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+{"segments": [{"id": 1, "seek": 4726, "start": 21.08, "end": 47.26, "text": "بسم الله الرحمن الرحيم والصلاة والسلام على أشرف الأنبياء والمرسلين سيدنا محمد وعلى أهلي وأصحابيها جميعا نكمل مع بعض بداية الموضوع ال matrices اللي بدأنا في بداية الأسبوع يوم الأحد نكمله اليوم ان شاء الله وصلنا كنا لعمليات مجموعة ال operations اللي ممكن نعملها على ال matrices عملية الجامعة وعملية الضرب أخدتوا عملية الجامعة قبل هيك جمعتوا matrices قبل هيك", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 29973, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 20292, 36725, 9381, 5016, 16758, 1829, 11296, 10874, 2304, 40228, 995, 8717, 24793, 1211, 20449, 45030, 11242, 4724, 28259, 10632, 9673, 2407, 11242, 45367, 2423, 32284, 13672, 1829, 47525, 10721, 8315, 8978, 4724, 28259, 10632, 16247, 35457, 45367, 7251, 20498, 16247, 24401, 8717, 24793, 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تلاتة اربعة هاي ال matrix بتاعتنا بدنا نفسك element by element ال element هنا ده ايش ايش عنوانه واحد واحد صح طيب الصف الأول طيب خلاص هاي الصف الأول في الأولى وضربه في العمود الأول في التانية", "tokens": [6027, 16296, 5296, 31377, 2304, 7251, 30544, 1975, 2655, 1863, 9957, 8978, 1975, 25513, 27884, 37495, 22653, 8978, 18871, 16254, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 8032, 47302, 2423, 8141, 39894, 995, 34268, 8315, 47525, 8315, 8717, 36178, 4117, 4478, 538, 4478, 2423, 4478, 34105, 11778, 3224, 1975, 1829, 8592, 1975, 1829, 8592, 18871, 2407, 7649, 3224, 36764, 24401, 36764, 24401, 20328, 5016, 23032, 1829, 3555, 31767, 5172, 16247, 12610, 23032, 1829, 3555, 16490, 1211, 33546, 8032, 47302, 31767, 5172, 16247, 12610, 8978, 16247, 12610, 7578, 4032, 11242, 25513, 3224, 8978, 18863, 2304, 23328, 16247, 12610, 8978, 16712, 7649, 10632], "avg_logprob": 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0.9434814453125}, {"start": 281.75, "end": 282.23, "word": " تلاتة", "probability": 0.8082275390625}, {"start": 282.23, "end": 282.63, "word": " اربعة", "probability": 0.87255859375}, {"start": 282.63, "end": 283.17, "word": " واحد", "probability": 0.781982421875}, {"start": 283.17, "end": 283.45, "word": " اتنين", "probability": 0.9737548828125}, {"start": 283.45, "end": 283.87, "word": " تلاتة", "probability": 0.9710693359375}, {"start": 283.87, "end": 284.17, "word": " اربعة", "probability": 0.9440104166666666}, {"start": 284.17, "end": 284.55, "word": " هاي", "probability": 0.569580078125}, {"start": 284.55, "end": 284.63, "word": " ال", "probability": 0.97412109375}, {"start": 284.63, "end": 284.91, "word": " matrix", "probability": 0.953125}, {"start": 284.91, "end": 285.35, "word": " بتاعتنا", "probability": 0.975830078125}, {"start": 285.35, "end": 285.83, "word": " بدنا", "probability": 0.767578125}, {"start": 285.83, "end": 286.11, "word": " نفسك", "probability": 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{"start": 291.55, "end": 292.99, "word": " صح", "probability": 0.8759765625}, {"start": 292.99, "end": 294.03, "word": " طيب", "probability": 0.8106282552083334}, {"start": 294.03, "end": 294.69, "word": " الصف", "probability": 0.990478515625}, {"start": 294.69, "end": 296.33, "word": " الأول", "probability": 0.758056640625}, {"start": 296.33, "end": 297.99, "word": " طيب", "probability": 0.8961588541666666}, {"start": 297.99, "end": 298.27, "word": " خلاص", "probability": 0.9899088541666666}, {"start": 298.27, "end": 298.47, "word": " هاي", "probability": 0.8076171875}, {"start": 298.47, "end": 298.81, "word": " الصف", "probability": 0.989990234375}, {"start": 298.81, "end": 299.17, "word": " الأول", "probability": 0.9541015625}, {"start": 299.17, "end": 299.33, "word": " في", "probability": 0.8798828125}, {"start": 299.33, "end": 300.05, "word": " الأولى", "probability": 0.8974609375}, {"start": 300.05, "end": 300.59, "word": " وضربه", "probability": 0.7978515625}, {"start": 300.59, "end": 300.69, "word": " في", "probability": 0.97509765625}, {"start": 300.69, "end": 301.07, "word": " العمود", "probability": 0.9571940104166666}, {"start": 301.07, "end": 301.61, "word": " الأول", "probability": 0.96533203125}, {"start": 301.61, "end": 301.87, "word": " في", "probability": 0.84716796875}, {"start": 301.87, "end": 302.97, "word": " التانية", "probability": 0.9052734375}], "temperature": 1.0}, {"id": 12, "seek": 32013, "start": 303.61, "end": 320.13, "text": "مدام هو أصلا واحد واحد الصف الأول باخده من ال matrix الأولى العمود الأول باخده من ال matrix التانية فبمسك element by element هذا في هذا صفر زائد اتنين زائد سلب واحد", "tokens": [2304, 3215, 10943, 31439, 5551, 9381, 15040, 36764, 24401, 36764, 24401, 31767, 5172, 16247, 12610, 4724, 47283, 3215, 3224, 9154, 2423, 8141, 16247, 12610, 7578, 18863, 2304, 23328, 16247, 12610, 4724, 47283, 3215, 3224, 9154, 2423, 8141, 16712, 7649, 10632, 6156, 3555, 2304, 3794, 4117, 4478, 538, 4478, 23758, 8978, 23758, 20328, 5172, 2288, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 8608, 46152, 36764, 24401], "avg_logprob": -0.1487771799598915, "compression_ratio": 1.769736842105263, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 303.61, "end": 303.99, "word": "مدام", "probability": 0.5018717447916666}, {"start": 303.99, "end": 304.11, "word": " هو", "probability": 0.93701171875}, {"start": 304.11, "end": 304.39, "word": " أصلا", "probability": 0.7849934895833334}, {"start": 304.39, "end": 304.73, "word": " واحد", "probability": 0.828125}, {"start": 304.73, "end": 305.21, "word": " واحد", "probability": 0.843505859375}, {"start": 305.21, "end": 306.47, "word": " الصف", "probability": 0.847412109375}, {"start": 306.47, "end": 307.29, "word": " الأول", "probability": 0.9326171875}, {"start": 307.29, "end": 308.35, "word": " باخده", "probability": 0.9495849609375}, {"start": 308.35, "end": 308.49, "word": " من", "probability": 0.99072265625}, {"start": 308.49, "end": 308.75, "word": " ال", "probability": 0.95263671875}, {"start": 308.75, "end": 309.43, "word": " matrix", "probability": 0.89111328125}, {"start": 309.43, "end": 310.19, "word": " الأولى", "probability": 0.9501953125}, {"start": 310.19, "end": 310.99, "word": " العمود", "probability": 0.908203125}, {"start": 310.99, "end": 311.49, "word": " الأول", "probability": 0.9638671875}, {"start": 311.49, "end": 311.95, "word": " باخده", "probability": 0.980712890625}, {"start": 311.95, "end": 312.05, "word": " من", "probability": 0.9951171875}, {"start": 312.05, "end": 312.17, "word": " ال", "probability": 0.962890625}, {"start": 312.17, "end": 312.43, "word": " matrix", "probability": 0.96240234375}, {"start": 312.43, "end": 312.95, "word": " التانية", "probability": 0.9422200520833334}, {"start": 312.95, "end": 313.61, "word": " فبمسك", "probability": 0.9232421875}, {"start": 313.61, "end": 313.83, "word": " element", "probability": 0.94677734375}, {"start": 313.83, "end": 314.01, "word": " by", 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العمود التاني فإذا الصف الأول زي ما هو بس هنا العنوان صار عند العمود التاني صفر تالتة حلو كويس", "tokens": [9566, 1829, 3555, 18863, 1863, 9381, 2288, 16712, 7649, 1829, 11933, 1829, 8592, 18871, 2407, 7649, 3224, 22807, 36764, 24401, 31767, 5172, 16247, 12610, 30767, 1829, 19446, 31439, 4724, 3794, 8978, 18863, 2304, 23328, 16712, 7649, 1829, 6156, 28814, 15730, 31767, 5172, 16247, 12610, 30767, 1829, 19446, 31439, 4724, 3794, 34105, 18863, 1863, 2407, 7649, 20328, 9640, 43242, 18863, 2304, 23328, 16712, 7649, 1829, 20328, 5172, 2288, 6055, 6027, 2655, 3660, 11331, 1211, 2407, 9122, 45865, 3794], "avg_logprob": -0.15494792335308516, "compression_ratio": 2.0071942446043165, "no_speech_prob": 1.8477439880371094e-06, "words": [{"start": 323.93, "end": 324.29, "word": "طيب", "probability": 0.9835611979166666}, {"start": 324.29, "end": 324.97, "word": " العنصر", "probability": 0.8428955078125}, {"start": 324.97, "end": 325.41, "word": " التاني", "probability": 0.9348958333333334}, {"start": 325.41, "end": 325.69, "word": " إيش", "probability": 0.8056640625}, {"start": 325.69, "end": 326.53, "word": " عنوانه؟", "probability": 0.9046875}, {"start": 326.53, "end": 326.97, "word": " واحد", "probability": 0.780029296875}, {"start": 326.97, "end": 330.09, "word": " الصف", "probability": 0.6099853515625}, {"start": 330.09, "end": 330.41, "word": " الأول", "probability": 0.899169921875}, {"start": 330.41, "end": 330.59, "word": " زي", "probability": 0.90234375}, {"start": 330.59, "end": 330.69, "word": " ما", "probability": 0.97998046875}, {"start": 330.69, "end": 330.89, "word": " هو", "probability": 0.998046875}, {"start": 330.89, "end": 331.09, "word": " بس", "probability": 0.953369140625}, {"start": 331.09, "end": 331.19, "word": " في", "probability": 0.92626953125}, {"start": 331.19, "end": 331.63, "word": " العمود", "probability": 0.9664713541666666}, {"start": 331.63, "end": 332.27, "word": " التاني", "probability": 0.9381510416666666}, {"start": 332.27, "end": 332.77, "word": " فإذا", "probability": 0.6935221354166666}, {"start": 332.77, "end": 333.07, "word": " الصف", "probability": 0.84765625}, {"start": 333.07, "end": 333.27, "word": " الأول", "probability": 0.979736328125}, {"start": 333.27, "end": 333.41, "word": " زي", "probability": 0.995361328125}, {"start": 333.41, "end": 333.45, "word": " ما", "probability": 0.9794921875}, {"start": 333.45, "end": 333.61, "word": " هو", "probability": 0.99658203125}, {"start": 333.61, "end": 334.11, "word": " بس", "probability": 0.96435546875}, {"start": 334.11, "end": 334.27, "word": " هنا", "probability": 0.93310546875}, {"start": 334.27, "end": 334.65, "word": " العنوان", "probability": 0.876953125}, {"start": 334.65, "end": 334.85, "word": " صار", "probability": 0.9609375}, {"start": 334.85, "end": 335.01, "word": " عند", "probability": 0.92041015625}, {"start": 335.01, "end": 335.39, "word": " العمود", "probability": 0.9915364583333334}, {"start": 335.39, "end": 335.91, "word": " التاني", "probability": 0.91796875}, {"start": 335.91, "end": 337.01, "word": " صفر", "probability": 0.9288736979166666}, {"start": 337.01, "end": 345.41, "word": " تالتة", "probability": 0.772308349609375}, {"start": 345.41, "end": 347.59, "word": " حلو", "probability": 0.8447265625}, {"start": 347.59, "end": 348.11, "word": " كويس", "probability": 0.7479654947916666}], "temperature": 1.0}, {"id": 14, "seek": 37553, "start": 349.69, "end": 375.53, "text": "الصفر سالب اتنين سالب تلاتة سالب خمسة طيب الرابع صف أول عمود رابع فطبيعه هيه و بتعطيني element في الصف الأول عمود رابع كويس صفر صفر سالب واحد طيب خلصنا من الصف الأول كله", "tokens": [6027, 9381, 5172, 2288, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 8608, 6027, 3555, 16490, 2304, 3794, 3660, 23032, 1829, 3555, 34892, 16758, 3615, 20328, 5172, 5551, 12610, 6225, 2304, 23328, 12602, 16758, 3615, 6156, 9566, 21292, 3615, 3224, 39896, 3224, 4032, 39894, 3615, 9566, 9957, 1829, 4478, 8978, 31767, 5172, 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"probability": 0.97265625}, {"start": 450.55, "end": 450.71, "word": " أن", "probability": 0.6064453125}, {"start": 450.71, "end": 451.69, "word": " عدد", "probability": 0.8758138020833334}, {"start": 451.69, "end": 452.09, "word": " الأعمد", "probability": 0.9656575520833334}, {"start": 452.09, "end": 452.29, "word": " هنا", "probability": 0.626953125}, {"start": 452.29, "end": 452.67, "word": " مختلف", "probability": 0.9886067708333334}, {"start": 452.67, "end": 452.81, "word": " عن", "probability": 0.982421875}, {"start": 452.81, "end": 453.07, "word": " عدد", "probability": 0.99072265625}, {"start": 453.07, "end": 453.51, "word": " الصفوف", "probability": 0.9871419270833334}, {"start": 453.51, "end": 454.09, "word": " فهنا", "probability": 0.9388020833333334}, {"start": 454.09, "end": 454.41, "word": " عملية", "probability": 0.9654947916666666}, {"start": 454.41, "end": 454.71, "word": " الضرب", "probability": 0.9798177083333334}, {"start": 454.71, "end": 454.93, "word": " غير", 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identity", "probability": 0.8857421875}, {"start": 466.65, "end": 467.21, "word": " matrices", "probability": 0.974609375}, {"start": 467.21, "end": 467.73, "word": " ال", "probability": 0.89306640625}, {"start": 467.73, "end": 467.99, "word": " identity", "probability": 0.85546875}, {"start": 467.99, "end": 468.43, "word": " matrices", "probability": 0.97802734375}, {"start": 468.43, "end": 469.11, "word": " أو", "probability": 0.64892578125}, {"start": 469.11, "end": 470.09, "word": " المحايد", "probability": 0.9427490234375}, {"start": 470.09, "end": 472.43, "word": " للمصفوفة،", "probability": 0.8807198660714286}, {"start": 472.43, "end": 472.87, "word": " المصفوفة", "probability": 0.9822265625}, {"start": 472.87, "end": 473.55, "word": " المحايدة", "probability": 0.98564453125}, {"start": 473.55, "end": 474.21, "word": " المصفوفة", "probability": 0.89619140625}, {"start": 474.21, "end": 474.59, "word": " المحايدة", "probability": 0.9892578125}, {"start": 474.59, "end": 474.75, "word": " هو", "probability": 0.931640625}, {"start": 474.75, "end": 474.99, "word": " نفس", "probability": 0.994384765625}, {"start": 474.99, "end": 475.37, "word": " المفهوم", "probability": 0.9940185546875}, {"start": 475.37, "end": 475.49, "word": " اللي", "probability": 0.85546875}, {"start": 475.49, "end": 475.63, "word": " كنا", "probability": 0.99560546875}, {"start": 475.63, "end": 476.09, "word": " نشتغله", "probability": 0.918212890625}, {"start": 476.09, "end": 476.29, "word": " عليه", "probability": 0.47509765625}], "temperature": 1.0}, {"id": 19, "seek": 50568, "start": 478.54, "end": 505.68, "text": "العنصر أو الرقم المحايد اللي هو أي رقم تاني بنضربه فيه بتغيرش أي رقم تاني اللي هو كان إيه؟ الواحد الواحد بنضربه في أي رقم هيظل نفس الرقم كويسة في ال identity برضه في matrix لو انضربت في أي matrix أخرى ال matrix الأخرى هتظل محافظة على نفس شكلها نفس ال elements بتاعتها كويسة هذه أول شغلة مهمة نعرفها أنه بتكون square", "tokens": [6027, 3615, 1863, 9381, 2288, 34051, 34892, 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{"start": 487.5, "end": 487.78, "word": " رقم", "probability": 0.9967447916666666}, {"start": 487.78, "end": 488.12, "word": " هيظل", "probability": 0.6952311197916666}, {"start": 488.12, "end": 488.3, "word": " نفس", "probability": 0.98486328125}, {"start": 488.3, "end": 488.76, "word": " الرقم", "probability": 0.9573567708333334}, {"start": 488.76, "end": 489.6, "word": " كويسة", "probability": 0.652252197265625}, {"start": 489.6, "end": 490.36, "word": " في", "probability": 0.76220703125}, {"start": 490.36, "end": 490.46, "word": " ال", "probability": 0.98828125}, {"start": 490.46, "end": 490.82, "word": " identity", "probability": 0.91552734375}, {"start": 490.82, "end": 491.3, "word": " برضه", "probability": 0.9856770833333334}, {"start": 491.3, "end": 491.64, "word": " في", "probability": 0.884765625}, {"start": 491.64, "end": 492.44, "word": " matrix", "probability": 0.58349609375}, {"start": 492.44, "end": 492.82, "word": " لو", "probability": 0.92138671875}, {"start": 492.82, "end": 493.28, "word": " انضربت", "probability": 0.8983154296875}, {"start": 493.28, "end": 493.42, "word": " في", "probability": 0.9755859375}, {"start": 493.42, "end": 493.6, "word": " أي", "probability": 0.83740234375}, {"start": 493.6, "end": 493.98, "word": " matrix", "probability": 0.94287109375}, {"start": 493.98, "end": 494.42, "word": " أخرى", "probability": 0.9703776041666666}, {"start": 494.42, "end": 494.56, "word": " ال", "probability": 0.77880859375}, {"start": 494.56, "end": 494.86, "word": " matrix", "probability": 0.9560546875}, {"start": 494.86, "end": 495.16, "word": " الأخرى", "probability": 0.9583333333333334}, {"start": 495.16, "end": 495.72, "word": " هتظل", "probability": 0.9329833984375}, {"start": 495.72, "end": 496.24, "word": " محافظة", "probability": 0.9890625}, {"start": 496.24, "end": 496.34, "word": " على", "probability": 0.91064453125}, {"start": 496.34, "end": 496.58, "word": " نفس", "probability": 0.984375}, {"start": 496.58, "end": 497.78, "word": " شكلها", "probability": 0.9775390625}, {"start": 497.78, "end": 499.0, "word": " نفس", "probability": 0.82666015625}, {"start": 499.0, "end": 499.38, "word": " ال", "probability": 0.96826171875}, {"start": 499.38, "end": 500.36, "word": " elements", "probability": 0.876953125}, {"start": 500.36, "end": 500.9, "word": " بتاعتها", "probability": 0.957763671875}, {"start": 500.9, "end": 501.78, "word": " كويسة", "probability": 0.9476318359375}, {"start": 501.78, "end": 502.0, "word": " هذه", "probability": 0.47509765625}, {"start": 502.0, "end": 502.2, "word": " أول", "probability": 0.971923828125}, {"start": 502.2, "end": 502.58, "word": " شغلة", "probability": 0.89306640625}, {"start": 502.58, "end": 503.52, "word": " مهمة", "probability": 0.9285481770833334}, {"start": 503.52, "end": 504.1, "word": " نعرفها", "probability": 0.9488525390625}, {"start": 504.1, "end": 504.32, "word": " أنه", "probability": 0.6552734375}, {"start": 504.32, "end": 504.76, "word": " بتكون", "probability": 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{"start": 507.22, "end": 508.52, "word": " square", "probability": 0.68310546875}, {"start": 508.52, "end": 508.64, "word": " و", "probability": 0.705078125}, {"start": 508.64, "end": 509.12, "word": " بنسميها", "probability": 0.8973388671875}, {"start": 509.12, "end": 509.5, "word": " order", "probability": 0.634765625}, {"start": 509.5, "end": 509.82, "word": " n", "probability": 0.50537109375}, {"start": 509.82, "end": 510.16, "word": " معناه", "probability": 0.8601888020833334}, {"start": 510.16, "end": 510.34, "word": " ذلك", "probability": 0.870361328125}, {"start": 510.34, "end": 510.6, "word": " أنها", "probability": 0.491455078125}, {"start": 510.6, "end": 510.82, "word": " n", "probability": 0.68017578125}, {"start": 510.82, "end": 511.02, "word": " في", "probability": 0.90869140625}, {"start": 511.02, "end": 511.34, "word": " n", "probability": 0.8837890625}, {"start": 511.34, "end": 512.3, "word": " ال", "probability": 0.90234375}, {"start": 512.3, "end": 512.86, "word": " diagonal", "probability": 0.6767578125}, {"start": 512.86, "end": 513.66, "word": " ones", "probability": 0.55029296875}, {"start": 513.66, "end": 514.6, "word": " otherwise", "probability": 0.7314453125}, {"start": 514.6, "end": 515.44, "word": " zeros", "probability": 0.74560546875}, {"start": 515.44, "end": 516.64, "word": " فإذا", "probability": 0.7423502604166666}, {"start": 516.64, "end": 516.8, "word": " ال", "probability": 0.97216796875}, {"start": 516.8, "end": 517.18, "word": " diagonal", "probability": 0.826171875}, {"start": 517.18, "end": 518.88, "word": " اللي", "probability": 0.776611328125}, {"start": 518.88, "end": 519.06, "word": " هو", "probability": 0.94091796875}, {"start": 519.06, "end": 519.18, "word": " ال", "probability": 0.9453125}, {"start": 519.18, "end": 519.44, "word": " elements", "probability": 0.861328125}, {"start": 519.44, "end": 519.84, "word": " هذه", "probability": 0.59814453125}, {"start": 519.84, "end": 520.7, "word": " من", "probability": 0.93212890625}, {"start": 520.7, "end": 522.44, "word": " أعلى", "probability": 0.9391276041666666}, {"start": 522.44, "end": 523.48, "word": " لشمال", "probability": 0.865478515625}, {"start": 523.48, "end": 524.5, "word": " لأدنى", "probability": 0.95732421875}, {"start": 524.5, "end": 524.98, "word": " اليمين", "probability": 0.7840983072916666}], "temperature": 1.0}, {"id": 21, "seek": 55448, "start": 525.86, "end": 554.48, "text": "المجموعة ال elements هذه كلها بتكون ones otherwise zeros فمعنى ذلك هي ال identity matrix عبارة عن matrix لمجموعة elements ال elements هذه تعرف بال I و J الصفوف و الأعمدة صفوف و الأعمدة إذا بيتفقوا مع بعض بيساوي بعض بنحطها بواحد فهنا واحد و واحد اتنين و اتنين تلاتة و تلاتة and و and otherwise لأ بيساويش بعض zero بنحطها يبقى zero", "tokens": [45340, 7435, 2304, 2407, 27884, 2423, 4959, 29538, 28242, 11296, 39894, 30544, 2306, 5911, 35193, 6156, 2304, 3615, 1863, 7578, 29910, 23275, 39896, 2423, 6575, 8141, 6225, 3555, 9640, 3660, 18871, 8141, 32767, 7435, 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682.23, "end": 682.53, "word": " عليها", "probability": 0.9873046875}, {"start": 682.53, "end": 682.77, "word": " فلو", "probability": 0.96240234375}, {"start": 682.77, "end": 683.03, "word": " قولنا", "probability": 0.7919921875}, {"start": 683.03, "end": 683.15, "word": " ال", "probability": 0.9521484375}, {"start": 683.15, "end": 683.55, "word": " inverse", "probability": 0.90625}, {"start": 683.55, "end": 683.85, "word": " ل", "probability": 0.923828125}, {"start": 683.85, "end": 684.77, "word": " A", "probability": 0.30810546875}, {"start": 684.77, "end": 685.21, "word": " B", "probability": 0.55029296875}, {"start": 685.21, "end": 685.71, "word": " C", "probability": 0.99267578125}, {"start": 685.71, "end": 686.15, "word": " D", "probability": 0.9912109375}, {"start": 686.15, "end": 686.67, "word": " بهذا", "probability": 0.791015625}, {"start": 686.67, "end": 687.03, "word": " الشكل", "probability": 0.994140625}, {"start": 687.03, "end": 688.45, "word": " خلينا", "probability": 0.8560791015625}, {"start": 688.45, "end": 689.77, "word": " نقول", "probability": 0.963623046875}, {"start": 689.77, "end": 690.11, "word": " مثلا", "probability": 0.89892578125}, {"start": 690.11, "end": 691.15, "word": " واحد", "probability": 0.919189453125}, {"start": 691.15, "end": 693.43, "word": " اتنين", "probability": 0.962158203125}, {"start": 693.43, "end": 694.83, "word": " تلاتة", "probability": 0.9652099609375}], "temperature": 1.0}, {"id": 28, "seek": 72204, "start": 698.74, "end": 722.04, "text": "2,2,3 أو 2,2,5 سهل خلّيني أقول بهذا الشكل هيا و بدنا نجيب لها ال inverse أول شغلة بدنا نحسبها نحسب ال determinant بتاعتها ال determinant بتاعتها المحددة بتاعتها جدّيش قيمة ال matrix جدّيش قيمة ال matrix ال diagonal minus ال co diagonal", "tokens": [17, 11, 17, 11, 18, 34051, 568, 11, 17, 11, 20, 8608, 3224, 1211, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 4724, 3224, 15730, 25124, 28820, 8032, 25528, 4032, 47525, 8315, 8717, 7435, 1829, 3555, 5296, 11296, 2423, 17340, 5551, 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"word": " ال", "probability": 0.9296875}, {"start": 721.64, "end": 721.74, "word": " co", "probability": 0.239013671875}, {"start": 721.74, "end": 722.04, "word": " diagonal", "probability": 0.34814453125}], "temperature": 1.0}, {"id": 29, "seek": 75094, "start": 723.02, "end": 750.94, "text": "diagonal بنطرح منه ال code diagonal بنسميها فهذه خمسة نقص واحد بطلع واحد فأول شي هنقسم كل اللي هيطلع ان هالوجه اللي هنتكلم كيف بيطلع كله بنجسمه على ال determinant واحد اتنين اتنين خمسة اللي هو هذا في النهاية هيساوي واحد تمام", "tokens": [4504, 6709, 304, 44945, 9566, 2288, 5016, 9154, 3224, 2423, 3089, 21539, 44945, 38251, 1829, 11296, 6156, 3224, 24192, 16490, 2304, 3794, 3660, 8717, 4587, 9381, 36764, 24401, 4724, 9566, 1211, 3615, 36764, 24401, 6156, 10721, 12610, 44049, 8032, 1863, 4587, 38251, 28242, 13672, 1829, 39896, 9566, 1211, 3615, 16472, 8032, 6027, 29245, 3224, 13672, 1829, 8032, 29399, 4117, 19528, 9122, 33911, 4724, 1829, 9566, 1211, 3615, 28242, 3224, 44945, 7435, 38251, 3224, 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{"start": 727.24, "end": 727.76, "word": " خمسة", "probability": 0.939453125}, {"start": 727.76, "end": 728.6, "word": " نقص", "probability": 0.90283203125}, {"start": 728.6, "end": 728.96, "word": " واحد", "probability": 0.98779296875}, {"start": 728.96, "end": 729.74, "word": " بطلع", "probability": 0.74615478515625}, {"start": 729.74, "end": 730.92, "word": " واحد", "probability": 0.97509765625}, {"start": 730.92, "end": 731.38, "word": " فأول", "probability": 0.9347330729166666}, {"start": 731.38, "end": 731.6, "word": " شي", "probability": 0.63330078125}, {"start": 731.6, "end": 732.26, "word": " هنقسم", "probability": 0.869873046875}, {"start": 732.26, "end": 732.58, "word": " كل", "probability": 0.96923828125}, {"start": 732.58, "end": 732.74, "word": " اللي", "probability": 0.94677734375}, {"start": 732.74, "end": 733.18, "word": " هيطلع", "probability": 0.8646240234375}, {"start": 733.18, "end": 733.32, "word": " ان", "probability": 0.312255859375}, {"start": 733.32, "end": 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"word": " اتنين", "probability": 0.9656982421875}, {"start": 741.94, "end": 742.82, "word": " خمسة", "probability": 0.9786376953125}, {"start": 742.82, "end": 743.32, "word": " اللي", "probability": 0.963134765625}, {"start": 743.32, "end": 743.44, "word": " هو", "probability": 0.97412109375}, {"start": 743.44, "end": 743.66, "word": " هذا", "probability": 0.62109375}, {"start": 743.66, "end": 743.8, "word": " في", "probability": 0.91357421875}, {"start": 743.8, "end": 744.14, "word": " النهاية", "probability": 0.9357096354166666}, {"start": 744.14, "end": 744.78, "word": " هيساوي", "probability": 0.88623046875}, {"start": 744.78, "end": 747.82, "word": " واحد", "probability": 0.981201171875}, {"start": 747.82, "end": 750.94, "word": " تمام", "probability": 0.815673828125}], "temperature": 1.0}, {"id": 30, "seek": 78166, "start": 753.1, "end": 781.66, "text": "هتكون عبارة عن matrix ال matrix هذه ال diagonal ال elements عند ال diagonal بنبدلها مع بعض بنبدلهم مع بعض المعنى هنا صارت إيه؟ 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"word": " نعمله", "probability": 0.8279622395833334}, {"start": 894.1, "end": 894.36, "word": " power", "probability": 0.6826171875}], "temperature": 1.0}, {"id": 36, "seek": 90723, "start": 895.05, "end": 907.23, "text": "لما بقول تلاتة to the power خمسة يعني التلاتة ضربتها في نفسها خمس مرات خمس مرات نفس الكلام هنا ال matrix ضربناها في نفسها في مرة for example هيفهمنا example", "tokens": [1211, 15042, 4724, 39648, 6055, 1211, 9307, 3660, 281, 264, 1347, 16490, 2304, 3794, 3660, 37495, 22653, 16712, 1211, 9307, 3660, 48812, 25513, 2655, 11296, 8978, 8717, 36178, 11296, 16490, 2304, 3794, 3714, 2288, 9307, 16490, 2304, 3794, 3714, 2288, 9307, 8717, 36178, 2423, 28820, 10943, 34105, 2423, 8141, 48812, 25513, 8315, 11296, 8978, 8717, 36178, 11296, 8978, 3714, 25720, 337, 1365, 39896, 5172, 16095, 8315, 1365], "avg_logprob": -0.12454043635550667, "compression_ratio": 1.644736842105263, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 895.05, "end": 895.23, "word": "لما", 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"probability": 0.9933268229166666}, {"start": 899.09, "end": 899.49, "word": " مرات", "probability": 0.9718424479166666}, {"start": 899.49, "end": 900.35, "word": " خمس", "probability": 0.8544921875}, {"start": 900.35, "end": 900.65, "word": " مرات", "probability": 0.9767252604166666}, {"start": 900.65, "end": 900.91, "word": " نفس", "probability": 0.9736328125}, {"start": 900.91, "end": 901.29, "word": " الكلام", "probability": 0.9796549479166666}, {"start": 901.29, "end": 901.51, "word": " هنا", "probability": 0.98095703125}, {"start": 901.51, "end": 901.81, "word": " ال", "probability": 0.90478515625}, {"start": 901.81, "end": 902.13, "word": " matrix", "probability": 0.93212890625}, {"start": 902.13, "end": 902.57, "word": " ضربناها", "probability": 0.9537353515625}, {"start": 902.57, "end": 902.71, "word": " في", "probability": 0.982421875}, {"start": 902.71, "end": 903.29, "word": " نفسها", "probability": 0.9912109375}, {"start": 903.29, "end": 904.13, "word": " في", "probability": 0.9111328125}, {"start": 904.13, "end": 904.69, "word": " مرة", "probability": 0.978271484375}, {"start": 904.69, "end": 905.79, "word": " for", "probability": 0.73583984375}, {"start": 905.79, "end": 906.21, "word": " example", "probability": 0.96875}, {"start": 906.21, "end": 906.83, "word": " هيفهمنا", "probability": 0.681640625}, {"start": 906.83, "end": 907.23, "word": " example", "probability": 0.8720703125}], "temperature": 1.0}, {"id": 37, "seek": 94053, "start": 911.57, "end": 940.53, "text": "تانية واحدة مانوس واحدة و Zero to the power of three يعني نفس ال matrix نفسها بده اضربها في نفسها كم مرة تلت مرات بكررها تلت مرات و بنضربها عندكم الحرية كاملة تضربوا التانية في التالتة و الناتج تضربه في الأولى او تضرب الأولى في التانية و الناتج تضربه في التالتة في الحالتين هو هو طيب هنا طبعا هنا في ال example ضرب التانية في التالتة نتيجة برضه هذا في هذا", "tokens": [2655, 7649, 10632, 36764, 24401, 3660, 3714, 7649, 41779, 36764, 24401, 3660, 4032, 17182, 281, 264, 1347, 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خلصنا ال element الأول طيب هذا في هذا اتنين طيب هذا في هذا لحظة هذا صف ثاني عمود أول يعني ناتج بدويش صف ثاني عمود أول هنا مش بدوش تمام", "tokens": [17, 87, 17, 1975, 25513, 27884, 8608, 6027, 3555, 36764, 24401, 8032, 47302, 16712, 1211, 9307, 3660, 8032, 47302, 16490, 1211, 9381, 8315, 2423, 4478, 16247, 12610, 23032, 1829, 3555, 23758, 8978, 23758, 1975, 2655, 1863, 9957, 23032, 1829, 3555, 23758, 8978, 23758, 5296, 5016, 19913, 3660, 23758, 20328, 5172, 38637, 7649, 1829, 6225, 2304, 23328, 5551, 12610, 37495, 22653, 8717, 9307, 7435, 47525, 45865, 8592, 20328, 5172, 38637, 7649, 1829, 6225, 2304, 23328, 5551, 12610, 34105, 37893, 47525, 2407, 8592, 46811, 10943], "avg_logprob": -0.2676711238565899, "compression_ratio": 1.826086956521739, "no_speech_prob": 1.5616416931152344e-05, "words": [{"start": 942.76, "end": 943.4, "word": "2x2", "probability": 0.607666015625}, {"start": 943.4, "end": 944.04, "word": " اربعة", "probability": 0.631324291229248}, {"start": 944.04, "end": 944.58, 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أعمدة و الأعمدة صفوف صفوف أعمدة و أعمدة صفوف ال diagonal لو تخيلنا هذه ورقة و ال diagonal هذه خشب عصية لذجناها و لفناها فبتصير صفوف أعمدة و الأعمدة صفوف عملنا flip across diagonal flip", "tokens": [8297, 6531, 38078, 34051, 2423, 6531, 43501, 44945, 38251, 1829, 11296, 5296, 15042, 4724, 39648, 6531, 43501, 295, 316, 34051, 2423, 8141, 316, 37495, 22653, 9122, 33456, 1829, 47525, 1211, 2655, 20328, 5172, 38688, 5551, 25957, 41891, 4032, 16247, 25957, 41891, 20328, 5172, 38688, 20328, 5172, 38688, 5551, 25957, 41891, 4032, 5551, 25957, 41891, 20328, 5172, 38688, 2423, 21539, 45164, 6055, 9778, 26895, 8315, 29538, 4032, 2288, 28671, 4032, 2423, 21539, 29538, 16490, 8592, 3555, 6225, 9381, 10632, 5296, 8848, 7435, 8315, 11296, 4032, 5296, 5172, 8315, 11296, 6156, 3555, 2655, 9381, 13546, 20328, 5172, 38688, 5551, 25957, 41891, 4032, 16247, 25957, 41891, 20328, 5172, 38688, 6225, 42213, 8315, 7929, 2108, 21539, 7929], "avg_logprob": -0.17105262909542052, "compression_ratio": 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{"start": 1320.03, "end": 1320.47, "word": " square", "probability": 0.90185546875}, {"start": 1320.47, "end": 1321.07, "word": " و", "probability": 0.94189453125}, {"start": 1321.07, "end": 1321.81, "word": " شرط", "probability": 0.8605143229166666}, {"start": 1321.81, "end": 1322.57, "word": " التاني", "probability": 0.9484049479166666}, {"start": 1322.57, "end": 1322.97, "word": " تساوي", "probability": 0.921142578125}, {"start": 1322.97, "end": 1323.51, "word": " لترانسبوز", "probability": 0.8949497767857143}, {"start": 1323.51, "end": 1323.93, "word": " تبعها", "probability": 0.9730224609375}], "temperature": 1.0}, {"id": 53, "seek": 135356, "start": 1324.28, "end": 1353.56, "text": "بتكون بتساوي ال a transpose تمام ال zero one matrices هذي نوع من أنواع ال matrices و اللي بتستخدم كتير في ال relations و في ال graphs و يمكن احنا المرة اللي فاتت حتى عشان نوضحها المرة اللي فاتت قلنا لو مثلا لنا صورة أبيض و أسود بقدر نمثلها ب one و zero بس نقدر نمثلها ب one و zero في النهاية لما نتكلم عن matrix عبارة عن one و zero", "tokens": [3555, 2655, 30544, 39894, 3794, 995, 45865, 2423, 257, 25167, 46811, 10943, 2423, 4018, 472, 32284, 8032, 8848, 1829, 8717, 45367, 9154, 14739, 14407, 3615, 2423, 32284, 4032, 13672, 1829, 39894, 14851, 9778, 40448, 9122, 2655, 13546, 8978, 2423, 2299, 4032, 8978, 2423, 24877, 4032, 7251, 43020, 1975, 5016, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 11331, 49975, 6225, 8592, 7649, 8717, 2407, 11242, 5016, 11296, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 12174, 1211, 8315, 45164, 50113, 15040, 5296, 8315, 20328, 13063, 3660, 5551, 21292, 11242, 4032, 5551, 3794, 23328, 4724, 28543, 2288, 8717, 2304, 12984, 1211, 11296, 4724, 472, 4032, 4018, 4724, 3794, 8717, 28543, 2288, 8717, 2304, 12984, 1211, 11296, 4724, 472, 4032, 4018, 8978, 28239, 11296, 10632, 5296, 15042, 8717, 2655, 4117, 19528, 18871, 8141, 6225, 3555, 9640, 3660, 18871, 472, 4032, 4018], "avg_logprob": -0.189073744008867, "compression_ratio": 1.943609022556391, 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"probability": 0.98388671875}, {"start": 1347.1, "end": 1347.44, "word": " نمثلها", "probability": 0.89775390625}, {"start": 1347.44, "end": 1347.56, "word": " ب", "probability": 0.66650390625}, {"start": 1347.56, "end": 1347.68, "word": " one", "probability": 0.5615234375}, {"start": 1347.68, "end": 1347.78, "word": " و", "probability": 0.9580078125}, {"start": 1347.78, "end": 1347.96, "word": " zero", "probability": 0.8564453125}, {"start": 1347.96, "end": 1348.26, "word": " بس", "probability": 0.974853515625}, {"start": 1348.26, "end": 1348.98, "word": " نقدر", "probability": 0.8663736979166666}, {"start": 1348.98, "end": 1349.4, "word": " نمثلها", "probability": 0.98642578125}, {"start": 1349.4, "end": 1349.5, "word": " ب", "probability": 0.76123046875}, {"start": 1349.5, "end": 1349.72, "word": " one", "probability": 0.77294921875}, {"start": 1349.72, "end": 1349.98, "word": " و", "probability": 0.98681640625}, {"start": 1349.98, "end": 1350.24, "word": " zero", "probability": 0.923828125}, {"start": 1350.24, "end": 1350.58, "word": " في", "probability": 0.464599609375}, {"start": 1350.58, "end": 1350.8, "word": " النهاية", "probability": 0.8551432291666666}, {"start": 1350.8, "end": 1350.88, "word": " لما", "probability": 0.6749267578125}, {"start": 1350.88, "end": 1351.08, "word": " نتكلم", "probability": 0.85888671875}, {"start": 1351.08, "end": 1351.22, "word": " عن", "probability": 0.98583984375}, {"start": 1351.22, "end": 1351.7, "word": " matrix", "probability": 0.81884765625}, {"start": 1351.7, "end": 1352.52, "word": " عبارة", "probability": 0.992431640625}, {"start": 1352.52, "end": 1352.68, "word": " عن", "probability": 0.99169921875}, {"start": 1352.68, "end": 1352.9, "word": " one", "probability": 0.95654296875}, {"start": 1352.9, "end": 1353.34, "word": " و", "probability": 0.98486328125}, {"start": 1353.34, "end": 1353.56, "word": " zero", "probability": 0.9287109375}], "temperature": 1.0}, {"id": 54, "seek": 138126, "start": 1353.84, "end": 1381.26, "text": "مجموعة ones على مجموعة zeros اعطاني matrix هذه بقدر اتعامل معها وفي applications كتير لها زي ما قلنا من اهمها ال relations اللي هناخدها لاحقا من اهمها ال directed graphs برضه هناخدها لاحقا اذا كان في relation بين عنصر و عنصر بحط نقطة التقاطع او ال element بتاع التقاطع بينهم انه بسوء واحد فهو true otherwise بنحطه false فبنقدر نجيب relation برضه دعونا نوضحها بالمثال", "tokens": [2304, 7435, 2304, 45367, 3660, 2306, 15844, 3714, 7435, 2304, 45367, 3660, 35193, 1975, 3615, 9566, 7649, 1829, 8141, 29538, 4724, 28543, 2288, 1975, 2655, 3615, 10943, 1211, 20449, 11296, 4032, 41185, 5821, 9122, 2655, 13546, 5296, 11296, 30767, 1829, 19446, 12174, 1211, 8315, 9154, 1975, 16095, 11296, 2423, 2299, 13672, 1829, 8032, 1863, 47283, 3215, 11296, 20193, 5016, 4587, 995, 9154, 1975, 16095, 11296, 2423, 12898, 24877, 4724, 43042, 3224, 8032, 1863, 47283, 3215, 11296, 20193, 5016, 4587, 995, 1975, 15730, 25961, 8978, 9721, 49374, 18871, 9381, 2288, 4032, 18871, 9381, 2288, 4724, 5016, 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اعطاني", "probability": 0.836083984375}, {"start": 1356.22, "end": 1356.56, "word": " matrix", "probability": 0.80908203125}, {"start": 1356.56, "end": 1356.98, "word": " هذه", "probability": 0.45654296875}, {"start": 1356.98, "end": 1357.3, "word": " بقدر", "probability": 0.8922526041666666}, {"start": 1357.3, "end": 1357.64, "word": " اتعامل", "probability": 0.94111328125}, {"start": 1357.64, "end": 1358.02, "word": " معها", "probability": 0.918212890625}, {"start": 1358.02, "end": 1358.36, "word": " وفي", "probability": 0.783203125}, {"start": 1358.36, "end": 1358.84, "word": " applications", "probability": 0.84521484375}, {"start": 1358.84, "end": 1359.26, "word": " كتير", "probability": 0.94287109375}, {"start": 1359.26, "end": 1359.48, "word": " لها", "probability": 0.62548828125}, {"start": 1359.48, "end": 1359.66, "word": " زي", "probability": 0.750732421875}, {"start": 1359.66, "end": 1359.72, "word": " ما", "probability": 0.97412109375}, {"start": 1359.72, "end": 1360.04, "word": " قلنا", "probability": 0.8863932291666666}, {"start": 1360.04, "end": 1360.52, "word": " من", "probability": 0.94384765625}, {"start": 1360.52, "end": 1360.84, "word": " اهمها", "probability": 0.802490234375}, {"start": 1360.84, "end": 1360.9, "word": " ال", "probability": 0.6142578125}, {"start": 1360.9, "end": 1361.14, "word": " relations", "probability": 0.91162109375}, {"start": 1361.14, "end": 1361.36, "word": " اللي", "probability": 0.827392578125}, {"start": 1361.36, "end": 1362.18, "word": " هناخدها", "probability": 0.90810546875}, {"start": 1362.18, "end": 1362.62, "word": " لاحقا", "probability": 0.9300537109375}, {"start": 1362.62, "end": 1363.1, "word": " من", "probability": 0.857421875}, {"start": 1363.1, "end": 1363.62, "word": " اهمها", "probability": 0.9371744791666666}, {"start": 1363.62, "end": 1364.08, "word": " ال", "probability": 0.94140625}, {"start": 1364.08, "end": 1364.4, "word": " directed", "probability": 0.86279296875}, {"start": 1364.4, "end": 1364.92, "word": " graphs", "probability": 0.91455078125}, {"start": 1364.92, "end": 1365.24, "word": " برضه", "probability": 0.7802734375}, {"start": 1365.24, "end": 1365.66, "word": " هناخدها", "probability": 0.9822265625}, {"start": 1365.66, "end": 1366.24, "word": " لاحقا", "probability": 0.9583740234375}, {"start": 1366.24, "end": 1366.78, "word": " اذا", "probability": 0.835693359375}, {"start": 1366.78, "end": 1366.94, "word": " كان", "probability": 0.98681640625}, {"start": 1366.94, "end": 1367.08, "word": " في", "probability": 0.87841796875}, {"start": 1367.08, "end": 1367.56, "word": " relation", "probability": 0.97998046875}, {"start": 1367.56, "end": 1368.1, "word": " بين", "probability": 0.943359375}, {"start": 1368.1, "end": 1368.72, "word": " عنصر", "probability": 0.86572265625}, {"start": 1368.72, "end": 1368.78, "word": " و", "probability": 0.9501953125}, {"start": 1368.78, "end": 1369.12, "word": " عنصر", "probability": 0.9127604166666666}, {"start": 1369.12, "end": 1369.56, "word": " بحط", "probability": 0.9705403645833334}, {"start": 1369.56, "end": 1370.28, "word": " نقطة", "probability": 0.96484375}, {"start": 1370.28, "end": 1370.78, "word": " التقاطع", "probability": 0.9305419921875}, {"start": 1370.78, "end": 1370.92, "word": " او", "probability": 0.8720703125}, {"start": 1370.92, "end": 1371.04, "word": " ال", "probability": 0.95361328125}, {"start": 1371.04, "end": 1371.28, "word": " element", "probability": 0.95361328125}, {"start": 1371.28, "end": 1371.46, "word": " بتاع", "probability": 0.53515625}, {"start": 1371.46, "end": 1371.88, "word": " التقاطع", "probability": 0.9686279296875}, {"start": 1371.88, "end": 1372.18, "word": " بينهم", "probability": 0.94921875}, {"start": 1372.18, "end": 1372.4, "word": " انه", "probability": 0.65380859375}, {"start": 1372.4, "end": 1372.94, "word": " بسوء", "probability": 0.67315673828125}, {"start": 1372.94, "end": 1373.3, "word": " واحد", "probability": 0.972412109375}, {"start": 1373.3, "end": 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1.0}, {"id": 55, "seek": 141257, "start": 1384.05, "end": 1412.57, "text": "لو قلنا أندي matrix، ال matrix هذه بتعطيني مجموعة ال courses المثاقات و كل مثاق في أي level في أي مستوى فهنا هنقول هدول المثاقات و هدول المستويات الدراسية تمام؟", "tokens": [1211, 2407, 12174, 1211, 8315, 14739, 16254, 8141, 12399, 2423, 8141, 29538, 39894, 3615, 9566, 9957, 1829, 3714, 7435, 2304, 2407, 27884, 2423, 7712, 9673, 12984, 995, 4587, 9307, 4032, 28242, 3714, 12984, 995, 4587, 8978, 36632, 1496, 8978, 36632, 3714, 14851, 2407, 7578, 6156, 3224, 8315, 8032, 1863, 39648, 8032, 3215, 12610, 9673, 12984, 995, 4587, 9307, 4032, 8032, 3215, 12610, 9673, 14851, 45865, 9307, 32748, 23557, 3794, 10632, 46811, 10943, 22807], "avg_logprob": -0.1506545594012415, "compression_ratio": 1.6280487804878048, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1384.05, "end": 1384.31, "word": "لو", "probability": 0.986328125}, {"start": 1384.31, "end": 1384.71, "word": " قلنا", "probability": 0.83984375}, 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نفسها بنفس القلية هذه انها تشبض رو في اللي بعدها انها تشبض رو في اللي بعدها عندما اخلص ال k times بتاعتنا عندما اخلص ال k times نفس الفكرة لل power اللي أخدناها سابقا تمام صور هذا هو الجزء اللي كان", "tokens": [1211, 1211, 257, 20449, 8717, 36178, 11296, 350, 3714, 25720, 1975, 2407, 1413, 4724, 11242, 25513, 11296, 8978, 8717, 36178, 11296, 44945, 36178, 25062, 1211, 10632, 29538, 16472, 11296, 6055, 8592, 3555, 11242, 12602, 2407, 8978, 13672, 1829, 39182, 11296, 16472, 11296, 6055, 8592, 3555, 11242, 12602, 2407, 8978, 13672, 1829, 39182, 11296, 43242, 15042, 1975, 9778, 1211, 9381, 2423, 350, 1413, 39894, 995, 34268, 8315, 43242, 15042, 1975, 9778, 1211, 9381, 2423, 350, 1413, 8717, 36178, 27188, 4117, 25720, 24976, 1347, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 8608, 16758, 4587, 995, 46811, 10943, 20328, 13063, 23758, 31439, 25724, 11622, 38207, 13672, 1829, 25961], "avg_logprob": -0.22641509560481557, "compression_ratio": 2.062176165803109, "no_speech_prob": 0.0, "words": 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"end": 2921.11, "text": "على طول بغير قيمته للقيمة اللي هي number بتاعة ال next اللي أنا روحتله هذا اللي هو ال AI طيب هنعمل repeating ل ال two steps هدولة خلصنا بعمل lock the next خلصنا next خلصنا next next next لحد ما نخلص كل ال sequence اللي موجود عندنا في الآخر خلصنا كل ال sequence كله كامل انتهى معانا return v", "tokens": [3615, 23942, 23032, 12610, 4724, 17082, 13546, 12174, 32640, 47395, 24976, 4587, 32640, 3660, 13672, 1829, 39896, 1230, 39894, 995, 27884, 2423, 958, 13672, 1829, 41850, 12602, 2407, 33753, 43761, 23758, 13672, 1829, 31439, 2423, 7318, 23032, 1829, 3555, 8032, 1863, 25957, 1211, 18617, 5296, 2423, 732, 4439, 8032, 3215, 12610, 3660, 16490, 1211, 9381, 8315, 4724, 25957, 1211, 4017, 264, 958, 16490, 1211, 9381, 8315, 958, 16490, 1211, 9381, 8315, 958, 958, 958, 5296, 24401, 19446, 8717, 9778, 1211, 9381, 28242, 2423, 8310, 13672, 1829, 3714, 29245, 23328, 43242, 8315, 8978, 6024, 95, 34740, 16490, 1211, 9381, 8315, 28242, 2423, 8310, 28242, 3224, 9122, 10943, 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"end": 2937.38, "word": " هذا", "probability": 0.822265625}, {"start": 2937.38, "end": 2937.76, "word": " بالمرة", "probability": 0.921875}, {"start": 2937.76, "end": 2938.02, "word": " معناه", "probability": 0.6696370442708334}, {"start": 2938.02, "end": 2938.46, "word": " حتى", "probability": 0.747802734375}, {"start": 2938.46, "end": 2938.7, "word": " بيصير", "probability": 0.8192138671875}, {"start": 2938.7, "end": 2939.04, "word": " يعطينا", "probability": 0.74395751953125}, {"start": 2939.04, "end": 2939.42, "word": " indication", "probability": 0.82958984375}, {"start": 2939.42, "end": 2939.74, "word": " كيف", "probability": 0.95654296875}, {"start": 2939.74, "end": 2940.1, "word": " مستوى", "probability": 0.9581298828125}, {"start": 2940.1, "end": 2940.62, "word": " الطالبات", "probability": 0.8988037109375}, {"start": 2940.62, "end": 2940.76, "word": " او", "probability": 0.826171875}, {"start": 2940.76, "end": 2940.94, "word": " كيف", "probability": 0.843017578125}, {"start": 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برضه لسه ماعملش code دي ربالكوا لسه ماعملناش code ماتكلمناش عن الأكواد بحدد ال sequence و find its maximum value فبقول set v ال temporary variable v بتسوي الأول a1 بتسوي 7 فإذا هذه seven look at the next element next element اللي هي 12", "tokens": [3555, 8592, 28820, 8496, 5551, 4117, 2655, 2288, 11331, 9957, 13412, 2407, 10632, 6225, 42213, 8315, 11296, 5296, 10721, 7251, 43020, 36764, 24401, 4724, 1829, 5016, 3555, 8592, 7251, 2655, 4117, 19528, 9122, 2655, 13546, 47525, 3224, 7251, 5016, 9566, 11296, 4439, 4724, 43042, 3224, 5296, 3794, 3224, 19446, 25957, 1211, 8592, 3089, 11778, 1829, 12602, 3555, 6027, 4117, 14407, 5296, 3794, 3224, 19446, 25957, 1211, 1863, 33599, 3089, 19446, 2655, 4117, 19528, 1863, 33599, 18871, 16247, 4117, 14407, 3215, 4724, 24401, 3215, 2423, 8310, 4032, 915, 1080, 6674, 2158, 6156, 3555, 39648, 992, 371, 2423, 13413, 7006, 371, 39894, 3794, 45865, 16247, 12610, 257, 16, 39894, 3794, 45865, 1614, 6156, 28814, 15730, 29538, 3407, 574, 412, 264, 958, 4478, 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الناتج، فهذا ال output، okay definiteness اللي هي ال precisely defined", "tokens": [6027, 29399, 16373, 7435, 13672, 1829, 41850, 3714, 14851, 22653, 11296, 50113, 15040, 9154, 9122, 23328, 6055, 3555, 34268, 45865, 3224, 31439, 691, 39894, 3794, 995, 45865, 11933, 1829, 8592, 22807, 2423, 8315, 2655, 7435, 12399, 1975, 3615, 9566, 9957, 1829, 2423, 8315, 2655, 7435, 12399, 6156, 3224, 15730, 2423, 5598, 12399, 1392, 1561, 6009, 442, 13672, 1829, 39896, 2423, 13402, 7642], "avg_logprob": -0.3772321570487249, "compression_ratio": 1.4171779141104295, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3064.92, "end": 3065.44, "word": "النتائج", "probability": 0.933349609375}, {"start": 3065.44, "end": 3065.54, "word": " اللي", "probability": 0.597900390625}, {"start": 3065.54, "end": 3065.62, "word": " أنا", "probability": 0.462158203125}, {"start": 3065.62, "end": 3066.02, "word": " مستنيها", "probability": 0.9017333984375}, {"start": 3066.02, "end": 3066.22, "word": " مثلا", 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و قد الغرض طيب ال correctness", "tokens": [1863, 36178, 13672, 1829, 12174, 1211, 8315, 3224, 14739, 6055, 30544, 1547, 2423, 3089, 6055, 3555, 3615, 8315, 1547, 4032, 13600, 20449, 28480, 47525, 28671, 7251, 30544, 20449, 28480, 47525, 28671, 20449, 28480, 4724, 13402, 7642, 4724, 2304, 3615, 1863, 7578, 14739, 3224, 6156, 3615, 15040, 7251, 30544, 28242, 3224, 20449, 28480, 28242, 16490, 9566, 2407, 3660, 9154, 16490, 9566, 2407, 9307, 3224, 20449, 28480, 3660, 47525, 28671, 37893, 3714, 4117, 2655, 38688, 3660, 11331, 33599, 2407, 9122, 2655, 13546, 4032, 12174, 3215, 6024, 118, 43042, 4032, 12174, 3215, 6024, 118, 43042, 23032, 1829, 3555, 2423, 3006, 1287], "avg_logprob": -0.15056817639957776, "compression_ratio": 1.815, "no_speech_prob": 0.0, "words": [{"start": 3082.89, "end": 3083.27, "word": "نفس", "probability": 0.922119140625}, {"start": 3083.27, "end": 3083.39, "word": " اللي", "probability": 0.865234375}, {"start": 3083.39, "end": 3083.87, "word": " قلناه", "probability": 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"word": " اتلتا", "probability": 0.9865234375}, {"start": 3486.52, "end": 3486.52, "word": " اتلتا", "probability": 0.9869140625}, {"start": 3486.52, "end": 3486.52, "word": " اتلتا", "probability": 0.9869140625}, {"start": 3486.52, "end": 3486.52, "word": " اتلتا", "probability": 0.987109375}, {"start": 3486.52, "end": 3486.52, "word": " اتلتا", "probability": 0.9875}, {"start": 3486.52, "end": 3486.7, "word": " اتلتا", "probability": 0.98759765625}, {"start": 3486.7, "end": 3487.38, "word": " اتلتا", "probability": 0.9876953125}, {"start": 3487.38, "end": 3487.72, "word": " اتلتا", "probability": 0.987890625}, {"start": 3487.72, "end": 3489.0, "word": " اتلتا", "probability": 0.98818359375}, {"start": 3489.0, "end": 3490.1, "word": " اتلتا", "probability": 0.98828125}, {"start": 3490.1, "end": 3491.06, "word": " اتلتا", "probability": 0.98837890625}, {"start": 3491.06, "end": 3492.26, "word": " اتلتا", "probability": 0.98837890625}, {"start": 3492.26, "end": 3492.88, "word": " اتلتا", "probability": 0.98857421875}, {"start": 3492.88, "end": 3493.54, "word": " اتلتا", "probability": 0.988671875}, {"start": 3493.54, "end": 3494.84, "word": " اتلتا", "probability": 0.9888671875}, {"start": 3494.84, "end": 3495.26, "word": " اتلت", "probability": 0.986328125}], "temperature": 1.0}, {"id": 141, "seek": 351563, "start": 3495.59, "end": 3515.63, "text": "انتجرز عشان انا بشتغل اكون عارف ان لا أنا بتكلمش عن real numbers فبحطله ايش نوع ال data اللي انا بده ادخلها ك input ال input data هذا او ال information او ال argument كما قلنا كويسة هذه لحالة هيك الجزء هذا بنقوله declaration هذا مجرد بتعمل تصريح اعلان عن code", "tokens": [7649, 2655, 7435, 2288, 11622, 6225, 8592, 7649, 1975, 8315, 4724, 8592, 2655, 17082, 1211, 1975, 30544, 6225, 9640, 5172, 16472, 20193, 41850, 4724, 2655, 4117, 19528, 8592, 18871, 957, 3547, 6156, 49628, 9566, 43761, 1975, 1829, 8592, 8717, 45367, 2423, 1412, 13672, 1829, 1975, 8315, 47525, 3224, 1975, 3215, 9778, 1211, 11296, 9122, 4846, 2423, 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otherwise داخل ال code إيش ممكن نكتب؟ ممكن نكتب حاجات كتيرة منها تعريف ال variables أن أكتب ال variable مثلا زي توي قولنا V بتساوي a1", "tokens": [4117, 8315, 44945, 4117, 2655, 3555, 28242, 10943, 4032, 9381, 5172, 4032, 9381, 5172, 4032, 28820, 10943, 3669, 4032, 3457, 559, 2662, 37893, 6225, 9640, 5172, 33599, 39182, 9957, 8608, 3555, 2655, 13412, 2407, 10632, 6156, 11242, 3660, 9122, 2655, 3555, 2655, 10747, 11469, 257, 16, 257, 17, 281, 364, 41674, 16490, 1211, 33546, 45030, 28480, 41850, 11778, 9778, 1211, 2655, 8978, 3089, 1975, 5016, 8315, 39896, 4117, 11778, 9778, 1211, 8315, 11933, 30241, 7649, 11778, 9778, 1211, 8315, 8978, 3089, 23032, 1829, 3555, 5911, 11778, 47283, 1211, 2423, 3089, 11933, 1829, 8592, 3714, 43020, 8717, 4117, 2655, 3555, 22807, 3714, 43020, 8717, 4117, 2655, 3555, 11331, 26108, 9307, 9122, 2655, 48923, 9154, 11296, 37279, 16572, 5172, 2423, 9102, 14739, 5551, 4117, 2655, 3555, 2423, 7006, 50113, 15040, 30767, 1829, 6055, 45865, 12174, 12610, 8315, 691, 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"probability": 0.998291015625}, {"start": 3536.26, "end": 3536.5, "word": " حاجات", "probability": 0.9609375}, {"start": 3536.5, "end": 3536.84, "word": " كتيرة", "probability": 0.94287109375}, {"start": 3536.84, "end": 3537.44, "word": " منها", "probability": 0.976318359375}, {"start": 3537.44, "end": 3537.88, "word": " تعريف", "probability": 0.9920247395833334}, {"start": 3537.88, "end": 3538.0, "word": " ال", "probability": 0.98291015625}, {"start": 3538.0, "end": 3538.46, "word": " variables", "probability": 0.9541015625}, {"start": 3538.46, "end": 3539.26, "word": " أن", "probability": 0.357177734375}, {"start": 3539.26, "end": 3539.6, "word": " أكتب", "probability": 0.9293212890625}, {"start": 3539.6, "end": 3539.78, "word": " ال", "probability": 0.97900390625}, {"start": 3539.78, "end": 3540.02, "word": " variable", "probability": 0.87841796875}, {"start": 3540.02, "end": 3540.34, "word": " مثلا", "probability": 0.986328125}, {"start": 3540.34, "end": 3540.52, "word": " زي", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6431c12536a78b38836c0688c4bbc64b58cbe82e
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_postprocess.srt
@@ -0,0 +1,3032 @@
+1
+00:00:20,740 --> 00:00:22,840
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:22,840 --> 00:00:25,560
+الأنبياء والمسؤالين سيدنا محمد وعلى الأقل هو صاحبي
+
+3
+00:00:25,560 --> 00:00:32,820
+أجمعي نكمل اليوم في ال order of growth ووصلنا
+
+4
+00:00:32,820 --> 00:00:37,800
+ل ال big O اتكلمنا عن ال big O و اتكلمنا عن مجموعة
+
+5
+00:00:37,800 --> 00:00:45,300
+facts about the big O وكان أهمها لما بتكلم عن جي
+
+6
+00:00:45,300 --> 00:00:49,100
+بتساوي big O of F
+
+7
+00:00:52,040 --> 00:00:56,800
+في حالة زي هذه معناته كأني بقول ان ال order مش ال
+
+8
+00:00:56,800 --> 00:01:00,400
+function و ركزوا معناه ال order بتكلم عن order مش
+
+9
+00:01:00,400 --> 00:01:05,780
+عن function ال order لأ ال function g مساوي لل
+
+10
+00:01:05,780 --> 00:01:10,180
+order of f أو أقل فإذا ال order مش ال function
+
+11
+00:01:10,180 --> 00:01:18,240
+بمعنى ممكن تكون هذه عبارة عن twox تربيع زائد x
+
+12
+00:01:18,240 --> 00:01:22,700
+ومساوية ل big O of function ال function هذه عبارة
+
+13
+00:01:22,700 --> 00:01:31,320
+عن x تربيع على اتنين في مثلا او مباشرة على طول
+
+14
+00:01:31,320 --> 00:01:40,380
+زائد او ناقص x تلاتة x لاحظوا ان هذه لا تساوي هذه
+
+15
+00:01:40,380 --> 00:01:44,420
+ولكن ال order نفس ال orderال order نفس ال order
+
+16
+00:01:44,420 --> 00:01:47,660
+احنا هنا جاعدين نتكلم عن order ال order نفس ال
+
+17
+00:01:47,660 --> 00:01:53,300
+order كويس ففي الحالة هذه لو قلنا a في f ال order
+
+18
+00:01:53,300 --> 00:01:57,840
+بتغيرش ال a هذا constant belonging to r to real
+
+19
+00:01:57,840 --> 00:02:02,080
+number فأي element او constant اللي بنضربه فيه ال
+
+20
+00:02:02,080 --> 00:02:05,300
+function مش هيغير ال order لل function ال function
+
+21
+00:02:05,300 --> 00:02:08,840
+تربيعية هتظل تربيعية تكعيبية هتظل تكعيبية first
+
+22
+00:02:08,840 --> 00:02:11,140
+order هتظل first order او ال linear هتظل ال linear
+
+23
+00:02:12,750 --> 00:02:18,190
+بمعنى تلاتة X تربيعية هي big O of X تربيع اف زائد
+
+24
+00:02:18,190 --> 00:02:23,650
+big O of F بمعنى لو كانت هذه تربيع هذه نفطرة
+
+25
+00:02:23,650 --> 00:02:28,790
+تربيعية طيب لما تقولوا big O of F هذه ايش هتكون
+
+26
+00:02:28,790 --> 00:02:36,210
+تربيعية او اقل تربيع هذا على الاكثر طيب مجموحهم
+
+27
+00:02:36,210 --> 00:02:40,910
+برضه هتكون تربيع فاذا big O of F ولو كانت اقل من
+
+28
+00:02:40,910 --> 00:02:45,520
+تربيعبرضه تربيع زائد linear او زائد constant او
+
+29
+00:02:45,520 --> 00:02:50,900
+زائد inverse هتظل برضه تربيع هتظل big O of second
+
+30
+00:02:50,900 --> 00:02:56,480
+order او big O of F نفسها فمعنى ذلك هنا لو قلنا X
+
+31
+00:02:56,480 --> 00:03:02,880
+تربيع plus X و X هذه big O of F ال F هنا اللي هي
+
+32
+00:03:02,880 --> 00:03:06,340
+تربيعية فهتظل ال function كلها على بعض برضه big O
+
+33
+00:03:06,340 --> 00:03:13,920
+of FOkay الجزء التاني في ال fact سبعتنا بدنا نعرف
+
+34
+00:03:13,920 --> 00:03:19,640
+إيش هي ال big omega one أولا ال order one هذا إيش
+
+35
+00:03:19,640 --> 00:03:26,700
+هو هذا constant بمعنى إنه كأنها F to the power
+
+36
+00:03:26,700 --> 00:03:27,920
+zero
+
+37
+00:03:31,000 --> 00:03:35,340
+فمعنى ذلك بيتكلم عن constant طيب نجى لجزء التانى
+
+38
+00:03:35,340 --> 00:03:41,340
+ال big omega معناته constant او اكبر constant او
+
+39
+00:03:41,340 --> 00:03:45,360
+اكبر تمام خلينا نجى نشوف constant او at least
+
+40
+00:03:45,360 --> 00:03:51,240
+order zero او order one then absolute f to the
+
+41
+00:03:51,240 --> 00:03:56,040
+power one minus b و b هنا اكبر من او يساوي zero
+
+42
+00:03:57,080 --> 00:04:00,680
+بتساوي big O of F طب أكبر قيمة .. أصغر قيمة ممكن
+
+43
+00:04:00,680 --> 00:04:07,900
+أنها تكون Zero لو قولنا Zero هنا هتطلع F نفسها ف F
+
+44
+00:04:07,900 --> 00:04:11,300
+نفسها هي big O of F هي نفس أصلا big O of F نفس
+
+45
+00:04:11,300 --> 00:04:16,940
+الدرجة ماتغيرتش طيب لو كانت one minus one constant
+
+46
+00:04:16,940 --> 00:04:21,980
+constant مع ال constant برضه big O of F طيب اتنين
+
+47
+00:04:23,630 --> 00:04:30,970
+-1 يعني 1 على F أقل من big O of F فنفس الكلام أو
+
+48
+00:04:30,970 --> 00:04:35,690
+أقل من ال order لل F فإذا تنفع مع big O of F زي X
+
+49
+00:04:35,690 --> 00:04:36,750
+to the power of minus 1
+
+50
+00:04:42,030 --> 00:04:50,390
+Log أقل من X فأي order نعمله log هيكون order أقل
+
+51
+00:04:50,390 --> 00:04:54,750
+مادام order أقل يتفق مع علامة أو ال notation بتاعة
+
+52
+00:04:54,750 --> 00:04:56,450
+big O of F
+
+53
+00:05:00,090 --> 00:05:03,050
+تبعت big O ببساطة جدا انتوا لما بيقولوا مثلا
+
+54
+00:05:03,050 --> 00:05:08,310
+linear ال linear الف ال output تبعها الف مليون ال
+
+55
+00:05:08,310 --> 00:05:14,370
+output تبعها مليون طب تعالى نشوف log log الف تلاتة
+
+56
+00:05:14,370 --> 00:05:19,610
+log مليون ستة ستة فواضح ان هي كقيمة اقل كتير و
+
+57
+00:05:19,610 --> 00:05:24,250
+بالعكس حتى الفرق بزيد بينهم الفرق بزيد بينهم فهدي
+
+58
+00:05:24,250 --> 00:05:30,470
+ال order تبعها كتير اقل من ال order ال Fطيب جي
+
+59
+00:05:30,470 --> 00:05:37,590
+بتساوي big O F of G تمام واضح برضه أنه هنا نتكلم
+
+60
+00:05:37,590 --> 00:05:46,760
+عن relation صحيحة على اعتبار أن ال F أكبر أكبرأو
+
+61
+00:05:46,760 --> 00:05:51,840
+تساوي 0 order بمعنى أكبر من constant فأقل قيمة لها
+
+62
+00:05:51,840 --> 00:05:56,120
+أقل order لها أنها تكون constant تكون constant فلو
+
+63
+00:05:56,120 --> 00:06:00,600
+كانت constant هنا فال G بتساوي big O of G منطقية
+
+64
+00:06:00,600 --> 00:06:06,620
+ال function هي نفس orderها صح طيب أكبرfirst order
+
+65
+00:06:06,620 --> 00:06:13,060
+first في جي بتزيد قاعدة الجي فالجي ضمن حدود ال big
+
+66
+00:06:13,060 --> 00:06:19,440
+O of FG فهتضمن
+
+67
+00:06:19,440 --> 00:06:29,450
+حدود ال big O بتاعتناوالعكس مش صحيح الحالة
+
+68
+00:06:29,450 --> 00:06:31,730
+الوحيدة اللي ممكن تساوي فيها إذا كانت ال F first
+
+69
+00:06:31,730 --> 00:06:35,530
+order بس Zero order عفوا Zero order بمعنى constant
+
+70
+00:06:35,530 --> 00:06:40,370
+إذا كانت constant it's okay otherwise لأ إذا كانت
+
+71
+00:06:40,370 --> 00:06:44,470
+first في حالة زي هذه X و هنا log X طبعا هذه لا
+
+72
+00:06:44,470 --> 00:06:51,050
+تساوي big O of Xتمام هذا لا تساوي big O of X ولا
+
+73
+00:06:51,050 --> 00:06:56,730
+تساوي big O of log X لأنه أكبر من التنتين أكبر من
+
+74
+00:06:56,730 --> 00:07:02,410
+التنتين او
+
+75
+00:07:02,410 --> 00:07:07,810
+فال X log X أكبر منها ال X log X هتكون أكبر من big
+
+76
+00:07:07,810 --> 00:07:14,650
+O of X طيب ال A أو ال constant equal to big O of F
+
+77
+00:07:14,650 --> 00:07:20,370
+constant هيكون ضمنضمن ال big O of X مدام أنا بقول
+
+78
+00:07:20,370 --> 00:07:26,130
+ان ال big O of X هي constant او اكبر zero order او
+
+79
+00:07:26,130 --> 00:07:29,610
+اكبر zero order او اكبر فممكن تكون first order
+
+80
+00:07:29,610 --> 00:07:33,810
+second order third logarithmic order اي شي بس في
+
+81
+00:07:33,810 --> 00:07:37,990
+جميع الأحوال ال constant هو اقل قيمة لها ف belong
+
+82
+00:07:37,990 --> 00:07:47,460
+to big O of F طيب لووصلنا إلى النتيجة أن ال F
+
+83
+00:07:47,460 --> 00:07:53,080
+belonged to big O of G and ال G belonged to big O
+
+84
+00:07:53,080 --> 00:07:58,340
+of F بمعنى كل واحدة منهم big O من التانية معناته
+
+85
+00:07:58,340 --> 00:08:02,060
+الإثنين بيسووا بعض وهذا لو متذكرين طريقة الإثبات
+
+86
+00:08:02,060 --> 00:08:06,140
+اللي كنا نعملها في ال matrices في ال sets أيام ما
+
+87
+00:08:06,140 --> 00:08:09,700
+كنا نتكلم في ال sets في ال set في المجموعات عشان
+
+88
+00:08:09,700 --> 00:08:12,400
+نثبت أن في مجموعتين بيسووا بعض كنا بدنا نثبت
+
+89
+00:08:12,400 --> 00:08:16,680
+شغلتين مع بعضكنا نثبت إن الأولى صبست من التانية،
+
+90
+00:08:16,680 --> 00:08:19,060
+وبعدين نثبت أن التانية صبست من الأولى، فبنقول إن
+
+91
+00:08:19,060 --> 00:08:24,460
+هم متساويتين طيب هنا نفس الكلام، لو قولنا ال F أقل
+
+92
+00:08:24,460 --> 00:08:28,980
+من أو تساوي ال order G طيب G أقل من أو تساوي ال
+
+93
+00:08:28,980 --> 00:08:32,480
+order F فالعمل المشترك بين التنتين، أن الأتنين
+
+94
+00:08:32,480 --> 00:08:37,520
+بيسووا بعض، فهذا بمعناه أن ال G and Fof the same
+
+95
+00:08:37,520 --> 00:08:43,140
+order of انما بنعطيها ال big theta بنعطيها big
+
+96
+00:08:43,140 --> 00:08:48,520
+theta فإذا f big theta of g او g big theta of f
+
+97
+00:08:48,520 --> 00:08:54,820
+تمام if is exactly order g لا أكبر ولا أقل هي
+
+98
+00:08:54,820 --> 00:08:59,700
+exactly نفس order g و بنكتبها if belong to big
+
+99
+00:08:59,700 --> 00:09:05,720
+theta of g و نفس الكلام نقدر نقول ان ال git
+
+100
+00:09:05,720 --> 00:09:11,900
+belongs to big theta of F طيب
+
+101
+00:09:11,900 --> 00:09:15,540
+نشوف بقى مجموعة rules او facts برضه about big
+
+102
+00:09:15,540 --> 00:09:18,220
+theta و هل تتناسب مع ال big O اللي احنا خدناها
+
+103
+00:09:18,220 --> 00:09:21,940
+سابقا او لا و اين بتختلف و انتوا تشبه نشوف اول
+
+104
+00:09:21,940 --> 00:09:27,760
+شغلةfor all f g أكبر من 0 ال two functions هدول
+
+105
+00:09:27,760 --> 00:09:32,580
+أكبر من 0 و في عندنا constants a و b belonging to
+
+106
+00:09:32,580 --> 00:09:36,820
+R و ال a و ال b أكبر من صفر أكبر من صفر فازم انا
+
+107
+00:09:36,820 --> 00:09:43,260
+بتكلم عن positive real number هد ال b a في f مش
+
+108
+00:09:43,260 --> 00:09:49,250
+هتتغير ال order هد ال constantالـ a constant فأي
+
+109
+00:09:49,250 --> 00:09:52,590
+constant في ال function مش هيغير ال order ال order
+
+110
+00:09:52,590 --> 00:09:56,510
+f حتضل f ال order تربيه حتضل تربيه أو second order
+
+111
+00:09:56,510 --> 00:09:58,830
+حتضل second order first order حتضل first order
+
+112
+00:09:58,830 --> 00:10:05,070
+فهذه مشابهة ل ال big O مشابه حتى لان ال big O طيب
+
+113
+00:10:05,070 --> 00:10:10,950
+و لكن ال f not belong to θ f و g احنا قلنا انه
+
+114
+00:10:10,950 --> 00:10:13,950
+أكبر من صفر فهذه ممكن تكون first order second
+
+115
+00:10:13,950 --> 00:10:18,530
+order third orderإذا كانتالتنتين هدولة first order
+
+116
+00:10:18,530 --> 00:10:23,190
+هدي first و هدي first ضربهم في بعض second order طب
+
+117
+00:10:23,190 --> 00:10:27,130
+كيف بده أقول first order big theta ل second order
+
+118
+00:10:27,130 --> 00:10:31,250
+لأ بيسووش بعض exactly هنا بيسووش بعض لو big O
+
+119
+00:10:31,250 --> 00:10:35,390
+بيمشي الحال ولكن big theta بيمشيش الحال إلا في
+
+120
+00:10:35,390 --> 00:10:40,590
+حالة واحدة إذا كان ال G first order zero order
+
+121
+00:10:40,590 --> 00:10:44,110
+بمعنى constant constant بصير نفس ال relation اللي
+
+122
+00:10:44,110 --> 00:10:48,540
+فوقها بصير نفس ال relation اللي فوقهافهذه unlike
+
+123
+00:10:48,540 --> 00:10:54,880
+big O okay absolute if to the power one minus b
+
+124
+00:10:54,880 --> 00:11:02,040
+one minus b احنا قلنا بي أكبر من صفر فإذا واحد لو
+
+125
+00:11:02,040 --> 00:11:07,600
+حاطين هنا واحد zero طب ال constant بسويش first
+
+126
+00:11:07,600 --> 00:11:09,960
+order صح؟
+
+127
+00:11:11,250 --> 00:11:14,730
+هنا واضح ان ال order لل F سواء first order second
+
+128
+00:11:14,730 --> 00:11:19,930
+order third order هينجس واحد او هصير zero order
+
+129
+00:11:19,930 --> 00:11:24,750
+هنا هصير zero order لا تساوي theta of F نفس الكلام
+
+130
+00:11:24,750 --> 00:11:28,390
+في ال log لان احنا عارفين ان ال log أقل abstractly
+
+131
+00:11:28,390 --> 00:11:34,190
+أقل من ال order ل F نفسها فلما بقول log F اكيد
+
+132
+00:11:34,190 --> 00:11:39,900
+هيكون أقل منF نفسها فلا يساوي .. لا يساوي ال order
+
+133
+00:11:39,900 --> 00:11:43,220
+F .. لا يساوي ال order F ال .. ال big theta لازم
+
+134
+00:11:43,220 --> 00:11:47,060
+exactly equal to نفس ال order .. equal .. the same
+
+135
+00:11:47,060 --> 00:11:51,960
+order أما هنا لأ هو strictly هيكون أقل في آخر
+
+136
+00:11:51,960 --> 00:11:56,140
+حالتين .. الحالتين هدولة دائما ال two operations
+
+137
+00:11:56,140 --> 00:12:00,960
+هدولة هيكونوا أقل من theta of F .. دائما هيكونوا
+
+138
+00:12:00,960 --> 00:12:01,660
+أقل من theta
+
+139
+00:12:06,810 --> 00:12:10,950
+حتى لو كان polylogarithmic ستكون أقل من ال order f
+
+140
+00:12:10,950 --> 00:12:15,730
+أقل من ال normal أقل من ال normal حتى لو S أي شاء
+
+141
+00:12:15,730 --> 00:12:23,370
+حتى لو S أي شاء ستكون أقل ستكون أقل على أساس أنه
+
+142
+00:12:23,370 --> 00:12:26,150
+واضح أن هذه polylogarithmic polylogarithmic
+
+143
+00:12:26,150 --> 00:12:29,930
+polylogarithmic function فال polylogarithmic
+
+144
+00:12:29,930 --> 00:12:36,910
+function أقل من ال linearطيب بدنا نحسب هالوجة إذا
+
+145
+00:12:36,910 --> 00:12:41,410
+فعلا عملت ال summation ل oiler من ذكرينه ل oiler
+
+146
+00:12:41,410 --> 00:12:46,050
+عبارة عن second order أو لأ هل فعلا هي كانت second
+
+147
+00:12:46,050 --> 00:12:50,210
+order أو لأ ال summation الذاكرية كيف كنا نحسبه n
+
+148
+00:12:50,210 --> 00:12:54,670
+في n plus 1 على 2 فهي ال summation نفسها n في n
+
+149
+00:12:54,670 --> 00:13:04,070
+plus 1 على 2 طيب ال n plus 1zero first order هذه
+
+150
+00:13:04,070 --> 00:13:09,930
+first order فبنقول theta of first order n مضروبة
+
+151
+00:13:09,930 --> 00:13:14,910
+في n على two طيب على two يعني كأني أنا بتكلم عن
+
+152
+00:13:14,910 --> 00:13:21,270
+theta n مضروبة في نصconstant انتوا هنا بتتكلموا عن
+
+153
+00:13:21,270 --> 00:13:23,970
+constant فconstant مايغيرش في ال order ال order
+
+154
+00:13:23,970 --> 00:13:28,670
+بيضل زي ما هو طيب في عندنا function برضه هدى هتكون
+
+155
+00:13:28,670 --> 00:13:35,710
+عبارة عن θ of n في θ of n n تربيع ضربهم في بعض
+
+156
+00:13:35,710 --> 00:13:41,030
+مباشرة هيساوي θ of n تربيع فال order second order
+
+157
+00:13:41,760 --> 00:13:44,640
+second order في الحالة اللي عندنا فلما تيجوا
+
+158
+00:13:44,640 --> 00:13:48,340
+تجمعوها بهذا الشكل و تشتغلوا على n في n plus واحد
+
+159
+00:13:48,340 --> 00:13:51,860
+على اتنين انتوا هنا بتتكلموا عن equation من الدرجة
+
+160
+00:13:51,860 --> 00:13:57,780
+أو من ال order الثاني من ال order التاني وهي عندكم
+
+161
+00:13:57,780 --> 00:14:02,620
+واضحة الترتيب تبعها طيب المرة اللي فاتت برضه
+
+162
+00:14:02,620 --> 00:14:04,360
+اتكلمنا عن other
+
+163
+00:14:06,600 --> 00:14:11,160
+relations other relations خلينا نرجع نعرج عليهم
+
+164
+00:14:11,160 --> 00:14:18,780
+كمان مرة لما كنا بنقول G هنا كله كاتبهم في G خلينا
+
+165
+00:14:18,780 --> 00:14:24,460
+نقول معناته F F بتساوي big O of G
+
+166
+00:14:26,790 --> 00:14:31,310
+هذه كانت إيش معناها؟ معناته إن ال order ل F أقل من
+
+167
+00:14:31,310 --> 00:14:35,090
+أو يساوي order G، أقل من أو يساوي order G، معناه
+
+168
+00:14:35,090 --> 00:14:41,190
+ذلك بقدر أقول إن ال F أقل من أو تساوي order G، هنا
+
+169
+00:14:41,190 --> 00:14:49,270
+بدأ أتكلم عن ال order، بتكلمش عن ال functionنتكلمش
+
+170
+00:14:49,270 --> 00:14:51,930
+عن مين؟ عن ال function، نتكلم عن ال order لل
+
+171
+00:14:51,930 --> 00:14:56,330
+function، معدلة التغير، جدش؟ أو ال growth تبعها،
+
+172
+00:14:56,330 --> 00:15:02,910
+كويس، طيب، كان في عندنا f small o of g، كانت
+
+173
+00:15:02,910 --> 00:15:09,070
+strictly أقل من، strictly أقل من، فهنا f أقل من g،
+
+174
+00:15:09,070 --> 00:15:17,980
+أقل من g، كان في عندنا big omega of gأكبر أو تساوي
+
+175
+00:15:17,980 --> 00:15:22,000
+دائما ال big أو يساوي مادام فيها big معناته فيها
+
+176
+00:15:22,000 --> 00:15:28,800
+يساوي طيب ف if أكبر من أو تساوي g طيب if بتساوي
+
+177
+00:15:28,800 --> 00:15:39,740
+small omega if strictly أكبر من g وأخيرا ال big
+
+178
+00:15:39,740 --> 00:15:45,020
+theta of g فهذه تساوي
+
+179
+00:15:47,620 --> 00:15:54,000
+G فلاحظوا كيف احنا بنكتبهم كمان لأنه
+
+180
+00:15:54,000 --> 00:15:57,720
+order نتكلم عن order نكتبش اكبر من او يساوي اللي
+
+181
+00:15:57,720 --> 00:16:03,220
+احنا عارفينها بالشكل هذا فيها ميالان شوية على اساس
+
+182
+00:16:03,220 --> 00:16:05,580
+تعرفوا بس انه احنا بنتكلم هنا عن ال order نتكلم مش
+
+183
+00:16:05,580 --> 00:16:08,080
+عن ال function نتكلم عن order نتكلم مش عن ال
+
+184
+00:16:08,080 --> 00:16:15,520
+function لأنه ببساطة تلاتة X تربيع ناقص X زائد مية
+
+185
+00:16:16,400 --> 00:16:22,720
+هي فعليا لا تساوي X تربيع، صحيح؟ ولكن ال order
+
+186
+00:16:22,720 --> 00:16:26,280
+بيساوي بعض، ال order بيساوي بعض، ك order لأ بيساوي
+
+187
+00:16:26,280 --> 00:16:33,660
+بعض الإتنين فالإتنين، الإتنين بيتفقوا إن الإتنين،
+
+188
+00:16:33,660 --> 00:16:40,440
+إيش بنقدر نقول عليهم؟ belong to X θ X تربيع،
+
+189
+00:16:40,440 --> 00:16:44,110
+الإتنين belong to θ X تربيعمتفقين ان الاتنين
+
+190
+00:16:44,110 --> 00:16:48,390
+second order برغم اختلافهم و بيساووش بعض فعليا،
+
+191
+00:16:48,390 --> 00:16:51,030
+بيساووش بعض فاحنا هنا متكلم عن ال order ماتنسوش
+
+192
+00:16:51,030 --> 00:16:53,410
+طيب فعنا ال big
+
+193
+00:17:02,580 --> 00:17:07,900
+أو أكبر بمعنى أنها نفس order g أو أكبر فكل ال
+
+194
+00:17:07,900 --> 00:17:10,800
+functions اللي بتتفق في هذا الكلام هي داخل ال set
+
+195
+00:17:10,800 --> 00:17:21,690
+big omega طيب small o of g هي كل ال functionsفاللي
+
+196
+00:17:21,690 --> 00:17:27,330
+هتكون إيش strictly أقل من order g، أقل من order g،
+
+197
+00:17:27,330 --> 00:17:31,990
+بينفعش تساوي، لا يجيزش تساوي، طيب small omega
+
+198
+00:17:31,990 --> 00:17:38,070
+strictly أكبر من order g، strictly أكبر من order g
+
+199
+00:17:38,070 --> 00:17:43,290
+أو الزمن لازم يكون أكبر من order g، لا تساوي، okay
+
+200
+00:17:44,830 --> 00:17:47,210
+مجموعة relations برضه هنتكلم عنها طبعا واضح أنه
+
+201
+00:17:47,210 --> 00:17:50,050
+احنا هنا أخدنا المجموعة ال notations الجديدة
+
+202
+00:17:50,050 --> 00:17:55,830
+بتاعتنا اللي هي ال order أقل من فهذه ال F have the
+
+203
+00:17:55,830 --> 00:17:59,350
+order أقل من order G فانا هنا بأتكلم عن مين عن
+
+204
+00:17:59,350 --> 00:18:04,650
+small O فش يساوي .. فش يساوي .. إذا فيه يساوي
+
+205
+00:18:04,650 --> 00:18:10,090
+بتصير ال big O فهنا to mean F belong to small O of
+
+206
+00:18:10,090 --> 00:18:13,630
+G طيب و F approximately
+
+207
+00:18:15,180 --> 00:18:19,800
+أو تقريبا تساوي G ك order فهي quality ك order
+
+208
+00:18:19,800 --> 00:18:23,340
+بتساوي G هذا معناه ان ال F برمته big theta of G
+
+209
+00:18:23,340 --> 00:18:31,410
+كويس عشان اقول ان ال F strictlysmall o of g او
+
+210
+00:18:31,410 --> 00:18:35,130
+strictly اقل من g في ال order طبعا ال order تبعها
+
+211
+00:18:35,130 --> 00:18:38,670
+اقل من g هذا امتى بيصير الكلام هذا اذا كان في ال
+
+212
+00:18:38,670 --> 00:18:44,810
+infinity لما بعمل limit to infinity f of x على g
+
+213
+00:18:44,810 --> 00:18:52,610
+of x equal to zero limit to zero limit to zero لما
+
+214
+00:18:52,610 --> 00:19:00,080
+اتكلموا عنال logarithmic logarithmic function بهذا
+
+215
+00:19:00,080 --> 00:19:11,580
+الشكل طبعا لحظه لما عند x بتساوي مليون مثلا جداش
+
+216
+00:19:11,580 --> 00:19:16,160
+قيمة ال logarithmic function ستة هتكون عند قيمة
+
+217
+00:19:16,160 --> 00:19:19,940
+الستة طيب لو بدنا نقارن هذه مع
+
+218
+00:19:22,960 --> 00:19:26,940
+مع cubic function مع تكعيبية مع function تكعيبية
+
+219
+00:19:26,940 --> 00:19:36,580
+هنا y بتساوي x تكعيب x تكعيب عند المليون تمانتاشر
+
+220
+00:19:36,580 --> 00:19:44,600
+صفر نتكلم عن تمانتاشر صفر فتمانتاشر صفر صحيح طيب
+
+221
+00:19:44,600 --> 00:19:52,610
+عند الألف هنا كانت تلاتة هنا كانت تسعةطيب لحظة
+
+222
+00:19:52,610 --> 00:19:56,890
+معدل التغير هذه معدل تغيرها بزيد أكبر بكتير من
+
+223
+00:19:56,890 --> 00:20:02,270
+معدل التغير هذه هنا كانت تلاتة هنا كانت عشرة to
+
+224
+00:20:02,270 --> 00:20:08,150
+the power تسعة هنا من تلاتة ل .. لجداش لستة الضعف
+
+225
+00:20:08,150 --> 00:20:15,070
+تطورت للضعف هنا لأ هنا تطورت لأضعاف ل
+
+226
+00:20:15,070 --> 00:20:19,390
+multiplication مش لمجرد ضعف يعني ماضربنهاش بس في
+
+227
+00:20:19,390 --> 00:20:23,510
+اتنين لأ احنا ضربناها في نفسهاأحنا ضربناها في
+
+228
+00:20:23,510 --> 00:20:27,470
+تكعيب، يعني كعبناها، تمام؟ مش مجرد ان ضربناها في
+
+229
+00:20:27,470 --> 00:20:32,130
+نفسها، تمام؟ فواضح ان معدل التغير بزيد كتير بينهم،
+
+230
+00:20:32,130 --> 00:20:34,930
+الفرق بزيد كتير بينهم طيب في ال infinity to
+
+231
+00:20:34,930 --> 00:20:42,770
+infinity ممكن تصل ان ال log على تكعيب limit to
+
+232
+00:20:42,770 --> 00:20:49,210
+zerolimit to zero هنا كنت بتتكلم عن تلاتة على عشرة
+
+233
+00:20:49,210 --> 00:20:53,370
+to the power تسعة قيمة كتير صغيرة بس لسه ستة على
+
+234
+00:20:53,370 --> 00:20:59,230
+عشرة to the power تمانتاش أقل كمان لو أخدته أكتر
+
+235
+00:20:59,230 --> 00:21:03,070
+عشرة مليون عشرين مليون خمسين مليون طبعا ال ratio
+
+236
+00:21:03,070 --> 00:21:08,310
+هتجل أكتر بينهم limit to infinity ال term هذا
+
+237
+00:21:08,310 --> 00:21:13,920
+limit to zeroفإذا f of x على g of x limit to zero
+
+238
+00:21:13,920 --> 00:21:16,860
+إذا كان تحقق الكلام ده بقدر أقوله مباشرة فإذا ال
+
+239
+00:21:16,860 --> 00:21:22,960
+order أقل strictly أقل من g strictly أقل من g إذا
+
+240
+00:21:22,960 --> 00:21:25,880
+نفس ال order يلهم نفس ال order بيكون بيكون كل
+
+241
+00:21:25,880 --> 00:21:30,140
+الفرج انه ماشيين مع بعض معدل التغير تبعهم ثابت
+
+242
+00:21:30,140 --> 00:21:36,680
+معدل تغيرهم ثابت تمام فأظن وضحت ال limitation هذه
+
+243
+00:21:39,470 --> 00:21:42,270
+مجموعة functions هتتعاملوا معها .. بتضطروا
+
+244
+00:21:42,270 --> 00:21:45,870
+تتعاملوا معها نشوف إيش ال relations بينهم ال one
+
+245
+00:21:45,870 --> 00:21:51,850
+zero order أو constant أقل من log of log M أقل من
+
+246
+00:21:51,850 --> 00:21:55,910
+ال log .. ليش؟ وإن كان معدل تغيره صغير ولكن في
+
+247
+00:21:55,910 --> 00:21:59,410
+معدل تغير ال constant مافي معدل تغير معدل تغير
+
+248
+00:21:59,410 --> 00:22:04,810
+zero constant معناته معدل تغير zero خلاص ثابت
+
+249
+00:22:04,810 --> 00:22:09,230
+مافيش معدل تغيره بتتغيرش مافيش growth بتصيرفيش نمو
+
+250
+00:22:09,230 --> 00:22:15,390
+بيصير في ال function بعكس ال log ال log بتتغير
+
+251
+00:22:15,390 --> 00:22:18,990
+okay بسيط احنا متفقين تغير بطيق ماشي بس في نهاية
+
+252
+00:22:18,990 --> 00:22:25,190
+في تغير في تغير فإذا ال order تبح أكبر من الواحد
+
+253
+00:22:25,190 --> 00:22:31,510
+طب في نفس الوجد log of n أكبر من log of log n ليش؟
+
+254
+00:22:31,510 --> 00:22:36,150
+لأنه ممكن نتعاملوا مع ال term هذا على أساس انه x
+
+255
+00:22:36,150 --> 00:22:45,710
+وهذا هيو xف log x أقل من x log x أقل من x نفس
+
+256
+00:22:45,710 --> 00:22:51,810
+الكلام سنقوله لاحقا ان log x دائما أقل من x في
+
+257
+00:22:51,810 --> 00:22:55,310
+الحالة اللي انا زى تقوى المليون في ال .. في ال ..
+
+258
+00:22:55,310 --> 00:22:59,950
+في ال linear هتسوى مليون input بيسوى مليون ال
+
+259
+00:22:59,950 --> 00:23:05,110
+output هتسوى مليون طيب مليون في ال log هسوى 6 أقل
+
+260
+00:23:05,110 --> 00:23:11,490
+بكتير فحتى معدل تغيره أقل طيب logال base تبعتك
+
+261
+00:23:11,490 --> 00:23:17,950
+تبعتنا decimal أو عشري هي هي لو ال log أي أساس آخر
+
+262
+00:23:17,950 --> 00:23:23,630
+لأي base تانية المعدل هو هو في تغير بيصير بينه قيم
+
+263
+00:23:23,630 --> 00:23:27,470
+اه بس بيظلوا ماشيين مع بعض بيظلوا ماشيين مع بعض
+
+264
+00:23:27,470 --> 00:23:30,990
+فمعدل تغيرهم بيظل ثابت مساوي لبعضه فهذا بيقول
+
+265
+00:23:30,990 --> 00:23:35,950
+بيساوي بعض بغض النظر عن مين عن الأساس الأساس ال
+
+266
+00:23:35,950 --> 00:23:41,090
+log بغض النظر عن أساس ال log تبعتناهنا هذه أقل من
+
+267
+00:23:41,090 --> 00:23:46,070
+ال poly logarithmic، أقل من ال poly logarithmic
+
+268
+00:23:46,070 --> 00:23:48,650
+function، أقل من ال poly logarithmic function ف
+
+269
+00:23:48,650 --> 00:23:54,210
+log الأساس k of n أقل من log to the power k، أقل
+
+270
+00:23:54,210 --> 00:23:56,670
+من ال poly logarithmic، فإذا في عندنا poly
+
+271
+00:23:56,670 --> 00:23:58,530
+logarithmic و في عندنا logarithmic function
+
+272
+00:23:59,550 --> 00:24:03,110
+بوليولغريثمك أكبر من ال logarithmic طيب و هذه
+
+273
+00:24:03,110 --> 00:24:08,470
+هتكون برضه نفس الكلام أقل من ان to the power one
+
+274
+00:24:08,470 --> 00:24:12,950
+over x من ال inverse من ال inverse ال inverse أقل
+
+275
+00:24:12,950 --> 00:24:18,710
+من ال n ال n أقل من n log n على اعتبار أن هذه
+
+276
+00:24:18,710 --> 00:24:22,110
+مضروبة في واحد هذه مضروبة في log n و احنا هنا لسه
+
+277
+00:24:22,110 --> 00:24:25,530
+بنقول ال واحد كانت أقل من log n فإذن طبيعي هذا
+
+278
+00:24:25,530 --> 00:24:37,310
+هيكونن أقل من ن في log n log n أقل من ال
+
+279
+00:24:37,310 --> 00:24:40,690
+polynomial من ال polynomial function n to the
+
+280
+00:24:40,690 --> 00:24:44,830
+power k تكعيب تربيع to the power four to the power
+
+281
+00:24:44,830 --> 00:24:49,950
+five polynomial أقل من ال polynomial اللي أكبر من
+
+282
+00:24:49,950 --> 00:24:56,480
+ال polynomial ال exponential اللي هيكي ثابت to the
+
+283
+00:24:56,480 --> 00:25:01,240
+power متغير to the power متغير هذه exponential هذه
+
+284
+00:25:01,240 --> 00:25:07,140
+exponential function فهذه أكبر من variable موجود
+
+285
+00:25:07,140 --> 00:25:11,020
+to the power constant to polynomial فال
+
+286
+00:25:11,020 --> 00:25:14,520
+exponential أكبر من ال polynomial functions okay
+
+287
+00:25:14,520 --> 00:25:19,120
+exponential اللي أكبر منها factorial
+
+288
+00:25:21,200 --> 00:25:24,280
+الفكتوري لما بيقول مية معناه ذلك أن أنا بتكلم عن
+
+289
+00:25:24,280 --> 00:25:27,720
+مية في تسعة وتسعين في تمانية وتسعين في سبعة وتسعين
+
+290
+00:25:27,720 --> 00:25:33,140
+لعند منصر لإيش؟ للواحد طيب هذه نفسها أقل من n to
+
+291
+00:25:33,140 --> 00:25:37,920
+the power n من مية to the power مية صحيح؟ لأن مية
+
+292
+00:25:37,920 --> 00:25:40,460
+to the power مية معناته بتضرب المية في نفسها ميت
+
+293
+00:25:40,460 --> 00:25:44,240
+مرة يعني مية في مية في مية في مية هناك كانت مية في
+
+294
+00:25:44,240 --> 00:25:47,320
+تسعة وتسعين في تمانية وتسعين في سبعة وتسعين غير
+
+295
+00:25:47,320 --> 00:25:49,680
+مية في مية في .. واضح أن مية في مية في مية في مية
+
+296
+00:25:49,680 --> 00:25:54,600
+أكبرأكبر ف N to the power of N أكيد أكبر من N
+
+297
+00:25:54,600 --> 00:25:59,300
+factorial و قصوا على ذلك يمكن هدول بس اللي هنتعامل
+
+298
+00:25:59,300 --> 00:26:03,760
+معهم و نقارن فيهم على أساس انه نحتاجهم في ال
+
+299
+00:26:03,760 --> 00:26:07,040
+complexity هالوجد كل الموضوع اللي فات بدنا نمهد ل
+
+300
+00:26:07,040 --> 00:26:12,260
+ال complexity بتاعتنا ال complexity ببساطة هي a
+
+301
+00:26:12,260 --> 00:26:15,880
+measure of how difficult it is to perform the
+
+302
+00:26:15,880 --> 00:26:21,810
+computation كيف أنابقدّي الحسابات في ال algorithm
+
+303
+00:26:21,810 --> 00:26:26,050
+تبعنا عندكم Algorithm هتكتبوه؟ هنطلب منك task
+
+304
+00:26:26,050 --> 00:26:29,570
+كتبنا ال algorithm أخدناه في أول محاضرة أشتغلناها
+
+305
+00:26:29,570 --> 00:26:34,250
+في ال algorithms كيف نكتب algorithm okay بعدين
+
+306
+00:26:34,250 --> 00:26:36,510
+أتعلمنا شوية عن ال order of growth و كيف ال
+
+307
+00:26:36,510 --> 00:26:39,610
+functions ال growth تبعها بنجيسوا مين أكبر من مين
+
+308
+00:26:39,610 --> 00:26:42,790
+طب هالوقت بدنا نمسك ال algorithm نفسه و ينجيس ال
+
+309
+00:26:42,790 --> 00:26:45,190
+complexity تبعته إن أنا أجيس ال order of growth
+
+310
+00:26:45,190 --> 00:26:49,750
+تبعهان احنا بدنا نجيس من أي درجة ال code اللي
+
+311
+00:26:49,750 --> 00:26:53,270
+انتوا كتبته كتبته code او كتبته algorithm طب ال
+
+312
+00:26:53,270 --> 00:26:55,750
+code تبعه ال .. ال .. ال complex اللي تبعته ال
+
+313
+00:26:55,750 --> 00:26:59,870
+order تبعه جداش؟ ليش؟ ليش محتاجينه؟ لأنه ممكن
+
+314
+00:26:59,870 --> 00:27:04,210
+يصلني كذا code بدعملهم analysis هذا ال order جداش؟
+
+315
+00:27:04,210 --> 00:27:07,450
+هذا ال order جداش؟ والله ال order الأقل أنسبلنا
+
+316
+00:27:07,450 --> 00:27:12,430
+ليش أنسبلنا؟ لأنه هيعطيني وقت أقل إذا اتفقنا لاحقا
+
+317
+00:27:12,430 --> 00:27:18,570
+ان احنا هنتكلم عن ال typeكويسة in general عادة كل
+
+318
+00:27:18,570 --> 00:27:23,110
+في الهندسة عموما بنتكلم عن ال cost هي ال criteria
+
+319
+00:27:23,110 --> 00:27:27,190
+بتاعتنا في القياسات ال cost هي ال criteria هي أهم
+
+320
+00:27:27,190 --> 00:27:30,250
+عنصر معظم ال design بشتغل عليه فاحنا لما بنشتغل
+
+321
+00:27:30,250 --> 00:27:34,490
+بنشتغل دايما على ال cost ال cost هذه ممكن نقيسها
+
+322
+00:27:34,490 --> 00:27:37,230
+بكذا طريقة أهم طريقة اللي احنا هنشتغل عليها هي ال
+
+323
+00:27:37,230 --> 00:27:43,570
+time ال processor لما بيزيد ال widgetفي حساباته
+
+324
+00:27:43,570 --> 00:27:47,930
+بضيع عليكم ال time ال time هذه معناته فيه energy
+
+325
+00:27:47,930 --> 00:27:52,810
+مستهلكة زيادة معناته ال code تبعكم لابد تطبقوه على
+
+326
+00:27:52,810 --> 00:27:57,750
+number of users او على n عددها كبير عدد ال inputs
+
+327
+00:27:57,750 --> 00:28:02,030
+تبعكم كبير ال delay هذا بصير اكبر ال time اللي
+
+328
+00:28:02,030 --> 00:28:07,280
+بضيع بصير اكبر لما نتكلم عنone millisecond فرق بين
+
+329
+00:28:07,280 --> 00:28:11,620
+two codes بين code والتاني one millisecond هذا لو
+
+330
+00:28:11,620 --> 00:28:15,460
+بتكون طبقه ال input تبعكم على مدينة زي غزة فيها
+
+331
+00:28:15,460 --> 00:28:18,720
+مليون و تمانمائة الف و بدنا نعمل search برقم
+
+332
+00:28:18,720 --> 00:28:23,360
+الهوية مثلاعشان نطلع صاحب رقم هوية معينة انتوا
+
+333
+00:28:23,360 --> 00:28:25,760
+عارفين كده هنضطر حسابات؟ معناه انتوا بدي اعمل
+
+334
+00:28:25,760 --> 00:28:30,340
+الاسوأ حالة ان انا بدور عن واحد رقم هويته اخر واحد
+
+335
+00:28:30,340 --> 00:28:34,340
+في السلسة في الموجودة صح؟ فده اسوأ حالة معناه ذلك
+
+336
+00:28:34,340 --> 00:28:37,860
+ان انا بدي اضطر اعمل مليون و تمانمائة الف مقارنة
+
+337
+00:28:37,860 --> 00:28:40,880
+مظبوط؟ او اتنين مليون مقارنة يعني بدي نشتغل على
+
+338
+00:28:40,880 --> 00:28:43,780
+اتنين مليون مقارنة اتنين مليون مقارنة اذا كل واحدة
+
+339
+00:28:43,780 --> 00:28:48,260
+بتتأخر لي one millisecond اللي احنا مش عارفين فيه
+
+340
+00:28:48,260 --> 00:28:52,000
+كده ال millisecondلحظوا جدش بتصير فيه delay، هصير
+
+341
+00:28:52,000 --> 00:28:54,460
+فيه كمية delay كبيرة جدا، معناته صار في عندكم
+
+342
+00:28:54,460 --> 00:29:02,680
+اتنين الف second، اتنين الف second صحيح؟ صارت two
+
+343
+00:29:02,680 --> 00:29:07,560
+K second عندك زيادة، فلحظوا اجسموه على سبتين على
+
+344
+00:29:07,560 --> 00:29:11,270
+سبتين بتطلعلكوا جدش عندكوا عدد أيام تأخيرتجدش ايام
+
+345
+00:29:11,270 --> 00:29:15,530
+تاخير بس عشان ينفذ ال code ال task تبعته فلأ مهم
+
+346
+00:29:15,530 --> 00:29:18,590
+جدا ال time في الحالة هذه وهو احد العناصر اللي
+
+347
+00:29:18,590 --> 00:29:22,110
+بيجيسوا فيها ال cost طبعا في عنصر تاني هو ال space
+
+348
+00:29:22,110 --> 00:29:25,290
+complexity ال space complexity تجدش ال memory اللي
+
+349
+00:29:25,290 --> 00:29:28,980
+انا محتاجهاقدش ال memory اللي انا محتاجها طبعا
+
+350
+00:29:28,980 --> 00:29:31,440
+احنا مش في صدد ان احنا اعمل اعلانات لبعض ال
+
+351
+00:29:31,440 --> 00:29:34,120
+softwares بس أحيانا جدا بتلاقوا في antivirus
+
+352
+00:29:34,120 --> 00:29:38,440
+بتحطوه على الجهاز بيروح الجهاز ليش؟ أخد space كبير
+
+353
+00:29:38,440 --> 00:29:43,860
+فخلاص حجز الجهاز عندكوا طبعا تيجوا تنفذولكوا
+
+354
+00:29:43,860 --> 00:29:47,540
+برنامجين تلاتة تفتحوا ال bar point على مش عارف على
+
+355
+00:29:47,540 --> 00:29:50,600
+ال excel على مش عارف اللي هتلاقوا الجهاز بتعملوا
+
+356
+00:29:50,600 --> 00:29:54,260
+click و بتستنوا قبل ما ..يعملكوا response قبل ما
+
+357
+00:29:54,260 --> 00:30:00,940
+يعطي ال response فواضح ان هنا ال space ضاعت في
+
+358
+00:30:00,940 --> 00:30:03,420
+المقابل في antivirus تاني ممكن تنزلوه و ما تحسوش
+
+359
+00:30:03,420 --> 00:30:07,860
+فيه مقد الغرض و مقد الغرض طبعا في الآخر هنا ال
+
+360
+00:30:07,860 --> 00:30:10,400
+space بتفرج معانا إذا والله انتوا ال space عندكوا
+
+361
+00:30:10,400 --> 00:30:14,200
+حجم صغير معاناة ال complexة بتحسبوها على ال space
+
+362
+00:30:14,200 --> 00:30:18,980
+في الحالة هذه in generalعموما احنا هنشتغل في ال
+
+363
+00:30:18,980 --> 00:30:21,880
+course تبعنا فقط على ال time عموما هنشتغل على ال
+
+364
+00:30:21,880 --> 00:30:25,600
+time بس انا حابب اوضحلكم ان لأ في criteria تانية
+
+365
+00:30:25,600 --> 00:30:28,240
+ممكن الواحد يشتغل عليها احنا هنشتغل على ال time
+
+366
+00:30:28,240 --> 00:30:31,940
+انتوا بعدين ممكن في وقت من الوقات او في مساهم
+
+367
+00:30:31,940 --> 00:30:38,920
+المساقات تضطروا تشتغلوا على اشي تاني okay طيب برضه
+
+368
+00:30:38,920 --> 00:30:41,720
+بنكون عارفين ان ال algorithms ممكن تتباع يعني كل
+
+369
+00:30:41,720 --> 00:30:45,340
+واحدة يكون لها complexity غير التانيوهنا بدو يصير
+
+370
+00:30:45,340 --> 00:30:49,960
+الاختيار انا بدأ اختار مين بناء على ال time search
+
+371
+00:30:49,960 --> 00:30:53,820
+الأقل هو اللي بدأ نختاره اللي بيعطينا time أقل
+
+372
+00:30:53,820 --> 00:30:57,740
+بمعنى ان انا هعمل click ال response تجيني أسرع
+
+373
+00:30:57,740 --> 00:31:01,520
+النتيجة تجيني أسرع طبعا هذا أنسبلي أفضلي هذا بيكون
+
+374
+00:31:01,520 --> 00:31:05,020
+كتير أفضلي طيب واضح ان احنا اشتغلنا هالواجهة على
+
+375
+00:31:05,020 --> 00:31:08,440
+ال time complexity بتاعتنا او ال complexity على
+
+376
+00:31:08,440 --> 00:31:11,420
+اساس ان هي function function في مين في عدد ال
+
+377
+00:31:11,420 --> 00:31:15,660
+inputsعدد ال inputs لما كان خمسة جدش كانت ال
+
+378
+00:31:15,660 --> 00:31:19,000
+complexity طب لما صاروا اتنين مليون جدش صارت ال
+
+379
+00:31:19,000 --> 00:31:22,060
+complexity طبعا بتتغير ال time جدش اللي استهلكته
+
+380
+00:31:22,060 --> 00:31:24,820
+هنا هيتغير عن هنا فواضح ان احنا بنتكلم هنا عن
+
+381
+00:31:24,820 --> 00:31:27,900
+function ال function هنا دي function في ال input
+
+382
+00:31:27,900 --> 00:31:33,240
+length جداش عدد ال inputs بتاعتنا كويسة في الغالب
+
+383
+00:31:33,240 --> 00:31:35,880
+او هذا ال general اللي الكل بيشتغل عليه احنا
+
+384
+00:31:35,880 --> 00:31:39,900
+بتشتغل دايما على ال worst caseعلى أسوأ حالة لما
+
+385
+00:31:39,900 --> 00:31:44,600
+بعمل search مثلا بنعمل search بتدور على رقم هوية
+
+386
+00:31:44,600 --> 00:31:48,560
+بعمل حساب أنه رقم هوية ممكن يكون أخر رقم نفترض
+
+387
+00:31:48,560 --> 00:31:53,280
+بدنا ندور على whatever يعني في صف عندى و بدور على
+
+388
+00:31:53,280 --> 00:31:57,100
+واحد اسمه خالد خالد هدا بده يبدأ من أول صف انت
+
+389
+00:31:57,100 --> 00:31:59,940
+خالد لأ انت خالد انت لأ هعمل حساب ايه في ال
+
+390
+00:31:59,940 --> 00:32:02,440
+algorithm و أنا بده اعمل algorithm مثلا او code
+
+391
+00:32:02,440 --> 00:32:05,280
+بدورلي على واحد اسمه خالد او واحد في مواصفة معينة
+
+392
+00:32:05,280 --> 00:32:08,370
+انه ممكن يكون اخر واحد في القائمةthe worst case
+
+393
+00:32:08,370 --> 00:32:12,250
+أسوأ حالة ممكنة هي اللي بنشتغل عليها عشان نكون
+
+394
+00:32:12,250 --> 00:32:15,790
+عملنا generalization لل code طبعنا إنه في أسوأ
+
+395
+00:32:15,790 --> 00:32:20,510
+حالة ممكن أجدش ممكن هيحتاج وقت، أجدش هيحتاج وقت،
+
+396
+00:32:20,510 --> 00:32:26,670
+كويسلو قلنا عشان نوضح أكتر بمثال لو قلنا في عندنا
+
+397
+00:32:26,670 --> 00:32:30,730
+ال system أو ال algorithm A has worst case time
+
+398
+00:32:30,730 --> 00:32:35,350
+complexity أحيانا بيسميها WCTC أو worst case time
+
+399
+00:32:35,350 --> 00:32:40,610
+complexity أو ممكن نسميها time has a time has a
+
+400
+00:32:40,610 --> 00:32:46,440
+time f of n ال n هذه قلنا عدد ال inputsالـ F الـ
+
+401
+00:32:46,440 --> 00:32:51,040
+Time سنسميها لسه الـ Time فإذا كان بيستغرق الـ
+
+402
+00:32:51,040 --> 00:32:56,980
+Time عبارة عن F of N لعدد Inputs N تفقنا عليها
+
+403
+00:32:56,980 --> 00:33:02,240
+اسمها F وعندنا ألغوريثم تاني B هذا هى يستغرق G of
+
+404
+00:33:02,240 --> 00:33:07,720
+N فإذا واحد هى يستغرق F of N واحد هى يستغرق G of N
+
+405
+00:33:07,720 --> 00:33:11,740
+وجهنا شفنا ال complex بتاعتهم أو شفنا ال order of
+
+406
+00:33:11,740 --> 00:33:20,980
+growth وجدنا ان ال Fمش هدى small omega small omega
+
+407
+00:33:20,980 --> 00:33:24,700
+of j small omega of j في الحالة هدى مين اللى
+
+408
+00:33:24,700 --> 00:33:30,920
+المفروض اختاره من الاتنين ال جي ال جي ليش ال جي ال
+
+409
+00:33:30,920 --> 00:33:34,400
+جي واضح انه اقل لانه بدأنا احنا هنا نتكلم عنه if
+
+410
+00:33:34,400 --> 00:33:44,260
+small omega of g معناته جي
+
+411
+00:33:46,040 --> 00:33:52,940
+small o of F فإذن ال G لازم تكون أقل من F ال G
+
+412
+00:33:52,940 --> 00:33:57,620
+دايما أقل من F فإذن طبيعي بدنا نختار ال system ال
+
+413
+00:33:57,620 --> 00:33:58,800
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+414
+00:33:58,800 --> 00:33:59,440
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+415
+00:33:59,440 --> 00:34:00,860
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+416
+00:34:00,860 --> 00:34:04,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+417
+00:34:04,840 --> 00:34:04,860
+ال ال ال ال ال ال ال
+
+418
+00:34:18,720 --> 00:34:21,520
+عشان احسب code هكتب ال code ال code يعني مثلا بدنا
+
+419
+00:34:21,520 --> 00:34:26,380
+نحسب ال maximum value او ال maximum element داخل
+
+420
+00:34:26,380 --> 00:34:30,340
+string معين او داخل list معينة و كتبنا ال code ده
+
+421
+00:34:30,340 --> 00:34:33,200
+سابقا لما بدنا نتكلم عن ال algorithm كتبنا ال code
+
+422
+00:34:33,200 --> 00:34:35,900
+قبلها هل واجد بدنا نحسب ال complexity تبعته؟
+
+423
+00:34:36,280 --> 00:34:39,460
+complexity أو الـ time المستغرب فكل line من ال
+
+424
+00:34:39,460 --> 00:34:43,380
+lines هذه إله time إله time هنقول إن والله ال line
+
+425
+00:34:43,380 --> 00:34:49,620
+الأولة مقارنة مجرد إن أحط ال V قيمتها ب A1 محتاجة
+
+426
+00:34:49,620 --> 00:34:53,820
+time T1 طيب ال four loop هذا عشان أعمل كلمة four
+
+427
+00:34:53,820 --> 00:35:02,160
+من كذا لكذا محتاجة T2 طيب if thenمحتاجة T3 زمن T3
+
+428
+00:35:02,160 --> 00:35:09,100
+return مجرد أن أرجع أعمل printing لأو أطبع قيمة V
+
+429
+00:35:09,100 --> 00:35:13,800
+على الشاشة أو أطلعها و أظهرها على الشاشة محتاجة T4
+
+430
+00:35:13,800 --> 00:35:17,820
+طيب هالواجهة بدنا نبسكهم جدش ال total لل algorithm
+
+431
+00:35:17,820 --> 00:35:20,760
+كله على بعضه ال total لل algorithm كله على بعضه
+
+432
+00:35:20,760 --> 00:35:27,780
+هيكون مجموحهم و بدنا بس ناخد بالنا إذا في تكرارات
+
+433
+00:35:27,780 --> 00:35:36,610
+ولا لأفإذا مبدأيا T1 زائد T2 زائد T3 زائد T4 لأ هو
+
+434
+00:35:36,610 --> 00:35:39,930
+مش هيك بس هو مش بس هيك انتوا لاحظوا انه عندكوا فيه
+
+435
+00:35:39,930 --> 00:35:45,630
+for loop معناته مين اللي بتكرر عنده T2 و T3 فإذا
+
+436
+00:35:45,630 --> 00:35:50,570
+بقدر أقول T1 زائد summation من مين لمين ل T2 زائد
+
+437
+00:35:50,570 --> 00:35:58,150
+T3 و هنا طبعا بعيد عنهم زائد T4 هذي من وين لوين؟من
+
+438
+00:35:58,150 --> 00:36:03,710
+I بيتساوي 2 to I صحيح؟
+
+439
+00:36:03,710 --> 00:36:07,370
+حلو، كويس جدا، في الحالة هذه عندنا هذا constant
+
+440
+00:36:07,370 --> 00:36:12,230
+ثابت خلاص تي واحد بتتنفذ مرة واحدة و بس جدش قيمتها
+
+441
+00:36:12,230 --> 00:36:15,510
+بعرف عن طريق جدش سرعة ال processor جدش مواصفات
+
+442
+00:36:15,510 --> 00:36:18,950
+الجهاز جدش ال operation الواحدة تستغرق في الجهاز
+
+443
+00:36:18,950 --> 00:36:24,520
+هذا بنعرفها فهذه constant، هذه constant كمانتنتين
+
+444
+00:36:24,520 --> 00:36:29,120
+مع بعض بقدر أقول أن هي theta of one theta of one
+
+445
+00:36:29,120 --> 00:36:33,180
+constant زائد هدول التنتين مع بعض لحالهم theta of
+
+446
+00:36:33,180 --> 00:36:40,600
+one بس هدول داخل ال summation من إتنين to n جدش
+
+447
+00:36:40,600 --> 00:36:46,880
+عدد التكرارات n ناقص واحد فإذا أنا بتكلم هنا عن n
+
+448
+00:36:46,880 --> 00:36:53,200
+ناقص واحد في theta of one plus theta one
+
+449
+00:36:56,570 --> 00:37:03,910
+ن نقص واحد ثيتا of n مضروبة
+
+450
+00:37:03,910 --> 00:37:09,710
+في constant ثيتا of one plus constant ثيتا of one
+
+451
+00:37:09,710 --> 00:37:14,890
+فإذا انتوا في الآخر ثيتا of n of n معناه ذلك أننا
+
+452
+00:37:14,890 --> 00:37:19,510
+بنتكلم عن first order فإذا في الآخر ال complex
+
+453
+00:37:19,510 --> 00:37:21,670
+بتاعتنا هنا ثيتا of n
+
+454
+00:37:26,870 --> 00:37:32,170
+هي ال analysis نفسه في الآخر بنصل ل theta of n او
+
+455
+00:37:32,170 --> 00:37:36,270
+first order فعزيزي نوضح ان كله بحياتك order بحياتك
+
+456
+00:37:36,270 --> 00:37:41,550
+first order كله اذا كان ال two elements بتاعونه مش
+
+457
+00:37:41,550 --> 00:37:47,600
+معروفينالـ two limits واحدة منهم to n و n هي عدد
+
+458
+00:37:47,600 --> 00:37:51,540
+ال inputs يعني هي ال variable تبعنا لحظة نوع n هي
+
+459
+00:37:51,540 --> 00:37:54,160
+عدد ال inputs و ال inputs هو ال variable تبعنا
+
+460
+00:37:54,160 --> 00:37:56,880
+فإذا واحدة من ال limits تبعون هدولة هي ال
+
+461
+00:37:56,880 --> 00:37:59,480
+variables اللي احنا بنشتغل عليه أساسا فإذا هنا
+
+462
+00:37:59,480 --> 00:38:03,400
+معتمد تماما على مين على عدد ال inputs إذا عدد ال
+
+463
+00:38:03,400 --> 00:38:07,780
+inputs مية هضطر أعمل تسعة وتسعين operation تكرار ل
+
+464
+00:38:07,780 --> 00:38:11,950
+T تنين و Tتلاتة إذا الف هنشطل على تسعمين تسعة
+
+465
+00:38:11,950 --> 00:38:16,390
+وتسعين iteration إذا جدش العدد ال inputs بفرج معاه
+
+466
+00:38:16,390 --> 00:38:19,290
+أنا جدش ال accumulation هنعمل accumulation هنعمل
+
+467
+00:38:19,290 --> 00:38:24,710
+فإذا فعلا إذا ال limits بتاعنا واحد منهم أو ال
+
+468
+00:38:24,710 --> 00:38:27,710
+limits بتاعتنا عبارة عن ال variable اللي بنشطل
+
+469
+00:38:27,710 --> 00:38:31,030
+عليه هو عدد ال inputs واضح إن أنا هنا هدخل في إيش
+
+470
+00:38:31,030 --> 00:38:34,990
+في first order كله بحيث يكون بده first order
+
+471
+00:38:38,620 --> 00:38:41,760
+كمان مثال ناخد ال linear search في ال linear
+
+472
+00:38:41,760 --> 00:38:44,980
+search متذكرين ال linear search ال linear search
+
+473
+00:38:44,980 --> 00:38:50,260
+مجرد أنه نبدأ procedure و بنعرف جد ايش الاسم و
+
+474
+00:38:50,260 --> 00:38:52,960
+حيكون في عندنا x integer هذا ال x اللي بدنا ندور
+
+475
+00:38:52,960 --> 00:38:56,620
+عليه element بدنا ندور هل هو موجود داخل ال list او
+
+476
+00:38:56,620 --> 00:39:00,780
+لأ ال list هذه بدنا نكون معرفينها a1, a2, a3, a4,
+
+477
+00:39:00,780 --> 00:39:04,460
+a5, a6, a7, a8, a9, a10, a11, a12, a13integers
+
+478
+00:39:04,460 --> 00:39:11,440
+متباينة مافيش اتنين بيساوي بعض ومرتبة ومرتبة ايام
+
+479
+00:39:11,440 --> 00:39:14,460
+اشتغلناها كان في عنا I بتساوي واحد في هذه ال
+
+480
+00:39:14,460 --> 00:39:20,140
+operation تبعتنا T واحد while مجرد ال operation
+
+481
+00:39:20,140 --> 00:39:25,340
+هذي while بتحتيه اتنين I بتساوي I زائد واحد بتحتيه
+
+482
+00:39:25,340 --> 00:39:34,450
+تلاتة if then بتحتيه اربعةelse بده T5 و return بده
+
+483
+00:39:34,450 --> 00:39:40,310
+T6 كويس في الحالة هذه الشغل عشان نشتغله كامل على
+
+484
+00:39:40,310 --> 00:39:45,190
+بعضه هيكون محتاج مجموحهم هيكون محتاجين برضه
+
+485
+00:39:45,190 --> 00:39:48,830
+مجموحهم بس برضه بدنا نرجع نركز وين وين بصير ال
+
+486
+00:39:48,830 --> 00:39:52,590
+iteration او وين بصير ال loop وين بصير في أنكو T1
+
+487
+00:39:52,590 --> 00:39:57,690
+T2 T6
+
+488
+00:39:58,980 --> 00:40:05,400
+ال loop هنا وين بيصيروا فعليا في اتنين تلاتة ولا
+
+489
+00:40:05,400 --> 00:40:09,200
+تلاتة اربع او اين بالظبط اتنين و تلاتة اتنين و
+
+490
+00:40:09,200 --> 00:40:19,720
+تلاتة هنا هيكون بدهم summation من I
+
+491
+00:40:19,720 --> 00:40:21,840
+بتساوي واحد
+
+492
+00:40:24,140 --> 00:40:27,800
+I بتساوي واحد، احنا بدأنا بواحد و بدأنا منه، بدأنا
+
+493
+00:40:27,800 --> 00:40:31,680
+من إيش؟ من I بتساوي واحد، هاي I كانت واحد، و ال
+
+494
+00:40:31,680 --> 00:40:35,800
+worst case تبعتنا أنه أصل to end، أسوأ حالة أنه
+
+495
+00:40:35,800 --> 00:40:39,620
+العنصر اللي بدور عليه في آخر عنصر أو أنه غير موجود
+
+496
+00:40:39,620 --> 00:40:42,730
+من أساسهأو أنه ممكن نكون غير موجود فانحطر أعمل
+
+497
+00:40:42,730 --> 00:40:46,650
+search على كل ال elements داخل ال list داخل ال
+
+498
+00:40:46,650 --> 00:40:50,630
+list okay فهيكون عندنا summation from i equal to
+
+499
+00:40:50,630 --> 00:40:57,130
+one to h to n لعند العدد كامل على بعضه لعند العدد
+
+500
+00:40:57,130 --> 00:40:59,970
+كله على بعضه في الحالة هاد واضح أنه مدام summation
+
+501
+00:40:59,970 --> 00:41:03,490
+واحدة هيكون عندكوا first order هيكون first order
+
+502
+00:41:03,490 --> 00:41:08,850
+على اعتبار أنه هاد هتكون مضروبة في h في n مضروبة
+
+503
+00:41:08,850 --> 00:41:09,870
+في h في theta
+
+504
+00:41:14,700 --> 00:41:20,580
+ال summation theta of n لأن هات جاية من n, n مرة
+
+505
+00:41:20,580 --> 00:41:26,560
+تكراراتها مضروبة في إيش هذا ال term? theta of one
+
+506
+00:41:27,490 --> 00:41:33,110
+كل هذا زائد theta of one plus theta of one كلهم
+
+507
+00:41:33,110 --> 00:41:35,870
+توتر على بعض theta of one كلهم توتر على بعض theta
+
+508
+00:41:35,870 --> 00:41:40,490
+of one ففي الآخر هيطلع ال order تبعكم first order
+
+509
+00:41:40,490 --> 00:41:45,550
+او theta of of n طيب the best case في افضل في افضل
+
+510
+00:41:45,550 --> 00:41:53,880
+حالة ممكنة هنالحظوا هنا في أفضل حالة ممكنة في ال
+
+511
+00:41:53,880 --> 00:41:56,320
+code اه موجود في ال code أفضل حالة أن يكون أول
+
+512
+00:41:56,320 --> 00:41:58,760
+عنصر طب أول عنصر خلّينا نتنبع ال algorithm تبعنا
+
+513
+00:41:58,760 --> 00:42:07,660
+خلّينا نتوب تحتها I بتساوي 1 okay هننفذها while X
+
+514
+00:42:07,660 --> 00:42:14,360
+بتساوي A1 مظبوط فإذا انت حققته وين هيروح هيطلع
+
+515
+00:42:14,360 --> 00:42:19,600
+هيجي هنا فإذا هذه ماتحققتشما نفذهاش، لم تنفذ، في
+
+516
+00:42:19,600 --> 00:42:24,760
+الحالة هذه بتاعتنا هتصير T1 زائد T2 زائد T4 تماما
+
+517
+00:42:24,760 --> 00:42:33,710
+زائد T5 T6 في الحالة هذه كله هكون θ of 1كله
+
+518
+00:42:33,710 --> 00:42:38,030
+constants طبعا هذه the best case هذه the best case
+
+519
+00:42:38,030 --> 00:42:44,730
+طب ال average case بين هدا و هدا ان لأنه هيكون بدل
+
+520
+00:42:44,730 --> 00:42:48,570
+I بتساوي واحد to N هتصير N over two و برضه هتكون
+
+521
+00:42:48,570 --> 00:42:52,650
+متغيرة هتظل متغيرة لإن أنا مش عارف جدش قيمة N N
+
+522
+00:42:52,650 --> 00:42:57,730
+over two هي هي كأنها N ليش لإن أنا بتعامل مع واحدة
+
+523
+00:42:57,730 --> 00:43:00,630
+من ال limits ان هي ال variable تبعنا و ال variable
+
+524
+00:43:00,630 --> 00:43:04,360
+تبعنا حددنا من ال inputsفالinputs أنا مش عارفهم
+
+525
+00:43:04,360 --> 00:43:10,060
+إذا خمسة غير خمسين غير ألف غير مليون بتختلف عدد ال
+
+526
+00:43:10,060 --> 00:43:12,760
+iterations في الحالة هذه فطبعا على اتنين أو مش على
+
+527
+00:43:12,760 --> 00:43:15,640
+اتنينية هي مش هتفرج معنا هيضل برضه بنتعامل مع
+
+528
+00:43:15,640 --> 00:43:21,000
+first order مع first order طيب ال binary في ال
+
+529
+00:43:21,000 --> 00:43:25,020
+binary كان لأ الوضع مختلف فإذا خلينا نحدد إنه في
+
+530
+00:43:25,020 --> 00:43:29,540
+ال search في ال linear search كان first order طيب
+
+531
+00:43:29,540 --> 00:43:34,210
+ال binary عشان نحدد مين أحسن من مينفي ال linear
+
+532
+00:43:34,210 --> 00:43:41,890
+كان عندنا θ of n طيب خلّيني أشوف ال binary في ال
+
+533
+00:43:41,890 --> 00:43:44,410
+binary هاي ال code اللي كتبته سابقا كتبناه
+
+534
+00:43:44,410 --> 00:43:50,630
+المحاضرة اللي فاتت أو اللي قبلها كان في عنده I و J
+
+535
+00:43:50,630 --> 00:43:54,890
+I و J هدولة كنا من حد بداية و نهاية ال interval
+
+536
+00:43:54,890 --> 00:43:59,270
+بتاعتنا ليش؟ لأنه كان الالـ Algorithm معتمد على
+
+537
+00:43:59,270 --> 00:44:02,890
+أساس أني أعمل check على ال midpoint على ال
+
+538
+00:44:02,890 --> 00:44:05,790
+midpoint أو ال element اللي موجود في ال midpoint
+
+539
+00:44:05,790 --> 00:44:12,030
+location في ال midpoint location بناءً عليه بعمل
+
+540
+00:44:12,030 --> 00:44:15,790
+اختزال أو elimination لنص ال interval كلها على بعض
+
+541
+00:44:15,790 --> 00:44:19,330
+ممكن كل هدول ال elements أشيلهم فانا بطلت مضطر
+
+542
+00:44:19,330 --> 00:44:23,190
+أعمل check عليهم واحدة واحدة اختزلهم كلهم مرة
+
+543
+00:44:23,190 --> 00:44:28,940
+واحدة خلاص مش محتاج مش محتاجين طيب نص المسافةبرضه
+
+544
+00:44:28,940 --> 00:44:31,700
+بنقارن مع ال element اللي موجود ممكن اختزل كل ال
+
+545
+00:44:31,700 --> 00:44:34,360
+elements اللي أكبر برضه كل ال elements اللي هنا مش
+
+546
+00:44:34,360 --> 00:44:37,940
+مضطر اقارن فيهم واضح ان احنا جالسين بنجلل حجم
+
+547
+00:44:37,940 --> 00:44:42,580
+المشكلة بنجلل حجم المشكلة طيب حددنا البداية و
+
+548
+00:44:42,580 --> 00:44:46,780
+النهاية بتاعوننا هدولة كل واحدة محتاجة time T1 T1
+
+549
+00:44:46,780 --> 00:44:52,040
+T1 مثلا T2 T1 T2 constants constants في النهاية
+
+550
+00:44:52,040 --> 00:44:57,120
+okay طيب سيبقوا من while هالوجدwhile و end هدول
+
+551
+00:44:57,120 --> 00:45:03,680
+سيبوهم داخل ال loop كل واحدة منهم هدول برضه محتاجة
+
+552
+00:45:03,680 --> 00:45:08,240
+T1 و T2 فهم التنتين لحالهم بدون ال while constant
+
+553
+00:45:08,240 --> 00:45:13,440
+خلاص ال operation هذه محتاجة زمن T3 او T4 خلاص هي
+
+554
+00:45:13,440 --> 00:45:17,620
+دايما T4 بس المشكلة دايما في قدش هتتكرر في قدش
+
+555
+00:45:17,620 --> 00:45:24,630
+هتتكرر okay thousand theta of oneخلصنا ال loop if
+
+556
+00:45:24,630 --> 00:45:28,610
+then بنعملها مرة واحدة إذا كان وصلت أو ماوصلتش و
+
+557
+00:45:28,610 --> 00:45:32,610
+return بال location برضه مرة واحدة هل وجدت السؤال
+
+558
+00:45:32,610 --> 00:45:37,430
+هنا ال loop هدق كم مرة هيتكرر؟ و أنا جاعت بجسم
+
+559
+00:45:37,430 --> 00:45:43,940
+انصاص هيك كم مرة هيتكرر؟إذا n معناته هتكون نفس ال
+
+560
+00:45:43,940 --> 00:45:46,900
+linear معناته ال order تبعها نفس ال linear في
+
+561
+00:45:46,900 --> 00:45:50,820
+الحالة دي مفرجش مين أستعمل لأن ال order تبع ال
+
+562
+00:45:50,820 --> 00:45:55,120
+اتنين نفس الاشي هنا هذه ال linear كانت first order
+
+563
+00:45:55,120 --> 00:45:59,760
+خليني أشوف هذه و خليني نبدأ نتخيل مدام بجسم اتنين
+
+564
+00:45:59,760 --> 00:46:04,280
+عن اتنينات يعني كإني بشغل على الأساس اتنين على
+
+565
+00:46:04,280 --> 00:46:09,600
+الأساس اتنين خليني أفترض أن عددهم من واحد to nو n
+
+566
+00:46:09,600 --> 00:46:14,200
+هذه أحد مشتقات الاتنين بمعنى بتساوي 2 to the power
+
+567
+00:46:14,200 --> 00:46:18,720
+k بصير
+
+568
+00:46:18,720 --> 00:46:23,300
+كل اللي بدنايا مدام في كل iteration أنا بجسم
+
+569
+00:46:23,300 --> 00:46:29,820
+المسافة تبعت نصين بعد أكم k هتصير n هذه بتساوي
+
+570
+00:46:29,820 --> 00:46:39,100
+واحد لأن احنا إمتى بنواجه هنا لما نصل في الآخرلأ
+
+571
+00:46:39,100 --> 00:46:44,460
+عنصر واحد بس وصلنا
+
+572
+00:46:44,460 --> 00:46:47,840
+لعنصر واحد العنصر الواحد هذا النهائي هو اللي بعمله
+
+573
+00:46:47,840 --> 00:46:53,600
+if then بنقارنه هل بيسوي x أو بيسويش x وخلاص سوى x
+
+574
+00:46:53,600 --> 00:46:55,600
+معناته هو العنصر هو ال x اللي أنا بدور عليها
+
+575
+00:46:55,600 --> 00:47:00,300
+ماسواش x خلاص غير موجودة x في الآخر أنا بصلها
+
+576
+00:47:00,300 --> 00:47:07,180
+لعنصر واحد العنصر الواحد ده انت بصله من عدد nو
+
+577
+00:47:07,180 --> 00:47:13,560
+هنفترض مبدئيا أن N أحد مشتقات ال .. او two to the
+
+578
+00:47:13,560 --> 00:47:18,920
+power of some K طيب خليني أجيبلكيها بالعكس افرضوا
+
+579
+00:47:18,920 --> 00:47:25,660
+أن ال N هذه اربعة و ستين نفرضهم اربعة و ستين اربعة
+
+580
+00:47:25,660 --> 00:47:30,080
+و ستين اول iteration جدش صاروا نص اتنين و تلاتين
+
+581
+00:47:30,080 --> 00:47:36,540
+هيخلصنا iteration طيب اتنين و تلاتينستاشر بعد two
+
+582
+00:47:36,540 --> 00:47:48,310
+iterations طيب تمانية أربعة اتنين واحد صحيح؟6 طيب
+
+583
+00:47:48,310 --> 00:47:51,170
+هل فعلا .. لحظوا احنا عملنا 6 iterations قبل ما
+
+584
+00:47:51,170 --> 00:47:54,370
+أصل ل element واحد عملنا 6 iterations فهل فعلا
+
+585
+00:47:54,370 --> 00:47:59,110
+صحيح ال 64 بتساوي 2 تطبعه 6؟ اه فعلا 2 تطبعه 6
+
+586
+00:47:59,110 --> 00:48:03,530
+معناه ان ال 6 هذي الصمكة اللي بنتكلم عنها الصمكة
+
+587
+00:48:03,530 --> 00:48:06,850
+هي عدد ال iterations فعليا اللي هيطلع هي فعليا عدد
+
+588
+00:48:06,850 --> 00:48:11,790
+ال iterations اللي هتظهر صح؟ صح كويس حسب قلية ال
+
+589
+00:48:11,790 --> 00:48:14,170
+.. ال worthing condition حسب ألغورية ال .. ال ..
+
+590
+00:48:15,210 --> 00:48:20,150
+الألية ال algorithm نفسه كيف بيشتغل فإذا بفترض أن
+
+591
+00:48:20,150 --> 00:48:24,890
+N هي two to the power of some K ك element و بعدين
+
+592
+00:48:24,890 --> 00:48:30,950
+ممكن نعممه إن إذا كانت لا تساوي مش مشكلة بنقربها
+
+593
+00:48:30,950 --> 00:48:35,290
+للرقم الأعلى يعني
+
+594
+00:48:35,290 --> 00:48:42,130
+إذا كانت مثلا ستينبنقربها لمن؟ لل 64 و بنشتغلها ل
+
+595
+00:48:42,130 --> 00:48:45,450
+64 فبتطلع بدنا 6 iterations حنكون محتاجين 6
+
+596
+00:48:45,450 --> 00:48:47,910
+iterations طيب كيف بده أجيب ال 6 iterations دي؟
+
+597
+00:48:47,910 --> 00:48:51,910
+لأن هي هي اللي هتحددلي جداش عدد التكرارات جداش عدد
+
+598
+00:48:51,910 --> 00:48:58,590
+التكرارات فكل اللي هنعمله log
+
+599
+00:48:58,590 --> 00:49:07,230
+n بتساوي log 2 to the power k فده بتساوي k في log
+
+600
+00:49:08,060 --> 00:49:19,220
+two log n كي ايش بتساوي هنا log n over log two طيب
+
+601
+00:49:19,220 --> 00:49:23,200
+في الحالة هذه ال
+
+602
+00:49:23,200 --> 00:49:28,020
+log هذا الأساس تبعه جديش ال base تبعه جديش عشرة و
+
+603
+00:49:28,020 --> 00:49:31,780
+هنا عشرة طيب في الحالة هذه كله بيصير بيساوي log
+
+604
+00:49:31,780 --> 00:49:40,390
+الأساس اتنين to n of nصح؟ كويس، تمام جدا، فإذا
+
+605
+00:49:40,390 --> 00:49:49,890
+واضح أن K هتساوي هذا ال term، اللي هي log N، log
+
+606
+00:49:49,890 --> 00:49:54,890
+N، فإذا نتكلم عن order logarithmic، واضح أن
+
+607
+00:49:54,890 --> 00:49:59,410
+التكرار طبعنا logarithmic، مش linear، مش linear،
+
+608
+00:49:59,410 --> 00:50:06,420
+فإذا التانية ال theta بتاعتنا log Nأقل طبعا هذه
+
+609
+00:50:06,420 --> 00:50:12,940
+هتكون أقل من N فإذا واضح أن ال binary search أفضل
+
+610
+00:50:12,940 --> 00:50:16,880
+و more efficient من ال linear search أفضل من ال
+
+611
+00:50:16,880 --> 00:50:20,800
+linear search واضحة لأن ال order تبعها أقل من
+
+612
+00:50:20,800 --> 00:50:25,220
+first order order أقل من first order لاحظوا احنا
+
+613
+00:50:25,220 --> 00:50:29,880
+اشتغلنا على 64 64 element عملناهم في 6 iterations
+
+614
+00:50:29,880 --> 00:50:34,770
+هناك في أسوأ حالة محتاج 64 iterationsفي ال linear
+
+615
+00:50:34,770 --> 00:50:38,950
+هحتاج 64 iterations صح؟ لأ هنا أسوأ case عندنا في
+
+616
+00:50:38,950 --> 00:50:42,350
+ال binary أني أشتغل على 6 iterations فقط بعد 6
+
+617
+00:50:42,350 --> 00:50:46,730
+iterations هكون وصلت لل X هل موجود أو غير موجود
+
+618
+00:50:46,730 --> 00:50:50,230
+okay
+
+619
+00:50:50,230 --> 00:50:55,470
+فهي التحليل تبعنا عشان في الآخر نحسب K و نشتغل على
+
+620
+00:50:55,470 --> 00:51:01,950
+K طيب ال matrix multiplication يمكن هذه احنا
+
+621
+00:51:01,950 --> 00:51:10,570
+ماخدناش في وقتهالما اتكلمنا عن ال matrices بس
+
+622
+00:51:10,570 --> 00:51:16,470
+قلنا ان كل for loop كل for loop هتعطينا ايش first
+
+623
+00:51:16,470 --> 00:51:22,110
+order هتعطينا تكرار وخصوصا اذا التكرار تبحة زي ما
+
+624
+00:51:22,110 --> 00:51:26,110
+قلنا ال limits تبعته ايش variables اذا ال limits
+
+625
+00:51:26,110 --> 00:51:29,670
+تبعته variables طيب خلينا نشوف في حالة ضرب
+
+626
+00:51:29,670 --> 00:51:38,060
+المصففاتاحنا بنضرب مصفوفات M في K بنضربها في مين؟
+
+627
+00:51:38,060 --> 00:51:47,660
+K في N عشان ينتج عندى مصفوفة M في N تمام واضح ان
+
+628
+00:51:47,660 --> 00:51:52,620
+في عندنا variable اتنين تلاتة في three variables
+
+629
+00:51:52,620 --> 00:51:55,760
+في
+
+630
+00:51:55,760 --> 00:52:00,090
+عدد الصفوفأنا ممكن أدخل matrix من عندي، يعني ليش
+
+631
+00:52:00,090 --> 00:52:04,350
+نلزمونه مثلا 2 في 3 أضربها في 3 ب 2؟ أنا بدي أدخل
+
+632
+00:52:04,350 --> 00:52:07,950
+5 في 7، إيش المشكلة؟ فعدد ال variables هذه
+
+633
+00:52:07,950 --> 00:52:11,530
+unvariable المفروض أنه ال algorithm يكون general
+
+634
+00:52:15,010 --> 00:52:17,970
+Dimension لل matrices اللي بدنا نضربها في بعض
+
+635
+00:52:17,970 --> 00:52:23,710
+يتقبلها أي dimension يتقبلها فهنا M في K .. K تاخد
+
+636
+00:52:23,710 --> 00:52:26,710
+أي قيمة M تاخد أي قيمة N تاخد أي قيمة فهذه
+
+637
+00:52:26,710 --> 00:52:30,610
+variables هذه بتحددنا عدد ال inputs بتحدد عدد ال
+
+638
+00:52:30,610 --> 00:52:34,290
+inputs اللي بدنا ندخله نضربه في بعض كويسة for I
+
+639
+00:52:34,290 --> 00:52:39,570
+one to H to M هذه هنا بنتكلم عن مين عن ال raw فإذا
+
+640
+00:52:39,570 --> 00:52:45,550
+بنبدأ بال raw رقم واحدبدينا فى الرقم واحد هى كل
+
+641
+00:52:45,550 --> 00:52:52,790
+عناصر الرقم واحد كويس بعدين for j from one to n
+
+642
+00:52:52,790 --> 00:53:00,070
+هنا بنتكلم عن كولوم التانية وهذا
+
+643
+00:53:00,070 --> 00:53:02,770
+قيمتها بواحد مع أننا بنتكلم عن كولوم الأول فى
+
+644
+00:53:02,770 --> 00:53:08,710
+التانية هنا حددناهم حددنا هذا ايش وهذا ايش انشطرعي
+
+645
+00:53:10,930 --> 00:53:14,070
+equal to zero ال summation اللي بدنا نجمع فيه بسوى
+
+646
+00:53:14,070 --> 00:53:20,070
+zero فهنا جيبنا النواعي عشان نجمع فيه نجمع نواعي
+
+647
+00:53:20,070 --> 00:53:27,030
+هذا هانيجي نجمع for q from one to k هنبدأ في أول
+
+648
+00:53:27,030 --> 00:53:37,660
+column في الأولى أول صف في التانية عشان نضربA I Q
+
+649
+00:53:37,660 --> 00:53:42,840
+و I حددنا واحد بدنا بواحد J حددنا واحد طبعا هنا
+
+650
+00:53:42,840 --> 00:53:49,300
+بدنا بمين و Q بواحد فال element الأول مع ال
+
+651
+00:53:49,300 --> 00:53:53,280
+element الأول هندربهم مع مين مع بعض هاي هندربناهم
+
+652
+00:53:53,280 --> 00:53:57,540
+مع بعض و نجمعهم على C كأنه هذه كانت صفر رمنا
+
+653
+00:53:57,540 --> 00:54:05,940
+قيمتهم هنا رمنا قيمتهم زائد ال Q بتساوي اتنينفهي
+
+654
+00:54:05,940 --> 00:54:09,840
+العنصر التاني مع العنصر التاني ضربناهم في بعض
+
+655
+00:54:09,840 --> 00:54:16,300
+وجمعنا قيمتهم التالت كيف تسوى نفطر التلاتة خلاص
+
+656
+00:54:16,300 --> 00:54:19,580
+خلصناها جمعنا قيمتهم هي دول هيك ساميشن جمعناهم
+
+657
+00:54:19,580 --> 00:54:23,860
+القيمة بتاعتهم هنحطها في التقاطع التانية دولة
+
+658
+00:54:23,860 --> 00:54:30,900
+بواحد وواحد هنحطها هنا خلصنا
+
+659
+00:54:30,900 --> 00:54:36,230
+ال four ال four بتاعة q كلها بنرجع لمينj بتساوى
+
+660
+00:54:36,230 --> 00:54:40,690
+اتنين فهنا نجلنا على مين على ال column التانى فى
+
+661
+00:54:40,690 --> 00:54:45,030
+التانى هذا ضغط لسه زى ما هو مازلنا زى ما هو فلحظوا
+
+662
+00:54:45,030 --> 00:54:50,810
+صارت الأولى العنصر الأول فى ال role أول مع العنصر
+
+663
+00:54:50,810 --> 00:54:54,930
+الأول فى ال column التانى لحظوا برضه هدا فى هدا
+
+664
+00:54:54,930 --> 00:54:59,830
+وهنا عشان هيك لازم نصفرها لإن هدى كانت فيها مجموعة
+
+665
+00:54:59,830 --> 00:55:02,350
+data بنصفرها
+
+666
+00:55:05,730 --> 00:55:08,030
+و تاخدوا بالكوا دايما فى بداية ال code تبعكوا و
+
+667
+00:55:08,030 --> 00:55:10,110
+حاولوا تصفروا كل ال algorithms تبعتكوا كتير فيه
+
+668
+00:55:10,110 --> 00:55:15,310
+بتصير مشاكل نتيجة ان ال variables هذه مخزنة قيم
+
+669
+00:55:15,310 --> 00:55:18,090
+سابقة مخزنة قيم سابقة فبتلاقيوا حالكوا طلعتوا
+
+670
+00:55:18,090 --> 00:55:20,810
+النتائج غلط طلعتوا النتائج غلط بتبدوا تجمعوا من
+
+671
+00:55:20,810 --> 00:55:25,770
+أول و جديد هذه مع هذه هذه في هذه هذه في هذه okay
+
+672
+00:55:25,770 --> 00:55:30,910
+جمعناهم عشان نحطهم فى نقطة تقطعهم هنا واحد مع
+
+673
+00:55:30,910 --> 00:55:35,640
+اتنين فإذا واحد اتنين بنحطال term التاني اللي
+
+674
+00:55:35,640 --> 00:55:40,560
+جمعناه و بنكمل بهذا الشكل لما نخلص كل لحظة انتوا
+
+675
+00:55:40,560 --> 00:55:43,880
+هنا Q جربتوها كذا مرة يعني ال loop ما اتكررش كمان
+
+676
+00:55:43,880 --> 00:55:47,560
+مرة واحدة ك loop ما اتكررش نفسه كمان مرة واحدة هو
+
+677
+00:55:47,560 --> 00:55:55,220
+قاعد بتكرر مع كل J طب لسه ال J هتتكرر مع كل I لما
+
+678
+00:55:55,220 --> 00:56:01,180
+تخلصوا N هناتخلص كل N تماما هتيجي هنا تاخد I تساوي
+
+679
+00:56:01,180 --> 00:56:06,940
+2 هتبدو كل اللي عملته هذا مع ال road تاني هتبدو ال
+
+680
+00:56:06,940 --> 00:56:09,040
+road تاني مع ال column الأول ال road تاني مع ال
+
+681
+00:56:09,040 --> 00:56:13,540
+column التاني مع التالت وكل مرة هترجع تعمله Q كمان
+
+682
+00:56:13,540 --> 00:56:18,820
+مرة طب ال for loop هذا Q هيتكرر K مرة أكم مرة
+
+683
+00:56:18,820 --> 00:56:24,680
+هتتكرر ال K مرة هذه حسب عدد ال elements اللي طلعها
+
+684
+00:56:24,680 --> 00:56:24,840
+هنا
+
+685
+00:56:27,910 --> 00:56:32,530
+إذا تلاتة في تلاتة هتتكرر تسعة مرات ال loop اللوب
+
+686
+00:56:32,530 --> 00:56:34,690
+اللي .. مش بس ال elements اللي داخل ال loop اللوب
+
+687
+00:56:34,690 --> 00:56:38,290
+نفسه هتتكرر تسعة مرات طيب تسعة مرات دول اللي هم
+
+688
+00:56:38,290 --> 00:56:44,830
+ايش M في N يعني لو كانت خمسة في خمسة هتتكرر خمسة
+
+689
+00:56:44,830 --> 00:56:54,170
+عشرين مرة فهنا M في N في عدد ال K في عدد K فهي
+
+690
+00:56:54,170 --> 00:56:59,890
+المعادلة هي دي أكم مرة هتنحسبهتنحسب التلتة في بعض
+
+691
+00:56:59,890 --> 00:57:06,650
+K في N في M K في N في M كويس نبدأ ال for loop
+
+692
+00:57:06,650 --> 00:57:10,490
+الأولى ال for loop الأولى هتكرر M مرة فهدي واضح أن
+
+693
+00:57:10,490 --> 00:57:15,490
+هي theta of M M first order هدي first order هي
+
+694
+00:57:15,490 --> 00:57:21,070
+لحالها طيب داخلها nested معاها متشابك معاها loop
+
+695
+00:57:21,070 --> 00:57:26,270
+تانية to N فبقول theta of Nبرضه first order طيب
+
+696
+00:57:26,270 --> 00:57:29,490
+داخلها ده طبعا constant بس هيتكرر حسب عدد
+
+697
+00:57:29,490 --> 00:57:35,550
+تكراراتها هنا في كمان for loop K مرة فده فيتا of K
+
+698
+00:57:35,550 --> 00:57:39,030
+بس كلهم في الآخر to the power one to the power one
+
+699
+00:57:39,030 --> 00:57:43,610
+to the power one first first first مشكلتنا وين انه
+
+700
+00:57:43,610 --> 00:57:49,330
+first في firstلأن هما في بعض متشابكين في بعض
+
+701
+00:57:49,330 --> 00:57:52,390
+متشابكين في بعض لحظوا هنا هاي ال order تبقى هاي ال
+
+702
+00:57:52,390 --> 00:57:55,230
+level هاي ال level هاي ال level هدولة داخل بعض
+
+703
+00:57:55,230 --> 00:58:00,730
+مادام داخل بعض كل واحدة هتتكرر بعدد التكرارات اللي
+
+704
+00:58:00,730 --> 00:58:04,210
+.. اللي أعلى منها بصير جداش عدد التكرارات كله على
+
+705
+00:58:04,210 --> 00:58:12,130
+بعضه theta M في N في K كأنها
+
+706
+00:58:12,130 --> 00:58:20,430
+G تكعيبتكعيب صارت sort of بتتكلم هنا عن function
+
+707
+00:58:20,430 --> 00:58:25,130
+تكعيب فتوقع هالواجهة صارت بتقدر تحسبوها مباشرة من
+
+708
+00:58:25,130 --> 00:58:28,230
+مين بس تشوف ال for أو ال while اعرف انه حيصير فيه
+
+709
+00:58:28,230 --> 00:58:33,190
+تكرار جديش عدد التكرارات حسب ال limits حسب ال
+
+710
+00:58:33,190 --> 00:58:37,610
+limits اللي جيته انه في four loops او while مع
+
+711
+00:58:37,610 --> 00:58:41,730
+while او while مع four loop nested مع بعض متشابكين
+
+712
+00:58:41,730 --> 00:58:44,950
+مع بعض معناته حصل ضربهم مع بعض هتصير حصل
+
+713
+00:58:50,130 --> 00:58:53,910
+معظم الحاجات اللي احنا خدناها ال orders اللي احنا
+
+714
+00:58:53,910 --> 00:59:00,370
+خدناها ممكن نرتبهم من الأبسط للأصعببنبدأ بال
+
+715
+00:59:00,370 --> 00:59:03,790
+constant first order وهدي عادة بتكون في ال best
+
+716
+00:59:03,790 --> 00:59:07,230
+case في ال best case بتكون عندكم ال code هتعملوه
+
+717
+00:59:07,230 --> 00:59:10,130
+مرة واحدة و خلاص هيطلع نتيجة فبتكون constant طبعا
+
+718
+00:59:10,130 --> 00:59:13,350
+هذا متحققش دائما اللي أكبر منها شوية زي اللي
+
+719
+00:59:13,350 --> 00:59:17,390
+شفناها when شفناها في ال binary search ال binary
+
+720
+00:59:17,390 --> 00:59:21,680
+search كانت logarithmicلوجاريثمك بغض النظر عن ال
+
+721
+00:59:21,680 --> 00:59:26,420
+pace تبعتنا ال pace دي اتنين او عشرة او decimal او
+
+722
+00:59:26,420 --> 00:59:29,260
+غير decimal او binary مش هتفرج كتير فان هي ال
+
+723
+00:59:29,260 --> 00:59:32,260
+function اسمها logarithmic نتعامل مع logarithmic
+
+724
+00:59:32,260 --> 00:59:36,960
+طيب logarithmic to the power k poly logarithmic
+
+725
+00:59:36,960 --> 00:59:41,780
+logarithmic متعددة متعددة كويس او مضروبة في بعضها
+
+726
+00:59:41,780 --> 00:59:44,360
+فدي بقوله logarithmic اعلى شوية من من ال
+
+727
+00:59:44,360 --> 00:59:48,480
+logarithmic طيب اللي اعلى منها ال linearاللينيار
+
+728
+00:59:48,480 --> 00:59:51,160
+أعلى منها شوية اللي أعلى من اللينيار ال polynomial
+
+729
+00:59:51,160 --> 00:59:57,380
+لينيار بس مضروبة to the power of C تكعيب تربيع to
+
+730
+00:59:57,380 --> 01:00:00,580
+the power of 5 to the power of 4 whatever يعني إيش
+
+731
+01:00:00,580 --> 01:00:05,860
+الشكل بتاع في الآخر زي تو ال matrices عملية ال
+
+732
+01:00:05,860 --> 01:00:09,320
+matrix ال matrix multiplication كانت polynomial
+
+733
+01:00:09,320 --> 01:00:13,780
+طيب اللي أكبر منها ال exponential أنه لأ هي مش N
+
+734
+01:00:13,780 --> 01:00:18,240
+to the power of C هي C to the power of Nالـ S هو
+
+735
+01:00:18,240 --> 01:00:21,540
+الـ variable الـ S تبعنا أو ال power هي ال
+
+736
+01:00:21,540 --> 01:00:24,580
+variable اللي أكبر منها ال factorial ال factorial
+
+737
+01:00:24,580 --> 01:00:28,480
+اللي أكبر منها ال N to the power N بس احنا
+
+738
+01:00:28,480 --> 01:00:31,060
+هالواجهة تخلّينا نسبر نجفل هنا هدول المعظم اللي
+
+739
+01:00:31,060 --> 01:00:34,540
+بنشتغل عليهم أو نحدد منهم هالواجهة طبيعة ال
+
+740
+01:00:34,540 --> 01:00:39,880
+function صعبة ولا مش صعبة اعملوا خط هنا أي
+
+741
+01:00:39,880 --> 01:00:42,900
+function أقل من polynomial .. polynomial فأقل
+
+742
+01:00:42,900 --> 01:00:49,900
+بنسميها tractableقابلة للحل قابلة للحل أو visible
+
+743
+01:00:49,900 --> 01:00:55,640
+ممكنة فإذا قابلة للحل attractable بنسميها لكل ال
+
+744
+01:00:55,640 --> 01:00:58,940
+functions اللي بتكون polynomial فأقل مدان
+
+745
+01:00:58,940 --> 01:01:05,120
+polynomial فأقل هذا بنقول يعني big
+
+746
+01:01:05,120 --> 01:01:07,880
+O of N to the power C
+
+747
+01:01:11,360 --> 01:01:14,920
+هدول ايش بنسميها tractable كل ال functions اللي
+
+748
+01:01:14,920 --> 01:01:20,180
+polynomial او اقل قابلة لحل اعملوله اكواد و انتم
+
+749
+01:01:20,180 --> 01:01:27,110
+مرتاحين طيب اكبر intractable او invisibleغير قابل
+
+750
+01:01:27,110 --> 01:01:30,010
+للحل لأن هنا اتعقدت فبصير حتى ال algorithm لما
+
+751
+01:01:30,010 --> 01:01:32,890
+بتتعملوه بياخد وقت طويل كل ما بتزيد عدد ال inputs
+
+752
+01:01:32,890 --> 01:01:37,630
+تبعته فبصير هنا غير ممكن الحل .. غير ممكن الحل او
+
+753
+01:01:37,630 --> 01:01:41,830
+بنقدر نصنفه ان هو غير ممكن الحل فهد المرة الجاية
+
+754
+01:01:41,830 --> 01:01:45,690
+بنرجع نتكلم عنها interactable و uninteractable هدي
+
+755
+01:01:45,690 --> 01:01:48,790
+إيش و هدي إيش و كيف العلاقة بينهم و كيف ال
+
+756
+01:01:48,790 --> 01:01:51,870
+relation بينهم و بعض الحالات الشاذة بين هدي و هدي
+
+757
+01:01:51,870 --> 01:01:54,490
+.. بين هدي و هدي يلا يعطيك الصحة العفو و برك الله
+
+758
+01:01:54,490 --> 01:01:54,770
+فيك
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1fd73dbaff4d0f75c194fa4263c95d6fcee0df7d
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_raw.json
@@ -0,0 +1 @@
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"text": "طيب جي بتساوي big O F of G تمام واضح برضه أنه هنا نتكلم عن relation صحيحة على اعتبار أن ال F أكبر أكبر", "tokens": [9566, 1829, 3555, 10874, 1829, 39894, 3794, 995, 45865, 955, 422, 479, 295, 460, 46811, 10943, 4032, 46958, 5016, 4724, 43042, 3224, 14739, 3224, 34105, 8717, 2655, 4117, 19528, 18871, 9721, 20328, 5016, 1829, 5016, 3660, 15844, 1975, 34268, 3555, 9640, 14739, 2423, 479, 5551, 4117, 26890, 5551, 4117, 26890], "avg_logprob": -0.2038909378005009, "compression_ratio": 1.251908396946565, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 329.57, "end": 329.91, "word": "طيب", "probability": 0.7044270833333334}, {"start": 329.91, "end": 330.47, "word": " جي", "probability": 0.73388671875}, {"start": 330.47, "end": 331.59, "word": " بتساوي", "probability": 0.864501953125}, {"start": 331.59, "end": 331.81, "word": " big", "probability": 0.671875}, {"start": 331.81, "end": 332.13, "word": " O", "probability": 0.8076171875}, {"start": 332.13, "end": 332.81, 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polylogarithmic polylogarithmic polylogarithmic function فال polylogarithmic function أقل من ال linear", "tokens": [5016, 49975, 45164, 25961, 6754, 4987, 289, 355, 13195, 8608, 2655, 30544, 5551, 4587, 1211, 9154, 2423, 1668, 283, 5551, 4587, 1211, 9154, 2423, 2710, 5551, 4587, 1211, 9154, 2423, 2710, 11331, 49975, 45164, 318, 36632, 13412, 16606, 11331, 49975, 45164, 318, 36632, 13412, 16606, 8608, 2655, 30544, 5551, 4587, 1211, 8608, 2655, 30544, 5551, 4587, 1211, 15844, 5551, 3794, 32277, 14739, 3224, 4032, 46958, 5016, 14739, 29538, 6754, 4987, 289, 355, 13195, 6754, 4987, 289, 355, 13195, 6754, 4987, 289, 355, 13195, 2445, 6156, 6027, 6754, 4987, 289, 355, 13195, 2445, 5551, 4587, 1211, 9154, 2423, 8213], "avg_logprob": -0.3257575679307032, "compression_ratio": 2.2546583850931676, "no_speech_prob": 0.0, "words": [{"start": 726.8100000000001, "end": 727.57, "word": "حتى", "probability": 0.561279296875}, {"start": 727.57, "end": 727.71, "word": " لو", "probability": 0.93310546875}, 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"text": "فاللي هتكون إيش strictly أقل من order g، أقل من order g، بينفعش تساوي، لا يجيزش تساوي، طيب small omega strictly أكبر من order g، strictly أكبر من order g أو الزمن لازم يكون أكبر من order g، لا تساوي، okay", "tokens": [5172, 6027, 20292, 8032, 2655, 30544, 11933, 1829, 8592, 20792, 5551, 4587, 1211, 9154, 1668, 290, 12399, 5551, 4587, 1211, 9154, 1668, 290, 12399, 4724, 9957, 5172, 3615, 8592, 6055, 3794, 995, 45865, 12399, 20193, 7251, 7435, 1829, 11622, 8592, 6055, 3794, 995, 45865, 12399, 23032, 1829, 3555, 1359, 10498, 20792, 5551, 4117, 26890, 9154, 1668, 290, 12399, 20792, 5551, 4117, 26890, 9154, 1668, 290, 34051, 6024, 110, 27842, 5296, 31377, 2304, 7251, 30544, 5551, 4117, 26890, 9154, 1668, 290, 12399, 20193, 6055, 3794, 995, 45865, 12399, 1392], "avg_logprob": -0.2457865181933628, "compression_ratio": 1.948051948051948, "no_speech_prob": 0.0, "words": [{"start": 1040.73, "end": 1041.69, "word": "فاللي", "probability": 0.4493001302083333}, {"start": 1041.69, "end": 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قيم اه بس بيظلوا ماشيين مع بعض بيظلوا ماشيين مع بعض فمعدل تغيرهم بيظل ثابت مساوي لبعضه فهذا بيقول بيساوي بعض بغض النظر عن مين عن الأساس الأساس ال log بغض النظر عن أساس ال log تبعتنا", "tokens": [6027, 3096, 6055, 3555, 34268, 4117, 6055, 3555, 34268, 8315, 26601, 34051, 6225, 8592, 16572, 39896, 39896, 45164, 2423, 3565, 36632, 5551, 3794, 32277, 19753, 34740, 5296, 10721, 1829, 3096, 6055, 7649, 10632, 9673, 22488, 1211, 31439, 31439, 8978, 6055, 17082, 13546, 4724, 1829, 9381, 13546, 49374, 3224, 12174, 32640, 1975, 3224, 4724, 3794, 4724, 1829, 19913, 1211, 14407, 3714, 33599, 1829, 9957, 20449, 45030, 11242, 4724, 1829, 19913, 1211, 14407, 3714, 33599, 1829, 9957, 20449, 45030, 11242, 6156, 2304, 22488, 1211, 6055, 17082, 13546, 16095, 4724, 1829, 19913, 1211, 38637, 16758, 2655, 47524, 995, 45865, 5296, 3555, 3615, 11242, 3224, 6156, 3224, 15730, 4724, 1829, 39648, 4724, 1829, 3794, 995, 45865, 45030, 11242, 4724, 17082, 11242, 28239, 19913, 2288, 18871, 3714, 9957, 18871, 16247, 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K طيب ال matrix multiplication يمكن هذه احنا ماخدناش في وقتها", "tokens": [41185, 2423, 8213, 8032, 33753, 26108, 12145, 36540, 20328, 5016, 22807, 5296, 10721, 34105, 5551, 3794, 2407, 10721, 1389, 43242, 8315, 8978, 2423, 17434, 14739, 1829, 5551, 8592, 2655, 17082, 1211, 15844, 1386, 36540, 6156, 47432, 39182, 1386, 36540, 8032, 30544, 4032, 36520, 2655, 24976, 1783, 8032, 1211, 3714, 29245, 23328, 34051, 32771, 13546, 3714, 29245, 23328, 1392, 6156, 3224, 1829, 16712, 5016, 20292, 1211, 6055, 3555, 3615, 8315, 6225, 8592, 7649, 8978, 6024, 95, 34740, 8717, 5016, 35457, 591, 4032, 8717, 8592, 2655, 17082, 1211, 15844, 591, 23032, 1829, 3555, 2423, 8141, 27290, 7251, 43020, 29538, 1975, 5016, 8315, 19446, 9778, 3215, 1863, 33599, 8978, 4032, 38149, 11296], "avg_logprob": -0.18636363853107799, "compression_ratio": 1.5954198473282444, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3034.21, "end": 3034.41, "word": "في", "probability": 0.55615234375}, {"start": 3034.41, 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{"start": 3075.39, "end": 3076.47, "word": " first", "probability": 0.48291015625}, {"start": 3076.47, "end": 3076.91, "word": " order", "probability": 0.94482421875}, {"start": 3076.91, "end": 3078.23, "word": " هتعطينا", "probability": 0.97265625}, {"start": 3078.23, "end": 3078.63, "word": " تكرار", "probability": 0.9420572916666666}, {"start": 3078.63, "end": 3079.53, "word": " وخصوصا", "probability": 0.9214680989583334}, {"start": 3079.53, "end": 3080.45, "word": " اذا", "probability": 0.81591796875}, {"start": 3080.45, "end": 3080.87, "word": " التكرار", "probability": 0.9519856770833334}, {"start": 3080.87, "end": 3081.65, "word": " تبحة", "probability": 0.6348063151041666}, {"start": 3081.65, "end": 3082.05, "word": " زي", "probability": 0.71923828125}, {"start": 3082.05, "end": 3082.11, "word": " ما", "probability": 0.9697265625}, {"start": 3082.11, "end": 3082.33, "word": " قلنا", "probability": 0.9544270833333334}, {"start": 3082.33, "end": 3082.41, "word": " ال", "probability": 0.6435546875}, {"start": 3082.41, "end": 3082.63, "word": " limits", "probability": 0.9658203125}, {"start": 3082.63, "end": 3082.99, "word": " تبعته", "probability": 0.8489990234375}, {"start": 3082.99, "end": 3083.35, "word": " ايش", "probability": 0.7398274739583334}, {"start": 3083.35, "end": 3084.83, "word": " variables", "probability": 0.78955078125}, {"start": 3084.83, "end": 3085.87, "word": " اذا", "probability": 0.806396484375}, {"start": 3085.87, "end": 3085.97, "word": " ال", "probability": 0.89990234375}, {"start": 3085.97, "end": 3086.11, "word": " limits", "probability": 0.9697265625}, {"start": 3086.11, "end": 3086.45, "word": " تبعته", "probability": 0.97265625}, {"start": 3086.45, "end": 3086.87, "word": " variables", "probability": 0.9521484375}, {"start": 3086.87, "end": 3088.09, "word": " طيب", "probability": 0.9055989583333334}, {"start": 3088.09, "end": 3088.37, "word": " خلينا", "probability": 0.79443359375}, {"start": 3088.37, "end": 3088.65, "word": " نشوف", "probability": 0.9973958333333334}, {"start": 3088.65, "end": 3088.87, "word": " في", "probability": 0.9404296875}, {"start": 3088.87, "end": 3089.31, "word": " حالة", "probability": 0.9973958333333334}, {"start": 3089.31, "end": 3089.67, "word": " ضرب", "probability": 0.97998046875}, {"start": 3089.67, "end": 3090.41, "word": " المصففات", "probability": 0.90712890625}], "temperature": 1.0}, {"id": 122, "seek": 311706, "start": 3091.72, "end": 3117.06, "text": "احنا بنضرب مصفوفات M في K بنضربها في مين؟ K في N عشان ينتج عندى مصفوفة M في N تمام واضح ان في عندنا variable اتنين تلاتة في three variables في عدد الصفوف", "tokens": [39319, 8315, 44945, 11242, 25513, 3714, 9381, 5172, 38688, 9307, 376, 8978, 591, 44945, 11242, 25513, 11296, 8978, 3714, 9957, 22807, 591, 8978, 426, 6225, 8592, 7649, 7251, 29399, 7435, 43242, 7578, 3714, 9381, 5172, 38688, 3660, 376, 8978, 426, 46811, 10943, 4032, 46958, 5016, 16472, 8978, 43242, 8315, 7006, 1975, 2655, 1863, 9957, 6055, 1211, 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K", "probability": 0.76220703125}, {"start": 3098.32, "end": 3098.78, "word": " في", "probability": 0.95947265625}, {"start": 3098.78, "end": 3099.22, "word": " N", "probability": 0.96630859375}, {"start": 3099.22, "end": 3099.84, "word": " عشان", "probability": 0.9759114583333334}, {"start": 3099.84, "end": 3100.22, "word": " ينتج", "probability": 0.9860026041666666}, {"start": 3100.22, "end": 3100.92, "word": " عندى", "probability": 0.71435546875}, {"start": 3100.92, "end": 3102.1, "word": " مصفوفة", "probability": 0.99306640625}, {"start": 3102.1, "end": 3102.88, "word": " M", "probability": 0.96044921875}, {"start": 3102.88, "end": 3103.28, "word": " في", "probability": 0.9658203125}, {"start": 3103.28, "end": 3103.94, "word": " N", "probability": 0.994140625}, {"start": 3103.94, "end": 3104.78, "word": " تمام", "probability": 0.764404296875}, {"start": 3104.78, "end": 3107.54, "word": " واضح", "probability": 0.7587076822916666}, {"start": 3107.54, "end": 3107.66, "word": " ان", "probability": 0.3486328125}, {"start": 3107.66, "end": 3107.82, "word": " في", "probability": 0.74267578125}, {"start": 3107.82, "end": 3108.22, "word": " عندنا", "probability": 0.895751953125}, {"start": 3108.22, "end": 3108.82, "word": " variable", "probability": 0.85693359375}, {"start": 3108.82, "end": 3110.44, "word": " اتنين", "probability": 0.9097900390625}, {"start": 3110.44, "end": 3111.48, "word": " تلاتة", "probability": 0.9053955078125}, {"start": 3111.48, "end": 3111.78, "word": " في", "probability": 0.8212890625}, {"start": 3111.78, "end": 3111.98, "word": " three", "probability": 0.78125}, {"start": 3111.98, "end": 3112.62, "word": " variables", "probability": 0.9580078125}, {"start": 3112.62, "end": 3115.76, "word": " في", "probability": 0.6591796875}, {"start": 3115.76, "end": 3116.52, "word": " عدد", "probability": 0.9876302083333334}, {"start": 3116.52, "end": 3117.06, "word": " الصفوف", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 123, "seek": 313153, "start": 3117.87, "end": 3131.53, "text": "أنا ممكن أدخل matrix من عندي، يعني ليش نلزمونه مثلا 2 في 3 أضربها في 3 ب 2؟ أنا بدي أدخل 5 في 7، إيش المشكلة؟ فعدد ال variables هذه unvariable المفروض أنه ال algorithm يكون general", "tokens": [10721, 8315, 3714, 43020, 5551, 3215, 9778, 1211, 8141, 9154, 18871, 16254, 12399, 37495, 22653, 32239, 8592, 8717, 1211, 11622, 2304, 11536, 3224, 50113, 15040, 568, 8978, 805, 5551, 11242, 25513, 11296, 8978, 805, 4724, 568, 22807, 41850, 4724, 16254, 5551, 3215, 9778, 1211, 1025, 8978, 1614, 12399, 11933, 1829, 8592, 9673, 8592, 28820, 3660, 22807, 6156, 22488, 3215, 2423, 9102, 29538, 517, 34033, 712, 9673, 5172, 32887, 11242, 14739, 3224, 2423, 9284, 7251, 30544, 2674], "avg_logprob": -0.2773944665859272, "compression_ratio": 1.4427083333333333, "no_speech_prob": 8.821487426757812e-06, "words": [{"start": 3117.87, "end": 3118.11, "word": "أنا", "probability": 0.7088623046875}, {"start": 3118.11, "end": 3118.35, "word": " ممكن", 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0.98115234375}, {"start": 3126.25, "end": 3127.31, "word": " فعدد", "probability": 0.94873046875}, {"start": 3127.31, "end": 3127.45, "word": " ال", "probability": 0.97216796875}, {"start": 3127.45, "end": 3127.73, "word": " variables", "probability": 0.77099609375}, {"start": 3127.73, "end": 3127.95, "word": " هذه", "probability": 0.5068359375}, {"start": 3127.95, "end": 3128.65, "word": " unvariable", "probability": 0.6893310546875}, {"start": 3128.65, "end": 3129.69, "word": " المفروض", "probability": 0.945068359375}, {"start": 3129.69, "end": 3129.87, "word": " أنه", "probability": 0.4986572265625}, {"start": 3129.87, "end": 3129.93, "word": " ال", "probability": 0.83984375}, {"start": 3129.93, "end": 3130.35, "word": " algorithm", "probability": 0.8603515625}, {"start": 3130.35, "end": 3131.05, "word": " يكون", "probability": 0.982421875}, {"start": 3131.05, "end": 3131.53, "word": " general", "probability": 0.92333984375}], "temperature": 1.0}, {"id": 124, "seek": 316133, "start": 3135.01, "end": 3161.33, "text": "Dimension لل matrices اللي بدنا نضربها في بعض يتقبلها أي dimension يتقبلها فهنا M في K .. K تاخد أي قيمة M تاخد أي قيمة N تاخد أي قيمة فهذه variables هذه بتحددنا عدد ال inputs بتحدد عدد ال inputs اللي بدنا ندخله نضربه في بعض كويسة for I one to H to M هذه هنا بنتكلم عن مين عن ال raw فإذا بنبدأ بال raw رقم واحد", "tokens": [35, 332, 3378, 24976, 32284, 13672, 1829, 47525, 8315, 8717, 11242, 25513, 11296, 8978, 45030, 11242, 7251, 2655, 4587, 36150, 11296, 36632, 10139, 7251, 2655, 4587, 36150, 11296, 6156, 3224, 8315, 376, 8978, 591, 4386, 591, 6055, 47283, 3215, 36632, 12174, 32640, 3660, 376, 6055, 47283, 3215, 36632, 12174, 32640, 3660, 426, 6055, 47283, 3215, 36632, 12174, 32640, 3660, 6156, 3224, 24192, 9102, 29538, 39894, 24401, 3215, 8315, 6225, 3215, 3215, 2423, 15743, 39894, 24401, 3215, 6225, 3215, 3215, 2423, 15743, 13672, 1829, 47525, 8315, 8717, 3215, 9778, 43761, 8717, 11242, 25513, 3224, 8978, 45030, 11242, 9122, 45865, 3794, 3660, 337, 286, 472, 281, 389, 281, 376, 29538, 34105, 44945, 2655, 4117, 19528, 18871, 3714, 9957, 18871, 2423, 8936, 6156, 28814, 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tractable", "probability": 0.97607421875}, {"start": 3672.9, "end": 3673.76, "word": " كل", "probability": 0.452392578125}, {"start": 3673.76, "end": 3673.92, "word": " ال", "probability": 0.95947265625}, {"start": 3673.92, "end": 3674.46, "word": " functions", "probability": 0.875}, {"start": 3674.46, "end": 3674.92, "word": " اللي", "probability": 0.958740234375}, {"start": 3674.92, "end": 3675.7, "word": " polynomial", "probability": 0.779296875}, {"start": 3675.7, "end": 3676.62, "word": " او", "probability": 0.83251953125}, {"start": 3676.62, "end": 3677.72, "word": " اقل", "probability": 0.95166015625}, {"start": 3677.72, "end": 3678.84, "word": " قابلة", "probability": 0.9210611979166666}, {"start": 3678.84, "end": 3679.22, "word": " لحل", "probability": 0.8663736979166666}, {"start": 3679.22, "end": 3679.7, "word": " اعملوله", "probability": 0.814501953125}, {"start": 3679.7, "end": 3680.02, "word": " اكواد", "probability": 0.708251953125}, {"start": 3680.02, "end": 3680.1, "word": " و", "probability": 0.9765625}, {"start": 3680.1, "end": 3680.18, "word": " انتم", "probability": 0.574951171875}, {"start": 3680.18, "end": 3680.8, "word": " مرتاحين", "probability": 0.9786376953125}, {"start": 3680.8, "end": 3681.5, "word": " طيب", "probability": 0.9308268229166666}, {"start": 3681.5, "end": 3682.22, "word": " اكبر", "probability": 0.919921875}, {"start": 3682.22, "end": 3684.08, "word": " intractable", "probability": 0.8416341145833334}, {"start": 3684.08, "end": 3684.66, "word": " او", "probability": 0.946533203125}, {"start": 3684.66, "end": 3685.52, "word": " invisible", "probability": 0.84033203125}], "temperature": 1.0}, {"id": 145, "seek": 371477, "start": 3686.39, "end": 3714.77, "text": "غير قابل للحل لأن هنا اتعقدت فبصير حتى ال algorithm لما بتتعملوه بياخد وقت طويل كل ما بتزيد عدد ال inputs تبعته فبصير هنا غير ممكن الحل .. غير ممكن الحل او بنقدر نصنفه ان هو غير ممكن الحل فهد المرة الجاية بنرجع نتكلم عنها interactable و uninteractable هدي إيش و هدي إيش و كيف العلاقة بينهم و كيف ال relation بينهم و بعض الحالات الشاذة بين هدي و هدي .. بين هدي و هدي يلا يعطيك الصحة العفو و برك الله فيك", "tokens": [17082, 13546, 12174, 16758, 1211, 24976, 5016, 1211, 5296, 33456, 34105, 1975, 2655, 3615, 28543, 2655, 6156, 3555, 9381, 13546, 11331, 49975, 2423, 9284, 5296, 15042, 39894, 2655, 25957, 1211, 2407, 3224, 4724, 1829, 47283, 3215, 4032, 38149, 23032, 2407, 26895, 28242, 19446, 39894, 11622, 25708, 6225, 3215, 3215, 2423, 15743, 6055, 3555, 34268, 3224, 6156, 3555, 9381, 13546, 34105, 32771, 13546, 3714, 43020, 21542, 1211, 4386, 32771, 13546, 3714, 43020, 21542, 1211, 1975, 2407, 44945, 28543, 2288, 8717, 9381, 1863, 5172, 3224, 16472, 31439, 32771, 13546, 3714, 43020, 21542, 1211, 6156, 3224, 3215, 9673, 25720, 25724, 995, 10632, 44945, 47341, 3615, 8717, 2655, 4117, 19528, 18871, 11296, 4648, 712, 4032, 49234, 578, 712, 8032, 16254, 11933, 1829, 8592, 4032, 8032, 16254, 11933, 1829, 8592, 4032, 9122, 33911, 18863, 15040, 28671, 49374, 16095, 4032, 9122, 33911, 2423, 9721, 49374, 16095, 4032, 45030, 11242, 21542, 6027, 9307, 25124, 45636, 3660, 49374, 8032, 16254, 4032, 8032, 16254, 4386, 49374, 8032, 16254, 4032, 8032, 16254, 7251, 15040, 37495, 9566, 1829, 4117, 31767, 5016, 3660, 18863, 5172, 2407, 4032, 4724, 31747, 21984, 8978, 4117], "avg_logprob": -0.16548687252550495, "compression_ratio": 2.09717868338558, "no_speech_prob": 3.0994415283203125e-06, "words": [{"start": 3686.39, "end": 3686.73, "word": "غير", "probability": 0.982177734375}, {"start": 3686.73, "end": 3687.11, "word": " قابل", "probability": 0.818603515625}, {"start": 3687.11, "end": 3687.55, "word": " للحل", "probability": 0.97705078125}, {"start": 3687.55, "end": 3687.77, "word": " لأن", "probability": 0.752685546875}, {"start": 3687.77, "end": 3687.95, "word": " هنا", "probability": 0.7392578125}, {"start": 3687.95, "end": 3688.57, "word": " اتعقدت", "probability": 0.89033203125}, {"start": 3688.57, "end": 3689.11, "word": " فبصير", "probability": 0.92041015625}, {"start": 3689.11, "end": 3689.37, "word": " حتى", "probability": 0.87744140625}, {"start": 3689.37, "end": 3689.49, "word": " ال", "probability": 0.966796875}, {"start": 3689.49, "end": 3689.81, "word": " algorithm", "probability": 0.96044921875}, {"start": 3689.81, "end": 3690.01, "word": " لما", "probability": 0.904052734375}, {"start": 3690.01, "end": 3690.77, "word": " بتتعملوه", "probability": 0.753173828125}, {"start": 3690.77, "end": 3691.23, "word": " بياخد", "probability": 0.9268798828125}, {"start": 3691.23, "end": 3691.43, "word": " وقت", "probability": 0.984375}, {"start": 3691.43, "end": 3691.73, "word": " طويل", "probability": 0.9332682291666666}, {"start": 3691.73, "end": 3691.89, "word": " كل", "probability": 0.9716796875}, {"start": 3691.89, "end": 3692.01, "word": " ما", "probability": 0.87060546875}, {"start": 3692.01, "end": 3692.33, "word": " بتزيد", "probability": 0.8377278645833334}, {"start": 3692.33, "end": 3692.57, "word": " عدد", "probability": 0.9892578125}, {"start": 3692.57, "end": 3692.67, "word": " ال", "probability": 0.93994140625}, {"start": 3692.67, "end": 3692.89, "word": " inputs", "probability": 0.81396484375}, {"start": 3692.89, "end": 3693.39, "word": " تبعته", "probability": 0.8935546875}, {"start": 3693.39, "end": 3694.07, "word": " فبصير", "probability": 0.95361328125}, {"start": 3694.07, "end": 3694.31, "word": " هنا", "probability": 0.99072265625}, {"start": 3694.31, "end": 3694.95, "word": " غير", "probability": 0.9970703125}, {"start": 3694.95, "end": 3695.35, "word": " ممكن", "probability": 0.98388671875}, {"start": 3695.35, "end": 3696.27, "word": " الحل", "probability": 0.99365234375}, {"start": 3696.27, "end": 3696.57, "word": " ..", "probability": 0.4296875}, {"start": 3696.57, "end": 3696.73, "word": " غير", "probability": 0.8837890625}, {"start": 3696.73, "end": 3696.97, "word": " ممكن", "probability": 0.9912109375}, {"start": 3696.97, "end": 3697.43, "word": " الحل", "probability": 0.991943359375}, {"start": 3697.43, "end": 3697.63, "word": " او", "probability": 0.6915283203125}, {"start": 3697.63, "end": 3697.95, "word": " بنقدر", "probability": 0.9054361979166666}, {"start": 3697.95, "end": 3698.39, "word": " نصنفه", "probability": 0.9388671875}, {"start": 3698.39, "end": 3698.49, "word": " ان", "probability": 0.69970703125}, {"start": 3698.49, "end": 3698.63, "word": " هو", "probability": 0.85107421875}, {"start": 3698.63, "end": 3698.95, "word": " غير", "probability": 0.995361328125}, {"start": 3698.95, "end": 3699.49, "word": " ممكن", "probability": 0.9912109375}, {"start": 3699.49, "end": 3700.81, "word": " الحل", "probability": 0.99072265625}, {"start": 3700.81, "end": 3701.37, "word": " فهد", "probability": 0.7627766927083334}, {"start": 3701.37, "end": 3701.61, "word": " المرة", "probability": 0.884521484375}, {"start": 3701.61, "end": 3701.83, "word": " الجاية", "probability": 0.7267252604166666}, {"start": 3701.83, "end": 3702.49, "word": " بنرجع", "probability": 0.8486328125}, {"start": 3702.49, "end": 3702.73, "word": " نتكلم", "probability": 0.9058837890625}, {"start": 3702.73, "end": 3702.95, "word": " عنها", "probability": 0.89404296875}, {"start": 3702.95, "end": 3703.41, "word": " interactable", "probability": 0.746337890625}, {"start": 3703.41, "end": 3703.55, "word": " و", "probability": 0.8466796875}, {"start": 3703.55, "end": 3704.95, "word": " uninteractable", "probability": 0.7021077473958334}, {"start": 3704.95, "end": 3705.69, "word": " هدي", "probability": 0.650390625}, {"start": 3705.69, "end": 3705.89, "word": " إيش", "probability": 0.7572428385416666}, {"start": 3705.89, "end": 3705.99, "word": " و", "probability": 0.9306640625}, {"start": 3705.99, "end": 3706.17, "word": " هدي", "probability": 0.953857421875}, {"start": 3706.17, "end": 3706.35, "word": " إيش", "probability": 0.9762369791666666}, {"start": 3706.35, "end": 3706.45, "word": " و", "probability": 0.9423828125}, {"start": 3706.45, "end": 3706.59, "word": " كيف", "probability": 0.93408203125}, {"start": 3706.59, "end": 3707.43, "word": " العلاقة", "probability": 0.8922526041666666}, {"start": 3707.43, "end": 3707.87, "word": " بينهم", "probability": 0.990234375}, {"start": 3707.87, "end": 3708.53, "word": " و", "probability": 0.95556640625}, {"start": 3708.53, "end": 3708.71, "word": " كيف", "probability": 0.729736328125}, {"start": 3708.71, "end": 3708.79, "word": " ال", "probability": 0.93798828125}, {"start": 3708.79, "end": 3709.07, "word": " relation", "probability": 0.98681640625}, {"start": 3709.07, "end": 3709.47, "word": " بينهم", "probability": 0.9912109375}, {"start": 3709.47, "end": 3709.61, "word": " و", "probability": 0.74609375}, {"start": 3709.61, "end": 3709.83, "word": " بعض", "probability": 0.983642578125}, {"start": 3709.83, "end": 3710.15, "word": " الحالات", "probability": 0.90576171875}, {"start": 3710.15, "end": 3710.69, "word": " الشاذة", "probability": 0.8448893229166666}, {"start": 3710.69, "end": 3711.27, "word": " بين", "probability": 0.97216796875}, {"start": 3711.27, "end": 3711.51, "word": " هدي", "probability": 0.916748046875}, {"start": 3711.51, "end": 3711.61, "word": " و", "probability": 0.78271484375}, {"start": 3711.61, "end": 3711.87, "word": " هدي", "probability": 0.968017578125}, {"start": 3711.87, "end": 3711.99, "word": " ..", "probability": 0.708984375}, {"start": 3711.99, "end": 3712.13, "word": " بين", "probability": 0.69482421875}, {"start": 3712.13, "end": 3712.41, "word": " هدي", "probability": 0.989501953125}, {"start": 3712.41, "end": 3712.59, "word": " و", "probability": 0.97900390625}, {"start": 3712.59, "end": 3712.85, "word": " هدي", "probability": 0.991943359375}, {"start": 3712.85, "end": 3713.35, "word": " يلا", "probability": 0.562744140625}, {"start": 3713.35, "end": 3713.61, "word": " يعطيك", "probability": 0.83172607421875}, {"start": 3713.61, "end": 3713.89, "word": " الصحة", "probability": 0.7919108072916666}, {"start": 3713.89, "end": 3714.07, "word": " العفو", "probability": 0.4905598958333333}, {"start": 3714.07, "end": 3714.19, "word": " و", "probability": 0.8173828125}, {"start": 3714.19, "end": 3714.37, "word": " برك", "probability": 0.728271484375}, {"start": 3714.37, "end": 3714.49, "word": " الله", "probability": 0.9482421875}, {"start": 3714.49, "end": 3714.77, "word": " فيك", "probability": 0.9384765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3715.56425, "duration_after_vad": 3580.6974999999866}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c31104b479840dc14bc5f263dbb1087105535c09
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/4ClPrE8tsnk_raw.srt
@@ -0,0 +1,3056 @@
+1
+00:00:20,740 --> 00:00:22,840
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:22,840 --> 00:00:25,560
+الأنبياء والمسؤالين سيدنا محمد وعلى الأقل هو صاحبي
+
+3
+00:00:25,560 --> 00:00:32,820
+أجمعي نكمل اليوم في ال order of growth ووصلنا
+
+4
+00:00:32,820 --> 00:00:37,800
+ل ال big O اتكلمنا عن ال big O و اتكلمنا عن مجموعة
+
+5
+00:00:37,800 --> 00:00:45,300
+facts about the big O وكان أهمها لما بتكلم عن جي
+
+6
+00:00:45,300 --> 00:00:49,100
+بتساوي big O of F
+
+7
+00:00:52,040 --> 00:00:56,800
+في حالة زي هذه معناته كأني بقول ان ال order مش ال
+
+8
+00:00:56,800 --> 00:01:00,400
+function و ركزوا معناه ال order بتكلم عن order مش
+
+9
+00:01:00,400 --> 00:01:05,780
+عن function ال order لأ ال function g مساوي لل
+
+10
+00:01:05,780 --> 00:01:10,180
+order of f أو أقل فإذا ال order مش ال function
+
+11
+00:01:10,180 --> 00:01:18,240
+بمعنى ممكن تكون هذه عبارة عن twox تربيع زائد x
+
+12
+00:01:18,240 --> 00:01:22,700
+ومساوية ل big O of function ال function هذه عبارة
+
+13
+00:01:22,700 --> 00:01:31,320
+عن x تربيع على اتنين في مثلا او مباشرة على طول
+
+14
+00:01:31,320 --> 00:01:40,380
+زائد او ناقص x تلاتة x لاحظوا ان هذه لا تساوي هذه
+
+15
+00:01:40,380 --> 00:01:44,420
+ولكن ال order نفس ال orderال order نفس ال order
+
+16
+00:01:44,420 --> 00:01:47,660
+احنا هنا جاعدين نتكلم عن order ال order نفس ال
+
+17
+00:01:47,660 --> 00:01:53,300
+order كويس ففي الحالة هذه لو قلنا a في f ال order
+
+18
+00:01:53,300 --> 00:01:57,840
+بتغيرش ال a هذا constant belonging to r to real
+
+19
+00:01:57,840 --> 00:02:02,080
+number فأي element او constant اللي بنضربه فيه ال
+
+20
+00:02:02,080 --> 00:02:05,300
+function مش هيغير ال order لل function ال function
+
+21
+00:02:05,300 --> 00:02:08,840
+تربيعية هتظل تربيعية تكعيبية هتظل تكعيبية first
+
+22
+00:02:08,840 --> 00:02:11,140
+order هتظل first order او ال linear هتظل ال linear
+
+23
+00:02:12,750 --> 00:02:18,190
+بمعنى تلاتة X تربيعية هي big O of X تربيع اف زائد
+
+24
+00:02:18,190 --> 00:02:23,650
+big O of F بمعنى لو كانت هذه تربيع هذه نفطرة
+
+25
+00:02:23,650 --> 00:02:28,790
+تربيعية طيب لما تقولوا big O of F هذه ايش هتكون
+
+26
+00:02:28,790 --> 00:02:36,210
+تربيعية او اقل تربيع هذا على الاكثر طيب مجموحهم
+
+27
+00:02:36,210 --> 00:02:40,910
+برضه هتكون تربيع فاذا big O of F ولو كانت اقل من
+
+28
+00:02:40,910 --> 00:02:45,520
+تربيعبرضه تربيع زائد linear او زائد constant او
+
+29
+00:02:45,520 --> 00:02:50,900
+زائد inverse هتظل برضه تربيع هتظل big O of second
+
+30
+00:02:50,900 --> 00:02:56,480
+order او big O of F نفسها فمعنى ذلك هنا لو قلنا X
+
+31
+00:02:56,480 --> 00:03:02,880
+تربيع plus X و X هذه big O of F ال F هنا اللي هي
+
+32
+00:03:02,880 --> 00:03:06,340
+تربيعية فهتظل ال function كلها على بعض برضه big O
+
+33
+00:03:06,340 --> 00:03:13,920
+of FOkay الجزء التاني في ال fact سبعتنا بدنا نعرف
+
+34
+00:03:13,920 --> 00:03:19,640
+إيش هي ال big omega one أولا ال order one هذا إيش
+
+35
+00:03:19,640 --> 00:03:26,700
+هو هذا constant بمعنى إنه كأنها F to the power
+
+36
+00:03:26,700 --> 00:03:27,920
+zero
+
+37
+00:03:31,000 --> 00:03:35,340
+فمعنى ذلك بيتكلم عن constant طيب نجى لجزء التانى
+
+38
+00:03:35,340 --> 00:03:41,340
+ال big omega معناته constant او اكبر constant او
+
+39
+00:03:41,340 --> 00:03:45,360
+اكبر تمام خلينا نجى نشوف constant او at least
+
+40
+00:03:45,360 --> 00:03:51,240
+order zero او order one then absolute f to the
+
+41
+00:03:51,240 --> 00:03:56,040
+power one minus b و b هنا اكبر من او يساوي zero
+
+42
+00:03:57,080 --> 00:04:00,680
+بتساوي big O of F طب أكبر قيمة .. أصغر قيمة ممكن
+
+43
+00:04:00,680 --> 00:04:07,900
+أنها تكون Zero لو قولنا Zero هنا هتطلع F نفسها ف F
+
+44
+00:04:07,900 --> 00:04:11,300
+نفسها هي big O of F هي نفس أصلا big O of F نفس
+
+45
+00:04:11,300 --> 00:04:16,940
+الدرجة ماتغيرتش طيب لو كانت one minus one constant
+
+46
+00:04:16,940 --> 00:04:21,980
+constant مع ال constant برضه big O of F طيب اتنين
+
+47
+00:04:23,630 --> 00:04:30,970
+-1 يعني 1 على F أقل من big O of F فنفس الكلام أو
+
+48
+00:04:30,970 --> 00:04:35,690
+أقل من ال order لل F فإذا تنفع مع big O of F زي X
+
+49
+00:04:35,690 --> 00:04:36,750
+to the power of minus 1
+
+50
+00:04:42,030 --> 00:04:50,390
+Log أقل من X فأي order نعمله log هيكون order أقل
+
+51
+00:04:50,390 --> 00:04:54,750
+مادام order أقل يتفق مع علامة أو ال notation بتاعة
+
+52
+00:04:54,750 --> 00:04:56,450
+big O of F
+
+53
+00:05:00,090 --> 00:05:03,050
+تبعت big O ببساطة جدا انتوا لما بيقولوا مثلا
+
+54
+00:05:03,050 --> 00:05:08,310
+linear ال linear الف ال output تبعها الف مليون ال
+
+55
+00:05:08,310 --> 00:05:14,370
+output تبعها مليون طب تعالى نشوف log log الف تلاتة
+
+56
+00:05:14,370 --> 00:05:19,610
+log مليون ستة ستة فواضح ان هي كقيمة اقل كتير و
+
+57
+00:05:19,610 --> 00:05:24,250
+بالعكس حتى الفرق بزيد بينهم الفرق بزيد بينهم فهدي
+
+58
+00:05:24,250 --> 00:05:30,470
+ال order تبعها كتير اقل من ال order ال Fطيب جي
+
+59
+00:05:30,470 --> 00:05:37,590
+بتساوي big O F of G تمام واضح برضه أنه هنا نتكلم
+
+60
+00:05:37,590 --> 00:05:46,760
+عن relation صحيحة على اعتبار أن ال F أكبر أكبرأو
+
+61
+00:05:46,760 --> 00:05:51,840
+تساوي 0 order بمعنى أكبر من constant فأقل قيمة لها
+
+62
+00:05:51,840 --> 00:05:56,120
+أقل order لها أنها تكون constant تكون constant فلو
+
+63
+00:05:56,120 --> 00:06:00,600
+كانت constant هنا فال G بتساوي big O of G منطقية
+
+64
+00:06:00,600 --> 00:06:06,620
+ال function هي نفس orderها صح طيب أكبرfirst order
+
+65
+00:06:06,620 --> 00:06:13,060
+first في جي بتزيد قاعدة الجي فالجي ضمن حدود ال big
+
+66
+00:06:13,060 --> 00:06:19,440
+O of FG فهتضمن
+
+67
+00:06:19,440 --> 00:06:29,450
+حدود ال big O بتاعتناوالعكس مش صحيح الحالة
+
+68
+00:06:29,450 --> 00:06:31,730
+الوحيدة اللي ممكن تساوي فيها إذا كانت ال F first
+
+69
+00:06:31,730 --> 00:06:35,530
+order بس Zero order عفوا Zero order بمعنى constant
+
+70
+00:06:35,530 --> 00:06:40,370
+إذا كانت constant it's okay otherwise لأ إذا كانت
+
+71
+00:06:40,370 --> 00:06:44,470
+first في حالة زي هذه X و هنا log X طبعا هذه لا
+
+72
+00:06:44,470 --> 00:06:51,050
+تساوي big O of Xتمام هذا لا تساوي big O of X ولا
+
+73
+00:06:51,050 --> 00:06:56,730
+تساوي big O of log X لأنه أكبر من التنتين أكبر من
+
+74
+00:06:56,730 --> 00:07:02,410
+التنتين او
+
+75
+00:07:02,410 --> 00:07:07,810
+فال X log X أكبر منها ال X log X هتكون أكبر من big
+
+76
+00:07:07,810 --> 00:07:14,650
+O of X طيب ال A أو ال constant equal to big O of F
+
+77
+00:07:14,650 --> 00:07:20,370
+constant هيكون ضمنضمن ال big O of X مدام أنا بقول
+
+78
+00:07:20,370 --> 00:07:26,130
+ان ال big O of X هي constant او اكبر zero order او
+
+79
+00:07:26,130 --> 00:07:29,610
+اكبر zero order او اكبر فممكن تكون first order
+
+80
+00:07:29,610 --> 00:07:33,810
+second order third logarithmic order اي شي بس في
+
+81
+00:07:33,810 --> 00:07:37,990
+جميع الأحوال ال constant هو اقل قيمة لها ف belong
+
+82
+00:07:37,990 --> 00:07:47,460
+to big O of F طيب لووصلنا إلى النتيجة أن ال F
+
+83
+00:07:47,460 --> 00:07:53,080
+belonged to big O of G and ال G belonged to big O
+
+84
+00:07:53,080 --> 00:07:58,340
+of F بمعنى كل واحدة منهم big O من التانية معناته
+
+85
+00:07:58,340 --> 00:08:02,060
+الإثنين بيسووا بعض وهذا لو متذكرين طريقة الإثبات
+
+86
+00:08:02,060 --> 00:08:06,140
+اللي كنا نعملها في ال matrices في ال sets أيام ما
+
+87
+00:08:06,140 --> 00:08:09,700
+كنا نتكلم في ال sets في ال set في المجموعات عشان
+
+88
+00:08:09,700 --> 00:08:12,400
+نثبت أن في مجموعتين بيسووا بعض كنا بدنا نثبت
+
+89
+00:08:12,400 --> 00:08:16,680
+شغلتين مع بعضكنا نثبت إن الأولى صبست من التانية،
+
+90
+00:08:16,680 --> 00:08:19,060
+وبعدين نثبت أن التانية صبست من الأولى، فبنقول إن
+
+91
+00:08:19,060 --> 00:08:24,460
+هم متساويتين طيب هنا نفس الكلام، لو قولنا ال F أقل
+
+92
+00:08:24,460 --> 00:08:28,980
+من أو تساوي ال order G طيب G أقل من أو تساوي ال
+
+93
+00:08:28,980 --> 00:08:32,480
+order F فالعمل المشترك بين التنتين، أن الأتنين
+
+94
+00:08:32,480 --> 00:08:37,520
+بيسووا بعض، فهذا بمعناه أن ال G and Fof the same
+
+95
+00:08:37,520 --> 00:08:43,140
+order of انما بنعطيها ال big theta بنعطيها big
+
+96
+00:08:43,140 --> 00:08:48,520
+theta فإذا f big theta of g او g big theta of f
+
+97
+00:08:48,520 --> 00:08:54,820
+تمام if is exactly order g لا أكبر ولا أقل هي
+
+98
+00:08:54,820 --> 00:08:59,700
+exactly نفس order g و بنكتبها if belong to big
+
+99
+00:08:59,700 --> 00:09:05,720
+theta of g و نفس الكلام نقدر نقول ان ال git
+
+100
+00:09:05,720 --> 00:09:11,900
+belongs to big theta of F طيب
+
+101
+00:09:11,900 --> 00:09:15,540
+نشوف بقى مجموعة rules او facts برضه about big
+
+102
+00:09:15,540 --> 00:09:18,220
+theta و هل تتناسب مع ال big O اللي احنا خدناها
+
+103
+00:09:18,220 --> 00:09:21,940
+سابقا او لا و اين بتختلف و انتوا تشبه نشوف اول
+
+104
+00:09:21,940 --> 00:09:27,760
+شغلةfor all f g أكبر من 0 ال two functions هدول
+
+105
+00:09:27,760 --> 00:09:32,580
+أكبر من 0 و في عندنا constants a و b belonging to
+
+106
+00:09:32,580 --> 00:09:36,820
+R و ال a و ال b أكبر من صفر أكبر من صفر فازم انا
+
+107
+00:09:36,820 --> 00:09:43,260
+بتكلم عن positive real number هد ال b a في f مش
+
+108
+00:09:43,260 --> 00:09:49,250
+هتتغير ال order هد ال constantالـ a constant فأي
+
+109
+00:09:49,250 --> 00:09:52,590
+constant في ال function مش هيغير ال order ال order
+
+110
+00:09:52,590 --> 00:09:56,510
+f حتضل f ال order تربيه حتضل تربيه أو second order
+
+111
+00:09:56,510 --> 00:09:58,830
+حتضل second order first order حتضل first order
+
+112
+00:09:58,830 --> 00:10:05,070
+فهذه مشابهة ل ال big O مشابه حتى لان ال big O طيب
+
+113
+00:10:05,070 --> 00:10:10,950
+و لكن ال f not belong to θ f و g احنا قلنا انه
+
+114
+00:10:10,950 --> 00:10:13,950
+أكبر من صفر فهذه ممكن تكون first order second
+
+115
+00:10:13,950 --> 00:10:18,530
+order third orderإذا كانتالتنتين هدولة first order
+
+116
+00:10:18,530 --> 00:10:23,190
+هدي first و هدي first ضربهم في بعض second order طب
+
+117
+00:10:23,190 --> 00:10:27,130
+كيف بده أقول first order big theta ل second order
+
+118
+00:10:27,130 --> 00:10:31,250
+لأ بيسووش بعض exactly هنا بيسووش بعض لو big O
+
+119
+00:10:31,250 --> 00:10:35,390
+بيمشي الحال ولكن big theta بيمشيش الحال إلا في
+
+120
+00:10:35,390 --> 00:10:40,590
+حالة واحدة إذا كان ال G first order zero order
+
+121
+00:10:40,590 --> 00:10:44,110
+بمعنى constant constant بصير نفس ال relation اللي
+
+122
+00:10:44,110 --> 00:10:48,540
+فوقها بصير نفس ال relation اللي فوقهافهذه unlike
+
+123
+00:10:48,540 --> 00:10:54,880
+big O okay absolute if to the power one minus b
+
+124
+00:10:54,880 --> 00:11:02,040
+one minus b احنا قلنا بي أكبر من صفر فإذا واحد لو
+
+125
+00:11:02,040 --> 00:11:07,600
+حاطين هنا واحد zero طب ال constant بسويش first
+
+126
+00:11:07,600 --> 00:11:09,960
+order صح؟
+
+127
+00:11:11,250 --> 00:11:14,730
+هنا واضح ان ال order لل F سواء first order second
+
+128
+00:11:14,730 --> 00:11:19,930
+order third order هينجس واحد او هصير zero order
+
+129
+00:11:19,930 --> 00:11:24,750
+هنا هصير zero order لا تساوي theta of F نفس الكلام
+
+130
+00:11:24,750 --> 00:11:28,390
+في ال log لان احنا عارفين ان ال log أقل abstractly
+
+131
+00:11:28,390 --> 00:11:34,190
+أقل من ال order ل F نفسها فلما بقول log F اكيد
+
+132
+00:11:34,190 --> 00:11:39,900
+هيكون أقل منF نفسها فلا يساوي .. لا يساوي ال order
+
+133
+00:11:39,900 --> 00:11:43,220
+F .. لا يساوي ال order F ال .. ال big theta لازم
+
+134
+00:11:43,220 --> 00:11:47,060
+exactly equal to نفس ال order .. equal .. the same
+
+135
+00:11:47,060 --> 00:11:51,960
+order أما هنا لأ هو strictly هيكون أقل في آخر
+
+136
+00:11:51,960 --> 00:11:56,140
+حالتين .. الحالتين هدولة دائما ال two operations
+
+137
+00:11:56,140 --> 00:12:00,960
+هدولة هيكونوا أقل من theta of F .. دائما هيكونوا
+
+138
+00:12:00,960 --> 00:12:01,660
+أقل من theta
+
+139
+00:12:06,810 --> 00:12:10,950
+حتى لو كان polylogarithmic ستكون أقل من ال order f
+
+140
+00:12:10,950 --> 00:12:15,730
+أقل من ال normal أقل من ال normal حتى لو S أي شاء
+
+141
+00:12:15,730 --> 00:12:23,370
+حتى لو S أي شاء ستكون أقل ستكون أقل على أساس أنه
+
+142
+00:12:23,370 --> 00:12:26,150
+واضح أن هذه polylogarithmic polylogarithmic
+
+143
+00:12:26,150 --> 00:12:29,930
+polylogarithmic function فال polylogarithmic
+
+144
+00:12:29,930 --> 00:12:36,910
+function أقل من ال linearطيب بدنا نحسب هالوجة إذا
+
+145
+00:12:36,910 --> 00:12:41,410
+فعلا عملت ال summation ل oiler من ذكرينه ل oiler
+
+146
+00:12:41,410 --> 00:12:46,050
+عبارة عن second order أو لأ هل فعلا هي كانت second
+
+147
+00:12:46,050 --> 00:12:50,210
+order أو لأ ال summation الذاكرية كيف كنا نحسبه n
+
+148
+00:12:50,210 --> 00:12:54,670
+في n plus 1 على 2 فهي ال summation نفسها n في n
+
+149
+00:12:54,670 --> 00:13:04,070
+plus 1 على 2 طيب ال n plus 1zero first order هذه
+
+150
+00:13:04,070 --> 00:13:09,930
+first order فبنقول theta of first order n مضروبة
+
+151
+00:13:09,930 --> 00:13:14,910
+في n على two طيب على two يعني كأني أنا بتكلم عن
+
+152
+00:13:14,910 --> 00:13:21,270
+theta n مضروبة في نصconstant انتوا هنا بتتكلموا عن
+
+153
+00:13:21,270 --> 00:13:23,970
+constant فconstant مايغيرش في ال order ال order
+
+154
+00:13:23,970 --> 00:13:28,670
+بيضل زي ما هو طيب في عندنا function برضه هدى هتكون
+
+155
+00:13:28,670 --> 00:13:35,710
+عبارة عن θ of n في θ of n n تربيع ضربهم في بعض
+
+156
+00:13:35,710 --> 00:13:41,030
+مباشرة هيساوي θ of n تربيع فال order second order
+
+157
+00:13:41,760 --> 00:13:44,640
+second order في الحالة اللي عندنا فلما تيجوا
+
+158
+00:13:44,640 --> 00:13:48,340
+تجمعوها بهذا الشكل و تشتغلوا على n في n plus واحد
+
+159
+00:13:48,340 --> 00:13:51,860
+على اتنين انتوا هنا بتتكلموا عن equation من الدرجة
+
+160
+00:13:51,860 --> 00:13:57,780
+أو من ال order الثاني من ال order التاني وهي عندكم
+
+161
+00:13:57,780 --> 00:14:02,620
+واضحة الترتيب تبعها طيب المرة اللي فاتت برضه
+
+162
+00:14:02,620 --> 00:14:04,360
+اتكلمنا عن other
+
+163
+00:14:06,600 --> 00:14:11,160
+relations other relations خلينا نرجع نعرج عليهم
+
+164
+00:14:11,160 --> 00:14:18,780
+كمان مرة لما كنا بنقول G هنا كله كاتبهم في G خلينا
+
+165
+00:14:18,780 --> 00:14:24,460
+نقول معناته F F بتساوي big O of G
+
+166
+00:14:26,790 --> 00:14:31,310
+هذه كانت إيش معناها؟ معناته إن ال order ل F أقل من
+
+167
+00:14:31,310 --> 00:14:35,090
+أو يساوي order G، أقل من أو يساوي order G، معناه
+
+168
+00:14:35,090 --> 00:14:41,190
+ذلك بقدر أقول إن ال F أقل من أو تساوي order G، هنا
+
+169
+00:14:41,190 --> 00:14:49,270
+بدأ أتكلم عن ال order، بتكلمش عن ال functionنتكلمش
+
+170
+00:14:49,270 --> 00:14:51,930
+عن مين؟ عن ال function، نتكلم عن ال order لل
+
+171
+00:14:51,930 --> 00:14:56,330
+function، معدلة التغير، جدش؟ أو ال growth تبعها،
+
+172
+00:14:56,330 --> 00:15:02,910
+كويس، طيب، كان في عندنا f small o of g، كانت
+
+173
+00:15:02,910 --> 00:15:09,070
+strictly أقل من، strictly أقل من، فهنا f أقل من g،
+
+174
+00:15:09,070 --> 00:15:17,980
+أقل من g، كان في عندنا big omega of gأكبر أو تساوي
+
+175
+00:15:17,980 --> 00:15:22,000
+دائما ال big أو يساوي مادام فيها big معناته فيها
+
+176
+00:15:22,000 --> 00:15:28,800
+يساوي طيب ف if أكبر من أو تساوي g طيب if بتساوي
+
+177
+00:15:28,800 --> 00:15:39,740
+small omega if strictly أكبر من g وأخيرا ال big
+
+178
+00:15:39,740 --> 00:15:45,020
+theta of g فهذه تساوي
+
+179
+00:15:47,620 --> 00:15:54,000
+G فلاحظوا كيف احنا بنكتبهم كمان لأنه
+
+180
+00:15:54,000 --> 00:15:57,720
+order نتكلم عن order نكتبش اكبر من او يساوي اللي
+
+181
+00:15:57,720 --> 00:16:03,220
+احنا عارفينها بالشكل هذا فيها ميالان شوية على اساس
+
+182
+00:16:03,220 --> 00:16:05,580
+تعرفوا بس انه احنا بنتكلم هنا عن ال order نتكلم مش
+
+183
+00:16:05,580 --> 00:16:08,080
+عن ال function نتكلم عن order نتكلم مش عن ال
+
+184
+00:16:08,080 --> 00:16:15,520
+function لأنه ببساطة تلاتة X تربيع ناقص X زائد مية
+
+185
+00:16:16,400 --> 00:16:22,720
+هي فعليا لا تساوي X تربيع، صحيح؟ ولكن ال order
+
+186
+00:16:22,720 --> 00:16:26,280
+بيساوي بعض، ال order بيساوي بعض، ك order لأ بيساوي
+
+187
+00:16:26,280 --> 00:16:33,660
+بعض الإتنين فالإتنين، الإتنين بيتفقوا إن الإتنين،
+
+188
+00:16:33,660 --> 00:16:40,440
+إيش بنقدر نقول عليهم؟ belong to X θ X تربيع،
+
+189
+00:16:40,440 --> 00:16:44,110
+الإتنين belong to θ X تربيعمتفقين ان الاتنين
+
+190
+00:16:44,110 --> 00:16:48,390
+second order برغم اختلافهم و بيساووش بعض فعليا،
+
+191
+00:16:48,390 --> 00:16:51,030
+بيساووش بعض فاحنا هنا متكلم عن ال order ماتنسوش
+
+192
+00:16:51,030 --> 00:16:53,410
+طيب فعنا ال big
+
+193
+00:17:02,580 --> 00:17:07,900
+أو أكبر بمعنى أنها نفس order g أو أكبر فكل ال
+
+194
+00:17:07,900 --> 00:17:10,800
+functions اللي بتتفق في هذا الكلام هي داخل ال set
+
+195
+00:17:10,800 --> 00:17:21,690
+big omega طيب small o of g هي كل ال functionsفاللي
+
+196
+00:17:21,690 --> 00:17:27,330
+هتكون إيش strictly أقل من order g، أقل من order g،
+
+197
+00:17:27,330 --> 00:17:31,990
+بينفعش تساوي، لا يجيزش تساوي، طيب small omega
+
+198
+00:17:31,990 --> 00:17:38,070
+strictly أكبر من order g، strictly أكبر من order g
+
+199
+00:17:38,070 --> 00:17:43,290
+أو الزمن لازم يكون أكبر من order g، لا تساوي، okay
+
+200
+00:17:44,830 --> 00:17:47,210
+مجموعة relations برضه هنتكلم عنها طبعا واضح أنه
+
+201
+00:17:47,210 --> 00:17:50,050
+احنا هنا أخدنا المجموعة ال notations الجديدة
+
+202
+00:17:50,050 --> 00:17:55,830
+بتاعتنا اللي هي ال order أقل من فهذه ال F have the
+
+203
+00:17:55,830 --> 00:17:59,350
+order أقل من order G فانا هنا بأتكلم عن مين عن
+
+204
+00:17:59,350 --> 00:18:04,650
+small O فش يساوي .. فش يساوي .. إذا فيه يساوي
+
+205
+00:18:04,650 --> 00:18:10,090
+بتصير ال big O فهنا to mean F belong to small O of
+
+206
+00:18:10,090 --> 00:18:13,630
+G طيب و F approximately
+
+207
+00:18:15,180 --> 00:18:19,800
+أو تقريبا تساوي G ك order فهي quality ك order
+
+208
+00:18:19,800 --> 00:18:23,340
+بتساوي G هذا معناه ان ال F برمته big theta of G
+
+209
+00:18:23,340 --> 00:18:31,410
+كويس عشان اقول ان ال F strictlysmall o of g او
+
+210
+00:18:31,410 --> 00:18:35,130
+strictly اقل من g في ال order طبعا ال order تبعها
+
+211
+00:18:35,130 --> 00:18:38,670
+اقل من g هذا امتى بيصير الكلام هذا اذا كان في ال
+
+212
+00:18:38,670 --> 00:18:44,810
+infinity لما بعمل limit to infinity f of x على g
+
+213
+00:18:44,810 --> 00:18:52,610
+of x equal to zero limit to zero limit to zero لما
+
+214
+00:18:52,610 --> 00:19:00,080
+اتكلموا عنال logarithmic logarithmic function بهذا
+
+215
+00:19:00,080 --> 00:19:11,580
+الشكل طبعا لحظه لما عند x بتساوي مليون مثلا جداش
+
+216
+00:19:11,580 --> 00:19:16,160
+قيمة ال logarithmic function ستة هتكون عند قيمة
+
+217
+00:19:16,160 --> 00:19:19,940
+الستة طيب لو بدنا نقارن هذه مع
+
+218
+00:19:22,960 --> 00:19:26,940
+مع cubic function مع تكعيبية مع function تكعيبية
+
+219
+00:19:26,940 --> 00:19:36,580
+هنا y بتساوي x تكعيب x تكعيب عند المليون تمانتاشر
+
+220
+00:19:36,580 --> 00:19:44,600
+صفر نتكلم عن تمانتاشر صفر فتمانتاشر صفر صحيح طيب
+
+221
+00:19:44,600 --> 00:19:52,610
+عند الألف هنا كانت تلاتة هنا كانت تسعةطيب لحظة
+
+222
+00:19:52,610 --> 00:19:56,890
+معدل التغير هذه معدل تغيرها بزيد أكبر بكتير من
+
+223
+00:19:56,890 --> 00:20:02,270
+معدل التغير هذه هنا كانت تلاتة هنا كانت عشرة to
+
+224
+00:20:02,270 --> 00:20:08,150
+the power تسعة هنا من تلاتة ل .. لجداش لستة الضعف
+
+225
+00:20:08,150 --> 00:20:15,070
+تطورت للضعف هنا لأ هنا تطورت لأضعاف ل
+
+226
+00:20:15,070 --> 00:20:19,390
+multiplication مش لمجرد ضعف يعني ماضربنهاش بس في
+
+227
+00:20:19,390 --> 00:20:23,510
+اتنين لأ احنا ضربناها في نفسهاأحنا ضربناها في
+
+228
+00:20:23,510 --> 00:20:27,470
+تكعيب، يعني كعبناها، تمام؟ مش مجرد ان ضربناها في
+
+229
+00:20:27,470 --> 00:20:32,130
+نفسها، تمام؟ فواضح ان معدل التغير بزيد كتير بينهم،
+
+230
+00:20:32,130 --> 00:20:34,930
+الفرق بزيد كتير بينهم طيب في ال infinity to
+
+231
+00:20:34,930 --> 00:20:42,770
+infinity ممكن تصل ان ال log على تكعيب limit to
+
+232
+00:20:42,770 --> 00:20:49,210
+zerolimit to zero هنا كنت بتتكلم عن تلاتة على عشرة
+
+233
+00:20:49,210 --> 00:20:53,370
+to the power تسعة قيمة كتير صغيرة بس لسه ستة على
+
+234
+00:20:53,370 --> 00:20:59,230
+عشرة to the power تمانتاش أقل كمان لو أخدته أكتر
+
+235
+00:20:59,230 --> 00:21:03,070
+عشرة مليون عشرين مليون خمسين مليون طبعا ال ratio
+
+236
+00:21:03,070 --> 00:21:08,310
+هتجل أكتر بينهم limit to infinity ال term هذا
+
+237
+00:21:08,310 --> 00:21:13,920
+limit to zeroفإذا f of x على g of x limit to zero
+
+238
+00:21:13,920 --> 00:21:16,860
+إذا كان تحقق الكلام ده بقدر أقوله مباشرة فإذا ال
+
+239
+00:21:16,860 --> 00:21:22,960
+order أقل strictly أقل من g strictly أقل من g إذا
+
+240
+00:21:22,960 --> 00:21:25,880
+نفس ال order يلهم نفس ال order بيكون بيكون كل
+
+241
+00:21:25,880 --> 00:21:30,140
+الفرج انه ماشيين مع بعض معدل التغير تبعهم ثابت
+
+242
+00:21:30,140 --> 00:21:36,680
+معدل تغيرهم ثابت تمام فأظن وضحت ال limitation هذه
+
+243
+00:21:39,470 --> 00:21:42,270
+مجموعة functions هتتعاملوا معها .. بتضطروا
+
+244
+00:21:42,270 --> 00:21:45,870
+تتعاملوا معها نشوف إيش ال relations بينهم ال one
+
+245
+00:21:45,870 --> 00:21:51,850
+zero order أو constant أقل من log of log M أقل من
+
+246
+00:21:51,850 --> 00:21:55,910
+ال log .. ليش؟ وإن كان معدل تغيره صغير ولكن في
+
+247
+00:21:55,910 --> 00:21:59,410
+معدل تغير ال constant مافي معدل تغير معدل تغير
+
+248
+00:21:59,410 --> 00:22:04,810
+zero constant معناته معدل تغير zero خلاص ثابت
+
+249
+00:22:04,810 --> 00:22:09,230
+مافيش معدل تغيره بتتغيرش مافيش growth بتصيرفيش نمو
+
+250
+00:22:09,230 --> 00:22:15,390
+بيصير في ال function بعكس ال log ال log بتتغير
+
+251
+00:22:15,390 --> 00:22:18,990
+okay بسيط احنا متفقين تغير بطيق ماشي بس في نهاية
+
+252
+00:22:18,990 --> 00:22:25,190
+في تغير في تغير فإذا ال order تبح أكبر من الواحد
+
+253
+00:22:25,190 --> 00:22:31,510
+طب في نفس الوجد log of n أكبر من log of log n ليش؟
+
+254
+00:22:31,510 --> 00:22:36,150
+لأنه ممكن نتعاملوا مع ال term هذا على أساس انه x
+
+255
+00:22:36,150 --> 00:22:45,710
+وهذا هيو xف log x أقل من x log x أقل من x نفس
+
+256
+00:22:45,710 --> 00:22:51,810
+الكلام سنقوله لاحقا ان log x دائما أقل من x في
+
+257
+00:22:51,810 --> 00:22:55,310
+الحالة اللي انا زى تقوى المليون في ال .. في ال ..
+
+258
+00:22:55,310 --> 00:22:59,950
+في ال linear هتسوى مليون input بيسوى مليون ال
+
+259
+00:22:59,950 --> 00:23:05,110
+output هتسوى مليون طيب مليون في ال log هسوى 6 أقل
+
+260
+00:23:05,110 --> 00:23:11,490
+بكتير فحتى معدل تغيره أقل طيب logال base تبعتك
+
+261
+00:23:11,490 --> 00:23:17,950
+تبعتنا decimal أو عشري هي هي لو ال log أي أساس آخر
+
+262
+00:23:17,950 --> 00:23:23,630
+لأي base تانية المعدل هو هو في تغير بيصير بينه قيم
+
+263
+00:23:23,630 --> 00:23:27,470
+اه بس بيظلوا ماشيين مع بعض بيظلوا ماشيين مع بعض
+
+264
+00:23:27,470 --> 00:23:30,990
+فمعدل تغيرهم بيظل ثابت مساوي لبعضه فهذا بيقول
+
+265
+00:23:30,990 --> 00:23:35,950
+بيساوي بعض بغض النظر عن مين عن الأساس الأساس ال
+
+266
+00:23:35,950 --> 00:23:41,090
+log بغض النظر عن أساس ال log تبعتناهنا هذه أقل من
+
+267
+00:23:41,090 --> 00:23:46,070
+ال poly logarithmic، أقل من ال poly logarithmic
+
+268
+00:23:46,070 --> 00:23:48,650
+function، أقل من ال poly logarithmic function ف
+
+269
+00:23:48,650 --> 00:23:54,210
+log الأساس k of n أقل من log to the power k، أقل
+
+270
+00:23:54,210 --> 00:23:56,670
+من ال poly logarithmic، فإذا في عندنا poly
+
+271
+00:23:56,670 --> 00:23:58,530
+logarithmic و في عندنا logarithmic function
+
+272
+00:23:59,550 --> 00:24:03,110
+بوليولغريثمك أكبر من ال logarithmic طيب و هذه
+
+273
+00:24:03,110 --> 00:24:08,470
+هتكون برضه نفس الكلام أقل من ان to the power one
+
+274
+00:24:08,470 --> 00:24:12,950
+over x من ال inverse من ال inverse ال inverse أقل
+
+275
+00:24:12,950 --> 00:24:18,710
+من ال n ال n أقل من n log n على اعتبار أن هذه
+
+276
+00:24:18,710 --> 00:24:22,110
+مضروبة في واحد هذه مضروبة في log n و احنا هنا لسه
+
+277
+00:24:22,110 --> 00:24:25,530
+بنقول ال واحد كانت أقل من log n فإذن طبيعي هذا
+
+278
+00:24:25,530 --> 00:24:37,310
+هيكونن أقل من ن في log n log n أقل من ال
+
+279
+00:24:37,310 --> 00:24:40,690
+polynomial من ال polynomial function n to the
+
+280
+00:24:40,690 --> 00:24:44,830
+power k تكعيب تربيع to the power four to the power
+
+281
+00:24:44,830 --> 00:24:49,950
+five polynomial أقل من ال polynomial اللي أكبر من
+
+282
+00:24:49,950 --> 00:24:56,480
+ال polynomial ال exponential اللي هيكي ثابت to the
+
+283
+00:24:56,480 --> 00:25:01,240
+power متغير to the power متغير هذه exponential هذه
+
+284
+00:25:01,240 --> 00:25:07,140
+exponential function فهذه أكبر من variable موجود
+
+285
+00:25:07,140 --> 00:25:11,020
+to the power constant to polynomial فال
+
+286
+00:25:11,020 --> 00:25:14,520
+exponential أكبر من ال polynomial functions okay
+
+287
+00:25:14,520 --> 00:25:19,120
+exponential اللي أكبر منها factorial
+
+288
+00:25:21,200 --> 00:25:24,280
+الفكتوري لما بيقول مية معناه ذلك أن أنا بتكلم عن
+
+289
+00:25:24,280 --> 00:25:27,720
+مية في تسعة وتسعين في تمانية وتسعين في سبعة وتسعين
+
+290
+00:25:27,720 --> 00:25:33,140
+لعند منصر لإيش؟ للواحد طيب هذه نفسها أقل من n to
+
+291
+00:25:33,140 --> 00:25:37,920
+the power n من مية to the power مية صحيح؟ لأن مية
+
+292
+00:25:37,920 --> 00:25:40,460
+to the power مية معناته بتضرب المية في نفسها ميت
+
+293
+00:25:40,460 --> 00:25:44,240
+مرة يعني مية في مية في مية في مية هناك كانت مية في
+
+294
+00:25:44,240 --> 00:25:47,320
+تسعة وتسعين في تمانية وتسعين في سبعة وتسعين غير
+
+295
+00:25:47,320 --> 00:25:49,680
+مية في مية في .. واضح أن مية في مية في مية في مية
+
+296
+00:25:49,680 --> 00:25:54,600
+أكبرأكبر ف N to the power of N أكيد أكبر من N
+
+297
+00:25:54,600 --> 00:25:59,300
+factorial و قصوا على ذلك يمكن هدول بس اللي هنتعامل
+
+298
+00:25:59,300 --> 00:26:03,760
+معهم و نقارن فيهم على أساس انه نحتاجهم في ال
+
+299
+00:26:03,760 --> 00:26:07,040
+complexity هالوجد كل الموضوع اللي فات بدنا نمهد ل
+
+300
+00:26:07,040 --> 00:26:12,260
+ال complexity بتاعتنا ال complexity ببساطة هي a
+
+301
+00:26:12,260 --> 00:26:15,880
+measure of how difficult it is to perform the
+
+302
+00:26:15,880 --> 00:26:21,810
+computation كيف أنابقدّي الحسابات في ال algorithm
+
+303
+00:26:21,810 --> 00:26:26,050
+تبعنا عندكم Algorithm هتكتبوه؟ هنطلب منك task
+
+304
+00:26:26,050 --> 00:26:29,570
+كتبنا ال algorithm أخدناه في أول محاضرة أشتغلناها
+
+305
+00:26:29,570 --> 00:26:34,250
+في ال algorithms كيف نكتب algorithm okay بعدين
+
+306
+00:26:34,250 --> 00:26:36,510
+أتعلمنا شوية عن ال order of growth و كيف ال
+
+307
+00:26:36,510 --> 00:26:39,610
+functions ال growth تبعها بنجيسوا مين أكبر من مين
+
+308
+00:26:39,610 --> 00:26:42,790
+طب هالوقت بدنا نمسك ال algorithm نفسه و ينجيس ال
+
+309
+00:26:42,790 --> 00:26:45,190
+complexity تبعته إن أنا أجيس ال order of growth
+
+310
+00:26:45,190 --> 00:26:49,750
+تبعهان احنا بدنا نجيس من أي درجة ال code اللي
+
+311
+00:26:49,750 --> 00:26:53,270
+انتوا كتبته كتبته code او كتبته algorithm طب ال
+
+312
+00:26:53,270 --> 00:26:55,750
+code تبعه ال .. ال .. ال complex اللي تبعته ال
+
+313
+00:26:55,750 --> 00:26:59,870
+order تبعه جداش؟ ليش؟ ليش محتاجينه؟ لأنه ممكن
+
+314
+00:26:59,870 --> 00:27:04,210
+يصلني كذا code بدعملهم analysis هذا ال order جداش؟
+
+315
+00:27:04,210 --> 00:27:07,450
+هذا ال order جداش؟ والله ال order الأقل أنسبلنا
+
+316
+00:27:07,450 --> 00:27:12,430
+ليش أنسبلنا؟ لأنه هيعطيني وقت أقل إذا اتفقنا لاحقا
+
+317
+00:27:12,430 --> 00:27:18,570
+ان احنا هنتكلم عن ال typeكويسة in general عادة كل
+
+318
+00:27:18,570 --> 00:27:23,110
+في الهندسة عموما بنتكلم عن ال cost هي ال criteria
+
+319
+00:27:23,110 --> 00:27:27,190
+بتاعتنا في القياسات ال cost هي ال criteria هي أهم
+
+320
+00:27:27,190 --> 00:27:30,250
+عنصر معظم ال design بشتغل عليه فاحنا لما بنشتغل
+
+321
+00:27:30,250 --> 00:27:34,490
+بنشتغل دايما على ال cost ال cost هذه ممكن نقيسها
+
+322
+00:27:34,490 --> 00:27:37,230
+بكذا طريقة أهم طريقة اللي احنا هنشتغل عليها هي ال
+
+323
+00:27:37,230 --> 00:27:43,570
+time ال processor لما بيزيد ال widgetفي حساباته
+
+324
+00:27:43,570 --> 00:27:47,930
+بضيع عليكم ال time ال time هذه معناته فيه energy
+
+325
+00:27:47,930 --> 00:27:52,810
+مستهلكة زيادة معناته ال code تبعكم لابد تطبقوه على
+
+326
+00:27:52,810 --> 00:27:57,750
+number of users او على n عددها كبير عدد ال inputs
+
+327
+00:27:57,750 --> 00:28:02,030
+تبعكم كبير ال delay هذا بصير اكبر ال time اللي
+
+328
+00:28:02,030 --> 00:28:07,280
+بضيع بصير اكبر لما نتكلم عنone millisecond فرق بين
+
+329
+00:28:07,280 --> 00:28:11,620
+two codes بين code والتاني one millisecond هذا لو
+
+330
+00:28:11,620 --> 00:28:15,460
+بتكون طبقه ال input تبعكم على مدينة زي غزة فيها
+
+331
+00:28:15,460 --> 00:28:18,720
+مليون و تمانمائة الف و بدنا نعمل search برقم
+
+332
+00:28:18,720 --> 00:28:23,360
+الهوية مثلاعشان نطلع صاحب رقم هوية معينة انتوا
+
+333
+00:28:23,360 --> 00:28:25,760
+عارفين كده هنضطر حسابات؟ معناه انتوا بدي اعمل
+
+334
+00:28:25,760 --> 00:28:30,340
+الاسوأ حالة ان انا بدور عن واحد رقم هويته اخر واحد
+
+335
+00:28:30,340 --> 00:28:34,340
+في السلسة في الموجودة صح؟ فده اسوأ حالة معناه ذلك
+
+336
+00:28:34,340 --> 00:28:37,860
+ان انا بدي اضطر اعمل مليون و تمانمائة الف مقارنة
+
+337
+00:28:37,860 --> 00:28:40,880
+مظبوط؟ او اتنين مليون مقارنة يعني بدي نشتغل على
+
+338
+00:28:40,880 --> 00:28:43,780
+اتنين مليون مقارنة اتنين مليون مقارنة اذا كل واحدة
+
+339
+00:28:43,780 --> 00:28:48,260
+بتتأخر لي one millisecond اللي احنا مش عارفين فيه
+
+340
+00:28:48,260 --> 00:28:52,000
+كده ال millisecondلحظوا جدش بتصير فيه delay، هصير
+
+341
+00:28:52,000 --> 00:28:54,460
+فيه كمية delay كبيرة جدا، معناته صار في عندكم
+
+342
+00:28:54,460 --> 00:29:02,680
+اتنين الف second، اتنين الف second صحيح؟ صارت two
+
+343
+00:29:02,680 --> 00:29:07,560
+K second عندك زيادة، فلحظوا اجسموه على سبتين على
+
+344
+00:29:07,560 --> 00:29:11,270
+سبتين بتطلعلكوا جدش عندكوا عدد أيام تأخيرتجدش ايام
+
+345
+00:29:11,270 --> 00:29:15,530
+تاخير بس عشان ينفذ ال code ال task تبعته فلأ مهم
+
+346
+00:29:15,530 --> 00:29:18,590
+جدا ال time في الحالة هذه وهو احد العناصر اللي
+
+347
+00:29:18,590 --> 00:29:22,110
+بيجيسوا فيها ال cost طبعا في عنصر تاني هو ال space
+
+348
+00:29:22,110 --> 00:29:25,290
+complexity ال space complexity تجدش ال memory اللي
+
+349
+00:29:25,290 --> 00:29:28,980
+انا محتاجهاقدش ال memory اللي انا محتاجها طبعا
+
+350
+00:29:28,980 --> 00:29:31,440
+احنا مش في صدد ان احنا اعمل اعلانات لبعض ال
+
+351
+00:29:31,440 --> 00:29:34,120
+softwares بس أحيانا جدا بتلاقوا في antivirus
+
+352
+00:29:34,120 --> 00:29:38,440
+بتحطوه على الجهاز بيروح الجهاز ليش؟ أخد space كبير
+
+353
+00:29:38,440 --> 00:29:43,860
+فخلاص حجز الجهاز عندكوا طبعا تيجوا تنفذولكوا
+
+354
+00:29:43,860 --> 00:29:47,540
+برنامجين تلاتة تفتحوا ال bar point على مش عارف على
+
+355
+00:29:47,540 --> 00:29:50,600
+ال excel على مش عارف اللي هتلاقوا الجهاز بتعملوا
+
+356
+00:29:50,600 --> 00:29:54,260
+click و بتستنوا قبل ما ..يعملكوا response قبل ما
+
+357
+00:29:54,260 --> 00:30:00,940
+يعطي ال response فواضح ان هنا ال space ضاعت في
+
+358
+00:30:00,940 --> 00:30:03,420
+المقابل في antivirus تاني ممكن تنزلوه و ما تحسوش
+
+359
+00:30:03,420 --> 00:30:07,860
+فيه مقد الغرض و مقد الغرض طبعا في الآخر هنا ال
+
+360
+00:30:07,860 --> 00:30:10,400
+space بتفرج معانا إذا والله انتوا ال space عندكوا
+
+361
+00:30:10,400 --> 00:30:14,200
+حجم صغير معاناة ال complexة بتحسبوها على ال space
+
+362
+00:30:14,200 --> 00:30:18,980
+في الحالة هذه in generalعموما احنا هنشتغل في ال
+
+363
+00:30:18,980 --> 00:30:21,880
+course تبعنا فقط على ال time عموما هنشتغل على ال
+
+364
+00:30:21,880 --> 00:30:25,600
+time بس انا حابب اوضحلكم ان لأ في criteria تانية
+
+365
+00:30:25,600 --> 00:30:28,240
+ممكن الواحد يشتغل عليها احنا هنشتغل على ال time
+
+366
+00:30:28,240 --> 00:30:31,940
+انتوا بعدين ممكن في وقت من الوقات او في مساهم
+
+367
+00:30:31,940 --> 00:30:38,920
+المساقات تضطروا تشتغلوا على اشي تاني okay طيب برضه
+
+368
+00:30:38,920 --> 00:30:41,720
+بنكون عارفين ان ال algorithms ممكن تتباع يعني كل
+
+369
+00:30:41,720 --> 00:30:45,340
+واحدة يكون لها complexity غير التانيوهنا بدو يصير
+
+370
+00:30:45,340 --> 00:30:49,960
+الاختيار انا بدأ اختار مين بناء على ال time search
+
+371
+00:30:49,960 --> 00:30:53,820
+الأقل هو اللي بدأ نختاره اللي بيعطينا time أقل
+
+372
+00:30:53,820 --> 00:30:57,740
+بمعنى ان انا هعمل click ال response تجيني أسرع
+
+373
+00:30:57,740 --> 00:31:01,520
+النتيجة تجيني أسرع طبعا هذا أنسبلي أفضلي هذا بيكون
+
+374
+00:31:01,520 --> 00:31:05,020
+كتير أفضلي طيب واضح ان احنا اشتغلنا هالواجهة على
+
+375
+00:31:05,020 --> 00:31:08,440
+ال time complexity بتاعتنا او ال complexity على
+
+376
+00:31:08,440 --> 00:31:11,420
+اساس ان هي function function في مين في عدد ال
+
+377
+00:31:11,420 --> 00:31:15,660
+inputsعدد ال inputs لما كان خمسة جدش كانت ال
+
+378
+00:31:15,660 --> 00:31:19,000
+complexity طب لما صاروا اتنين مليون جدش صارت ال
+
+379
+00:31:19,000 --> 00:31:22,060
+complexity طبعا بتتغير ال time جدش اللي استهلكته
+
+380
+00:31:22,060 --> 00:31:24,820
+هنا هيتغير عن هنا فواضح ان احنا بنتكلم هنا عن
+
+381
+00:31:24,820 --> 00:31:27,900
+function ال function هنا دي function في ال input
+
+382
+00:31:27,900 --> 00:31:33,240
+length جداش عدد ال inputs بتاعتنا كويسة في الغالب
+
+383
+00:31:33,240 --> 00:31:35,880
+او هذا ال general اللي الكل بيشتغل عليه احنا
+
+384
+00:31:35,880 --> 00:31:39,900
+بتشتغل دايما على ال worst caseعلى أسوأ حالة لما
+
+385
+00:31:39,900 --> 00:31:44,600
+بعمل search مثلا بنعمل search بتدور على رقم هوية
+
+386
+00:31:44,600 --> 00:31:48,560
+بعمل حساب أنه رقم هوية ممكن يكون أخر رقم نفترض
+
+387
+00:31:48,560 --> 00:31:53,280
+بدنا ندور على whatever يعني في صف عندى و بدور على
+
+388
+00:31:53,280 --> 00:31:57,100
+واحد اسمه خالد خالد هدا بده يبدأ من أول صف انت
+
+389
+00:31:57,100 --> 00:31:59,940
+خالد لأ انت خالد انت لأ هعمل حساب ايه في ال
+
+390
+00:31:59,940 --> 00:32:02,440
+algorithm و أنا بده اعمل algorithm مثلا او code
+
+391
+00:32:02,440 --> 00:32:05,280
+بدورلي على واحد اسمه خالد او واحد في مواصفة معينة
+
+392
+00:32:05,280 --> 00:32:08,370
+انه ممكن يكون اخر واحد في القائمةthe worst case
+
+393
+00:32:08,370 --> 00:32:12,250
+أسوأ حالة ممكنة هي اللي بنشتغل عليها عشان نكون
+
+394
+00:32:12,250 --> 00:32:15,790
+عملنا generalization لل code طبعنا إنه في أسوأ
+
+395
+00:32:15,790 --> 00:32:20,510
+حالة ممكن أجدش ممكن هيحتاج وقت، أجدش هيحتاج وقت،
+
+396
+00:32:20,510 --> 00:32:26,670
+كويسلو قلنا عشان نوضح أكتر بمثال لو قلنا في عندنا
+
+397
+00:32:26,670 --> 00:32:30,730
+ال system أو ال algorithm A has worst case time
+
+398
+00:32:30,730 --> 00:32:35,350
+complexity أحيانا بيسميها WCTC أو worst case time
+
+399
+00:32:35,350 --> 00:32:40,610
+complexity أو ممكن نسميها time has a time has a
+
+400
+00:32:40,610 --> 00:32:46,440
+time f of n ال n هذه قلنا عدد ال inputsالـ F الـ
+
+401
+00:32:46,440 --> 00:32:51,040
+Time سنسميها لسه الـ Time فإذا كان بيستغرق الـ
+
+402
+00:32:51,040 --> 00:32:56,980
+Time عبارة عن F of N لعدد Inputs N تفقنا عليها
+
+403
+00:32:56,980 --> 00:33:02,240
+اسمها F وعندنا ألغوريثم تاني B هذا هى يستغرق G of
+
+404
+00:33:02,240 --> 00:33:07,720
+N فإذا واحد هى يستغرق F of N واحد هى يستغرق G of N
+
+405
+00:33:07,720 --> 00:33:11,740
+وجهنا شفنا ال complex بتاعتهم أو شفنا ال order of
+
+406
+00:33:11,740 --> 00:33:20,980
+growth وجدنا ان ال Fمش هدى small omega small omega
+
+407
+00:33:20,980 --> 00:33:24,700
+of j small omega of j في الحالة هدى مين اللى
+
+408
+00:33:24,700 --> 00:33:30,920
+المفروض اختاره من الاتنين ال جي ال جي ليش ال جي ال
+
+409
+00:33:30,920 --> 00:33:34,400
+جي واضح انه اقل لانه بدأنا احنا هنا نتكلم عنه if
+
+410
+00:33:34,400 --> 00:33:44,260
+small omega of g معناته جي
+
+411
+00:33:46,040 --> 00:33:52,940
+small o of F فإذن ال G لازم تكون أقل من F ال G
+
+412
+00:33:52,940 --> 00:33:57,620
+دايما أقل من F فإذن طبيعي بدنا نختار ال system ال
+
+413
+00:33:57,620 --> 00:33:58,800
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+414
+00:33:58,800 --> 00:33:59,440
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+415
+00:33:59,440 --> 00:33:59,440
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+416
+00:33:59,440 --> 00:34:00,860
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+417
+00:34:00,860 --> 00:34:04,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+418
+00:34:04,840 --> 00:34:04,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+419
+00:34:04,840 --> 00:34:04,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+420
+00:34:04,840 --> 00:34:04,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+421
+00:34:04,840 --> 00:34:04,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+422
+00:34:04,840 --> 00:34:04,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+423
+00:34:04,840 --> 00:34:04,860
+ال ال ال ال ال ال ال
+
+424
+00:34:18,720 --> 00:34:21,520
+عشان احسب code هكتب ال code ال code يعني مثلا بدنا
+
+425
+00:34:21,520 --> 00:34:26,380
+نحسب ال maximum value او ال maximum element داخل
+
+426
+00:34:26,380 --> 00:34:30,340
+string معين او داخل list معينة و كتبنا ال code ده
+
+427
+00:34:30,340 --> 00:34:33,200
+سابقا لما بدنا نتكلم عن ال algorithm كتبنا ال code
+
+428
+00:34:33,200 --> 00:34:35,900
+قبلها هل واجد بدنا نحسب ال complexity تبعته؟
+
+429
+00:34:36,280 --> 00:34:39,460
+complexity أو الـ time المستغرب فكل line من ال
+
+430
+00:34:39,460 --> 00:34:43,380
+lines هذه إله time إله time هنقول إن والله ال line
+
+431
+00:34:43,380 --> 00:34:49,620
+الأولة مقارنة مجرد إن أحط ال V قيمتها ب A1 محتاجة
+
+432
+00:34:49,620 --> 00:34:53,820
+time T1 طيب ال four loop هذا عشان أعمل كلمة four
+
+433
+00:34:53,820 --> 00:35:02,160
+من كذا لكذا محتاجة T2 طيب if thenمحتاجة T3 زمن T3
+
+434
+00:35:02,160 --> 00:35:09,100
+return مجرد أن أرجع أعمل printing لأو أطبع قيمة V
+
+435
+00:35:09,100 --> 00:35:13,800
+على الشاشة أو أطلعها و أظهرها على الشاشة محتاجة T4
+
+436
+00:35:13,800 --> 00:35:17,820
+طيب هالواجهة بدنا نبسكهم جدش ال total لل algorithm
+
+437
+00:35:17,820 --> 00:35:20,760
+كله على بعضه ال total لل algorithm كله على بعضه
+
+438
+00:35:20,760 --> 00:35:27,780
+هيكون مجموحهم و بدنا بس ناخد بالنا إذا في تكرارات
+
+439
+00:35:27,780 --> 00:35:36,610
+ولا لأفإذا مبدأيا T1 زائد T2 زائد T3 زائد T4 لأ هو
+
+440
+00:35:36,610 --> 00:35:39,930
+مش هيك بس هو مش بس هيك انتوا لاحظوا انه عندكوا فيه
+
+441
+00:35:39,930 --> 00:35:45,630
+for loop معناته مين اللي بتكرر عنده T2 و T3 فإذا
+
+442
+00:35:45,630 --> 00:35:50,570
+بقدر أقول T1 زائد summation من مين لمين ل T2 زائد
+
+443
+00:35:50,570 --> 00:35:58,150
+T3 و هنا طبعا بعيد عنهم زائد T4 هذي من وين لوين؟من
+
+444
+00:35:58,150 --> 00:36:03,710
+I بيتساوي 2 to I صحيح؟
+
+445
+00:36:03,710 --> 00:36:07,370
+حلو، كويس جدا، في الحالة هذه عندنا هذا constant
+
+446
+00:36:07,370 --> 00:36:12,230
+ثابت خلاص تي واحد بتتنفذ مرة واحدة و بس جدش قيمتها
+
+447
+00:36:12,230 --> 00:36:15,510
+بعرف عن طريق جدش سرعة ال processor جدش مواصفات
+
+448
+00:36:15,510 --> 00:36:18,950
+الجهاز جدش ال operation الواحدة تستغرق في الجهاز
+
+449
+00:36:18,950 --> 00:36:24,520
+هذا بنعرفها فهذه constant، هذه constant كمانتنتين
+
+450
+00:36:24,520 --> 00:36:29,120
+مع بعض بقدر أقول أن هي theta of one theta of one
+
+451
+00:36:29,120 --> 00:36:33,180
+constant زائد هدول التنتين مع بعض لحالهم theta of
+
+452
+00:36:33,180 --> 00:36:40,600
+one بس هدول داخل ال summation من إتنين to n جدش
+
+453
+00:36:40,600 --> 00:36:46,880
+عدد التكرارات n ناقص واحد فإذا أنا بتكلم هنا عن n
+
+454
+00:36:46,880 --> 00:36:53,200
+ناقص واحد في theta of one plus theta one
+
+455
+00:36:56,570 --> 00:37:03,910
+ن نقص واحد ثيتا of n مضروبة
+
+456
+00:37:03,910 --> 00:37:09,710
+في constant ثيتا of one plus constant ثيتا of one
+
+457
+00:37:09,710 --> 00:37:14,890
+فإذا انتوا في الآخر ثيتا of n of n معناه ذلك أننا
+
+458
+00:37:14,890 --> 00:37:19,510
+بنتكلم عن first order فإذا في الآخر ال complex
+
+459
+00:37:19,510 --> 00:37:21,670
+بتاعتنا هنا ثيتا of n
+
+460
+00:37:26,870 --> 00:37:32,170
+هي ال analysis نفسه في الآخر بنصل ل theta of n او
+
+461
+00:37:32,170 --> 00:37:36,270
+first order فعزيزي نوضح ان كله بحياتك order بحياتك
+
+462
+00:37:36,270 --> 00:37:41,550
+first order كله اذا كان ال two elements بتاعونه مش
+
+463
+00:37:41,550 --> 00:37:47,600
+معروفينالـ two limits واحدة منهم to n و n هي عدد
+
+464
+00:37:47,600 --> 00:37:51,540
+ال inputs يعني هي ال variable تبعنا لحظة نوع n هي
+
+465
+00:37:51,540 --> 00:37:54,160
+عدد ال inputs و ال inputs هو ال variable تبعنا
+
+466
+00:37:54,160 --> 00:37:56,880
+فإذا واحدة من ال limits تبعون هدولة هي ال
+
+467
+00:37:56,880 --> 00:37:59,480
+variables اللي احنا بنشتغل عليه أساسا فإذا هنا
+
+468
+00:37:59,480 --> 00:38:03,400
+معتمد تماما على مين على عدد ال inputs إذا عدد ال
+
+469
+00:38:03,400 --> 00:38:07,780
+inputs مية هضطر أعمل تسعة وتسعين operation تكرار ل
+
+470
+00:38:07,780 --> 00:38:11,950
+T تنين و Tتلاتة إذا الف هنشطل على تسعمين تسعة
+
+471
+00:38:11,950 --> 00:38:16,390
+وتسعين iteration إذا جدش العدد ال inputs بفرج معاه
+
+472
+00:38:16,390 --> 00:38:19,290
+أنا جدش ال accumulation هنعمل accumulation هنعمل
+
+473
+00:38:19,290 --> 00:38:24,710
+فإذا فعلا إذا ال limits بتاعنا واحد منهم أو ال
+
+474
+00:38:24,710 --> 00:38:27,710
+limits بتاعتنا عبارة عن ال variable اللي بنشطل
+
+475
+00:38:27,710 --> 00:38:31,030
+عليه هو عدد ال inputs واضح إن أنا هنا هدخل في إيش
+
+476
+00:38:31,030 --> 00:38:34,990
+في first order كله بحيث يكون بده first order
+
+477
+00:38:38,620 --> 00:38:41,760
+كمان مثال ناخد ال linear search في ال linear
+
+478
+00:38:41,760 --> 00:38:44,980
+search متذكرين ال linear search ال linear search
+
+479
+00:38:44,980 --> 00:38:50,260
+مجرد أنه نبدأ procedure و بنعرف جد ايش الاسم و
+
+480
+00:38:50,260 --> 00:38:52,960
+حيكون في عندنا x integer هذا ال x اللي بدنا ندور
+
+481
+00:38:52,960 --> 00:38:56,620
+عليه element بدنا ندور هل هو موجود داخل ال list او
+
+482
+00:38:56,620 --> 00:39:00,780
+لأ ال list هذه بدنا نكون معرفينها a1, a2, a3, a4,
+
+483
+00:39:00,780 --> 00:39:04,460
+a5, a6, a7, a8, a9, a10, a11, a12, a13integers
+
+484
+00:39:04,460 --> 00:39:11,440
+متباينة مافيش اتنين بيساوي بعض ومرتبة ومرتبة ايام
+
+485
+00:39:11,440 --> 00:39:14,460
+اشتغلناها كان في عنا I بتساوي واحد في هذه ال
+
+486
+00:39:14,460 --> 00:39:20,140
+operation تبعتنا T واحد while مجرد ال operation
+
+487
+00:39:20,140 --> 00:39:25,340
+هذي while بتحتيه اتنين I بتساوي I زائد واحد بتحتيه
+
+488
+00:39:25,340 --> 00:39:34,450
+تلاتة if then بتحتيه اربعةelse بده T5 و return بده
+
+489
+00:39:34,450 --> 00:39:40,310
+T6 كويس في الحالة هذه الشغل عشان نشتغله كامل على
+
+490
+00:39:40,310 --> 00:39:45,190
+بعضه هيكون محتاج مجموحهم هيكون محتاجين برضه
+
+491
+00:39:45,190 --> 00:39:48,830
+مجموحهم بس برضه بدنا نرجع نركز وين وين بصير ال
+
+492
+00:39:48,830 --> 00:39:52,590
+iteration او وين بصير ال loop وين بصير في أنكو T1
+
+493
+00:39:52,590 --> 00:39:57,690
+T2 T6
+
+494
+00:39:58,980 --> 00:40:05,400
+ال loop هنا وين بيصيروا فعليا في اتنين تلاتة ولا
+
+495
+00:40:05,400 --> 00:40:09,200
+تلاتة اربع او اين بالظبط اتنين و تلاتة اتنين و
+
+496
+00:40:09,200 --> 00:40:19,720
+تلاتة هنا هيكون بدهم summation من I
+
+497
+00:40:19,720 --> 00:40:21,840
+بتساوي واحد
+
+498
+00:40:24,140 --> 00:40:27,800
+I بتساوي واحد، احنا بدأنا بواحد و بدأنا منه، بدأنا
+
+499
+00:40:27,800 --> 00:40:31,680
+من إيش؟ من I بتساوي واحد، هاي I كانت واحد، و ال
+
+500
+00:40:31,680 --> 00:40:35,800
+worst case تبعتنا أنه أصل to end، أسوأ حالة أنه
+
+501
+00:40:35,800 --> 00:40:39,620
+العنصر اللي بدور عليه في آخر عنصر أو أنه غير موجود
+
+502
+00:40:39,620 --> 00:40:42,730
+من أساسهأو أنه ممكن نكون غير موجود فانحطر أعمل
+
+503
+00:40:42,730 --> 00:40:46,650
+search على كل ال elements داخل ال list داخل ال
+
+504
+00:40:46,650 --> 00:40:50,630
+list okay فهيكون عندنا summation from i equal to
+
+505
+00:40:50,630 --> 00:40:57,130
+one to h to n لعند العدد كامل على بعضه لعند العدد
+
+506
+00:40:57,130 --> 00:40:59,970
+كله على بعضه في الحالة هاد واضح أنه مدام summation
+
+507
+00:40:59,970 --> 00:41:03,490
+واحدة هيكون عندكوا first order هيكون first order
+
+508
+00:41:03,490 --> 00:41:08,850
+على اعتبار أنه هاد هتكون مضروبة في h في n مضروبة
+
+509
+00:41:08,850 --> 00:41:09,870
+في h في theta
+
+510
+00:41:14,700 --> 00:41:20,580
+ال summation theta of n لأن هات جاية من n, n مرة
+
+511
+00:41:20,580 --> 00:41:26,560
+تكراراتها مضروبة في إيش هذا ال term? theta of one
+
+512
+00:41:27,490 --> 00:41:33,110
+كل هذا زائد theta of one plus theta of one كلهم
+
+513
+00:41:33,110 --> 00:41:35,870
+توتر على بعض theta of one كلهم توتر على بعض theta
+
+514
+00:41:35,870 --> 00:41:40,490
+of one ففي الآخر هيطلع ال order تبعكم first order
+
+515
+00:41:40,490 --> 00:41:45,550
+او theta of of n طيب the best case في افضل في افضل
+
+516
+00:41:45,550 --> 00:41:53,880
+حالة ممكنة هنالحظوا هنا في أفضل حالة ممكنة في ال
+
+517
+00:41:53,880 --> 00:41:56,320
+code اه موجود في ال code أفضل حالة أن يكون أول
+
+518
+00:41:56,320 --> 00:41:58,760
+عنصر طب أول عنصر خلّينا نتنبع ال algorithm تبعنا
+
+519
+00:41:58,760 --> 00:42:07,660
+خلّينا نتوب تحتها I بتساوي 1 okay هننفذها while X
+
+520
+00:42:07,660 --> 00:42:14,360
+بتساوي A1 مظبوط فإذا انت حققته وين هيروح هيطلع
+
+521
+00:42:14,360 --> 00:42:19,600
+هيجي هنا فإذا هذه ماتحققتشما نفذهاش، لم تنفذ، في
+
+522
+00:42:19,600 --> 00:42:24,760
+الحالة هذه بتاعتنا هتصير T1 زائد T2 زائد T4 تماما
+
+523
+00:42:24,760 --> 00:42:33,710
+زائد T5 T6 في الحالة هذه كله هكون θ of 1كله
+
+524
+00:42:33,710 --> 00:42:38,030
+constants طبعا هذه the best case هذه the best case
+
+525
+00:42:38,030 --> 00:42:44,730
+طب ال average case بين هدا و هدا ان لأنه هيكون بدل
+
+526
+00:42:44,730 --> 00:42:48,570
+I بتساوي واحد to N هتصير N over two و برضه هتكون
+
+527
+00:42:48,570 --> 00:42:52,650
+متغيرة هتظل متغيرة لإن أنا مش عارف جدش قيمة N N
+
+528
+00:42:52,650 --> 00:42:57,730
+over two هي هي كأنها N ليش لإن أنا بتعامل مع واحدة
+
+529
+00:42:57,730 --> 00:43:00,630
+من ال limits ان هي ال variable تبعنا و ال variable
+
+530
+00:43:00,630 --> 00:43:04,360
+تبعنا حددنا من ال inputsفالinputs أنا مش عارفهم
+
+531
+00:43:04,360 --> 00:43:10,060
+إذا خمسة غير خمسين غير ألف غير مليون بتختلف عدد ال
+
+532
+00:43:10,060 --> 00:43:12,760
+iterations في الحالة هذه فطبعا على اتنين أو مش على
+
+533
+00:43:12,760 --> 00:43:15,640
+اتنينية هي مش هتفرج معنا هيضل برضه بنتعامل مع
+
+534
+00:43:15,640 --> 00:43:21,000
+first order مع first order طيب ال binary في ال
+
+535
+00:43:21,000 --> 00:43:25,020
+binary كان لأ الوضع مختلف فإذا خلينا نحدد إنه في
+
+536
+00:43:25,020 --> 00:43:29,540
+ال search في ال linear search كان first order طيب
+
+537
+00:43:29,540 --> 00:43:34,210
+ال binary عشان نحدد مين أحسن من مينفي ال linear
+
+538
+00:43:34,210 --> 00:43:41,890
+كان عندنا θ of n طيب خلّيني أشوف ال binary في ال
+
+539
+00:43:41,890 --> 00:43:44,410
+binary هاي ال code اللي كتبته سابقا كتبناه
+
+540
+00:43:44,410 --> 00:43:50,630
+المحاضرة اللي فاتت أو اللي قبلها كان في عنده I و J
+
+541
+00:43:50,630 --> 00:43:54,890
+I و J هدولة كنا من حد بداية و نهاية ال interval
+
+542
+00:43:54,890 --> 00:43:59,270
+بتاعتنا ليش؟ لأنه كان الالـ Algorithm معتمد على
+
+543
+00:43:59,270 --> 00:44:02,890
+أساس أني أعمل check على ال midpoint على ال
+
+544
+00:44:02,890 --> 00:44:05,790
+midpoint أو ال element اللي موجود في ال midpoint
+
+545
+00:44:05,790 --> 00:44:12,030
+location في ال midpoint location بناءً عليه بعمل
+
+546
+00:44:12,030 --> 00:44:15,790
+اختزال أو elimination لنص ال interval كلها على بعض
+
+547
+00:44:15,790 --> 00:44:19,330
+ممكن كل هدول ال elements أشيلهم فانا بطلت مضطر
+
+548
+00:44:19,330 --> 00:44:23,190
+أعمل check عليهم واحدة واحدة اختزلهم كلهم مرة
+
+549
+00:44:23,190 --> 00:44:28,940
+واحدة خلاص مش محتاج مش محتاجين طيب نص المسافةبرضه
+
+550
+00:44:28,940 --> 00:44:31,700
+بنقارن مع ال element اللي موجود ممكن اختزل كل ال
+
+551
+00:44:31,700 --> 00:44:34,360
+elements اللي أكبر برضه كل ال elements اللي هنا مش
+
+552
+00:44:34,360 --> 00:44:37,940
+مضطر اقارن فيهم واضح ان احنا جالسين بنجلل حجم
+
+553
+00:44:37,940 --> 00:44:42,580
+المشكلة بنجلل حجم المشكلة طيب حددنا البداية و
+
+554
+00:44:42,580 --> 00:44:46,780
+النهاية بتاعوننا هدولة كل واحدة محتاجة time T1 T1
+
+555
+00:44:46,780 --> 00:44:52,040
+T1 مثلا T2 T1 T2 constants constants في النهاية
+
+556
+00:44:52,040 --> 00:44:57,120
+okay طيب سيبقوا من while هالوجدwhile و end هدول
+
+557
+00:44:57,120 --> 00:45:03,680
+سيبوهم داخل ال loop كل واحدة منهم هدول برضه محتاجة
+
+558
+00:45:03,680 --> 00:45:08,240
+T1 و T2 فهم التنتين لحالهم بدون ال while constant
+
+559
+00:45:08,240 --> 00:45:13,440
+خلاص ال operation هذه محتاجة زمن T3 او T4 خلاص هي
+
+560
+00:45:13,440 --> 00:45:17,620
+دايما T4 بس المشكلة دايما في قدش هتتكرر في قدش
+
+561
+00:45:17,620 --> 00:45:24,630
+هتتكرر okay thousand theta of oneخلصنا ال loop if
+
+562
+00:45:24,630 --> 00:45:28,610
+then بنعملها مرة واحدة إذا كان وصلت أو ماوصلتش و
+
+563
+00:45:28,610 --> 00:45:32,610
+return بال location برضه مرة واحدة هل وجدت السؤال
+
+564
+00:45:32,610 --> 00:45:37,430
+هنا ال loop هدق كم مرة هيتكرر؟ و أنا جاعت بجسم
+
+565
+00:45:37,430 --> 00:45:43,940
+انصاص هيك كم مرة هيتكرر؟إذا n معناته هتكون نفس ال
+
+566
+00:45:43,940 --> 00:45:46,900
+linear معناته ال order تبعها نفس ال linear في
+
+567
+00:45:46,900 --> 00:45:50,820
+الحالة دي مفرجش مين أستعمل لأن ال order تبع ال
+
+568
+00:45:50,820 --> 00:45:55,120
+اتنين نفس الاشي هنا هذه ال linear كانت first order
+
+569
+00:45:55,120 --> 00:45:59,760
+خليني أشوف هذه و خليني نبدأ نتخيل مدام بجسم اتنين
+
+570
+00:45:59,760 --> 00:46:04,280
+عن اتنينات يعني كإني بشغل على الأساس اتنين على
+
+571
+00:46:04,280 --> 00:46:09,600
+الأساس اتنين خليني أفترض أن عددهم من واحد to nو n
+
+572
+00:46:09,600 --> 00:46:14,200
+هذه أحد مشتقات الاتنين بمعنى بتساوي 2 to the power
+
+573
+00:46:14,200 --> 00:46:18,720
+k بصير
+
+574
+00:46:18,720 --> 00:46:23,300
+كل اللي بدنايا مدام في كل iteration أنا بجسم
+
+575
+00:46:23,300 --> 00:46:29,820
+المسافة تبعت نصين بعد أكم k هتصير n هذه بتساوي
+
+576
+00:46:29,820 --> 00:46:39,100
+واحد لأن احنا إمتى بنواجه هنا لما نصل في الآخرلأ
+
+577
+00:46:39,100 --> 00:46:44,460
+عنصر واحد بس وصلنا
+
+578
+00:46:44,460 --> 00:46:47,840
+لعنصر واحد العنصر الواحد هذا النهائي هو اللي بعمله
+
+579
+00:46:47,840 --> 00:46:53,600
+if then بنقارنه هل بيسوي x أو بيسويش x وخلاص سوى x
+
+580
+00:46:53,600 --> 00:46:55,600
+معناته هو العنصر هو ال x اللي أنا بدور عليها
+
+581
+00:46:55,600 --> 00:47:00,300
+ماسواش x خلاص غير موجودة x في الآخر أنا بصلها
+
+582
+00:47:00,300 --> 00:47:07,180
+لعنصر واحد العنصر الواحد ده انت بصله من عدد nو
+
+583
+00:47:07,180 --> 00:47:13,560
+هنفترض مبدئيا أن N أحد مشتقات ال .. او two to the
+
+584
+00:47:13,560 --> 00:47:18,920
+power of some K طيب خليني أجيبلكيها بالعكس افرضوا
+
+585
+00:47:18,920 --> 00:47:25,660
+أن ال N هذه اربعة و ستين نفرضهم اربعة و ستين اربعة
+
+586
+00:47:25,660 --> 00:47:30,080
+و ستين اول iteration جدش صاروا نص اتنين و تلاتين
+
+587
+00:47:30,080 --> 00:47:36,540
+هيخلصنا iteration طيب اتنين و تلاتينستاشر بعد two
+
+588
+00:47:36,540 --> 00:47:48,310
+iterations طيب تمانية أربعة اتنين واحد صحيح؟6 طيب
+
+589
+00:47:48,310 --> 00:47:51,170
+هل فعلا .. لحظوا احنا عملنا 6 iterations قبل ما
+
+590
+00:47:51,170 --> 00:47:54,370
+أصل ل element واحد عملنا 6 iterations فهل فعلا
+
+591
+00:47:54,370 --> 00:47:59,110
+صحيح ال 64 بتساوي 2 تطبعه 6؟ اه فعلا 2 تطبعه 6
+
+592
+00:47:59,110 --> 00:48:03,530
+معناه ان ال 6 هذي الصمكة اللي بنتكلم عنها الصمكة
+
+593
+00:48:03,530 --> 00:48:06,850
+هي عدد ال iterations فعليا اللي هيطلع هي فعليا عدد
+
+594
+00:48:06,850 --> 00:48:11,790
+ال iterations اللي هتظهر صح؟ صح كويس حسب قلية ال
+
+595
+00:48:11,790 --> 00:48:14,170
+.. ال worthing condition حسب ألغورية ال .. ال ..
+
+596
+00:48:15,210 --> 00:48:20,150
+الألية ال algorithm نفسه كيف بيشتغل فإذا بفترض أن
+
+597
+00:48:20,150 --> 00:48:24,890
+N هي two to the power of some K ك element و بعدين
+
+598
+00:48:24,890 --> 00:48:30,950
+ممكن نعممه إن إذا كانت لا تساوي مش مشكلة بنقربها
+
+599
+00:48:30,950 --> 00:48:35,290
+للرقم الأعلى يعني
+
+600
+00:48:35,290 --> 00:48:42,130
+إذا كانت مثلا ستينبنقربها لمن؟ لل 64 و بنشتغلها ل
+
+601
+00:48:42,130 --> 00:48:45,450
+64 فبتطلع بدنا 6 iterations حنكون محتاجين 6
+
+602
+00:48:45,450 --> 00:48:47,910
+iterations طيب كيف بده أجيب ال 6 iterations دي؟
+
+603
+00:48:47,910 --> 00:48:51,910
+لأن هي هي اللي هتحددلي جداش عدد التكرارات جداش عدد
+
+604
+00:48:51,910 --> 00:48:58,590
+التكرارات فكل اللي هنعمله log
+
+605
+00:48:58,590 --> 00:49:07,230
+n بتساوي log 2 to the power k فده بتساوي k في log
+
+606
+00:49:08,060 --> 00:49:19,220
+two log n كي ايش بتساوي هنا log n over log two طيب
+
+607
+00:49:19,220 --> 00:49:23,200
+في الحالة هذه ال
+
+608
+00:49:23,200 --> 00:49:28,020
+log هذا الأساس تبعه جديش ال base تبعه جديش عشرة و
+
+609
+00:49:28,020 --> 00:49:31,780
+هنا عشرة طيب في الحالة هذه كله بيصير بيساوي log
+
+610
+00:49:31,780 --> 00:49:40,390
+الأساس اتنين to n of nصح؟ كويس، تمام جدا، فإذا
+
+611
+00:49:40,390 --> 00:49:49,890
+واضح أن K هتساوي هذا ال term، اللي هي log N، log
+
+612
+00:49:49,890 --> 00:49:54,890
+N، فإذا نتكلم عن order logarithmic، واضح أن
+
+613
+00:49:54,890 --> 00:49:59,410
+التكرار طبعنا logarithmic، مش linear، مش linear،
+
+614
+00:49:59,410 --> 00:50:06,420
+فإذا التانية ال theta بتاعتنا log Nأقل طبعا هذه
+
+615
+00:50:06,420 --> 00:50:12,940
+هتكون أقل من N فإذا واضح أن ال binary search أفضل
+
+616
+00:50:12,940 --> 00:50:16,880
+و more efficient من ال linear search أفضل من ال
+
+617
+00:50:16,880 --> 00:50:20,800
+linear search واضحة لأن ال order تبعها أقل من
+
+618
+00:50:20,800 --> 00:50:25,220
+first order order أقل من first order لاحظوا احنا
+
+619
+00:50:25,220 --> 00:50:29,880
+اشتغلنا على 64 64 element عملناهم في 6 iterations
+
+620
+00:50:29,880 --> 00:50:34,770
+هناك في أسوأ حالة محتاج 64 iterationsفي ال linear
+
+621
+00:50:34,770 --> 00:50:38,950
+هحتاج 64 iterations صح؟ لأ هنا أسوأ case عندنا في
+
+622
+00:50:38,950 --> 00:50:42,350
+ال binary أني أشتغل على 6 iterations فقط بعد 6
+
+623
+00:50:42,350 --> 00:50:46,730
+iterations هكون وصلت لل X هل موجود أو غير موجود
+
+624
+00:50:46,730 --> 00:50:50,230
+okay
+
+625
+00:50:50,230 --> 00:50:55,470
+فهي التحليل تبعنا عشان في الآخر نحسب K و نشتغل على
+
+626
+00:50:55,470 --> 00:51:01,950
+K طيب ال matrix multiplication يمكن هذه احنا
+
+627
+00:51:01,950 --> 00:51:10,570
+ماخدناش في وقتهالما اتكلمنا عن ال matrices بس
+
+628
+00:51:10,570 --> 00:51:16,470
+قلنا ان كل for loop كل for loop هتعطينا ايش first
+
+629
+00:51:16,470 --> 00:51:22,110
+order هتعطينا تكرار وخصوصا اذا التكرار تبحة زي ما
+
+630
+00:51:22,110 --> 00:51:26,110
+قلنا ال limits تبعته ايش variables اذا ال limits
+
+631
+00:51:26,110 --> 00:51:29,670
+تبعته variables طيب خلينا نشوف في حالة ضرب
+
+632
+00:51:29,670 --> 00:51:38,060
+المصففاتاحنا بنضرب مصفوفات M في K بنضربها في مين؟
+
+633
+00:51:38,060 --> 00:51:47,660
+K في N عشان ينتج عندى مصفوفة M في N تمام واضح ان
+
+634
+00:51:47,660 --> 00:51:52,620
+في عندنا variable اتنين تلاتة في three variables
+
+635
+00:51:52,620 --> 00:51:55,760
+في
+
+636
+00:51:55,760 --> 00:52:00,090
+عدد الصفوفأنا ممكن أدخل matrix من عندي، يعني ليش
+
+637
+00:52:00,090 --> 00:52:04,350
+نلزمونه مثلا 2 في 3 أضربها في 3 ب 2؟ أنا بدي أدخل
+
+638
+00:52:04,350 --> 00:52:07,950
+5 في 7، إيش المشكلة؟ فعدد ال variables هذه
+
+639
+00:52:07,950 --> 00:52:11,530
+unvariable المفروض أنه ال algorithm يكون general
+
+640
+00:52:15,010 --> 00:52:17,970
+Dimension لل matrices اللي بدنا نضربها في بعض
+
+641
+00:52:17,970 --> 00:52:23,710
+يتقبلها أي dimension يتقبلها فهنا M في K .. K تاخد
+
+642
+00:52:23,710 --> 00:52:26,710
+أي قيمة M تاخد أي قيمة N تاخد أي قيمة فهذه
+
+643
+00:52:26,710 --> 00:52:30,610
+variables هذه بتحددنا عدد ال inputs بتحدد عدد ال
+
+644
+00:52:30,610 --> 00:52:34,290
+inputs اللي بدنا ندخله نضربه في بعض كويسة for I
+
+645
+00:52:34,290 --> 00:52:39,570
+one to H to M هذه هنا بنتكلم عن مين عن ال raw فإذا
+
+646
+00:52:39,570 --> 00:52:45,550
+بنبدأ بال raw رقم واحدبدينا فى الرقم واحد هى كل
+
+647
+00:52:45,550 --> 00:52:52,790
+عناصر الرقم واحد كويس بعدين for j from one to n
+
+648
+00:52:52,790 --> 00:53:00,070
+هنا بنتكلم عن كولوم التانية وهذا
+
+649
+00:53:00,070 --> 00:53:02,770
+قيمتها بواحد مع أننا بنتكلم عن كولوم الأول فى
+
+650
+00:53:02,770 --> 00:53:08,710
+التانية هنا حددناهم حددنا هذا ايش وهذا ايش انشطرعي
+
+651
+00:53:10,930 --> 00:53:14,070
+equal to zero ال summation اللي بدنا نجمع فيه بسوى
+
+652
+00:53:14,070 --> 00:53:20,070
+zero فهنا جيبنا النواعي عشان نجمع فيه نجمع نواعي
+
+653
+00:53:20,070 --> 00:53:27,030
+هذا هانيجي نجمع for q from one to k هنبدأ في أول
+
+654
+00:53:27,030 --> 00:53:37,660
+column في الأولى أول صف في التانية عشان نضربA I Q
+
+655
+00:53:37,660 --> 00:53:42,840
+و I حددنا واحد بدنا بواحد J حددنا واحد طبعا هنا
+
+656
+00:53:42,840 --> 00:53:49,300
+بدنا بمين و Q بواحد فال element الأول مع ال
+
+657
+00:53:49,300 --> 00:53:53,280
+element الأول هندربهم مع مين مع بعض هاي هندربناهم
+
+658
+00:53:53,280 --> 00:53:57,540
+مع بعض و نجمعهم على C كأنه هذه كانت صفر رمنا
+
+659
+00:53:57,540 --> 00:54:05,940
+قيمتهم هنا رمنا قيمتهم زائد ال Q بتساوي اتنينفهي
+
+660
+00:54:05,940 --> 00:54:09,840
+العنصر التاني مع العنصر التاني ضربناهم في بعض
+
+661
+00:54:09,840 --> 00:54:16,300
+وجمعنا قيمتهم التالت كيف تسوى نفطر التلاتة خلاص
+
+662
+00:54:16,300 --> 00:54:19,580
+خلصناها جمعنا قيمتهم هي دول هيك ساميشن جمعناهم
+
+663
+00:54:19,580 --> 00:54:23,860
+القيمة بتاعتهم هنحطها في التقاطع التانية دولة
+
+664
+00:54:23,860 --> 00:54:30,900
+بواحد وواحد هنحطها هنا خلصنا
+
+665
+00:54:30,900 --> 00:54:36,230
+ال four ال four بتاعة q كلها بنرجع لمينj بتساوى
+
+666
+00:54:36,230 --> 00:54:40,690
+اتنين فهنا نجلنا على مين على ال column التانى فى
+
+667
+00:54:40,690 --> 00:54:45,030
+التانى هذا ضغط لسه زى ما هو مازلنا زى ما هو فلحظوا
+
+668
+00:54:45,030 --> 00:54:50,810
+صارت الأولى العنصر الأول فى ال role أول مع العنصر
+
+669
+00:54:50,810 --> 00:54:54,930
+الأول فى ال column التانى لحظوا برضه هدا فى هدا
+
+670
+00:54:54,930 --> 00:54:59,830
+وهنا عشان هيك لازم نصفرها لإن هدى كانت فيها مجموعة
+
+671
+00:54:59,830 --> 00:55:02,350
+data بنصفرها
+
+672
+00:55:05,730 --> 00:55:08,030
+و تاخدوا بالكوا دايما فى بداية ال code تبعكوا و
+
+673
+00:55:08,030 --> 00:55:10,110
+حاولوا تصفروا كل ال algorithms تبعتكوا كتير فيه
+
+674
+00:55:10,110 --> 00:55:15,310
+بتصير مشاكل نتيجة ان ال variables هذه مخزنة قيم
+
+675
+00:55:15,310 --> 00:55:18,090
+سابقة مخزنة قيم سابقة فبتلاقيوا حالكوا طلعتوا
+
+676
+00:55:18,090 --> 00:55:20,810
+النتائج غلط طلعتوا النتائج غلط بتبدوا تجمعوا من
+
+677
+00:55:20,810 --> 00:55:25,770
+أول و جديد هذه مع هذه هذه في هذه هذه في هذه okay
+
+678
+00:55:25,770 --> 00:55:30,910
+جمعناهم عشان نحطهم فى نقطة تقطعهم هنا واحد مع
+
+679
+00:55:30,910 --> 00:55:35,640
+اتنين فإذا واحد اتنين بنحطال term التاني اللي
+
+680
+00:55:35,640 --> 00:55:40,560
+جمعناه و بنكمل بهذا الشكل لما نخلص كل لحظة انتوا
+
+681
+00:55:40,560 --> 00:55:43,880
+هنا Q جربتوها كذا مرة يعني ال loop ما اتكررش كمان
+
+682
+00:55:43,880 --> 00:55:47,560
+مرة واحدة ك loop ما اتكررش نفسه كمان مرة واحدة هو
+
+683
+00:55:47,560 --> 00:55:55,220
+قاعد بتكرر مع كل J طب لسه ال J هتتكرر مع كل I لما
+
+684
+00:55:55,220 --> 00:56:01,180
+تخلصوا N هناتخلص كل N تماما هتيجي هنا تاخد I تساوي
+
+685
+00:56:01,180 --> 00:56:06,940
+2 هتبدو كل اللي عملته هذا مع ال road تاني هتبدو ال
+
+686
+00:56:06,940 --> 00:56:09,040
+road تاني مع ال column الأول ال road تاني مع ال
+
+687
+00:56:09,040 --> 00:56:13,540
+column التاني مع التالت وكل مرة هترجع تعمله Q كمان
+
+688
+00:56:13,540 --> 00:56:18,820
+مرة طب ال for loop هذا Q هيتكرر K مرة أكم مرة
+
+689
+00:56:18,820 --> 00:56:24,680
+هتتكرر ال K مرة هذه حسب عدد ال elements اللي طلعها
+
+690
+00:56:24,680 --> 00:56:24,840
+هنا
+
+691
+00:56:27,910 --> 00:56:32,530
+إذا تلاتة في تلاتة هتتكرر تسعة مرات ال loop اللوب
+
+692
+00:56:32,530 --> 00:56:34,690
+اللي .. مش بس ال elements اللي داخل ال loop اللوب
+
+693
+00:56:34,690 --> 00:56:38,290
+نفسه هتتكرر تسعة مرات طيب تسعة مرات دول اللي هم
+
+694
+00:56:38,290 --> 00:56:44,830
+ايش M في N يعني لو كانت خمسة في خمسة هتتكرر خمسة
+
+695
+00:56:44,830 --> 00:56:54,170
+عشرين مرة فهنا M في N في عدد ال K في عدد K فهي
+
+696
+00:56:54,170 --> 00:56:59,890
+المعادلة هي دي أكم مرة هتنحسبهتنحسب التلتة في بعض
+
+697
+00:56:59,890 --> 00:57:06,650
+K في N في M K في N في M كويس نبدأ ال for loop
+
+698
+00:57:06,650 --> 00:57:10,490
+الأولى ال for loop الأولى هتكرر M مرة فهدي واضح أن
+
+699
+00:57:10,490 --> 00:57:15,490
+هي theta of M M first order هدي first order هي
+
+700
+00:57:15,490 --> 00:57:21,070
+لحالها طيب داخلها nested معاها متشابك معاها loop
+
+701
+00:57:21,070 --> 00:57:26,270
+تانية to N فبقول theta of Nبرضه first order طيب
+
+702
+00:57:26,270 --> 00:57:29,490
+داخلها ده طبعا constant بس هيتكرر حسب عدد
+
+703
+00:57:29,490 --> 00:57:35,550
+تكراراتها هنا في كمان for loop K مرة فده فيتا of K
+
+704
+00:57:35,550 --> 00:57:39,030
+بس كلهم في الآخر to the power one to the power one
+
+705
+00:57:39,030 --> 00:57:43,610
+to the power one first first first مشكلتنا وين انه
+
+706
+00:57:43,610 --> 00:57:49,330
+first في firstلأن هما في بعض متشابكين في بعض
+
+707
+00:57:49,330 --> 00:57:52,390
+متشابكين في بعض لحظوا هنا هاي ال order تبقى هاي ال
+
+708
+00:57:52,390 --> 00:57:55,230
+level هاي ال level هاي ال level هدولة داخل بعض
+
+709
+00:57:55,230 --> 00:58:00,730
+مادام داخل بعض كل واحدة هتتكرر بعدد التكرارات اللي
+
+710
+00:58:00,730 --> 00:58:04,210
+.. اللي أعلى منها بصير جداش عدد التكرارات كله على
+
+711
+00:58:04,210 --> 00:58:12,130
+بعضه theta M في N في K كأنها
+
+712
+00:58:12,130 --> 00:58:20,430
+G تكعيبتكعيب صارت sort of بتتكلم هنا عن function
+
+713
+00:58:20,430 --> 00:58:25,130
+تكعيب فتوقع هالواجهة صارت بتقدر تحسبوها مباشرة من
+
+714
+00:58:25,130 --> 00:58:28,230
+مين بس تشوف ال for أو ال while اعرف انه حيصير فيه
+
+715
+00:58:28,230 --> 00:58:33,190
+تكرار جديش عدد التكرارات حسب ال limits حسب ال
+
+716
+00:58:33,190 --> 00:58:37,610
+limits اللي جيته انه في four loops او while مع
+
+717
+00:58:37,610 --> 00:58:41,730
+while او while مع four loop nested مع بعض متشابكين
+
+718
+00:58:41,730 --> 00:58:44,950
+مع بعض معناته حصل ضربهم مع بعض هتصير حصل
+
+719
+00:58:50,130 --> 00:58:53,910
+معظم الحاجات اللي احنا خدناها ال orders اللي احنا
+
+720
+00:58:53,910 --> 00:59:00,370
+خدناها ممكن نرتبهم من الأبسط للأصعببنبدأ بال
+
+721
+00:59:00,370 --> 00:59:03,790
+constant first order وهدي عادة بتكون في ال best
+
+722
+00:59:03,790 --> 00:59:07,230
+case في ال best case بتكون عندكم ال code هتعملوه
+
+723
+00:59:07,230 --> 00:59:10,130
+مرة واحدة و خلاص هيطلع نتيجة فبتكون constant طبعا
+
+724
+00:59:10,130 --> 00:59:13,350
+هذا متحققش دائما اللي أكبر منها شوية زي اللي
+
+725
+00:59:13,350 --> 00:59:17,390
+شفناها when شفناها في ال binary search ال binary
+
+726
+00:59:17,390 --> 00:59:21,680
+search كانت logarithmicلوجاريثمك بغض النظر عن ال
+
+727
+00:59:21,680 --> 00:59:26,420
+pace تبعتنا ال pace دي اتنين او عشرة او decimal او
+
+728
+00:59:26,420 --> 00:59:29,260
+غير decimal او binary مش هتفرج كتير فان هي ال
+
+729
+00:59:29,260 --> 00:59:32,260
+function اسمها logarithmic نتعامل مع logarithmic
+
+730
+00:59:32,260 --> 00:59:36,960
+طيب logarithmic to the power k poly logarithmic
+
+731
+00:59:36,960 --> 00:59:41,780
+logarithmic متعددة متعددة كويس او مضروبة في بعضها
+
+732
+00:59:41,780 --> 00:59:44,360
+فدي بقوله logarithmic اعلى شوية من من ال
+
+733
+00:59:44,360 --> 00:59:48,480
+logarithmic طيب اللي اعلى منها ال linearاللينيار
+
+734
+00:59:48,480 --> 00:59:51,160
+أعلى منها شوية اللي أعلى من اللينيار ال polynomial
+
+735
+00:59:51,160 --> 00:59:57,380
+لينيار بس مضروبة to the power of C تكعيب تربيع to
+
+736
+00:59:57,380 --> 01:00:00,580
+the power of 5 to the power of 4 whatever يعني إيش
+
+737
+01:00:00,580 --> 01:00:05,860
+الشكل بتاع في الآخر زي تو ال matrices عملية ال
+
+738
+01:00:05,860 --> 01:00:09,320
+matrix ال matrix multiplication كانت polynomial
+
+739
+01:00:09,320 --> 01:00:13,780
+طيب اللي أكبر منها ال exponential أنه لأ هي مش N
+
+740
+01:00:13,780 --> 01:00:18,240
+to the power of C هي C to the power of Nالـ S هو
+
+741
+01:00:18,240 --> 01:00:21,540
+الـ variable الـ S تبعنا أو ال power هي ال
+
+742
+01:00:21,540 --> 01:00:24,580
+variable اللي أكبر منها ال factorial ال factorial
+
+743
+01:00:24,580 --> 01:00:28,480
+اللي أكبر منها ال N to the power N بس احنا
+
+744
+01:00:28,480 --> 01:00:31,060
+هالواجهة تخلّينا نسبر نجفل هنا هدول المعظم اللي
+
+745
+01:00:31,060 --> 01:00:34,540
+بنشتغل عليهم أو نحدد منهم هالواجهة طبيعة ال
+
+746
+01:00:34,540 --> 01:00:39,880
+function صعبة ولا مش صعبة اعملوا خط هنا أي
+
+747
+01:00:39,880 --> 01:00:42,900
+function أقل من polynomial .. polynomial فأقل
+
+748
+01:00:42,900 --> 01:00:49,900
+بنسميها tractableقابلة للحل قابلة للحل أو visible
+
+749
+01:00:49,900 --> 01:00:55,640
+ممكنة فإذا قابلة للحل attractable بنسميها لكل ال
+
+750
+01:00:55,640 --> 01:00:58,940
+functions اللي بتكون polynomial فأقل مدان
+
+751
+01:00:58,940 --> 01:01:05,120
+polynomial فأقل هذا بنقول يعني big
+
+752
+01:01:05,120 --> 01:01:07,880
+O of N to the power C
+
+753
+01:01:11,360 --> 01:01:14,920
+هدول ايش بنسميها tractable كل ال functions اللي
+
+754
+01:01:14,920 --> 01:01:20,180
+polynomial او اقل قابلة لحل اعملوله اكواد و انتم
+
+755
+01:01:20,180 --> 01:01:27,110
+مرتاحين طيب اكبر intractable او invisibleغير قابل
+
+756
+01:01:27,110 --> 01:01:30,010
+للحل لأن هنا اتعقدت فبصير حتى ال algorithm لما
+
+757
+01:01:30,010 --> 01:01:32,890
+بتتعملوه بياخد وقت طويل كل ما بتزيد عدد ال inputs
+
+758
+01:01:32,890 --> 01:01:37,630
+تبعته فبصير هنا غير ممكن الحل .. غير ممكن الحل او
+
+759
+01:01:37,630 --> 01:01:41,830
+بنقدر نصنفه ان هو غير ممكن الحل فهد المرة الجاية
+
+760
+01:01:41,830 --> 01:01:45,690
+بنرجع نتكلم عنها interactable و uninteractable هدي
+
+761
+01:01:45,690 --> 01:01:48,790
+إيش و هدي إيش و كيف العلاقة بينهم و كيف ال
+
+762
+01:01:48,790 --> 01:01:51,870
+relation بينهم و بعض الحالات الشاذة بين هدي و هدي
+
+763
+01:01:51,870 --> 01:01:54,490
+.. بين هدي و هدي يلا يعطيك الصحة العفو و برك الله
+
+764
+01:01:54,490 --> 01:01:54,770
+فيك
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig.srt
new file mode 100644
index 0000000000000000000000000000000000000000..993c052240d3a01f27e04e3cd05529288d4c106f
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig.srt
@@ -0,0 +1,2286 @@
+
+1
+00:00:20,770 --> 00:00:23,090
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,090 --> 00:00:25,970
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,970 --> 00:00:30,470
+أُشمين، بدأنا المرة اللي فاتت مع الـalgorithms
+
+4
+00:00:30,470 --> 00:00:34,170
+واتكلمنا كيف ممكن نعمل code، واتكلمنا عن الـ
+
+5
+00:00:34,170 --> 00:00:37,070
+language المتعرف عليها اللي هنشتغل عليها اللي هي
+
+6
+00:00:37,070 --> 00:00:40,670
+الـpseudocode، الـalgorithm اللي هنكتب فيها الـ
+
+7
+00:00:40,670 --> 00:00:45,530
+algorithms بتاعتنا خلال الـcourse. وصلنا لشوية
+
+8
+00:00:45,530 --> 00:00:49,350
+examples. أخدنا الـsearching، واتكلمنا عن نوعين أو
+
+9
+00:00:49,350 --> 00:00:52,790
+two codes أو two algorithms مشهورين جداً اللي هو الـ
+
+10
+00:00:52,790 --> 00:00:57,370
+linear search و الـbinary search. وصلنا لعملية الـ
+
+11
+00:00:57,370 --> 00:01:01,770
+sorting، لأنه لما كنا بنعمل searching، حقيقة كنا
+
+12
+00:01:01,770 --> 00:01:06,580
+بنعمل searching على ordered list. طيب ممكن
+
+13
+00:01:06,580 --> 00:01:10,040
+تجيكوا list مش ordered أساساً، يعني ممكن أساساً تكون
+
+14
+00:01:10,040 --> 00:01:15,320
+unordered list، أرقام عشوائية مبعثرة، مش مرتبة، لا أَت-
+
+15
+00:01:15,320 --> 00:01:18,760
+زايد ولا نازلة، أيه ولا يعني، لا هي تصاعدي ولا هي تنازلي
+
+16
+00:01:18,760 --> 00:01:23,480
+فبدنا نعمل code يعملنا الموضوع هذا، هو يعملنا عملية
+
+17
+00:01:23,480 --> 00:01:29,180
+sorting، عملية تصنيف، عملية ترتيب. اتكلمنا عن نوعين
+
+18
+00:01:29,180 --> 00:01:32,220
+المرة اللي فاتت، قولنا هنتكلم عن نوعين، النوع الأول
+
+19
+00:01:32,220 --> 00:01:39,160
+الـbubble sort و الـinsertion sort. بداية الـbubble
+
+20
+00:01:39,160 --> 00:01:43,940
+sort code بالشكل اللي احنا شايفينه، أو sequence
+
+21
+00:01:43,940 --> 00:01:48,210
+بهذا الشكل اللي احنا شايفينه، هذا هو الـsequence، الـ
+
+22
+00:01:48,210 --> 00:01:52,730
+left sequence هو الـinitial sequence تبعنا، بداية
+
+23
+00:01:52,730 --> 00:01:55,950
+الـsequence، كيف جاي ترتيبه؟ جاي ترتيبه تلاتين و
+
+24
+00:01:55,950 --> 00:01:58,550
+واحد، و تلاتين و واحد، و تلاتين و تلاتين، و
+
+25
+00:01:58,550 --> 00:01:59,870
+تلاتين و تلاتين، و تلاتين و تلاتين، و
+
+26
+00:01:59,870 --> 00:02:02,110
+تلاتين و تلاتين، و تلاتين و تلاتين، و
+
+27
+00:02:02,110 --> 00:02:02,130
+تلاتين و تلاتين، و تلاتين و تلاتين، و
+
+28
+00:02:02,130 --> 00:02:02,310
+تلاتين و تلاتين، و تلاتين و تلاتين، و
+
+29
+00:02:02,310 --> 00:02:07,830
+تلاتين و تلاتين، و تلاتين و تلاتين، و
+
+30
+00:02:07,830 --> 00:02:13,250
+تلاتين و تلاتين، و
+
+31
+00:02:19,170 --> 00:02:23,810
+وزنه بيكون أقل، فبيطلع as a bubble كفقاعة هواء على
+
+32
+00:02:23,810 --> 00:02:26,490
+السطح. لأ، احنا الـcode تبعنا، رغم أن هو اسمه bubble
+
+33
+00:02:26,490 --> 00:02:30,010
+sort، بس احنا هنشتغل على القيم الكبيرة من بداية الـ
+
+34
+00:02:30,010 --> 00:02:34,770
+sequence. يعني هنيجي نعمل عملية مقارنات، عملية
+
+35
+00:02:34,770 --> 00:02:38,830
+المقارنات هذه بتبدأ من أول element في الـsequence.
+
+36
+00:02:38,830 --> 00:02:42,310
+نبدأ بأول element في الـlist بتاعتنا، وبنعمل
+
+37
+00:02:42,310 --> 00:02:45,880
+مقارنة مع الثاني. هيكون عندنا مقارنة أولى. طيب
+
+38
+00:02:45,880 --> 00:02:50,920
+تلاتين، واحد، تلاتين. دائماً بنحاول نخلي الأقل في
+
+39
+00:02:50,920 --> 00:02:54,940
+الترتيب، الأقل للأول. طيب هنا عندنا location واحد،
+
+40
+00:02:54,940 --> 00:02:58,160
+location اتنين، location واحد أقل من location اتنين،
+
+41
+00:02:58,160 --> 00:03:01,600
+فبنحط فيه الرقم الأقل، فتلاتين، واحد، تلاتين، مش
+
+42
+00:03:01,600 --> 00:03:07,080
+محتاجة تغيير. بنعمل مقارنة، مين الـlocation أو
+
+43
+00:03:07,080 --> 00:03:08,680
+الرقم في الـlocation الثاني مع الرقم في الـ
+
+44
+00:03:08,680 --> 00:03:14,880
+location الثالث، واحد، تلاتين مع واحد. أه، الواحد أقل،
+
+45
+00:03:14,880 --> 00:03:21,140
+فبنعمل swap أو interchange، بنعكس هذا مكان هذا، و
+
+46
+00:03:21,140 --> 00:03:27,300
+هذا مكان هذا، فهيبقى عكسه هنا. كويس، مدام عكسنا، بده
+
+47
+00:03:27,300 --> 00:03:29,900
+يصير هنا عندي الواحد، وهنا بده يصير الواحد، تلاتين.
+
+48
+00:03:29,900 --> 00:03:33,600
+بنقارنها، لوجه التلاتة مع أربعة، تلاتة مع أربعة، و
+
+49
+00:03:33,600 --> 00:03:37,700
+واحد، و تلاتين مع اتنين و تلاتين، بتظل زي ما هي. طيب
+
+50
+00:03:37,700 --> 00:03:41,660
+اتنين و تلاتين مع تلاتة و تلاتين، تلاتة و تلاتين مع
+
+51
+00:03:41,660 --> 00:03:46,420
+اتنين، swap، تصير هنا الاتنين، وهنا تلاتة و تلاتين.
+
+52
+00:03:46,420 --> 00:03:51,660
+طيب، بنكمل، لسه احنا مازلنا في أول مرحلة، كل هذه لسه
+
+53
+00:03:51,660 --> 00:03:56,440
+مرحلة واحدة، مرحلة أولى، بقارن كل رقم مع اللي وراه.
+
+54
+00:03:56,440 --> 00:03:59,000
+كل رقم مع اللي وراه، كل element مع الـelement اللي
+
+55
+00:03:59,000 --> 00:04:01,580
+بعده. طيب صارت تلاتة و تلاتين مع أربعة و تلاتين،
+
+56
+00:04:01,580 --> 00:04:06,370
+ثابت. بعدين أربعة و تلاتين مع تلاتة، swap، بتصير هنا
+
+57
+00:04:06,370 --> 00:04:09,950
+التلاتة، وهنا الأربعة و تلاتين. لاحظوا أن هو هذا
+
+58
+00:04:09,950 --> 00:04:13,230
+الـsequence صار بالشكل ده، بس أنا لسه مخلصتش، أنا كل
+
+59
+00:04:13,230 --> 00:04:18,870
+اللي عملته إيش؟ سويت، أخدت element حطيته في القاع، بس
+
+60
+00:04:18,870 --> 00:04:24,930
+فعلياً، أول مرحلة، أكبر رقم موجود، حطيته في الـlast
+
+61
+00:04:24,930 --> 00:04:27,890
+location، حطيناه في إيش؟ في الـlast location، فصار
+
+62
+00:04:27,890 --> 00:04:30,230
+في الـlast location. هلوجد، لما بدي أجي أعمل عدد
+
+63
+00:04:30,230 --> 00:04:32,770
+مقارنات، لاحظوا هنا واحد، اتنين، تلاتة، أربعة،
+
+64
+00:04:32,770 --> 00:04:37,150
+خمسة، ستة، سبعة، تمانية، الـN بتاعتنا بتمانية، عندنا
+
+65
+00:04:37,150 --> 00:04:42,010
+ثمانية elements، صحيح؟ ثمانية elements، محتاجين N
+
+66
+00:04:42,010 --> 00:04:44,230
+minus one comparisons.
+
+67
+00:04:46,270 --> 00:04:53,830
+هذه مقارنة، اتنين، تلاتة، أربعة، خمسة، ستة، سبعة، تمام؟
+
+68
+00:04:53,830 --> 00:04:59,490
+كويس، آخر رقم هنا ثابت، خلاص أنا من المرحلة الأولى
+
+69
+00:04:59,490 --> 00:05:02,870
+ثبتت أن هذا أكبر رقم موجود، بقرنه، وبقرنه كمان
+
+70
+00:05:02,870 --> 00:05:07,370
+مرة، ففي المرحلة الثانية كان عندي سبعة comparisons.
+
+71
+00:05:07,370 --> 00:05:13,220
+بصيروا ستة، بصير عندي واحد، اتنين، تلاتة، أربعة، خمسة، ستة،
+
+72
+00:05:13,220 --> 00:05:15,740
+الاربعة و تلاتين لأ، لأن احنا عارفين من المرحلة
+
+73
+00:05:15,740 --> 00:05:17,840
+الأولى أن الأربعة و تلاتين هو أكبر رقم كان موجود
+
+74
+00:05:17,840 --> 00:05:24,140
+بدليل أنه صفة في الآخر، في قاع الـsequence تبعكم، أو
+
+75
+00:05:24,140 --> 00:05:28,260
+الـlist بتاعتكم، as a last element، موجود في الـlist.
+
+76
+00:05:28,260 --> 00:05:34,240
+كويس، اللي بعدها، هتلاقوا صار اتنين، صاروا تحت، ومش
+
+77
+00:05:34,240 --> 00:05:36,760
+محتاجين يتقارنوا فيهم كمان مرة. بتصير أنك تشتغلوا
+
+78
+00:05:36,760 --> 00:05:42,580
+على خمسة comparisons، أربعة comparisons، تلاتة
+
+79
+00:05:42,580 --> 00:05:50,960
+comparisons، two comparisons، و stop. فلاحظوا حتى عدد
+
+80
+00:05:50,960 --> 00:05:56,020
+المقارنات اللي هتحتاجوها كل مرة بتقل. طيب، فصار
+
+81
+00:05:56,020 --> 00:06:02,420
+عندنا عدد مقارنات بدنا نعملها في كل مرحلة، وعندنا
+
+82
+00:06:02,420 --> 00:06:06,240
+إيش كمان؟ عندنا عدد مراحل. مرحلة أولى، مرحلة ثانية،
+
+83
+00:06:06,240 --> 00:06:09,620
+مرحلة ثالثة، رابعة، خامسة، سادسة، ولاحظوا أن عدد
+
+84
+00:06:09,620 --> 00:06:17,500
+المراحل برضه minus two هنا، هتطلع، فاحنا هنا هنعدلها
+
+85
+00:06:17,500 --> 00:06:22,620
+في الـcode تبعنا. لاحظوا، ففي عندنا عدد مراحل، وفي
+
+86
+00:06:22,620 --> 00:06:27,860
+عندنا عدد conversions داخل كل مرحلة من مراحل الشغل.
+
+87
+00:06:27,860 --> 00:06:32,640
+كويس، هنبدأ نفهمها، لوجه الـcode، الـsequence نفسه
+
+88
+00:06:32,640 --> 00:06:35,600
+كيف القيم نفسها. هلوجد، مننا نعملها code، نكتب لها
+
+89
+00:06:35,600 --> 00:06:42,040
+code، نشتغل عليه، نكتب
+
+90
+00:06:42,040 --> 00:06:46,100
+لنا code معين، ونشتغل عليه. طيب، الـcode هذا، خلينا
+
+91
+00:06:46,100 --> 00:06:49,960
+نكتب معانا sequence على الجنب، ونشتغله مع الـcode
+
+92
+00:06:49,960 --> 00:06:53,640
+parallel مع الـcode، عشان نكون متابعين الـcode كويس.
+
+93
+00:06:53,640 --> 00:06:58,220
+مع real list، مع قائمة بنجرب عليها. خلينا نقول أن في
+
+94
+00:06:58,220 --> 00:07:04,510
+الـlist بتاعتنا، say مثلاً، خليني أقول، طبعاً احنا عرفنا
+
+95
+00:07:04,510 --> 00:07:07,770
+الـprocedure، و before sort، على أساس أنه هي الاسم
+
+96
+00:07:07,770 --> 00:07:10,910
+تبعنا، الـprocedure. أنا داخل هنا على algorithm، على
+
+97
+00:07:10,910 --> 00:07:17,970
+code، عرفناهم، an element داخل list، وسمنهم إيش؟ real
+
+98
+00:07:17,970 --> 00:07:24,650
+numbers within، أكبر من أو تساوي اتنين، لأن واحد بدي
+
+99
+00:07:24,650 --> 00:07:29,030
+أقارنه مع مين؟ خلاص هو sorted لحاله، لحاله، رقم واحد،
+
+100
+00:07:29,030 --> 00:07:34,130
+رقمين، بكون محتاج عملية comparison واحدة. هما موجودين
+
+101
+00:07:34,130 --> 00:07:36,710
+الاثنين، بعمل comparison بينهم، مين الأقل؟ بخليه في
+
+102
+00:07:36,710 --> 00:07:40,530
+الأول، بحطه في الأول. طيب، real numbers، خليني أشوف
+
+103
+00:07:40,530 --> 00:07:43,610
+إنها مجموعة real numbers، لو قلنا مثلاً عندنا three
+
+104
+00:07:43,610 --> 00:07:52,790
+three point two مثلاً، و
+
+105
+00:07:52,790 --> 00:08:00,480
+two point five، one point one، three
+
+106
+00:08:00,480 --> 00:08:04,500
+point one، واحد، اتنين، أربعة، اتنين، أربعة، اتنين، أربعة،
+
+107
+00:08:04,500 --> 00:08:06,400
+اتنين، أربعة، اتنين، أربعة، اتنين، أربعة، اتنين، أربعة،
+
+108
+00:08:06,400 --> 00:08:07,360
+اتنين، أربعة، اتنين، أربعة، اتنين، أربعة، اتنين، أربعة،
+
+109
+00:08:07,360 --> 00:08:09,280
+اتنين، أربعة، اتنين، أربعة، اتنين، أربعة، اتنين، أربعة،
+
+110
+00:08:09,280 --> 00:08:11,420
+اتنين، أربعة، اتنين، أربعة، اتنين، أربعة، اتنين، أربعة،
+
+111
+00:08:11,420 --> 00:08:24,320
+اتنين، أربعة، اتنين، أربعة، اتنين، أربعة، اتنين، أرب-
+
+112
+00:08:25,350 --> 00:08:29,290
+عة، واحد، اتنين، تلاتة، أربعة، خمسة، لأربعة،
+
+113
+00:08:29,290 --> 00:08:35,710
+تمام؟ كويس، هذه اللوب هذا، هيعطينا المراحل اللي
+
+114
+00:08:35,710 --> 00:08:39,350
+هنشتغل عليها، كم مرحلة أنا محتاجها؟ كانت مرحلة
+
+115
+00:08:39,350 --> 00:08:42,390
+اتنين، تلاتة، أربعة، خمسة، زي ما كان التو مرسومة،
+
+116
+00:08:42,390 --> 00:08:48,010
+طيب، في كل مرحلة، كم comparison هنعمل؟ بص، طيب، كم comparison هنعمل؟ برضه من واحد to N
+
+117
+00:08:48,010 --> 00:08:51,370
+minus I. ليش؟ لأن في كل مرحلة، هنجس عدد الـ
+
+118
+00:08:51,370 --> 00:08:55,940
+conversions، صح؟ جربناها، وقلنا أن في كل مرحلة بتقل
+
+119
+00:08:55,940 --> 00:09:00,940
+عدد الـconversions اللي أنا محتاجها. طيب، فكل مرة
+
+120
+00:09:00,940 --> 00:09:04,180
+أول ما هنبدأ، هنبدأ، كان عندي ثمانية، صار بدي
+
+121
+00:09:04,180 --> 00:09:07,560
+محتاج سبعة conversions، سبعة conversions. فهبدأ to N
+
+122
+00:09:07,560 --> 00:09:11,600
+minus I، I هنا واحد، فأنا في المرحلة الأولى محتاج N
+
+123
+00:09:11,600 --> 00:09:16,620
+minus one comparisons. طب في المرحلة الثانية، minus
+
+124
+00:09:16,620 --> 00:09:20,900
+two، بتكون هنا i صارت اتنين. في المرحلة الأخيرة، n
+
+125
+00:09:20,900 --> 00:09:26,020
+minus one، بتصير أنا محتاج comparison واحدة، لأنه
+
+126
+00:09:26,020 --> 00:09:30,060
+بيكون فاضل رقمين بس، بيكون فاضل رقمين. خلينا نشوف
+
+127
+00:09:30,060 --> 00:09:33,680
+الكلام هذا فعلاً على list موجودة قدامنا. هنبدأ هنا بـ
+
+128
+00:09:33,680 --> 00:09:37,980
+i بتساوي واحد، فإذا two n minus one، يعني معنى
+
+129
+00:09:37,980 --> 00:09:43,940
+ذلك، بتكلم عن إيش؟ عن أربعة، بتكلم عن أربعة هنا.
+
+130
+00:09:43,940 --> 00:09:47,320
+وأربعة هنا. Okay، أربعة وأربعة، نبدأ، if a one، هاي الـ
+
+131
+00:09:56,220 --> 00:10:01,360
+j بدينها بين واحد، أكبر من j plus one، أكبر من اتنين،
+
+132
+00:10:01,360 --> 00:10:05,780
+فبشوف الـelement الأول مع الـelement الثاني، if الـ
+
+133
+00:10:05,780 --> 00:10:08,640
+element الأول أكبر من الـelement الثاني، نعمل
+
+134
+00:10:08,640 --> 00:10:13,740
+interchange، swap، نبدلهم مع بعض. كويس، خلينا نشوف
+
+135
+00:10:13,740 --> 00:10:18,560
+هاي الأول، وهاي الثاني. هل فعلاً الأول أكبر من
+
+136
+00:10:18,560 --> 00:10:24,500
+الثاني؟ الأول أكبر من الثاني، في الحالة هذه، بنقول على طول، two point five، و three
+
+137
+00:10:24,500 --> 00:10:28,660
+point two، بهذا الشكل. طيب، خلصنا I بتساوي واحد، I
+
+138
+00:10:28,660 --> 00:10:34,840
+بتساوي اتنين، صار بقارن اتنين مع تلاتة، هاي اتنين مع
+
+139
+00:10:34,840 --> 00:10:41,680
+تلاتة.
+
+140
+00:10:44,880 --> 00:10:51,340
+3.2 مع 1.1، الثاني أكبر من الثالث، فبنحط هنا الثالث،
+
+141
+00:10:51,340 --> 00:10:57,080
+بيصير هو الثاني، والثاني بيصير هو الثالث. طيب، خلصنا
+
+142
+00:10:57,080 --> 00:11:05,180
+I سوى تلاتة، صار بقارن تلاتة مع أربعة، هي تلاتة، واحد،
+
+143
+00:11:05,180 --> 00:11:09,960
+اتنين، هي تلاتة مع أربعة، أكبر، بدلناهم.
+
+144
+00:11:14,800 --> 00:11:20,680
+خلاص، آخر رقم، أربعة، أربعة، أربعة،
+
+145
+00:11:20,680 --> 00:11:23,920
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+146
+00:11:23,920 --> 00:11:24,080
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+147
+00:11:24,080 --> 00:11:24,480
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+148
+00:11:24,480 --> 00:11:26,660
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+149
+00:11:26,660 --> 00:11:26,880
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+150
+00:11:26,880 --> 00:11:28,000
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+151
+00:11:28,000 --> 00:11:34,400
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+152
+00:11:34,400 --> 00:11:39,600
+أربعة، أربعة، أربعة، أربعة،
+
+153
+00:11:39,600 --> 00:11:42,100
+أربعة،
+
+154
+00:11:44,880 --> 00:11:48,400
+اتنين، هذا المفروض من واحد لأربعة، احنا لسه ماوصلناش
+
+155
+00:11:48,400 --> 00:11:53,220
+لأربعة، لسه اتنين، اتنين، معناته هنبدأ هنا من واحد
+
+156
+00:11:53,220 --> 00:11:59,120
+لخمسة، minus اتنين، لتلاتة، لأنه هحتاج تلاتة
+
+157
+00:11:59,120 --> 00:12:01,600
+conversions، بس في المرحلة الأولى كنت محتاج أربعة
+
+158
+00:12:01,600 --> 00:12:05,360
+conversions، واحدة، اتنين، تلاتة، أربعة، في المرحلة
+
+159
+00:12:05,360 --> 00:12:09,420
+الثانية، هنحتاج تلاتة بس، ليش؟ لأن تلاتة فاصلة اتنين
+
+160
+00:12:09,420 --> 00:12:13,510
+هذه خلاص هتبقى ثابتة، ومش هقارن فيها مرة ثانية. قارنّا
+
+161
+00:12:13,510 --> 00:12:18,070
+وما وصلناها للـlast location إلا لأن هي أكبر رقم
+
+162
+00:12:18,070 --> 00:12:22,270
+موجود، لو لأن هي أكبر رقم موجود، كان ماوصلتش في الـ
+
+163
+00:12:22,270 --> 00:12:27,850
+last location. كويسة، نشوف عند الواحد، واحد مع اتنين،
+
+164
+00:12:27,850 --> 00:12:35,110
+واحد مع اتنين، one point one، two point five. طيب، عند
+
+165
+00:12:35,110 --> 00:12:41,110
+الاتنين، اتنين مع تلاتة، اتنين مع تلاتة، بيضلوا. خلاص
+
+166
+00:12:41,110 --> 00:12:47,450
+بتنزل زي ما هي. طيب، تلاتة مع أربعة، تلاتة مع أربعة،
+
+167
+
+223
+00:17:50,460 --> 00:17:54,100
+الـ location هذا مش تبعها طيب بنشوف الـ location
+
+224
+00:17:54,100 --> 00:18:01,940
+التاني 3.1 مع 2.3  لـ location هذا مش تبعها طيب
+
+225
+00:18:01,940 --> 00:18:08,400
+3.1 مع 3.2 أقل من .. مدام أقل من هذه لازم تشوف
+
+226
+00:18:08,400 --> 00:18:11,220
+location تاني، يعملها shift على الـ location اللي
+
+227
+00:18:11,220 --> 00:18:15,200
+وراها، و بنعمل insertion للـ X هذا اللي كنت بعمله ..
+
+228
+00:18:15,200 --> 00:18:18,480
+بعمله search عرفت إن المفروض الـ location يكون
+
+229
+00:18:18,480 --> 00:18:21,160
+فبدخله في الـ location  طبعاً، و بعمله insertion في الـ
+
+230
+00:18:21,160 --> 00:18:29,760
+location الطبيعي، طبعاً الصحيح، كويس. آخر رقم 2.4، 2.4
+
+231
+00:18:29,760 --> 00:18:35,760
+برضه بنرجع بنقارنها مع، طبعاً احنا هنا ماكتبناش بس
+
+232
+00:18:35,760 --> 00:18:43,160
+3.2 أكبر من 1.1 فسيب الـ 1.1 في حالها مالهاش علاقة
+
+233
+00:18:43,160 --> 00:18:47,560
+فيها، طيب 2.5 لأ أقل من 2.5 معناته الـ location
+
+234
+00:18:47,560 --> 00:18:51,080
+تبعها هو هذا الـ 2.5، مكان الـ 2.5 المفروض الـ
+
+235
+00:18:51,080 --> 00:18:56,550
+location التاني، معناته إن من 2.5 كله هذا بدنا
+
+236
+00:18:56,550 --> 00:19:03,870
+نعمله shift نضغط فيه هنا A5، A5 هذه هتاخد الرقم
+
+237
+00:19:03,870 --> 00:19:08,190
+اللي كان في A4، A4 هينعملها shift بالرقم اللي كان
+
+238
+00:19:08,190 --> 00:19:14,750
+في A3، A3 هتاخد الرقم تبع A2، عشان نعمل insertion
+
+239
+00:19:14,750 --> 00:19:20,190
+لمن؟ للرقم الجديد، نعمل insertion للرقم الجديد، لحظة
+
+240
+00:19:20,190 --> 00:19:26,340
+إن برضه اترتب، ترتب الـ sequence عندكم، ترتب الـ
+
+241
+00:19:26,340 --> 00:19:31,840
+sequence عندكم، تمام. فهنا بتكلم برضه، بتقدر تستخدم
+
+242
+00:19:31,840 --> 00:19:35,440
+إما الـ linear أو الـ binary search، الطريقة اللي
+
+243
+00:19:35,440 --> 00:19:38,320
+بتحبي تستخدموها، استخدموها، إما تستخدموها أنتو في
+
+244
+00:19:38,320 --> 00:19:42,180
+الآخر، صارت عبارة عن search، عبارة عن search X، و
+
+245
+00:19:42,180 --> 00:19:44,460
+بتحاولوا تشوف وين الـ location تبعه، بتحاولوا تشوف
+
+246
+00:19:44,460 --> 00:19:48,160
+وين الـ location تبعه، فبتقدروا تشتغلوا على الـ
+
+247
+00:19:48,160 --> 00:19:51,480
+linear أو على الـ binary، وبعدين بتعملوا shift إذا
+
+248
+00:19:51,480 --> 00:19:57,100
+كان الـ item أو الـ X أقل من قيمة الـ element في الـ
+
+249
+00:19:57,100 --> 00:19:59,510
+location، قيمة الـ element في الـ location، وبتعمله
+
+250
+00:19:59,510 --> 00:20:03,590
+shift للـ item أو للـ element بـ one position، بـ one
+
+251
+00:20:03,590 --> 00:20:08,510
+position على الـ location اللي أعلى منه، على الـ
+
+252
+00:20:08,510 --> 00:20:10,790
+location اللي أعلى منه، بحيث إنه يصير في عندكوا هنا
+
+253
+00:20:10,790 --> 00:20:16,290
+فضاء، hall، الـ hall هذا بتضيفه في الـ new item اللي
+
+254
+00:20:16,290 --> 00:20:18,910
+هو الـ x اللي بتدوروا عليه، الـ x اللي كنتوا بتعملوا
+
+255
+00:20:18,910 --> 00:20:22,930
+الـ search عليه هذا
+
+256
+00:20:22,930 --> 00:20:25,850
+كانت جزئية ضايلة من الـ algorithm
+
+257
+00:20:31,220 --> 00:20:35,240
+بتاعتنا، عشان نكمل برضه في الـ algorithm، بس عشان
+
+258
+00:20:35,240 --> 00:20:38,160
+أشتغل على الـ algorithm محتاج أدرس حاجة اسمها الـ
+
+259
+00:20:38,160 --> 00:20:44,960
+complexity، complexity بمعنى إنه عندنا أكتر من code
+
+260
+00:20:44,960 --> 00:20:49,100
+ممكن يعملوا نفس الـ task، نفس الـ task، بس بدي أحسب الـ
+
+261
+00:20:49,100 --> 00:20:53,960
+complexity للكل، ليش؟ عشان أعرف إنه منهم أختار، لأنه
+
+262
+00:20:53,960 --> 00:20:59,210
+ممكن جداً يكون عندنا code، code، كل واحدة كتبت لنا
+
+263
+00:20:59,210 --> 00:21:02,290
+code، أجي أفحصهم، أعملهم analysis، وهذا اللي بدنا
+
+264
+00:21:02,290 --> 00:21:06,010
+نتعلمه، نعمل analysis لهم، نطلع المعادلة بتاعة كل
+
+265
+00:21:06,010 --> 00:21:09,070
+واحد منهم، معادلة إيش؟ هنعرف احنا بنتكلم هنا عن
+
+266
+00:21:09,070 --> 00:21:14,130
+معادلة الـ variable فيها عدد الـ inputs، variable عدد
+
+267
+00:21:14,130 --> 00:21:17,070
+الـ inputs، بحيث إنه كل ما زادت عدد الـ inputs أكيد
+
+268
+00:21:17,070 --> 00:21:19,330
+هيزيد الـ function، في إيش؟ أنا بدي أعملها الـ
+
+269
+00:21:19,330 --> 00:21:23,130
+complexity في الـ time، ورغم إنه طبعاً في criteria
+
+270
+00:21:23,130 --> 00:21:26,430
+تانية ممكن اللي واحد يشتغل عليها زي الـ energy، كم
+
+271
+00:21:26,430 --> 00:21:30,630
+تستهلك الـ energy أو الـ space، بس احنا مش هنشتغل
+
+272
+00:21:30,630 --> 00:21:33,310
+فيهم هدول، هنركز على الـ complexity بتاعتنا، مفهومها
+
+273
+00:21:33,310 --> 00:21:36,610
+أكثر على الـ time، إنه code اللي بيستغرق الـ time
+
+274
+00:21:36,610 --> 00:21:41,770
+أكبر، عندنا two codes، باجي بحسب الـ equation بتاعت
+
+275
+00:21:41,770 --> 00:21:43,830
+هذا، مع الـ equation بتاعت هذا، الـ equation ده إيش،
+
+276
+00:21:43,830 --> 00:21:47,980
+بتحسب ليه؟ بتحسب الـ time، variable في إيش؟ أو
+
+277
+00:21:47,980 --> 00:21:51,960
+function، في variable عبارة عن عدد الـ inputs للكود
+
+278
+00:21:51,960 --> 00:21:56,020
+لأن كل ما زاد عدد الـ inputs، سيزيد الـ time، سيزيد
+
+279
+00:21:56,020 --> 00:21:59,640
+معاها الـ time، فبكون عملت equation أو formula، الـ
+
+280
+00:21:59,640 --> 00:22:02,480
+formula دي بنشوف الـ complexity بتاعتها، والله اللي
+
+281
+00:22:02,480 --> 00:22:05,880
+أعلى complexity بديش إياه، لأنه معناه إنّه
+
+282
+00:22:05,880 --> 00:22:11,100
+هيستغرق وقت أكبر، بظل بس كيف بدنا نعرف
+
+283
+00:22:11,100 --> 00:22:14,020
+إنّه مين الـ complexity أعلى؟ بدنا نشوف كل equation
+
+284
+00:22:14,020 --> 00:22:18,540
+من اللي بيطلع، هدول هيتلعوا functions، الـ orders of
+
+285
+00:22:18,540 --> 00:22:23,780
+growth، جديش معدل النمو للـ function هذه، وجديش معدل
+
+286
+00:22:23,780 --> 00:22:26,260
+النمو للـ function هذه، عشان نقول والله اللي معدل
+
+287
+00:22:26,260 --> 00:22:31,540
+نموه أعلى، بمعنى بزود input واحد، بزيد مقابله خمسة
+
+288
+00:22:31,540 --> 00:22:35,550
+في الـ time، وفوق code تاني، بزود input واحد، بزيد
+
+289
+00:22:35,550 --> 00:22:39,450
+مقابله أربعة في الـ time، يعني الـ time بتضعف أربع
+
+290
+00:22:39,450 --> 00:22:41,930
+مرات، هنا بتضعف خمس مرات، لا والله الخمس مرات مديش
+
+291
+00:22:41,930 --> 00:22:46,490
+إياه، لأنه الـ order of growth، معدل النمو تبعه أكبر
+
+292
+00:22:46,490 --> 00:22:53,090
+فهو faster، أسرع، أسرع، بس أنا بدور على أسرع، احنا
+
+293
+00:22:53,090 --> 00:22:57,670
+بالعكس، بدنا الأقل، بدنا الـ time complexity الأقل، فالـ
+
+294
+00:22:57,670 --> 00:22:59,630
+time complexity، قبل ما نبدأ نتكلم عن الـ time
+
+295
+00:22:59,630 --> 00:23:02,850
+complexity، بدنا نتكلم عن الـ orders of growth، كيف
+
+296
+00:23:02,850 --> 00:23:09,050
+بقدر أحسب الـ order of growth، وكيف لـ codeين نحسب
+
+297
+00:23:09,050 --> 00:23:12,950
+الـ order لهذا، ولهذا، عشان نقدر نقارنهم ببعض، ففي
+
+298
+00:23:12,950 --> 00:23:16,690
+جزئية هنا لازم نتكلم عنها، اللي هي الـ growth أو الـ
+
+299
+00:23:16,690 --> 00:23:22,530
+orders of growth، orders of growth، كويسة. الشكل اللي
+
+300
+00:23:22,530 --> 00:23:28,400
+قدامنا هنا، هنبدأ طبعاً بناءً على الـ knowledge السابقة
+
+301
+00:23:28,400 --> 00:23:30,780
+اللي عندنا، بناءً على الـ knowledge السابقة، بقدر أقول
+
+302
+00:23:30,780 --> 00:23:34,400
+إنّ الـ order تبعت المعادلة دي إيش؟ طبعاً هن .. هن ..
+
+303
+00:23:34,400 --> 00:23:37,800
+بعدين هنشرحها من وجهة نظر الـ discrete، كيف بحسب الـ
+
+304
+00:23:37,800 --> 00:23:41,580
+order بالظبط، ولكن مبدئياً أنتو بتتكلموا هنا عن خط
+
+305
+00:23:41,580 --> 00:23:48,750
+مستقيم، بغض النظر إنّ الـ slope مختلف، وليس واحد مثلما
+
+306
+00:23:48,750 --> 00:23:53,810
+احنا نعرف إنّ الـ slope مختلف، الـ shift ليس بعيداً عن
+
+307
+00:23:53,810 --> 00:23:58,230
+صفر، صفر، بل بعيداً عن صفر وثمانية، ببدأ عن صفر و
+
+308
+00:23:58,230 --> 00:24:03,590
+ثمانية، موجود عندنا، بس في جميع الأحوال لو قلتلكوا
+
+309
+00:24:03,590 --> 00:24:06,770
+إيش الـ order أو أي درجة هذه المعادلة اللي هي 30n
+
+310
+00:24:06,770 --> 00:24:13,050
+plus ثمانية، الأولى، الأولى هذه first order، درجة
+
+311
+00:24:13,050 --> 00:24:15,190
+أولى، احنا إيش عرفناها درجة أولى؟ من الـ knowledge
+
+312
+00:24:15,190 --> 00:24:18,850
+السابق، اتفقنا، بس برضه هنعرف احنا كيف ممكن نشتغلها
+
+313
+00:24:18,850 --> 00:24:21,350
+بالـ discrete، واعرف جديش الـ order تبعها، لإنه بدي
+
+314
+00:24:21,350 --> 00:24:25,290
+أقارنها بـ orders ثانية، بدي نقارنها بـ orders ثانية
+
+315
+00:24:25,290 --> 00:24:30,920
+معادلة التانية هذه، المعادلة التانية هنا تربيع
+
+316
+00:24:30,920 --> 00:24:36,940
+plus واحد، تربيع plus واحد، وهي الشكل، الشكل تبعها
+
+317
+00:24:36,940 --> 00:24:42,320
+طبعاً واضح إنّ في shift بقيمة واحد، قيمة الـ shift
+
+318
+00:24:42,320 --> 00:24:45,560
+اللي موجود، طيب التربيع واضح إنّ أنا بتكلم عن
+
+319
+00:24:45,560 --> 00:24:50,040
+second order، بتكلم عن second order، okay. في أجزاء
+
+320
+00:24:51,310 --> 00:24:55,330
+أقل، وفي أجزاء أكبر، طب أنا بشتغل عالمين؟ عشان أقول
+
+321
+00:24:55,330 --> 00:24:58,350
+والله أي order اللي أنا بنصبني أكتر، دائماً بندور
+
+322
+00:24:58,350 --> 00:25:04,250
+على K معينة، الـ K هذه قيمة، قيمة N، بمعنى عند عدد
+
+323
+00:25:04,250 --> 00:25:11,410
+users محدد، معين، هسميه K، فالـ N هذه أكبر من K دائماً
+
+324
+00:25:11,410 --> 00:25:14,370
+واحد منهم بيكون أكبر من الثاني، فالأكبر هو الـ
+
+325
+00:25:14,370 --> 00:25:19,550
+faster، بسميه، وهذا بديش إياه، فواضح إنّ التربيع عنده
+
+326
+00:25:19,550 --> 00:25:26,570
+نقطة هذه، هنقول عليها K، فكل N أكبر من K دائماً
+
+327
+00:25:26,570 --> 00:25:30,470
+التربيع أكبر من الـ linear، دائماً التربيع أكبر من الـ
+
+328
+00:25:30,470 --> 00:25:33,910
+linear، بغض النظر عن الـ coefficient اللي مضروبة فيه
+
+329
+00:25:33,910 --> 00:25:37,610
+الـ linear، بس الـ coefficient هذه فقط هتغيرلكوا وين
+
+330
+00:25:37,610 --> 00:25:42,050
+موجود التقاطع هذا، بس دائماً في قيمة لـ K بعدها
+
+331
+00:25:42,050 --> 00:25:45,430
+التربيع دائماً أكبر من الـ linear، دائماً التربيع
+
+332
+00:25:45,430 --> 00:25:50,410
+بيكون أكبر من الـ linear، بعد قيمة معينة لـ N، و
+
+333
+00:25:50,410 --> 00:25:56,990
+هنسميها K، اللي هي النقطة هذه، فإذا for all N أكبر
+
+334
+00:25:56,990 --> 00:26:01,130
+من K، دائماً
+
+335
+00:26:01,130 --> 00:26:06,650
+المعادلة بالخط الأحمر هذه، بالـ red line، هتكون أكبر
+
+336
+00:26:06,650 --> 00:26:11,830
+من الـ black line، second order دائماً هتكون أكبر من
+
+337
+00:26:11,830 --> 00:26:15,150
+الـ first order، وهتلاقوا إنّ المعدل كبير جداً، يعني
+
+338
+00:26:15,150 --> 00:26:17,370
+هنا كان الفرق بينهم بالشكل هذا، هنا الفرق لحظوا
+
+339
+00:26:17,370 --> 00:26:21,870
+جديش صار، ولسه ما وصلناش، شايفين جديش صار الفرق؟
+
+340
+00:26:21,870 --> 00:26:26,210
+معدل الفرق، معدل التغير، فواضح إنّ المعادلة
+
+341
+00:26:26,210 --> 00:26:33,770
+التربعية أسرع، أسرع بالنسبة لزيادة N من المعادلة الـ
+
+342
+00:26:33,770 --> 00:26:37,230
+linear أو الخطية
+
+343
+00:26:42,540 --> 00:26:46,880
+كويس، في الحلقة دي عشان نعرف كل واحدة منهم، بنعرفها
+
+344
+00:26:46,880 --> 00:26:51,220
+بحاجة هنسميها الـ order of growth، الـ .. هنقول الـ
+
+345
+00:26:51,220 --> 00:26:56,160
+function الأولى، هفترض إنّ هذه الـ time لـ code أول
+
+346
+00:26:56,160 --> 00:26:59,520
+الـ code الأول، جينا حسبناه، لجينا إنّ الـ complexity
+
+347
+00:26:59,520 --> 00:27:05,380
+تبعته 30n plus ثمانية، والـ n هذه جديش عدد لو
+
+348
+00:27:05,380 --> 00:27:08,120
+بدنا نقول إنّ الـ code هذه بيحسبلنا، بيعملنا sorting
+
+349
+00:27:10,040 --> 00:27:14,720
+جديش عدد الـ items اللي بدنا نعملهم sorting؟ قيمتهم
+
+350
+00:27:14,720 --> 00:27:18,860
+n، فخمسة عشرة، يعني هنا مثلاً كنا بنتكلم عن خمسة،
+
+351
+00:27:18,860 --> 00:27:23,140
+عشرة، عشرين، خمسين، سبعين، مية، ألف، ألفين، مليون، جديش
+
+352
+00:27:23,140 --> 00:27:27,900
+فهذه اللي هي قيمة n، الـ f of n، الـ time اللي بنحتاجه
+
+353
+00:27:27,900 --> 00:27:31,860
+لتنفيذ البرنامج هذا، أو للـ code هذا، خلينا نقول في
+
+354
+00:27:31,860 --> 00:27:36,410
+عندنا system أول، لهذا الـ system أول، وهيكون فيه
+
+355
+00:27:36,410 --> 00:27:41,630
+system ثاني، أو code ثاني، الـ complexity اللي تتبعته، أو
+
+356
+00:27:41,630 --> 00:27:47,570
+الـ time بيحسبها عن طريق n2 plus 1، n2 plus 1، ونفس
+
+357
+00:27:47,570 --> 00:27:50,790
+الكلام، الـ n هنا هتكون عدد الـ items اللي بدي أعملها
+
+358
+00:27:50,790 --> 00:27:55,650
+sorting، الـ f of n، الـ time اللي هحتاجه، الـ time اللي
+
+359
+00:27:55,650 --> 00:27:58,170
+هحتاجه، فهذا code وهذا code، بدنا نشوف مين أحسن من
+
+360
+00:27:58,170 --> 00:28:02,740
+التاني، طيب بدنا نعرف الـ code الأول، و نعرف الـ order
+
+361
+00:28:02,740 --> 00:28:09,580
+تبعته، بعرف الـ order تبعته بالنسبة لـ Big O، طب مش
+
+362
+00:28:09,580 --> 00:28:13,800
+هي Big O، Big O of N، يعني كأني بقول إنّه 30N
+
+363
+00:28:13,800 --> 00:28:20,560
+plus واحد، at most first order، لأنه لحظة أنا أقول
+
+364
+00:28:20,560 --> 00:28:30,140
+Big O of N، طيب N هذه هي first order، هذه first order
+
+365
+00:28:30,140 --> 00:28:38,100
+صحيح؟ كأني بقول إنّ المعادلة هذه بالكتير first order
+
+366
+00:28:38,100 --> 00:28:43,620
+ممكن تكون أقل، أقل أو تساوي first order، فهي ضمن
+
+367
+00:28:43,620 --> 00:28:46,240
+التعريف، احنا عارفين إنّ هي first order، احنا عارفين
+
+368
+00:28:46,240 --> 00:28:49,760
+إنّ هي first order، فهي تنطبق مع الـ Big O، الـ Big O
+
+369
+00:28:49,760 --> 00:28:55,660
+دي معناها at most proportional to n، تتناسب مع n
+
+370
+00:28:55,660 --> 00:29:01,340
+بالكتير، يعني ممكن تكون أقل، ممكن أقول إنّه constant
+
+371
+00:29:01,340 --> 00:29:05,080
+أو log، الـ log احنا عارفين إنّه أقل من الـ .. الـ
+
+372
+00:29:05,080 --> 00:29:08,280
+order تبعه أقل من الـ first، log أقل من الـ first
+
+373
+00:29:08,280 --> 00:29:16,800
+صحيح، فممكن أقول إنّ الـ log of N برضه is Big O of N
+
+374
+00:29:16,800 --> 00:29:23,340
+على اعتبار إنّ هي أقل من، فالـ Big O بيسمح لنا إنّه أقل
+
+375
+00:29:23,340 --> 00:29:28,200
+من أو يساوي first order، أقل من أو يساوي، ممكن تكون
+
+376
+00:29:28,200 --> 00:29:35,220
+constant، أقول مثلاً ثلاثة is Big O of N، ثلاثة
+
+377
+00:29:35,220 --> 00:29:41,040
+constant، يعني الـ order zero، order zero، تمام، فالـ
+
+378
+00:29:41,040 --> 00:29:47,140
+order zero، فهنا الـ Big O هذه معناها إنّه بشوف العنصر
+
+379
+00:29:47,140 --> 00:29:51,420
+اللي جوه، العنصر اللي جوه N، N هذا linear، ممكن تكتب
+
+380
+00:29:51,420 --> 00:29:56,880
+N تربيع، فأنا بتكلم هنا عن تربيع، second order، third
+
+381
+00:29:56,880 --> 00:30:01,340
+order، فبشُوف N هذه كلها ثابتة، هتكون منها بس الـ
+
+382
+00:30:01,340 --> 00:30:05,780
+power، جديش هي، ده اللي هتحدد الـ order تبعنا، طيب
+
+383
+00:30:05,780 --> 00:30:16,750
+ممكن تنحط Big O of N to the power 0، بـ 1
+
+384
+00:30:16,750 --> 00:30:21,430
+فبنكتبها Big O of 1
+
+385
+00:30:21,430 --> 00:30:30,470
+فبعرف إنّ هذه constant أو order 0، تمام، على اعتبار
+
+386
+00:30:30,470 --> 00:30:36,880
+إنّها n to the power 0، فطلع لنا الواحد، كويس، هذا كل
+
+387
+00:30:36,880 --> 00:30:39,540
+الكلام اللي ع
+
+445
+00:34:57,440 --> 00:35:02,680
+معناته كل الـfunctions هذه بقدر أحطها في set فالـ
+
+446
+00:35:02,680 --> 00:35:07,390
+function صارت element داخل الـset. الـset هذه كل الـ
+
+447
+00:35:07,390 --> 00:35:12,430
+elements اللي تتفق أن هي big O للـfirst order تمام.
+
+448
+00:35:12,430 --> 00:35:18,350
+معناه ذلك لما أنا بدي أجعل ريفي بقول set of
+
+449
+00:35:18,350 --> 00:35:25,910
+functions. الـfunction هذه from R to R نسبة
+
+450
+00:35:25,910 --> 00:35:28,410
+لميه؟ للـfunction اللي أنا بدي أنسب إليها، اللي بدي
+
+451
+00:35:28,410 --> 00:35:32,010
+أنسب الـorder إليها، فهي function from R to R such
+
+452
+00:35:32,010 --> 00:35:35,640
+that. إيش اللي بده يحقق لنا إياه؟ يعني عشان هذه
+
+453
+00:35:35,640 --> 00:35:39,000
+تكون الـfunction فعلاً element داخل الـset بتاعة الـ
+
+454
+00:35:39,000 --> 00:35:41,820
+big O of G. إيش اللي لازم يتحققه؟ لازم يتحقق التالي:
+
+455
+00:35:41,820 --> 00:35:47,040
+there exist C و K،  كي هي النقطة اللي كنا نتكلم عنها
+
+456
+00:35:47,040 --> 00:35:54,820
+اللي بعدها دائماً. التربيعية أكبر من الـlinear. معناته أن
+
+457
+00:35:54,820 --> 00:35:59,500
+أنا فعلاً بدور على قيمة constant K و there exist لـ
+
+458
+00:35:59,500 --> 00:36:04,660
+C برضه constant... constant. طيب، there exist C, K
+
+459
+00:36:04,660 --> 00:36:08,920
+such that for all X أكبر من K، لكل القيم اللي بعد K،
+
+460
+00:36:08,920 --> 00:36:16,580
+لكل القيم اللي بعد K، F of X، الـfunction اللي داخل
+
+461
+00:36:16,580 --> 00:36:22,690
+الـset، أقل من أو تساوي C في G of X. نسبنا هنا
+
+462
+00:36:22,690 --> 00:36:25,010
+بالنسبة لمن؟ للـfunction اللي... اللي احنا عارفين
+
+463
+00:36:25,010 --> 00:36:27,550
+الـorder تبعها و بدنا نعرف هل الـfunction F belong
+
+464
+00:36:27,550 --> 00:36:30,930
+إليها أو لأ. جينا example هالوجد، حنعرف كيف أطلع
+
+465
+00:36:30,930 --> 00:36:35,510
+برضه الـC و الـK، حنعرف نطلع هالوجد الـC و الـK بس
+
+466
+00:36:35,510 --> 00:36:41,810
+مبدئياً بنقول إنه بعد النقطة K، الـfunction F is at
+
+467
+00:36:41,810 --> 00:36:45,650
+most a constant C times of G.
+
+468
+00:36:47,600 --> 00:36:53,040
+معناته أن هي proportional to G، تتناسب مع G، تتناسب
+
+469
+00:36:53,040 --> 00:36:57,420
+هنا مع G. هناخد example و هنرسم الرسم تبعهم عشان
+
+470
+00:36:57,420 --> 00:37:02,020
+نشوف كيف العملية التناسب. طيب، نقرأها: if is at most
+
+471
+00:37:02,020 --> 00:37:09,520
+order G، أو if is big O of G، أو ممكن نقول if بتساوي
+
+472
+00:37:09,520 --> 00:37:14,680
+big O of G، أو ممكن نكتبها if belong، لأن احنا عرفنا
+
+473
+00:37:14,680 --> 00:37:18,460
+الـif إن هي function داخل الـset اللي تحتوي على كل
+
+474
+00:37:18,460 --> 00:37:22,740
+الـfunctions بتاعة الـbig O، فهي واحدة منهم، فبقدر
+
+475
+00:37:22,740 --> 00:37:27,040
+أقول أن هي element أو function belong to big O of
+
+476
+00:37:27,040 --> 00:37:30,820
+G. بناءً على التعريف، بناءً على تعريفنا أن احنا بنتكلم
+
+477
+00:37:30,820 --> 00:37:36,860
+عن set of functions. أحياناً ممكن نقلش منها الـat
+
+478
+00:37:36,860 --> 00:37:42,240
+most بتاعتنا، فبقول if is order g، خلاص ممكن جداً
+
+479
+00:37:42,240 --> 00:37:46,920
+نختصرها. طيب، خلينا نشوف كيف نحسبها، الـK و الـC اللي
+
+480
+00:37:46,920 --> 00:37:50,360
+قلت لكم بدنا نجيبهم. ناخد الـtwo examples اللي
+
+481
+00:37:50,360 --> 00:37:55,980
+اتكلمنا عنهم، اللي واحدة linear، واحدة square، و بدنا
+
+482
+00:37:55,980 --> 00:37:59,920
+نجيب هل فعلاً هي big O of N أو لأ. نمسك الأولى:
+
+483
+00:37:59,920 --> 00:38:05,120
+30 N plus 8 is big O of N first order.
+
+484
+00:38:05,120 --> 00:38:09,730
+بدنا نثبت الكلام هذا، و بدنا نوضح الكلام هذا ليش
+
+485
+00:38:09,730 --> 00:38:12,830
+يقول لنا 130؟ ليش احنا امتى قلنا ممكن تكون فعلاً
+
+486
+00:38:12,830 --> 00:38:20,670
+first order إذا كان يوجد C و K اللي بيحققوا لنا الـ
+
+487
+00:38:20,670 --> 00:38:28,330
+condition أن F of X أقل من أو تساوي C في N في الـ
+
+488
+00:38:28,330 --> 00:38:35,030
+order. طبعاً F of N، تمام؟ بدنا نحقق الكلام هذا. فعشان
+
+489
+00:38:35,030 --> 00:38:40,450
+أحققه، بدي أثبت أنه موجودة الـC و الـK. طب كيف نقدر
+
+490
+00:38:40,450 --> 00:38:45,790
+نجيب الـC و الـK؟ من هنا الـC مباشرة تقدر تاخدها
+
+491
+00:38:45,790 --> 00:38:52,610
+من الـcoefficient بتاعت N هنا. طيب وين الـorder N
+
+492
+00:38:52,610 --> 00:38:56,810
+هنا؟ هيها.  قديش الـcoefficient تبعها؟ 30. معناته
+
+493
+00:38:56,810 --> 00:39:04,070
+الـC بتساوي الـcoefficient زائد واحد. زائد
+
+494
+00:39:04,070 --> 00:39:10,030
+واحد. طيب، الـK، قيمة الـshift، 8. 8
+
+495
+00:39:10,030 --> 00:39:13,110
+بالمعادلات.
+
+496
+00:39:13,110 --> 00:39:15,230
+خليني أنا أعمل check، هل فعلاً تحقق الـcondition
+
+497
+00:39:15,230 --> 00:39:20,230
+تبعنا ولا لأ. بدنا نتأكد. خليني أقول: let C = 31.
+
+498
+00:39:20,230 --> 00:39:31,470
+عرفنا ليش؟ أقل رقم بيحقق
+
+499
+00:39:31,470 --> 00:39:35,050
+المعادلة، أقل رقم بيحقق المعادلة.
+
+500
+00:39:42,870 --> 00:39:45,970
+31. قلنا: لأ، الـcoefficient تبع N هنا، احنا بنتكلم عن
+
+501
+00:39:45,970 --> 00:39:49,770
+الـfirst order، صح؟ طب وين الـcoefficient تبع الـ
+
+502
+00:39:49,770 --> 00:39:53,410
+first order في المعادلة؟ إيه اللي هو 30، فهذا
+
+503
+00:39:53,410 --> 00:39:58,030
+بنزوده: 31. يعني كأنه بدور على أقل رقم يكون أكبر
+
+504
+00:39:58,030 --> 00:40:01,770
+منها. أقل رقم يكون أكبر منها. أنتم في الآخر ممكن
+
+505
+00:40:01,770 --> 00:40:06,350
+تفترضوا 35، هيمشي الحال. المهم احنا كل الفكرة أن
+
+506
+00:40:06,350 --> 00:40:12,700
+there exist K و C. مجرد أنه في رقم حقق المعادلة
+
+507
+00:40:12,700 --> 00:40:16,920
+بكفي. أنا من عندي بحاول افترضه أنه أقل رقم ممكن
+
+508
+00:40:16,920 --> 00:40:21,640
+اللي أقل منه مش هتصحح المعادلة. بس هو الحد الفاصل.
+
+509
+00:40:21,640 --> 00:40:25,940
+أنتم ممكن في الآخر تفترضوه مثلاً C بـ60، و الـK تعمله
+
+510
+00:40:25,940 --> 00:40:29,840
+10. هتتحقق باريحية كبيرة جداً المعادلة. معاكم هتلاقوا
+
+511
+00:40:29,840 --> 00:40:33,500
+أن المعادلة هتتحقق باريحية كبيرة. احنا هنا زي ما
+
+512
+00:40:33,500 --> 00:40:38,500
+بقوله بالظبط، حوالين بالظبط اللي أكبر من، أقل قيمة
+
+513
+00:40:38,500 --> 00:40:42,500
+ممكنة للـC و الـK. تمام، هذه الـC، 31، K، 8،
+
+514
+00:40:42,500 --> 00:40:48,100
+أسيوم لكل قيم N اللي أكبر من K، المفروض يتحقق الـ
+
+515
+00:40:48,100 --> 00:40:54,300
+condition. لكل قيم K اللي أكبر من 8. فاحنا نقول
+
+516
+00:40:54,300 --> 00:40:59,280
+هنا for N أكبر من K، يعني أكبر من 8. طيب، نمسك
+
+517
+00:40:59,280 --> 00:41:04,000
+الـterm هذا، لأن احنا بدنا نحقق هذه الشرطة. بدنا
+
+518
+00:41:04,000 --> 00:41:10,120
+نثبت أن فيه C و فيه K بيحققوا لنا الشرط هذه. أن N، لكل N
+
+519
+00:41:10,120 --> 00:41:15,560
+أكبر من K. هذا الشرط ده. هنمسك الشرط هذا. هاي الـC N،
+
+520
+00:41:15,560 --> 00:41:19,640
+هاي الـC N، الـC احنا فرضناها قديش؟ واحد و تلاتين. طيب،
+
+521
+00:41:19,640 --> 00:41:24,100
+ما هذه؟ بقدر أقول أن هي 30 زائد N، صحيح؟ طيب هذه
+
+522
+00:41:24,100 --> 00:41:29,840
+أكيد أكبر من 30 N، لأن هذه بتساوي هذه، أكبر من
+
+523
+00:41:29,840 --> 00:41:33,380
+30 N زائد 8. باعتبار أن أنا بتكلم على كل
+
+524
+00:41:33,380 --> 00:41:39,090
+قيم N اللي أكبر من 8. فالـN أكيد أكبر من 8.
+
+525
+00:41:39,090 --> 00:41:50,550
+صح؟ فإذا 30 N زائد 8 أقل من 31 N، فحقق الشرط.
+
+526
+00:41:50,550 --> 00:41:54,950
+يكفيني من الشرط أن يوجد رقمين حققوا ليّا. مدام يوجد
+
+527
+00:41:54,950 --> 00:41:59,570
+رقمين حققوا، فإذا هي فعلاً الـfunction هذه first
+
+528
+00:41:59,570 --> 00:42:06,590
+order أو big O of N first، أو أقل. first أو أقل أو
+
+529
+00:42:06,590 --> 00:42:12,470
+تتناسب، let's say proportional مع الـfirst order.
+
+530
+00:42:12,470 --> 00:42:15,450
+تتناسب مع الـfirst order. نفس الكلام ممكن نعمله
+
+531
+00:42:15,450 --> 00:42:22,210
+لمن؟ للتربيعية. التربيعية هنا. C كم ممكن تقترحوها؟
+
+532
+00:42:25,250 --> 00:42:29,530
+هي N تربيع، و N تربيع، قديش الـcoefficient هنا؟ C
+
+533
+00:42:29,530 --> 00:42:36,610
+قديش؟ نعملها 2 زائد 1، 1 زائد 1. فـC بتساوي 2. طيب K
+
+534
+00:42:36,610 --> 00:42:42,970
+بـ1. هدول أقل رقمين ممكن تختاروهم. ممكن تختاروا
+
+535
+00:42:42,970 --> 00:42:46,870
+أكبر، ممكن تختاروا أكبر، هتلاقوا إنه برضه هتتحقق الـ
+
+536
+00:42:46,870 --> 00:42:51,350
+equation، و هتتحقق بزيادة. يعني هيكون الفرق كمان في
+
+537
+00:42:51,350 --> 00:42:57,090
+أكبر منه بزيادة. حنشوف: there exists C, K for all N
+
+538
+00:42:57,090 --> 00:43:03,210
+أكبر من K، يعني لكل قيم N أكبر من 1، لكل قيم N أكبر
+
+539
+00:43:03,210 --> 00:43:07,570
+من 1. فإذا N لازم تكون أكبر من 1 عشانها أكبر من
+
+540
+00:43:07,570 --> 00:43:12,970
+K. نمسك هذه: C N تربيع. نمسك C N تربيع، و C حاطينها بـ2.
+
+541
+00:43:12,970 --> 00:43:17,590
+2 N تربيع. عبارة عن N تربيع زائد N تربيع. أكبر من N
+
+542
+00:43:17,590 --> 00:43:21,470
+تربيع زائد 1، على اعتبار أن الـN قلنا أكبر من
+
+543
+00:43:21,470 --> 00:43:23,950
+1. مدام أكبر من 1، التربيع تبعها أكبر من 1.
+
+544
+00:43:23,950 --> 00:43:28,210
+مدام قيمة أكبر من 1، تربيعها أكيد أكبر من 1.
+
+545
+00:43:28,210 --> 00:43:32,890
+فأكيد الـterm هذا أكبر من الـterm هذا. فإذا الـN
+
+546
+00:43:32,890 --> 00:43:37,530
+تربيع زائد 1 أقل من C N تربيع. حققنا الـ
+
+547
+00:43:37,530 --> 00:43:40,950
+condition. مدام أقل من C N تربيع، معناته هي ضمن الـ
+
+548
+00:43:40,950 --> 00:43:46,130
+order تربيعية. الـfunction هي ضمن الـorder تربيعية، فبقدر
+
+549
+00:43:46,130 --> 00:43:52,090
+أقول اللي هي big O of N square، و أنا مرتاح. okay.
+
+550
+00:43:52,090 --> 00:44:01,950
+هاي الشكل تبعنا. لو اتكلمنا عن 30
+
+551
+00:44:01,950 --> 00:44:06,670
+N زائد 8. طب وين الرقم اللي فعلاً قلت لكم K و
+
+552
+00:44:06,670 --> 00:44:09,670
+مش K و مش عارف إيش و بقى أكبر من K، المعادلة
+
+553
+00:44:09,670 --> 00:44:14,470
+دائماً أقل من N تربيع، من الـN، من O، big O of N. لحظة
+
+554
+00:44:14,470 --> 00:44:22,330
+أنه هادي N مش 31 N. 31 N، قديش تطلع؟ واحد و تلاتين N.
+
+555
+00:44:22,330 --> 00:44:24,790
+واحد و تلاتين N، هترسم معاكم بهذا الشكل.
+
+556
+00:44:27,750 --> 00:44:32,490
+هتكون هذه 31 N. بعد قيمة معينة، عن نقطة معينة اللي
+
+557
+00:44:32,490 --> 00:44:40,130
+هو عن 8. هتلاقوا دائماً 31 N أكبر من 30 N زائد 8. أكبر
+
+558
+00:44:40,130 --> 00:44:45,450
+من 30 N زائد 8. فبيكون لكل N اللي أكبر من 8، دائماً
+
+559
+00:44:45,450 --> 00:44:50,370
+linear. فإذا الـfunction كلها على بعض linear. تصور
+
+560
+00:44:50,370 --> 00:44:51,450
+مرسومة؟ اه مرسومة.
+
+561
+00:44:59,730 --> 00:45:04,850
+K. فكل الجزء اللي أكبر من 8 ينطبق عليه الـ
+
+562
+00:45:04,850 --> 00:45:08,810
+condition. بنقدر ساعتها نقول أن: اه والله في موجود
+
+563
+00:45:08,810 --> 00:45:14,870
+أو في وجود لـK و الـC. مدام موجودة automatically.
+
+564
+00:45:14,870 --> 00:45:22,750
+المعادلة هي دي. بقول: belong to O of N، أو is O of N.
+
+565
+00:45:22,750 --> 00:45:26,770
+زي ما بتكون، خدوا لكم أي مسمى من مسميات متوسطة منها.
+
+566
+00:45:27,540 --> 00:45:32,100
+تمام. هلوجد مجموعة rules، مجموعة facts، مجموعة
+
+567
+00:45:32,100 --> 00:45:37,220
+relations مهمة ممكن تتعاملوا معاها، خاصة بالـbig
+
+568
+00:45:37,220 --> 00:45:43,880
+بالـbig O، خاصة بمين؟ بالـbig O. أول شغلة هي
+
+569
+00:45:43,880 --> 00:45:47,140
+transitive. إيش يعني transitive؟ يعني لو قلنا if
+
+570
+00:45:47,140 --> 00:45:55,450
+relation مع G. باعتبار أن الـF belong to big O G. Big
+
+571
+00:45:55,450 --> 00:46:05,190
+O of G. يعني واضح أن F نفس order G أو أقل، و G نفس
+
+572
+00:46:05,190 --> 00:46:12,490
+order H أو أقل. معناته G belong to big O of H. هذا
+
+573
+00:46:12,490 --> 00:46:18,900
+هيقودنا تماماً أن F برضه big O of H. Big O of H.
+
+574
+00:46:18,900 --> 00:46:23,380
+Transitive، أو انتقالية. يعني الـrelation هنا مع الـ
+
+575
+00:46:23,380 --> 00:46:28,440
+relation هنا. إذا كان الـF أقل من G، و الـG أقل من H،
+
+576
+00:46:28,440 --> 00:46:33,780
+فبالضرورة F أقل من H. صحيح؟ بالضرورة هتكون أقل منها
+
+577
+00:46:33,780 --> 00:46:38,300
+أو تساوي بالكثير. كويس. هاي أول relation. relation
+
+578
+00:46:38,300 --> 00:46:42,480
+الثانية: big O with constant. سواء هيكون مضروب أو
+
+579
+00:46:42,480 --> 00:46:47,160
+root أو log. بدنا نشوف كيف نتعامل مع الـconstants.
+
+580
+00:46:47,160 --> 00:46:52,300
+أول شغلة: إذا ضربناها ضرب مباشرة، بقى constant A،
+
+581
+00:46:52,300 --> 00:46:57,140
+و هذه. قلنا أن الـconstant A و B هدول constants، بيـ
+
+582
+00:46:57,140 --> 00:47:00,180
+بس هتكون أكبر من صفر، أكبر أو تساوي صفر، أكبر أو
+
+583
+00:47:00,180 --> 00:47:08,660
+تساوي صفر. لو قلنا F big O of F. Big O of F. معناته
+
+584
+00:47:08,660 --> 00:47:13,920
+الـfunction F لها نفس الـorder. طب لو انضربت في a
+
+585
+00:47:13,920 --> 00:47:18,380
+constant، مجرد constant، حضرت، هي هي برضه belonged to
+
+586
+00:47:18,380 --> 00:47:24,020
+big O of F. زي لما تقولوا N هي first order. طب meet
+
+587
+00:47:24,020 --> 00:47:28,950
+N برضه first order. السلوك بس اللي اتغير، سلوب تبعها
+
+588
+00:47:28,950 --> 00:47:32,670
+فقط اللي اتغير. أما ما اتغيرش شيء، هتظل نفس الـorder.
+
+589
+00:47:32,670 --> 00:47:37,550
+فهي مجرد أضرب الـfunction في constant، هتظل نفس الـ
+
+590
+00:47:37,550 --> 00:47:43,290
+function. طيب، F هذه الـcondition تبعنا، بس اللي بدنا
+
+591
+00:47:43,290 --> 00:47:52,470
+ناخد بالنا منه هنا. نرجع له: small omega of 1، big
+
+592
+00:47:52,470 --> 00:48:02,560
+O of N. إيش معناه؟ لما أقول: if بتساوي big O of N،
+
+593
+00:48:02,560 --> 00:48:08,060
+معناها أن الـfunction هذه الـorder تبعها linear أو
+
+594
+00:48:08,060 --> 00:48:20,280
+أقل. صح؟ أو أقل. طيب، if تساوي small O of N، معناها if
+
+595
+00:48:20,280 --> 00:48:28,800
+الـorder تبعها أقل من N، لا يساوي N، لا يساوي N، أقل
+
+596
+00:48:28,800 --> 00:48:33,980
+من N. يعني ممكن التربيعية، اللي لو قلنا 3 N
+
+597
+00:48:33,980 --> 00:48:43,480
+plus 7، ممكن أقول عنها is small o of N تربيع، بس
+
+598
+00:48:43,480 --> 00:48:49,360
+بقولش small n of N، لأن أنا عارف إنها first order.
+
+599
+00:48:50,260 --> 00:48:55,300
+هنا الـsmall o أقل من first order. تعريفها أقل من
+
+600
+00:48:55,300 --> 00:49:04,900
+first order. تمام. هاي الثانية، الثالثة: big omega، big
+
+601
+00:49:04,900 --> 00:49:12,300
+omega of N. معناته الـorder تبع F أكبر من أو يساوي
+
+602
+00:49:12,300 --> 00:49:17,160
+N، اللي هو first order. يعني first order أو أكبر.
+
+603
+00:49:18,880 --> 00:49:24,620
+first order أو أكبر. اكتبوا عندكم. ممكن نضطر نحتاجهم.
+
+604
+00:49:24,620 --> 00:49:27,380
+وإن كان هي الـbig O هي الأكثر استخداماً، يعني أكثر
+
+605
+00:49:27,380 --> 00:49:30,780
+استخداماً. بس أنا مضطر أستخدمها لغة أشرح لكم إياها، علشان تطلع
+
+606
+00:49:30,780 --> 00:49:35,060
+النتيجة، عشان نفهمها الشيء هذا. بس تمام، فعشان نفهمها،
+
+607
+00:49:35,060 --> 00:49:42,620
+بدنا نحطهم كلهم و نخلص. طيب، هذه الـbig omega. طيب، الـ
+
+667
+00:54:47,200 --> 00:54:56,880
+of F جي أقل من أو تساوي ال order تبع f وال h برضه
+
+668
+00:54:56,880 --> 00:55:02,080
+أقل من أو تساوي ال order تبع f فمجموع الاتنين g و h
+
+669
+00:55:02,080 --> 00:55:08,300
+برضه هيكون ضمن التعريف يعني first order زائد first
+
+670
+00:55:08,300 --> 00:55:12,580
+order هيظل first order هيظل first order second
+
+671
+00:55:12,580 --> 00:55:16,300
+order زائد first order second order المهم أنه مش
+
+672
+00:55:16,300 --> 00:55:19,460
+هيزيد عن أي واحدة منهم مدام summation مش هيزيد عن أي
+
+673
+00:55:19,460 --> 00:55:26,420
+واحدة منهم هيظل ال order هو order واحدة منهم اللي
+
+674
+00:55:26,420 --> 00:55:33,960
+هي الأكبر اللي هي الأكبر okay بنكمل برضه بمجموعة
+
+675
+00:55:33,960 --> 00:55:39,620
+facts about ال big O for all c أكبر من صفر
+
+676
+00:55:39,620 --> 00:55:42,580
+constant مجرد constant ال constant هذا ضربناه في
+
+677
+00:55:42,580 --> 00:55:50,240
+ال function مش هيتغير هتظل برضه big O of F طيب
+
+678
+00:55:50,240 --> 00:55:59,550
+جمعنا لما تقولوا N belong to O of N first طيب بفرق
+
+679
+00:55:59,550 --> 00:56:03,530
+لو قولنا ثلاثة N ما هي برضه belong to first order
+
+680
+00:56:03,530 --> 00:56:09,650
+نفس الكلام لو قولنا ثلاثة N زائد C كمان زائد خمسة
+
+681
+00:56:09,650 --> 00:56:16,070
+first order طيب ناقص عشرة نفس الكلام first order
+
+682
+00:56:17,410 --> 00:56:22,470
+نفس الفكرة ف constant ضربناه أو جمعناه أو طرحناه
+
+683
+00:56:22,470 --> 00:56:25,270
+على ال function مش هيغير ال order تاع ال function
+
+684
+00:56:25,270 --> 00:56:34,210
+مدام constant مدام رقم ثابت okay if one belong to
+
+685
+00:56:34,210 --> 00:56:40,430
+O of G1 هذا إيه ال order ال order تبع F1 هو order
+
+686
+00:56:40,430 --> 00:56:46,790
+G أو أقل and F2 function مختلفة belong to O ل
+
+687
+00:56:46,790 --> 00:56:53,270
+order مختلف هدول إختلفت ال orders F1 غير F2 G1
+
+688
+00:56:53,270 --> 00:57:00,110
+غير G2 طيب لما أقول F1 في F2 F1 مضروبة في F2 belong
+
+689
+00:57:00,110 --> 00:57:05,370
+to big O of G1 مضروبة في G2 زي لما نقول first
+
+690
+00:57:05,370 --> 00:57:15,230
+order في second order لأ third في ضرب ضرب مضروب
+
+691
+00:57:15,230 --> 00:57:19,210
+ضرب لما تكون عندكوا N تربيع زائد واحد مضروبة في
+
+692
+00:57:19,210 --> 00:57:26,090
+N هيصير في عندكوا N تكعيب زائد N هنا صارت mean
+
+693
+00:57:26,090 --> 00:57:31,630
+third order صارت هنا third order فنفس الكلام بدنا
+
+694
+00:57:31,630 --> 00:57:34,090
+نضرب ال orders بتاعتهم .. بدنا نضرب ال orders
+
+695
+00:57:34,090 --> 00:57:37,810
+بتاعتهم واحدة مثلاً ال order الخامس ال five order
+
+696
+00:57:37,810 --> 00:57:41,150
+مضروبة في
+
+697
+00:57:42,360 --> 00:57:51,300
+fourth order تسعة تسعة تسعة تسعة تسعة
+
+698
+00:57:51,300 --> 00:57:55,080
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+699
+00:57:55,080 --> 00:57:56,980
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+700
+00:57:56,980 --> 00:57:57,480
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+701
+00:57:57,480 --> 00:57:57,860
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+702
+00:57:57,860 --> 00:57:58,300
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+703
+00:57:58,300 --> 00:58:01,260
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+704
+00:58:01,260 --> 00:58:08,290
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسfirst
+
+705
+00:58:08,290 --> 00:58:11,630
+order زائد second order مين الأكبر؟ ال second
+
+706
+00:58:11,630 --> 00:58:14,670
+معناته مجموعهم بيعطينا second order مجموعهم
+
+707
+00:58:14,670 --> 00:58:18,170
+بيعطي second order اللي لو بده يجمعهم هدول مش
+
+708
+00:58:18,170 --> 00:58:22,570
+هيتغير هتظل خمسة هتظل ال order تبعنا خمسة طيب
+
+709
+00:58:22,570 --> 00:58:29,110
+بناخد مين منهم ال big G1 من الاتنين أمتى باخد G1؟
+
+710
+00:58:29,110 --> 00:58:34,530
+إذا كانت G2 belonged to big O G1 بمعنى أن ال G1 هي
+
+711
+00:58:34,530 --> 00:58:40,190
+الأكبر أو تساوي G1 أكبر أو تساوي فهنا بالظبط كأنه
+
+712
+00:58:40,190 --> 00:58:51,470
+ال G1 هي ال big O of N to the power 5 هي
+
+713
+00:58:51,470 --> 00:58:56,470
+الأكبر من to the power 4 فهي اللي بناخدها طبعاً
+
+714
+00:58:56,470 --> 00:59:01,130
+واضح جداً أنه بقدر ببساطة أقول أن ال N to the power
+
+715
+00:59:01,130 --> 00:59:07,710
+4 هي big O of N to the power 5 صحيح فهي هي نفسها
+
+716
+00:59:07,710 --> 00:59:14,570
+هي belong belong هذه هي نفسها دي فاللي هنختارها
+
+717
+00:59:14,570 --> 00:59:19,790
+فعلاً هي ال n to the power four اللي هي جي واحد جي
+
+718
+00:59:19,790 --> 00:59:27,450
+واحد كويس مجموعة
+
+719
+00:59:27,450 --> 00:59:30,190
+ال facts هي نفسها هي نفس اللي إحنا خدناهم هدول
+
+720
+00:59:30,190 --> 00:59:36,430
+أيه نفسهم لو ما نضرب function في constant هيظل نفس
+
+721
+00:59:36,430 --> 00:59:41,590
+ال function هو معاه example ثلاثة X تربيع برضه ال
+
+722
+00:59:41,590 --> 00:59:47,030
+second order برضه second order لو قولنا F plus big
+
+723
+00:59:47,030 --> 00:59:52,050
+O of F هي نفس big O of F لاحظوا هنا ال order هو ال
+
+724
+00:59:52,050 --> 00:59:54,830
+order ال function طبعاً هنا مدخل نفس ال function
+
+725
+00:59:55,390 --> 00:59:59,590
+يعني معناته ال orders متشابهة ال orders متشابهة
+
+726
+00:59:59,590 --> 01:00:04,490
+هنا قد تكون big O هذه إما نفس ال order أو أقل أو
+
+727
+01:00:04,490 --> 01:00:12,310
+أقل فهنا F تربيعية big O of F ممكن تكون إما تربيع
+
+728
+01:00:12,310 --> 01:00:15,430
+أو first order إما second order أو first order فلو
+
+729
+01:00:15,430 --> 01:00:18,910
+إفترضنا first order هيظل تربيع هيظل نفس ال order
+
+730
+01:00:18,910 --> 01:00:22,550
+تبع مين بتاع ال function هيظل نفس ال order ال
+
+731
+01:00:22,550 --> 01:00:27,070
+function كويس خلي هدول للمرة الجاية عشان إيش
+
+732
+01:00:27,070 --> 01:00:31,050
+نراجع فيهم برضه، كويس إن بيظلوا موجودين نراجعهم،
+
+733
+01:00:31,050 --> 01:00:36,950
+فضل ال order إحنا بدأنا محاضرتنا لما بدأت أنا
+
+734
+01:00:36,950 --> 01:00:39,410
+ما بدأت في ال order عارفة؟ اتكلمتلكوا شوية عن ال
+
+735
+01:00:39,410 --> 01:00:42,750
+complexity ال complexity عشان أحسبها بحسبها من
+
+736
+01:00:42,750 --> 01:00:49,060
+هنا، بحسبها أنه ال function بتاعتنا big of إيش بشوف
+
+737
+01:00:49,060 --> 01:00:52,800
+ال order تبع ال .. ال code الأول و ال order بتاع
+
+738
+01:00:52,800 --> 01:00:57,700
+ال code الثاني ال order الأقل هو اللي باخده مين ال
+
+739
+01:00:57,700 --> 01:01:00,740
+order تبعه أقل هو اللي بناخده بنقول لأ هذا ال code
+
+740
+01:01:00,740 --> 01:01:05,360
+أفضل more efficient للشغل اللي .. أو لل task
+
+741
+01:01:05,360 --> 01:01:08,180
+اللي بنشتغل عليها لل task اللي بنشتغل عليها على
+
+742
+01:01:08,180 --> 01:01:10,080
+بركة الله يعطيكم العافية و نشوفكم المرة الجاية إن
+
+743
+01:01:10,080 --> 01:01:10,300
+شاء الله
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c8199477d98edf04e5421cdc9f7f96f7f2149f17
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_postprocess.srt
@@ -0,0 +1,2972 @@
+1
+00:00:20,770 --> 00:00:23,090
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,090 --> 00:00:25,970
+الأنبياء والمرسلين سيدنا محمد وعلى أليه وصحبيه
+
+3
+00:00:25,970 --> 00:00:30,470
+أشمين بدأنا المرة اللي فاتت مع ال algorithms
+
+4
+00:00:30,470 --> 00:00:34,170
+واتكلمنا كيف ممكن نعمل code واتكلمنا عن ال
+
+5
+00:00:34,170 --> 00:00:37,070
+language المتعرف عليها اللي هنشتغل عليها اللي هي
+
+6
+00:00:37,070 --> 00:00:40,670
+ال pseudocode ال algorithm اللي هنكتب فيها ال
+
+7
+00:00:40,670 --> 00:00:45,530
+algorithms بتاعتنا خلال ال courseوصلنا لشوية
+
+8
+00:00:45,530 --> 00:00:49,350
+examples أخدنا ال searching و اتكلمنا عن نوعين او
+
+9
+00:00:49,350 --> 00:00:52,790
+two codes او two algorithms مشهورين جدا اللي هو ال
+
+10
+00:00:52,790 --> 00:00:57,370
+linear search و ال binary search وصلنا لعملية ال
+
+11
+00:00:57,370 --> 00:01:01,770
+sorting لانه لما كنا بنعمل searching حقيقة كنا
+
+12
+00:01:01,770 --> 00:01:06,580
+بنعمل searching على order او ordered listطيب ممكن
+
+13
+00:01:06,580 --> 00:01:10,040
+تجيكوا list مش ordered أساسا يعني ممكن أساسا تكون
+
+14
+00:01:10,040 --> 00:01:15,320
+unordered list أرقام عشوائية مبعثرة مش مرتبة لا ات
+
+15
+00:01:15,320 --> 00:01:18,760
+زد ولا زد ايه ولا يعني لا هى تصعدي ولا هى تنازلي
+
+16
+00:01:18,760 --> 00:01:23,480
+فبدنا نعمل code يعملنا الموضوع هذا هو يعملنا عملية
+
+17
+00:01:23,480 --> 00:01:29,180
+sorting عملية تصنيف عملية ترتيباتكلمنا عن نوعين
+
+18
+00:01:29,180 --> 00:01:32,220
+المرة اللى فاتت قولنا هنتكلم عن نوعين النوع الاول
+
+19
+00:01:32,220 --> 00:01:39,160
+ال bubble sort و ال insertion sort بداية ال bubble
+
+20
+00:01:39,160 --> 00:01:43,940
+sort code بالشكل اللى احنا شايفينه او sequence
+
+21
+00:01:43,940 --> 00:01:48,210
+بهذا الشكل اللى احنا شايفينه هذا هو ال sequenceالـ
+
+22
+00:01:48,210 --> 00:01:52,730
+left sequence هو ال initial sequence تبعنا بداية
+
+23
+00:01:52,730 --> 00:01:55,950
+ال sequence كيف جاي ترتيبه جاي ترتيبه تلاتين و
+
+24
+00:01:55,950 --> 00:01:58,550
+واحد و تلاتين و واحد و تلاتين و تلاتين و تلاتين و
+
+25
+00:01:58,550 --> 00:01:59,870
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+26
+00:01:59,870 --> 00:02:02,110
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+27
+00:02:02,110 --> 00:02:02,130
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+28
+00:02:02,130 --> 00:02:02,310
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+29
+00:02:02,310 --> 00:02:07,830
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+30
+00:02:07,830 --> 00:02:13,250
+تلاتين و تلاتين و
+
+31
+00:02:19,170 --> 00:02:23,810
+وزنه بكون أقل فبطلع as a bubble كفقاعة هوة على
+
+32
+00:02:23,810 --> 00:02:26,490
+السطح لأ احنا ال code تبعنا رغم ان هو اسمه bubble
+
+33
+00:02:26,490 --> 00:02:30,010
+sort بس احنا هنشتغل على القيم الكبيرة من بداية ال
+
+34
+00:02:30,010 --> 00:02:34,770
+sequence يعني هنيجي نعمل عملية مقارنات عملية
+
+35
+00:02:34,770 --> 00:02:38,830
+المقارنات هذه بتبدأ من أول element في ال sequence
+
+36
+00:02:38,830 --> 00:02:42,310
+نبدأ بأول element في ال list بتاعتنا و بنعمله
+
+37
+00:02:42,310 --> 00:02:45,880
+مقارنة مع التانيفهيكون عندنا مقارنة أولى طيب
+
+38
+00:02:45,880 --> 00:02:50,920
+تلاتين واحد تلاتين دايما بنحاول نخلي الأقل في
+
+39
+00:02:50,920 --> 00:02:54,940
+الترتيب الأقل للأول طيب هنا عندنا location واحد
+
+40
+00:02:54,940 --> 00:02:58,160
+location اتنين location واحد أقل من location اتنين
+
+41
+00:02:58,160 --> 00:03:01,600
+فبنحط فيه الرقم الأقل فتلاتين واحد تلاتين مش
+
+42
+00:03:01,600 --> 00:03:07,080
+محتاجة تغيير ابنش بنعمل مقارنة مين ال location او
+
+43
+00:03:07,080 --> 00:03:08,680
+الرقم في ال location التاني مع الرقم في ال
+
+44
+00:03:08,680 --> 00:03:14,880
+location التالت واحد تلاتين مع واحدأه الواحد أقل
+
+45
+00:03:14,880 --> 00:03:21,140
+فبنعمل swap أو interchange بنعكس هذا مكان هذا و
+
+46
+00:03:21,140 --> 00:03:27,300
+هذا مكان هذا فهيبقى عكسه هنا كويس مدام عكسنا بده
+
+47
+00:03:27,300 --> 00:03:29,900
+يصير هنا عندي الواحد و هنا بده يصير الواحد تلاتين
+
+48
+00:03:29,900 --> 00:03:33,600
+بنقارنها لوجه التلاتة مع أربعة تلاتة مع أربعة و
+
+49
+00:03:33,600 --> 00:03:37,700
+واحد و تلاتين مع اتنين و تلاتين بتظل زي ما هي طيب
+
+50
+00:03:37,700 --> 00:03:41,660
+اتنين و تلاتين مع تلاتة و تلاتينتلاتة و تلاتين مع
+
+51
+00:03:41,660 --> 00:03:46,420
+اتنين سواب تصير هنا الاتنين و هنا تلاتة و تلاتين
+
+52
+00:03:46,420 --> 00:03:51,660
+طيب بنكمل لسه احنا مازلنا في اول مرحلة كل هذه لسه
+
+53
+00:03:51,660 --> 00:03:56,440
+مرحلة واحدة مرحلة أولى بقارن كل رقم مع اللي وراه
+
+54
+00:03:56,440 --> 00:03:59,000
+كل رقم مع اللي وراه كل element مع ال element اللي
+
+55
+00:03:59,000 --> 00:04:01,580
+بعده طيب صارت تلاتة و تلاتين مع اربعة و تلاتين
+
+56
+00:04:01,580 --> 00:04:06,370
+ثابتبعدين اربعة و تلاتين مع تلاتة سواب بتصير هنا
+
+57
+00:04:06,370 --> 00:04:09,950
+التلاتة و هنا الأربعة و تلاتين لاحظوا انه هو هذا
+
+58
+00:04:09,950 --> 00:04:13,230
+ال sequence صار بالشجرة بس انا لسه مخلصتش انا كل
+
+59
+00:04:13,230 --> 00:04:18,870
+اللي عملته ايش سويت اتجل element حطته في القاعبس
+
+60
+00:04:18,870 --> 00:04:24,930
+فعليا أول مرحلة أكبر رقم موجود حطيته في ال last
+
+61
+00:04:24,930 --> 00:04:27,890
+location حطيناه في ايش؟ في ال last location فصار
+
+62
+00:04:27,890 --> 00:04:30,230
+في ال last location هلوجد لما بدي أجي أعمل عدد
+
+63
+00:04:30,230 --> 00:04:32,770
+مقارنات، لاحظوا هنا واحد، اتنين، تلاتة، أربعة،
+
+64
+00:04:32,770 --> 00:04:37,150
+خمس، ستة، سبعة، تمانية ال N بتاعتنا بتمانية، عندنا
+
+65
+00:04:37,150 --> 00:04:42,010
+تمانية elements، صحيح؟ تمانية elements، محتاجين N
+
+66
+00:04:42,010 --> 00:04:44,230
+minus one comparisons
+
+67
+00:04:46,270 --> 00:04:53,830
+هذه مقارنة تنتين تلاتة أربعة خمسة ستة سبعة تمام؟
+
+68
+00:04:53,830 --> 00:04:59,490
+كويس آخر رقم هنا ثابت خلاص أنا من المرحلة الأولى
+
+69
+00:04:59,490 --> 00:05:02,870
+ثبتت أن هذا أكبر رقم موجود بقرنوه و بقرنوش كمان
+
+70
+00:05:02,870 --> 00:05:07,370
+مرة ففي المرحلة التانية كان عندي سبعة comparisons
+
+71
+00:05:07,370 --> 00:05:13,220
+بصيروا ستةبصير عندى واحد اتنين تلاتة اربع خمسة ستة
+
+72
+00:05:13,220 --> 00:05:15,740
+الاربعة و تلاتين لأ لان احنا عارفين من المرحلة
+
+73
+00:05:15,740 --> 00:05:17,840
+الأولى ان الاربعة و تلاتين هو اكبر رقم كان موجود
+
+74
+00:05:17,840 --> 00:05:24,140
+بدليل انه صفة في الاخر في قاع ال sequence تبعكم او
+
+75
+00:05:24,140 --> 00:05:28,260
+ال list بتاعتكم as a last element موجود في ال list
+
+76
+00:05:28,260 --> 00:05:34,240
+كويس اللي بعدها هتلاقوا صار اتنين صاروا تحت و مش
+
+77
+00:05:34,240 --> 00:05:36,760
+محتاجين يتقارنوا فيهم كمان مرة بتصير انك تشتغلوا
+
+78
+00:05:36,760 --> 00:05:42,580
+على خمسةcomparisons أربعة comparisons تلاتة
+
+79
+00:05:42,580 --> 00:05:50,960
+comparisons two comparisons و stop فلاحظوا حتى عدد
+
+80
+00:05:50,960 --> 00:05:56,020
+المقارنات اللي هتحتاجوها كل مرة بتجيل طيب فصار
+
+81
+00:05:56,020 --> 00:06:02,420
+عندنا عدد مقارنات بدنا نعملها في كل مرحلة و عندنا
+
+82
+00:06:02,420 --> 00:06:06,240
+أيش كمان عندنا عدد مراحلمرحلة أولى، مرحلة تانية،
+
+83
+00:06:06,240 --> 00:06:09,620
+مرحلة تالتة، مرابعة، خمسة، سادسة و لاحظوا أن عدد
+
+84
+00:06:09,620 --> 00:06:17,500
+المراحل برضه minus two هنا هتطلع فإحنا هنا هنعدلها
+
+85
+00:06:17,500 --> 00:06:22,620
+في ال code تبعنا لاحظوا ففي عندنا عدد مراحل و في
+
+86
+00:06:22,620 --> 00:06:27,860
+عندنا عدد conversions داخل كل مرحلة من مراحل الشغل
+
+87
+00:06:27,860 --> 00:06:32,640
+كويس هنبدأ مفهومها لوجة ال code ال sequence نفسه
+
+88
+00:06:32,640 --> 00:06:35,600
+كيف القالية نفسهاهلوجد مننا نعملها code نكتب لها
+
+89
+00:06:35,600 --> 00:06:42,040
+code نشتغل عليه نكتب
+
+90
+00:06:42,040 --> 00:06:46,100
+لنا code معين و نشتغل عليه طيب ال code هذا خلينا
+
+91
+00:06:46,100 --> 00:06:49,960
+نكتب معانا sequence على الجنب و نشتغله مع ال code
+
+92
+00:06:49,960 --> 00:06:53,640
+parallel مع ال code عشان نكون متابعين ال code كويس
+
+93
+00:06:53,640 --> 00:06:58,220
+مع real list مع قائمة بنجرب عليها خلينا نقول ان في
+
+94
+00:06:58,220 --> 00:07:04,510
+ال list بتاعتناsay مثلا خليني اقول طبعا احنا عرفنا
+
+95
+00:07:04,510 --> 00:07:07,770
+ال procedure و before sort على اساس انه هي الاسم
+
+96
+00:07:07,770 --> 00:07:10,910
+تبعنا ال procedure انا داخل هنا على algorithm على
+
+97
+00:07:10,910 --> 00:07:17,970
+code عرفناهم an element داخل list و سمنهم ايش real
+
+98
+00:07:17,970 --> 00:07:24,650
+numbers within أكبر من أو تساوي اتنين لان واحد بدي
+
+99
+00:07:24,650 --> 00:07:29,030
+اقارنه مع مينفخلاص هو sorted لحاله لحاله رقم واحد
+
+100
+00:07:29,030 --> 00:07:34,130
+رقمين بكون محتاج عملية comparison واحدة هم موجودين
+
+101
+00:07:34,130 --> 00:07:36,710
+الإتنين بعمل comparison بينهم مين الأقل بخلوه في
+
+102
+00:07:36,710 --> 00:07:40,530
+الأول بحطه في الأول طيب real numbers خليني أشوف
+
+103
+00:07:40,530 --> 00:07:43,610
+إنها مجموعة real numbers لو قلنا مثلا عندنا three
+
+104
+00:07:43,610 --> 00:07:52,790
+three point two مثلا و
+
+105
+00:07:52,790 --> 00:08:00,480
+two point fiveone point one three
+
+106
+00:08:00,480 --> 00:08:04,500
+point one احد اتنين اربعة اتنين اربعة اتنين اربعة
+
+107
+00:08:04,500 --> 00:08:06,400
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+108
+00:08:06,400 --> 00:08:07,360
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+109
+00:08:07,360 --> 00:08:09,280
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+110
+00:08:09,280 --> 00:08:11,420
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+111
+00:08:11,420 --> 00:08:24,320
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين ارب
+
+112
+00:08:25,350 --> 00:08:29,290
+لأربعة، واحد، اتنين، تلاتة، أربعة، خمسة، لأربعة،
+
+113
+00:08:29,290 --> 00:08:35,710
+تمام؟ كويس، هذه اللوب هذا هيعطينا المراحل اللي
+
+114
+00:08:35,710 --> 00:08:39,350
+هنشتغل عليها، أكم مرحلة أنا محتاجها، كانت مرحلة
+
+115
+00:08:39,350 --> 00:08:42,390
+اتنين، تلاتة، أربعة، خمسة، زي ما كان التو مرسومة،
+
+116
+00:08:42,390 --> 00:08:48,010
+طيب في فرد داخلي في كل مرحلة أكم comparison هنعمل،
+
+117
+00:08:48,010 --> 00:08:51,370
+بصبوت، طيب أكم comparison هنعمل برضه من واحد to N
+
+118
+00:08:51,370 --> 00:08:55,940
+minus Iليش؟ لأن في كل مرحلة هنجس عدد ال
+
+119
+00:08:55,940 --> 00:09:00,940
+conversions صح؟ جربناها وقلنا إن في كل مرحلة بتجل
+
+120
+00:09:00,940 --> 00:09:04,180
+عدد ال conversions اللي أنا محتاجها طيب فكل مرة
+
+121
+00:09:04,180 --> 00:09:07,560
+أول ما هنبدأ .. هنبدأ كان عندي تمانية صار بدي
+
+122
+00:09:07,560 --> 00:09:11,600
+محتاج سبعة conversions سبعة conversions فهبدأ to N
+
+123
+00:09:11,600 --> 00:09:16,620
+minus I I هنا واحد فانا في المرحلة الأولى محتاج N
+
+124
+00:09:16,620 --> 00:09:20,900
+minus onecomparisons طب فى المرحلة التانية minus
+
+125
+00:09:20,900 --> 00:09:26,020
+two بتكون هنا i صارت اتنين فى المرحلة الأخيرة n
+
+126
+00:09:26,020 --> 00:09:30,060
+minus one بتصير انا محتاج comparison واحدة لأنه
+
+127
+00:09:30,060 --> 00:09:33,680
+بيكون ضال رقمين بس بيكون ضال رقمين خلّينى نشوف
+
+128
+00:09:33,680 --> 00:09:37,980
+الكلام هذا فعلا على list موجودة جدامنا هنبدأ هنا ب
+
+129
+00:09:37,980 --> 00:09:43,940
+i بتساوي واحد فإذا two n minus one يعني مدى معنى
+
+130
+00:09:43,940 --> 00:09:47,320
+ذلك بتكلم عن ايش عن أربعة بتكلم عن أربعة هنا
+
+131
+00:09:47,320 --> 00:09:56,220
+وأربعة هناOkay أربعة و أربعة نبدأ if a one هاي ال
+
+132
+00:09:56,220 --> 00:10:01,360
+j بدينها بين واحد أكبر من j plus one أكبر من اتنين
+
+133
+00:10:01,360 --> 00:10:05,780
+فبشوف ال element الأول مع ال element التاني if ال
+
+134
+00:10:05,780 --> 00:10:08,640
+element الأول أكبر من ال element التاني نعمل
+
+135
+00:10:08,640 --> 00:10:13,740
+interchange swap بنبدلهم مع بعض كويس فلينا نشوف
+
+136
+00:10:13,740 --> 00:10:18,560
+هاي الأول و هاي التانيهل فعلا الأول أكبر من
+
+137
+00:10:18,560 --> 00:10:24,500
+التاني؟ الأول أكبر من التاني فالأول أكبر من التاني
+
+138
+00:10:24,500 --> 00:10:28,660
+في الحالة هذي بنقول على طول two point five و three
+
+139
+00:10:28,660 --> 00:10:34,840
+point two بهذا الشكل طيب خلصنا I بتساوي واحد I
+
+140
+00:10:34,840 --> 00:10:41,680
+بتساوي اتنين صار بقارن اتنين مع تلاتة هاي اتنين مع
+
+141
+00:10:41,680 --> 00:10:43,280
+تلاتة
+
+142
+00:10:44,880 --> 00:10:51,340
+3.2 مع 1.1 التاني أكبر من التالت فبنحط هنا التالت
+
+143
+00:10:51,340 --> 00:10:57,080
+بيصير هو التاني و التاني بيصير هو التالت طيب خلصنا
+
+144
+00:10:57,080 --> 00:11:05,180
+I سوى تلاتة صار بقارن تلاتة مع أربعة هي تلاتة واحد
+
+145
+00:11:05,180 --> 00:11:09,960
+اتنين هي تلاتة مع أربعة أكبر بدلناهم
+
+146
+00:11:14,800 --> 00:11:20,680
+خلاص اخر رقم اربعة اربعة اربعة
+
+147
+00:11:20,680 --> 00:11:23,920
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+148
+00:11:23,920 --> 00:11:24,080
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+149
+00:11:24,080 --> 00:11:24,480
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+150
+00:11:24,480 --> 00:11:26,660
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+151
+00:11:26,660 --> 00:11:26,880
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+152
+00:11:26,880 --> 00:11:28,000
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+153
+00:11:28,000 --> 00:11:34,400
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+154
+00:11:34,400 --> 00:11:39,600
+اربعة اربعة اربعة اربعة
+
+155
+00:11:39,600 --> 00:11:42,100
+اربعة
+
+156
+00:11:44,880 --> 00:11:48,400
+تنين هذا المفروض من واحد لاربعة احنا لسه ماوصلناش
+
+157
+00:11:48,400 --> 00:11:53,220
+لاربعة لسه اتنين اتنين معناته هنبدأ هنا من واحد
+
+158
+00:11:53,220 --> 00:11:59,120
+تخمسة minus اتنين لتلاتة لانه هحتاج تلاتة
+
+159
+00:11:59,120 --> 00:12:01,600
+conversions بس في المرحلة الأولى كنت محتاج اربعة
+
+160
+00:12:01,600 --> 00:12:05,360
+conversions واحدة اتنين تلاتة اربعة في المرحلة
+
+161
+00:12:05,360 --> 00:12:09,420
+التانية هنحتاج تلاتة بس ليش لان تلاتة فاصلة اتنين
+
+162
+00:12:09,420 --> 00:12:13,510
+هذه خلاص هتبقى ثابتة ومش هقارن فيها مرة تانيةقرننا
+
+163
+00:12:13,510 --> 00:12:18,070
+وما وصلها لل last location إلا إن هي أكبر رقم
+
+164
+00:12:18,070 --> 00:12:22,270
+موجود لو لإن هي أكبر رقم موجود كان ماوصلتش في ال
+
+165
+00:12:22,270 --> 00:12:27,850
+last location كويسة نشوف عند الواحد واحد مع اتنين
+
+166
+00:12:27,850 --> 00:12:35,110
+واحد مع اتنين one point one two point five طيب عند
+
+167
+00:12:35,110 --> 00:12:41,110
+الاتنين اتنين مع تلاتة اتنين مع تلاتة بيضلواخلاص
+
+168
+00:12:41,110 --> 00:12:47,450
+بتنزل زي ما هي طيب تلاتة مع أربعة تلاتة مع أربعة
+
+169
+00:12:47,450 --> 00:12:53,390
+swap خلاص
+
+170
+00:12:53,390 --> 00:12:59,090
+stop أنا وصلت التلاتة هذه بتبقى زي ما هي هتبقى
+
+171
+00:12:59,090 --> 00:13:03,710
+ثابتة لأنه ماوصلنالهاش في ال loop كويسة هيخلصنا
+
+172
+00:13:03,710 --> 00:13:10,530
+كمان مرة بنصل هنا لمين ل I بتساوي تلاتةصار هنا
+
+173
+00:13:10,530 --> 00:13:16,650
+كده؟ خمسة ناقص تلاتة اتنين مقارنة
+
+174
+00:13:16,650 --> 00:13:19,230
+محتاجة تقوم بارزوز اللي هنعملهم فعليا تقوم بارزوز
+
+175
+00:13:19,230 --> 00:13:24,610
+خلينا نشوف ا بواحد مع ا باتنين ا واحد أكبر من
+
+176
+00:13:24,610 --> 00:13:30,850
+اتنين؟ لأ بنزلوا زي ما هم طيب اتنين مع ا تلاتة
+
+177
+00:13:30,850 --> 00:13:31,430
+أكبر
+
+178
+00:13:38,400 --> 00:13:44,440
+و هدولة خلاص خلصنا اللوب بيظلوا زي ما هما خلصنا
+
+179
+00:13:44,440 --> 00:13:49,860
+هاي اللوب هادى هنرجع نطلع للوب العلوية جديش أربعة
+
+180
+00:13:49,860 --> 00:13:56,320
+آخر رقم عند I بتساوي أربعة طيب خمسة نقص أربعة واحد
+
+181
+00:13:58,080 --> 00:14:01,500
+خلاص انا هعمل مقارنة واحدة اللي هي بين اول اتنين
+
+182
+00:14:01,500 --> 00:14:10,300
+بس اول اتنين ماتغيروش بيظل 1.1 2.4 2.5 3.1 و 3.2
+
+183
+00:14:10,300 --> 00:14:18,980
+sorted list لحظة sorted عملنا لها sorting عملنا
+
+184
+00:14:18,980 --> 00:14:22,460
+لها ترتيب عملنا لها ترتيب في الحالة التاعتناها دي
+
+185
+00:14:22,460 --> 00:14:28,710
+okay واضح ليه ال codeواضح و انا فهمنا ليش n-i و
+
+186
+00:14:28,710 --> 00:14:33,710
+هذه نتيجة ان انا كل مرة في element بصفة في الآخر
+
+187
+00:14:33,710 --> 00:14:36,750
+مش محتاج راجع اقارن فيه لان انا قارنته في المرحلة
+
+188
+00:14:36,750 --> 00:14:39,170
+الأولى قارنناه في المرحلة الأولى مش هنقعد نقارن
+
+189
+00:14:39,170 --> 00:14:50,430
+فيه كمان مرة طيب هذه ال sort ال bubble sort خلوها
+
+190
+00:14:50,430 --> 00:14:52,070
+.. خلوها لكم
+
+191
+00:14:59,840 --> 00:15:03,320
+النوع التانى اللى هى insertion sort algorithm
+
+192
+00:15:03,320 --> 00:15:06,180
+insertion sort algorithm بيعتمد على عملية ال
+
+193
+00:15:06,180 --> 00:15:09,520
+search اللى أخدناها سابقا جماله كنا أخدنا search
+
+194
+00:15:09,520 --> 00:15:17,080
+سواء بال linear أو بال binary و خلينا نمسك برضه
+
+195
+00:15:17,080 --> 00:15:22,800
+نفس ال sequence تبعنا و نحاول نشتغل معاه الفكرة
+
+196
+00:15:22,800 --> 00:15:26,420
+كيف بتتم؟ بتتم انه انا بفترض في عندنا sequence انا
+
+197
+00:15:26,420 --> 00:15:30,610
+بدي أعمله creation انا بدي أنشئهبنبدأ بأول element
+
+198
+00:15:30,610 --> 00:15:38,170
+ال element الأول هنا بنحطه كأول element في ال set
+
+199
+00:15:38,170 --> 00:15:43,170
+هذه أو في ال list طيب ال element التاني بتعامل
+
+200
+00:15:43,170 --> 00:15:49,390
+معاه كأنه بيعمل search x مش كنا بنسميه في element
+
+201
+00:15:49,390 --> 00:15:53,110
+x وفي ال list و ال element x بدور عليه داخل ال
+
+202
+00:15:53,110 --> 00:15:56,410
+list عشان أعرف إيش ال location تبعه نعرف مين ال
+
+203
+00:15:56,410 --> 00:16:02,840
+location تبعه كويسةالـ X هذا اللي هو 2.5 هنقارنه
+
+204
+00:16:02,840 --> 00:16:10,000
+مع 3.2 إذا أقل بياخد ال location تبعها و بيعمل لها
+
+205
+00:16:10,000 --> 00:16:15,940
+shift إذا أقل بياخد ال location تبع الرقم اللي
+
+206
+00:16:15,940 --> 00:16:20,000
+جدامه اللي أكبر منه و بيعمل shift له لكل اللي وراه
+
+207
+00:16:20,000 --> 00:16:25,940
+فإذا هذه كانت A1ماكنش في عناقية 2 طب انا بده ادخل
+
+208
+00:16:25,940 --> 00:16:36,020
+2.5 فبندخل 2.5 و بنقارنها مع 3.2 3.2 أكبر معناته
+
+209
+00:16:36,020 --> 00:16:41,380
+هت سيب تتخلى عن مكانها وهذه هنعملها insertion
+
+210
+00:16:41,380 --> 00:16:44,940
+insertion
+
+211
+00:16:44,940 --> 00:16:51,390
+في ال location اللي ثابته 3.2بتصير هنا اتنين و نص
+
+212
+00:16:51,390 --> 00:16:54,850
+صار عندنا ال list بتاعتنا فيه two elements بنكرر
+
+213
+00:16:54,850 --> 00:17:00,590
+نفس الكلام على ال X الجديدة one point one برضه
+
+214
+00:17:00,590 --> 00:17:07,130
+عمليت search بعمل search على ال one point one one
+
+215
+00:17:07,130 --> 00:17:13,050
+point one one point one بالنسبة ل two point five
+
+216
+00:17:13,050 --> 00:17:17,550
+اقل اقل معناته CP لل location تبعيlocation تبحر
+
+217
+00:17:17,550 --> 00:17:20,470
+بسبب معناه ذلك ان كل هذا كل ال sequence اللى كان
+
+218
+00:17:20,470 --> 00:17:24,490
+موجود هنا كله بدى نعمله shift كانوا a2 بيصير ل a3
+
+219
+00:17:24,490 --> 00:17:31,710
+هدى صارت 3.2 2.5 shift لكل الأرقام اللى وراها و
+
+220
+00:17:31,710 --> 00:17:35,550
+هنا بنعملها insertion في ال location اللى جديد في
+
+221
+00:17:35,550 --> 00:17:43,750
+المكان اللى فضل okay اللى وراها 3.1 بنعمل مقارنة
+
+222
+00:17:43,750 --> 00:17:50,460
+مع ال 1.1هل هي أقل من .. لأ خلاص بتسيبها واضح أن
+
+223
+00:17:50,460 --> 00:17:54,100
+ال location هذا مش تبعها طيب بنشوف ال location
+
+224
+00:17:54,100 --> 00:18:01,940
+التاني 3.1 مع 2.3 لأالـ location هذا مش تبحها طيب
+
+225
+00:18:01,940 --> 00:18:08,400
+3.1 مع 3.2 أقل من .. مدام أقل من هذه لازم تشوف
+
+226
+00:18:08,400 --> 00:18:11,220
+location تاني يعملها shift على ال location اللي
+
+227
+00:18:11,220 --> 00:18:15,200
+وراها و بنعمل insertion لل X هذا اللي كنت بعمله ..
+
+228
+00:18:15,200 --> 00:18:18,480
+بعمله search عرفت كون المفروض ال location يكون
+
+229
+00:18:18,480 --> 00:18:21,160
+فبدخله في ال location طبعه و بعمله insertion في ال
+
+230
+00:18:21,160 --> 00:18:29,760
+location الطبيعي طبعه الصحيح كويسأخر رقم 2.4 2.4
+
+231
+00:18:29,760 --> 00:18:35,760
+برضه بنرجع بنقارنها مع طبعا احنا هنا ماكتبناش بس
+
+232
+00:18:35,760 --> 00:18:43,160
+32 أكبر من 1.1 فسيب ال 1.1 في حالها ماليناهش علاقة
+
+233
+00:18:43,160 --> 00:18:47,560
+فيها طيب 2.5 لأ أقل من 2.5 معناته ال location
+
+234
+00:18:47,560 --> 00:18:51,080
+تبعها هو هذا ال 2.5 مكان ال 2.5 المفروض ال
+
+235
+00:18:51,080 --> 00:18:56,550
+location التاني معناه ذلك منمن 2.5 كله هذا بدنا
+
+236
+00:18:56,550 --> 00:19:03,870
+نعمله shift نضغط فيه هنا A5 A5 هذه هتاخد الرقم
+
+237
+00:19:03,870 --> 00:19:08,190
+اللي كان في A4 A4 هينعملها shift بالرقم اللي كان
+
+238
+00:19:08,190 --> 00:19:14,750
+في A3 A3 هتاخد الرقم تبع A2 عشان نعمل insertion
+
+239
+00:19:14,750 --> 00:19:20,190
+لمن؟ للرقم الجديد نعمل insertion للرقم الجديد لحظة
+
+240
+00:19:20,190 --> 00:19:26,340
+انه برضه اترتبتترتب ال sequence عندكم ترتب ال
+
+241
+00:19:26,340 --> 00:19:31,840
+sequence عندكم تمام فهنا بتكلم برضه بتقدر تستخدم
+
+242
+00:19:31,840 --> 00:19:35,440
+اما ال linear او ال binary searchالطريقة اللى
+
+243
+00:19:35,440 --> 00:19:38,320
+بتحبى تستخدموها استخدموها اما تستخدموها انتوا فى
+
+244
+00:19:38,320 --> 00:19:42,180
+الآخر صارت عبارة عن search عبارة عن search X و
+
+245
+00:19:42,180 --> 00:19:44,460
+بتحاولوا تشوف وين ال location تبعه بتحاولوا تشوف
+
+246
+00:19:44,460 --> 00:19:48,160
+وين ال location تبعه فبتقدروا تشتغلوا على ال
+
+247
+00:19:48,160 --> 00:19:51,480
+linear او على ال binary و بعدين بتعملوا shift اذا
+
+248
+00:19:51,480 --> 00:19:57,100
+كان ال item او ال X اقل من قيمة ال element فى ال
+
+249
+00:19:57,100 --> 00:19:59,510
+locationقيمة ال element في ال location و بتعمله
+
+250
+00:19:59,510 --> 00:20:03,590
+shift ل ال item او ال element ب one position ب one
+
+251
+00:20:03,590 --> 00:20:08,510
+position على ال location اللي اعلى منه على ال
+
+252
+00:20:08,510 --> 00:20:10,790
+location اللي اعلى منه بحيث انه يصير في عندكوا هنا
+
+253
+00:20:10,790 --> 00:20:16,290
+فضاء hall ال hall هذا بتضيفه في ال new item اللي
+
+254
+00:20:16,290 --> 00:20:18,910
+هو ال x اللي بتدوروا عليها ال x اللي كنتوا بتعمله
+
+255
+00:20:18,910 --> 00:20:22,930
+ال search عليها هذا
+
+256
+00:20:22,930 --> 00:20:25,850
+كانت جزئية ضايلة من ال algorithm
+
+257
+00:20:31,220 --> 00:20:35,240
+بتاعتنا عشان نكمل برضه في ال algorithm بس عشان
+
+258
+00:20:35,240 --> 00:20:38,160
+أشتغل على ال algorithm محتاج أدرس حاجة اسمها ال
+
+259
+00:20:38,160 --> 00:20:44,960
+complexity complexity بمعنى أنه عندنا أكتر من code
+
+260
+00:20:44,960 --> 00:20:49,100
+ممكن يعملوا نفس ال task نفس ال task بس بدي أحسب ال
+
+261
+00:20:49,100 --> 00:20:53,960
+complexity للكل ليش؟ عشان أعرف أنه منهم أختار لأنه
+
+262
+00:20:53,960 --> 00:20:59,210
+ممكن جدا يكون عند codeتو code كل واحدة كتبت لنا
+
+263
+00:20:59,210 --> 00:21:02,290
+code أجي أفحصهم أعملهم analysis وهذا اللي بدنا
+
+264
+00:21:02,290 --> 00:21:06,010
+نتعلمه نعمل analysis لهم نطلع المعادلة بتاعة كل
+
+265
+00:21:06,010 --> 00:21:09,070
+واحد منهم معادلة إيش هنعرف احنا بنتكلم هنا عن
+
+266
+00:21:09,070 --> 00:21:14,130
+معادلة ال variable فيها عدد ال inputs variable عدد
+
+267
+00:21:14,130 --> 00:21:17,070
+ال inputs بحيث أنه كل ما زادت عدد ال inputs أكيد
+
+268
+00:21:17,070 --> 00:21:19,330
+هيزيد ال function في إيش أنا بدي أعملها ال
+
+269
+00:21:19,330 --> 00:21:23,130
+complexity في ال timeو رغم أنه طبعا في criteria
+
+270
+00:21:23,130 --> 00:21:26,430
+تانية ممكن اللي واحد يشتغل عليها زي ال energy، كم
+
+271
+00:21:26,430 --> 00:21:30,630
+تستهلك ال energy أو ال space بس احنا مش هنشتغل
+
+272
+00:21:30,630 --> 00:21:33,310
+فيهم هدول، هنخلق ال complexity بتاعتنا مفهومها
+
+273
+00:21:33,310 --> 00:21:36,610
+أكثر على ال time أنه code اللي بيستغرق ال time
+
+274
+00:21:36,610 --> 00:21:41,770
+أكبر عندنا two codes، باجي بحسب ال equation بتاعت
+
+275
+00:21:41,770 --> 00:21:43,830
+هذا مع ال equation بتاعت هذا ال equation ده إيش،
+
+276
+00:21:43,830 --> 00:21:47,980
+بتحسب ليه؟ بتحسب ال time variable في إيش؟أو
+
+277
+00:21:47,980 --> 00:21:51,960
+function في variable عبارة عن عدد ال inputs للكود
+
+278
+00:21:51,960 --> 00:21:56,020
+لأن كل ما زاد عدد ال inputs سيزيد ال time سيزيد
+
+279
+00:21:56,020 --> 00:21:59,640
+معاها ال time فبكون عملت equation أو formula ال
+
+280
+00:21:59,640 --> 00:22:02,480
+formula دي بنشوف ال complexity بتاعتها والله اللي
+
+281
+00:22:02,480 --> 00:22:05,880
+أعلى complexity بديش إياه لأنه معناه ذلك أنه
+
+282
+00:22:05,880 --> 00:22:11,100
+سيصغرق و أكبرهيستغرق وقت أكبر بظل بس كيف بدنا نعرف
+
+283
+00:22:11,100 --> 00:22:14,020
+أنه مين ال complexity أعلى بدنا نشوف كل equation
+
+284
+00:22:14,020 --> 00:22:18,540
+من اللي بيطلع هدولة هيتلعوا functions ال orders of
+
+285
+00:22:18,540 --> 00:22:23,780
+growth جديش معدل النمو لل function هذه و جديش معدل
+
+286
+00:22:23,780 --> 00:22:26,260
+النمو لل function هذه عشان نقول والله اللي معدل
+
+287
+00:22:26,260 --> 00:22:31,540
+نموه أعلى بمعنى بزود input واحد بزيد مقابله خمسة
+
+288
+00:22:31,540 --> 00:22:35,550
+في ال timeو فوق code تاني بزود input واحد بزيد
+
+289
+00:22:35,550 --> 00:22:39,450
+مقابله أربعة في ال time يعني ال time بتضعف أربع
+
+290
+00:22:39,450 --> 00:22:41,930
+مرات هنا بتضعف خمس مرات لا والله الخمس مرات مديش
+
+291
+00:22:41,930 --> 00:22:46,490
+يام لأنه ال order of growth معدل النمو تبعه أكبر
+
+292
+00:22:46,490 --> 00:22:53,090
+فهو faster أسرع أسرع بس أنا بدورش على أسرع احنا
+
+293
+00:22:53,090 --> 00:22:57,670
+بالعكس بدنا الأقل بدنا ال time complexity الأقلفال
+
+294
+00:22:57,670 --> 00:22:59,630
+time complexity قبل ما نبدأ نتكلم عن ال time
+
+295
+00:22:59,630 --> 00:23:02,850
+complexity بدنا نتكلم عن ال orders of growth كيف
+
+296
+00:23:02,850 --> 00:23:09,050
+بقدر أحسب ال order of growth و كيف ل codeين نحسب
+
+297
+00:23:09,050 --> 00:23:12,950
+ال order لهذا و لهذا عشان نقدر نقارنهم البعض ففي
+
+298
+00:23:12,950 --> 00:23:16,690
+جزئية هنا لازم نتكلم عنها اللي هي ال growth أو ال
+
+299
+00:23:16,690 --> 00:23:22,530
+orders of growth orders of growth كويسة الشكل اللي
+
+300
+00:23:22,530 --> 00:23:28,400
+قدامنا هناهنبدأ طبعا بناء على ال knowledge السابقة
+
+301
+00:23:28,400 --> 00:23:30,780
+اللي عندنا بناء على ال knowledge السابقة بقدر أقول
+
+302
+00:23:30,780 --> 00:23:34,400
+أن ال order تبعت المعادلة دي إيش طبعا هن .. هن ..
+
+303
+00:23:34,400 --> 00:23:37,800
+بعدين هنشرحها من وجه نظر ال discrete كيف بحسب ال
+
+304
+00:23:37,800 --> 00:23:41,580
+order بالظبط ولكن مبدأيا انتوا بتتكلموا هنا عن خط
+
+305
+00:23:41,580 --> 00:23:48,750
+مستقيمبغض النظر ان ال slope مختلف و ليس واحد مثلما
+
+306
+00:23:48,750 --> 00:23:53,810
+احنا نعرف ان ال slope مختلف ال shift ليس بعيد من
+
+307
+00:23:53,810 --> 00:23:58,230
+صفر صفر بل بعيد من صفر و تمانية بدا عن صفر و
+
+308
+00:23:58,230 --> 00:24:03,590
+تمانيةموجود عندنا بس في جميع الأحوال لو قلتلكوا
+
+309
+00:24:03,590 --> 00:24:06,770
+ايش ال order او اي درجة هذه المعادلة اللي هي 30n
+
+310
+00:24:06,770 --> 00:24:13,050
+plus تمانية الأولى الأولى هذه first order درجة
+
+311
+00:24:13,050 --> 00:24:15,190
+أولى احنا اين عرفناها درجة أولى من ال knowledge
+
+312
+00:24:15,190 --> 00:24:18,850
+السابق اتنى بس برضه هنعرف احنا كيف ممكن نشتغلها
+
+313
+00:24:18,850 --> 00:24:21,350
+بال discrete و اعرف جدتش ال order تبعها لإنه بده
+
+314
+00:24:21,350 --> 00:24:25,290
+اقارنها ب orders تانية بده نقارنها ب orders تانية
+
+315
+00:24:25,290 --> 00:24:30,920
+معادلة التانية هذهالمعادلة التانية هنا انتربيع
+
+316
+00:24:30,920 --> 00:24:36,940
+plus واحد انتربيع plus واحد وهي الشكل الشكل تبعها
+
+317
+00:24:36,940 --> 00:24:42,320
+طبعا واضح انه في shift بقيمة واحد قيمة ال shift
+
+318
+00:24:42,320 --> 00:24:45,560
+اللي موجود طيب الانتربيع واضح ان انا بتكلم عن
+
+319
+00:24:45,560 --> 00:24:50,040
+second order بتكلم عن second order okay في أجزاء
+
+320
+00:24:51,310 --> 00:24:55,330
+أقل وفي أجزاء أكبر طب أنا بشتغل عالمين عشان أقول
+
+321
+00:24:55,330 --> 00:24:58,350
+والله any order اللي أنا بنصبني أكتر دائما بندور
+
+322
+00:24:58,350 --> 00:25:04,250
+على K معينة ال K هذه قيمة قيمة N بمعنى عند عدد
+
+323
+00:25:04,250 --> 00:25:11,410
+users محدد معين هسميه K فال N هذه أكبر من K دائما
+
+324
+00:25:11,410 --> 00:25:14,370
+واحد منهم بيكون أكبر من الثاني فالأكبر هو ال
+
+325
+00:25:14,370 --> 00:25:19,550
+faster بسميه وهذا بديش إياه فواضح أن التربيع عنده
+
+326
+00:25:19,550 --> 00:25:26,570
+نقطة هذههنقول عليها K فكل N أكبر من K دائما
+
+327
+00:25:26,570 --> 00:25:30,470
+التربيع أكبر من ال linear دائما التربيع أكبر من ال
+
+328
+00:25:30,470 --> 00:25:33,910
+linear بغض النظر عن ال coefficient اللي مضروبة فيه
+
+329
+00:25:33,910 --> 00:25:37,610
+ال linear بس ال coefficient هذي فقط هتغيرلكوا وين
+
+330
+00:25:37,610 --> 00:25:42,050
+موجود التقاطع هذا بس دائما في قيمة ل K بعدها
+
+331
+00:25:42,050 --> 00:25:45,430
+التربيع دائما أكبر من ال linear دائما التربيع
+
+332
+00:25:45,430 --> 00:25:50,410
+بيكون أكبر من ال linear بعد قيمة معينة لهل N و
+
+333
+00:25:50,410 --> 00:25:56,990
+هنسميها K اللي هي النقطة هذه فإذا for all N أكبر
+
+334
+00:25:56,990 --> 00:26:01,130
+من K دائما
+
+335
+00:26:01,130 --> 00:26:06,650
+المعادلة بالخط الأحمر هذه بال red line هتكون أكبر
+
+336
+00:26:06,650 --> 00:26:11,830
+من ال black linesecond order دائما هتكون اكبر من
+
+337
+00:26:11,830 --> 00:26:15,150
+ال first order و هتلاقوا ان المعدل كبير جدا يعني
+
+338
+00:26:15,150 --> 00:26:17,370
+هنا كان الفرق بينهم بالشكل هذا هنا الفرق لحظوا
+
+339
+00:26:17,370 --> 00:26:21,870
+جداش صار و لسه ماصلنهاش شايفين جداش صار الفرق؟
+
+340
+00:26:21,870 --> 00:26:26,210
+معدل الفرق، معدل التغير فواضح انه المعادلة
+
+341
+00:26:26,210 --> 00:26:33,770
+التربعية أسرع أسرع بالنسبة لزيادة N من المعادلة ال
+
+342
+00:26:33,770 --> 00:26:37,230
+linear أو الخطية
+
+343
+00:26:42,540 --> 00:26:46,880
+كويس في الحلقة دي عشان نعرف كل واحدة منهم بنعرفها
+
+344
+00:26:46,880 --> 00:26:51,220
+بحاجة هنسميها ال order of growth ال .. هنقول ال
+
+345
+00:26:51,220 --> 00:26:56,160
+function الأولى هفترض انه هدى ال time ل code أول
+
+346
+00:26:56,160 --> 00:26:59,520
+ال code الأول جينا حسبناه لجينا ان ال complexity
+
+347
+00:26:59,520 --> 00:27:05,380
+تبعته تلتين and plus تمانية وال and هدى جدش عدد لو
+
+348
+00:27:05,380 --> 00:27:08,120
+بدنا نقول ان ال code هدى بيحسبلنا بيعملنا sorting
+
+349
+00:27:10,040 --> 00:27:14,720
+جديش عدد ال items اللي بدنا نعملهم sorting؟ قيمتهم
+
+350
+00:27:14,720 --> 00:27:18,860
+n فخمسة عشرة يعني هنا مثلا كنا بنتش نطلع على خمسة
+
+351
+00:27:18,860 --> 00:27:23,140
+عشرة عشرين خمسين سبعين مية ألف ألفين مليون جديش
+
+352
+00:27:23,140 --> 00:27:27,900
+فهذه اللي هي قيمة n ال f of n ال time اللي بنحتاجه
+
+353
+00:27:27,900 --> 00:27:31,860
+لتنفيذ البرنامج هذا أو لل code هذا خيص فهنقول في
+
+354
+00:27:31,860 --> 00:27:36,410
+عندنا system أولهذا ال system أول و هيكون فيه
+
+355
+00:27:36,410 --> 00:27:41,630
+system تاني أو code تاني ال complex اللي تتبعته أو
+
+356
+00:27:41,630 --> 00:27:47,570
+ال time بيحسبها عن طريق n2 plus 1 n2 plus 1 و نفس
+
+357
+00:27:47,570 --> 00:27:50,790
+الكلام ال n هنا هتكون عدد ال items اللي بده أعملها
+
+358
+00:27:50,790 --> 00:27:55,650
+sorting ال f of n ال time اللي هحتاجه ال time اللي
+
+359
+00:27:55,650 --> 00:27:58,170
+هحتاجه فهذا code و هذا code بدنا نشوف مين أحسن من
+
+360
+00:27:58,170 --> 00:28:02,740
+التاني طيب بدنا نعرف ال code الأولوانعرف ال order
+
+361
+00:28:02,740 --> 00:28:09,580
+تبعته، بعرف ال order تبعته بالنسبة ل big O، طب مش
+
+362
+00:28:09,580 --> 00:28:13,800
+هي big O، big O of N يعني كأني بقول انه تلاتين N
+
+363
+00:28:13,800 --> 00:28:20,560
+plus واحد at most first order لأنه لحظة انا اقول
+
+364
+00:28:20,560 --> 00:28:30,140
+big O of N طيب N هذه هي first orderهذه first order
+
+365
+00:28:30,140 --> 00:28:38,100
+صحيح؟ كأن بقول إن المعادلة هذه بالكتير first order
+
+366
+00:28:38,100 --> 00:28:43,620
+ممكن تكون أقل أقل أو تساوي first order فهي ضمن
+
+367
+00:28:43,620 --> 00:28:46,240
+التعريف احنا عارفين إن هي first order احنا عارفين
+
+368
+00:28:46,240 --> 00:28:49,760
+إن هي first order فهي تنطبق مع ال big O ال big O
+
+369
+00:28:49,760 --> 00:28:55,660
+دي معناها at most proportional to n تتناسب مع n
+
+370
+00:28:55,660 --> 00:29:01,340
+بالكتيريعني ممكن تكون اقل ممكن اقول انه constant
+
+371
+00:29:01,340 --> 00:29:05,080
+او log ال log احنا عارفين انه اقل من ال .. ال
+
+372
+00:29:05,080 --> 00:29:08,280
+order تبعه اقل من ال first log اقل من ال first
+
+373
+00:29:08,280 --> 00:29:16,800
+صحيح فممكن اقول ان ال log of N برضه is big O of N
+
+374
+00:29:16,800 --> 00:29:23,340
+على اعتبار ان هيأقل من فال big O بيسمح لنا أنه أقل
+
+375
+00:29:23,340 --> 00:29:28,200
+من أو يساوي first order أقل من أو يساوي ممكن تكون
+
+376
+00:29:28,200 --> 00:29:35,220
+constant أقول مثلا تلاتة is big O of N تلاتة
+
+377
+00:29:35,220 --> 00:29:41,040
+constant يعني ال order zero order zero تمام فال
+
+378
+00:29:41,040 --> 00:29:47,140
+order zero فهنا ال big O هذه معناها أنهبشوف العنصر
+
+379
+00:29:47,140 --> 00:29:51,420
+اللي جوه العنصر اللي جوه N N هذا linear ممكن تكتب
+
+380
+00:29:51,420 --> 00:29:56,880
+N تربيع فانا بتكلم هنا عن تربيع second order third
+
+381
+00:29:56,880 --> 00:30:01,340
+order فبشوف N هذه كلها ثابتة هتكون منها بس ال
+
+382
+00:30:01,340 --> 00:30:05,780
+power جديش هي ده اللي هتحدد ال order تبعنا طيب
+
+383
+00:30:05,780 --> 00:30:16,750
+ممكن تنحط big O of N 00 order n to the power 0 ب 1
+
+384
+00:30:16,750 --> 00:30:21,430
+فبنكتبها big O of 1
+
+385
+00:30:21,430 --> 00:30:30,470
+فبعرف أن هذه constant أو order 0 تمام على اعتبار
+
+386
+00:30:30,470 --> 00:30:36,880
+أنها n to the power 0 فطلع لنا الواحدكويس هذا كل
+
+387
+00:30:36,880 --> 00:30:39,540
+الكلام اللي عايشه ممكن نقوله عن ال big O حتى الآن
+
+388
+00:30:39,540 --> 00:30:42,900
+و لاحقا هتتطور الأمور معناه شويه شويه في ال big O
+
+389
+00:30:42,900 --> 00:30:49,060
+تمام هذا بالنسبالي الأولى big O of N في rest order
+
+390
+00:30:49,060 --> 00:30:54,960
+الطيب التانية تانية تربية هي is order N squared
+
+391
+00:30:54,960 --> 00:31:01,080
+فبنقولها big O of N squared فهذه بالكتير N squared
+
+392
+00:31:01,080 --> 00:31:03,900
+بس هي ممكن تكون N squared يعني ممكن تكون أقل أو
+
+393
+00:31:03,900 --> 00:31:08,300
+تساويsecond order هي فعلا تسوى second order هي
+
+394
+00:31:08,300 --> 00:31:11,240
+ممكن تسوى .. فعلا تسوى second order طب في الحالة
+
+395
+00:31:11,240 --> 00:31:16,660
+هذه for large .. large numbers of user records لو
+
+396
+00:31:16,660 --> 00:31:20,720
+في عندنا user records كبيرة أو عدد ال inputs كبير
+
+397
+00:31:20,720 --> 00:31:28,000
+جدا هنتوقع مين منهم more time دائما هياخد وقت
+
+398
+00:31:28,000 --> 00:31:34,900
+زيادة الأولى اللي هو a أو bتربية مدام أنا بتكلم عن
+
+399
+00:31:34,900 --> 00:31:38,900
+large numbers عدد كبير احنا لو بدنا نعمل sorting
+
+400
+00:31:38,900 --> 00:31:42,680
+هنا مثلا لمجموعة
+
+401
+00:31:42,680 --> 00:31:45,520
+الطالبات او مجموعة البنات اللي مثلا سجلين احد
+
+402
+00:31:45,520 --> 00:31:48,800
+المثقات طبعا تقولكوا هتسجلوا المثقات بس لما اجي
+
+403
+00:31:48,800 --> 00:31:52,920
+انا اسحب الكشف عن طريق القراكل مثلا برنامج الجامعة
+
+404
+00:31:52,920 --> 00:31:56,460
+بيحسب ليه بيرتب ليه حسب أرقامك الدراسية او أرقامك
+
+405
+00:31:56,460 --> 00:31:59,800
+الجامعية صحيح؟ حسب الرقم الجامعي مع أن اتعمل
+
+406
+00:31:59,800 --> 00:32:04,210
+sortingمعناته في code في النصر رتبلكم يعني عملكم
+
+407
+00:32:04,210 --> 00:32:07,450
+sorting عمل sorting احنا مش هنتكلم عن عددنا اربعين
+
+408
+00:32:07,450 --> 00:32:09,990
+و لا تخمسة و تلاتين طالبة مش .. مش .. مش الرقم
+
+409
+00:32:09,990 --> 00:32:14,470
+الكبير لو بنتكلم عن مساق من مساقات متضلبات الجامعة
+
+410
+00:32:14,470 --> 00:32:18,510
+اللي عددهم كبير جدا ممكن يصل متينات و بتكون تعملوا
+
+411
+00:32:18,510 --> 00:32:21,350
+sorting هيفرق طبعا code عن code في الحالة هذه في
+
+412
+00:32:21,350 --> 00:32:25,830
+الحالة هذه هتبين ان لأ ال linear كتير احسن لمنكالـ
+
+413
+00:32:25,830 --> 00:32:28,570
+quadratic او اللي هي second order ال first order
+
+414
+00:32:28,570 --> 00:32:30,830
+أكيد هحصل من ال second order ال second order هياخد
+
+415
+00:32:30,830 --> 00:32:36,950
+وقت أكبر في عملية ال sorting لو مثلا عندكوا two
+
+416
+00:32:36,950 --> 00:32:41,990
+codes واحد linear و واحد .. يعني واحد first order
+
+417
+00:32:41,990 --> 00:32:44,610
+و واحد second order ال second order طبعا هياخد
+
+418
+00:32:44,610 --> 00:32:50,130
+more time أكيد هياخد more timeOkay نرجع لل Big O
+
+419
+00:32:50,130 --> 00:32:55,230
+هذي نرجع نعرج شوية كمان مرة على ال Big O و نستفيد
+
+420
+00:32:55,230 --> 00:33:01,730
+شوية في الشرحة هنقول Big O of G فانا هنا بتكلم عن
+
+421
+00:33:01,730 --> 00:33:08,490
+Big O of G, G هذي function هذي function زي توي لما
+
+422
+00:33:08,490 --> 00:33:11,630
+كنا بيقول Big O of N أنا بتعامل مع أنها هذي
+
+423
+00:33:11,630 --> 00:33:15,780
+function من أي درجةمن الدرجة الأولى فهذه نفس
+
+424
+00:33:15,780 --> 00:33:21,020
+الكلام g function هنحددها لاحقا بس احنا هنا سمناها
+
+425
+00:33:21,020 --> 00:33:24,160
+خليناها undefined بالشكل هذا ان هي function و خلاص
+
+426
+00:33:24,160 --> 00:33:28,340
+function و خلاص أولى تانية تالتة من أي درجة من أي
+
+427
+00:33:28,340 --> 00:33:30,300
+order مش إشكال المهم ان في النهاية function
+
+428
+00:33:30,300 --> 00:33:35,580
+النهاية function okay ف let g be any function from
+
+429
+00:33:35,580 --> 00:33:38,200
+real number to real number ال domain real number و
+
+430
+00:33:38,200 --> 00:33:43,380
+ال codomain real number defineat most order g فال
+
+431
+00:33:43,380 --> 00:33:45,960
+big O هذا بنعرفه على أساس أنه at most order g
+
+432
+00:33:45,960 --> 00:33:50,680
+فممكن أقول if .. بدي أشوف if بالنسبة لل big O
+
+433
+00:33:50,680 --> 00:34:00,340
+فبقول if at most .. رجعنا تاني هنا okay at most
+
+434
+00:34:00,340 --> 00:34:06,140
+order g بمعنى هل هي .. إذا قولناها بهذا الشكل
+
+435
+00:34:06,140 --> 00:34:13,110
+معناته أن ال if نفس order g أو أقلأو أقل أو كأني
+
+436
+00:34:13,110 --> 00:34:18,850
+بقول هي من ال order بالكتير order g بالكتير order
+
+437
+00:34:18,850 --> 00:34:23,010
+g يعني ممكن يكون أقل، ممكن يكون أقل، كويس فهي تعرف
+
+438
+00:34:23,010 --> 00:34:28,310
+أنه يقول at most order g تنكتب big O of g to be
+
+439
+00:34:28,310 --> 00:34:33,050
+set of functions فإذا أنا لغة إيش اللي بدي أعرفه؟
+
+440
+00:34:33,050 --> 00:34:38,230
+بدي أعرف ال big O of g لو افترضنا، فرضنا إن ال G
+
+441
+00:34:38,230 --> 00:34:42,960
+هي the first orderأيش ال functions اللي بقدر
+
+442
+00:34:42,960 --> 00:34:47,720
+اكتبها ان هي فعلا تساوي big O of G كل ال first
+
+443
+00:34:47,720 --> 00:34:52,500
+order functions صح؟ كل ال function اللي ال order
+
+444
+00:34:52,500 --> 00:34:57,440
+طبعها first order بقدر اعرفها big O of first order
+
+445
+00:34:57,440 --> 00:35:02,680
+معناته كل ال functions هذه بقدر احطها في set فال
+
+446
+00:35:02,680 --> 00:35:07,390
+function صارت element داخل setالset هذي كل ال
+
+447
+00:35:07,390 --> 00:35:12,430
+elements اللي تتفق ان هي big O لل first order تمام
+
+448
+00:35:12,430 --> 00:35:18,350
+معناه ذلك لما انا بدي أجعل ريفا بقول set of
+
+449
+00:35:18,350 --> 00:35:25,910
+functions ال function هذي from R to R نسبة
+
+450
+00:35:25,910 --> 00:35:28,410
+لميه؟ لل function اللي أنا بدي أنسب إلها اللي بدي
+
+451
+00:35:28,410 --> 00:35:32,010
+أنسب ال order إلها فهي function from R to R such
+
+452
+00:35:32,010 --> 00:35:35,640
+thatأيش اللي بده يحقق لنا إياها؟ يعني عشان هذه
+
+453
+00:35:35,640 --> 00:35:39,000
+تكون ال function فعلا element داخل ال set بتاعة ال
+
+454
+00:35:39,000 --> 00:35:41,820
+big O of G إيش اللي لازم يتحققه؟ لازم يتحقق التالي
+
+455
+00:35:41,820 --> 00:35:47,040
+there exist C و K كي هي النقطة اللي كنا نتكلم عنها
+
+456
+00:35:47,040 --> 00:35:54,820
+اللي بعدها دائماالتربيه أكبر من الlinear معناته أن
+
+457
+00:35:54,820 --> 00:35:59,500
+أنا فعلا بدور على قيمة constant K و there exist ل
+
+458
+00:35:59,500 --> 00:36:04,660
+C برضه constant .. constant طيب there exist CK
+
+459
+00:36:04,660 --> 00:36:08,920
+such that for all X أكبر من K لكل القيم اللي بعد K
+
+460
+00:36:08,920 --> 00:36:16,580
+لكل القيم اللي بعد K F of X ال function اللي داخل
+
+461
+00:36:16,580 --> 00:36:22,690
+ال setأقل من أو تساوي C في G of X نسبنا هنا
+
+462
+00:36:22,690 --> 00:36:25,010
+بالنسبة لمن؟ لل function اللي .. اللي احنا عارفين
+
+463
+00:36:25,010 --> 00:36:27,550
+ال order تبعها و بدنا نعرف هل ال function F belong
+
+464
+00:36:27,550 --> 00:36:30,930
+إلها أو لأ جينا example هالوجد، حنعرف كيف أطلع
+
+465
+00:36:30,930 --> 00:36:35,510
+برضه ال C و ال K، حنعرف نطلع هالوجد ال C و ال K بس
+
+466
+00:36:35,510 --> 00:36:41,810
+مبدأيا بنقول إنه بعد النقطة K ال function F is at
+
+467
+00:36:41,810 --> 00:36:45,650
+most a constant C times of G
+
+468
+00:36:47,600 --> 00:36:53,040
+معناته ان هي proportional to G تتناسب مع G تتناسب
+
+469
+00:36:53,040 --> 00:36:57,420
+هنا مع G هناخد example و هنرسم الرسم تبعهم عشان
+
+470
+00:36:57,420 --> 00:37:02,020
+نشوف كيف العملية التناسب طيب نقرأها if is at most
+
+471
+00:37:02,020 --> 00:37:09,520
+order G او if is big O of G او ممكن نقول if بتساوي
+
+472
+00:37:09,520 --> 00:37:14,680
+big O of Gأو ممكن نكتبها if belong لإن احنا عرفنا
+
+473
+00:37:14,680 --> 00:37:18,460
+ال if إن هي function داخل ال set اللي تحتوي على كل
+
+474
+00:37:18,460 --> 00:37:22,740
+ال functions بتاعة ال big O فهي واحدة منهم فبقدر
+
+475
+00:37:22,740 --> 00:37:27,040
+أقول إن هي element أو function belong to big O of
+
+476
+00:37:27,040 --> 00:37:30,820
+Gبناء على التعريف بناء على تعريفنا ان احنا بتكلم
+
+477
+00:37:30,820 --> 00:37:36,860
+عن set of functions أحيانا ممكن نقلش منها ال at
+
+478
+00:37:36,860 --> 00:37:42,240
+most بتاعتنا فبقول if is order g خلاص ممكن جدا
+
+479
+00:37:42,240 --> 00:37:46,920
+نختصرها طيب خلينا نشوف كيف نحسبها ال K و ال C اللي
+
+480
+00:37:46,920 --> 00:37:50,360
+قلتلكم بدنا نجيبهم ناخد ال two examples اللي
+
+481
+00:37:50,360 --> 00:37:55,980
+اتكلمنا عنهم اللي واحدة linear واحدة squareو بدنا
+
+482
+00:37:55,980 --> 00:37:59,920
+نجيب هل فعلا هي big O of N او لأ نمسك الأولى
+
+483
+00:37:59,920 --> 00:38:05,120
+تلاتين N plus تمانية is big O of N first order
+
+484
+00:38:05,120 --> 00:38:09,730
+بدنا نثبت الكلام هذا و بدنا نوضح الكلام هذاليش
+
+485
+00:38:09,730 --> 00:38:12,830
+يقولنا 130؟ ليش احنا امتى قولنا ممكن تكون فعلا
+
+486
+00:38:12,830 --> 00:38:20,670
+first order إذا كان يوجد C و K اللي بيحققولنا ال
+
+487
+00:38:20,670 --> 00:38:28,330
+condition أن F of X أقل من أو تساوي C في N في ال
+
+488
+00:38:28,330 --> 00:38:35,030
+order طبعا F of Nتمام؟ بدنا نحقق الكلام هذا فعشان
+
+489
+00:38:35,030 --> 00:38:40,450
+أحققه بدي أثبت أنه موجودة ال c و ال k طب كيف نقدر
+
+490
+00:38:40,450 --> 00:38:45,790
+نجيب ال c و ال k؟ من هنا ال c مباشرة تقدر تاخدها
+
+491
+00:38:45,790 --> 00:38:52,610
+من ال coefficient تبعت n هنا n طيب وين ال order n
+
+492
+00:38:52,610 --> 00:38:56,810
+هنا؟ هيها كدوش ال coefficient تبعها؟ تلاتين معناته
+
+493
+00:38:56,810 --> 00:39:04,070
+ال cبتساوي ال coefficient زائد واحد زائد
+
+494
+00:39:04,070 --> 00:39:10,030
+واحد طيب ال K قيمة ال shift تمانية تمانية
+
+495
+00:39:10,030 --> 00:39:13,110
+بالمعادلات
+
+496
+00:39:13,110 --> 00:39:15,230
+خليني انا اعمل check هل فعلا تحقق ال condition
+
+497
+00:39:15,230 --> 00:39:20,230
+تبعنا ولا لأ بدنا نتأكد خليني اقول هي let C 31
+
+498
+00:39:20,230 --> 00:39:31,470
+عرفنا ليشأقل رقم بيحقق
+
+499
+00:39:31,470 --> 00:39:35,050
+المعادلة أقل رقم بيحقق المعادلة
+
+500
+00:39:42,870 --> 00:39:45,970
+31 قلنا لأ ال coefficient تبع n هنا احنا بتكلم عن
+
+501
+00:39:45,970 --> 00:39:49,770
+ال first order صح طب وين ال coefficient تبع ال
+
+502
+00:39:49,770 --> 00:39:53,410
+first order في المعادلة ايه اللي هو 30 فهذا
+
+503
+00:39:53,410 --> 00:39:58,030
+بنزودها 31 يعني كأنه بدور على اقل رقم يكون اكبر
+
+504
+00:39:58,030 --> 00:40:01,770
+منها اقل رقم يكون اكبر منها انتوا في الآخر ممكن
+
+505
+00:40:01,770 --> 00:40:06,350
+تفترضوا 35 هيمشي الحال المهم احنا كل الفكرة ان
+
+506
+00:40:06,350 --> 00:40:12,700
+there exist k و cمجرد أنه في رقم حقق المعادلة
+
+507
+00:40:12,700 --> 00:40:16,920
+بكافي انا من عندى بحاول افترضه انه اقل رقم ممكن
+
+508
+00:40:16,920 --> 00:40:21,640
+اللى اقل منه مش هتصبط المعادلة بس هو الحد الفاصل
+
+509
+00:40:21,640 --> 00:40:25,940
+انتوا ممكن في الآخر تفترضه مثلا C ب60 وال K تعمله
+
+510
+00:40:25,940 --> 00:40:29,840
+10 هتتحقق باريحية كبيرة جدا المعادلة معاكم هتلاقوا
+
+511
+00:40:29,840 --> 00:40:33,500
+ان المعادلة هتتحقق باريحية كبيرة احنا هنا زى ما
+
+512
+00:40:33,500 --> 00:40:38,500
+بقوله بالظبط حوالين بالظبط اللى اكبر منكأقل قيمة
+
+513
+00:40:38,500 --> 00:40:42,500
+ممكنة للـC والـK تمام، هذه الـC و 31، K تمانية،
+
+514
+00:40:42,500 --> 00:40:48,100
+أسيوم لكل قيم N اللي أكبر من K المفروض يتحقق ال
+
+515
+00:40:48,100 --> 00:40:54,300
+condition لكل قيم K اللي أكبر من تمانية فاحنا نقول
+
+516
+00:40:54,300 --> 00:40:59,280
+هنا for N أكبر من K يعني أكبر من تمانية طيب، نمسك
+
+517
+00:40:59,280 --> 00:41:04,000
+ال term هذا لأن احنا بدنا نحقق هذه الشرطة بدنا
+
+518
+00:41:04,000 --> 00:41:10,120
+نثبت أن فيه C و فيه Kبحققولنا الشرط هذه أن N لكل N
+
+519
+00:41:10,120 --> 00:41:15,560
+أكبر من K هذا الشرط ده هنمسك الشرط هذا هاي ال C N
+
+520
+00:41:15,560 --> 00:41:19,640
+هاي ال C N ال C احنا فرضناها جديش واحد تلاتين طيب
+
+521
+00:41:19,640 --> 00:41:24,100
+ما هذه بقدر أقول أن هي تلاتين زائد N صحيح؟ طيب هذه
+
+522
+00:41:24,100 --> 00:41:29,840
+أكيد أكبر من تلاتين N لأن هذه بتسوي هذه أكبر من
+
+523
+00:41:29,840 --> 00:41:33,380
+تلاتين N زائد تمانية باعتبار أن أنا بتكلم على كل
+
+524
+00:41:33,380 --> 00:41:39,090
+قيم N اللي أكبر من تمانيةفال N أكيد أكبر من تمانية
+
+525
+00:41:39,090 --> 00:41:50,550
+صح فإذا تلاتين N زائد تمانية أقل من CCN فحقق الشرط
+
+526
+00:41:50,550 --> 00:41:54,950
+يكفيني من الشرط أن يوجد رقمين حققوا ليا مدان يوجد
+
+527
+00:41:54,950 --> 00:41:59,570
+رقمين حققوا فإذا هي فعلا ال function هذه first
+
+528
+00:41:59,570 --> 00:42:06,590
+order أو big O of N first أو أقلfirst او اقل او
+
+529
+00:42:06,590 --> 00:42:12,470
+تتناسب let's say proportional مع ال first order
+
+530
+00:42:12,470 --> 00:42:15,450
+تتناسب مع ال first order نفس الكلام ممكن نعمله
+
+531
+00:42:15,450 --> 00:42:22,210
+لمن؟ للتربية التربية هنا C كم ممكن تقترحوها؟
+
+532
+00:42:25,250 --> 00:42:29,530
+هي n تربيع و n تربيع جداش ال coefficient هنا C
+
+533
+00:42:29,530 --> 00:42:36,610
+بجداش نعملها 2 زائد 1 1 زائد 1 ف C بتساوي 2 طيب K
+
+534
+00:42:36,610 --> 00:42:42,970
+بواحد هدول أقل رقمين ممكن تختاروهم ممكن تختاروا
+
+535
+00:42:42,970 --> 00:42:46,870
+أكبر ممكن تختاروا أكبر هتلاقي انه برضه هتتحقق ال
+
+536
+00:42:46,870 --> 00:42:51,350
+equation و هتتحقق بزيادة يعني هتكون الفرق كمان في
+
+537
+00:42:51,350 --> 00:42:57,090
+أكبر منه بزيادةحنشوف there exists ck for all n
+
+538
+00:42:57,090 --> 00:43:03,210
+أكبر من k يعني لكل قيم n أكبر من 1 لكل قيم n أكبر
+
+539
+00:43:03,210 --> 00:43:07,570
+من 1 فإذا n لازم تكون أكبر من 1 عساس أنها أكبر من
+
+540
+00:43:07,570 --> 00:43:12,970
+k نمسك هذه cn تربيع نمسك cn تربيع و c حاطناها ب2
+
+541
+00:43:12,970 --> 00:43:17,590
+2n تربيع عبارة عن n تربيع زاد n تربيعأكبر من N
+
+542
+00:43:17,590 --> 00:43:21,470
+تربيع زائد واحد على اعتبار أن ال N قلنا أكبر من
+
+543
+00:43:21,470 --> 00:43:23,950
+واحد مدام أكبر من واحد التربيع تباع أكبر من واحد
+
+544
+00:43:23,950 --> 00:43:28,210
+مدام كقيمة أكبر من واحد تربيعها أكيد أكبر من واحد
+
+545
+00:43:28,210 --> 00:43:32,890
+فأكيد ال term هذا أكبر من ال term هذا فإذا ال N
+
+546
+00:43:32,890 --> 00:43:37,530
+تربيع زائد واحد أقل من C N تربيع حققنا ال
+
+547
+00:43:37,530 --> 00:43:40,950
+condition مدام أقل من C N تربيع معناته هي ضمن ال
+
+548
+00:43:40,950 --> 00:43:46,130
+order تربيعك function هي ضمن ال order تربية فبقدر
+
+549
+00:43:46,130 --> 00:43:52,090
+أقول اللي هي big O of N square و أنا مرتاح okay
+
+550
+00:43:52,090 --> 00:44:01,950
+هاي الشكل تبعنا لو اتكلمنا عن تلاتين
+
+551
+00:44:01,950 --> 00:44:06,670
+N زائد تمانيةطب وين الرقم اللى فعلا قلتلنا كيه و
+
+552
+00:44:06,670 --> 00:44:09,670
+مش كيه و مش عارفاش و بقى أكبر من كيه المعادلة
+
+553
+00:44:09,670 --> 00:44:14,470
+دايما أقل من N تربيه من ال N من O big O of N لحظة
+
+554
+00:44:14,470 --> 00:44:22,330
+أنه هادي N مش CNN CNN جداش تطلع واحد و تلاتين N
+
+555
+00:44:22,330 --> 00:44:24,790
+واحد و تلاتين N هترسم معاكم بهذا الشكل
+
+556
+00:44:27,750 --> 00:44:32,490
+هتكون هذه 31 أن فبعد قيمة معينة عن تقطع معين اللي
+
+557
+00:44:32,490 --> 00:44:40,130
+هو عن 8 هتلاقوا دايما 31 أكبر من 30 أن زائد 8 أكبر
+
+558
+00:44:40,130 --> 00:44:45,450
+من 30 أن زائد 8 فبيكون لكل أن اللي أكبر من 8 دايما
+
+559
+00:44:45,450 --> 00:44:50,370
+linear فإذا ال function كلها على بعض linear تصور
+
+560
+00:44:50,370 --> 00:44:51,450
+مرسومة؟ أه مرسومة
+
+561
+00:44:59,730 --> 00:45:04,850
+ك فكل الجزء اللي أكبر من تمانية ينطبق عليه ال
+
+562
+00:45:04,850 --> 00:45:08,810
+condition بنقدر ساعتها نقول ان اه والله في موجود
+
+563
+00:45:08,810 --> 00:45:14,870
+او في وجود لك و ال c مدان موجودة automatic
+
+564
+00:45:14,870 --> 00:45:22,750
+المعادلة هي دي بقول belong of O of N او is O of N
+
+565
+00:45:22,750 --> 00:45:26,770
+زي ما بتكون خدولكوا اي مسمة من مسمات متويسة منها
+
+566
+00:45:27,540 --> 00:45:32,100
+تمام هلوجد مجموعة rules مجموعة facts مجموعة
+
+567
+00:45:32,100 --> 00:45:37,220
+relations مهمة ممكن تتعاملوا معاها خاصة بال big
+
+568
+00:45:37,220 --> 00:45:43,880
+بال big O خاصة بمين بال big O أول شغلة هي
+
+569
+00:45:43,880 --> 00:45:47,140
+transitive ايش يعني transitive يعني لو قولنا if
+
+570
+00:45:47,140 --> 00:45:55,450
+relation مع G باعتبار أن ال F belong to big O GBig
+
+571
+00:45:55,450 --> 00:46:05,190
+O of G يعني واضح ان F نفس order G او اقل و G نفس
+
+572
+00:46:05,190 --> 00:46:12,490
+order H او اقل معناته G belong to big O of H هذا
+
+573
+00:46:12,490 --> 00:46:18,900
+هيقودنا تماما ان F برضه big O of HBig O of H
+
+574
+00:46:18,900 --> 00:46:23,380
+Transitive أو انتقالية يعني ال relation هنا مع ال
+
+575
+00:46:23,380 --> 00:46:28,440
+relation هنا إذا كان ال F أقل من G و ال G أقل من H
+
+576
+00:46:28,440 --> 00:46:33,780
+فبالضرورة F أقل من H صحيح؟ بالضرورة هتكون أقل منها
+
+577
+00:46:33,780 --> 00:46:38,300
+أو تساوي بالكتير، كويس، هاي أول relationrelation
+
+578
+00:46:38,300 --> 00:46:42,480
+التانية big O with constant سواء هيكون مضروب او
+
+579
+00:46:42,480 --> 00:46:47,160
+root او log بدنا نشوف كيف يتعامل مع ال constants
+
+580
+00:46:47,160 --> 00:46:52,300
+اول شغلة اذا ضربناها ضرب مباشرة بقى constant A
+
+581
+00:46:52,300 --> 00:46:57,140
+وهذه قولنا ان ال constant A وB هدول constants بي
+
+582
+00:46:57,140 --> 00:47:00,180
+بس هتكون اكبر من صفر اكبر او تساوي صفر اكبر او
+
+583
+00:47:00,180 --> 00:47:08,660
+تساوي صفر لو قولنا F big O of FBig O of F معناته
+
+584
+00:47:08,660 --> 00:47:13,920
+ال function F لها نفس ال order طب لو انضربت في a
+
+585
+00:47:13,920 --> 00:47:18,380
+constant مجرد constant حضر هي هي برضه belonged to
+
+586
+00:47:18,380 --> 00:47:24,020
+big O of F زي لما تقولوا n هي first order طب meet
+
+587
+00:47:24,020 --> 00:47:28,950
+n برضه first order السلوك بس اللي اتغيرسلوب تبعها
+
+588
+00:47:28,950 --> 00:47:32,670
+فقط اللي اتغير اما ما اتغيرش شي هتظل نفس ال order
+
+589
+00:47:32,670 --> 00:47:37,550
+فهي مجرد اضرب ال function في constant هتظل نفس ال
+
+590
+00:47:37,550 --> 00:47:43,290
+function طيب f هذه ال condition تبعنا بس اللي بدنا
+
+591
+00:47:43,290 --> 00:47:52,470
+ناخد بالنا منه هنا نرجعله small omega of واحد big
+
+592
+00:47:52,470 --> 00:48:02,560
+O of N ايش معناهالما اقول if بتساوي big O of N
+
+593
+00:48:02,560 --> 00:48:08,060
+معناها ان ال function هذه ال order تبعها linear او
+
+594
+00:48:08,060 --> 00:48:20,280
+اقل صح او اقل طيب if ساوي small O of N معناها if
+
+595
+00:48:20,280 --> 00:48:28,800
+ال order تبعها اقل من N لا يساوي N لا يساوي Nأقل
+
+596
+00:48:28,800 --> 00:48:33,980
+من n يعني ممكن التربيعية اللي لو قولنا تلاتة n
+
+597
+00:48:33,980 --> 00:48:43,480
+plus سبعة ممكن أقول عنها is small o of n تربيع بس
+
+598
+00:48:43,480 --> 00:48:49,360
+بقولش small n of n لإن أنا عارف إن هي first order
+
+599
+00:48:50,260 --> 00:48:55,300
+هنا ال small o أقل من first order تعريفها أقل من
+
+600
+00:48:55,300 --> 00:49:04,900
+first order تمام هاي التانية التالتة big omega big
+
+601
+00:49:04,900 --> 00:49:12,300
+omega of n معناته ال order تبع f أكبر من أو يساوي
+
+602
+00:49:12,300 --> 00:49:17,160
+n اللي هو first order يعني first order أو أكبر
+
+603
+00:49:18,880 --> 00:49:24,620
+first order أو أكبر كتبوه عندكم ممكن نضطر نحتاجهم
+
+604
+00:49:24,620 --> 00:49:27,380
+وإن كان هي ال big O هي الأكثر استخداما يعني أكثر
+
+605
+00:49:27,380 --> 00:49:30,780
+استخداما بس أنا مضطرها لغة أشرحلكم هي علشان طلعة
+
+606
+00:49:30,780 --> 00:49:35,060
+النهد عشان نفهمها الشيء هذا بس تمام فعشان نفهمها
+
+607
+00:49:35,060 --> 00:49:42,620
+بدنا نحطهم كلهم و نخلص طيب هذه ال big omega طيب ال
+
+608
+00:49:42,620 --> 00:49:50,780
+small omega of Nأكبر من أكبر
+
+609
+00:49:50,780 --> 00:49:57,440
+من أكبر
+
+610
+00:49:57,440 --> 00:49:57,600
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+611
+00:49:57,600 --> 00:49:58,220
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+612
+00:49:58,220 --> 00:50:01,200
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+613
+00:50:01,200 --> 00:50:05,060
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+614
+00:50:05,060 --> 00:50:05,080
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+615
+00:50:05,080 --> 00:50:05,100
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+616
+00:50:05,100 --> 00:50:15,220
+أكبر من أكبر من أكبر من أكبر من أكبر
+
+617
+00:50:15,220 --> 00:50:20,370
+منتساوي F او F تساوي big theta of N معناته ان هي
+
+618
+00:50:20,370 --> 00:50:25,710
+exactly تساوي ال order هذا فهنا F الزمن لا هي اكبر
+
+619
+00:50:25,710 --> 00:50:28,590
+ولا هي اصغر من ال first order هي بالظبط first
+
+620
+00:50:28,590 --> 00:50:34,770
+order هي exactly first order هاي معناته theta of N
+
+621
+00:50:34,770 --> 00:50:36,870
+فهي ال relations اللي ممكن نعملها لها ال functions
+
+622
+00:50:36,870 --> 00:50:40,210
+عشان نحسب ال order بتاع ال function فاحنا هلوجت
+
+623
+00:50:40,210 --> 00:50:48,940
+ألزمنا هو بمين؟بال Omega of one معناه ذلك ان ال F
+
+624
+00:50:48,940 --> 00:50:57,860
+دائما اكبر من ال order ال
+
+625
+00:50:57,860 --> 00:51:01,380
+order ايش ده Zero ال order Zero هي اذا اكبر من
+
+626
+00:51:01,380 --> 00:51:06,800
+constant اكبر من constant يعني هي كل الفكرة ان ال
+
+627
+00:51:06,800 --> 00:51:10,400
+F هي لازم تكون اكبر من ال constant ممكن تكون
+
+628
+00:51:10,400 --> 00:51:14,880
+linear و ممكن تكون اقل من linear زي loglogarithmic
+
+629
+00:51:14,880 --> 00:51:19,360
+أقل من ال linear log أقل من ال linear ببساطة جدا
+
+630
+00:51:19,360 --> 00:51:25,720
+لو قلنا linear لو أنا بتكلم linear العشرة يقابلها
+
+631
+00:51:25,720 --> 00:51:31,380
+ال output عشرة المية يقابلها مية طيب المية log log
+
+632
+00:51:31,380 --> 00:51:35,820
+مية جداش log
+
+633
+00:51:35,820 --> 00:51:41,780
+للأساس ال base تبعكوا عشرة اتنين log مليون
+
+634
+00:51:52,670 --> 00:51:54,750
+6 ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+635
+00:51:54,750 --> 00:51:56,730
+ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+636
+00:51:56,730 --> 00:52:01,010
+ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+637
+00:52:01,010 --> 00:52:02,550
+ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+638
+00:52:02,550 --> 00:52:06,770
+ستة، ستة، ستة، ستة، ستة، ستة،
+
+639
+00:52:06,770 --> 00:52:11,890
+ستة
+
+640
+00:52:12,490 --> 00:52:24,590
+الـ log معدل تغيرها بطيق معدل تغيرها بيكون
+
+641
+00:52:24,590 --> 00:52:32,230
+بطيق عند الواحد بواحد فبتكون تقريبا بهذا الشكل بس
+
+642
+00:52:32,230 --> 00:52:37,370
+فيه تغير تغير بطيق اه بس فيه تغير مش constant مش
+
+643
+00:52:37,370 --> 00:52:41,210
+constant في المقابل بتلاقي ال linear مش بهذا الشكل
+
+644
+00:52:46,060 --> 00:52:49,300
+خلصنا ال constant مضروف في function مش هيغير في ال
+
+645
+00:52:49,300 --> 00:52:53,760
+order طيب لو قلنا f to the power one minus b و b
+
+646
+00:52:53,760 --> 00:52:59,120
+أكبر من أو تساوي صفر لو بتساوي صفر معناته هي نفس f
+
+647
+00:52:59,120 --> 00:53:04,480
+ال order هو هو كله هيكون big of f ال order مش
+
+648
+00:53:04,480 --> 00:53:09,560
+هيتغير القصد طيب لو كان هنا أكبر من صفر لو قلنا
+
+649
+00:53:09,560 --> 00:53:16,760
+واحدأصبحت 0 أصبحت constant ضمن التعريف big O of F
+
+650
+00:53:16,760 --> 00:53:23,340
+لأنه أقل من ال order فهو ضمن التعريف big O حتى لان
+
+651
+00:53:23,340 --> 00:53:28,660
+بالنسبة لل big O ضمن التعريف اتنين to the power
+
+652
+00:53:28,660 --> 00:53:34,990
+minus نص يعني واحد على Fفال order inverse أقل من
+
+653
+00:53:34,990 --> 00:53:41,890
+ال F طيب و log لسه توي كنا بنحكي عن ال log ال log
+
+654
+00:53:41,890 --> 00:53:45,430
+دايما أقل من مين من ال linear فما دايما أنا بقول
+
+655
+00:53:45,430 --> 00:53:50,430
+log F بغض النظر ال base تبعنا إيش و بغض النظر حتى
+
+656
+00:53:50,430 --> 00:53:57,990
+لو إلها أس أو تتباور كذا تتباور أي قيمة في الآخر
+
+657
+00:53:57,990 --> 00:54:04,110
+هي أقل من ال big O of Fأقل من ال big O of F قيمتها
+
+658
+00:54:04,110 --> 00:54:08,350
+أقل من قيمة ال function نفسها اتوا احنا أخدنا مثال
+
+659
+00:54:08,350 --> 00:54:11,650
+لو ال function linear هي أصغر حاجة احنا متوقعينها
+
+660
+00:54:11,650 --> 00:54:16,110
+مية طبقنا عليها ال linear function هتسوى مية ال
+
+661
+00:54:16,110 --> 00:54:20,790
+output طب ال input الف هيسوى الف مليون هيسوى مليون
+
+662
+00:54:20,790 --> 00:54:24,090
+طب لأ ال output اللي ظهر ده او القيمة اللي ظهرت
+
+663
+00:54:24,090 --> 00:54:29,800
+logهتلاقوها بدل عشرة صارت واحد بدل مية صارت اتنين
+
+664
+00:54:29,800 --> 00:54:36,220
+بدل مليون صارت ستة تمام؟ كويس فهنا برضه هتظل كلهم
+
+665
+00:54:36,220 --> 00:54:40,320
+جميع الصياغ واحد اتنين تلات صياغ كلهم ضمن ال big O
+
+666
+00:54:40,320 --> 00:54:47,200
+of F sum of functions لو قلنا جي belong to big O
+
+667
+00:54:47,200 --> 00:54:56,880
+of F جي اقل من او تساويال order تبع f وال h برضه
+
+668
+00:54:56,880 --> 00:55:02,080
+اقل من او تسوي ال order تبع f فمجموع الاتنين g و h
+
+669
+00:55:02,080 --> 00:55:08,300
+برضه هيكون ضمن التعريف يعني first order زائد first
+
+670
+00:55:08,300 --> 00:55:12,580
+order هيظل first order هيظل first order second
+
+671
+00:55:12,580 --> 00:55:16,300
+order زائد first order second order المهم انه مش
+
+672
+00:55:16,300 --> 00:55:19,460
+هيزيد عن اي واحدة منهم مدام صماشن مش هيزيد عن اي
+
+673
+00:55:19,460 --> 00:55:26,420
+واحدة منهم هيظلالـ order هو order واحدة منهم اللي
+
+674
+00:55:26,420 --> 00:55:33,960
+هي الأكبر اللي هي الأكبر okay بنكمل برضه بمجموعة
+
+675
+00:55:33,960 --> 00:55:39,620
+facts about ال big O for all c أكبر من صفر
+
+676
+00:55:39,620 --> 00:55:42,580
+constant مجرد constant ال constant هذا ضربناه في
+
+677
+00:55:42,580 --> 00:55:50,240
+ال function مش هيتغير هتظل برضه big O of F طيب
+
+678
+00:55:50,240 --> 00:55:59,550
+جمعنالما تقولوا N belong to O of N first طيب بفرق
+
+679
+00:55:59,550 --> 00:56:03,530
+لو قولنا تلاتة N ما هي برضه belong to first order
+
+680
+00:56:03,530 --> 00:56:09,650
+نفس الكلام لو قولنا تلاتة N زائد C كمان زائد خمسة
+
+681
+00:56:09,650 --> 00:56:16,070
+first order طيب ناقص عشرة نفس الكلام first order
+
+682
+00:56:17,410 --> 00:56:22,470
+نفس الفكرة ف constant ضربناه أو جمعناه أو طرحناه
+
+683
+00:56:22,470 --> 00:56:25,270
+على ال function مش هيغير ال order تاع ال function
+
+684
+00:56:25,270 --> 00:56:34,210
+مادام constant مادام رقم ثابت okay if onebelong to
+
+685
+00:56:34,210 --> 00:56:40,430
+O of G1 هدا إيه ال order ال order تبع F1 هو order
+
+686
+00:56:40,430 --> 00:56:46,790
+G أو أقل and F2 function مختلفة belong to O ل
+
+687
+00:56:46,790 --> 00:56:53,270
+order مختلف هدوليك اختلفت ال orders F1 غير F2 G1
+
+688
+00:56:53,270 --> 00:57:00,110
+غير G2 طيب لما أقول F1 في F2F1 مضروبة في F2 belong
+
+689
+00:57:00,110 --> 00:57:05,370
+to big O of G1 مضروبة في G2 زي لما نقول first
+
+690
+00:57:05,370 --> 00:57:15,230
+order في second order لأ third في ضرب ضرب مضروب
+
+691
+00:57:15,230 --> 00:57:19,210
+ضرب لما تكونوا عندكوا N تربيع زائد واحد مضروبة في
+
+692
+00:57:19,210 --> 00:57:26,090
+N هيصير في عندكوا N تكعيب زائد N هنا صارت mean
+
+693
+00:57:26,090 --> 00:57:31,630
+third orderصارت هنا third order فنفس الكلام بدنا
+
+694
+00:57:31,630 --> 00:57:34,090
+نضرب ال orders بتاعتهم .. بدنا نضرب ال orders
+
+695
+00:57:34,090 --> 00:57:37,810
+بتاعتهم واحدة مثلا ال order الخامس ال five order
+
+696
+00:57:37,810 --> 00:57:41,150
+مضروفة ان
+
+697
+00:57:42,360 --> 00:57:51,300
+fourth order تسعة تسعة تسعة تسعة تسعة
+
+698
+00:57:51,300 --> 00:57:55,080
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+699
+00:57:55,080 --> 00:57:56,980
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+700
+00:57:56,980 --> 00:57:57,480
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+701
+00:57:57,480 --> 00:57:57,860
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+702
+00:57:57,860 --> 00:57:58,300
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+703
+00:57:58,300 --> 00:58:01,260
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+704
+00:58:01,260 --> 00:58:08,290
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسfirst
+
+705
+00:58:08,290 --> 00:58:11,630
+order زائد second order مين الأكبر؟ ال second
+
+706
+00:58:11,630 --> 00:58:14,670
+معناته مجموح ان بيعطيين second order مجموح ان
+
+707
+00:58:14,670 --> 00:58:18,170
+بيعطي second order اللي لو بده اجمحهم هدوله مش
+
+708
+00:58:18,170 --> 00:58:22,570
+هيتغير هتظل خمسة هتظل ال order تبعنا خمسة طيب
+
+709
+00:58:22,570 --> 00:58:29,110
+بناخد مين منهم ال big G1 من التنتين امتى باخد G1؟
+
+710
+00:58:29,110 --> 00:58:34,530
+اذا كانت G2 belonged to big O G1 بمعنى ان ال G1 هي
+
+711
+00:58:34,530 --> 00:58:40,190
+الأكبرأو تساوي G1 أكبر أو تساوي فهنا بالظبط كأنه
+
+712
+00:58:40,190 --> 00:58:51,470
+ال G1 هي ال big O of N to the power 5 هي
+
+713
+00:58:51,470 --> 00:58:56,470
+الأكبر من to the power 4 فهي اللي بناخدها طبعا
+
+714
+00:58:56,470 --> 00:59:01,130
+واضح جدا أنه بقدر ببساطة أقول أن ال N to the power
+
+715
+00:59:01,130 --> 00:59:07,710
+4 هي big O of N to the power 5صحيح فهيها هي نفسها
+
+716
+00:59:07,710 --> 00:59:14,570
+هي belong belong هذه هي نفسها دي فاللي هنختارها
+
+717
+00:59:14,570 --> 00:59:19,790
+فعلا هي ال n to the power four اللي هي جي واحد جي
+
+718
+00:59:19,790 --> 00:59:27,450
+واحد كويس مجموعة
+
+719
+00:59:27,450 --> 00:59:30,190
+ال facts هي نفسها هي نفس اللي احنا خدناهم هدولاك
+
+720
+00:59:30,190 --> 00:59:36,430
+ايه نفسهملو ما نضرب function في constant هيظل نفس
+
+721
+00:59:36,430 --> 00:59:41,590
+ال function هو معاه example تلاتة X تربيع برضه ال
+
+722
+00:59:41,590 --> 00:59:47,030
+second order برضه second order لو قولنا F plus big
+
+723
+00:59:47,030 --> 00:59:52,050
+O of F هي نفس big O of F لاحظوا هنا ال order هو ال
+
+724
+00:59:52,050 --> 00:59:54,830
+order ال function طبعا هنا مدخل نفس ال function
+
+725
+00:59:55,390 --> 00:59:59,590
+يعني معناته ال orders متشابهة ال orders متشابهة
+
+726
+00:59:59,590 --> 01:00:04,490
+هنا قد تكون big O هذه اما نفس ال order او اقل او
+
+727
+01:00:04,490 --> 01:00:12,310
+اقل فهنا F تربيعية big O of F ممكن تكون اما تربيع
+
+728
+01:00:12,310 --> 01:00:15,430
+او first order اما second order او first order فلو
+
+729
+01:00:15,430 --> 01:00:18,910
+افترضنا first order هيظل تربيع هيظل نفس ال order
+
+730
+01:00:18,910 --> 01:00:22,550
+تبع مين بتاع ال function هيظل نفس ال order ال
+
+731
+01:00:22,550 --> 01:00:27,070
+functionكويس خلّي هدول المرة الجاية عشان إيش
+
+732
+01:00:27,070 --> 01:00:31,050
+ننراجع فيهم برضه، كويس إن بيظلوا موجودين نرجحهم،
+
+733
+01:00:31,050 --> 01:00:36,950
+فضلوا ال order احنا بدأنا محاضرتنا لما بدأت انا
+
+734
+01:00:36,950 --> 01:00:39,410
+مابدتش في ال order عارفة؟ اتكلمتلكوا شوية عن ال
+
+735
+01:00:39,410 --> 01:00:42,750
+complexity ال complexity عشان أحسبها بحسبها من
+
+736
+01:00:42,750 --> 01:00:49,060
+هنا، بحسبها إنه ال function بتاعتنا big of إيشبشوف
+
+737
+01:00:49,060 --> 01:00:52,800
+ال order تبع ال .. ال code الأول و ال order بتاع
+
+738
+01:00:52,800 --> 01:00:57,700
+ال code التاني ال order الأقل هو اللي باخده مين ال
+
+739
+01:00:57,700 --> 01:01:00,740
+order تبعه أقل هو اللي بناخده بنقول لأ هذا ال code
+
+740
+01:01:00,740 --> 01:01:05,360
+أفضل more efficient ل الشغل اللي .. او لل task
+
+741
+01:01:05,360 --> 01:01:08,180
+اللي بنشتغل عليها لل task اللي بنشتغل عليها على
+
+742
+01:01:08,180 --> 01:01:10,080
+بركة الله يعطيكم العافية و نشوفكم المرة الجاية ان
+
+743
+01:01:10,080 --> 01:01:10,300
+شاء الله
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f604ace4988f0caaed02096ae99be103830ff96
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_raw.json
@@ -0,0 +1 @@
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"text": "comparisons أربعة comparisons تلاتة comparisons two comparisons و stop فلاحظوا حتى عدد المقارنات اللي هتحتاجوها كل مرة بتجيل طيب فصار عندنا عدد مقارنات بدنا نعملها في كل مرحلة و عندنا أيش كمان عندنا عدد مراحل", "tokens": [1112, 2181, 23886, 5551, 25513, 27884, 33157, 6055, 1211, 9307, 3660, 33157, 732, 33157, 4032, 1590, 6156, 15040, 5016, 19913, 14407, 11331, 49975, 6225, 3215, 3215, 9673, 4587, 9640, 8315, 2655, 13672, 1829, 8032, 2655, 33753, 26108, 2407, 11296, 28242, 3714, 25720, 39894, 7435, 26895, 23032, 1829, 3555, 6156, 9381, 9640, 43242, 8315, 6225, 3215, 3215, 3714, 4587, 9640, 8315, 2655, 47525, 8315, 8717, 25957, 1211, 11296, 8978, 28242, 3714, 2288, 5016, 37977, 4032, 43242, 8315, 36632, 8592, 9122, 2304, 7649, 43242, 8315, 6225, 3215, 3215, 3714, 23557, 5016, 1211], "avg_logprob": -0.15693681580679758, "compression_ratio": 1.8186813186813187, "no_speech_prob": 0.0, "words": [{"start": 338.26, "end": 338.92, "word": "comparisons", "probability": 0.7047119140625}, 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فإحنا هنا هنعدلها في ال code تبعنا لاحظوا ففي عندنا عدد مراحل و في عندنا عدد conversions داخل كل مرحلة من مراحل الشغل كويس هنبدأ مفهومها لوجة ال code ال sequence نفسه كيف القالية نفسها", "tokens": [29973, 5016, 37977, 5551, 12610, 7578, 12399, 3714, 2288, 5016, 37977, 6055, 7649, 10632, 12399, 3714, 2288, 5016, 37977, 6055, 6027, 2655, 3660, 12399, 3714, 2288, 16758, 27884, 12399, 16490, 2304, 3794, 3660, 12399, 8608, 18513, 3794, 3660, 4032, 20193, 5016, 19913, 14407, 14739, 6225, 3215, 3215, 9673, 23557, 5016, 1211, 4724, 43042, 3224, 3175, 732, 34105, 8032, 2655, 9566, 1211, 3615, 6156, 28814, 5016, 8315, 34105, 8032, 1863, 22488, 1211, 11296, 8978, 2423, 3089, 6055, 3555, 3615, 8315, 20193, 5016, 19913, 14407, 6156, 41185, 43242, 8315, 6225, 3215, 3215, 3714, 23557, 5016, 1211, 4032, 8978, 43242, 8315, 6225, 3215, 3215, 42256, 11778, 47283, 1211, 28242, 3714, 2288, 5016, 37977, 9154, 3714, 23557, 5016, 1211, 25124, 17082, 1211, 9122, 45865, 3794, 8032, 1863, 44510, 10721, 3714, 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بغض النظر عن ال coefficient اللي مضروبة فيه ال linear بس ال coefficient هذي فقط هتغيرلكوا وين موجود التقاطع هذا بس دائما في قيمة ل K بعدها التربيع دائما أكبر من ال linear دائما التربيع بيكون أكبر من ال linear بعد قيمة معينة له", "tokens": [3224, 1863, 39648, 25894, 11296, 591, 6156, 28820, 426, 5551, 4117, 26890, 9154, 591, 11778, 16373, 15042, 16712, 2288, 21292, 3615, 5551, 4117, 26890, 9154, 2423, 8213, 11778, 16373, 15042, 16712, 2288, 21292, 3615, 5551, 4117, 26890, 9154, 2423, 8213, 4724, 17082, 11242, 28239, 19913, 2288, 18871, 2423, 17619, 13672, 1829, 3714, 11242, 32887, 49401, 8978, 3224, 2423, 8213, 4724, 3794, 2423, 17619, 8032, 8848, 1829, 6156, 47432, 8032, 2655, 17082, 13546, 23275, 14407, 4032, 9957, 3714, 29245, 23328, 16712, 4587, 41193, 3615, 23758, 4724, 3794, 11778, 16373, 15042, 8978, 12174, 32640, 3660, 5296, 591, 39182, 11296, 16712, 2288, 21292, 3615, 11778, 16373, 15042, 5551, 4117, 26890, 9154, 2423, 8213, 11778, 16373, 15042, 16712, 2288, 21292, 3615, 4724, 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1541.09, "word": " K", "probability": 0.6884765625}, {"start": 1541.09, "end": 1542.05, "word": " بعدها", "probability": 0.96337890625}, {"start": 1542.05, "end": 1542.83, "word": " التربيع", "probability": 0.982421875}, {"start": 1542.83, "end": 1543.07, "word": " دائما", "probability": 0.8639322916666666}, {"start": 1543.07, "end": 1543.37, "word": " أكبر", "probability": 0.9597981770833334}, {"start": 1543.37, "end": 1543.53, "word": " من", "probability": 0.99560546875}, {"start": 1543.53, "end": 1543.63, "word": " ال", "probability": 0.94140625}, {"start": 1543.63, "end": 1543.87, "word": " linear", "probability": 0.955078125}, {"start": 1543.87, "end": 1544.95, "word": " دائما", "probability": 0.9637044270833334}, {"start": 1544.95, "end": 1545.43, "word": " التربيع", "probability": 0.9832763671875}, {"start": 1545.43, "end": 1545.67, "word": " بيكون", "probability": 0.7823893229166666}, {"start": 1545.67, "end": 1545.97, "word": " أكبر", "probability": 0.9488932291666666}, {"start": 1545.97, "end": 1546.11, "word": " من", "probability": 0.9951171875}, {"start": 1546.11, "end": 1546.21, "word": " ال", "probability": 0.92578125}, {"start": 1546.21, "end": 1546.37, "word": " linear", "probability": 0.939453125}, {"start": 1546.37, "end": 1546.63, "word": " بعد", "probability": 0.9619140625}, {"start": 1546.63, "end": 1546.99, "word": " قيمة", "probability": 0.9884440104166666}, {"start": 1546.99, "end": 1547.47, "word": " معينة", "probability": 0.9892578125}, {"start": 1547.47, "end": 1547.67, "word": " له", "probability": 0.83349609375}], "temperature": 1.0}, {"id": 60, "seek": 156819, "start": 1548.45, "end": 1568.19, "text": "ل N و هنسميها K اللي هي النقطة هذه فإذا for all N أكبر من K دائما المعادلة بالخط الأحمر هذه بال red line هتكون أكبر من ال black line", "tokens": [1211, 426, 4032, 8032, 1863, 38251, 1829, 11296, 591, 13672, 1829, 39896, 28239, 47432, 3660, 29538, 6156, 28814, 15730, 337, 439, 426, 5551, 4117, 26890, 9154, 591, 11778, 16373, 15042, 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و لسه ماصلنهاش شايفين جداش صار الفرق؟ معدل الفرق، معدل التغير فواضح انه المعادلة التربعية أسرع أسرع بالنسبة لزيادة N من المعادلة ال linear أو الخطية", "tokens": [27375, 1668, 11778, 16373, 15042, 8032, 2655, 30544, 1975, 4117, 26890, 9154, 2423, 700, 1668, 4032, 8032, 2655, 15040, 4587, 14407, 16472, 9673, 22488, 1211, 9122, 3555, 13546, 10874, 28259, 37495, 22653, 34105, 25961, 27188, 2288, 4587, 49374, 16095, 20666, 8592, 28820, 23758, 34105, 27188, 2288, 4587, 5296, 5016, 19913, 14407, 10874, 3215, 33599, 20328, 9640, 4032, 5296, 3794, 3224, 19446, 36520, 1863, 3224, 33599, 13412, 995, 33911, 9957, 10874, 3215, 33599, 20328, 9640, 27188, 2288, 4587, 22807, 20449, 3215, 1211, 27188, 2288, 4587, 12399, 20449, 3215, 1211, 16712, 17082, 13546, 6156, 2407, 46958, 5016, 16472, 3224, 9673, 3615, 18513, 37977, 16712, 25513, 3615, 10632, 5551, 3794, 2288, 3615, 5551, 3794, 2288, 3615, 20666, 1863, 35457, 3660, 5296, 11622, 1829, 18513, 3660, 426, 9154, 9673, 3615, 18513, 37977, 2423, 8213, 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if .. بدي أشوف if بالنسبة لل big O فبقول if at most .. رجعنا تاني هنا okay at most order g بمعنى هل هي .. إذا قولناها بهذا الشكل معناته أن ال if نفس order g أو أقل", "tokens": [267, 881, 1668, 290, 6156, 6027, 955, 422, 23758, 44945, 3615, 28480, 3224, 15844, 5551, 3794, 32277, 14739, 3224, 412, 881, 1668, 290, 6156, 2304, 43020, 5551, 39648, 498, 4386, 4724, 16254, 5551, 8592, 38688, 498, 20666, 1863, 35457, 3660, 24976, 955, 422, 6156, 3555, 39648, 498, 412, 881, 4386, 12602, 7435, 3615, 8315, 6055, 7649, 1829, 34105, 1392, 412, 881, 1668, 290, 4724, 2304, 3615, 1863, 7578, 8032, 1211, 39896, 4386, 11933, 15730, 12174, 12610, 8315, 11296, 39627, 15730, 25124, 28820, 20449, 8315, 47395, 14739, 2423, 498, 8717, 36178, 1668, 290, 34051, 5551, 4587, 1211], "avg_logprob": -0.20183633529033856, "compression_ratio": 1.6826923076923077, "no_speech_prob": 5.4836273193359375e-06, "words": [{"start": 2021.3, "end": 2021.68, "word": "at", "probability": 0.54052734375}, {"start": 2021.68, "end": 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"probability": 0.9580078125}, {"start": 2102.68, "end": 2102.92, "word": " function", "probability": 0.86279296875}, {"start": 2102.92, "end": 2103.28, "word": " صارت", "probability": 0.9720052083333334}, {"start": 2103.28, "end": 2103.62, "word": " element", "probability": 0.9814453125}, {"start": 2103.62, "end": 2103.98, "word": " داخل", "probability": 0.9777018229166666}, {"start": 2103.98, "end": 2104.38, "word": " set", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 81, "seek": 213231, "start": 2105.21, "end": 2132.31, "text": "الset هذي كل ال elements اللي تتفق ان هي big O لل first order تمام معناه ذلك لما انا بدي أجعل ريفا بقول set of functions ال function هذي from R to R نسبة لميه؟ لل function اللي أنا بدي أنسب إلها اللي بدي أنسب ال order إلها فهي function from R to R such that", "tokens": [6027, 3854, 8032, 8848, 1829, 28242, 2423, 4959, 13672, 1829, 6055, 2655, 5172, 4587, 16472, 39896, 955, 422, 24976, 700, 1668, 6055, 15042, 2304, 20449, 8315, 3224, 29910, 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إلها", "probability": 0.7135416666666666}, {"start": 2127.71, "end": 2128.25, "word": " اللي", "probability": 0.890869140625}, {"start": 2128.25, "end": 2128.41, "word": " بدي", "probability": 0.8837890625}, {"start": 2128.41, "end": 2128.73, "word": " أنسب", "probability": 0.9615885416666666}, {"start": 2128.73, "end": 2128.83, "word": " ال", "probability": 0.9072265625}, {"start": 2128.83, "end": 2129.05, "word": " order", "probability": 0.97021484375}, {"start": 2129.05, "end": 2129.37, "word": " إلها", "probability": 0.8546549479166666}, {"start": 2129.37, "end": 2129.99, "word": " فهي", "probability": 0.7724609375}, {"start": 2129.99, "end": 2130.67, "word": " function", "probability": 0.84814453125}, {"start": 2130.67, "end": 2130.93, "word": " from", "probability": 0.9189453125}, {"start": 2130.93, "end": 2131.17, "word": " R", "probability": 0.9921875}, {"start": 2131.17, "end": 2131.33, "word": " to", "probability": 0.984375}, {"start": 2131.33, "end": 2131.55, "word": " R", 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"end": 2175.88, "word": " function", "probability": 0.89453125}, {"start": 2175.88, "end": 2176.3, "word": " اللي", "probability": 0.9541015625}, {"start": 2176.3, "end": 2176.58, "word": " داخل", "probability": 0.97705078125}, {"start": 2176.58, "end": 2176.72, "word": " ال", "probability": 0.923828125}, {"start": 2176.72, "end": 2177.02, "word": " set", "probability": 0.91552734375}], "temperature": 1.0}, {"id": 84, "seek": 220565, "start": 2177.87, "end": 2205.65, "text": "أقل من أو تساوي C في G of X نسبنا هنا بالنسبة لمن؟ لل function اللي .. اللي احنا عارفين ال order تبعها و بدنا نعرف هل ال function F belong إلها أو لأ جينا example هالوجد، حنعرف كيف أطلع برضه ال C و ال K، حنعرف نطلع هالوجد ال C و ال K بس مبدأيا بنقول إنه بعد النقطة K ال function F is at most a constant C times of G", "tokens": [10721, 4587, 1211, 9154, 34051, 6055, 3794, 995, 45865, 383, 8978, 460, 295, 1783, 8717, 35457, 8315, 34105, 20666, 1863, 35457, 3660, 5296, 27842, 22807, 24976, 2445, 13672, 1829, 4386, 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"probability": 0.982421875}, {"start": 2194.11, "end": 2194.55, "word": " و", "probability": 0.91455078125}, {"start": 2194.55, "end": 2194.65, "word": " ال", "probability": 0.78564453125}, {"start": 2194.65, "end": 2194.79, "word": " K", "probability": 0.98828125}, {"start": 2194.79, "end": 2195.51, "word": " بس", "probability": 0.770751953125}, {"start": 2195.51, "end": 2196.67, "word": " مبدأيا", "probability": 0.846435546875}, {"start": 2196.67, "end": 2196.97, "word": " بنقول", "probability": 0.7398681640625}, {"start": 2196.97, "end": 2197.35, "word": " إنه", "probability": 0.6876220703125}, {"start": 2197.35, "end": 2197.81, "word": " بعد", "probability": 0.951171875}, {"start": 2197.81, "end": 2198.57, "word": " النقطة", "probability": 0.8411458333333334}, {"start": 2198.57, "end": 2198.93, "word": " K", "probability": 0.951171875}, {"start": 2198.93, "end": 2199.43, "word": " ال", "probability": 0.77099609375}, {"start": 2199.43, "end": 2199.75, "word": " function", "probability": 0.958984375}, {"start": 2199.75, "end": 2200.81, "word": " F", "probability": 0.72021484375}, {"start": 2200.81, "end": 2201.47, "word": " is", "probability": 0.93798828125}, {"start": 2201.47, "end": 2201.81, "word": " at", "probability": 0.90869140625}, {"start": 2201.81, "end": 2202.37, "word": " most", "probability": 0.916015625}, {"start": 2202.37, "end": 2203.01, "word": " a", "probability": 0.97216796875}, {"start": 2203.01, "end": 2203.45, "word": " constant", "probability": 0.95556640625}, {"start": 2203.45, "end": 2203.75, "word": " C", "probability": 0.82763671875}, {"start": 2203.75, "end": 2204.15, "word": " times", "probability": 0.87548828125}, {"start": 2204.15, "end": 2204.51, "word": " of", "probability": 0.93701171875}, {"start": 2204.51, "end": 2205.65, "word": " G", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 85, "seek": 223019, "start": 2207.6, "end": 2230.2, "text": "معناته ان هي proportional to G تتناسب مع G تتناسب هنا مع G هناخد example و هنرسم الرسم تبعهم عشان نشوف كيف العملية التناسب طيب نقرأها if is at most order G او if is big O of G او ممكن نقول if بتساوي big O of G", "tokens": [2304, 3615, 8315, 47395, 16472, 39896, 24969, 281, 460, 6055, 2655, 8315, 35457, 20449, 460, 6055, 2655, 8315, 35457, 34105, 20449, 460, 8032, 1863, 47283, 3215, 1365, 4032, 8032, 1863, 2288, 38251, 34892, 38251, 6055, 3555, 3615, 16095, 6225, 8592, 7649, 8717, 8592, 38688, 9122, 33911, 18863, 42213, 10632, 16712, 8315, 35457, 23032, 1829, 3555, 8717, 4587, 2288, 10721, 11296, 498, 307, 412, 881, 1668, 460, 1975, 2407, 498, 307, 955, 422, 295, 460, 1975, 2407, 3714, 43020, 8717, 39648, 498, 39894, 3794, 995, 45865, 955, 422, 295, 460], "avg_logprob": -0.13993055903249316, "compression_ratio": 1.5786802030456852, "no_speech_prob": 0.0, "words": [{"start": 2207.6, "end": 2208.12, "word": "معناته", "probability": 0.9151611328125}, {"start": 2208.12, "end": 2208.24, "word": " ان", "probability": 0.81982421875}, {"start": 2208.24, 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"probability": 0.98974609375}, {"start": 2227.08, "end": 2227.94, "word": " او", "probability": 0.97265625}, {"start": 2227.94, "end": 2228.5, "word": " ممكن", "probability": 0.93505859375}, {"start": 2228.5, "end": 2228.74, "word": " نقول", "probability": 0.9775390625}, {"start": 2228.74, "end": 2229.06, "word": " if", "probability": 0.8369140625}, {"start": 2229.06, "end": 2229.52, "word": " بتساوي", "probability": 0.814208984375}, {"start": 2229.52, "end": 2229.72, "word": " big", "probability": 0.84130859375}, {"start": 2229.72, "end": 2229.86, "word": " O", "probability": 0.95458984375}, {"start": 2229.86, "end": 2230.04, "word": " of", "probability": 0.97802734375}, {"start": 2230.04, "end": 2230.2, "word": " G", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 86, "seek": 224730, "start": 2231.16, "end": 2247.3, "text": "أو ممكن نكتبها if belong لإن احنا عرفنا ال if إن هي function داخل ال set اللي تحتوي على كل ال functions بتاعة ال big O فهي واحدة منهم فبقدر أقول إن هي element أو function belong to big O of G", "tokens": [10721, 2407, 3714, 43020, 8717, 4117, 2655, 3555, 11296, 498, 5784, 5296, 28814, 1863, 1975, 5016, 8315, 6225, 28480, 8315, 2423, 498, 36145, 39896, 2445, 11778, 47283, 1211, 2423, 992, 13672, 1829, 6055, 33753, 45865, 15844, 28242, 2423, 6828, 39894, 995, 27884, 2423, 955, 422, 6156, 3224, 1829, 36764, 24401, 3660, 9154, 16095, 6156, 3555, 28543, 2288, 5551, 39648, 36145, 39896, 4478, 34051, 2445, 5784, 281, 955, 422, 295, 460], "avg_logprob": -0.19586267815509312, "compression_ratio": 1.5303867403314917, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2231.16, "end": 2231.44, "word": "أو", "probability": 0.883056640625}, {"start": 2231.44, "end": 2231.66, "word": " ممكن", "probability": 0.846923828125}, {"start": 2231.66, "end": 2232.3, "word": " نكتبها", "probability": 0.9734375}, {"start": 2232.3, "end": 2233.0, "word": " if", "probability": 0.1888427734375}, {"start": 2233.0, "end": 2233.72, "word": " belong", 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0.9619140625}, {"start": 2247.04, "end": 2247.3, "word": " G", "probability": 0.8896484375}], "temperature": 1.0}, {"id": 87, "seek": 227452, "start": 2248.36, "end": 2274.52, "text": "بناء على التعريف بناء على تعريفنا ان احنا بتكلم عن set of functions أحيانا ممكن نقلش منها ال at most بتاعتنا فبقول if is order g خلاص ممكن جدا نختصرها طيب خلينا نشوف كيف نحسبها ال K و ال C اللي قلتلكم بدنا نجيبهم ناخد ال two examples اللي اتكلمنا عنهم اللي واحدة linear واحدة square", "tokens": [3555, 1863, 16606, 15844, 16712, 3615, 16572, 5172, 44945, 16606, 15844, 37279, 16572, 5172, 8315, 16472, 1975, 5016, 8315, 39894, 4117, 19528, 18871, 992, 295, 6828, 5551, 5016, 1829, 7649, 995, 3714, 43020, 8717, 4587, 1211, 8592, 9154, 11296, 2423, 412, 881, 39894, 995, 34268, 8315, 6156, 3555, 39648, 498, 307, 1668, 290, 16490, 1211, 33546, 3714, 43020, 10874, 28259, 8717, 46456, 9381, 2288, 11296, 23032, 1829, 3555, 16490, 1211, 9957, 995, 8717, 8592, 38688, 9122, 33911, 8717, 5016, 35457, 11296, 2423, 591, 4032, 2423, 383, 13672, 1829, 12174, 1211, 2655, 23275, 2304, 47525, 8315, 8717, 7435, 1829, 3555, 16095, 8717, 47283, 3215, 2423, 732, 5110, 13672, 1829, 1975, 2655, 4117, 19528, 8315, 18871, 16095, 13672, 1829, 36764, 24401, 3660, 8213, 36764, 24401, 3660, 3732], "avg_logprob": -0.19233630940554633, "compression_ratio": 1.6940298507462686, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2248.36, "end": 2248.72, "word": "بناء", "probability": 0.7970377604166666}, {"start": 2248.72, "end": 2248.86, "word": " على", "probability": 0.6708984375}, {"start": 2248.86, "end": 2249.4, "word": " التعريف", "probability": 0.82281494140625}, {"start": 2249.4, "end": 2249.92, "word": " بناء", "probability": 0.57275390625}, {"start": 2249.92, "end": 2250.0, "word": " على", "probability": 0.8330078125}, {"start": 2250.0, "end": 2250.38, "word": " تعريفنا", "probability": 0.8599853515625}, {"start": 2250.38, "end": 2250.46, "word": " ان", "probability": 0.38623046875}, {"start": 2250.46, "end": 2250.58, "word": " احنا", "probability": 0.83203125}, {"start": 2250.58, "end": 2250.82, "word": " بتكلم", "probability": 0.701171875}, {"start": 2250.82, "end": 2251.02, "word": " عن", "probability": 0.9794921875}, {"start": 2251.02, "end": 2251.32, "word": " set", "probability": 0.75048828125}, {"start": 2251.32, "end": 2251.62, "word": " of", "probability": 0.97607421875}, {"start": 2251.62, "end": 2254.04, "word": " functions", "probability": 0.86962890625}, {"start": 2254.04, "end": 2254.9, "word": " أحيانا", "probability": 0.85888671875}, {"start": 2254.9, "end": 2255.18, "word": " ممكن", "probability": 0.909912109375}, {"start": 2255.18, "end": 2256.08, "word": " نقلش", "probability": 0.649658203125}, {"start": 2256.08, "end": 2256.36, "word": " منها", "probability": 0.828125}, {"start": 2256.36, "end": 2256.62, "word": " ال", "probability": 0.417724609375}, {"start": 2256.62, "end": 2256.86, "word": " at", "probability": 0.81640625}, {"start": 2256.86, "end": 2257.3, "word": " most", "probability": 0.8095703125}, {"start": 2257.3, "end": 2258.52, "word": " بتاعتنا", "probability": 0.919921875}, {"start": 2258.52, "end": 2259.04, "word": " فبقول", "probability": 0.8836263020833334}, {"start": 2259.04, "end": 2259.34, "word": " if", "probability": 0.8837890625}, {"start": 2259.34, "end": 2259.7, "word": " is", "probability": 0.84375}, {"start": 2259.7, "end": 2260.14, "word": " order", "probability": 0.9404296875}, {"start": 2260.14, "end": 2260.46, "word": " g", "probability": 0.697265625}, {"start": 2260.46, "end": 2261.0, "word": " خلاص", "probability": 0.7178548177083334}, {"start": 2261.0, "end": 2261.9, "word": " ممكن", "probability": 0.946044921875}, {"start": 2261.9, "end": 2262.24, "word": " جدا", "probability": 0.9873046875}, {"start": 2262.24, "end": 2263.02, "word": " نختصرها", "probability": 0.98095703125}, {"start": 2263.02, "end": 2264.42, "word": " طيب", "probability": 0.8624674479166666}, {"start": 2264.42, "end": 2265.0, "word": " خلينا", "probability": 0.741455078125}, {"start": 2265.0, "end": 2265.2, "word": " نشوف", "probability": 0.9280598958333334}, {"start": 2265.2, "end": 2265.3, "word": " كيف", "probability": 0.9716796875}, {"start": 2265.3, "end": 2265.8, "word": " نحسبها", "probability": 0.771240234375}, {"start": 2265.8, "end": 2265.96, "word": " ال", "probability": 0.7607421875}, {"start": 2265.96, "end": 2266.14, "word": " K", "probability": 0.58984375}, {"start": 2266.14, "end": 2266.56, "word": " و", "probability": 0.65087890625}, {"start": 2266.56, "end": 2266.68, "word": " ال", "probability": 0.62548828125}, {"start": 2266.68, "end": 2266.8, "word": " C", "probability": 0.86962890625}, {"start": 2266.8, "end": 2266.92, "word": " اللي", "probability": 0.886962890625}, {"start": 2266.92, "end": 2267.26, "word": " قلتلكم", "probability": 0.8595703125}, {"start": 2267.26, "end": 2267.46, "word": " بدنا", "probability": 0.856689453125}, {"start": 2267.46, "end": 2267.94, "word": " نجيبهم", "probability": 0.9888671875}, {"start": 2267.94, "end": 2269.38, "word": " ناخد", "probability": 0.9837239583333334}, {"start": 2269.38, "end": 2269.52, "word": " ال", "probability": 0.982421875}, {"start": 2269.52, "end": 2269.64, "word": " two", "probability": 0.90966796875}, {"start": 2269.64, "end": 2270.04, "word": " examples", "probability": 0.759765625}, {"start": 2270.04, "end": 2270.36, "word": " اللي", "probability": 0.976806640625}, {"start": 2270.36, "end": 2271.4, "word": " اتكلمنا", "probability": 0.98076171875}, {"start": 2271.4, "end": 2271.72, "word": " عنهم", "probability": 0.987548828125}, {"start": 2271.72, "end": 2271.94, "word": " اللي", "probability": 0.937744140625}, {"start": 2271.94, "end": 2272.2, "word": " واحدة", "probability": 0.9759114583333334}, {"start": 2272.2, "end": 2272.4, "word": " linear", "probability": 0.68994140625}, {"start": 2272.4, "end": 2272.92, "word": " واحدة", "probability": 0.94775390625}, {"start": 2272.92, "end": 2274.52, "word": " square", "probability": 0.87060546875}], "temperature": 1.0}, {"id": 88, "seek": 228880, "start": 2275.58, "end": 2288.8, "text": "و بدنا نجيب هل فعلا هي big O of N او لأ نمسك الأولى تلاتين N plus تمانية is big O of N first order بدنا نثبت الكلام هذا و بدنا نوضح الكلام هذا", "tokens": [2407, 47525, 8315, 8717, 7435, 1829, 3555, 8032, 1211, 6156, 3615, 15040, 39896, 955, 422, 295, 426, 1975, 2407, 5296, 10721, 8717, 2304, 3794, 4117, 16247, 12610, 7578, 6055, 1211, 9307, 9957, 426, 1804, 46811, 7649, 10632, 307, 955, 422, 295, 426, 700, 1668, 47525, 8315, 8717, 12984, 3555, 2655, 2423, 28820, 10943, 23758, 4032, 47525, 8315, 8717, 2407, 11242, 5016, 2423, 28820, 10943, 23758], "avg_logprob": -0.161458332881783, "compression_ratio": 1.5384615384615385, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2275.58, "end": 2275.78, "word": "و", "probability": 0.354736328125}, {"start": 2275.78, "end": 2275.98, "word": " بدنا", "probability": 0.783203125}, {"start": 2275.98, "end": 2276.26, "word": " نجيب", "probability": 0.9794921875}, {"start": 2276.26, "end": 2276.44, "word": " هل", "probability": 0.92431640625}, {"start": 2276.44, "end": 2276.72, "word": " فعلا", "probability": 0.9256184895833334}, {"start": 2276.72, "end": 2276.92, "word": " هي", "probability": 0.72314453125}, {"start": 2276.92, "end": 2277.16, "word": " big", "probability": 0.61083984375}, {"start": 2277.16, "end": 2277.44, "word": " O", "probability": 0.88720703125}, {"start": 2277.44, "end": 2277.96, "word": " of", "probability": 0.91845703125}, {"start": 2277.96, "end": 2278.2, "word": " N", "probability": 0.8779296875}, {"start": 2278.2, "end": 2278.58, "word": " او", "probability": 0.789794921875}, {"start": 2278.58, "end": 2278.82, "word": " لأ", "probability": 0.833740234375}, {"start": 2278.82, "end": 2279.36, "word": " نمسك", "probability": 0.88037109375}, {"start": 2279.36, "end": 2279.92, "word": " الأولى", "probability": 0.9091796875}, {"start": 2279.92, "end": 2280.5, "word": " تلاتين", "probability": 0.79559326171875}, {"start": 2280.5, "end": 2280.76, "word": " N", "probability": 0.64013671875}, {"start": 2280.76, "end": 2281.14, "word": " plus", "probability": 0.5810546875}, {"start": 2281.14, "end": 2281.74, "word": " تمانية", "probability": 0.9729817708333334}, {"start": 2281.74, "end": 2282.3, "word": " is", "probability": 0.748046875}, {"start": 2282.3, "end": 2283.4, "word": " big", "probability": 0.81787109375}, {"start": 2283.4, "end": 2283.6, "word": " O", "probability": 0.9716796875}, {"start": 2283.6, "end": 2283.78, "word": " of", "probability": 0.974609375}, {"start": 2283.78, "end": 2284.04, "word": " N", "probability": 0.9873046875}, {"start": 2284.04, "end": 2284.62, "word": " first", "probability": 0.3232421875}, {"start": 2284.62, "end": 2285.12, "word": " order", "probability": 0.94482421875}, {"start": 2285.12, "end": 2286.38, "word": " بدنا", "probability": 0.903564453125}, {"start": 2286.38, "end": 2286.7, "word": " نثبت", "probability": 0.99560546875}, {"start": 2286.7, "end": 2287.04, "word": " الكلام", "probability": 0.9431966145833334}, {"start": 2287.04, "end": 2287.26, "word": " هذا", "probability": 0.86083984375}, {"start": 2287.26, "end": 2287.64, "word": " و", "probability": 0.6904296875}, {"start": 2287.64, "end": 2287.82, "word": " بدنا", "probability": 0.8369140625}, {"start": 2287.82, "end": 2288.24, "word": " نوضح", "probability": 0.9820556640625}, {"start": 2288.24, "end": 2288.6, "word": " الكلام", "probability": 0.96435546875}, {"start": 2288.6, "end": 2288.8, "word": " هذا", "probability": 0.96142578125}], "temperature": 1.0}, {"id": 89, "seek": 230939, "start": 2289.23, "end": 2309.39, "text": "ليش يقولنا 130؟ ليش احنا امتى قولنا ممكن تكون فعلا first order إذا كان يوجد C و K اللي بيحققولنا ال condition أن F of X أقل من أو تساوي C في N في ال order طبعا F of N", "tokens": [20292, 8592, 7251, 39648, 8315, 19966, 22807, 32239, 8592, 1975, 5016, 8315, 1975, 2304, 49975, 12174, 12610, 8315, 3714, 43020, 6055, 30544, 6156, 3615, 15040, 700, 1668, 11933, 15730, 25961, 7251, 29245, 3215, 383, 4032, 591, 13672, 1829, 4724, 1829, 5016, 4587, 4587, 12610, 8315, 2423, 4188, 14739, 479, 295, 1783, 5551, 4587, 1211, 9154, 34051, 6055, 3794, 995, 45865, 383, 8978, 426, 8978, 2423, 1668, 23032, 3555, 3615, 995, 479, 295, 426], "avg_logprob": -0.20893158461596514, "compression_ratio": 1.4033149171270718, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2289.23, "end": 2289.73, "word": "ليش", "probability": 0.6671142578125}, {"start": 2289.73, "end": 2290.21, "word": " يقولنا", "probability": 0.7222493489583334}, {"start": 2290.21, "end": 2290.73, "word": " 130؟", "probability": 0.66845703125}, {"start": 2290.73, "end": 2291.01, "word": " ليش", "probability": 0.676513671875}, {"start": 2291.01, "end": 2291.37, "word": " احنا", "probability": 0.757568359375}, {"start": 2291.37, "end": 2291.57, "word": " امتى", "probability": 0.79052734375}, {"start": 2291.57, "end": 2291.81, "word": " قولنا", "probability": 0.7547200520833334}, {"start": 2291.81, "end": 2292.09, "word": " ممكن", "probability": 0.897216796875}, {"start": 2292.09, "end": 2292.39, "word": " تكون", "probability": 0.97119140625}, {"start": 2292.39, "end": 2292.83, "word": " فعلا", "probability": 0.86572265625}, {"start": 2292.83, "end": 2294.99, "word": " first", "probability": 0.70654296875}, {"start": 2294.99, "end": 2295.47, "word": " order", "probability": 0.943359375}, {"start": 2295.47, "end": 2296.03, "word": " إذا", "probability": 0.7357177734375}, {"start": 2296.03, "end": 2296.33, "word": " كان", "probability": 0.98095703125}, {"start": 2296.33, "end": 2297.33, "word": " يوجد", "probability": 0.98193359375}, {"start": 2297.33, "end": 2297.83, "word": " C", "probability": 0.55029296875}, {"start": 2297.83, "end": 2298.71, "word": " و", "probability": 0.96533203125}, {"start": 2298.71, "end": 2298.95, "word": " K", "probability": 0.603515625}, {"start": 2298.95, "end": 2299.35, "word": " اللي", "probability": 0.90185546875}, {"start": 2299.35, "end": 2300.13, "word": " بيحققولنا", "probability": 0.93115234375}, {"start": 2300.13, "end": 2300.67, "word": " ال", "probability": 0.931640625}, {"start": 2300.67, "end": 2301.13, "word": " condition", "probability": 0.9921875}, {"start": 2301.13, "end": 2302.11, "word": " أن", "probability": 0.415771484375}, {"start": 2302.11, "end": 2303.09, "word": " F", "probability": 0.493896484375}, {"start": 2303.09, "end": 2303.65, "word": " of", "probability": 0.404296875}, {"start": 2303.65, "end": 2304.11, "word": " X", "probability": 0.95849609375}, {"start": 2304.11, "end": 2304.89, "word": " أقل", "probability": 0.9415690104166666}, {"start": 2304.89, "end": 2305.09, "word": " من", "probability": 0.99169921875}, {"start": 2305.09, "end": 2305.31, "word": " أو", "probability": 0.89794921875}, {"start": 2305.31, "end": 2305.79, "word": " تساوي", "probability": 0.96142578125}, {"start": 2305.79, "end": 2306.93, "word": " C", "probability": 0.84130859375}, {"start": 2306.93, "end": 2307.59, "word": " في", "probability": 0.89990234375}, {"start": 2307.59, "end": 2307.79, "word": " N", "probability": 0.87060546875}, {"start": 2307.79, "end": 2308.25, "word": " في", "probability": 0.79150390625}, {"start": 2308.25, "end": 2308.33, "word": " ال", "probability": 0.92529296875}, {"start": 2308.33, "end": 2308.57, "word": " order", "probability": 0.95654296875}, {"start": 2308.57, "end": 2308.83, "word": " طبعا", "probability": 0.9271240234375}, {"start": 2308.83, "end": 2309.05, "word": " F", "probability": 0.50048828125}, {"start": 2309.05, "end": 2309.21, "word": " of", "probability": 0.88037109375}, {"start": 2309.21, "end": 2309.39, "word": " N", "probability": 0.9765625}], "temperature": 1.0}, {"id": 90, "seek": 233721, "start": 2310.65, "end": 2337.21, "text": "تمام؟ بدنا نحقق الكلام هذا فعشان أحققه بدي أثبت أنه موجودة ال c و ال k طب كيف نقدر نجيب ال c و ال k؟ من هنا ال c مباشرة تقدر تاخدها من ال coefficient تبعت n هنا n طيب وين ال order n هنا؟ هيها كدوش ال coefficient تبعها؟ تلاتين معناته ال c", "tokens": [2655, 15042, 2304, 22807, 47525, 8315, 8717, 5016, 4587, 4587, 2423, 28820, 10943, 23758, 6156, 3615, 8592, 7649, 5551, 5016, 4587, 4587, 3224, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 3224, 3714, 29245, 23328, 3660, 2423, 269, 4032, 2423, 350, 23032, 3555, 9122, 33911, 8717, 28543, 2288, 8717, 7435, 1829, 3555, 2423, 269, 4032, 2423, 350, 22807, 9154, 34105, 2423, 269, 3714, 3555, 33599, 25720, 6055, 28543, 2288, 6055, 47283, 3215, 11296, 9154, 2423, 17619, 6055, 3555, 34268, 297, 34105, 297, 23032, 1829, 3555, 4032, 9957, 2423, 1668, 297, 34105, 22807, 39896, 11296, 9122, 3215, 2407, 8592, 2423, 17619, 6055, 3555, 3615, 11296, 22807, 6055, 1211, 9307, 9957, 20449, 8315, 47395, 2423, 269], "avg_logprob": -0.2568530610256028, "compression_ratio": 1.7990654205607477, "no_speech_prob": 1.3113021850585938e-06, "words": [{"start": 2310.65, "end": 2311.39, "word": "تمام؟", 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337607, "start": 3352.37, "end": 3376.07, "text": "لما تقولوا N belong to O of N first طيب بفرق لو قولنا تلاتة N ما هي برضه belong to first order نفس الكلام لو قولنا تلاتة N زائد C كمان زائد خمسة first order طيب ناقص عشرة نفس الكلام first order", "tokens": [1211, 15042, 6055, 39648, 14407, 426, 5784, 281, 422, 295, 426, 700, 23032, 1829, 3555, 4724, 5172, 2288, 4587, 45164, 12174, 12610, 8315, 6055, 1211, 9307, 3660, 426, 19446, 39896, 4724, 43042, 3224, 5784, 281, 700, 1668, 8717, 36178, 2423, 28820, 10943, 45164, 12174, 12610, 8315, 6055, 1211, 9307, 3660, 426, 30767, 16373, 3215, 383, 9122, 2304, 7649, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 700, 1668, 23032, 1829, 3555, 8717, 995, 4587, 9381, 6225, 8592, 25720, 8717, 36178, 2423, 28820, 10943, 700, 1668], "avg_logprob": -0.2023896995712729, "compression_ratio": 1.7763975155279503, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 3352.37, "end": 3352.67, "word": "لما", "probability": 0.7666015625}, {"start": 3352.67, 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{"start": 3543.27, "end": 3543.55, "word": " of", "probability": 0.97705078125}, {"start": 3543.55, "end": 3543.75, "word": " N", "probability": 0.98046875}, {"start": 3543.75, "end": 3543.89, "word": " to", "probability": 0.98388671875}, {"start": 3543.89, "end": 3544.01, "word": " the", "probability": 0.91748046875}, {"start": 3544.01, "end": 3544.15, "word": " power", "probability": 0.88818359375}, {"start": 3544.15, "end": 3544.51, "word": " 5", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 137, "seek": 357197, "start": 3545.25, "end": 3571.97, "text": "صحيح فهيها هي نفسها هي belong belong هذه هي نفسها دي فاللي هنختارها فعلا هي ال n to the power four اللي هي جي واحد جي واحد كويس مجموعة ال facts هي نفسها هي نفس اللي احنا خدناهم هدولاك ايه نفسهم", "tokens": [9381, 5016, 1829, 5016, 6156, 3224, 1829, 11296, 39896, 8717, 36178, 11296, 39896, 5784, 5784, 29538, 39896, 8717, 36178, 11296, 11778, 1829, 6156, 6027, 20292, 8032, 1863, 46456, 9640, 11296, 6156, 3615, 15040, 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نضرب function في constant هيظل نفس ال function هو معاه example تلاتة X تربيع برضه ال second order برضه second order لو قولنا F plus big O of F هي نفس big O of F لاحظوا هنا ال order هو ال order ال function طبعا هنا مدخل نفس ال function", "tokens": [1211, 2407, 19446, 8717, 11242, 25513, 2445, 8978, 5754, 39896, 19913, 1211, 8717, 36178, 2423, 2445, 31439, 20449, 40294, 1365, 6055, 1211, 9307, 3660, 1783, 6055, 2288, 21292, 3615, 4724, 43042, 3224, 2423, 1150, 1668, 4724, 43042, 3224, 1150, 1668, 45164, 12174, 12610, 8315, 479, 1804, 955, 422, 295, 479, 39896, 8717, 36178, 955, 422, 295, 479, 20193, 5016, 19913, 14407, 34105, 2423, 1668, 31439, 2423, 1668, 2423, 2445, 23032, 3555, 3615, 995, 34105, 3714, 3215, 9778, 1211, 8717, 36178, 2423, 2445], "avg_logprob": -0.23004518215914807, "compression_ratio": 1.71875, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3572.71, "end": 3573.01, "word": "لو", "probability": 0.773681640625}, {"start": 3573.01, "end": 3573.13, "word": " 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..", "probability": 0.26953125}, {"start": 3651.04, "end": 3651.28, "word": " ال", "probability": 0.84130859375}, {"start": 3651.28, "end": 3651.46, "word": " code", "probability": 0.6376953125}, {"start": 3651.46, "end": 3651.92, "word": " الأول", "probability": 0.952392578125}, {"start": 3651.92, "end": 3652.36, "word": " و", "probability": 0.62548828125}, {"start": 3652.36, "end": 3652.46, "word": " ال", "probability": 0.94775390625}, {"start": 3652.46, "end": 3652.64, "word": " order", "probability": 0.9638671875}, {"start": 3652.64, "end": 3652.8, "word": " بتاع", "probability": 0.7381591796875}, {"start": 3652.8, "end": 3652.9, "word": " ال", "probability": 0.91650390625}, {"start": 3652.9, "end": 3653.06, "word": " code", "probability": 0.98095703125}, {"start": 3653.06, "end": 3653.52, "word": " التاني", "probability": 0.8338216145833334}, {"start": 3653.52, "end": 3654.2, "word": " ال", "probability": 0.476806640625}, {"start": 3654.2, "end": 3654.56, "word": " order", "probability": 0.98095703125}, {"start": 3654.56, "end": 3655.18, "word": " الأقل", "probability": 0.986328125}, {"start": 3655.18, "end": 3655.76, "word": " هو", "probability": 0.98681640625}, {"start": 3655.76, "end": 3655.92, "word": " اللي", "probability": 0.93310546875}, {"start": 3655.92, "end": 3656.34, "word": " باخده", "probability": 0.971435546875}, {"start": 3656.34, "end": 3657.6, "word": " مين", "probability": 0.779296875}, {"start": 3657.6, "end": 3657.7, "word": " ال", "probability": 0.9951171875}, {"start": 3657.7, "end": 3657.92, "word": " order", "probability": 0.97265625}, {"start": 3657.92, "end": 3658.24, "word": " تبعه", "probability": 0.9605712890625}, {"start": 3658.24, "end": 3658.66, "word": " أقل", "probability": 0.9617513020833334}, {"start": 3658.66, "end": 3658.96, "word": " هو", "probability": 0.93408203125}, {"start": 3658.96, "end": 3659.08, "word": " اللي", "probability": 0.990478515625}, {"start": 3659.08, "end": 3659.42, "word": " بناخده", "probability": 0.928955078125}, {"start": 3659.42, "end": 3659.9, "word": " بنقول", "probability": 0.640380859375}, {"start": 3659.9, "end": 3660.06, "word": " لأ", "probability": 0.904296875}, {"start": 3660.06, "end": 3660.3, "word": " هذا", "probability": 0.91064453125}, {"start": 3660.3, "end": 3660.46, "word": " ال", "probability": 0.94384765625}, {"start": 3660.46, "end": 3660.74, "word": " code", "probability": 0.98779296875}, {"start": 3660.74, "end": 3661.32, "word": " أفضل", "probability": 0.9771728515625}, {"start": 3661.32, "end": 3662.18, "word": " more", "probability": 0.8818359375}, {"start": 3662.18, "end": 3662.66, "word": " efficient", "probability": 0.92919921875}, {"start": 3662.66, "end": 3663.32, "word": " ل", "probability": 0.765625}, {"start": 3663.32, "end": 3664.32, "word": " الشغل", "probability": 0.8356119791666666}, {"start": 3664.32, "end": 3664.42, "word": " اللي", "probability": 0.69189453125}, {"start": 3664.42, "end": 3664.58, "word": " ..", "probability": 0.56201171875}, {"start": 3664.58, "end": 3664.88, "word": " او", "probability": 0.83935546875}, {"start": 3664.88, "end": 3665.06, "word": " لل", "probability": 0.87890625}, {"start": 3665.06, "end": 3665.36, "word": " task", "probability": 0.9052734375}, {"start": 3665.36, "end": 3665.6, "word": " اللي", "probability": 0.986572265625}, {"start": 3665.6, "end": 3665.96, "word": " بنشتغل", "probability": 0.98115234375}, {"start": 3665.96, "end": 3666.46, "word": " عليها", "probability": 0.98828125}, {"start": 3666.46, "end": 3666.64, "word": " لل", "probability": 0.4140625}, {"start": 3666.64, "end": 3666.86, "word": " task", "probability": 0.95751953125}, {"start": 3666.86, "end": 3666.96, "word": " اللي", "probability": 0.993896484375}, {"start": 3666.96, "end": 3667.32, "word": " بنشتغل", "probability": 0.97939453125}, {"start": 3667.32, "end": 3667.7, "word": " عليها", "probability": 0.992919921875}, {"start": 3667.7, "end": 3668.18, "word": " على", "probability": 0.62939453125}, {"start": 3668.18, "end": 3668.46, "word": " بركة", "probability": 0.8924153645833334}, {"start": 3668.46, "end": 3668.54, "word": " الله", "probability": 0.9501953125}, {"start": 3668.54, "end": 3668.8, "word": " يعطيكم", "probability": 0.8251953125}, {"start": 3668.8, "end": 3669.16, "word": " العافية", "probability": 0.84423828125}, {"start": 3669.16, "end": 3669.3, "word": " و", "probability": 0.9638671875}, {"start": 3669.3, "end": 3669.58, "word": " نشوفكم", "probability": 0.8834228515625}, {"start": 3669.58, "end": 3669.74, "word": " المرة", "probability": 0.844482421875}, {"start": 3669.74, "end": 3669.94, "word": " الجاية", "probability": 0.6429036458333334}, {"start": 3669.94, "end": 3670.08, "word": " ان", "probability": 0.6279296875}, {"start": 3670.08, "end": 3670.24, "word": " شاء", "probability": 0.943603515625}, {"start": 3670.24, "end": 3670.3, "word": " الله", "probability": 0.94921875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3671.0285, "duration_after_vad": 3534.102499999984}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3a387570a836d9acc07d7a6fa3d05a5620c54ffb
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/5xrgOnF9Wig_raw.srt
@@ -0,0 +1,3000 @@
+1
+00:00:20,770 --> 00:00:23,090
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,090 --> 00:00:25,970
+الأنبياء والمرسلين سيدنا محمد وعلى أليه وصحبيه
+
+3
+00:00:25,970 --> 00:00:30,470
+أشمين بدأنا المرة اللي فاتت مع ال algorithms
+
+4
+00:00:30,470 --> 00:00:34,170
+واتكلمنا كيف ممكن نعمل code واتكلمنا عن ال
+
+5
+00:00:34,170 --> 00:00:37,070
+language المتعرف عليها اللي هنشتغل عليها اللي هي
+
+6
+00:00:37,070 --> 00:00:40,670
+ال pseudocode ال algorithm اللي هنكتب فيها ال
+
+7
+00:00:40,670 --> 00:00:45,530
+algorithms بتاعتنا خلال ال courseوصلنا لشوية
+
+8
+00:00:45,530 --> 00:00:49,350
+examples أخدنا ال searching و اتكلمنا عن نوعين او
+
+9
+00:00:49,350 --> 00:00:52,790
+two codes او two algorithms مشهورين جدا اللي هو ال
+
+10
+00:00:52,790 --> 00:00:57,370
+linear search و ال binary search وصلنا لعملية ال
+
+11
+00:00:57,370 --> 00:01:01,770
+sorting لانه لما كنا بنعمل searching حقيقة كنا
+
+12
+00:01:01,770 --> 00:01:06,580
+بنعمل searching على order او ordered listطيب ممكن
+
+13
+00:01:06,580 --> 00:01:10,040
+تجيكوا list مش ordered أساسا يعني ممكن أساسا تكون
+
+14
+00:01:10,040 --> 00:01:15,320
+unordered list أرقام عشوائية مبعثرة مش مرتبة لا ات
+
+15
+00:01:15,320 --> 00:01:18,760
+زد ولا زد ايه ولا يعني لا هى تصعدي ولا هى تنازلي
+
+16
+00:01:18,760 --> 00:01:23,480
+فبدنا نعمل code يعملنا الموضوع هذا هو يعملنا عملية
+
+17
+00:01:23,480 --> 00:01:29,180
+sorting عملية تصنيف عملية ترتيباتكلمنا عن نوعين
+
+18
+00:01:29,180 --> 00:01:32,220
+المرة اللى فاتت قولنا هنتكلم عن نوعين النوع الاول
+
+19
+00:01:32,220 --> 00:01:39,160
+ال bubble sort و ال insertion sort بداية ال bubble
+
+20
+00:01:39,160 --> 00:01:43,940
+sort code بالشكل اللى احنا شايفينه او sequence
+
+21
+00:01:43,940 --> 00:01:48,210
+بهذا الشكل اللى احنا شايفينه هذا هو ال sequenceالـ
+
+22
+00:01:48,210 --> 00:01:52,730
+left sequence هو ال initial sequence تبعنا بداية
+
+23
+00:01:52,730 --> 00:01:55,950
+ال sequence كيف جاي ترتيبه جاي ترتيبه تلاتين و
+
+24
+00:01:55,950 --> 00:01:58,550
+واحد و تلاتين و واحد و تلاتين و تلاتين و تلاتين و
+
+25
+00:01:58,550 --> 00:01:59,870
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+26
+00:01:59,870 --> 00:02:02,110
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+27
+00:02:02,110 --> 00:02:02,130
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+28
+00:02:02,130 --> 00:02:02,130
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+29
+00:02:02,130 --> 00:02:02,310
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+30
+00:02:02,310 --> 00:02:07,830
+تلاتين و تلاتين و تلاتين و تلاتين و تلاتين و
+
+31
+00:02:07,830 --> 00:02:13,250
+تلاتين و تلاتين و
+
+32
+00:02:19,170 --> 00:02:23,810
+وزنه بكون أقل فبطلع as a bubble كفقاعة هوة على
+
+33
+00:02:23,810 --> 00:02:26,490
+السطح لأ احنا ال code تبعنا رغم ان هو اسمه bubble
+
+34
+00:02:26,490 --> 00:02:30,010
+sort بس احنا هنشتغل على القيم الكبيرة من بداية ال
+
+35
+00:02:30,010 --> 00:02:34,770
+sequence يعني هنيجي نعمل عملية مقارنات عملية
+
+36
+00:02:34,770 --> 00:02:38,830
+المقارنات هذه بتبدأ من أول element في ال sequence
+
+37
+00:02:38,830 --> 00:02:42,310
+نبدأ بأول element في ال list بتاعتنا و بنعمله
+
+38
+00:02:42,310 --> 00:02:45,880
+مقارنة مع التانيفهيكون عندنا مقارنة أولى طيب
+
+39
+00:02:45,880 --> 00:02:50,920
+تلاتين واحد تلاتين دايما بنحاول نخلي الأقل في
+
+40
+00:02:50,920 --> 00:02:54,940
+الترتيب الأقل للأول طيب هنا عندنا location واحد
+
+41
+00:02:54,940 --> 00:02:58,160
+location اتنين location واحد أقل من location اتنين
+
+42
+00:02:58,160 --> 00:03:01,600
+فبنحط فيه الرقم الأقل فتلاتين واحد تلاتين مش
+
+43
+00:03:01,600 --> 00:03:07,080
+محتاجة تغيير ابنش بنعمل مقارنة مين ال location او
+
+44
+00:03:07,080 --> 00:03:08,680
+الرقم في ال location التاني مع الرقم في ال
+
+45
+00:03:08,680 --> 00:03:14,880
+location التالت واحد تلاتين مع واحدأه الواحد أقل
+
+46
+00:03:14,880 --> 00:03:21,140
+فبنعمل swap أو interchange بنعكس هذا مكان هذا و
+
+47
+00:03:21,140 --> 00:03:27,300
+هذا مكان هذا فهيبقى عكسه هنا كويس مدام عكسنا بده
+
+48
+00:03:27,300 --> 00:03:29,900
+يصير هنا عندي الواحد و هنا بده يصير الواحد تلاتين
+
+49
+00:03:29,900 --> 00:03:33,600
+بنقارنها لوجه التلاتة مع أربعة تلاتة مع أربعة و
+
+50
+00:03:33,600 --> 00:03:37,700
+واحد و تلاتين مع اتنين و تلاتين بتظل زي ما هي طيب
+
+51
+00:03:37,700 --> 00:03:41,660
+اتنين و تلاتين مع تلاتة و تلاتينتلاتة و تلاتين مع
+
+52
+00:03:41,660 --> 00:03:46,420
+اتنين سواب تصير هنا الاتنين و هنا تلاتة و تلاتين
+
+53
+00:03:46,420 --> 00:03:51,660
+طيب بنكمل لسه احنا مازلنا في اول مرحلة كل هذه لسه
+
+54
+00:03:51,660 --> 00:03:56,440
+مرحلة واحدة مرحلة أولى بقارن كل رقم مع اللي وراه
+
+55
+00:03:56,440 --> 00:03:59,000
+كل رقم مع اللي وراه كل element مع ال element اللي
+
+56
+00:03:59,000 --> 00:04:01,580
+بعده طيب صارت تلاتة و تلاتين مع اربعة و تلاتين
+
+57
+00:04:01,580 --> 00:04:06,370
+ثابتبعدين اربعة و تلاتين مع تلاتة سواب بتصير هنا
+
+58
+00:04:06,370 --> 00:04:09,950
+التلاتة و هنا الأربعة و تلاتين لاحظوا انه هو هذا
+
+59
+00:04:09,950 --> 00:04:13,230
+ال sequence صار بالشجرة بس انا لسه مخلصتش انا كل
+
+60
+00:04:13,230 --> 00:04:18,870
+اللي عملته ايش سويت اتجل element حطته في القاعبس
+
+61
+00:04:18,870 --> 00:04:24,930
+فعليا أول مرحلة أكبر رقم موجود حطيته في ال last
+
+62
+00:04:24,930 --> 00:04:27,890
+location حطيناه في ايش؟ في ال last location فصار
+
+63
+00:04:27,890 --> 00:04:30,230
+في ال last location هلوجد لما بدي أجي أعمل عدد
+
+64
+00:04:30,230 --> 00:04:32,770
+مقارنات، لاحظوا هنا واحد، اتنين، تلاتة، أربعة،
+
+65
+00:04:32,770 --> 00:04:37,150
+خمس، ستة، سبعة، تمانية ال N بتاعتنا بتمانية، عندنا
+
+66
+00:04:37,150 --> 00:04:42,010
+تمانية elements، صحيح؟ تمانية elements، محتاجين N
+
+67
+00:04:42,010 --> 00:04:44,230
+minus one comparisons
+
+68
+00:04:46,270 --> 00:04:53,830
+هذه مقارنة تنتين تلاتة أربعة خمسة ستة سبعة تمام؟
+
+69
+00:04:53,830 --> 00:04:59,490
+كويس آخر رقم هنا ثابت خلاص أنا من المرحلة الأولى
+
+70
+00:04:59,490 --> 00:05:02,870
+ثبتت أن هذا أكبر رقم موجود بقرنوه و بقرنوش كمان
+
+71
+00:05:02,870 --> 00:05:07,370
+مرة ففي المرحلة التانية كان عندي سبعة comparisons
+
+72
+00:05:07,370 --> 00:05:13,220
+بصيروا ستةبصير عندى واحد اتنين تلاتة اربع خمسة ستة
+
+73
+00:05:13,220 --> 00:05:15,740
+الاربعة و تلاتين لأ لان احنا عارفين من المرحلة
+
+74
+00:05:15,740 --> 00:05:17,840
+الأولى ان الاربعة و تلاتين هو اكبر رقم كان موجود
+
+75
+00:05:17,840 --> 00:05:24,140
+بدليل انه صفة في الاخر في قاع ال sequence تبعكم او
+
+76
+00:05:24,140 --> 00:05:28,260
+ال list بتاعتكم as a last element موجود في ال list
+
+77
+00:05:28,260 --> 00:05:34,240
+كويس اللي بعدها هتلاقوا صار اتنين صاروا تحت و مش
+
+78
+00:05:34,240 --> 00:05:36,760
+محتاجين يتقارنوا فيهم كمان مرة بتصير انك تشتغلوا
+
+79
+00:05:36,760 --> 00:05:42,580
+على خمسةcomparisons أربعة comparisons تلاتة
+
+80
+00:05:42,580 --> 00:05:50,960
+comparisons two comparisons و stop فلاحظوا حتى عدد
+
+81
+00:05:50,960 --> 00:05:56,020
+المقارنات اللي هتحتاجوها كل مرة بتجيل طيب فصار
+
+82
+00:05:56,020 --> 00:06:02,420
+عندنا عدد مقارنات بدنا نعملها في كل مرحلة و عندنا
+
+83
+00:06:02,420 --> 00:06:06,240
+أيش كمان عندنا عدد مراحلمرحلة أولى، مرحلة تانية،
+
+84
+00:06:06,240 --> 00:06:09,620
+مرحلة تالتة، مرابعة، خمسة، سادسة و لاحظوا أن عدد
+
+85
+00:06:09,620 --> 00:06:17,500
+المراحل برضه minus two هنا هتطلع فإحنا هنا هنعدلها
+
+86
+00:06:17,500 --> 00:06:22,620
+في ال code تبعنا لاحظوا ففي عندنا عدد مراحل و في
+
+87
+00:06:22,620 --> 00:06:27,860
+عندنا عدد conversions داخل كل مرحلة من مراحل الشغل
+
+88
+00:06:27,860 --> 00:06:32,640
+كويس هنبدأ مفهومها لوجة ال code ال sequence نفسه
+
+89
+00:06:32,640 --> 00:06:35,600
+كيف القالية نفسهاهلوجد مننا نعملها code نكتب لها
+
+90
+00:06:35,600 --> 00:06:42,040
+code نشتغل عليه نكتب
+
+91
+00:06:42,040 --> 00:06:46,100
+لنا code معين و نشتغل عليه طيب ال code هذا خلينا
+
+92
+00:06:46,100 --> 00:06:49,960
+نكتب معانا sequence على الجنب و نشتغله مع ال code
+
+93
+00:06:49,960 --> 00:06:53,640
+parallel مع ال code عشان نكون متابعين ال code كويس
+
+94
+00:06:53,640 --> 00:06:58,220
+مع real list مع قائمة بنجرب عليها خلينا نقول ان في
+
+95
+00:06:58,220 --> 00:07:04,510
+ال list بتاعتناsay مثلا خليني اقول طبعا احنا عرفنا
+
+96
+00:07:04,510 --> 00:07:07,770
+ال procedure و before sort على اساس انه هي الاسم
+
+97
+00:07:07,770 --> 00:07:10,910
+تبعنا ال procedure انا داخل هنا على algorithm على
+
+98
+00:07:10,910 --> 00:07:17,970
+code عرفناهم an element داخل list و سمنهم ايش real
+
+99
+00:07:17,970 --> 00:07:24,650
+numbers within أكبر من أو تساوي اتنين لان واحد بدي
+
+100
+00:07:24,650 --> 00:07:29,030
+اقارنه مع مينفخلاص هو sorted لحاله لحاله رقم واحد
+
+101
+00:07:29,030 --> 00:07:34,130
+رقمين بكون محتاج عملية comparison واحدة هم موجودين
+
+102
+00:07:34,130 --> 00:07:36,710
+الإتنين بعمل comparison بينهم مين الأقل بخلوه في
+
+103
+00:07:36,710 --> 00:07:40,530
+الأول بحطه في الأول طيب real numbers خليني أشوف
+
+104
+00:07:40,530 --> 00:07:43,610
+إنها مجموعة real numbers لو قلنا مثلا عندنا three
+
+105
+00:07:43,610 --> 00:07:52,790
+three point two مثلا و
+
+106
+00:07:52,790 --> 00:08:00,480
+two point fiveone point one three
+
+107
+00:08:00,480 --> 00:08:04,500
+point one احد اتنين اربعة اتنين اربعة اتنين اربعة
+
+108
+00:08:04,500 --> 00:08:06,400
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+109
+00:08:06,400 --> 00:08:07,360
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+110
+00:08:07,360 --> 00:08:07,360
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+111
+00:08:07,360 --> 00:08:07,360
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+112
+00:08:07,360 --> 00:08:09,280
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+113
+00:08:09,280 --> 00:08:11,420
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين اربعة
+
+114
+00:08:11,420 --> 00:08:24,320
+اتنين اربعة اتنين اربعة اتنين اربعة اتنين ارب
+
+115
+00:08:25,350 --> 00:08:29,290
+لأربعة، واحد، اتنين، تلاتة، أربعة، خمسة، لأربعة،
+
+116
+00:08:29,290 --> 00:08:35,710
+تمام؟ كويس، هذه اللوب هذا هيعطينا المراحل اللي
+
+117
+00:08:35,710 --> 00:08:39,350
+هنشتغل عليها، أكم مرحلة أنا محتاجها، كانت مرحلة
+
+118
+00:08:39,350 --> 00:08:42,390
+اتنين، تلاتة، أربعة، خمسة، زي ما كان التو مرسومة،
+
+119
+00:08:42,390 --> 00:08:48,010
+طيب في فرد داخلي في كل مرحلة أكم comparison هنعمل،
+
+120
+00:08:48,010 --> 00:08:51,370
+بصبوت، طيب أكم comparison هنعمل برضه من واحد to N
+
+121
+00:08:51,370 --> 00:08:55,940
+minus Iليش؟ لأن في كل مرحلة هنجس عدد ال
+
+122
+00:08:55,940 --> 00:09:00,940
+conversions صح؟ جربناها وقلنا إن في كل مرحلة بتجل
+
+123
+00:09:00,940 --> 00:09:04,180
+عدد ال conversions اللي أنا محتاجها طيب فكل مرة
+
+124
+00:09:04,180 --> 00:09:07,560
+أول ما هنبدأ .. هنبدأ كان عندي تمانية صار بدي
+
+125
+00:09:07,560 --> 00:09:11,600
+محتاج سبعة conversions سبعة conversions فهبدأ to N
+
+126
+00:09:11,600 --> 00:09:16,620
+minus I I هنا واحد فانا في المرحلة الأولى محتاج N
+
+127
+00:09:16,620 --> 00:09:20,900
+minus onecomparisons طب فى المرحلة التانية minus
+
+128
+00:09:20,900 --> 00:09:26,020
+two بتكون هنا i صارت اتنين فى المرحلة الأخيرة n
+
+129
+00:09:26,020 --> 00:09:30,060
+minus one بتصير انا محتاج comparison واحدة لأنه
+
+130
+00:09:30,060 --> 00:09:33,680
+بيكون ضال رقمين بس بيكون ضال رقمين خلّينى نشوف
+
+131
+00:09:33,680 --> 00:09:37,980
+الكلام هذا فعلا على list موجودة جدامنا هنبدأ هنا ب
+
+132
+00:09:37,980 --> 00:09:43,940
+i بتساوي واحد فإذا two n minus one يعني مدى معنى
+
+133
+00:09:43,940 --> 00:09:47,320
+ذلك بتكلم عن ايش عن أربعة بتكلم عن أربعة هنا
+
+134
+00:09:47,320 --> 00:09:56,220
+وأربعة هناOkay أربعة و أربعة نبدأ if a one هاي ال
+
+135
+00:09:56,220 --> 00:10:01,360
+j بدينها بين واحد أكبر من j plus one أكبر من اتنين
+
+136
+00:10:01,360 --> 00:10:05,780
+فبشوف ال element الأول مع ال element التاني if ال
+
+137
+00:10:05,780 --> 00:10:08,640
+element الأول أكبر من ال element التاني نعمل
+
+138
+00:10:08,640 --> 00:10:13,740
+interchange swap بنبدلهم مع بعض كويس فلينا نشوف
+
+139
+00:10:13,740 --> 00:10:18,560
+هاي الأول و هاي التانيهل فعلا الأول أكبر من
+
+140
+00:10:18,560 --> 00:10:24,500
+التاني؟ الأول أكبر من التاني فالأول أكبر من التاني
+
+141
+00:10:24,500 --> 00:10:28,660
+في الحالة هذي بنقول على طول two point five و three
+
+142
+00:10:28,660 --> 00:10:34,840
+point two بهذا الشكل طيب خلصنا I بتساوي واحد I
+
+143
+00:10:34,840 --> 00:10:41,680
+بتساوي اتنين صار بقارن اتنين مع تلاتة هاي اتنين مع
+
+144
+00:10:41,680 --> 00:10:43,280
+تلاتة
+
+145
+00:10:44,880 --> 00:10:51,340
+3.2 مع 1.1 التاني أكبر من التالت فبنحط هنا التالت
+
+146
+00:10:51,340 --> 00:10:57,080
+بيصير هو التاني و التاني بيصير هو التالت طيب خلصنا
+
+147
+00:10:57,080 --> 00:11:05,180
+I سوى تلاتة صار بقارن تلاتة مع أربعة هي تلاتة واحد
+
+148
+00:11:05,180 --> 00:11:09,960
+اتنين هي تلاتة مع أربعة أكبر بدلناهم
+
+149
+00:11:14,800 --> 00:11:20,680
+خلاص اخر رقم اربعة اربعة اربعة
+
+150
+00:11:20,680 --> 00:11:23,920
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+151
+00:11:23,920 --> 00:11:24,080
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+152
+00:11:24,080 --> 00:11:24,480
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+153
+00:11:24,480 --> 00:11:26,660
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+154
+00:11:26,660 --> 00:11:26,880
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+155
+00:11:26,880 --> 00:11:28,000
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+156
+00:11:28,000 --> 00:11:34,400
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+157
+00:11:34,400 --> 00:11:34,400
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+158
+00:11:34,400 --> 00:11:39,600
+اربعة اربعة اربعة اربعة
+
+159
+00:11:39,600 --> 00:11:42,100
+اربعة
+
+160
+00:11:44,880 --> 00:11:48,400
+تنين هذا المفروض من واحد لاربعة احنا لسه ماوصلناش
+
+161
+00:11:48,400 --> 00:11:53,220
+لاربعة لسه اتنين اتنين معناته هنبدأ هنا من واحد
+
+162
+00:11:53,220 --> 00:11:59,120
+تخمسة minus اتنين لتلاتة لانه هحتاج تلاتة
+
+163
+00:11:59,120 --> 00:12:01,600
+conversions بس في المرحلة الأولى كنت محتاج اربعة
+
+164
+00:12:01,600 --> 00:12:05,360
+conversions واحدة اتنين تلاتة اربعة في المرحلة
+
+165
+00:12:05,360 --> 00:12:09,420
+التانية هنحتاج تلاتة بس ليش لان تلاتة فاصلة اتنين
+
+166
+00:12:09,420 --> 00:12:13,510
+هذه خلاص هتبقى ثابتة ومش هقارن فيها مرة تانيةقرننا
+
+167
+00:12:13,510 --> 00:12:18,070
+وما وصلها لل last location إلا إن هي أكبر رقم
+
+168
+00:12:18,070 --> 00:12:22,270
+موجود لو لإن هي أكبر رقم موجود كان ماوصلتش في ال
+
+169
+00:12:22,270 --> 00:12:27,850
+last location كويسة نشوف عند الواحد واحد مع اتنين
+
+170
+00:12:27,850 --> 00:12:35,110
+واحد مع اتنين one point one two point five طيب عند
+
+171
+00:12:35,110 --> 00:12:41,110
+الاتنين اتنين مع تلاتة اتنين مع تلاتة بيضلواخلاص
+
+172
+00:12:41,110 --> 00:12:47,450
+بتنزل زي ما هي طيب تلاتة مع أربعة تلاتة مع أربعة
+
+173
+00:12:47,450 --> 00:12:53,390
+swap خلاص
+
+174
+00:12:53,390 --> 00:12:59,090
+stop أنا وصلت التلاتة هذه بتبقى زي ما هي هتبقى
+
+175
+00:12:59,090 --> 00:13:03,710
+ثابتة لأنه ماوصلنالهاش في ال loop كويسة هيخلصنا
+
+176
+00:13:03,710 --> 00:13:10,530
+كمان مرة بنصل هنا لمين ل I بتساوي تلاتةصار هنا
+
+177
+00:13:10,530 --> 00:13:16,650
+كده؟ خمسة ناقص تلاتة اتنين مقارنة
+
+178
+00:13:16,650 --> 00:13:19,230
+محتاجة تقوم بارزوز اللي هنعملهم فعليا تقوم بارزوز
+
+179
+00:13:19,230 --> 00:13:24,610
+خلينا نشوف ا بواحد مع ا باتنين ا واحد أكبر من
+
+180
+00:13:24,610 --> 00:13:30,850
+اتنين؟ لأ بنزلوا زي ما هم طيب اتنين مع ا تلاتة
+
+181
+00:13:30,850 --> 00:13:31,430
+أكبر
+
+182
+00:13:38,400 --> 00:13:44,440
+و هدولة خلاص خلصنا اللوب بيظلوا زي ما هما خلصنا
+
+183
+00:13:44,440 --> 00:13:49,860
+هاي اللوب هادى هنرجع نطلع للوب العلوية جديش أربعة
+
+184
+00:13:49,860 --> 00:13:56,320
+آخر رقم عند I بتساوي أربعة طيب خمسة نقص أربعة واحد
+
+185
+00:13:58,080 --> 00:14:01,500
+خلاص انا هعمل مقارنة واحدة اللي هي بين اول اتنين
+
+186
+00:14:01,500 --> 00:14:10,300
+بس اول اتنين ماتغيروش بيظل 1.1 2.4 2.5 3.1 و 3.2
+
+187
+00:14:10,300 --> 00:14:18,980
+sorted list لحظة sorted عملنا لها sorting عملنا
+
+188
+00:14:18,980 --> 00:14:22,460
+لها ترتيب عملنا لها ترتيب في الحالة التاعتناها دي
+
+189
+00:14:22,460 --> 00:14:28,710
+okay واضح ليه ال codeواضح و انا فهمنا ليش n-i و
+
+190
+00:14:28,710 --> 00:14:33,710
+هذه نتيجة ان انا كل مرة في element بصفة في الآخر
+
+191
+00:14:33,710 --> 00:14:36,750
+مش محتاج راجع اقارن فيه لان انا قارنته في المرحلة
+
+192
+00:14:36,750 --> 00:14:39,170
+الأولى قارنناه في المرحلة الأولى مش هنقعد نقارن
+
+193
+00:14:39,170 --> 00:14:50,430
+فيه كمان مرة طيب هذه ال sort ال bubble sort خلوها
+
+194
+00:14:50,430 --> 00:14:52,070
+.. خلوها لكم
+
+195
+00:14:59,840 --> 00:15:03,320
+النوع التانى اللى هى insertion sort algorithm
+
+196
+00:15:03,320 --> 00:15:06,180
+insertion sort algorithm بيعتمد على عملية ال
+
+197
+00:15:06,180 --> 00:15:09,520
+search اللى أخدناها سابقا جماله كنا أخدنا search
+
+198
+00:15:09,520 --> 00:15:17,080
+سواء بال linear أو بال binary و خلينا نمسك برضه
+
+199
+00:15:17,080 --> 00:15:22,800
+نفس ال sequence تبعنا و نحاول نشتغل معاه الفكرة
+
+200
+00:15:22,800 --> 00:15:26,420
+كيف بتتم؟ بتتم انه انا بفترض في عندنا sequence انا
+
+201
+00:15:26,420 --> 00:15:30,610
+بدي أعمله creation انا بدي أنشئهبنبدأ بأول element
+
+202
+00:15:30,610 --> 00:15:38,170
+ال element الأول هنا بنحطه كأول element في ال set
+
+203
+00:15:38,170 --> 00:15:43,170
+هذه أو في ال list طيب ال element التاني بتعامل
+
+204
+00:15:43,170 --> 00:15:49,390
+معاه كأنه بيعمل search x مش كنا بنسميه في element
+
+205
+00:15:49,390 --> 00:15:53,110
+x وفي ال list و ال element x بدور عليه داخل ال
+
+206
+00:15:53,110 --> 00:15:56,410
+list عشان أعرف إيش ال location تبعه نعرف مين ال
+
+207
+00:15:56,410 --> 00:16:02,840
+location تبعه كويسةالـ X هذا اللي هو 2.5 هنقارنه
+
+208
+00:16:02,840 --> 00:16:10,000
+مع 3.2 إذا أقل بياخد ال location تبعها و بيعمل لها
+
+209
+00:16:10,000 --> 00:16:15,940
+shift إذا أقل بياخد ال location تبع الرقم اللي
+
+210
+00:16:15,940 --> 00:16:20,000
+جدامه اللي أكبر منه و بيعمل shift له لكل اللي وراه
+
+211
+00:16:20,000 --> 00:16:25,940
+فإذا هذه كانت A1ماكنش في عناقية 2 طب انا بده ادخل
+
+212
+00:16:25,940 --> 00:16:36,020
+2.5 فبندخل 2.5 و بنقارنها مع 3.2 3.2 أكبر معناته
+
+213
+00:16:36,020 --> 00:16:41,380
+هت سيب تتخلى عن مكانها وهذه هنعملها insertion
+
+214
+00:16:41,380 --> 00:16:44,940
+insertion
+
+215
+00:16:44,940 --> 00:16:51,390
+في ال location اللي ثابته 3.2بتصير هنا اتنين و نص
+
+216
+00:16:51,390 --> 00:16:54,850
+صار عندنا ال list بتاعتنا فيه two elements بنكرر
+
+217
+00:16:54,850 --> 00:17:00,590
+نفس الكلام على ال X الجديدة one point one برضه
+
+218
+00:17:00,590 --> 00:17:07,130
+عمليت search بعمل search على ال one point one one
+
+219
+00:17:07,130 --> 00:17:13,050
+point one one point one بالنسبة ل two point five
+
+220
+00:17:13,050 --> 00:17:17,550
+اقل اقل معناته CP لل location تبعيlocation تبحر
+
+221
+00:17:17,550 --> 00:17:20,470
+بسبب معناه ذلك ان كل هذا كل ال sequence اللى كان
+
+222
+00:17:20,470 --> 00:17:24,490
+موجود هنا كله بدى نعمله shift كانوا a2 بيصير ل a3
+
+223
+00:17:24,490 --> 00:17:31,710
+هدى صارت 3.2 2.5 shift لكل الأرقام اللى وراها و
+
+224
+00:17:31,710 --> 00:17:35,550
+هنا بنعملها insertion في ال location اللى جديد في
+
+225
+00:17:35,550 --> 00:17:43,750
+المكان اللى فضل okay اللى وراها 3.1 بنعمل مقارنة
+
+226
+00:17:43,750 --> 00:17:50,460
+مع ال 1.1هل هي أقل من .. لأ خلاص بتسيبها واضح أن
+
+227
+00:17:50,460 --> 00:17:54,100
+ال location هذا مش تبعها طيب بنشوف ال location
+
+228
+00:17:54,100 --> 00:18:01,940
+التاني 3.1 مع 2.3 لأالـ location هذا مش تبحها طيب
+
+229
+00:18:01,940 --> 00:18:08,400
+3.1 مع 3.2 أقل من .. مدام أقل من هذه لازم تشوف
+
+230
+00:18:08,400 --> 00:18:11,220
+location تاني يعملها shift على ال location اللي
+
+231
+00:18:11,220 --> 00:18:15,200
+وراها و بنعمل insertion لل X هذا اللي كنت بعمله ..
+
+232
+00:18:15,200 --> 00:18:18,480
+بعمله search عرفت كون المفروض ال location يكون
+
+233
+00:18:18,480 --> 00:18:21,160
+فبدخله في ال location طبعه و بعمله insertion في ال
+
+234
+00:18:21,160 --> 00:18:29,760
+location الطبيعي طبعه الصحيح كويسأخر رقم 2.4 2.4
+
+235
+00:18:29,760 --> 00:18:35,760
+برضه بنرجع بنقارنها مع طبعا احنا هنا ماكتبناش بس
+
+236
+00:18:35,760 --> 00:18:43,160
+32 أكبر من 1.1 فسيب ال 1.1 في حالها ماليناهش علاقة
+
+237
+00:18:43,160 --> 00:18:47,560
+فيها طيب 2.5 لأ أقل من 2.5 معناته ال location
+
+238
+00:18:47,560 --> 00:18:51,080
+تبعها هو هذا ال 2.5 مكان ال 2.5 المفروض ال
+
+239
+00:18:51,080 --> 00:18:56,550
+location التاني معناه ذلك منمن 2.5 كله هذا بدنا
+
+240
+00:18:56,550 --> 00:19:03,870
+نعمله shift نضغط فيه هنا A5 A5 هذه هتاخد الرقم
+
+241
+00:19:03,870 --> 00:19:08,190
+اللي كان في A4 A4 هينعملها shift بالرقم اللي كان
+
+242
+00:19:08,190 --> 00:19:14,750
+في A3 A3 هتاخد الرقم تبع A2 عشان نعمل insertion
+
+243
+00:19:14,750 --> 00:19:20,190
+لمن؟ للرقم الجديد نعمل insertion للرقم الجديد لحظة
+
+244
+00:19:20,190 --> 00:19:26,340
+انه برضه اترتبتترتب ال sequence عندكم ترتب ال
+
+245
+00:19:26,340 --> 00:19:31,840
+sequence عندكم تمام فهنا بتكلم برضه بتقدر تستخدم
+
+246
+00:19:31,840 --> 00:19:35,440
+اما ال linear او ال binary searchالطريقة اللى
+
+247
+00:19:35,440 --> 00:19:38,320
+بتحبى تستخدموها استخدموها اما تستخدموها انتوا فى
+
+248
+00:19:38,320 --> 00:19:42,180
+الآخر صارت عبارة عن search عبارة عن search X و
+
+249
+00:19:42,180 --> 00:19:44,460
+بتحاولوا تشوف وين ال location تبعه بتحاولوا تشوف
+
+250
+00:19:44,460 --> 00:19:48,160
+وين ال location تبعه فبتقدروا تشتغلوا على ال
+
+251
+00:19:48,160 --> 00:19:51,480
+linear او على ال binary و بعدين بتعملوا shift اذا
+
+252
+00:19:51,480 --> 00:19:57,100
+كان ال item او ال X اقل من قيمة ال element فى ال
+
+253
+00:19:57,100 --> 00:19:59,510
+locationقيمة ال element في ال location و بتعمله
+
+254
+00:19:59,510 --> 00:20:03,590
+shift ل ال item او ال element ب one position ب one
+
+255
+00:20:03,590 --> 00:20:08,510
+position على ال location اللي اعلى منه على ال
+
+256
+00:20:08,510 --> 00:20:10,790
+location اللي اعلى منه بحيث انه يصير في عندكوا هنا
+
+257
+00:20:10,790 --> 00:20:16,290
+فضاء hall ال hall هذا بتضيفه في ال new item اللي
+
+258
+00:20:16,290 --> 00:20:18,910
+هو ال x اللي بتدوروا عليها ال x اللي كنتوا بتعمله
+
+259
+00:20:18,910 --> 00:20:22,930
+ال search عليها هذا
+
+260
+00:20:22,930 --> 00:20:25,850
+كانت جزئية ضايلة من ال algorithm
+
+261
+00:20:31,220 --> 00:20:35,240
+بتاعتنا عشان نكمل برضه في ال algorithm بس عشان
+
+262
+00:20:35,240 --> 00:20:38,160
+أشتغل على ال algorithm محتاج أدرس حاجة اسمها ال
+
+263
+00:20:38,160 --> 00:20:44,960
+complexity complexity بمعنى أنه عندنا أكتر من code
+
+264
+00:20:44,960 --> 00:20:49,100
+ممكن يعملوا نفس ال task نفس ال task بس بدي أحسب ال
+
+265
+00:20:49,100 --> 00:20:53,960
+complexity للكل ليش؟ عشان أعرف أنه منهم أختار لأنه
+
+266
+00:20:53,960 --> 00:20:59,210
+ممكن جدا يكون عند codeتو code كل واحدة كتبت لنا
+
+267
+00:20:59,210 --> 00:21:02,290
+code أجي أفحصهم أعملهم analysis وهذا اللي بدنا
+
+268
+00:21:02,290 --> 00:21:06,010
+نتعلمه نعمل analysis لهم نطلع المعادلة بتاعة كل
+
+269
+00:21:06,010 --> 00:21:09,070
+واحد منهم معادلة إيش هنعرف احنا بنتكلم هنا عن
+
+270
+00:21:09,070 --> 00:21:14,130
+معادلة ال variable فيها عدد ال inputs variable عدد
+
+271
+00:21:14,130 --> 00:21:17,070
+ال inputs بحيث أنه كل ما زادت عدد ال inputs أكيد
+
+272
+00:21:17,070 --> 00:21:19,330
+هيزيد ال function في إيش أنا بدي أعملها ال
+
+273
+00:21:19,330 --> 00:21:23,130
+complexity في ال timeو رغم أنه طبعا في criteria
+
+274
+00:21:23,130 --> 00:21:26,430
+تانية ممكن اللي واحد يشتغل عليها زي ال energy، كم
+
+275
+00:21:26,430 --> 00:21:30,630
+تستهلك ال energy أو ال space بس احنا مش هنشتغل
+
+276
+00:21:30,630 --> 00:21:33,310
+فيهم هدول، هنخلق ال complexity بتاعتنا مفهومها
+
+277
+00:21:33,310 --> 00:21:36,610
+أكثر على ال time أنه code اللي بيستغرق ال time
+
+278
+00:21:36,610 --> 00:21:41,770
+أكبر عندنا two codes، باجي بحسب ال equation بتاعت
+
+279
+00:21:41,770 --> 00:21:43,830
+هذا مع ال equation بتاعت هذا ال equation ده إيش،
+
+280
+00:21:43,830 --> 00:21:47,980
+بتحسب ليه؟ بتحسب ال time variable في إيش؟أو
+
+281
+00:21:47,980 --> 00:21:51,960
+function في variable عبارة عن عدد ال inputs للكود
+
+282
+00:21:51,960 --> 00:21:56,020
+لأن كل ما زاد عدد ال inputs سيزيد ال time سيزيد
+
+283
+00:21:56,020 --> 00:21:59,640
+معاها ال time فبكون عملت equation أو formula ال
+
+284
+00:21:59,640 --> 00:22:02,480
+formula دي بنشوف ال complexity بتاعتها والله اللي
+
+285
+00:22:02,480 --> 00:22:05,880
+أعلى complexity بديش إياه لأنه معناه ذلك أنه
+
+286
+00:22:05,880 --> 00:22:11,100
+سيصغرق و أكبرهيستغرق وقت أكبر بظل بس كيف بدنا نعرف
+
+287
+00:22:11,100 --> 00:22:14,020
+أنه مين ال complexity أعلى بدنا نشوف كل equation
+
+288
+00:22:14,020 --> 00:22:18,540
+من اللي بيطلع هدولة هيتلعوا functions ال orders of
+
+289
+00:22:18,540 --> 00:22:23,780
+growth جديش معدل النمو لل function هذه و جديش معدل
+
+290
+00:22:23,780 --> 00:22:26,260
+النمو لل function هذه عشان نقول والله اللي معدل
+
+291
+00:22:26,260 --> 00:22:31,540
+نموه أعلى بمعنى بزود input واحد بزيد مقابله خمسة
+
+292
+00:22:31,540 --> 00:22:35,550
+في ال timeو فوق code تاني بزود input واحد بزيد
+
+293
+00:22:35,550 --> 00:22:39,450
+مقابله أربعة في ال time يعني ال time بتضعف أربع
+
+294
+00:22:39,450 --> 00:22:41,930
+مرات هنا بتضعف خمس مرات لا والله الخمس مرات مديش
+
+295
+00:22:41,930 --> 00:22:46,490
+يام لأنه ال order of growth معدل النمو تبعه أكبر
+
+296
+00:22:46,490 --> 00:22:53,090
+فهو faster أسرع أسرع بس أنا بدورش على أسرع احنا
+
+297
+00:22:53,090 --> 00:22:57,670
+بالعكس بدنا الأقل بدنا ال time complexity الأقلفال
+
+298
+00:22:57,670 --> 00:22:59,630
+time complexity قبل ما نبدأ نتكلم عن ال time
+
+299
+00:22:59,630 --> 00:23:02,850
+complexity بدنا نتكلم عن ال orders of growth كيف
+
+300
+00:23:02,850 --> 00:23:09,050
+بقدر أحسب ال order of growth و كيف ل codeين نحسب
+
+301
+00:23:09,050 --> 00:23:12,950
+ال order لهذا و لهذا عشان نقدر نقارنهم البعض ففي
+
+302
+00:23:12,950 --> 00:23:16,690
+جزئية هنا لازم نتكلم عنها اللي هي ال growth أو ال
+
+303
+00:23:16,690 --> 00:23:22,530
+orders of growth orders of growth كويسة الشكل اللي
+
+304
+00:23:22,530 --> 00:23:28,400
+قدامنا هناهنبدأ طبعا بناء على ال knowledge السابقة
+
+305
+00:23:28,400 --> 00:23:30,780
+اللي عندنا بناء على ال knowledge السابقة بقدر أقول
+
+306
+00:23:30,780 --> 00:23:34,400
+أن ال order تبعت المعادلة دي إيش طبعا هن .. هن ..
+
+307
+00:23:34,400 --> 00:23:37,800
+بعدين هنشرحها من وجه نظر ال discrete كيف بحسب ال
+
+308
+00:23:37,800 --> 00:23:41,580
+order بالظبط ولكن مبدأيا انتوا بتتكلموا هنا عن خط
+
+309
+00:23:41,580 --> 00:23:48,750
+مستقيمبغض النظر ان ال slope مختلف و ليس واحد مثلما
+
+310
+00:23:48,750 --> 00:23:53,810
+احنا نعرف ان ال slope مختلف ال shift ليس بعيد من
+
+311
+00:23:53,810 --> 00:23:58,230
+صفر صفر بل بعيد من صفر و تمانية بدا عن صفر و
+
+312
+00:23:58,230 --> 00:24:03,590
+تمانيةموجود عندنا بس في جميع الأحوال لو قلتلكوا
+
+313
+00:24:03,590 --> 00:24:06,770
+ايش ال order او اي درجة هذه المعادلة اللي هي 30n
+
+314
+00:24:06,770 --> 00:24:13,050
+plus تمانية الأولى الأولى هذه first order درجة
+
+315
+00:24:13,050 --> 00:24:15,190
+أولى احنا اين عرفناها درجة أولى من ال knowledge
+
+316
+00:24:15,190 --> 00:24:18,850
+السابق اتنى بس برضه هنعرف احنا كيف ممكن نشتغلها
+
+317
+00:24:18,850 --> 00:24:21,350
+بال discrete و اعرف جدتش ال order تبعها لإنه بده
+
+318
+00:24:21,350 --> 00:24:25,290
+اقارنها ب orders تانية بده نقارنها ب orders تانية
+
+319
+00:24:25,290 --> 00:24:30,920
+معادلة التانية هذهالمعادلة التانية هنا انتربيع
+
+320
+00:24:30,920 --> 00:24:36,940
+plus واحد انتربيع plus واحد وهي الشكل الشكل تبعها
+
+321
+00:24:36,940 --> 00:24:42,320
+طبعا واضح انه في shift بقيمة واحد قيمة ال shift
+
+322
+00:24:42,320 --> 00:24:45,560
+اللي موجود طيب الانتربيع واضح ان انا بتكلم عن
+
+323
+00:24:45,560 --> 00:24:50,040
+second order بتكلم عن second order okay في أجزاء
+
+324
+00:24:51,310 --> 00:24:55,330
+أقل وفي أجزاء أكبر طب أنا بشتغل عالمين عشان أقول
+
+325
+00:24:55,330 --> 00:24:58,350
+والله any order اللي أنا بنصبني أكتر دائما بندور
+
+326
+00:24:58,350 --> 00:25:04,250
+على K معينة ال K هذه قيمة قيمة N بمعنى عند عدد
+
+327
+00:25:04,250 --> 00:25:11,410
+users محدد معين هسميه K فال N هذه أكبر من K دائما
+
+328
+00:25:11,410 --> 00:25:14,370
+واحد منهم بيكون أكبر من الثاني فالأكبر هو ال
+
+329
+00:25:14,370 --> 00:25:19,550
+faster بسميه وهذا بديش إياه فواضح أن التربيع عنده
+
+330
+00:25:19,550 --> 00:25:26,570
+نقطة هذههنقول عليها K فكل N أكبر من K دائما
+
+331
+00:25:26,570 --> 00:25:30,470
+التربيع أكبر من ال linear دائما التربيع أكبر من ال
+
+332
+00:25:30,470 --> 00:25:33,910
+linear بغض النظر عن ال coefficient اللي مضروبة فيه
+
+333
+00:25:33,910 --> 00:25:37,610
+ال linear بس ال coefficient هذي فقط هتغيرلكوا وين
+
+334
+00:25:37,610 --> 00:25:42,050
+موجود التقاطع هذا بس دائما في قيمة ل K بعدها
+
+335
+00:25:42,050 --> 00:25:45,430
+التربيع دائما أكبر من ال linear دائما التربيع
+
+336
+00:25:45,430 --> 00:25:50,410
+بيكون أكبر من ال linear بعد قيمة معينة لهل N و
+
+337
+00:25:50,410 --> 00:25:56,990
+هنسميها K اللي هي النقطة هذه فإذا for all N أكبر
+
+338
+00:25:56,990 --> 00:26:01,130
+من K دائما
+
+339
+00:26:01,130 --> 00:26:06,650
+المعادلة بالخط الأحمر هذه بال red line هتكون أكبر
+
+340
+00:26:06,650 --> 00:26:11,830
+من ال black linesecond order دائما هتكون اكبر من
+
+341
+00:26:11,830 --> 00:26:15,150
+ال first order و هتلاقوا ان المعدل كبير جدا يعني
+
+342
+00:26:15,150 --> 00:26:17,370
+هنا كان الفرق بينهم بالشكل هذا هنا الفرق لحظوا
+
+343
+00:26:17,370 --> 00:26:21,870
+جداش صار و لسه ماصلنهاش شايفين جداش صار الفرق؟
+
+344
+00:26:21,870 --> 00:26:26,210
+معدل الفرق، معدل التغير فواضح انه المعادلة
+
+345
+00:26:26,210 --> 00:26:33,770
+التربعية أسرع أسرع بالنسبة لزيادة N من المعادلة ال
+
+346
+00:26:33,770 --> 00:26:37,230
+linear أو الخطية
+
+347
+00:26:42,540 --> 00:26:46,880
+كويس في الحلقة دي عشان نعرف كل واحدة منهم بنعرفها
+
+348
+00:26:46,880 --> 00:26:51,220
+بحاجة هنسميها ال order of growth ال .. هنقول ال
+
+349
+00:26:51,220 --> 00:26:56,160
+function الأولى هفترض انه هدى ال time ل code أول
+
+350
+00:26:56,160 --> 00:26:59,520
+ال code الأول جينا حسبناه لجينا ان ال complexity
+
+351
+00:26:59,520 --> 00:27:05,380
+تبعته تلتين and plus تمانية وال and هدى جدش عدد لو
+
+352
+00:27:05,380 --> 00:27:08,120
+بدنا نقول ان ال code هدى بيحسبلنا بيعملنا sorting
+
+353
+00:27:10,040 --> 00:27:14,720
+جديش عدد ال items اللي بدنا نعملهم sorting؟ قيمتهم
+
+354
+00:27:14,720 --> 00:27:18,860
+n فخمسة عشرة يعني هنا مثلا كنا بنتش نطلع على خمسة
+
+355
+00:27:18,860 --> 00:27:23,140
+عشرة عشرين خمسين سبعين مية ألف ألفين مليون جديش
+
+356
+00:27:23,140 --> 00:27:27,900
+فهذه اللي هي قيمة n ال f of n ال time اللي بنحتاجه
+
+357
+00:27:27,900 --> 00:27:31,860
+لتنفيذ البرنامج هذا أو لل code هذا خيص فهنقول في
+
+358
+00:27:31,860 --> 00:27:36,410
+عندنا system أولهذا ال system أول و هيكون فيه
+
+359
+00:27:36,410 --> 00:27:41,630
+system تاني أو code تاني ال complex اللي تتبعته أو
+
+360
+00:27:41,630 --> 00:27:47,570
+ال time بيحسبها عن طريق n2 plus 1 n2 plus 1 و نفس
+
+361
+00:27:47,570 --> 00:27:50,790
+الكلام ال n هنا هتكون عدد ال items اللي بده أعملها
+
+362
+00:27:50,790 --> 00:27:55,650
+sorting ال f of n ال time اللي هحتاجه ال time اللي
+
+363
+00:27:55,650 --> 00:27:58,170
+هحتاجه فهذا code و هذا code بدنا نشوف مين أحسن من
+
+364
+00:27:58,170 --> 00:28:02,740
+التاني طيب بدنا نعرف ال code الأولوانعرف ال order
+
+365
+00:28:02,740 --> 00:28:09,580
+تبعته، بعرف ال order تبعته بالنسبة ل big O، طب مش
+
+366
+00:28:09,580 --> 00:28:13,800
+هي big O، big O of N يعني كأني بقول انه تلاتين N
+
+367
+00:28:13,800 --> 00:28:20,560
+plus واحد at most first order لأنه لحظة انا اقول
+
+368
+00:28:20,560 --> 00:28:30,140
+big O of N طيب N هذه هي first orderهذه first order
+
+369
+00:28:30,140 --> 00:28:38,100
+صحيح؟ كأن بقول إن المعادلة هذه بالكتير first order
+
+370
+00:28:38,100 --> 00:28:43,620
+ممكن تكون أقل أقل أو تساوي first order فهي ضمن
+
+371
+00:28:43,620 --> 00:28:46,240
+التعريف احنا عارفين إن هي first order احنا عارفين
+
+372
+00:28:46,240 --> 00:28:49,760
+إن هي first order فهي تنطبق مع ال big O ال big O
+
+373
+00:28:49,760 --> 00:28:55,660
+دي معناها at most proportional to n تتناسب مع n
+
+374
+00:28:55,660 --> 00:29:01,340
+بالكتيريعني ممكن تكون اقل ممكن اقول انه constant
+
+375
+00:29:01,340 --> 00:29:05,080
+او log ال log احنا عارفين انه اقل من ال .. ال
+
+376
+00:29:05,080 --> 00:29:08,280
+order تبعه اقل من ال first log اقل من ال first
+
+377
+00:29:08,280 --> 00:29:16,800
+صحيح فممكن اقول ان ال log of N برضه is big O of N
+
+378
+00:29:16,800 --> 00:29:23,340
+على اعتبار ان هيأقل من فال big O بيسمح لنا أنه أقل
+
+379
+00:29:23,340 --> 00:29:28,200
+من أو يساوي first order أقل من أو يساوي ممكن تكون
+
+380
+00:29:28,200 --> 00:29:35,220
+constant أقول مثلا تلاتة is big O of N تلاتة
+
+381
+00:29:35,220 --> 00:29:41,040
+constant يعني ال order zero order zero تمام فال
+
+382
+00:29:41,040 --> 00:29:47,140
+order zero فهنا ال big O هذه معناها أنهبشوف العنصر
+
+383
+00:29:47,140 --> 00:29:51,420
+اللي جوه العنصر اللي جوه N N هذا linear ممكن تكتب
+
+384
+00:29:51,420 --> 00:29:56,880
+N تربيع فانا بتكلم هنا عن تربيع second order third
+
+385
+00:29:56,880 --> 00:30:01,340
+order فبشوف N هذه كلها ثابتة هتكون منها بس ال
+
+386
+00:30:01,340 --> 00:30:05,780
+power جديش هي ده اللي هتحدد ال order تبعنا طيب
+
+387
+00:30:05,780 --> 00:30:16,750
+ممكن تنحط big O of N 00 order n to the power 0 ب 1
+
+388
+00:30:16,750 --> 00:30:21,430
+فبنكتبها big O of 1
+
+389
+00:30:21,430 --> 00:30:30,470
+فبعرف أن هذه constant أو order 0 تمام على اعتبار
+
+390
+00:30:30,470 --> 00:30:36,880
+أنها n to the power 0 فطلع لنا الواحدكويس هذا كل
+
+391
+00:30:36,880 --> 00:30:39,540
+الكلام اللي عايشه ممكن نقوله عن ال big O حتى الآن
+
+392
+00:30:39,540 --> 00:30:42,900
+و لاحقا هتتطور الأمور معناه شويه شويه في ال big O
+
+393
+00:30:42,900 --> 00:30:49,060
+تمام هذا بالنسبالي الأولى big O of N في rest order
+
+394
+00:30:49,060 --> 00:30:54,960
+الطيب التانية تانية تربية هي is order N squared
+
+395
+00:30:54,960 --> 00:31:01,080
+فبنقولها big O of N squared فهذه بالكتير N squared
+
+396
+00:31:01,080 --> 00:31:03,900
+بس هي ممكن تكون N squared يعني ممكن تكون أقل أو
+
+397
+00:31:03,900 --> 00:31:08,300
+تساويsecond order هي فعلا تسوى second order هي
+
+398
+00:31:08,300 --> 00:31:11,240
+ممكن تسوى .. فعلا تسوى second order طب في الحالة
+
+399
+00:31:11,240 --> 00:31:16,660
+هذه for large .. large numbers of user records لو
+
+400
+00:31:16,660 --> 00:31:20,720
+في عندنا user records كبيرة أو عدد ال inputs كبير
+
+401
+00:31:20,720 --> 00:31:28,000
+جدا هنتوقع مين منهم more time دائما هياخد وقت
+
+402
+00:31:28,000 --> 00:31:34,900
+زيادة الأولى اللي هو a أو bتربية مدام أنا بتكلم عن
+
+403
+00:31:34,900 --> 00:31:38,900
+large numbers عدد كبير احنا لو بدنا نعمل sorting
+
+404
+00:31:38,900 --> 00:31:42,680
+هنا مثلا لمجموعة
+
+405
+00:31:42,680 --> 00:31:45,520
+الطالبات او مجموعة البنات اللي مثلا سجلين احد
+
+406
+00:31:45,520 --> 00:31:48,800
+المثقات طبعا تقولكوا هتسجلوا المثقات بس لما اجي
+
+407
+00:31:48,800 --> 00:31:52,920
+انا اسحب الكشف عن طريق القراكل مثلا برنامج الجامعة
+
+408
+00:31:52,920 --> 00:31:56,460
+بيحسب ليه بيرتب ليه حسب أرقامك الدراسية او أرقامك
+
+409
+00:31:56,460 --> 00:31:59,800
+الجامعية صحيح؟ حسب الرقم الجامعي مع أن اتعمل
+
+410
+00:31:59,800 --> 00:32:04,210
+sortingمعناته في code في النصر رتبلكم يعني عملكم
+
+411
+00:32:04,210 --> 00:32:07,450
+sorting عمل sorting احنا مش هنتكلم عن عددنا اربعين
+
+412
+00:32:07,450 --> 00:32:09,990
+و لا تخمسة و تلاتين طالبة مش .. مش .. مش الرقم
+
+413
+00:32:09,990 --> 00:32:14,470
+الكبير لو بنتكلم عن مساق من مساقات متضلبات الجامعة
+
+414
+00:32:14,470 --> 00:32:18,510
+اللي عددهم كبير جدا ممكن يصل متينات و بتكون تعملوا
+
+415
+00:32:18,510 --> 00:32:21,350
+sorting هيفرق طبعا code عن code في الحالة هذه في
+
+416
+00:32:21,350 --> 00:32:25,830
+الحالة هذه هتبين ان لأ ال linear كتير احسن لمنكالـ
+
+417
+00:32:25,830 --> 00:32:28,570
+quadratic او اللي هي second order ال first order
+
+418
+00:32:28,570 --> 00:32:30,830
+أكيد هحصل من ال second order ال second order هياخد
+
+419
+00:32:30,830 --> 00:32:36,950
+وقت أكبر في عملية ال sorting لو مثلا عندكوا two
+
+420
+00:32:36,950 --> 00:32:41,990
+codes واحد linear و واحد .. يعني واحد first order
+
+421
+00:32:41,990 --> 00:32:44,610
+و واحد second order ال second order طبعا هياخد
+
+422
+00:32:44,610 --> 00:32:50,130
+more time أكيد هياخد more timeOkay نرجع لل Big O
+
+423
+00:32:50,130 --> 00:32:55,230
+هذي نرجع نعرج شوية كمان مرة على ال Big O و نستفيد
+
+424
+00:32:55,230 --> 00:33:01,730
+شوية في الشرحة هنقول Big O of G فانا هنا بتكلم عن
+
+425
+00:33:01,730 --> 00:33:08,490
+Big O of G, G هذي function هذي function زي توي لما
+
+426
+00:33:08,490 --> 00:33:11,630
+كنا بيقول Big O of N أنا بتعامل مع أنها هذي
+
+427
+00:33:11,630 --> 00:33:15,780
+function من أي درجةمن الدرجة الأولى فهذه نفس
+
+428
+00:33:15,780 --> 00:33:21,020
+الكلام g function هنحددها لاحقا بس احنا هنا سمناها
+
+429
+00:33:21,020 --> 00:33:24,160
+خليناها undefined بالشكل هذا ان هي function و خلاص
+
+430
+00:33:24,160 --> 00:33:28,340
+function و خلاص أولى تانية تالتة من أي درجة من أي
+
+431
+00:33:28,340 --> 00:33:30,300
+order مش إشكال المهم ان في النهاية function
+
+432
+00:33:30,300 --> 00:33:35,580
+النهاية function okay ف let g be any function from
+
+433
+00:33:35,580 --> 00:33:38,200
+real number to real number ال domain real number و
+
+434
+00:33:38,200 --> 00:33:43,380
+ال codomain real number defineat most order g فال
+
+435
+00:33:43,380 --> 00:33:45,960
+big O هذا بنعرفه على أساس أنه at most order g
+
+436
+00:33:45,960 --> 00:33:50,680
+فممكن أقول if .. بدي أشوف if بالنسبة لل big O
+
+437
+00:33:50,680 --> 00:34:00,340
+فبقول if at most .. رجعنا تاني هنا okay at most
+
+438
+00:34:00,340 --> 00:34:06,140
+order g بمعنى هل هي .. إذا قولناها بهذا الشكل
+
+439
+00:34:06,140 --> 00:34:13,110
+معناته أن ال if نفس order g أو أقلأو أقل أو كأني
+
+440
+00:34:13,110 --> 00:34:18,850
+بقول هي من ال order بالكتير order g بالكتير order
+
+441
+00:34:18,850 --> 00:34:23,010
+g يعني ممكن يكون أقل، ممكن يكون أقل، كويس فهي تعرف
+
+442
+00:34:23,010 --> 00:34:28,310
+أنه يقول at most order g تنكتب big O of g to be
+
+443
+00:34:28,310 --> 00:34:33,050
+set of functions فإذا أنا لغة إيش اللي بدي أعرفه؟
+
+444
+00:34:33,050 --> 00:34:38,230
+بدي أعرف ال big O of g لو افترضنا، فرضنا إن ال G
+
+445
+00:34:38,230 --> 00:34:42,960
+هي the first orderأيش ال functions اللي بقدر
+
+446
+00:34:42,960 --> 00:34:47,720
+اكتبها ان هي فعلا تساوي big O of G كل ال first
+
+447
+00:34:47,720 --> 00:34:52,500
+order functions صح؟ كل ال function اللي ال order
+
+448
+00:34:52,500 --> 00:34:57,440
+طبعها first order بقدر اعرفها big O of first order
+
+449
+00:34:57,440 --> 00:35:02,680
+معناته كل ال functions هذه بقدر احطها في set فال
+
+450
+00:35:02,680 --> 00:35:07,390
+function صارت element داخل setالset هذي كل ال
+
+451
+00:35:07,390 --> 00:35:12,430
+elements اللي تتفق ان هي big O لل first order تمام
+
+452
+00:35:12,430 --> 00:35:18,350
+معناه ذلك لما انا بدي أجعل ريفا بقول set of
+
+453
+00:35:18,350 --> 00:35:25,910
+functions ال function هذي from R to R نسبة
+
+454
+00:35:25,910 --> 00:35:28,410
+لميه؟ لل function اللي أنا بدي أنسب إلها اللي بدي
+
+455
+00:35:28,410 --> 00:35:32,010
+أنسب ال order إلها فهي function from R to R such
+
+456
+00:35:32,010 --> 00:35:35,640
+thatأيش اللي بده يحقق لنا إياها؟ يعني عشان هذه
+
+457
+00:35:35,640 --> 00:35:39,000
+تكون ال function فعلا element داخل ال set بتاعة ال
+
+458
+00:35:39,000 --> 00:35:41,820
+big O of G إيش اللي لازم يتحققه؟ لازم يتحقق التالي
+
+459
+00:35:41,820 --> 00:35:47,040
+there exist C و K كي هي النقطة اللي كنا نتكلم عنها
+
+460
+00:35:47,040 --> 00:35:54,820
+اللي بعدها دائماالتربيه أكبر من الlinear معناته أن
+
+461
+00:35:54,820 --> 00:35:59,500
+أنا فعلا بدور على قيمة constant K و there exist ل
+
+462
+00:35:59,500 --> 00:36:04,660
+C برضه constant .. constant طيب there exist CK
+
+463
+00:36:04,660 --> 00:36:08,920
+such that for all X أكبر من K لكل القيم اللي بعد K
+
+464
+00:36:08,920 --> 00:36:16,580
+لكل القيم اللي بعد K F of X ال function اللي داخل
+
+465
+00:36:16,580 --> 00:36:22,690
+ال setأقل من أو تساوي C في G of X نسبنا هنا
+
+466
+00:36:22,690 --> 00:36:25,010
+بالنسبة لمن؟ لل function اللي .. اللي احنا عارفين
+
+467
+00:36:25,010 --> 00:36:27,550
+ال order تبعها و بدنا نعرف هل ال function F belong
+
+468
+00:36:27,550 --> 00:36:30,930
+إلها أو لأ جينا example هالوجد، حنعرف كيف أطلع
+
+469
+00:36:30,930 --> 00:36:35,510
+برضه ال C و ال K، حنعرف نطلع هالوجد ال C و ال K بس
+
+470
+00:36:35,510 --> 00:36:41,810
+مبدأيا بنقول إنه بعد النقطة K ال function F is at
+
+471
+00:36:41,810 --> 00:36:45,650
+most a constant C times of G
+
+472
+00:36:47,600 --> 00:36:53,040
+معناته ان هي proportional to G تتناسب مع G تتناسب
+
+473
+00:36:53,040 --> 00:36:57,420
+هنا مع G هناخد example و هنرسم الرسم تبعهم عشان
+
+474
+00:36:57,420 --> 00:37:02,020
+نشوف كيف العملية التناسب طيب نقرأها if is at most
+
+475
+00:37:02,020 --> 00:37:09,520
+order G او if is big O of G او ممكن نقول if بتساوي
+
+476
+00:37:09,520 --> 00:37:14,680
+big O of Gأو ممكن نكتبها if belong لإن احنا عرفنا
+
+477
+00:37:14,680 --> 00:37:18,460
+ال if إن هي function داخل ال set اللي تحتوي على كل
+
+478
+00:37:18,460 --> 00:37:22,740
+ال functions بتاعة ال big O فهي واحدة منهم فبقدر
+
+479
+00:37:22,740 --> 00:37:27,040
+أقول إن هي element أو function belong to big O of
+
+480
+00:37:27,040 --> 00:37:30,820
+Gبناء على التعريف بناء على تعريفنا ان احنا بتكلم
+
+481
+00:37:30,820 --> 00:37:36,860
+عن set of functions أحيانا ممكن نقلش منها ال at
+
+482
+00:37:36,860 --> 00:37:42,240
+most بتاعتنا فبقول if is order g خلاص ممكن جدا
+
+483
+00:37:42,240 --> 00:37:46,920
+نختصرها طيب خلينا نشوف كيف نحسبها ال K و ال C اللي
+
+484
+00:37:46,920 --> 00:37:50,360
+قلتلكم بدنا نجيبهم ناخد ال two examples اللي
+
+485
+00:37:50,360 --> 00:37:55,980
+اتكلمنا عنهم اللي واحدة linear واحدة squareو بدنا
+
+486
+00:37:55,980 --> 00:37:59,920
+نجيب هل فعلا هي big O of N او لأ نمسك الأولى
+
+487
+00:37:59,920 --> 00:38:05,120
+تلاتين N plus تمانية is big O of N first order
+
+488
+00:38:05,120 --> 00:38:09,730
+بدنا نثبت الكلام هذا و بدنا نوضح الكلام هذاليش
+
+489
+00:38:09,730 --> 00:38:12,830
+يقولنا 130؟ ليش احنا امتى قولنا ممكن تكون فعلا
+
+490
+00:38:12,830 --> 00:38:20,670
+first order إذا كان يوجد C و K اللي بيحققولنا ال
+
+491
+00:38:20,670 --> 00:38:28,330
+condition أن F of X أقل من أو تساوي C في N في ال
+
+492
+00:38:28,330 --> 00:38:35,030
+order طبعا F of Nتمام؟ بدنا نحقق الكلام هذا فعشان
+
+493
+00:38:35,030 --> 00:38:40,450
+أحققه بدي أثبت أنه موجودة ال c و ال k طب كيف نقدر
+
+494
+00:38:40,450 --> 00:38:45,790
+نجيب ال c و ال k؟ من هنا ال c مباشرة تقدر تاخدها
+
+495
+00:38:45,790 --> 00:38:52,610
+من ال coefficient تبعت n هنا n طيب وين ال order n
+
+496
+00:38:52,610 --> 00:38:56,810
+هنا؟ هيها كدوش ال coefficient تبعها؟ تلاتين معناته
+
+497
+00:38:56,810 --> 00:39:04,070
+ال cبتساوي ال coefficient زائد واحد زائد
+
+498
+00:39:04,070 --> 00:39:10,030
+واحد طيب ال K قيمة ال shift تمانية تمانية
+
+499
+00:39:10,030 --> 00:39:13,110
+بالمعادلات
+
+500
+00:39:13,110 --> 00:39:15,230
+خليني انا اعمل check هل فعلا تحقق ال condition
+
+501
+00:39:15,230 --> 00:39:20,230
+تبعنا ولا لأ بدنا نتأكد خليني اقول هي let C 31
+
+502
+00:39:20,230 --> 00:39:31,470
+عرفنا ليشأقل رقم بيحقق
+
+503
+00:39:31,470 --> 00:39:35,050
+المعادلة أقل رقم بيحقق المعادلة
+
+504
+00:39:42,870 --> 00:39:45,970
+31 قلنا لأ ال coefficient تبع n هنا احنا بتكلم عن
+
+505
+00:39:45,970 --> 00:39:49,770
+ال first order صح طب وين ال coefficient تبع ال
+
+506
+00:39:49,770 --> 00:39:53,410
+first order في المعادلة ايه اللي هو 30 فهذا
+
+507
+00:39:53,410 --> 00:39:58,030
+بنزودها 31 يعني كأنه بدور على اقل رقم يكون اكبر
+
+508
+00:39:58,030 --> 00:40:01,770
+منها اقل رقم يكون اكبر منها انتوا في الآخر ممكن
+
+509
+00:40:01,770 --> 00:40:06,350
+تفترضوا 35 هيمشي الحال المهم احنا كل الفكرة ان
+
+510
+00:40:06,350 --> 00:40:12,700
+there exist k و cمجرد أنه في رقم حقق المعادلة
+
+511
+00:40:12,700 --> 00:40:16,920
+بكافي انا من عندى بحاول افترضه انه اقل رقم ممكن
+
+512
+00:40:16,920 --> 00:40:21,640
+اللى اقل منه مش هتصبط المعادلة بس هو الحد الفاصل
+
+513
+00:40:21,640 --> 00:40:25,940
+انتوا ممكن في الآخر تفترضه مثلا C ب60 وال K تعمله
+
+514
+00:40:25,940 --> 00:40:29,840
+10 هتتحقق باريحية كبيرة جدا المعادلة معاكم هتلاقوا
+
+515
+00:40:29,840 --> 00:40:33,500
+ان المعادلة هتتحقق باريحية كبيرة احنا هنا زى ما
+
+516
+00:40:33,500 --> 00:40:38,500
+بقوله بالظبط حوالين بالظبط اللى اكبر منكأقل قيمة
+
+517
+00:40:38,500 --> 00:40:42,500
+ممكنة للـC والـK تمام، هذه الـC و 31، K تمانية،
+
+518
+00:40:42,500 --> 00:40:48,100
+أسيوم لكل قيم N اللي أكبر من K المفروض يتحقق ال
+
+519
+00:40:48,100 --> 00:40:54,300
+condition لكل قيم K اللي أكبر من تمانية فاحنا نقول
+
+520
+00:40:54,300 --> 00:40:59,280
+هنا for N أكبر من K يعني أكبر من تمانية طيب، نمسك
+
+521
+00:40:59,280 --> 00:41:04,000
+ال term هذا لأن احنا بدنا نحقق هذه الشرطة بدنا
+
+522
+00:41:04,000 --> 00:41:10,120
+نثبت أن فيه C و فيه Kبحققولنا الشرط هذه أن N لكل N
+
+523
+00:41:10,120 --> 00:41:15,560
+أكبر من K هذا الشرط ده هنمسك الشرط هذا هاي ال C N
+
+524
+00:41:15,560 --> 00:41:19,640
+هاي ال C N ال C احنا فرضناها جديش واحد تلاتين طيب
+
+525
+00:41:19,640 --> 00:41:24,100
+ما هذه بقدر أقول أن هي تلاتين زائد N صحيح؟ طيب هذه
+
+526
+00:41:24,100 --> 00:41:29,840
+أكيد أكبر من تلاتين N لأن هذه بتسوي هذه أكبر من
+
+527
+00:41:29,840 --> 00:41:33,380
+تلاتين N زائد تمانية باعتبار أن أنا بتكلم على كل
+
+528
+00:41:33,380 --> 00:41:39,090
+قيم N اللي أكبر من تمانيةفال N أكيد أكبر من تمانية
+
+529
+00:41:39,090 --> 00:41:50,550
+صح فإذا تلاتين N زائد تمانية أقل من CCN فحقق الشرط
+
+530
+00:41:50,550 --> 00:41:54,950
+يكفيني من الشرط أن يوجد رقمين حققوا ليا مدان يوجد
+
+531
+00:41:54,950 --> 00:41:59,570
+رقمين حققوا فإذا هي فعلا ال function هذه first
+
+532
+00:41:59,570 --> 00:42:06,590
+order أو big O of N first أو أقلfirst او اقل او
+
+533
+00:42:06,590 --> 00:42:12,470
+تتناسب let's say proportional مع ال first order
+
+534
+00:42:12,470 --> 00:42:15,450
+تتناسب مع ال first order نفس الكلام ممكن نعمله
+
+535
+00:42:15,450 --> 00:42:22,210
+لمن؟ للتربية التربية هنا C كم ممكن تقترحوها؟
+
+536
+00:42:25,250 --> 00:42:29,530
+هي n تربيع و n تربيع جداش ال coefficient هنا C
+
+537
+00:42:29,530 --> 00:42:36,610
+بجداش نعملها 2 زائد 1 1 زائد 1 ف C بتساوي 2 طيب K
+
+538
+00:42:36,610 --> 00:42:42,970
+بواحد هدول أقل رقمين ممكن تختاروهم ممكن تختاروا
+
+539
+00:42:42,970 --> 00:42:46,870
+أكبر ممكن تختاروا أكبر هتلاقي انه برضه هتتحقق ال
+
+540
+00:42:46,870 --> 00:42:51,350
+equation و هتتحقق بزيادة يعني هتكون الفرق كمان في
+
+541
+00:42:51,350 --> 00:42:57,090
+أكبر منه بزيادةحنشوف there exists ck for all n
+
+542
+00:42:57,090 --> 00:43:03,210
+أكبر من k يعني لكل قيم n أكبر من 1 لكل قيم n أكبر
+
+543
+00:43:03,210 --> 00:43:07,570
+من 1 فإذا n لازم تكون أكبر من 1 عساس أنها أكبر من
+
+544
+00:43:07,570 --> 00:43:12,970
+k نمسك هذه cn تربيع نمسك cn تربيع و c حاطناها ب2
+
+545
+00:43:12,970 --> 00:43:17,590
+2n تربيع عبارة عن n تربيع زاد n تربيعأكبر من N
+
+546
+00:43:17,590 --> 00:43:21,470
+تربيع زائد واحد على اعتبار أن ال N قلنا أكبر من
+
+547
+00:43:21,470 --> 00:43:23,950
+واحد مدام أكبر من واحد التربيع تباع أكبر من واحد
+
+548
+00:43:23,950 --> 00:43:28,210
+مدام كقيمة أكبر من واحد تربيعها أكيد أكبر من واحد
+
+549
+00:43:28,210 --> 00:43:32,890
+فأكيد ال term هذا أكبر من ال term هذا فإذا ال N
+
+550
+00:43:32,890 --> 00:43:37,530
+تربيع زائد واحد أقل من C N تربيع حققنا ال
+
+551
+00:43:37,530 --> 00:43:40,950
+condition مدام أقل من C N تربيع معناته هي ضمن ال
+
+552
+00:43:40,950 --> 00:43:46,130
+order تربيعك function هي ضمن ال order تربية فبقدر
+
+553
+00:43:46,130 --> 00:43:52,090
+أقول اللي هي big O of N square و أنا مرتاح okay
+
+554
+00:43:52,090 --> 00:44:01,950
+هاي الشكل تبعنا لو اتكلمنا عن تلاتين
+
+555
+00:44:01,950 --> 00:44:06,670
+N زائد تمانيةطب وين الرقم اللى فعلا قلتلنا كيه و
+
+556
+00:44:06,670 --> 00:44:09,670
+مش كيه و مش عارفاش و بقى أكبر من كيه المعادلة
+
+557
+00:44:09,670 --> 00:44:14,470
+دايما أقل من N تربيه من ال N من O big O of N لحظة
+
+558
+00:44:14,470 --> 00:44:22,330
+أنه هادي N مش CNN CNN جداش تطلع واحد و تلاتين N
+
+559
+00:44:22,330 --> 00:44:24,790
+واحد و تلاتين N هترسم معاكم بهذا الشكل
+
+560
+00:44:27,750 --> 00:44:32,490
+هتكون هذه 31 أن فبعد قيمة معينة عن تقطع معين اللي
+
+561
+00:44:32,490 --> 00:44:40,130
+هو عن 8 هتلاقوا دايما 31 أكبر من 30 أن زائد 8 أكبر
+
+562
+00:44:40,130 --> 00:44:45,450
+من 30 أن زائد 8 فبيكون لكل أن اللي أكبر من 8 دايما
+
+563
+00:44:45,450 --> 00:44:50,370
+linear فإذا ال function كلها على بعض linear تصور
+
+564
+00:44:50,370 --> 00:44:51,450
+مرسومة؟ أه مرسومة
+
+565
+00:44:59,730 --> 00:45:04,850
+ك فكل الجزء اللي أكبر من تمانية ينطبق عليه ال
+
+566
+00:45:04,850 --> 00:45:08,810
+condition بنقدر ساعتها نقول ان اه والله في موجود
+
+567
+00:45:08,810 --> 00:45:14,870
+او في وجود لك و ال c مدان موجودة automatic
+
+568
+00:45:14,870 --> 00:45:22,750
+المعادلة هي دي بقول belong of O of N او is O of N
+
+569
+00:45:22,750 --> 00:45:26,770
+زي ما بتكون خدولكوا اي مسمة من مسمات متويسة منها
+
+570
+00:45:27,540 --> 00:45:32,100
+تمام هلوجد مجموعة rules مجموعة facts مجموعة
+
+571
+00:45:32,100 --> 00:45:37,220
+relations مهمة ممكن تتعاملوا معاها خاصة بال big
+
+572
+00:45:37,220 --> 00:45:43,880
+بال big O خاصة بمين بال big O أول شغلة هي
+
+573
+00:45:43,880 --> 00:45:47,140
+transitive ايش يعني transitive يعني لو قولنا if
+
+574
+00:45:47,140 --> 00:45:55,450
+relation مع G باعتبار أن ال F belong to big O GBig
+
+575
+00:45:55,450 --> 00:46:05,190
+O of G يعني واضح ان F نفس order G او اقل و G نفس
+
+576
+00:46:05,190 --> 00:46:12,490
+order H او اقل معناته G belong to big O of H هذا
+
+577
+00:46:12,490 --> 00:46:18,900
+هيقودنا تماما ان F برضه big O of HBig O of H
+
+578
+00:46:18,900 --> 00:46:23,380
+Transitive أو انتقالية يعني ال relation هنا مع ال
+
+579
+00:46:23,380 --> 00:46:28,440
+relation هنا إذا كان ال F أقل من G و ال G أقل من H
+
+580
+00:46:28,440 --> 00:46:33,780
+فبالضرورة F أقل من H صحيح؟ بالضرورة هتكون أقل منها
+
+581
+00:46:33,780 --> 00:46:38,300
+أو تساوي بالكتير، كويس، هاي أول relationrelation
+
+582
+00:46:38,300 --> 00:46:42,480
+التانية big O with constant سواء هيكون مضروب او
+
+583
+00:46:42,480 --> 00:46:47,160
+root او log بدنا نشوف كيف يتعامل مع ال constants
+
+584
+00:46:47,160 --> 00:46:52,300
+اول شغلة اذا ضربناها ضرب مباشرة بقى constant A
+
+585
+00:46:52,300 --> 00:46:57,140
+وهذه قولنا ان ال constant A وB هدول constants بي
+
+586
+00:46:57,140 --> 00:47:00,180
+بس هتكون اكبر من صفر اكبر او تساوي صفر اكبر او
+
+587
+00:47:00,180 --> 00:47:08,660
+تساوي صفر لو قولنا F big O of FBig O of F معناته
+
+588
+00:47:08,660 --> 00:47:13,920
+ال function F لها نفس ال order طب لو انضربت في a
+
+589
+00:47:13,920 --> 00:47:18,380
+constant مجرد constant حضر هي هي برضه belonged to
+
+590
+00:47:18,380 --> 00:47:24,020
+big O of F زي لما تقولوا n هي first order طب meet
+
+591
+00:47:24,020 --> 00:47:28,950
+n برضه first order السلوك بس اللي اتغيرسلوب تبعها
+
+592
+00:47:28,950 --> 00:47:32,670
+فقط اللي اتغير اما ما اتغيرش شي هتظل نفس ال order
+
+593
+00:47:32,670 --> 00:47:37,550
+فهي مجرد اضرب ال function في constant هتظل نفس ال
+
+594
+00:47:37,550 --> 00:47:43,290
+function طيب f هذه ال condition تبعنا بس اللي بدنا
+
+595
+00:47:43,290 --> 00:47:52,470
+ناخد بالنا منه هنا نرجعله small omega of واحد big
+
+596
+00:47:52,470 --> 00:48:02,560
+O of N ايش معناهالما اقول if بتساوي big O of N
+
+597
+00:48:02,560 --> 00:48:08,060
+معناها ان ال function هذه ال order تبعها linear او
+
+598
+00:48:08,060 --> 00:48:20,280
+اقل صح او اقل طيب if ساوي small O of N معناها if
+
+599
+00:48:20,280 --> 00:48:28,800
+ال order تبعها اقل من N لا يساوي N لا يساوي Nأقل
+
+600
+00:48:28,800 --> 00:48:33,980
+من n يعني ممكن التربيعية اللي لو قولنا تلاتة n
+
+601
+00:48:33,980 --> 00:48:43,480
+plus سبعة ممكن أقول عنها is small o of n تربيع بس
+
+602
+00:48:43,480 --> 00:48:49,360
+بقولش small n of n لإن أنا عارف إن هي first order
+
+603
+00:48:50,260 --> 00:48:55,300
+هنا ال small o أقل من first order تعريفها أقل من
+
+604
+00:48:55,300 --> 00:49:04,900
+first order تمام هاي التانية التالتة big omega big
+
+605
+00:49:04,900 --> 00:49:12,300
+omega of n معناته ال order تبع f أكبر من أو يساوي
+
+606
+00:49:12,300 --> 00:49:17,160
+n اللي هو first order يعني first order أو أكبر
+
+607
+00:49:18,880 --> 00:49:24,620
+first order أو أكبر كتبوه عندكم ممكن نضطر نحتاجهم
+
+608
+00:49:24,620 --> 00:49:27,380
+وإن كان هي ال big O هي الأكثر استخداما يعني أكثر
+
+609
+00:49:27,380 --> 00:49:30,780
+استخداما بس أنا مضطرها لغة أشرحلكم هي علشان طلعة
+
+610
+00:49:30,780 --> 00:49:35,060
+النهد عشان نفهمها الشيء هذا بس تمام فعشان نفهمها
+
+611
+00:49:35,060 --> 00:49:42,620
+بدنا نحطهم كلهم و نخلص طيب هذه ال big omega طيب ال
+
+612
+00:49:42,620 --> 00:49:50,780
+small omega of Nأكبر من أكبر
+
+613
+00:49:50,780 --> 00:49:57,440
+من أكبر
+
+614
+00:49:57,440 --> 00:49:57,440
+من أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+615
+00:49:57,440 --> 00:49:57,600
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+616
+00:49:57,600 --> 00:49:58,220
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+617
+00:49:58,220 --> 00:50:01,200
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+618
+00:50:01,200 --> 00:50:05,060
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+619
+00:50:05,060 --> 00:50:05,080
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+620
+00:50:05,080 --> 00:50:05,080
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+621
+00:50:05,080 --> 00:50:05,100
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+622
+00:50:05,100 --> 00:50:15,220
+أكبر من أكبر من أكبر من أكبر من أكبر
+
+623
+00:50:15,220 --> 00:50:20,370
+منتساوي F او F تساوي big theta of N معناته ان هي
+
+624
+00:50:20,370 --> 00:50:25,710
+exactly تساوي ال order هذا فهنا F الزمن لا هي اكبر
+
+625
+00:50:25,710 --> 00:50:28,590
+ولا هي اصغر من ال first order هي بالظبط first
+
+626
+00:50:28,590 --> 00:50:34,770
+order هي exactly first order هاي معناته theta of N
+
+627
+00:50:34,770 --> 00:50:36,870
+فهي ال relations اللي ممكن نعملها لها ال functions
+
+628
+00:50:36,870 --> 00:50:40,210
+عشان نحسب ال order بتاع ال function فاحنا هلوجت
+
+629
+00:50:40,210 --> 00:50:48,940
+ألزمنا هو بمين؟بال Omega of one معناه ذلك ان ال F
+
+630
+00:50:48,940 --> 00:50:57,860
+دائما اكبر من ال order ال
+
+631
+00:50:57,860 --> 00:51:01,380
+order ايش ده Zero ال order Zero هي اذا اكبر من
+
+632
+00:51:01,380 --> 00:51:06,800
+constant اكبر من constant يعني هي كل الفكرة ان ال
+
+633
+00:51:06,800 --> 00:51:10,400
+F هي لازم تكون اكبر من ال constant ممكن تكون
+
+634
+00:51:10,400 --> 00:51:14,880
+linear و ممكن تكون اقل من linear زي loglogarithmic
+
+635
+00:51:14,880 --> 00:51:19,360
+أقل من ال linear log أقل من ال linear ببساطة جدا
+
+636
+00:51:19,360 --> 00:51:25,720
+لو قلنا linear لو أنا بتكلم linear العشرة يقابلها
+
+637
+00:51:25,720 --> 00:51:31,380
+ال output عشرة المية يقابلها مية طيب المية log log
+
+638
+00:51:31,380 --> 00:51:35,820
+مية جداش log
+
+639
+00:51:35,820 --> 00:51:41,780
+للأساس ال base تبعكوا عشرة اتنين log مليون
+
+640
+00:51:52,670 --> 00:51:54,750
+6 ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+641
+00:51:54,750 --> 00:51:56,730
+ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+642
+00:51:56,730 --> 00:52:01,010
+ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+643
+00:52:01,010 --> 00:52:02,550
+ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+644
+00:52:02,550 --> 00:52:02,550
+ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة، ستة،
+
+645
+00:52:02,550 --> 00:52:06,770
+ستة، ستة، ستة، ستة، ستة، ستة،
+
+646
+00:52:06,770 --> 00:52:11,890
+ستة
+
+647
+00:52:12,490 --> 00:52:24,590
+الـ log معدل تغيرها بطيق معدل تغيرها بيكون
+
+648
+00:52:24,590 --> 00:52:32,230
+بطيق عند الواحد بواحد فبتكون تقريبا بهذا الشكل بس
+
+649
+00:52:32,230 --> 00:52:37,370
+فيه تغير تغير بطيق اه بس فيه تغير مش constant مش
+
+650
+00:52:37,370 --> 00:52:41,210
+constant في المقابل بتلاقي ال linear مش بهذا الشكل
+
+651
+00:52:46,060 --> 00:52:49,300
+خلصنا ال constant مضروف في function مش هيغير في ال
+
+652
+00:52:49,300 --> 00:52:53,760
+order طيب لو قلنا f to the power one minus b و b
+
+653
+00:52:53,760 --> 00:52:59,120
+أكبر من أو تساوي صفر لو بتساوي صفر معناته هي نفس f
+
+654
+00:52:59,120 --> 00:53:04,480
+ال order هو هو كله هيكون big of f ال order مش
+
+655
+00:53:04,480 --> 00:53:09,560
+هيتغير القصد طيب لو كان هنا أكبر من صفر لو قلنا
+
+656
+00:53:09,560 --> 00:53:16,760
+واحدأصبحت 0 أصبحت constant ضمن التعريف big O of F
+
+657
+00:53:16,760 --> 00:53:23,340
+لأنه أقل من ال order فهو ضمن التعريف big O حتى لان
+
+658
+00:53:23,340 --> 00:53:28,660
+بالنسبة لل big O ضمن التعريف اتنين to the power
+
+659
+00:53:28,660 --> 00:53:34,990
+minus نص يعني واحد على Fفال order inverse أقل من
+
+660
+00:53:34,990 --> 00:53:41,890
+ال F طيب و log لسه توي كنا بنحكي عن ال log ال log
+
+661
+00:53:41,890 --> 00:53:45,430
+دايما أقل من مين من ال linear فما دايما أنا بقول
+
+662
+00:53:45,430 --> 00:53:50,430
+log F بغض النظر ال base تبعنا إيش و بغض النظر حتى
+
+663
+00:53:50,430 --> 00:53:57,990
+لو إلها أس أو تتباور كذا تتباور أي قيمة في الآخر
+
+664
+00:53:57,990 --> 00:54:04,110
+هي أقل من ال big O of Fأقل من ال big O of F قيمتها
+
+665
+00:54:04,110 --> 00:54:08,350
+أقل من قيمة ال function نفسها اتوا احنا أخدنا مثال
+
+666
+00:54:08,350 --> 00:54:11,650
+لو ال function linear هي أصغر حاجة احنا متوقعينها
+
+667
+00:54:11,650 --> 00:54:16,110
+مية طبقنا عليها ال linear function هتسوى مية ال
+
+668
+00:54:16,110 --> 00:54:20,790
+output طب ال input الف هيسوى الف مليون هيسوى مليون
+
+669
+00:54:20,790 --> 00:54:24,090
+طب لأ ال output اللي ظهر ده او القيمة اللي ظهرت
+
+670
+00:54:24,090 --> 00:54:29,800
+logهتلاقوها بدل عشرة صارت واحد بدل مية صارت اتنين
+
+671
+00:54:29,800 --> 00:54:36,220
+بدل مليون صارت ستة تمام؟ كويس فهنا برضه هتظل كلهم
+
+672
+00:54:36,220 --> 00:54:40,320
+جميع الصياغ واحد اتنين تلات صياغ كلهم ضمن ال big O
+
+673
+00:54:40,320 --> 00:54:47,200
+of F sum of functions لو قلنا جي belong to big O
+
+674
+00:54:47,200 --> 00:54:56,880
+of F جي اقل من او تساويال order تبع f وال h برضه
+
+675
+00:54:56,880 --> 00:55:02,080
+اقل من او تسوي ال order تبع f فمجموع الاتنين g و h
+
+676
+00:55:02,080 --> 00:55:08,300
+برضه هيكون ضمن التعريف يعني first order زائد first
+
+677
+00:55:08,300 --> 00:55:12,580
+order هيظل first order هيظل first order second
+
+678
+00:55:12,580 --> 00:55:16,300
+order زائد first order second order المهم انه مش
+
+679
+00:55:16,300 --> 00:55:19,460
+هيزيد عن اي واحدة منهم مدام صماشن مش هيزيد عن اي
+
+680
+00:55:19,460 --> 00:55:26,420
+واحدة منهم هيظلالـ order هو order واحدة منهم اللي
+
+681
+00:55:26,420 --> 00:55:33,960
+هي الأكبر اللي هي الأكبر okay بنكمل برضه بمجموعة
+
+682
+00:55:33,960 --> 00:55:39,620
+facts about ال big O for all c أكبر من صفر
+
+683
+00:55:39,620 --> 00:55:42,580
+constant مجرد constant ال constant هذا ضربناه في
+
+684
+00:55:42,580 --> 00:55:50,240
+ال function مش هيتغير هتظل برضه big O of F طيب
+
+685
+00:55:50,240 --> 00:55:59,550
+جمعنالما تقولوا N belong to O of N first طيب بفرق
+
+686
+00:55:59,550 --> 00:56:03,530
+لو قولنا تلاتة N ما هي برضه belong to first order
+
+687
+00:56:03,530 --> 00:56:09,650
+نفس الكلام لو قولنا تلاتة N زائد C كمان زائد خمسة
+
+688
+00:56:09,650 --> 00:56:16,070
+first order طيب ناقص عشرة نفس الكلام first order
+
+689
+00:56:17,410 --> 00:56:22,470
+نفس الفكرة ف constant ضربناه أو جمعناه أو طرحناه
+
+690
+00:56:22,470 --> 00:56:25,270
+على ال function مش هيغير ال order تاع ال function
+
+691
+00:56:25,270 --> 00:56:34,210
+مادام constant مادام رقم ثابت okay if onebelong to
+
+692
+00:56:34,210 --> 00:56:40,430
+O of G1 هدا إيه ال order ال order تبع F1 هو order
+
+693
+00:56:40,430 --> 00:56:46,790
+G أو أقل and F2 function مختلفة belong to O ل
+
+694
+00:56:46,790 --> 00:56:53,270
+order مختلف هدوليك اختلفت ال orders F1 غير F2 G1
+
+695
+00:56:53,270 --> 00:57:00,110
+غير G2 طيب لما أقول F1 في F2F1 مضروبة في F2 belong
+
+696
+00:57:00,110 --> 00:57:05,370
+to big O of G1 مضروبة في G2 زي لما نقول first
+
+697
+00:57:05,370 --> 00:57:15,230
+order في second order لأ third في ضرب ضرب مضروب
+
+698
+00:57:15,230 --> 00:57:19,210
+ضرب لما تكونوا عندكوا N تربيع زائد واحد مضروبة في
+
+699
+00:57:19,210 --> 00:57:26,090
+N هيصير في عندكوا N تكعيب زائد N هنا صارت mean
+
+700
+00:57:26,090 --> 00:57:31,630
+third orderصارت هنا third order فنفس الكلام بدنا
+
+701
+00:57:31,630 --> 00:57:34,090
+نضرب ال orders بتاعتهم .. بدنا نضرب ال orders
+
+702
+00:57:34,090 --> 00:57:37,810
+بتاعتهم واحدة مثلا ال order الخامس ال five order
+
+703
+00:57:37,810 --> 00:57:41,150
+مضروفة ان
+
+704
+00:57:42,360 --> 00:57:51,300
+fourth order تسعة تسعة تسعة تسعة تسعة
+
+705
+00:57:51,300 --> 00:57:55,080
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+706
+00:57:55,080 --> 00:57:56,980
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+707
+00:57:56,980 --> 00:57:57,480
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+708
+00:57:57,480 --> 00:57:57,860
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+709
+00:57:57,860 --> 00:57:58,300
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+710
+00:57:58,300 --> 00:58:01,260
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+711
+00:58:01,260 --> 00:58:08,290
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسfirst
+
+712
+00:58:08,290 --> 00:58:11,630
+order زائد second order مين الأكبر؟ ال second
+
+713
+00:58:11,630 --> 00:58:14,670
+معناته مجموح ان بيعطيين second order مجموح ان
+
+714
+00:58:14,670 --> 00:58:18,170
+بيعطي second order اللي لو بده اجمحهم هدوله مش
+
+715
+00:58:18,170 --> 00:58:22,570
+هيتغير هتظل خمسة هتظل ال order تبعنا خمسة طيب
+
+716
+00:58:22,570 --> 00:58:29,110
+بناخد مين منهم ال big G1 من التنتين امتى باخد G1؟
+
+717
+00:58:29,110 --> 00:58:34,530
+اذا كانت G2 belonged to big O G1 بمعنى ان ال G1 هي
+
+718
+00:58:34,530 --> 00:58:40,190
+الأكبرأو تساوي G1 أكبر أو تساوي فهنا بالظبط كأنه
+
+719
+00:58:40,190 --> 00:58:51,470
+ال G1 هي ال big O of N to the power 5 هي
+
+720
+00:58:51,470 --> 00:58:56,470
+الأكبر من to the power 4 فهي اللي بناخدها طبعا
+
+721
+00:58:56,470 --> 00:59:01,130
+واضح جدا أنه بقدر ببساطة أقول أن ال N to the power
+
+722
+00:59:01,130 --> 00:59:07,710
+4 هي big O of N to the power 5صحيح فهيها هي نفسها
+
+723
+00:59:07,710 --> 00:59:14,570
+هي belong belong هذه هي نفسها دي فاللي هنختارها
+
+724
+00:59:14,570 --> 00:59:19,790
+فعلا هي ال n to the power four اللي هي جي واحد جي
+
+725
+00:59:19,790 --> 00:59:27,450
+واحد كويس مجموعة
+
+726
+00:59:27,450 --> 00:59:30,190
+ال facts هي نفسها هي نفس اللي احنا خدناهم هدولاك
+
+727
+00:59:30,190 --> 00:59:36,430
+ايه نفسهملو ما نضرب function في constant هيظل نفس
+
+728
+00:59:36,430 --> 00:59:41,590
+ال function هو معاه example تلاتة X تربيع برضه ال
+
+729
+00:59:41,590 --> 00:59:47,030
+second order برضه second order لو قولنا F plus big
+
+730
+00:59:47,030 --> 00:59:52,050
+O of F هي نفس big O of F لاحظوا هنا ال order هو ال
+
+731
+00:59:52,050 --> 00:59:54,830
+order ال function طبعا هنا مدخل نفس ال function
+
+732
+00:59:55,390 --> 00:59:59,590
+يعني معناته ال orders متشابهة ال orders متشابهة
+
+733
+00:59:59,590 --> 01:00:04,490
+هنا قد تكون big O هذه اما نفس ال order او اقل او
+
+734
+01:00:04,490 --> 01:00:12,310
+اقل فهنا F تربيعية big O of F ممكن تكون اما تربيع
+
+735
+01:00:12,310 --> 01:00:15,430
+او first order اما second order او first order فلو
+
+736
+01:00:15,430 --> 01:00:18,910
+افترضنا first order هيظل تربيع هيظل نفس ال order
+
+737
+01:00:18,910 --> 01:00:22,550
+تبع مين بتاع ال function هيظل نفس ال order ال
+
+738
+01:00:22,550 --> 01:00:27,070
+functionكويس خلّي هدول المرة الجاية عشان إيش
+
+739
+01:00:27,070 --> 01:00:31,050
+ننراجع فيهم برضه، كويس إن بيظلوا موجودين نرجحهم،
+
+740
+01:00:31,050 --> 01:00:36,950
+فضلوا ال order احنا بدأنا محاضرتنا لما بدأت انا
+
+741
+01:00:36,950 --> 01:00:39,410
+مابدتش في ال order عارفة؟ اتكلمتلكوا شوية عن ال
+
+742
+01:00:39,410 --> 01:00:42,750
+complexity ال complexity عشان أحسبها بحسبها من
+
+743
+01:00:42,750 --> 01:00:49,060
+هنا، بحسبها إنه ال function بتاعتنا big of إيشبشوف
+
+744
+01:00:49,060 --> 01:00:52,800
+ال order تبع ال .. ال code الأول و ال order بتاع
+
+745
+01:00:52,800 --> 01:00:57,700
+ال code التاني ال order الأقل هو اللي باخده مين ال
+
+746
+01:00:57,700 --> 01:01:00,740
+order تبعه أقل هو اللي بناخده بنقول لأ هذا ال code
+
+747
+01:01:00,740 --> 01:01:05,360
+أفضل more efficient ل الشغل اللي .. او لل task
+
+748
+01:01:05,360 --> 01:01:08,180
+اللي بنشتغل عليها لل task اللي بنشتغل عليها على
+
+749
+01:01:08,180 --> 01:01:10,080
+بركة الله يعطيكم العافية و نشوفكم المرة الجاية ان
+
+750
+01:01:10,080 --> 01:01:10,300
+شاء الله
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/79nrEVc1ARE.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/79nrEVc1ARE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..582908b293775e1581e6f93881c9c19dc52fd645
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/79nrEVc1ARE.srt
@@ -0,0 +1,2027 @@
+1
+00:00:21,280 --> 00:00:23,160
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,160 --> 00:00:26,160
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه أجمعين
+
+3
+00:00:26,160 --> 00:00:30,480
+نبدأ اليوم نكمل الجزئية  الـ examples اللي كنا
+
+4
+00:00:30,480 --> 00:00:34,620
+بنتكلم فيها عن الـ counting كان في ضايلة كم من
+
+5
+00:00:34,620 --> 00:00:37,540
+example عشان نبدأ في الموضوع الجديد إن شاء الله
+
+6
+00:00:37,540 --> 00:00:42,020
+تعالَ بنحاول نكملهم في الـ...  هلوجة عشان نبدأ نخلص
+
+7
+00:00:42,020 --> 00:00:45,780
+الموضوع اللي بـremaining examples وصلنا المرة اللي فاتت
+
+8
+00:00:45,780 --> 00:00:49,060
+كان عبارة عن password بدنا نشوف قداش عدد الـ
+
+9
+00:00:49,060 --> 00:00:52,860
+passwords اللي ممكن نعملها generation باستخدام two
+
+10
+00:00:52,860 --> 00:00:56,260
+digits أو أو أو two characters بمعنى فيه هيكون
+
+11
+00:00:56,260 --> 00:01:02,080
+عندك الـ password عبارة عن two positions position
+
+12
+00:01:02,080 --> 00:01:05,840
+number one and position number two. الـ two
+
+13
+00:01:05,840 --> 00:01:08,360
+positions هدول إيش الشروط اللي لهم؟ أو إيش الـ
+
+14
+00:01:08,360 --> 00:01:11,280
+... الـ ... الـ characters اللي ممكن نستخدمها لكل
+
+15
+00:01:11,280 --> 00:01:13,560
+position من الـ two positions هدول؟ الـ two
+
+16
+00:01:13,560 --> 00:01:17,100
+positions اللي ممكن يكونوا عبارة عن letters from A
+
+17
+00:01:17,100 --> 00:01:23,800
+to Z, or digits from 0 to 9, or واحدة أو one of the
+
+18
+00:01:23,800 --> 00:01:26,920
+10 punctuation characters, 10 punctuations اللي
+
+19
+00:01:26,920 --> 00:01:29,780
+ممثلين بهذا الشكل، الشكل اللي موجود هنا في الـ slide
+
+20
+00:01:29,780 --> 00:01:33,260
+وهدول اللي نقدر نجيبهم من shift 1, shift 2, أو
+
+21
+00:01:33,260 --> 00:01:37,000
+shift 3 to shift 0. فهدول اللي هم الـ punctuations
+
+22
+00:01:37,000 --> 00:01:41,240
+طيب هدول اللي هم الممكنية اللي بنقدر نختار منهم
+
+23
+00:01:41,240 --> 00:01:45,740
+الـ characters بتاعة الـ two positions. طيب في عندنا
+
+24
+00:01:45,740 --> 00:01:50,300
+شرط ثاني لعملية الـ generation للـ passwords هذه، أن
+
+25
+00:01:50,300 --> 00:01:54,960
+each password must contain at least one digit or
+
+26
+00:01:55,370 --> 00:01:58,650
+punctuation characters. فإذا واحدة من الـ position
+
+27
+00:01:58,650 --> 00:02:01,210
+يا الـ position الأول يا الـ position الثاني at
+
+28
+00:02:01,210 --> 00:02:07,570
+least لازم يكون فيه digit أو punctuation. بمعنى أنه
+
+29
+00:02:07,570 --> 00:02:14,430
+لا يمكن أن يكون فيه two letters في الـ password. لازم
+
+30
+00:02:14,430 --> 00:02:19,010
+يكون واحد منهم digit أو punctuation at least. يعني
+
+31
+00:02:19,010 --> 00:02:23,010
+ممكن يكونوا الإثنين digits أو الإثنين punctuations
+
+32
+00:02:23,010 --> 00:02:27,360
+أو واحد digit وواحد punctuation.  كيف
+
+33
+00:02:27,360 --> 00:02:28,220
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+34
+00:02:28,220 --> 00:02:28,580
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+35
+00:02:28,580 --> 00:02:30,960
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+36
+00:02:30,960 --> 00:02:32,020
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+37
+00:02:32,020 --> 00:02:33,680
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+38
+00:02:33,680 --> 00:02:34,600
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+39
+00:02:34,600 --> 00:02:35,460
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+40
+00:02:35,460 --> 00:02:35,540
+نستطيع أن نستطيع أن نستطيع أن نستطيع أن نستطيع أن
+
+41
+00:02:35,540 --> 00:02:42,880
+نستطيع أن نستطيع أن نستطيع
+
+42
+00:02:42,880 --> 00:02:51,940
+أن
+
+43
+00:02:51,940 --> 00:02:56,490
+نستَطْرِد أنه عشرة punctuations. ف أنا بالنسبة للـ
+
+44
+00:02:56,490 --> 00:03:00,170
+position number one في عندي إمكانية لـ 2 لـ 20
+
+45
+00:03:00,170 --> 00:03:04,650
+character نستخدمهم في حالة الـ position الأول. إذا
+
+46
+00:03:04,650 --> 00:03:08,030
+تم استخدام فعلاً digit أو punctuation في الـ
+
+47
+00:03:08,030 --> 00:03:11,530
+position الأول، فالـ position الثاني أنا في حل من
+
+48
+00:03:11,530 --> 00:03:15,350
+الشرط هذا، فبقدر بقدر أقول أنه ممكن يكون letters
+
+49
+00:03:15,350 --> 00:03:20,150
+26 أو ممكن يكون برضه digit أو ممكن يكون
+
+50
+00:03:20,150 --> 00:03:25,810
+punctuation. فهذا هتصير 46. طيب الإثنين هدول الـ two
+
+51
+00:03:25,810 --> 00:03:29,510
+positions لازم الإثنين موجودين. بمعنى الـ position
+
+52
+00:03:29,510 --> 00:03:35,770
+الأول موجود بعدد الحالات اللي بقدر أمثلها فيها، وand
+
+53
+00:03:35,770 --> 00:03:38,210
+الـ position الثاني موجود بعدد الحالات اللي بقدر
+
+54
+00:03:38,210 --> 00:03:43,830
+أمَثِّلها فيها. فهنا بتصير عملية ضرب. صارت 20 في 46 حالة
+
+55
+00:03:43,830 --> 00:03:48,960
+طيب هذا كانت حالة أولى. الحالة الثانية، هفترض أنه لـ
+
+56
+00:03:48,960 --> 00:03:52,540
+الـ position الثاني هو اللي حقق لي شرط الـ
+
+57
+00:03:52,540 --> 00:03:57,700
+punctuation أو digit فقط في الـ position هذا. فهنا
+
+58
+00:03:57,700 --> 00:04:02,380
+أصبحت عشرة زائد عشرة. عشرة digits زائد عشرة
+
+59
+00:04:02,380 --> 00:04:07,080
+punctuations. أصبح عندي عشرين character محددين، إما
+
+60
+00:04:07,080 --> 00:04:12,620
+digit أو punctuation. صار الـ position الأول ممكن
+
+61
+00:04:12,620 --> 00:04:17,900
+يكون letters، ممكن يكون برضه punctuation، وممكن يكون
+
+62
+00:04:17,900 --> 00:04:22,900
+digits. فصار هذه عندي 46. قداش عددهم؟ نفس الكلام.
+
+63
+00:04:22,900 --> 00:04:28,660
+صاروا برضه 46 في 20. طيب، هلاحظ أنه الحالتين بدهم
+
+64
+00:04:28,660 --> 00:04:33,200
+نجمعهم، لأنه إما هتظهر عندي الـ characters بتاعة الـ
+
+65
+00:04:33,200 --> 00:04:36,500
+punctuation أو الـ digit في الـ position الثاني أو
+
+66
+00:04:36,500 --> 00:04:40,000
+في الـ position الأول. إما هذه أو هذه. ففي الحالة دي
+
+67
+00:04:40,000 --> 00:04:50,110
+صارت عندي 20 في 46 زائد 46 في 20. طيب، بقدرش
+
+68
+00:04:50,110 --> 00:04:53,710
+أَسْكُت، هو أقول خلاص، مجموع هو عدد الـ passwords
+
+69
+00:04:53,710 --> 00:04:58,430
+الممكنة. ليش؟ لأنه في حالات انعدت هنا، واتكررت هنا.
+
+70
+00:04:58,430 --> 00:05:01,070
+إيش هي الحالات اللي اتكررت هنا؟ آه، في حالات اتكررت
+
+71
+00:05:01,070 --> 00:05:05,190
+لأنه أنا لما بقول هنا عندي عشرين punctuations أو
+
+72
+00:05:05,190 --> 00:05:08,430
+digits، تكرر معاها أنه في الحالة الثانية برضه
+
+73
+00:05:08,430 --> 00:05:12,950
+موجودة الـ digit أو punctuation. فإذا أصبح في عندي
+
+74
+00:05:12,950 --> 00:05:16,250
+هنا digit and punctuations، وفي الحالة الثانية صار
+
+75
+00:05:16,250 --> 00:05:19,910
+في عندي برضه هنا مجموعة digits، وموجود هنا في حالة
+
+76
+00:05:19,910 --> 00:05:22,790
+الـ punctuations برضه في الحالة الأولى. فهذه حالة
+
+77
+00:05:22,790 --> 00:05:27,770
+متوفرة، حالة متوفرة وموجودة. فإذا بدنا نطرحهم، أو
+
+78
+00:05:27,770 --> 00:05:30,370
+بدنا نطرح الـ intersection between them. طب كيف أطرح
+
+79
+00:05:30,370 --> 00:05:33,190
+الـ intersection between them؟ أنه أعمل التقاطع
+
+80
+00:05:33,190 --> 00:05:37,410
+التقاطع، أن الشرط تحقق الـ two positions مع بعض. الـ
+
+81
+00:05:37,410 --> 00:05:40,010
+two positions مع بعض. كيف ممكن يتحقق الـ two
+
+82
+00:05:40,010 --> 00:05:44,690
+positions مع بعض؟ أن الـ position الأول عبارة عن
+
+83
+00:05:44,690 --> 00:05:50,270
+digit أو punctuation. عشرة زائد عشرة، و الـ position
+
+84
+00:05:50,270 --> 00:05:56,010
+الثاني أيضاً برضه digit and punctuation. برضه إما
+
+85
+00:05:56,010 --> 00:06:01,110
+عشرة أو عشرة. فصار في عندنا عشرين في عشرين. هدول
+
+86
+00:06:01,110 --> 00:06:04,630
+تكرروا هنا، تكرروا هنا، تكرروا في الحالتين، في
+
+87
+00:06:04,630 --> 00:06:08,570
+الحالتين، في الحالتين. فأنا مضطر أطرحهم مرة، لأن
+
+88
+00:06:08,570 --> 00:06:10,990
+جمعتهم مرتين. فأبدأ أطرحهم مرة عشان يكونوا مجموعين
+
+89
+00:06:10,990 --> 00:06:16,880
+بس مرة واحدة فقط. فهنا صار سالب أو minus عشرين في
+
+90
+00:06:16,880 --> 00:06:24,560
+عشرين. أصبح لنا بهذا الشكل الحل: 920
+
+91
+00:06:24,560 --> 00:06:30,140
+زائد 920 ناقص 400 بيعطينا 1440
+
+92
+00:06:30,140 --> 00:06:33,820
+ألف وأربعمائة وأربعين password
+
+93
+00:06:33,820 --> 00:06:37,260
+أو different passwords ممكنة في الحالة اللي عندنا.
+
+94
+00:06:37,260 --> 00:06:41,940
+في الحالة اللي عندنا. okay. More examples. لو بدنا أن
+
+95
+00:06:41,940 --> 00:06:46,320
+نجيب find the number of three-letter initials
+
+96
+00:06:46,320 --> 00:06:50,600
+where none of the letters are repeated. إذا كان بدنا
+
+97
+00:06:50,600 --> 00:06:55,440
+نجيب مجموعة الحروف الأولى... مجموعة الحروف الأولى
+
+98
+00:06:55,440 --> 00:06:58,640
+أو الـ abbreviations... abbreviations لـ three
+
+99
+00:06:58,640 --> 00:07:02,980
+letters as initials. ممكن نقول مجموعة abbreviations
+
+100
+00:07:02,980 --> 00:07:09,600
+متكونة من three letters: a, b, c. بهذا الشكل، بهذا الشكل.
+
+101
+00:07:09,600 --> 00:07:14,320
+كم abbreviations أو كم abbreviations ممكن أكون
+
+102
+00:07:14,320 --> 00:07:19,000
+من الـ three letters بشرط أنه ما تتكرر الـ letters.
+
+103
+00:07:19,000 --> 00:07:24,400
+إذا كان في الـ a أصبحت في الـ position الأول، لا يمكن
+
+104
+00:07:24,400 --> 00:07:26,900
+قبولها في الـ position الثاني أو الـ position الثالث.
+
+105
+00:07:26,900 --> 00:07:32,080
+فهنا ممنوع التكرار للـ letters ساعتها. فجدِشْ في
+
+106
+00:07:32,080 --> 00:07:37,540
+إمكانية لعدد initials في الحالة هذه، أو عدد
+
+107
+00:07:37,540 --> 00:07:41,140
+abbreviations في الحالة، مختصرات في الحالة هذه طبعاً
+
+108
+00:07:41,140 --> 00:07:44,600
+بالنسبة للـ location الأول، هو هختار من واحد من 26
+
+109
+00:07:44,600 --> 00:07:48,980
+letter. في الحالة الثانية ممنوع التكرار.
+
+110
+00:07:48,980 --> 00:07:51,800
+ممنوع التكرار، معناته ذلك أن في عندي 26 بس
+
+111
+00:07:51,800 --> 00:07:55,260
+أنا هنا في character اخترته، في letter اخترتها، فصار
+
+112
+00:07:55,260 --> 00:07:59,800
+اختياري من 25.  الثالثة 24، لأن
+
+113
+00:07:59,800 --> 00:08:02,560
+فيه رقمين، في two letters تم اختيارهم في الخانة
+
+114
+00:08:02,560 --> 00:08:05,820
+الأولى والخانة الثانية. فصار عندي عدد الاحتمالات
+
+115
+00:08:05,820 --> 00:08:09,200
+أو عدد الـ letters اللي ممكن اختار منهم فقط 24.
+
+116
+00:08:09,200 --> 00:08:14,400
+أصبح أجدِشْ 26 في 25 في
+
+117
+00:08:14,400 --> 00:08:21,910
+24. تمام. طيب، مثال بسيط جداً، المثال
+
+118
+00:08:21,910 --> 00:08:24,230
+اللي بعده: count the number of bit strings of
+
+119
+00:08:24,230 --> 00:08:27,110
+length 4. وهذه أخذتها وأنتم بتشتغلوا في الـ binary
+
+120
+00:08:27,110 --> 00:08:30,150
+وجدِشْ عدد الـ bit strings اللي بتقدروا تعملوه
+
+121
+00:08:30,150 --> 00:08:33,710
+generation من عدد bits محدد بالنسبة لكم، أو عدد
+
+122
+00:08:33,710 --> 00:08:36,770
+digit محدد. فلو نتكلم عن أربعة، معناته ذلك أن أنتم
+
+123
+00:08:36,770 --> 00:08:41,710
+في عندكم أربعة digits. هذي جدِشْ الاختيارات؟ وجدِشْ عدد
+
+124
+00:08:41,710 --> 00:08:44,930
+الـ possibilities بتاعتها؟ إما zero أو one. فهذه
+
+125
+00:08:44,930 --> 00:08:48,110
+إثنين، الثانية برضه إثنين، ثلاثة إثنين، أربعة إثنين،
+
+126
+00:08:48,110 --> 00:08:51,490
+فجدِشْ عددهم أربعة؟ صار عندي two to the power أربعة
+
+127
+00:08:51,490 --> 00:08:56,050
+مضروبهم في بعض. فهذا two to the power أربعة. مثال
+
+128
+00:08:56,050 --> 00:09:01,700
+سهل، ما فيه أي أشكال، ما فيه أي مشاكل. Okay, count
+
+129
+00:09:01,700 --> 00:09:05,400
+the number of bit strings of length four or less.
+
+130
+00:09:05,400 --> 00:09:08,880
+four or less معناته ذلك ممكن يكون طوله أربعة أو
+
+131
+00:09:08,880 --> 00:09:15,740
+ثلاثة أو إثنين أو واحد أو  هل مجرد كلمة؟ أو معناته أن
+
+132
+00:09:15,740 --> 00:09:19,500
+أنا بعمل جمع بالنسبة لأربعة. صارت 2 <sup>4</sup>
+
+133
+00:09:19,500 --> 00:09:24,060
+أو هي أو بتترجم لجمع، لـ summation.
+
+134
+00:09:26,110 --> 00:09:30,170
+ثلاثة أو إثنين أو إثنين أو إثنين أو إثنين إثنين
+
+135
+00:09:30,170 --> 00:09:30,570
+إثنين إثنين إثنين إثنين إثنين إثنين إثنين إثنين
+
+136
+00:09:30,570 --> 00:09:31,330
+إثنين إثنين إثنين إثنين إثنين إثنين إثنين إثنين
+
+137
+00:09:31,330 --> 00:09:37,150
+إثنين إثنين إثنين إثنين إثنين إثنين إثنين إثنين
+
+138
+00:09:37,150 --> 00:09:42,430
+إثنين
+
+139
+00:09:42,430 --> 00:09:44,870
+إثنين إثنين إثنين إثنين إثنين إثنين إثنين إثنين
+
+140
+00:09:44,870 --> 00:09:46,230
+إثنين إثنين إثنين إثنين إثنين إثنين إثنين إثنين
+
+141
+00:09:46,230 --> 00:09:51,430
+إثنين إثنين إثنين إثنين إثنين إثنين إثنين
+
+142
+00:09:55,130 --> 00:10:00,450
+two ways للجمع أو two tasks. بحسب جدِشْ عدد الـ ways
+
+143
+00:10:00,450 --> 00:10:03,770
+للـ task الأولى اللي هي any task أولى: begin with
+
+144
+00:10:03,770 --> 00:10:09,090
+an even digit. الـ task الثانية: end with an even digit.
+
+145
+00:10:09,090 --> 00:10:12,930
+وبنجمعهم مع بعض. ليش بنجمعهم مع بعض؟ لأن في بينهم or.
+
+146
+00:10:12,930 --> 00:10:19,230
+في بينهم or. okay. بنمسك الأولى اللي هي begin with
+
+147
+00:10:19,230 --> 00:10:21,350
+with an even
+
+148
+00:10:27,010 --> 00:10:30,650
+هي three digit. هذه طبعاً احنا بنتكلم عن decimal هنا.
+
+149
+00:10:30,650 --> 00:10:34,290
+في الحالة بتاعتنا، أنا بتكلم من صفر لتسعة. قداش
+
+150
+00:10:34,290 --> 00:10:37,930
+أرقام even من صفر لتسعة؟ عندي الصفر، عندي الإثنين،
+
+151
+00:10:37,930 --> 00:10:42,990
+عندي الأربعة، عندي الستة، وعندي الثمانية. تمام. هلأ
+
+152
+00:10:42,990 --> 00:10:45,110
+وجهة لما بدنا نبدأ بالحالة الأولى
+
+153
+00:10:48,430 --> 00:10:55,710
+begin with an even digit. جدِشْ الأرقام الـ even اللي أنا
+
+154
+00:10:55,710 --> 00:10:59,190
+بقدر أبدأ فيها الرقم؟ نبدأ فيها معناته هتيجي في أول
+
+155
+00:10:59,190 --> 00:11:04,970
+location، في أول bit أو في أول digit هنا. okay. هيكون
+
+156
+00:11:04,970 --> 00:11:11,090
+جدِشْ عددهم؟ واحد، إثنين، ثلاثة، أربعة، خمسة. خمسة؟ لأ، مش
+
+157
+00:11:11,090 --> 00:11:14,150
+خمسة. ليش مش خمسة؟ لأن الصفر غير مسموح فيه لما نقول
+
+158
+00:11:14,150 --> 00:11:19,870
+صفر، ستة، خمسة. هذا فعلياً number من two digits، مش من
+
+159
+00:11:19,870 --> 00:11:22,810
+three digits. هذا من two digits. فإذا الـ zero لا
+
+160
+00:11:22,810 --> 00:11:28,810
+يمكن استخدام الـ zero في مرحلة أو في خانة المئات.
+
+161
+00:11:28,810 --> 00:11:32,250
+فإذا هنا مش أربعة، مش خمسة، هنا في عندي أربعة احتمالات
+
+162
+00:11:32,250 --> 00:11:35,710
+فقط، أو أربعة اختيارات. بقدر أربعة أرقام بقدر اختار
+
+163
+00:11:35,710 --> 00:11:38,650
+منهم، أو أربعة ديجت، بقدر اختار منهم منهم إيش؟ أربعة
+
+164
+00:11:38,650 --> 00:11:44,470
+أربعة، ستة، ثمانية. أربعة فقط. فهذه هتكون أربعة. ثانية
+
+165
+00:11:44,470 --> 00:11:49,730
+خلاص، الثانية free، ممكن تكون من صفر لتسعة. من صفر لتسعة
+
+166
+00:11:50,150 --> 00:11:54,410
+ممكن تكون 59. هي هي. three digits أو
+
+167
+00:11:54,410 --> 00:11:59,770
+ممكن تكون 99. فهيهم من صفر لتسعة. أي رقم
+
+168
+00:11:59,770 --> 00:12:04,030
+ممكن جداً. وبيظل اسمها رقم من الـ three digits. فمن
+
+169
+00:12:04,030 --> 00:12:07,670
+صفر لتسعة، عندي عشر حالات. الرقم الأخير برضه من صفر
+
+170
+00:12:07,670 --> 00:12:11,390
+لتسعة، فيه عشر احتمالات. هذه هي بدأت تسعة، وهي استخدمنا
+
+171
+00:12:11,390 --> 00:12:16,550
+الصفر موجود، فالصفر في الأحاد هيظل موجود في المئات.
+
+172
+00:12:16,550 --> 00:12:21,050
+لأ، في المئات ما لوش قيمة. Okay، مضروب في إيش؟ في عشر.
+
+173
+00:12:21,050 --> 00:12:25,730
+صار عندي 400 ways to represent this
+
+174
+00:12:25,73
+
+223
+00:15:54,120 --> 00:15:59,670
+نقول if the function from A to B, from A to B, الـ A
+
+224
+00:15:59,670 --> 00:16:03,870
+نسميها الـ domain, الـ B نسميها الـ codomain, and
+
+225
+00:16:03,870 --> 00:16:07,950
+cardinality of A أكبر من أو تساوي cardinality of B
+
+226
+00:16:07,950 --> 00:16:11,770
+plus واحد. فإذا الـ domain أكبر من الـ
+
+227
+00:16:11,770 --> 00:16:16,130
+codomain, automatically معنى ذلك أنه في عندنا عناصر
+
+228
+00:16:16,130 --> 00:16:20,550
+موجودة، أو أكثر من عنصر موجود في الـ domain لهم نفس
+
+229
+00:16:20,550 --> 00:16:24,930
+الناتج في الـ codomain، صحيح؟ لما بنعمل assignment
+
+230
+00:16:24,930 --> 00:16:31,650
+لهم، أكيد هيكون في عندنا two pre-images لهم القيم اللي
+
+231
+00:16:31,650 --> 00:16:35,030
+موجودة في الـ domain، كنا نسميهم pre-image، بتذكرينهم
+
+232
+00:16:35,030 --> 00:16:40,010
+pre-image، الـ قيم اللي موجودة في الـ codomain كنا
+
+233
+00:16:40,010 --> 00:16:43,510
+نسميها image. فمعنى ذلك أن يوجد image لأكثر من one
+
+234
+00:16:43,510 --> 00:16:49,630
+pre-image. Then some element of B has
+
+235
+00:16:52,690 --> 00:16:56,430
+under function f. في الحالة دي معناته أن أنا بتكلم
+
+236
+00:16:56,430 --> 00:17:04,570
+عن not one to one. ليش؟ لأنه مش كل image جاية من pre-
+
+237
+00:17:04,570 --> 00:17:08,110
+image واحدة، لأ هي فيه two pre-images هيروحوا لنفس
+
+238
+00:17:08,110 --> 00:17:11,850
+الـ image. لنفس الـ image هيكون في عندنا two pigeons
+
+239
+00:17:11,850 --> 00:17:16,930
+لنفس الـ hole، لنفس الـ pigeon hole، تمام؟ فهيكون أكثر
+
+240
+00:17:16,930 --> 00:17:27,280
+من pre-images. Okay، توضيح للفكرة، و
+
+241
+00:17:27,280 --> 00:17:32,280
+أنه فعلاً مجرد أنه في هنا مثلاً عندي ثمان.. تسع
+
+242
+00:17:32,280 --> 00:17:36,740
+خانات. التسع خانات هدول أكثر من عشر.. من عشرة
+
+243
+00:17:36,740 --> 00:17:40,100
+pigeons، أكيد أكثر من تسعة pigeons، أكيد هيكون في
+
+244
+00:17:40,100 --> 00:17:42,540
+two pigeons في نفس الـ.. في نفس الخانة، أو في نفس
+
+245
+00:17:42,540 --> 00:17:47,890
+الـ.. okay، بتتوزع كيف؟ مش فارقة معايا يعني أن أنا
+
+246
+00:17:47,890 --> 00:17:49,790
+ماليش علاقة بالتوزيع، بس أنا اللي بقدر أحكم عليه
+
+247
+00:17:49,790 --> 00:17:54,670
+exactly، أنه at least في مكان يوجد فيه أكثر من
+
+248
+00:17:54,670 --> 00:17:58,410
+واحدة. هذا اللي بقدر أقوله وأنا متطمن بس
+
+249
+00:17:58,410 --> 00:18:02,710
+بقدرش أعمم الحالة هذه، وبقدرش أعمم الحالة هذه أني
+
+250
+00:18:02,710 --> 00:18:05,730
+أقول اه، والله فيه تلقائيًا، لأ، بضمنش أنه دائمًا هتكون
+
+251
+00:18:05,730 --> 00:18:10,190
+هيك، بس أنا ضامن أنه دائمًا في خانة فيها أكثر من one
+
+252
+00:18:10,190 --> 00:18:14,330
+pigeon. في دائمًا خانة فيها أكثر من one pigeon. Okay،
+
+253
+00:18:14,330 --> 00:18:18,550
+examples، كيف ممكن تيجي examples على الموضوع هذا، أو
+
+254
+00:18:18,550 --> 00:18:21,210
+إيش في examples توضح الفكرة هذه؟ هتوضح ببساطة جدًا
+
+255
+00:18:21,210 --> 00:18:27,370
+there are 101 possible numeric grades من 0 إلى 100.
+
+256
+00:18:27,370 --> 00:18:30,830
+هذا اللي هي rounded، إما round up أو round down.
+
+257
+00:18:30,830 --> 00:18:34,450
+بمعنى أن الدرجة اللي هتكون موجودة، إما بعملها تقريب
+
+258
+00:18:34,450 --> 00:18:37,530
+بعملها ceiling أو floor، بعملها round up أو round
+
+259
+00:18:37,530 --> 00:18:41,550
+down. كلهم لازم يكونوا integers، integers في
+
+260
+00:18:41,550 --> 00:18:44,630
+الحالة هذه. الـ grades اللي موجودة عندي عددهم 101
+
+261
+00:18:44,630 --> 00:18:49,310
+grades. لو عندي عدد طلاب أكبر من 101، أكيد في طالبين
+
+262
+00:18:49,310 --> 00:18:53,470
+هيشتركوا بنفس الـ grade، أكيد في طالبين هيأخذوا نفس
+
+263
+00:18:53,470 --> 00:18:57,090
+العلامة، هذا على الأقل.. هذا على الأقل.. يمكن
+
+264
+00:18:57,090 --> 00:19:00,190
+يكون في أكثر.. يمكن يكون في أكثر.. بس أنا بتكلم
+
+265
+00:19:00,190 --> 00:19:04,680
+هنا at least، هذا الـ.. يعني الكلمة المضمونة. I am
+
+266
+00:19:04,680 --> 00:19:09,360
+sure that أن فعلاً في أكثر من طالب لهم نفس الـ grade،
+
+267
+00:19:09,360 --> 00:19:14,440
+okay. ففي الحالة دي اللي أنا around it مش هيكون فيه
+
+268
+00:19:14,440 --> 00:19:17,460
+قصور، أنه يكبر.. يكثر عدد الـ grades اللي موجودة
+
+269
+00:19:17,460 --> 00:19:20,220
+لهم. الـ grades خلاص 101. فإذا عدد الطلاب أكثر من
+
+270
+00:19:20,220 --> 00:19:24,340
+101، automatically هنقول فيه two students at least
+
+271
+00:19:24,340 --> 00:19:27,240
+في نهاية الـ semester هيكون إنهم نفس الـ grade، نفس
+
+272
+00:19:27,240 --> 00:19:30,740
+الـ grade. طبعاً واضح أن احنا هنا بنتكلم عن none أو
+
+273
+00:19:30,740 --> 00:19:34,080
+not a one to one function، not a one to one
+
+274
+00:19:34,080 --> 00:19:37,740
+function، لأنه في two students، في two pre-images
+
+275
+00:19:37,740 --> 00:19:42,250
+اللي يمثلوا للطلاب موجودين إنهم نفس الـ grade، الـ
+
+276
+00:19:42,250 --> 00:19:44,490
+image، نفس القيمة في الـ.. في الـ.. في الـ codomain.
+
+277
+00:19:44,490 --> 00:19:51,670
+okay. طيب في.. اه بس بدنا نشوف طبعاً واحدة من هدول
+
+278
+00:19:53,960 --> 00:19:59,300
+خليني أشوف كمان examples. Among any group of 367
+
+279
+00:19:59,300 --> 00:20:03,260
+people, there must be at least two with the same
+
+280
+00:20:03,260 --> 00:20:07,780
+birthday. لو كان في عندنا ثلاثمية وسبعة وستون شخص،
+
+281
+00:20:07,780 --> 00:20:11,640
+أكيد في على الأقل اثنين انولدوا في نفس اليوم، أكيد
+
+282
+00:20:12,450 --> 00:20:15,690
+sure. يمكن يكون فيه أكثر، يعني صدفة في حالة من
+
+283
+00:20:15,690 --> 00:20:18,570
+الحالات، يمكن في خمسة أو عشرة.. يمكن في إحدى الحالات
+
+284
+00:20:18,570 --> 00:20:22,530
+نصفهم، بس أنا بتكلم في المضمون، المضمون اللي أنا فعلاً
+
+285
+00:20:22,530 --> 00:20:25,490
+..to guarantee that أن على الأقل في عندنا اثنين
+
+286
+00:20:25,490 --> 00:20:30,590
+have the same birthday، have the same أو لهم نفس
+
+287
+00:20:30,590 --> 00:20:33,730
+.. أو have the same birthday، أو لهم نفس يوم
+
+288
+00:20:33,730 --> 00:20:39,840
+الميلاد. In any group of 27 English words، لو في
+
+289
+00:20:39,840 --> 00:20:44,320
+عندنا مجموعة فيها 27 كلمة، برضه at least في كلمتين
+
+290
+00:20:44,320 --> 00:20:48,670
+بدأوا بنفس الـ letter، صحيح؟ بيولوجيًا يعني منطق كل
+
+291
+00:20:48,670 --> 00:20:52,470
+اللي احنا بقوله، لأنه عندكم 26 حرف، فلو افترضنا أسوأ
+
+292
+00:20:52,470 --> 00:20:55,990
+حالة ممكنة أنه كل كلمة مختلفة عن الثانية، الـ
+
+293
+00:20:55,990 --> 00:21:00,010
+maximum اللي لهم في الاختلاف 26. الـ 27 هذه لازم
+
+294
+00:21:00,010 --> 00:21:02,450
+تكون مشابهة لواحدة منهم، لازم تكون مشابهة لواحدة
+
+295
+00:21:02,450 --> 00:21:05,290
+منهم. طيب، how many people must be selected from a
+
+296
+00:21:05,290 --> 00:21:09,670
+collection of 15 married couples to ensure that at
+
+297
+00:21:09,670 --> 00:21:14,870
+least two of the persons chosen are married to
+
+298
+00:21:14,870 --> 00:21:20,370
+each other. هل يوجد في عندنا خمسة عشر couple، أزواج، و
+
+299
+00:21:20,370 --> 00:21:24,350
+خلاص، وتوزعوا. بدنا نختار، جديش عدد الناس اللي بدنا
+
+300
+00:21:24,350 --> 00:21:26,730
+نختارهم، عشان أكون ضامن أنه من المجموعة اللي تم
+
+301
+00:21:26,730 --> 00:21:30,990
+اختيارها يوجد زوجين؟ 16، أكثر من عدد الشباب اللي
+
+302
+00:21:30,990 --> 00:21:37,130
+.. أسوأ حالة ممكنة أني أضل أختار كله males أو كله
+
+303
+00:21:37,130 --> 00:21:43,790
+females، أو أختارهم بهذا الشكل. بس maximum الاختيار
+
+304
+00:21:43,790 --> 00:21:48,910
+تبعي 15. الرقم 16، أكيد هيكون couple مع واحد من الـ
+
+305
+00:21:48,910 --> 00:21:51,530
+.. من الـ.. الـ.. الـ selected، أكيد هيتن couple مع
+
+306
+00:21:51,530 --> 00:21:53,950
+الـ selected. ففي الحالة دي، عشان فعلاً أضمن الـ
+
+307
+00:21:53,950 --> 00:21:57,270
+condition هذا، بدي أعمل اختيار لـ 16 persons، يكون
+
+308
+00:21:57,270 --> 00:22:04,150
+ضامن at least يوجد one couple، at least. Okay، كمان
+
+309
+00:22:04,150 --> 00:22:07,950
+مثال، لحظة. كلهم هندرجهم تحت نفس المنطقة
+
+310
+00:22:07,950 --> 00:22:11,170
+اللي أنتم شايفينه سهل لعندنا، لو ما بصفيش فيه مشكلة،
+
+311
+00:22:11,170 --> 00:22:17,310
+هنشوف كمان الـ grades نفسها. لو عندنا five grades
+
+312
+00:22:17,310 --> 00:22:23,610
+اللي هم A امتياز، B جيد جدًا، C جيد، و D pass أو
+
+313
+00:22:23,610 --> 00:22:30,390
+مقبول، وفي عندنا الـ F، ففي عندنا خمسة grades.
+
+314
+00:22:32,750 --> 00:22:36,670
+في عندنا خمسة grade. Okay، how many students do we
+
+315
+00:22:36,670 --> 00:22:41,190
+need to be sure at least six get the same grade?
+
+316
+00:22:41,190 --> 00:22:44,750
+عشان أضمن أنه في ستة طلاب أخذوا نفس الـ
+
+317
+00:22:44,750 --> 00:22:47,630
+grade، المفروض أنه جديش عدد الطلاب أصلاً عشان أقول
+
+318
+00:22:47,630 --> 00:22:52,590
+أن أنا ضامن تمامًا في ستة طلاب أخذوا نفس الـ grade.
+
+319
+00:22:52,590 --> 00:22:56,910
+ستة. طب، هاي الستة، هاه، هاي الطالب الأول إجه هنا، طالب
+
+320
+00:22:56,910 --> 00:22:58,730
+الثاني إجه هنا، طالب الثالث هنا، والرابع هنا، و
+
+321
+00:22:58,730 --> 00:23:01,370
+الخامس هنا. طب، هاي الـ grade ده في اثنين بس، ما فيش
+
+322
+00:23:01,370 --> 00:23:07,350
+فيه ستة. 37، طب
+
+323
+00:23:07,350 --> 00:23:12,030
+ناخذ أسوأ حالة ممكنة. أسوأ حالة ممكنة أن الطلاب، أنا
+
+324
+00:23:12,030 --> 00:23:15,990
+قاعد بوزع، قاعدين بيتوزعوا على grades، بيجوا كلهم تحت
+
+325
+00:23:15,990 --> 00:23:19,310
+نفس الـ grade الواحد، قاعدين بيتوزعوا معاهم، فهيجي هنا
+
+326
+00:23:19,310 --> 00:23:23,570
+واحد، اثنين، ثلاثة، واحد بهذا الشكل، لعند ما يصير لكل
+
+327
+00:23:23,570 --> 00:23:32,030
+grade فيه خمسة. كملنا؟ واحد، اثنين؟ ايوه، هاي وصلتوا
+
+328
+00:23:32,030 --> 00:23:37,730
+هاي وصلتوا للجواب. هذه الـ worst case، أنه والله
+
+329
+00:23:37,730 --> 00:23:40,910
+يتوزعوا معايا بهذا الشكل. أنا لعند ما أقدر أقول إن
+
+330
+00:23:40,910 --> 00:23:45,550
+لو عندي خمسة وعشرون طالب، أكيد هيكون فيه ستة نفس
+
+331
+00:23:45,550 --> 00:23:48,510
+الـ grade، لأ، بضمنهاش، مش دائمًا ممكن تصبح معايا، بس
+
+332
+00:23:48,510 --> 00:23:52,450
+عشان أكون sure من كلامي، معناته لازم يكون فيه كمان
+
+333
+00:23:52,450 --> 00:23:56,060
+ستة وعشرون طالب. لزيادة هذا بضمن ليه؟ معلومتي
+
+334
+00:23:56,060 --> 00:23:59,860
+باطمئنان، لأن هي أسوأ case ممكنة في التوزيع، أو خلاني
+
+335
+00:23:59,860 --> 00:24:06,880
+أقول إن الـ uniform هنا، الـ uniform. فالرقم 26 يأخذ
+
+336
+00:24:06,880 --> 00:24:10,130
+الـ grade اللي بدي إياه. بدي يجي هنا، بدي يجي هنا، بدي
+
+337
+00:24:10,130 --> 00:24:14,050
+يجي هنا، يجي هنا. معنى ذلك أن الـ grade C فيه 6
+
+338
+00:24:14,050 --> 00:24:17,850
+طلاب حصلوا على grade C. يجي هنا grade A فيه 6 طلاب
+
+339
+00:24:17,850 --> 00:24:21,490
+حصلوا على grade A. يجي هنا F فيه 6 طلاب حصلوا على F.
+
+340
+00:24:21,490 --> 00:24:26,510
+فرقم 26 هو الإجابة في الحالة هذه اللي احنا محتاجين
+
+341
+00:24:26,510 --> 00:24:30,070
+عدد طلاب مساوي له، عشان أضمن أنه في 6 طلاب اللي هم
+
+342
+00:24:30,070 --> 00:24:36,770
+نفس الـ grade. okay. فهي try to fill the boxes، بتجربوا
+
+343
+00:24:36,770 --> 00:24:41,630
+تعملوا، تملوا الـ boxes كاملة، كأنه الطلاب بيتوزعوا
+
+344
+00:24:41,630 --> 00:24:47,490
+uniformly، كأنها بتتوزع بالتساوي. okay، كمان مثال
+
+345
+00:24:47,490 --> 00:24:52,090
+مثال كتير كويس. Assume the telephone number is as
+
+346
+00:24:52,090 --> 00:25:01,200
+follows aaa و 5x. إيش الـ aaa و 5x هذه؟ الأرقام
+
+347
+00:25:01,200 --> 00:25:06,900
+التليفونات. ممكن يكون في عندنا خمسة أرقام، الخمسة
+
+348
+00:25:06,900 --> 00:25:11,360
+أرقام هدول خاصين بمين؟ بـ Central معين، أكمل Central
+
+349
+00:25:11,360 --> 00:25:14,960
+محتاج عشان أغطي خمسة وعشرين user، أي خمسة وعشرون
+
+350
+00:25:14,960 --> 00:25:19,930
+مليون user. هذه هي باختصار. طيب نشوف هي أصلاً بتكون من
+
+351
+00:25:19,930 --> 00:25:23,130
+إيش؟ الرقم بتكون من الخمسة هدول اللي بيقدر
+
+352
+00:25:23,130 --> 00:25:25,750
+يوفرلي إياها الـ Central الواحد، أو الـ area Central لـ
+
+353
+00:25:25,750 --> 00:25:29,950
+area واحدة. بيصير جديش عدد الـ code اللي محتاجها لكل
+
+354
+00:25:29,950 --> 00:25:33,810
+area، أو جديش عدد الـ area codes اللي محتاجينها؟ عدد
+
+355
+00:25:33,810 --> 00:25:39,190
+الـ area codes. معنى ذلك، كم أيه محتاج هنا؟ ثلاثة.
+
+356
+00:25:39,190 --> 00:25:43,460
+خمسة عشر. جديش الأرقام اللي أنا محتاجها عشان أقول
+
+357
+00:25:43,460 --> 00:25:45,820
+والله فعلاً الرقم كله على بعضه وهيك، رقم التليفون
+
+358
+00:25:45,820 --> 00:25:49,020
+كله على بعضه، وبيقدر يكفي لخمسة وعشرين مليون user.
+
+359
+00:25:49,020 --> 00:25:52,660
+خمسة وعشرون مليون مشترك، خمسة وعشرون مليون بني
+
+360
+00:25:52,660 --> 00:25:56,360
+آدم عايشين في المدينة، كل واحد من حقه يأخذ رقم
+
+361
+00:25:56,360 --> 00:25:59,100
+تليفون مختلف، أو different telephone number،
+
+362
+00:25:59,100 --> 00:26:02,900
+telephone number. أنتم عادة تعرفوا أن كلنا مثلاً
+
+363
+00:26:02,900 --> 00:26:07,450
+مشترك بـ 2 8، وبعدين ممكن تختلف. طب ما هذه الأرقام
+
+364
+00:26:07,450 --> 00:26:10,290
+هذه الـ area، هذه الـ area الكبيرة، ممكن ساعتها تلاقوا
+
+365
+00:26:10,290 --> 00:26:15,790
+فيه ستة، بأعرف أنه هذه آه، هذه منطقة كذا. لو سبعة، آه
+
+366
+00:26:15,790 --> 00:26:18,150
+هذه منطقة كذا. لو اثنين ثمانية ثمانية، آه ده الـ
+
+367
+00:26:18,150 --> 00:26:21,250
+Central الجديد ركبه، مش عارف، هذه معظمهم منطقة كذا.
+
+368
+00:26:21,250 --> 00:26:24,150
+صحيح، من الرقم ممكن نعرفه أن المنطقة. معناته أنا
+
+369
+00:26:24,150 --> 00:26:29,670
+بتكلم عن الـ area. طيب، كم Code أو كم digit محتاج للـ
+
+370
+00:26:29,670 --> 00:26:34,510
+area، عشان زي ما قلنا نوفر خمسة وعشرين مليون رقم
+
+371
+00:26:34,510 --> 00:26:38,290
+خمسة وعشرون مليون different number. okay، بنمسك
+
+372
+00:26:38,290 --> 00:26:40,570
+الخمسة وعشرين اللي أنا محتاجهم أصلاً، خمسة وعشرون
+
+373
+00:26:40,570 --> 00:26:46,810
+مليون. هدول عبارة عن إيش؟ بيساوي two to the power
+
+374
+00:26:46,810 --> 00:26:49,570
+of five، في ten to the power of seven.
+
+375
+00:26:52,090 --> 00:26:58,090
+صح؟ على أساس أنه 25 في 10⁶. لأ، هنا نأخذ كمان واحد
+
+376
+00:26:58,090 --> 00:27:01,550
+وتصير بهذا الشكل. احنا عارفين أن هدول خمسة، واحد،
+
+377
+00:27:01,550 --> 00:27:03,530
+اثنين، ثلاثة، أربعة، خمسة، كل Central بيعطيني
+
+378
+00:27:03,530 --> 00:27:08,830
+الـ hand خمسة. فهذه ten to the power of five. كم Central
+
+379
+00:27:08,830 --> 00:27:14,270
+محتاج؟ لو هنا زودنا.. كان hand الـ Central واحد بس،
+
+380
+00:27:14,270 --> 00:27:18,490
+هيعطيني فقط الـ ten to the power of five. عشرة to the
+
+381
+00:27:18,490 --> 00:27:25,100
+power of five. طب لو كانوا اثنين، two digits، بيصير زائد
+
+382
+00:27:25,100 --> 00:27:28,080
+..زائد واحد، زائد اثنين، زائد ثلاثة، لأن أنا بقعد
+
+383
+00:27:28,080 --> 00:27:34,240
+بزود عدد digits. لو حطينا واحدة، صار عدد الـ total
+
+384
+00:27:34,240 --> 00:27:38,540
+تبعي بدل خمسة صار ستة. صار في ممكنية أحط هنا كمان
+
+385
+00:27:38,540 --> 00:27:44,150
+واحد. طب لو حطينا اثنين، بيصير اثنين كمان، ثلاثة، على
+
+386
+00:27:44,150 --> 00:27:48,810
+اعتبار أنه، تخيلوا هاي الأرقام بتاعتكم، كل رقم بياخذ
+
+387
+00:27:48,810 --> 00:27:52,550
+من صفر إلى تسعة، فإذا ممكن يكون له عشرة، الرقم اللي
+
+388
+00:27:52,550 --> 00:27:55,890
+جنبه برضه من صفر إلى تسعة، فإذا عشرة، الاثنين مع بعض
+
+389
+00:27:55,890 --> 00:27:59,150
+عشرة في عشرة. طيب واحد، اثنين
+
+445
+00:32:00,590 --> 00:32:05,490
+نعمل نفس الكلام بس لأ في الشهر على تلاتين .. على
+
+446
+00:32:05,490 --> 00:32:08,810
+إثنا عشر على إثنا عشر على إثنا عشر، مئتين وثمانين على إثنا عشر
+
+447
+00:32:08,810 --> 00:32:12,470
+مئتين وثمانين على إثنا عشر، وبنعمل ceiling
+
+448
+00:32:12,470 --> 00:32:17,710
+على اليوم مش هيبقى صفر، على اليوم بتطلع واحد، أما
+
+449
+00:32:17,710 --> 00:32:18,290
+احنا ceiling
+
+450
+00:32:21,180 --> 00:32:26,860
+أقول لك لو كان عندي طالب واحد، هيطلع واحد لأنه at
+
+451
+00:32:26,860 --> 00:32:30,360
+least أنه آه والله، إله عيد ميلاد ما هو موجود مدى
+
+452
+00:32:30,360 --> 00:32:34,000
+ما في طالب ما هو موجود، صار موجود، يعني بتقول لي والله
+
+453
+00:32:34,000 --> 00:32:41,700
+مئتين وثمانين على الثلاثمية خمسة وستين، okay أقل
+
+454
+00:32:41,700 --> 00:32:47,060
+من واحد، معك أقل من واحد، أقول لك: ه طالب واحد عندي
+
+455
+00:32:49,070 --> 00:32:53,970
+أقول لك: في 82 عندي طالب واحد على 360، بتطلع جد ما
+
+456
+00:32:53,970 --> 00:33:00,910
+بتطلع على الألف، إيش بتطلع؟ 0.001، ceiling واحد يعني
+
+457
+00:33:00,910 --> 00:33:03,790
+معنى ذلك أن في يوم على الأقل يوجد فيه عيد ميلاد
+
+458
+00:33:03,790 --> 00:33:07,190
+واحد، هو نفسه اللي هو عيد ميلاد، هو نفسه، فلأ هذه
+
+459
+00:33:07,190 --> 00:33:13,650
+موجودة، هذه هتكون طبعاً هنا قيمة، okay، الـ permutation
+
+460
+00:33:13,650 --> 00:33:16,970
+والـ combination، بدنا نحاول نفهمهم على الأقل، ون
+
+461
+00:33:16,970 --> 00:33:20,370
+.. طبعاً إحنا كملناهم مع الشعب الثاني، كملنا الـ ..
+
+462
+00:33:20,370 --> 00:33:25,630
+الاثنين، نفهمهم أجل ما فيها الـ .. إيش permutation و
+
+463
+00:33:25,630 --> 00:33:28,190
+إيش الـ combination؟ الـ permutation والـ combination
+
+464
+00:33:28,190 --> 00:33:31,150
+هي طريقة اختيار، أو عدد الـ ways اللي بقدر أختار
+
+465
+00:33:31,150 --> 00:33:36,690
+فيها، بقدر أختار فيها مجموعة objects من set تحتوي
+
+466
+00:33:36,690 --> 00:33:40,590
+على objects، من set تحتوي على objects، زي لما نقول
+
+467
+00:33:40,590 --> 00:33:43,970
+والله بدنا نختار منكم ثلاث طالبات لمسابقة ثقافية
+
+468
+00:33:43,970 --> 00:33:47,850
+فرضاً في مسابقة ثقافية، بدنا نختار منكم ثلاث، الثلاث
+
+469
+00:33:47,850 --> 00:33:52,200
+دولة، كم طريقة بقدر أختار فيها الثلاث؟ عشان أختارهم
+
+470
+00:33:52,200 --> 00:33:55,740
+بدي أعرف أصلاً جدش العين اللي موجودة، صحيح؟ فبنعرف
+
+471
+00:33:55,740 --> 00:34:00,460
+جدش عدد فضاء العين، أو الـ cardinality للـ S نفسها
+
+472
+00:34:00,460 --> 00:34:04,600
+للـ S نفسها، جدش العدد؟ لأنه منها بدي أختار، إذا كان
+
+473
+00:34:04,600 --> 00:34:08,640
+والله بدي أختار ثلاثة، طب هم كلهم ثلاثة، فكان طريقة
+
+474
+00:34:08,640 --> 00:34:11,020
+بقدر أختار فيها هي واحدة، هم إن هم ثلاثة، هي هم
+
+475
+00:34:11,020 --> 00:34:15,060
+ثلاثة، خلصنا، لو كان أربعة معناته بنعمل combination
+
+476
+00:34:16,660 --> 00:34:20,060
+يكون الأول والثاني والثالث، أو الأول والثاني
+
+477
+00:34:20,060 --> 00:34:26,240
+والرابع، أو الأول والثالث والرابع، الأول والثاني
+
+478
+00:34:26,240 --> 00:34:29,140
+والرابع، يعني تعملوا combine، تبدأ تعملوا إيش
+
+479
+00:34:29,140 --> 00:34:31,500
+الاختيارات الممكنة، تجد إيش العدد؟ العدد الطرق اللي
+
+480
+00:34:31,500 --> 00:34:37,020
+ممكن نختار فيها، هذه الطريقة، أو هذا الشيء، هذه مفهوم
+
+481
+00:34:37,020 --> 00:34:40,120
+طيب، ممكن يكون مفهوم ثاني، أقول لكم: لأ، بدنا نختار
+
+482
+00:34:40,120 --> 00:34:45,960
+ثلاث، بس أول واحدة هأختارها هتكون هي قائدة اللجنة
+
+483
+00:34:45,960 --> 00:34:50,380
+هي رئيسة اللجنة، الثانية بدها تكون أمين سر اللجنة
+
+484
+00:34:50,380 --> 00:34:55,200
+الثالثة بدها تكون عضو اللجنة، آه، معناته هنا الـ order
+
+485
+00:34:55,200 --> 00:35:01,620
+بيختلف، سر، بمعنى لو اخترنا الأنصار الأول، بدنا نخففها
+
+486
+00:35:01,620 --> 00:35:05,780
+شوية، لو افترض أن أنا عندي أربعة، بس أختار الأول
+
+487
+00:35:05,780 --> 00:35:11,860
+والثاني والثالث، لحظة، ممكن أرجع أختار الثالث
+
+488
+00:35:11,860 --> 00:35:16,140
+والثاني والأول، يكون هذا هو الـ first، وهذا الـ
+
+489
+00:35:16,140 --> 00:35:20,340
+second، وهذا الـ third، أو ممكن يكون هذا الـ first، و
+
+490
+00:35:20,340 --> 00:35:28,650
+هذا الـ third مثلاً، وهذا الـ second، أو عدد الاحتمالات
+
+491
+00:35:28,650 --> 00:35:33,150
+أكبر، لماذا؟ لأنه مهم الترتيب هنا، أما لا والله
+
+492
+00:35:33,150 --> 00:35:36,330
+اللجنة، كلهم قعدوا في اللجنة وخلاص، بيصير كل الحالة
+
+493
+00:35:36,330 --> 00:35:40,530
+دي حالة واحدة، هي طريقة واحدة، خلاص الثلاث وبس، لكن
+
+494
+00:35:40,530 --> 00:35:44,510
+لما أقول: لأ، في order، بمعنى أنه هتفرق الاختيار
+
+495
+00:35:44,510 --> 00:35:48,750
+الأول عن الثاني عن الثالث، بيصير لها طريقة التعامل
+
+496
+00:35:48,750 --> 00:35:53,360
+مختلفة تماماً في الـ permutation، في عملية الـ
+
+497
+00:35:53,360 --> 00:35:58,940
+permutation، خلينا نقول إن إحنا برضه بنختار من 6، S
+
+498
+00:35:58,940 --> 00:36:04,980
+of objects، بنختار عدد معين، حسب إيش اللي ما جدش
+
+499
+00:36:04,980 --> 00:36:09,400
+قيمة العدد المطلوب، ولكن exactly once، بنختاره مرة
+
+500
+00:36:09,400 --> 00:36:13,540
+واحدة، يعني ما فيش repetition، ما فيش replacement
+
+501
+00:36:14,340 --> 00:36:17,560
+ما فيش إن هو بختار الشيء، وبعد ما يختاره برجع
+
+502
+00:36:17,560 --> 00:36:21,520
+بأعيدها ثاني في القرعة ثاني، الجرعة، بس أختار منها
+
+503
+00:36:21,520 --> 00:36:26,160
+خلاص، اللي تم اختياره بيطلع برة الجرعة، بأختار لون
+
+504
+00:36:26,160 --> 00:36:28,480
+ثاني، يعني ما فيش إمكانية مثلاً يقول: والله بدي أختار
+
+505
+00:36:28,480 --> 00:36:32,860
+من الألوان الأربعة دول، طب آه عشوائياً يلا أختارنا،
+
+506
+00:36:32,860 --> 00:36:36,780
+آه اللون الأحمر، أول اختيار كان لون الأحمر، في
+
+507
+00:36:36,780 --> 00:36:41,180
+إمكانية لو جيت أما أرجعه وأخبطه وأختار كمان مرة
+
+508
+00:36:41,180 --> 00:36:45,860
+يمكن يطلع، يمكن يطلع كمان مرة، أو أنه لأ، without
+
+509
+00:36:45,860 --> 00:36:50,180
+replacement، اخترته وأطلعه، أختار من غيره، ففي
+
+510
+00:36:50,180 --> 00:36:52,740
+طريقتين في الاختيار، ديروا بالكم، في طريقتين في
+
+511
+00:36:52,740 --> 00:36:56,120
+الاختيار، خلينا نأجلها شوية، طريقتين في الاختيار
+
+512
+00:36:56,120 --> 00:37:00,260
+هدول مهمين جداً، يعني لما يطلبكم في الـ urn model
+
+513
+00:37:00,260 --> 00:37:04,900
+مثلاً الـ urn model، أو نموذج الجرة، واللي دائماً أنتم
+
+514
+00:37:04,900 --> 00:37:07,740
+بتسمعوه في الـ probability، بتقول: والله جرة وفيها
+
+515
+00:37:07,740 --> 00:37:11,300
+مجموعة كرات، إيش احتمال نحط يد نطلع كرة صفراء؟ طب
+
+516
+00:37:11,300 --> 00:37:14,980
+هو أصلاً إيش اللي موجود؟ جالك عشر كرات حمراء، وعشر كرات
+
+517
+00:37:14,980 --> 00:37:18,500
+صفراء، وعشر كرات زرقاء، طب هأحط إيد، كل خبطة؟ يطلع إيش
+
+518
+00:37:18,500 --> 00:37:22,040
+احتمال يطلع كذا؟ خلينا نشتغل على الموديل هذا، يمكن
+
+519
+00:37:22,040 --> 00:37:25,320
+يوضح لنا أمورنا هالوقت، طيب لما أقول: من مجموعة n
+
+520
+00:37:25,320 --> 00:37:29,940
+objects موجودين داخل الـ urn، هدول بدنا نختار منهم R
+
+521
+00:37:29,940 --> 00:37:35,600
+objects، طبعاً R لازم تكون أقل، maximum تساوي N، لأنه
+
+522
+00:37:35,600 --> 00:37:38,240
+لما أقول: والله إذا كان العدد خمسة، بدي أختار ستة
+
+523
+00:37:38,240 --> 00:37:42,280
+ما فيش فيها احتمالات هذه، ولا فيها طرق selection
+
+524
+00:37:42,280 --> 00:37:46,880
+خلاص، كلهم بدي إياهم وخلصنا، لأنه اختيار واحد هنا من
+
+525
+00:37:46,880 --> 00:37:50,860
+خمسة، بدي ستة، خلاص كلهم مرة واحدة، ما فيش لا
+
+526
+00:37:50,860 --> 00:37:56,470
+permutation ولا تبديل ولا combination، توافق، أنتم
+
+527
+00:37:56,470 --> 00:37:59,550
+أخذتوها تبديل وتوافق صحيح؟ ليها permutation and
+
+528
+00:37:59,550 --> 00:38:04,850
+combination، هل وقت عملية الاختيار، أو الـ topic to
+
+529
+00:38:04,850 --> 00:38:09,290
+select، يعني اقتناء أو انتقاء أو selection، اختيار
+
+530
+00:38:09,290 --> 00:38:14,130
+بدنا نسأل حالنا: هل اختيارها ده لازم يكون with
+
+531
+00:38:14,130 --> 00:38:17,430
+replacement، زي ما قلنا، ممكن أختار الشيء وبعدين
+
+532
+00:38:17,430 --> 00:38:20,790
+أرجعه ثاني، مرتين على الجرعة الجاية، ولا without
+
+533
+00:38:20,790 --> 00:38:24,810
+replacement، with replacement، هنسيبكم إياها تأخذوها
+
+534
+00:38:24,810 --> 00:38:28,170
+لاحقاً إن شاء الله، في مصدق الـ probability هتشتغلوا
+
+535
+00:38:28,170 --> 00:38:31,510
+في الـ probability، تعملوا replacement، ما عرفش فينا
+
+536
+00:38:31,510 --> 00:38:34,430
+تقولوا، اخذوها، تأخذوا الـ probability، إحنا هنشتغل
+
+537
+00:38:34,430 --> 00:38:38,050
+على without replacement، هنشتغل على without
+
+538
+00:38:38,050 --> 00:38:41,690
+replacement، without replacement، برضه بيضل فيه سؤال
+
+539
+00:38:41,690 --> 00:38:44,230
+فبيفهمنا إن أنت هتشتغل without replacement، اللي
+
+540
+00:38:44,230 --> 00:38:48,830
+هتختاره خلاص، طلع، طيب هل الـ order مهم ولا غير مهم؟
+
+541
+00:38:49,640 --> 00:38:53,780
+إذا والله مهم الـ order، صار اسمها تباديل، لأنه بيفرق
+
+542
+00:38:53,780 --> 00:38:56,640
+أنا اخترت .. okay، الشخص اخترته في جميع الأحوال
+
+543
+00:38:56,640 --> 00:38:59,680
+اخترته، ولكن أنا اخترته أول واحد ولا ثاني واحد ولا
+
+544
+00:38:59,680 --> 00:39:04,060
+ثالث واحد، بيفرق، فهنا إذا كان والله without
+
+545
+00:39:04,060 --> 00:39:10,600
+replacement، تمام، ordered list، معنى ذلك بنسميه هذه
+
+546
+00:39:10,600 --> 00:39:14,080
+permutation، تباديل، إذا والله لأ، أنا ordered مش
+
+547
+00:39:14,080 --> 00:39:19,430
+هتفرق، بنسميها combination، توافق، توافق، وهذه لها
+
+548
+00:39:19,430 --> 00:39:22,090
+examples، وهذه لها examples، هذه فيها أمثلة، وهذه
+
+549
+00:39:22,090 --> 00:39:28,590
+لها أمثلة، الـ permutation اللي عملنا جنب قانونها،
+
+550
+00:39:28,590 --> 00:39:33,850
+قانونها ببساطة أنه بدي أختار R من M، R هذه لازم تكون
+
+551
+00:39:33,850 --> 00:39:37,210
+أقل من أو تساوي maximum، طبعاً بدنا نأخذ بالنا
+
+552
+00:39:37,210 --> 00:39:40,690
+arrangement using R arrangement، معناته مرتبة، بدها
+
+553
+00:39:40,690 --> 00:39:44,730
+يكون فيها ترتيب، بمعنى إن الـ order مهم، الـ order مهم
+
+554
+00:39:44,730 --> 00:39:48,070
+ممكن أنا أختار نفس الشخص، ولكن بيفرق أنا اخترته
+
+555
+00:39:48,070 --> 00:39:50,930
+واحد، ولا يعني في أول اختيار، ولا اخترته في ثاني
+
+556
+00:39:50,930 --> 00:39:53,670
+اختيار، بتفرق تماماً زي لما نقول: والله بدنا نختار
+
+557
+00:39:53,670 --> 00:39:56,710
+أول واحد هأختاره هيكون هو رئيس اللجنة، الثاني هأختاره
+
+558
+00:39:56,710 --> 00:39:59,770
+هيكون أمين سر اللجنة، الثالث اللي هأختاره هيكون عضو في
+
+559
+00:39:59,770 --> 00:40:04,270
+اللجنة، لو اختلفوا هم نفس الثلاث، صار فيهم تبديل
+
+560
+00:40:04,270 --> 00:40:07,610
+كمان، ممكن يبدلوا مع بعض المناصب اللي أخذوها، هذه
+
+561
+00:40:07,610 --> 00:40:10,830
+بناءً على مين تم اختياره في الأول، فالترتيب هنا هيكون
+
+562
+00:40:10,830 --> 00:40:13,890
+مهم، القانون تبعنا عشان نشتغل على number of
+
+563
+00:40:13,890 --> 00:40:18,650
+different r permutation of a set of n distinct
+
+564
+00:40:18,650 --> 00:40:24,290
+elements is denoted by permutation of n وr
+
+565
+00:40:25,160 --> 00:40:33,260
+Permutation من N أختار R، هذه هتساوي N في N-1 في N
+
+566
+00:40:33,260 --> 00:40:39,900
+-2، لحد ما نصل to N-R plus 1، بمعنى أن عدد الـ terms
+
+567
+00:40:39,900 --> 00:40:46,820
+يطلع قيمته بيساوي R، 1، 2، 3، 4، 5، R، خلاص نضربهم في بعض
+
+568
+00:40:46,820 --> 00:40:51,200
+تنازلياً من N للأرقام اللي أقل، مجدداً، عدد الـ terms R
+
+569
+00:40:51,200 --> 00:40:56,530
+هذه ممكن نعملها بشكل مضروب الـ n، أو n factorial على
+
+570
+00:40:56,530 --> 00:41:01,030
+n minus r factorial، على n minus r factorial، على n
+
+571
+00:41:01,030 --> 00:41:11,190
+minus r factorial، okay، ماتش
+
+572
+00:41:11,190 --> 00:41:16,380
+المثال اللي كان وراه، طيب نأخذ المثال هذا ونخلي
+
+573
+00:41:16,380 --> 00:41:20,480
+باقي الأمثلة للمرة الجاية، عشان بس يعني يكون في
+
+574
+00:41:20,480 --> 00:41:23,880
+مثال، أجل ما فيها مثال واحد، طبعاً في كذا مثال جايين
+
+575
+00:41:23,880 --> 00:41:27,900
+لسه، خلينا نفترض أن في عندنا .. سريع هيك .. أن في
+
+576
+00:41:27,900 --> 00:41:32,320
+عندنا bomb مزروعة في your city، في قنبلة تم زراعتها
+
+577
+00:41:32,320 --> 00:41:37,320
+في المدينة عندكم، و your task أو your job is to
+
+578
+00:41:37,320 --> 00:41:44,220
+disable it، مطلوب إنكم .. ت .. ت .. ت .. تحطوا
+
+579
+00:41:44,220 --> 00:41:47,720
+التجربة، أو توقفوا انفجارها، توقفوا انفجارها، كيف؟
+
+580
+00:41:47,720 --> 00:41:51,580
+by cutting wires of the trigger device، بتكون تشوف
+
+581
+00:41:51,580 --> 00:41:53,840
+وين الـ trigger device تبعها، أنتم تبعون كهربا وأنا
+
+582
+00:41:53,840 --> 00:41:58,620
+كل يوم دوائر، بتكون تشوف وين الـ trigger device
+
+583
+00:41:58,620 --> 00:42:02,160
+بتاعتها عشان تقطع أسلاكها، تقطع وين الأسلاك اللي
+
+584
+00:42:02,160 --> 00:42:05,520
+رايحة الـ trigger، بتلاقيهم، بدنا نقطعهم، إذا جئتم
+
+585
+00:42:05,520 --> 00:42:08,760
+تطلعتوا، إذا جئتم إن الـ trigger رايح على box، الـ box
+
+586
+00:42:08,760 --> 00:42:13,020
+هذه بتطلع عشر wires، إذا جئتم، إذا جئتم إن الـ
+
+587
+00:42:13,020 --> 00:42:16,100
+trigger طبعاً رايح على box، الـ box هذه فيها عشر wires
+
+588
+00:42:16,100 --> 00:42:20,980
+العشر wires هدول، مطلوب منكم تقطع منهم ثلاثة to
+
+589
+00:42:20,980 --> 00:42:27,800
+disable it، أو ترتيبهم، لو واحدة سيليك انقطع، جبل
+
+590
+00:42:27,800 --> 00:42:32,680
+الثانية برضه هتنجح، برضه هتنجح، فإذا إحنا مهتمين،
+
+591
+00:42:32,680 --> 00:42:38,380
+بدنا نعمل cutting لـ three right wires، and three
+
+592
+00:42:38,380 --> 00:42:45,600
+orders، right order، لهم، okay، otherwise it will
+
+593
+00:42:45,600 --> 00:42:50,860
+explode، هتنفجر، otherwise هتنفجر، طيب if the wire all
+
+594
+00:42:50,860 --> 00:42:54,380
+look the same، إذا كل الـ wires عندكم كلهم لونهم أسود
+
+595
+00:42:54,380 --> 00:42:56,820
+يعني مش زي ما بتشوفوا في الأفلام، لون أحمر، لون أسود، لون
+
+596
+00:42:56,820 --> 00:42:59,920
+أزرق، ومش عارف إيش، يعطيكم hint أو شيء، كلهم نفس
+
+597
+00:42:59,920 --> 00:43:05,620
+اللون، متشابهات تماماً، ما فيش أي شيء، كلهم رايحين على
+
+598
+00:43:05,620 --> 00:43:08,740
+حاجة هيك عاملة زي الـ chip، box، مش معروف مين الـ input
+
+599
+00:43:08,740 --> 00:43:12,080
+ومين الـ output تبعها، فما فيش أي شيء يميز أي select
+
+600
+00:43:12,080 --> 00:43:17,640
+فيهم، طيب what are your chances of survival؟ جدش
+
+601
+00:43:17,640 --> 00:43:20,520
+فرصة نجاحكم في المهمة؟ جدش فرصة نجاتكم في
+
+602
+00:43:20,520 --> 00:43:24,400
+المهمة؟ جدش، شوي شوي، هالوجهة أنتم ببساطة
+
+603
+00:43:24,400 --> 00:43:28,920
+بتختاروا جدش؟ ثلاثة من أصل عشرة، يعني أنتم
+
+604
+00:43:28,920 --> 00:43:31,840
+بتتكلموا عن، طبعاً الترتيب مهم، لأن لو بدون ترتيب
+
+605
+00:43:31,840 --> 00:43:35,920
+بنسميها combination، بنسميها توفيق، لأ، هنا بنتكلم عن
+
+606
+00:43:35,920 --> 00:43:38,980
+تباديل، تباديل، معناه تتكلم عن permutation، عشرة
+
+607
+00:43:38,980 --> 00:43:44,540
+ثلاثة، خلاص، هذه تساوي N factorial، زي ما قلنا N
+
+608
+00:43:44,540 --> 00:43:49,000
+minus R factorial، يعني أنتم بتتكلموا عن جدش عشرة
+
+609
+00:43:49,000 --> 00:43:55,260
+factorial على سبعة، خلاصنا، خلاص، أو مدام عددهم
+
+610
+00:43:55,260 --> 00:44:00,020
+قليل هنا، بتقدروا تقولوا: عشرة في تسعة في ثمانية، هذا
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/79nrEVc1ARE_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/79nrEVc1ARE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..42f54b1145cfb06dfb056a8641ef5f03e8f82a49
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/79nrEVc1ARE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4280, "start": 21.28, "end": 42.8, "text": "بسم الله الرحمن الرحيم الصلاة والسلام علي أشرف الأنبياء ومرسلين سيدنا محمد وعلى آله وصحبه أجمعين نبدأ اليوم نكمل الجزئية ال examples اللي كنا بنتكلم فيها عن ال counting كان في ضايلة أكام من example عشان نبدأ في الموضوع الجديد ان شاء الله تعالى بنحاول نكملهم في ال .. هلوجة عشان نبدأ نخلص الموضوع اللي براهم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 16070, 3794, 37440, 25894, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 4032, 2304, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 8717, 44510, 10721, 45595, 20498, 8717, 24793, 1211, 25724, 11622, 19986, 10632, 2423, 5110, 13672, 1829, 9122, 8315, 4724, 29399, 4117, 19528, 8978, 11296, 18871, 2423, 13251, 25961, 8978, 48812, 995, 26895, 3660, 5551, 4117, 10943, 9154, 1365, 6225, 8592, 7649, 8717, 44510, 10721, 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تكرروا في الحالتين في الحالتين في الحالتين فانا مضطر اطرحهم مرة لان جمعتهم مرتين فابدأ اطرحهم مرة عشان يكونوا جامعوا بس مرة واحدة فقط فهنا صار", "tokens": [3615, 8592, 25720, 30767, 16373, 3215, 6225, 8592, 25720, 4032, 2423, 2535, 16712, 7649, 1829, 36632, 11242, 995, 4724, 43042, 3224, 14293, 293, 27006, 16073, 4724, 43042, 3224, 1975, 15042, 6225, 8592, 25720, 1975, 2407, 6225, 8592, 25720, 6156, 9381, 9640, 8978, 6225, 8315, 6225, 46309, 9957, 8978, 6225, 46309, 9957, 8032, 3215, 12610, 3660, 6055, 37983, 2288, 14407, 34105, 6055, 37983, 2288, 14407, 34105, 6055, 37983, 2288, 14407, 8978, 21542, 6027, 2655, 9957, 8978, 21542, 6027, 2655, 9957, 8978, 21542, 6027, 2655, 9957, 6156, 7649, 995, 3714, 11242, 9566, 2288, 1975, 9566, 2288, 5016, 16095, 3714, 25720, 5296, 7649, 10874, 2304, 34268, 16095, 3714, 43500, 9957, 6156, 16758, 3215, 10721, 1975, 9566, 2288, 5016, 16095, 3714, 25720, 6225, 8592, 7649, 7251, 30544, 14407, 10874, 10943, 3615, 14407, 4724, 3794, 3714, 25720, 36764, 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عندنا okay", "tokens": [3794, 6027, 3555, 34051, 3175, 6225, 46309, 9957, 8978, 6225, 46309, 9957, 5551, 9381, 49628, 5296, 8315, 39627, 15730, 25124, 28820, 21542, 1211, 6055, 3794, 25957, 16373, 3660, 4032, 6225, 46309, 9957, 30767, 16373, 3215, 6055, 3794, 25957, 16373, 3660, 4032, 6225, 46309, 9957, 8717, 995, 4587, 9381, 5551, 25513, 25957, 10632, 4724, 40228, 9566, 1829, 8315, 5551, 46538, 4032, 5551, 25513, 25957, 10632, 4032, 5551, 25513, 3615, 9957, 5551, 46538, 4032, 5551, 25513, 25957, 10632, 4032, 5551, 25513, 3615, 9957, 11524, 34051, 819, 33149, 3714, 43020, 3660, 8978, 21542, 6027, 3660, 13672, 1829, 43242, 8315, 8978, 21542, 6027, 3660, 13672, 1829, 43242, 8315, 1392], "avg_logprob": -0.1941332551387121, "compression_ratio": 2.1315789473684212, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 374.2, "end": 374.76, "word": "سالب", "probability": 0.6326090494791666}, {"start": 374.76, "end": 374.88, "word": " أو", "probability": 0.38427734375}, {"start": 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"probability": 0.57720947265625}, {"start": 392.04, "end": 392.14, "word": " و", "probability": 0.99267578125}, {"start": 392.14, "end": 392.48, "word": " أربعمية", "probability": 0.940185546875}, {"start": 392.48, "end": 392.58, "word": " و", "probability": 0.98046875}, {"start": 392.58, "end": 392.94, "word": " أربعين", "probability": 0.962890625}, {"start": 392.94, "end": 393.82, "word": " password", "probability": 0.67236328125}, {"start": 393.82, "end": 394.06, "word": " أو", "probability": 0.583984375}, {"start": 394.06, "end": 394.4, "word": " different", "probability": 0.85595703125}, {"start": 394.4, "end": 395.02, "word": " passwords", "probability": 0.79052734375}, {"start": 395.02, "end": 395.82, "word": " ممكنة", "probability": 0.9736328125}, {"start": 395.82, "end": 396.28, "word": " في", "probability": 0.943359375}, {"start": 396.28, "end": 396.66, "word": " الحالة", "probability": 0.97119140625}, {"start": 396.66, "end": 396.92, "word": " اللي", "probability": 0.9189453125}, {"start": 396.92, "end": 397.26, "word": " عندنا", "probability": 0.693115234375}, {"start": 397.26, "end": 397.42, "word": " في", "probability": 0.5048828125}, {"start": 397.42, "end": 397.72, "word": " الحالة", "probability": 0.9851888020833334}, {"start": 397.72, "end": 397.84, "word": " اللي", "probability": 0.990966796875}, {"start": 397.84, "end": 398.22, "word": " عندنا", "probability": 0.957275390625}, {"start": 398.22, "end": 398.6, "word": " okay", "probability": 0.72216796875}], "temperature": 1.0}, {"id": 17, "seek": 42766, "start": 399.7, "end": 427.66, "text": "more examples لو بدنا ان نجيب find the number of three letter initials where none of letters are repeated إذا كان بدنا نجيب مجموعة الحروف الأولى .. مجموعة الحروف الأولى أو ال abbreviations .. abbreviations لthree letters as initials ممكن نقول مجموعة abbreviations متكونة من three letters a,b,c بهذا الشكل", "tokens": [3138, 5110, 45164, 47525, 8315, 16472, 8717, 7435, 1829, 3555, 915, 264, 1230, 295, 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409.1, "word": " are", "probability": 0.96337890625}, {"start": 409.1, "end": 409.56, "word": " repeated", "probability": 0.47314453125}, {"start": 409.56, "end": 410.16, "word": " إذا", "probability": 0.623779296875}, {"start": 410.16, "end": 410.32, "word": " كان", "probability": 0.97802734375}, {"start": 410.32, "end": 410.6, "word": " بدنا", "probability": 0.940673828125}, {"start": 410.6, "end": 411.06, "word": " نجيب", "probability": 0.997314453125}, {"start": 411.06, "end": 411.9, "word": " مجموعة", "probability": 0.9357421875}, {"start": 411.9, "end": 412.64, "word": " الحروف", "probability": 0.96630859375}, {"start": 412.64, "end": 413.94, "word": " الأولى", "probability": 0.97021484375}, {"start": 413.94, "end": 414.36, "word": " ..", "probability": 0.267333984375}, {"start": 414.36, "end": 414.78, "word": " مجموعة", "probability": 0.89228515625}, {"start": 414.78, "end": 415.12, "word": " الحروف", "probability": 0.9737955729166666}, {"start": 415.12, "end": 415.44, "word": " الأولى", "probability": 0.9928385416666666}, {"start": 415.44, "end": 415.62, "word": " أو", "probability": 0.7529296875}, {"start": 415.62, "end": 416.14, "word": " ال", "probability": 0.94921875}, {"start": 416.14, "end": 416.98, "word": " abbreviations", "probability": 0.782470703125}, {"start": 416.98, "end": 417.32, "word": " ..", "probability": 0.7998046875}, {"start": 417.32, "end": 418.0, "word": " abbreviations", "probability": 0.966552734375}, {"start": 418.0, "end": 418.64, "word": " لthree", "probability": 0.728759765625}, {"start": 418.64, "end": 419.46, "word": " letters", "probability": 0.84912109375}, {"start": 419.46, "end": 419.9, "word": " as", "probability": 0.97314453125}, {"start": 419.9, "end": 420.9, "word": " initials", "probability": 0.768310546875}, {"start": 420.9, "end": 421.18, "word": " ممكن", "probability": 0.969970703125}, {"start": 421.18, "end": 421.5, "word": " نقول", "probability": 0.981201171875}, {"start": 421.5, "end": 422.38, "word": " مجموعة", "probability": 0.97109375}, {"start": 422.38, "end": 422.98, "word": " abbreviations", "probability": 0.952392578125}, {"start": 422.98, "end": 423.48, "word": " متكونة", "probability": 0.9694010416666666}, {"start": 423.48, "end": 423.6, "word": " من", "probability": 0.998046875}, {"start": 423.6, "end": 424.02, "word": " three", "probability": 0.78076171875}, {"start": 424.02, "end": 424.78, "word": " letters", "probability": 0.83447265625}, {"start": 424.78, "end": 426.52, "word": " a", "probability": 0.5546875}, {"start": 426.52, "end": 426.72, "word": ",b", "probability": 0.685791015625}, {"start": 426.72, "end": 426.94, "word": ",c", "probability": 0.981689453125}, {"start": 426.94, "end": 427.3, "word": " بهذا", "probability": 0.873046875}, {"start": 427.3, "end": 427.66, "word": " الشكل", "probability": 0.995849609375}], "temperature": 1.0}, {"id": 18, "seek": 45412, "start": 428.44, "end": 454.12, "text": "بهذا الشكل أكم abbreviations أو أكم abbreviations ممكن أكون من ال three letters بشرط أنه ماتتكررش ال letters إذا كان في ال a أصبحت في ال position الأول لا يمكن قبولها في ال position التاني أو ال position التالق فهنا ممنوع التكرار لل letters ساعتنا فجدتش في إمكانية لعدد", "tokens": [3555, 3224, 15730, 25124, 28820, 5551, 24793, 35839, 763, 34051, 5551, 24793, 35839, 763, 3714, 43020, 5551, 30544, 9154, 2423, 1045, 7825, 4724, 46309, 9566, 14739, 3224, 3714, 9307, 2655, 37983, 2288, 8592, 2423, 7825, 11933, 15730, 25961, 8978, 2423, 257, 5551, 9381, 3555, 33753, 8978, 2423, 2535, 16247, 12610, 20193, 7251, 43020, 12174, 3555, 12610, 11296, 8978, 2423, 2535, 16712, 7649, 1829, 34051, 2423, 2535, 16712, 6027, 4587, 6156, 3224, 8315, 3714, 27842, 45367, 16712, 37983, 9640, 24976, 7825, 8608, 995, 34268, 8315, 6156, 7435, 3215, 2655, 8592, 8978, 11933, 2304, 41361, 10632, 5296, 22488, 3215], "avg_logprob": -0.15465561224489796, "compression_ratio": 1.9389671361502347, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 428.44, "end": 428.98, "word": 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"start": 455.3, "end": 477.84, "text": "initials في الحالة لأن او عدد abbreviations في الحالة مختصرات في الحالة هذه طبعا بالنسبة لل location الأول هو هختار من واحد من ستة و عشرين letter K في الحالة التانية ممنوع التكرار ممنوع التكرار معناه ذلك ان في عندى ستة و عشرين بس انا هنا في character اخترته في letter اخترتها فصار اختياري من خمسة و عشرين التالتة", "tokens": [259, 270, 12356, 8978, 21542, 6027, 3660, 5296, 33456, 1975, 2407, 6225, 3215, 3215, 35839, 763, 8978, 21542, 6027, 3660, 3714, 46456, 9381, 2288, 9307, 8978, 21542, 6027, 3660, 29538, 23032, 3555, 3615, 995, 20666, 1863, 35457, 3660, 24976, 4914, 16247, 12610, 31439, 8032, 46456, 9640, 9154, 36764, 24401, 9154, 8608, 2655, 3660, 4032, 6225, 46309, 9957, 5063, 591, 8978, 21542, 6027, 3660, 16712, 7649, 10632, 3714, 27842, 45367, 16712, 37983, 9640, 3714, 27842, 45367, 16712, 37983, 9640, 20449, 8315, 3224, 29910, 23275, 16472, 8978, 43242, 7578, 8608, 2655, 3660, 4032, 6225, 46309, 9957, 4724, 3794, 1975, 8315, 34105, 8978, 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47283, 3215, 2423, 7204, 13672, 1829, 47525, 22653, 995], "avg_logprob": -0.36534091992811724, "compression_ratio": 1.380952380952381, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1435.44, "end": 1436.06, "word": "معلومتي", "probability": 0.70458984375}, {"start": 1436.06, "end": 1436.58, "word": " باطمان", "probability": 0.5491943359375}, {"start": 1436.58, "end": 1437.02, "word": " لأن", "probability": 0.53857421875}, {"start": 1437.02, "end": 1437.18, "word": " هي", "probability": 0.2705078125}, {"start": 1437.18, "end": 1437.58, "word": " أسوأ", "probability": 0.91357421875}, {"start": 1437.58, "end": 1437.78, "word": " case", "probability": 0.90283203125}, {"start": 1437.78, "end": 1438.34, "word": " ممكنة", "probability": 0.8763020833333334}, {"start": 1438.34, "end": 1438.5, "word": " في", "probability": 0.88671875}, {"start": 1438.5, "end": 1439.08, "word": " التوزيع", "probability": 0.981201171875}, {"start": 1439.08, "end": 1439.64, "word": " او", "probability": 0.751220703125}, {"start": 1439.64, "end": 1439.86, "word": " خلاني", "probability": 0.62017822265625}, {"start": 1439.86, "end": 1440.02, "word": " اقول", "probability": 0.74462890625}, {"start": 1440.02, "end": 1440.16, "word": " ان", "probability": 0.278564453125}, {"start": 1440.16, "end": 1440.28, "word": " ال", "probability": 0.6513671875}, {"start": 1440.28, "end": 1440.74, "word": " uniform", "probability": 0.96826171875}, {"start": 1440.74, "end": 1441.04, "word": " هنا", "probability": 0.97998046875}, {"start": 1441.04, "end": 1441.52, "word": " ال", "probability": 0.2388916015625}, {"start": 1441.52, "end": 1441.86, "word": " uniform", "probability": 0.41357421875}, {"start": 1441.86, "end": 1443.94, "word": " فالرقم", "probability": 0.8794921875}, {"start": 1443.94, "end": 1444.64, "word": " 26", "probability": 0.64599609375}, {"start": 1444.64, "end": 1446.88, "word": " ياخد", "probability": 0.95458984375}, {"start": 1446.88, "end": 1446.96, "word": " ال", "probability": 0.8662109375}, {"start": 1446.96, "end": 1447.14, "word": " grade", "probability": 0.9677734375}, {"start": 1447.14, "end": 1447.24, "word": " اللي", "probability": 0.92822265625}, {"start": 1447.24, "end": 1447.7, "word": " بدنيا", "probability": 0.5232747395833334}], "temperature": 1.0}, {"id": 61, "seek": 147157, "start": 1448.99, "end": 1471.57, "text": "بدو ييجي هنا بدو ييجي هنا بدو ييجي هنا ايجي هنا معناه ذلك انها ل grade C في 6 طلاب حصلوا على grade C ايجي هنا grade A في 6 طلاب حصلوا على grade A ايجي هنا F في 6 طلاب حصلوا على F فرقم 26 هو الإجابة في الحالة هذه اللي احنا محتاجين عدد طلاب مساوي له عشان اضمن انه في 6 طلاب اللي هم نفس ل grade okay", "tokens": [44510, 2407, 7251, 1829, 7435, 1829, 34105, 47525, 2407, 7251, 1829, 7435, 1829, 34105, 47525, 2407, 7251, 1829, 7435, 1829, 34105, 1975, 1829, 7435, 1829, 34105, 20449, 8315, 3224, 29910, 23275, 16472, 11296, 5296, 7204, 383, 8978, 1386, 23032, 15040, 3555, 11331, 36520, 14407, 15844, 7204, 383, 1975, 1829, 7435, 1829, 34105, 7204, 316, 8978, 1386, 23032, 15040, 3555, 11331, 36520, 14407, 15844, 7204, 316, 1975, 1829, 7435, 1829, 34105, 479, 8978, 1386, 23032, 15040, 3555, 11331, 36520, 14407, 15844, 479, 6156, 2288, 4587, 2304, 7551, 31439, 33688, 7435, 16758, 3660, 8978, 21542, 6027, 3660, 29538, 13672, 1829, 1975, 5016, 8315, 3714, 33753, 26108, 9957, 6225, 3215, 3215, 23032, 15040, 3555, 47524, 995, 45865, 46740, 6225, 8592, 7649, 1975, 11242, 27842, 16472, 3224, 8978, 1386, 23032, 15040, 3555, 13672, 1829, 8032, 2304, 8717, 36178, 5296, 7204, 1392], "avg_logprob": -0.20063405138426932, "compression_ratio": 2.3173076923076925, "no_speech_prob": 9.059906005859375e-06, "words": [{"start": 1448.99, "end": 1449.29, "word": "بدو", "probability": 0.477630615234375}, {"start": 1449.29, "end": 1449.45, "word": " ييجي", "probability": 0.80145263671875}, {"start": 1449.45, "end": 1449.57, "word": " هنا", "probability": 0.97900390625}, {"start": 1449.57, "end": 1449.73, "word": " بدو", "probability": 0.6197509765625}, {"start": 1449.73, "end": 1449.87, "word": " ييجي", "probability": 0.9259033203125}, {"start": 1449.87, "end": 1449.97, "word": " هنا", "probability": 0.9873046875}, {"start": 1449.97, "end": 1450.13, "word": " بدو", "probability": 0.8193359375}, {"start": 1450.13, "end": 1450.27, "word": " ييجي", "probability": 0.959228515625}, {"start": 1450.27, "end": 1450.43, "word": " هنا", "probability": 0.875}, {"start": 1450.43, "end": 1450.63, "word": " ايجي", "probability": 0.488006591796875}, {"start": 1450.63, "end": 1450.87, "word": " هنا", "probability": 0.94140625}, {"start": 1450.87, "end": 1451.53, "word": " معناه", "probability": 0.687744140625}, {"start": 1451.53, "end": 1451.75, "word": " ذلك", "probability": 0.9150390625}, {"start": 1451.75, "end": 1452.03, "word": " انها", "probability": 0.6590576171875}, {"start": 1452.03, "end": 1452.25, "word": " ل", "probability": 0.390380859375}, {"start": 1452.25, "end": 1452.45, "word": " grade", "probability": 0.90869140625}, {"start": 1452.45, "end": 1452.81, "word": " C", "probability": 0.62890625}, {"start": 1452.81, "end": 1453.53, "word": " في", "probability": 0.84765625}, {"start": 1453.53, "end": 1454.05, "word": " 6", "probability": 0.480224609375}, {"start": 1454.05, "end": 1454.43, "word": " طلاب", "probability": 0.931640625}, {"start": 1454.43, "end": 1454.75, "word": " حصلوا", "probability": 0.96240234375}, {"start": 1454.75, "end": 1454.87, "word": " على", "probability": 0.58056640625}, {"start": 1454.87, "end": 1455.07, "word": " grade", "probability": 0.9375}, {"start": 1455.07, "end": 1455.35, "word": " C", "probability": 0.88134765625}, {"start": 1455.35, "end": 1455.99, "word": " ايجي", "probability": 0.86083984375}, {"start": 1455.99, "end": 1456.21, "word": " هنا", "probability": 0.97998046875}, {"start": 1456.21, "end": 1456.61, "word": " grade", "probability": 0.8212890625}, {"start": 1456.61, "end": 1457.03, "word": " A", "probability": 0.96728515625}, {"start": 1457.03, "end": 1457.29, "word": " في", "probability": 0.8662109375}, {"start": 1457.29, "end": 1457.57, "word": " 6", "probability": 0.98193359375}, {"start": 1457.57, "end": 1457.85, "word": " طلاب", "probability": 0.9508463541666666}, {"start": 1457.85, "end": 1458.13, "word": " حصلوا", "probability": 0.9853515625}, {"start": 1458.13, "end": 1458.19, "word": " على", "probability": 0.80322265625}, {"start": 1458.19, "end": 1458.29, "word": " grade", "probability": 0.9619140625}, {"start": 1458.29, "end": 1458.51, "word": " A", "probability": 0.9736328125}, {"start": 1458.51, "end": 1459.15, "word": " ايجي", "probability": 0.9598388671875}, {"start": 1459.15, "end": 1459.39, "word": " هنا", "probability": 0.98779296875}, {"start": 1459.39, "end": 1459.83, "word": " F", "probability": 0.775390625}, {"start": 1459.83, "end": 1460.27, "word": " في", "probability": 0.9189453125}, {"start": 1460.27, "end": 1460.47, "word": " 6", "probability": 0.98779296875}, {"start": 1460.47, "end": 1460.73, "word": " طلاب", "probability": 0.9365234375}, {"start": 1460.73, "end": 1461.07, "word": " حصلوا", "probability": 0.9505208333333334}, {"start": 1461.07, "end": 1461.17, "word": " على", "probability": 0.75732421875}, {"start": 1461.17, "end": 1461.49, "word": " F", "probability": 0.449951171875}, {"start": 1461.49, "end": 1462.47, "word": " فرقم", "probability": 0.873779296875}, {"start": 1462.47, "end": 1463.09, "word": " 26", "probability": 0.9111328125}, {"start": 1463.09, "end": 1463.39, "word": " هو", "probability": 0.97021484375}, {"start": 1463.39, "end": 1464.43, "word": " الإجابة", "probability": 0.93603515625}, {"start": 1464.43, "end": 1464.53, "word": " في", "probability": 0.94921875}, {"start": 1464.53, "end": 1464.81, "word": " الحالة", "probability": 0.9654947916666666}, {"start": 1464.81, "end": 1465.05, "word": " هذه", "probability": 0.44677734375}, {"start": 1465.05, "end": 1465.99, "word": " اللي", "probability": 0.942138671875}, {"start": 1465.99, "end": 1466.13, "word": " احنا", "probability": 0.9402669270833334}, {"start": 1466.13, "end": 1466.51, "word": " محتاجين", "probability": 0.988525390625}, {"start": 1466.51, "end": 1466.75, "word": " عدد", "probability": 0.9571940104166666}, {"start": 1466.75, "end": 1467.57, "word": " طلاب", "probability": 0.9755859375}, {"start": 1467.57, "end": 1468.03, "word": " مساوي", "probability": 0.7635091145833334}, {"start": 1468.03, "end": 1468.25, "word": " له", "probability": 0.76416015625}, {"start": 1468.25, "end": 1468.53, "word": " عشان", "probability": 0.96142578125}, {"start": 1468.53, "end": 1468.75, "word": " اضمن", "probability": 0.751953125}, {"start": 1468.75, "end": 1468.89, "word": " انه", "probability": 0.642578125}, {"start": 1468.89, "end": 1469.01, "word": " في", "probability": 0.78759765625}, {"start": 1469.01, "end": 1469.13, "word": " 6", "probability": 0.9306640625}, {"start": 1469.13, "end": 1469.63, "word": " طلاب", "probability": 0.9635416666666666}, {"start": 1469.63, "end": 1469.93, "word": " اللي", "probability": 0.944091796875}, {"start": 1469.93, "end": 1470.07, "word": " هم", "probability": 0.733642578125}, {"start": 1470.07, "end": 1470.35, "word": " نفس", "probability": 0.98681640625}, {"start": 1470.35, "end": 1470.69, "word": " ل", "probability": 0.59521484375}, {"start": 1470.69, "end": 1470.93, "word": " grade", "probability": 0.9697265625}, {"start": 1470.93, "end": 1471.57, "word": " okay", "probability": 0.50927734375}], "temperature": 1.0}, {"id": 62, "seek": 149993, "start": 1472.85, "end": 1499.93, "text": "فهي try to fill the boxes بتجربوا تعملوا اتملوا ال boxes كاملة كأنه الطلاب بتتوزع uniformly كأنها بتتوزع بالتساوي okay كمان مثال مثال كتير كويس assume ال telephone number is as follows aaa و 5x ايش ال aaa و 5x هذه؟", "tokens": [5172, 3224, 1829, 853, 281, 2836, 264, 9002, 39894, 7435, 25513, 14407, 6055, 25957, 1211, 14407, 1975, 39237, 1211, 14407, 2423, 9002, 9122, 10943, 37977, 9122, 33456, 3224, 41950, 15040, 3555, 39894, 2655, 2407, 11622, 3615, 48806, 9122, 33456, 11296, 39894, 2655, 2407, 11622, 3615, 20666, 2655, 3794, 995, 45865, 1392, 9122, 2304, 7649, 50113, 6027, 50113, 6027, 9122, 2655, 13546, 9122, 45865, 3794, 6552, 2423, 19800, 1230, 307, 382, 10002, 257, 4332, 4032, 1025, 87, 1975, 1829, 8592, 2423, 257, 4332, 4032, 1025, 87, 29538, 22807], "avg_logprob": -0.1896306767382405, "compression_ratio": 1.5628140703517588, "no_speech_prob": 0.0, "words": [{"start": 1472.85, "end": 1473.31, "word": "فهي", "probability": 0.8912760416666666}, {"start": 1473.31, "end": 1474.01, "word": " try", "probability": 0.61865234375}, {"start": 1474.01, "end": 1474.23, "word": " to", "probability": 0.98193359375}, {"start": 1474.23, "end": 1474.45, "word": " fill", "probability": 0.8837890625}, {"start": 1474.45, "end": 1474.91, "word": " the", "probability": 0.84765625}, {"start": 1474.91, "end": 1475.31, "word": " boxes", "probability": 0.912109375}, {"start": 1475.31, "end": 1476.77, "word": " بتجربوا", "probability": 0.7281494140625}, {"start": 1476.77, "end": 1477.29, "word": " تعملوا", "probability": 0.90869140625}, {"start": 1477.29, "end": 1477.93, "word": " اتملوا", "probability": 0.78497314453125}, {"start": 1477.93, "end": 1478.01, "word": " ال", "probability": 0.8642578125}, {"start": 1478.01, "end": 1478.25, "word": " boxes", "probability": 0.939453125}, {"start": 1478.25, "end": 1478.93, "word": " كاملة", "probability": 0.958984375}, {"start": 1478.93, "end": 1479.83, "word": " كأنه", "probability": 0.7430013020833334}, {"start": 1479.83, "end": 1480.89, "word": " الطلاب", "probability": 0.9415690104166666}, {"start": 1480.89, "end": 1481.63, "word": " بتتوزع", "probability": 0.8998046875}, {"start": 1481.63, "end": 1483.39, "word": " uniformly", "probability": 0.93505859375}, {"start": 1483.39, "end": 1484.03, "word": " كأنها", "probability": 0.8650716145833334}, {"start": 1484.03, "end": 1484.51, "word": " بتتوزع", "probability": 0.97041015625}, {"start": 1484.51, "end": 1485.11, "word": " بالتساوي", "probability": 0.94033203125}, {"start": 1485.11, "end": 1486.63, "word": " okay", "probability": 0.5888671875}, {"start": 1486.63, "end": 1487.05, "word": " كمان", "probability": 0.9275716145833334}, {"start": 1487.05, "end": 1487.49, "word": " مثال", "probability": 0.87841796875}, {"start": 1487.49, "end": 1488.47, "word": " مثال", "probability": 0.854248046875}, {"start": 1488.47, "end": 1488.73, "word": " كتير", "probability": 0.9283854166666666}, {"start": 1488.73, "end": 1489.23, "word": " كويس", "probability": 0.9876302083333334}, {"start": 1489.23, "end": 1490.13, "word": " assume", "probability": 0.73291015625}, {"start": 1490.13, "end": 1490.31, "word": " ال", "probability": 0.646484375}, {"start": 1490.31, "end": 1490.59, "word": " telephone", "probability": 0.88427734375}, {"start": 1490.59, "end": 1491.05, "word": " number", "probability": 0.9765625}, {"start": 1491.05, "end": 1491.49, "word": " is", "probability": 0.9541015625}, {"start": 1491.49, "end": 1492.09, "word": " as", "probability": 0.96142578125}, {"start": 1492.09, "end": 1492.89, "word": " follows", "probability": 0.82373046875}, {"start": 1492.89, "end": 1494.63, "word": " aaa", "probability": 0.544189453125}, {"start": 1494.63, "end": 1495.77, "word": " و", "probability": 0.9228515625}, {"start": 1495.77, "end": 1496.57, "word": " 5x", "probability": 0.691162109375}, {"start": 1496.57, "end": 1498.39, "word": " ايش", "probability": 0.7814127604166666}, {"start": 1498.39, "end": 1498.53, "word": " ال", "probability": 0.86767578125}, {"start": 1498.53, "end": 1498.79, "word": " aaa", "probability": 0.8603515625}, {"start": 1498.79, "end": 1498.95, "word": " و", "probability": 0.82568359375}, {"start": 1498.95, "end": 1499.35, "word": " 5x", "probability": 0.835205078125}, {"start": 1499.35, "end": 1499.93, "word": " هذه؟", "probability": 0.635498046875}], "temperature": 1.0}, {"id": 63, "seek": 151546, "start": 1500.54, "end": 1515.46, "text": "الأرقام التليفونات ممكن يكون في عندنا خمس أرقام الخمس أرقام هدولة خاصين بمين ب Central معين أكمل Central محتاج عشان أغطي خمسة و عشرين user أي خمسة و عشرين مليون user", "tokens": [6027, 10721, 2288, 4587, 10943, 16712, 20292, 5172, 2407, 8315, 2655, 3714, 43020, 7251, 30544, 8978, 43242, 8315, 16490, 2304, 3794, 5551, 2288, 4587, 10943, 33962, 2304, 3794, 5551, 2288, 4587, 10943, 8032, 3215, 12610, 3660, 16490, 33546, 9957, 4724, 2304, 9957, 4724, 9701, 20449, 9957, 5551, 24793, 1211, 9701, 3714, 33753, 26108, 6225, 8592, 7649, 5551, 17082, 9566, 1829, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 4195, 36632, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 3714, 20292, 11536, 4195], "avg_logprob": -0.21912650315158338, "compression_ratio": 1.748427672955975, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1500.54, "end": 1501.2, "word": "الأرقام", "probability": 0.83349609375}, {"start": 1501.2, "end": 1502.0, "word": " التليفونات", "probability": 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{"start": 1525.75, "end": 1526.01, "word": " area", "probability": 0.67041015625}, {"start": 1526.01, "end": 1526.49, "word": " واحدة", "probability": 0.9661458333333334}, {"start": 1526.49, "end": 1527.09, "word": " بيصير", "probability": 0.84716796875}, {"start": 1527.09, "end": 1527.71, "word": " جديش", "probability": 0.6649576822916666}, {"start": 1527.71, "end": 1528.35, "word": " عدد", "probability": 0.9908854166666666}, {"start": 1528.35, "end": 1528.61, "word": " ال", "probability": 0.73193359375}, {"start": 1528.61, "end": 1528.89, "word": " code", "probability": 0.9677734375}, {"start": 1528.89, "end": 1529.03, "word": " اللي", "probability": 0.97607421875}, {"start": 1529.03, "end": 1529.51, "word": " محتاجها", "probability": 0.9793701171875}, {"start": 1529.51, "end": 1529.95, "word": " لكل", "probability": 0.973388671875}, {"start": 1529.95, "end": 1530.37, "word": " area", "probability": 0.88525390625}, {"start": 1530.37, "end": 1531.13, "word": " أو", "probability": 0.6650390625}, {"start": 1531.13, "end": 1531.41, "word": " جديش", "probability": 0.94384765625}, {"start": 1531.41, "end": 1531.67, "word": " عدد", "probability": 0.9962565104166666}, {"start": 1531.67, "end": 1531.79, "word": " ال", "probability": 0.96142578125}, {"start": 1531.79, "end": 1532.15, "word": " area", "probability": 0.92626953125}, {"start": 1532.15, "end": 1532.83, "word": " codes", "probability": 0.716796875}, {"start": 1532.83, "end": 1533.09, "word": " اللي", "probability": 0.991455078125}, {"start": 1533.09, "end": 1533.61, "word": " محتاجينها", "probability": 0.98408203125}, {"start": 1533.61, "end": 1533.81, "word": " عدد", "probability": 0.9718424479166666}, {"start": 1533.81, "end": 1533.91, "word": " ال", "probability": 0.9619140625}, {"start": 1533.91, "end": 1534.07, "word": " area", "probability": 0.90966796875}, {"start": 1534.07, "end": 1534.33, "word": " codes", "probability": 0.8837890625}, {"start": 1534.33, "end": 1534.83, "word": " معناه", "probability": 0.8160807291666666}, {"start": 1534.83, "end": 1535.09, "word": " ذلك", "probability": 0.991455078125}, {"start": 1535.09, "end": 1535.43, "word": " أكم", "probability": 0.857421875}, {"start": 1535.43, "end": 1536.63, "word": " ايه", "probability": 0.7350260416666666}, {"start": 1536.63, "end": 1537.05, "word": " محتاج", "probability": 0.9879557291666666}, {"start": 1537.05, "end": 1537.29, "word": " هنا", "probability": 0.994140625}, {"start": 1537.29, "end": 1539.19, "word": " تلاتة", "probability": 0.897705078125}, {"start": 1539.19, "end": 1539.79, "word": " خمسة", "probability": 0.9173583984375}, {"start": 1539.79, "end": 1540.25, "word": " عشرة", "probability": 0.9327799479166666}], "temperature": 1.0}, {"id": 65, "seek": 156400, "start": 1541.36, "end": 1564.0, "text": "جدّيش الأرقام اللي أنا محتاجها عشان أقول والله فعلا الرقم كله على بعض و هيك رقم التليفون كله على بعض و بيقدر يكفي لخمسة و عشرين مليون user خمسة و عشرين مليون مشترك خمسة و عشرين مليون بني آدم عايشين في المدينة كل واحد من حقه ياخد رقم، تليفون مختلف أو different telephone number، telephone number أنتوا عادة تعرفين أن كلنا مثلا مشترك ب 2 8", "tokens": [7435, 3215, 11703, 1829, 8592, 16247, 2288, 4587, 10943, 13672, 1829, 41850, 3714, 33753, 26108, 11296, 6225, 8592, 7649, 5551, 39648, 16070, 43761, 6156, 3615, 15040, 34892, 4587, 2304, 28242, 3224, 15844, 45030, 11242, 4032, 39896, 4117, 12602, 4587, 2304, 16712, 20292, 5172, 11536, 28242, 3224, 15844, 45030, 11242, 4032, 4724, 1829, 28543, 2288, 7251, 4117, 41185, 5296, 9778, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 3714, 20292, 11536, 4195, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 3714, 20292, 11536, 37893, 2655, 31747, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 3714, 20292, 11536, 4724, 22653, 19753, 40448, 6225, 47302, 8592, 9957, 8978, 9673, 3215, 9957, 3660, 28242, 36764, 24401, 9154, 11331, 4587, 3224, 7251, 47283, 3215, 12602, 4587, 2304, 12399, 6055, 20292, 5172, 11536, 3714, 46456, 46538, 34051, 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"word": " مشترك", "probability": 0.919921875}, {"start": 1550.84, "end": 1551.38, "word": " خمسة", "probability": 0.8905029296875}, {"start": 1551.38, "end": 1551.44, "word": " و", "probability": 0.99853515625}, {"start": 1551.44, "end": 1551.64, "word": " عشرين", "probability": 0.9705403645833334}, {"start": 1551.64, "end": 1552.04, "word": " مليون", "probability": 0.9938151041666666}, {"start": 1552.04, "end": 1552.66, "word": " بني", "probability": 0.885498046875}, {"start": 1552.66, "end": 1552.92, "word": " آدم", "probability": 0.7244873046875}, {"start": 1552.92, "end": 1553.3, "word": " عايشين", "probability": 0.9927978515625}, {"start": 1553.3, "end": 1553.4, "word": " في", "probability": 0.8984375}, {"start": 1553.4, "end": 1553.92, "word": " المدينة", "probability": 0.9923095703125}, {"start": 1553.92, "end": 1554.38, "word": " كل", "probability": 0.82666015625}, {"start": 1554.38, "end": 1554.8, "word": " واحد", "probability": 0.997802734375}, {"start": 1554.8, "end": 1555.2, "word": " من", "probability": 0.9921875}, {"start": 1555.2, "end": 1555.52, "word": " حقه", "probability": 0.9938151041666666}, {"start": 1555.52, "end": 1555.86, "word": " ياخد", "probability": 0.9832356770833334}, {"start": 1555.86, "end": 1556.36, "word": " رقم،", "probability": 0.86492919921875}, {"start": 1556.36, "end": 1556.62, "word": " تليفون", "probability": 0.9168701171875}, {"start": 1556.62, "end": 1557.18, "word": " مختلف", "probability": 0.98583984375}, {"start": 1557.18, "end": 1557.34, "word": " أو", "probability": 0.7900390625}, {"start": 1557.34, "end": 1557.68, "word": " different", "probability": 0.890625}, {"start": 1557.68, "end": 1558.32, "word": " telephone", "probability": 0.83251953125}, {"start": 1558.32, "end": 1559.1, "word": " number،", "probability": 0.6422119140625}, {"start": 1559.1, "end": 1559.44, "word": " telephone", "probability": 0.81396484375}, {"start": 1559.44, "end": 1561.1, "word": " number", "probability": 0.97216796875}, {"start": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I.srt
new file mode 100644
index 0000000000000000000000000000000000000000..47c61d67e52bd7143aee733ddf9c6399aca55a87
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I.srt
@@ -0,0 +1,2033 @@
+
+1
+00:00:20,790 --> 00:00:23,010
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:23,010 --> 00:00:25,850
+الأنبياء والمسلمين سيدنا محمد عليه الصلاة والسلام
+
+3
+00:00:25,850 --> 00:00:29,950
+جماعة، نكمل اليوم إن شاء الله تعالى في موضوع ال
+
+4
+00:00:29,950 --> 00:00:35,050
+inductive أو الـ induction، الـ inductive proof و كان
+
+5
+00:00:35,050 --> 00:00:38,370
+ضايق لنا، اتكلمنا يمكن بعد ما اتكلمنا على الـ first
+
+6
+00:00:38,370 --> 00:00:41,370
+principle examples، أخدنا two examples على الـ first
+
+7
+00:00:41,370 --> 00:00:45,850
+principle، و الـ first principle تفكيرا كان يعتمد
+
+8
+00:00:45,850 --> 00:00:52,000
+على فكرة أن P of N بأثبتها من P of N minus one، من
+
+9
+00:00:52,000 --> 00:00:55,980
+العنصر اللي قبله مباشرة. طيب، اتكلمنا المرة اللي
+
+10
+00:00:55,980 --> 00:00:58,600
+فاتت برضه في آخر المحاضرة عن الـ second principle
+
+11
+00:00:58,600 --> 00:01:02,000
+example، وقلنا إنه بتختلف عن الـ first إنه أنا
+
+12
+00:01:02,000 --> 00:01:06,940
+بأخذ P of N من كل الـ elements اللي قبله، من جميع
+
+13
+00:01:06,940 --> 00:01:10,340
+الـ elements اللي قبله، مش ضروري أثبتهم واحد واحد،
+
+14
+00:01:10,340 --> 00:01:15,700
+ولكن ببدأ دائما بالـ base case، وبعدين by logic كل
+
+15
+00:01:15,700 --> 00:01:20,730
+element أقل من P of N بيعتمد على الـ base، ممكن الـ
+
+16
+00:01:20,730 --> 00:01:25,010
+sequence تبعهم يوصلنا لـ الـ base case. أخدنا مثال
+
+17
+00:01:25,010 --> 00:01:27,630
+المرة اللي فاتت اللي كان له علاقة بالـ primes، أن
+
+18
+00:01:27,630 --> 00:01:32,190
+كل element بيتكون من مجموعة الـ primes. اليوم بنكمل
+
+19
+00:01:32,190 --> 00:01:36,370
+الـ example الثاني لـ second principle example اللي
+
+20
+00:01:36,370 --> 00:01:39,610
+هو زي ما إحنا شايفينه، نخلص فيه جزئية الـ inductive
+
+21
+00:01:39,610 --> 00:01:43,230
+عشان ننتقل على section هو نفسه inductive، يعني هو
+
+22
+00:01:43,230 --> 00:01:48,210
+يعني تكميل لجزئية الـ inductive. طيب، نشوف المثال
+
+23
+00:01:48,210 --> 00:01:51,700
+الثاني، الـ proof: I prove that every amount of
+
+24
+00:01:51,700 --> 00:01:55,440
+postage of twelve cents or more can be formed
+
+25
+00:01:55,440 --> 00:02:01,480
+using just four cent and five cent stamps. إيش
+
+26
+00:02:01,480 --> 00:02:04,400
+يعني؟ الـ postage اللي هو تتكلموا أنتم عن جواب
+
+27
+00:02:04,400 --> 00:02:10,100
+البُسط، أو الجواب البريدي، الجواب البريدي. كل جواب
+
+28
+00:02:10,100 --> 00:02:15,560
+بريدي، أو حوالة بريدية، شيء اللي له علاقة بالبريد.
+
+29
+00:02:15,560 --> 00:02:22,120
+يمكن وضع عليه طوابع أي قيمة، له أكثر من اثنا عشر
+
+30
+00:02:22,120 --> 00:02:27,400
+أو أكثر سنت، بقدر أمثلها بـ two stems، الـ stems اللي
+
+31
+00:02:27,400 --> 00:02:31,580
+هي الطوابع، بقدر أمثلها بطابعين فقط، أو بنوعين من
+
+32
+00:02:31,580 --> 00:02:36,200
+الطوابع، اللي هو طابع قيمته أربعة سنت، وطابع قيمته
+
+33
+00:02:36,200 --> 00:02:40,460
+خمسة سنت. طابع أربعة سنت، وخمسة سنت. زي لما تروحوا
+
+34
+00:02:40,460 --> 00:02:43,540
+مثلا، تكونوا تعملوا روشتة في أي مستوصف، أي أو أي
+
+35
+00:02:43,540 --> 00:02:50,070
+هيئة صحية، وتكونوا محتاجين ثلاثة، شكل، هحط لكم
+
+36
+00:02:50,070 --> 00:02:57,310
+ثلاثة stems، شكل شكل شكل، صحيح؟ فعمل تكوين للرقم
+
+37
+00:02:57,310 --> 00:03:01,190
+ثلاثة من الـ three stems من نفس الفئة، اللي هي الفئة
+
+38
+00:03:01,190 --> 00:03:07,490
+one، شكل. طيب، هنا نفس الكلام، بده نثبت إنه أي روشتة،
+
+39
+00:03:07,490 --> 00:03:14,310
+أي جواب، أي بريد قيمته أكثر أو تساوي اثنا عشر cent،
+
+40
+00:03:14,310 --> 00:03:19,950
+بقدر أمثلها بنوعين من الـ stems، نوعين من الـ
+
+41
+00:03:19,950 --> 00:03:25,550
+stems اللي هما ماجدداش أربعة سنت أو خمسة سنت. هل فعلا
+
+42
+00:03:25,550 --> 00:03:28,590
+نقدر الكلام هذا؟ نشوف، هو مطلوب نعمل إثبات للكلام
+
+43
+00:03:28,590 --> 00:03:31,430
+هذا. طيب، في الحالة دي، الـ initial condition بتاعتنا
+
+44
+00:03:31,430 --> 00:03:34,830
+أول، الـ base case بتاعتنا، الـ base case بتاعتنا
+
+45
+00:03:34,830 --> 00:03:39,540
+هنبدأ من الأساس، اثنا عشر أو أكثر، هو بيقول اثنا عشر أو
+
+46
+00:03:39,540 --> 00:03:42,500
+أكثر. فإذا بدي أبدأ من أولها، الاثنا عشر، هل فعلا الاثنا عشر
+
+47
+00:03:42,500 --> 00:03:49,600
+بقدر أمثلها بمجموعة stamps أربعة أو خمسة؟ طبيعي، ليش؟
+
+48
+00:03:49,600 --> 00:03:54,940
+لأنه عبارة عن ثلاثة four cents stamp، مظبوط؟
+
+49
+00:03:54,940 --> 00:04:00,520
+ثلاثة، ثلاثة أربعة أربعة، أربعة أربعة. فإذا بقدر
+
+50
+00:04:00,520 --> 00:04:05,840
+أمثل أنه هي ثلاثة مضروبة في مين؟ في four cent stamp.
+
+51
+00:04:07,980 --> 00:04:14,380
+الثلاثة عشر هنا طبعا لاحظوا أنه إحنا هنحتاج الـ base
+
+52
+00:04:14,380 --> 00:04:18,040
+case بتاعتنا على الأقل يكون فيها أربعة، ليش أربعة؟
+
+53
+00:04:18,040 --> 00:04:23,500
+لأنه التكرار بيبدا من أربعة، أقل stamp موجودة عندكم
+
+54
+00:04:23,500 --> 00:04:27,200
+عشان تعملوا تكرار للقيمة، هي أربعة، أقل واحدة لأربعة.
+
+55
+00:04:27,200 --> 00:04:29,960
+فأنتم محتاجين الـ base case بتاعتكم على الأقل أربعة
+
+56
+00:04:29,960 --> 00:04:35,140
+قيم، عشان تضمنوا بعد أنه في تكرار في recursion، في
+
+57
+00:04:35,140 --> 00:04:40,600
+تكرار للعملية، بزيادة، موجود لها stamp بزيادة،
+
+58
+00:04:40,600 --> 00:04:43,400
+موجودة، لها قيمة للـ stamp بتاعتها. okay، فبناخد
+
+59
+00:04:43,400 --> 00:04:47,820
+الثلاثة عشر، ثلاثة عشر عبارة عن اثنين في أربعة زائد خمسة.
+
+60
+00:04:47,820 --> 00:04:52,830
+اثنين في أربعة زائد خمسة. الأربعة عشر: واحد واثنين.
+
+61
+00:04:52,830 --> 00:04:57,350
+الخمسة عشر: ثلاثة. فلاحظوا هنا: ثلاثة، اثنين، واحد، واحد،
+
+62
+00:04:57,350 --> 00:05:02,350
+اثنين، ثلاثة. تبديل وتوفيق، لأن الفرق بينهم واحد، فكل
+
+63
+00:05:02,350 --> 00:05:07,530
+مرة بنزود... بنزود قيمة أو cent من الـ combination
+
+64
+00:05:07,530 --> 00:05:11,250
+اللي عملناها لمجموعة الـ stamps بتاعتنا. okay، في
+
+65
+00:05:11,250 --> 00:05:15,430
+الحالة هذه، أنا ضمنت أن من الاثنا عشر لخمسة عشر،
+
+66
+00:05:15,430 --> 00:05:19,950
+is true، لأن إحنا اللي عاملينها هي... إحنا عاملينها
+
+67
+00:05:19,950 --> 00:05:24,870
+فعلا من اثنا عشر لخمسة عشر... اثنا عشر لخمسة عشر، P of N is
+
+68
+00:05:24,870 --> 00:05:28,370
+true... P of N is true. فهذه كل هذا اللي هي الـ base
+
+69
+00:05:28,370 --> 00:05:32,830
+case اللي إحنا بنحله بإيدينا، هنشتغل واحدة واحدة،
+
+70
+00:05:32,830 --> 00:05:36,990
+عشان نخلصهم، خلصناهم. الـ inductive step في الـ
+
+71
+00:05:36,990 --> 00:05:40,870
+inductive step بنبدأ نشتغل على اللي أعلى من الـ
+
+72
+00:05:40,870 --> 00:05:46,210
+base case. فإذا حد من خمسة عشر فأعلى من خمسة عشر، فإيش؟
+
+73
+00:05:46,210 --> 00:05:49,810
+فأعلى من خمسة عشر، فأعلى، بقول n أكبر من أو تساوي
+
+74
+00:05:49,810 --> 00:05:56,830
+fifteen. assume for all twelve أقل من أو تساوي k،
+
+75
+00:05:56,830 --> 00:06:03,180
+أقل من أو تساوي n، k... حطيناها variable اسمه k...
+
+76
+00:06:03,180 --> 00:06:06,740
+والـ n ممكن تكون أي... أي شيء، ممكن تكون أكبر من
+
+77
+00:06:06,740 --> 00:06:09,620
+الخمسة عشر... ما دام أنا في الـ inductive بتكون أكبر
+
+78
+00:06:09,620 --> 00:06:12,320
+من الخمسة عشر. هذا ممكن برضه أكتبه بطريقة ثانية، أقول
+
+79
+00:06:12,320 --> 00:06:17,960
+أن هي n minus three أقل من أو يساوي m، على أساس لما
+
+80
+00:06:17,960 --> 00:06:25,190
+بدنا نحسب n plus one، إيش الفرق بينها؟ لاحظوا، من
+
+81
+00:06:25,190 --> 00:06:29,630
+اثنا عشر لـ n اللي إحنا أساسا قلنا إن هي approved،
+
+82
+00:06:29,630 --> 00:06:38,090
+assume هي assume، لاحظوا هنا k بنمثلها بـ n minus
+
+83
+00:06:38,090 --> 00:06:40,890
+three. طيب، n minus three، إذا أنا فعلا عامل
+
+84
+00:06:40,890 --> 00:06:44,990
+assumption للـ condition هذا، n minus three أقل من
+
+85
+00:06:44,990 --> 00:06:54,040
+n، فإذا true، فإذا كان فعلا هي true، بقدر أجيب منها n
+
+86
+00:06:54,040 --> 00:07:01,540
+plus واحد، لإيش؟ لأنه كده الفرق بينهم أربعة، يعني
+
+87
+00:07:01,540 --> 00:07:07,000
+بزود stamp واحدة قيمتها أربعة سنت. فإذا، إذا قدرنا
+
+88
+00:07:07,000 --> 00:07:13,950
+نثبت أن n minus three is true، باللوجيك n زائد واحد
+
+89
+00:07:13,950 --> 00:07:18,130
+is true، لأن كل اللي هضيفه كمان stamp واحدة بقيمة
+
+90
+00:07:18,130 --> 00:07:24,570
+أربعة cent، أربعة cent. فإذا بنقدر نمثلها، k، الـ k
+
+91
+00:07:24,570 --> 00:07:29,530
+بتاعتنا هنا بنقدر نمثلها بـ n minus three، وأنا
+
+92
+00:07:29,530 --> 00:07:33,350
+ضامن أن n minus three هي ضمن الـ region هذه، لازم
+
+93
+00:07:33,350 --> 00:07:37,150
+تكون... لأن أقل من n، أقل من n، أقل من n، الثلاثة.
+
+94
+00:07:37,150 --> 00:07:44,110
+okay، فإذا، so P of n minus 3 is true، كل اللي هنعمله
+
+95
+00:07:44,110 --> 00:07:51,910
+add لمين؟ لـ 4 cent stamp. فـ 4 cent stamp to get
+
+96
+00:07:51,910 --> 00:07:58,870
+postage for n plus 1، لأن n plus 1 و n minus 3
+
+97
+00:07:58,870 --> 00:08:02,530
+الفرق بينهم أربعة، والأربعة موجود، عند قيمة الفرق
+
+98
+00:08:02,530 --> 00:08:05,290
+هذا، يعني أنا بزود بس كمان stamp واحدة أو طابع
+
+99
+00:08:05,290 --> 00:08:10,080
+بريدي واحد، طابع بريدي واحد. فإذا كان قدرنا نثبت هيو
+
+100
+00:08:10,080 --> 00:08:16,080
+بإيدنا الاثنا عشر، فإذا الستة عشر أكيد برضه ممكن نعملها
+
+101
+00:08:16,080 --> 00:08:22,480
+generation، باستخدام، هنا كنا قد إيش نستخدم؟ ثلاثة في
+
+102
+00:08:22,480 --> 00:08:26,880
+أربعة stamp في أربعة cent stamp، كل اللي هنعمله هنا،
+
+103
+00:08:26,880 --> 00:08:32,880
+هنزود أربعة، فبتصير أربعة من فئة الأربعة cent، من
+
+104
+00:08:32,880 --> 00:08:39,790
+فئة الأربعة cent. طيب، لو قلنا ثمانية عشر، كل ما ستفعلونه، ثمانية عشر، n
+
+105
+00:08:39,790 --> 00:08:44,530
+plus 1 تكافئ
+
+106
+00:08:44,530 --> 00:08:49,350
+اللي قبلها، الأربعة، اللي هي n minus 3، minus 3.
+
+107
+00:08:49,350 --> 00:08:55,980
+بالنسبة للثمانية عشر، نقص أربعة، يعني تمثل الأربعة عشر. طب
+
+108
+00:08:55,980 --> 00:08:59,240
+الأربعة عشر، إحنا أثبتناها، just now، كانت بتساوي عبارة
+
+109
+00:08:59,240 --> 00:09:06,020
+عن واحد في أربعة سنت زائد اثنين في خمسة سنت. فكل
+
+110
+00:09:06,020 --> 00:09:09,720
+اللي هنعمل، من الطوابع، هتصير اثنين في أربعة سنت
+
+111
+00:09:09,720 --> 00:09:19,400
+زائد اثنين في خمسة سنت. فكل n plus واحد هتطرح منها
+
+112
+00:09:19,400 --> 00:09:25,980
+أربعة، هتكون تمثل الأربعة عشر قبلها. طب، لو قلنا خمسة
+
+113
+00:09:25,980 --> 00:09:31,380
+وخمسين، بس عشان نوضح ليش هي second principle،
+
+114
+00:09:31,380 --> 00:09:35,320
+second principle، لازم تثبت كل اللي قبله، صح؟ لازم
+
+115
+00:09:35,320 --> 00:09:39,480
+نثبت كل اللي قبله، لعند ما نصل للـ base case.
+
+116
+00:09:39,480 --> 00:09:45,820
+فالأربعة وأربعين هذه تكافئ إيش؟ زائد أربعة stamp،
+
+117
+00:09:45,820 --> 00:09:51,540
+قيمتها أربعة سنت. الواحد وخمسين تكافئ برضه، نزيد
+
+118
+00:09:51,540 --> 00:09:59,700
+أربعة. سبعة وأربعين تكافئ ثلاثة وأربعين تكافئ، و
+
+119
+00:09:59,700 --> 00:10:05,360
+هكذا، لعندما تصلوا لوحدة من... من الأربع قيم بتاعتنا.
+
+120
+00:10:05,360 --> 00:10:11,960
+هتصلوا لأربع قيم، أكيد، جدد، القيم اللي هتصلوها، كيف
+
+121
+00:10:11,960 --> 00:10:18,000
+مثلناها؟ زائد عدد الأربعات، الفروق، زائد عدد الأربعات
+
+122
+00:10:18,000 --> 00:10:22,480
+اللي أنتم عملتُهم ك... كفروق... كفروق عندكم. okay،
+
+123
+00:10:22,480 --> 00:10:26,780
+فلاحظوا
+
+124
+00:10:26,780 --> 00:10:29,660
+إنه فعلا إحنا بنتكلم هنا عن second principle، على
+
+125
+00:10:29,660 --> 00:10:36,100
+أساس أثبت إنه فعلا n plus واحد، أو P of n plus واحد
+
+126
+00:10:36,100 --> 00:10:41,470
+is true for all numbers أكبر من اثنا عشر، لكل الأرقام التي
+
+127
+00:10:41,470 --> 00:10:46,690
+أكبر من اثنا عشر. ليست لديها قيمة، هذه قيمة، لو قلنا حتى الـ
+
+128
+00:10:46,690 --> 00:10:51,590
+خمسة وخمسين، نقدر نمثلها من الـ base cases اللي موجودة عندنا،
+
+129
+00:10:51,590 --> 00:10:54,610
+من الأربع base cases اللي موجودين عندنا. ففي الحالة
+
+130
+00:10:54,610 --> 00:10:59,660
+هذه، لو أثبتنا عند الخمسة وخمسين، معناته كل اللي أقل
+
+131
+00:10:59,660 --> 00:11:02,900
+من الخمسة وخمسين تم إثباته مسبقا، قبل ما أصل لخمسة
+
+132
+00:11:02,900 --> 00:11:05,800
+وخمسين. صحيح؟ لحظة، إن إحنا عشان نثبت أن الخمسة و
+
+133
+00:11:05,800 --> 00:11:10,560
+خمسين، بقدر أجيبها من أربعة وخمسة cent، لازم أثبت
+
+134
+00:11:10,560 --> 00:11:14,440
+كل اللي قبلها، لما نصل مين؟ للـ base case. فإذا أنا
+
+135
+00:11:14,440 --> 00:11:17,020
+بتكلم عن second principle فعلا، مش مجرد اللي قبله،
+
+136
+00:11:17,020 --> 00:11:20,780
+فقط، كل اللي قبله لازم يكونوا is true، كل اللي
+
+137
+00:11:20,780 --> 00:11:24,830
+قبله لازم يكونوا is true. Okay، كان هذا المثال
+
+138
+00:11:24,830 --> 00:11:32,670
+المتبقي هنا من المرة اللي فاتت، نكمل.
+
+139
+00:11:32,670 --> 00:11:36,590
+ماقدرش أقول إن إحنا هندخل على موضوع جديد، لأنه هو
+
+140
+00:11:36,590 --> 00:11:39,870
+تكميل له، وبالعكس، هنرجع نشتغل على inductive فيه،
+
+141
+00:11:39,870 --> 00:11:43,710
+اللي هو عمل الـ recursion. فـ inductive، لما بقول بدي
+
+142
+00:11:43,710 --> 00:11:49,030
+أثبت P of N من P of N minus 1، P of N minus 1، بدي
+
+143
+00:11:49,030 --> 00:11:52,900
+أثبتها من P of N minus 2. لاحظوا إن إحنا بنعمل تكرار،
+
+144
+00:11:52,900 --> 00:11:57,080
+جاعدين بنعمل عملية تكرار لعملية الـ proof نفسها.
+
+145
+00:11:57,080 --> 00:12:00,820
+فإذا هذه بتقودنا لحاجة اسمها recursion، عملية
+
+146
+00:12:00,820 --> 00:12:04,260
+التكرار، عملية التكرار. فهي مبنية على بعض، ماقدرش
+
+147
+00:12:04,260 --> 00:12:07,580
+أقول إن الموضوعين مفصولين عن بعض، الاثنين related
+
+148
+00:12:07,580 --> 00:12:10,560
+لبعض. الحقيقة، الاثنين الموضوعين related لبعض. فالـ
+
+149
+00:12:10,560 --> 00:12:13,560
+recursion هي in general إن أنا بعمل generation أو
+
+150
+00:12:13,560 --> 00:12:20,310
+بعمل... بعمل definition لـ object أو term منه نفسه، لما
+
+151
+00:12:20,310 --> 00:12:22,590
+بقول بده أعمل تعريف لمجموعة الـ elements داخل
+
+152
+00:12:22,590 --> 00:12:25,330
+sequence معين، بعملها من نفس الـ sequence، من
+
+153
+00:12:25,330 --> 00:12:28,570
+elements موجودة في الـ sequence نفسه، من elements
+
+154
+00:12:28,570 --> 00:12:32,410
+موجودة داخل نفس الـ sequence، هي هي نفسها. فإذا، إما
+
+155
+00:12:32,410 --> 00:12:36,220
+إن بعملها definition، هذا الـ object منه نفسه، أو من
+
+156
+00:12:36,220 --> 00:12:39,740
+جزء منه، أو من جزء من جزء منه. فأنتم لاحظوا هنا، لما
+
+157
+00:12:39,740 --> 00:12:44,340
+بتتكلموا عن الـ... الـ postage، كنتوا من جزء من القيم
+
+158
+00:12:44,340 --> 00:12:49,100
+السابقة اللي ممكن أثبتها باستخدام أربعة أو خمسة
+
+159
+00:12:49,100 --> 00:12:55,590
+cent stamps، أربعة أو خمسة cent stamps. okay، بحيث إن
+
+160
+00:12:55,590 --> 00:13:00,930
+أنا، الـ inductive proof هو أحد الصور الواضحة جدا
+
+161
+00:13:00,930 --> 00:13:03,270
+لعملية الـ recursion، أحد الصور الواضحة جدا لعملية
+
+162
+00:13:03,270 --> 00:13:06,350
+الـ recursion. ليش؟ لأن أنا بأثبت P of N plus
+
+163
+00:13:06,350 --> 00:13:12,330
+واحد recursively، من P of N، بشكل متكرر، من P of N.
+
+164
+00:13:12,330 --> 00:13:16,690
+إذا أثبتنا P of N، automatically P of N plus
+
+165
+00:13:16,690 --> 00:13:21,450
+واحد is true. إذا أثبتت P of N plus 1 is true، بقدر
+
+166
+00:13:21,450 --> 00:13:26,190
+أثبت منها P of N plus 2، بنقدر نثبت منها plus 3،
+
+167
+00:13:26,190 --> 00:13:31,190
+plus 4. فهذه عملية الـ recursion أو الـ recursively
+
+168
+00:13:31,190 --> 00:13:36,330
+proof. في الحالة هذه بنقدر نقول كلمة recursive على
+
+169
+00:13:36,330 --> 0
+
+223
+00:17:42,230 --> 00:17:48,490
+n ناقص واحد في 2 to the power of one، ال base واحد
+
+224
+00:17:48,490 --> 00:17:52,990
+نفس ال base، فهذه اتنين، ومجموع ال powers مجموع ال
+
+225
+00:17:52,990 --> 00:17:56,870
+powers، ف 3 to the power of n، ف a of n، 2 to the
+
+226
+00:17:56,870 --> 00:18:01,410
+power of n، مظبوط. نفس ال condition، فبنبدأ نعرف ال a
+
+227
+00:18:01,410 --> 00:18:05,570
+node ال initial بتاعتنا، initial بتاعتنا عند zero
+
+228
+00:18:05,570 --> 00:18:10,710
+two to the power zero، ف a zero بيساوي واحد، for n
+
+229
+00:18:10,710 --> 00:18:15,770
+أكبر منه، يساوي صفر. let a n بتساوي a n minus one في
+
+230
+00:18:15,770 --> 00:18:20,290
+اتنين في اتنين، فبقدر أكون مثلته بالعنصر اللي جابله
+
+231
+00:18:20,290 --> 00:18:24,310
+بالعنصر أو ال element السابق، بال element السابق له
+
+232
+00:18:24,310 --> 00:18:27,150
+okay، هذا مثال، ناخد كمان مثال
+
+233
+00:18:36,040 --> 00:18:38,620
+نبدأ بالإنشيال، الإنشيال زي ما قلنا بالمبادرة
+
+234
+00:18:38,620 --> 00:18:44,140
+بالزيرو، f of zero اتانية given، تلاتة، طيب لاتكفي
+
+235
+00:18:44,140 --> 00:18:48,880
+لحالها، محتاج ال initial elements، هو يعطيني element
+
+236
+00:18:48,880 --> 00:18:51,020
+واحد من ال initial elements، من ال initial elements
+
+237
+00:18:51,020 --> 00:18:56,620
+أو القيم المعروفة مسبقًا، f of zero بتساوي تلاتة
+
+238
+00:18:56,620 --> 00:19:02,590
+محتاج ال rule لسه، كيف أربط f of n ب f of n minus
+
+239
+00:19:02,590 --> 00:19:07,290
+واحد؟ برضه أعطاني ال rule تبعته، for all، for all n
+
+240
+00:19:07,290 --> 00:19:10,950
+belong to natural number، let f of n plus واحد تساوي
+
+241
+00:19:10,950 --> 00:19:16,590
+اثنين في f of n، زي التلاتة، هل واجد بقدر أجيب كل ال
+
+242
+00:19:16,590 --> 00:19:19,210
+sequence تبعه؟ نقدر نجيب حاليًا، مدام صار عند ال
+
+243
+00:19:19,210 --> 00:19:23,130
+rule وعند ال initial، كله بتجيبه بعدين، أي element
+
+244
+00:19:23,130 --> 00:19:26,610
+بتحكيه، بتقدر تجيبه، تقدروا تجيبوه، خلينا نقول f of
+
+245
+00:19:26,610 --> 00:19:27,950
+واحد، كده هتساوي
+
+246
+00:19:33,170 --> 00:19:38,690
+عودوا هنا، zero بالظبط، فتلاتة
+
+247
+00:19:38,690 --> 00:19:42,090
+في الست... تلاتة في اتنين ستة، زائد تلاتة تسعة، تسعة
+
+248
+00:19:42,090 --> 00:19:50,690
+okay، طيب F of اتنين، واحد
+
+249
+00:19:50,690 --> 00:19:55,590
+وعشرين، طيب التالت، F of three، واحد وعشرين في اتنين
+
+250
+00:19:55,590 --> 00:19:58,890
+اثنين وأربعين، زائد تلاتة، خمسة وأربعين، طيب خمسة
+
+251
+00:19:58,890 --> 00:20:03,650
+وأربعين في اتنين، تسعين، زائد تلاتة، تلاتة وتسعين. Okay
+
+252
+00:20:03,650 --> 00:20:06,930
+فكل element بيجيب ال element اللي وراه، كل element
+
+253
+00:20:06,930 --> 00:20:18,390
+بيجيب ال element اللي وراه. Okay
+
+254
+00:20:18,390 --> 00:20:24,270
+نكمل برضه ال factorial، ال factorial بنقدر نمثلها ك
+
+255
+00:20:24,270 --> 00:20:28,790
+multiplication، ك multiplication، فلما بقول n
+
+256
+00:20:28,790 --> 00:20:35,550
+factorial، هي عبارة عن multiplication ل i from 1 to
+
+257
+00:20:35,550 --> 00:20:41,110
+n، كيف؟
+
+258
+00:20:41,110 --> 00:20:44,970
+نقدر نمثلها ببساطة جدًا، عشان نمثلها، معناه أن أنا
+
+259
+00:20:44,970 --> 00:20:50,100
+بدي أعرفها، مش to n، to n minus one، to n minus one، ف
+
+260
+00:20:50,100 --> 00:20:55,640
+n factorial تساوي n minus one factorial... إيش
+
+261
+00:20:55,640 --> 00:21:01,020
+الفرق اللي بينهم؟ أن هي مضروبة في n، فهي ال
+
+262
+00:21:01,020 --> 00:21:05,060
+recursive form
+
+263
+00:21:05,060 --> 00:21:09,920
+أو ال rule بتاعتنا، okay، فال base case بتاعتنا، f of
+
+264
+00:21:09,920 --> 00:21:14,760
+zero، عند ال zero factorial، zero factorial واحد
+
+265
+00:21:14,760 --> 00:21:18,360
+طيب ال recursive part اللي هو ال rule اللي بدنا
+
+266
+00:21:18,360 --> 00:21:23,640
+نستخدمها، ب F of N equivalent to N مضروبة في F of N
+
+267
+00:21:23,640 --> 00:21:28,100
+minus واحد، F of N minus واحد، فمعطينا هاي العنصر
+
+268
+00:21:28,100 --> 00:21:31,660
+الأول، والثاني، والثالث، بعد العنصر zero، بعد zero
+
+269
+00:21:31,660 --> 00:21:37,020
+فهنا واحد factorial بواحد، طيب هنا اتنين factorial
+
+270
+00:21:37,020 --> 00:21:41,080
+باتنين، بس أنا عارف أنه هاد عبارة عن إيش؟ اتنين في
+
+271
+00:21:41,080 --> 00:21:45,760
+واحد factorial، واحد factorial، هنا عارفين أنه هاد
+
+272
+00:21:45,760 --> 00:21:50,860
+عبارة عن تلاتة في اتنين factorial، من العنصر اللي
+
+273
+00:21:50,860 --> 00:21:54,360
+جابلها، من العنصر اللي جابلها، بيمكننا نجيبها، طيب
+
+274
+00:21:54,360 --> 00:21:57,760
+شوية easy examples، مول easy examples، شوية examples
+
+275
+00:21:57,760 --> 00:22:07,990
+بسيطة، ممكن نتكلم فيها بسرعة. لو قلنا a في n، طيب،
+
+276
+00:22:07,990 --> 00:22:15,070
+بتجيبها في دلالة n-1، فبتكون عبارة عن إيش؟ a في n-1
+
+277
+00:22:15,070 --> 00:22:24,410
+زائد a، زائد a، خدوا ال a مشترك، بتبقى a-1 زائد 1
+
+278
+00:22:24,410 --> 00:22:34,370
+فصرت في إيش؟ في a في n. Okay، طيب a to the power n
+
+279
+00:22:34,370 --> 00:22:40,590
+بده تصير a to the power n minus واحد، إيش ال term
+
+280
+00:22:40,590 --> 00:22:44,950
+اللي بدي أجمعه، وأضربه، وأقسمه؟ في a، في a، على
+
+281
+00:22:44,950 --> 00:22:48,070
+اعتبار أنه a عبارة عن to the power واحد، عبارة عن
+
+282
+00:22:48,070 --> 00:22:55,410
+to the power واحد. okay، summation، summation
+
+283
+00:22:55,410 --> 00:22:59,810
+من zero to n، بده أمثلها بإيش؟ summation to n minus
+
+284
+00:22:59,810 --> 00:23:04,780
+واحد. طب إيش اللي دلالة An؟ نفسها، آخر element اللي
+
+285
+00:23:04,780 --> 00:23:11,020
+ما انجمعش معها، ال multiplication، ال factorial اللي كنا
+
+286
+00:23:11,020 --> 00:23:13,740
+نتكلم عنه، نفس ال factorial اللي كنا نتكلم عنه، ال
+
+287
+00:23:13,740 --> 00:23:18,460
+intersection، عشان
+
+288
+00:23:18,460 --> 00:23:24,510
+نجيبها بدلالة to n-1، إيش هتساوي؟ Intersection من 0
+
+289
+00:23:24,510 --> 00:23:28,510
+ل N-1، من Intersection من N؟ Intersection زائد N
+
+290
+00:23:28,510 --> 00:23:33,050
+فإذا هنا كأنها صارت ال intersection الكبيرة، زي ال
+
+291
+00:23:33,050 --> 00:23:42,290
+summation من 0 to N-1، Intersection صغيرة مع A N، أو
+
+292
+00:23:42,290 --> 00:23:51,310
+مع S، هنا معرفين احنا لل S، S، S N، لل S N، تمام؟ okay
+
+293
+00:23:54,340 --> 00:23:58,440
+هي مجموعة examples بسيطة، سهلة، مش فيها كتير مشاكل
+
+294
+00:23:58,440 --> 00:24:02,520
+okay، Fibonacci series، واحدة من ال series برضه اللي
+
+295
+00:24:02,520 --> 00:24:07,140
+هنشتغل عليها كتير، اللي هي ال Fibonacci series، برضه
+
+296
+00:24:07,140 --> 00:24:13,200
+من ال series اللي بتعرف بال previous terms بتاعتها
+
+297
+00:24:13,200 --> 00:24:17,480
+بال terms السابقة لها، بس هنا بنعرفهاش term واحد
+
+298
+00:24:17,480 --> 00:24:22,890
+سابق، بنعرفه two terms، two terms سابقين لها، فلما
+
+299
+00:24:22,890 --> 00:24:28,630
+نقول Fibonacci series، FF of N، هو N أكبر من أو
+
+300
+00:24:28,630 --> 00:24:34,590
+يساوي صفر، من السيريز المشهورة جدًا، بتعرف كتالة، F of
+
+301
+00:24:34,590 --> 00:24:41,470
+0 equal to 0، F of 1 equal to 1، طب F of N أو أكثر
+
+302
+00:24:41,470 --> 00:24:47,190
+بتعرف ك F of N minus 1 plus F of N minus 2، ال two
+
+303
+00:24:47,190 --> 00:24:49,490
+elements اللي جابلتها، مجموعة ال two elements اللي
+
+304
+00:24:49,490 --> 00:24:52,250
+جابلتها، فكل element بيساوي ال two elements اللي
+
+305
+00:24:52,250 --> 00:24:57,060
+جابله، فلو قلنا صفر وواحد، هاي two initials، دعونا
+
+306
+00:24:57,060 --> 00:25:02,580
+مجموحهم، بيجيبولي ال element اللي بعدهم، هنا ال
+
+307
+00:25:02,580 --> 00:25:06,080
+element صفر، ال element الأول، مجموحهم هيساوي ال
+
+308
+00:25:06,080 --> 00:25:11,020
+element التاني واحد، طيب التاني أو الأول مع التاني
+
+309
+00:25:11,020 --> 00:25:16,020
+هيعطينا تلاتة، اتنين، طيب التاني مع التالت هيعطينا
+
+310
+00:25:16,020 --> 00:25:19,740
+الرابع، فإذا واحد زائد اتنين بيساوي تلاتة، تلاتة
+
+311
+00:25:19,740 --> 00:25:22,460
+زائد اتنين بيساوي خمسة، تلاتة زائد خمسة بيساوي
+
+312
+00:25:22,460 --> 00:25:26,100
+ثمانية، ثمانية زائد خمسة بيساوي تلاتاشر، تلاتاشر زائد
+
+313
+00:25:26,100 --> 00:25:29,200
+ثمانية بيساوي واحد وعشرين، وهكذا، بتبقى لكم كاملين
+
+314
+00:25:29,200 --> 00:25:33,980
+هاي ال series، طبعًا واضح أنها بتزيد، كل ما زادت قيمة
+
+315
+00:25:33,980 --> 00:25:38,620
+n، كل ما زادت قيمة n بتزيد، هذه واحدة من النماذج
+
+316
+00:25:38,620 --> 00:25:41,500
+لمين؟ لل recursive
+
+317
+00:25:46,470 --> 00:25:49,810
+Okay، ناخد Inductive Proof، لحظوا هنا رجعنا ل
+
+318
+00:25:49,810 --> 00:25:52,410
+Inductive، لأن هم أصلا الموضوعين مترابطين جدًا، فبعض
+
+319
+00:25:52,410 --> 00:25:55,110
+ما بقدرش أقول أن هذا موضوع غير ال Inductive، هم
+
+320
+00:25:55,110 --> 00:25:59,210
+الاثنين نفس الموضوع أساسًا، ففي theorem about
+
+321
+00:25:59,210 --> 00:26:02,870
+Fibonacci Series، بدنا نثبتها باستخدام ال Inductive
+
+322
+00:26:02,870 --> 00:26:09,180
+و تحديدا ال second principle of induction، فهنقول f
+
+323
+00:26:09,180 --> 00:26:14,580
+of n أقل من 2 to the power of n، أو f of n أقل من 2
+
+324
+00:26:14,580 --> 00:26:17,560
+to the power of n، هل فعلاً هذا الكلام حقيقي لكل ال
+
+325
+00:26:17,560 --> 00:26:21,120
+elements في Fibonacci Series؟ Fibonacci Series، خلاص احنا
+
+326
+00:26:21,120 --> 00:26:28,060
+عارفين أن هي صفر، واحد، واحد، اتنين، تلاتة، خمسة، ثمانية،
+
+327
+00:26:28,060 --> 00:26:32,080
+تلاتاشر، واحد وعشرين، وهكذا، هل ال elements هذه فعلاً
+
+328
+00:26:32,080 --> 00:26:34,860
+دائمًا هتكون أقل من two to the power of the element
+
+329
+00:26:35,950 --> 00:26:39,030
+بدنا نشوف، هنبدأ بال إيش؟ بال base case، ال base
+
+330
+00:26:39,030 --> 00:26:42,150
+case، طبعًا ال two cases الحقيقة هيكون عندنا اللي هو
+
+331
+00:26:42,150 --> 00:26:45,250
+ال F0 وال F1، هدول دائمًا ال initial بتاعهم، ليش؟
+
+332
+00:26:45,250 --> 00:26:48,170
+لأن أنا محتاجهم عشان أجيب اللي وراهم، محتاجهم
+
+333
+00:26:48,170 --> 00:26:54,570
+أجيب العنصر الثالث بعدهم، ف F of 0، 0 أقل من 2 to the power of
+
+334
+00:26:54,570 --> 00:26:59,420
+zero، فإذا ال condition الأول اتحقق، طيب التاني ال
+
+335
+00:26:59,420 --> 00:27:03,420
+F1 بتساوي واحد، أقل من two to the power
+
+336
+00:27:03,420 --> 00:27:07,440
+واحد، ليش؟ لأن قيمتها باتنين، فالواحد أقل، أقل من اتنين
+
+337
+00:27:07,440 --> 00:27:12,920
+okay، اتحقق الثاني، خلصنا ال base cases، ال inductive
+
+338
+00:27:12,920 --> 00:27:17,280
+ال inductive، نكتب ال rule نفسها، فطبعًا احنا Fibonacci
+
+339
+00:27:17,280 --> 00:27:20,760
+خلاص عرفنا ال rule بتاعتها، فبنادش، عرفنا ال rule، FN
+
+340
+00:27:20,760 --> 00:27:25,060
+بتساوي FN minus واحد زائد FN minus اتنين، كتبناها
+
+341
+00:27:26,340 --> 00:27:32,100
+Okay، هنا هنقول عشان أثبت ال... وين راحت... لكل قيم
+
+342
+00:27:32,100 --> 00:27:41,240
+K أقل من N، is true، أقل من N، is true، عشان أجيب FN
+
+343
+00:27:41,240 --> 00:27:44,880
+طيب إيش يعني true؟ ال true معناته أن هي محقق
+
+344
+00:27:44,880 --> 00:27:49,360
+النظرية، ال theory هذه، فإذا كانت فعلاً احنا K أقل من
+
+345
+00:27:49,360 --> 00:27:54,220
+n، فإذا fk أقل من 2 to the power of k، 2 to the
+
+346
+00:27:54,220 --> 00:27:57,360
+power of k، هي الحقيقة ال theorem تبعتها، طيب نيجي نصل
+
+347
+00:27:57,360 --> 00:28:05,360
+إلى ال fn، fn بتساوي fn-1 plus fn-2، n-1 بتنطبق على ال
+
+348
+00:28:05,360 --> 00:28:11,230
+k هذه، لأنه أقل من n، فإذا بقدر أمثلها بإيش؟ two to
+
+349
+00:28:11,230 --> 00:28:15,330
+the power of the term، 2 to the power of n-1، طيب
+
+350
+00:28:15,330 --> 00:28:20,250
+plus، if n-2، 2 to the power of n-2، هل وجد هذا ال
+
+351
+00:28:20,250 --> 00:28:28,150
+term كله بدنا نجيبه بدلالة n، مش n-1، عشان نشوف هل
+
+352
+00:28:28,150 --> 00:28:31,350
+فعلاً أقل منه؟ يمكن يطلع أكبر منه، يمكن يطلع بيساوي، مش
+
+353
+00:28:31,350 --> 00:28:35,290
+عارفين، نشوفه، هل فعلاً بحقيقة لأ ال condition هذه، أو
+
+354
+00:28:35,290 --> 00:28:40,520
+لأ، أولًا بدنا نوحد ال two terms هاتول، بدنا نوحد
+
+355
+00:28:40,520 --> 00:28:42,360
+ال two terms، بس خدوا بالكوا، بتكونوا توحدوا الـ
+
+356
+00:28:42,360 --> 00:28:46,700
+two terms، في سبيل أن ال inequality هذه، عدم
+
+357
+00:28:46,700 --> 00:28:51,160
+المساواة هذه، اللي هي أقل من، ما تتغيرش، في سبيل
+
+358
+00:28:51,160 --> 00:28:55,760
+أنها ما تتغيرش، لو بدنا نغير ل N minus two، يعني
+
+359
+00:28:55,760 --> 00:28:58,940
+هذا بدنا نحطه، نقول والله two to the power of N
+
+360
+00:28:58,940 --> 00:29:04,070
+minus two، أنا كبرتها ولا صغرتها؟ صغرتها، صغرناها،
+
+361
+00:29:04,070 --> 00:29:08,890
+فإذا بصير في خوف عليها، الأقل منها دي، ممكن تنجلب،
+
+362
+00:29:08,890 --> 00:29:13,670
+ممكن تكون عكسها، فلأ بلاش من هذه، بنشتغل على مين؟
+
+363
+00:29:13,670 --> 00:29:17,690
+على تحويل two to the power n minus two، ل two to
+
+364
+00:29:17,690 --> 00:29:21,230
+the power n minus one، مين أكبر منهم من التانية؟
+
+365
+00:29:23,420 --> 00:29:27,980
+فإذن بمجرد أن أنا استبدلت هذه بقيمة أكبر منها، أنا
+
+366
+00:29:27,980 --> 00:29:31,420
+محافظ على أكبر منها، بالعكس، زودت ال inequality هذه
+
+367
+00:29:31,420 --> 00:29:35,580
+زودت ال inequality، عدم المساواة، زودتها، فأنا بالعكس
+
+368
+00:29:35,580 --> 00:29:41,040
+أكبر من ال term ده، أكبر من if، إن ما زالت مضمونة
+
+369
+00:29:41,040 --> 00:29:44,230
+بالعكس حتى زودناها، ال inequality اللي بينهم، فصارت
+
+370
+00:29:44,230 --> 00:29:46,650
+two to the power of n minus one، plus two to the
+
+371
+00:29:46,650 --> 00:29:49,790
+power of n minus one، هدول بجمعهم، بقدر أجيبها
+
+372
+00:29:49,790 --> 00:29:53,510
+بدلالة n، على اعتبار أن هنا two to the power of n
+
+373
+00:29:53,510 --> 00:29:56,930
+minus one، مضروبة في اتنين، ممكن أكررها مرتين، هيها
+
+374
+00:29:56,930 --> 00:30:00,250
+طب هذه عبارة عن two to the power of one، to the
+
+375
+00:30:00,250 --> 00:30:03,790
+power of one، to the power of one، بتصير two to the
+
+376
+00:30:03,790 --> 00:30:08,190
+power of n minus one plus one، صارت إيه؟ two to the
+
+377
+00:30:08,190 --> 00:30:12,160
+power of n، 2 to the power n، فإذا النتيجة في النهاية
+
+378
+00:30:12,160 --> 00:30:20,960
+أن f of n أقل من 2 to the power n، أقل من 2 to the
+
+379
+00:30:20,960 --> 00:30:23,280
+power n، طب ما هو نفس ال theorem، فعلاً مطلوب أثبتها
+
+380
+00:30:23,280 --> 00:30:28,260
+هي نفس ال theorem المطلوب أثبتها، تمام، هذا باستخدام
+
+381
+00:30:28,260 --> 00:30:31,880
+... باستخدام إيش؟ ال inductive، باستخدام إيش؟ ال
+
+382
+00:30:31,880 --> 00:30:32,360
+inductive
+
+383
+00:30:42,780 --> 00:30:48,880
+Okay، في theorem ل Lame، أو Lame's theorem، واضح من
+
+384
+00:30:48,880 --> 00:30:53,400
+اسمه، فرنسي، واضح من الاسم أنه فرنسي
+
+385
+00:30:56,420 --> 00:31:00,740
+فبوناتشي إيطالي، طبعًا، حتى اسمه باين، فبوناتشي إيطالي
+
+386
+00:31:00,740 --> 00:31:06,180
+هنا متكلم علمي، عالم فرنسي، وجدلنا relation لواحدة
+
+387
+00:31:06,180 --> 00:31:11,060
+من ال algorithms اللي هي بطبيعتها recursive...
+
+388
+00:31:11,060 --> 00:31:14,340
+recursive algorithm، أهمها، واحنا أخدناها اللي هي
+
+389
+00:31:14,340 --> 00:31:17,450
+Euclid's algorithm، Euclid's algorithm، عشان نجيب
+
+390
+00:31:17,450 --> 00:31:20,290
+منها ال greatest common divisor، لو متذكرين كنا
+
+391
+00:31:20,
+
+445
+00:35:55,710 --> 00:36:01,310
+iterations أو عدد المراحل. الألغوريثم نفسه كم مرة
+
+446
+00:36:01,310 --> 00:36:07,800
+هتتكرر. عدد الـ iterations recursively defined sets
+
+447
+00:36:07,800 --> 00:36:11,280
+عملية الـ recursively أو التكرار في تعريف الـ sets
+
+448
+00:36:11,280 --> 00:36:16,880
+نبدأ الـ algorithm وهناخد examples، نبدأ نشتغل على
+
+449
+00:36:16,880 --> 00:36:20,860
+الـ set، هل فعلا ممكن نمثلها أو تمثل باستخدام
+
+450
+00:36:20,860 --> 00:36:26,600
+recursive بشكل recursively؟ آه، ممكن. ممكن، كيف ممكن؟
+
+451
+00:36:26,600 --> 00:36:30,120
+إذا كان حددنا small finite set of base elements of
+
+452
+00:36:30,120 --> 00:36:34,460
+S، إذا كان حددنا الـ elements، ويعني على الأقل رقم من
+
+453
+00:36:34,460 --> 00:36:38,880
+element small numbers أو small finite elements
+
+454
+00:36:38,880 --> 00:36:41,840
+مجموعة elements في الأول، على أساس أقدر أعمل منهم
+
+455
+00:36:41,840 --> 00:36:44,000
+generation للباقي. نقدر نعمل منهم generation ممكن
+
+456
+00:36:44,000 --> 00:36:47,420
+يكون element واحد، ممكن يكون اتنين، نقدر نعمل منهم
+
+457
+00:36:47,420 --> 00:36:51,280
+generation. طيب لو عرفنا مجموعة الـ elements small
+
+458
+00:36:51,280 --> 00:36:56,280
+finite set of elements، هل كافي؟ لأ، محتاج الـ rule
+
+459
+00:36:56,280 --> 00:36:59,940
+محتاج المعادلة اللي أعمل فيها generation، فمحتاج
+
+460
+00:36:59,940 --> 00:37:03,870
+rule of constructing new elements of S. إذا اتحقق
+
+461
+00:37:03,870 --> 00:37:07,510
+الشرط ده، بقدر أعرف الـ set بدون ما أضطر أحط
+
+462
+00:37:07,510 --> 00:37:10,450
+كل الـ elements، ساعتها بدون أن أضطر نحط كل الـ
+
+463
+00:37:10,450 --> 00:37:17,490
+elements بشكل منطقي وبشكل ضمني. S has no other
+
+464
+00:37:17,490 --> 00:37:21,530
+elements but these اللي بنقدر نعمله generation فقط
+
+465
+00:37:21,530 --> 00:37:24,030
+هم الـ elements. يعني ما تقولوش طب ما يمكن يكون في
+
+466
+00:37:24,030 --> 00:37:29,070
+elements تانية، لأ، مدام فيه rule، ففقط الـ elements
+
+467
+00:37:29,070 --> 00:37:32,630
+اللي belong to this set هي اللي تم عملية الـ
+
+468
+00:37:32,630 --> 00:37:35,670
+generation بتاعتها من الـ rule بتاعتنا فقط. لو يوجد
+
+469
+00:37:35,670 --> 00:37:39,470
+أي elements أخرى، for example، لو قولنا three belong
+
+470
+00:37:39,470 --> 00:37:46,020
+to set S، set S، وأعطاني معلومة واحدة أن التلاتة
+
+471
+00:37:46,020 --> 00:37:50,640
+belong to this set فقط، ما أعطانيش حاجة تانية، وبعدين
+
+472
+00:37:50,640 --> 00:37:56,420
+let x plus y belong to S، برضه مجموعة symbols، قالنا
+
+473
+00:37:56,420 --> 00:38:03,360
+أن two elements x و y belong to S. طيب if x و y
+
+474
+00:38:03,360 --> 00:38:08,420
+belong to، mean to S، فهنا بيعطيني إذن أن مجموعهم
+
+475
+00:38:08,420 --> 00:38:12,540
+belong to S، إذا كانوا الاتنين داخل S. إذا كانوا
+
+476
+00:38:12,540 --> 00:38:17,460
+الاثنين نفسهم داخل الـ set S. مطلوب مننا أن نجيب
+
+477
+00:38:17,460 --> 00:38:21,480
+الـ elements للـ set S first، لأن أنا عارف element الـ
+
+478
+00:38:21,480 --> 00:38:26,020
+element هذا، بعدين بتكلم عن set، ممكن يكون هو Y، هو X
+
+479
+00:38:26,020 --> 00:38:30,440
+في الـ set، ممكن يكون نفس الـ element، نفس الـ element
+
+480
+00:38:30,440 --> 00:38:37,120
+فإذا ممكن تكون تلاتة، تلاتة، تلاتة زائد تلاتة ستة
+
+481
+00:38:37,120 --> 00:38:42,600
+معناه ذلك أنه برضه الستة belong to S. طيب مدام 6
+
+482
+00:38:42,600 --> 00:38:48,180
+belong to S، طب ممكن تكون الـ X هي الـ 6، أو Y الـ 6، أو
+
+483
+00:38:48,180 --> 00:38:55,800
+الـ 2، فإذا ممكن تكون برضه 9، أو 12. طيب مدام صار في
+
+484
+00:38:55,800 --> 00:39:04,360
+عند الـ 6، و 9، و 12، طب ممكن تكون هذه 9 و 12، معناه
+
+485
+00:39:04,360 --> 00:39:09,120
+ذلك سوف أتحدث عن 21، طبعا بما في اللي بينهم كمان
+
+486
+00:39:09,790 --> 00:39:13,690
+18، تقول 16، فواضح أن احنا بنتكلم عن set
+
+487
+00:39:13,690 --> 00:39:17,990
+لمضاعفات الرقم تلاتة. بقدر أعمل أي generation لأي
+
+488
+00:39:17,990 --> 00:39:22,770
+رقم آخر غير مضاعفات التلاتة، ما فيش إمكانية، معناته
+
+489
+00:39:22,770 --> 00:39:26,270
+الـ set لا يمكن أن هي تكون تحتوي على أي element
+
+490
+00:39:26,270 --> 00:39:30,610
+باستثناء مضاعفات الرقم تلاتة، باستخدام مضاعفات رقم
+
+491
+00:39:30,610 --> 00:39:36,930
+تلاتة. okay
+
+492
+00:39:38,460 --> 00:39:41,660
+set of all strings. نحن نتكلم عن الـ strings، هالـ
+
+493
+00:39:41,660 --> 00:39:44,500
+هالـ recursive اللي بقدر أمثلها، آه، بنقدر نمثلها
+
+494
+00:39:44,500 --> 00:39:49,100
+بشكل recursive. كيف؟ ناخد بس بقى من two symbols
+
+495
+00:39:49,100 --> 00:39:53,760
+هالـ، هنشتغل عليه، أو من علامتين هناخدهم، أو
+
+496
+00:39:53,760 --> 00:39:57,820
+notation. الـ notation الأولى اللي هي الـ sigma big
+
+497
+00:39:57,820 --> 00:40:01,780
+sigma، الـ big sigma، وفي notation تانية اللي هي big
+
+498
+00:40:01,780 --> 00:40:05,840
+sigma star. إيش هذه؟ وإيش هذه؟ في فرق شاسع بين
+
+499
+00:40:05,840 --> 00:40:09,340
+الاثنين. كتبت لكم الفرق اللي هي تحت، اكتبوا الفرق تحت
+
+500
+00:40:09,340 --> 00:40:12,260
+عشان تبقوا متذكرينه. يمكن أقول المحاضرة، وبعدين
+
+501
+00:40:12,260 --> 00:40:16,780
+تنسوهم بكرة، بعد وتكونوا نسيتوهم، لأنه كتير بضخامة
+
+502
+00:40:16,780 --> 00:40:24,360
+فـ الـ sigma لحالها هي set of symbols، set of
+
+503
+00:40:24,360 --> 00:40:29,660
+alphabet، بس، معناته الـ elements، الـ elements هذه عبارة
+
+504
+00:40:29,660 --> 00:40:35,440
+عن إيش؟ الـ alphabet أو symbols، element by element
+
+505
+00:40:35,440 --> 00:40:42,280
+طيب، الـ sigma star، set of strings، strings، الـ string
+
+506
+00:40:42,280 --> 00:40:45,860
+ممكن يكون له أطوال مختلفة. فلو اتكلمنا مثلا، والله
+
+507
+00:40:45,860 --> 00:40:49,280
+أن الـ alphabet هي مجموعة الـ symbols بتاعتنا، لما
+
+508
+00:40:49,280 --> 00:40:52,660
+بقول الـ universe of discourse بتاعتنا، alphabet
+
+509
+00:40:52,660 --> 00:40:55,840
+معناته الـ sigma star بكل بساطة ممكن تكون الـ
+
+510
+00:40:55,840 --> 00:41:02,500
+dictionary كله، كل كلمة string، صح؟ فإذا لما أقول
+
+511
+00:41:04,250 --> 00:41:12,090
+Sigma to the power تلاتة مثلا، ممكن تكون
+
+512
+00:41:12,090 --> 00:41:19,830
+في كلمات كتير طولها تلاتة، bad، the، boy، صحيح؟ كل
+
+513
+00:41:19,830 --> 00:41:23,810
+الكلمات اللي طولها تلاتة. طيب لما أقول star، مش محدد
+
+514
+00:41:23,810 --> 00:41:27,590
+الطول، معناه ذلك أن كل الكلمات الممكنة، كل الكلمات
+
+515
+00:41:27,590 --> 00:41:33,340
+إيش الممكنة؟ لاحظوا في sigma هذه، لأ، الـ sigma هذه فقط
+
+516
+00:41:33,340 --> 00:41:37,200
+هم الـ 26 element بتاع الـ language بتاعتنا اللي هي
+
+517
+00:41:37,200 --> 00:41:42,620
+الـ letters بتاعتنا فقط، هي الـ alphabet فقط. فهذه غير
+
+518
+00:41:42,620 --> 00:41:46,940
+هذه. خذوا بالكم، الفرق شاسع جدا بينهم، شاسع شاسع
+
+519
+00:41:46,940 --> 00:41:50,500
+شاسع فعلا، هذه احنا بنتكلم عن alphabet elements أو
+
+520
+00:41:50,500 --> 00:41:54,660
+symbols، هناك بنتكلم عن strings، والـ strings هذه
+
+521
+00:41:54,660 --> 00:42:00,140
+أطوالها مختلفة. بدأتوا تلاحظوا star، star مش معروف
+
+522
+00:42:00,140 --> 00:42:04,950
+الطول. فإذا أطوال مختلفة تماما. خلينا نبدأ نحط
+
+523
+00:42:04,950 --> 00:42:09,530
+recursively شوية تعريفات هنا. لما نمشي نحط the set
+
+524
+00:42:09,530 --> 00:42:17,650
+sigma star of all strings over sigma. طب sigma الشيء
+
+525
+00:42:17,650 --> 00:42:21,530
+احنا قلنا اللي هي الـ alphabet. لما بقول over sigma
+
+526
+00:42:21,530 --> 00:42:24,470
+وكل strings اللي هي over sigma، معناته كل الكلمات
+
+527
+00:42:24,470 --> 00:42:28,430
+اللي بتتكون من الـ letters هذه. كل الكلمات اللي ممكن
+
+528
+00:42:28,430 --> 00:42:34,310
+تتكون من الـ letters. ممكن مثلا، ده لحظة، هذا لحالها
+
+529
+00:42:34,310 --> 00:42:39,370
+symbol، هاي كمان symbol، هاي كمان symbol، تلاتة مع
+
+530
+00:42:39,370 --> 00:42:45,910
+بعض، عملولي string، فهي صار عندنا string أو series
+
+531
+00:42:45,910 --> 00:42:52,360
+أو ما هي string أفضل من الـ symbols. أعطوني معنى
+
+532
+00:42:52,360 --> 00:42:57,320
+أعطوني معنى. okay، هدول belong to مين؟ to sigma star
+
+533
+00:42:57,320 --> 00:43:01,160
+to sigma star. طيب lambda اللي هي الـ empty string
+
+534
+00:43:01,160 --> 00:43:05,960
+هذه subset من أي string ممكنة من أي sigma star
+
+535
+00:43:05,960 --> 00:43:13,480
+ممكنة، لأنه هذه string، string هذه not belong لو
+
+536
+00:43:13,480 --> 00:43:19,920
+مافيش الـ star. ليش؟ لأنه sigma لحالها symbols مش
+
+537
+00:43:19,920 --> 00:43:26,060
+string، فـ not belong، ولكن لما بتكلم عن star، آه star
+
+538
+00:43:26,060 --> 00:43:30,300
+معناته string، مظبوط كلامها هيك، صح؟ تنطبق، بمشي لحالك
+
+539
+00:43:30,300 --> 00:43:35,220
+فإذا lambda belong to star sigma، على أساس أنه
+
+540
+00:43:35,220 --> 00:43:39,180
+lambda زي ما قلنا الـ empty string، okay، و belong to
+
+541
+00:43:39,180 --> 00:43:46,240
+sigma star. فإذا هذه ليست symbol، هذه string، واضحة؟
+
+542
+00:43:46,240 --> 00:43:51,080
+جدًا، طولها مش عارف، هذه string لأنها belong to مين؟
+
+543
+00:43:51,080 --> 00:43:57,960
+to sigma star. طيب، and x belong to sigma، فإذن هذه
+
+544
+00:43:57,960 --> 00:44:01,840
+symbol، هذه حرف الـ x، أنا بتكلم هنا عن الـ element
+
+545
+00:44:01,840 --> 00:44:08,320
+نفسه، element اسمه x، جدًا طوله واحد، هو واحد، هو نفسه
+
+546
+00:44:08,320 --> 00:44:12,500
+واحدة، مش ماشي string، هذا لحاله هو simple، هو لحاله
+
+547
+00:44:12,500 --> 00:44:18,060
+simple. كويس. فلما بقول concatenation لـ W مع X، أكيد
+
+548
+00:44:18,060 --> 00:44:22,420
+belong to Sigma Star، لأن أنا مش عارف جدًا الـ W، فكل
+
+549
+00:44:22,420 --> 00:44:25,140
+اللي بقدر أقوله إن الـ string هذا كله على بعضه الـ
+
+550
+00:44:25,140 --> 00:44:33,160
+concatenated string، عبارة عن طول W زائد واحد الـ X
+
+551
+00:44:33,160 --> 00:44:37,230
+أنا ضامنه واحد، خلاص ما فيش مشكلة، لأن هو element
+
+552
+00:44:37,230 --> 00:44:41,230
+واحد اللي انضاف، ولكن w أنا مش عارف، هي اتعرفت على
+
+553
+00:44:41,230 --> 00:44:45,490
+أساس أنها string، وما عرفليش طولها، ففي الآخر الطول
+
+554
+00:44:45,490 --> 00:44:50,250
+ككل، صار طول w زائد الواحد اللي هو j من x، بأعتبر أن
+
+555
+00:44:50,250 --> 00:44:54,770
+أنا عارف x belong لمين؟ belonging to alphabet، لـ
+
+556
+00:44:54,770 --> 00:45:03,020
+alphabet symbols. example، يمكن توضح معانا أكتر لو
+
+557
+00:45:03,020 --> 00:45:08,140
+قلنا if sigma لحالها، big sigma لحالها equal to
+
+558
+00:45:08,140 --> 00:45:12,100
+zero one، فهدول الـ symbols، هدول الـ symbols ساعتها
+
+559
+00:45:12,100 --> 00:45:17,140
+صفر واحد. okay، the strings found in sigma star over
+
+560
+00:45:17,140 --> 00:45:22,100
+the sigma. إيش sigma الـ star اللي ممكن أعملها
+
+561
+00:45:22,100 --> 00:45:27,250
+generation من sigma لحالها، of all bit strings، لكل
+
+562
+00:45:27,250 --> 00:45:29,070
+الـ bit strings اللي ممكن ناخدها من الـ two bits
+
+563
+00:45:29,070 --> 00:45:33,710
+هدول الـ symbols، هدول الـ two symbols فقط. أول حالة
+
+564
+00:45:33,710 --> 00:45:37,410
+اللي هي الـ lambda، أول واحدة lambda، ليش؟ لأن دي
+
+565
+00:45:37,410 --> 00:45:44,310
+اللي كنا هناك بنتكلم عن إيش؟ الـ star، كلام عن الـ
+
+566
+00:45:44,310 --> 00:45:49,030
+star هذه، عرفتوها خلاص، معرفة وانتهينا. صفر واحد بس
+
+567
+00:45:49,030 --> 00:45:51,690
+هاي الـ two symbols بتوعكم، ما فيش symbols تانية
+
+568
+00:45:51,690 --> 00:45:55,070
+ولكن لما بتكلم عن الـ strings، لأ، الـ strings ممكن
+
+569
+00:45:55,070 --> 00:46:00,050
+تكون empty، ممكن تكون الـ واحد، صفر، لحاله هو string
+
+570
+00:46:00,050 --> 00:46:04,710
+الـ string في element واحد، طيب، أو الـ واحد لحاله، أو
+
+571
+00:46:04,710 --> 00:46:09,670
+صفر، صفر، أو صفر واحد، أو واحد صفر، أو واحد واحد، أو أو
+
+572
+00:46:09,670 --> 00:46:13,070
+أو أو to infinity. إيش ممكن يكون في؟ أو كمان زيادة
+
+573
+00:46:13,070 --> 00:46:23,210
+أربعة، ثلاثة صفار، صفرين وواحد، صفر واحد صفر، مش محدد طول
+
+574
+00:46:23,210 --> 00:46:27,370
+الـ string، طول الـ string ممكن يكون أي شيء، ممكن يكون
+
+575
+00:46:27,370 --> 00:46:31,390
+أي شيء، فواضح.. واضحة الفرق بين الاتنين، الـ sigma
+
+576
+00:46:31,390 --> 00:46:34,350
+مختلف عن الـ sigma star. ما تلخبطوش بكرة فيهم في
+
+577
+00:46:34,350 --> 00:46:39,430
+الامتحانات، ما تلخبطوش فيهم في الامتحانات. واحدة
+
+578
+00:46:39,430 --> 00:46:43,330
+symbols، واحدة strings، واحدة strings ومش محددين الـ
+
+579
+00:46:43,330 --> 00:46:46,790
+string جدًا طوله، أهم شيء أن احنا مش محددين، مدام
+
+580
+00:46:46,790 --> 00:46:48,070
+حاطينها star
+
+581
+00:46:50,830 --> 00:46:54,010
+Okay، recursively برضه نقدر نعمل concatenation
+
+582
+00:46:54,010 --> 00:46:56,590
+عمليّة recursively، as a concatenation، لأن كل الـ
+
+583
+00:46:56,590 --> 00:46:59,570
+concatenation هو أساسًا أن احنا عملنا له generation
+
+584
+00:46:59,570 --> 00:47:04,030
+من two strands، من two strands، فممكن يكون two
+
+585
+00:47:04,030 --> 00:47:08,770
+strings، ممكن منهم أعمل generation لـ string تالت، هو
+
+586
+00:47:08,770 --> 00:47:11,650
+جاي من اللي جابلهم، جاي من اللي جابلهم، في الطريقة
+
+587
+00:47:11,650 --> 00:47:15,830
+recursively. ممكن نعرف الـ concatenation of strings
+
+588
+00:47:15,830 --> 00:47:23,730
+w1 و w2، هذه string جدًا طوله مش عارف، string جدًا
+
+589
+00:47:23,730 --> 00:47:27,810
+طوله برضه مش عارف. okay، الـ business بتاعتنا، if w
+
+590
+00:47:27,810 --> 00:47:33,980
+belong to sigma star، then w، الـ dot هذه معناته
+
+591
+00:47:33,980 --> 00:47:41,580
+concatenation. الـ lambda هي نفسها w، لأن أنت بتتكلم
+
+592
+00:47:41,580 --> 00:47:46,860
+عن empty string، where الـ lambda هنا عرفناها اللي
+
+593
+00:47:46,860 --> 00:47:53,180
+هي الـ empty string. الـ recursive ليش هنا اشتغلنا على
+
+594
+00:47:53,180 --> 00:47:58,080
+الـ lambda؟ لأن أقل lambda ممكنة، أقل string ممكنة للـ
+
+595
+00:47:58,080 --> 00:48:03,440
+W2 هي تكون lambda. طيب لأ، أكتر من lambda، معناه ذلك
+
+596
+00:48:03,440 --> 00:48:09,130
+أن W1 زي ما هي هي belong to sigma star، و W2 ليس
+
+597
+00:48:09,130 --> 00:48:13,250
+فارغًا، لأ، خلاص سيبنا الـ base case، في الـ inductive
+
+598
+00:48:13,250 --> 00:48:17,370
+case، أنه ممكن يكون هنا قيمة أكبر، يكون W2 belong to
+
+599
+00:48:17,370 --> 00:48:20,430
+برضه sigma star. مش هم عارفين هالـ sigma star في
+
+600
+00:48:20,430 --> 00:48:27,370
+الحالة هذه، and X belong to، هنا إيش؟ sigma بس، فأنا
+
+601
+00:48:27,370 --> 00:48:34,250
+هنا بتكلم عن X لحاله، element واحد فقط، then W في W2
+
+602
+00:48:34,250 --> 00:48:40,650
+X، كأنه بيعمل concatenation لـ W2 مع الـ X، فهيساوي له
+
+603
+00:48:40,650 --> 00:48:46,690
+نفس الطول لـ W2، زي 1 concatenation مع W1، هي نفسها
+
+604
+00:48:46,690 --> 00:48:50,990
+لو عملنا concatenation لـ W1 مع W2، والـ
+
+605
+00:48:50,990 --> 00:48:54,370
+concatenated string عملنا له concatenation كمان
+
+606
+00:48:54,370 --> 00:48:59,390
+مرة مع X لحالها، مع X، مع X لحالها، فهذا في الآخر كـ
+
+607
+00:48:59,390 --> 00:49:07,280
+length كامل هيساوي الـ length لأ w1 زائد الـ length
+
+608
+00:49:07,280 --> 00:49:14,220
+تبع w2 زائد واحد بالظبط، زائد واحد، تمام. فهي عملية
+
+609
+00:49:14,220 --> 00:49:18,080
+الـ concatenation، أساسًا أن احنا دايما بنحسبها من الـ
+
+610
+00:49:18,080 --> 00:49:20,720
+concatenated string اللي جابها من الـ concatenated
+
+611
+00:49:20,720 --> 00:49:25,680
+string اللي جابها. other easy string examples، لو
+
+612
+00:49:25,680 --> 00:49:28,900
+قولنا الـ length هنا.. هنا.. رجع يتكلم عن مين؟
+
+613
+00:49:28,900 --> 00:49:32,220
+عن الـ length لـ الـ strings، عن الـ length لـ الـ
+
+614
+00:49:32,220 --> 00:49:38,740
+strings. فالـ length L of W، of a string W، فأنا بتكلم
+
+615
+00:49:38,740 --> 
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8a7848d4429d629a05ce454dce1281bf23b63118
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2609, "start": 20.79, "end": 26.09, "text": "بسم الله الرحمن الرحيم والصلاة والسلام على أشرف الأنبياء والمسلمين سيدنا محمد الله عليه الصحة يا جماعة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 2304, 3794, 19528, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 21984, 6225, 20292, 3224, 31767, 5016, 3660, 35186, 10874, 15042, 27884], "avg_logprob": -0.21110372594062318, "compression_ratio": 1.606837606837607, "no_speech_prob": 0.0, "words": [{"start": 20.79, "end": 21.09, "word": "بسم", "probability": 0.884765625}, {"start": 21.09, "end": 21.21, "word": " الله", "probability": 0.95947265625}, {"start": 21.21, "end": 21.57, "word": " الرحمن", "probability": 0.9817708333333334}, {"start": 21.57, "end": 21.91, "word": " الرحيم", "probability": 0.9923502604166666}, {"start": 21.91, "end": 22.25, "word": " والصلاة", "probability": 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دايما بال base case و بعدين by logic كل element اقل من P of N بيعتمد على ال base", "tokens": [27842, 18863, 1863, 9381, 2288, 13672, 1829, 10874, 16758, 1211, 11296, 3714, 3555, 33599, 25720, 23032, 1829, 3555, 1975, 2655, 4117, 19528, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 4724, 43042, 3224, 8978, 1975, 34740, 9673, 5016, 46958, 25720, 18871, 2423, 1150, 8665, 1365, 4032, 39648, 8315, 16472, 3224, 39894, 46456, 46538, 18871, 2423, 700, 16472, 3224, 1975, 8315, 4724, 47283, 3555, 9566, 430, 295, 426, 9154, 28242, 2423, 4959, 13672, 1829, 10874, 16758, 1211, 11296, 9154, 10874, 2304, 40228, 2423, 4959, 13672, 1829, 10874, 16758, 1211, 11296, 37893, 4724, 11242, 2288, 13063, 1829, 1975, 12984, 3555, 2655, 16095, 36764, 24401, 36764, 24401, 35525, 19452, 4724, 44510, 10721, 11778, 47302, 15042, 20666, 3096, 1389, 4032, 39182, 9957, 538, 9952, 28242, 4478, 1975, 4587, 1211, 9154, 430, 295, 426, 4724, 1829, 34268, 2304, 3215, 15844, 2423, 3096], "avg_logprob": 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four cents stamp مظبوط تلاتة تلت أربعة أربعة أو أربعة أو أربعة فإذا بقدر أمثل أن هي تلاتة مضروبة في مين في four cent stamp", "tokens": [4762, 34051, 5551, 4117, 2655, 2288, 6156, 28814, 15730, 4724, 16254, 5551, 44510, 10721, 9154, 5551, 12610, 11296, 2423, 2272, 8032, 1211, 6156, 3615, 15040, 2423, 2272, 4724, 28543, 2288, 5551, 2304, 12984, 1211, 11296, 4724, 2304, 7435, 2304, 2407, 27884, 30800, 5551, 25513, 27884, 34051, 16490, 2304, 3794, 3660, 23032, 21292, 3615, 1829, 32239, 8592, 5296, 33456, 3224, 6225, 3555, 9640, 3660, 18871, 2423, 1045, 1451, 14941, 9921, 3714, 19913, 3555, 2407, 9566, 6055, 1211, 9307, 3660, 6055, 1211, 2655, 5551, 25513, 27884, 5551, 25513, 27884, 34051, 5551, 25513, 27884, 34051, 5551, 25513, 27884, 6156, 28814, 15730, 4724, 28543, 2288, 5551, 2304, 12984, 1211, 14739, 39896, 6055, 1211, 9307, 3660, 3714, 11242, 32887, 49401, 8978, 3714, 9957, 8978, 1451, 1489, 9921], "avg_logprob": -0.17187500387672486, "compression_ratio": 1.8967136150234742, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 219.04, "end": 219.32, "word": "12", "probability": 0.261474609375}, {"start": 219.32, "end": 219.54, "word": " أو", "probability": 0.371337890625}, {"start": 219.54, "end": 219.8, "word": " أكتر", "probability": 0.90185546875}, {"start": 219.8, "end": 220.04, "word": " فإذا", "probability": 0.6749674479166666}, {"start": 220.04, "end": 220.26, "word": " بدي", "probability": 0.792236328125}, {"start": 220.26, "end": 220.48, "word": " أبدأ", "probability": 0.9402669270833334}, {"start": 220.48, "end": 220.6, "word": " من", "probability": 0.978515625}, {"start": 220.6, "end": 221.02, "word": " أولها", "probability": 0.9908854166666666}, {"start": 221.02, "end": 221.16, "word": " ال", "probability": 0.6572265625}, {"start": 221.16, "end": 221.52, "word": " 12", "probability": 0.78369140625}, {"start": 221.52, "end": 221.98, "word": " هل", "probability": 0.927001953125}, {"start": 221.98, "end": 222.18, "word": " فعلا", 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0.74169921875}, {"start": 229.84, "end": 230.1, "word": " عبارة", "probability": 0.9921875}, {"start": 230.1, "end": 230.24, "word": " عن", "probability": 0.99462890625}, {"start": 230.24, "end": 230.36, "word": " ال", "probability": 0.65673828125}, {"start": 230.36, "end": 230.66, "word": " three", "probability": 0.7255859375}, {"start": 230.66, "end": 231.52, "word": " four", "probability": 0.6845703125}, {"start": 231.52, "end": 232.5, "word": " cents", "probability": 0.63427734375}, {"start": 232.5, "end": 233.42, "word": " stamp", "probability": 0.8935546875}, {"start": 233.42, "end": 234.94, "word": " مظبوط", "probability": 0.8396484375}, {"start": 234.94, "end": 236.42, "word": " تلاتة", "probability": 0.84765625}, {"start": 236.42, "end": 237.62, "word": " تلت", "probability": 0.6328938802083334}, {"start": 237.62, "end": 237.96, "word": " أربعة", "probability": 0.9435221354166666}, {"start": 237.96, "end": 239.2, "word": " أربعة", "probability": 0.8826497395833334}, {"start": 239.2, "end": 239.32, "word": " أو", "probability": 0.6064453125}, {"start": 239.32, "end": 239.58, "word": " أربعة", "probability": 0.9225260416666666}, {"start": 239.58, "end": 239.64, "word": " أو", "probability": 0.642578125}, {"start": 239.64, "end": 239.92, "word": " أربعة", "probability": 0.9593098958333334}, {"start": 239.92, "end": 240.24, "word": " فإذا", "probability": 0.88671875}, {"start": 240.24, "end": 240.52, "word": " بقدر", "probability": 0.9890950520833334}, {"start": 240.52, "end": 240.78, "word": " أمثل", "probability": 0.9029541015625}, {"start": 240.78, "end": 240.86, "word": " أن", "probability": 0.5771484375}, {"start": 240.86, "end": 240.94, "word": " هي", "probability": 0.79736328125}, {"start": 240.94, "end": 241.76, "word": " تلاتة", "probability": 0.97509765625}, {"start": 241.76, "end": 242.68, "word": " مضروبة", "probability": 0.97705078125}, {"start": 242.68, "end": 242.86, "word": " في", "probability": 0.96044921875}, {"start": 242.86, "end": 243.12, "word": " مين", "probability": 0.74755859375}, {"start": 243.12, "end": 243.6, "word": " في", "probability": 0.853515625}, {"start": 243.6, "end": 244.4, "word": " four", "probability": 0.85205078125}, {"start": 244.4, "end": 245.1, "word": " cent", "probability": 0.537109375}, {"start": 245.1, "end": 245.84, "word": " stamp", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 10, "seek": 26039, "start": 247.98, "end": 260.4, "text": "الـ 13 هنا طبعا لاحظوا أنه احنا هنحتاج ال base case بتاعتنا على الأقل يكون فينا أربعة، ليش أربعة؟ لأنه التكرار ببدأ من أربعة", "tokens": [6027, 39184, 3705, 34105, 23032, 3555, 3615, 995, 20193, 5016, 19913, 14407, 14739, 3224, 1975, 5016, 8315, 8032, 1863, 33753, 26108, 2423, 3096, 1389, 39894, 995, 34268, 8315, 15844, 16247, 4587, 1211, 7251, 30544, 8978, 8315, 5551, 25513, 27884, 12399, 32239, 8592, 5551, 25513, 27884, 22807, 5296, 33456, 3224, 16712, 37983, 9640, 4724, 44510, 10721, 9154, 5551, 25513, 27884], "avg_logprob": 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"probability": 0.9453125}, {"start": 254.58, "end": 254.92, "word": " بتاعتنا", "probability": 0.886474609375}, {"start": 254.92, "end": 255.02, "word": " على", "probability": 0.76513671875}, {"start": 255.02, "end": 255.32, "word": " الأقل", "probability": 0.9811197916666666}, {"start": 255.32, "end": 255.56, "word": " يكون", "probability": 0.952880859375}, {"start": 255.56, "end": 255.84, "word": " فينا", "probability": 0.643310546875}, {"start": 255.84, "end": 257.0, "word": " أربعة،", "probability": 0.7022705078125}, {"start": 257.0, "end": 257.28, "word": " ليش", "probability": 0.9072265625}, {"start": 257.28, "end": 258.04, "word": " أربعة؟", "probability": 0.9359130859375}, {"start": 258.04, "end": 258.38, "word": " لأنه", "probability": 0.77392578125}, {"start": 258.38, "end": 259.08, "word": " التكرار", "probability": 0.94140625}, {"start": 259.08, "end": 259.76, "word": " ببدأ", "probability": 0.9527994791666666}, {"start": 259.76, "end": 259.92, "word": " من", "probability": 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موجودة", "probability": 0.9635009765625}, {"start": 263.12, "end": 263.5, "word": " عندكم", "probability": 0.96875}, {"start": 263.5, "end": 263.78, "word": " عشان", "probability": 0.92333984375}, {"start": 263.78, "end": 264.16, "word": " تعملوا", "probability": 0.97802734375}, {"start": 264.16, "end": 264.74, "word": " تكرار", "probability": 0.9430338541666666}, {"start": 264.74, "end": 265.74, "word": " للقيمة", "probability": 0.8026123046875}, {"start": 265.74, "end": 265.9, "word": " هي", "probability": 0.8017578125}, {"start": 265.9, "end": 266.36, "word": " أربعة", "probability": 0.8577473958333334}, {"start": 266.36, "end": 266.72, "word": " أقل", "probability": 0.87744140625}, {"start": 266.72, "end": 266.96, "word": " واحدة", "probability": 0.9656575520833334}, {"start": 266.96, "end": 267.2, "word": " لأربعة", "probability": 0.7894287109375}, {"start": 267.2, "end": 267.44, "word": " فانتم", "probability": 0.8048502604166666}, {"start": 267.44, "end": 267.88, "word": " 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"probability": 0.5159912109375}, {"start": 271.94, "end": 272.1, "word": " في", "probability": 0.888671875}, {"start": 272.1, "end": 273.38, "word": " تكرار", "probability": 0.8951822916666666}, {"start": 273.38, "end": 273.6, "word": " في", "probability": 0.80908203125}, {"start": 273.6, "end": 274.38, "word": " recursion", "probability": 0.888671875}, {"start": 274.38, "end": 275.14, "word": " في", "probability": 0.8076171875}, {"start": 275.14, "end": 275.64, "word": " تكرار", "probability": 0.9803059895833334}, {"start": 275.64, "end": 276.76, "word": " للعملية", "probability": 0.9293212890625}, {"start": 276.76, "end": 277.84, "word": " بزيادة", "probability": 0.991015625}, {"start": 277.84, "end": 278.74, "word": " موجود", "probability": 0.98486328125}, {"start": 278.74, "end": 279.42, "word": " إلها", "probability": 0.640625}, {"start": 279.42, "end": 279.9, "word": " stamp", "probability": 0.98486328125}, {"start": 279.9, "end": 280.6, "word": " بزيادة", "probability": 0.9826171875}, {"start": 280.6, "end": 280.96, "word": " موجودة", "probability": 0.9140625}, {"start": 280.96, "end": 281.06, "word": " إلها", "probability": 0.7742513020833334}, {"start": 281.06, "end": 281.38, "word": " قيمة", "probability": 0.9908854166666666}, {"start": 281.38, "end": 281.52, "word": " لل", "probability": 0.53369140625}, {"start": 281.52, "end": 281.78, "word": " stamp", "probability": 0.9248046875}, {"start": 281.78, "end": 282.2, "word": " بتاعتها", "probability": 0.969482421875}, {"start": 282.2, "end": 282.68, "word": " okay", "probability": 0.61572265625}, {"start": 282.68, "end": 283.4, "word": " فناخد", "probability": 0.9727783203125}, {"start": 283.4, "end": 284.0, "word": " التلتاش", "probability": 0.69830322265625}, {"start": 284.0, "end": 284.46, "word": " التلتاش", "probability": 0.84344482421875}, {"start": 284.46, "end": 284.82, "word": " عبارة", "probability": 0.994873046875}, {"start": 284.82, "end": 285.5, "word": " عن", "probability": 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"text": "واحد و اتنين الخمستاشر تلاتة فلاحظوا هنا تلاتة اتنين واحد واحد اتنين تلاتة تبديل و توفيق لأن الفرق بينهم واحد فكل مرة بنزود .. بنزود قيمة او cent من ال combination اللي عملناها لمجموعة ال stamps بتاعتنا okay في الحالة هذه انا ضمنت ان ان من ال twelve to fifteen is true", "tokens": [14407, 24401, 4032, 1975, 2655, 1863, 9957, 33962, 2304, 14851, 33599, 2288, 6055, 1211, 9307, 3660, 6156, 15040, 5016, 19913, 14407, 34105, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 36764, 24401, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 6055, 3555, 16254, 1211, 4032, 6055, 38688, 1829, 4587, 5296, 33456, 27188, 2288, 4587, 49374, 16095, 36764, 24401, 6156, 28820, 3714, 25720, 44945, 11622, 23328, 4386, 44945, 11622, 23328, 12174, 32640, 3660, 1975, 2407, 1489, 9154, 2423, 6562, 13672, 1829, 6225, 42213, 8315, 11296, 32767, 7435, 2304, 2407, 27884, 2423, 30800, 39894, 995, 34268, 8315, 1392, 8978, 21542, 6027, 3660, 29538, 1975, 8315, 48812, 27842, 2655, 16472, 16472, 9154, 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لأن N plus 1 و N minus 3 الفرق بينهم أربعة و الأربعة موجود عند قيمة الفرق هذا يعني أنا بزود بس كمان stamp واحدة أو طابع بريدة واحد طابع بريدة واحد", "tokens": [47, 295, 426, 3175, 805, 307, 2074, 28242, 13672, 1829, 8032, 1863, 25957, 43761, 909, 5296, 2304, 9957, 5296, 1017, 10657, 9921, 6156, 19, 10657, 9921, 281, 483, 2183, 609, 337, 426, 1804, 502, 5296, 33456, 426, 1804, 502, 4032, 426, 3175, 805, 27188, 2288, 4587, 49374, 16095, 5551, 25513, 27884, 4032, 16247, 25513, 27884, 3714, 29245, 23328, 43242, 12174, 32640, 3660, 27188, 2288, 4587, 23758, 37495, 22653, 41850, 4724, 11622, 23328, 4724, 3794, 9122, 2304, 7649, 9921, 36764, 24401, 3660, 34051, 23032, 16758, 3615, 4724, 16572, 41891, 36764, 24401, 23032, 16758, 3615, 4724, 16572, 41891, 36764, 24401], "avg_logprob": -0.23453282707869405, "compression_ratio": 1.660633484162896, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 460.75, "end": 461.03, "word": "P", "probability": 0.771484375}, {"start": 461.03, "end": 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{"start": 510.56, "end": 511.08, "word": " الأربعة", "probability": 0.98388671875}, {"start": 511.08, "end": 511.68, "word": " cent", "probability": 0.7216796875}, {"start": 511.68, "end": 512.88, "word": " من", "probability": 0.75}, {"start": 512.88, "end": 513.14, "word": " فئة", "probability": 0.9920247395833334}, {"start": 513.14, "end": 513.48, "word": " الأربعة", "probability": 0.9837239583333334}, {"start": 513.48, "end": 513.74, "word": " cent", "probability": 0.68359375}, {"start": 513.74, "end": 514.14, "word": " طيب", "probability": 0.9436848958333334}, {"start": 514.14, "end": 514.42, "word": " لو", "probability": 0.95654296875}, {"start": 514.42, "end": 514.66, "word": " قلنا", "probability": 0.8486328125}, {"start": 514.66, "end": 515.06, "word": " 18", "probability": 0.460693359375}], "temperature": 1.0}, {"id": 21, "seek": 53303, "start": 517.27, "end": 533.03, "text": "كل ما ستفعلونه 18 n plus 1 تكافئ اللي جابها الاربعة اللي هي n minus 3 minus 3 بالنسبة لل 18 نقص 4 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S", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 90, "seek": 229134, "start": 2261.84, "end": 2291.34, "text": "set S و اعطاني معلومة واحدة ان التلاتة belong to this set فقط ماعطانيش اش تاني و بعدين let x plus y belong to S برضه مجموعة symbols قالنا ان two elements x و y belong to S طيب if x و y belong to mean to S فهنا بيعطيني اذن ان مجموحهم belong to S اذا كانوا الاتنين داخل S", "tokens": [3854, 318, 4032, 1975, 3615, 9566, 7649, 1829, 20449, 1211, 20498, 3660, 36764, 24401, 3660, 16472, 16712, 1211, 9307, 3660, 5784, 281, 341, 992, 6156, 47432, 19446, 3615, 9566, 7649, 1829, 8592, 1975, 8592, 6055, 7649, 1829, 4032, 39182, 9957, 718, 2031, 1804, 288, 5784, 281, 318, 4724, 43042, 3224, 3714, 7435, 2304, 2407, 27884, 16944, 50239, 8315, 16472, 732, 4959, 2031, 4032, 288, 5784, 281, 318, 23032, 1829, 3555, 498, 2031, 4032, 288, 5784, 281, 914, 281, 318, 6156, 3224, 8315, 4724, 40228, 9566, 9957, 1829, 1975, 8848, 1863, 16472, 3714, 7435, 2304, 2407, 5016, 16095, 5784, 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طولها تلاتة طيب لما أقول star مش محدد الطول معناه ذلك إن كل الكلمات الممكنة كل الكلمات إيش الممكنة لحظو في sigma هذه لأ", "tokens": [50, 16150, 281, 264, 1347, 6055, 1211, 9307, 3660, 50113, 15040, 3714, 43020, 6055, 30544, 8978, 9122, 19528, 9307, 9122, 2655, 13546, 23032, 12610, 11296, 6055, 1211, 9307, 3660, 1578, 264, 3237, 20328, 5016, 1829, 5016, 22807, 28242, 33251, 19528, 9307, 13672, 1829, 23032, 12610, 11296, 6055, 1211, 9307, 3660, 23032, 1829, 3555, 5296, 15042, 5551, 39648, 3543, 37893, 3714, 24401, 3215, 41950, 12610, 20449, 8315, 3224, 29910, 23275, 36145, 28242, 33251, 19528, 9307, 9673, 43020, 3660, 28242, 33251, 19528, 9307, 11933, 1829, 8592, 9673, 43020, 3660, 5296, 5016, 19913, 2407, 8978, 12771, 29538, 5296, 10721], "avg_logprob": -0.22422680412371135, "compression_ratio": 1.846938775510204, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 2464.25, "end": 2465.01, "word": "Sigma", "probability": 0.58978271484375}, {"start": 2465.01, "end": 2465.53, 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star", "probability": 0.8212890625}, {"start": 2482.03, "end": 2483.45, "word": " مش", "probability": 0.93701171875}, {"start": 2483.45, "end": 2483.81, "word": " محدد", "probability": 0.9931640625}, {"start": 2483.81, "end": 2484.19, "word": " الطول", "probability": 0.9716796875}, {"start": 2484.19, "end": 2484.97, "word": " معناه", "probability": 0.8037109375}, {"start": 2484.97, "end": 2485.17, "word": " ذلك", "probability": 0.95458984375}, {"start": 2485.17, "end": 2485.31, "word": " إن", "probability": 0.35205078125}, {"start": 2485.31, "end": 2485.59, "word": " كل", "probability": 0.89453125}, {"start": 2485.59, "end": 2485.99, "word": " الكلمات", "probability": 0.97509765625}, {"start": 2485.99, "end": 2486.75, "word": " الممكنة", "probability": 0.9788411458333334}, {"start": 2486.75, "end": 2487.05, "word": " كل", "probability": 0.75244140625}, {"start": 2487.05, "end": 2487.59, "word": " الكلمات", "probability": 0.9765625}, {"start": 2487.59, "end": 2487.91, "word": " إيش", 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"word": " احنا", "probability": 0.8772786458333334}, {"start": 2508.16, "end": 2508.44, "word": " بنتكلم", "probability": 0.81982421875}, {"start": 2508.44, "end": 2508.6, "word": " عن", "probability": 0.94189453125}, {"start": 2508.6, "end": 2509.0, "word": " alphabet", "probability": 0.69970703125}, {"start": 2509.0, "end": 2510.1, "word": " elements", "probability": 0.8828125}, {"start": 2510.1, "end": 2510.5, "word": " او", "probability": 0.89697265625}, {"start": 2510.5, "end": 2511.08, "word": " symbols", "probability": 0.85205078125}, {"start": 2511.08, "end": 2511.94, "word": " هناك", "probability": 0.93505859375}, {"start": 2511.94, "end": 2512.32, "word": " بنتكلم", "probability": 0.88623046875}, {"start": 2512.32, "end": 2512.52, "word": " عن", "probability": 0.9931640625}, {"start": 2512.52, "end": 2513.12, "word": " strings", "probability": 0.8740234375}, {"start": 2513.12, "end": 2513.86, "word": " و", "probability": 0.53515625}, {"start": 2513.86, "end": 2513.94, "word": " ال", "probability": 0.87060546875}, {"start": 2513.94, "end": 2514.26, "word": " strings", "probability": 0.96044921875}, {"start": 2514.26, "end": 2514.66, "word": " هدى", "probability": 0.9140625}, {"start": 2514.66, "end": 2515.58, "word": " الأطوار", "probability": 0.64599609375}, {"start": 2515.58, "end": 2516.18, "word": " مختلفة", "probability": 0.9381103515625}, {"start": 2516.18, "end": 2516.62, "word": " بدأتوا", "probability": 0.514312744140625}, {"start": 2516.62, "end": 2517.0, "word": " تبوار", "probability": 0.7957763671875}, {"start": 2517.0, "end": 2517.86, "word": " star", "probability": 0.72607421875}, {"start": 2517.86, "end": 2519.14, "word": " star", "probability": 0.246826171875}, {"start": 2519.14, "end": 2519.84, "word": " مش", "probability": 0.9892578125}, {"start": 2519.84, "end": 2520.14, "word": " معروف", "probability": 0.9923502604166666}, {"start": 2520.14, "end": 2520.46, "word": " الطول", "probability": 0.846435546875}], "temperature": 1.0}, {"id": 99, "seek": 254655, "start": 2521.31, "end": 2546.55, "text": "فإذا انقلها طول مختلفة تمام خلينا نبدأ نحط recursively شوية تعريفات هنا لما نمشي نحط the set sigma star of all strings over sigma طب sigma الشي احنا قولنا اللي هي ال alphabet لما بقول over sigma وكل strings اللي هي over sigma معناته كل الكلمات اللي بتتكون من ال letters هذه", "tokens": [5172, 28814, 15730, 16472, 4587, 1211, 11296, 23032, 12610, 3714, 46456, 46538, 3660, 46811, 10943, 16490, 20292, 8315, 8717, 44510, 10721, 8717, 5016, 9566, 20560, 3413, 13412, 2407, 10632, 37279, 16572, 5172, 9307, 34105, 5296, 15042, 8717, 2304, 8592, 1829, 8717, 5016, 9566, 264, 992, 12771, 3543, 295, 439, 13985, 670, 12771, 23032, 3555, 12771, 25124, 1829, 1975, 5016, 8315, 12174, 12610, 8315, 13672, 1829, 39896, 2423, 23339, 5296, 15042, 4724, 39648, 670, 12771, 4032, 28820, 13985, 13672, 1829, 39896, 670, 12771, 20449, 8315, 47395, 28242, 33251, 19528, 9307, 13672, 1829, 39894, 2655, 30544, 9154, 2423, 7825, 29538], "avg_logprob": 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" بقول", "probability": 0.980224609375}, {"start": 2540.67, "end": 2541.03, "word": " over", "probability": 0.94921875}, {"start": 2541.03, "end": 2541.53, "word": " sigma", "probability": 0.91943359375}, {"start": 2541.53, "end": 2542.11, "word": " وكل", "probability": 0.818359375}, {"start": 2542.11, "end": 2542.49, "word": " strings", "probability": 0.83837890625}, {"start": 2542.49, "end": 2542.61, "word": " اللي", "probability": 0.9755859375}, {"start": 2542.61, "end": 2542.75, "word": " هي", "probability": 0.9345703125}, {"start": 2542.75, "end": 2543.01, "word": " over", "probability": 0.9404296875}, {"start": 2543.01, "end": 2543.37, "word": " sigma", "probability": 0.9609375}, {"start": 2543.37, "end": 2543.85, "word": " معناته", "probability": 0.9114583333333334}, {"start": 2543.85, "end": 2544.01, "word": " كل", "probability": 0.990234375}, {"start": 2544.01, "end": 2544.47, "word": " الكلمات", "probability": 0.96728515625}, {"start": 2544.47, "end": 2544.73, "word": " اللي", "probability": 0.956787109375}, {"start": 2544.73, "end": 2545.25, "word": " بتتكون", "probability": 0.9728190104166666}, {"start": 2545.25, "end": 2545.87, "word": " من", "probability": 0.99609375}, {"start": 2545.87, "end": 2546.01, "word": " ال", "probability": 0.89111328125}, {"start": 2546.01, "end": 2546.25, "word": " letters", "probability": 0.8486328125}, {"start": 2546.25, "end": 2546.55, "word": " هذه", "probability": 0.56640625}], "temperature": 1.0}, {"id": 100, "seek": 256715, "start": 2547.57, "end": 2567.15, "text": "كل الكلمات اللي ممكن تتكون من ال letters ممكن مثلا ده لحظة هذا لحالها symbol هاي كمان symbol هاي كمان symbol تلاتة مع بعض عملولي string فهي صار عندنا string او series او ما هي string افضل", "tokens": [28820, 33251, 19528, 9307, 13672, 1829, 3714, 43020, 6055, 2655, 30544, 9154, 2423, 7825, 3714, 43020, 50113, 15040, 11778, 3224, 5296, 5016, 19913, 3660, 23758, 5296, 5016, 6027, 11296, 5986, 8032, 47302, 9122, 2304, 7649, 5986, 8032, 47302, 9122, 2304, 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"probability": 0.9287109375}, {"start": 2565.91, "end": 2566.11, "word": " او", "probability": 0.90478515625}, {"start": 2566.11, "end": 2566.29, "word": " ما", "probability": 0.70703125}, {"start": 2566.29, "end": 2566.39, "word": " هي", "probability": 0.56787109375}, {"start": 2566.39, "end": 2566.77, "word": " string", "probability": 0.85595703125}, {"start": 2566.77, "end": 2567.15, "word": " افضل", "probability": 0.9659423828125}], "temperature": 1.0}, {"id": 101, "seek": 259438, "start": 2568.8, "end": 2594.38, "text": "من ال symbols اعطونى معنى اعطونى معنى okay هدول belong to مين؟ to sigma star to sigma star طيب lambda اللى هى ال empty string هدى subset من أي string ممكنه من أي sigma star ممكنه لأنه هدى string string هدى not belong لو مفيش ال star", "tokens": [27842, 2423, 16944, 1975, 3615, 9566, 11536, 7578, 20449, 1863, 7578, 1975, 3615, 9566, 11536, 7578, 20449, 1863, 7578, 1392, 8032, 3215, 12610, 5784, 281, 3714, 9957, 22807, 281, 12771, 3543, 281, 12771, 3543, 23032, 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2573.24, "end": 2573.68, "word": " okay", "probability": 0.5166015625}, {"start": 2573.68, "end": 2574.48, "word": " هدول", "probability": 0.9607747395833334}, {"start": 2574.48, "end": 2574.76, "word": " belong", "probability": 0.83837890625}, {"start": 2574.76, "end": 2574.92, "word": " to", "probability": 0.9560546875}, {"start": 2574.92, "end": 2575.58, "word": " مين؟", "probability": 0.7496744791666666}, {"start": 2575.58, "end": 2576.16, "word": " to", "probability": 0.8583984375}, {"start": 2576.16, "end": 2576.48, "word": " sigma", "probability": 0.73681640625}, {"start": 2576.48, "end": 2577.32, "word": " star", "probability": 0.7470703125}, {"start": 2577.32, "end": 2578.0, "word": " to", "probability": 0.34375}, {"start": 2578.0, "end": 2578.3, "word": " sigma", "probability": 0.94873046875}, {"start": 2578.3, "end": 2578.76, "word": " star", "probability": 0.90625}, {"start": 2578.76, "end": 2579.24, "word": " طيب", "probability": 0.8758138020833334}, {"start": 2579.24, "end": 2579.74, "word": " lambda", "probability": 0.376953125}, {"start": 2579.74, "end": 2580.22, "word": " اللى", "probability": 0.793701171875}, {"start": 2580.22, "end": 2580.32, "word": " هى", "probability": 0.927734375}, {"start": 2580.32, "end": 2580.4, "word": " ال", "probability": 0.97216796875}, {"start": 2580.4, "end": 2580.64, "word": " empty", "probability": 0.72412109375}, {"start": 2580.64, "end": 2581.16, "word": " string", "probability": 0.8759765625}, {"start": 2581.16, "end": 2582.1, "word": " هدى", "probability": 0.7080078125}, {"start": 2582.1, "end": 2582.66, "word": " subset", "probability": 0.95849609375}, {"start": 2582.66, "end": 2582.92, "word": " من", "probability": 0.98779296875}, {"start": 2582.92, "end": 2583.24, "word": " أي", "probability": 0.5390625}, {"start": 2583.24, "end": 2583.66, "word": " string", "probability": 0.88818359375}, {"start": 2583.66, "end": 2584.16, "word": " ممكنه", "probability": 0.8868815104166666}, {"start": 2584.16, "end": 2584.36, "word": " من", "probability": 0.888671875}, {"start": 2584.36, "end": 2584.66, "word": " أي", "probability": 0.495849609375}, {"start": 2584.66, "end": 2585.68, "word": " sigma", "probability": 0.876953125}, {"start": 2585.68, "end": 2585.96, "word": " star", "probability": 0.93115234375}, {"start": 2585.96, "end": 2586.72, "word": " ممكنه", "probability": 0.986328125}, {"start": 2586.72, "end": 2587.06, "word": " لأنه", "probability": 0.7023111979166666}, {"start": 2587.06, "end": 2587.48, "word": " هدى", "probability": 0.9654947916666666}, {"start": 2587.48, "end": 2588.68, "word": " string", "probability": 0.9150390625}, {"start": 2588.68, "end": 2590.48, "word": " string", "probability": 0.60009765625}, {"start": 2590.48, "end": 2591.78, "word": " هدى", "probability": 0.98583984375}, {"start": 2591.78, "end": 2592.16, "word": " not", "probability": 0.96875}, {"start": 2592.16, "end": 2592.72, "word": " belong", "probability": 0.90380859375}, {"start": 2592.72, "end": 2593.48, "word": " لو", "probability": 0.98828125}, {"start": 2593.48, "end": 2593.92, "word": " مفيش", "probability": 0.7412109375}, {"start": 2593.92, "end": 2594.04, "word": " ال", "probability": 0.80517578125}, {"start": 2594.04, "end": 2594.38, "word": " star", "probability": 0.82373046875}], "temperature": 1.0}, {"id": 102, "seek": 262476, "start": 2596.18, "end": 2624.76, "text": "ليش؟ لأنه sigma لحالها symbols مش string ف not belong ولكن لما بتكلم عن star أه star معناته string مظبوط كلامها هيك صح تنطبخ بمشي لحالك فإذا lambda belong to star sigma على أساس أنه lambda زي ما قلنا ال empty string okay و belong to sigma star فإذا هذه ليست symbol هذه string", "tokens": [20292, 8592, 22807, 5296, 33456, 3224, 12771, 5296, 5016, 6027, 11296, 16944, 37893, 6798, 6156, 406, 5784, 35525, 19452, 5296, 15042, 39894, 4117, 19528, 18871, 3543, 5551, 3224, 3543, 20449, 8315, 47395, 6798, 3714, 19913, 3555, 2407, 9566, 28242, 10943, 11296, 39896, 4117, 20328, 5016, 6055, 1863, 9566, 3555, 9778, 4724, 2304, 8592, 1829, 5296, 5016, 6027, 4117, 6156, 28814, 15730, 13607, 5784, 281, 3543, 12771, 15844, 5551, 3794, 32277, 14739, 3224, 13607, 30767, 1829, 19446, 12174, 1211, 8315, 2423, 6707, 6798, 1392, 4032, 5784, 281, 12771, 3543, 6156, 28814, 15730, 29538, 32239, 14851, 5986, 29538, 6798], "avg_logprob": -0.2739158123731613, "compression_ratio": 1.6437768240343347, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2596.18, "end": 2597.0, "word": "ليش؟", "probability": 0.8470052083333334}, {"start": 2597.0, "end": 2597.5, "word": " لأنه", "probability": 0.6491292317708334}, {"start": 2597.5, "end": 2598.2, "word": " sigma", "probability": 0.69091796875}, {"start": 2598.2, "end": 2598.74, "word": " لحالها", "probability": 0.9886474609375}, {"start": 2598.74, "end": 2599.42, "word": " symbols", "probability": 0.8447265625}, {"start": 2599.42, "end": 2599.92, "word": " مش", "probability": 0.493896484375}, {"start": 2599.92, "end": 2600.46, "word": " string", 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0.8076171875}, {"start": 2613.66, "end": 2614.14, "word": " sigma", "probability": 0.86865234375}, {"start": 2614.14, "end": 2614.78, "word": " على", "probability": 0.880859375}, {"start": 2614.78, "end": 2615.02, "word": " أساس", "probability": 0.9453125}, {"start": 2615.02, "end": 2615.22, "word": " أنه", "probability": 0.5810546875}, {"start": 2615.22, "end": 2615.48, "word": " lambda", "probability": 0.615234375}, {"start": 2615.48, "end": 2615.66, "word": " زي", "probability": 0.97509765625}, {"start": 2615.66, "end": 2615.76, "word": " ما", "probability": 0.9716796875}, {"start": 2615.76, "end": 2616.12, "word": " قلنا", "probability": 0.82861328125}, {"start": 2616.12, "end": 2616.38, "word": " ال", "probability": 0.88037109375}, {"start": 2616.38, "end": 2616.68, "word": " empty", "probability": 0.444580078125}, {"start": 2616.68, "end": 2617.22, "word": " string", "probability": 0.828125}, {"start": 2617.22, "end": 2617.56, "word": " okay", "probability": 0.434326171875}, {"start": 2617.56, "end": 2618.34, "word": " و", "probability": 0.546875}, {"start": 2618.34, "end": 2618.76, "word": " belong", "probability": 0.62451171875}, {"start": 2618.76, "end": 2619.18, "word": " to", "probability": 0.98046875}, {"start": 2619.18, "end": 2620.74, "word": " sigma", "probability": 0.83740234375}, {"start": 2620.74, "end": 2621.58, "word": " star", "probability": 0.830078125}, {"start": 2621.58, "end": 2622.18, "word": " فإذا", "probability": 0.9137369791666666}, {"start": 2622.18, "end": 2622.5, "word": " هذه", "probability": 0.6591796875}, {"start": 2622.5, "end": 2623.04, "word": " ليست", "probability": 0.9580078125}, {"start": 2623.04, "end": 2623.46, "word": " symbol", "probability": 0.71533203125}, {"start": 2623.46, "end": 2624.3, "word": " هذه", "probability": 0.5546875}, {"start": 2624.3, "end": 2624.76, "word": " string", "probability": 0.85595703125}], "temperature": 1.0}, {"id": 103, "seek": 264612, "start": 2625.58, "end": 2646.12, "text": "واضحة؟ جدش طوله مش عارف هذي string لأنها belong to مين؟ to sigma star طيب and x belong to sigma فإذن هذي symbol هذي حرف ال x أنا بتكلم هنا عن ال element نفسه element اسمه x جدش طوله واحد هو واحد", "tokens": [2407, 46958, 5016, 3660, 22807, 10874, 3215, 8592, 23032, 12610, 3224, 37893, 6225, 9640, 5172, 8032, 8848, 1829, 6798, 5296, 33456, 11296, 5784, 281, 3714, 9957, 22807, 281, 12771, 3543, 23032, 1829, 3555, 293, 2031, 5784, 281, 12771, 6156, 28814, 8848, 1863, 8032, 8848, 1829, 5986, 8032, 8848, 1829, 11331, 28480, 2423, 2031, 41850, 39894, 4117, 19528, 34105, 18871, 2423, 4478, 8717, 36178, 3224, 4478, 24525, 2304, 3224, 2031, 10874, 3215, 8592, 23032, 12610, 3224, 36764, 24401, 31439, 36764, 24401], "avg_logprob": -0.23707562022738987, "compression_ratio": 1.5380434782608696, "no_speech_prob": 2.9206275939941406e-06, "words": [{"start": 2625.58, "end": 2626.24, "word": "واضحة؟", "probability": 0.771875}, {"start": 2626.24, "end": 2626.5, "word": " جدش", "probability": 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"probability": 0.9091796875}, {"start": 2639.34, "end": 2639.6, "word": " x", "probability": 0.485107421875}, {"start": 2639.6, "end": 2640.72, "word": " أنا", "probability": 0.70263671875}, {"start": 2640.72, "end": 2640.94, "word": " بتكلم", "probability": 0.9339192708333334}, {"start": 2640.94, "end": 2641.08, "word": " هنا", "probability": 0.67236328125}, {"start": 2641.08, "end": 2641.18, "word": " عن", "probability": 0.9951171875}, {"start": 2641.18, "end": 2641.58, "word": " ال", "probability": 0.95751953125}, {"start": 2641.58, "end": 2641.84, "word": " element", "probability": 0.884765625}, {"start": 2641.84, "end": 2642.24, "word": " نفسه", "probability": 0.99560546875}, {"start": 2642.24, "end": 2642.62, "word": " element", "probability": 0.74072265625}, {"start": 2642.62, "end": 2642.96, "word": " اسمه", "probability": 0.9479166666666666}, {"start": 2642.96, "end": 2643.28, "word": " x", "probability": 0.95849609375}, {"start": 2643.28, "end": 2644.1, "word": " جدش", 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ل", "probability": 0.9306640625}, {"start": 2655.2, "end": 2655.54, "word": " W", "probability": 0.477294921875}, {"start": 2655.54, "end": 2655.78, "word": " مع", "probability": 0.99169921875}, {"start": 2655.78, "end": 2656.22, "word": " X", "probability": 0.939453125}, {"start": 2656.22, "end": 2658.06, "word": " أكيد", "probability": 0.9378255208333334}, {"start": 2658.06, "end": 2658.34, "word": " belong", "probability": 0.332763671875}, {"start": 2658.34, "end": 2658.6, "word": " to", "probability": 0.96630859375}, {"start": 2658.6, "end": 2659.26, "word": " Sigma", "probability": 0.40576171875}, {"start": 2659.26, "end": 2659.52, "word": " Star", "probability": 0.1806640625}, {"start": 2659.52, "end": 2659.74, "word": " لإن", "probability": 0.7858072916666666}, {"start": 2659.74, "end": 2659.86, "word": " أنا", "probability": 0.73193359375}, {"start": 2659.86, "end": 2659.98, "word": " مش", "probability": 0.98974609375}, {"start": 2659.98, "end": 2660.3, "word": " عارف", 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2700.65, "end": 2701.07, "word": " معانا", "probability": 0.9749348958333334}, {"start": 2701.07, "end": 2702.07, "word": " أكتر", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 106, "seek": 272348, "start": 2702.8, "end": 2723.48, "text": "لو قلنا if sigma لحالها big sigma لحالها equal to zero one فهدولة ال symbols هدولة ال symbols ساعتنا صفر واحد okay the strings found in sigma star over the sigma ايش sigma ال star اللي ممكن اعملها generation من sigma لحالها", "tokens": [1211, 2407, 12174, 1211, 8315, 498, 12771, 5296, 5016, 6027, 11296, 955, 12771, 5296, 5016, 6027, 11296, 2681, 281, 4018, 472, 6156, 3224, 3215, 12610, 3660, 2423, 16944, 8032, 3215, 12610, 3660, 2423, 16944, 8608, 995, 34268, 8315, 20328, 5172, 2288, 36764, 24401, 1392, 264, 13985, 1352, 294, 12771, 3543, 670, 264, 12771, 1975, 1829, 8592, 12771, 2423, 3543, 13672, 1829, 3714, 43020, 1975, 25957, 1211, 11296, 5125, 9154, 12771, 5296, 5016, 6027, 11296], "avg_logprob": -0.19239583214124042, 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"end": 2721.2, "word": " اللي", "probability": 0.869384765625}, {"start": 2721.2, "end": 2721.42, "word": " ممكن", "probability": 0.985595703125}, {"start": 2721.42, "end": 2722.1, "word": " اعملها", "probability": 0.9056396484375}, {"start": 2722.1, "end": 2722.54, "word": " generation", "probability": 0.875}, {"start": 2722.54, "end": 2722.74, "word": " من", "probability": 0.98681640625}, {"start": 2722.74, "end": 2723.0, "word": " sigma", "probability": 0.89306640625}, {"start": 2723.0, "end": 2723.48, "word": " لحالها", "probability": 0.9964599609375}], "temperature": 1.0}, {"id": 107, "seek": 275341, "start": 2724.37, "end": 2753.41, "text": "of all bit strings لكل ال bit strings اللي ممكن ناخدها من ال two bits هدولة ال symbols هدولة ال two symbols فقط أول حالة اللي هي ال lambda أول واحدة lambda ليش لأن دي ربع اللي كنتوا هناك تتكلم عن إيش ال star كلام عن ال star هذه عرفتوها خلاص معرفة و انتهينا صفر واحد بس هاي ال two symbols بتاعونكوا مافيش symbols تانية ولكن لما بتكلم عن ال strings", "tokens": [2670, 439, 857, 13985, 5296, 28820, 2423, 857, 13985, 13672, 1829, 3714, 43020, 8717, 47283, 3215, 11296, 9154, 2423, 732, 9239, 8032, 3215, 12610, 3660, 2423, 16944, 8032, 3215, 12610, 3660, 2423, 732, 16944, 6156, 47432, 5551, 12610, 11331, 6027, 3660, 13672, 1829, 39896, 2423, 13607, 5551, 12610, 36764, 24401, 3660, 13607, 32239, 8592, 5296, 33456, 11778, 1829, 12602, 3555, 3615, 13672, 1829, 9122, 29399, 14407, 34105, 4117, 6055, 2655, 4117, 19528, 18871, 11933, 1829, 8592, 2423, 3543, 28242, 10943, 18871, 2423, 3543, 29538, 6225, 28480, 2655, 2407, 11296, 16490, 1211, 33546, 20449, 28480, 3660, 4032, 16472, 47395, 1829, 8315, 20328, 5172, 2288, 36764, 24401, 4724, 3794, 8032, 47302, 2423, 732, 16944, 39894, 45761, 11536, 4117, 14407, 19446, 41185, 8592, 16944, 6055, 7649, 10632, 35525, 19452, 5296, 15042, 39894, 4117, 19528, 18871, 2423, 13985], "avg_logprob": -0.21435184677441915, "compression_ratio": 1.966542750929368, "no_speech_prob": 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"start": 2754.03, "end": 2778.73, "text": "لأ ال strings ممكن تكون empty ممكن تكون ال واحد صفر لحاله هو string ال string في element واحد طيب او ال واحد لحاله او صفر صفر او صفر واحد او واحد صفر او واحد واحد او او او او to infinity ايش ممكن يكون في او كمان زيادة اربع تلت صفار صفرين و واحد صفر واحد صفر", "tokens": [1211, 10721, 2423, 13985, 3714, 43020, 6055, 30544, 6707, 3714, 43020, 6055, 30544, 2423, 36764, 24401, 20328, 5172, 2288, 5296, 5016, 6027, 3224, 31439, 6798, 2423, 6798, 8978, 4478, 36764, 24401, 23032, 1829, 3555, 1975, 2407, 2423, 36764, 24401, 5296, 5016, 6027, 3224, 1975, 2407, 20328, 5172, 2288, 20328, 5172, 2288, 1975, 2407, 20328, 5172, 2288, 36764, 24401, 1975, 2407, 36764, 24401, 20328, 5172, 2288, 1975, 2407, 36764, 24401, 36764, 24401, 1975, 2407, 1975, 2407, 1975, 2407, 1975, 2407, 281, 13202, 1975, 1829, 8592, 3714, 43020, 7251, 30544, 8978, 1975, 2407, 9122, 2304, 7649, 30767, 1829, 18513, 3660, 1975, 25513, 3615, 6055, 1211, 2655, 20328, 5172, 9640, 20328, 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عارف، string جدش طوله برضه مش عارف okay ال business بتاعتنا if w belong to sigma star", "tokens": [20534, 13985, 3714, 43020, 9154, 16095, 5551, 25957, 1211, 5125, 5296, 6798, 6055, 6027, 2655, 31439, 10874, 47302, 9154, 13672, 1829, 10874, 16758, 1211, 16095, 10874, 47302, 9154, 13672, 1829, 10874, 16758, 1211, 16095, 8978, 41950, 16572, 28671, 20560, 3413, 3714, 43020, 8717, 3615, 28480, 2423, 1588, 7186, 399, 295, 13985, 261, 16, 4032, 261, 17, 8032, 3215, 7578, 6798, 10874, 3215, 8592, 23032, 12610, 3224, 37893, 6225, 9640, 5172, 12399, 6798, 10874, 3215, 8592, 23032, 12610, 3224, 4724, 43042, 3224, 37893, 6225, 9640, 5172, 1392, 2423, 1606, 39894, 995, 34268, 8315, 498, 261, 5784, 281, 12771, 3543], "avg_logprob": -0.21938131915198433, "compression_ratio": 1.6977777777777778, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2823.79, "end": 2824.03, "word": "two", "probability": 0.2467041015625}, {"start": 2824.03, "end": 2824.55, "word": " strings", "probability": 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جدش", "probability": 0.9850260416666666}, {"start": 2843.73, "end": 2843.97, "word": " طوله", "probability": 0.9967447916666666}, {"start": 2843.97, "end": 2844.17, "word": " برضه", "probability": 0.8277180989583334}, {"start": 2844.17, "end": 2844.33, "word": " مش", "probability": 0.990234375}, {"start": 2844.33, "end": 2844.99, "word": " عارف", "probability": 0.9947916666666666}, {"start": 2844.99, "end": 2845.45, "word": " okay", "probability": 0.466796875}, {"start": 2845.45, "end": 2845.83, "word": " ال", "probability": 0.947265625}, {"start": 2845.83, "end": 2846.05, "word": " business", "probability": 0.93701171875}, {"start": 2846.05, "end": 2846.65, "word": " بتاعتنا", "probability": 0.9229736328125}, {"start": 2846.65, "end": 2846.97, "word": " if", "probability": 0.865234375}, {"start": 2846.97, "end": 2847.81, "word": " w", "probability": 0.8486328125}, {"start": 2847.81, "end": 2848.11, "word": " belong", "probability": 0.40380859375}, {"start": 2848.11, "end": 2848.39, "word": " to", "probability": 0.984375}, {"start": 2848.39, "end": 2849.07, "word": " sigma", "probability": 0.6845703125}, {"start": 2849.07, "end": 2849.49, "word": " star", "probability": 0.759765625}], "temperature": 1.0}, {"id": 112, "seek": 286810, "start": 2850.78, "end": 2868.1, "text": "then w ال dot هذه معناته concatenation ال lambda هي نفسها w لإن انت بتتكلم عن empty string where ال lambda هنا عرفناها اللي هي ال empty string", "tokens": [19096, 261, 2423, 5893, 29538, 20449, 8315, 47395, 1588, 7186, 399, 2423, 13607, 39896, 8717, 36178, 11296, 261, 5296, 28814, 1863, 16472, 2655, 39894, 2655, 4117, 19528, 18871, 6707, 6798, 689, 2423, 13607, 34105, 6225, 28480, 8315, 11296, 13672, 1829, 39896, 2423, 6707, 6798], "avg_logprob": -0.4399305476082696, "compression_ratio": 1.3900709219858156, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2850.78, "end": 2851.16, "word": "then", "probability": 0.320068359375}, {"start": 2851.16, "end": 2852.04, "word": " w", 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"word": " انت", "probability": 0.769287109375}, {"start": 2861.32, "end": 2861.58, "word": " بتتكلم", "probability": 0.8775634765625}, {"start": 2861.58, "end": 2861.8, "word": " عن", "probability": 0.97119140625}, {"start": 2861.8, "end": 2862.16, "word": " empty", "probability": 0.257080078125}, {"start": 2862.16, "end": 2863.38, "word": " string", "probability": 0.368896484375}, {"start": 2863.38, "end": 2865.06, "word": " where", "probability": 0.41015625}, {"start": 2865.06, "end": 2865.8, "word": " ال", "probability": 0.7109375}, {"start": 2865.8, "end": 2866.02, "word": " lambda", "probability": 0.9501953125}, {"start": 2866.02, "end": 2866.2, "word": " هنا", "probability": 0.6064453125}, {"start": 2866.2, "end": 2866.7, "word": " عرفناها", "probability": 0.662872314453125}, {"start": 2866.7, "end": 2866.86, "word": " اللي", "probability": 0.870361328125}, {"start": 2866.86, "end": 2867.0, "word": " هي", "probability": 0.6943359375}, {"start": 2867.0, "end": 2867.12, "word": " ال", "probability": 0.888671875}, {"start": 2867.12, "end": 2867.38, "word": " empty", "probability": 0.76806640625}, {"start": 2867.38, "end": 2868.1, "word": " string", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 113, "seek": 288758, "start": 2869.9, "end": 2887.58, "text": "ال recursive ليش هنا أشتغلنا على ال lambda لأن أقل lambda ممكنة أقل string ممكن لل W2 هي تكون lambda طيب لأ أكتر من lambda معناه ذلك أن W1 زي ما هي هي belong to sigma star", "tokens": [6027, 20560, 488, 32239, 8592, 34105, 5551, 8592, 2655, 17082, 1211, 8315, 15844, 2423, 13607, 5296, 33456, 5551, 4587, 1211, 13607, 3714, 43020, 3660, 5551, 4587, 1211, 6798, 3714, 43020, 24976, 343, 17, 39896, 6055, 30544, 13607, 23032, 1829, 3555, 5296, 10721, 5551, 4117, 2655, 2288, 9154, 13607, 20449, 8315, 3224, 29910, 23275, 14739, 343, 16, 30767, 1829, 19446, 39896, 39896, 5784, 281, 12771, 3543], "avg_logprob": -0.2623106087699081, "compression_ratio": 1.455621301775148, "no_speech_prob": 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"end": 3064.66, "word": " عملية", "probability": 0.98974609375}, {"start": 3064.66, "end": 3064.8, "word": " ال", "probability": 0.91943359375}, {"start": 3064.8, "end": 3065.42, "word": " concatenation", "probability": 0.8313802083333334}, {"start": 3065.42, "end": 3065.68, "word": " ال", "probability": 0.740234375}, {"start": 3065.68, "end": 3066.86, "word": " recursive", "probability": 0.85986328125}, {"start": 3066.86, "end": 3067.74, "word": " هنستعمل", "probability": 0.91337890625}, {"start": 3067.74, "end": 3067.98, "word": " عملية", "probability": 0.9905598958333334}, {"start": 3067.98, "end": 3068.1, "word": " ال", "probability": 0.97216796875}, {"start": 3068.1, "end": 3068.64, "word": " recursion", "probability": 0.963623046875}, {"start": 3068.64, "end": 3069.2, "word": " من", "probability": 0.9921875}, {"start": 3069.2, "end": 3069.7, "word": " ال", "probability": 0.97021484375}, {"start": 3069.7, "end": 3070.02, "word": " element", "probability": 0.97216796875}, {"start": 3070.02, "end": 3070.64, "word": " السابق", "probability": 0.99462890625}, {"start": 3070.64, "end": 3071.9, "word": " فبنخليها", "probability": 0.9026692708333334}, {"start": 3071.9, "end": 3072.36, "word": " تكرار", "probability": 0.9617513020833334}, {"start": 3072.36, "end": 3072.92, "word": " بنخليها", "probability": 0.79888916015625}, {"start": 3072.92, "end": 3073.12, "word": " عملية", "probability": 0.9801432291666666}, {"start": 3073.12, "end": 3073.52, "word": " تكرار", "probability": 0.9866536458333334}, {"start": 3073.52, "end": 3074.12, "word": " بناخدها", "probability": 0.8690185546875}, {"start": 3074.12, "end": 3074.36, "word": " المرة", "probability": 0.905029296875}, {"start": 3074.36, "end": 3074.7, "word": " الجاية", "probability": 0.9114583333333334}, {"start": 3074.7, "end": 3075.06, "word": " هتلاقي", "probability": 0.894287109375}, {"start": 3075.06, "end": 3075.4, "word": " انه", "probability": 0.71923828125}, {"start": 3075.4, "end": 3076.14, "word": " هنبسط", "probability": 0.97373046875}, {"start": 3076.14, "end": 3076.64, "word": " كتير", "probability": 0.9401041666666666}, {"start": 3076.64, "end": 3077.22, "word": " algorithms", "probability": 0.74072265625}, {"start": 3077.22, "end": 3077.7, "word": " أخدناها", "probability": 0.9193359375}, {"start": 3077.7, "end": 3078.16, "word": " سابقا", "probability": 0.9923095703125}, {"start": 3078.16, "end": 3078.84, "word": " هتتبسط", "probability": 0.9169921875}, {"start": 3078.84, "end": 3079.06, "word": " كتير", "probability": 0.98876953125}, {"start": 3079.06, "end": 3079.32, "word": " وعدد", "probability": 0.9088541666666666}, {"start": 3079.32, "end": 3079.66, "word": " صوره", "probability": 0.67236328125}, {"start": 3079.66, "end": 3079.92, "word": " هتصير", "probability": 0.94287109375}, {"start": 3079.92, "end": 3080.16, "word": " أجل", "probability": 0.7635091145833334}, {"start": 3080.16, "end": 3080.5, "word": " كتير", "probability": 0.974609375}], "temperature": 1.0}, {"id": 122, "seek": 308563, "start": 3081.95, "end": 3085.63, "text": "يلا يعطيكوا العافية تشوفوا يوم ال .. ال ..", "tokens": [1829, 15040, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 6055, 8592, 38688, 14407, 7251, 20498, 2423, 4386, 2423, 4386], "avg_logprob": -0.28311011337098624, "compression_ratio": 1.1428571428571428, "no_speech_prob": 0.0, "words": [{"start": 3081.95, "end": 3082.27, "word": "يلا", "probability": 0.5250244140625}, {"start": 3082.27, "end": 3082.59, "word": " يعطيكوا", "probability": 0.8615234375}, {"start": 3082.59, "end": 3083.07, "word": " العافية", "probability": 0.8509114583333334}, {"start": 3083.07, "end": 3083.75, "word": " تشوفوا", "probability": 0.78289794921875}, {"start": 3083.75, "end": 3084.93, "word": " يوم", "probability": 0.9814453125}, {"start": 3084.93, "end": 3085.25, "word": " ال", "probability": 0.81396484375}, {"start": 3085.25, "end": 3085.25, "word": " ..", "probability": 0.86962890625}, {"start": 3085.25, "end": 3085.45, "word": " ال", "probability": 0.71826171875}, {"start": 3085.45, "end": 3085.63, "word": " ..", "probability": 0.7548828125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3087.0, "duration_after_vad": 2979.2143749999877}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a72a3a9441dc7bb9fc1198fdc5d532187080feae
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/9pcVsVjQE6I_raw.srt
@@ -0,0 +1,2564 @@
+1
+00:00:20,790 --> 00:00:23,010
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:23,010 --> 00:00:25,850
+الأنبياء والمسلمين سيدنا محمد الله عليه الصحة يا
+
+3
+00:00:25,850 --> 00:00:29,950
+جماعةنكمل اليوم إن شاء الله تعالى في موضوع ال
+
+4
+00:00:29,950 --> 00:00:35,050
+inductive او ال induction ال inductive proof و كان
+
+5
+00:00:35,050 --> 00:00:38,370
+ضايق لنا اتكلمنا يمكن بعد ما اتكلمنا على ال first
+
+6
+00:00:38,370 --> 00:00:41,370
+principle examples أخدنا two examples على ال first
+
+7
+00:00:41,370 --> 00:00:45,850
+principle و ال first principle تفكيرا كان يعتمد
+
+8
+00:00:45,850 --> 00:00:52,000
+على فكرة ان P of N بأثبتها من P of N minus oneمن
+
+9
+00:00:52,000 --> 00:00:55,980
+العنصر اللي جابلها مباشرة طيب اتكلمنا المرة اللي
+
+10
+00:00:55,980 --> 00:00:58,600
+فاتت برضه في اخر المحاضرة عن ال second principle
+
+11
+00:00:58,600 --> 00:01:02,000
+example وقولنا انه بتختلف عن ال first انه انا
+
+12
+00:01:02,000 --> 00:01:06,940
+باخبط P of N من كل ال elements اللي جابلها من جميع
+
+13
+00:01:06,940 --> 00:01:10,340
+ال elements اللي جابلها مش بضروري اثبتهم واحد واحد
+
+14
+00:01:10,340 --> 00:01:15,700
+ولكن ببدأ دايما بال base case و بعدين by logic كل
+
+15
+00:01:15,700 --> 00:01:20,730
+element اقل من P of N بيعتمد على ال baseممكن ال
+
+16
+00:01:20,730 --> 00:01:25,010
+sequence تبعهم يوصلنا ل ال base case أخدنا مثال
+
+17
+00:01:25,010 --> 00:01:27,630
+المرة اللى فاترة اللى كان له علاقة بال primes ان
+
+18
+00:01:27,630 --> 00:01:32,190
+كل element بيتكون من مجموعة ال primes اليوم بنكمل
+
+19
+00:01:32,190 --> 00:01:36,370
+ال example التانى ل second principle example اللى
+
+20
+00:01:36,370 --> 00:01:39,610
+هو زى ما احنا نشوفه نخلص فيه جزئية ال inductive
+
+21
+00:01:39,610 --> 00:01:43,230
+عشان ننجل على section هو نفسه inductive يعني هو
+
+22
+00:01:43,230 --> 00:01:48,210
+يعني تكميل لجزئية ال inductive طيب نشوف المثال
+
+23
+00:01:48,210 --> 00:01:51,700
+التانى ال proofI prove that every amount of
+
+24
+00:01:51,700 --> 00:01:55,440
+postage of twelve cents or more can be formed
+
+25
+00:01:55,440 --> 00:02:01,480
+using just four cent and five cent stamps إيش
+
+26
+00:02:01,480 --> 00:02:04,400
+يعني؟ ال postage اللي هو تتكلموا أنتوا عن جواب
+
+27
+00:02:04,400 --> 00:02:10,100
+البُسطة أو الجواب البريدي الجواب البريدي كل جواب
+
+28
+00:02:10,100 --> 00:02:15,560
+بريدي أو حوالة بريدية شئ اللي له علاقة بالبريد
+
+29
+00:02:15,560 --> 00:02:22,120
+يمكنوضع عليه طوابع أي قيمة له أكتر من اتناش اتناش
+
+30
+00:02:22,120 --> 00:02:27,400
+او اكتر سنت بقدر امثلها ب two stems ال stems اللي
+
+31
+00:02:27,400 --> 00:02:31,580
+هي الطوابع بقدر امثلها بطابعين فقط او بنوعين من
+
+32
+00:02:31,580 --> 00:02:36,200
+الطوابع اللي هو طابع قيمته اربعة سنت و طابع قيمته
+
+33
+00:02:36,200 --> 00:02:40,460
+خمسة سنت طابع اربعة سنت و خمسة سنت زي لما تروحوا
+
+34
+00:02:40,460 --> 00:02:43,540
+مثلا تكونوا تعملوا روشيتة في اي مستوصف اي او اي
+
+35
+00:02:43,540 --> 00:02:50,070
+هيئة صحية و تكونوا محتاجين فرضاتلاتة شكل هحطلكوا
+
+36
+00:02:50,070 --> 00:02:57,310
+تلاتة stems شكل شكل شكل صحيح فعمل تكوين للرقم
+
+37
+00:02:57,310 --> 00:03:01,190
+تلاتة من ال three stems من نفس الفئة اللي هي الفئة
+
+38
+00:03:01,190 --> 00:03:07,490
+one شكل طيب هنا نفس الكلام بده نثبت انه اي روشتة
+
+39
+00:03:07,490 --> 00:03:14,310
+اي جواب اي بريد قيمته اكتر او تساوي اتناشر cent
+
+40
+00:03:14,310 --> 00:03:19,950
+بقدر امثلها twoأو نوعين من ال stems نوعين من ال
+
+41
+00:03:19,950 --> 00:03:25,550
+stems اللي هم ماجدداش أربع سن أو خمس سنة هل فعلا
+
+42
+00:03:25,550 --> 00:03:28,590
+نقدر الكلام هذا؟ نشوف هو مطلوب نعمل إثبات للكلام
+
+43
+00:03:28,590 --> 00:03:31,430
+هذا طيب في الحالة دي ال initial condition تبعتنا
+
+44
+00:03:31,430 --> 00:03:34,830
+أول ال base case بتاعتنا ال base case بتاعتنا
+
+45
+00:03:34,830 --> 00:03:39,540
+هنبدأ من الأساس اتمعش هو بيقول نتمعش أو أكتر12 أو
+
+46
+00:03:39,540 --> 00:03:42,500
+أكتر فإذا بدي أبدأ من أولها ال 12 هل فعلا ال 12
+
+47
+00:03:42,500 --> 00:03:49,600
+بقدر أمثلها بمجموعة stamps أربعة أو خمسة طبيعي ليش
+
+48
+00:03:49,600 --> 00:03:54,940
+لأنه عبارة عن ال three four cents stamp مظبوط
+
+49
+00:03:54,940 --> 00:04:00,520
+تلاتة تلت أربعة أربعة أو أربعة أو أربعة فإذا بقدر
+
+50
+00:04:00,520 --> 00:04:05,840
+أمثل أن هي تلاتة مضروبة في مين في four cent stamp
+
+51
+00:04:07,980 --> 00:04:14,380
+الـ 13 هنا طبعا لاحظوا أنه احنا هنحتاج ال base
+
+52
+00:04:14,380 --> 00:04:18,040
+case بتاعتنا على الأقل يكون فينا أربعة، ليش أربعة؟
+
+53
+00:04:18,040 --> 00:04:23,500
+لأنه التكرار ببدأ من أربعةأقل stamp موجودة عندكم
+
+54
+00:04:23,500 --> 00:04:27,200
+عشان تعملوا تكرار للقيمة هي أربعة أقل واحدة لأربعة
+
+55
+00:04:27,200 --> 00:04:29,960
+فانتم محتاجين ال base case بتاعتكم على الأقل أربع
+
+56
+00:04:29,960 --> 00:04:35,140
+قيم عشان تضمنوا بعد أنه في تكرار في recursion في
+
+57
+00:04:35,140 --> 00:04:40,600
+تكرار للعملية بزيادة موجود إلها stamp بزيادة
+
+58
+00:04:40,600 --> 00:04:43,400
+موجودة إلها قيمة لل stamp بتاعتها okay فناخد
+
+59
+00:04:43,400 --> 00:04:47,820
+التلتاش التلتاش عبارة عن اتنين في أربعة زائد خمسة
+
+60
+00:04:47,820 --> 00:04:52,830
+اتنين في أربعة زائد خمسة الاربعتاشواحد و اتنين
+
+61
+00:04:52,830 --> 00:04:57,350
+الخمستاشر تلاتة فلاحظوا هنا تلاتة اتنين واحد واحد
+
+62
+00:04:57,350 --> 00:05:02,350
+اتنين تلاتة تبديل و توفيق لأن الفرق بينهم واحد فكل
+
+63
+00:05:02,350 --> 00:05:07,530
+مرة بنزود .. بنزود قيمة او cent من ال combination
+
+64
+00:05:07,530 --> 00:05:11,250
+اللي عملناها لمجموعة ال stamps بتاعتنا okay في
+
+65
+00:05:11,250 --> 00:05:15,430
+الحالة هذه انا ضمنت ان ان من ال twelve to fifteen
+
+66
+00:05:15,430 --> 00:05:19,950
+is trueلأن احنا اللي عاملينها هي .. احنا عاملينها
+
+67
+00:05:19,950 --> 00:05:24,870
+فعلا من اتناش لخمستاش .. اتناش لخمستاش P of N is
+
+68
+00:05:24,870 --> 00:05:28,370
+true .. P of N is true فهذه كل هذا اللي هي ال base
+
+69
+00:05:28,370 --> 00:05:32,830
+caseاللي احنا بحنحله بإيدنا هنشتغل واحدة واحدة
+
+70
+00:05:32,830 --> 00:05:36,990
+عشان نخلصهم خلصناهم ال inductive step في ال
+
+71
+00:05:36,990 --> 00:05:40,870
+inductive step بنبدأ نشتغل على اللي أعلى من ال
+
+72
+00:05:40,870 --> 00:05:46,210
+base case فإذا حد من خمستاش فأعلى من خمستاش فإيش
+
+73
+00:05:46,210 --> 00:05:49,810
+فأعلى من خمستاش فأعلى بقول n أكبر من أو تساوي
+
+74
+00:05:49,810 --> 00:05:56,830
+fifteen assume for all twelve أقل من أو تساوي k
+
+75
+00:05:56,830 --> 00:06:03,180
+أقل من أو تساوي nك .. حطيناها variable اسمه ك ..
+
+76
+00:06:03,180 --> 00:06:06,740
+والان ممكن تكون أي .. أي شيء ممكن تكون أكبر من
+
+77
+00:06:06,740 --> 00:06:09,620
+الخمستاش .. ماداما أنا في ال inductive بتكون أكبر
+
+78
+00:06:09,620 --> 00:06:12,320
+من الخمستاش هذا ممكن برضه أكتبها بطريقة تانية أقول
+
+79
+00:06:12,320 --> 00:06:17,960
+أن هي n minus three أقل من أو يساوي m على أساس لما
+
+80
+00:06:17,960 --> 00:06:25,190
+بدنا نحسب n plus one إيش الفرق بينها؟ لحظوامن
+
+81
+00:06:25,190 --> 00:06:29,630
+twelve to n اللي احنا أساسا قلنا ان هي approved
+
+82
+00:06:29,630 --> 00:06:38,090
+assume هي assume لاحظوا هنا K بنمثلها ب N minus
+
+83
+00:06:38,090 --> 00:06:40,890
+three طيب N minus three إذا أنا فعلا عامل
+
+84
+00:06:40,890 --> 00:06:44,990
+assumption ل ال condition هذا N minus three أقل من
+
+85
+00:06:44,990 --> 00:06:54,040
+N فإذا true فإذا كان فعلا هي trueبقدر أجيب منها n
+
+86
+00:06:54,040 --> 00:07:01,540
+plus واحد لإيش لأنه كده الفرق بينهم أربعة يعني
+
+87
+00:07:01,540 --> 00:07:07,000
+بزود stamp واحدة قيمتها أربعة سنت فإذا إذا جدرنا
+
+88
+00:07:07,000 --> 00:07:13,950
+نثبت أن n minus three is trueباللوجيك n زائد واحد
+
+89
+00:07:13,950 --> 00:07:18,130
+is true لأن كل اللي هضيفه كمان stamp واحدة بقيمة
+
+90
+00:07:18,130 --> 00:07:24,570
+أربعة cent أربعة cent فإذا بنقدر نمثلها K ال K
+
+91
+00:07:24,570 --> 00:07:29,530
+بتاعتنا هنا بنقدر نمثلها ب N minus three و أنا
+
+92
+00:07:29,530 --> 00:07:33,350
+ضامن أن N minus three هي ضمن ال region هذه لازم
+
+93
+00:07:33,350 --> 00:07:37,150
+تكون .. لأن أقل من N أقل من N أقل من N التلاتة
+
+94
+00:07:37,150 --> 00:07:44,110
+okay فإذا soP of N minus 3 is true كل اللي هنعمله
+
+95
+00:07:44,110 --> 00:07:51,910
+add لمين ل 4 synth stamp ف4 synth stamp to get
+
+96
+00:07:51,910 --> 00:07:58,870
+postage for N plus 1 لأن N plus 1 و N minus 3
+
+97
+00:07:58,870 --> 00:08:02,530
+الفرق بينهم أربعة و الأربعة موجود عند قيمة الفرق
+
+98
+00:08:02,530 --> 00:08:05,290
+هذا يعني أنا بزود بس كمان stamp واحدة أو طابع
+
+99
+00:08:05,290 --> 00:08:10,080
+بريدة واحد طابع بريدة واحدفإذا كان قدرنا نثبت هيو
+
+100
+00:08:10,080 --> 00:08:16,080
+بإيدنا ال 12 فإذا ال 16 أكيد برضه ممكن نعملها
+
+101
+00:08:16,080 --> 00:08:22,480
+generation باستخدام هنا كنا قدش نستخدم تلاتة في
+
+102
+00:08:22,480 --> 00:08:26,880
+أربعة stamp في أربعة cent stamp كل اللي هنعمله هنا
+
+103
+00:08:26,880 --> 00:08:32,880
+هنزود أربعة فبتصير أربعة من فئة الأربعة cent من
+
+104
+00:08:32,880 --> 00:08:39,790
+فئة الأربعة cent طيب لو قلنا 18كل ما ستفعلونه 18 n
+
+105
+00:08:39,790 --> 00:08:44,530
+plus 1 تكافئ
+
+106
+00:08:44,530 --> 00:08:49,350
+اللي جابها الاربعة اللي هي n minus 3 minus 3
+
+107
+00:08:49,350 --> 00:08:55,980
+بالنسبة لل 18 نقص 4 يعني تمثلالاربعتاش طب
+
+108
+00:08:55,980 --> 00:08:59,240
+الاربعتاش احنا أثبتناها جوي توي كانت بتسوي عبارة
+
+109
+00:08:59,240 --> 00:09:06,020
+عن واحد في أربعة سنت زائد اتنين في خمسة سنت فكل
+
+110
+00:09:06,020 --> 00:09:09,720
+اللي هنعمل منه الطماطش هتصير اتنين في أربعة سنت
+
+111
+00:09:09,720 --> 00:09:19,400
+زائد اتنين في خمسة سنتفكل n plus واحد هتطرح منها
+
+112
+00:09:19,400 --> 00:09:25,980
+أربعة هتكون تم تمثيل الأربعة جبالك طب لو قلنا خمسة
+
+113
+00:09:25,980 --> 00:09:31,380
+و خمسين بس عشان نوضح ليش هي second principle
+
+114
+00:09:31,380 --> 00:09:35,320
+second principle لازم تثبت كل اللي جابلها صح لازم
+
+115
+00:09:35,320 --> 00:09:39,480
+نثبت كل اللي جابلها لعند ما نصل لل base case
+
+116
+00:09:39,480 --> 00:09:45,820
+فالاربعة و اربعين هده تكافئ أيش؟ زائد أربعةstamp
+
+117
+00:09:45,820 --> 00:09:51,540
+قيمته اربعة سن الواحد وخمسين تكافئ برضه نقل زيادة
+
+118
+00:09:51,540 --> 00:09:59,700
+اربعة سبعة واربعين تكافئ تلاتة واربعين تكافئ و
+
+119
+00:09:59,700 --> 00:10:05,360
+هكذا لعندما تصلوا لوحدة من من الاربع قيم بتاعنا
+
+120
+00:10:05,360 --> 00:10:11,960
+هتصلوا لاربع قيم اكيد جدش القيم اللي هتصلوهاكيف
+
+121
+00:10:11,960 --> 00:10:18,000
+مثلناها زائد عدد الأربعات الفروق زائد عدد الأربعات
+
+122
+00:10:18,000 --> 00:10:22,480
+اللي انتوا عملتهم ك .. كفروق .. كفروق عندكم okay
+
+123
+00:10:22,480 --> 00:10:26,780
+فلاحظوا
+
+124
+00:10:26,780 --> 00:10:29,660
+انه فعلا احنا نتكلم هنا عن second principle على
+
+125
+00:10:29,660 --> 00:10:36,100
+اساس اثبت انه فعلا N plus واحد او P of N plus واحد
+
+126
+00:10:36,100 --> 00:10:41,470
+is true for allNumbers أكبر من 12 لكل الأرقام التي
+
+127
+00:10:41,470 --> 00:10:46,690
+أكبر من 12 ليست لديها قيمة هذه قيمة لو قلنا حتى ال
+
+128
+00:10:46,690 --> 00:10:51,590
+55 نقدر نمثلها من ال base cases اللي موجودة عندنا
+
+129
+00:10:51,590 --> 00:10:54,610
+من الأربع base cases اللي موجودين عندنا ففي الحالة
+
+130
+00:10:54,610 --> 00:10:59,660
+هذه لوأثبتنا عند الخمسة و خمسين معناته كل اللي أقل
+
+131
+00:10:59,660 --> 00:11:02,900
+من الخمسة و خمسين تم أثبته مسبقا جابل ما أصل لخمسة
+
+132
+00:11:02,900 --> 00:11:05,800
+و خمسين صحيح؟ لحظة ان احنا عشان نثبت أن الخمسة و
+
+133
+00:11:05,800 --> 00:11:10,560
+خمسين بقدر أجيبها من أربعة و خمسة cent لازم أثبت
+
+134
+00:11:10,560 --> 00:11:14,440
+كل اللي جابلها لما نصل مين لل base case فإذا أنا
+
+135
+00:11:14,440 --> 00:11:17,020
+بتكلم عن second principle فعلا مش مجرد اللي جابلها
+
+136
+00:11:17,020 --> 00:11:20,780
+فقط كل اللي جابلها لازم يكونوا is true كل اللي
+
+137
+00:11:20,780 --> 00:11:24,830
+جابلها لازم يكونوا is trueOkay كان هذا المثال
+
+138
+00:11:24,830 --> 00:11:32,670
+المتبقى هنا من المرة اللى فاتت نكمل
+
+139
+00:11:32,670 --> 00:11:36,590
+ماقدرش اقول ان احنا هندخل على موضوع جديد لانه هو
+
+140
+00:11:36,590 --> 00:11:39,870
+تكميل له و بالعكس هنرجع نشتغل على inductive فيه
+
+141
+00:11:39,870 --> 00:11:43,710
+اللى هو عملت ال recursion فinductive لما بقول بدي
+
+142
+00:11:43,710 --> 00:11:49,030
+اثبت P of N من P of N minus 1 P of N minus 1 بدي
+
+143
+00:11:49,030 --> 00:11:52,900
+اثبتها من P of N minus 2لحظوا ان احنا بنعمل تكرار
+
+144
+00:11:52,900 --> 00:11:57,080
+جاعدين بنعمل عملية تكرار لعملية ال proof نفسها
+
+145
+00:11:57,080 --> 00:12:00,820
+فإذا هذه بتقودنا لحاجة اسمها recursion عملية
+
+146
+00:12:00,820 --> 00:12:04,260
+التكرار عملية التكرار فهي مبنية على بعض ماقدرش
+
+147
+00:12:04,260 --> 00:12:07,580
+اقول ان الموضوعين مفصلين عن بعض، الاتنين related
+
+148
+00:12:07,580 --> 00:12:10,560
+لبعض الحقيقة الاتنين الموضوعين related لبعض فال
+
+149
+00:12:10,560 --> 00:12:13,560
+recursion هي in general ان انا بعمل generation او
+
+150
+00:12:13,560 --> 00:12:20,310
+بعملبعمل definition ل object أو term منه نفسه لما
+
+151
+00:12:20,310 --> 00:12:22,590
+بقول بده اعمل تعريف لمجموعة ال elements داخل
+
+152
+00:12:22,590 --> 00:12:25,330
+sequence معين بعملها من نفس ال sequence من
+
+153
+00:12:25,330 --> 00:12:28,570
+elements موجودة في ال sequence نفسه من elements
+
+154
+00:12:28,570 --> 00:12:32,410
+موجودة داخل نفس ال sequence هي هي نفسها فإذا اما
+
+155
+00:12:32,410 --> 00:12:36,220
+ان بعملها definition هذا ال objectمنه نفسه او من
+
+156
+00:12:36,220 --> 00:12:39,740
+جزء منه او من جزء من جزء منه فانتوا لاحظوا هنا لما
+
+157
+00:12:39,740 --> 00:12:44,340
+بتتكلموا عن ال .. ال postage كنتوا من جزء من القيم
+
+158
+00:12:44,340 --> 00:12:49,100
+السابقة اللي ممكن اثبتها باستخدام اربعة او خمسة
+
+159
+00:12:49,100 --> 00:12:55,590
+cent stamps اربعة او خمسة cent stamps okayبحيث إن
+
+160
+00:12:55,590 --> 00:13:00,930
+أنا ال inductive proof هو أحد الصور الواضحة جدا
+
+161
+00:13:00,930 --> 00:13:03,270
+لعملية ال recursion أحد الصور الواضحة جدا لعملية
+
+162
+00:13:03,270 --> 00:13:06,350
+ال recursion ليش؟ لأن أنا بثبت P of N مائة plus
+
+163
+00:13:06,350 --> 00:13:12,330
+واحد recursively من P of N بشكل متكرر من P of N
+
+164
+00:13:12,330 --> 00:13:16,690
+إذا أثبتنا P of N automatically P of N مائة plus
+
+165
+00:13:16,690 --> 00:13:21,450
+واحد is trueإذا أثبتت P of N plus 1 is true بقدر
+
+166
+00:13:21,450 --> 00:13:26,190
+أثبت منها P of N plus 2 بنقدر نثبت منها plus 3
+
+167
+00:13:26,190 --> 00:13:31,190
+plus 4 فهذه عملية ال recursion أو ال recursively
+
+168
+00:13:31,190 --> 00:13:36,330
+proof في الحالة هذه بنقدر نقول كلمة recursive على
+
+169
+00:13:36,330 --> 00:13:39,350
+ال algorithm فنقول recursive algorithms زي اللي
+
+170
+00:13:39,350 --> 00:13:45,170
+هناخدها في آخر الموضوع إذا لحجناأو ممكن تكون
+
+171
+00:13:45,170 --> 00:13:48,950
+recursive definitions, recursive functions,
+
+172
+00:13:49,130 --> 00:13:53,090
+recursive sequences, recursive sets ففي مجالات
+
+173
+00:13:53,090 --> 00:13:55,490
+كتير ممكن أستخدم فيها عملية ال recursion .. ال
+
+174
+00:13:55,490 --> 00:13:57,350
+recursion بتاعتنا .. هناخدهم شوية .. شوية .. شوية
+
+175
+00:13:57,350 --> 00:14:00,450
+.. واحدة .. واحدة أثناء المحاضرة بتاعتنا .. أثناء
+
+176
+00:14:00,450 --> 00:14:04,230
+المحاضرة okay recursively defined functions ال
+
+177
+00:14:04,230 --> 00:14:07,590
+functions برضه بنقدر نعرفها as a ..
+
+178
+00:14:10,140 --> 00:14:14,340
+recursion form أبسط حللة اللي هي simplest case one
+
+179
+00:14:14,340 --> 00:14:19,620
+way to define a function ك if of function from
+
+180
+00:14:19,620 --> 00:14:23,440
+natural number to set natural number to set
+
+181
+00:14:23,440 --> 00:14:27,440
+natural number to set الحكيش احنا فعلا اشتغلناها
+
+182
+00:14:27,440 --> 00:14:34,640
+قبل هيك احنا فعلا اشتغلناها سابقا كيف اشتغلناها
+
+183
+00:14:34,640 --> 00:14:39,050
+سابقا ان انتوا تقولواهنا بدنا نمثل نفس التمثيل
+
+184
+00:14:39,050 --> 00:14:41,070
+اللي أخدناه أيام ال function لما اتكلمنا عن ال
+
+185
+00:14:41,070 --> 00:14:43,790
+function كنا نقول والله في عنا ايش كنا نسمي هذا
+
+186
+00:14:43,790 --> 00:14:48,850
+domain codomain
+
+187
+00:14:48,850 --> 00:14:53,110
+كنا بنقول مثلا natural number معناه ان انا بتكلم
+
+188
+00:14:53,110 --> 00:15:00,250
+صفر واحد اتنين to n مظبوط طيب set ال set هذه معناه
+
+189
+00:15:00,250 --> 00:15:04,790
+ان انا بقول element داخل ال set بنعرفهابال
+
+190
+00:15:04,790 --> 00:15:08,090
+location تبعها نعرفها بال location location تبعها
+
+191
+00:15:08,090 --> 00:15:16,090
+ممكن نقول a node فهذا related لهذه function فهذه
+
+192
+00:15:16,090 --> 00:15:23,250
+function of zero بعناك اللي هي ال a zero طيب
+
+193
+00:15:23,250 --> 00:15:29,930
+الواحد a واحد الاتنين a اتنين to a n فلاحظوا ان
+
+194
+00:15:29,930 --> 00:15:33,090
+احنا بنعرف ال element عن طريق ال location تبعه عن
+
+195
+00:15:33,090 --> 00:15:38,400
+طريقجديش الترتيب أو ال location تبعه في ال set
+
+196
+00:15:38,400 --> 00:15:43,500
+okay فبنقدر هنا عشان نعرف الكلام هذا ل set او
+
+197
+00:15:43,500 --> 00:15:48,940
+series او sequence او string بنقدر نعرفه باستخدام
+
+198
+00:15:48,940 --> 00:15:51,080
+ال location تبعه فبقدر اقول ان ال function فعليا
+
+199
+00:15:51,080 --> 00:15:55,700
+ال function f of n location in بنعرف منه ال
+
+200
+00:15:55,700 --> 00:15:59,840
+element في ال location هذا بنعرف ال element في ال
+
+201
+00:15:59,840 --> 00:16:03,040
+location هذا فبنقدر نعرفها كتالي بنفس فكرة ال
+
+202
+00:16:03,040 --> 00:16:07,130
+inductionأو الـ inductive proof اللي أخدناها محتاج
+
+203
+00:16:07,130 --> 00:16:10,730
+ال base الأساسي فبنعمل تعريف ل ال initial
+
+204
+00:16:10,730 --> 00:16:15,090
+condition أو ال base case بتاعتنا ال F of 0 أنا
+
+205
+00:16:15,090 --> 00:16:18,730
+بتكلم عن ال natural فأول element فيها 0 فبدنا نثبت
+
+206
+00:16:18,730 --> 00:16:23,750
+ان ال F of 0 is true فعلا موجودة لها قيمة for N
+
+207
+00:16:23,750 --> 00:16:27,310
+أكبر من 0 هنا بدأنا كأنه في ال inductive كأنه
+
+208
+00:16:27,310 --> 00:16:34,350
+بدأنا في إيش في ال inductive define F of Nك term
+
+209
+00:16:34,350 --> 00:16:40,950
+of 0, f of 1, f of 2, f of 3, to f of n minus 1
+
+210
+00:16:40,950 --> 00:16:45,990
+إذا كان فعلا to f of n minus 1 مثبتة منهم بقدر
+
+211
+00:16:45,990 --> 00:16:51,690
+أجيب f of n بشكل recursively بشكل تكراري بشكل
+
+212
+00:16:51,690 --> 00:16:56,230
+تكراري زي ناخد شوية أمثلة توضح الأمور لو قلنا مثلا
+
+213
+00:16:56,230 --> 00:17:00,890
+السيريز عندنا معرفة كتالي a n equivalent to 2 to
+
+214
+00:17:00,890 --> 00:17:05,200
+the power nبدنا نمثلها recursively بشكل recursive
+
+215
+00:17:05,200 --> 00:17:09,200
+recursively معناته ان انا بتحول ال form اللي عندى
+
+216
+00:17:09,200 --> 00:17:19,660
+هنا ل form كتالي a n بدلالة a n minus واحد من
+
+217
+00:17:19,660 --> 00:17:22,540
+العنصر اللى جابله طب هل ممكن نمثلها بالعنصر اللى
+
+218
+00:17:22,540 --> 00:17:24,380
+جابله او نقدر نمثلها بالعنصر اللى جابله كل اللى
+
+219
+00:17:24,380 --> 00:17:29,020
+بقدر اقول انه مضروب فتنة لحظوا
+
+220
+00:17:31,290 --> 00:17:33,710
+2 to the power of n هي عبارة عن 2 to the power of
+
+221
+00:17:33,710 --> 00:17:38,430
+n minus واحد في اتنين لان ماعرفين ان كل الموضوع
+
+222
+00:17:38,430 --> 00:17:42,230
+هنا الاتنين مضروبة في اتنين فهذه 2 to the power of
+
+223
+00:17:42,230 --> 00:17:48,490
+n minus واحد في 2 to the power of one ال base واحد
+
+224
+00:17:48,490 --> 00:17:52,990
+نفس ال base فهذه اتنين ومجموع ال powers مجموع ال
+
+225
+00:17:52,990 --> 00:17:56,870
+powers ف3 to the power of n ف a of n 2 to the
+
+226
+00:17:56,870 --> 00:18:01,410
+power of n مظبوطنفس ال condition فبنبدأ نعرف ال a
+
+227
+00:18:01,410 --> 00:18:05,570
+node ال initial تبعتنا initial بتاعتنا عند zero
+
+228
+00:18:05,570 --> 00:18:10,710
+two to the power zero ف a zero بيساوي واحد for n
+
+229
+00:18:10,710 --> 00:18:15,770
+أكبر منه يساوي صفر let a n بتساوي a n minus one في
+
+230
+00:18:15,770 --> 00:18:20,290
+اتنين في اتنين فبقدر اكون مثلته بالعنصر اللي جابله
+
+231
+00:18:20,290 --> 00:18:24,310
+بالعنصر او ال element السابق بال element السابق له
+
+232
+00:18:24,310 --> 00:18:27,150
+okay هذا مثال ناخد كمان مثال
+
+233
+00:18:36,040 --> 00:18:38,620
+نبدأ بالإنشيال الانشيال زي ما قلنا بالمبادرة
+
+234
+00:18:38,620 --> 00:18:44,140
+بالزيرو f of zero اتانية given تلاتة طيب لاتكفي
+
+235
+00:18:44,140 --> 00:18:48,880
+لحالها محتاج ال initial elements هو يعطيني element
+
+236
+00:18:48,880 --> 00:18:51,020
+واحد من ال initial elements من ال initial elements
+
+237
+00:18:51,020 --> 00:18:56,620
+او القيم المعروفة مسبقا f of zero بتسوي تلاتة
+
+238
+00:18:56,620 --> 00:19:02,590
+محتاج ال rule لسهكيف أربط f of n ب f of n minus
+
+239
+00:19:02,590 --> 00:19:07,290
+واحد برضه أعطاني ال rule تبعته for all for all and
+
+240
+00:19:07,290 --> 00:19:10,950
+belong to natural number let f of n plus واحد تسوي
+
+241
+00:19:10,950 --> 00:19:16,590
+two في f of n زي التلاتة هل واجد بقدر أجيب كل ال
+
+242
+00:19:16,590 --> 00:19:19,210
+sequence تبعيه نقدر نجيب حاليا مدام صار عند ال
+
+243
+00:19:19,210 --> 00:19:23,130
+rule و عند ال initial كله بتجيب بعدين أي element
+
+244
+00:19:23,130 --> 00:19:26,610
+بتكويه بتقدر تجيبه تقدروا اتجيبوا خلينا نقول f of
+
+245
+00:19:26,610 --> 00:19:27,950
+واحد كده هتساوي
+
+246
+00:19:33,170 --> 00:19:38,690
+عودوا هنا zero بالظبط فتلاتة
+
+247
+00:19:38,690 --> 00:19:42,090
+في الست .. تلاتة في اتنين ستة زائد تلاتة تسعة تسعة
+
+248
+00:19:42,090 --> 00:19:50,690
+okay طيب F of اتنين واحد
+
+249
+00:19:50,690 --> 00:19:55,590
+وعشرين طيب التالت F of three واحد وعشرين في اتنين
+
+250
+00:19:55,590 --> 00:19:58,890
+اتنين واربعين زائد تلاتة خمسة واربعين طيب خمسة
+
+251
+00:19:58,890 --> 00:20:03,650
+واربعين في اتنين تسعين زائد تلاتة تلاتة وتسعينOkay
+
+252
+00:20:03,650 --> 00:20:06,930
+فكل element بيجيب ال element اللي ورا كل element
+
+253
+00:20:06,930 --> 00:20:18,390
+بيجيب ال element اللي ورا Okay
+
+254
+00:20:18,390 --> 00:20:24,270
+نكمل برضه ال factorial ال factorial بنقدر نمثلها ك
+
+255
+00:20:24,270 --> 00:20:28,790
+multiplication ك multiplication فلما بقولn
+
+256
+00:20:28,790 --> 00:20:35,550
+factorial هي عبارة عن multiplication ل i from 1 to
+
+257
+00:20:35,550 --> 00:20:41,110
+n كيف
+
+258
+00:20:41,110 --> 00:20:44,970
+نقدر نمثلها ببساطة جدا عشان نمثلها معناه ان انا
+
+259
+00:20:44,970 --> 00:20:50,100
+بدى اعرفها مش to n to n minus one to n minus oneف
+
+260
+00:20:50,100 --> 00:20:55,640
+n factorial تساوي n minus one factorial .. إيش
+
+261
+00:20:55,640 --> 00:21:01,020
+الفرق اللي بينهم؟ إن هي مضروبة في n فهي ال
+
+262
+00:21:01,020 --> 00:21:05,060
+recursive form
+
+263
+00:21:05,060 --> 00:21:09,920
+أو ال rule بتاعتنا okay فال base case تبعتنا f of
+
+264
+00:21:09,920 --> 00:21:14,760
+zeroعند ال zero factorial zero zero factorial واحد
+
+265
+00:21:14,760 --> 00:21:18,360
+طيب ال recursive part اللي هو ال rule اللي بدنا
+
+266
+00:21:18,360 --> 00:21:23,640
+نستخدمها ب F of N equivalent to N مضروبة في F of N
+
+267
+00:21:23,640 --> 00:21:28,100
+minus واحد F of N minus واحد فمعطينا هاي العنصر
+
+268
+00:21:28,100 --> 00:21:31,660
+الأول والتاني والتالت بعد العنصر zero بعد zero
+
+269
+00:21:31,660 --> 00:21:37,020
+فهنا واحد factorialبواحد طيب هنا اتنين factorial
+
+270
+00:21:37,020 --> 00:21:41,080
+بتنين بس انا عارف انه هاد عبارة عن ايش اتنين في
+
+271
+00:21:41,080 --> 00:21:45,760
+واحد factorial واحد factorial هنا عارفين انه هاد
+
+272
+00:21:45,760 --> 00:21:50,860
+عبارة عن ثلاثة في اتنين factorial من العنصر اللي
+
+273
+00:21:50,860 --> 00:21:54,360
+جابلها من العنصر اللي جابلها بيمكننا انجيبها طيب
+
+274
+00:21:54,360 --> 00:21:57,760
+شوية easy examples مول easy examples شوية examples
+
+275
+00:21:57,760 --> 00:22:07,990
+بسيطة ممكن نتكلم فيها بسرعةلو قلنا a في n طيب،
+
+276
+00:22:07,990 --> 00:22:15,070
+بتجيبها في دلالة n-1 فبتكون عبارة عن إيش؟ a في n-1
+
+277
+00:22:15,070 --> 00:22:24,410
+زائد a زائد a خدوا ال a مشترك، بتبقى a-1 زائد 1
+
+278
+00:22:24,410 --> 00:22:34,370
+فصرت في إيش؟ في a في nOkay طيب a to the power n
+
+279
+00:22:34,370 --> 00:22:40,590
+بده تصير a to the power n minus واحد ايش ال term
+
+280
+00:22:40,590 --> 00:22:44,950
+اللي بدي اجمعه و ادربه و اقسمه في a في a على
+
+281
+00:22:44,950 --> 00:22:48,070
+اعتبار انه a عبارة عن to the power واحد عبارة عن
+
+282
+00:22:48,070 --> 00:22:55,410
+to the power واحد okay summation summation
+
+283
+00:22:55,410 --> 00:22:59,810
+من zero to n بده امثلها باش summation to n minus
+
+284
+00:22:59,810 --> 00:23:04,780
+واحد طب ايش اللي دلالـ An نفسها آخر element اللي
+
+285
+00:23:04,780 --> 00:23:11,020
+ما انجمعش معها ال multiplication الفكتوري اللي كنا
+
+286
+00:23:11,020 --> 00:23:13,740
+نتكلم عنه نفس الفكتوري اللي كنا نتكلم عنه ال
+
+287
+00:23:13,740 --> 00:23:18,460
+intersection عشان
+
+288
+00:23:18,460 --> 00:23:24,510
+نجيبها بدلالة to n-1 إيش هتساوي؟Intersection من 0
+
+289
+00:23:24,510 --> 00:23:28,510
+ل N-1 من Intersection من N؟ Intersection زاد N
+
+290
+00:23:28,510 --> 00:23:33,050
+فإذا هنا كأنها صارت ال intersection الكبيرة زي ال
+
+291
+00:23:33,050 --> 00:23:42,290
+summation من 0 to N-1 Intersection صغيرة مع A N أو
+
+292
+00:23:42,290 --> 00:23:51,310
+مع S هنا معرفين أحنا لل S S S N لل S N تمام؟ okay
+
+293
+00:23:54,340 --> 00:23:58,440
+هي مجموعة examples بسيطة سهلة مش فيها كتير مشاكل
+
+294
+00:23:58,440 --> 00:24:02,520
+okay Fibonacci series واحدة من ال series برضه اللي
+
+295
+00:24:02,520 --> 00:24:07,140
+هنشتغل عليها كتير اللي هي ال Fibonacci series برضه
+
+296
+00:24:07,140 --> 00:24:13,200
+من ال series اللي تعرف بال previous terms بتاعتها
+
+297
+00:24:13,200 --> 00:24:17,480
+بال terms السابقة لها بس هنا بنعرفهاش term واحد
+
+298
+00:24:17,480 --> 00:24:22,890
+سابق بنعرفه two termstwo terms سابقين لها فلما
+
+299
+00:24:22,890 --> 00:24:28,630
+نقول Fapanacci series FF of N هو N أكبر من أو
+
+300
+00:24:28,630 --> 00:24:34,590
+تساوي صفر من السيريز المشهورة جدا تعرف كتالة F of
+
+301
+00:24:34,590 --> 00:24:41,470
+0 equal to 0 F of 1 equal to 1 طب F of N أو أكثر
+
+302
+00:24:41,470 --> 00:24:47,190
+تعرف ك F of N minus 1 plus F of N minus 2 ال two
+
+303
+00:24:47,190 --> 00:24:49,490
+elements اللي جابلها مجموعة ال two elements اللي
+
+304
+00:24:49,490 --> 00:24:52,250
+جابلها فكل element يساوي ال two elements اللي
+
+305
+00:24:52,250 --> 00:24:57,060
+جابله فلو قلنا صفرو واحد هاي two initials دعونا
+
+306
+00:24:57,060 --> 00:25:02,580
+مجموحهم بيجيبولي ال element اللي بعدهم هنا ال
+
+307
+00:25:02,580 --> 00:25:06,080
+element صفر ال element الأول مجموحهم هيساوي ال
+
+308
+00:25:06,080 --> 00:25:11,020
+element التاني واحد طيب التاني أو الأول مع التاني
+
+309
+00:25:11,020 --> 00:25:16,020
+هيعطينا تالتالاتنين طيب التاني مع التالت هيعطينا
+
+310
+00:25:16,020 --> 00:25:19,740
+الرابع فإذا واحد زائد اتنين بيساوي تلاتة تلاتة
+
+311
+00:25:19,740 --> 00:25:22,460
+زائد اتنين بيساوي خمسة تلاتة زائد خمسة بيساوي
+
+312
+00:25:22,460 --> 00:25:26,100
+تمانية تمانية زائد خمسة بيساوي تلتاشر تلتاشر زائد
+
+313
+00:25:26,100 --> 00:25:29,200
+تمانية بيساوي واحد وعشرين و هكذا بتبقى لكم كاملين
+
+314
+00:25:29,200 --> 00:25:33,980
+هاي ال series طبعا واضح أنها بتزيد كل ما زادت قيمة
+
+315
+00:25:33,980 --> 00:25:38,620
+n كل ما زادت قيمة n بتزيد هذه واحدة من النماذج
+
+316
+00:25:38,620 --> 00:25:41,500
+لمين لل recursive
+
+317
+00:25:46,470 --> 00:25:49,810
+Okay ناخد Inductive Proof لحظوا هنا رجعنا ل
+
+318
+00:25:49,810 --> 00:25:52,410
+Inductive لأن هم أصلا الموضوعين مترابطنين جدا فبعض
+
+319
+00:25:52,410 --> 00:25:55,110
+ما بقدرش أقول أن هذا موضوع غير ال Inductive هم
+
+320
+00:25:55,110 --> 00:25:59,210
+الأثنين نفس الموضوع أساسا ففي theorem about
+
+321
+00:25:59,210 --> 00:26:02,870
+Fapinacci Series بدنا نثبتها باستخدام ال Inductive
+
+322
+00:26:02,870 --> 00:26:09,180
+و تحديدا ال second principle of inductionفحنقول f
+
+323
+00:26:09,180 --> 00:26:14,580
+of n أقل من 2 to the power of n او f of n أقل من 2
+
+324
+00:26:14,580 --> 00:26:17,560
+to the power of n هل فعلا هذا الكلام حقيقي لكل ال
+
+325
+00:26:17,560 --> 00:26:21,120
+elements في فبناتشي سيريز فبناتشي سيريز خلاص احنا
+
+326
+00:26:21,120 --> 00:26:28,060
+عارفين ان هي صفر واحد واحد اتنين تلاتة خمسة تمانية
+
+327
+00:26:28,060 --> 00:26:32,080
+تلتاشة واحد وعشرين و هكذا هل ال elements هذه فعلا
+
+328
+00:26:32,080 --> 00:26:34,860
+دائما هتكون أقل من two to the power of the element
+
+329
+00:26:35,950 --> 00:26:39,030
+بدنا نشوف، هنبدأ بال إيش؟ بال base case ال base
+
+330
+00:26:39,030 --> 00:26:42,150
+case طبعا ال two cases الحقيقة هيكون عندنا اللي هو
+
+331
+00:26:42,150 --> 00:26:45,250
+ال F0 و ال F1 هدول دايما ال initial بتاعهم ليش؟
+
+332
+00:26:45,250 --> 00:26:48,170
+لإن أنا محتاجهم عشان أجيبي اللي وراهم محتاجهم
+
+333
+00:26:48,170 --> 00:26:54,570
+أجيبي العنصر التالت بعدهم ف F of 0، 0 أقل منته
+
+334
+00:26:54,570 --> 00:26:59,420
+تتبارزيفإذا ال condition الأول اتحقق طيب التاني ال
+
+335
+00:26:59,420 --> 00:27:03,420
+N شريط تاني F1 بتسوي واحد أقل من two to the power
+
+336
+00:27:03,420 --> 00:27:07,440
+واحد ليش لإن قمتها باتنين فالواحد أقل أقل من اتنين
+
+337
+00:27:07,440 --> 00:27:12,920
+okay اتحقق التاني خلصنا ال base cases ال inductive
+
+338
+00:27:12,920 --> 00:27:17,280
+ال inductive نكتب ال rule نفسها فطبعا احنا فبنادش
+
+339
+00:27:17,280 --> 00:27:20,760
+خلاص عرفنا ال rule بتاعتها فبنادش عرفنا ال rule FN
+
+340
+00:27:20,760 --> 00:27:25,060
+بتسوي FN minus واحد زائد FN minus اتنين كتبناها
+
+341
+00:27:26,340 --> 00:27:32,100
+Okay هنا هنقول عشان أثبت ال .. وين راحت .. لكل قيم
+
+342
+00:27:32,100 --> 00:27:41,240
+K أقل من N is true أقل من N is true عشان أجيب FN
+
+343
+00:27:41,240 --> 00:27:44,880
+طيب إيش يعني true؟ ال true معناته ان هي محقق
+
+344
+00:27:44,880 --> 00:27:49,360
+النظرية ال theory هذيفإذا كانت فعلًا احنا k أقل من
+
+345
+00:27:49,360 --> 00:27:54,220
+n فإذا fk أقل من 2 to the power of k 2 to the
+
+346
+00:27:54,220 --> 00:27:57,360
+power of k هي الحقيقة ال theorem تبعد طيب نيجي نصل
+
+347
+00:27:57,360 --> 00:28:05,360
+إلى ال fn fn بتسوي fn-1 plus fn-2 n-1 تنطبق على ال
+
+348
+00:28:05,360 --> 00:28:11,230
+k هذه لأنه أقل من n فإذا بقدر امثلها بإيش twoto
+
+349
+00:28:11,230 --> 00:28:15,330
+the power of the term 2 to the power of n-1 طيب
+
+350
+00:28:15,330 --> 00:28:20,250
+plus if n-2 2 to the power of n-2 هلوجد هذا ال
+
+351
+00:28:20,250 --> 00:28:28,150
+term كله بدنا نجيبه بدلالة n مش n-1 عشان نشوف هل
+
+352
+00:28:28,150 --> 00:28:31,350
+فعلا أقل منه يمكن يطلع أكبر منه يمكن يطلع بساوي مش
+
+353
+00:28:31,350 --> 00:28:35,290
+عارفين نشوفه هل فعلا بحقيقة لأ ال condition هذ أو
+
+354
+00:28:35,290 --> 00:28:40,520
+لأ أولا بدنا نوحدالـ two terms هاتولا، بدنا نوحد
+
+355
+00:28:40,520 --> 00:28:42,360
+الـ two terms بس خدوا بالكوا بتكونوا توحدوا الـ
+
+356
+00:28:42,360 --> 00:28:46,700
+two terms في سبيل إن ال inequality هذه، عدم
+
+357
+00:28:46,700 --> 00:28:51,160
+المساواة هذه، اللي هي أقل من، ما تتغيرش، في سبيل
+
+358
+00:28:51,160 --> 00:28:55,760
+إنها ما تتغيرش، لو بدنا نغير ل N minus two، يعني
+
+359
+00:28:55,760 --> 00:28:58,940
+هذا بدنا نحطها، نقول والله two to the power of N
+
+360
+00:28:58,940 --> 00:29:04,070
+minus two، أنا كبرتها ولا جللتها؟زغرتها، زغرناها،
+
+361
+00:29:04,070 --> 00:29:08,890
+فإذا بصير في خوف عليها الأقل منها دي، ممكن تنجلب،
+
+362
+00:29:08,890 --> 00:29:13,670
+ممكن تكون عكسها، فلأ بلاش من هذه، بنشتغل على مين؟
+
+363
+00:29:13,670 --> 00:29:17,690
+على تحويل two to the power n minus two ل two to
+
+364
+00:29:17,690 --> 00:29:21,230
+the power n minus one، مين أكبر منهم من التانية؟
+
+365
+00:29:23,420 --> 00:29:27,980
+فإذن بمجرد إن أنا استبدلت هذه بقيمة أكبر منها أنا
+
+366
+00:29:27,980 --> 00:29:31,420
+محافظ على أكبر منها بالعكس زودت ال inequality هذه
+
+367
+00:29:31,420 --> 00:29:35,580
+زودت ال inequality عدم المساوية زودتها فانا بالعكس
+
+368
+00:29:35,580 --> 00:29:41,040
+أكبر من ال term ده أكبر من if ان ما زالت مضمونة
+
+369
+00:29:41,040 --> 00:29:44,230
+بالعكس حتى زودناهاالـ inequality اللي بينهم فصارت
+
+370
+00:29:44,230 --> 00:29:46,650
+two to the power of n minus one plus two to the
+
+371
+00:29:46,650 --> 00:29:49,790
+power of n minus one هدول بجمحهم بقدر أجيبها
+
+372
+00:29:49,790 --> 00:29:53,510
+بدلالة n على اعتبار ان هنا two to the power of n
+
+373
+00:29:53,510 --> 00:29:56,930
+minus one مضروبة في اتنين ممكن اكررها مرتين هيها
+
+374
+00:29:56,930 --> 00:30:00,250
+طب هذه عبارة عن two to the power of one to the
+
+375
+00:30:00,250 --> 00:30:03,790
+power of one to the power of one بتصيرت two to the
+
+376
+00:30:03,790 --> 00:30:08,190
+power of n minus one plus one صارت ايه؟ two to the
+
+377
+00:30:08,190 --> 00:30:12,160
+power of n2 to the power n فإذا النتيجة في النهاية
+
+378
+00:30:12,160 --> 00:30:20,960
+أن f of n أقل من 2 to the power n أقل من 2 to the
+
+379
+00:30:20,960 --> 00:30:23,280
+power n طب ما هو نفس ال theorem فعلا مطلوب أثبتها
+
+380
+00:30:23,280 --> 00:30:28,260
+هي نفس ال theorem المطلوب أثبتها تمام هذا باستخدام
+
+381
+00:30:28,260 --> 00:30:31,880
+.. باستخدام إيش؟ ال inductive باستخدام إيش؟ ال
+
+382
+00:30:31,880 --> 00:30:32,360
+inductive
+
+383
+00:30:42,780 --> 00:30:48,880
+Okay في theorem ل lame أو lame's theorem واضح من
+
+384
+00:30:48,880 --> 00:30:53,400
+اسمه فرنسي واضح من الاسم انه فرنسي
+
+385
+00:30:56,420 --> 00:31:00,740
+فبناتشي إيطالي طبعا حتى اسمه باين فبناتشي إيطالي
+
+386
+00:31:00,740 --> 00:31:06,180
+هنا متكلم علمي عالم فرنسي وجدلنا relation لواحدة
+
+387
+00:31:06,180 --> 00:31:11,060
+من ال algorithms اللي هي بطبيعتها recursive ..
+
+388
+00:31:11,060 --> 00:31:14,340
+recursive algorithm أهمها و احنا أخدناها اللي هي
+
+389
+00:31:14,340 --> 00:31:17,450
+Euclide's algorithmEuclides algorithm عشان نجيب
+
+390
+00:31:17,450 --> 00:31:20,290
+منها ال greatest common divisor لو متذكرين كنا
+
+391
+00:31:20,290 --> 00:31:24,570
+نجيبها باستخدام ال modular ال modular كنا بنكررها
+
+392
+00:31:24,570 --> 00:31:28,310
+كذا مرة ال modular لعند ما نصل ايش ل b equal to
+
+393
+00:31:28,310 --> 00:31:33,090
+zero او يعني ال ناتج تبع ال modular كان يطلع zero
+
+394
+00:31:33,090 --> 00:31:35,390
+فبناخد ال element التاني هو ال greatest common
+
+395
+00:31:35,390 --> 00:31:39,750
+divisor كان معنا ذلك انه ال modular كنا نستخدمه
+
+396
+00:31:39,750 --> 00:31:46,240
+كذا مرة في تكرار في recursionفي recursion في تكرار
+
+397
+00:31:46,240 --> 00:31:50,880
+عملناه هنا في الحالة بتاعتنا okay لما كنا بنقول
+
+398
+00:31:50,880 --> 00:31:56,200
+the greatest common divisor كانت بتساوي ل a و b
+
+399
+00:31:56,200 --> 00:31:58,700
+طبعا خلينا ناخدها ل a و b بعد ما بنقول بتساوي
+
+400
+00:31:58,700 --> 00:32:04,080
+نذكركوا فيها فهذه كانت تساوي the greatest common
+
+401
+00:32:04,080 --> 00:32:12,650
+divisor لمن a mod b و bطبعا الناتج هذا يقولنا أنه
+
+402
+00:32:12,650 --> 00:32:20,150
+يطلع أقل من B أو 0 إذا equal to B معناته equal to
+
+403
+00:32:20,150 --> 00:32:23,810
+0 فعلا equal to 0 ففي الحالة هذه كنا نقول برضه to
+
+404
+00:32:23,810 --> 00:32:27,930
+sell greatest common divisor للناتج هنا اللي هو R
+
+405
+00:32:27,930 --> 00:32:37,990
+نفترض أن قيمته R ف B mod R و R لحظوا في تكرارالـ
+
+406
+00:32:37,990 --> 00:32:40,530
+greatest common divisor اللي احنا بنكرره فانتوا ..
+
+407
+00:32:40,530 --> 00:32:43,670
+فاحنا فعليا ال .. ال Euclides algorithm بتكرر جاعد
+
+408
+00:32:43,670 --> 00:32:48,870
+طب أكم مرة هيتكرر؟ ال recursion تبعتنا أكم مرة؟ ال
+
+409
+00:32:48,870 --> 00:32:52,030
+recursion تكرر فواحدة من الأمثلة الواضحة جدا لل
+
+410
+00:32:52,030 --> 00:32:54,370
+recursion الموضوع اللي احنا بنحكي فيه هي ال
+
+411
+00:32:54,370 --> 00:32:58,910
+Euclides algorithm أكم مرة بتتكرر؟ بتتكرر أقل من
+
+412
+00:32:58,910 --> 00:33:02,950
+أو تسوى 5K الشيء ال K .. K عرفناه على أساس أن هي
+
+413
+00:33:02,950 --> 00:33:12,290
+floor log Bلل base 10 plus 1 او عدد ال digits
+
+414
+00:33:12,290 --> 00:33:18,510
+للرقم الأقل للرقم بي عدد ال digits للرقم بي ليش؟
+
+415
+00:33:18,510 --> 00:33:25,070
+خلّيني افترض ان ال بي هدي 99 هي أكبر رقم ممكن لل
+
+416
+00:33:25,070 --> 00:33:29,830
+two digits مثلا فلما نقول log base 10
+
+417
+00:33:33,740 --> 00:33:41,080
+floor زائد واحد log تسعة وتسعين لأ أقل من اتنين
+
+418
+00:33:41,080 --> 00:33:45,860
+بيدوب لإيش لأنه عند المية ال log بيساوي اتنين فهدي
+
+419
+00:33:45,860 --> 00:33:50,780
+لأ واحد فاصلة تسعة يمكن تسعة مش فاكر بس رقم كبير
+
+420
+00:33:50,780 --> 00:33:54,760
+ولكن ماوصلش للاتنين أقل من اتنين مدام في الحالة
+
+421
+00:33:54,760 --> 00:34:01,250
+هدي floor هيساوي واحدزائد واحد يساوي اتنين طبعا من
+
+422
+00:34:01,250 --> 00:34:05,050
+الاول اتنين معناته two digits هيها و خلاص two
+
+423
+00:34:05,050 --> 00:34:09,390
+digits و خلاص طيب لو قولنا مية log مية يساوي اتنين
+
+424
+00:34:09,390 --> 00:34:13,890
+زائد واحد تلاتة ما هي فعلا three digits3 digits
+
+425
+00:34:13,890 --> 00:34:19,810
+فإذا سواء أقول K بتساوي floor log V plus 1 أو أقول
+
+426
+00:34:19,810 --> 00:34:24,990
+إن هي number of decimal digits in V .. in B اللي
+
+427
+00:34:24,990 --> 00:34:30,250
+هو ال element الأقل منهم ال element إيش؟ الأقل فلو
+
+428
+00:34:30,250 --> 00:34:33,590
+بدنا نعمل greatest common divisor فرضا جدلا ل
+
+429
+00:34:33,590 --> 00:34:36,910
+سبعمية
+
+430
+00:34:36,910 --> 00:34:42,430
+مثلا تلاتة وأربعين وستمية
+
+431
+00:34:43,540 --> 00:34:51,340
+بلاش ال 43 انا شاك ان يكون .. مالوش نفترض 44 و 650
+
+432
+00:34:51,340 --> 00:34:55,140
+هدول
+
+433
+00:34:55,140 --> 00:34:59,400
+اكبر عدد ممكن لعدد ال iterations بتاعتهم او عدد
+
+434
+00:34:59,400 --> 00:35:05,480
+التكرار ل ال Euclid's algorithm جداش؟ خمسة في
+
+435
+00:35:05,480 --> 00:35:10,640
+تلاتة الرقم الأصغر هيه كم digit فيه؟ تلاتة طب لو
+
+436
+00:35:10,640 --> 00:35:17,420
+قولنا 65هي سبعمية اربع واربع وخمسة وستين في اتنين
+
+437
+00:35:17,420 --> 00:35:21,860
+عشرة لانه صار two digits فأكبر عدد iterations
+
+438
+00:35:21,860 --> 00:35:26,920
+ممكنة تكون بتساوي two digits في .. في من؟ في
+
+439
+00:35:26,920 --> 00:35:31,220
+الخمسة .. في الخمسة ممكن تكون أقل .. ممكن تكون أقل
+
+440
+00:35:31,220 --> 00:35:36,160
+.. ممكن تكون أقل .. okay ففي الآخر أثبت .. يعني
+
+441
+00:35:36,160 --> 00:35:41,490
+أثبت لميه أنهالألغوريثم يوخليتس هو الوقت اللينيار
+
+442
+00:35:41,490 --> 00:35:46,730
+في الكترين في B هو فعلا لينيار ليش لأنه أقل من أو
+
+443
+00:35:46,730 --> 00:35:50,830
+يسوى خمسة K والخمسة K لينيار لينيار فهي relation
+
+444
+00:35:50,830 --> 00:35:55,710
+لينيار كل ما زادت عدد ال digits كل ما هتزيد عدد ال
+
+445
+00:35:55,710 --> 00:36:01,310
+iterations أو عدد المراحل الألغوريثم نفسها كم مرة
+
+446
+00:36:01,310 --> 00:36:07,800
+هتتكرر عدد ال iterationsrecursively defined sets
+
+447
+00:36:07,800 --> 00:36:11,280
+عملية ال recursively او التكرار في تعريف ال sets
+
+448
+00:36:11,280 --> 00:36:16,880
+نبدأ ال algorithm و هناخد examples نبدأ نشتغل على
+
+449
+00:36:16,880 --> 00:36:20,860
+ال set هل فعلا ممكن نمثلها او تمثل باستخدام
+
+450
+00:36:20,860 --> 00:36:26,600
+recursive بشكل recursively اه ممكن ممكن كيف ممكن
+
+451
+00:36:26,600 --> 00:36:30,120
+اذا كان حددنا small finite set of base elements of
+
+452
+00:36:30,120 --> 00:36:34,460
+S اذا كان حددنا elements و يعني على الأقلأكم من
+
+453
+00:36:34,460 --> 00:36:38,880
+element small numbers أو small finite elements
+
+454
+00:36:38,880 --> 00:36:41,840
+مجموعة elements في الأول على أساس أقدر أعمل منهم
+
+455
+00:36:41,840 --> 00:36:44,000
+generation للباقي نقدر نعمل منهم generation ممكن
+
+456
+00:36:44,000 --> 00:36:47,420
+يكون element واحد ممكن يكون اتنين نقدر نعمل منهم
+
+457
+00:36:47,420 --> 00:36:51,280
+generation طيب لو عرفنا مجموعة ال elements small
+
+458
+00:36:51,280 --> 00:36:56,280
+finite set of elements هل كافي؟ لأ محتاج ال rule
+
+459
+00:36:56,280 --> 00:36:59,940
+محتاج المعادلة اللي أعمل فيها generation فمحتاج
+
+460
+00:36:59,940 --> 00:37:03,870
+rule of constructing new elements of usإذا اتحقق
+
+461
+00:37:03,870 --> 00:37:07,510
+كنت انتها دولة بقدر أعرف ال set بدون ما أضطر أحط
+
+462
+00:37:07,510 --> 00:37:10,450
+كل ال elements ساعتها بدون أن أضطر نحط كل ال
+
+463
+00:37:10,450 --> 00:37:17,490
+elementsبشكل منطقي و بشكل ضمني S has no other
+
+464
+00:37:17,490 --> 00:37:21,530
+elements but these اللي بنقدر نعمله generation فقط
+
+465
+00:37:21,530 --> 00:37:24,030
+هم ال elements يعني ما تقولوش طب ما يمكن يكون في
+
+466
+00:37:24,030 --> 00:37:29,070
+elements تانية لأ مدان فيه rule ففقط ال elements
+
+467
+00:37:29,070 --> 00:37:32,630
+اللي belong to this set هي اللي تم عملية ال
+
+468
+00:37:32,630 --> 00:37:35,670
+generation بتاعتها من ال rule بتاعتنا فقط لو يوجد
+
+469
+00:37:35,670 --> 00:37:39,470
+أي elements أخرى for example لو قولنا three belong
+
+470
+00:37:39,470 --> 00:37:46,020
+to set Sset S و اعطاني معلومة واحدة ان التلاتة
+
+471
+00:37:46,020 --> 00:37:50,640
+belong to this set فقط ماعطانيش اش تاني و بعدين
+
+472
+00:37:50,640 --> 00:37:56,420
+let x plus y belong to S برضه مجموعة symbols قالنا
+
+473
+00:37:56,420 --> 00:38:03,360
+ان two elements x و y belong to S طيب if x و y
+
+474
+00:38:03,360 --> 00:38:08,420
+belong to mean to S فهنا بيعطيني اذن ان مجموحهم
+
+475
+00:38:08,420 --> 00:38:12,540
+belong to S اذا كانوا الاتنين داخل Sإذا كانوا
+
+476
+00:38:12,540 --> 00:38:17,460
+الأثنين نفسهم داخل ال set S مطلوب مننا أن نجيب
+
+477
+00:38:17,460 --> 00:38:21,480
+الشيء لل set S first لأن أنا عارف element ال
+
+478
+00:38:21,480 --> 00:38:26,020
+element هذا بعدين بتكلم عن set ممكن يكون هو Y هو X
+
+479
+00:38:26,020 --> 00:38:30,440
+في ال set ممكن يكون نفس ال element نفس ال element
+
+480
+00:38:30,440 --> 00:38:37,120
+فإذا ممكن تكون تلاتة تلاتة تلاتة زائد تلاتة ستة
+
+481
+00:38:37,120 --> 00:38:42,600
+معناه ذلك أنه برضه الستة belong to Sطيب مدام 6
+
+482
+00:38:42,600 --> 00:38:48,180
+belong to S طب ممكن تكون ال X هي ال 6 او Y ال 6 او
+
+483
+00:38:48,180 --> 00:38:55,800
+ال 2 فإذا ممكن تكون برضه 9 او 12 طيب مدام صار في
+
+484
+00:38:55,800 --> 00:39:04,360
+عند ال 6 و 9 و 12 طب ممكن تكون هذه 9 و 12 معناه
+
+485
+00:39:04,360 --> 00:39:09,120
+ذلك سوف اتكلم عن 21 طبعا بما في اللي بينهم كمان
+
+486
+00:39:09,790 --> 00:39:13,690
+تمنتاشر تقول الستناشر فواضح ان احنا بكلم عن set
+
+487
+00:39:13,690 --> 00:39:17,990
+لمضاعفات الرقم تلاتة بقدر اعمل اي generation لأي
+
+488
+00:39:17,990 --> 00:39:22,770
+رقم اخر غير مضاعفات التلاتة مافيش إمكانية معناته
+
+489
+00:39:22,770 --> 00:39:26,270
+ال set لا يمكن ان هي تكون تحتوي على اي element
+
+490
+00:39:26,270 --> 00:39:30,610
+باستثناء مضاعفات الرقم تلاتة باستخدام مضاعفات رقم
+
+491
+00:39:30,610 --> 00:39:36,930
+تلاتة okay
+
+492
+00:39:38,460 --> 00:39:41,660
+set of all strings نجن نتكلم عن ال strings هالوجد
+
+493
+00:39:41,660 --> 00:39:44,500
+هال recursive اللي بقدر امثلها اه بنقدر نمثلها
+
+494
+00:39:44,500 --> 00:39:49,100
+بشكل recursive كيف ناخد بس بقى ما من two symbols
+
+495
+00:39:49,100 --> 00:39:53,760
+هالوجد هنشتغل عليه او من علامتين هناخدهم او
+
+496
+00:39:53,760 --> 00:39:57,820
+notation ال notation الأولى اللي هي ال sigma big
+
+497
+00:39:57,820 --> 00:40:01,780
+sigma ال big sigma وفي notation تانية اللي هي big
+
+498
+00:40:01,780 --> 00:40:05,840
+sigma star ايش هذي و ايش هذي في فرق شاسة بين
+
+499
+00:40:05,840 --> 00:40:09,340
+الاتنين كتبتلكوا الفرق اللي هي تحتكتبوا الفرق تحت
+
+500
+00:40:09,340 --> 00:40:12,260
+عشان تبقوا متذكرينه يمكن اقول المحاضرة و بعدين
+
+501
+00:40:12,260 --> 00:40:16,780
+تنسوهم بكرة بعد و تكونوا نسيتوهم لأنه كتير بضخبته
+
+502
+00:40:16,780 --> 00:40:24,360
+ف ال sigma لحالها هي set of symbols set of
+
+503
+00:40:24,360 --> 00:40:29,660
+alphabet بس معناته elements ال elements هذه عبارة
+
+504
+00:40:29,660 --> 00:40:35,440
+عن ايش ال alphabet او symbolselement by element
+
+505
+00:40:35,440 --> 00:40:42,280
+طيب ال sigma star set of strings strings ال string
+
+506
+00:40:42,280 --> 00:40:45,860
+ممكن يكون له أطوال مختلفة فلو اتكلمنا مثلا والله
+
+507
+00:40:45,860 --> 00:40:49,280
+أن ال alphabet هي مجموعة ال symbols بتاعتنا لما
+
+508
+00:40:49,280 --> 00:40:52,660
+بقول ال universe of discourse بتاعتنا alphabet
+
+509
+00:40:52,660 --> 00:40:55,840
+معناته ال sigma star بكل بساطة ممكن تكون ال
+
+510
+00:40:55,840 --> 00:41:02,500
+dictionary كله كل كلمة string صح فإذا لما أقول
+
+511
+00:41:04,250 --> 00:41:12,090
+Sigma to the power تلاتة مثلا ممكن تكون
+
+512
+00:41:12,090 --> 00:41:19,830
+في كلمات كتير طولها تلاتة bad the boy صحيح؟ كل
+
+513
+00:41:19,830 --> 00:41:23,810
+الكلمات اللي طولها تلاتة طيب لما أقول star مش محدد
+
+514
+00:41:23,810 --> 00:41:27,590
+الطول معناه ذلك إن كل الكلمات الممكنة كل الكلمات
+
+515
+00:41:27,590 --> 00:41:33,340
+إيش الممكنة لحظو في sigma هذه لأالـ sigma هادى فقط
+
+516
+00:41:33,340 --> 00:41:37,200
+هم ال 26 element بتاع ال language بتاعتنا اللى هى
+
+517
+00:41:37,200 --> 00:41:42,620
+ال letters بتاعتنا فقط هى ال alphabet فقط فهدى غير
+
+518
+00:41:42,620 --> 00:41:46,940
+هدى تاخدوا بالكوا الفرق شاسع جدا بينهم شاسع شاسع
+
+519
+00:41:46,940 --> 00:41:50,500
+شاسع فعلا هدى احنا بنتكلم عن alphabet elements او
+
+520
+00:41:50,500 --> 00:41:54,660
+symbols هناك بنتكلم عن strings و ال strings هدى
+
+521
+00:41:54,660 --> 00:42:00,140
+الأطوار مختلفة بدأتوا تبوار star star مش معروف
+
+522
+00:42:00,140 --> 00:42:04,950
+الطولفإذا انقلها طول مختلفة تمام خلينا نبدأ نحط
+
+523
+00:42:04,950 --> 00:42:09,530
+recursively شوية تعريفات هنا لما نمشي نحط the set
+
+524
+00:42:09,530 --> 00:42:17,650
+sigma star of all strings over sigma طب sigma الشي
+
+525
+00:42:17,650 --> 00:42:21,530
+احنا قولنا اللي هي ال alphabet لما بقول over sigma
+
+526
+00:42:21,530 --> 00:42:24,470
+وكل strings اللي هي over sigma معناته كل الكلمات
+
+527
+00:42:24,470 --> 00:42:28,430
+اللي بتتكون من ال letters هذهكل الكلمات اللي ممكن
+
+528
+00:42:28,430 --> 00:42:34,310
+تتكون من ال letters ممكن مثلا ده لحظة هذا لحالها
+
+529
+00:42:34,310 --> 00:42:39,370
+symbol هاي كمان symbol هاي كمان symbol تلاتة مع
+
+530
+00:42:39,370 --> 00:42:45,910
+بعض عملولي string فهي صار عندنا string او series
+
+531
+00:42:45,910 --> 00:42:52,360
+او ما هي string افضلمن ال symbols اعطونى معنى
+
+532
+00:42:52,360 --> 00:42:57,320
+اعطونى معنى okay هدول belong to مين؟ to sigma star
+
+533
+00:42:57,320 --> 00:43:01,160
+to sigma star طيب lambda اللى هى ال empty string
+
+534
+00:43:01,160 --> 00:43:05,960
+هدى subset من أي string ممكنه من أي sigma star
+
+535
+00:43:05,960 --> 00:43:13,480
+ممكنه لأنه هدى string string هدى not belong لو
+
+536
+00:43:13,480 --> 00:43:19,920
+مفيش ال starليش؟ لأنه sigma لحالها symbols مش
+
+537
+00:43:19,920 --> 00:43:26,060
+string ف not belong ولكن لما بتكلم عن star أه star
+
+538
+00:43:26,060 --> 00:43:30,300
+معناته string مظبوط كلامها هيك صح تنطبخ بمشي لحالك
+
+539
+00:43:30,300 --> 00:43:35,220
+فإذا lambda belong to star sigma على أساس أنه
+
+540
+00:43:35,220 --> 00:43:39,180
+lambda زي ما قلنا ال empty string okay و belong to
+
+541
+00:43:39,180 --> 00:43:46,240
+sigma star فإذا هذه ليست symbol هذه stringواضحة؟
+
+542
+00:43:46,240 --> 00:43:51,080
+جدش طوله مش عارف هذي string لأنها belong to مين؟
+
+543
+00:43:51,080 --> 00:43:57,960
+to sigma star طيب and x belong to sigma فإذن هذي
+
+544
+00:43:57,960 --> 00:44:01,840
+symbol هذي حرف ال x أنا بتكلم هنا عن ال element
+
+545
+00:44:01,840 --> 00:44:08,320
+نفسه element اسمه x جدش طوله واحد هو واحدهو نفسه
+
+546
+00:44:08,320 --> 00:44:12,500
+واحدة مش ماش string هذا لحاله هو simple هو لحاله
+
+547
+00:44:12,500 --> 00:44:18,060
+simple كويس فلما بقول concatenation ل W مع X أكيد
+
+548
+00:44:18,060 --> 00:44:22,420
+belong to Sigma Star لإن أنا مش عارف جداش ال W فكل
+
+549
+00:44:22,420 --> 00:44:25,140
+اللي بقدر أقول إن ال string هذا كله على بعضه ال
+
+550
+00:44:25,140 --> 00:44:33,160
+concatenated string عبارة عن طول W زائد واحد ال X
+
+551
+00:44:33,160 --> 00:44:37,230
+أنا ضامنها واحدخلاص مافيش مشكلة لإن هو element
+
+552
+00:44:37,230 --> 00:44:41,230
+واحد اللي انضاف ولكن w أنا مش عارف هي اتعرفت على
+
+553
+00:44:41,230 --> 00:44:45,490
+أساس إن هي string وماعرفليش طولها ففي الآخر الطول
+
+554
+00:44:45,490 --> 00:44:50,250
+ككل صار طول w زائد الواحد اللي هو j من x بعتبر إن
+
+555
+00:44:50,250 --> 00:44:54,770
+أنا عارف x belong لمين belonging to alphabet ل
+
+556
+00:44:54,770 --> 00:45:03,020
+alphabet symbols example يمكن توضح معانا أكترلو
+
+557
+00:45:03,020 --> 00:45:08,140
+قلنا if sigma لحالها big sigma لحالها equal to
+
+558
+00:45:08,140 --> 00:45:12,100
+zero one فهدولة ال symbols هدولة ال symbols ساعتنا
+
+559
+00:45:12,100 --> 00:45:17,140
+صفر واحد okay the strings found in sigma star over
+
+560
+00:45:17,140 --> 00:45:22,100
+the sigma ايش sigma ال star اللي ممكن اعملها
+
+561
+00:45:22,100 --> 00:45:27,250
+generation من sigma لحالهاof all bit strings لكل
+
+562
+00:45:27,250 --> 00:45:29,070
+ال bit strings اللي ممكن ناخدها من ال two bits
+
+563
+00:45:29,070 --> 00:45:33,710
+هدولة ال symbols هدولة ال two symbols فقط أول حالة
+
+564
+00:45:33,710 --> 00:45:37,410
+اللي هي ال lambda أول واحدة lambda ليش لأن دي ربع
+
+565
+00:45:37,410 --> 00:45:44,310
+اللي كنتوا هناك تتكلم عن إيش ال star كلام عن ال
+
+566
+00:45:44,310 --> 00:45:49,030
+star هذه عرفتوها خلاص معرفة و انتهينا صفر واحد بس
+
+567
+00:45:49,030 --> 00:45:51,690
+هاي ال two symbols بتاعونكوا مافيش symbols تانية
+
+568
+00:45:51,690 --> 00:45:55,070
+ولكن لما بتكلم عن ال stringsلأ ال strings ممكن
+
+569
+00:45:55,070 --> 00:46:00,050
+تكون empty ممكن تكون ال واحد صفر لحاله هو string
+
+570
+00:46:00,050 --> 00:46:04,710
+ال string في element واحد طيب او ال واحد لحاله او
+
+571
+00:46:04,710 --> 00:46:09,670
+صفر صفر او صفر واحد او واحد صفر او واحد واحد او او
+
+572
+00:46:09,670 --> 00:46:13,070
+او او to infinity ايش ممكن يكون في او كمان زيادة
+
+573
+00:46:13,070 --> 00:46:23,210
+اربع تلت صفار صفرين و واحد صفر واحد صفرمش محدد طول
+
+574
+00:46:23,210 --> 00:46:27,370
+ال string طول ال string ممكن يكون أي شئ ممكن يكون
+
+575
+00:46:27,370 --> 00:46:31,390
+أي شئ فواضح .. واضحة الفرق بين التنتين ال sigma
+
+576
+00:46:31,390 --> 00:46:34,350
+مختلف عن ال sigma star ماتلخبطوش بكرا فيهم في
+
+577
+00:46:34,350 --> 00:46:39,430
+الامتحانات ماتلخبطوش فيهم في الامتحانات واحدة
+
+578
+00:46:39,430 --> 00:46:43,330
+symbols واحدة strings واحدة strings ومش محددين ال
+
+579
+00:46:43,330 --> 00:46:46,790
+string جدش طوله اهم شي ان احنا مش محددين مدام
+
+580
+00:46:46,790 --> 00:46:48,070
+حاطينها star
+
+581
+00:46:50,830 --> 00:46:54,010
+Okay recursively برضه نقدر نعمل concatenation
+
+582
+00:46:54,010 --> 00:46:56,590
+عمريت recursively as a concatenation لأن كل ال
+
+583
+00:46:56,590 --> 00:46:59,570
+concatenation هو أساسا ان احنا عملاله generation
+
+584
+00:46:59,570 --> 00:47:04,030
+من two strands من two strands فممكن يكونtwo
+
+585
+00:47:04,030 --> 00:47:08,770
+strings ممكن منهم أعمل generation ل string تالت هو
+
+586
+00:47:08,770 --> 00:47:11,650
+جاي من اللي جابلهم جاي من اللي جابلهم في الطريقة
+
+587
+00:47:11,650 --> 00:47:15,830
+recursively ممكن نعرف ال concatenation of strings
+
+588
+00:47:15,830 --> 00:47:23,730
+w1 و w2 هدى string جدش طوله مش عارف، string جدش
+
+589
+00:47:23,730 --> 00:47:27,810
+طوله برضه مش عارف okay ال business بتاعتنا if w
+
+590
+00:47:27,810 --> 00:47:33,980
+belong to sigma starthen w ال dot هذه معناته
+
+591
+00:47:33,980 --> 00:47:41,580
+concatenation ال lambda هي نفسها w لإن انت بتتكلم
+
+592
+00:47:41,580 --> 00:47:46,860
+عن empty string where ال lambda هنا عرفناها اللي
+
+593
+00:47:46,860 --> 00:47:53,180
+هي ال empty stringال recursive ليش هنا أشتغلنا على
+
+594
+00:47:53,180 --> 00:47:58,080
+ال lambda لأن أقل lambda ممكنة أقل string ممكن لل
+
+595
+00:47:58,080 --> 00:48:03,440
+W2 هي تكون lambda طيب لأ أكتر من lambda معناه ذلك
+
+596
+00:48:03,440 --> 00:48:09,130
+أن W1 زي ما هي هي belong to sigma starو W2 ليس
+
+597
+00:48:09,130 --> 00:48:13,250
+فارغاً لأ خلاص سيبنا ال base case في ال indicative
+
+598
+00:48:13,250 --> 00:48:17,370
+case انه ممكن يكون هنا قيمة أكبر يكون W2 بelong to
+
+599
+00:48:17,370 --> 00:48:20,430
+برضه sigma star مش هم عارفين هال sigma star في
+
+600
+00:48:20,430 --> 00:48:27,370
+الحالة هذه and X belong to هنا إيش sigma بس فانا
+
+601
+00:48:27,370 --> 00:48:34,250
+هنا بتكلم عن X لحاله element واحد فقط thenW في W2
+
+602
+00:48:34,250 --> 00:48:40,650
+X كأنه بيعمل concatenation ل W2 مع ال X فهيسوي ليه
+
+603
+00:48:40,650 --> 00:48:46,690
+نفس الطول ل W2 زي 1 concatenation مع W1 هي نفسها
+
+604
+00:48:46,690 --> 00:48:50,990
+لو عملنا concatenation ل W1 مع W2 و ال
+
+605
+00:48:50,990 --> 00:48:54,370
+concatenated string عملنا له concatenation كمان
+
+606
+00:48:54,370 --> 00:48:59,390
+مرة مع X لحالها مع X مع X لحالها فهذا في الأخر ك
+
+607
+00:48:59,390 --> 00:49:07,280
+length كامل هيسوي ال lengthلأ w1 زائد ال length
+
+608
+00:49:07,280 --> 00:49:14,220
+تبع w2 زائد واحد بالظبط زائد واحد تمام فهي عملية
+
+609
+00:49:14,220 --> 00:49:18,080
+ال concatenation عساس ان احنا دايما بنحسبها من ال
+
+610
+00:49:18,080 --> 00:49:20,720
+concatenated string اللي جابلها من ال concatenated
+
+611
+00:49:20,720 --> 00:49:25,680
+string اللي جابلهاother easy string examples لو
+
+612
+00:49:25,680 --> 00:49:28,900
+قولنا ال length هينا .. هينا .. رجع يتكلم عن مين؟
+
+613
+00:49:28,900 --> 00:49:32,220
+عن ال length ل ال strings عن ال length ل ال
+
+614
+00:49:32,220 --> 00:49:38,740
+stringsفال length L of W of a string W فانا بتكلم
+
+615
+00:49:38,740 --> 00:49:42,080
+هنا عن ال length of a string W هاي معناه احنا طبعا
+
+616
+00:49:42,080 --> 00:49:45,320
+توي ضمنها كنت بكتبها فوصلتكوا الفكرة ووصلتكوا
+
+617
+00:49:45,320 --> 00:49:49,380
+الفكرة ضمن ان توي احنا بنكتبها فلما بقول L of W
+
+618
+00:49:49,380 --> 00:49:52,660
+معناته اللي مقصود فيها ال length ل string W ال
+
+619
+00:49:52,660 --> 00:49:56,760
+base step بتاعتنا ان ال string هتكون lambda ف0
+
+620
+00:49:56,760 --> 00:50:04,270
+okay recursive steplength of w concatenated مع x
+
+621
+00:50:04,270 --> 00:50:09,030
+ال length ل ال w plus واحد طبعا هذا الكلام اذا
+
+622
+00:50:09,030 --> 00:50:12,410
+كانت ال w فعلا انا مش عارف ال length تبعها فهي
+
+623
+00:50:12,410 --> 00:50:14,510
+معناه ذلك مدام مش عارف ال length تبعها belong to
+
+624
+00:50:14,510 --> 00:50:20,810
+sigma star و ال x مدام حطيناها واحد معناته ضمن ان
+
+625
+00:50:20,810 --> 00:50:27,630
+انا معرفها ان هي belong to sigma to sigma المرة
+
+626
+00:50:27,630 --> 00:50:31,060
+الجاية عشانبكون ضايلنا الجزئية الوحيدة اللي هي
+
+627
+00:50:31,060 --> 00:50:34,540
+recursive algorithms أخدنا ال recursive function
+
+628
+00:50:34,540 --> 00:50:38,400
+أخدنا ال recursive set و أخدنا ال recursive string
+
+629
+00:50:38,400 --> 00:50:43,020
+دل بس ال recursive algorithms هناخد شوية
+
+630
+00:50:43,020 --> 00:50:46,260
+algorithms أخدناها سابقا بس لحظوا هنا هنحطلكوا
+
+631
+00:50:46,260 --> 00:50:48,920
+إياها هنعملكوا إياها بصطرين تلاتة بس بتم حلها
+
+632
+00:50:48,920 --> 00:50:53,160
+بصطرين تلاتة هي بتلت أسطور بنحل مثلا عملية
+
+633
+00:50:54,360 --> 00:50:57,820
+الألغوريثم هنا كانت خاصة بمين؟ خاصة بالpower نفترض
+
+634
+00:50:57,820 --> 00:51:02,140
+a to the power n بدون ما أضطر أعمل code كبير لأ
+
+635
+00:51:02,140 --> 00:51:04,800
+بعمله صغير جدا على أساس ان انا هستعمل عملية ال
+
+636
+00:51:04,800 --> 00:51:08,100
+concatenation ال recursive هنستعمل عملية ال
+
+637
+00:51:08,100 --> 00:51:12,360
+recursion من ال element السابق فبنخليها تكرار
+
+638
+00:51:12,360 --> 00:51:15,060
+بنخليها عملية تكرار بناخدها المرة الجاية هتلاقي
+
+639
+00:51:15,060 --> 00:51:18,840
+انه هنبسط كتير algorithms أخدناها سابقا هتتبسط
+
+640
+00:51:18,840 --> 00:51:23,070
+كتير وعدد صوره هتصير أجل كتيريلا يعطيكوا العافية
+
+641
+00:51:23,070 --> 00:51:25,630
+تشوفوا يوم ال .. ال ..
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8eabd785c60bf208ae9e03529f539d0aad04b9a9
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk.srt
@@ -0,0 +1,2594 @@
+1
+00:00:21,110 --> 00:00:23,430
+بسم الله الرحمن الرحيم، الصلاة والسلام على أشرف
+
+2
+00:00:23,430 --> 00:00:25,930
+الأنبياء والمرسلين، سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,930 --> 00:00:31,250
+أجمعين. اليوم سنتكمل في الـ cryptology أو علم
+
+4
+00:00:31,250 --> 00:00:34,130
+التشفير. علم التشفير واحدة من الـ applications
+
+5
+00:00:34,130 --> 00:00:39,130
+المهمة للـ number theory. ليش؟ لأننا سنستخدم فيها
+
+6
+00:00:39,130 --> 00:00:43,780
+معلومات من التي أخذناها في number theory، وتعتمد
+
+7
+00:00:43,780 --> 00:00:46,960
+أصلًا على أرقام لأننا في الآخر سنشفر الـ message
+
+8
+00:00:46,960 --> 00:00:50,320
+التي نريد إرسالها إلى أرقام، مجموعة أرقام، مجموعة
+
+9
+00:00:50,320 --> 00:00:53,880
+الأرقام هذه سنعمل عليها شوية process معينة، شوية
+
+10
+00:00:53,880 --> 00:00:57,960
+معالجة بحيث أننا نغير الأرقام، الأرقام هذه إذا
+
+11
+00:00:57,960 --> 00:01:00,900
+تغيرت، الذي سيرى ذلك في الطريق لن يعرف الشيء بالظبط.
+
+12
+00:01:00,900 --> 00:01:04,380
+لن يعرف الشيء. الأرقام هذه الأصلية.  أنا أحتاج
+
+13
+00:01:04,380 --> 00:01:07,940
+مجموعة الأرقام، وأكون أعرف الـ code التي شُفرت به
+
+14
+00:01:07,940 --> 00:01:13,400
+لكي أعرف  أعمل decryption، إعادة التشفير أو فك
+
+15
+00:01:13,400 --> 00:01:17,560
+التشفير. واليوم سنتكلم عن هذا الموضوع في الـ
+
+16
+00:01:17,560 --> 00:01:21,640
+cryptology أو الـ cryptography. الـ cryptography التي
+
+17
+00:01:21,640 --> 00:01:24,280
+هي الـ methods التي تُستخدم  لإجراء encryption
+
+18
+00:01:24,280 --> 00:01:30,200
+نفعل فيها encryption أو decryption. هذه هي الطرق
+
+19
+00:01:30,200 --> 00:01:33,500
+التي نستخدمها في الـ encryption والـ decryption
+
+20
+00:01:33,500 --> 00:01:38,560
+للمسج بحيث أن تصبح coded message. هذه نسميها
+
+21
+00:01:38,560 --> 00:01:43,200
+الـ cryptography أو الـ cryptology، الذي هو علم
+
+22
+00:01:43,200 --> 00:01:47,320
+التشفير أو علم، عملية الاختيار للطرق أو علم الطرق
+
+23
+00:01:47,320 --> 00:01:52,830
+التي تُستخدم في التشفير. طيب، في الـ crypto
+
+24
+00:01:52,830 --> 00:01:58,590
+analysis، هذا الذي هو علم كسر التشفير. هذا يستخدمه
+
+25
+00:01:58,590 --> 00:02:01,390
+عادة الناس الذين يعملون كـ hackers، يحاولون
+
+26
+00:02:01,390 --> 00:02:04,350
+يُجيدوا أيضًا علمهم وكيفية فك التشفير و
+
+27
+00:02:04,350 --> 00:02:08,070
+الـ message عندما تأتينا مشفرة، كيف نحاول استخراج منها
+
+28
+00:02:08,070 --> 00:02:12,630
+شوية الـ numbers المهمة في عملية تشفيرها. فهذا علم، و
+
+29
+00:02:12,630 --> 00:02:16,630
+هذا علم. لكل واحد منهما علمه الخاص، وله ناس الذين يعملون
+
+30
+00:02:16,630 --> 00:02:20,530
+فيه. طيب، سنتكلم شوية عن هذا الموضوع، وسنأخذ مثالًا
+
+31
+00:02:20,530 --> 00:02:26,570
+بسيطًا، وهو Caesar cipher أو الذي هو شفرة القيصر.
+
+32
+00:02:27,350 --> 00:02:30,670
+شفرة القيصر، كان عندما يذهب إلى الحروب أو يبعث إلى
+
+33
+00:02:30,670 --> 00:02:34,670
+... للقوات التابعة له أو للحكام... للولايات المحيطة
+
+34
+00:02:34,670 --> 00:02:37,430
+الـ ... الـ ... الـ ... كان يبعث  رسائله مشفرة، يبعث الـ
+
+35
+00:02:37,430 --> 00:02:40,130
+message التي يريد إرسالها، يرسلها بطريقة مشفرة بحيث
+
+36
+00:02:40,130 --> 00:02:43,490
+أنها لو وقعت مع الأعداء لن يعرفوا بالضبط ما الذي يريد
+
+37
+00:02:43,490 --> 00:02:46,290
+إرساله.  طبعًا كانت الـ ... الـ ... الـ cipher  تبعه أو
+
+38
+00:02:46,290 --> 00:02:50,150
+الشفرة تبعته كانت  كتير modest، يعني كتير متواضعة أو
+
+39
+00:02:50,150 --> 00:02:53,370
+كتير بسيطة. فكان كل ما يفعله أنه يُرتب كل
+
+40
+00:02:53,370 --> 00:02:58,520
+الحروف... حروف اللغة الـ 26، ويكتبها، ولكل واحد يعطيه
+
+41
+00:02:58,520 --> 00:03:04,120
+رقمًا، يبدأ من الـ A صفر، B واحد، اثنين، ثلاثة، إلى الـ Z
+
+42
+00:03:04,120 --> 00:03:10,160
+خمسة وعشرين. وكل ما يفعله يكتب الرسالة، يأخذ
+
+43
+00:03:10,160 --> 00:03:14,570
+حرفًا حرفًا من الرسالة، الحرف الأول في الرسالة، كم
+
+44
+00:03:14,570 --> 00:03:19,090
+المطابق للرقم التابع له. هذا يمثل الرقم التابع للحرف الأول.
+
+45
+00:03:19,090 --> 00:03:23,070
+فيُرتّب، ويُصبح أرقامًا. والأرقام هذه يأخذ رقمًا رقمًا، ويُجمع
+
+46
+00:03:23,070 --> 00:03:28,790
+عليه ثلاثة، ويُجري modulo 26، modulo 26. فطبعًا
+
+47
+00:03:28,790 --> 00:03:32,090
+الأرقام تغيرت هكذا، الأرقام كلها تغيرت، ويرسل
+
+48
+00:03:32,090 --> 00:03:36,150
+الرسالة بناءً على الأرقام التي تغيرت، فيعود إلى اللغة
+
+49
+00:03:36,150 --> 00:03:39,470
+ثانيًا، فتظهر حروف ليس لها أي علاقة بالـ message
+
+50
+00:03:39,470 --> 00:03:43,810
+الأصلية. تكون هي نفس الـ message ولكن شُفرت، صارت لها
+
+51
+00:03:43,810 --> 00:03:48,710
+عملية shift، shift بمقدار ثلاثة، shift بمقدار ثلاثة.
+
+52
+00:03:48,710 --> 00:03:51,030
+هذا الذي كان الـ encryption، كان يُجري encryption
+
+53
+00:03:51,030 --> 00:03:56,090
+بهذا الشكل، تشفير بهذا الشكل. أو فك التشفير، يُجرونه
+
+54
+00:03:56,090 --> 00:04:00,170
+كيف؟ يُجرون نفس الفكرة ولكن بالعكس. هنا كنا نجمع
+
+55
+00:04:00,170 --> 00:04:04,210
+ثلاثة، الآن سنضطر ماذا نفعل؟ ننقص ثلاثة، ننقص ثلاثة، و
+
+56
+00:04:04,210 --> 00:04:08,950
+نعمل أيضًا modulo 26، نعمل modulo 26. طيب،
+
+57
+00:04:08,950 --> 00:04:15,030
+in general، الـ shift cipher هذا N + K، بغض النظر
+
+58
+00:04:15,030 --> 00:04:18,050
+عن K، ثلاثة كما هو مُستخدم أو خمسة أو عشرة، نستطيع
+
+59
+00:04:18,050 --> 00:04:21,630
+استخدامه. in general، K، ونكتب أي رقم نريده.
+
+60
+00:04:21,630 --> 00:04:28,060
+modulo M، modulo عام نعمل عليه. طيب، تطور الموضوع
+
+61
+00:04:28,060 --> 00:04:31,900
+شوية، فصار في transformation أنني أستطيع أيضًا الـ N
+
+62
+00:04:31,900 --> 00:04:36,480
+أُضربها في multiplier، أُعَقّدها شوية، أُعَقّدها شوية، فعلت
+
+63
+00:04:36,480 --> 00:04:40,060
+التشفير أني لست مُجبرًا على N + ثلاثة، ما أجعلها
+
+64
+00:04:40,060 --> 00:04:47,090
+سبعة N + ثلاثة modulo 26. هنا أصبحت more secure،
+
+65
+00:04:47,090 --> 00:04:51,230
+ولكن برضه بالنسبة للعلم الذي نحن فيه حاليًا، كل
+
+66
+00:04:51,230 --> 00:04:54,030
+الطريقة على بعضها insecure، كل الطريقة على بعضها
+
+67
+00:04:54,030 --> 00:04:57,870
+غير آمنة، سهّلت الكشف. الطريقة هذه كلها على بعضها هكذا
+
+68
+00:04:57,870 --> 00:05:00,970
+سهّلت الكشف. ولكن كما أقول، إننا كنا نستخدمها منذ
+
+69
+00:05:00,970 --> 00:05:06,410
+قرون بعيدة جدًّا، منذ قرون بعيدة جدًّا، من أيام القيصر، من
+
+70
+00:05:06,410 --> 00:05:12,330
+أيام القيصر أو Caesar.  كويس، نأخذ مثالًا، for example، لو
+
+71
+00:05:12,330 --> 00:05:16,070
+أخذنا جملةً ونريد تشفيرها، فكل ما نفعله أننا
+
+72
+00:05:16,070 --> 00:05:20,230
+نكتب مجموعة الأرقام، مجموعة الحروف بتاعتنا، لكل حرف
+
+73
+00:05:20,230 --> 00:05:27,090
+ما يقابله الرقم الذي يقابله، لكل حرف الرقم، والشفرة
+
+74
+00:05:27,090 --> 00:05:32,610
+بتاعتنا هنا واضح أننا... نحن لسنا نعرف أن
+
+75
+00:05:32,610 --> 00:05:33,390
+الحقيقة...
+
+76
+00:05:37,530 --> 00:05:45,110
+لماذا؟ لماذا؟
+
+77
+00:05:45,110 --> 00:05:52,070
+آه والله، برضه ممكن، برضه يعني، وجهة نظرك صحيحة، ممكن
+
+78
+00:05:52,070 --> 00:05:58,130
+احتجنا الكهرباء. خلاص، نجعلها is not easy.
+
+79
+00:06:02,120 --> 00:06:04,600
+لا، ولكن هذه الكلمة لازالت من الكهرباء، لست أعرفها، هي
+
+80
+00:06:04,600 --> 00:06:12,080
+لمن بعده، okay.
+
+81
+00:06:12,080 --> 00:06:19,850
+فلاحظوا أننا هنا...  تظهر الشاشة. كل ما
+
+82
+00:06:19,850 --> 00:06:23,570
+سنفعله، لكل حرف، سنرتب كل الحروف، حافظين الحروف؟
+
+83
+00:06:23,570 --> 00:06:27,230
+فتكتبوا
+
+84
+00:06:27,230 --> 00:06:31,850
+الحروف ترتيبًا مرتبًا، وعند الـ A صفر، B واحد، تكتبوا
+
+85
+00:06:31,850 --> 00:06:37,470
+برضه تحت مجموعة الأرقام التابعة لها، لكل ترتيبها في الـ
+
+86
+00:06:37,470 --> 00:06:42,330
+sequence التابع لها، وبعدين نستطيع العمل هنا على Caesar
+
+87
+00:06:43,990 --> 00:06:46,770
+Caesar، الذي كما قلنا N + ثلاثة، كل ما
+
+88
+00:06:46,770 --> 00:06:51,650
+سنفعله، لكل حرف، نضيف عليه ثلاثة. فـ T مثلًا، نضيف
+
+89
+00:06:51,650 --> 00:06:56,330
+عليها ثلاثة، تصبح W. فأول حرف يُصبح أنّه الـ W في
+
+90
+00:06:56,330 --> 00:07:00,810
+الرسالة، فعليًّا الـ encoded message  بتاعنا يُصبح حرفًا
+
+91
+00:07:00,810 --> 00:07:08,350
+الـ W. الـ H مثلًا نضيف عليه أيضًا ثلاثة، يُصبح K، الـ E
+
+92
+00:07:08,350 --> 00:07:13,470
+نضيف عليه ثلاثة، يُصبح H وهكذا، نكمل الـ message
+
+93
+00:07:13,470 --> 00:07:18,130
+بتاعتنا، وتظهر  شيء بهذا الشكل. هذه تُرسل الـ
+
+94
+00:07:18,130 --> 00:07:20,570
+message. هذه هي التي تُرسل. طبعًا الـ message هذه
+
+95
+00:07:20,570 --> 00:07:25,110
+الـ الكهرباء لن تعرفها، فسنحمي أنفسنا منها. الـ message زي
+
+96
+00:07:25,110 --> 00:07:30,250
+هذه لن تُظهر، لن تُعرف، لن تُعرف. لماذا؟ لأنها مشفرة.
+
+97
+00:07:30,250 --> 00:07:32,950
+الحروف أنتم لن تعرفوا منها شيء، لن تعرفوا منها
+
+98
+00:07:32,950 --> 00:07:35,990
+شيء. ومع ذلك، ومع ذلك، كما قلت لكم، أجيبكم أن
+
+99
+00:07:35,990 --> 00:07:39,490
+هي insecure، unsecure. لماذا؟ لأن أبسط شيء، ما عليك إلا
+
+100
+00:07:39,490 --> 00:07:44,710
+أن تنظر إلى الرقم أو إلى الـ letter المتكرر كثيرًا، هدف
+
+101
+00:07:44,710 --> 00:07:46,750
+في الغالب... في الغالب يكون أحد حروف الـ
+
+102
+00:07:46,750 --> 00:07:51,870
+vowels، غالبًا حرف من الحروف الساكنة، صحيح؟ لأنها
+
+103
+00:07:51,870 --> 00:07:55,730
+الأكثر استخدامًا في اللغة، هي الأكثر، وأكثرهم حرف
+
+104
+00:07:55,730 --> 00:08:00,230
+الـ E. يعني بتأتون لتروا أين الحرف الأكثر استخدامًا
+
+105
+00:08:00,230 --> 00:08:04,570
+مثلًا هو حرف الـ H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ
+
+106
+00:08:04,570 --> 00:08:05,870
+H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ
+
+107
+00:08:05,870 --> 00:08:05,990
+H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ
+
+108
+00:08:05,990 --> 00:08:06,050
+H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ
+
+109
+00:08:06,050 --> 00:08:06,750
+H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ
+
+110
+00:08:06,750 --> 00:08:09,870
+H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ
+
+111
+00:08:09,870 --> 00:08:15,210
+H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ H، الـ
+
+112
+00:08:15,210 --> 00:08:20,810
+H، الـ H
+
+113
+00:08:28,270 --> 00:08:32,470
+Okay، نجرب الـ relation هذه التي استنتجتها على
+
+114
+00:08:32,470 --> 00:08:35,470
+كل شيء، ونرى ما تظهره الـ message. والله، الـ message
+
+115
+00:08:35,470 --> 00:08:38,490
+لها معنى واضح، خلاص، فككتها. ليس لها معنى واضح،
+
+116
+00:08:38,490 --> 00:08:42,790
+ممكن ألا يكون الـ E، تكون الـ A أو الـ I أو الـ U، المهم
+
+117
+00:08:42,790 --> 00:08:45,230
+واحد من الحروف لأن هذا ما نحن مُعتادون عليه أنه
+
+118
+00:08:45,230 --> 00:08:49,370
+أكثر استخدامًا في اللغة، وهي الـ vowels أو الحروف
+
+119
+00:08:49,370 --> 00:08:52,090
+العلة، أو الحروف التي هي الساكنة، الحروف الساكنة.
+
+120
+00:08:57,990 --> 00:09:00,590
+فنستخدمها، لهذا السبب، أنها insecure، حقيقة أنها
+
+121
+00:09:00,590 --> 00:09:03,010
+insecure. أقول لكم حتى لو ضربت في multiplier، حتى
+
+122
+00:09:03,010 --> 00:09:06,170
+لو ضربت في multiplier، تظل برضه insecure، ستظل
+
+123
+00:09:06,170 --> 00:09:13,190
+insecure. طيب، في الـ cryptography، عادة نحن نعمل
+
+124
+00:09:13,190 --> 00:09:16,510
+على two keys مهمين، فيه الـ public وفيه الـ private.
+
+125
+00:09:16,510 --> 00:09:20,730
+ولكي لا أطيل عليكم أكثر، الـ public، نحن نستخدمه
+
+126
+00:09:20,730 --> 00:09:24,170
+لكي نعمل communication بشكل آمن، securely
+
+127
+00:09:24,170 --> 00:09:29,210
+نتواصل مع الآخر أو الـ key strings، نستخدمها
+
+128
+00:09:29,210 --> 00:09:33,310
+في التواصل، كالـ email التابع لكم، الـ email الذي فيه
+
+129
+00:09:33,310 --> 00:09:36,810
+عندكم الـ username أو الـ email address، هذا public.
+
+130
+00:09:37,880 --> 00:09:41,120
+هذا الكل يعرفه.  لكي أرسل لكم message، يجب أن
+
+131
+00:09:41,120 --> 00:09:44,360
+أعرفه. لكي أرسل لكم، فهذا public. طيب، private، عندما أنا
+
+132
+00:09:44,360 --> 00:09:49,180
+أريد الدخول إلى الـ email، هذا private، فيه password، الـ
+
+133
+00:09:49,180 --> 00:09:52,300
+password، من المفترض أن هذا private، هذا لكم خاصّ
+
+134
+00:09:52,300 --> 00:09:55,220
+بكم أنتم، أو خاصّ بصاحب الـ email address، فهذا
+
+135
+00:09:55,220 --> 00:09:59,800
+private. فإذن، فينا public وفينا private.  private في
+
+136
+00:09:59,800 --> 00:10:02,540
+عندنا public، وفي عندنا private. طيب، في عندنا أيضًا
+
+137
+00:10:02,540 --> 00:10:06,720
+نفس الكلام للـ websites، الـ websites عمومًا، لكي أقرأ
+
+138
+00:10:06,720 --> 00:10:10,230
+أي معلومة موجودة على الـ websites، إما أنني أريد الكتابة
+
+139
+00:10:10,230 --> 00:10:13,150
+معلومة، أو أريد قراءة معلومة. فعندما أكتب معلومة،
+
+140
+00:10:13,150 --> 00:10:15,590
+المفترض أنني أملك الـ user name،  بتاع الـ path بتاع
+
+141
+00:10:15,590 --> 00:10:20,930
+الـ website أو الـ web page، لأدخل وأكتب
+
+142
+00:10:20,930 --> 00:10:25,390
+أجري insertion لمعلومات، أو لمقالة، أو لصور، أو أو أو
+
+143
+00:10:25,390 --> 00:10:29,670
+ف... وبعدين نعمل publishing. الـ publishing  ظهرت
+
+144
+00:10:29,670 --> 00:10:34,830
+طبعًا، لكي أقرأها، أحتاج ماذا؟ أحتاج الـ browser، الـ
+
+145
+00:10:34,830 --> 00:10:37,370
+browser، فقط.  أحتاج الـ browser. فممكن هذا يكون
+
+146
+00:10:37,370 --> 00:10:41,870
+public، لكي أقرأها هي public. لكي أفتح مع
+
+147
+00:10:41,870 --> 00:10:44,870
+الصفحة وأقرأها، ستكون public. لو أنا ليس عندي الـ
+
+148
+00:10:44,870 --> 00:10:48,030
+browser، لن أعرف قراءتها. ففي هذه الحالة أكون أنا
+
+149
+00:10:48,030 --> 00:10:53,650
+أحتاج الـ public key. آه، جبنا الـ explorer مثلًا برضه،
+
+150
+00:10:53,650 --> 00:10:56,950
+ستجدون فيه مرات صور، أو مرات فيديوهات، سيقول لكم لا
+
+151
+00:10:56,950 --> 00:11:00,550
+نحتاج... لا نعرف ماذا... الـ ... الـ latest version، okay.
+
+152
+00:11:00,550 --> 00:11:04,310
+معنى ذلك أنه هذا ليس قادرًا كـ decoder، ليس قادرًا على الفتح،
+
+153
+00:11:04,310 --> 00:11:08,170
+أضطر البحث عن شيء... ولكن في النهاية هذا كله ماذا؟
+
+154
+00:11:08,170 --> 00:11:11,610
+public. هذا كله نحن نتكلم عن شيء public، لماذا؟ لأنه
+
+155
+00:11:11,610 --> 00:11:13,910
+أنزل إلى السوق، أنزل إلى... أفتح على الـ net على
+
+156
+00:11:13,910 --> 00:11:16,670
+موقع آخر، أبحث عن الـ browser، وأحصل على آخر version، و
+
+157
+00:11:16,670 --> 00:11:21,390
+أنزله، يعني هذا public، ليس فيه private. الـ
+
+158
+00:11:21,390 --> 00:11:24,150
+private سيكون عندي الذي يريد الكتابة، عندما أريد أنا الدخول
+
+159
+00:11:24,150 --> 00:11:28,230
+لا، أريد تغييرها على الصفحة. لا، هذه private، public
+
+160
+00:11:28,230 --> 00:11:31,450
+issue و private issue. الـ email نفس الشيء، public
+
+161
+00:11:31,450 --> 00:11:35,320
+أنني أستطيع إرسال الـ message
+
+162
+00:11:35,320 --> 00:11:38,920
+التي أُرسلها، تراها كل فرد، كل واحدة تدخل
+
+163
+00:11:38,920 --> 00:11:42,540
+على حسابها، لستم جميعًا ستدخلون على حساب واحد، كل
+
+164
+00:11:42,540 --> 00:11:46,260
+واحدة تدخل على حسابها، private، private. فهذا الفرق
+
+165
+00:11:46,260 --> 00:11:51,130
+بين الـ public، الذي هو can be made public، والـ
+
+166
+00:11:51,130 --> 00:11:55,270
+private، الذي هو can be kept secret from
+
+167
+00:11:55,270 --> 00:11:58,110
+everyone. هذا المفترض. يقولون لا والله، الـ password
+
+168
+00:11:58,110 --> 00:12:01,410
+تبع هذا خاص بي، لا أحد سيأخذ الـ password  ويعمل email
+
+169
+00:12:01,410
+
+223
+00:15:51,180 --> 00:15:56,920
+وجد في معادلة انكريبشن باستخدام الـ RSA relative الـ
+
+224
+00:15:56,920 --> 00:16:01,580
+prime للـ P minus one, P minus one في Q minus one
+
+225
+00:16:01,580 --> 00:16:10,050
+فإذًا في E صار أنا كل اللي محتاجه P, Q و E, ولاحظوا
+
+226
+00:16:10,050 --> 00:16:13,190
+هذا prime وهذا prime وهذا لازم تكون relatively
+
+227
+00:16:13,190 --> 00:16:23,610
+prime مع مين؟ مع P-1 في Q-1 كلهم prime أو co-prime
+
+228
+00:16:23,610 --> 00:16:27,610
+يعني أو co-prime فهذا هيفيدنا جدًا في عملية الـ
+
+229
+00:16:27,610 --> 00:16:32,800
+security. طيب الـ public key، الشيء اللي بدنا نستعمله
+
+230
+00:16:32,800 --> 00:16:37,940
+فعلاً هالوقت في الأرقام الـ N هذي هتكون عبارة عن الـ
+
+231
+00:16:37,940 --> 00:16:42,400
+P في الـ Q, N عبارة عن P في Q, وهذي هستخدمها كـ
+
+232
+00:16:42,400 --> 00:16:46,100
+modulo أو كـ modulus في الـ system تبعنا، هي هذي الـ
+
+233
+00:16:46,100 --> 00:16:49,440
+modulus تبعنا، الـ N هتكون هي الـ modulus وما تكونش
+
+234
+00:16:49,440 --> 00:16:52,540
+هي الـ P نفسها أو الـ Q نفسها، لأن إذا الـ P نفسها أو
+
+235
+00:16:52,540 --> 00:16:54,740
+الـ Q نفسها أنتم كشفتوا الـ P والـ Q في الحالة هذي
+
+236
+00:16:54,740 --> 00:16:57,560
+إذا كانت واحدة من الاثنين، لا، ما نفعش، لازم تكون
+
+237
+00:16:57,560 --> 00:17:02,050
+ضرب الاثنين، مضروب الاثنين بحيث أن أنت تطلع عليها
+
+238
+00:17:02,050 --> 00:17:09,230
+تشعر أنها رقم not prime أو composite number بس
+
+239
+00:17:09,230 --> 00:17:14,870
+فعليًا مش هتعرف تطلع منه الـ P والـ Q، رقم ممكن يكسب على
+
+240
+00:17:14,870 --> 00:17:18,110
+أرقام ثانية غير الـ P والـ Q، كمان يكون بيكسب على أرقام
+
+241
+00:17:18,110 --> 00:17:21,730
+أخرى، بس في الآخر ممكن تعرف الـ P والـ Q منه
+
+242
+00:17:24,510 --> 00:17:28,910
+لما بجي هأعمل لوغاريتم، أعمل هنا، طبعًا خلصنا عملية الـ
+
+243
+00:17:28,910 --> 00:17:32,530
+encryption باستخدام الـ private key، بيصير بدنا
+
+244
+00:17:32,530 --> 00:17:34,970
+نعمل decryption باستخدام
+
+245
+00:17:37,170 --> 00:17:40,910
+public key. طيب استخدم الـ public key، خلاص اتفقنا
+
+246
+00:17:40,910 --> 00:17:44,050
+هاي الـ modulus نفسه هو هو اللي هيستخدم في الـ
+
+247
+00:17:44,050 --> 00:17:47,010
+encryption، هنستخدمه برضه في الـ decryption، بس الـ
+
+248
+00:17:47,010 --> 00:17:52,270
+exponent محتاجين نجيب له الـ inverse تبعه مرة أخرى
+
+249
+00:17:52,270 --> 00:17:55,150
+أخذنا الـ inverse، كيف نجيبها؟ محتاجين الـ inverse والـ
+
+250
+00:17:55,150 --> 00:17:59,810
+inverse مهم جدًا، فمحتاج أجيب D، وهذا D هو الـ
+
+251
+00:17:59,810 --> 00:18:00,870
+inverse of E
+
+252
+00:18:03,540 --> 00:18:07,500
+حاجة عملتها زي تَوّي لما كنا بنشتغل على الـ...الـ
+
+253
+00:18:07,500 --> 00:18:12,180
+scissors, الـ cipher كنا بنقول plus ثلاثة، فإذا العكس
+
+254
+00:18:12,180 --> 00:18:16,280
+تبعها سالب ثلاثة، لما بدي أعمل decryption كنا نعمل
+
+255
+00:18:16,280 --> 00:18:18,700
+بالعكس، فهنا نفس الكلام بدي أجيب العكس، بس أنا هنا
+
+256
+00:18:18,700 --> 00:18:22,120
+شغال على modulo، على مجموعة، فَالـ inverse
+
+257
+00:18:22,120 --> 00:18:28,540
+تبعنا للـ E هتكون D، وهذي عبارة عن E modulo P minus
+
+258
+00:18:28,540 --> 00:18:33,850
+واحد في Q minus واحد، بيعطينا D، وبنستخدمش الـ E
+
+259
+00:18:33,850 --> 00:18:40,970
+نفسها، نستخدمش الـ E نفسها، لا نستخدم الـ E نفسها، كويس
+
+260
+00:18:40,970 --> 00:18:44,470
+فعملية الـ encryption هالوقت بدأنا نحدد مجموعة الـ
+
+261
+00:18:44,470 --> 00:18:46,450
+parameters اللي أنا محتاجها، مجموعة الأرقام اللي
+
+262
+00:18:46,450 --> 00:18:50,170
+أنا محتاجها عشان أعمل encryption هتكون الـ
+
+263
+00:18:50,170 --> 00:18:54,430
+encrypted signal هتساوي الـ message الأصلية to the
+
+264
+00:18:54,430 --> 00:19:00,710
+power E, exponent modulo N, والـ N هي اللي هي إيه؟ قلنا
+
+265
+00:19:00,710 --> 00:19:05,490
+P في Q, P في Q, كويسة، هذي بتكون، هيك الـ message هي
+
+266
+00:19:05,490 --> 00:19:09,830
+اللي بتنبعث، أو الـ encrypted message, الـ encoded
+
+267
+00:19:09,830 --> 00:19:12,390
+message، بعتناها، وخلاص، اللي هيشوفها مش هيفهم منها
+
+268
+00:19:12,390 --> 00:19:15,750
+حاجة، هذي اللي هيشوفها مش هيفهم منها أي شيء، طيب
+
+269
+00:19:15,750 --> 00:19:19,910
+وصلتني، بدي أعكسها، بدي أجيبها، طبعًا عشان أجيبها لازم
+
+270
+00:19:19,910 --> 00:19:26,470
+أنا الوحيد اللي هيكون عارف إيش الـ E، ولاحظوا، مش الـ
+
+271
+00:19:26,470 --> 00:19:34,130
+N، مش الـ N، بدي أكون عارف الـ P والـ Q، يعني حتى لو
+
+272
+00:19:34,130 --> 00:19:38,930
+انكسفت هنا، هو اللي عرف الـ N، ما عرفش الـ P والـ Q، طب
+
+273
+00:19:38,930 --> 00:19:42,270
+أنا عشان أفتحها، الـ message تبعيتي بدي أكون عارف مين
+
+274
+00:19:42,270 --> 00:19:48,150
+P و Q، لإني بدي أجيب inverse الـ E، طب inverse الـ E
+
+275
+00:19:49,260 --> 00:19:54,460
+بدنا نعمله modulo P-1 Q-1، فأنا لازم أكون أعرف الـ P والـ
+
+276
+00:19:54,460 --> 00:19:58,560
+Q، الـ primes العناصر المهمة جدًا، هذه الـ primes
+
+277
+00:19:58,560 --> 00:20:03,280
+اللي صعب تتكرر، اللي بيكون صعب شوية تتكرر، كويسة
+
+278
+00:20:03,280 --> 00:20:08,040
+فإذا الـ message تبعيتي هتساوي C، الـ encrypted to the
+
+279
+00:20:08,040 --> 00:20:12,480
+power D اللي هو الـ inverse، الـ D هذا ماحدش هيعرفها
+
+280
+00:20:12,480 --> 00:20:16,430
+لإن أنا العارف الـ code اللي اتشفرت فيه، الـ code
+
+281
+00:20:16,430 --> 00:20:20,910
+اللي اتشفرت فيه، عارف الـ D، خلاص نحصل على D mod N
+
+282
+00:20:20,910 --> 00:20:24,170
+okay، هو عارف الـ N، فليكن عارفها من الـ message اللي
+
+283
+00:20:24,170 --> 00:20:27,790
+قطعها، شافها في الطريق وقطعها، ومشكلة، okay، هيعرف
+
+284
+00:20:27,790 --> 00:20:32,630
+الـ N، ومشتغل على N، بس الـ D لا، هو مش عارف لا P ولا
+
+285
+00:20:32,630 --> 00:20:36,170
+Q، لأنه مش موجودة في الـ message، هنا مش موجودة في الـ
+
+286
+00:20:36,170 --> 00:20:41,850
+message، كويس، نأخذ example للـ Encryption وللـ
+
+287
+00:20:41,850 --> 00:20:45,530
+Decryption، نبدأ بالـ Encryption، Encryption خلاص
+
+288
+00:20:45,530 --> 00:20:50,870
+إحنا عارفين القانون تبعنا اللي هي C بتساوي M to
+
+289
+00:20:50,870 --> 00:20:57,390
+the power E mod أو modulo M, modulo N، إيش الكلمة
+
+290
+00:20:57,390 --> 00:21:00,960
+اللي بدنا نبعتها؟ بدنا نبعت كلمة stop، مثلًا بدنا نبعت
+
+291
+00:21:00,960 --> 00:21:05,420
+كلمة stop، فـ stop برضه بشوف إيش ترتيب الـ S، إيش
+
+292
+00:21:05,420 --> 00:21:11,060
+ترتيب الـ T، إيش ترتيب الـ O، الـ P في الـ sequence تبع
+
+293
+00:21:11,060 --> 00:21:17,000
+الـ alphabet string، فهنشوف الأولى هذه مثلًا، بدنا
+
+294
+00:21:17,000 --> 00:21:20,060
+نعرف إيش ترتيبها، ترتيب، ترتيب، ترتيب، هنكون عملنا
+
+295
+00:21:20,060 --> 00:21:23,300
+شفرة لها لحالها، هنكون عملنا شفرة لحالها، طيب
+
+296
+00:21:23,300 --> 00:21:29,360
+هتلاقوا الـ S ترتيبها 18، الـ T وراها على طول 19
+
+297
+00:21:30,900 --> 00:21:33,700
+ناخدهم أربعة أربعة، ناخدهم يعني two letters, two
+
+298
+00:21:33,700 --> 00:21:36,720
+letters, two letters، هدول مع بعض، بعدين في two
+
+299
+00:21:36,720 --> 00:21:38,900
+letters، الـ O والـ P برضه الاثنين هدول ورا بعض
+
+300
+00:21:38,900 --> 00:21:42,840
+فواحدة خمسة عشر وواحدة أربعة عشر، هيك الـ message
+
+301
+00:21:42,840 --> 00:21:46,120
+اللي أنا بدي أبعتها، بس ما عملتلهاش أي encryption، بس
+
+302
+00:21:46,120 --> 00:21:48,380
+ما عملناش أي encryption، هي الـ message بتاعتنا اللي
+
+303
+00:21:48,380 --> 00:21:52,780
+بدنا نبعثها، كويسة، مبدأيًا بيعطيني المعلومات
+
+304
+00:21:52,780 --> 00:21:56,140
+okay، ميعطينيش هي الـ key، ميعطينيش الـ Q، prime, prime
+
+305
+00:21:56,930 --> 00:22:02,250
+بينها، بنقدر نطلعها لإن مضروب الاثنين في بعض في ألفين
+
+306
+00:22:02,250 --> 00:22:05,130
+وخمسمائة سبعة وثلاثين، وميعطينيش كمان الـ exponent
+
+307
+00:22:05,130 --> 00:22:09,430
+اللي هو الـ power، طبعًا الـ exponential، جزء الـ power
+
+308
+00:22:09,430 --> 00:22:14,570
+الـ E ثلاثة عشر، برضه prime، برضه الـ prime، فلاحظوا
+
+309
+00:22:14,570 --> 00:22:17,050
+بقالكم...خدوا، بقالكم من الأرقام كلها primes فعليًا
+
+310
+00:22:17,050 --> 00:22:20,110
+يعني الـ given كلها ده كله primes، عندكوا هاي prime
+
+311
+00:22:20,110 --> 00:22:24,190
+هاي اثنين، هاي ثلاثة، okay، خليني أعمل check, check
+
+312
+00:22:24,190 --> 00:22:32,610
+مهم جدًا أن الـ E لازم تكون co-prime كمان مع P-1 وQ
+
+313
+00:22:32,610 --> 00:22:39,950
+-1، ليش؟ اللي حضر معنا المرة اللي فاتت، الـ inverse
+
+314
+00:22:39,950 --> 00:22:44,810
+ليش؟
+
+315
+00:22:44,810 --> 00:22:50,930
+لما هنكون بدنا نجيب الـ inverse تبع A mod
+
+316
+00:22:52,830 --> 00:23:00,670
+M، كنا بنقول إن الـ A والـ M لازم يكونوا relatively
+
+317
+00:23:00,670 --> 00:23:08,410
+prime، عشان أضمن إن داخل M لا يوجد إلا inverse واحد
+
+318
+00:23:08,410 --> 00:23:14,100
+للـ A، ارجعوا على المحاضرة السابقة، كويس إنها بتسجل
+
+319
+00:23:14,100 --> 00:23:19,300
+عشان ما تقولوش لما ما سمعناش، بتسجل، فهذه عشان تقولوا
+
+320
+00:23:19,300 --> 00:23:23,340
+آه والله فيه inverse، لازم يكون الـ a والـ m
+
+321
+00:23:23,340 --> 00:23:29,440
+relatively prime أو co-prime، في الحالة هذه نفس
+
+322
+00:23:29,440 --> 00:23:32,940
+الكلام هنا، طب أنا محتاج الـ E هذه بعدين أعملها
+
+323
+00:23:32,940 --> 00:23:37,020
+inverse، عشان أحسب D، مش محتاجين نحسب D دي من وين؟
+
+324
+00:23:37,020 --> 00:23:40,220
+بدنا نجيبها، inverse الـ E، ما تجيبش
+
+325
+00:23:42,780 --> 00:23:48,200
+P-1، P-1، فعشان فعلاً خليني أعمل تشيك قبل ما نبدأ
+
+326
+00:23:48,200 --> 00:23:51,900
+نشتغل، هل الأرقام بتاعتنا كلها مناسبة للـ encryption
+
+327
+00:23:51,900 --> 00:23:56,860
+اللي بدنا نعمله أو لا، فإذا GCD بتاعتهم okay هتطلع
+
+328
+00:23:56,860 --> 00:24:00,920
+one، okay، من الثمانين رقم مناسبة جدًا، عندنا ثلاثة
+
+329
+00:24:00,920 --> 00:24:04,560
+primes، والـ prime اللي أنا محتاجه، الـ exponent اللي
+
+330
+00:24:04,560 --> 00:24:07,160
+أنا محتاجه أجيب له الـ inverse بالنسبة له، الـ prime
+
+331
+00:24:07,160 --> 00:24:10,180
+الأول minus one في الـ prime الثاني minus one برضه
+
+332
+00:24:10,180 --> 00:24:13,920
+relatively prime مع بعض، فإذا بقدر أقول إن دي اللي
+
+333
+00:24:13,920 --> 00:24:22,580
+هأحسبها، هي inverse واحدة، unique inverse للـ E، كويس
+
+334
+00:24:26,400 --> 00:24:30,620
+هذا الأصل، إن هتكون، يعني إذا كان في سؤال هتكون معطاة
+
+335
+00:24:30,620 --> 00:24:33,660
+ولكن إذا كنت أنت designer، المفروض أنت اللي تصممهم
+
+336
+00:24:33,660 --> 00:24:38,040
+إذا كانت مجرد مهندسة وبتعملوا تشفير، تعملوا code
+
+337
+00:24:38,040 --> 00:24:42,340
+لحالكم، بدك تختارينهم بهذا الشكل، اختاري رقمين
+
+338
+00:24:42,340 --> 00:24:46,320
+الـ primes، الرقمين الـ primes، هتقولي، خذي بالك هذا
+
+339
+00:24:46,320 --> 00:24:50,480
+minus one في هذا minus one، تختاري رقم prime ثالث
+
+340
+00:24:52,170 --> 00:24:55,750
+يكون relatively prime مع مضروبهم، مضروبهم minus واحد
+
+341
+00:24:55,750 --> 00:24:59,250
+مضروبهم minus واحد، مع بعض، يعني الشبكة هيك تاخدي
+
+342
+00:24:59,250 --> 00:25:01,810
+بالك في الـ design تبعها عشان تختاريهم، بس طبعًا في
+
+343
+00:25:01,810 --> 00:25:09,050
+السؤال هتكون given، هنا في السؤال هتكون given، خلصنا
+
+344
+00:25:09,050 --> 00:25:19,160
+في الحالة هذه، الـ S 18، T 19، O 14، P 15، هي خلصنا الـ
+
+345
+00:25:19,160 --> 00:25:21,500
+code تبعنا، بناخدهم إيش؟ بناخدهم two letters و two
+
+346
+00:25:21,500 --> 00:25:24,560
+letters، بناخد الاثنين هدول مع بعض بنعتبرهم message
+
+347
+00:25:24,560 --> 00:25:36,900
+وبنعمل لهم modulo N اللي هي PQ، طيب لحظة، طبعًا هيطلع
+
+348
+00:25:36,900 --> 00:25:40,580
+الرقم الأول رقم كبير جدًا، لإيش؟ لإنه 1819 to the
+
+349
+00:25:40,580 --> 00:25:43,740
+power 13، على calculator مش هيطلع معاكم، القِيمة اللي معاكم مش
+
+350
+00:25:43,740 --> 00:25:47,860
+هيطلع، لأن أنتم بتتكلموا هنا عن قد إيش؟ 1819 to the
+
+351
+00:25:47,860 --> 00:25:52,520
+power 13، to the power 13، طبعًا هذا كمان هيتوه أكتر
+
+352
+00:25:52,520 --> 00:25:57,420
+المعلومة لو شفناها في نص الطريق، ليش؟ لأن كل رقم أو
+
+353
+00:25:57,420 --> 00:26:01,480
+كل letter مبنية مع اللي جانبها، بمعنى إنه مش دايمًا
+
+354
+00:26:01,480 --> 00:26:04,940
+الـ letter نفسها في نفس الـ system هتأخذ نفس القيمة
+
+355
+00:26:04,940 --> 00:26:08,620
+في الـ encryption، لا، ليش؟ لأنها معتمدة على اللي
+
+356
+00:26:08,620 --> 00:26:11,650
+جانبها، أو على اللي بعدها، فالجابل أو اللي بعده هو
+
+357
+00:26:11,650 --> 00:26:14,970
+هيغير كل الرقم على بعضه، هيتغير كل الرقم، فهذا كمان
+
+358
+00:26:14,970 --> 00:26:18,370
+more secure في الشغل، هذا بيعطيكم more secure في
+
+359
+00:26:18,370 --> 00:26:22,070
+الشغل، فصار هنا بعمل...بعملش encryption لـ 18 لحالها
+
+360
+00:26:22,070 --> 00:26:26,830
+اللي هي خاصة بالاسم، لا، أنا بعملش للـ 18، بعمل لـ 1819
+
+361
+00:26:26,830 --> 00:26:31,970
+هذا مش letter، رقم بس أنا عارف إنه كيف...إيش يمثل
+
+362
+00:26:31,970 --> 00:26:35,230
+يمثل two letters مع بعض، كويسة، أربطه لـ 13، وأعمل
+
+363
+00:26:35,230 --> 00:26:41,290
+mod، mod n، هيساوي رقم جديد، بنكمل الجزء الثاني نفس
+
+364
+00:26:41,290 --> 00:26:45,990
+الكلام، أربطهم
+
+365
+00:26:45,990 --> 00:26:49,750
+كتر، أربطهم، عشرين، واحد، ثمانين، واحد وعشرين، اثنين،
+
+366
+00:26:49,750 --> 00:26:53,050
+وثمانين، هاي الـ message اللي هتنبعث، هذا الـ message
+
+367
+00:26:53,050 --> 00:26:59,870
+هي الرسالة اللي هنبعتها، الرسالة هذه اللي راحت، لو
+
+368
+00:26:59,870 --> 00:27:02,830
+شفناها في نص الطريق مش هتعرفوا منها شيء، هذه مش
+
+369
+00:27:02,830 --> 00:27:05,950
+هتعرفوا منها حاجة، هتعرف تطلع منها الكلمة، ومش هتعرف
+
+370
+00:27:05,950 --> 00:27:09,330
+تطلع منها الكلمة، كويس، مين اللي هيعرف يطلع منها
+
+371
+00:27:09,330 --> 00:27:13,350
+الكلمة؟ المستقبل هناك اللي عارف شوية parameters
+
+372
+00:27:13,350 --> 00:27:17,530
+محددة، عارف شوية parameters معينة، من أهمها زي ما
+
+373
+00:27:17,530 --> 00:27:21,950
+قلنا الـ E، عشان بده يجيب لها الـ inverse، الـ P والـ Q
+
+374
+00:27:21,950 --> 00:27:27,530
+عشان برضه بده يشتغل على P-1 وQ-1، وبده يجيب الـ N
+
+375
+00:27:27,530 --> 00:27:32,430
+منهم، كويس، خلينا نشوف بالعكس لو بدنا نعمل
+
+376
+00:27:32,430 --> 00:27:40,010
+decryption لـ message بهذا الشكل: 0 9 8 1 0 4 6 1
+
+377
+00:27:40,010 --> 00:27:43,950
+هنفترض أن هذه وصلتنا، بدنا نشوف الشيء هذا بالظبط
+
+378
+00:27:43,950 --> 00:27:47,090
+طبعًا على نفس المثال السابق، على نفس المثال السابق
+
+379
+00:27:47,090 --> 00:27:49,890
+كنا نشتغل على ثلاثة وأربعين، تسعة وخمسين، اللي هي
+
+380
+00:27:49,890 --> 00:27:55,830
+الـ P والـ Q، والـ E ثلاثة عشر، okay، فنفس الكلام okay
+
+381
+00:27:55,830 --> 00:28:02,560
+عندنا، فالـ N هي هي PQ، N، exponent ثلاثة عشر، تمام، تمام
+
+382
+00:28:02,560 --> 00:28:06,780
+بدنا نحسب مين؟ D، D ممكن ترجع للمثال اللي كان دبل
+
+383
+00:28:06,780 --> 00:28:10,040
+هذا اللي هو في exercise أربعة في نفس الكتاب...
+
+384
+00:28:10,040 --> 00:28:13,980
+الكتاب هذا عشان تعرفي، بس هو الـ inverse هذه جابها
+
+385
+00:28:13,980 --> 00:28:20,140
+مين؟ لثلاثة عشر، فإذا التسعمئة وثلاثة وسبعين هذه اللي
+
+386
+00:28:20,140 --> 00:28:24,700
+هي سبعة وثلاثين، سبعة وثلاثين، هذا
+
+445
+00:32:48,260 --> 00:32:52,180
+بالحجم وبال... بيكونوا عاملينها كبيرة جدا بمجرد
+
+446
+00:32:52,180 --> 00:32:54,640
+ما وجع أول واحد خلاص احنا قاعدين نتفرج أنه آه آخر
+
+447
+00:32:54,640 --> 00:32:58,080
+واحد خلاص متوقعين أن آخر... آخر حجر هيجع... آخر
+
+448
+00:32:58,080 --> 00:33:02,800
+حجر هيجع... كويس فإذا الأول شرط أن الحجر الأول is
+
+449
+00:33:02,800 --> 00:33:08,150
+true، وإذا هنا بتعامل أنا مع ال... الـ predicate
+
+450
+00:33:08,150 --> 00:33:13,410
+function أو الـ predicate تبعتي أنه الحجر رقم صفر
+
+451
+00:33:13,410 --> 00:33:21,410
+is failed، وجاء كويس هل هو fails فعلا بيقع، جاعد
+
+452
+00:33:21,410 --> 00:33:29,050
+إذا وجاء بدي أضمن الشرط الثاني أنه كل حجر في الـ
+
+453
+00:33:29,050 --> 00:33:34,400
+location N، إذا وجاء then الحجر في location n plus
+
+454
+00:33:34,400 --> 00:33:39,040
+واحد هيجع، لأنه ممكن يطلعوا بعض عن بعض، هذا يجع
+
+455
+00:33:39,040 --> 00:33:45,860
+ما يوجعش الثاني، صح؟ فإذن شرطين، شرط أول أن أول حجر
+
+456
+00:33:45,860 --> 00:33:49,680
+is true، هو فعلا P of Zero، ال... ال... الـ
+
+457
+00:33:49,680 --> 00:33:53,520
+predicate عند Zero، عند ال... ال... الـ basis step
+
+458
+00:33:53,520 --> 00:33:59,040
+هذه عند أول خطوة، وجع هذا شرط أول أن فعلا وجعت
+
+459
+00:33:59,040 --> 00:34:02,460
+الأولى، عشان أقول والله كله وجع، خلاص أكيد كله
+
+460
+00:34:02,460 --> 00:34:10,500
+هيجع، الأولى وجع، الشرط الثاني والأهم أنه كل حجر
+
+461
+00:34:10,500 --> 00:34:15,580
+مرتبط باللي وراه، إذا وجع الحجر أكيد هيجع اللي وراه، ف
+
+462
+00:34:15,580 --> 00:34:24,140
+if then، if P of N then P of N plus 1، P of N plus 1
+
+463
+00:34:24,140 --> 00:34:31,500
+تمام، هذه فعليا عملية induction بتاعتنا، وهي حقيقة
+
+464
+00:34:31,500 --> 00:34:36,780
+powerful، فعلا قوية جدا في الإثبات، ومهمة جدا، واحدة
+
+465
+00:34:36,780 --> 00:34:40,800
+من الطرق اللي كتير بتستخدم لل proving، لعملية الـ
+
+466
+00:34:40,800 --> 00:34:45,240
+proving لمين؟ لل predicate P of N is true for
+
+467
+00:34:45,240 --> 00:34:51,560
+every natural number N، للكل، عشان أضمن أن فعلا عندكم
+
+468
+00:34:51,560 --> 00:34:56,060
+ثيورة معينة وبتعملوا prove أن هي لكل الأرقام
+
+469
+00:34:56,060 --> 00:34:59,940
+صحيحة، يعني إذا نطبق على كل الأرقام، ممكن نشتغل على
+
+470
+00:34:59,940 --> 00:35:05,180
+induction approval، وهناخد شوية examples عليها بس
+
+471
+00:35:05,180 --> 00:35:08,460
+قاعدين احنا بنوضح الفكرة نفسها، من وين اجت الفكرة؟
+
+472
+00:35:08,460 --> 00:35:11,580
+من وين؟ عشان الفكرة هذه معتمدة على الـ domino
+
+473
+00:35:11,580 --> 00:35:16,160
+effect principle، على مبدأ عمل تأثير الـ domino أو
+
+474
+00:35:16,160 --> 00:35:19,060
+حجار الـ domino على بعضها، حجار الـ domino على بعضها
+
+475
+00:35:19,060 --> 00:35:23,740
+طيب الـ inference rule اللي هنشتغل عليه هيكون كالتالي، if
+
+476
+00:35:23,740 --> 00:35:29,480
+P of 0 is true، لحظة، الحجر الأول وقع is true فعلا
+
+477
+00:35:29,480 --> 00:35:38,060
+خلاص وقع، and for all N أكبر من أو تساوي الصفر، if P of
+
+478
+00:35:38,060 --> 00:35:44,000
+N is true then P of N plus 1 is true، فإذا كل حجر
+
+479
+00:35:44,000 --> 00:35:48,100
+إذا وقع أكيد حيوقع اللي وراه، إذا تحققوا الشرطين فإذا
+
+480
+00:35:48,100 --> 00:35:52,940
+بقول for all N أكبر من صفر P of N is true، بغض
+
+481
+00:35:52,940 --> 00:36:00,640
+النظر عن N، آنية للكل، لكل N أكبر من صفر، للكل، فإذا
+
+482
+00:36:00,640 --> 00:36:04,800
+بكون ضامن أن كل الحجار وقعت، كل الحجار وقعت
+
+483
+00:36:04,800 --> 00:36:08,560
+هنشتغل على الـ rule هذه فقط، هي اللي بنعمل منها كل
+
+484
+00:36:08,560 --> 00:36:12,640
+إثباتاتنا اللي هنشتغل عليها، على إثباتاتنا، زي ما
+
+485
+00:36:12,640 --> 00:36:16,580
+قلنا الـ domino، الـ premise number one، أنه domino
+
+486
+00:36:16,580 --> 00:36:21,780
+number zero falls، الدومينو الأولى وقعت، الدومينو الـ
+
+487
+00:36:21,780 --> 00:36:25,720
+premise number two، for every n belong to natural
+
+488
+00:36:25,720 --> 00:36:31,570
+number، if domino number n falls then domino n plus
+
+489
+00:36:31,570 --> 00:36:33,610
+واحد، number n plus واحد، number n plus واحد، number
+
+490
+00:36:33,610 --> 00:36:38,710
+n plus واحد، number n plus واحد، number n plus واحد
+
+491
+00:36:38,710 --> 00:36:43,550
+number n plus واحد، number n plus واحد، number n
+
+492
+00:36:43,550 --> 00:36:44,050
+plus واحد، number n plus واحد، number n plus واحد
+
+493
+00:36:44,050 --> 00:36:44,310
+plus واحد، number n plus واحد، number n plus واحد
+
+494
+00:36:44,310 --> 00:36:45,430
+number n plus واحد، number n plus واحد، number n
+
+495
+00:36:45,430 --> 00:36:47,570
+plus واحد، number n plus واحد، number n plus واحد
+
+496
+00:36:47,570 --> 00:36:50,890
+number n plus واحد، number n plus واحد، number n
+
+497
+00:36:50,890 --> 00:36:53,490
+plus واحد، number n plus واحد، number n plus واحد
+
+498
+00:36:53,490 --> 00:36:53,930
+number n plus واحد، number n plus واحد، number n
+
+499
+00:36:53,930 --> 00:36:55,130
+plus واحد، number n plus واحد، number n plus واحد
+
+500
+00:36:55,130 --> 00:36:56,130
+number n plus واحد، number n plus واحد، number n
+
+501
+00:36:56,130 --> 00:36:56,650
+number n plus واحد، number n plus واحد، number n
+
+502
+00:36:56,650 --> 00:37:01,130
+plus واحد، number n plus زاد أن أنا وقعت أول حجر
+
+503
+00:37:01,130 --> 00:37:05,110
+فخلاص كلنا عارفين، إذا فعلا الشرطين تحققوا، أن آخر
+
+504
+00:37:05,110 --> 00:37:12,070
+حجر هيقع، أن آخر حجر برضه هيقع، طيب الـ outline of an
+
+505
+00:37:12,070 --> 00:37:15,250
+inductive proof، عشان نشوف الـ inductive proof هذه
+
+506
+00:37:15,250 --> 00:37:17,630
+تبعنا كيف ممكن تتم، احنا كل اللي بدنا نعمله method
+
+507
+00:37:17,630 --> 00:37:22,050
+هو أن for all n، P of n، النظرية P of n is true
+
+508
+00:37:25,070 --> 00:37:28,610
+بدنا نوصل على two steps، step الأولى اللي هي الـ base
+
+509
+00:37:28,610 --> 00:37:33,230
+case أو الـ basis step، أن أنا أعوض عند الـ zero أو
+
+510
+00:37:33,230 --> 00:37:38,950
+أعوض عند أول element للـ N اللي هو الـ initial
+
+511
+00:37:38,950 --> 00:37:42,130
+ببعضها، أول element موجود في الـ sequence، أول
+
+512
+00:37:42,130 --> 00:37:45,990
+element بتعود مباشرة، أعوضه مباشرة، هل بيحقق الـ P of
+
+513
+00:37:45,990 --> 00:37:48,790
+N ولا لأ، بتشوف إيش المعادلة هذه الـ P of N عبارة عن
+
+514
+00:37:48,790 --> 00:37:53,870
+إيش، أعوضوا فيها، is it true؟ okay، هاي أول خطوة
+
+515
+00:37:53,870 --> 00:37:59,370
+خلصناها، الشرط الثاني بدنا نقول for all n، أفرض أنا
+
+516
+00:37:59,370 --> 00:38:03,970
+من عندي أن الـ P of N is it true؟ هنفرض أن الـ P of
+
+517
+00:38:03,970 --> 00:38:08,850
+N is true؟، وهشوف هل الـ P of N plus واحد، بناء على
+
+518
+00:38:08,850 --> 00:38:11,490
+معلومة أن الـ P of N is true؟ هل هي كمان الـ true؟
+
+519
+00:38:11,490 --> 00:38:15,550
+ولا لأ، إذا تحققت true، فتحقق الشرطين، فإذا النظرية
+
+520
+00:38:15,550 --> 00:38:19,650
+دي دائما صحيحة، خلاص بتقول أنه دائما صحيح
+
+521
+00:38:20,400 --> 00:38:24,020
+automatically، دائما معناته كل الحجار، يعني مادام
+
+522
+00:38:24,020 --> 00:38:27,260
+دائم خلاص معناته دائما صحيحة، إذا تحقق الـ two
+
+523
+00:38:27,260 --> 00:38:31,420
+conditions هدول، طيب بنستخدم direct proof، إيه عفوا
+
+524
+00:38:31,420 --> 00:38:34,840
+الـ direct proof، direct proof مش فيها مشكلة على طول
+
+525
+00:38:34,840 --> 00:38:38,120
+جربوا هنا وجربوا هنا، خلصنا يعني مالهاش أي
+
+526
+00:38:38,120 --> 00:38:44,390
+techniques تانية، مباشرة، تعود مباشر على طول، okay هذا
+
+527
+00:38:44,390 --> 00:38:48,210
+بالنسبة لمين؟ للـ inductive step، direct ما تشتغلوش
+
+528
+00:38:48,210 --> 00:38:50,950
+لا indirect ولا contrapositive ولا contradiction
+
+529
+00:38:50,950 --> 00:38:56,170
+ولا غيره، هي بسيطة جدا، أفرضوا هذه true، وثبتوا هذه
+
+530
+00:38:56,170 --> 00:38:59,730
+منها بس يعني ما تغلبوش حالكم في شيء، ولا تقعدوا
+
+531
+00:38:59,730 --> 00:39:02,530
+تشوشوا حالكم، ولا تقعدوا تقولوا يمكن الدكتور قصده
+
+532
+00:39:02,530 --> 00:39:07,170
+يعملنا خدع، هذه مباشرة، شغلوها direct على طول دائما
+
+533
+00:39:07,170 --> 00:39:11,970
+طيب، let n belong to natural number، assume p of n
+
+534
+00:39:12,390 --> 00:39:18,370
+فإذا هنا عشان أشتغلها، بفرض أن P of N is true، و
+
+535
+00:39:18,370 --> 00:39:25,590
+under this assumption، prove P of N plus 1 is true
+
+536
+00:39:25,590 --> 00:39:30,730
+ثبتنا والله إذا true، معناته تتحقق في الشرط، إذا not
+
+537
+00:39:30,730 --> 00:39:34,270
+معناته كلها لا تتحقق، معناته هنا بتقول for all دي
+
+538
+00:39:34,270 --> 00:39:38,480
+غلط، كلمة for all غلط، معناته ماقدرش أقول أن الـ
+
+539
+00:39:38,480 --> 00:39:42,180
+predicate دي للكل صحيحة، لأ هي مش للكل صحيحة، فإذا
+
+540
+00:39:42,180 --> 00:39:45,300
+بكون أثبت العكس، طبعا لأ، أنتم بتكونوا تفتقروا أن هي
+
+541
+00:39:45,300 --> 00:39:48,380
+فعلا صحيحة، فبتكونوا تتأكدوا أن هذا true وهذا
+
+542
+00:39:48,380 --> 00:39:52,660
+true، عشان تثبتوا في الآخر أن والله فعلا for all
+
+543
+00:39:52,660 --> 00:39:57,900
+and P of N is true، طيب
+
+544
+00:39:57,900 --> 00:40:00,340
+in general، in general ممكن احنا ما نبدأش من الـ
+
+545
+00:40:00,340 --> 00:40:06,340
+zero، ممكن نبدأ من C، أي element، فهيكون الـ initial
+
+546
+00:40:06,340 --> 00:40:10,440
+case بتاعتنا أو الـ base case بتاعتنا هي الـ C
+
+547
+00:40:10,440 --> 00:40:15,210
+نفسها، فبنصير نشتغل هنا على P of C، الـ predicate of
+
+548
+00:40:15,210 --> 00:40:21,270
+C بدل الـ P of 0، بدل P of 0، وبصير بدنا نثبت إيش أن
+
+549
+00:40:21,270 --> 00:40:25,150
+for all n أكبر من أو تساوي C، مضروبة في ال... في الـ
+
+550
+00:40:25,150 --> 00:40:27,950
+term هذا، بس طبعا أنا C constant، فأنا النظرية ضالة
+
+551
+00:40:27,950 --> 00:40:32,310
+زي ما هي، بدي أفرض P of N implies P of N plus 1
+
+552
+00:40:32,310 --> 00:40:35,470
+ما حدش يقولي implies هذه، معناته إذا هذه false
+
+553
+00:40:35,470 --> 00:40:38,230
+معناته وهذه false، معناته true، ليش؟ لأن إحنا
+
+554
+00:40:38,230 --> 00:40:44,370
+assumption تبعنا من الأساس أن هذه true، this is true
+
+555
+00:40:44,370 --> 00:40:48,570
+فعشان تكون هذه is true وكل true، لازم تكون true
+
+556
+00:40:48,570 --> 00:40:53,310
+صحيح؟ ما حدش يقول، إحنا في الـ implication إحنا
+
+557
+00:40:53,310 --> 00:40:55,790
+عارفين أن هذه ممكن تكون false وهذه false، كله true
+
+558
+00:40:55,790 --> 00:40:59,090
+لأ، إحنا هنا من الأساس عاملين assumption أساسا أن
+
+559
+00:40:59,090 --> 00:41:03,950
+هذه is true، أنتم بتفرضوها فرض، هذه true ومنها
+
+560
+00:41:03,950 --> 00:41:05,790
+تحاولوا تثبتوا الثانية true
+
+561
+00:41:11,560 --> 00:41:14,800
+هناخد أمثلة، هالواجهة، قبل أن ناخد أمثلة نرجع كمان
+
+562
+00:41:14,800 --> 00:41:22,220
+مرة، هاي اللي هنعمله، الـ first عادي كده اسمها طريقة
+
+563
+00:41:22,220 --> 00:41:28,540
+الـ first principle، طب في طريقة ثانية اسمها second
+
+564
+00:41:28,540 --> 00:41:31,680
+principle، second principle مختلفة شوية في الـ
+
+565
+00:41:31,680 --> 00:41:37,520
+induction، ليش؟ هو لا يكتفي أنه يقول P of zero is
+
+566
+00:41:37,520 --> 00:41:45,740
+true and if P of N is true than P of N plus 1 is
+
+567
+00:41:45,740 --> 00:41:50,100
+true، لأ عشان أثبت P of N plus 1، أثبت لي أن كل اللي
+
+568
+00:41:50,100 --> 00:41:56,520
+قبله is true، مش بس الوحيدة اللي هي P of N اللي
+
+569
+00:41:56,520 --> 00:41:59,320
+قبلها واحدة لحالها، لأ أثبت لي كل اللي قبلها، لمن
+
+570
+00:41:59,320 --> 00:42:02,640
+عندي الصفر أن هي true، طبعا أوضح أن هذا أصعب شوية
+
+571
+00:42:04,190 --> 00:42:09,590
+في الإثبات، عشان أقول أن فعلا P of N plus واحد is
+
+572
+00:42:09,590 --> 00:42:13,690
+true، لأ أنا لن أكتفي بس تقول P of N is true خلاص
+
+573
+00:42:13,690 --> 00:42:20,190
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+574
+00:42:20,190 --> 00:42:22,290
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+575
+00:42:22,290 --> 00:42:24,890
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+576
+00:42:24,890 --> 00:42:27,150
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+577
+00:42:27,150 --> 00:42:29,730
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ ل
+
+578
+00:42:33,270 --> 00:42:38,390
+طبعا هذا الـ strong proof، واضح أن هذا الإثبات
+
+579
+00:42:38,390 --> 00:42:42,030
+الأقوى، الإثبات الأقوى، طبعا ممكن يستخدم، يعني أنتم
+
+580
+00:42:42,030 --> 00:42:44,530
+ما تقلقوش، مش هتلاقوا الصعب، ساعات التطبيق على وجهه
+
+581
+00:42:44,530 --> 00:42:48,210
+هتلاقوا أن أموره مش... مش صعبة لهذه الدرجة يعني، مش
+
+582
+00:42:48,210 --> 00:42:52,420
+صعبة لهذه الدرجة، طيب مثال، خلّيني نبدأ بالـ first
+
+583
+00:42:52,420 --> 00:42:56,440
+principle، البسيط، السهل، وخلاص، مجرد لو أثبتت أن P
+
+584
+00:42:56,440 --> 00:42:59,220
+of N is true، خلاص وهذه أثبتت منها true، بكفي
+
+585
+00:42:59,220 --> 00:43:03,520
+خلّيني نشوف لو مطلوب أن أprove that the summation
+
+586
+00:43:03,520 --> 00:43:11,740
+of the first N positive integers is N squared، إيش
+
+587
+00:43:11,740 --> 00:43:19,070
+يعني؟ بمعنى لو أخذنا أول and odd positive، أول and
+
+588
+00:43:19,070 --> 00:43:24,150
+odd positive، إيش معناه؟ واحد، ثلاثة، خمسة، سبعة،
+
+589
+00:43:24,150 --> 00:43:30,990
+تسعة، أحد عشر، and so on، هدول إيش بيساووا؟ بيساووا
+
+590
+00:43:30,990 --> 00:43:37,430
+N تربيع، خلينا نجرب، هذه إيش location تبعها؟ واحد،
+
+591
+00:43:37,430 --> 00:43:42,210
+location اثنين، ثلاثة، أربعة، خمسة، ستة، هذه الـ
+
+592
+00:43:42,210 --> 00:43:46,930
+N، وهي قيمة الـ N، وهنا الـ summation بدنا نعمل
+
+593
+00:43:46,930 --> 00:43:51,470
+summation، مثلا خلينا ناخد أول element، الأولى، الأول
+
+594
+00:43:51,470 --> 00:43:58,750
+بيساوي الـ location تربيع، صح، طيب الثانية، فإذا الـ
+
+595
+00:43:58,750 --> 00:44:02,670
+summation الأول مع الثاني، أربعة، يساوي الـ location
+
+596
+00:44:02,670 --> 00:44:09,040
+الثاني تربيع، مجموع الثلاثة، يساوي ثلاثة تربيع، يساوي
+
+597
+00:44:09,040 --> 00:44:12,980
+أربعة تربيع، يساوي أربعة تربيع، وهكذا، خمسة تربيع
+
+598
+00:44:12,980 --> 00:44:19,660
+ستة تربيع، مجموع الستة elements من بداية الـ
+
+599
+00:44:19,660 --> 00:44:22,860
+sequence الـ odd أو الـ string تبع الـ odd
+
+600
+00:44:25,810 --> 00:44:29,250
+بنكون هذه النظرية بدنا نثبتها، أو بنكون حددنا إيش
+
+601
+00:44:29,250 --> 00:44:33,810
+النظرية أساسا بتاعتنا، ف for all n أكبر من أو يساوي
+
+602
+00:44:33,810 --> 00:44:43,270
+واحد، summation، لاحظوا، 2I minus one، خلينا نجرب
+
+603
+00:44:43,270 --> 00:44:48,210
+عندي الواحد، واحد في اثنين ناقص واحد، آه هاي الـ
+
+604
+00:44:48,210 --> 00:44:51,210
+element الأول اللي هو الواحد، فعلا عندي الـ location
+
+605
+00:44:51,210 --> 00:44:55,630
+واحد، بكون جبت الـ element الأول، طب عند الـ element
+
+606
+00:44:55,630 --> 00:45:01,050
+اثنين، عند
+
+607
+00:45:01,050 --> 00:45:10,230
+الثلاثة، ستة، خمسة، ففعلا الـ summation هيك صحيح، بدنا
+
+608
+00:45:10,230 --> 00:45:17,090
+نثبت أنه يساوي N تربيع، زي
+
+609
+00:45:17,090 --> 00:45:19,830
+ما قلنا، عندنا two conditions، الأول
+
+610
+00:45:21,600 --> 00:45:28,040
+الـ base step، الشيء أني أعوض بأصغر رقم موجود
+
+611
+00:45:28,040 --> 00:45:31,600
+خلينا نعوض بأصغر رقم موجود، أصغر رقم موجود، الواحد
+
+612
+00:45:31,600 --> 00:45:40,280
+فإذا من واحد لواحد، هل يساوي واحد تربيع؟ واحد بيساوي
+
+613
+00:45:40,280 --> 00:45:44,900
+واحد، فده هيثبت أن واحد بيساوي واحد، فإذا and الـ P of
+
+614
+00:45:44,900 --> 00:45:52,220
+واحد is true
+
+667
+00:50:30,750 --> 00:50:35,960
+هنا هنحط معناته أن P of n تساوي، و الـ n هنا معناته
+
+668
+00:50:35,960 --> 00:50:38,700
+أن n أقل من two to the power of n، لأن هذه الـ
+
+669
+00:50:38,700 --> 00:50:41,600
+assumption اللي هنبدأ فيه الـ inductive step بتاعتي
+
+670
+00:50:41,600 --> 00:50:45,320
+الـ inductive step، بس خلينا مبدأيا نبدأ بالـ base
+
+671
+00:50:45,320 --> 00:50:51,720
+step. أول أقل رقم ممكن واحد، خلينا نجرب الواحد عشان
+
+672
+00:50:51,720 --> 00:50:55,320
+نشتغل على الـ base case أو الـ base step. واحد أقل من
+
+673
+00:50:55,320 --> 00:50:58,340
+two to the power واحد. اه صحيح، واحد أقل من اتنين.
+
+674
+00:50:58,340 --> 00:51:02,260
+الكلام صحيح. فإذا هاي أول شرط خلصناه. الـ inductive
+
+675
+00:51:02,260 --> 00:51:09,230
+step. for all n أكبر من صفر، بدنا نعمل approve لإيش؟ P
+
+676
+00:51:09,230 --> 00:51:14,770
+of n implies P of n plus واحد. فإذن هنقول أن P of n
+
+677
+00:51:14,770 --> 00:51:20,090
+is true، معناته أن فعلا المعادلة هذه صحيحة، أن n أقل
+
+678
+00:51:20,090 --> 00:51:24,410
+من 2 to the power n. معناته أن n أقل من 2 to the
+
+679
+00:51:24,410 --> 00:51:28,810
+power n. هذه الـ logic مسلم فيها أن هي صحيحة.  مثلمة
+
+680
+00:51:28,810 --> 00:51:33,050
+فيها أنها صحيحة، و هنعمل هى assuming  هى تمام، إجتنا
+
+681
+00:51:33,050 --> 00:51:36,070
+كمان مرة، و بدنا منها نعمل proof لهذا الـ term. خلاص
+
+682
+00:51:36,070 --> 00:51:40,390
+نمسك هذا الـ term، إن هو الـ term اللي هنا، هذا هي اه
+
+683
+00:51:40,390 --> 00:51:44,390
+من واجبنا، الكلام هذا استلمه. احنا قاعدين بنقول n
+
+684
+00:51:44,390 --> 00:51:49,630
+أقل من two to the power n، صح؟ طيب اجمعوا زائد واحد.
+
+685
+00:51:49,630 --> 00:51:57,120
+زائد واحد، بتغير إشي؟ خمسة أقل من ستة، ستة أقل من
+
+686
+00:51:57,120 --> 00:52:07,540
+سبعة، صحيح، okay. بعد هيك، ضمنين إنه دايما الواحد
+
+687
+00:52:07,540 --> 00:52:12,980
+أقل من two to the power n، ليش؟ لأن أقل n ممكنة هي
+
+688
+00:52:12,980 --> 00:52:17,640
+الواحد، هي الواحد، و احنا أصلا هي أثبتناها من الأول،
+
+689
+00:52:17,640 --> 00:52:21,830
+إن واحد هتكون أقل من two to the power one. أقل قيمة
+
+690
+00:52:21,830 --> 00:52:26,730
+ممكن للـ N هي الواحد. فإذا كان الـ term هذا أكبر من N
+
+691
+00:52:26,730 --> 00:52:30,890
+زائد واحد، طب لما نزوده كمان برضه حيظل أكبر من N
+
+692
+00:52:30,890 --> 00:52:33,770
+زائد واحد، حيظل أكبر من N زائد واحد. طب ليش أنا بدي
+
+693
+00:52:33,770 --> 00:52:37,910
+إياها N زائد واحد؟ اتنين. أجمع الـ two N هذه عشان
+
+694
+00:52:37,910 --> 00:52:41,470
+أجمعها مع الـ two N اللي موجودة، أجيب الـ N plus واحد.
+
+695
+00:52:41,470 --> 00:52:46,460
+عشان نجيب الـ N plus واحد. ليش؟ لأن الـ term هذا ببساطة
+
+696
+00:52:46,460 --> 00:52:49,140
+two to the power of n plus two to the power of n
+
+697
+00:52:49,140 --> 00:52:52,000
+ما هي هذي تساوي two to the power of n في اتنين.
+
+698
+00:52:52,000 --> 00:52:56,900
+اتنين يعني to the power of one. يعني معناه ذلك
+
+699
+00:52:56,900 --> 00:53:02,120
+اتنين to the power، مجموعهم تمام.
+
+700
+00:53:02,120 --> 00:53:05,260
+معناه ذلك ان هذي two to the power of n plus one هي
+
+701
+00:53:05,260 --> 00:53:08,700
+ان زائد واحد أقل من two to the power of n زائد
+
+702
+00:53:08,700 --> 00:53:14,810
+واحد. أقل من two to the power n زي الواحد. تمام. فإذا طول
+
+703
+00:53:14,810 --> 00:53:19,270
+ما هي P of N is true، برضه P of N زي الواحد is true
+
+704
+00:53:19,270 --> 00:53:23,510
+is true. هذه automatic. ليه؟ معناته هذا الكلام للكل
+
+705
+00:53:23,510 --> 00:53:28,230
+صحيح. نظرية هذه أو المعادلة، الـ relation هذه لكل
+
+706
+00:53:28,230 --> 00:53:33,510
+الأرقام صحيحة، لكل الـ natural number لأكبر من صفر
+
+707
+00:53:33,510 --> 00:53:35,630
+صحيحة. تمام.
+
+708
+00:53:44,900 --> 00:53:52,800
+طيب، سلسلة. الـ second principle، second principle
+
+709
+00:53:52,800 --> 00:53:58,320
+زي ما قولنا، إيش بتقدر تكتب؟ أن كل السابق is true.
+
+710
+00:53:58,320 --> 00:54:01,840
+طيب، شوية شوية، خلينا ناخد إيش هي النظرية أصلا، بدوية.
+
+711
+00:54:01,840 --> 00:54:06,280
+show that every n أكبر من واحد، لكل الأرقام اللي
+
+712
+00:54:06,280 --> 00:54:11,950
+أكبر من واحد، can be written as a product P1 P2 to P
+
+713
+00:54:11,950 --> 00:54:17,370
+S of some series of S' number. هذي قلناها لما
+
+714
+00:54:17,370 --> 00:54:20,970
+اتكلمنا عن الـ primes، لما اتكلمنا عن الـ prime أو الـ
+
+715
+00:54:20,970 --> 00:54:26,870
+factorization. قلنا أن كل رقم عبارة عن مضروب مجموعة
+
+716
+00:54:26,870 --> 00:54:30,410
+أرقام، صحيح، مجموعة الـ primes. عبارة عن مضروب مجموعة
+
+717
+00:54:30,410 --> 00:54:34,990
+الـ primes. فهو بده يدينا نثبتها. لحظة، بدنا هنا عملية
+
+718
+00:54:34,990 --> 00:54:40,210
+إثبات لها. okay. عشان أثبتها، هنقول إن الكاشه الأولى
+
+719
+00:54:40,210 --> 00:54:45,010
+عندنا هنا، كاشه الـ P of،  كائنها الـ of zero بتاعتنا
+
+720
+00:54:45,010 --> 00:54:49,110
+اللي هو أول element أكبر من واحد. HP للإتنين. فبدنا
+
+721
+00:54:49,110 --> 00:54:53,550
+نجرب عند الإتنين. عند الإتنين، N بتساوي اتنين، لت الـ
+
+722
+00:54:53,550 --> 00:54:57,850
+S تبعنا أو الـ string تبعنا يحتوي على element واحد
+
+723
+00:54:57,850 --> 00:55:02,290
+اللي هو إيش؟ الـ prime، إتنين. فهو فعلا هو prime.
+
+724
+00:55:02,290 --> 00:55:06,990
+فإذا الـ string عبارة عن prime واحد، فإذا يساوي واحد
+
+725
+00:55:06,990 --> 00:55:10,230
+الـ cardinality بتاعته بتساوي واحد. الـ cardinality
+
+726
+00:55:10,230 --> 00:55:13,270
+بتساوي واحد. okay. هل وجدنا، دخلنا في الـ inductive step
+
+727
+00:55:13,270 --> 00:55:19,150
+في الـ inductive step. let n أكبر أو تساوي اتنين، أكبر
+
+728
+00:55:19,150 --> 00:55:24,530
+من اتنين. اتنين أثبتناها. الأتنين أثبتناها. assume for
+
+729
+00:55:24,530 --> 00:55:28,010
+all k أكبر
+
+730
+00:55:28,010 --> 00:55:34,210
+من اتنين، و أقل من n. يعني كله، نثبت لكله. for all k
+
+731
+00:55:34,210 --> 00:55:41,610
+من اتنين to n، P of k is true. إذا فعلا is true، عشان
+
+732
+00:55:41,610 --> 00:55:47,990
+هنا من ذهنك بنقول، consider n plus واحد، في الحالة
+
+733
+00:55:47,990 --> 00:55:55,410
+التاعتنا. okay. هدول is true، تمام؟ هدول بقدر أقول
+
+734
+00:55:55,410 --> 00:56:00,830
+إن هم مثبتين، بس لحد، هم مش عارف، صح؟ يعني عند n
+
+735
+00:56:00,830 --> 00:56:04,330
+plus واحد، أنا مش عارف، إحنا بدنا نثبتها هي صح ولا
+
+736
+00:56:04,330 --> 00:56:11,070
+غلط. لعند n، كل السابق مظبوط. مدام أنا بتكلم عن اتنين
+
+737
+00:56:11,070 --> 00:56:14,190
+من اتنين، فهنا الـ K، أول K ممكن أتعامل معاها حاليا
+
+738
+00:56:14,190 --> 00:56:20,250
+تكون اتنين نفسها. الاتنين نفسها صحيحة. لو تكلمنا عن
+
+739
+00:56:20,250 --> 00:56:24,980
+n بتساوي اتنين. طب أكتر من اتنين، مش عارف. فبدنا نثبت
+
+740
+00:56:24,980 --> 00:56:29,200
+هالوجهة. إذا كان فعلا عن n زائد واحد، فهنا هنفرض إنه
+
+741
+00:56:29,200 --> 00:56:32,360
+أنا بدي أتعامل مع n زائد واحد. والله إذا هي prime
+
+742
+00:56:32,360 --> 00:56:37,980
+إذا هي نفسها prime، معناته الـ string تبعها بواحد. هي
+
+743
+00:56:37,980 --> 00:56:42,690
+نفسها. فده is a prime. هذا is a prime. ممكن تتحقق مع
+
+744
+00:56:42,690 --> 00:56:47,190
+بعض elements أو مع بعض numbers، بس مش الكل، مش الكل.
+
+745
+00:56:47,190 --> 00:56:50,070
+فإذا في شرط تاني لازم أخد بالي منه هنا. if prime
+
+746
+00:56:50,070 --> 00:56:55,330
+نتكذا. okay، مش مشكلة. ولكن else if زائد واحد مش
+
+747
+00:56:55,330 --> 00:57:00,620
+prime، مش معناته مش prime، معناته عبارة عن A مضروبة في B.
+
+748
+00:57:00,620 --> 00:57:08,820
+مضروبة في B، صح؟ composite number، مضروبة في B، مضروبة
+
+749
+00:57:08,820 --> 00:57:10,820
+في B، مضروبة في B، مضروبة في B، مضروبة في
+
+750
+00:57:10,820 --> 00:57:13,620
+B، مضروبة في B، مضروبة في B، مضروبة في B.
+
+751
+00:57:13,620 --> 00:57:16,180
+مضروبة في B، مضروبة في B، مضروبة في B، مضروبة في B.
+
+752
+00:57:16,180 --> 00:57:16,240
+مضروبة في B، مضروبة في B، مضروبة في B، مضروبة في B.
+
+753
+00:57:16,240 --> 00:57:16,480
+مضروبة في B، مضروبة في B، مضروبة في B، مضروبة في B.
+
+754
+00:57:16,480 --> 00:57:17,400
+مضروبة في B، مضروبة في B، مضروبة في B، مضروبة في B.
+
+755
+00:57:17,400 --> 00:57:18,600
+مضروبة في B.
+
+756
+00:57:22,630 --> 00:57:28,030
+لأ، هو composite أو مؤلف من رقمين مضروبين في بعض،
+
+757
+00:57:28,030 --> 00:57:35,130
+فليكن A هتكون طبيعيا أقل من N، صح؟
+
+758
+00:57:35,130 --> 00:57:38,250
+أكيد هتكون أقل من N، أنا بتكلم عن N زائد واحد، و
+
+759
+00:57:38,250 --> 00:57:42,090
+متألف من رقمين مضروبين في بعض، فالرقمين المضروبين في
+
+760
+00:57:42,090 --> 00:57:46,640
+بعض، كل واحد منهم أقل من n زائد واحد. أكيد، أكيد كل
+
+761
+00:57:46,640 --> 00:57:49,920
+واحد منهم هتكون أقل من n زائد واحد. فإذا A هتكون
+
+762
+00:57:49,920 --> 00:57:54,320
+أكبر من واحد، و أقل من أو تساوي n، اللي هي أقل من n
+
+763
+00:57:54,320 --> 00:57:59,840
+زائد واحد. طيب، بي نفس الكلام، الرقمين هدول اللي
+
+764
+00:57:59,840 --> 00:58:05,870
+لايمكن يكونوا بيساووا n، إذا ماكنتش prime، صح؟ إذا لم
+
+765
+00:58:05,870 --> 00:58:11,010
+تكن الـ prime، هل ممكن A تساوي n زائد واحد؟ لأ، ولا
+
+766
+00:58:11,010 --> 00:58:13,550
+الـ B ممكن تكون بتساوي n زائد واحد. لازم يكون قيمهم
+
+767
+00:58:13,550 --> 00:58:17,970
+أقل منها، أقل منها. إذا واحدة منهم تساوي n زائد واحد،
+
+768
+00:58:17,970 --> 00:58:22,610
+معناته هي prime، معناته هي أصلا prime. طيب، لا تساوي،
+
+769
+00:58:22,610 --> 00:58:29,750
+معناته أقل. معنى ذلك، وبناء على الـ condition هذا، إن
+
+770
+00:58:29,750 --> 00:58:35,740
+كل اللي أقل is true. فإذا A is it true؟ هي متكونة من
+
+771
+00:58:35,740 --> 00:58:41,000
+مجموعة الـ primes، و B برضه أقل، فإذا is it true؟ هي
+
+772
+00:58:41,000 --> 00:58:44,720
+متكونة برضه من مجموعة الـ primes. هي متكونة أصلا من
+
+773
+00:58:44,720 --> 00:58:48,560
+مجموعة الـ primes. فمعنى ذلك بقدر أقول أن الـ A متكونة
+
+774
+00:58:48,560 --> 00:58:54,160
+أساسا من مجموعة الـ primes، عددهم T. فالـ string تبعنا
+
+775
+00:58:54,160 --> 00:58:59,770
+T، و A مضروب، عبارة عن prime أول في تاني في تالت في
+
+776
+00:58:59,770 --> 00:59:04,630
+prime رقم T. الـ B نفس الكلام، بيعتبر أنها أقل من N
+
+777
+00:59:04,630 --> 00:59:08,930
+زائد واحد، فهي مثبتة مسبقا. طب اللحظة، أنتو كيف
+
+778
+00:59:08,930 --> 00:59:13,790
+أثبتت أساسا من الأول؟ أنتو برضه هتسألوا، طب أساسا
+
+779
+00:59:13,790 --> 00:59:19,310
+إيه؟ مين جالها أن هي مجموعة الـ primes؟ لأن هي نفسها لو
+
+780
+00:59:19,310 --> 00:59:22,430
+اتعاملت معها أنها N زائد واحد.
+
+781
+00:59:25,050 --> 00:59:29,690
+برضه نفس الكلام، هقول إن هي مضروب مجموعة أرقام. هقول
+
+782
+00:59:29,690 --> 00:59:35,670
+إن هي برضه مضروب مجموعة أرقام أقل منها. طيب، مجموعة
+
+783
+00:59:35,670 --> 00:59:41,090
+الأرقام اللي أقل منها برضه، إما إن هي prime، نفس الـ
+
+784
+00:59:41,090 --> 00:59:43,970
+condition. لاحظوا إن الـ condition بتكرر. لاحظوا إن
+
+785
+00:59:43,970 --> 00:59:48,790
+هنا الـ condition بتكرر، أو رقمين أقل منها، لعدم أصل
+
+786
+00:59:48,790 --> 00:59:54,260
+لمين؟ للـ initial، لعندي نصل الـ initial condition
+
+787
+00:59:54,260 --> 00:59:58,120
+تبعنا، أو الـ base case بتاعتنا. نصل الـ base case
+
+788
+00:59:58,120 --> 01:00:04,300
+بتاعتنا. لاحظتوا كده؟ فإذن واضح إنه هنا أنا ما
+
+789
+01:00:04,300 --> 01:00:08,480
+أقفلتش اللي أقل منها، لأ بالعكس، و مثبتين اللي أقل
+
+790
+01:00:08,480 --> 01:00:13,360
+منها، نتيجة إن هم كانوا قبلها n زائد واحد. نتيجة أن
+
+791
+01:00:13,360 --> 01:00:17,380
+هما كانوا أصلا قبلها n زائد واحد، صح؟ عشان أصل لـ n
+
+792
+01:00:17,380 --> 01:00:20,620
+زائد واحد هنا، و أقول أن كل اللي قبلها مثبت، هم
+
+793
+01:00:20,620 --> 01:00:24,300
+أساسا، كل اللي قبلها، ما تم إثباتهم إلا لأنه كانوا
+
+794
+01:00:24,300 --> 01:00:30,040
+عند n زائد واحد. فعند n زائد واحد، أقل الواحدة ممكنة
+
+795
+01:00:30,040 --> 01:00:35,520
+عند التلاتة مثلا، إبراهيم. عند الأربعة، عند الأربعة
+
+796
+01:00:35,520 --> 01:00:42,130
+اتنين في اتنين، فهي مثبتة مسبقا، لاتنين. هي هالاحظتها؟
+
+797
+01:00:42,130 --> 01:00:44,850
+فالسلسلة ماشية، مش معناه أن أنا بدأت من n زائد
+
+798
+01:00:44,850 --> 01:00:48,310
+واحد، معناته أنا نسيت اللي قبلها، لأ، المطلوب أن
+
+799
+01:00:48,310 --> 01:00:52,450
+احنا هنا كلّه، قاعدين نتكلم عن الكل، فكل واحدة جاية
+
+800
+01:00:52,450 --> 01:00:56,690
+من مضروب رقمين، الرقمين هدولة قبلها، بس هم
+
+801
+01:00:56,690 --> 01:01:00,910
+مثبتين، لأنه كانوا قبلها n زائد واحد. واضحة؟
+
+802
+01:01:00,910 --> 01:01:06,550
+واضحة، كويسة. فالقصد هنا أن كل واحدة منهم أثبتت أنها
+
+803
+01:01:06,550 --> 01:01:09,990
+فعلا مجموعة برايمز. هذه مجموعة برايمز، وهذه مجموعة
+
+804
+01:01:09,990 --> 01:01:16,610
+برايمز. فمعنى ذلك أن N زائد واحد عبارة عن A في B.
+
+805
+01:01:16,610 --> 01:01:22,950
+معناته الـ B كلها في الـ Q، كلها الـ B كلها في الـ Q.
+
+806
+01:01:22,950 --> 01:01:30,160
+كلها. فستجد أنها primes في primes، جد عددها T زائد U. فإذن
+
+807
+01:01:30,160 --> 01:01:36,060
+عبارة عن sequence of primes T plus U.
+
+808
+01:01:38,360 --> 01:01:43,200
+تمام. المرة الجاية بناخد الـ example اللي وراها عشان
+
+809
+01:01:43,200 --> 01:01:45,300
+الأمور توضح. هو ضايقنا الـ slide، هذا الـ example
+
+810
+01:01:45,300 --> 01:01:48,880
+التاني، بناخده المرة الجاية عمدا عشان نرجع
+
+811
+01:01:48,880 --> 01:01:51,960
+للموضوع كمان مرة، نوضح لكم يا عزيزي. يعطيكم الصحة و
+
+812
+01:01:51,960 --> 01:01:52,700
+الراحة، و بارك الله فيكم.
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2d10b66977e4172b41713d3f2563550cd7933fc1
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_postprocess.srt
@@ -0,0 +1,3248 @@
+1
+00:00:21,110 --> 00:00:23,430
+بسم الله الرحمن الرحيم الصلاة و السلام على أشرف
+
+2
+00:00:23,430 --> 00:00:25,930
+الأنبياء والمسلمين سيدنا محمد وعلى أهلي وصحيح
+
+3
+00:00:25,930 --> 00:00:31,250
+أجمعين اليوم بنتكمل في ال cryptology أو علم
+
+4
+00:00:31,250 --> 00:00:34,130
+التشفير علم التشفير واحدة من ال applications
+
+5
+00:00:34,130 --> 00:00:39,130
+المهمة لل number theory ليش؟ لأن هنستخدم فيها
+
+6
+00:00:39,130 --> 00:00:43,780
+معلومات من اللي أخدناها في number theoryو بتعتمد
+
+7
+00:00:43,780 --> 00:00:46,960
+أصلا على أرقام لإن احنا في الآخر هنشفر ال message
+
+8
+00:00:46,960 --> 00:00:50,320
+اللي بدنا نبعتها لأرقام مجموعة أرقام مجموعة
+
+9
+00:00:50,320 --> 00:00:53,880
+الأرقام هذه هنعمل عليها شوية process معينة شوية
+
+10
+00:00:53,880 --> 00:00:57,960
+معالجة بحيث ان احنا نغير الأرقام الأرقام هذه إذا
+
+11
+00:00:57,960 --> 00:01:00,900
+اتغيرت اللي هيشوفها في الطريق مش هيعرف الشي بالظبط
+
+12
+00:01:00,900 --> 00:01:04,380
+مش هيعرف الشي الأرقام هذه الأصل أنه أنا بستجبل
+
+13
+00:01:04,380 --> 00:01:07,940
+مجموعة الأرقام أكون عارف ال code اللي اتشفرت فيه
+
+14
+00:01:07,940 --> 00:01:13,400
+عشان أعرف أعملهاdecryption اعادة التشفير او فك
+
+15
+00:01:13,400 --> 00:01:17,560
+التشفير فاليوم هنتكلم عن الموضوع هذا في ال
+
+16
+00:01:17,560 --> 00:01:21,640
+cryptology او ال cryptography ال cryptography اللي
+
+17
+00:01:21,640 --> 00:01:24,280
+هي ال methods اللي بتستخدم اعمل فيها encryption
+
+18
+00:01:24,280 --> 00:01:30,200
+نعمل فيها encryption او decryptionهدولة إيش الطرق
+
+19
+00:01:30,200 --> 00:01:33,500
+اللى بنستخدمها في ال encryption و ال decryption
+
+20
+00:01:33,500 --> 00:01:38,560
+للمسجد بحيث ان هي تصبح coded message هدى بنسميها
+
+21
+00:01:38,560 --> 00:01:43,200
+ال cryptography او ال cryptography اللى هو علم
+
+22
+00:01:43,200 --> 00:01:47,320
+التشفير أو علم عملي الاختيار الطرق أو علم الطرق
+
+23
+00:01:47,320 --> 00:01:52,830
+اللى تستخدم في التشفيرالتشفير طيب في ال crypto
+
+24
+00:01:52,830 --> 00:01:58,590
+analysis هذا اللي هو علم كسر التشفير هذا بيستخدمه
+
+25
+00:01:58,590 --> 00:02:01,390
+عادة الناس اللي بيشتغلوا ك hackers بيحاولوا
+
+26
+00:02:01,390 --> 00:02:04,350
+يشتغلوا برضه يلهم علمهم و كيف احنا نفك التشفير و
+
+27
+00:02:04,350 --> 00:02:08,070
+ال message لما تجينا مشفرة كيف احاول ا stamp منها
+
+28
+00:02:08,070 --> 00:02:12,630
+شوية ال numbers المهمة في عملية تشفيرها فهذا علم و
+
+29
+00:02:12,630 --> 00:02:16,630
+هذا علم كل واحد منهم علمو فيه له ناس اللي بيشتغلوا
+
+30
+00:02:16,630 --> 00:02:20,530
+فيه، طيب هنتكلم شوية عن المضوح هذا و بناخد مثال
+
+31
+00:02:20,530 --> 00:02:26,570
+بسيط اللي هو caesars cyber او اللي هو شفرة القيصر
+
+32
+00:02:27,350 --> 00:02:30,670
+شفرة القيصر كان لما بيروح على الحروب او بيبعت لل
+
+33
+00:02:30,670 --> 00:02:34,670
+.. للقوات تبعونه او للحكام .. للولايات اللي حوالي
+
+34
+00:02:34,670 --> 00:02:37,430
+ال .. ال .. ال .. كان يبعتله مياها مشفرة يبعت ال
+
+35
+00:02:37,430 --> 00:02:40,130
+message اللي بده يبعتها يبعتها بطريقة مشفرة بحيث
+
+36
+00:02:40,130 --> 00:02:43,490
+انه لو وقعت مع الاعداء مايعرفوش بالظبط اش اللي بده
+
+37
+00:02:43,490 --> 00:02:46,290
+يبعته طبعا كانت ال .. ال .. ال cypher تبعه او
+
+38
+00:02:46,290 --> 00:02:50,150
+الشفرة تبعته كانت كتير modest يعني كتير متواضعة او
+
+39
+00:02:50,150 --> 00:02:53,370
+كتير بسيطة فكان كل اللي بيعمله انه بيشيبلنا كل
+
+40
+00:02:53,370 --> 00:02:58,520
+الحروف .. حروف اللغةالـ 26 بكتبهم و كل واحد بيعطيه
+
+41
+00:02:58,520 --> 00:03:04,120
+رقم ببدأ من ال A صفر B واحد اتنين تلاتة لعند ال Z
+
+42
+00:03:04,120 --> 00:03:10,160
+خمسة و عشرين و كل اللي بيعمله بكتب الرسالة بياخد
+
+43
+00:03:10,160 --> 00:03:14,570
+حرف حرف الرسالةالحرف الأول في الرسالة جدّاش
+
+44
+00:03:14,570 --> 00:03:19,090
+المطرود الرقم تبعه فهذا يمثل الرقم تبع الحرف الأول
+
+45
+00:03:19,090 --> 00:03:23,070
+فبرتقم و بيصير أرقام الأرقام هتمسك رقم رقم و بيجمع
+
+46
+00:03:23,070 --> 00:03:28,790
+عليه تلاتة و بيعمل modulo 26 modulo 26 فطبعا
+
+47
+00:03:28,790 --> 00:03:32,090
+الأرقام اتغيرت هيك الأرقام كلها اتغيرت و بيبعت
+
+48
+00:03:32,090 --> 00:03:36,150
+الرسالة بناء على الأرقام اللي اتغيرت فبرجع اللغة
+
+49
+00:03:36,150 --> 00:03:39,470
+تاني فبتطلع حروف مالهاش أي علاقة بال message
+
+50
+00:03:39,470 --> 00:03:43,810
+الأصليةبتكون هي نفس ال message ولكن اتشفتت صار لها
+
+51
+00:03:43,810 --> 00:03:48,710
+عملية shift shift بمقدار تلاتة shift بمقدار تلاتة
+
+52
+00:03:48,710 --> 00:03:51,030
+هذا اللي كانت ال encryption كان بيعمل encryption
+
+53
+00:03:51,030 --> 00:03:56,090
+بهذا الشكل تشفير بهذا الشكلأو فك التشفير بيعملوا
+
+54
+00:03:56,090 --> 00:04:00,170
+كيف؟ بيعملوا نفس الفكرة ولكن بالعكس هنا كنا نجمع
+
+55
+00:04:00,170 --> 00:04:04,210
+تلاتة، لأ هنضطر إيش نعمل؟ نقص تلاتة نقص تلاتة و
+
+56
+00:04:04,210 --> 00:04:08,950
+برضه نشتغل على موديولو 26 نشتغل على موديولو 26 طيب
+
+57
+00:04:08,950 --> 00:04:15,030
+in general ال shift cipher هذا N plus K بغض النظر
+
+58
+00:04:15,030 --> 00:04:18,050
+K تلاتة زي ما هو مستعمل أو خمسة أو عشرة نقدر
+
+59
+00:04:18,050 --> 00:04:21,630
+نستعملها in general K و نكتب أي رقم بدنا يه
+
+60
+00:04:21,630 --> 00:04:28,060
+موديولو Mموديولو عامو نشتغل عليه طيب اتطور الموضوع
+
+61
+00:04:28,060 --> 00:04:31,900
+شوية فصار في transformation ان انا ممكن كمان ال N
+
+62
+00:04:31,900 --> 00:04:36,480
+أضربها في multiplier ان عجدها شوية عجدها شوية عملت
+
+63
+00:04:36,480 --> 00:04:40,060
+التشفير انه ليش اشتغل على N plus تلاتة ما اخليها
+
+64
+00:04:40,060 --> 00:04:47,090
+سبعة N plus تلاتةmodulo 26 فهنا صارت more secure
+
+65
+00:04:47,090 --> 00:04:51,230
+ولكن برضه بالنسبة للعلم اللي احنا حاليا موجود كل
+
+66
+00:04:51,230 --> 00:04:54,030
+الطريقة على بعضها insecure كل الطريقة على بعضها
+
+67
+00:04:54,030 --> 00:04:57,870
+غير آمنة سهلت الكشف الطريقة دي كلها على بعضها هيك
+
+68
+00:04:57,870 --> 00:05:00,970
+سهلت الكشف ولكن زي ما اقول ان احنا كنا مستعمل من
+
+69
+00:05:00,970 --> 00:05:06,410
+قرون بعيدة جدا من قرون بعيدة جدا من أيام القيصر من
+
+70
+00:05:06,410 --> 00:05:12,330
+أيام القيصر او Caesarكويس ناخد مثال for example لو
+
+71
+00:05:12,330 --> 00:05:16,070
+أخدنا جملة و بدنا نشفرها فكل اللي بنعمله ان احنا
+
+72
+00:05:16,070 --> 00:05:20,230
+بنكتب مجموعة الأرقام مجموعة الحروف بتاعتنا كل حرف
+
+73
+00:05:20,230 --> 00:05:27,090
+ما يقابله الرقم اللي مقابلله كل حرف الرقم و الشفرة
+
+74
+00:05:27,090 --> 00:05:32,610
+بتاعتنا هنا واضح ان احنا .. احنا مش عارفين ان
+
+75
+00:05:32,610 --> 00:05:33,390
+حقيقة ..
+
+76
+00:05:37,530 --> 00:05:45,110
+عشان ايش؟ عشان ايش؟
+
+77
+00:05:45,110 --> 00:05:52,070
+اه والله برضه ممكن برضه يعني وجهي لسببك صحيح ممكن
+
+78
+00:05:52,070 --> 00:05:58,130
+احتجت الكهربا خلاص نخليها is not easy
+
+79
+00:06:02,120 --> 00:06:04,600
+لأ بس هذه الكلمة لسه هو من الكهربا مش عارفها هي
+
+80
+00:06:04,600 --> 00:06:12,080
+للي بعده okay
+
+81
+00:06:12,080 --> 00:06:19,850
+فلاحظوا أن احنا هنا .. بس تظهر الشاشةكل اللي
+
+82
+00:06:19,850 --> 00:06:23,570
+هنعمله كل حرف هنرتب كل الحروف حافظين الحروف؟
+
+83
+00:06:23,570 --> 00:06:27,230
+فتكتبوا
+
+84
+00:06:27,230 --> 00:06:31,850
+الحروف ترتيبا مرتبة و عند ال a صفر بواحد تكتبوا
+
+85
+00:06:31,850 --> 00:06:37,470
+برضه تحت مجموعة الأرقام بتاعتها كل ترتيبهم في ال
+
+86
+00:06:37,470 --> 00:06:42,330
+sequence تبعهم و بعدين ممكن نشتغل هنا على Caesar
+
+87
+00:06:43,990 --> 00:06:46,770
+Caesar اللي هو زي ما قلنا N plus تلاتة كل اللي
+
+88
+00:06:46,770 --> 00:06:51,650
+هنعمله كل حرف بنزود عليه تلاتة ف ال T مثلا بنزود
+
+89
+00:06:51,650 --> 00:06:56,330
+عليها تلاتة بتصير W فأول حرف بيصبح أن هو ال W في
+
+90
+00:06:56,330 --> 00:07:00,810
+الرسالة فعليا ال encoded message بتاعنا بتصير حرف
+
+91
+00:07:00,810 --> 00:07:08,350
+ال W ال H مثلا بنزود عليه كمان تلاتة بيصير K ال E
+
+92
+00:07:08,350 --> 00:07:13,470
+بنزود عليه تلاتة بيصير H وهكذابنكمل ال message
+
+93
+00:07:13,470 --> 00:07:18,130
+بتاعتنا بتطلع حاجة بهذا الشكل هذه بتنبعد ال
+
+94
+00:07:18,130 --> 00:07:20,570
+message هذه هي اللي بتنبعد طبعا ال message هذه
+
+95
+00:07:20,570 --> 00:07:25,110
+الكهربا مش هتعرفها فهتعديلنا منها فال message زي
+
+96
+00:07:25,110 --> 00:07:30,250
+هذه مش هتبين مش هتنعرف مش هتنعرف ليش لأنه مشفرة
+
+97
+00:07:30,250 --> 00:07:32,950
+الحروف انتوا مش هتعرفوا منها اشي مش هتعرفوا منها
+
+98
+00:07:32,950 --> 00:07:35,990
+حاجة ومع ذلك ومع ذلك زي ما قلتلكوا انا أجابكوا ان
+
+99
+00:07:35,990 --> 00:07:39,490
+هي insecureunsecure ليش؟ لأنه أبسط شغلة، مابتيش
+
+100
+00:07:39,490 --> 00:07:44,710
+تتطلع على الرقم أو على ال letter المتكرر كتير، هدف
+
+101
+00:07:44,710 --> 00:07:46,750
+في الغالب .. في الغالب يكون واحدة من حروف ال
+
+102
+00:07:46,750 --> 00:07:51,870
+vowels، غالبا حرف من حروف اللي لينة، صحيح؟ لإن هي
+
+103
+00:07:51,870 --> 00:07:55,730
+الأكثر استخداما في اللغة، هي الأكتر و أكثرهم حرف
+
+104
+00:07:55,730 --> 00:08:00,230
+ال Eيعني بتيجي تتطلعوا وين الحرف الأكتر استخدامه
+
+105
+00:08:00,230 --> 00:08:04,570
+مثلا هو حرف ال H ال H ال H ال H ال H ال H ال H ال
+
+106
+00:08:04,570 --> 00:08:05,870
+H ال H ال H ال H ال H ال H ال H ال H ال H ال H ال
+
+107
+00:08:05,870 --> 00:08:05,990
+H ال H ال H ال H ال H ال H ال H ال H ال H ال H ال
+
+108
+00:08:05,990 --> 00:08:06,050
+H ال H ال H ال H ال H ال H ال H ال H ال H ال H ال
+
+109
+00:08:06,050 --> 00:08:06,750
+H ال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال
+
+110
+00:08:06,750 --> 00:08:09,870
+Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال
+
+111
+00:08:09,870 --> 00:08:15,210
+Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال
+
+112
+00:08:15,210 --> 00:08:20,810
+Hال H
+
+113
+00:08:28,270 --> 00:08:32,470
+Okay بجرب ال relation هذه اللي انا أستنتجتها على
+
+114
+00:08:32,470 --> 00:08:35,470
+كل و بنشوف إيش بتطلع ال message و الله ال message
+
+115
+00:08:35,470 --> 00:08:38,490
+إلها معنى واضح خلاص أنا فكيتها مالهاش معنى واضح
+
+116
+00:08:38,490 --> 00:08:42,790
+ممكن مايكنش ال E تكون ال A أو ال I أو ال U المهم
+
+117
+00:08:42,790 --> 00:08:45,230
+واحدة من الحروف لإنه هذا اللي احنا متعودين أنه
+
+118
+00:08:45,230 --> 00:08:49,370
+أكثر استخداما في اللغة اللي هي ال vowels أو الحروف
+
+119
+00:08:49,370 --> 00:08:52,090
+العلة أو الحروف اللي هي اللينة الحروف اللينة
+
+120
+00:08:57,990 --> 00:09:00,590
+فبنستخدمها عشان هيك انها insecure حقيقة انها
+
+121
+00:09:00,590 --> 00:09:03,010
+insecure اقولكوا حتى لو انضربت في multiplier حتى
+
+122
+00:09:03,010 --> 00:09:06,170
+لو انضربت في multiplier بتظل برضه insecure هتظل
+
+123
+00:09:06,170 --> 00:09:13,190
+insecure طيب في ال cryptography عادة احنا بتشتغل
+
+124
+00:09:13,190 --> 00:09:16,510
+على two keys مهمين فيه ال public و فيه ال private
+
+125
+00:09:16,510 --> 00:09:20,730
+و عشان مابضحكوا ايها اكترال public احنا بنستخدمه
+
+126
+00:09:20,730 --> 00:09:24,170
+عشان نعمل communication ل ال .. ال .. securely
+
+127
+00:09:24,170 --> 00:09:29,210
+communicate the other أو the key strings بتستخدموه
+
+128
+00:09:29,210 --> 00:09:33,310
+في التواصل زي ال email تبعكم ال email اللي فيه
+
+129
+00:09:33,310 --> 00:09:36,810
+عندكم ال username او ال email address هذا public
+
+130
+00:09:37,880 --> 00:09:41,120
+هذا الكل بعرفه عشان ابعتلكم message لازم يكون
+
+131
+00:09:41,120 --> 00:09:44,360
+عارفه عشان ابعتلكم فده public طيب private لما انا
+
+132
+00:09:44,360 --> 00:09:49,180
+بدي ادخل على ال email هذا private فى password ال
+
+133
+00:09:49,180 --> 00:09:52,300
+password المفروض ان هذا private هذا إلكوا خاص
+
+134
+00:09:52,300 --> 00:09:55,220
+فيكوا انتوا او خاص بصاحب ال email address فهذا
+
+135
+00:09:55,220 --> 00:09:59,800
+private فإذا فينا public وفينا privateprivate في
+
+136
+00:09:59,800 --> 00:10:02,540
+عندنا public و في عندنا private طيب في عندنا برضه
+
+137
+00:10:02,540 --> 00:10:06,720
+نفس الكلام لل websites ال websites عموما عشان اقرأ
+
+138
+00:10:06,720 --> 00:10:10,230
+اي معلومة موجودة على ال websitesاما اني بدى اكتب
+
+139
+00:10:10,230 --> 00:10:13,150
+معلومة او بدى اقرأ معلومة فعشان اكتب معلومة
+
+140
+00:10:13,150 --> 00:10:15,590
+المفروض ان انا عندي ال user name بتاع ال path بتاع
+
+141
+00:10:15,590 --> 00:10:20,930
+ال website او ال web page عشان ادخل و ادخل اكتب
+
+142
+00:10:20,930 --> 00:10:25,390
+اعمل insertion لمعلومات او لمقالة او لصور او او او
+
+143
+00:10:25,390 --> 00:10:29,670
+ف .. و بعدين بنعمل publishing ال publishing طلعت
+
+144
+00:10:29,670 --> 00:10:34,830
+طبعا عشان اقرأهامحتاج ايه؟ محتاج ال browser ال
+
+145
+00:10:34,830 --> 00:10:37,370
+browser كله انا محتاج ال browser فممكن هذا بتكون
+
+146
+00:10:37,370 --> 00:10:41,870
+public عشان اقراها هي public عشان انا افتح مع
+
+147
+00:10:41,870 --> 00:10:44,870
+السفحة و اقراها هتكون public لو انا ماعندش ال
+
+148
+00:10:44,870 --> 00:10:48,030
+browser مش هعرف اقراها ففي الحالة دي بكون انا
+
+149
+00:10:48,030 --> 00:10:53,650
+محتاج ال public keyأه جبنا ال explorer مثلا برضه
+
+150
+00:10:53,650 --> 00:10:56,950
+هتلاقي فيه مرات صور أو مرات الفيديوهات هيقولكوا لأ
+
+151
+00:10:56,950 --> 00:11:00,550
+محتاجين مش عارف إيش ال .. ال latest version okay
+
+152
+00:11:00,550 --> 00:11:04,310
+معناه ذلك إنه هذا مش جادر ك decoder مش جادر يفتح
+
+153
+00:11:04,310 --> 00:11:08,170
+بضطر أدور على إشي .. بس في النهاية ده كله إيش
+
+154
+00:11:08,170 --> 00:11:11,610
+publicهذا كله احنا متكلم عن حاجة public ليش؟ لأنه
+
+155
+00:11:11,610 --> 00:11:13,910
+بنزل على السوق بنزل على .. بفتح على ال net على
+
+156
+00:11:13,910 --> 00:11:16,670
+موقع تاني بدور على ال browser و بجيب أخر version و
+
+157
+00:11:16,670 --> 00:11:21,390
+بنزله يعني هذه public مافيش فيها private ال
+
+158
+00:11:21,390 --> 00:11:24,150
+private هتكون عندي اللي بده يكتب لما بدي أنا أدخل
+
+159
+00:11:24,150 --> 00:11:28,230
+لأ بدي أغير عليها الصفحة لأ هذه private public
+
+160
+00:11:28,230 --> 00:11:31,450
+issue و private issue ال email نفس الجثة public
+
+161
+00:11:31,450 --> 00:11:35,320
+أنه والله أنا ممكن أبعت للكلبس عشان ال message
+
+162
+00:11:35,320 --> 00:11:38,920
+اللي أنا بعطتها تشوفوها individual كل واحدة بتدخل
+
+163
+00:11:38,920 --> 00:11:42,540
+على حسابها مش كلكوا هتدخلوا على حساب واحدة كل
+
+164
+00:11:42,540 --> 00:11:46,260
+واحدة بتدخل على حسابها private private فهذا الفرق
+
+165
+00:11:46,260 --> 00:11:51,130
+من ال publicاللي هو can be made public و ال
+
+166
+00:11:51,130 --> 00:11:55,270
+private اللي هو ده can be kept secret from
+
+167
+00:11:55,270 --> 00:11:58,110
+everyone هذا المفروض يقولوا لأ والله ال password
+
+168
+00:11:58,110 --> 00:12:01,410
+تبع هذا خاص فيا ماحدش هيمسك ال password يعمل email
+
+169
+00:12:01,410 --> 00:12:03,550
+و يغلب حاله و بعدين ال password تبعه يقعد يعطيه
+
+170
+00:12:03,550 --> 00:12:06,570
+يوزه عن الناس ماحدش بيعمل هيف فهذه private هذه
+
+171
+00:12:06,570 --> 00:12:10,790
+خاصة .. خاصة فيكم .. خاصة فيكم .. فيكم انتوا كويس
+
+172
+00:12:10,790 --> 00:12:14,230
+ال .. ال .. ال ..for examples يعني احنا اتكلمنا عن
+
+173
+00:12:14,230 --> 00:12:17,050
+examples يعني انت الاول ممكن يعمل encryption لل
+
+174
+00:12:17,050 --> 00:12:21,230
+message و ال private يفتحها فانا ممكن برضه فعلا اي
+
+175
+00:12:21,230 --> 00:12:24,670
+واحد يعمل encryption نعمل encryption ال encryption
+
+176
+00:12:24,670 --> 00:12:28,410
+تكون anyone بقدر يعملها زي لما بدي اعملكوا email
+
+177
+00:12:28,410 --> 00:12:32,110
+بدي ابعتلكوا email طبعا انتوا email كوا اي واحد
+
+178
+00:12:32,110 --> 00:12:36,610
+بقدر يبعتلكوا صح ف anyone بقدر يعمل encryption
+
+179
+00:12:38,300 --> 00:12:41,380
+encryption للمسجل اللي بصمتكم بس مين اللي بيقدر
+
+180
+00:12:41,380 --> 00:12:45,900
+يعمل decryption يفتحها فقط انتوا private فقط انتوا
+
+181
+00:12:45,900 --> 00:12:50,980
+private في المقابل ال website مثلا نموذج لها ان
+
+182
+00:12:50,980 --> 00:12:54,300
+انا اعمل encryption باستخدام ال private key
+
+183
+00:12:56,020 --> 00:12:58,820
+encryption للمعلومة باستخدام ال private مش اي حد
+
+184
+00:12:58,820 --> 00:13:01,500
+اللي بيعمل .. اللي بدخل على ال website و بينزل
+
+185
+00:13:01,500 --> 00:13:05,400
+معلومات فقط صاحب ال website طيب و في المقابل
+
+186
+00:13:05,400 --> 00:13:10,300
+anyone بيقدر يعمل decryption اي واحد بيقدر يشوف اش
+
+187
+00:13:10,300 --> 00:13:12,980
+اللي مكتوب اي حد بيقدر يشوف فهي فوق two examples
+
+188
+00:13:12,980 --> 00:13:19,610
+لهاللموضوع طيب من ال .. يمكن نقول ال systems او ال
+
+189
+00:13:19,610 --> 00:13:23,490
+.. ال .. ال crypto system المشهور جدا لل
+
+190
+00:13:23,490 --> 00:13:30,750
+encryption اللي هو ال RSA ال RSA system اللي هو
+
+191
+00:13:30,750 --> 00:13:38,610
+rivest او rivest شمير و أدلمان او ال RSA متعرف
+
+192
+00:13:38,610 --> 00:13:42,380
+عليه RSAهدول برضه خلاص اتفقنا هيكون في عندي two
+
+193
+00:13:42,380 --> 00:13:47,340
+keys ال key الأولى ال private key و ال public key
+
+194
+00:13:47,340 --> 00:13:52,160
+ال private keyبتذكرى لما اتكلمنا في ال numbers ..
+
+195
+00:13:52,160 --> 00:13:54,340
+في ال primes عفوا .. في ال primes و قولنا ان ال
+
+196
+00:13:54,340 --> 00:13:59,240
+primes من اهم الارقام اللى هنحتاجها لاحقا و فعلا
+
+197
+00:13:59,240 --> 00:14:02,740
+هنحتاجها في ال encryption هنحتاجها ليش؟ برضه لما
+
+198
+00:14:02,740 --> 00:14:07,160
+اتكلمنا في ال pseudo prime لو فاكرين .. pseudo
+
+199
+00:14:07,160 --> 00:14:11,360
+prime قولنا انه جداش بقدر استخدم عشان اعمل
+
+200
+00:14:11,360 --> 00:14:16,300
+generation ل random sequence primesبيكون في الحالة
+
+201
+00:14:16,300 --> 00:14:21,100
+هذه التكرار بعيد جدا او ال period نفسها كتير بعيدة
+
+202
+00:14:21,100 --> 00:14:25,200
+او كتير ان انت بحث كبير عبل ما يتكرر الرقم هيكون
+
+203
+00:14:25,200 --> 00:14:30,340
+بده عدد كبير جدا من الأرقام بين كل رقم و تكراره لو
+
+204
+00:14:30,340 --> 00:14:33,600
+فمذاكرين قولنا الكلام هذا و قولنا يمكن الرقم
+
+205
+00:14:33,600 --> 00:14:36,240
+الأكثر استخداما لو فاكرين ليه اتنين to the power
+
+206
+00:14:36,240 --> 00:14:40,290
+واحد و تلاتين minus واحدقلتلكوا أكثر استخداما لأن
+
+207
+00:14:40,290 --> 00:14:44,650
+بعد اتنين to the power واحد و تلاتين بتكرر كمان
+
+208
+00:14:44,650 --> 00:14:47,970
+مرة فانتوا بتتكلموا عن رقم كتير كبير جدا فهذا
+
+209
+00:14:47,970 --> 00:14:52,410
+بيكون more secure في التعامل نفس الكلام ان لما بدي
+
+210
+00:14:52,410 --> 00:14:55,010
+اشتغل على ال private على ال private في طريقة ال
+
+211
+00:14:55,010 --> 00:15:02,290
+RSA بيكون بدنا two primes و random prime numbers
+
+212
+00:15:02,290 --> 00:15:09,040
+محتاجين رقمين كبار جدا نسبيا و primesالـprimes
+
+213
+00:15:09,040 --> 00:15:12,280
+دائما الـprimes بيعطيكوا more secure ليش؟ لأنه لا
+
+214
+00:15:12,280 --> 00:15:17,600
+يختصر تقدروش تختصروه فمعنى ذلك لو كان بده يتكرر
+
+215
+00:15:17,600 --> 00:15:22,180
+بعد الف iteration أو بعد الف number مافيش إمكانية
+
+216
+00:15:22,180 --> 00:15:25,440
+تختصروه بعد خمسمية لو بيكسب مع اتنين لو بيكسب مع
+
+217
+00:15:25,440 --> 00:15:30,080
+اتنين هتلاقوه في الألف هيظهر مرتين إذا كان بيكسب
+
+218
+00:15:30,080 --> 00:15:33,380
+مع اتنين إذا بيكسب مع تلاتة هتلاقوه في خلال الألف
+
+219
+00:15:33,380 --> 00:15:38,280
+هيكسب مع تلاتةأما إذا كان prime لو قيمته جريبة من
+
+220
+00:15:38,280 --> 00:15:43,220
+الألف هخلص بعد قيمة ال prime أو قيمة كبيرة جدا عبل
+
+221
+00:15:43,220 --> 00:15:47,000
+ما يتكرر عبل ما يتكرر فبيميروا أكتر لاستخدام ال
+
+222
+00:15:47,000 --> 00:15:51,180
+prime بعدين في ال exponent E هنستخدمه برضه هو اللي
+
+223
+00:15:51,180 --> 00:15:56,920
+وجد في معادل انكريبشن باستخدام ال RSA relative ال
+
+224
+00:15:56,920 --> 00:16:01,580
+prime لل P minus one P minus one في Q minus one
+
+225
+00:16:01,580 --> 00:16:10,050
+فإذافي E صار انا كل اللي محتاجه P Q و E و لاحظوا
+
+226
+00:16:10,050 --> 00:16:13,190
+هذا prime وهذا prime و هذا لازم تكون relatively
+
+227
+00:16:13,190 --> 00:16:23,610
+prime مع مين؟ مع P-1 في Q-1 كلهم prime او co-prime
+
+228
+00:16:23,610 --> 00:16:27,610
+يعني او co-prime فهذا هتفيدنا جدا في عملية ال
+
+229
+00:16:27,610 --> 00:16:32,800
+security طيب ال public keyأشي اللي بدنا نستعمله
+
+230
+00:16:32,800 --> 00:16:37,940
+فعلا هالوقت في الأرقام ال N هذي هتكون عبارة عن ال
+
+231
+00:16:37,940 --> 00:16:42,400
+P في ال Q ن عبارة عن P في Q و هذي هستخدمها ك
+
+232
+00:16:42,400 --> 00:16:46,100
+modulo او ك modulus في ال system تبعنا هي هذي ال
+
+233
+00:16:46,100 --> 00:16:49,440
+modulus تبعنا ال N هتكون هي ال modulus و ماتكونش
+
+234
+00:16:49,440 --> 00:16:52,540
+هي ال P نفسها أو ال Q نفسها لأن إذا ال P نفسها أو
+
+235
+00:16:52,540 --> 00:16:54,740
+ال Q نفسها انتوا كشفتوا ال P و ال Q في الحالة هذي
+
+236
+00:16:54,740 --> 00:16:57,560
+إذا كان واحدة من اتنين اتنين لأ مانفعش لازم تكون
+
+237
+00:16:57,560 --> 00:17:02,050
+ضرب الأتنينمضروب لاتنين بحيث ان انت تتطلع عليها
+
+238
+00:17:02,050 --> 00:17:09,230
+تشعر ان هي رقم not prime او composite number بس
+
+239
+00:17:09,230 --> 00:17:14,870
+فعليا مش هتعرف تطلع منه ال P و Q رقم ممكن يكسب على
+
+240
+00:17:14,870 --> 00:17:18,110
+أرقام تانية غير ال P و Q كمان يكون بيكسب على أرقام
+
+241
+00:17:18,110 --> 00:17:21,730
+أخرى بس في الآخر ممكن تعرف ال P و Q منه
+
+242
+00:17:24,510 --> 00:17:28,910
+لما بجي هلوجت اعمل هنا طبعا خلصنا encryption عملية
+
+243
+00:17:28,910 --> 00:17:32,530
+ال encryption باستخدام ال private key بصير بدنا
+
+244
+00:17:32,530 --> 00:17:34,970
+نعمل decryption باستخدام
+
+245
+00:17:37,170 --> 00:17:40,910
+public key طيب استخدم ال public key خلاص اتفجنا
+
+246
+00:17:40,910 --> 00:17:44,050
+هاي ال modulus نفسه هو هو اللي هيستخدم في ال
+
+247
+00:17:44,050 --> 00:17:47,010
+encryption هنستخدمه برضه في ال decryption بس ال
+
+248
+00:17:47,010 --> 00:17:52,270
+exponent محتاجين تجيبله ال inverse تبعه مرة أخرى
+
+249
+00:17:52,270 --> 00:17:55,150
+أتخدنا ال inverse كيف نجيبها محتاجين ال inverse و
+
+250
+00:17:55,150 --> 00:17:59,810
+ال inverse مهم جدا فمحتاج أجيب D و هذا D هو ال
+
+251
+00:17:59,810 --> 00:18:00,870
+inverse of E
+
+252
+00:18:03,540 --> 00:18:07,500
+حاجة عملتها زى توى لما كنا بنشتغل على ال .. ال
+
+253
+00:18:07,500 --> 00:18:12,180
+scissors ال cypher كنا بنقول plus تلاتة فإذا العكس
+
+254
+00:18:12,180 --> 00:18:16,280
+تبعها سالب تلاتة لما بدى اعمل decryption كنا نعمل
+
+255
+00:18:16,280 --> 00:18:18,700
+بالعكس فهنا نفس الكلام بدي أجيب العكس بس أنا هنا
+
+256
+00:18:18,700 --> 00:18:22,120
+شغال على modulo على مجموعة braille فال inverse
+
+257
+00:18:22,120 --> 00:18:28,540
+تبعنا لل E هتكون D وهدى عبارة عن E modulo P minus
+
+258
+00:18:28,540 --> 00:18:33,850
+واحد في Q minus واحد بيعطينادى وبنستخدمش ال E
+
+259
+00:18:33,850 --> 00:18:40,970
+نفسها نستخدمش ال E نفسها لاتستخدم ال E نفسها كويس
+
+260
+00:18:40,970 --> 00:18:44,470
+فعملية ال encryption هالوجت بدأت محددنا مجموعة ال
+
+261
+00:18:44,470 --> 00:18:46,450
+parameters اللى انا محتاجها مجموعة الأرقام اللى
+
+262
+00:18:46,450 --> 00:18:50,170
+انا محتاجها عشان اعمل encryption هتكون ال
+
+263
+00:18:50,170 --> 00:18:54,430
+encrypted signal هتساوي ال message الأصلية to the
+
+264
+00:18:54,430 --> 00:19:00,710
+power E exponentmode N و ال N هى اللى هى ايه قولنا
+
+265
+00:19:00,710 --> 00:19:05,490
+P فى Q P فى Q كويسة هذى بتكون هيك ال message هى
+
+266
+00:19:05,490 --> 00:19:09,830
+اللى بتنبعها او ال encrypted message ال encoded
+
+267
+00:19:09,830 --> 00:19:12,390
+message بعتناها و خلاص اللى هشوفها مش هفهم منها
+
+268
+00:19:12,390 --> 00:19:15,750
+حاجة هذى اللى هشوفها مش هفهم منها اى شىء طيب
+
+269
+00:19:15,750 --> 00:19:19,910
+وصلتنى بدي اعكسها بدي اجيبها طبعا عشان اجيبها لازم
+
+270
+00:19:19,910 --> 00:19:26,470
+انا الوحيد اللى هكون عارف ايش ال E و لاحظوا مش ال
+
+271
+00:19:26,470 --> 00:19:34,130
+Nمش ال N بدي أكون عارف ال P و ال Q يعني حتى لو
+
+272
+00:19:34,130 --> 00:19:38,930
+انكسفت هنا هو اللي عرفه ال N ماعرفش ال P و ال Q طب
+
+273
+00:19:38,930 --> 00:19:42,270
+أنا عشان أفتحها ال message تبعتي بدي أكون عارف مين
+
+274
+00:19:42,270 --> 00:19:48,150
+P و Q لإني بدي أجيب inverse ال E طب inverse ال E
+
+275
+00:19:49,260 --> 00:19:54,460
+بدنا نعمل module P-1Q-1 فانا لازم اكون اعرف ال P و
+
+276
+00:19:54,460 --> 00:19:58,560
+ال Q ال Primes العناصر المهمة جدا هذه ال Primes
+
+277
+00:19:58,560 --> 00:20:03,280
+اللي صعب تتكرر اللي بيكون صعب شوية تتكرر كويسة
+
+278
+00:20:03,280 --> 00:20:08,040
+فإذا ال message تبعتي هتساوي C ال encrypted to the
+
+279
+00:20:08,040 --> 00:20:12,480
+power D اللي هو ال inverse ال D هذا ماحدش هيعرفها
+
+280
+00:20:12,480 --> 00:20:16,430
+لنالأن أنا العارف ال code اللي اتشفرت فيه ال code
+
+281
+00:20:16,430 --> 00:20:20,910
+اللي اتشفرت فينا عارف ال D خلاص نحصل على D mod N
+
+282
+00:20:20,910 --> 00:20:24,170
+okay هو عارف ال N فليكن عارفها من ال message اللي
+
+283
+00:20:24,170 --> 00:20:27,790
+قطعها شافها في الطريق و قطعها و مشكلة okay هيعرف
+
+284
+00:20:27,790 --> 00:20:32,630
+ال N و مشتغل على N بس ال D لأ هو مش عارف لا P ولا
+
+285
+00:20:32,630 --> 00:20:36,170
+Q لأنه مش موجودة في ال message هنا مش موجودة في ال
+
+286
+00:20:36,170 --> 00:20:41,850
+message كويس ناخد exampleلل Encryption و لل
+
+287
+00:20:41,850 --> 00:20:45,530
+Decryption نبدأ بال Encryption Encryption خلاص
+
+288
+00:20:45,530 --> 00:20:50,870
+احنا عارفين القانون تبعنا اللي هي C بتساوي M to
+
+289
+00:20:50,870 --> 00:20:57,390
+the power E mod او modulo M modulo N ايش الكلمة
+
+290
+00:20:57,390 --> 00:21:00,960
+اللي بدنا نبعتها؟ بدنا نبعت كلمة stop مثلاده نبعد
+
+291
+00:21:00,960 --> 00:21:05,420
+كلمة stop ف stop برضه بشوف جدش ترتيب ال S جدش
+
+292
+00:21:05,420 --> 00:21:11,060
+ترتيب ال T جدش ترتيب ال O ال P في ال sequence تبع
+
+293
+00:21:11,060 --> 00:21:17,000
+ال alphabet string فحنشوف الأولى هذه مثلا بدنا
+
+294
+00:21:17,000 --> 00:21:20,060
+نعرف جدش ترتيبها ترتيب ترتيب ترتيب هنكون عملنا
+
+295
+00:21:20,060 --> 00:21:23,300
+شفرة لها لحالها هنكون عملنا شفرة لحالها طيب
+
+296
+00:21:23,300 --> 00:21:29,360
+هتلاقوا ال S ترتيبها 18 ال T وراها على طول 19
+
+297
+00:21:30,900 --> 00:21:33,700
+ناخدهم اربعة اربعة ناخدهم يعني two letters two
+
+298
+00:21:33,700 --> 00:21:36,720
+letters two letters هدول مع بعض بعدين في two
+
+299
+00:21:36,720 --> 00:21:38,900
+letters ال O و ال B برضه الاتنين هدول ورا بعض
+
+300
+00:21:38,900 --> 00:21:42,840
+فواحدة خمستاش و واحدة اربعتاش هد هيك ال message
+
+301
+00:21:42,840 --> 00:21:46,120
+اللي انا بده ابعتها بس ماعملتلهاش اي encryption بس
+
+302
+00:21:46,120 --> 00:21:48,380
+ماعملناش اي encryption هد ال message بتاعتنا اللي
+
+303
+00:21:48,380 --> 00:21:52,780
+بدنا تتصل كويسة مبدأ ينقش كمان ميعطيني المعلومات
+
+304
+00:21:52,780 --> 00:21:56,140
+okay ميعطيني هى ال key ميعطيني ال Q prime prime
+
+305
+00:21:56,930 --> 00:22:02,250
+بينها بنقدر نطلع لإن مضروب الأثنين في بعض في ألفين
+
+306
+00:22:02,250 --> 00:22:05,130
+وخمسمية سبعة و تلاتين وميعطيني كمان ال exponent
+
+307
+00:22:05,130 --> 00:22:09,430
+اللي هو ال power طبعا ال exponential جزيط ال power
+
+308
+00:22:09,430 --> 00:22:14,570
+ال E تلات عشر برضه prime برضه ال prime فلحظوا
+
+309
+00:22:14,570 --> 00:22:17,050
+بقالكم .. خدوا بقالكم من الأرقام كلها primes فعليا
+
+310
+00:22:17,050 --> 00:22:20,110
+يعني ال given كلها ده كله primes عندكوا هاي prime
+
+311
+00:22:20,110 --> 00:22:24,190
+هاي اتنين هاي تلاتة okayخلّيني اعمل check check
+
+312
+00:22:24,190 --> 00:22:32,610
+مهم جدا ان ال E لازم تكون co-prime كمان مع P-1 و Q
+
+313
+00:22:32,610 --> 00:22:39,950
+-1 ليش؟ اللي حضر معانا المرة اللي فتت ال inverse
+
+314
+00:22:39,950 --> 00:22:44,810
+ليش؟
+
+315
+00:22:44,810 --> 00:22:50,930
+لما هنكون بدنا نجيب ال inverse تبع A مد
+
+316
+00:22:52,830 --> 00:23:00,670
+م كنا بنقول إن ال A و M لازم يكونوا relatively
+
+317
+00:23:00,670 --> 00:23:08,410
+prime عشان أضمن إن داخل M لا يوجد إلا inverse واحد
+
+318
+00:23:08,410 --> 00:23:14,100
+لل Aارجعوا على المحاضرة السابقة كويس انه بتسجل
+
+319
+00:23:14,100 --> 00:23:19,300
+عشان ما تقولوش لما ماسمعناش بتسجل فهذه عشان تقولوا
+
+320
+00:23:19,300 --> 00:23:23,340
+اه والله فيه inverse لازم يكون ال a و ال m
+
+321
+00:23:23,340 --> 00:23:29,440
+relatively prime او co-prime في الحالة هذه نفس
+
+322
+00:23:29,440 --> 00:23:32,940
+الكلام هنا طب انا محتاج ال E هذه بعدين اعملها
+
+323
+00:23:32,940 --> 00:23:37,020
+inverse عشان احسب D مش محتاجين نحسب D دي من وين
+
+324
+00:23:37,020 --> 00:23:40,220
+بدنا نجيبها inverse ال E ماتجداش
+
+325
+00:23:42,780 --> 00:23:48,200
+P-1 P-1 فعشان فعلا خلّيني اعمل تشك جبل ما نبدأ
+
+326
+00:23:48,200 --> 00:23:51,900
+نشتغل هل الرقم بتاعتنا كلها مناسبة لل encryption
+
+327
+00:23:51,900 --> 00:23:56,860
+اللي بدنا نعمله او لا فإذا GCD بتاعتهم okay هتطلع
+
+328
+00:23:56,860 --> 00:24:00,920
+one okay من التمنين الأرقام مناسبة جدا عندنا تلاتة
+
+329
+00:24:00,920 --> 00:24:04,560
+primesو ال prime اللي انا محتاجه ال exponent اللي
+
+330
+00:24:04,560 --> 00:24:07,160
+انا محتاجه اجيبله ال inverse بالنسبة له ال prime
+
+331
+00:24:07,160 --> 00:24:10,180
+الأول minus one في ال prime التاني minus one برضه
+
+332
+00:24:10,180 --> 00:24:13,920
+relative ال prime مع بعض فإذا بقدر اقول ان دي اللي
+
+333
+00:24:13,920 --> 00:24:22,580
+هحسبها هي inverse واحدة unique inverse لل E كويس
+
+334
+00:24:26,400 --> 00:24:30,620
+هذا الاصل إن هتكون يعني إذا كان في سؤال هتكون معطق
+
+335
+00:24:30,620 --> 00:24:33,660
+ولكن إذا كان انت designer المفروض انت اللي تصمميهم
+
+336
+00:24:33,660 --> 00:24:38,040
+إذا كانت مجرد مهندسات و بتعملوا تشفوا تعملوا code
+
+337
+00:24:38,040 --> 00:24:42,340
+لحالكم بدك تختارينه بهذا الشكل اتحولوا تنجي رقمين
+
+338
+00:24:42,340 --> 00:24:46,320
+الprimes الرقمين الprimes هتقول تاخدي بالك هذا
+
+339
+00:24:46,320 --> 00:24:50,480
+minus one في هذا minus one تختاري رقم prime تالت
+
+340
+00:24:52,170 --> 00:24:55,750
+يكون relative prime مع مضروبهم مضروبهم minus واحد
+
+341
+00:24:55,750 --> 00:24:59,250
+مضروبهم minus واحد مع بعض يعني الشبكة هيك تاخد
+
+342
+00:24:59,250 --> 00:25:01,810
+بالك في ال design تبعها عشان تختاريهم بس طبعا في
+
+343
+00:25:01,810 --> 00:25:09,050
+السؤال هتكون given هنا في السؤال هتكون given خلصنا
+
+344
+00:25:09,050 --> 00:25:19,160
+في الحالة هذه ال S 18 T 19 O 14 P 15هي خلصنا ال
+
+345
+00:25:19,160 --> 00:25:21,500
+code تبعنا بناخدهم ايش ناخدهم two letters و two
+
+346
+00:25:21,500 --> 00:25:24,560
+letters بناخد الاتنين هذول مع بعض بنعتبرهم message
+
+347
+00:25:24,560 --> 00:25:36,900
+و بنعملهم modulo N اللي هي PQ طيب لحظة طبعا هيطلع
+
+348
+00:25:36,900 --> 00:25:40,580
+الرقم الاول رقم كبير جدا لإيش لإنه 13 ع ال
+
+349
+00:25:40,580 --> 00:25:43,740
+calculator مش هطلع معاكعالقلة الحسبة اللي معاكم مش
+
+350
+00:25:43,740 --> 00:25:47,860
+هيطلع لأن انتوا بتتكلموا هنا عن قداش 1819 to the
+
+351
+00:25:47,860 --> 00:25:52,520
+power 13 to the power 13 طبعا هذا كمان هيتوه اكتر
+
+352
+00:25:52,520 --> 00:25:57,420
+المعلومة لو شفناها في نص الطريق ليش لأن كل رقم او
+
+353
+00:25:57,420 --> 00:26:01,480
+كل letter مبنية مع اللي جابلها بمعنى انه مش دايما
+
+354
+00:26:01,480 --> 00:26:04,940
+ال letter نفسها في نفس ال system هتاخد نفس القيمة
+
+355
+00:26:04,940 --> 00:26:08,620
+في ال encryption لأ ليش لأنها معتمدة على اللي
+
+356
+00:26:08,620 --> 00:26:11,650
+جابلها او على اللي بعدهافالجابل أو اللي بعد هو
+
+357
+00:26:11,650 --> 00:26:14,970
+هيغيروا كل الرقم على بعضه هيتغير كل الرقم فهد كمان
+
+358
+00:26:14,970 --> 00:26:18,370
+more secure في الشغل هد بتعطيكوا more secure في
+
+359
+00:26:18,370 --> 00:26:22,070
+الشغل فصرا هنا بعمل .. بعملش encryption ل 18 لحالة
+
+360
+00:26:22,070 --> 00:26:26,830
+اللي هي خاصة بالاسم لأ أنا بعملش لل 18 بعمل ل 1819
+
+361
+00:26:26,830 --> 00:26:31,970
+هد مش letter رقم بس أنا عارف إن هو كيف .. إيش يمثل
+
+362
+00:26:31,970 --> 00:26:35,230
+يمثل two letters مع بعض كويسة تتبارط ل 13 و بعمل
+
+363
+00:26:35,230 --> 00:26:41,290
+mod g mod n هيسوي رقم جديدبنكمل الجزء التاني نفس
+
+364
+00:26:41,290 --> 00:26:45,990
+الكلام بارطبهم
+
+365
+00:26:45,990 --> 00:26:49,750
+كتر تبهم عشرين واحد تمانين و واحد و عشرين اتنين و
+
+366
+00:26:49,750 --> 00:26:53,050
+تمانين هاي ال message اللي هتنبعتها هذا ال message
+
+367
+00:26:53,050 --> 00:26:59,870
+هي الرسالة اللي هنبعتها ارسالة هذه اللي راحت لو
+
+368
+00:26:59,870 --> 00:27:02,830
+شفتواها في نص الطريق مش هتعرفوا منها اشي هذه مش
+
+369
+00:27:02,830 --> 00:27:05,950
+هتعرفوا منها حاجةهتعرف تطلع منها الكلمة ومش هتعرف
+
+370
+00:27:05,950 --> 00:27:09,330
+تطلع منها الكلمة كويس، مين اللي هعرف يطلع منها
+
+371
+00:27:09,330 --> 00:27:13,350
+كلمة؟ المستقبل هناك اللي عارف شوية parameters
+
+372
+00:27:13,350 --> 00:27:17,530
+محددة عارف شوية parameters معينة، من أهمها زي ما
+
+373
+00:27:17,530 --> 00:27:21,950
+قلنا ال E عشان بده يجيبلها ال inverse ال P و ال Q
+
+374
+00:27:21,950 --> 00:27:27,530
+عشان برضه بده يشتغل على P-1 و Q-1 و بده يجيب ال N
+
+375
+00:27:27,530 --> 00:27:32,430
+منهمكويس خلّينا نشوف بالعكس لو بدنا نعمل
+
+376
+00:27:32,430 --> 00:27:40,010
+decryption ل message بهذا الشكل 0 9 8 1 0 4 6 1
+
+377
+00:27:40,010 --> 00:27:43,950
+هنفترض أن هذه وصلتنا بدنا نشوف الشيء هذا بالظبط
+
+378
+00:27:43,950 --> 00:27:47,090
+طبعا على نفس المثال السابق على نفس المثال السابق
+
+379
+00:27:47,090 --> 00:27:49,890
+كنا نشتغل على تلاتة و أربعين تسعة و خمسين اللي هي
+
+380
+00:27:49,890 --> 00:27:55,830
+ال P و ال Q و ال E تلات عشر okay فنفس الكلام okay
+
+381
+00:27:55,830 --> 00:28:02,560
+عايا ف ال N هي هي PPQ N exponent تلت عشر تمام تمام
+
+382
+00:28:02,560 --> 00:28:06,780
+بدنا نحسب مين D D ممكن ترجع للمثال اللي كان دبل
+
+383
+00:28:06,780 --> 00:28:10,040
+هذا اللي هو في exercise أربعة في نفس الكتاب ..
+
+384
+00:28:10,040 --> 00:28:13,980
+الكتاب هذا عشان تعرفى بس هو ال inverse هذه جابها
+
+385
+00:28:13,980 --> 00:28:20,140
+مين لتلت عشر فإذا التسعمية تلاتة و سبعين هذه اللي
+
+386
+00:28:20,140 --> 00:28:24,700
+هي سبعة و تلاتين سبعة و تلاتين هذا ال inverse
+
+387
+00:28:27,610 --> 00:28:39,190
+ال inverse لمن؟ لل تلتاش مدت اتنين خمسة
+
+388
+00:28:39,190 --> 00:28:44,550
+تلاتة سبعة فمن هنا اجه الرقم الرقم من هنا اجه
+
+389
+00:28:44,550 --> 00:28:50,710
+الرقم الرقم كويسةبتقدر تشتغلوها تعملوها فاكرين
+
+390
+00:28:50,710 --> 00:28:54,050
+الطريقة اللى خدناها المطولة ترجعوا تجمعوا تانى
+
+391
+00:28:54,050 --> 00:28:57,250
+فبتقدروا تجيبوا منها ال turn تبعكوا حد اوكى
+
+392
+00:28:57,250 --> 00:29:01,930
+خلصناها بدنا نجيب ال message الاصلية اللى هى P
+
+393
+00:29:01,930 --> 00:29:08,130
+تساوي ال encrypted message to the power D mod N زى
+
+394
+00:29:08,130 --> 00:29:14,760
+ما هى ال N ال N زى ما هى كويسبرضه هبناخدهم أربع
+
+395
+00:29:14,760 --> 00:29:17,140
+أرقام two letters two letters هاي الأربع أرقام
+
+396
+00:29:17,140 --> 00:29:19,620
+الأولى to the power تسعمية سبعة و تلاتية طبعا برضه
+
+397
+00:29:19,620 --> 00:29:23,300
+على الأقل الحاسوب مش هتطلع معاكوا ماتطلعش معاكوا
+
+398
+00:29:23,300 --> 00:29:27,000
+هدى عادة كل الأقوات هدى بتنعمل على chip
+
+399
+00:29:27,000 --> 00:29:31,640
+microcontroller ال microcontroller هدى بتعملوا
+
+400
+00:29:31,640 --> 00:29:33,760
+عليه ال code تبعكم بحيث ال data مباشرة تدخل
+
+401
+00:29:33,760 --> 00:29:37,720
+بنعملها encryption فهو بتصير chip كأنها encryption
+
+402
+00:29:37,720 --> 00:29:41,780
+بنعملها encryption أو encoderصارت على خلاص ال chip
+
+403
+00:29:41,780 --> 00:29:44,260
+هذه اسمها encoder طب ال chip هذه اسمها ال decoder
+
+404
+00:29:44,260 --> 00:29:48,500
+تبعه خلاص بيصيروا يتفاهموا مع بعض اتوماتيك اللي
+
+405
+00:29:48,500 --> 00:29:50,400
+بيصيروا يتفاهموا مع بعض هيك الصناعة بتتبع خلاص هذا
+
+406
+00:29:50,400 --> 00:29:53,100
+encoder و هذا decoder بيكون ال design كله معمول
+
+407
+00:29:53,100 --> 00:29:56,180
+جوا و الاتنين هذول ا synchronize مع بعض لإن هذول
+
+408
+00:29:56,180 --> 00:29:58,960
+بيفهموا مع بعض لإن نفس ال code و نفس ال E هنا
+
+409
+00:29:58,960 --> 00:30:02,180
+موجودة ال D هنا موجودة ما يقابلها ال D تحتها
+
+410
+00:30:02,180 --> 00:30:09,730
+خلاصنا طلعت 0704هذا بالنسبة للرقم الأول الرقم
+
+411
+00:30:09,730 --> 00:30:13,450
+التاني الجزء التاني برضه تتباور تسعمية سبعة و
+
+412
+00:30:13,450 --> 00:30:16,950
+تلاتين من الفين و خمسمية سبعة و تلاتين بساوي
+
+413
+00:30:16,950 --> 00:30:22,050
+احداشر و خمستاشر بنشوف خلاص ترتيب صفر سبعة صفر
+
+414
+00:30:22,050 --> 00:30:25,290
+سبعة في ال .. في ال bit string او في ال alphabet
+
+415
+00:30:25,290 --> 00:30:28,950
+string فعلا ال alphabet string جدش مش بيساوي بساوي
+
+416
+00:30:28,950 --> 00:30:37,020
+ال H صفر أربعة ال E11 قال فبتلاقوا طلعت معاكم ال
+
+417
+00:30:37,020 --> 00:30:43,200
+message الحقيقية فعليا اللي كانت ممثلة 09810461
+
+418
+00:30:43,200 --> 00:30:47,040
+هي عملية ال encryption الطريقة دي ما زالت مستخدمة
+
+419
+00:30:47,040 --> 00:30:50,160
+يعني معظم ال applications ال .. ال .. ال
+
+420
+00:30:50,160 --> 00:30:52,480
+commercial applications مستخدمة لعندي الآن الطريقة
+
+421
+00:30:52,480 --> 00:30:58,510
+اللي هي ال RSAشائعة يعني شائعة الاستخدام وسلسة
+
+422
+00:30:58,510 --> 00:31:01,350
+بسيطة كما انتوا شايفين الأمور فيها مش كتير صعبة
+
+423
+00:31:01,350 --> 00:31:04,110
+المهم انكوا تجيبوا مجموعة برايم مناسبة تجيبوا
+
+424
+00:31:04,110 --> 00:31:08,390
+أرقام برايم مناسبة طبعا في encryption techniques
+
+425
+00:31:08,390 --> 00:31:12,190
+طلعت أفضل من هذه بس طبعا دلوقتي ممكن معظمها بيروح
+
+426
+00:31:12,190 --> 00:31:15,510
+ل ال military applications في الغالب و الحاجات
+
+427
+00:31:15,510 --> 00:31:20,390
+المحتاجة ال security أعلى تمام
+
+428
+00:31:22,610 --> 00:31:34,890
+هذه كانت أخر جزء كان عندنا من مين؟ من
+
+429
+00:31:34,890 --> 00:31:40,270
+number theory okay نكمل في جزئية من الحاجات المهمة
+
+430
+00:31:40,270 --> 00:31:45,170
+برضه اللي بتستخدم لل improving عملية الإثباتات
+
+431
+00:31:45,170 --> 00:31:48,290
+عملية الإثباتات هذه في حاجة اسمها mathematical
+
+432
+00:31:48,290 --> 00:31:53,900
+induction أو induction proofالإثبات بالحث، إيش
+
+433
+00:31:53,900 --> 00:31:56,260
+الإثبات بالحث؟ induction احنا عارفين ان هو الحث
+
+434
+00:31:56,260 --> 00:32:00,280
+يعني، حث عشان نوضحلكوا إياها الدومينو عارفين حجار
+
+435
+00:32:00,280 --> 00:32:03,440
+الدومينو؟ حجار الدومينو عارفين الناس اللي بيصفطوا
+
+436
+00:32:03,440 --> 00:32:09,600
+الحجار؟ بتلاقوا بيصفطوا الحجار هيك؟ و بعدين لو رمى
+
+437
+00:32:09,600 --> 00:32:14,700
+أول حجر أكيد أخر حجر هيجي عناطبعا هذا عشان اقول
+
+438
+00:32:14,700 --> 00:32:18,180
+انه فعلا اكيد اخر حجر هيجع او اكيد انه كل حجر هتجع
+
+439
+00:32:18,180 --> 00:32:23,960
+بمجرد ما عملت induction للأولى حفظ ان اوجع الأولى
+
+440
+00:32:23,960 --> 00:32:28,800
+بدي اضمن انه عشان كلهم يجعوا في شرطين مهمين عشان
+
+441
+00:32:28,800 --> 00:32:33,560
+فعلا اضمن انه كل وجع في شرطين كتير مهمين ايش هم
+
+442
+00:32:33,560 --> 00:32:39,740
+الشرطين المهمين انه الأولى وجعت فعلاالتعاون الدوم
+
+443
+00:32:39,740 --> 00:32:42,240
+أنه بتشوفون بيكونوا حاطين خمستاشر ألف اشتين ألف
+
+444
+00:32:42,240 --> 00:32:48,260
+جطعة بيركبوها و بيدخلوا فيها موصوعة جنس و بالعدد و
+
+445
+00:32:48,260 --> 00:32:52,180
+بالحجم و بال .. بيكونوا عاملينها كبيرة جدا بمجرد
+
+446
+00:32:52,180 --> 00:32:54,640
+ما وجع أول واحد خلاص احنا قاعدين نتفرج أنه آه أخر
+
+447
+00:32:54,640 --> 00:32:58,080
+واحد خلاص متوقعين أن أخر .. أخر حجر هيجع .. أخر
+
+448
+00:32:58,080 --> 00:33:02,800
+حجر هيجع .. كويس فإذا الأول شرط أنه الحجر الأول is
+
+449
+00:33:02,800 --> 00:33:08,150
+true و جعفإذا هنا بتعامل أنا مع ال .. ال predicate
+
+450
+00:33:08,150 --> 00:33:13,410
+function أو ال predicate تبعتي إنه الحجر رقم صفر
+
+451
+00:33:13,410 --> 00:33:21,410
+is failed و جاء كويس هل هو fails فعلا بيقع جاعد
+
+452
+00:33:21,410 --> 00:33:29,050
+إذا و جاء بدي أضمن الشرط التاني إنه كل حجر في ال
+
+453
+00:33:29,050 --> 00:33:34,400
+location N إذا و جاء thenالحجر في location n plus
+
+454
+00:33:34,400 --> 00:33:39,040
+واحد هيجع لأنه ممكن يطلعوا بعض عن بعض هذا يجع
+
+455
+00:33:39,040 --> 00:33:45,860
+مايوجعش التاني، صح؟ فإذن شرطين شرط أول إن أول حجر
+
+456
+00:33:45,860 --> 00:33:49,680
+is true هو فعلاً P of Zero ال .. ال .. ال
+
+457
+00:33:49,680 --> 00:33:53,520
+predicate عند Zero عند ال .. ال .. ال basis tip
+
+458
+00:33:53,520 --> 00:33:59,040
+هذه عند أول خطوة وجعهذا شرط أول إن فعلًا وجعت
+
+459
+00:33:59,040 --> 00:34:02,460
+الأولى عشان أقول والله كله وجعك خلاص أكيد كله
+
+460
+00:34:02,460 --> 00:34:10,500
+هيجعك الأولى وجعك الشرط التاني و الأهم إنه كل حجر
+
+461
+00:34:10,500 --> 00:34:15,580
+مرتبط باللي ورا إذا وجع الحجر أكيد هيجع اللي ورا ف
+
+462
+00:34:15,580 --> 00:34:24,140
+if then if P of N then P of N plus 1 P of N plus 1
+
+463
+00:34:24,140 --> 00:34:31,500
+تمامهذه فعلياً عملية induction بتاعتنا وهي حقيقة
+
+464
+00:34:31,500 --> 00:34:36,780
+powerful فعلا قوية جدا في الإثبات ومهمة جدا واحدة
+
+465
+00:34:36,780 --> 00:34:40,800
+من الطرق اللي كتير بتستخدم لل proving لعملية ال
+
+466
+00:34:40,800 --> 00:34:45,240
+proving لمين؟ لل predicate P of N is true for
+
+467
+00:34:45,240 --> 00:34:51,560
+every natural number Nللكل عشان اضمن ان فعلا عندكم
+
+468
+00:34:51,560 --> 00:34:56,060
+ثيورة معينة و بتعملوا prove ان هي لكل الأرقام
+
+469
+00:34:56,060 --> 00:34:59,940
+صحيحة يعني اذا نطبق على كل الأرقام ممكن نشتغل على
+
+470
+00:34:59,940 --> 00:35:05,180
+induction approval و هناخد شوية examples عليها بس
+
+471
+00:35:05,180 --> 00:35:08,460
+قاعدين احنا بنوضح الفكرة نفسها من وين اجت الفكرة؟
+
+472
+00:35:08,460 --> 00:35:11,580
+من وين؟عشان الفكرة فهذه معتمدة على ال domino
+
+473
+00:35:11,580 --> 00:35:16,160
+effect principle على مبدأ عمل تأثير ال domino أو
+
+474
+00:35:16,160 --> 00:35:19,060
+حجار ال domino على بعضها حجار ال domino على بعضها
+
+475
+00:35:19,060 --> 00:35:23,740
+طيب ال inference rule اللي هنشتغل عليه هكت تالي if
+
+476
+00:35:23,740 --> 00:35:29,480
+P of 0 is true لحظه الحجر الأول وجه is true فعلا
+
+477
+00:35:29,480 --> 00:35:38,060
+خلاص و جه and for all N أكبر أو تساوي الصفرif P of
+
+478
+00:35:38,060 --> 00:35:44,000
+N is true then P of N plus 1 is true فإذا كل حجر
+
+479
+00:35:44,000 --> 00:35:48,100
+إذا وجع أكيد حيجع اللي ورا إذا تحققوا الشرطين فإذا
+
+480
+00:35:48,100 --> 00:35:52,940
+بقول for all N أكبر من صفر P of N is true بغض
+
+481
+00:35:52,940 --> 00:36:00,640
+النظر عن N أنية للكل لكل N أكبر من صفر للكل فإذا
+
+482
+00:36:00,640 --> 00:36:04,800
+بكون ضامن إن كل الحجار وجعين كل الحجار وجعين
+
+483
+00:36:04,800 --> 00:36:08,560
+هنشتغل علىالرول هذه فقط هي اللي بنعمل منها كل
+
+484
+00:36:08,560 --> 00:36:12,640
+إثباتاتنا اللي هنشتغل عليها على إثباتاتنا زي ما
+
+485
+00:36:12,640 --> 00:36:16,580
+قلنا ال domino ال premise number one انه domino
+
+486
+00:36:16,580 --> 00:36:21,780
+number zero fails الدومينو الأولى وجعت الدجاع ال
+
+487
+00:36:21,780 --> 00:36:25,720
+premise number two for every n belong to natural
+
+488
+00:36:25,720 --> 00:36:31,570
+number if domino number n fails thendomino n plus
+
+489
+00:36:31,570 --> 00:36:33,610
+واحد number n plus واحد number n plus واحد number
+
+490
+00:36:33,610 --> 00:36:38,710
+n plus واحد number n plus واحد number n plus واحد
+
+491
+00:36:38,710 --> 00:36:43,550
+number n plus واحد number n plus واحد number n
+
+492
+00:36:43,550 --> 00:36:44,050
+plus واحد number n plus واحد number n plus واحد
+
+493
+00:36:44,050 --> 00:36:44,310
+plus واحد number n plus واحد number n plus واحد
+
+494
+00:36:44,310 --> 00:36:45,430
+number n plus واحد number n plus واحد number n
+
+495
+00:36:45,430 --> 00:36:47,570
+plus واحد number n plus واحد number n plus واحد
+
+496
+00:36:47,570 --> 00:36:50,890
+number n plus واحد number n plus واحد number n
+
+497
+00:36:50,890 --> 00:36:53,490
+plus واحد number n plus واحد number n plus واحد
+
+498
+00:36:53,490 --> 00:36:53,930
+number n plus واحد number n plus واحد number n
+
+499
+00:36:53,930 --> 00:36:55,130
+plus واحد number n plus واحد number n plus واحد
+
+500
+00:36:55,130 --> 00:36:56,130
+number n plus واحد number n plus واحد number n
+
+501
+00:36:56,130 --> 00:36:56,650
+number n plus واحد number n plus واحد number n
+
+502
+00:36:56,650 --> 00:37:01,130
+plus واحد number n plusزاد ان انا وجعت اول حجر
+
+503
+00:37:01,130 --> 00:37:05,110
+فخلاص كلنا عارفين اذا فعلا الشرطين تحققوا ان اخر
+
+504
+00:37:05,110 --> 00:37:12,070
+حجر حاجع ان اخر حجر برضه حاجع طيب ال outline of an
+
+505
+00:37:12,070 --> 00:37:15,250
+inductive proof عشان نشوف ال inductive proof هذه
+
+506
+00:37:15,250 --> 00:37:17,630
+تبعنا كيف ممكن تتم احنا كل اللي بدنا نعمل method
+
+507
+00:37:17,630 --> 00:37:22,050
+هو ان for all n P of n النظرية P of n is true
+
+508
+00:37:25,070 --> 00:37:28,610
+بدنا نصل على two steps step الأولى اللى هى ال base
+
+509
+00:37:28,610 --> 00:37:33,230
+case او ال basis step ان انا اعوض عند ال zero او
+
+510
+00:37:33,230 --> 00:37:38,950
+اعوض عند أول element لل N اللى هو ال initial
+
+511
+00:37:38,950 --> 00:37:42,130
+ببعضها أول element موجود في ال sequence أول
+
+512
+00:37:42,130 --> 00:37:45,990
+element بتعود مباشرة اعوضه مباشرة هل بيحقق ال P of
+
+513
+00:37:45,990 --> 00:37:48,790
+N ولا لأ بتشوف ايش المعادلة هذه ال P of N عبارة عن
+
+514
+00:37:48,790 --> 00:37:53,870
+ايشعوضوا فيها is it true؟ okay هاي أول شرطة
+
+515
+00:37:53,870 --> 00:37:59,370
+خلصناها الشرط التاني بدنا نقول for all n أفرض أنا
+
+516
+00:37:59,370 --> 00:38:03,970
+من عندي أن ال P of N is it true؟ هنفرض أن ال P of
+
+517
+00:38:03,970 --> 00:38:08,850
+N is true؟ و هشوف هل ال P of N plus واحد بناء على
+
+518
+00:38:08,850 --> 00:38:11,490
+معلومة أن ال P of N is true؟ هل هي كمان ال true؟
+
+519
+00:38:11,490 --> 00:38:15,550
+ولا لأ إذا تحققت true فتحقق الشرطين فإذا النظرية
+
+520
+00:38:15,550 --> 00:38:19,650
+دي دائما صحيحة خلاص بتقول إنه دائما صحيح
+
+521
+00:38:20,400 --> 00:38:24,020
+automatically دائما معناته كل إحشار يعني مادام
+
+522
+00:38:24,020 --> 00:38:27,260
+دائم خلاص معناته دائما صحيحة إذا تحقق ال two
+
+523
+00:38:27,260 --> 00:38:31,420
+conditions هدول طيب بنستخدم direct search ايه عفوا
+
+524
+00:38:31,420 --> 00:38:34,840
+ال direct proof direct proof مش فيها مشكلة على طول
+
+525
+00:38:34,840 --> 00:38:38,120
+جربوا هنا وجربوا هنا خلصنا يعني مالهاش أي
+
+526
+00:38:38,120 --> 00:38:44,390
+techniques تانية مباشرة تعود مباشر على طول okayهذا
+
+527
+00:38:44,390 --> 00:38:48,210
+بالنسبة لمين؟ لل inductive step direct ما تشتغلوش
+
+528
+00:38:48,210 --> 00:38:50,950
+لا indirect ولا contrapositive ولا contradiction
+
+529
+00:38:50,950 --> 00:38:56,170
+ولا غيره هي بسيطة جدا افرضوا هذه true وثقتوا هذه
+
+530
+00:38:56,170 --> 00:38:59,730
+منها بس يعني ما تغلبوش حالكوا في اشي ولا تقعدوا
+
+531
+00:38:59,730 --> 00:39:02,530
+تشوشوا حالكوا ولا تقعدوا تقولوا يمكن الدكتور جصده
+
+532
+00:39:02,530 --> 00:39:07,170
+يعملنا خدع هذي مباشرة شغلوها direct على طول دايما
+
+533
+00:39:07,170 --> 00:39:11,970
+طيب let n belong to natural number assume p of n
+
+534
+00:39:12,390 --> 00:39:18,370
+فإذا هنا عشان أشتغلها بفرض أن P of N is true و
+
+535
+00:39:18,370 --> 00:39:25,590
+under this assumption prove P of N plus 1 is true
+
+536
+00:39:25,590 --> 00:39:30,730
+قرنا و الله إذا true معناته تتحقق في الشرط إذا not
+
+537
+00:39:30,730 --> 00:39:34,270
+معناته كلها لاتتحقق معناته هنا بتقول for all دي
+
+538
+00:39:34,270 --> 00:39:38,480
+غلطكلمة for all غلط، معناته ماقدرش أقول إن ال
+
+539
+00:39:38,480 --> 00:39:42,180
+predicate دي للكل صحيحة، لأ هي مش للكل صحيحة، فإذا
+
+540
+00:39:42,180 --> 00:39:45,300
+بكون أثبت العكس طبعا لأ أنتوا بتكونوا تفتقوا إن هي
+
+541
+00:39:45,300 --> 00:39:48,380
+فعلا صحيحة، فبتكونوا تتأكدوا إن هذا true و هذا
+
+542
+00:39:48,380 --> 00:39:52,660
+true عشان تثبتوا في الآخر إن والله فعلا for all
+
+543
+00:39:52,660 --> 00:39:57,900
+and P of N is true طيب
+
+544
+00:39:57,900 --> 00:40:00,340
+in general، in general ممكن احنا مانبداش من ال
+
+545
+00:40:00,340 --> 00:40:06,340
+zeroممكن نبدأ من C، أي element، فهيكون ال initial
+
+546
+00:40:06,340 --> 00:40:10,440
+case بتاعتنا أو ال base case بتاعتنا هي ال C
+
+547
+00:40:10,440 --> 00:40:15,210
+نفسها، فبنصيب نشتغل هنا على P of Cالـ predicate of
+
+548
+00:40:15,210 --> 00:40:21,270
+C بدل الـ P of 0 بدل P of 0 وبصير بدنا نثبت إيش أن
+
+549
+00:40:21,270 --> 00:40:25,150
+for all n أكبر من أو تساوي C مضروبة في ال .. في ال
+
+550
+00:40:25,150 --> 00:40:27,950
+term هذا بس طبعا أنا C constant فانا النظرية ضالت
+
+551
+00:40:27,950 --> 00:40:32,310
+زي ما هي بدي أفرض P of N employees P of N plus 1
+
+552
+00:40:32,310 --> 00:40:35,470
+ماحدش يقولي employees هذه معناته إذا هذه false
+
+553
+00:40:35,470 --> 00:40:38,230
+معناته و هذه false معناته true ليش؟ لأن أحنا
+
+554
+00:40:38,230 --> 00:40:44,370
+assumption تبعنا من الأساس إن هذه truethis is true
+
+555
+00:40:44,370 --> 00:40:48,570
+فعشان تكون هذه is true و كل true لازم تكون true
+
+556
+00:40:48,570 --> 00:40:53,310
+صحيح؟ ماحدش يقول اه احنا في ال implication احنا
+
+557
+00:40:53,310 --> 00:40:55,790
+عارفين ان هذه ممكن تكون false و هذه false كله true
+
+558
+00:40:55,790 --> 00:40:59,090
+لأ احنا هنا من الأساس عاملين assumption أساسا ان
+
+559
+00:40:59,090 --> 00:41:03,950
+هذه is true انتوا بتفرضوها فرض هذه true و منها
+
+560
+00:41:03,950 --> 00:41:05,790
+تحاولوا تفضطوا التانية true
+
+561
+00:41:11,560 --> 00:41:14,800
+هناخد أمثلة هالواجهة قبل أن ناخد أمثلة نرجع كمان
+
+562
+00:41:14,800 --> 00:41:22,220
+مرة هاي اللي هنعمله ال first عادي كده اسمها طريقة
+
+563
+00:41:22,220 --> 00:41:28,540
+ال first principle طب في طريقة تانية اسمها second
+
+564
+00:41:28,540 --> 00:41:31,680
+principle second principle مختلفة شوية في ال
+
+565
+00:41:31,680 --> 00:41:37,520
+induction ليش؟ هو لا يكتفي انه يقول P of zero is
+
+566
+00:41:37,520 --> 00:41:45,740
+true and ifP of N is true than P of N plus 1 is
+
+567
+00:41:45,740 --> 00:41:50,100
+true لأ عشان أثبت P of N plus 1 أثبتلي أن كل اللي
+
+568
+00:41:50,100 --> 00:41:56,520
+جابلها is true مش بس الوحيدة اللي هي P of N اللي
+
+569
+00:41:56,520 --> 00:41:59,320
+جابلها واحدة لحالها لأ أثبتلي كل اللي جابلها لمن
+
+570
+00:41:59,320 --> 00:42:02,640
+عندي الصفر أن هي true طبعا أوضح أن هذا أصعب شوية
+
+571
+00:42:04,190 --> 00:42:09,590
+بدوا إثبات عشان أقول إن فعلا P of N plus واحد is
+
+572
+00:42:09,590 --> 00:42:13,690
+true لأ أنا لن أكتفي بس تقولي P of N is true خلاص
+
+573
+00:42:13,690 --> 00:42:20,190
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+574
+00:42:20,190 --> 00:42:22,290
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+575
+00:42:22,290 --> 00:42:24,890
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+576
+00:42:24,890 --> 00:42:27,150
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+577
+00:42:27,150 --> 00:42:29,730
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ ل
+
+578
+00:42:33,270 --> 00:42:38,390
+طبعا هذا ال strong proof واضح أن هذا الأثبات
+
+579
+00:42:38,390 --> 00:42:42,030
+الأقوى، الأثبات الأقوى طبعا ممكن يستخدم يعني انتوا
+
+580
+00:42:42,030 --> 00:42:44,530
+ماتجلغوش مش هلاقش الصعب ساعات التطبيق على وجهك
+
+581
+00:42:44,530 --> 00:42:48,210
+هتلاقي ان أمورهم مش .. مش صعبة لها الدرجة يعنى، مش
+
+582
+00:42:48,210 --> 00:42:52,420
+صعبة لها الدرجةطيب مثال خلّيني نبدأ بال first
+
+583
+00:42:52,420 --> 00:42:56,440
+principle البسيط السهل و خلاص مجرد لو أثبتت أن P
+
+584
+00:42:56,440 --> 00:42:59,220
+of N is true خلاص و هذه أثبتت منها true بكفي
+
+585
+00:42:59,220 --> 00:43:03,520
+خلّيني نشوف لو مطلوب ان ا prove that the summation
+
+586
+00:43:03,520 --> 00:43:11,740
+of the first N positive integers is N squared ايش
+
+587
+00:43:11,740 --> 00:43:19,070
+يعني؟ بمعنىلو أخدنا أول and odd positive أول and
+
+588
+00:43:19,070 --> 00:43:24,150
+odd positive إيش معناه؟ واحد، تلاتة، خمسة، سبعة،
+
+589
+00:43:24,150 --> 00:43:30,990
+تسعة، احداشر and so on هدول إيش بيساووا؟ بيساووا
+
+590
+00:43:30,990 --> 00:43:37,430
+and تربية خلينا نجرب هدي إيش location تبعها؟ واحد،
+
+591
+00:43:37,430 --> 00:43:42,210
+location اتنين، تلاتة، أربعة، خمسة، ستة، هدي ال
+
+592
+00:43:42,210 --> 00:43:46,930
+andهي قيمة الأمن و هنا ال summation بدنا نعمل
+
+593
+00:43:46,930 --> 00:43:51,470
+summation مثلا خلينا ناخد أول element الأولة الأول
+
+594
+00:43:51,470 --> 00:43:58,750
+بساوي ال location تربيع صح طيب التانية فإذا ال
+
+595
+00:43:58,750 --> 00:44:02,670
+summation الأول مع التاني أربعة يساوي ال location
+
+596
+00:44:02,670 --> 00:44:09,040
+التاني تربيعمجموع التلاتة يساوي تلاتة تربيع يساوي
+
+597
+00:44:09,040 --> 00:44:12,980
+أربعة تربيع يساوي أربعة تربيع و هكذا خمسة تربيع
+
+598
+00:44:12,980 --> 00:44:19,660
+ستة تربيع مجموع الستة elements من بداية ال
+
+599
+00:44:19,660 --> 00:44:22,860
+sequence ال odd أو ال string تبع ال odd
+
+600
+00:44:25,810 --> 00:44:29,250
+بنكون هذه النظرية بدنا نثبتها أو بنكون حددنا إيش
+
+601
+00:44:29,250 --> 00:44:33,810
+النظرية أساساً بتاعتنا ف for all n أكبر من أو يسوى
+
+602
+00:44:33,810 --> 00:44:43,270
+واحد summation لاحظوا two I minus one فلينا نجرب
+
+603
+00:44:43,270 --> 00:44:48,210
+عندي الواحد واحد في اتنين ناقص واحد اه هاي ال
+
+604
+00:44:48,210 --> 00:44:51,210
+element الأول اللي هو الواحد فعلا عندي ال location
+
+605
+00:44:51,210 --> 00:44:55,630
+واحد بكون جبت ال element الأولطب عند ال element
+
+606
+00:44:55,630 --> 00:45:01,050
+اتنين عند
+
+607
+00:45:01,050 --> 00:45:10,230
+التلاتة ستة خمسة ففعلا ال summation هيك صحيح بدنا
+
+608
+00:45:10,230 --> 00:45:17,090
+نثبت انه يساوي N تربيع زي
+
+609
+00:45:17,090 --> 00:45:19,830
+ما قلنا عندنا اتو conditions الاول
+
+610
+00:45:21,600 --> 00:45:28,040
+ال base is step الشيء أني أعوض بأصغر رقم موجود
+
+611
+00:45:28,040 --> 00:45:31,600
+خلينا نعوض بأصغر رقم موجود أصغر رقم موجود الواحد
+
+612
+00:45:31,600 --> 00:45:40,280
+فإذا من واحد لواحد هل يسوى واحد تربيع واحد بيسوى
+
+613
+00:45:40,280 --> 00:45:44,900
+واحد فده هتقدر ان واحد بيسوى واحد فإذا and ال P of
+
+614
+00:45:44,900 --> 00:45:52,220
+واحد is trueهذه ال base step أول element دائما
+
+615
+00:45:52,220 --> 00:45:55,600
+بتجربوا أول element و بتجربوا عليه ال theory
+
+616
+00:45:55,600 --> 00:45:59,660
+المقلوب إثباتها الأولى خلصت مش الحاجة طيب دلها
+
+617
+00:45:59,660 --> 00:46:04,120
+الوقت نجرب التاني
+
+618
+00:46:04,120 --> 00:46:09,920
+التاني
+
+619
+00:46:09,920 --> 00:46:17,340
+كالتالي هنقول انه summation I بتسوي واحد and plus
+
+620
+00:46:17,340 --> 00:46:22,220
+oneهلق بنثبت اللي هو ال N plus one صحيح؟ فبنجيب ال
+
+621
+00:46:22,220 --> 00:46:27,860
+N plus one و بنحاول نجيبه بدلالة N بنحاول نجيبه
+
+622
+00:46:27,860 --> 00:46:32,560
+بدلالة N ليش؟ لأن أثبتنا أن N is true فانا هلق
+
+623
+00:46:32,560 --> 00:46:42,240
+هقول assumption تبعتي أن I بتساوي 1 to N to I
+
+624
+00:46:42,240 --> 00:46:49,710
+minus 1 فعلا بتساوي N تربيعبنانة على ال assumption
+
+625
+00:46:49,710 --> 00:46:55,550
+تبعي هذا بتثبتها الوجد هل to n plus واحد برضه
+
+626
+00:46:55,550 --> 00:47:00,350
+هتطلع n plus واحد تربيه و لا لأ طيب خليني امسكها
+
+627
+00:47:00,350 --> 00:47:10,730
+هنا صارت اتنين I ناقص واحد هذه
+
+628
+00:47:10,730 --> 00:47:14,690
+ايش ممكن تساوي عشان احطها بدلالةن اللي انا عارف ان
+
+629
+00:47:14,690 --> 00:47:22,810
+هي true فتساوي summation I بتساوي واحد to N minus
+
+630
+00:47:22,810 --> 00:47:28,210
+واحد plus .. لاحظ عوضه بس في العنصر الأخير اللي
+
+631
+00:47:28,210 --> 00:47:33,950
+ضال اخر عنصر ضال فحنعوض بإيش؟ ب2 مضروبها في N plus
+
+632
+00:47:33,950 --> 00:47:39,530
+واحد N plus واحد ناقص واحد بس
+
+633
+00:47:42,390 --> 00:47:46,010
+Okay هذا احنا ضمنين دايما ان هو true احنا اصلا
+
+634
+00:47:46,010 --> 00:47:48,270
+عاملين assumption اصلا ان هو true فإذا هذا بيساوي
+
+635
+00:47:48,270 --> 00:47:54,150
+n تربيع مدامي صح مدامي صح بيضالي جزء اللي ضايل هنا
+
+636
+00:47:54,150 --> 00:48:01,790
+طبعا هنا هيكون عندكوا اتنين n وزائد واحد طيب ال
+
+637
+00:48:01,790 --> 00:48:07,430
+term هذا ايش بيساوي n زائد واحد تربيع طب ما هي صح
+
+638
+00:48:07,430 --> 00:48:13,600
+فإذا المعادلة صحيحةالنظرية او المعادلة بتاعتنا
+
+639
+00:48:13,600 --> 00:48:18,580
+فعلا صحيحة واضح ان النظرية صحيحة لحظة الموضوع بسيط
+
+640
+00:48:18,580 --> 00:48:23,340
+جدا كل اللي بيصير بتجربوا اول element في ال
+
+641
+00:48:23,340 --> 00:48:26,520
+sequence عندكم اول element موجود بتجربوا على ال
+
+642
+00:48:26,520 --> 00:48:30,480
+theory المطلوب اثباتها بتضمن ان هو is true حسب
+
+643
+00:48:30,480 --> 00:48:34,260
+النظرية خلصنا اول شرط او ال base step او ال bases
+
+644
+00:48:34,260 --> 00:48:40,460
+step تمام خلصناها الشرط التاني بتفرضه ان عند n
+
+645
+00:48:41,430 --> 00:48:46,950
+التيوري صحيحة is true و بتحاولوا تحسبوا عند n plus
+
+646
+00:48:46,950 --> 00:48:50,450
+واحد طبعا عشان تحسبوا عند n plus واحد تحاولوا
+
+647
+00:48:50,450 --> 00:48:53,590
+دايما تجيبوها بدلالة n اللي انتوا ضمنيه ان هي is
+
+648
+00:48:53,590 --> 00:49:00,370
+true بحيث انكم مباشرة تعوضوا بقيمتها او بقيمتها في
+
+649
+00:49:00,370 --> 00:49:03,850
+التيوري باعتبار ان هي true وشوفوا ايش ال summation
+
+650
+00:49:03,850 --> 00:49:08,200
+او كيف شكل المعادلة بتتطلع معاكمالـ sequence كله
+
+651
+00:49:08,200 --> 00:49:10,840
+هيظل ماشي معاكم الجزئية هذه بس هي اللي هتختلف من
+
+652
+00:49:10,840 --> 00:49:15,380
+مثال لمثال ان كيف عمليت التجميل هتصير بس ماقدرش
+
+653
+00:49:15,380 --> 00:49:18,600
+أقولكوا هذا الاشي ثابت ليش لأنه حسب النظرية نفسها
+
+654
+00:49:18,600 --> 00:49:21,960
+هتتغير مجموعة الأقام اللي هنا بس بس بتكون شطرتكوا
+
+655
+00:49:21,960 --> 00:49:26,280
+كيف تدمجوها مع بعض عشان توصلوا ان حتى عند N plus
+
+656
+00:49:26,280 --> 00:49:27,940
+واحد ال theory is true
+
+657
+00:49:32,950 --> 00:49:35,050
+طماما ماهي هاد ال assumption تبعنا هاد ال
+
+658
+00:49:35,050 --> 00:49:38,510
+inductive step ال inductive step مبنيه على الموضوع
+
+659
+00:49:38,510 --> 00:49:42,930
+هذا اني بفرض P of N is true و بحاول بناء على
+
+660
+00:49:42,930 --> 00:49:50,510
+الفرضية هذه أثبت ان P of N plus 1 is true okay فهي
+
+661
+00:49:50,510 --> 00:49:57,850
+الفكرة اللي احنا عملناها فعليا ناخد المثال التاني
+
+662
+00:49:57,850 --> 00:50:01,050
+كمان مثال approve
+
+663
+00:50:08,490 --> 00:50:15,070
+تانى بيقول النظرية بتاعتنا for all n أكبر من صفر n
+
+664
+00:50:15,070 --> 00:50:20,930
+دائما أقل من two to the power n طبعا ال biometric
+
+665
+00:50:20,930 --> 00:50:25,190
+معروف يعني دائما إذا كان فعلا for all n أكبر من
+
+666
+00:50:25,190 --> 00:50:30,750
+صفر دائما n أقل من two to the power n منطقى طيب
+
+667
+00:50:30,750 --> 00:50:35,960
+هنا هنحط معناته أن P of nتساوي and ال n هنا معناته
+
+668
+00:50:35,960 --> 00:50:38,700
+أن n أقل من two to the power of n لأن هذه ال
+
+669
+00:50:38,700 --> 00:50:41,600
+assumption اللي هنبدأ فيه ال inductive step بتاعتي
+
+670
+00:50:41,600 --> 00:50:45,320
+ال inductive step بس خلينا مبدأيا نبدأ بال base
+
+671
+00:50:45,320 --> 00:50:51,720
+step أول أقل رقم ممكن واحد خلينا نجرب الواحد عشان
+
+672
+00:50:51,720 --> 00:50:55,320
+نشتغل على ال base case او ال base step واحد أقل من
+
+673
+00:50:55,320 --> 00:50:58,340
+two to the power واحد اه صحيح واحد أقل من اتنين
+
+674
+00:50:58,340 --> 00:51:02,260
+الكلام صحيح فإذا هاي أول شرط خلصناه ال inductive
+
+675
+00:51:02,260 --> 00:51:09,230
+stepfor all n أكبر من صفر بدنا نعمل approve لإيش P
+
+676
+00:51:09,230 --> 00:51:14,770
+of n employs P of n plus واحد فإذن هنقول أن P of n
+
+677
+00:51:14,770 --> 00:51:20,090
+is true معناته أن فعلا المعادلة هذه صحيحة أن n أقل
+
+678
+00:51:20,090 --> 00:51:24,410
+من 2 to the power n معناته أن n أقل من 2 to the
+
+679
+00:51:24,410 --> 00:51:28,810
+power n هذه ال logic مسلم فيها أن هي صحيحةمثلمة
+
+680
+00:51:28,810 --> 00:51:33,050
+فيها أنها صحيحة و هنعمل هى assuming هى تمام إجتنا
+
+681
+00:51:33,050 --> 00:51:36,070
+كمان مرة و بدنا منها نعمل proof لهذا ال term خلاص
+
+682
+00:51:36,070 --> 00:51:40,390
+نمسك هذا ال term ان هو ال term اللى هنا هذا هى اه
+
+683
+00:51:40,390 --> 00:51:44,390
+من واجبنا الكلام هذا استلمه احنا قاعدين بنقول n
+
+684
+00:51:44,390 --> 00:51:49,630
+أقل من two to the power n صح طيب اجمعوا زائد واحد
+
+685
+00:51:49,630 --> 00:51:57,120
+زائد واحدبتغير إشي؟ خمسة أقل من ستة، ستة أقل من
+
+686
+00:51:57,120 --> 00:52:07,540
+سبعة، صحيح، okay بعد هيك، ضمنين إنه دايما الواحد
+
+687
+00:52:07,540 --> 00:52:12,980
+أقل من two to the power n، ليش؟ لأن أقل n ممكنة هي
+
+688
+00:52:12,980 --> 00:52:17,640
+الواحد، هي الواحد، و احنا أصلا هي أثنتنا من الأول،
+
+689
+00:52:17,640 --> 00:52:21,830
+إن واحد هتكون أقل من two to the power oneأقل قيمة
+
+690
+00:52:21,830 --> 00:52:26,730
+ممكن لل N هي الواحد فإذا كان ال term هذا أكبر من N
+
+691
+00:52:26,730 --> 00:52:30,890
+زائد واحد طب لما نزوده كمان برضه حيظل أكبر من N
+
+692
+00:52:30,890 --> 00:52:33,770
+زائد واحد حيظل أكبر من N زائد واحد طب ليش أنا بدي
+
+693
+00:52:33,770 --> 00:52:37,910
+إياها N زائد واحد اتنين أجمع ال two N هذه عشان
+
+694
+00:52:37,910 --> 00:52:41,470
+أجمعها مع ال two N اللي موجودة أجيب ال N plus واحد
+
+695
+00:52:41,470 --> 00:52:46,460
+عشان نجيب ال N plus واحد ليش لإن ال term هذاببساطة
+
+696
+00:52:46,460 --> 00:52:49,140
+two to the power of n plus two to the power of n
+
+697
+00:52:49,140 --> 00:52:52,000
+ما هي هذي تساوي two to the power of n في اتنين
+
+698
+00:52:52,000 --> 00:52:56,900
+اتنين يعني to the power of one يعني معناه ذلك
+
+699
+00:52:56,900 --> 00:53:02,120
+اتنين to the power مجموحهم تمام
+
+700
+00:53:02,120 --> 00:53:05,260
+معناه ذلك ان هذي two to the power of n plus one هي
+
+701
+00:53:05,260 --> 00:53:08,700
+ان زائد واحد اقل من two to the power of n زائد
+
+702
+00:53:08,700 --> 00:53:14,810
+واحدأقل من two to four N زي الواحد تمام فإذا طول
+
+703
+00:53:14,810 --> 00:53:19,270
+ما هي P of N is true برضه P of N زي الواحد is true
+
+704
+00:53:19,270 --> 00:53:23,510
+is true هذه automatic ليه؟ معناته هذا الكلام للكل
+
+705
+00:53:23,510 --> 00:53:28,230
+صحيح نظرية هذه أو المعادلة ال relation هذه لكل
+
+706
+00:53:28,230 --> 00:53:33,510
+الأرقام صحيحة لكل ال natural number لأكبر من صفر
+
+707
+00:53:33,510 --> 00:53:35,630
+صحيحة تمام
+
+708
+00:53:44,900 --> 00:53:52,800
+تو سلسلة طيب ال second principle second principle
+
+709
+00:53:52,800 --> 00:53:58,320
+زي ما قولنا ايش بتقدر تكتب ان كل السابق is true
+
+710
+00:53:58,320 --> 00:54:01,840
+طيب شوية شوية خلينا ناخد إيش هي النظرية أصلا بدوية
+
+711
+00:54:01,840 --> 00:54:06,280
+show that every n أكبر من واحد لكل الأرقام اللي
+
+712
+00:54:06,280 --> 00:54:11,950
+أكبر من واحد can be written as a productP1 P2 to P
+
+713
+00:54:11,950 --> 00:54:17,370
+S of some series of S' number هذي قلناها لما
+
+714
+00:54:17,370 --> 00:54:20,970
+اتكلمنا عن الprimes لما اتكلمنا عن ال prime او ال
+
+715
+00:54:20,970 --> 00:54:26,870
+factorization قلنا ان كل رقم عبارة عن مضروب مجموعة
+
+716
+00:54:26,870 --> 00:54:30,410
+ارقام صحيح مجموعة الprimes عبارة عن مضروب مجموعة
+
+717
+00:54:30,410 --> 00:54:34,990
+الprimes فهو بده يدينا نثبتها لحظة بدنا هنا اعملية
+
+718
+00:54:34,990 --> 00:54:40,210
+اثبات لها okayعشان أثبتها، هنقول إن الكاشة الأولى
+
+719
+00:54:40,210 --> 00:54:45,010
+عندنا هنا كاشة الـP of كائنها الـof zero بتاعتنا
+
+720
+00:54:45,010 --> 00:54:49,110
+اللي هو أول element أكبر من واحد HP للإتنين فبدنا
+
+721
+00:54:49,110 --> 00:54:53,550
+نجرب عند الإتنين عند الإتنين N بتساوي اتنين لت ال
+
+722
+00:54:53,550 --> 00:54:57,850
+S تبعنا أو ال string تبعنا يحتوي على element واحد
+
+723
+00:54:57,850 --> 00:55:02,290
+اللي هو إيش ال prime إتنينفهو فعلا هي يقيم prime
+
+724
+00:55:02,290 --> 00:55:06,990
+فإذا ال string عبارة عن prime واحد فإذا يسوى واحد
+
+725
+00:55:06,990 --> 00:55:10,230
+ال cardinality بتبعته بتسوى واحد ال cardinality
+
+726
+00:55:10,230 --> 00:55:13,270
+بتسوى واحد okay هلوجد دخلنا في ال inductive step
+
+727
+00:55:13,270 --> 00:55:19,150
+في ال inductive step let n أكبر أو تسوى اتنين أكبر
+
+728
+00:55:19,150 --> 00:55:24,530
+من اتنين اتنين أثبتناها الأتنين أثبتت assumefor
+
+729
+00:55:24,530 --> 00:55:28,010
+all كأكبر
+
+730
+00:55:28,010 --> 00:55:34,210
+من اتنين و اقل من ن يعني كله نثبت لكله for all k
+
+731
+00:55:34,210 --> 00:55:41,610
+من اتنين to n P of k is true إذا فعلا is true عشان
+
+732
+00:55:41,610 --> 00:55:47,990
+هنا من ذهنك بنقول consider n plus واحد في الحالة
+
+733
+00:55:47,990 --> 00:55:55,410
+التاعتنا okay هدول is trueتمام؟ هدول بقدروا أقول
+
+734
+00:55:55,410 --> 00:56:00,830
+إن هم مثبتين بس لبعد هم مش عارف صح؟ يعني عند n
+
+735
+00:56:00,830 --> 00:56:04,330
+plus واحد أنا مش عارف إحنا بدنا نثبتها هي صح ولا
+
+736
+00:56:04,330 --> 00:56:11,070
+غلط لعند n كل السابق مظبوط مدام أنا بتكلم عن اتنين
+
+737
+00:56:11,070 --> 00:56:14,190
+من اتنين فهنا ال K أول K ممكن أتعامل معاها حاليا
+
+738
+00:56:14,190 --> 00:56:20,250
+تكون اتنين نفسها الاتنين نفسها صحيحة لو تكلمنا عن
+
+739
+00:56:20,250 --> 00:56:24,980
+n بتساوي اتنين طب أكتر من اتنينمش عارف فبدنا نثبت
+
+740
+00:56:24,980 --> 00:56:29,200
+هالوجهة إذا كان فعلا عن n زائد واحد فهنا هنفرض إنه
+
+741
+00:56:29,200 --> 00:56:32,360
+أنا بدي أتعامل مع n زائد واحد والله إذا هي prime
+
+742
+00:56:32,360 --> 00:56:37,980
+إذا هي نفسها prime معناته ال string تبعها بواحد هي
+
+743
+00:56:37,980 --> 00:56:42,690
+نفسها فده is a primeهذا is a prime ممكن تتحقق مع
+
+744
+00:56:42,690 --> 00:56:47,190
+بعض elements أو مع بعض numbers بس مش الكل مش الكل
+
+745
+00:56:47,190 --> 00:56:50,070
+فإذا في شرط تاني لازم أخد بالي منه هنا if prime
+
+746
+00:56:50,070 --> 00:56:55,330
+نتكذا okay مش مشكلة ولكن else if زائد واحد مش
+
+747
+00:56:55,330 --> 00:57:00,620
+prime مش معناته مش prime معناته عبارة عن ايهزائد B
+
+748
+00:57:00,620 --> 00:57:08,820
+مضروبة في B صح composite number مضروبة في B مضروبة
+
+749
+00:57:08,820 --> 00:57:10,820
+في B مضروبة في B مضروبة في B مضروبة في B مضروبة في
+
+750
+00:57:10,820 --> 00:57:13,620
+B مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+751
+00:57:13,620 --> 00:57:16,180
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+752
+00:57:16,180 --> 00:57:16,240
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+753
+00:57:16,240 --> 00:57:16,480
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+754
+00:57:16,480 --> 00:57:17,400
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+755
+00:57:17,400 --> 00:57:18,600
+مضروبة في B
+
+756
+00:57:22,630 --> 00:57:28,030
+لأ هو composite أو مؤلف من رقمين مضربين في بعض،
+
+757
+00:57:28,030 --> 00:57:35,130
+فليكن A هتكون طبيعي أقل من N صح؟
+
+758
+00:57:35,130 --> 00:57:38,250
+أكيد هتكون أقل من N، أنا بتكلم عن N زائد واحد، و
+
+759
+00:57:38,250 --> 00:57:42,090
+متألف من رقمين مضربين في بعض، فالرقمين المضربين في
+
+760
+00:57:42,090 --> 00:57:46,640
+بعض، كل واحد منهم أقلمن n زائد واحد اكيد اكيد كل
+
+761
+00:57:46,640 --> 00:57:49,920
+واحد منهم هتكون اقل من n زائد واحد فإذا a هتكون
+
+762
+00:57:49,920 --> 00:57:54,320
+اكبر من واحد و اقل من او تسوى n اللي هي اقل من n
+
+763
+00:57:54,320 --> 00:57:59,840
+زائد واحد طيب بي نفس الكلام الرقمين هدول اللي
+
+764
+00:57:59,840 --> 00:58:05,870
+لايمكن يكونوا بيسووا n إذا ماكنتش prime صح؟إذا لم
+
+765
+00:58:05,870 --> 00:58:11,010
+تكن الـ prime هل ممكن a تسوى n زائد واحد؟ لأ ولا
+
+766
+00:58:11,010 --> 00:58:13,550
+البيئة ممكن تكون بتسوى n زائد واحد لازم يكون قيمهم
+
+767
+00:58:13,550 --> 00:58:17,970
+أقل منها أقل منها إذا واحدة منهم تسوى n زائد واحد
+
+768
+00:58:17,970 --> 00:58:22,610
+معناته هي prime معناته هي أصلا prime طيب، لا تساوي
+
+769
+00:58:22,610 --> 00:58:29,750
+معناته أقل، معنى ذلك وبناء على ال condition هذا إن
+
+770
+00:58:29,750 --> 00:58:35,740
+كل اللي أقل is true فإذا ais it true؟ هي متكونة من
+
+771
+00:58:35,740 --> 00:58:41,000
+مجموعة الprimes و B برضه أقل فإذا is it true؟ هي
+
+772
+00:58:41,000 --> 00:58:44,720
+متكونة برضه من مجموعة الprimes هي متكونة أصلا من
+
+773
+00:58:44,720 --> 00:58:48,560
+مجموعة الprimes فمعنا ذلك بقدر أقول أن ال A متكونة
+
+774
+00:58:48,560 --> 00:58:54,160
+أساسا من مجموعة الprimes عددهم T فال string تبعنا
+
+775
+00:58:54,160 --> 00:58:59,770
+T و A مضروم عبارة عنprime أول في تاني في تالت في
+
+776
+00:58:59,770 --> 00:59:04,630
+prime رقم T ال B نفس الكلام بيعتبر أنها أقل من N
+
+777
+00:59:04,630 --> 00:59:08,930
+زائد واحد فهي مثبتة مسبقا طب اللحظة أنتوا كيف
+
+778
+00:59:08,930 --> 00:59:13,790
+أثبتت أساسا من الأول أنتوا برضه هتسأله طب أساسا
+
+779
+00:59:13,790 --> 00:59:19,310
+ايه مين جل من أنها مجموعة الprimes لأن هي نفسها لو
+
+780
+00:59:19,310 --> 00:59:22,430
+اتعاملت معها أنها N زائد واحد
+
+781
+00:59:25,050 --> 00:59:29,690
+برضه نفس الكلام هقول إن هي مضروب مجموعة أرقام هقول
+
+782
+00:59:29,690 --> 00:59:35,670
+إن هي برضه مضروب مجموعة أرقام أقل منها طيب مجموعة
+
+783
+00:59:35,670 --> 00:59:41,090
+الأرقام اللي أقل منها برضه إما إن هي prime نفس ال
+
+784
+00:59:41,090 --> 00:59:43,970
+condition لاحظوا إن ال condition بتكرر لاحظوا إن
+
+785
+00:59:43,970 --> 00:59:48,790
+هنا ال condition بتكرر أو رقمين أقل منها لعدم أصل
+
+786
+00:59:48,790 --> 00:59:54,260
+لمين لل initialلعندي نصل ال initial condition
+
+787
+00:59:54,260 --> 00:59:58,120
+تبعنا أو ال base case بتاعتنا نصل ال base case
+
+788
+00:59:58,120 --> 01:00:04,300
+بتاعتنا لاحظتوا كده؟ فإذن واضح إنه هنا أنا ما
+
+789
+01:00:04,300 --> 01:00:08,480
+أقفلتش اللي أقل منها لأ بالعكس و مثبتين اللي أقل
+
+790
+01:00:08,480 --> 01:00:13,360
+منها نتيجة إن هم كانوا قبلها n زائد واحدنتيجة ان
+
+791
+01:00:13,360 --> 01:00:17,380
+هما كانوا أصلا قبلها n زائد واحد صح؟ عشان أصل ل n
+
+792
+01:00:17,380 --> 01:00:20,620
+زائد واحد هنا و أقول ان كل اللي جابلها مثبت هم
+
+793
+01:00:20,620 --> 01:00:24,300
+أساسا كل اللي جابلها ماتمش إثباتهم إلا لأنه كانوا
+
+794
+01:00:24,300 --> 01:00:30,040
+عند n زائد واحد فعند n زائد واحد أقل الواحدة ممكنة
+
+795
+01:00:30,040 --> 01:00:35,520
+عند التلاتة مثلا إبراهيم عند الأربعة عند الأربعة
+
+796
+01:00:35,520 --> 01:00:42,130
+اتنين في اتنين فهي مثبتة مسبقا لاتنين هيهالاحظته؟
+
+797
+01:00:42,130 --> 01:00:44,850
+فالسلسلة ماشية، مش معناه أن أنا بدأت من n زائد
+
+798
+01:00:44,850 --> 01:00:48,310
+واحد، معناته أنا انسيت اللي جابلها، لأ، المطلوب أن
+
+799
+01:00:48,310 --> 01:00:52,450
+احنا هنا كله، قاعدين نتكلم عن الكل، فكل واحدة جاية
+
+800
+01:00:52,450 --> 01:00:56,690
+من مضروب رقمين، الرقمين هدولة جابلها، بس هم
+
+801
+01:00:56,690 --> 01:01:00,910
+مثبتين، لأنه كانوا جابلها n زائد واحد، واضحة؟
+
+802
+01:01:00,910 --> 01:01:06,550
+واضحة، كويسةفالقصد هنا أن كل واحدة منهم أثبتت أنها
+
+803
+01:01:06,550 --> 01:01:09,990
+فعلا مجموعة براينز هذه مجموعة براينز وهذه مجموعة
+
+804
+01:01:09,990 --> 01:01:16,610
+براينز فمعنى ذلك أن N زائد واحد عبارة عن A في B
+
+805
+01:01:16,610 --> 01:01:22,950
+معناته ال B كلها في ال Q كلها ال B كلها في ال Q
+
+806
+01:01:22,950 --> 01:01:30,160
+كلها فستجد أنها بيز في كيوز جدش عددهم T زائد Uفإذن
+
+807
+01:01:30,160 --> 01:01:36,060
+عبارة عن sequence of primes T plus U'
+
+808
+01:01:38,360 --> 01:01:43,200
+تمام المرة الجاية بناخد ال example اللي وراها عشان
+
+809
+01:01:43,200 --> 01:01:45,300
+الأمور توضح هو ضايقنا ال slide هذا ال example
+
+810
+01:01:45,300 --> 01:01:48,880
+التاني بناخده المرة الجاية بالعمد عشان نرجع
+
+811
+01:01:48,880 --> 01:01:51,960
+للموضوع كمان مرة نوضحكوا يا عزيزي يعطيكوا الصحة و
+
+812
+01:01:51,960 --> 01:01:52,700
+رحة و برك الله فيكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ab68ed233845ecd21195cc6eeb10c69739db59d1
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4109, "start": 21.11, "end": 41.09, "text": "بسم الله الرحمن الرحيم الصلاة و السلام على أشرف الأنبياء والمسلمين سيدنا محمد وعلى أهلي وصحيح أجمعين اليوم بنتكمل في ال cryptology أو علم التشفير علم التشفير واحدة من ال applications المهمة لل number theory ليش؟ لأن هنستخدم فيها معلومات من اللي أخدناها في number theory", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 4032, 21136, 37440, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 2304, 3794, 19528, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 20292, 4032, 9381, 5016, 1829, 5016, 5551, 7435, 2304, 3615, 9957, 45595, 20498, 4724, 29399, 24793, 1211, 8978, 2423, 9844, 1793, 34051, 11203, 2304, 16712, 8592, 5172, 13546, 11203, 2304, 16712, 8592, 5172, 13546, 36764, 24401, 3660, 9154, 2423, 5821, 9673, 16095, 3660, 24976, 1230, 5261, 32239, 8592, 22807, 5296, 33456, 8032, 1863, 14851, 9778, 40448, 8978, 11296, 20449, 1211, 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قولنا انه جداش بقدر استخدم عشان اعمل generation ل random sequence primes", "tokens": [3555, 2655, 8848, 37983, 7578, 5296, 15042, 1975, 2655, 4117, 19528, 8315, 8978, 2423, 3547, 4386, 8978, 2423, 582, 1532, 6225, 5172, 14407, 4386, 8978, 2423, 582, 1532, 4032, 12174, 12610, 8315, 16472, 2423, 582, 1532, 9154, 1975, 16095, 2423, 9640, 4587, 10943, 13672, 7578, 8032, 1863, 33753, 26108, 11296, 20193, 5016, 4587, 995, 4032, 6156, 3615, 15040, 8032, 1863, 33753, 26108, 11296, 8978, 2423, 29575, 8032, 1863, 33753, 26108, 11296, 32239, 8592, 22807, 4724, 43042, 3224, 5296, 15042, 1975, 2655, 4117, 19528, 8315, 8978, 2423, 35899, 5835, 45164, 6156, 995, 37983, 9957, 4386, 35899, 5835, 12174, 12610, 8315, 16472, 3224, 10874, 3215, 33599, 4724, 28543, 2288, 44713, 9778, 40448, 6225, 8592, 7649, 1975, 25957, 1211, 5125, 5296, 4974, 8310, 2886, 279], "avg_logprob": -0.19461381823066773, "compression_ratio": 1.9253112033195021, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 830.16, 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cypher كنا بنقول plus تلاتة فإذا العكس تبعها سالب تلاتة لما بدى اعمل decryption كنا نعمل بالعكس فهنا نفس الكلام بدي أجيب العكس بس أنا هنا شغال على modulo على مجموعة braille فال inverse تبعنا لل E هتكون D وهدى عبارة عن E modulo P minus واحد في Q minus واحد بيعطينا", "tokens": [5016, 26108, 3660, 6225, 42213, 2655, 11296, 30767, 7578, 33427, 7578, 5296, 15042, 9122, 8315, 44945, 8592, 2655, 17082, 1211, 15844, 2423, 4386, 2423, 16066, 2423, 3185, 79, 511, 9122, 8315, 44945, 39648, 1804, 6055, 1211, 9307, 3660, 6156, 28814, 15730, 18863, 4117, 3794, 6055, 3555, 3615, 11296, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 5296, 15042, 47525, 7578, 1975, 25957, 1211, 979, 627, 1695, 9122, 8315, 8717, 25957, 1211, 20666, 3615, 4117, 3794, 6156, 3224, 8315, 8717, 36178, 2423, 28820, 10943, 4724, 16254, 5551, 7435, 1829, 3555, 18863, 4117, 3794, 4724, 3794, 41850, 34105, 13412, 17082, 6027, 15844, 1072, 13455, 15844, 3714, 7435, 2304, 2407, 27884, 1548, 3409, 6156, 6027, 17340, 6055, 3555, 3615, 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صعب شوية تتكرر كويسة فإذا ال message تبعتي هتساوي C ال encrypted to the power D اللي هو ال inverse ال D هذا ماحدش هيعرفها لنا", "tokens": [44510, 8315, 8717, 25957, 1211, 10088, 430, 12, 16, 48, 12, 16, 6156, 7649, 995, 5296, 31377, 2304, 1975, 30544, 1975, 3615, 28480, 2423, 430, 4032, 2423, 1249, 2423, 2114, 1532, 18863, 1863, 33546, 2288, 9673, 16095, 3660, 10874, 28259, 29538, 2423, 2114, 1532, 13672, 1829, 20328, 3615, 3555, 6055, 2655, 37983, 2288, 13672, 1829, 4724, 1829, 30544, 20328, 3615, 3555, 13412, 2407, 10632, 6055, 2655, 37983, 2288, 9122, 45865, 3794, 3660, 6156, 28814, 15730, 2423, 3636, 6055, 3555, 3615, 31371, 8032, 2655, 3794, 995, 45865, 383, 2423, 36663, 281, 264, 1347, 413, 13672, 1829, 31439, 2423, 17340, 2423, 413, 23758, 19446, 24401, 8592, 39896, 3615, 28480, 11296, 5296, 8315], "avg_logprob": -0.25619368563901196, "compression_ratio": 1.5925925925925926, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1189.26, "end": 1189.58, "word": "بدنا", 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"word": " بعدين", "probability": 0.927978515625}, {"start": 1927.34, "end": 1929.08, "word": " لو", "probability": 0.8837890625}, {"start": 1929.08, "end": 1929.6, "word": " رمى", "probability": 0.9523111979166666}, {"start": 1929.6, "end": 1929.9, "word": " أول", "probability": 0.952392578125}, {"start": 1929.9, "end": 1931.06, "word": " حجر", "probability": 0.8173828125}, {"start": 1931.06, "end": 1931.44, "word": " أكيد", "probability": 0.943359375}, {"start": 1931.44, "end": 1931.66, "word": " أخر", "probability": 0.9208984375}, {"start": 1931.66, "end": 1931.92, "word": " حجر", "probability": 0.9943033854166666}, {"start": 1931.92, "end": 1932.22, "word": " هيجي", "probability": 0.8269856770833334}, {"start": 1932.22, "end": 1932.4, "word": " عنا", "probability": 0.4013671875}], "temperature": 1.0}, {"id": 81, "seek": 195780, "start": 1933.7, "end": 1957.8, "text": "طبعا هذا عشان اقول انه فعلا اكيد اخر حجر هيجع او اكيد انه كل حجر هتجع بمجرد ما عملت induction للأولى حفظ ان اوجع الأولى بدي اضمن انه عشان كلهم يجعوا في شرطين مهمين عشان فعلا اضمن انه كل وجع في شرطين كتير مهمين ايش هم الشرطين المهمين انه الأولى وجعت فعلا", "tokens": [9566, 3555, 3615, 995, 23758, 6225, 8592, 7649, 1975, 39648, 16472, 3224, 6156, 3615, 15040, 1975, 4117, 25708, 1975, 34740, 11331, 7435, 2288, 39896, 7435, 3615, 1975, 2407, 1975, 4117, 25708, 16472, 3224, 28242, 11331, 7435, 2288, 8032, 2655, 7435, 3615, 4724, 2304, 7435, 2288, 3215, 19446, 6225, 42213, 2655, 33371, 24976, 10721, 12610, 7578, 11331, 5172, 19913, 16472, 1975, 29245, 3615, 16247, 12610, 7578, 4724, 16254, 1975, 11242, 27842, 16472, 3224, 6225, 8592, 7649, 28242, 16095, 7251, 7435, 3615, 14407, 8978, 13412, 2288, 9566, 9957, 3714, 16095, 9957, 6225, 8592, 7649, 6156, 3615, 15040, 1975, 11242, 27842, 16472, 3224, 28242, 4032, 7435, 3615, 8978, 13412, 2288, 9566, 9957, 9122, 2655, 13546, 3714, 16095, 9957, 1975, 1829, 8592, 8032, 2304, 25124, 2288, 9566, 9957, 9673, 16095, 9957, 16472, 3224, 16247, 12610, 7578, 49610, 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"probability": 0.905517578125}, {"start": 2047.24, "end": 2048.78, "word": " إنه", "probability": 0.560791015625}, {"start": 2048.78, "end": 2049.26, "word": " كل", "probability": 0.9775390625}, {"start": 2049.26, "end": 2050.5, "word": " حجر", "probability": 0.9930013020833334}, {"start": 2050.5, "end": 2051.12, "word": " مرتبط", "probability": 0.993896484375}, {"start": 2051.12, "end": 2051.36, "word": " باللي", "probability": 0.869384765625}, {"start": 2051.36, "end": 2051.58, "word": " ورا", "probability": 0.9853515625}, {"start": 2051.58, "end": 2052.48, "word": " إذا", "probability": 0.9345703125}, {"start": 2052.48, "end": 2052.76, "word": " وجع", "probability": 0.78759765625}, {"start": 2052.76, "end": 2053.26, "word": " الحجر", "probability": 0.9951171875}, {"start": 2053.26, "end": 2053.86, "word": " أكيد", "probability": 0.978515625}, {"start": 2053.86, "end": 2054.62, "word": " هيجع", "probability": 0.9763997395833334}, {"start": 2054.62, "end": 2054.78, "word": " اللي", "probability": 0.9306640625}, {"start": 2054.78, "end": 2055.0, "word": " ورا", "probability": 0.927978515625}, {"start": 2055.0, "end": 2055.58, "word": " ف", "probability": 0.91259765625}, {"start": 2055.58, "end": 2055.86, "word": " if", "probability": 0.88134765625}, {"start": 2055.86, "end": 2056.46, "word": " then", "probability": 0.82275390625}, {"start": 2056.46, "end": 2057.54, "word": " if", "probability": 0.65087890625}, {"start": 2057.54, "end": 2058.2, "word": " P", "probability": 0.7275390625}, {"start": 2058.2, "end": 2058.46, "word": " of", "probability": 0.5703125}, {"start": 2058.46, "end": 2058.72, "word": " N", "probability": 0.62548828125}, {"start": 2058.72, "end": 2059.3, "word": " then", "probability": 0.841796875}, {"start": 2059.3, "end": 2059.86, "word": " P", "probability": 0.97802734375}, {"start": 2059.86, "end": 2060.08, "word": " of", "probability": 0.97314453125}, {"start": 2060.08, "end": 2060.28, "word": " N", "probability": 0.982421875}, {"start": 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{"start": 2076.88, "end": 2077.26, "word": " الطرق", "probability": 0.9720052083333334}, {"start": 2077.26, "end": 2077.7, "word": " اللي", "probability": 0.906982421875}, {"start": 2077.7, "end": 2078.06, "word": " كتير", "probability": 0.8961588541666666}, {"start": 2078.06, "end": 2078.64, "word": " بتستخدم", "probability": 0.946533203125}, {"start": 2078.64, "end": 2079.06, "word": " لل", "probability": 0.397216796875}, {"start": 2079.06, "end": 2079.48, "word": " proving", "probability": 0.7900390625}, {"start": 2079.48, "end": 2080.68, "word": " لعملية", "probability": 0.7760009765625}, {"start": 2080.68, "end": 2080.8, "word": " ال", "probability": 0.935546875}, {"start": 2080.8, "end": 2081.16, "word": " proving", "probability": 0.9140625}, {"start": 2081.16, "end": 2082.06, "word": " لمين؟", "probability": 0.5198567708333334}, {"start": 2082.06, "end": 2082.2, "word": " لل", "probability": 0.53662109375}, {"start": 2082.2, "end": 2082.76, "word": " predicate", "probability": 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اذا نطبق على كل الأرقام ممكن نشتغل على induction approval و هناخد شوية examples عليها بس قاعدين احنا بنوضح الفكرة نفسها من وين اجت الفكرة؟ من وين؟", "tokens": [1211, 23275, 1211, 6225, 8592, 7649, 1975, 11242, 27842, 16472, 6156, 3615, 15040, 43242, 24793, 38637, 1829, 13063, 3660, 20449, 9957, 3660, 4032, 39894, 25957, 1211, 14407, 7081, 16472, 39896, 5296, 28820, 16247, 2288, 4587, 10943, 20328, 5016, 1829, 5016, 3660, 37495, 22653, 1975, 15730, 8717, 9566, 3555, 4587, 15844, 28242, 16247, 2288, 4587, 10943, 3714, 43020, 8717, 8592, 2655, 17082, 1211, 15844, 33371, 13317, 4032, 8032, 1863, 47283, 3215, 13412, 2407, 10632, 5110, 25894, 11296, 4724, 3794, 12174, 995, 22488, 9957, 1975, 5016, 8315, 44945, 2407, 11242, 5016, 27188, 4117, 25720, 8717, 36178, 11296, 9154, 4032, 9957, 1975, 7435, 2655, 27188, 4117, 25720, 22807, 9154, 4032, 9957, 22807], "avg_logprob": -0.23920454247431322, "compression_ratio": 1.6359832635983265, "no_speech_prob": 1.1324882507324219e-06, "words": 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"probability": 0.91650390625}, {"start": 2099.74, "end": 2099.94, "word": " على", "probability": 0.8310546875}, {"start": 2099.94, "end": 2100.54, "word": " induction", "probability": 0.8896484375}, {"start": 2100.54, "end": 2101.3, "word": " approval", "probability": 0.419189453125}, {"start": 2101.3, "end": 2101.44, "word": " و", "probability": 0.4306640625}, {"start": 2101.44, "end": 2102.74, "word": " هناخد", "probability": 0.709075927734375}, {"start": 2102.74, "end": 2103.12, "word": " شوية", "probability": 0.7644856770833334}, {"start": 2103.12, "end": 2103.54, "word": " examples", "probability": 0.75}, {"start": 2103.54, "end": 2103.82, "word": " عليها", "probability": 0.771728515625}, {"start": 2103.82, "end": 2105.18, "word": " بس", "probability": 0.600341796875}, {"start": 2105.18, "end": 2105.42, "word": " قاعدين", "probability": 0.7618408203125}, {"start": 2105.42, "end": 2105.52, "word": " احنا", "probability": 0.8050944010416666}, {"start": 2105.52, "end": 2106.04, "word": " بنوضح", "probability": 0.9578857421875}, {"start": 2106.04, "end": 2106.86, "word": " الفكرة", "probability": 0.9899088541666666}, {"start": 2106.86, "end": 2107.32, "word": " نفسها", "probability": 0.9752604166666666}, {"start": 2107.32, "end": 2107.54, "word": " من", "probability": 0.68115234375}, {"start": 2107.54, "end": 2107.7, "word": " وين", "probability": 0.8076171875}, {"start": 2107.7, "end": 2107.94, "word": " اجت", "probability": 0.666259765625}, {"start": 2107.94, "end": 2108.46, "word": " الفكرة؟", "probability": 0.9185791015625}, {"start": 2108.46, "end": 2108.6, "word": " من", "probability": 0.9619140625}, {"start": 2108.6, "end": 2109.02, "word": " وين؟", "probability": 0.9150390625}], "temperature": 1.0}, {"id": 88, "seek": 213554, "start": 2109.42, "end": 2135.54, "text": "عشان الفكرة فهذه معتمدة على ال domino effect principle على مبدأ عمل تأثير ال domino أو حجار ال domino على بعضها حجار ال domino على بعضها طيب ال inference rule اللي هنشتغل عليه هكت تالي if P of 0 is true لحظه الحجر الأول وجه is true فعلا خلاص و جه and for all N أكبر أو تساوي الصفر", "tokens": [3615, 8592, 7649, 27188, 4117, 25720, 6156, 3224, 24192, 3714, 34268, 2304, 41891, 15844, 2423, 3285, 2982, 1802, 8665, 15844, 3714, 44510, 10721, 6225, 42213, 6055, 10721, 12984, 13546, 2423, 3285, 2982, 34051, 11331, 7435, 9640, 2423, 3285, 2982, 15844, 45030, 11242, 11296, 11331, 7435, 9640, 2423, 3285, 2982, 15844, 45030, 11242, 11296, 23032, 1829, 3555, 2423, 38253, 4978, 13672, 1829, 8032, 1863, 8592, 2655, 17082, 1211, 47356, 8032, 4117, 2655, 6055, 6027, 1829, 498, 430, 295, 1958, 307, 2074, 5296, 5016, 19913, 3224, 21542, 7435, 2288, 16247, 12610, 4032, 7435, 3224, 307, 2074, 6156, 3615, 15040, 16490, 1211, 33546, 4032, 10874, 3224, 293, 337, 439, 426, 5551, 4117, 26890, 34051, 6055, 3794, 995, 45865, 31767, 5172, 2288], "avg_logprob": -0.20627626375991756, "compression_ratio": 1.7016129032258065, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2109.42, "end": 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2235.85, "end": 2236.11, "word": " ممكن", "probability": 0.98388671875}, {"start": 2236.11, "end": 2236.39, "word": " تتم", "probability": 0.612548828125}, {"start": 2236.39, "end": 2236.63, "word": " احنا", "probability": 0.923828125}, {"start": 2236.63, "end": 2236.91, "word": " كل", "probability": 0.72265625}, {"start": 2236.91, "end": 2237.03, "word": " اللي", "probability": 0.923828125}, {"start": 2237.03, "end": 2237.25, "word": " بدنا", "probability": 0.7998046875}, {"start": 2237.25, "end": 2237.43, "word": " نعمل", "probability": 0.6884765625}, {"start": 2237.43, "end": 2237.63, "word": " method", "probability": 0.9326171875}, {"start": 2237.63, "end": 2237.95, "word": " هو", "probability": 0.31005859375}, {"start": 2237.95, "end": 2238.27, "word": " ان", "probability": 0.273193359375}, {"start": 2238.27, "end": 2238.49, "word": " for", "probability": 0.93310546875}, {"start": 2238.49, "end": 2238.83, "word": " all", "probability": 0.9560546875}, {"start": 2238.83, "end": 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اللى هو ال initial ببعضها أول element موجود في ال sequence أول element بتعود مباشرة اعوضه مباشرة هل بيحقق ال P of N ولا لأ بتشوف ايش المعادلة هذه ال P of N عبارة عن ايش", "tokens": [44510, 8315, 8717, 36520, 15844, 732, 4439, 1823, 16247, 12610, 7578, 13672, 7578, 8032, 7578, 2423, 3096, 1389, 1975, 2407, 2423, 5143, 1823, 16472, 1975, 8315, 1975, 3615, 2407, 11242, 43242, 2423, 4018, 1975, 2407, 1975, 3615, 2407, 11242, 43242, 5551, 12610, 4478, 24976, 426, 13672, 7578, 31439, 2423, 5883, 4724, 3555, 3615, 11242, 11296, 5551, 12610, 4478, 3714, 29245, 23328, 8978, 2423, 8310, 5551, 12610, 4478, 39894, 3615, 23328, 3714, 3555, 33599, 25720, 1975, 3615, 2407, 11242, 3224, 3714, 3555, 33599, 25720, 8032, 1211, 4724, 1829, 5016, 4587, 4587, 2423, 430, 295, 426, 49429, 5296, 10721, 39894, 8592, 38688, 1975, 1829, 8592, 9673, 3615, 18513, 37977, 29538, 2423, 430, 295, 426, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 8592], "avg_logprob": -0.24380165683336494, "compression_ratio": 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element", "probability": 0.9716796875}, {"start": 2260.79, "end": 2261.23, "word": " موجود", "probability": 0.9762369791666666}, {"start": 2261.23, "end": 2261.35, "word": " في", "probability": 0.60205078125}, {"start": 2261.35, "end": 2261.45, "word": " ال", "probability": 0.90966796875}, {"start": 2261.45, "end": 2261.81, "word": " sequence", "probability": 0.99072265625}, {"start": 2261.81, "end": 2262.13, "word": " أول", "probability": 0.788818359375}, {"start": 2262.13, "end": 2262.31, "word": " element", "probability": 0.95751953125}, {"start": 2262.31, "end": 2262.69, "word": " بتعود", "probability": 0.7569173177083334}, {"start": 2262.69, "end": 2263.13, "word": " مباشرة", "probability": 0.9425048828125}, {"start": 2263.13, "end": 2263.51, "word": " اعوضه", "probability": 0.755078125}, {"start": 2263.51, "end": 2263.91, "word": " مباشرة", "probability": 0.990966796875}, {"start": 2263.91, "end": 2264.75, "word": " هل", "probability": 0.96728515625}, {"start": 2264.75, "end": 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0.98466796875}, {"start": 2296.79, "end": 2298.25, "word": " خلاص", "probability": 0.97607421875}, {"start": 2298.25, "end": 2298.53, "word": " بتقول", "probability": 0.66845703125}, {"start": 2298.53, "end": 2298.71, "word": " إنه", "probability": 0.70361328125}, {"start": 2298.71, "end": 2299.15, "word": " دائما", "probability": 0.97314453125}, {"start": 2299.15, "end": 2299.65, "word": " صحيح", "probability": 0.99853515625}], "temperature": 1.0}, {"id": 95, "seek": 232240, "start": 2300.4, "end": 2322.4, "text": "automatically دائما معناته كل إحشار يعني مادام دائم خلاص معناته دائما صحيحة إذا تحقق ال two conditions هدول طيب بنستخدم direct search ايه عفوا ال direct proof direct proof مش فيها مشكلة على طول جربوا هنا وجربوا هنا خلصنا يعني مالهاش أي techniques تانية مباشرة تعود مباشر على طول okay", "tokens": [1375, 298, 5030, 11778, 16373, 15042, 20449, 8315, 47395, 28242, 11933, 5016, 8592, 9640, 37495, 22653, 3714, 18513, 10943, 11778, 16373, 2304, 16490, 1211, 33546, 20449, 8315, 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"text": "هذا بالنسبة لمين؟ لل inductive step direct ما تشتغلوش لا indirect ولا contrapositive ولا contradiction ولا غيره هي بسيطة جدا افرضوا هذه true وثقتوا هذه منها بس يعني ما تغلبوش حالكوا في اشي ولا تقعدوا تشوشوا حالكوا ولا تقعدوا تقولوا يمكن الدكتور جصده يعملنا خدع هذي مباشرة شغلوها direct على طول دايما طيب let n belong to natural number assume p of n", "tokens": [3224, 15730, 20666, 1863, 35457, 3660, 32767, 9957, 22807, 24976, 31612, 488, 1823, 2047, 19446, 6055, 8592, 2655, 17082, 1211, 2407, 8592, 20193, 19523, 49429, 660, 4007, 329, 2187, 49429, 34937, 49429, 32771, 13546, 3224, 39896, 4724, 3794, 1829, 9566, 3660, 10874, 28259, 1975, 5172, 43042, 14407, 29538, 2074, 4032, 12984, 38149, 14407, 29538, 9154, 11296, 4724, 3794, 37495, 22653, 19446, 6055, 17082, 46152, 2407, 8592, 11331, 6027, 4117, 14407, 8978, 1975, 8592, 1829, 49429, 6055, 4587, 22488, 14407, 6055, 8592, 2407, 8592, 14407, 11331, 6027, 4117, 14407, 49429, 6055, 4587, 22488, 14407, 6055, 39648, 14407, 7251, 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"probability": 0.79449462890625}, {"start": 2342.53, "end": 2343.03, "word": " يعملنا", "probability": 0.9525146484375}, {"start": 2343.03, "end": 2343.49, "word": " خدع", "probability": 0.81396484375}, {"start": 2343.49, "end": 2344.33, "word": " هذي", "probability": 0.54541015625}, {"start": 2344.33, "end": 2344.81, "word": " مباشرة", "probability": 0.991455078125}, {"start": 2344.81, "end": 2345.49, "word": " شغلوها", "probability": 0.866259765625}, {"start": 2345.49, "end": 2345.81, "word": " direct", "probability": 0.935546875}, {"start": 2345.81, "end": 2345.99, "word": " على", "probability": 0.90087890625}, {"start": 2345.99, "end": 2346.27, "word": " طول", "probability": 0.984130859375}, {"start": 2346.27, "end": 2347.17, "word": " دايما", "probability": 0.567138671875}, {"start": 2347.17, "end": 2347.65, "word": " طيب", "probability": 0.8894856770833334}, {"start": 2347.65, "end": 2348.07, "word": " let", "probability": 0.798828125}, {"start": 2348.07, "end": 2348.37, "word": 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{"start": 3184.26, "end": 3184.3, "word": " of", "probability": 0.95751953125}, {"start": 3184.3, "end": 3184.44, "word": " n", "probability": 0.9443359375}, {"start": 3184.44, "end": 3184.6, "word": " plus", "probability": 0.7041015625}, {"start": 3184.6, "end": 3184.86, "word": " one", "probability": 0.67919921875}, {"start": 3184.86, "end": 3185.26, "word": " هي", "probability": 0.443359375}, {"start": 3185.26, "end": 3186.18, "word": " ان", "probability": 0.275146484375}, {"start": 3186.18, "end": 3186.82, "word": " زائد", "probability": 0.7286783854166666}, {"start": 3186.82, "end": 3187.18, "word": " واحد", "probability": 0.98876953125}, {"start": 3187.18, "end": 3187.54, "word": " اقل", "probability": 0.9498697916666666}, {"start": 3187.54, "end": 3187.74, "word": " من", "probability": 0.98779296875}, {"start": 3187.74, "end": 3187.94, "word": " two", "probability": 0.93896484375}, {"start": 3187.94, "end": 3188.04, "word": " to", "probability": 0.98486328125}, {"start": 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وهذه مجموعة براينز فمعنى ذلك أن N زائد واحد عبارة عن A في B معناته ال B كلها في ال Q كلها ال B كلها في ال Q كلها فستجد أنها بيز في كيوز جدش عددهم T زائد U", "tokens": [5172, 6027, 4587, 9381, 3215, 34105, 14739, 28242, 36764, 24401, 3660, 9154, 16095, 5551, 12984, 3555, 2655, 2655, 14739, 11296, 6156, 3615, 15040, 3714, 7435, 2304, 2407, 27884, 4724, 23557, 9957, 11622, 29538, 3714, 7435, 2304, 2407, 27884, 4724, 23557, 9957, 11622, 37037, 24192, 3714, 7435, 2304, 2407, 27884, 4724, 23557, 9957, 11622, 6156, 2304, 3615, 1863, 7578, 29910, 23275, 14739, 426, 30767, 16373, 3215, 36764, 24401, 6225, 3555, 9640, 3660, 18871, 316, 8978, 363, 20449, 8315, 47395, 2423, 363, 28242, 11296, 8978, 2423, 1249, 28242, 11296, 2423, 363, 28242, 11296, 8978, 2423, 1249, 28242, 11296, 6156, 14851, 7435, 3215, 14739, 11296, 4724, 1829, 11622, 8978, 9122, 1829, 2407, 11622, 10874, 3215, 8592, 6225, 3215, 3215, 16095, 314, 30767, 16373, 3215, 624], "avg_logprob": -0.18470528237218778, "compression_ratio": 2.089005235602094, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3663.31, "end": 3664.01, "word": "فالقصد", "probability": 0.7615234375}, {"start": 3664.01, "end": 3664.21, "word": " هنا", "probability": 0.96923828125}, {"start": 3664.21, "end": 3664.49, "word": " أن", "probability": 0.50048828125}, {"start": 3664.49, "end": 3665.13, "word": " كل", "probability": 0.6396484375}, {"start": 3665.13, "end": 3665.41, "word": " واحدة", "probability": 0.9913736979166666}, {"start": 3665.41, "end": 3665.65, "word": " منهم", "probability": 0.955078125}, {"start": 3665.65, "end": 3666.23, "word": " أثبتت", "probability": 0.93583984375}, {"start": 3666.23, "end": 3666.55, "word": " أنها", "probability": 0.666748046875}, {"start": 3666.55, "end": 3666.85, "word": " فعلا", "probability": 0.8408203125}, {"start": 3666.85, "end": 3667.21, "word": " مجموعة", "probability": 0.937109375}, {"start": 3667.21, "end": 3667.77, "word": " براينز", "probability": 0.60308837890625}, {"start": 3667.77, "end": 3668.51, "word": " هذه", "probability": 0.21435546875}, {"start": 3668.51, "end": 3668.85, "word": " مجموعة", "probability": 0.9634765625}, {"start": 3668.85, "end": 3669.25, "word": " براينز", "probability": 0.969970703125}, {"start": 3669.25, "end": 3669.67, "word": " وهذه", "probability": 0.90185546875}, {"start": 3669.67, "end": 3669.99, "word": " مجموعة", "probability": 0.973046875}, {"start": 3669.99, "end": 3670.45, "word": " براينز", "probability": 0.9932861328125}, {"start": 3670.45, "end": 3670.99, "word": " فمعنى", "probability": 0.89931640625}, {"start": 3670.99, "end": 3671.21, "word": " ذلك", "probability": 0.9873046875}, {"start": 3671.21, "end": 3671.39, "word": " أن", "probability": 0.7802734375}, {"start": 3671.39, "end": 3671.61, "word": " N", "probability": 0.25048828125}, {"start": 3671.61, "end": 3671.85, "word": " زائد", "probability": 0.7179361979166666}, {"start": 3671.85, "end": 3672.27, "word": " واحد", "probability": 0.75146484375}, {"start": 3672.27, "end": 3672.87, "word": " عبارة", "probability": 0.99560546875}, {"start": 3672.87, "end": 3673.07, "word": " عن", "probability": 0.9873046875}, {"start": 3673.07, "end": 3675.91, "word": " A", "probability": 0.416748046875}, {"start": 3675.91, "end": 3676.35, "word": " في", "probability": 0.69384765625}, {"start": 3676.35, "end": 3676.61, "word": " B", "probability": 0.91552734375}, {"start": 3676.61, "end": 3677.11, "word": " معناته", "probability": 0.865234375}, {"start": 3677.11, "end": 3678.19, "word": " ال", "probability": 0.86181640625}, {"start": 3678.19, "end": 3678.35, "word": " B", "probability": 0.5400390625}, {"start": 3678.35, "end": 3678.87, "word": " كلها", "probability": 0.812255859375}, {"start": 3678.87, "end": 3679.65, "word": " في", "probability": 0.958984375}, {"start": 3679.65, "end": 3679.79, "word": " ال", "probability": 0.90185546875}, {"start": 3679.79, "end": 3680.03, "word": " Q", "probability": 0.84033203125}, {"start": 3680.03, "end": 3680.69, "word": " كلها", "probability": 0.98779296875}, {"start": 3680.69, "end": 3681.53, "word": " ال", "probability": 0.53271484375}, {"start": 3681.53, "end": 3681.69, "word": " B", "probability": 0.83935546875}, {"start": 3681.69, "end": 3681.97, "word": " كلها", "probability": 0.970947265625}, {"start": 3681.97, "end": 3682.15, "word": " في", "probability": 0.9892578125}, {"start": 3682.15, "end": 3682.69, "word": " ال", "probability": 0.8681640625}, {"start": 3682.69, "end": 3682.95, "word": " Q", "probability": 0.876953125}, {"start": 3682.95, "end": 3683.63, "word": " كلها", "probability": 0.9921875}, {"start": 3683.63, "end": 3684.15, "word": " فستجد", "probability": 0.7926025390625}, {"start": 3684.15, "end": 3684.65, "word": " أنها", "probability": 0.4365234375}, {"start": 3684.65, "end": 3685.93, "word": " بيز", "probability": 0.670654296875}, {"start": 3685.93, "end": 3686.17, "word": " في", "probability": 0.9521484375}, {"start": 3686.17, "end": 3686.61, "word": " كيوز", "probability": 0.91796875}, {"start": 3686.61, "end": 3687.07, "word": " جدش", "probability": 0.80615234375}, {"start": 3687.07, "end": 3687.51, "word": " عددهم", "probability": 0.9720458984375}, {"start": 3687.51, "end": 3687.93, "word": " T", "probability": 0.783203125}, {"start": 3687.93, "end": 3688.49, "word": " زائد", "probability": 0.9640299479166666}, {"start": 3688.49, "end": 3688.71, "word": " U", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 149, "seek": 371270, "start": 3689.58, "end": 3712.7, "text": "فإذن عبارة عن sequence of primes T plus U' تمام المرة الجاية بناخد ال example اللي وراها عشان الأمور توضح هو ضايقنا ال slide هذا ال example التاني بناخده المرة الجاية بالعمد عشان نرجع للموضوع كمان مرة نوضحكوا يا عزيزي يعطيكوا الصحة و رحة و برك الله فيكم", "tokens": [5172, 28814, 8848, 1863, 6225, 3555, 9640, 3660, 18871, 8310, 295, 582, 1532, 314, 1804, 624, 6, 46811, 10943, 9673, 25720, 25724, 995, 10632, 44945, 47283, 3215, 2423, 1365, 13672, 1829, 4032, 23557, 11296, 6225, 8592, 7649, 16247, 2304, 13063, 33427, 11242, 5016, 31439, 48812, 47302, 4587, 8315, 2423, 4137, 23758, 2423, 1365, 16712, 7649, 1829, 44945, 47283, 3215, 3224, 9673, 25720, 25724, 995, 10632, 20666, 25957, 3215, 6225, 8592, 7649, 8717, 47341, 3615, 5296, 19528, 2407, 11242, 45367, 9122, 2304, 7649, 3714, 25720, 8717, 2407, 11242, 5016, 4117, 14407, 35186, 6225, 11622, 1829, 11622, 1829, 37495, 9566, 1829, 4117, 14407, 31767, 5016, 3660, 4032, 12602, 5016, 3660, 4032, 4724, 31747, 21984, 8978, 24793], "avg_logprob": -0.2283967393895854, "compression_ratio": 1.759493670886076, "no_speech_prob": 0.0, "words": [{"start": 3689.58, "end": 3690.16, "word": "فإذن", "probability": 0.75457763671875}, {"start": 3690.16, "end": 3690.82, "word": " عبارة", "probability": 0.9873046875}, {"start": 3690.82, "end": 3691.08, "word": " عن", "probability": 0.99609375}, {"start": 3691.08, "end": 3691.56, "word": " sequence", "probability": 0.78564453125}, {"start": 3691.56, "end": 3692.58, "word": " of", "probability": 0.94091796875}, {"start": 3692.58, "end": 3693.18, "word": " primes", "probability": 0.7410888671875}, {"start": 3693.18, "end": 3694.56, "word": " T", "probability": 0.3779296875}, {"start": 3694.56, "end": 3695.22, "word": " plus", "probability": 0.1263427734375}, {"start": 3695.22, "end": 3696.06, "word": " U'", "probability": 0.98486328125}, {"start": 3698.36, "end": 3699.32, "word": " تمام", "probability": 0.6937255859375}, {"start": 3699.32, "end": 3701.4, "word": " المرة", "probability": 0.93017578125}, {"start": 3701.4, "end": 3701.78, "word": " الجاية", "probability": 0.8992513020833334}, {"start": 3701.78, "end": 3702.18, "word": " بناخد", "probability": 0.785400390625}, {"start": 3702.18, "end": 3702.26, "word": " ال", "probability": 0.77197265625}, {"start": 3702.26, "end": 3702.56, "word": " example", "probability": 0.85205078125}, {"start": 3702.56, "end": 3702.72, "word": " اللي", "probability": 0.8935546875}, {"start": 3702.72, "end": 3703.0, "word": " وراها", "probability": 0.96826171875}, {"start": 3703.0, "end": 3703.2, "word": " عشان", "probability": 0.9617513020833334}, {"start": 3703.2, "end": 3703.48, "word": " الأمور", "probability": 0.9314778645833334}, {"start": 3703.48, "end": 3703.84, "word": " توضح", "probability": 0.935546875}, {"start": 3703.84, "end": 3704.16, "word": " هو", "probability": 0.72607421875}, {"start": 3704.16, "end": 3704.44, "word": " ضايقنا", "probability": 0.8568115234375}, {"start": 3704.44, "end": 3704.56, "word": " ال", "probability": 0.6318359375}, {"start": 3704.56, "end": 3704.76, "word": " slide", "probability": 0.97998046875}, {"start": 3704.76, "end": 3704.96, "word": " هذا", "probability": 0.461181640625}, {"start": 3704.96, "end": 3705.04, "word": " ال", "probability": 0.92578125}, {"start": 3705.04, "end": 3705.3, "word": " example", "probability": 0.90478515625}, {"start": 3705.3, "end": 3705.82, "word": " التاني", "probability": 0.9453125}, {"start": 3705.82, "end": 3706.9, "word": " بناخده", "probability": 0.9368896484375}, {"start": 3706.9, "end": 3707.12, "word": " المرة", "probability": 0.974365234375}, {"start": 3707.12, "end": 3707.54, "word": " الجاية", "probability": 0.97900390625}, {"start": 3707.54, "end": 3708.1, "word": " بالعمد", "probability": 0.7081705729166666}, {"start": 3708.1, "end": 3708.48, "word": " عشان", "probability": 0.7742513020833334}, {"start": 3708.48, "end": 3708.88, "word": " نرجع", "probability": 0.970703125}, {"start": 3708.88, "end": 3709.3, "word": " للموضوع", "probability": 0.9158203125}, {"start": 3709.3, "end": 3709.54, "word": " كمان", "probability": 0.8870442708333334}, {"start": 3709.54, "end": 3709.76, "word": " مرة", "probability": 0.9794921875}, {"start": 3709.76, "end": 3710.62, "word": " نوضحكوا", "probability": 0.72216796875}, {"start": 3710.62, "end": 3710.76, "word": " يا", "probability": 0.53369140625}, {"start": 3710.76, "end": 3710.92, "word": " عزيزي", "probability": 0.865185546875}, {"start": 3710.92, "end": 3711.66, "word": " يعطيكوا", "probability": 0.8916015625}, {"start": 3711.66, "end": 3711.86, "word": " الصحة", "probability": 0.5634765625}, {"start": 3711.86, "end": 3711.96, "word": " و", "probability": 0.57080078125}, {"start": 3711.96, "end": 3712.0, "word": " رحة", "probability": 0.4160563151041667}, {"start": 3712.0, "end": 3712.12, "word": " و", "probability": 0.9033203125}, {"start": 3712.12, "end": 3712.24, "word": " برك", "probability": 0.829345703125}, {"start": 3712.24, "end": 3712.38, "word": " الله", "probability": 0.373046875}, {"start": 3712.38, "end": 3712.7, "word": " فيكم", "probability": 0.908203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3713.56725, "duration_after_vad": 3574.802499999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6e761f033d9c6c48c81984112b8231c77a802e6b
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/COT_ZuFXjkk_raw.srt
@@ -0,0 +1,3284 @@
+1
+00:00:21,110 --> 00:00:23,430
+بسم الله الرحمن الرحيم الصلاة و السلام على أشرف
+
+2
+00:00:23,430 --> 00:00:25,930
+الأنبياء والمسلمين سيدنا محمد وعلى أهلي وصحيح
+
+3
+00:00:25,930 --> 00:00:31,250
+أجمعين اليوم بنتكمل في ال cryptology أو علم
+
+4
+00:00:31,250 --> 00:00:34,130
+التشفير علم التشفير واحدة من ال applications
+
+5
+00:00:34,130 --> 00:00:39,130
+المهمة لل number theory ليش؟ لأن هنستخدم فيها
+
+6
+00:00:39,130 --> 00:00:43,780
+معلومات من اللي أخدناها في number theoryو بتعتمد
+
+7
+00:00:43,780 --> 00:00:46,960
+أصلا على أرقام لإن احنا في الآخر هنشفر ال message
+
+8
+00:00:46,960 --> 00:00:50,320
+اللي بدنا نبعتها لأرقام مجموعة أرقام مجموعة
+
+9
+00:00:50,320 --> 00:00:53,880
+الأرقام هذه هنعمل عليها شوية process معينة شوية
+
+10
+00:00:53,880 --> 00:00:57,960
+معالجة بحيث ان احنا نغير الأرقام الأرقام هذه إذا
+
+11
+00:00:57,960 --> 00:01:00,900
+اتغيرت اللي هيشوفها في الطريق مش هيعرف الشي بالظبط
+
+12
+00:01:00,900 --> 00:01:04,380
+مش هيعرف الشي الأرقام هذه الأصل أنه أنا بستجبل
+
+13
+00:01:04,380 --> 00:01:07,940
+مجموعة الأرقام أكون عارف ال code اللي اتشفرت فيه
+
+14
+00:01:07,940 --> 00:01:13,400
+عشان أعرف أعملهاdecryption اعادة التشفير او فك
+
+15
+00:01:13,400 --> 00:01:17,560
+التشفير فاليوم هنتكلم عن الموضوع هذا في ال
+
+16
+00:01:17,560 --> 00:01:21,640
+cryptology او ال cryptography ال cryptography اللي
+
+17
+00:01:21,640 --> 00:01:24,280
+هي ال methods اللي بتستخدم اعمل فيها encryption
+
+18
+00:01:24,280 --> 00:01:30,200
+نعمل فيها encryption او decryptionهدولة إيش الطرق
+
+19
+00:01:30,200 --> 00:01:33,500
+اللى بنستخدمها في ال encryption و ال decryption
+
+20
+00:01:33,500 --> 00:01:38,560
+للمسجد بحيث ان هي تصبح coded message هدى بنسميها
+
+21
+00:01:38,560 --> 00:01:43,200
+ال cryptography او ال cryptography اللى هو علم
+
+22
+00:01:43,200 --> 00:01:47,320
+التشفير أو علم عملي الاختيار الطرق أو علم الطرق
+
+23
+00:01:47,320 --> 00:01:52,830
+اللى تستخدم في التشفيرالتشفير طيب في ال crypto
+
+24
+00:01:52,830 --> 00:01:58,590
+analysis هذا اللي هو علم كسر التشفير هذا بيستخدمه
+
+25
+00:01:58,590 --> 00:02:01,390
+عادة الناس اللي بيشتغلوا ك hackers بيحاولوا
+
+26
+00:02:01,390 --> 00:02:04,350
+يشتغلوا برضه يلهم علمهم و كيف احنا نفك التشفير و
+
+27
+00:02:04,350 --> 00:02:08,070
+ال message لما تجينا مشفرة كيف احاول ا stamp منها
+
+28
+00:02:08,070 --> 00:02:12,630
+شوية ال numbers المهمة في عملية تشفيرها فهذا علم و
+
+29
+00:02:12,630 --> 00:02:16,630
+هذا علم كل واحد منهم علمو فيه له ناس اللي بيشتغلوا
+
+30
+00:02:16,630 --> 00:02:20,530
+فيه، طيب هنتكلم شوية عن المضوح هذا و بناخد مثال
+
+31
+00:02:20,530 --> 00:02:26,570
+بسيط اللي هو caesars cyber او اللي هو شفرة القيصر
+
+32
+00:02:27,350 --> 00:02:30,670
+شفرة القيصر كان لما بيروح على الحروب او بيبعت لل
+
+33
+00:02:30,670 --> 00:02:34,670
+.. للقوات تبعونه او للحكام .. للولايات اللي حوالي
+
+34
+00:02:34,670 --> 00:02:37,430
+ال .. ال .. ال .. كان يبعتله مياها مشفرة يبعت ال
+
+35
+00:02:37,430 --> 00:02:40,130
+message اللي بده يبعتها يبعتها بطريقة مشفرة بحيث
+
+36
+00:02:40,130 --> 00:02:43,490
+انه لو وقعت مع الاعداء مايعرفوش بالظبط اش اللي بده
+
+37
+00:02:43,490 --> 00:02:46,290
+يبعته طبعا كانت ال .. ال .. ال cypher تبعه او
+
+38
+00:02:46,290 --> 00:02:50,150
+الشفرة تبعته كانت كتير modest يعني كتير متواضعة او
+
+39
+00:02:50,150 --> 00:02:53,370
+كتير بسيطة فكان كل اللي بيعمله انه بيشيبلنا كل
+
+40
+00:02:53,370 --> 00:02:58,520
+الحروف .. حروف اللغةالـ 26 بكتبهم و كل واحد بيعطيه
+
+41
+00:02:58,520 --> 00:03:04,120
+رقم ببدأ من ال A صفر B واحد اتنين تلاتة لعند ال Z
+
+42
+00:03:04,120 --> 00:03:10,160
+خمسة و عشرين و كل اللي بيعمله بكتب الرسالة بياخد
+
+43
+00:03:10,160 --> 00:03:14,570
+حرف حرف الرسالةالحرف الأول في الرسالة جدّاش
+
+44
+00:03:14,570 --> 00:03:19,090
+المطرود الرقم تبعه فهذا يمثل الرقم تبع الحرف الأول
+
+45
+00:03:19,090 --> 00:03:23,070
+فبرتقم و بيصير أرقام الأرقام هتمسك رقم رقم و بيجمع
+
+46
+00:03:23,070 --> 00:03:28,790
+عليه تلاتة و بيعمل modulo 26 modulo 26 فطبعا
+
+47
+00:03:28,790 --> 00:03:32,090
+الأرقام اتغيرت هيك الأرقام كلها اتغيرت و بيبعت
+
+48
+00:03:32,090 --> 00:03:36,150
+الرسالة بناء على الأرقام اللي اتغيرت فبرجع اللغة
+
+49
+00:03:36,150 --> 00:03:39,470
+تاني فبتطلع حروف مالهاش أي علاقة بال message
+
+50
+00:03:39,470 --> 00:03:43,810
+الأصليةبتكون هي نفس ال message ولكن اتشفتت صار لها
+
+51
+00:03:43,810 --> 00:03:48,710
+عملية shift shift بمقدار تلاتة shift بمقدار تلاتة
+
+52
+00:03:48,710 --> 00:03:51,030
+هذا اللي كانت ال encryption كان بيعمل encryption
+
+53
+00:03:51,030 --> 00:03:56,090
+بهذا الشكل تشفير بهذا الشكلأو فك التشفير بيعملوا
+
+54
+00:03:56,090 --> 00:04:00,170
+كيف؟ بيعملوا نفس الفكرة ولكن بالعكس هنا كنا نجمع
+
+55
+00:04:00,170 --> 00:04:04,210
+تلاتة، لأ هنضطر إيش نعمل؟ نقص تلاتة نقص تلاتة و
+
+56
+00:04:04,210 --> 00:04:08,950
+برضه نشتغل على موديولو 26 نشتغل على موديولو 26 طيب
+
+57
+00:04:08,950 --> 00:04:15,030
+in general ال shift cipher هذا N plus K بغض النظر
+
+58
+00:04:15,030 --> 00:04:18,050
+K تلاتة زي ما هو مستعمل أو خمسة أو عشرة نقدر
+
+59
+00:04:18,050 --> 00:04:21,630
+نستعملها in general K و نكتب أي رقم بدنا يه
+
+60
+00:04:21,630 --> 00:04:28,060
+موديولو Mموديولو عامو نشتغل عليه طيب اتطور الموضوع
+
+61
+00:04:28,060 --> 00:04:31,900
+شوية فصار في transformation ان انا ممكن كمان ال N
+
+62
+00:04:31,900 --> 00:04:36,480
+أضربها في multiplier ان عجدها شوية عجدها شوية عملت
+
+63
+00:04:36,480 --> 00:04:40,060
+التشفير انه ليش اشتغل على N plus تلاتة ما اخليها
+
+64
+00:04:40,060 --> 00:04:47,090
+سبعة N plus تلاتةmodulo 26 فهنا صارت more secure
+
+65
+00:04:47,090 --> 00:04:51,230
+ولكن برضه بالنسبة للعلم اللي احنا حاليا موجود كل
+
+66
+00:04:51,230 --> 00:04:54,030
+الطريقة على بعضها insecure كل الطريقة على بعضها
+
+67
+00:04:54,030 --> 00:04:57,870
+غير آمنة سهلت الكشف الطريقة دي كلها على بعضها هيك
+
+68
+00:04:57,870 --> 00:05:00,970
+سهلت الكشف ولكن زي ما اقول ان احنا كنا مستعمل من
+
+69
+00:05:00,970 --> 00:05:06,410
+قرون بعيدة جدا من قرون بعيدة جدا من أيام القيصر من
+
+70
+00:05:06,410 --> 00:05:12,330
+أيام القيصر او Caesarكويس ناخد مثال for example لو
+
+71
+00:05:12,330 --> 00:05:16,070
+أخدنا جملة و بدنا نشفرها فكل اللي بنعمله ان احنا
+
+72
+00:05:16,070 --> 00:05:20,230
+بنكتب مجموعة الأرقام مجموعة الحروف بتاعتنا كل حرف
+
+73
+00:05:20,230 --> 00:05:27,090
+ما يقابله الرقم اللي مقابلله كل حرف الرقم و الشفرة
+
+74
+00:05:27,090 --> 00:05:32,610
+بتاعتنا هنا واضح ان احنا .. احنا مش عارفين ان
+
+75
+00:05:32,610 --> 00:05:33,390
+حقيقة ..
+
+76
+00:05:37,530 --> 00:05:45,110
+عشان ايش؟ عشان ايش؟
+
+77
+00:05:45,110 --> 00:05:52,070
+اه والله برضه ممكن برضه يعني وجهي لسببك صحيح ممكن
+
+78
+00:05:52,070 --> 00:05:58,130
+احتجت الكهربا خلاص نخليها is not easy
+
+79
+00:06:02,120 --> 00:06:04,600
+لأ بس هذه الكلمة لسه هو من الكهربا مش عارفها هي
+
+80
+00:06:04,600 --> 00:06:12,080
+للي بعده okay
+
+81
+00:06:12,080 --> 00:06:19,850
+فلاحظوا أن احنا هنا .. بس تظهر الشاشةكل اللي
+
+82
+00:06:19,850 --> 00:06:23,570
+هنعمله كل حرف هنرتب كل الحروف حافظين الحروف؟
+
+83
+00:06:23,570 --> 00:06:27,230
+فتكتبوا
+
+84
+00:06:27,230 --> 00:06:31,850
+الحروف ترتيبا مرتبة و عند ال a صفر بواحد تكتبوا
+
+85
+00:06:31,850 --> 00:06:37,470
+برضه تحت مجموعة الأرقام بتاعتها كل ترتيبهم في ال
+
+86
+00:06:37,470 --> 00:06:42,330
+sequence تبعهم و بعدين ممكن نشتغل هنا على Caesar
+
+87
+00:06:43,990 --> 00:06:46,770
+Caesar اللي هو زي ما قلنا N plus تلاتة كل اللي
+
+88
+00:06:46,770 --> 00:06:51,650
+هنعمله كل حرف بنزود عليه تلاتة ف ال T مثلا بنزود
+
+89
+00:06:51,650 --> 00:06:56,330
+عليها تلاتة بتصير W فأول حرف بيصبح أن هو ال W في
+
+90
+00:06:56,330 --> 00:07:00,810
+الرسالة فعليا ال encoded message بتاعنا بتصير حرف
+
+91
+00:07:00,810 --> 00:07:08,350
+ال W ال H مثلا بنزود عليه كمان تلاتة بيصير K ال E
+
+92
+00:07:08,350 --> 00:07:13,470
+بنزود عليه تلاتة بيصير H وهكذابنكمل ال message
+
+93
+00:07:13,470 --> 00:07:18,130
+بتاعتنا بتطلع حاجة بهذا الشكل هذه بتنبعد ال
+
+94
+00:07:18,130 --> 00:07:20,570
+message هذه هي اللي بتنبعد طبعا ال message هذه
+
+95
+00:07:20,570 --> 00:07:25,110
+الكهربا مش هتعرفها فهتعديلنا منها فال message زي
+
+96
+00:07:25,110 --> 00:07:30,250
+هذه مش هتبين مش هتنعرف مش هتنعرف ليش لأنه مشفرة
+
+97
+00:07:30,250 --> 00:07:32,950
+الحروف انتوا مش هتعرفوا منها اشي مش هتعرفوا منها
+
+98
+00:07:32,950 --> 00:07:35,990
+حاجة ومع ذلك ومع ذلك زي ما قلتلكوا انا أجابكوا ان
+
+99
+00:07:35,990 --> 00:07:39,490
+هي insecureunsecure ليش؟ لأنه أبسط شغلة، مابتيش
+
+100
+00:07:39,490 --> 00:07:44,710
+تتطلع على الرقم أو على ال letter المتكرر كتير، هدف
+
+101
+00:07:44,710 --> 00:07:46,750
+في الغالب .. في الغالب يكون واحدة من حروف ال
+
+102
+00:07:46,750 --> 00:07:51,870
+vowels، غالبا حرف من حروف اللي لينة، صحيح؟ لإن هي
+
+103
+00:07:51,870 --> 00:07:55,730
+الأكثر استخداما في اللغة، هي الأكتر و أكثرهم حرف
+
+104
+00:07:55,730 --> 00:08:00,230
+ال Eيعني بتيجي تتطلعوا وين الحرف الأكتر استخدامه
+
+105
+00:08:00,230 --> 00:08:04,570
+مثلا هو حرف ال H ال H ال H ال H ال H ال H ال H ال
+
+106
+00:08:04,570 --> 00:08:05,870
+H ال H ال H ال H ال H ال H ال H ال H ال H ال H ال
+
+107
+00:08:05,870 --> 00:08:05,870
+H ال H ال H ال H ال H ال H ال H ال H ال H ال H ال
+
+108
+00:08:05,870 --> 00:08:05,990
+H ال H ال H ال H ال H ال H ال H ال H ال H ال H ال
+
+109
+00:08:05,990 --> 00:08:06,050
+H ال H ال H ال H ال H ال H ال H ال H ال H ال H ال
+
+110
+00:08:06,050 --> 00:08:06,750
+H ال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال
+
+111
+00:08:06,750 --> 00:08:06,750
+Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال
+
+112
+00:08:06,750 --> 00:08:09,870
+Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال
+
+113
+00:08:09,870 --> 00:08:15,210
+Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال Hال
+
+114
+00:08:15,210 --> 00:08:20,810
+Hال H
+
+115
+00:08:28,270 --> 00:08:32,470
+Okay بجرب ال relation هذه اللي انا أستنتجتها على
+
+116
+00:08:32,470 --> 00:08:35,470
+كل و بنشوف إيش بتطلع ال message و الله ال message
+
+117
+00:08:35,470 --> 00:08:38,490
+إلها معنى واضح خلاص أنا فكيتها مالهاش معنى واضح
+
+118
+00:08:38,490 --> 00:08:42,790
+ممكن مايكنش ال E تكون ال A أو ال I أو ال U المهم
+
+119
+00:08:42,790 --> 00:08:45,230
+واحدة من الحروف لإنه هذا اللي احنا متعودين أنه
+
+120
+00:08:45,230 --> 00:08:49,370
+أكثر استخداما في اللغة اللي هي ال vowels أو الحروف
+
+121
+00:08:49,370 --> 00:08:52,090
+العلة أو الحروف اللي هي اللينة الحروف اللينة
+
+122
+00:08:57,990 --> 00:09:00,590
+فبنستخدمها عشان هيك انها insecure حقيقة انها
+
+123
+00:09:00,590 --> 00:09:03,010
+insecure اقولكوا حتى لو انضربت في multiplier حتى
+
+124
+00:09:03,010 --> 00:09:06,170
+لو انضربت في multiplier بتظل برضه insecure هتظل
+
+125
+00:09:06,170 --> 00:09:13,190
+insecure طيب في ال cryptography عادة احنا بتشتغل
+
+126
+00:09:13,190 --> 00:09:16,510
+على two keys مهمين فيه ال public و فيه ال private
+
+127
+00:09:16,510 --> 00:09:20,730
+و عشان مابضحكوا ايها اكترال public احنا بنستخدمه
+
+128
+00:09:20,730 --> 00:09:24,170
+عشان نعمل communication ل ال .. ال .. securely
+
+129
+00:09:24,170 --> 00:09:29,210
+communicate the other أو the key strings بتستخدموه
+
+130
+00:09:29,210 --> 00:09:33,310
+في التواصل زي ال email تبعكم ال email اللي فيه
+
+131
+00:09:33,310 --> 00:09:36,810
+عندكم ال username او ال email address هذا public
+
+132
+00:09:37,880 --> 00:09:41,120
+هذا الكل بعرفه عشان ابعتلكم message لازم يكون
+
+133
+00:09:41,120 --> 00:09:44,360
+عارفه عشان ابعتلكم فده public طيب private لما انا
+
+134
+00:09:44,360 --> 00:09:49,180
+بدي ادخل على ال email هذا private فى password ال
+
+135
+00:09:49,180 --> 00:09:52,300
+password المفروض ان هذا private هذا إلكوا خاص
+
+136
+00:09:52,300 --> 00:09:55,220
+فيكوا انتوا او خاص بصاحب ال email address فهذا
+
+137
+00:09:55,220 --> 00:09:59,800
+private فإذا فينا public وفينا privateprivate في
+
+138
+00:09:59,800 --> 00:10:02,540
+عندنا public و في عندنا private طيب في عندنا برضه
+
+139
+00:10:02,540 --> 00:10:06,720
+نفس الكلام لل websites ال websites عموما عشان اقرأ
+
+140
+00:10:06,720 --> 00:10:10,230
+اي معلومة موجودة على ال websitesاما اني بدى اكتب
+
+141
+00:10:10,230 --> 00:10:13,150
+معلومة او بدى اقرأ معلومة فعشان اكتب معلومة
+
+142
+00:10:13,150 --> 00:10:15,590
+المفروض ان انا عندي ال user name بتاع ال path بتاع
+
+143
+00:10:15,590 --> 00:10:20,930
+ال website او ال web page عشان ادخل و ادخل اكتب
+
+144
+00:10:20,930 --> 00:10:25,390
+اعمل insertion لمعلومات او لمقالة او لصور او او او
+
+145
+00:10:25,390 --> 00:10:29,670
+ف .. و بعدين بنعمل publishing ال publishing طلعت
+
+146
+00:10:29,670 --> 00:10:34,830
+طبعا عشان اقرأهامحتاج ايه؟ محتاج ال browser ال
+
+147
+00:10:34,830 --> 00:10:37,370
+browser كله انا محتاج ال browser فممكن هذا بتكون
+
+148
+00:10:37,370 --> 00:10:41,870
+public عشان اقراها هي public عشان انا افتح مع
+
+149
+00:10:41,870 --> 00:10:44,870
+السفحة و اقراها هتكون public لو انا ماعندش ال
+
+150
+00:10:44,870 --> 00:10:48,030
+browser مش هعرف اقراها ففي الحالة دي بكون انا
+
+151
+00:10:48,030 --> 00:10:53,650
+محتاج ال public keyأه جبنا ال explorer مثلا برضه
+
+152
+00:10:53,650 --> 00:10:56,950
+هتلاقي فيه مرات صور أو مرات الفيديوهات هيقولكوا لأ
+
+153
+00:10:56,950 --> 00:11:00,550
+محتاجين مش عارف إيش ال .. ال latest version okay
+
+154
+00:11:00,550 --> 00:11:04,310
+معناه ذلك إنه هذا مش جادر ك decoder مش جادر يفتح
+
+155
+00:11:04,310 --> 00:11:08,170
+بضطر أدور على إشي .. بس في النهاية ده كله إيش
+
+156
+00:11:08,170 --> 00:11:11,610
+publicهذا كله احنا متكلم عن حاجة public ليش؟ لأنه
+
+157
+00:11:11,610 --> 00:11:13,910
+بنزل على السوق بنزل على .. بفتح على ال net على
+
+158
+00:11:13,910 --> 00:11:16,670
+موقع تاني بدور على ال browser و بجيب أخر version و
+
+159
+00:11:16,670 --> 00:11:21,390
+بنزله يعني هذه public مافيش فيها private ال
+
+160
+00:11:21,390 --> 00:11:24,150
+private هتكون عندي اللي بده يكتب لما بدي أنا أدخل
+
+161
+00:11:24,150 --> 00:11:28,230
+لأ بدي أغير عليها الصفحة لأ هذه private public
+
+162
+00:11:28,230 --> 00:11:31,450
+issue و private issue ال email نفس الجثة public
+
+163
+00:11:31,450 --> 00:11:35,320
+أنه والله أنا ممكن أبعت للكلبس عشان ال message
+
+164
+00:11:35,320 --> 00:11:38,920
+اللي أنا بعطتها تشوفوها individual كل واحدة بتدخل
+
+165
+00:11:38,920 --> 00:11:42,540
+على حسابها مش كلكوا هتدخلوا على حساب واحدة كل
+
+166
+00:11:42,540 --> 00:11:46,260
+واحدة بتدخل على حسابها private private فهذا الفرق
+
+167
+00:11:46,260 --> 00:11:51,130
+من ال publicاللي هو can be made public و ال
+
+168
+00:11:51,130 --> 00:11:55,270
+private اللي هو ده can be kept secret from
+
+169
+00:11:55,270 --> 00:11:58,110
+everyone هذا المفروض يقولوا لأ والله ال password
+
+170
+00:11:58,110 --> 00:12:01,410
+تبع هذا خاص فيا ماحدش هيمسك ال password يعمل email
+
+171
+00:12:01,410 --> 00:12:03,550
+و يغلب حاله و بعدين ال password تبعه يقعد يعطيه
+
+172
+00:12:03,550 --> 00:12:06,570
+يوزه عن الناس ماحدش بيعمل هيف فهذه private هذه
+
+173
+00:12:06,570 --> 00:12:10,790
+خاصة .. خاصة فيكم .. خاصة فيكم .. فيكم انتوا كويس
+
+174
+00:12:10,790 --> 00:12:14,230
+ال .. ال .. ال ..for examples يعني احنا اتكلمنا عن
+
+175
+00:12:14,230 --> 00:12:17,050
+examples يعني انت الاول ممكن يعمل encryption لل
+
+176
+00:12:17,050 --> 00:12:21,230
+message و ال private يفتحها فانا ممكن برضه فعلا اي
+
+177
+00:12:21,230 --> 00:12:24,670
+واحد يعمل encryption نعمل encryption ال encryption
+
+178
+00:12:24,670 --> 00:12:28,410
+تكون anyone بقدر يعملها زي لما بدي اعملكوا email
+
+179
+00:12:28,410 --> 00:12:32,110
+بدي ابعتلكوا email طبعا انتوا email كوا اي واحد
+
+180
+00:12:32,110 --> 00:12:36,610
+بقدر يبعتلكوا صح ف anyone بقدر يعمل encryption
+
+181
+00:12:38,300 --> 00:12:41,380
+encryption للمسجل اللي بصمتكم بس مين اللي بيقدر
+
+182
+00:12:41,380 --> 00:12:45,900
+يعمل decryption يفتحها فقط انتوا private فقط انتوا
+
+183
+00:12:45,900 --> 00:12:50,980
+private في المقابل ال website مثلا نموذج لها ان
+
+184
+00:12:50,980 --> 00:12:54,300
+انا اعمل encryption باستخدام ال private key
+
+185
+00:12:56,020 --> 00:12:58,820
+encryption للمعلومة باستخدام ال private مش اي حد
+
+186
+00:12:58,820 --> 00:13:01,500
+اللي بيعمل .. اللي بدخل على ال website و بينزل
+
+187
+00:13:01,500 --> 00:13:05,400
+معلومات فقط صاحب ال website طيب و في المقابل
+
+188
+00:13:05,400 --> 00:13:10,300
+anyone بيقدر يعمل decryption اي واحد بيقدر يشوف اش
+
+189
+00:13:10,300 --> 00:13:12,980
+اللي مكتوب اي حد بيقدر يشوف فهي فوق two examples
+
+190
+00:13:12,980 --> 00:13:19,610
+لهاللموضوع طيب من ال .. يمكن نقول ال systems او ال
+
+191
+00:13:19,610 --> 00:13:23,490
+.. ال .. ال crypto system المشهور جدا لل
+
+192
+00:13:23,490 --> 00:13:30,750
+encryption اللي هو ال RSA ال RSA system اللي هو
+
+193
+00:13:30,750 --> 00:13:38,610
+rivest او rivest شمير و أدلمان او ال RSA متعرف
+
+194
+00:13:38,610 --> 00:13:42,380
+عليه RSAهدول برضه خلاص اتفقنا هيكون في عندي two
+
+195
+00:13:42,380 --> 00:13:47,340
+keys ال key الأولى ال private key و ال public key
+
+196
+00:13:47,340 --> 00:13:52,160
+ال private keyبتذكرى لما اتكلمنا في ال numbers ..
+
+197
+00:13:52,160 --> 00:13:54,340
+في ال primes عفوا .. في ال primes و قولنا ان ال
+
+198
+00:13:54,340 --> 00:13:59,240
+primes من اهم الارقام اللى هنحتاجها لاحقا و فعلا
+
+199
+00:13:59,240 --> 00:14:02,740
+هنحتاجها في ال encryption هنحتاجها ليش؟ برضه لما
+
+200
+00:14:02,740 --> 00:14:07,160
+اتكلمنا في ال pseudo prime لو فاكرين .. pseudo
+
+201
+00:14:07,160 --> 00:14:11,360
+prime قولنا انه جداش بقدر استخدم عشان اعمل
+
+202
+00:14:11,360 --> 00:14:16,300
+generation ل random sequence primesبيكون في الحالة
+
+203
+00:14:16,300 --> 00:14:21,100
+هذه التكرار بعيد جدا او ال period نفسها كتير بعيدة
+
+204
+00:14:21,100 --> 00:14:25,200
+او كتير ان انت بحث كبير عبل ما يتكرر الرقم هيكون
+
+205
+00:14:25,200 --> 00:14:30,340
+بده عدد كبير جدا من الأرقام بين كل رقم و تكراره لو
+
+206
+00:14:30,340 --> 00:14:33,600
+فمذاكرين قولنا الكلام هذا و قولنا يمكن الرقم
+
+207
+00:14:33,600 --> 00:14:36,240
+الأكثر استخداما لو فاكرين ليه اتنين to the power
+
+208
+00:14:36,240 --> 00:14:40,290
+واحد و تلاتين minus واحدقلتلكوا أكثر استخداما لأن
+
+209
+00:14:40,290 --> 00:14:44,650
+بعد اتنين to the power واحد و تلاتين بتكرر كمان
+
+210
+00:14:44,650 --> 00:14:47,970
+مرة فانتوا بتتكلموا عن رقم كتير كبير جدا فهذا
+
+211
+00:14:47,970 --> 00:14:52,410
+بيكون more secure في التعامل نفس الكلام ان لما بدي
+
+212
+00:14:52,410 --> 00:14:55,010
+اشتغل على ال private على ال private في طريقة ال
+
+213
+00:14:55,010 --> 00:15:02,290
+RSA بيكون بدنا two primes و random prime numbers
+
+214
+00:15:02,290 --> 00:15:09,040
+محتاجين رقمين كبار جدا نسبيا و primesالـprimes
+
+215
+00:15:09,040 --> 00:15:12,280
+دائما الـprimes بيعطيكوا more secure ليش؟ لأنه لا
+
+216
+00:15:12,280 --> 00:15:17,600
+يختصر تقدروش تختصروه فمعنى ذلك لو كان بده يتكرر
+
+217
+00:15:17,600 --> 00:15:22,180
+بعد الف iteration أو بعد الف number مافيش إمكانية
+
+218
+00:15:22,180 --> 00:15:25,440
+تختصروه بعد خمسمية لو بيكسب مع اتنين لو بيكسب مع
+
+219
+00:15:25,440 --> 00:15:30,080
+اتنين هتلاقوه في الألف هيظهر مرتين إذا كان بيكسب
+
+220
+00:15:30,080 --> 00:15:33,380
+مع اتنين إذا بيكسب مع تلاتة هتلاقوه في خلال الألف
+
+221
+00:15:33,380 --> 00:15:38,280
+هيكسب مع تلاتةأما إذا كان prime لو قيمته جريبة من
+
+222
+00:15:38,280 --> 00:15:43,220
+الألف هخلص بعد قيمة ال prime أو قيمة كبيرة جدا عبل
+
+223
+00:15:43,220 --> 00:15:47,000
+ما يتكرر عبل ما يتكرر فبيميروا أكتر لاستخدام ال
+
+224
+00:15:47,000 --> 00:15:51,180
+prime بعدين في ال exponent E هنستخدمه برضه هو اللي
+
+225
+00:15:51,180 --> 00:15:56,920
+وجد في معادل انكريبشن باستخدام ال RSA relative ال
+
+226
+00:15:56,920 --> 00:16:01,580
+prime لل P minus one P minus one في Q minus one
+
+227
+00:16:01,580 --> 00:16:10,050
+فإذافي E صار انا كل اللي محتاجه P Q و E و لاحظوا
+
+228
+00:16:10,050 --> 00:16:13,190
+هذا prime وهذا prime و هذا لازم تكون relatively
+
+229
+00:16:13,190 --> 00:16:23,610
+prime مع مين؟ مع P-1 في Q-1 كلهم prime او co-prime
+
+230
+00:16:23,610 --> 00:16:27,610
+يعني او co-prime فهذا هتفيدنا جدا في عملية ال
+
+231
+00:16:27,610 --> 00:16:32,800
+security طيب ال public keyأشي اللي بدنا نستعمله
+
+232
+00:16:32,800 --> 00:16:37,940
+فعلا هالوقت في الأرقام ال N هذي هتكون عبارة عن ال
+
+233
+00:16:37,940 --> 00:16:42,400
+P في ال Q ن عبارة عن P في Q و هذي هستخدمها ك
+
+234
+00:16:42,400 --> 00:16:46,100
+modulo او ك modulus في ال system تبعنا هي هذي ال
+
+235
+00:16:46,100 --> 00:16:49,440
+modulus تبعنا ال N هتكون هي ال modulus و ماتكونش
+
+236
+00:16:49,440 --> 00:16:52,540
+هي ال P نفسها أو ال Q نفسها لأن إذا ال P نفسها أو
+
+237
+00:16:52,540 --> 00:16:54,740
+ال Q نفسها انتوا كشفتوا ال P و ال Q في الحالة هذي
+
+238
+00:16:54,740 --> 00:16:57,560
+إذا كان واحدة من اتنين اتنين لأ مانفعش لازم تكون
+
+239
+00:16:57,560 --> 00:17:02,050
+ضرب الأتنينمضروب لاتنين بحيث ان انت تتطلع عليها
+
+240
+00:17:02,050 --> 00:17:09,230
+تشعر ان هي رقم not prime او composite number بس
+
+241
+00:17:09,230 --> 00:17:14,870
+فعليا مش هتعرف تطلع منه ال P و Q رقم ممكن يكسب على
+
+242
+00:17:14,870 --> 00:17:18,110
+أرقام تانية غير ال P و Q كمان يكون بيكسب على أرقام
+
+243
+00:17:18,110 --> 00:17:21,730
+أخرى بس في الآخر ممكن تعرف ال P و Q منه
+
+244
+00:17:24,510 --> 00:17:28,910
+لما بجي هلوجت اعمل هنا طبعا خلصنا encryption عملية
+
+245
+00:17:28,910 --> 00:17:32,530
+ال encryption باستخدام ال private key بصير بدنا
+
+246
+00:17:32,530 --> 00:17:34,970
+نعمل decryption باستخدام
+
+247
+00:17:37,170 --> 00:17:40,910
+public key طيب استخدم ال public key خلاص اتفجنا
+
+248
+00:17:40,910 --> 00:17:44,050
+هاي ال modulus نفسه هو هو اللي هيستخدم في ال
+
+249
+00:17:44,050 --> 00:17:47,010
+encryption هنستخدمه برضه في ال decryption بس ال
+
+250
+00:17:47,010 --> 00:17:52,270
+exponent محتاجين تجيبله ال inverse تبعه مرة أخرى
+
+251
+00:17:52,270 --> 00:17:55,150
+أتخدنا ال inverse كيف نجيبها محتاجين ال inverse و
+
+252
+00:17:55,150 --> 00:17:59,810
+ال inverse مهم جدا فمحتاج أجيب D و هذا D هو ال
+
+253
+00:17:59,810 --> 00:18:00,870
+inverse of E
+
+254
+00:18:03,540 --> 00:18:07,500
+حاجة عملتها زى توى لما كنا بنشتغل على ال .. ال
+
+255
+00:18:07,500 --> 00:18:12,180
+scissors ال cypher كنا بنقول plus تلاتة فإذا العكس
+
+256
+00:18:12,180 --> 00:18:16,280
+تبعها سالب تلاتة لما بدى اعمل decryption كنا نعمل
+
+257
+00:18:16,280 --> 00:18:18,700
+بالعكس فهنا نفس الكلام بدي أجيب العكس بس أنا هنا
+
+258
+00:18:18,700 --> 00:18:22,120
+شغال على modulo على مجموعة braille فال inverse
+
+259
+00:18:22,120 --> 00:18:28,540
+تبعنا لل E هتكون D وهدى عبارة عن E modulo P minus
+
+260
+00:18:28,540 --> 00:18:33,850
+واحد في Q minus واحد بيعطينادى وبنستخدمش ال E
+
+261
+00:18:33,850 --> 00:18:40,970
+نفسها نستخدمش ال E نفسها لاتستخدم ال E نفسها كويس
+
+262
+00:18:40,970 --> 00:18:44,470
+فعملية ال encryption هالوجت بدأت محددنا مجموعة ال
+
+263
+00:18:44,470 --> 00:18:46,450
+parameters اللى انا محتاجها مجموعة الأرقام اللى
+
+264
+00:18:46,450 --> 00:18:50,170
+انا محتاجها عشان اعمل encryption هتكون ال
+
+265
+00:18:50,170 --> 00:18:54,430
+encrypted signal هتساوي ال message الأصلية to the
+
+266
+00:18:54,430 --> 00:19:00,710
+power E exponentmode N و ال N هى اللى هى ايه قولنا
+
+267
+00:19:00,710 --> 00:19:05,490
+P فى Q P فى Q كويسة هذى بتكون هيك ال message هى
+
+268
+00:19:05,490 --> 00:19:09,830
+اللى بتنبعها او ال encrypted message ال encoded
+
+269
+00:19:09,830 --> 00:19:12,390
+message بعتناها و خلاص اللى هشوفها مش هفهم منها
+
+270
+00:19:12,390 --> 00:19:15,750
+حاجة هذى اللى هشوفها مش هفهم منها اى شىء طيب
+
+271
+00:19:15,750 --> 00:19:19,910
+وصلتنى بدي اعكسها بدي اجيبها طبعا عشان اجيبها لازم
+
+272
+00:19:19,910 --> 00:19:26,470
+انا الوحيد اللى هكون عارف ايش ال E و لاحظوا مش ال
+
+273
+00:19:26,470 --> 00:19:34,130
+Nمش ال N بدي أكون عارف ال P و ال Q يعني حتى لو
+
+274
+00:19:34,130 --> 00:19:38,930
+انكسفت هنا هو اللي عرفه ال N ماعرفش ال P و ال Q طب
+
+275
+00:19:38,930 --> 00:19:42,270
+أنا عشان أفتحها ال message تبعتي بدي أكون عارف مين
+
+276
+00:19:42,270 --> 00:19:48,150
+P و Q لإني بدي أجيب inverse ال E طب inverse ال E
+
+277
+00:19:49,260 --> 00:19:54,460
+بدنا نعمل module P-1Q-1 فانا لازم اكون اعرف ال P و
+
+278
+00:19:54,460 --> 00:19:58,560
+ال Q ال Primes العناصر المهمة جدا هذه ال Primes
+
+279
+00:19:58,560 --> 00:20:03,280
+اللي صعب تتكرر اللي بيكون صعب شوية تتكرر كويسة
+
+280
+00:20:03,280 --> 00:20:08,040
+فإذا ال message تبعتي هتساوي C ال encrypted to the
+
+281
+00:20:08,040 --> 00:20:12,480
+power D اللي هو ال inverse ال D هذا ماحدش هيعرفها
+
+282
+00:20:12,480 --> 00:20:16,430
+لنالأن أنا العارف ال code اللي اتشفرت فيه ال code
+
+283
+00:20:16,430 --> 00:20:20,910
+اللي اتشفرت فينا عارف ال D خلاص نحصل على D mod N
+
+284
+00:20:20,910 --> 00:20:24,170
+okay هو عارف ال N فليكن عارفها من ال message اللي
+
+285
+00:20:24,170 --> 00:20:27,790
+قطعها شافها في الطريق و قطعها و مشكلة okay هيعرف
+
+286
+00:20:27,790 --> 00:20:32,630
+ال N و مشتغل على N بس ال D لأ هو مش عارف لا P ولا
+
+287
+00:20:32,630 --> 00:20:36,170
+Q لأنه مش موجودة في ال message هنا مش موجودة في ال
+
+288
+00:20:36,170 --> 00:20:41,850
+message كويس ناخد exampleلل Encryption و لل
+
+289
+00:20:41,850 --> 00:20:45,530
+Decryption نبدأ بال Encryption Encryption خلاص
+
+290
+00:20:45,530 --> 00:20:50,870
+احنا عارفين القانون تبعنا اللي هي C بتساوي M to
+
+291
+00:20:50,870 --> 00:20:57,390
+the power E mod او modulo M modulo N ايش الكلمة
+
+292
+00:20:57,390 --> 00:21:00,960
+اللي بدنا نبعتها؟ بدنا نبعت كلمة stop مثلاده نبعد
+
+293
+00:21:00,960 --> 00:21:05,420
+كلمة stop ف stop برضه بشوف جدش ترتيب ال S جدش
+
+294
+00:21:05,420 --> 00:21:11,060
+ترتيب ال T جدش ترتيب ال O ال P في ال sequence تبع
+
+295
+00:21:11,060 --> 00:21:17,000
+ال alphabet string فحنشوف الأولى هذه مثلا بدنا
+
+296
+00:21:17,000 --> 00:21:20,060
+نعرف جدش ترتيبها ترتيب ترتيب ترتيب هنكون عملنا
+
+297
+00:21:20,060 --> 00:21:23,300
+شفرة لها لحالها هنكون عملنا شفرة لحالها طيب
+
+298
+00:21:23,300 --> 00:21:29,360
+هتلاقوا ال S ترتيبها 18 ال T وراها على طول 19
+
+299
+00:21:30,900 --> 00:21:33,700
+ناخدهم اربعة اربعة ناخدهم يعني two letters two
+
+300
+00:21:33,700 --> 00:21:36,720
+letters two letters هدول مع بعض بعدين في two
+
+301
+00:21:36,720 --> 00:21:38,900
+letters ال O و ال B برضه الاتنين هدول ورا بعض
+
+302
+00:21:38,900 --> 00:21:42,840
+فواحدة خمستاش و واحدة اربعتاش هد هيك ال message
+
+303
+00:21:42,840 --> 00:21:46,120
+اللي انا بده ابعتها بس ماعملتلهاش اي encryption بس
+
+304
+00:21:46,120 --> 00:21:48,380
+ماعملناش اي encryption هد ال message بتاعتنا اللي
+
+305
+00:21:48,380 --> 00:21:52,780
+بدنا تتصل كويسة مبدأ ينقش كمان ميعطيني المعلومات
+
+306
+00:21:52,780 --> 00:21:56,140
+okay ميعطيني هى ال key ميعطيني ال Q prime prime
+
+307
+00:21:56,930 --> 00:22:02,250
+بينها بنقدر نطلع لإن مضروب الأثنين في بعض في ألفين
+
+308
+00:22:02,250 --> 00:22:05,130
+وخمسمية سبعة و تلاتين وميعطيني كمان ال exponent
+
+309
+00:22:05,130 --> 00:22:09,430
+اللي هو ال power طبعا ال exponential جزيط ال power
+
+310
+00:22:09,430 --> 00:22:14,570
+ال E تلات عشر برضه prime برضه ال prime فلحظوا
+
+311
+00:22:14,570 --> 00:22:17,050
+بقالكم .. خدوا بقالكم من الأرقام كلها primes فعليا
+
+312
+00:22:17,050 --> 00:22:20,110
+يعني ال given كلها ده كله primes عندكوا هاي prime
+
+313
+00:22:20,110 --> 00:22:24,190
+هاي اتنين هاي تلاتة okayخلّيني اعمل check check
+
+314
+00:22:24,190 --> 00:22:32,610
+مهم جدا ان ال E لازم تكون co-prime كمان مع P-1 و Q
+
+315
+00:22:32,610 --> 00:22:39,950
+-1 ليش؟ اللي حضر معانا المرة اللي فتت ال inverse
+
+316
+00:22:39,950 --> 00:22:44,810
+ليش؟
+
+317
+00:22:44,810 --> 00:22:50,930
+لما هنكون بدنا نجيب ال inverse تبع A مد
+
+318
+00:22:52,830 --> 00:23:00,670
+م كنا بنقول إن ال A و M لازم يكونوا relatively
+
+319
+00:23:00,670 --> 00:23:08,410
+prime عشان أضمن إن داخل M لا يوجد إلا inverse واحد
+
+320
+00:23:08,410 --> 00:23:14,100
+لل Aارجعوا على المحاضرة السابقة كويس انه بتسجل
+
+321
+00:23:14,100 --> 00:23:19,300
+عشان ما تقولوش لما ماسمعناش بتسجل فهذه عشان تقولوا
+
+322
+00:23:19,300 --> 00:23:23,340
+اه والله فيه inverse لازم يكون ال a و ال m
+
+323
+00:23:23,340 --> 00:23:29,440
+relatively prime او co-prime في الحالة هذه نفس
+
+324
+00:23:29,440 --> 00:23:32,940
+الكلام هنا طب انا محتاج ال E هذه بعدين اعملها
+
+325
+00:23:32,940 --> 00:23:37,020
+inverse عشان احسب D مش محتاجين نحسب D دي من وين
+
+326
+00:23:37,020 --> 00:23:40,220
+بدنا نجيبها inverse ال E ماتجداش
+
+327
+00:23:42,780 --> 00:23:48,200
+P-1 P-1 فعشان فعلا خلّيني اعمل تشك جبل ما نبدأ
+
+328
+00:23:48,200 --> 00:23:51,900
+نشتغل هل الرقم بتاعتنا كلها مناسبة لل encryption
+
+329
+00:23:51,900 --> 00:23:56,860
+اللي بدنا نعمله او لا فإذا GCD بتاعتهم okay هتطلع
+
+330
+00:23:56,860 --> 00:24:00,920
+one okay من التمنين الأرقام مناسبة جدا عندنا تلاتة
+
+331
+00:24:00,920 --> 00:24:04,560
+primesو ال prime اللي انا محتاجه ال exponent اللي
+
+332
+00:24:04,560 --> 00:24:07,160
+انا محتاجه اجيبله ال inverse بالنسبة له ال prime
+
+333
+00:24:07,160 --> 00:24:10,180
+الأول minus one في ال prime التاني minus one برضه
+
+334
+00:24:10,180 --> 00:24:13,920
+relative ال prime مع بعض فإذا بقدر اقول ان دي اللي
+
+335
+00:24:13,920 --> 00:24:22,580
+هحسبها هي inverse واحدة unique inverse لل E كويس
+
+336
+00:24:26,400 --> 00:24:30,620
+هذا الاصل إن هتكون يعني إذا كان في سؤال هتكون معطق
+
+337
+00:24:30,620 --> 00:24:33,660
+ولكن إذا كان انت designer المفروض انت اللي تصمميهم
+
+338
+00:24:33,660 --> 00:24:38,040
+إذا كانت مجرد مهندسات و بتعملوا تشفوا تعملوا code
+
+339
+00:24:38,040 --> 00:24:42,340
+لحالكم بدك تختارينه بهذا الشكل اتحولوا تنجي رقمين
+
+340
+00:24:42,340 --> 00:24:46,320
+الprimes الرقمين الprimes هتقول تاخدي بالك هذا
+
+341
+00:24:46,320 --> 00:24:50,480
+minus one في هذا minus one تختاري رقم prime تالت
+
+342
+00:24:52,170 --> 00:24:55,750
+يكون relative prime مع مضروبهم مضروبهم minus واحد
+
+343
+00:24:55,750 --> 00:24:59,250
+مضروبهم minus واحد مع بعض يعني الشبكة هيك تاخد
+
+344
+00:24:59,250 --> 00:25:01,810
+بالك في ال design تبعها عشان تختاريهم بس طبعا في
+
+345
+00:25:01,810 --> 00:25:09,050
+السؤال هتكون given هنا في السؤال هتكون given خلصنا
+
+346
+00:25:09,050 --> 00:25:19,160
+في الحالة هذه ال S 18 T 19 O 14 P 15هي خلصنا ال
+
+347
+00:25:19,160 --> 00:25:21,500
+code تبعنا بناخدهم ايش ناخدهم two letters و two
+
+348
+00:25:21,500 --> 00:25:24,560
+letters بناخد الاتنين هذول مع بعض بنعتبرهم message
+
+349
+00:25:24,560 --> 00:25:36,900
+و بنعملهم modulo N اللي هي PQ طيب لحظة طبعا هيطلع
+
+350
+00:25:36,900 --> 00:25:40,580
+الرقم الاول رقم كبير جدا لإيش لإنه 13 ع ال
+
+351
+00:25:40,580 --> 00:25:43,740
+calculator مش هطلع معاكعالقلة الحسبة اللي معاكم مش
+
+352
+00:25:43,740 --> 00:25:47,860
+هيطلع لأن انتوا بتتكلموا هنا عن قداش 1819 to the
+
+353
+00:25:47,860 --> 00:25:52,520
+power 13 to the power 13 طبعا هذا كمان هيتوه اكتر
+
+354
+00:25:52,520 --> 00:25:57,420
+المعلومة لو شفناها في نص الطريق ليش لأن كل رقم او
+
+355
+00:25:57,420 --> 00:26:01,480
+كل letter مبنية مع اللي جابلها بمعنى انه مش دايما
+
+356
+00:26:01,480 --> 00:26:04,940
+ال letter نفسها في نفس ال system هتاخد نفس القيمة
+
+357
+00:26:04,940 --> 00:26:08,620
+في ال encryption لأ ليش لأنها معتمدة على اللي
+
+358
+00:26:08,620 --> 00:26:11,650
+جابلها او على اللي بعدهافالجابل أو اللي بعد هو
+
+359
+00:26:11,650 --> 00:26:14,970
+هيغيروا كل الرقم على بعضه هيتغير كل الرقم فهد كمان
+
+360
+00:26:14,970 --> 00:26:18,370
+more secure في الشغل هد بتعطيكوا more secure في
+
+361
+00:26:18,370 --> 00:26:22,070
+الشغل فصرا هنا بعمل .. بعملش encryption ل 18 لحالة
+
+362
+00:26:22,070 --> 00:26:26,830
+اللي هي خاصة بالاسم لأ أنا بعملش لل 18 بعمل ل 1819
+
+363
+00:26:26,830 --> 00:26:31,970
+هد مش letter رقم بس أنا عارف إن هو كيف .. إيش يمثل
+
+364
+00:26:31,970 --> 00:26:35,230
+يمثل two letters مع بعض كويسة تتبارط ل 13 و بعمل
+
+365
+00:26:35,230 --> 00:26:41,290
+mod g mod n هيسوي رقم جديدبنكمل الجزء التاني نفس
+
+366
+00:26:41,290 --> 00:26:45,990
+الكلام بارطبهم
+
+367
+00:26:45,990 --> 00:26:49,750
+كتر تبهم عشرين واحد تمانين و واحد و عشرين اتنين و
+
+368
+00:26:49,750 --> 00:26:53,050
+تمانين هاي ال message اللي هتنبعتها هذا ال message
+
+369
+00:26:53,050 --> 00:26:59,870
+هي الرسالة اللي هنبعتها ارسالة هذه اللي راحت لو
+
+370
+00:26:59,870 --> 00:27:02,830
+شفتواها في نص الطريق مش هتعرفوا منها اشي هذه مش
+
+371
+00:27:02,830 --> 00:27:05,950
+هتعرفوا منها حاجةهتعرف تطلع منها الكلمة ومش هتعرف
+
+372
+00:27:05,950 --> 00:27:09,330
+تطلع منها الكلمة كويس، مين اللي هعرف يطلع منها
+
+373
+00:27:09,330 --> 00:27:13,350
+كلمة؟ المستقبل هناك اللي عارف شوية parameters
+
+374
+00:27:13,350 --> 00:27:17,530
+محددة عارف شوية parameters معينة، من أهمها زي ما
+
+375
+00:27:17,530 --> 00:27:21,950
+قلنا ال E عشان بده يجيبلها ال inverse ال P و ال Q
+
+376
+00:27:21,950 --> 00:27:27,530
+عشان برضه بده يشتغل على P-1 و Q-1 و بده يجيب ال N
+
+377
+00:27:27,530 --> 00:27:32,430
+منهمكويس خلّينا نشوف بالعكس لو بدنا نعمل
+
+378
+00:27:32,430 --> 00:27:40,010
+decryption ل message بهذا الشكل 0 9 8 1 0 4 6 1
+
+379
+00:27:40,010 --> 00:27:43,950
+هنفترض أن هذه وصلتنا بدنا نشوف الشيء هذا بالظبط
+
+380
+00:27:43,950 --> 00:27:47,090
+طبعا على نفس المثال السابق على نفس المثال السابق
+
+381
+00:27:47,090 --> 00:27:49,890
+كنا نشتغل على تلاتة و أربعين تسعة و خمسين اللي هي
+
+382
+00:27:49,890 --> 00:27:55,830
+ال P و ال Q و ال E تلات عشر okay فنفس الكلام okay
+
+383
+00:27:55,830 --> 00:28:02,560
+عايا ف ال N هي هي PPQ N exponent تلت عشر تمام تمام
+
+384
+00:28:02,560 --> 00:28:06,780
+بدنا نحسب مين D D ممكن ترجع للمثال اللي كان دبل
+
+385
+00:28:06,780 --> 00:28:10,040
+هذا اللي هو في exercise أربعة في نفس الكتاب ..
+
+386
+00:28:10,040 --> 00:28:13,980
+الكتاب هذا عشان تعرفى بس هو ال inverse هذه جابها
+
+387
+00:28:13,980 --> 00:28:20,140
+مين لتلت عشر فإذا التسعمية تلاتة و سبعين هذه اللي
+
+388
+00:28:20,140 --> 00:28:24,700
+هي سبعة و تلاتين سبعة و تلاتين هذا ال inverse
+
+389
+00:28:27,610 --> 00:28:39,190
+ال inverse لمن؟ لل تلتاش مدت اتنين خمسة
+
+390
+00:28:39,190 --> 00:28:44,550
+تلاتة سبعة فمن هنا اجه الرقم الرقم من هنا اجه
+
+391
+00:28:44,550 --> 00:28:50,710
+الرقم الرقم كويسةبتقدر تشتغلوها تعملوها فاكرين
+
+392
+00:28:50,710 --> 00:28:54,050
+الطريقة اللى خدناها المطولة ترجعوا تجمعوا تانى
+
+393
+00:28:54,050 --> 00:28:57,250
+فبتقدروا تجيبوا منها ال turn تبعكوا حد اوكى
+
+394
+00:28:57,250 --> 00:29:01,930
+خلصناها بدنا نجيب ال message الاصلية اللى هى P
+
+395
+00:29:01,930 --> 00:29:08,130
+تساوي ال encrypted message to the power D mod N زى
+
+396
+00:29:08,130 --> 00:29:14,760
+ما هى ال N ال N زى ما هى كويسبرضه هبناخدهم أربع
+
+397
+00:29:14,760 --> 00:29:17,140
+أرقام two letters two letters هاي الأربع أرقام
+
+398
+00:29:17,140 --> 00:29:19,620
+الأولى to the power تسعمية سبعة و تلاتية طبعا برضه
+
+399
+00:29:19,620 --> 00:29:23,300
+على الأقل الحاسوب مش هتطلع معاكوا ماتطلعش معاكوا
+
+400
+00:29:23,300 --> 00:29:27,000
+هدى عادة كل الأقوات هدى بتنعمل على chip
+
+401
+00:29:27,000 --> 00:29:31,640
+microcontroller ال microcontroller هدى بتعملوا
+
+402
+00:29:31,640 --> 00:29:33,760
+عليه ال code تبعكم بحيث ال data مباشرة تدخل
+
+403
+00:29:33,760 --> 00:29:37,720
+بنعملها encryption فهو بتصير chip كأنها encryption
+
+404
+00:29:37,720 --> 00:29:41,780
+بنعملها encryption أو encoderصارت على خلاص ال chip
+
+405
+00:29:41,780 --> 00:29:44,260
+هذه اسمها encoder طب ال chip هذه اسمها ال decoder
+
+406
+00:29:44,260 --> 00:29:48,500
+تبعه خلاص بيصيروا يتفاهموا مع بعض اتوماتيك اللي
+
+407
+00:29:48,500 --> 00:29:50,400
+بيصيروا يتفاهموا مع بعض هيك الصناعة بتتبع خلاص هذا
+
+408
+00:29:50,400 --> 00:29:53,100
+encoder و هذا decoder بيكون ال design كله معمول
+
+409
+00:29:53,100 --> 00:29:56,180
+جوا و الاتنين هذول ا synchronize مع بعض لإن هذول
+
+410
+00:29:56,180 --> 00:29:58,960
+بيفهموا مع بعض لإن نفس ال code و نفس ال E هنا
+
+411
+00:29:58,960 --> 00:30:02,180
+موجودة ال D هنا موجودة ما يقابلها ال D تحتها
+
+412
+00:30:02,180 --> 00:30:09,730
+خلاصنا طلعت 0704هذا بالنسبة للرقم الأول الرقم
+
+413
+00:30:09,730 --> 00:30:13,450
+التاني الجزء التاني برضه تتباور تسعمية سبعة و
+
+414
+00:30:13,450 --> 00:30:16,950
+تلاتين من الفين و خمسمية سبعة و تلاتين بساوي
+
+415
+00:30:16,950 --> 00:30:22,050
+احداشر و خمستاشر بنشوف خلاص ترتيب صفر سبعة صفر
+
+416
+00:30:22,050 --> 00:30:25,290
+سبعة في ال .. في ال bit string او في ال alphabet
+
+417
+00:30:25,290 --> 00:30:28,950
+string فعلا ال alphabet string جدش مش بيساوي بساوي
+
+418
+00:30:28,950 --> 00:30:37,020
+ال H صفر أربعة ال E11 قال فبتلاقوا طلعت معاكم ال
+
+419
+00:30:37,020 --> 00:30:43,200
+message الحقيقية فعليا اللي كانت ممثلة 09810461
+
+420
+00:30:43,200 --> 00:30:47,040
+هي عملية ال encryption الطريقة دي ما زالت مستخدمة
+
+421
+00:30:47,040 --> 00:30:50,160
+يعني معظم ال applications ال .. ال .. ال
+
+422
+00:30:50,160 --> 00:30:52,480
+commercial applications مستخدمة لعندي الآن الطريقة
+
+423
+00:30:52,480 --> 00:30:58,510
+اللي هي ال RSAشائعة يعني شائعة الاستخدام وسلسة
+
+424
+00:30:58,510 --> 00:31:01,350
+بسيطة كما انتوا شايفين الأمور فيها مش كتير صعبة
+
+425
+00:31:01,350 --> 00:31:04,110
+المهم انكوا تجيبوا مجموعة برايم مناسبة تجيبوا
+
+426
+00:31:04,110 --> 00:31:08,390
+أرقام برايم مناسبة طبعا في encryption techniques
+
+427
+00:31:08,390 --> 00:31:12,190
+طلعت أفضل من هذه بس طبعا دلوقتي ممكن معظمها بيروح
+
+428
+00:31:12,190 --> 00:31:15,510
+ل ال military applications في الغالب و الحاجات
+
+429
+00:31:15,510 --> 00:31:20,390
+المحتاجة ال security أعلى تمام
+
+430
+00:31:22,610 --> 00:31:34,890
+هذه كانت أخر جزء كان عندنا من مين؟ من
+
+431
+00:31:34,890 --> 00:31:40,270
+number theory okay نكمل في جزئية من الحاجات المهمة
+
+432
+00:31:40,270 --> 00:31:45,170
+برضه اللي بتستخدم لل improving عملية الإثباتات
+
+433
+00:31:45,170 --> 00:31:48,290
+عملية الإثباتات هذه في حاجة اسمها mathematical
+
+434
+00:31:48,290 --> 00:31:53,900
+induction أو induction proofالإثبات بالحث، إيش
+
+435
+00:31:53,900 --> 00:31:56,260
+الإثبات بالحث؟ induction احنا عارفين ان هو الحث
+
+436
+00:31:56,260 --> 00:32:00,280
+يعني، حث عشان نوضحلكوا إياها الدومينو عارفين حجار
+
+437
+00:32:00,280 --> 00:32:03,440
+الدومينو؟ حجار الدومينو عارفين الناس اللي بيصفطوا
+
+438
+00:32:03,440 --> 00:32:09,600
+الحجار؟ بتلاقوا بيصفطوا الحجار هيك؟ و بعدين لو رمى
+
+439
+00:32:09,600 --> 00:32:14,700
+أول حجر أكيد أخر حجر هيجي عناطبعا هذا عشان اقول
+
+440
+00:32:14,700 --> 00:32:18,180
+انه فعلا اكيد اخر حجر هيجع او اكيد انه كل حجر هتجع
+
+441
+00:32:18,180 --> 00:32:23,960
+بمجرد ما عملت induction للأولى حفظ ان اوجع الأولى
+
+442
+00:32:23,960 --> 00:32:28,800
+بدي اضمن انه عشان كلهم يجعوا في شرطين مهمين عشان
+
+443
+00:32:28,800 --> 00:32:33,560
+فعلا اضمن انه كل وجع في شرطين كتير مهمين ايش هم
+
+444
+00:32:33,560 --> 00:32:39,740
+الشرطين المهمين انه الأولى وجعت فعلاالتعاون الدوم
+
+445
+00:32:39,740 --> 00:32:42,240
+أنه بتشوفون بيكونوا حاطين خمستاشر ألف اشتين ألف
+
+446
+00:32:42,240 --> 00:32:48,260
+جطعة بيركبوها و بيدخلوا فيها موصوعة جنس و بالعدد و
+
+447
+00:32:48,260 --> 00:32:52,180
+بالحجم و بال .. بيكونوا عاملينها كبيرة جدا بمجرد
+
+448
+00:32:52,180 --> 00:32:54,640
+ما وجع أول واحد خلاص احنا قاعدين نتفرج أنه آه أخر
+
+449
+00:32:54,640 --> 00:32:58,080
+واحد خلاص متوقعين أن أخر .. أخر حجر هيجع .. أخر
+
+450
+00:32:58,080 --> 00:33:02,800
+حجر هيجع .. كويس فإذا الأول شرط أنه الحجر الأول is
+
+451
+00:33:02,800 --> 00:33:08,150
+true و جعفإذا هنا بتعامل أنا مع ال .. ال predicate
+
+452
+00:33:08,150 --> 00:33:13,410
+function أو ال predicate تبعتي إنه الحجر رقم صفر
+
+453
+00:33:13,410 --> 00:33:21,410
+is failed و جاء كويس هل هو fails فعلا بيقع جاعد
+
+454
+00:33:21,410 --> 00:33:29,050
+إذا و جاء بدي أضمن الشرط التاني إنه كل حجر في ال
+
+455
+00:33:29,050 --> 00:33:34,400
+location N إذا و جاء thenالحجر في location n plus
+
+456
+00:33:34,400 --> 00:33:39,040
+واحد هيجع لأنه ممكن يطلعوا بعض عن بعض هذا يجع
+
+457
+00:33:39,040 --> 00:33:45,860
+مايوجعش التاني، صح؟ فإذن شرطين شرط أول إن أول حجر
+
+458
+00:33:45,860 --> 00:33:49,680
+is true هو فعلاً P of Zero ال .. ال .. ال
+
+459
+00:33:49,680 --> 00:33:53,520
+predicate عند Zero عند ال .. ال .. ال basis tip
+
+460
+00:33:53,520 --> 00:33:59,040
+هذه عند أول خطوة وجعهذا شرط أول إن فعلًا وجعت
+
+461
+00:33:59,040 --> 00:34:02,460
+الأولى عشان أقول والله كله وجعك خلاص أكيد كله
+
+462
+00:34:02,460 --> 00:34:10,500
+هيجعك الأولى وجعك الشرط التاني و الأهم إنه كل حجر
+
+463
+00:34:10,500 --> 00:34:15,580
+مرتبط باللي ورا إذا وجع الحجر أكيد هيجع اللي ورا ف
+
+464
+00:34:15,580 --> 00:34:24,140
+if then if P of N then P of N plus 1 P of N plus 1
+
+465
+00:34:24,140 --> 00:34:31,500
+تمامهذه فعلياً عملية induction بتاعتنا وهي حقيقة
+
+466
+00:34:31,500 --> 00:34:36,780
+powerful فعلا قوية جدا في الإثبات ومهمة جدا واحدة
+
+467
+00:34:36,780 --> 00:34:40,800
+من الطرق اللي كتير بتستخدم لل proving لعملية ال
+
+468
+00:34:40,800 --> 00:34:45,240
+proving لمين؟ لل predicate P of N is true for
+
+469
+00:34:45,240 --> 00:34:51,560
+every natural number Nللكل عشان اضمن ان فعلا عندكم
+
+470
+00:34:51,560 --> 00:34:56,060
+ثيورة معينة و بتعملوا prove ان هي لكل الأرقام
+
+471
+00:34:56,060 --> 00:34:59,940
+صحيحة يعني اذا نطبق على كل الأرقام ممكن نشتغل على
+
+472
+00:34:59,940 --> 00:35:05,180
+induction approval و هناخد شوية examples عليها بس
+
+473
+00:35:05,180 --> 00:35:08,460
+قاعدين احنا بنوضح الفكرة نفسها من وين اجت الفكرة؟
+
+474
+00:35:08,460 --> 00:35:11,580
+من وين؟عشان الفكرة فهذه معتمدة على ال domino
+
+475
+00:35:11,580 --> 00:35:16,160
+effect principle على مبدأ عمل تأثير ال domino أو
+
+476
+00:35:16,160 --> 00:35:19,060
+حجار ال domino على بعضها حجار ال domino على بعضها
+
+477
+00:35:19,060 --> 00:35:23,740
+طيب ال inference rule اللي هنشتغل عليه هكت تالي if
+
+478
+00:35:23,740 --> 00:35:29,480
+P of 0 is true لحظه الحجر الأول وجه is true فعلا
+
+479
+00:35:29,480 --> 00:35:38,060
+خلاص و جه and for all N أكبر أو تساوي الصفرif P of
+
+480
+00:35:38,060 --> 00:35:44,000
+N is true then P of N plus 1 is true فإذا كل حجر
+
+481
+00:35:44,000 --> 00:35:48,100
+إذا وجع أكيد حيجع اللي ورا إذا تحققوا الشرطين فإذا
+
+482
+00:35:48,100 --> 00:35:52,940
+بقول for all N أكبر من صفر P of N is true بغض
+
+483
+00:35:52,940 --> 00:36:00,640
+النظر عن N أنية للكل لكل N أكبر من صفر للكل فإذا
+
+484
+00:36:00,640 --> 00:36:04,800
+بكون ضامن إن كل الحجار وجعين كل الحجار وجعين
+
+485
+00:36:04,800 --> 00:36:08,560
+هنشتغل علىالرول هذه فقط هي اللي بنعمل منها كل
+
+486
+00:36:08,560 --> 00:36:12,640
+إثباتاتنا اللي هنشتغل عليها على إثباتاتنا زي ما
+
+487
+00:36:12,640 --> 00:36:16,580
+قلنا ال domino ال premise number one انه domino
+
+488
+00:36:16,580 --> 00:36:21,780
+number zero fails الدومينو الأولى وجعت الدجاع ال
+
+489
+00:36:21,780 --> 00:36:25,720
+premise number two for every n belong to natural
+
+490
+00:36:25,720 --> 00:36:31,570
+number if domino number n fails thendomino n plus
+
+491
+00:36:31,570 --> 00:36:33,610
+واحد number n plus واحد number n plus واحد number
+
+492
+00:36:33,610 --> 00:36:38,710
+n plus واحد number n plus واحد number n plus واحد
+
+493
+00:36:38,710 --> 00:36:43,550
+number n plus واحد number n plus واحد number n
+
+494
+00:36:43,550 --> 00:36:44,050
+plus واحد number n plus واحد number n plus واحد
+
+495
+00:36:44,050 --> 00:36:44,050
+number n plus واحد number n plus واحد number n
+
+496
+00:36:44,050 --> 00:36:44,310
+plus واحد number n plus واحد number n plus واحد
+
+497
+00:36:44,310 --> 00:36:45,430
+number n plus واحد number n plus واحد number n
+
+498
+00:36:45,430 --> 00:36:47,570
+plus واحد number n plus واحد number n plus واحد
+
+499
+00:36:47,570 --> 00:36:50,890
+number n plus واحد number n plus واحد number n
+
+500
+00:36:50,890 --> 00:36:53,490
+plus واحد number n plus واحد number n plus واحد
+
+501
+00:36:53,490 --> 00:36:53,930
+number n plus واحد number n plus واحد number n
+
+502
+00:36:53,930 --> 00:36:55,130
+plus واحد number n plus واحد number n plus واحد
+
+503
+00:36:55,130 --> 00:36:56,130
+number n plus واحد number n plus واحد number n
+
+504
+00:36:56,130 --> 00:36:56,130
+plus واحد number n plus واحد number n plus واحد
+
+505
+00:36:56,130 --> 00:36:56,130
+number n plus واحد number n plus واحد number n
+
+506
+00:36:56,130 --> 00:36:56,130
+plus واحد number n plus واحد number n plus واحد
+
+507
+00:36:56,130 --> 00:36:56,650
+number n plus واحد number n plus واحد number n
+
+508
+00:36:56,650 --> 00:37:01,130
+plus واحد number n plusزاد ان انا وجعت اول حجر
+
+509
+00:37:01,130 --> 00:37:05,110
+فخلاص كلنا عارفين اذا فعلا الشرطين تحققوا ان اخر
+
+510
+00:37:05,110 --> 00:37:12,070
+حجر حاجع ان اخر حجر برضه حاجع طيب ال outline of an
+
+511
+00:37:12,070 --> 00:37:15,250
+inductive proof عشان نشوف ال inductive proof هذه
+
+512
+00:37:15,250 --> 00:37:17,630
+تبعنا كيف ممكن تتم احنا كل اللي بدنا نعمل method
+
+513
+00:37:17,630 --> 00:37:22,050
+هو ان for all n P of n النظرية P of n is true
+
+514
+00:37:25,070 --> 00:37:28,610
+بدنا نصل على two steps step الأولى اللى هى ال base
+
+515
+00:37:28,610 --> 00:37:33,230
+case او ال basis step ان انا اعوض عند ال zero او
+
+516
+00:37:33,230 --> 00:37:38,950
+اعوض عند أول element لل N اللى هو ال initial
+
+517
+00:37:38,950 --> 00:37:42,130
+ببعضها أول element موجود في ال sequence أول
+
+518
+00:37:42,130 --> 00:37:45,990
+element بتعود مباشرة اعوضه مباشرة هل بيحقق ال P of
+
+519
+00:37:45,990 --> 00:37:48,790
+N ولا لأ بتشوف ايش المعادلة هذه ال P of N عبارة عن
+
+520
+00:37:48,790 --> 00:37:53,870
+ايشعوضوا فيها is it true؟ okay هاي أول شرطة
+
+521
+00:37:53,870 --> 00:37:59,370
+خلصناها الشرط التاني بدنا نقول for all n أفرض أنا
+
+522
+00:37:59,370 --> 00:38:03,970
+من عندي أن ال P of N is it true؟ هنفرض أن ال P of
+
+523
+00:38:03,970 --> 00:38:08,850
+N is true؟ و هشوف هل ال P of N plus واحد بناء على
+
+524
+00:38:08,850 --> 00:38:11,490
+معلومة أن ال P of N is true؟ هل هي كمان ال true؟
+
+525
+00:38:11,490 --> 00:38:15,550
+ولا لأ إذا تحققت true فتحقق الشرطين فإذا النظرية
+
+526
+00:38:15,550 --> 00:38:19,650
+دي دائما صحيحة خلاص بتقول إنه دائما صحيح
+
+527
+00:38:20,400 --> 00:38:24,020
+automatically دائما معناته كل إحشار يعني مادام
+
+528
+00:38:24,020 --> 00:38:27,260
+دائم خلاص معناته دائما صحيحة إذا تحقق ال two
+
+529
+00:38:27,260 --> 00:38:31,420
+conditions هدول طيب بنستخدم direct search ايه عفوا
+
+530
+00:38:31,420 --> 00:38:34,840
+ال direct proof direct proof مش فيها مشكلة على طول
+
+531
+00:38:34,840 --> 00:38:38,120
+جربوا هنا وجربوا هنا خلصنا يعني مالهاش أي
+
+532
+00:38:38,120 --> 00:38:44,390
+techniques تانية مباشرة تعود مباشر على طول okayهذا
+
+533
+00:38:44,390 --> 00:38:48,210
+بالنسبة لمين؟ لل inductive step direct ما تشتغلوش
+
+534
+00:38:48,210 --> 00:38:50,950
+لا indirect ولا contrapositive ولا contradiction
+
+535
+00:38:50,950 --> 00:38:56,170
+ولا غيره هي بسيطة جدا افرضوا هذه true وثقتوا هذه
+
+536
+00:38:56,170 --> 00:38:59,730
+منها بس يعني ما تغلبوش حالكوا في اشي ولا تقعدوا
+
+537
+00:38:59,730 --> 00:39:02,530
+تشوشوا حالكوا ولا تقعدوا تقولوا يمكن الدكتور جصده
+
+538
+00:39:02,530 --> 00:39:07,170
+يعملنا خدع هذي مباشرة شغلوها direct على طول دايما
+
+539
+00:39:07,170 --> 00:39:11,970
+طيب let n belong to natural number assume p of n
+
+540
+00:39:12,390 --> 00:39:18,370
+فإذا هنا عشان أشتغلها بفرض أن P of N is true و
+
+541
+00:39:18,370 --> 00:39:25,590
+under this assumption prove P of N plus 1 is true
+
+542
+00:39:25,590 --> 00:39:30,730
+قرنا و الله إذا true معناته تتحقق في الشرط إذا not
+
+543
+00:39:30,730 --> 00:39:34,270
+معناته كلها لاتتحقق معناته هنا بتقول for all دي
+
+544
+00:39:34,270 --> 00:39:38,480
+غلطكلمة for all غلط، معناته ماقدرش أقول إن ال
+
+545
+00:39:38,480 --> 00:39:42,180
+predicate دي للكل صحيحة، لأ هي مش للكل صحيحة، فإذا
+
+546
+00:39:42,180 --> 00:39:45,300
+بكون أثبت العكس طبعا لأ أنتوا بتكونوا تفتقوا إن هي
+
+547
+00:39:45,300 --> 00:39:48,380
+فعلا صحيحة، فبتكونوا تتأكدوا إن هذا true و هذا
+
+548
+00:39:48,380 --> 00:39:52,660
+true عشان تثبتوا في الآخر إن والله فعلا for all
+
+549
+00:39:52,660 --> 00:39:57,900
+and P of N is true طيب
+
+550
+00:39:57,900 --> 00:40:00,340
+in general، in general ممكن احنا مانبداش من ال
+
+551
+00:40:00,340 --> 00:40:06,340
+zeroممكن نبدأ من C، أي element، فهيكون ال initial
+
+552
+00:40:06,340 --> 00:40:10,440
+case بتاعتنا أو ال base case بتاعتنا هي ال C
+
+553
+00:40:10,440 --> 00:40:15,210
+نفسها، فبنصيب نشتغل هنا على P of Cالـ predicate of
+
+554
+00:40:15,210 --> 00:40:21,270
+C بدل الـ P of 0 بدل P of 0 وبصير بدنا نثبت إيش أن
+
+555
+00:40:21,270 --> 00:40:25,150
+for all n أكبر من أو تساوي C مضروبة في ال .. في ال
+
+556
+00:40:25,150 --> 00:40:27,950
+term هذا بس طبعا أنا C constant فانا النظرية ضالت
+
+557
+00:40:27,950 --> 00:40:32,310
+زي ما هي بدي أفرض P of N employees P of N plus 1
+
+558
+00:40:32,310 --> 00:40:35,470
+ماحدش يقولي employees هذه معناته إذا هذه false
+
+559
+00:40:35,470 --> 00:40:38,230
+معناته و هذه false معناته true ليش؟ لأن أحنا
+
+560
+00:40:38,230 --> 00:40:44,370
+assumption تبعنا من الأساس إن هذه truethis is true
+
+561
+00:40:44,370 --> 00:40:48,570
+فعشان تكون هذه is true و كل true لازم تكون true
+
+562
+00:40:48,570 --> 00:40:53,310
+صحيح؟ ماحدش يقول اه احنا في ال implication احنا
+
+563
+00:40:53,310 --> 00:40:55,790
+عارفين ان هذه ممكن تكون false و هذه false كله true
+
+564
+00:40:55,790 --> 00:40:59,090
+لأ احنا هنا من الأساس عاملين assumption أساسا ان
+
+565
+00:40:59,090 --> 00:41:03,950
+هذه is true انتوا بتفرضوها فرض هذه true و منها
+
+566
+00:41:03,950 --> 00:41:05,790
+تحاولوا تفضطوا التانية true
+
+567
+00:41:11,560 --> 00:41:14,800
+هناخد أمثلة هالواجهة قبل أن ناخد أمثلة نرجع كمان
+
+568
+00:41:14,800 --> 00:41:22,220
+مرة هاي اللي هنعمله ال first عادي كده اسمها طريقة
+
+569
+00:41:22,220 --> 00:41:28,540
+ال first principle طب في طريقة تانية اسمها second
+
+570
+00:41:28,540 --> 00:41:31,680
+principle second principle مختلفة شوية في ال
+
+571
+00:41:31,680 --> 00:41:37,520
+induction ليش؟ هو لا يكتفي انه يقول P of zero is
+
+572
+00:41:37,520 --> 00:41:45,740
+true and ifP of N is true than P of N plus 1 is
+
+573
+00:41:45,740 --> 00:41:50,100
+true لأ عشان أثبت P of N plus 1 أثبتلي أن كل اللي
+
+574
+00:41:50,100 --> 00:41:56,520
+جابلها is true مش بس الوحيدة اللي هي P of N اللي
+
+575
+00:41:56,520 --> 00:41:59,320
+جابلها واحدة لحالها لأ أثبتلي كل اللي جابلها لمن
+
+576
+00:41:59,320 --> 00:42:02,640
+عندي الصفر أن هي true طبعا أوضح أن هذا أصعب شوية
+
+577
+00:42:04,190 --> 00:42:09,590
+بدوا إثبات عشان أقول إن فعلا P of N plus واحد is
+
+578
+00:42:09,590 --> 00:42:13,690
+true لأ أنا لن أكتفي بس تقولي P of N is true خلاص
+
+579
+00:42:13,690 --> 00:42:20,190
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+580
+00:42:20,190 --> 00:42:22,290
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+581
+00:42:22,290 --> 00:42:24,890
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+582
+00:42:24,890 --> 00:42:27,150
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+583
+00:42:27,150 --> 00:42:27,150
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+584
+00:42:27,150 --> 00:42:29,730
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ ل
+
+585
+00:42:33,270 --> 00:42:38,390
+طبعا هذا ال strong proof واضح أن هذا الأثبات
+
+586
+00:42:38,390 --> 00:42:42,030
+الأقوى، الأثبات الأقوى طبعا ممكن يستخدم يعني انتوا
+
+587
+00:42:42,030 --> 00:42:44,530
+ماتجلغوش مش هلاقش الصعب ساعات التطبيق على وجهك
+
+588
+00:42:44,530 --> 00:42:48,210
+هتلاقي ان أمورهم مش .. مش صعبة لها الدرجة يعنى، مش
+
+589
+00:42:48,210 --> 00:42:52,420
+صعبة لها الدرجةطيب مثال خلّيني نبدأ بال first
+
+590
+00:42:52,420 --> 00:42:56,440
+principle البسيط السهل و خلاص مجرد لو أثبتت أن P
+
+591
+00:42:56,440 --> 00:42:59,220
+of N is true خلاص و هذه أثبتت منها true بكفي
+
+592
+00:42:59,220 --> 00:43:03,520
+خلّيني نشوف لو مطلوب ان ا prove that the summation
+
+593
+00:43:03,520 --> 00:43:11,740
+of the first N positive integers is N squared ايش
+
+594
+00:43:11,740 --> 00:43:19,070
+يعني؟ بمعنىلو أخدنا أول and odd positive أول and
+
+595
+00:43:19,070 --> 00:43:24,150
+odd positive إيش معناه؟ واحد، تلاتة، خمسة، سبعة،
+
+596
+00:43:24,150 --> 00:43:30,990
+تسعة، احداشر and so on هدول إيش بيساووا؟ بيساووا
+
+597
+00:43:30,990 --> 00:43:37,430
+and تربية خلينا نجرب هدي إيش location تبعها؟ واحد،
+
+598
+00:43:37,430 --> 00:43:42,210
+location اتنين، تلاتة، أربعة، خمسة، ستة، هدي ال
+
+599
+00:43:42,210 --> 00:43:46,930
+andهي قيمة الأمن و هنا ال summation بدنا نعمل
+
+600
+00:43:46,930 --> 00:43:51,470
+summation مثلا خلينا ناخد أول element الأولة الأول
+
+601
+00:43:51,470 --> 00:43:58,750
+بساوي ال location تربيع صح طيب التانية فإذا ال
+
+602
+00:43:58,750 --> 00:44:02,670
+summation الأول مع التاني أربعة يساوي ال location
+
+603
+00:44:02,670 --> 00:44:09,040
+التاني تربيعمجموع التلاتة يساوي تلاتة تربيع يساوي
+
+604
+00:44:09,040 --> 00:44:12,980
+أربعة تربيع يساوي أربعة تربيع و هكذا خمسة تربيع
+
+605
+00:44:12,980 --> 00:44:19,660
+ستة تربيع مجموع الستة elements من بداية ال
+
+606
+00:44:19,660 --> 00:44:22,860
+sequence ال odd أو ال string تبع ال odd
+
+607
+00:44:25,810 --> 00:44:29,250
+بنكون هذه النظرية بدنا نثبتها أو بنكون حددنا إيش
+
+608
+00:44:29,250 --> 00:44:33,810
+النظرية أساساً بتاعتنا ف for all n أكبر من أو يسوى
+
+609
+00:44:33,810 --> 00:44:43,270
+واحد summation لاحظوا two I minus one فلينا نجرب
+
+610
+00:44:43,270 --> 00:44:48,210
+عندي الواحد واحد في اتنين ناقص واحد اه هاي ال
+
+611
+00:44:48,210 --> 00:44:51,210
+element الأول اللي هو الواحد فعلا عندي ال location
+
+612
+00:44:51,210 --> 00:44:55,630
+واحد بكون جبت ال element الأولطب عند ال element
+
+613
+00:44:55,630 --> 00:45:01,050
+اتنين عند
+
+614
+00:45:01,050 --> 00:45:10,230
+التلاتة ستة خمسة ففعلا ال summation هيك صحيح بدنا
+
+615
+00:45:10,230 --> 00:45:17,090
+نثبت انه يساوي N تربيع زي
+
+616
+00:45:17,090 --> 00:45:19,830
+ما قلنا عندنا اتو conditions الاول
+
+617
+00:45:21,600 --> 00:45:28,040
+ال base is step الشيء أني أعوض بأصغر رقم موجود
+
+618
+00:45:28,040 --> 00:45:31,600
+خلينا نعوض بأصغر رقم موجود أصغر رقم موجود الواحد
+
+619
+00:45:31,600 --> 00:45:40,280
+فإذا من واحد لواحد هل يسوى واحد تربيع واحد بيسوى
+
+620
+00:45:40,280 --> 00:45:44,900
+واحد فده هتقدر ان واحد بيسوى واحد فإذا and ال P of
+
+621
+00:45:44,900 --> 00:45:52,220
+واحد is trueهذه ال base step أول element دائما
+
+622
+00:45:52,220 --> 00:45:55,600
+بتجربوا أول element و بتجربوا عليه ال theory
+
+623
+00:45:55,600 --> 00:45:59,660
+المقلوب إثباتها الأولى خلصت مش الحاجة طيب دلها
+
+624
+00:45:59,660 --> 00:46:04,120
+الوقت نجرب التاني
+
+625
+00:46:04,120 --> 00:46:09,920
+التاني
+
+626
+00:46:09,920 --> 00:46:17,340
+كالتالي هنقول انه summation I بتسوي واحد and plus
+
+627
+00:46:17,340 --> 00:46:22,220
+oneهلق بنثبت اللي هو ال N plus one صحيح؟ فبنجيب ال
+
+628
+00:46:22,220 --> 00:46:27,860
+N plus one و بنحاول نجيبه بدلالة N بنحاول نجيبه
+
+629
+00:46:27,860 --> 00:46:32,560
+بدلالة N ليش؟ لأن أثبتنا أن N is true فانا هلق
+
+630
+00:46:32,560 --> 00:46:42,240
+هقول assumption تبعتي أن I بتساوي 1 to N to I
+
+631
+00:46:42,240 --> 00:46:49,710
+minus 1 فعلا بتساوي N تربيعبنانة على ال assumption
+
+632
+00:46:49,710 --> 00:46:55,550
+تبعي هذا بتثبتها الوجد هل to n plus واحد برضه
+
+633
+00:46:55,550 --> 00:47:00,350
+هتطلع n plus واحد تربيه و لا لأ طيب خليني امسكها
+
+634
+00:47:00,350 --> 00:47:10,730
+هنا صارت اتنين I ناقص واحد هذه
+
+635
+00:47:10,730 --> 00:47:14,690
+ايش ممكن تساوي عشان احطها بدلالةن اللي انا عارف ان
+
+636
+00:47:14,690 --> 00:47:22,810
+هي true فتساوي summation I بتساوي واحد to N minus
+
+637
+00:47:22,810 --> 00:47:28,210
+واحد plus .. لاحظ عوضه بس في العنصر الأخير اللي
+
+638
+00:47:28,210 --> 00:47:33,950
+ضال اخر عنصر ضال فحنعوض بإيش؟ ب2 مضروبها في N plus
+
+639
+00:47:33,950 --> 00:47:39,530
+واحد N plus واحد ناقص واحد بس
+
+640
+00:47:42,390 --> 00:47:46,010
+Okay هذا احنا ضمنين دايما ان هو true احنا اصلا
+
+641
+00:47:46,010 --> 00:47:48,270
+عاملين assumption اصلا ان هو true فإذا هذا بيساوي
+
+642
+00:47:48,270 --> 00:47:54,150
+n تربيع مدامي صح مدامي صح بيضالي جزء اللي ضايل هنا
+
+643
+00:47:54,150 --> 00:48:01,790
+طبعا هنا هيكون عندكوا اتنين n وزائد واحد طيب ال
+
+644
+00:48:01,790 --> 00:48:07,430
+term هذا ايش بيساوي n زائد واحد تربيع طب ما هي صح
+
+645
+00:48:07,430 --> 00:48:13,600
+فإذا المعادلة صحيحةالنظرية او المعادلة بتاعتنا
+
+646
+00:48:13,600 --> 00:48:18,580
+فعلا صحيحة واضح ان النظرية صحيحة لحظة الموضوع بسيط
+
+647
+00:48:18,580 --> 00:48:23,340
+جدا كل اللي بيصير بتجربوا اول element في ال
+
+648
+00:48:23,340 --> 00:48:26,520
+sequence عندكم اول element موجود بتجربوا على ال
+
+649
+00:48:26,520 --> 00:48:30,480
+theory المطلوب اثباتها بتضمن ان هو is true حسب
+
+650
+00:48:30,480 --> 00:48:34,260
+النظرية خلصنا اول شرط او ال base step او ال bases
+
+651
+00:48:34,260 --> 00:48:40,460
+step تمام خلصناها الشرط التاني بتفرضه ان عند n
+
+652
+00:48:41,430 --> 00:48:46,950
+التيوري صحيحة is true و بتحاولوا تحسبوا عند n plus
+
+653
+00:48:46,950 --> 00:48:50,450
+واحد طبعا عشان تحسبوا عند n plus واحد تحاولوا
+
+654
+00:48:50,450 --> 00:48:53,590
+دايما تجيبوها بدلالة n اللي انتوا ضمنيه ان هي is
+
+655
+00:48:53,590 --> 00:49:00,370
+true بحيث انكم مباشرة تعوضوا بقيمتها او بقيمتها في
+
+656
+00:49:00,370 --> 00:49:03,850
+التيوري باعتبار ان هي true وشوفوا ايش ال summation
+
+657
+00:49:03,850 --> 00:49:08,200
+او كيف شكل المعادلة بتتطلع معاكمالـ sequence كله
+
+658
+00:49:08,200 --> 00:49:10,840
+هيظل ماشي معاكم الجزئية هذه بس هي اللي هتختلف من
+
+659
+00:49:10,840 --> 00:49:15,380
+مثال لمثال ان كيف عمليت التجميل هتصير بس ماقدرش
+
+660
+00:49:15,380 --> 00:49:18,600
+أقولكوا هذا الاشي ثابت ليش لأنه حسب النظرية نفسها
+
+661
+00:49:18,600 --> 00:49:21,960
+هتتغير مجموعة الأقام اللي هنا بس بس بتكون شطرتكوا
+
+662
+00:49:21,960 --> 00:49:26,280
+كيف تدمجوها مع بعض عشان توصلوا ان حتى عند N plus
+
+663
+00:49:26,280 --> 00:49:27,940
+واحد ال theory is true
+
+664
+00:49:32,950 --> 00:49:35,050
+طماما ماهي هاد ال assumption تبعنا هاد ال
+
+665
+00:49:35,050 --> 00:49:38,510
+inductive step ال inductive step مبنيه على الموضوع
+
+666
+00:49:38,510 --> 00:49:42,930
+هذا اني بفرض P of N is true و بحاول بناء على
+
+667
+00:49:42,930 --> 00:49:50,510
+الفرضية هذه أثبت ان P of N plus 1 is true okay فهي
+
+668
+00:49:50,510 --> 00:49:57,850
+الفكرة اللي احنا عملناها فعليا ناخد المثال التاني
+
+669
+00:49:57,850 --> 00:50:01,050
+كمان مثال approve
+
+670
+00:50:08,490 --> 00:50:15,070
+تانى بيقول النظرية بتاعتنا for all n أكبر من صفر n
+
+671
+00:50:15,070 --> 00:50:20,930
+دائما أقل من two to the power n طبعا ال biometric
+
+672
+00:50:20,930 --> 00:50:25,190
+معروف يعني دائما إذا كان فعلا for all n أكبر من
+
+673
+00:50:25,190 --> 00:50:30,750
+صفر دائما n أقل من two to the power n منطقى طيب
+
+674
+00:50:30,750 --> 00:50:35,960
+هنا هنحط معناته أن P of nتساوي and ال n هنا معناته
+
+675
+00:50:35,960 --> 00:50:38,700
+أن n أقل من two to the power of n لأن هذه ال
+
+676
+00:50:38,700 --> 00:50:41,600
+assumption اللي هنبدأ فيه ال inductive step بتاعتي
+
+677
+00:50:41,600 --> 00:50:45,320
+ال inductive step بس خلينا مبدأيا نبدأ بال base
+
+678
+00:50:45,320 --> 00:50:51,720
+step أول أقل رقم ممكن واحد خلينا نجرب الواحد عشان
+
+679
+00:50:51,720 --> 00:50:55,320
+نشتغل على ال base case او ال base step واحد أقل من
+
+680
+00:50:55,320 --> 00:50:58,340
+two to the power واحد اه صحيح واحد أقل من اتنين
+
+681
+00:50:58,340 --> 00:51:02,260
+الكلام صحيح فإذا هاي أول شرط خلصناه ال inductive
+
+682
+00:51:02,260 --> 00:51:09,230
+stepfor all n أكبر من صفر بدنا نعمل approve لإيش P
+
+683
+00:51:09,230 --> 00:51:14,770
+of n employs P of n plus واحد فإذن هنقول أن P of n
+
+684
+00:51:14,770 --> 00:51:20,090
+is true معناته أن فعلا المعادلة هذه صحيحة أن n أقل
+
+685
+00:51:20,090 --> 00:51:24,410
+من 2 to the power n معناته أن n أقل من 2 to the
+
+686
+00:51:24,410 --> 00:51:28,810
+power n هذه ال logic مسلم فيها أن هي صحيحةمثلمة
+
+687
+00:51:28,810 --> 00:51:33,050
+فيها أنها صحيحة و هنعمل هى assuming هى تمام إجتنا
+
+688
+00:51:33,050 --> 00:51:36,070
+كمان مرة و بدنا منها نعمل proof لهذا ال term خلاص
+
+689
+00:51:36,070 --> 00:51:40,390
+نمسك هذا ال term ان هو ال term اللى هنا هذا هى اه
+
+690
+00:51:40,390 --> 00:51:44,390
+من واجبنا الكلام هذا استلمه احنا قاعدين بنقول n
+
+691
+00:51:44,390 --> 00:51:49,630
+أقل من two to the power n صح طيب اجمعوا زائد واحد
+
+692
+00:51:49,630 --> 00:51:57,120
+زائد واحدبتغير إشي؟ خمسة أقل من ستة، ستة أقل من
+
+693
+00:51:57,120 --> 00:52:07,540
+سبعة، صحيح، okay بعد هيك، ضمنين إنه دايما الواحد
+
+694
+00:52:07,540 --> 00:52:12,980
+أقل من two to the power n، ليش؟ لأن أقل n ممكنة هي
+
+695
+00:52:12,980 --> 00:52:17,640
+الواحد، هي الواحد، و احنا أصلا هي أثنتنا من الأول،
+
+696
+00:52:17,640 --> 00:52:21,830
+إن واحد هتكون أقل من two to the power oneأقل قيمة
+
+697
+00:52:21,830 --> 00:52:26,730
+ممكن لل N هي الواحد فإذا كان ال term هذا أكبر من N
+
+698
+00:52:26,730 --> 00:52:30,890
+زائد واحد طب لما نزوده كمان برضه حيظل أكبر من N
+
+699
+00:52:30,890 --> 00:52:33,770
+زائد واحد حيظل أكبر من N زائد واحد طب ليش أنا بدي
+
+700
+00:52:33,770 --> 00:52:37,910
+إياها N زائد واحد اتنين أجمع ال two N هذه عشان
+
+701
+00:52:37,910 --> 00:52:41,470
+أجمعها مع ال two N اللي موجودة أجيب ال N plus واحد
+
+702
+00:52:41,470 --> 00:52:46,460
+عشان نجيب ال N plus واحد ليش لإن ال term هذاببساطة
+
+703
+00:52:46,460 --> 00:52:49,140
+two to the power of n plus two to the power of n
+
+704
+00:52:49,140 --> 00:52:52,000
+ما هي هذي تساوي two to the power of n في اتنين
+
+705
+00:52:52,000 --> 00:52:56,900
+اتنين يعني to the power of one يعني معناه ذلك
+
+706
+00:52:56,900 --> 00:53:02,120
+اتنين to the power مجموحهم تمام
+
+707
+00:53:02,120 --> 00:53:05,260
+معناه ذلك ان هذي two to the power of n plus one هي
+
+708
+00:53:05,260 --> 00:53:08,700
+ان زائد واحد اقل من two to the power of n زائد
+
+709
+00:53:08,700 --> 00:53:14,810
+واحدأقل من two to four N زي الواحد تمام فإذا طول
+
+710
+00:53:14,810 --> 00:53:19,270
+ما هي P of N is true برضه P of N زي الواحد is true
+
+711
+00:53:19,270 --> 00:53:23,510
+is true هذه automatic ليه؟ معناته هذا الكلام للكل
+
+712
+00:53:23,510 --> 00:53:28,230
+صحيح نظرية هذه أو المعادلة ال relation هذه لكل
+
+713
+00:53:28,230 --> 00:53:33,510
+الأرقام صحيحة لكل ال natural number لأكبر من صفر
+
+714
+00:53:33,510 --> 00:53:35,630
+صحيحة تمام
+
+715
+00:53:44,900 --> 00:53:52,800
+تو سلسلة طيب ال second principle second principle
+
+716
+00:53:52,800 --> 00:53:58,320
+زي ما قولنا ايش بتقدر تكتب ان كل السابق is true
+
+717
+00:53:58,320 --> 00:54:01,840
+طيب شوية شوية خلينا ناخد إيش هي النظرية أصلا بدوية
+
+718
+00:54:01,840 --> 00:54:06,280
+show that every n أكبر من واحد لكل الأرقام اللي
+
+719
+00:54:06,280 --> 00:54:11,950
+أكبر من واحد can be written as a productP1 P2 to P
+
+720
+00:54:11,950 --> 00:54:17,370
+S of some series of S' number هذي قلناها لما
+
+721
+00:54:17,370 --> 00:54:20,970
+اتكلمنا عن الprimes لما اتكلمنا عن ال prime او ال
+
+722
+00:54:20,970 --> 00:54:26,870
+factorization قلنا ان كل رقم عبارة عن مضروب مجموعة
+
+723
+00:54:26,870 --> 00:54:30,410
+ارقام صحيح مجموعة الprimes عبارة عن مضروب مجموعة
+
+724
+00:54:30,410 --> 00:54:34,990
+الprimes فهو بده يدينا نثبتها لحظة بدنا هنا اعملية
+
+725
+00:54:34,990 --> 00:54:40,210
+اثبات لها okayعشان أثبتها، هنقول إن الكاشة الأولى
+
+726
+00:54:40,210 --> 00:54:45,010
+عندنا هنا كاشة الـP of كائنها الـof zero بتاعتنا
+
+727
+00:54:45,010 --> 00:54:49,110
+اللي هو أول element أكبر من واحد HP للإتنين فبدنا
+
+728
+00:54:49,110 --> 00:54:53,550
+نجرب عند الإتنين عند الإتنين N بتساوي اتنين لت ال
+
+729
+00:54:53,550 --> 00:54:57,850
+S تبعنا أو ال string تبعنا يحتوي على element واحد
+
+730
+00:54:57,850 --> 00:55:02,290
+اللي هو إيش ال prime إتنينفهو فعلا هي يقيم prime
+
+731
+00:55:02,290 --> 00:55:06,990
+فإذا ال string عبارة عن prime واحد فإذا يسوى واحد
+
+732
+00:55:06,990 --> 00:55:10,230
+ال cardinality بتبعته بتسوى واحد ال cardinality
+
+733
+00:55:10,230 --> 00:55:13,270
+بتسوى واحد okay هلوجد دخلنا في ال inductive step
+
+734
+00:55:13,270 --> 00:55:19,150
+في ال inductive step let n أكبر أو تسوى اتنين أكبر
+
+735
+00:55:19,150 --> 00:55:24,530
+من اتنين اتنين أثبتناها الأتنين أثبتت assumefor
+
+736
+00:55:24,530 --> 00:55:28,010
+all كأكبر
+
+737
+00:55:28,010 --> 00:55:34,210
+من اتنين و اقل من ن يعني كله نثبت لكله for all k
+
+738
+00:55:34,210 --> 00:55:41,610
+من اتنين to n P of k is true إذا فعلا is true عشان
+
+739
+00:55:41,610 --> 00:55:47,990
+هنا من ذهنك بنقول consider n plus واحد في الحالة
+
+740
+00:55:47,990 --> 00:55:55,410
+التاعتنا okay هدول is trueتمام؟ هدول بقدروا أقول
+
+741
+00:55:55,410 --> 00:56:00,830
+إن هم مثبتين بس لبعد هم مش عارف صح؟ يعني عند n
+
+742
+00:56:00,830 --> 00:56:04,330
+plus واحد أنا مش عارف إحنا بدنا نثبتها هي صح ولا
+
+743
+00:56:04,330 --> 00:56:11,070
+غلط لعند n كل السابق مظبوط مدام أنا بتكلم عن اتنين
+
+744
+00:56:11,070 --> 00:56:14,190
+من اتنين فهنا ال K أول K ممكن أتعامل معاها حاليا
+
+745
+00:56:14,190 --> 00:56:20,250
+تكون اتنين نفسها الاتنين نفسها صحيحة لو تكلمنا عن
+
+746
+00:56:20,250 --> 00:56:24,980
+n بتساوي اتنين طب أكتر من اتنينمش عارف فبدنا نثبت
+
+747
+00:56:24,980 --> 00:56:29,200
+هالوجهة إذا كان فعلا عن n زائد واحد فهنا هنفرض إنه
+
+748
+00:56:29,200 --> 00:56:32,360
+أنا بدي أتعامل مع n زائد واحد والله إذا هي prime
+
+749
+00:56:32,360 --> 00:56:37,980
+إذا هي نفسها prime معناته ال string تبعها بواحد هي
+
+750
+00:56:37,980 --> 00:56:42,690
+نفسها فده is a primeهذا is a prime ممكن تتحقق مع
+
+751
+00:56:42,690 --> 00:56:47,190
+بعض elements أو مع بعض numbers بس مش الكل مش الكل
+
+752
+00:56:47,190 --> 00:56:50,070
+فإذا في شرط تاني لازم أخد بالي منه هنا if prime
+
+753
+00:56:50,070 --> 00:56:55,330
+نتكذا okay مش مشكلة ولكن else if زائد واحد مش
+
+754
+00:56:55,330 --> 00:57:00,620
+prime مش معناته مش prime معناته عبارة عن ايهزائد B
+
+755
+00:57:00,620 --> 00:57:08,820
+مضروبة في B صح composite number مضروبة في B مضروبة
+
+756
+00:57:08,820 --> 00:57:10,820
+في B مضروبة في B مضروبة في B مضروبة في B مضروبة في
+
+757
+00:57:10,820 --> 00:57:13,620
+B مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+758
+00:57:13,620 --> 00:57:13,620
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+759
+00:57:13,620 --> 00:57:16,180
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+760
+00:57:16,180 --> 00:57:16,240
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+761
+00:57:16,240 --> 00:57:16,240
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+762
+00:57:16,240 --> 00:57:16,480
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+763
+00:57:16,480 --> 00:57:17,400
+مضروبة في B مضروبة في B مضروبة في B مضروبة في B
+
+764
+00:57:17,400 --> 00:57:18,600
+مضروبة في B
+
+765
+00:57:22,630 --> 00:57:28,030
+لأ هو composite أو مؤلف من رقمين مضربين في بعض،
+
+766
+00:57:28,030 --> 00:57:35,130
+فليكن A هتكون طبيعي أقل من N صح؟
+
+767
+00:57:35,130 --> 00:57:38,250
+أكيد هتكون أقل من N، أنا بتكلم عن N زائد واحد، و
+
+768
+00:57:38,250 --> 00:57:42,090
+متألف من رقمين مضربين في بعض، فالرقمين المضربين في
+
+769
+00:57:42,090 --> 00:57:46,640
+بعض، كل واحد منهم أقلمن n زائد واحد اكيد اكيد كل
+
+770
+00:57:46,640 --> 00:57:49,920
+واحد منهم هتكون اقل من n زائد واحد فإذا a هتكون
+
+771
+00:57:49,920 --> 00:57:54,320
+اكبر من واحد و اقل من او تسوى n اللي هي اقل من n
+
+772
+00:57:54,320 --> 00:57:59,840
+زائد واحد طيب بي نفس الكلام الرقمين هدول اللي
+
+773
+00:57:59,840 --> 00:58:05,870
+لايمكن يكونوا بيسووا n إذا ماكنتش prime صح؟إذا لم
+
+774
+00:58:05,870 --> 00:58:11,010
+تكن الـ prime هل ممكن a تسوى n زائد واحد؟ لأ ولا
+
+775
+00:58:11,010 --> 00:58:13,550
+البيئة ممكن تكون بتسوى n زائد واحد لازم يكون قيمهم
+
+776
+00:58:13,550 --> 00:58:17,970
+أقل منها أقل منها إذا واحدة منهم تسوى n زائد واحد
+
+777
+00:58:17,970 --> 00:58:22,610
+معناته هي prime معناته هي أصلا prime طيب، لا تساوي
+
+778
+00:58:22,610 --> 00:58:29,750
+معناته أقل، معنى ذلك وبناء على ال condition هذا إن
+
+779
+00:58:29,750 --> 00:58:35,740
+كل اللي أقل is true فإذا ais it true؟ هي متكونة من
+
+780
+00:58:35,740 --> 00:58:41,000
+مجموعة الprimes و B برضه أقل فإذا is it true؟ هي
+
+781
+00:58:41,000 --> 00:58:44,720
+متكونة برضه من مجموعة الprimes هي متكونة أصلا من
+
+782
+00:58:44,720 --> 00:58:48,560
+مجموعة الprimes فمعنا ذلك بقدر أقول أن ال A متكونة
+
+783
+00:58:48,560 --> 00:58:54,160
+أساسا من مجموعة الprimes عددهم T فال string تبعنا
+
+784
+00:58:54,160 --> 00:58:59,770
+T و A مضروم عبارة عنprime أول في تاني في تالت في
+
+785
+00:58:59,770 --> 00:59:04,630
+prime رقم T ال B نفس الكلام بيعتبر أنها أقل من N
+
+786
+00:59:04,630 --> 00:59:08,930
+زائد واحد فهي مثبتة مسبقا طب اللحظة أنتوا كيف
+
+787
+00:59:08,930 --> 00:59:13,790
+أثبتت أساسا من الأول أنتوا برضه هتسأله طب أساسا
+
+788
+00:59:13,790 --> 00:59:19,310
+ايه مين جل من أنها مجموعة الprimes لأن هي نفسها لو
+
+789
+00:59:19,310 --> 00:59:22,430
+اتعاملت معها أنها N زائد واحد
+
+790
+00:59:25,050 --> 00:59:29,690
+برضه نفس الكلام هقول إن هي مضروب مجموعة أرقام هقول
+
+791
+00:59:29,690 --> 00:59:35,670
+إن هي برضه مضروب مجموعة أرقام أقل منها طيب مجموعة
+
+792
+00:59:35,670 --> 00:59:41,090
+الأرقام اللي أقل منها برضه إما إن هي prime نفس ال
+
+793
+00:59:41,090 --> 00:59:43,970
+condition لاحظوا إن ال condition بتكرر لاحظوا إن
+
+794
+00:59:43,970 --> 00:59:48,790
+هنا ال condition بتكرر أو رقمين أقل منها لعدم أصل
+
+795
+00:59:48,790 --> 00:59:54,260
+لمين لل initialلعندي نصل ال initial condition
+
+796
+00:59:54,260 --> 00:59:58,120
+تبعنا أو ال base case بتاعتنا نصل ال base case
+
+797
+00:59:58,120 --> 01:00:04,300
+بتاعتنا لاحظتوا كده؟ فإذن واضح إنه هنا أنا ما
+
+798
+01:00:04,300 --> 01:00:08,480
+أقفلتش اللي أقل منها لأ بالعكس و مثبتين اللي أقل
+
+799
+01:00:08,480 --> 01:00:13,360
+منها نتيجة إن هم كانوا قبلها n زائد واحدنتيجة ان
+
+800
+01:00:13,360 --> 01:00:17,380
+هما كانوا أصلا قبلها n زائد واحد صح؟ عشان أصل ل n
+
+801
+01:00:17,380 --> 01:00:20,620
+زائد واحد هنا و أقول ان كل اللي جابلها مثبت هم
+
+802
+01:00:20,620 --> 01:00:24,300
+أساسا كل اللي جابلها ماتمش إثباتهم إلا لأنه كانوا
+
+803
+01:00:24,300 --> 01:00:30,040
+عند n زائد واحد فعند n زائد واحد أقل الواحدة ممكنة
+
+804
+01:00:30,040 --> 01:00:35,520
+عند التلاتة مثلا إبراهيم عند الأربعة عند الأربعة
+
+805
+01:00:35,520 --> 01:00:42,130
+اتنين في اتنين فهي مثبتة مسبقا لاتنين هيهالاحظته؟
+
+806
+01:00:42,130 --> 01:00:44,850
+فالسلسلة ماشية، مش معناه أن أنا بدأت من n زائد
+
+807
+01:00:44,850 --> 01:00:48,310
+واحد، معناته أنا انسيت اللي جابلها، لأ، المطلوب أن
+
+808
+01:00:48,310 --> 01:00:52,450
+احنا هنا كله، قاعدين نتكلم عن الكل، فكل واحدة جاية
+
+809
+01:00:52,450 --> 01:00:56,690
+من مضروب رقمين، الرقمين هدولة جابلها، بس هم
+
+810
+01:00:56,690 --> 01:01:00,910
+مثبتين، لأنه كانوا جابلها n زائد واحد، واضحة؟
+
+811
+01:01:00,910 --> 01:01:06,550
+واضحة، كويسةفالقصد هنا أن كل واحدة منهم أثبتت أنها
+
+812
+01:01:06,550 --> 01:01:09,990
+فعلا مجموعة براينز هذه مجموعة براينز وهذه مجموعة
+
+813
+01:01:09,990 --> 01:01:16,610
+براينز فمعنى ذلك أن N زائد واحد عبارة عن A في B
+
+814
+01:01:16,610 --> 01:01:22,950
+معناته ال B كلها في ال Q كلها ال B كلها في ال Q
+
+815
+01:01:22,950 --> 01:01:30,160
+كلها فستجد أنها بيز في كيوز جدش عددهم T زائد Uفإذن
+
+816
+01:01:30,160 --> 01:01:36,060
+عبارة عن sequence of primes T plus U'
+
+817
+01:01:38,360 --> 01:01:43,200
+تمام المرة الجاية بناخد ال example اللي وراها عشان
+
+818
+01:01:43,200 --> 01:01:45,300
+الأمور توضح هو ضايقنا ال slide هذا ال example
+
+819
+01:01:45,300 --> 01:01:48,880
+التاني بناخده المرة الجاية بالعمد عشان نرجع
+
+820
+01:01:48,880 --> 01:01:51,960
+للموضوع كمان مرة نوضحكوا يا عزيزي يعطيكوا الصحة و
+
+821
+01:01:51,960 --> 01:01:52,700
+رحة و برك الله فيكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..13b179557eb9596deeadfffba55cbf8e868d47f4
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA.srt
@@ -0,0 +1,3039 @@
+1
+00:00:21,090 --> 00:00:22,950
+بسم الله الرحمن الرحيم الصلاة والسلام عليكم ورحمة
+
+2
+00:00:22,950 --> 00:00:25,290
+الله وبركاته يا أبو حميد وسيدنا محمد وعلى أهله
+
+3
+00:00:25,290 --> 00:00:30,070
+وصحابه أجمعين. نبدأ اليوم محاضرتنا من الـ graph اللي
+
+4
+00:00:30,070 --> 00:00:32,570
+بدأنا المرة اللي فاتت، والمرة اللي فاتت أخذنا
+
+5
+00:00:32,570 --> 00:00:37,010
+مجموعة أنواع، هيك في عجلة يعني، بس أخذنا إيش يعني ..
+
+6
+00:00:37,010 --> 00:00:40,610
+لما نتكلم عن undirected graph أو simple graph، إيش
+
+7
+00:00:40,610 --> 00:00:44,730
+معناه؟ اتكلمنا عن الـ multiple أو الـ
+
+8
+00:00:44,730 --> 00:00:47,670
+multigraph، اتكلمنا عن الـ pseudograph، واتكلمنا عن
+
+9
+00:00:47,670 --> 00:00:51,910
+الـ directed graph، والـ multi أو الـ directed
+
+10
+00:00:51,910 --> 00:00:55,370
+multigraph. اتكلمنا عن الخمسة في واحد، وللمرة اللي
+
+11
+00:00:55,370 --> 00:00:59,370
+فاتت اتكلمنا ووقفنا عندهم لعند ما وصلنا لـ section
+
+12
+00:00:59,370 --> 00:01:03,130
+عشرة اثنين، وقلنا إن المرة الجاية هناخدها، هنتكلم
+
+13
+00:01:03,130 --> 00:01:07,250
+عن .. عن الـ شوية terminology خاصة بالـ graphs
+
+14
+00:01:07,250 --> 00:01:10,290
+خاصة بإيش؟ بالـ graphs. الـ graphs هذه، هنتكلم عن الـ
+
+15
+00:01:10,290 --> 00:01:14,570
+adjacent، هنتكلم عن الـ connects، هنتكلم عن الـ end
+
+16
+00:01:14,570 --> 00:01:18,450
+points، الـ degree مهم جدا، إيش يعني degree، الـ initial
+
+17
+00:01:18,450 --> 00:01:21,670
+والـ terminal، الـ in degree، الـ out degree، الـ
+
+18
+00:01:21,670 --> 00:01:24,730
+complete. هنا من الـ complete ولتحت هنتكلم عن
+
+19
+00:01:24,730 --> 00:01:29,210
+مجموعة أنواع عن أنواع من الـ graphs، الـ cycles، الـ
+
+20
+00:01:29,210 --> 00:01:32,770
+wheels، الـ cubes
+
+21
+00:01:33,570 --> 00:01:36,770
+الـ bipartite، وبعدين هنتكلم عن two properties هيك
+
+22
+00:01:36,770 --> 00:01:39,970
+سريعين، اللي هي الـ subgraph، إيش يعني subgraph، و
+
+23
+00:01:39,970 --> 00:01:43,430
+إيش يعني union، كيف نعمل union للـ graphs مع بعض، و
+
+24
+00:01:43,430 --> 00:01:46,330
+بعدين بنشوف إيش بيكون باقي علينا، لو بيكون باقي
+
+25
+00:01:46,330 --> 00:01:48,910
+علينا، يمكن الـ isomorphism، وعملية الـ
+
+26
+00:01:48,910 --> 00:01:54,490
+representation للـ graphs. نبدأ بالـ adjacency أو
+
+27
+00:01:54,490 --> 00:02:01,470
+المجاورة. المجاورة لما يكون في عندنا two nodes، و
+
+28
+00:02:01,470 --> 00:02:06,610
+الاتنين هدول متصلين مع بعض U و V، فهم متجاورين.
+
+29
+00:02:06,610 --> 00:02:11,090
+بعدين في طريق بينهم أو في link بينهم، في edge بينهم.
+
+30
+00:02:11,090 --> 00:02:15,630
+فهم بنسميهم متجاورين، فـ U و V are adjacent، أو
+
+31
+00:02:15,630 --> 00:02:21,760
+neighbors، جيران، أو connected، متصلين، في توصيل بينهم.
+
+32
+00:02:21,760 --> 00:02:25,000
+يوجد توصيل بينهم. الـ edge E is incident with
+
+33
+00:02:25,000 --> 00:02:30,440
+vertices U و V، وماحددتش هي incident من مين لأنه
+
+34
+00:02:30,440 --> 00:02:36,780
+بشتغل هنا undirected، ما فيش اتجاه، فـ from U to V بمشي
+
+35
+00:02:36,780 --> 00:02:41,820
+الحال، from V to U برضه بمشي،  الحال أنا مش محدد
+
+36
+00:02:41,820 --> 00:02:45,120
+مين الاتجاه، مش محددين اتجاهنا، ففي الحالة هذه
+
+37
+00:02:45,120 --> 00:02:50,580
+بنسميها incident with vertices u and v. هذه هذه بمشي
+
+38
+00:02:50,580 --> 00:02:55,560
+الحال،  عشان إن هي undirected، الـ connect u و v هي
+
+39
+00:02:55,560 --> 00:03:01,390
+توصل u بـ v، صحيح ما حددناش لسه اتجاهها. الـ vertices U
+
+40
+00:03:01,390 --> 00:03:04,330
+vertices اللي هي جمع الـ vertex. الـ vertex اللي
+
+41
+00:03:04,330 --> 00:03:06,350
+قلنا المرة اللي فاتت، اللي هي قمة، أو بمعنى node
+
+42
+00:03:06,350 --> 00:03:10,510
+المقصود فيها الـ node تبعتنا هذه، فهذه vertex V و
+
+43
+00:03:10,510 --> 00:03:15,170
+vertex U. طيب الـ vertices U و V are end points of
+
+44
+00:03:15,170 --> 00:03:21,990
+edge E، هي النهايات للـ link E هذا، للـ link E هذه
+
+45
+00:03:21,990 --> 00:03:25,250
+النهاية، وهذه النهاية، اللي هم أطرافه، يعني الأطراف
+
+46
+00:03:26,040 --> 00:03:31,480
+للـ link. من هنا بدنا نتكلم عن الـ degree، الـ degree
+
+47
+00:03:31,480 --> 00:03:36,740
+لكل vertex لحالها. كل vertex فيه لها degree. طيب الـ
+
+48
+00:03:36,740 --> 00:03:41,220
+total أو الـ graph كله على بعضه فيه له برضه degree.
+
+49
+00:03:41,220 --> 00:03:44,020
+بدنا نحسبها. degree هذا إيش يعني degree؟ الـ degree
+
+50
+00:03:44,020 --> 00:03:49,060
+بمعنى إنه كم edge connected لـ الـ vertex، فالـ
+
+51
+00:03:49,060 --> 00:03:52,680
+vertex هذه هنا connected بـ edge واحدة، معناه ذلك إن
+
+52
+00:03:52,680 --> 00:03:55,180
+الـ degree بتاعتها واحدة، معناه ذلك إن الـ degree
+
+53
+00:03:55,180 --> 00:04:00,320
+بتاعتها بواحد. نفترض إنه في إلها self loop، الـ self
+
+54
+00:04:00,320 --> 00:04:04,880
+loop بتحسب مرتين، بتحسب مرتين. أنا ماليش علاقة كيف
+
+55
+00:04:04,880 --> 00:04:08,700
+شكلها هنا، أنا بالنسبالي وأنا داخل الـ U، كم طريق
+
+56
+00:04:08,700 --> 00:04:13,840
+بقدر أطلع منه من الـ U؟ في عندي طريق اتنين، تلاتة، فالـ
+
+57
+00:04:13,840 --> 00:04:18,120
+degree هنا صارت تلاتة، فإذا الـ لما بتكلم هنا عن
+
+58
+00:04:18,120 --> 00:04:23,140
+الـ self loop تنعد مرتين، تنحسب مرتين، ليش؟ لأن في
+
+59
+00:04:23,140 --> 00:04:27,900
+إلها طريقين، واحد، اتنين، فهنا الـ degree هذه، degree u
+
+60
+00:04:27,900 --> 00:04:34,920
+هتساوي تلاتة. طيب degree v هتساوي
+
+61
+00:04:34,920 --> 00:04:39,580
+واحد، هتساوي في الحالة هذه واحد. طيب لو في عندنا
+
+62
+00:04:39,580 --> 00:04:47,350
+vertex، الـ degree بتاعتها zero بهذا الشكل، وبس zero.
+
+63
+00:04:47,350 --> 00:04:51,370
+معناته ما فيش أي طريق حولها، city، الـ city هذه نائية.
+
+64
+00:04:51,370 --> 00:04:54,870
+بلد نائية، مالهاش أي طريق عليها، ففي الحالة هذه
+
+65
+00:04:54,870 --> 00:05:00,270
+بنسميها isolated، منعزلة، معزولة تماما، isolated في
+
+66
+00:05:00,270 --> 00:05:04,210
+الحالات. طيب لما نكونها degree واحد بهذا الشكل،
+
+67
+00:05:04,210 --> 00:05:11,330
+بنسميها pendant، أو معلقة، بالضبط عامل زي معلقة بخيط.
+
+68
+00:05:11,330 --> 00:05:14,630
+يعني مثلا مربوطة بخيط، على جد، خيط، على جد، طريق واحد.
+
+69
+00:05:14,630 --> 00:05:19,430
+فهذا اسمها dependent. في الحالة اللي بيكون فيها الـ
+
+70
+00:05:19,430 --> 00:05:24,390
+degree بتاعتها واحد، okay. الـ handshaking theorem، الـ
+
+71
+00:05:24,390 --> 00:05:28,070
+handshaking theorem، فعليا هي نظرية بنستخدمها عشان
+
+72
+00:05:28,070 --> 00:05:31,510
+نحسب فيها الـ degrees، نوجد الـ degrees للرسم تبعنا
+
+73
+00:05:31,510 --> 00:05:34,570
+كله على بعضه. فالـ degree في الحالة اللي عندنا هنا
+
+74
+00:05:34,570 --> 00:05:41,070
+summation degree of V، و V هذه belong to capital V.
+
+75
+00:05:41,070 --> 00:05:45,450
+capital V هي set of vertices، set of vertices، أو
+
+76
+00:05:45,450 --> 00:05:50,170
+set of nodes، set of nodes، بمعنى كل الـ nodes تبعتنا.
+
+77
+00:05:50,170 --> 00:05:54,030
+معنى ذلك إن أنا بتكلم عن الـ graph كله، كل graph على
+
+78
+00:05:54,030 --> 00:05:57,010
+بعضه، ومجموع الـ degree تبعته، الـ degree تبعته عبارة
+
+79
+00:05:57,010 --> 00:05:59,290
+عن الـ degree للـ node الأولى، زي الـ degree للـ node
+
+80
+00:05:59,290 --> 00:06:01,210
+التانية، لو في node تالتة، وزيادة الـ degree للـ node
+
+81
+00:06:01,210 --> 00:06:04,690
+التالتة، زيادة الرابعة، لما نخلص كل الـ nodes اللي
+
+82
+00:06:04,690 --> 00:06:08,710
+موجودة للي graph، للي graph طبعا، فهنا الـ summation
+
+83
+00:06:08,710 --> 00:06:13,970
+في الحالة دي هيساوي 2E، ليش اتنين؟ لأنه كل E أنا
+
+84
+00:06:13,970 --> 00:06:18,270
+حسبته مرتين، مرة بالنسبة للـ node اللي في أوله، ومرة
+
+85
+00:06:18,270 --> 00:06:22,110
+بالنسبة للـ node اللي في آخره، مظبوط. لحظوا هنا أنا
+
+86
+00:06:22,110 --> 00:06:26,260
+حسبت degree واحد، ليش واحد؟ من الـ E. طيب هنا لما حسبت
+
+87
+00:06:26,260 --> 00:06:29,140
+تلاتة، واحدة منهم كانت للـ E، يعني الـ E هتنحسب مرتين.
+
+88
+00:06:29,140 --> 00:06:33,040
+عشان هيك فعلا الـ degree للكل على بعضه هتكون مرة
+
+89
+00:06:33,040 --> 00:06:35,920
+اجت من هنا، ومرة اجت من هنا، فالـ E مرتين انحسبت.
+
+90
+00:06:35,920 --> 00:06:41,750
+فعشان هيك بنقول 2 في E، اللي هو جدّاش عدد الـ
+
+91
+00:06:41,750 --> 00:06:46,250
+edges اللي موجودة، على اعتبار إن الـ E هنا هي الـ set
+
+92
+00:06:46,250 --> 00:06:50,430
+of edges، لما بأخذها cardinality، معناه نوجد عدد الـ
+
+93
+00:06:50,430 --> 00:06:55,950
+edges اللي موجودة، في اتنين. عرفنا ليش في اتنين؟ لأن
+
+94
+00:06:55,950 --> 00:07:00,730
+فعليا الـ node اللي في الأول انحسب بالنسبالها، والـ
+
+95
+00:07:00,730 --> 00:07:03,030
+node اللي في الآخر برضه انحسب بالنسبالها. طبعا هنا
+
+96
+00:07:03,030 --> 00:07:05,750
+ما فيش لا أول ولا آخر، يعني الصراحة، بس أنا بقول لكم
+
+97
+00:07:05,750 --> 00:07:08,350
+في الأول وفي الآخر، بس لأن هو undirected، مش معروف
+
+98
+00:07:08,350 --> 00:07:11,470
+مين الأول ومين الآخر أساسا، مين الأولى ومين التانية،
+
+99
+00:07:11,470 --> 00:07:13,890
+مش معروف. المهم إن هي connected between two
+
+100
+00:07:13,890 --> 00:07:19,170
+vertices، وبس. في الآخر هيساوي 2 في cardinality للـ
+
+101
+00:07:19,170 --> 00:07:24,870
+set E، بمعنى عدد الـ edges تبعتكم، عدد الـ edges في 2
+
+102
+00:07:24,870 --> 00:07:30,090
+يعطينا الـ degree لكل الرسم على بعضه، اوكي. من هنا إذا
+
+103
+00:07:30,090 --> 00:07:33,870
+كانت عدد الـ edges تبعتكم فردي، الـ degree ده منزوجي،
+
+104
+00:07:34,970 --> 00:07:37,670
+by logic، ما هي .. إيش ما يكون .. إيش ما تكون عدد
+
+105
+00:07:37,670 --> 00:07:40,730
+الـ الـ lectures تبعتكم، الـ degree للـ graph كله
+
+106
+00:07:40,730 --> 00:07:43,690
+على بعضه دائما زوجي، لأنها هي 2 في some integer.
+
+107
+00:07:43,690 --> 00:07:48,510
+2 في some integer، فدائما هتكون زوجي، هي الـ
+
+108
+00:07:48,510 --> 00:07:52,110
+النتيجة من النظرية. طيب كل هذا الكلام كان إيه؟
+
+109
+00:07:52,110 --> 00:07:56,290
+undirected. لما نيجي على الـ directed، الأمور بتختلف
+
+110
+00:07:56,290 --> 00:07:59,130
+شوية، بيصير المسميات، حتى الـ terminology بتاعتنا
+
+111
+00:07:59,130 --> 00:08:02,970
+هتختلف، هتختلف، لأنه بدنا نحددها logic من البداية، ومن
+
+112
+00:08:02,970 --> 00:08:07,680
+النهاية، في شغل، من البداية ومن النهاية، هنا
+
+113
+00:08:07,680 --> 00:08:11,000
+حاطين relation لمين؟ أو عاملين mapping لمين؟ لـ U و V.
+
+114
+00:08:11,000 --> 00:08:19,620
+U و V، معناته الـ link جاي من U لـ V بهذا الشكل. طيب
+
+115
+00:08:19,620 --> 00:08:26,590
+في الحالة دي، U is adjacent to V، to V، أنا رايح to V.
+
+116
+00:08:26,590 --> 00:08:32,830
+فإذا V هي النهاية، طبعتي، طيب إذا بدأ، أنسبها للـ V، V
+
+117
+00:08:32,830 --> 00:08:39,370
+اسمها adjacent from U. بعرف من المصطلحين دول، to و
+
+118
+00:08:39,370 --> 00:08:42,170
+from، إن هذا directed، بنعرف إن إحنا بنتكلم عن
+
+119
+00:08:42,170 --> 00:08:47,090
+directed graph، E graph، كويس، أو directed link، أو
+
+120
+00:08:47,090 --> 00:08:53,990
+directed link، أو edge، كويس. E هيها، E comes from U،
+
+121
+00:08:53,990 --> 00:09:02,210
+هيها بادية من U، طيب، أو goes to V، فالمصطلحات هذه في
+
+122
+00:09:02,210 --> 00:09:05,530
+الـ undirected بنقولهاش connected to كذا، وخلاص. هي
+
+123
+00:09:05,530 --> 00:09:09,210
+A و B connected together، وخلصنا. ممكن نقول are
+
+124
+00:09:09,210 --> 00:09:11,710
+connected، U و V are connected، و stop، خلاص خلصنا.
+
+125
+00:09:11,710 --> 00:09:15,590
+متواصلين، مين قبل مين، مين بعد مين، ما حدش بعرف، بس
+
+126
+00:09:15,590 --> 00:09:19,070
+هنا لأ، هنا بدنا نكون دقيقين، بدنا نعرف بالضبط E،
+
+127
+00:09:19,070 --> 00:09:24,690
+الـ E هذه من وين بادية، من وين منتهية. E connects U
+
+128
+00:09:24,690 --> 00:09:31,610
+to V، هي مش U and V، هناك سميناها U and V، بتوصل U
+
+129
+00:09:31,610 --> 00:09:38,130
+و V، هنا لأ، U to V، بتوصل إلى U، رايح لـ V، أو E
+
+130
+00:09:38,130 --> 00:09:45,650
+goes from U، رايح من U لـ V، فالمصطلحات كلمتين، تلاتة،
+
+131
+00:09:45,650 --> 00:09:49,670
+بيميزوه، لأن أنا بتكلم عن directed. طيب الـ initial
+
+132
+00:09:49,670 --> 00:09:52,870
+vertex of E، الـ initial vertex، الـ الـ الـ
+
+133
+00:09:52,870 --> 00:09:55,570
+vertex اللي بادية منها، الـ initial value تبعتك ..
+
+134
+00:09:55,570 --> 00:10:01,830
+تبعتك هي الـ U، فإذن is U، طيب أو الـ terminal، الـ
+
+135
+00:10:01,830 --> 00:10:05,170
+terminal، النهاية، النهاية الـ الـ الـ أو
+
+136
+00:10:05,170 --> 00:10:07,870
+النهاية، الطرفية تبعتكم، الطرف النهائي تبعتكم، اللي
+
+137
+00:10:07,870 --> 00:10:13,080
+هو V، فهذا هيكون الـ vertex، أو الـ terminal vertex للـ
+
+138
+00:10:13,080 --> 00:10:22,200
+E، هي الـ V. طيب في الـ directed degree، عشان نحسب الـ
+
+139
+00:10:22,200 --> 00:10:26,400
+degree في الحالة هذه، بقدرش أقول إن هي خلاص، في
+
+140
+00:10:26,400 --> 00:10:29,440
+الحالة اللي زي هذه، هي هي الـ connection، وخلاص، و
+
+141
+00:10:29,440 --> 00:10:32,660
+نوجدش عدد اللي طالع لأ، إنتوا هنا ديروا بالكم، وفي in
+
+142
+00:10:32,660 --> 00:10:37,720
+وفي out، معنى ذلك، لأن في link هيكون طالع من الـ
+
+143
+00:10:37,720 --> 00:10:41,270
+vertex، وفي link داخل الـ vertex. في الحلقة دي، حاسب
+
+144
+00:10:41,270 --> 00:10:48,930
+في عندي in degree، وفي out degree، in degree، و out
+
+145
+00:10:48,930 --> 00:10:54,330
+degree. هذه الـ in degree بنسميها degree سالب، و
+
+146
+00:10:54,330 --> 00:11:02,950
+degree موجب، موجب. فإذا أنا بتكلم، طالع منها موجب،
+
+147
+00:11:02,950 --> 00:11:05,830
+معناته طالع من الـ link اللي طالع من مين؟ من الـ
+
+148
+00:11:05,830 --> 00:11:10,490
+vertex. سالب لأ، الـ link اللي داخل للـ vertex، داخل للـ
+
+149
+00:11:10,490 --> 00:11:14,550
+vertex. خلينا نأخذ، طبعا في النهاية الـ degree للـ
+
+150
+00:11:14,550 --> 00:11:17,530
+total كله على بعضه، اللي هو مجموع التنتين، اللي هو
+
+151
+00:11:17,530 --> 00:11:20,850
+مجموع in degree، و out degree، أو الـ in degree، والـ
+
+152
+00:11:20,850 --> 00:11:23,870
+out degree، كويسة. لو نمسكهم للـ example اللي إحنا
+
+153
+00:11:23,870 --> 00:11:32,650
+حاطينه هنا، هنا الـ out degree جدّاش of v يساوي zero.
+
+154
+00:11:32,650 --> 00:11:34,310
+صحيح، الـ in degree
+
+155
+00:11:37,700 --> 00:11:46,240
+يساوي واحد. طيب هنا الـ out degree هيساوي اتنين، طيب الـ
+
+156
+00:11:46,240 --> 00:11:54,100
+in degree واحد، صحيح. المجموع عند هنا تلاتة، المجموع
+
+157
+00:11:54,100 --> 00:11:56,680
+عند هنا واحد، المجموع عند هنا واحد، وعندنا تلاتة.
+
+158
+00:11:56,680 --> 00:12:01,700
+طيب الـ degree totally هنا للـ اتنين، اتنين، والـ in
+
+159
+00:12:01,700 --> 00:12:04,880
+degree، الـ out degree اتنين، والـ in degree اتنين.
+
+160
+00:12:04,880 --> 00:12:10,990
+لازم يساوي بعض، لأن كل edge هي in بالنسبة لواحد أكيد،
+
+161
+00:12:10,990 --> 00:12:15,890
+out بالنسبة للتاني، مدام طالعة من U رايحة لـ V، فهي
+
+162
+00:12:15,890 --> 00:12:20,230
+in لواحد منهم، و out للتاني. هتنحسب مرتين، إحنا زي
+
+163
+00:12:20,230 --> 00:12:23,250
+الـ مرة اللي فاتت قلنا هتنحسب مرتين، بس هنا هنميزهم،
+
+164
+00:12:23,250 --> 00:12:27,990
+إن هي مرة هتكون in، ومرة هتكون out، فمعنى ذلك إن
+
+165
+00:12:27,990 --> 00:12:31,890
+مجموع الـ in لازم يطلع بيساوي مجموع الـ out للـ graph
+
+166
+00:12:31,890 --> 00:12:35,710
+كله على بعضه، صح؟ biological، منطقية، لازم تطلع هنا،
+
+167
+00:12:35,710 --> 00:12:39,750
+okay، ما فيش link بالنسبالك، وهيكون طالع هيك، وسايب
+
+168
+00:12:39,750 --> 00:12:44,690
+هذا، ما بنحسبش
+
+223
+00:16:29,920 --> 00:16:33,660
+متصلة مع الثلاثة اللي ضايقينها كل point هتكون متصلة
+
+224
+00:16:33,660 --> 00:16:37,870
+مع الثلاثة اللي ضايقينهم أمام أربعة كل واحدة هتكون
+
+225
+00:16:37,870 --> 00:16:39,830
+متصلة مع الثلاثة اللي ضايلة فكل واحدة degree
+
+226
+00:16:39,830 --> 00:16:43,770
+بتاعتها ثلاثة كل واحدة degree بتاعتها ثلاثة، K خمسة
+
+227
+00:16:43,770 --> 00:16:46,830
+برضه خمسة nodes، معناه ذلك أنه كل node degree
+
+228
+00:16:46,830 --> 00:16:50,030
+بتاعتها أربعة، تمام، أربعة، والكلام نفس الكلام
+
+229
+00:16:50,030 --> 00:16:55,270
+بنكمله طيب في الـ K أو الـ complete graphs، جدش عدد
+
+230
+00:16:55,270 --> 00:16:59,790
+الـ edges بتاعتنا، جدش عدد الـ edges اللي هنا اللي
+
+231
+00:16:59,790 --> 00:17:04,090
+موجودين عندنا هيكونوا بساوة summation from 1 to n
+
+232
+00:17:04,090 --> 00:17:09,590
+-1 للـ I، وهذا طبعا بنحلها باستخدام الـ Euler theorem
+
+233
+00:17:09,590 --> 00:17:15,090
+بتاعة Euler theorem، بس ناخد بأنه n to minus one n
+
+234
+00:17:15,090 --> 00:17:20,850
+minus one، القانون تبعنا لما كان summation to n كان
+
+235
+00:17:20,850 --> 00:17:27,940
+بساوة n في n plus 1 على 2، طب هنا minus one بصير هنا
+
+236
+00:17:27,940 --> 00:17:32,000
+minus one وهنا minus one، هذه صارت minus one هنا
+
+237
+00:17:32,000 --> 00:17:40,880
+وهذه صارت one، zero صارت n في n minus one، الـ
+
+238
+00:17:40,880 --> 00:17:45,520
+degree
+
+239
+00:17:45,520 --> 00:17:50,260
+لكل واحدة منهم برضه سهل، جدش عددهم نقص واحد، الـ
+
+240
+00:17:50,260 --> 00:17:53,580
+degree للنقطة هذه، عددهم أربعة، نقص واحد، فإذا الـ
+
+241
+00:17:53,580 --> 00:17:55,500
+degree ثلاثة، هي ثلاثة، والـ degree هنا ثلاثة، والـ
+
+242
+00:17:55,500 --> 00:17:59,420
+degree هنا ثلاثة، الـ degree لكل واحدة منهم ثلاثة
+
+243
+00:17:59,420 --> 00:18:03,920
+طيب مجموعهم اثنا عشر، اثنا عشر، من وين جبناها اثنا عشر؟ ثلاثة
+
+244
+00:18:03,920 --> 00:18:08,000
+في أربعة، ثلاثة في أربعة، جبناها من الـ edges، كم يمكن
+
+245
+00:18:08,000 --> 00:18:12,620
+نجيبها من الـ edges؟ في اثنين صحيح، مش احنا قلنا أن الـ
+
+246
+00:18:12,620 --> 00:18:16,820
+degree للكل بيساوي اثنين في absolute E، برضه هنا
+
+247
+00:18:16,820 --> 00:18:19,820
+أعطيناكوا إياها، الـ edges، معناه ذلك مباشرة من هنا
+
+248
+00:18:19,820 --> 00:18:22,960
+بتقدروا تجيبوا عدد الـ degrees، الـ total من هنا
+
+249
+00:18:22,960 --> 00:18:27,080
+مباشرة، من خلاص ممكن عدد number of nodes مضروب بالـ
+
+250
+00:18:27,080 --> 00:18:30,120
+… بالظبط، ممكن تعملوا بنفس الفكرة عساس أن كل واحدة
+
+251
+00:18:30,120 --> 00:18:36,760
+إلها three degrees، three، في عددهم بالظبط، Okay، الـ
+
+252
+00:18:36,760 --> 00:18:41,360
+cycles، هذه واحدة من أنواع الـ topologies اللي ممكن
+
+253
+00:18:41,360 --> 00:18:46,460
+تمر عليكم في الشبكات، للـ ring connection، في الـ ring
+
+254
+00:18:46,460 --> 00:18:50,660
+connection، بتتوصل عادة بهذا الشكل، الـ BC بتكون كل
+
+255
+00:18:50,660 --> 00:18:54,580
+BC متوصل مع الثاني، كل BC بتكون متوصل مع الثاني
+
+256
+00:18:54,580 --> 00:18:58,420
+فبتكون في النهاية عاملة ring، بتكون عاملة شكل ring
+
+257
+00:18:58,420 --> 00:19:01,820
+طبعا عشان تكون شكل ring، الأصل أنه بيبدأ من C ثلاثة
+
+258
+00:19:01,820 --> 00:19:07,460
+C2 بعملش ring، بعملش cycle، C ثلاثة بيعملش cycle، طيب
+
+259
+00:19:07,460 --> 00:19:11,360
+في الآخر لازم يكون أكبر من أو يساوي ثلاثة لأنه
+
+260
+00:19:11,360 --> 00:19:16,040
+اثنين بعملش cycle، تمام، فالـ cycle on N vertices
+
+261
+00:19:16,040 --> 00:19:21,000
+بنسميها C، من كلمة cycle، بنسميها Cn، عبارة عن
+
+262
+00:19:21,000 --> 00:19:25,240
+simple graph، هذا الـ graph بيحتوي على N vertices
+
+263
+00:19:25,240 --> 00:19:29,940
+باعتبار أن احنا بسميه Cn، الـ N هنا عدد الـ
+
+264
+00:19:29,940 --> 00:19:34,080
+nodes، معناه ذلك أنه هيكون عندنا N nodes أو N nodes
+
+265
+00:19:34,080 --> 00:19:39,720
+الـ E، الـ connection، الـ connection اللي بينهم هتكون
+
+266
+00:19:39,720 --> 00:19:45,800
+بين كل نقطة واللي جنبها بس، خلاص، فإذا V1 V2، stop
+
+267
+00:19:45,800 --> 00:19:54,250
+من V2 لـ V3، transitivity، من V3 لـ V4، من V4 لـ V5، من V
+
+268
+00:19:54,250 --> 00:20:01,190
+N-1 to V N، عشان أحقق، أعمل الـ transitive closure
+
+269
+00:20:02,000 --> 00:20:08,120
+محتاج إيش تسوي؟ من V1 to N، بس هنعكسها هتصير VN to
+
+270
+00:20:08,120 --> 00:20:11,960
+V1، VN to V1، هيك سكرنا مين؟ الـ loop تبعنا أو سكرنا
+
+271
+00:20:11,960 --> 00:20:16,520
+الـ cycle بتاعتنا، فهيك اتسكت علنا الـ cycle، okay
+
+272
+00:20:16,520 --> 00:20:20,340
+هاي مجموعة منهم، وهي واضح أنه هاد الـ architecture
+
+273
+00:20:20,340 --> 00:20:23,320
+هاد أو الـ topology هاد ممكن تحتاجوها لاحقا في
+
+274
+00:20:23,320 --> 00:20:27,240
+الشبكات، كنوع من انواع، من أنواع الـ networks، نوع من
+
+275
+00:20:27,240 --> 00:20:31,850
+أنواع أو الـ topology للـ networks، Okay، how many
+
+276
+00:20:31,850 --> 00:20:39,550
+edges are there in Cn؟ قدش عدد الـ edges؟ عندكم N
+
+277
+00:20:39,550 --> 00:20:43,430
+edges موجودة فعليا، إذا كانت ثلاثة، في عندكم هيكون
+
+278
+00:20:43,430 --> 00:20:47,630
+ثلاثة edges، هنا أربعة، هيكون في عندكم أربعة edges
+
+279
+00:20:47,630 --> 00:20:50,570
+خمسة، هيكون في عندكم خمسة edges، فهذه بتساوي…
+
+280
+00:20:50,570 --> 00:20:53,530
+بتساوي N، الـ degree؟ نفس الشيء
+
+281
+00:20:57,330 --> 00:21:05,250
+total degree تبعكم اثنين في عدد الـ edges، الـ wheels
+
+282
+00:21:05,250 --> 00:21:13,790
+مختلفة شوية عن الـ cycle، لما
+
+283
+00:21:13,790 --> 00:21:17,050
+أقول في wheel معينة عندي، معناته في عندي عجلة، يعني
+
+284
+00:21:17,050 --> 00:21:22,110
+العجلة تمشي شكل بالشكل هذا، cycle، وخلاص، بدها
+
+285
+00:21:22,110 --> 00:21:26,220
+المحور تبعها، مش بدها محور، بدها نقطة الارتكاز
+
+286
+00:21:26,220 --> 00:21:30,340
+بتاعتها، نقطة ارتكازها عبارة عن node، عبارة عن node
+
+287
+00:21:30,340 --> 00:21:35,040
+لو افترض أن هدول عددهم خمسة مثلا، خمسة nodes وهي
+
+288
+00:21:35,040 --> 00:21:39,820
+متواصلين مع بعض بـ ring، يعني كـ ring topology بالشكل
+
+289
+00:21:39,820 --> 00:21:44,560
+هذا أو cycle C5
+
+290
+00:21:44,560 --> 00:21:48,880
+بالشكل هذا، محتاجين center، الـ center هذا connected
+
+291
+00:21:48,880 --> 00:21:55,310
+مع H أو مع every other node… مع every other node
+
+292
+00:21:55,310 --> 00:21:58,810
+كويس؟ بالشكل هذا، إيش اللي زودنا احنا هنا فعليا؟
+
+293
+00:21:58,810 --> 00:22:04,010
+star، برضه ممكن تمر عليكم كـ star connection، الـ
+
+294
+00:22:04,010 --> 00:22:08,230
+star connection، وهذه واحدة من صورها ال… ال… الـ
+
+295
+00:22:08,230 --> 00:22:11,270
+router، الـ router اللي بتشتغلوا عليه، الـ router هو
+
+296
+00:22:11,270 --> 00:22:15,570
+ماخد input وبعدين كده بيوزع star، بوزع star بشكل
+
+297
+00:22:15,570 --> 00:22:19,110
+star، بحيث أنه لو واحدة منهم صار لها أي… أي فصل
+
+298
+00:22:19,110 --> 00:22:21,670
+بتأثرش على الباقين، بتأثرش على الباقين، طبعا اللي
+
+299
+00:22:21,670 --> 00:22:24,770
+أخدوا الشبكات عارفين الجزئية دي، إذا ما أخدتهاش
+
+300
+00:22:24,770 --> 00:22:27,130
+الناس اللي ما أخدوا الشبكات، هيأخدوها، بس القصد اللي
+
+301
+00:22:27,130 --> 00:22:29,450
+أنا بحاول أوصلكم أنه الـ topologies هذه أنتو هتمر
+
+302
+00:22:29,450 --> 00:22:34,210
+عليكم، هتمر عليكم كـ as graphs، هتحتاجوها، ففي عندكم
+
+303
+00:22:34,210 --> 00:22:37,150
+هنا صار هي الـ ring، وصار في عندكم الـ star، هدول هيك
+
+304
+00:22:37,150 --> 00:22:42,400
+مع بعض بنسميهم Wheel أو شكل عجلة، فمعنى ذلك أن هذه
+
+305
+00:22:42,400 --> 00:22:47,220
+هي كـ Cycle هنضيف لها نقطة في النص و connected مع
+
+306
+00:22:47,220 --> 00:22:53,380
+الـ all nodes، أربعة، نفس الكلام، نقطة في النص و
+
+307
+00:22:53,380 --> 00:22:56,560
+هنوصلها مع الكل، خمسة نفس الشيء، ستة نفس الموضوع
+
+308
+00:22:56,560 --> 00:23:01,940
+سبعة وهكذا، تمام؟ بصير هيك شكلها أو كلهم بصيروا
+
+309
+00:23:01,940 --> 00:23:05,200
+عبارة عن… كل واحدة منهم عبارة عن wheel أو كلهم
+
+310
+00:23:05,200 --> 00:23:08,120
+wheels، في الحالة اللي، وأنا طيب، جدش عدد الـ edges
+
+311
+00:23:08,120 --> 00:23:12,340
+تبعتكم؟ أن في n نقص واحد، طب خلينا نشوف… اقصوا
+
+312
+00:23:12,340 --> 00:23:16,580
+اقصوا، اهدوا الـ cycle، جدش كان فيها؟ n، طيب ال… الـ
+
+313
+00:23:16,580 --> 00:23:23,180
+star لحالها؟ سؤال، سؤال خالص، إيه أصله هدول؟ احنا
+
+314
+00:23:23,180 --> 00:23:26,620
+قلنا اللي في المحورية، هذه بتتوصل مع كل واحدة منهم
+
+315
+00:23:26,620 --> 00:23:31,060
+طب هما جدش عددهم؟ N، معنى ذلك أنه محتاجة N link
+
+316
+00:23:31,060 --> 00:23:35,500
+زيادة، طب وهي أصلا جدش كان فيها؟ الـ cycle N، صار
+
+317
+00:23:35,500 --> 00:23:40,000
+في عندي N زائد N، اثنين N، اثنين N، مظبوط، فصار في
+
+318
+00:23:40,000 --> 00:23:43,160
+عندي هنا N جاية من الـ cycle، وN جاية من الـ star
+
+319
+00:23:43,160 --> 00:23:46,430
+اللي جوا، صار عندنا ال… ال… الـ wheels كلهم على
+
+320
+00:23:46,430 --> 00:23:51,630
+بعض، العدد الـ edges بتاعتها بيساوي اثنين N، اثنين N
+
+321
+00:23:51,630 --> 00:23:57,070
+طب عدد الـ degrees؟ أربعين، أربعين، تمام، okay، طب الـ N
+
+322
+00:23:57,070 --> 00:24:01,470
+cubes أو الـ hyper cubes، الـ hyper cubes هذه ببساطة
+
+323
+00:24:01,470 --> 00:24:07,720
+كل اللي بنعمله أنه بنسميها طبعا Q، من الـ Q كلفظة الـ
+
+324
+00:24:07,720 --> 00:24:17,840
+N، لدرجة الـ index، لو كانت zero بتكون عبارة عن node
+
+325
+00:24:17,840 --> 00:24:23,220
+واحدة، وإيش معناها zero هنا؟ واحد، وحاطين الـ index
+
+326
+00:24:23,220 --> 00:24:27,140
+zero، لأن الـ zero هذا يمثل جدش عدد الـ copies اللي عملت
+
+327
+00:24:27,140 --> 00:24:33,790
+احنا لسه ما عملناش أي نسخ هنا، إيش بيقولنا؟ الـ qn هي
+
+328
+00:24:33,790 --> 00:24:39,670
+عبارة عن copy من qn-1، من اللي قبلها، طب هذه اللي
+
+329
+00:24:39,670 --> 00:24:42,250
+قبلها، ما كانش فيه قبلها، هي أصغر عنصر، أن يكون node
+
+330
+00:24:42,250 --> 00:24:46,270
+واحدة، فهي مش ماخدة copy من إيش، مدام مش ماخدة copy
+
+331
+00:24:46,270 --> 00:24:50,020
+من إيش، فهي zero، قبل أنْ نعرف أنها وجدت، ليش الـ
+
+332
+00:24:50,020 --> 00:24:54,400
+index zero؟ لأن هنا zero copy، هي نقطة وخلاص ما فيش
+
+333
+00:24:54,400 --> 00:24:57,720
+أي connection، ما ربطناها مع أي شيء، طيب لما أقول q1
+
+334
+00:24:57,720 --> 00:25:01,840
+معناته بتعمل one copy، one copy هذه بتعملها copy
+
+335
+00:25:01,840 --> 00:25:07,740
+زيادة، بمعنى هذه النقطة الأصلية، هنعملها copy ونوصل
+
+336
+00:25:07,740 --> 00:25:12,260
+بين كل نقطة والنقطة اللي سُنسخت منها بهذا الشكل
+
+337
+00:25:12,260 --> 00:25:22,250
+خلاص، هذه q1، طيب q2، نسخة من Q1، بتصير هاي هذا، وQ1
+
+338
+00:25:22,250 --> 00:25:27,830
+نسخة منها، طيب النقطة هذه مستنسخة من أي نقطة من هذه
+
+339
+00:25:27,830 --> 00:25:31,190
+بوصلهم مع بعض، طيب هذه النقطة مستنسخة من مين؟ النقطة
+
+340
+00:25:31,190 --> 00:25:36,250
+هذه، بوصلهم مع بعض، بس بعملش الـ full connection، يعني
+
+341
+00:25:36,250 --> 00:25:40,130
+مش بروح بوصل هذه في كل اللي موجود، لأ، كل واحدة في
+
+342
+00:25:40,130 --> 00:25:43,410
+النسخة في النقطة اللي انسخت منها بس
+
+343
+00:25:46,680 --> 00:25:53,460
+Q3، هذه الأصلية، بعمل منها نسخة copy، وبنوصل كل نقطة
+
+344
+00:25:53,460 --> 00:25:59,540
+بالنقطة اللي انسخت منها، فهي فعلا copies of Q and
+
+345
+00:25:59,540 --> 00:26:02,620
+minus one، من اللي قبلها، طب هذه لما بدنا نجيب Q4
+
+346
+00:26:02,620 --> 00:26:08,240
+هي الأصلية، المكعب، وهي نسخة من المكعب، كل نقطة
+
+347
+00:26:08,240 --> 00:26:12,940
+بالنقطة اللي انسخت منها، فهي
+
+348
+00:26:12,940 --> 00:26:14,080
+بصير هذه الشكل Q
+
+349
+00:26:27,630 --> 00:26:31,490
+ممتاز، ما يعطيكم، طبعا جدش عدد الـ vertices لكل واحدة
+
+350
+00:26:31,490 --> 00:26:35,990
+لكل حالة منهم، لكل حالة منهم، هي number of vertices
+
+351
+00:26:35,990 --> 00:26:37,210
+two to the power
+
+352
+00:26:39,970 --> 00:26:45,750
+طيب هنا q0، q1، q2، q3، بتقدروا تجيبوه بحيث أنه لو
+
+353
+00:26:45,750 --> 00:26:50,610
+عوضتوا هنا بـ 0 و1، فأنتوا node واحدة، طيب لو عوضتوا
+
+354
+00:26:50,610 --> 00:26:55,590
+بالواحد، بالاثنين، بالاثنين، هاي الأربعة، هنا صار
+
+355
+00:26:55,590 --> 00:26:58,550
+ثمانية، صار ستة عشر، اثنين وثلاثين وهكذا، بتكملوا
+
+356
+00:26:58,550 --> 00:27:00,450
+عليها، عدد الـ edges
+
+357
+00:27:19,450 --> 00:27:35,470
+جربوها، نجربها مظبوط
+
+358
+00:27:35,470 --> 00:27:39,810
+بتجربوا معايا ولا إيش؟ بتجربوا معنا؟ أنا شوفتكم
+
+359
+00:27:39,810 --> 00:27:43,930
+ساكتهم، اللحظة تكونوا سايفين أن أنا بتجرب لحالي، جربوها
+
+360
+00:27:43,930 --> 00:27:50,850
+مظبوطة
+
+361
+00:27:50,850 --> 00:27:55,430
+طيب هي ما كانتش موجودة أساسا، وليه الأمانة برضه صدقا
+
+362
+00:27:55,430 --> 00:28:00,110
+بشرحها عند الشباب، واحد من الشباب طلعها، واحد من
+
+363
+00:28:00,110 --> 00:28:02,130
+الشباب طلع لنا الـ relation، بيقول لي طب دكتورة، دم هاد
+
+364
+00:28:02,130 --> 00:28:07,710
+الـ relation بتنفع، بتقول آه، بتنفع، صح، فممكن n في
+
+365
+00:28:07,710 --> 00:28:09,730
+اثنين to the power of n minus one
+
+366
+00:28:14,540 --> 00:28:18,960
+كويس، هذه شطارتكم عاد، أن كل اللي اخذتو في الـ
+
+367
+00:28:18,960 --> 00:28:23,140
+discrete، لو أنتم بتراجعوا على الـ net، ال… الـ IQ
+
+368
+00:28:23,140 --> 00:28:27,280
+test، هتلاقيه أن كل اللي بتيجي في مسابقات الذكاء
+
+369
+00:28:27,280 --> 00:28:30,380
+العقلي والأمور، الأسئلة اللي بيجيبوها للأذكياء و
+
+370
+00:28:30,380 --> 00:28:33,060
+للحاجات هذه، وبيحسبوا منها المقياس كله، احنا أخدناه
+
+371
+00:28:33,060 --> 00:28:37,420
+في المساق، يعني المساق هو كأنه مخصص للـ IQ، لأنه
+
+372
+00:28:37,420 --> 00:28:40,040
+المطلوب منكم، أنتم لو بتدوروا على الـ net، كان لجاته
+
+373
+00:28:40,040 --> 00:28:43,420
+كتير أسئلة زي هذه، بتقدروا تطلعوا منها relations و
+
+374
+00:28:43,420 --> 00:28:48,000
+بتقدروا تسبجوا حتى في المصطلحات تبعنا، فهذه موجودة
+
+375
+00:28:48,000 --> 00:28:53,620
+كتير في الـ IQ، في الـ IQ test أو الـ intelligent test
+
+376
+00:28:53,620 --> 00:28:57,620
+بتلاقوا كتير أسئلة زي هذه، جدش عدد الـ edges تبعتها،
+
+377
+00:28:57,620 --> 00:29:00,160
+جدش عدد الـ nodes، جدش عدد، مش عارفين، طب جيبلنا
+
+378
+00:29:00,160 --> 00:29:05,520
+relation للـ index مع عدد ال… كتير موجودة…
+
+379
+00:29:05,520 --> 00:29:13,080
+كتير موجودة، طيب جزء ثاني، الـ bipartite، الـ bi
+
+380
+00:29:13,080 --> 00:29:15,780
+partite، ببساطة جدا، بيكون عندي مجموعة الـ vertices
+
+381
+00:29:15,780 --> 00:29:20,660
+بجسمهم نصين، بجسمهم إيش؟ فريقين، كل فريق connected مع
+
+382
+00:29:20,660 --> 00:29:29,740
+each node of other part، بس داخل الـ part نفسه لأ
+
+383
+00:29:29,740 --> 00:29:32,780
+ما فيش أي connection، لا يوجد أي connection، لا يوجد أي
+
+384
+00:29:32,780 --> 00:29:37,230
+connection، فهتلاحظوا هنا، part number one، part
+
+385
+00:29:37,230 --> 00:29:42,610
+number two، هنا هتوزع خمسة vertices، وهنا هيكون خمسة
+
+386
+00:29:42,610 --> 00:29:47,510
+vertices، كويس، كل node هنا connected أو مسموح أنه
+
+387
+00:29:47,510 --> 00:29:50,690
+يكون connected مع الـ other numbers في الـ part
+
+388
+00:29:50,690 --> 00:29:54,390
+الثاني، في الـ part الثاني، مش في نفس الـ part، والعكس
+
+389
+00:29:54,390 --> 00:29:59,810
+صحيح، فهذه V1، V2، في الحالة اللي عندنا هنا، جدش عدد الـ
+
+390
+
+445
+00:33:54,020 --> 00:33:59,530
+اتنين تلاتة، هذه subset منها، خلاص هذه subset من الـ G
+
+446
+00:33:59,530 --> 00:34:02,950
+في الحلقة هذه، عندي هنا صار الـ graph هو subset من الـ
+
+447
+00:34:02,950 --> 00:34:06,630
+graph، طب لو زودنا كمان واحد هنا وعملنا بهذا الشكل
+
+448
+00:34:06,630 --> 00:34:11,990
+بس برضه sub graph، برضه sub graph، ما تقولوش طب لأ
+
+449
+00:34:11,990 --> 00:34:15,270
+ماهو في هاي خط، طب ما جاهاش الخط، مش المشكلة مش
+
+450
+00:34:15,270 --> 00:34:20,930
+المشكلة، أنا اللي بهمني أنه كل node هنا، كل node
+
+451
+00:34:20,930 --> 00:34:25,950
+belong to this graph، بيولوجيك هي برضه هتكون belong
+
+452
+00:34:25,950 --> 00:34:29,590
+to this graph، صحيح الـ node هذه موجودة، الـ node هذه
+
+453
+00:34:29,590 --> 00:34:33,830
+موجودة، الـ node هذه موجودة، تمام، الـ links برضه، مدام الـ
+
+454
+00:34:33,830 --> 00:34:38,330
+link موجود هنا، لازم يكون موجود هنا، فكل link موجود
+
+455
+00:34:38,330 --> 00:34:42,870
+هنا، موجود هنا، خلاص، العكس مش صحيح، العكس غير صحيح، الـ
+
+456
+00:34:42,870 --> 00:34:45,330
+link اللي موجود هنا، مش بالضرورة يكون موجود هنا، هذه
+
+457
+00:34:45,330 --> 00:34:50,330
+subset، هذه فئة جزئية من الفئة اللي هنا، الفئة هذه
+
+458
+00:34:50,330 --> 00:34:55,110
+بنقيسها على الـ nodes، إنه الـ nodes اللي هنا جزء من
+
+459
+00:34:55,110 --> 00:34:58,290
+الـ nodes اللي هنا، وبنقيسها كمان على مين؟ على الـ
+
+460
+00:34:58,290 --> 00:35:02,570
+connections، على الـ edges، على الـ links، فكل link
+
+461
+00:35:02,570 --> 00:35:04,690
+موجود هنا، المفروض إنه في الأصل كان موجود هنا
+
+462
+00:35:04,690 --> 00:35:12,330
+فبنقول إن هذا subset of g، فهنا هناخد هاي subset
+
+463
+00:35:12,330 --> 00:35:16,910
+منها، جزء منها، مش بالضروري كلها، مش بالضروري كلها،
+
+464
+00:35:16,910 --> 00:35:20,250
+مدام جزء منها، كيف نقدر نقول إن هو جزء منها؟ بنمسك
+
+465
+00:35:20,250 --> 00:35:24,350
+الـ vertices بتاعنا، هل هما فعلا كل vertex موجودة
+
+466
+00:35:24,350 --> 00:35:27,970
+هنا موجودة هنا؟ موجودة، طب هل كل link موجود هنا
+
+467
+00:35:27,970 --> 00:35:32,430
+فعلا موجود هنا؟ خلاص، بإذن الله هذه الـ H هي subset of G
+
+468
+00:35:36,900 --> 00:35:42,880
+Okay، بالعكس، الـ union، الاتحاد، الاتحاد طبعا هيكون في
+
+469
+00:35:42,880 --> 00:35:45,700
+عندنا two graphs، في عندنا graph number one، graph
+
+470
+00:35:45,700 --> 00:35:50,060
+number two، بدنا نجيب الـ union، أو g1 union g2 of
+
+471
+00:35:50,060 --> 00:35:54,690
+two simple graphs، g1 معرفينه على أساس أنه هو v1 اللي
+
+472
+00:35:54,690 --> 00:35:57,630
+هو عدد الـ vertices بتاعونه، أو الـ set of vertices
+
+473
+00:35:57,630 --> 00:36:03,330
+بتاعونه، وE1 اللي هو عدد الـ edges بتاعونه، طيب مع
+
+474
+00:36:03,330 --> 00:36:06,810
+مين هنعمل union؟ مع G2 اللي برضه له set of
+
+475
+00:36:06,810 --> 00:36:11,370
+vertices اسمها V2، وليه set of edges اسمها E2
+
+476
+00:36:11,370 --> 00:36:14,950
+simply هتكوني graph جديد، لـ graph جديد، هذا إيش اللي
+
+477
+00:36:14,950 --> 00:36:18,790
+بيميزه؟ بيميزه أن الـ vertices بتاعونه عبارة عن V1
+
+478
+00:36:18,790 --> 00:36:26,820
+union V2، و الـ edges بتاعونه E1 union E2، فهنا هذي
+
+479
+00:36:26,820 --> 00:36:35,100
+هي الـ V total، وهنا الـ E total للكل، إذا رسمناهم
+
+480
+00:36:35,100 --> 00:36:38,660
+هدول مع هدول الاتنين، وحطناهم مع بعض، هتلاقوا الـ
+
+481
+00:36:38,660 --> 00:36:41,840
+union تبعنا، فهتلاقوه في الحالة اللي زي اللي عندنا
+
+482
+00:36:41,840 --> 00:36:46,500
+هنا، هتكون بهذا الشكل، الاتنين مع بعض، يعني ارسموا هذا
+
+483
+00:36:46,500 --> 00:36:48,940
+الحال على ورقة شفاف، و هذا الحال على ورقة شفاف، و
+
+484
+00:36:48,940 --> 00:36:52,500
+اجعوهم مع بعض على بعض، هيك إيش الشكل اللي هيطلع في
+
+485
+00:36:52,500 --> 00:36:55,720
+ده، الورقة الشفاف هو هذا الـ union للكل مع بعضه
+
+486
+00:36:55,720 --> 00:36:57,300
+للكل مع بعضه
+
+487
+00:37:02,520 --> 00:37:07,820
+Okay، هي خلصنا بعض أنواع .. بعض أنواع من مين؟ من الـ
+
+488
+00:37:07,820 --> 00:37:10,660
+graphs، خلينا نشوف اللي هو كيف بقدر أمثل الـ graph، و
+
+489
+00:37:10,660 --> 00:37:13,380
+احنا مثلناها قبل هيك، ليش؟ لأنه احنا في النهاية
+
+490
+00:37:13,380 --> 00:37:16,140
+نتكلم عن الـ graph، الـ graph عبارة عن إيش؟ relation
+
+491
+00:37:16,140 --> 00:37:21,480
+أيام الـ relation، كيف كنا نمثل الـ relation؟ كنا
+
+492
+00:37:21,480 --> 00:37:23,380
+نستخدم طرق تانية، الشمعة
+
+493
+00:37:27,280 --> 00:37:32,500
+استخدمنا الـ one zero matrix، واستخدمنا الـ directed
+
+494
+00:37:32,500 --> 00:37:35,520
+graph، أو الـ diagraph، متذكرين؟ طب احنا اصلا نشتغل
+
+495
+00:37:35,520 --> 00:37:39,340
+diagraph أساسا، فمعنى ذلك التمثيل المتوقع أنه بيسكن
+
+496
+00:37:39,340 --> 00:37:42,280
+باستخدام الـ matrix، استخدام matrix، احنا فعليا
+
+497
+00:37:42,280 --> 00:37:46,720
+هنشتغل على الـ matrix بطرق تانية، واحدة الـ adjacency
+
+498
+00:37:46,720 --> 00:37:50,840
+matrices، و الـ incidence matrices، جايبلهم، هنتكلم بس
+
+499
+00:37:50,840 --> 00:37:54,620
+عن الـ list، هذه بسيطة جدا، بنعمل قائمة بعدد الـ
+
+500
+00:37:54,620 --> 00:37:57,660
+vertices، وكل واحدة connected مع مين؟ و بس، فهذه
+
+501
+00:37:57,660 --> 00:38:02,120
+طريقة تمثيل ممكنة للـ graph representations، هناخد
+
+502
+00:38:02,120 --> 00:38:05,480
+تلت طرق، بساطين جدا لإنه مرت أفكارهم علينا، one zero
+
+503
+00:38:05,480 --> 00:38:07,980
+بحط one إذا كان الـ relation موجودة، zero إذا كان مش
+
+504
+00:38:07,980 --> 00:38:12,120
+موجودة، فـ one بحطها إذا كان الـ link موجود، و zero إذا
+
+505
+00:38:12,120 --> 00:38:15,280
+ما كانش الـ link موجود في الرسمة، بس هنشوفها مراجعة
+
+506
+00:38:15,280 --> 00:38:17,560
+بالتفاصيل بعدين، في جزئية تانية اللي هي الـ graph
+
+507
+00:38:17,560 --> 00:38:21,310
+isomorphism،Isomorphism اللي هي المشابهة، هل هم
+
+508
+00:38:21,310 --> 00:38:23,950
+متشابهين ولا لأ، الرسومات، وهذه برضه من الحاجات اللي
+
+509
+00:38:23,950 --> 00:38:30,630
+كتير موجودة في الـ IQ test، أو في الـ intelligence
+
+510
+00:38:30,630 --> 00:38:33,650
+test
+
+511
+00:38:33,650 --> 00:38:37,530
+اللي بتعملوها عادة، بيجيبوا الرسمة معينة، وبعدين
+
+512
+00:38:37,530 --> 00:38:40,030
+تحتها بيجيبوا مجموعة رسومات، وبيقولوا هذا matching
+
+513
+00:38:40,030 --> 00:38:45,150
+مع مين؟ ممكن يكون فيها مجموعة nodes بس ملوّحين شوية
+
+514
+00:38:45,940 --> 00:38:49,540
+لفّهم، عملهم، دورهم، محركهم تسعين درجة، مائة و
+
+515
+00:38:49,540 --> 00:38:53,660
+عشرين درجة، مغير، مظبط، هنا الشطارة كيف تعرف أن هذا
+
+516
+00:38:53,660 --> 00:38:57,000
+هو مش شبه لهذا، الـ isomorphism، هذا اللي هي التناظر
+
+517
+00:38:57,000 --> 00:39:00,740
+ممكن في النهاية الرسمة تكون مختلفة، شكلها تماما
+
+518
+00:39:00,740 --> 00:39:04,660
+مختلف، بس لأ، هي نفس الرسمة، بمعنى لو في two nodes
+
+519
+00:39:04,660 --> 00:39:08,560
+منهم، لفتوهم، هيطلع نفس الرسمة بنفس الـ connections
+
+520
+00:39:08,560 --> 00:39:12,640
+بتاعتهم، هناخدها وهنتكلم عليها إذا وصلنا إليها
+
+521
+00:39:12,640 --> 00:39:15,200
+هناخد بس شوية أفكار اللي هي عملية الـ connections
+
+522
+00:39:15,200 --> 00:39:18,680
+عشان نحدد الـ isomorphism موجودة أو لا
+
+523
+00:39:18,680 --> 00:39:23,280
+هنتكلم عن الـ connection، وبيكون خلصنا كل ما يخص الـ
+
+524
+00:39:23,280 --> 00:39:31,400
+graph في شغلنا، نبدأ بالـ representation، أول شغل
+
+525
+00:39:31,400 --> 00:39:35,350
+اللي هي الـ adjacency list، بسيطة جدا، عندكوا graph
+
+526
+00:39:35,350 --> 00:39:39,470
+معين، بتعمله representation، مثله، تمثيله مافيش أبسط
+
+527
+00:39:39,470 --> 00:39:45,450
+منه، ليش؟  جداش عدد الـ nodes تبعونه، رتبوهم عندكوا
+
+528
+00:39:45,450 --> 00:39:50,050
+A,B,C,D to F، فلس، A,B,C,D تمام، بنمسكهم هدول،
+
+529
+00:39:50,050 --> 00:39:52,810
+بنسميها vertex، الـ column هدول بنسميه vertex في الـ
+
+530
+00:39:52,810 --> 00:39:56,030
+list اللي عندنا، الـ list أو الـ column التاني بنسميه
+
+531
+00:39:56,030 --> 00:40:01,830
+الـ adjacent vertices، كل اللي بنعمله، A هي إيه؟ هي
+
+532
+00:40:01,830 --> 00:40:07,070
+إيه؟ مجاورة مع مين؟ ب و سي، خلاص نكتب ب و سي، انتهى
+
+533
+00:40:07,070 --> 00:40:16,050
+الكلام، طيب الـ b، وين بي؟ هذه بي، لاحظوا مع a، مع c، مع
+
+534
+00:40:16,050 --> 00:40:23,590
+e، مع f، طيب الـ d إيش
+
+535
+00:40:23,590 --> 00:40:27,830
+بنسميها هذه isolated، isolated، تمام، isolated degree
+
+536
+00:40:27,830 --> 00:40:31,730
+بتاعتها صفر، فهذه مش متواصلة مع أي حد، هذه zero، فمدام
+
+537
+00:40:31,730 --> 00:40:38,490
+zero، زيرو فهي زيرو فعلا، كويس، سهل، التمثيل
+
+538
+00:40:38,490 --> 00:40:42,070
+بالشكل هذا، مافيش فيه أي شيء، لما تشوفوا adjacency
+
+539
+00:40:42,070 --> 00:40:45,770
+list، list، مافيش فيه أي شيء، بس تحطوا كل الـ vertices
+
+540
+00:40:45,770 --> 00:40:52,370
+وكل واحدة مجاورة لمين؟ وانتهى الكلام، الـ adjacency
+
+541
+00:40:52,370 --> 00:40:57,270
+list، في حالة الـ direct، في حالة الـ direct بنعملها
+
+542
+00:40:57,270 --> 00:41:02,550
+للـ incident edges، إذا في incident edges أو لا، كيف
+
+543
+00:41:02,550 --> 00:41:07,630
+يعني نفس الكلام، بنحط مجموعة الـ edges تبعوننا، عفوا
+
+544
+00:41:07,630 --> 00:41:11,130
+الـ vertices بتاعوننا، اللي هو الـ nodes، و بنفترضهم
+
+545
+00:41:11,130 --> 00:41:14,970
+هدول مين؟ الـ initial vertex، هدول الـ initial
+
+546
+00:41:14,970 --> 00:41:19,730
+vertex، بمعنى كل link طالع محسوب، أما كل link داخل
+
+547
+00:41:19,730 --> 00:41:28,110
+لأ، نمسك a، و نمسكهم، a هي إيه؟ كم link طالع؟ بي على
+
+548
+00:41:28,110 --> 00:41:33,790
+بي، و على دي، و على ايه، لحظوا فعلا بنحطهم، لحظوا هذا
+
+549
+00:41:33,790 --> 00:41:40,410
+ما حسبتش هذا، بحسبش لإني من الأول حاططها
+
+550
+00:41:40,410 --> 00:41:45,270
+initial vertex، initial vertex، ما نحطهاش، طيب لو
+
+551
+00:41:45,270 --> 00:41:51,670
+أخدنا B، أخدنا B، إيش اللي طالع منها؟ هاي واحد، هاي
+
+552
+00:41:51,670 --> 00:41:57,030
+اتنين، هدول؟ لأ، هدول لأ، طيب، ففي الحالة هذا هيكون
+
+553
+00:41:57,030 --> 00:42:02,050
+عندي B، من B طالع رايح لمين؟ لـ B، خلاص بنحط بي، ورايح
+
+554
+00:42:02,050 --> 00:42:09,030
+التاني لمين؟ لـ D، هاي D، طيب نمسك D،
+
+555
+00:42:09,030 --> 00:42:14,490
+Zero، فبتظل فاقية، رغم أن هي في إلى three lengths، بس
+
+556
+00:42:14,490 --> 00:42:18,030
+الـ links كلها in in degree، كلهم in degree، لأ، مش
+
+557
+00:42:18,030 --> 00:42:20,070
+محسوبة لـ in degree، أنا هنا بتعامل معها أساس أنها
+
+558
+00:42:20,070 --> 00:42:23,030
+تكون هي الـ initial، ما تكونش هي الـ terminal، هي الـ
+
+559
+00:42:23,030 --> 00:42:26,790
+terminal، آه ليش؟ بدليل أن هي وصفتها هي هي E، هي E
+
+560
+00:42:26,790 --> 00:42:31,060
+في كمان E تانية، آه، المفروض في E تانية، ع دي .. دي ..
+
+561
+00:42:31,060 --> 00:42:33,060
+دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي
+
+562
+00:42:33,060 --> 00:42:34,680
+دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي
+
+563
+00:42:34,680 --> 00:42:39,200
+.. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي ..
+
+564
+00:42:39,200 --> 00:42:45,480
+دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي
+
+565
+00:42:45,480 --> 00:42:52,090
+دي .. دي .. دي .. دي .. د، تمام، هاي عملية التنفيذ في
+
+566
+00:42:52,090 --> 00:42:57,450
+حالة الـ directed graph، ناخد النوع التاني، الـ
+
+567
+00:42:57,450 --> 00:43:00,270
+adjacency matrices، adjacency matrices، اسمها
+
+568
+00:43:00,270 --> 00:43:02,670
+matrices، خلاص، معناه أن أنا بتكلم عن matrix، يعني في
+
+569
+00:43:02,670 --> 00:43:05,490
+النهاية هيكون في عندي row، وهيكون في عندي column
+
+570
+00:43:05,490 --> 00:43:08,610
+هاي الـ matrix، وهيكون في عندي row، وهيكون عندي
+
+571
+00:43:08,610 --> 00:43:14,820
+column، وهيكون مجموعة عناصر i,j، مجاورة عن i,j دائما
+
+572
+00:43:14,820 --> 00:43:22,180
+i هتكون للـ row، الـ row هذا بنحط مين؟ الـ node، هنحط
+
+573
+00:43:22,180 --> 00:43:24,580
+مجموعة الـ nodes بتاعتنا، كل الـ nodes بتاعتكم
+
+574
+00:43:24,580 --> 00:43:31,140
+بترتبهم هنا، كويس، هنا الـ adjacency معناته أنا بتكلم
+
+575
+00:43:31,140 --> 00:43:35,600
+عن الـ node adjacent لمين؟ لـ node برضه، فإذا برضه هنا
+
+576
+00:43:35,600 --> 00:43:40,850
+بنحط nodes، بس احنا دائما نتطلع على المصطلح تبعنا
+
+577
+00:43:40,850 --> 00:43:43,810
+adjacency، آه الـ adjacency مع مين؟ عادة الـ adjacency
+
+578
+00:43:43,810 --> 00:43:48,330
+بنحط node مع node، هل هم adjacent لبعض أو لأ، معنا
+
+579
+00:43:48,330 --> 00:43:51,290
+ذلك أن الـ input بالنسبالي node، و الـ output هيكون
+
+580
+00:43:51,290 --> 00:43:54,450
+برضه node، بنرتبهم هنا، بنرتبهم هنا، إذا والله هم
+
+581
+00:43:54,450 --> 00:43:58,410
+الاثنين adjacent لبعض، بمعنى أن فيه link بينهم، i,j
+
+582
+00:43:58,410 --> 00:44:07,100
+المقابلة لهم بنحطها واحد، otherwise بنحطها zero، خلاص
+
+583
+00:44:07,100 --> 00:44:13,380
+هاي طريقة التمثيل بتاعتنا، مثلًا ناخد example بهذا
+
+584
+00:44:13,380 --> 00:44:19,620
+الشكل، graph زي اللي احنا شايفينها هنا، كم
+
+585
+00:44:19,620 --> 00:44:25,080
+node في عندك؟ أربعة، هاي A,B,C و D، ونفس الكلام هنا
+
+586
+00:44:25,080 --> 00:44:27,660
+برضه A,B,C و D
+
+587
+00:44:33,740 --> 00:44:40,220
+between a و a، هل في أي self loop؟ لأ، zero، طيب هل
+
+588
+00:44:40,220 --> 00:44:45,440
+في relation between a و b؟ آه، آه في، طب a و c؟ آه
+
+589
+00:44:45,440 --> 00:44:54,310
+واحد، a و d؟ one، طيب بين b و a، آه، feeling، طب بين b و
+
+590
+00:44:54,310 --> 00:45:00,470
+b نفسها، طب b و c، ب و د، فإذا فعلا a و d فقط، و
+
+591
+00:45:00,470 --> 00:45:03,670
+بنكمل التمثيل طبعا، طيب، لأنه احنا بنتكلم عن
+
+592
+00:45:03,670 --> 00:45:10,570
+undirected، لحظة، لازم تكون symmetric، بمعنى أن a,b
+
+593
+00:45:10,570 --> 00:45:20,530
+هي نفسها b,a، صحيح، الـ b,a هي نفس a,b، فلو عملتوا الـ
+
+594
+00:45:20,530 --> 00:45:23,390
+diagonal هنا، هتلاقوا أن هما symmetric، الاثنين
+
+595
+00:45:23,390 --> 00:45:26,130
+هيكونوا symmetric، في الحالة بتاعتنا، فهذه لازم
+
+596
+00:45:26,130 --> 00:45:28,230
+تاخدوا بالكم منها، مدام أن أنا بتكلم عن undirected
+
+597
+00:45:28,230 --> 00:45:31,710
+لازم تكون symmetric، طيب إذا كانت نتكلم عن
+
+598
+00:45:31,710 --> 00:45:36,590
+multigraph، multigraph، ما نشتغلش على 01 matrix،
+
+599
+00:45:36,590 --> 00:45:40,840
+بنشتغل على natural matrix، natural matrix، بمعنى أنه
+
+600
+00:45:40,840 --> 00:45:44,700
+في عندنا عدد natural، مستخدمة كده، عدد العدد؟ هنا
+
+601
+00:45:44,700 --> 00:45:49,940
+بحكوا 1، عصر أنه في relation، لأ، بحكوا 2، على عدد الـ
+
+602
+00:45:49,940 --> 00:45:53,140
+paths الموجودة، أو عدد الـ links الموجودة، أو عدد الـ
+
+603
+00:45:53,140 --> 00:45:57,820
+links الموجودة، for example، لو
+
+604
+00:45:57,820 --> 00:46:03,320
+أخدنا شكل بهذا الشكل، a,b,c,d، برضه نفس الكلام، هنعمل
+
+605
+00:46:03,320 --> 00:46:11,770
+a,b,c,d، a,b,c,d، الـ A و الـ A مافيش بينهم إشي، طيب
+
+606
+00:46:11,770 --> 00:46:21,350
+خلينا نشوف، ناخد مثلًا الـ C و الـ D، هاي C و D، تلاتة
+
+607
+00:46:21,350 --> 00:46:23,710
+واحد، اتنين، تلاتة، فبنكتبها تلاتة، natural number
+
+608
+00:46:23,710 --> 00:46:27,910
+ما نشتغلش هنا zero one matrix، لأ، خلاص، natural matrix
+
+609
+00:46:27,910 --> 00:46:30,830
+natural matrix، ليش؟ لأنه بيصير بهمني أنا الـ logic
+
+610
+00:46:30,830 --> 00:46:35,11
+
+667
+00:51:06,880 --> 00:51:09,060
+one
+
+668
+00:51:11,150 --> 00:51:15,530
+عند الـ a مع الـ one هل هما الـ a تعتبر أحد الأطراف
+
+669
+00:51:15,530 --> 00:51:19,670
+الـ end points بتاعة الـ one؟ مظبوط، معناته one، طب هل الـ
+
+670
+00:51:19,670 --> 00:51:24,290
+a تعتبر برضه أحد الـ end nodes بتاعة الـ link اتنين؟
+
+671
+00:51:24,290 --> 00:51:30,070
+okay للتلاتة؟ لأ للاربعة؟ للخمسة؟ اه خمسة هي
+
+672
+00:51:30,070 --> 00:51:36,660
+الخمسة هي التلاتة وهي الخمسة والستة، بقيد كتير، طيب
+
+673
+00:51:36,660 --> 00:51:40,760
+تعالوا نفحصها بطريقة مختلفة شوية، احنا هنا امسكنا
+
+674
+00:51:40,760 --> 00:51:45,320
+row by row، طب نمسكها column by column، اتنين
+
+675
+00:51:45,320 --> 00:51:50,940
+connected بين ايش وايه، خلاص، قدام الـ a واحد وقدام
+
+676
+00:51:50,940 --> 00:51:54,480
+الـ d واحد، otherwise zeros، لإن هو فعلا بيوصل اتنين
+
+677
+00:51:54,480 --> 00:52:00,280
+بقى طيب، الستة self-loop معناته فقط مع نفسها، مع الـ C
+
+678
+00:52:00,280 --> 00:52:05,620
+هتلاقيه حتى هنا عبارة عن one واحد فقط، بعرف أن هذا
+
+679
+00:52:05,620 --> 00:52:11,260
+self-loop، أي شيء تاني بعرف أنه وجد أربعة، المفروض
+
+680
+00:52:11,260 --> 00:52:16,680
+بوصله لـ C مع دي، طيب ستة أو هذا واحد لحاله، معناته
+
+681
+00:52:16,680 --> 00:52:20,360
+هذا self-loop مع الـ C، self-loop، بنعرف أن هنا تتكلم
+
+682
+00:52:20,360 --> 00:52:23,460
+عن self-loop، طيب لما يكون directed
+
+683
+00:52:26,380 --> 00:52:29,640
+بتتكلم هنا عن directed، في الحالة هذه لأ، بيصير
+
+684
+00:52:29,640 --> 00:52:38,600
+بتكون تمثله الشكل تبعكم فعليا بـ two digits، طيب زي
+
+685
+00:52:38,600 --> 00:52:43,260
+ما قلنا هنا الـ incidence matrix اللي نقدر نمثلها
+
+686
+00:52:43,260 --> 00:52:49,480
+باستخدام اللي بنستعمل الـ rows vertices والـ columns
+
+687
+00:52:49,480 --> 00:52:55,120
+بنمثل فيهم الـ edges أو الـ legs لو قلنا إنه بدنا
+
+688
+00:52:55,120 --> 00:52:58,000
+نشتغل على directed graph، الـ directed graph بيصير
+
+689
+00:52:58,000 --> 00:53:02,540
+بدي two bits أنثلهم لكل E، one بيصير فعلا دي two
+
+690
+00:53:02,540 --> 00:53:07,040
+bits هنا في الحالة اللي عندنا هنا
+
+691
+00:53:16,280 --> 00:53:23,640
+فيه بيستخدموا تلاتة، واحدة للـ in، واحدة للـ out، واحدة
+
+692
+00:53:23,640 --> 00:53:27,760
+للـ self loop، واحدة للـ self loop، وإن كان بنقدر
+
+693
+00:53:27,760 --> 00:53:31,500
+نمثلهم باتنين بس، على اعتبار أن لو ظهر عندكم الـ in
+
+694
+00:53:31,500 --> 00:53:37,540
+one والـ out one، معناته self loop، معناته هذا يعتبر
+
+695
+00:53:37,540 --> 00:53:43,750
+in للـ B و out للـ B برضه، معناته منها الها، هذا
+
+696
+00:53:43,750 --> 00:53:47,610
+يعتبر self loop، بتقدر تمثلها، ولكن لأن عنوان الكتاب
+
+697
+00:53:47,610 --> 00:53:51,710
+كان بيتكلم عن two ones بيستخدمهم للـ edges، للـ two
+
+698
+00:53:51,710 --> 00:53:54,270
+edges تبعونا اللي هي الـ in والـ out، وفي one
+
+699
+00:53:54,270 --> 00:53:58,770
+مستخدمة للـ loop، زي ما قلت لكم أنا أتصور أنه لأ
+
+700
+00:53:58,770 --> 00:54:01,870
+باتنين بكفي جداً، لأنه إذا كان اتفقوا one مع one
+
+701
+00:54:01,870 --> 00:54:04,670
+one one، هذه معناته هذا self loop، هذا بيحول في
+
+702
+00:54:04,670 --> 00:54:11,160
+الحالة هذه أصبح self loop، تمام، بتقدروا تمثلوها بس
+
+703
+00:54:11,160 --> 00:54:14,880
+بتكونوا تزودوا عدد الـ digits بتاعتكم، عدد الـ digits
+
+704
+00:54:14,880 --> 00:54:20,460
+بتاعتكم، طيب الـ isomorphism مدام عرفناها لوقت عملية
+
+705
+00:54:20,460 --> 00:54:25,480
+التمثيل، بيصير عملية الـ isomorphism، هذه  المشابهة، كيف
+
+706
+00:54:25,480 --> 00:54:29,560
+بدي أعرف أنه two graphs مش شبه بعض أو لأ، two graphs
+
+707
+00:54:29,560 --> 00:54:33,920
+عشان شبه بعض، لازم في شواهد في الأول، عناصر نتأكد
+
+708
+00:54:33,920 --> 00:54:37,080
+منها، هل هي متساوية مع بعض ولا لأ، قبل ما أقعد أقول
+
+709
+00:54:37,080 --> 00:54:40,040
+لأ، طب أنا بدي أتخيل هذا لو اتحركت، لو هذه لأ، من غير
+
+710
+00:54:40,040 --> 00:54:43,920
+تخيلها، بدون تخيلات أو إنه كيف، لأ، الـ node هذي لو
+
+711
+00:54:43,920 --> 00:54:46,760
+حركناها هيك، لأ، لأ، بدون شيء، كل اللي هتعملوه أول
+
+712
+00:54:46,760 --> 00:54:51,840
+شيء، عدد الـ nodes متساوي، فبدنا نجمع، نحط عشان أقول
+
+713
+00:54:51,840 --> 00:54:58,460
+G1 و G2 أو G1 isomorphic to G2، مشابهة ومناظرة لـ G2
+
+714
+00:54:58,460 --> 00:55:02,180
+بدنا نشوف أول شغلة، هل الـ cardinality للـ vertices
+
+715
+00:55:02,180 --> 00:55:06,360
+بتساوي، بمعنى عدد الـ nodes متساويين، نعم، بنيجي نفحص
+
+716
+00:55:06,360 --> 00:55:08,980
+لها الأولى، أو الله فيها خمسة nodes، طب التانية فيها
+
+717
+00:55:08,980 --> 00:55:12,200
+ستة، خلاص stop، وقف، مش بيشابهوا بعض، خلاص انتهى من غير
+
+718
+00:55:12,200 --> 00:55:15,100
+ما تدوروا على شيء ثاني، و الله يطلعوا يشابهوا بعض
+
+719
+00:55:15,100 --> 00:55:19,180
+بدنا نشوف عدد الـ lengths، عدد الـ lengths بتاعتهم، هل
+
+720
+00:55:19,180 --> 00:55:23,600
+بيشابهوا، بيساووا بعض أو لأ، طيب طلعوا يساووا بعض، الـ
+
+721
+00:55:23,600 --> 00:55:29,800
+degree، number of vertices with degree n، إذا كان الـ
+
+722
+00:55:29,800 --> 00:55:32,340
+degree واحد، إذا كان الـ degree واحد، إذا كان الـ
+
+723
+00:55:32,340 --> 00:55:34,600
+degree واحد، إذا كان الـ degree واحد، إذا كان الـ
+
+724
+00:55:34,600 --> 00:55:37,200
+degree واحد، إذا كان الـ degree واحد، إذا كان الـ
+
+725
+00:55:37,200 --> 00:55:43,350
+degree واحد، إذا كان الـ degree واحد، طب كم واحدة من
+
+726
+00:55:43,350 --> 00:55:46,410
+الـ vertices، طبعاً الـ degree بتاعتها بتساوي اتنين
+
+727
+00:55:46,410 --> 00:55:49,810
+خلصنا الاتنين، التلاتة لعندي، بتصلوا لأكبر degree
+
+728
+00:55:49,810 --> 00:55:52,370
+ممكنة في الـ nodes اللي موجودة عندكم، طبعاً أنتم
+
+729
+00:55:52,370 --> 00:55:54,610
+بتواصلوا، هتشوفوا أكبر degree ممكنة، ممكن تطلع اتنين
+
+730
+00:55:54,610 --> 00:55:57,750
+أو تلاتة أو أربعة مثلاً، بتعملوا check على كل اللي
+
+731
+00:55:57,750 --> 00:56:01,850
+أقل منها، قد ايه عدد الـ degrees هنا، وقد ايه عدد الـ
+
+732
+00:56:01,850 --> 00:56:04,670
+degrees هنا، لكل degree من الـ degrees، قد ايه عدد الـ
+
+733
+00:56:04,670 --> 00:56:07,170
+nodes اللي بتحقق الـ degree، يعني إذا واحدة منهم
+
+734
+00:56:07,170 --> 00:56:10,190
+اختلفت، خلاص الـ stop، وقفوا، مش هتوصلوا، الـ stop مستحيل
+
+735
+00:56:10,190 --> 00:56:14,130
+يظبطوا أن يكونوا مشابهين لبعض، ضبطوا خير وبركة، طيب
+
+736
+00:56:14,130 --> 00:56:18,790
+فإذا عدد الـ degree، degree n is the same in both
+
+737
+00:56:18,790 --> 00:56:21,890
+graphs، هذا برضه شرط ضروري لازم يتحقق، طيب for
+
+738
+00:56:21,890 --> 00:56:27,590
+every prepared sub graph G of one graph there is a
+
+739
+00:56:27,590 --> 00:56:30,790
+prepared sub graph of the other graph is
+
+740
+00:56:30,790 --> 00:56:37,030
+isomorphic to G، فإذا كان في sub graph طلعناه من G
+
+741
+00:56:37,030 --> 00:56:40,650
+مشابه، هو نفسه بالظبط، مشابهة بقدر أطلع نفس الـ sub
+
+742
+00:56:40,650 --> 00:56:43,490
+graph من الـ graph التاني، بقى نفسه، هذا عنصر برضه
+
+743
+00:56:43,490 --> 00:56:47,030
+بقدر أمثل فيه، إن والله الاتنين ممكن يكونوا متشابهين
+
+744
+00:56:47,030 --> 00:56:49,730
+بس لازم يتحققوا جميع العناصر، احنا طبعاً لما نيجي
+
+745
+00:56:49,730 --> 00:56:53,310
+نحقق، هنحقق العنصر الأول والثاني اللي بنعتمد عليهم
+
+746
+00:56:53,310 --> 00:56:56,450
+لأن الـ sub graph مافي احتمالات كتيرة، الـ sub graph
+
+747
+00:56:56,450 --> 00:56:58,850
+الـ sub graph اللي هي كتير احتمالات أنه ممكن نطلع
+
+748
+00:56:58,850 --> 00:57:01,710
+sub graph يطلع من هنا لهنا، فحنعمل check على
+
+749
+00:57:01,710 --> 00:57:04,370
+التنتين هدول، ومنهم نؤكد، هل الكلام صحيح أو لا
+
+750
+00:57:04,370 --> 00:57:09,410
+طيب مثال الـ isomorphism example، ناخد isomorphism
+
+751
+00:57:09,410 --> 00:57:13,210
+example، هل الـ two graphs هدول isomorphic، كل واحدة
+
+752
+00:57:13,210 --> 00:57:18,640
+منهم للتانية أو لأ، is isomorphic، اعملوا لنا إعادة
+
+753
+00:57:18,640 --> 00:57:22,340
+تسميات، يعني قولوا لنا، اديها دي وين مكانها هنا، طبعاً
+
+754
+00:57:22,340 --> 00:57:24,960
+هنا اتغيرت، طبعاً واضح أن هنا اتغير الشكل، هذا بعيد
+
+755
+00:57:24,960 --> 00:57:27,840
+تماماً، بتحس أنه مالوش علاقة بالشكل التاني، بس خليني
+
+756
+00:57:27,840 --> 00:57:35,140
+أديهم واحدة واحدة، عدد الـ vertices قد ايه؟ هنا عندي ستة
+
+757
+00:57:35,140 --> 00:57:40,880
+قد ايه هناك؟ ستة، هاي أول شرط، تحقق، الشرط الثاني الـ edges
+
+758
+00:57:40,880 --> 00:57:46,870
+واحد، تلاتة، أربعة، خمسة، ستة، سبعة، تمانية، تسعة، طب هنا
+
+759
+00:57:46,870 --> 00:57:49,730
+واحد، اتنين، تلاتة، أربعة، خمسة، ستة، سبعة، تمانية، تسعة
+
+760
+00:57:49,730 --> 00:57:53,450
+okay، هاي عدينا من التاني، التالت، الشرط التالت الـ
+
+761
+00:57:53,450 --> 00:57:58,050
+degree، طيب بدنا نشوف في degree zero هنا أو هنا
+
+762
+00:57:58,050 --> 00:58:01,370
+مافيش degree zero، مافيش أي isolated node، طيب الـ
+
+763
+00:58:01,370 --> 00:58:06,030
+degree one، مافيش أي واحدة منفصلة، صحيح؟ ولا واحدة
+
+764
+00:58:06,030 --> 00:58:09,810
+معلقة، طيب الـ ... الـ isolated، عفواً الـ degree اتنين
+
+765
+00:58:19,690 --> 00:58:25,830
+خلينا نقول هدي G1 أو هدي G2، خلينا نشوف هنا لأ
+
+766
+00:58:25,830 --> 00:58:30,490
+هدي الـ degree أكبر، أكبر، هاي واحدة وهاي اتنين، صار
+
+767
+00:58:30,490 --> 00:58:34,530
+الـ graph الأول فيه اتنين، طيب هنا هاي في واحدة و
+
+768
+00:58:34,530 --> 00:58:38,570
+هاي اتنين، في ايش غيرهم؟ طيب معناته هنا في two
+
+769
+00:58:38,570 --> 00:58:42,130
+vertices، الـ degree بتاعتهم اتنين، اتنين، تشابهوا، طيب
+
+770
+00:58:42,130 --> 00:58:47,030
+تلاتة، إذا الـ degree بتساوي تلاتة، هاي في عندي واحدة
+
+771
+00:58:48,480 --> 00:58:55,440
+وهاي كمان واحدة، في غيرهم؟ فش، إذا هاي اتنين، طيب
+
+772
+00:58:55,440 --> 00:59:01,520
+هنا هاي في واحدة، وهاي واحدة، هاي في هنا واحدة، و
+
+773
+00:59:01,520 --> 00:59:07,740
+هنا في واحدة، تمام، نتين، طيب degree أربعة، هنا هاي
+
+774
+00:59:07,740 --> 00:59:12,300
+في واحدة، وهاي واحدة، طيب في الرسمة التانية
+
+775
+00:59:15,900 --> 00:59:20,280
+كويس، هاي اتنين، طيب degree خامسة، مافيش لا هنا ولا
+
+776
+00:59:20,280 --> 00:59:22,700
+هنا، خلاص، هي أكبر degree كانت الأربع، واضح أنه
+
+777
+00:59:22,700 --> 00:59:26,660
+معناته في isomorphism، مبدئياً في isomorphism، لضال
+
+778
+00:59:26,660 --> 00:59:33,980
+مدام اتفقنا أن في isomorphism، بدنا أن
+
+779
+00:59:33,980 --> 00:59:38,440
+نغير المسميات هذه لهناك، طبعاً هتلاحظوا أنه مدام كله
+
+780
+00:59:38,440 --> 00:59:40,860
+كان اتنين اتنين اتنين اتنين، في إمكانية لحلين
+
+781
+00:59:40,860 --> 00:59:45,100
+حقيقةً، في إمكانية هنا لحلين، لأنه symmetric الشكل
+
+782
+00:59:45,100 --> 00:59:52,060
+الشكل symmetric، ممكن نحط D مكان F و F مكان D، ممكن
+
+783
+00:59:52,060 --> 00:59:56,320
+تظبط، يعني الوقت احنا هنجرب حل منهم، وبقى مش متذكر
+
+784
+00:59:56,320 --> 00:59:58,860
+أنا الحل اللي رأيه، حطه هناك، بس احنا خلينا نحل واحد
+
+785
+00:59:58,860 --> 01:00:02,080
+منهم الاتنين، هيطلعوا صح، لو اختلفوا خلينا نبدأ
+
+786
+01:00:02,080 --> 01:00:05,480
+الدرجة اتنين، مين في هنا الـ degree بتاعه اتنين
+
+787
+01:00:05,480 --> 01:00:11,550
+دي، خلينا ناخد دي نحطها دي، دي connected مع واحدة
+
+788
+01:00:11,550 --> 01:00:15,570
+degree أربعة، وواحدة degree تلاتة، صحيح؟ طيب، مين
+
+789
+01:00:15,570 --> 01:00:22,210
+الـ degree أربعة؟ الـ B، ومين الـ degree تلاتة؟ الـ A،
+
+790
+01:00:22,210 --> 01:00:27,470
+كويس، التانية اللي هي الـ F، برضه نفس الكلام، مع
+
+791
+01:00:27,470 --> 01:00:30,890
+واحدة تلاتة وواحدة اتنين، مين التلاتة كانت؟ الـ C
+
+792
+01:00:30,890 --> 01:00:38,170
+تلاتة، والـ E، الـ C تلاتة، تخضع تخضع تخضع تخضع تخضع
+
+793
+01:00:38,170 --> 01:00:39,050
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+794
+01:00:39,050 --> 01:00:39,950
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+795
+01:00:39,950 --> 01:00:41,650
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+796
+01:00:41,650 --> 01:00:41,830
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+797
+01:00:41,830 --> 01:00:49,950
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+798
+01:00:49,950 --> 01:00:55,150
+تخضع، هذا حل موجود، وممكن نشوف احنا ايش اللي كنا
+
+799
+01:00:55,150 --> 01:00:58,310
+عاملينه، برضه كانت دي، اه دي كنا بدنا نشتغلنا برضه في
+
+800
+01:00:58,310 --> 01:01:00,730
+دي، ممكن الـ F على فكرة تبدأ من الـ F وتطلع معاك و
+
+801
+01:01:00,730 --> 01:01:04,430
+ماشية في الحالة هذه، ممكن تظبط حالتنا لأن هي
+
+802
+01:01:04,430 --> 01:01:07,390
+symmetric أصلاً الرسمة، الرسمة symmetric، لما جينا
+
+803
+01:01:07,390 --> 01:01:09,450
+نطلعنا على الـ degrees، رجعناهم كلهم اتنين اتنين اتنين
+
+804
+01:01:09,450 --> 01:01:15,450
+اتنين، كلهم متشابهة، طيب فهتلاحظوا أنه قدرنا نعمل
+
+805
+01:01:15,450 --> 01:01:18,090
+renaming لمين؟ لقى الرسم، طبعاً، طيب هي دي
+
+806
+01:01:23,710 --> 01:01:28,810
+نشوف عدد الـ nodes الأول هنا خمسة وهناك خمسة، مش
+
+807
+01:01:28,810 --> 01:01:34,490
+الحال، عدد الـ edges تبعتنا نتصور هنا the same
+
+808
+01:01:34,490 --> 01:01:40,310
+vertices، بمش الحال، طيب عدد الـ edges برضه نفس العدد
+
+809
+01:01:40,310 --> 01:01:47,640
+نمسك الـ degrees، لو أخدنا degree بتساوي اتنين، زيرو في
+
+810
+01:01:47,640 --> 01:01:51,860
+زيرو، فش زيرو، في واحد، فش واحد، طب نبدأ معناته في
+
+811
+01:01:51,860 --> 01:01:54,300
+اتنين، طبعاً اللي جابلها زيرو واحد، ده دولت زيرو
+
+812
+01:01:54,300 --> 01:01:59,440
+مافيش شيء، نبدأ ديجري اتنين، خلينا نقول جي وان وهدي
+
+813
+01:01:59,440 --> 01:02:03,680
+جي تو، نبدأ
+
+814
+01:02:03,680 --> 01:02:08,540
+ديجري اتنين، هنا في عندي واحدة، تلاتة، تلاتة، تلاتة
+
+815
+01:02:08,540 --> 01:02:13,440
+تلاتة، هنا في عندي فقط نود واحدة، هنا واحد، اتنين
+
+816
+01:02:13,440 --> 01:02:17,180
+تلاتة، تلاتة، تلاتة، تلاتة، stop، خلاص وقف، مافيش دلوقت
+
+817
+01:02:17,180 --> 01:02:21,700
+أكمل، not isomorphic، فإذا كل واحدة منهم not
+
+818
+01:02:21,700 --> 01:02:24,760
+isomorphic للتانية، not isomorphic لمين؟ للتانية
+
+819
+01:02:24,760 --> 01:02:29,460
+لأنه مبدئياً degree اتنين كان في هنا عندي واحد، و
+
+820
+01:02:29,460 --> 01:02:36,680
+هنا تلاتة، واحد versus three، مش شبه بعض، مش شبه بعض، تمام
+
+821
+01:02:44,640 --> 01:02:49,620
+ومع ذلك، خليني أقول، ومع ذلك... ممكن أخلص كل يوم
+
+822
+01:02:49,620 --> 01:02:58,600
+... ومع ذلك لاحظوا أن الـ ... مش دائماً بتظبط، مش
+
+823
+01:02:58,600 --> 01:03:01,660
+دائماً، بس الشروط هذه اللي حالتها بتظبط، هادي بنسميها
+
+824
+01:03:01,660 --> 01:03:04,640
+necessary condition but not sufficient condition
+
+825
+01:03:05,840 --> 01:03:10,260
+بمعنى شروط ضرورية لازم تتحقق، بس مش كافية، ليست
+
+826
+01:03:10,260 --> 01:03:15,160
+كافية، ليش؟ مش... مش كافية، عشان هسبقكم شوية، شوفوا ليش
+
+827
+01:03:15,160 --> 01:03:19,540
+الشكل هذا، خلينا
+
+828
+01:03:19,540 --> 01:03:22,920
+نسابق شوية، عشان نقول والله لأ، معناته في جزئية صغيرة
+
+829
+01:03:22,920 --> 01:03:24,920
+بدنا نعمل test عليها، وبدنا نخلصنا
+
+830
+01:03:27,910 --> 01:03:36,770
+لحظة، 123456 123456 123456 123456 123456 123456
+
+831
+01:03:36,770 --> 01:03:45
+
+889
+01:07:31,000 --> 01:07:34,440
+باقي النقاط هتظل متصلة مع بعض، فإذا هنا ما فيش لا
+
+890
+01:07:34,440 --> 01:07:40,130
+cut vertex ولا cut edge، تمام. في هذا الـ cut vertex
+
+891
+01:07:40,130 --> 01:07:42,770
+أو الـ cut edge اللي هي بتعمل لنا separation أو
+
+892
+01:07:42,770 --> 01:07:47,430
+separates one connected component أو component
+
+893
+01:07:47,430 --> 01:07:53,370
+into two components if removed. إذا كان إزالته
+
+894
+01:07:53,370 --> 01:07:57,310
+بتخلي الـ one connected component تصير أكثر من one
+
+895
+01:07:57,310 --> 01:08:01,290
+أو من اثنين أو أكثر components، اثنين أو أكثر
+
+896
+01:08:01,290 --> 01:08:05,380
+components. مصطلح ثاني اللي هي الـ weakly connected و
+
+897
+01:08:05,380 --> 01:08:07,960
+الـ strongly connected، weakly connected والـ
+
+898
+01:08:07,960 --> 01:08:11,680
+strongly connected عادة تستخدم في الـ directed graph
+
+899
+01:08:11,680 --> 01:08:16,960
+في الـ directed graph، بمعنى إذا والله كل النقاط متصلة
+
+900
+01:08:16,960 --> 01:08:22,180
+مع بعض، ولكن الاكتشاف بساعدنيش أن أنا امشي بين أي
+
+901
+01:08:22,180 --> 01:08:26,340
+نقطة والـ ثانية، بنسميها weakly connected. طيب إذا
+
+902
+01:08:26,340 --> 01:08:29,400
+واحدة منهم منفصلة تماماً، واضح أن هي not connected
+
+903
+01:08:29,400 --> 01:08:35,600
+أصلاً بتكون connected. أساساً لكن إذا كان حتى بالأسهم
+
+904
+01:08:35,600 --> 01:08:38,960
+من أي نقطة لأي نقطة ثانية بقدر أنشئ، من أي نقطة
+
+905
+01:08:38,960 --> 01:08:42,360
+لأي نقطة بقدر أروح، حسب الاتجاه، بنسميها strongly
+
+906
+01:08:42,360 --> 01:08:47,180
+connected. هنا في الحالة اللي زي هذه، بدي أطلع من A
+
+907
+01:08:47,180 --> 01:08:47,940
+مثلاً للـ B
+
+908
+01:08:52,400 --> 01:08:56,080
+ما فيش... مضطر... هو في connection ولكن اتجاهه مش
+
+909
+01:08:56,080 --> 01:09:00,060
+مظبوط، اتجاهه بالعكس، بنسميها أنه لأ، ما أقدرش أقول أن
+
+910
+01:09:00,060 --> 01:09:02,800
+هو ما فيش connection، بس بقول weakly connected
+
+911
+01:09:02,800 --> 01:09:06,080
+بنسميها weakly connected. طب حالة زي هذه، بدي أروح
+
+912
+01:09:06,080 --> 01:09:09,860
+من A لـ B، طيب
+
+913
+01:09:09,860 --> 01:09:18,360
+بدي أروح من A لـ C، طب A لـ D، طب من B لـ C، طب
+
+914
+01:09:18,360 --> 01:09:25,230
+من الـ... الـ B للـ D، طب من دي لإيه؟ ففي طريق بأمشي
+
+915
+01:09:25,230 --> 01:09:28,550
+مع الـ directed تبعنا، مع الاتجاه تبعنا، من أي نقطة و
+
+916
+01:09:28,550 --> 01:09:32,210
+أي نقطة ثانية، فهنا بنسميها strongly connected
+
+917
+01:09:32,210 --> 01:09:35,950
+فواضحة ثاني، وجهة الفرق بين الـ weakly connected والـ
+
+918
+01:09:35,950 --> 01:09:39,870
+الـ strongly connected. هذه في حالة أنه as a
+
+919
+01:09:39,870 --> 01:09:44,250
+directed graph، ما فيش طريق، ولكن لو نفسها تحولت لـ
+
+920
+01:09:44,250 --> 01:09:48,050
+undirected، بيصير في طريق، بنسميها weakly، بنسميها
+
+921
+01:09:48,050 --> 01:09:51,730
+weakly connection، ولكن ضعيف، الثانية لأ،
+
+922
+01:09:51,730 --> 01:09:56,510
+connection قوي، strongly connected. معنى ذلك أنه
+
+923
+01:09:56,510 --> 01:09:59,330
+هنجد الحاجة الثانية اللي بدي أشتغل عليها، بدنا
+
+924
+01:09:59,330 --> 01:10:03,890
+نشتغل على الـ connection عشان نحدد هل هم isomorphic
+
+925
+01:10:03,890 --> 01:10:08,630
+ولا لأ، إيش الـ connection؟ إنه من أي نقطة عشان
+
+926
+01:10:08,630 --> 01:10:12,390
+أعمله وأرجع لنفس النقطة، جدش الـ degree تبعتي، جدش
+
+927
+01:10:12,390 --> 01:10:16,630
+عدد الـ points اللي أنا مرت عليهم، جدش عدد الـ points
+
+928
+01:10:16,630 --> 01:10:19,950
+اللي مرينا عليهم، الـ path تبعنا، جدش حجمه، جدش الـ size
+
+929
+01:10:19,950 --> 01:10:24,010
+تبعه، فهنا the number and size of connected
+
+930
+01:10:24,010 --> 01:10:27,950
+components، connected components. لما أقول والله بدي
+
+931
+01:10:27,950 --> 01:10:30,250
+أطلع من النقطة هذه وأرجع لها ثاني، معناته ممكن أطلع
+
+932
+01:10:30,250 --> 01:10:36,250
+أشطر بهذا الشكل، ما جدش عدد الـ... اللي هي الـ circle
+
+933
+01:10:36,250 --> 01:10:38,250
+تبعتنا أو الـ circuit، بنتعمل circuit أو... أو
+
+934
+01:10:38,250 --> 01:10:45,450
+circle، لـ individual terms أو individual point
+
+935
+01:10:45,450 --> 01:10:51,050
+هتكون عندي واحد، اثنين، ثلاثة، أربعة، آه، معنى ذلك أن
+
+936
+01:10:51,050 --> 01:10:56,280
+في عندي نقطة، الـ connectivity بتاعتها أربعة، أو الـ
+
+937
+01:10:56,280 --> 01:10:59,300
+path تبعها أربعة. طيب هل هنا، هنا، هنا نقطة فيها
+
+938
+01:10:59,300 --> 01:11:03,280
+أربعة، في نقطة أربعة بس، هل هي نفسها مرتبطة هنا،
+
+939
+01:11:03,280 --> 01:11:08,040
+مرتبطة، ممكن تكون مرتبطة بناء على الـ condition اللي
+
+940
+01:11:08,040 --> 01:11:16,340
+إحنا قلناها، أكمل. وهنا الـ degree تبعته ثلاثة، ما فيش
+
+941
+01:11:16,340 --> 01:11:19,660
+أي loop، الـ degree تبعته ثلاثة، صح؟ طب هنا أكمل، في
+
+942
+01:11:19,660 --> 01:11:22,360
+الـ degree تبعته ثلاثة، أو يعني الـ length تبعته
+
+943
+01:11:22,360 --> 01:11:24,900
+ثلاثة، الـ size تبعته ثلاثة، فيه اثنين، طب ليش ما ظهرش
+
+944
+01:11:24,900 --> 01:11:28,840
+هنا؟ معناته مش... مش... مش isomorphic الاثنين
+
+945
+01:11:28,840 --> 01:11:34,880
+الاثنين مش isomorphic. هي من النقطة هذه عشان
+
+946
+01:11:34,880 --> 01:11:38,520
+أرجع لها، في عندي path واحد، اثنين، ثلاثة. هنا ما فيش أي
+
+947
+01:11:38,520 --> 01:11:42,880
+نقطة برجع لها بـ... بـ... بـ path، الـ size تبعه ثلاثة
+
+948
+01:11:42,880 --> 01:11:49,440
+وإليه؟
+
+949
+01:11:49,440 --> 01:11:53,910
+مش هتلاقوا. خلاص، معناته not isomorphic، رغم أن هي
+
+950
+01:11:53,910 --> 01:11:57,030
+حققت الشروط السابقة، الشروط اللي بدأنا فيها كلها
+
+951
+01:11:57,030 --> 01:12:01,110
+كانت متحققة، بس واضح أنه لأ، مش isomorphic. زودنا بس
+
+952
+01:12:01,110 --> 01:12:04,570
+جزئية الـ connectivity هذه، الـ connectivity اللي
+
+953
+01:12:04,570 --> 01:12:08,050
+زودناها، الجزئية بتاعتنا، أنه عشان يكون في connection
+
+954
+01:12:08,050 --> 01:12:13,510
+بين النقطة ونفسها، النقطة لنفسها connected، جدش الـ
+
+955
+01:12:13,510 --> 01:12:16,770
+size تبع الـ length تبعنا، جدش الـ size تبعنا، واضح أن
+
+956
+01:12:16,770 --> 01:12:20,890
+هنا في ثلاثة، طيب هنا لو اتكلمنا عن الأربعة مثلاً
+
+957
+01:12:22,330 --> 01:12:27,610
+أكمبث هنا أربعة؟ واحد، واحد، واحد، واحد، واحد،
+
+958
+01:12:27,610 --> 01:12:29,810
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+959
+01:12:29,810 --> 01:12:30,850
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+960
+01:12:30,850 --> 01:12:32,850
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+961
+01:12:32,850 --> 01:12:35,930
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+962
+01:12:35,930 --> 01:12:37,470
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+963
+01:12:37,470 --> 01:12:40,370
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+964
+01:12:40,370 --> 01:12:41,070
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+965
+01:12:41,070 --> 01:12:49,090
+واحد، واحد، واحد
+
+966
+01:12:58,920 --> 01:13:03,140
+إحنا في الشرط
+
+967
+01:13:03,140 --> 01:13:06,700
+الأول، كنا بنقول أن عدد الـ edges يساوي بعض، بس هنا
+
+968
+01:13:06,700 --> 01:13:11,340
+لأ، هنا صرنا بنحدد قد إيش طول مجموع الـ edges عشان
+
+969
+01:13:11,340 --> 01:13:15,120
+أرجع لنفس النقطة عشان أعمل loop أو أعمل circuit
+
+970
+01:13:16,090 --> 01:13:20,810
+عشان أعمل circuit، جدش عدد الـ edges اللي محتاجها،
+
+971
+01:13:20,810 --> 01:13:24,770
+فواضح أنه هنا كنت محتاج أعمل أو أكمل loop بثلاثة
+
+972
+01:13:24,770 --> 01:13:27,330
+edges، هنا ما كانش في إمكاني أعملها بثلاثة edges
+
+973
+01:13:27,330 --> 01:13:32,350
+فواضح أنه هذه لأ، مش مماثلة لها، هذه مماثلة، أنه كان
+
+974
+01:13:32,350 --> 01:13:35,190
+ممكن نفس الـ characteristic اللي بقدر أطلّعها من هنا
+
+975
+01:13:35,190 --> 01:13:38,130
+هي هي أطلّعها من هنا، بس هو هذا ماصارش فعلياً، هذا
+
+976
+01:13:38,130 --> 01:13:41,110
+ما حصلش، معناه واضح أن هنا كان في ثلاثة، هناك ما كانش
+
+977
+01:13:41,110 --> 01:13:45,340
+في ثلاثة، فهيك بنقدر نقول أن هدول الاثنين مش
+
+978
+01:13:45,340 --> 01:13:48,480
+isomorphic، وبناء على هيك بنكون خلصنا إن شاء الله
+
+979
+01:13:48,480 --> 01:13:50,920
+محاضرتنا لـ graphs، وبنكون خلصنا المصاق إن شاء الله
+
+980
+01:13:50,920 --> 01:13:53,940
+طالع، بنشوفكوا إن شاء الله في مصاقات أخرى، ويعطيكوا
+
+981
+01:13:53,940 --> 01:13:55,860
+الصحة، والعفو، يا كل عام وأنتم بخير، وربنا يوفقكم
+
+982
+01:13:55,860 --> 01:13:56,480
+في امتحاناتكم
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..92669b50b232d50dcdeb9f0b65f26ff4c54c5356
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA_postprocess.srt
@@ -0,0 +1,3928 @@
+1
+00:00:21,090 --> 00:00:22,950
+بسم الله الرحمن الرحيم الصلاة والسلام عليكم ورحمة
+
+2
+00:00:22,950 --> 00:00:25,290
+الله وبركاته يا أبو حميد وسيدنا محمد وعلى أهلي
+
+3
+00:00:25,290 --> 00:00:30,070
+وصحابي أجمعين نبدأ اليوم حاضرتنا من ال graph اللي
+
+4
+00:00:30,070 --> 00:00:32,570
+بدأنا المرة اللي فاتت و المرة اللي فاتت أخدنا
+
+5
+00:00:32,570 --> 00:00:37,010
+مجموعة أنواع هيك في قجلة يعني بس أخدنا إيش يعني ..
+
+6
+00:00:37,010 --> 00:00:40,610
+لما نتكلم عن undirected graph أو simple graph إيش
+
+7
+00:00:40,610 --> 00:00:44,730
+معناه؟ اتكلمنا عن ال .. ال multiple أو ال
+
+8
+00:00:44,730 --> 00:00:47,670
+multigraph اتكلمنا عن ال pseudograph و اتكلمنا عن
+
+9
+00:00:47,670 --> 00:00:51,910
+ال directed graphو ال multi .. او ال directed
+
+10
+00:00:51,910 --> 00:00:55,370
+multi graph اتكلمنا عن الخمسة ان واحد و للمرة اللي
+
+11
+00:00:55,370 --> 00:00:59,370
+فاتت اتكلمنا و وجفنا عندهم لعند ما وصلنا ل section
+
+12
+00:00:59,370 --> 00:01:03,130
+عشرة اتنين و قولنا ان المرة الجاية هناخدها هنتكلم
+
+13
+00:01:03,130 --> 00:01:07,250
+عن .. عن ال .. شوية terminology خاصة بال graphs
+
+14
+00:01:07,250 --> 00:01:10,290
+خاصة بإيش؟ بال graphs ال graphs هذه هنتكلم عن ال
+
+15
+00:01:10,290 --> 00:01:14,570
+adjacent هنتكلم عن ال connects هنتكلم عن ال end
+
+16
+00:01:14,570 --> 00:01:18,450
+pointsال degree مهم جدا إيش يعني degree ال initial
+
+17
+00:01:18,450 --> 00:01:21,670
+و ال terminal ال in degree ال out degree ال
+
+18
+00:01:21,670 --> 00:01:24,730
+complete هنا من ال complete و لتحت هنتكلم عن
+
+19
+00:01:24,730 --> 00:01:29,210
+مجموعة أنواع عن أنواع من ال graphs ال cycles ال
+
+20
+00:01:29,210 --> 00:01:32,770
+wheels ال cubes
+
+21
+00:01:33,570 --> 00:01:36,770
+الـ bipartate و بعدين هنتكلم عن two properties هيك
+
+22
+00:01:36,770 --> 00:01:39,970
+سريعين اللي هي ال sub graph إيش يعني sub graph و
+
+23
+00:01:39,970 --> 00:01:43,430
+إيش يعني union كيف نعمل union لل graphs مع بعض و
+
+24
+00:01:43,430 --> 00:01:46,330
+بعدين بنشوف إيش بيكون ضايل علينا لو بيكون ضايل
+
+25
+00:01:46,330 --> 00:01:48,910
+علينا يمكن ال isomorphism و عملية ال
+
+26
+00:01:48,910 --> 00:01:54,490
+representation لل graphs نبدأ بال adjacency أو
+
+27
+00:01:54,490 --> 00:02:01,470
+المجاورة المجاورة لما يكون في عندنا two nodesو
+
+28
+00:02:01,470 --> 00:02:06,610
+الاتنين هدولة متصلين مع بعض U و V فهم متجاورين
+
+29
+00:02:06,610 --> 00:02:11,090
+بعدين في طريق بينهم او في link بينهم في edge بينهم
+
+30
+00:02:11,090 --> 00:02:15,630
+فهم بنتسميهم متجاورين ف U و V are adjacent او
+
+31
+00:02:15,630 --> 00:02:21,760
+neighborsجيران أو connected متصلين في توصيل بينهم
+
+32
+00:02:21,760 --> 00:02:25,000
+يوجد توصيل بينهم ال edge E is incident with
+
+33
+00:02:25,000 --> 00:02:30,440
+vertices U و V و ماحددتش هي incident من مين لأنه
+
+34
+00:02:30,440 --> 00:02:36,780
+بشطل هنا undirected مافيش اتجاه ف from U to V بمشي
+
+35
+00:02:36,780 --> 00:02:41,820
+الحال from V to U برضه بمشيبمش الحال انا مش محدد
+
+36
+00:02:41,820 --> 00:02:45,120
+مين الاتجاه مش محددين اتجاهنا ففي الحالة هذه
+
+37
+00:02:45,120 --> 00:02:50,580
+بنسميها incident with vertices u and v هذه هذي بمش
+
+38
+00:02:50,580 --> 00:02:55,560
+الحال عساس ان هي undirected الhe connect u وv هي
+
+39
+00:02:55,560 --> 00:03:01,390
+توصل u بv صحيحما حددناش لسه اتجاهها ال vertices U
+
+40
+00:03:01,390 --> 00:03:04,330
+vertices اللي هي جمع ال vertex ال vertex اللي
+
+41
+00:03:04,330 --> 00:03:06,350
+قولنا المرة اللي فاتت اللي هي قمة أو بمعنى node
+
+42
+00:03:06,350 --> 00:03:10,510
+المقصود فيها ال node تبعتنا هذه فهذه vertex V و
+
+43
+00:03:10,510 --> 00:03:15,170
+vertex U طيب ال vertices U و V are end points of
+
+44
+00:03:15,170 --> 00:03:21,990
+edge E هي النهايات لل link E هذا لل link E هذه
+
+45
+00:03:21,990 --> 00:03:25,250
+النهاية و هذه النهاية اللي هم أطرافه يعني الأطراف
+
+46
+00:03:26,040 --> 00:03:31,480
+لل link من هنا بدنا نتكلم عن ال degree ال degree
+
+47
+00:03:31,480 --> 00:03:36,740
+لكل vertex لحالها كل vertex فيه لها degree طيب ال
+
+48
+00:03:36,740 --> 00:03:41,220
+total او ال graph كله على بعضه فيه له برضه degree
+
+49
+00:03:41,220 --> 00:03:44,020
+بدنا نحسبها degree هذا ايش يعني degree ال degree
+
+50
+00:03:44,020 --> 00:03:49,060
+بمعنى انه اكم edge connected ل ال vertex فال
+
+51
+00:03:49,060 --> 00:03:52,680
+vertex هذه هنا connected ب edge واحدة معناه ذلك ان
+
+52
+00:03:52,680 --> 00:03:55,180
+ال degree بتاعتها واحدةمعناه ذلك أن ال degree
+
+53
+00:03:55,180 --> 00:04:00,320
+بتاعتها بواحد نفترض أنه في إلها self loop ال self
+
+54
+00:04:00,320 --> 00:04:04,880
+loop بتنحسب مرتين بتنحسب مرتين أنا ماليش علاقة كيف
+
+55
+00:04:04,880 --> 00:04:08,700
+شكلها هنا أنا بالنسبالي و أنا داخل ال U أكم طريق
+
+56
+00:04:08,700 --> 00:04:13,840
+بقدر أطلع منه من ال U؟ في عندى طريق اتنين تلاتةفال
+
+57
+00:04:13,840 --> 00:04:18,120
+degree هنا صارت تلاتة فإذا ال .. لما بتكلم هنا عن
+
+58
+00:04:18,120 --> 00:04:23,140
+ال self loop تنعد مرتين تنحسب مرتين ليش؟ لأن في
+
+59
+00:04:23,140 --> 00:04:27,900
+لها طريقين واحد اتنين فهنا ال degree هذه degree u
+
+60
+00:04:27,900 --> 00:04:34,920
+هتساوي تلاتة طيب degree v هتساوي
+
+61
+00:04:34,920 --> 00:04:39,580
+واحد هتساوي في الحالة هذه واحد طيب لو في عندنا
+
+62
+00:04:39,580 --> 00:04:47,350
+vertex ال degree بتاعتها zeroبهذا الشكل و بس zero
+
+63
+00:04:47,350 --> 00:04:51,370
+معناته مافيش اي طريق حولها city ال city هذه نائية
+
+64
+00:04:51,370 --> 00:04:54,870
+بلد نائية مالهاش اي طريق عليها ففي الحالة هذه
+
+65
+00:04:54,870 --> 00:05:00,270
+بنسميها isolated منعزلة معزولة تمام isolated في
+
+66
+00:05:00,270 --> 00:05:04,210
+الحالات طيب لما نكونها degree واحد بهذا الشكل
+
+67
+00:05:04,210 --> 00:05:11,330
+بنسميها pendant او معلق بالظبط عامل زي معلقةبخيط
+
+68
+00:05:11,330 --> 00:05:14,630
+يعني مثلا مربوطة بخيط على جد خيط على جد طريق واحد
+
+69
+00:05:14,630 --> 00:05:19,430
+فهذا اسمها dependent في الحالة اللي بيكون فيها ال
+
+70
+00:05:19,430 --> 00:05:24,390
+degree بتاعتها واحد okay ال handshaking theorem ال
+
+71
+00:05:24,390 --> 00:05:28,070
+handshaking theorem فعليا هي نظرية بنستخدمها عشان
+
+72
+00:05:28,070 --> 00:05:31,510
+نحسب فيها ال degrees نجدش ال degrees للرسم تبعنا
+
+73
+00:05:31,510 --> 00:05:34,570
+كله على بعض فال degree في الحالة اللي عندنا هنا
+
+74
+00:05:34,570 --> 00:05:41,070
+summationdegree of V و V هذه belong to capital V
+
+75
+00:05:41,070 --> 00:05:45,450
+capital V هي set of vertices set of vertices او
+
+76
+00:05:45,450 --> 00:05:50,170
+set of nodes set of nodes بمعنى كل ال nodes تبعتنا
+
+77
+00:05:50,170 --> 00:05:54,030
+معنا ذلك ان انا بتكلم عن ال graph كله كل graph على
+
+78
+00:05:54,030 --> 00:05:57,010
+بعض وموجدش ال degree تبعته ال degree تبعته عبارة
+
+79
+00:05:57,010 --> 00:05:59,290
+عن ال degree لل node الأولى زي ال degree لل node
+
+80
+00:05:59,290 --> 00:06:01,210
+التانية لو في node تارتة وزيادة ال degree لل node
+
+81
+00:06:01,210 --> 00:06:04,690
+التارتة زيادة الرابع لما نخلص كل ال nodes اللي
+
+82
+00:06:04,690 --> 00:06:08,710
+موجودةلالي graph لالي graph طبعا فهنا ال summation
+
+83
+00:06:08,710 --> 00:06:13,970
+في الحالة ده هسوي اتنين E ليش اتنين لأنه كل E انا
+
+84
+00:06:13,970 --> 00:06:18,270
+حسبته مرتين مرة بالنسبة لل node اللي في أوله و مرة
+
+85
+00:06:18,270 --> 00:06:22,110
+بالنسبة لل node اللي في اخره مظبوط لحظوا هنا انا
+
+86
+00:06:22,110 --> 00:06:26,260
+حسب degree واحد ليش واحد من ال Eطيب هنا لما حسبت
+
+87
+00:06:26,260 --> 00:06:29,140
+تلاتة واحدة منهم كانت لل E يعني ال E هتنحسبت مرتين
+
+88
+00:06:29,140 --> 00:06:33,040
+عشان هيك فعلا ال degree للكل على بعضه هتكون مرة
+
+89
+00:06:33,040 --> 00:06:35,920
+اجت من هنا و مرة اجت من هنا فال E مرتين انحسبت
+
+90
+00:06:35,920 --> 00:06:41,750
+فعشان يمكن نقول اتنين في E اللي هو جداشة عددال
+
+91
+00:06:41,750 --> 00:06:46,250
+edges اللي موجودة على اعتبار ان ال E هنا هي ال set
+
+92
+00:06:46,250 --> 00:06:50,430
+of edges لما باخدها cardinality معناه تجدش عدد ال
+
+93
+00:06:50,430 --> 00:06:55,950
+edges اللي موجودة في اتنين عرفنا ليش في اتنين لإن
+
+94
+00:06:55,950 --> 00:07:00,730
+فعليا ال node اللي في الأول انحسب بالنسبالها و ال
+
+95
+00:07:00,730 --> 00:07:03,030
+node اللي في الآخر برضه انحسب بالنسبالها طبعا هنا
+
+96
+00:07:03,030 --> 00:07:05,750
+مافيش لا أول ولا آخر يعني الصراحة بس أنا بقولكوا
+
+97
+00:07:05,750 --> 00:07:08,350
+في الأول و في الآخر بس لإن هو undirected مش معروف
+
+98
+00:07:08,350 --> 00:07:11,470
+مين الأول و مين الآخر أساسامين الأولى ومين التانية
+
+99
+00:07:11,470 --> 00:07:13,890
+مش معروف المهم ان هي connected between two
+
+100
+00:07:13,890 --> 00:07:19,170
+vertices و بس في الآخر هيساوي 2 في cardinality لل
+
+101
+00:07:19,170 --> 00:07:24,870
+set E بمعنى عدد ال edges تبعتكم عدد ال edges في 2
+
+102
+00:07:24,870 --> 00:07:30,090
+يعطينا ال degree لكل الرسم على بعض اوكي من هنا اذا
+
+103
+00:07:30,090 --> 00:07:33,870
+كانت عدد ال edges تبعتكم فردي ال degree ده منزوجي
+
+104
+00:07:34,970 --> 00:07:37,670
+by logic ما هي .. إيش ما يكون .. إيش ما تكون عدد
+
+105
+00:07:37,670 --> 00:07:40,730
+ال .. ال lectures تبعتكم ال degree لل graph كله
+
+106
+00:07:40,730 --> 00:07:43,690
+على بعضه دائما زوجي لأنها هي اتنين في some integer
+
+107
+00:07:43,690 --> 00:07:48,510
+اتنين في some integer فدائما هتكون زوجي هي ال ..
+
+108
+00:07:48,510 --> 00:07:52,110
+النتيجة من النظرية طيب كل هذا الكلام كان إيه؟
+
+109
+00:07:52,110 --> 00:07:56,290
+undirected لما نيجي على ال directed الأمور بتختلف
+
+110
+00:07:56,290 --> 00:07:59,130
+شوية بصير المسميات حتى ال terminology بتاعتنا
+
+111
+00:07:59,130 --> 00:08:02,970
+هتختلف هتختلف لأنه بدنا نحددها logic من البداية و
+
+112
+00:08:02,970 --> 00:08:07,680
+من النهايةفي شغل، من البداية و من النهاية هنا
+
+113
+00:08:07,680 --> 00:08:11,000
+حاطين relation لمين أو عاملين mapping لمين ل U و V
+
+114
+00:08:11,000 --> 00:08:19,620
+U و V معناته ال link جاي من U ل V بهذا الشكل طيب
+
+115
+00:08:19,620 --> 00:08:26,590
+في الحالة دي U is adjacent to Vto V أنا رايح to V
+
+116
+00:08:26,590 --> 00:08:32,830
+فإذا V هي النهاية طبعتي طيب إذا بدأ أنسبها لل V V
+
+117
+00:08:32,830 --> 00:08:39,370
+اسم adjacent from you بعرف من المصطلحين دول to و
+
+118
+00:08:39,370 --> 00:08:42,170
+from إن هذا directed نعرف إن أحنا بتكلم عن
+
+119
+00:08:42,170 --> 00:08:47,090
+directed graphE graph كويس او directed link او
+
+120
+00:08:47,090 --> 00:08:53,990
+directed link او edge كويس E هيها E comes from U
+
+121
+00:08:53,990 --> 00:09:02,210
+هيها بادية من U طيب او goes to V فالمصطلحات هذه في
+
+122
+00:09:02,210 --> 00:09:05,530
+ال undirected بنقولهاش connected to كذا و خلاص هي
+
+123
+00:09:05,530 --> 00:09:09,210
+A و B connected together و خلصنا ممكن نقول are
+
+124
+00:09:09,210 --> 00:09:11,710
+connected U و V are connected و stop خلاص خلصنا
+
+125
+00:09:11,710 --> 00:09:15,590
+متواصلينمين قبل مين، مين بعد مين، ماحدش بعرف، بس
+
+126
+00:09:15,590 --> 00:09:19,070
+هنا لأ، هنا بدنا نكون دقيقين، بدنا نعرف بالظبط E
+
+127
+00:09:19,070 --> 00:09:24,690
+ال E هذه من وين بادية، من وين منتهية، E connects U
+
+128
+00:09:24,690 --> 00:09:31,610
+to V هي مش U and V، هناك سميناها U and V، بتوصل U
+
+129
+00:09:31,610 --> 00:09:38,130
+و V، هنا لأ، U to V، بتوصل إلى U، رايح ل V أو E
+
+130
+00:09:38,130 --> 00:09:45,650
+goes from Uرايح من U ل V فالمصطلحات كلمتين تلاتة
+
+131
+00:09:45,650 --> 00:09:49,670
+بيميزوه لأن أنا بتكلم عن directed طيب ال initial
+
+132
+00:09:49,670 --> 00:09:52,870
+vertex of E ال initial vertex ال .. ال .. ال
+
+133
+00:09:52,870 --> 00:09:55,570
+vertex اللي بادي منها ال initial value تبعتك ..
+
+134
+00:09:55,570 --> 00:10:01,830
+تبعتك هي ال U فإذا is U طيب او ال terminal ال
+
+135
+00:10:01,830 --> 00:10:05,170
+terminal النهاية النهاية ال .. ال .. ال .. او
+
+136
+00:10:05,170 --> 00:10:07,870
+النهاية الطرفية تبعتكم الطرف النهائي تبعتكم اللي
+
+137
+00:10:07,870 --> 00:10:13,080
+هو V فهذا هيكونالـ vertex أو ال terminal vertex لل
+
+138
+00:10:13,080 --> 00:10:22,200
+E هي ال V طيب في ال directed degree عشان نحسب ال
+
+139
+00:10:22,200 --> 00:10:26,400
+degree في الحالة هذه بقدرش أقول إن هي خلاص في
+
+140
+00:10:26,400 --> 00:10:29,440
+الحالة اللي زي هذه هي هي ال connection و خلاص و
+
+141
+00:10:29,440 --> 00:10:32,660
+جديش عدد اللي طالع لأ انتوا هنا ديروا برك و في in
+
+142
+00:10:32,660 --> 00:10:37,720
+و في out معناه ذلك لإن في link هيكون طالع من ال
+
+143
+00:10:37,720 --> 00:10:41,270
+vertex و في link داخل ال vertexفي الحلقة دي حاسيب
+
+144
+00:10:41,270 --> 00:10:48,930
+في عندي in degree و في out degree in degree و out
+
+145
+00:10:48,930 --> 00:10:54,330
+degree هذه ال in degree بتسميها degree سالب و
+
+146
+00:10:54,330 --> 00:11:02,950
+degree موجب موجب فإذا أنا بتكلم طالع منها موجب
+
+147
+00:11:02,950 --> 00:11:05,830
+معناته طالع من ال link اللي طالع من مين من ال
+
+148
+00:11:05,830 --> 00:11:10,490
+vertexسالب لأ ال link اللي داخل لل vertex داخل لل
+
+149
+00:11:10,490 --> 00:11:14,550
+vertex خلّينا ناخد طبعا في النهاية ال degree لل
+
+150
+00:11:14,550 --> 00:11:17,530
+total كله على بعضه اللي هو مجموع التنتين اللي هو
+
+151
+00:11:17,530 --> 00:11:20,850
+مجموع degree in و degree out او ال in degree و ال
+
+152
+00:11:20,850 --> 00:11:23,870
+out degree كويسة لو نمسكهم لل example اللي احنا
+
+153
+00:11:23,870 --> 00:11:32,650
+حاطينه هنا هنا ال out degree جداش of v يساوي zero
+
+154
+00:11:32,650 --> 00:11:34,310
+صحيح ال in degree
+
+155
+00:11:37,700 --> 00:11:46,240
+يساوي واحد طيب هنا ال out degree هيساوي نين طيب ال
+
+156
+00:11:46,240 --> 00:11:54,100
+in degree واحد صحيح المجموع عند هنا تلاتة المجموع
+
+157
+00:11:54,100 --> 00:11:56,680
+عند هنا واحد المجموع عند هنا واحد و عندنا تلاتة
+
+158
+00:11:56,680 --> 00:12:01,700
+طيب ال degree totally هنا لتنتين اتنين و ال in
+
+159
+00:12:01,700 --> 00:12:04,880
+degree ال out degree اتنين و ال in degree اتنين
+
+160
+00:12:04,880 --> 00:12:10,990
+لازم يساوي بعضلأن كل edge هي in بالنسبة لواحد اكيد
+
+161
+00:12:10,990 --> 00:12:15,890
+out بالنسبة للتاني مدام طالعة من U رايحة ل V فهي
+
+162
+00:12:15,890 --> 00:12:20,230
+in لواحد منهم و out للتاني هتنحسب مرتين احنا زي
+
+163
+00:12:20,230 --> 00:12:23,250
+المرة اللي فاتت قولنا هتنحسب مرتين بس هنا هنميزهم
+
+164
+00:12:23,250 --> 00:12:27,990
+ان هي مرة هتكون in و مرة هتكون out فمعنى ذلك ان
+
+165
+00:12:27,990 --> 00:12:31,890
+مجموع ال in لازم يطلع بساوء مجموع ال out لل graph
+
+166
+00:12:31,890 --> 00:12:35,710
+كله على بعضه صح؟ biological منطقية لازم تطلع هنا
+
+167
+00:12:35,710 --> 00:12:39,750
+okayمافيش link بالنسبالك و هيكون طالع هيك و سايب
+
+168
+00:12:39,750 --> 00:12:44,690
+هذا مابنحسبش مادام مش واصل ل vertex معناته ده طريق
+
+169
+00:12:44,690 --> 00:12:49,050
+مش كاملة مش كاملة مابنحسبش هذه غير محسوب ال link
+
+170
+00:12:49,050 --> 00:12:52,150
+هدا هيك غير محسوب إذا ماوصلش ل vertex okay في
+
+171
+00:12:52,150 --> 00:12:55,790
+النهاية ال degree لل total هتكون عبارة عن ال
+
+172
+00:12:55,790 --> 00:13:01,230
+degree minus plus ال degree plus ل ال vertex نفسها
+
+173
+00:13:01,850 --> 00:13:04,810
+أو ال total كله على بعضه فال total كله على بعضه
+
+174
+00:13:04,810 --> 00:13:08,390
+المفروض انه كل ال in يساوي كل ال out مع بعضهم
+
+175
+00:13:08,390 --> 00:13:11,470
+ومجموحه في النهاية هو ال degree لل graph كله على
+
+176
+00:13:11,470 --> 00:13:14,830
+بعضه لل graph كله على بعضه نرجع لل directed hand
+
+177
+00:13:14,830 --> 00:13:19,570
+tracking theorem ناخدها النظرية دي مدام احنا قولنا
+
+178
+00:13:19,570 --> 00:13:22,830
+ان ال in degree بيساوي ال out degree معناته فعلا
+
+179
+00:13:22,830 --> 00:13:26,930
+ال summation لكل ال vertices لل in هيهم احنا هنا
+
+180
+00:13:26,930 --> 00:13:30,490
+عملنا ال summation هيها ال out زاد ال outسوّالنا
+
+181
+00:13:30,490 --> 00:13:33,670
+اتنين، اتنين هذا لمن؟ لجراف كله على بعضه فهو هذا
+
+182
+00:13:33,670 --> 00:13:35,930
+كل ال summation على بعضه لان احنا عملنا summation
+
+183
+00:13:35,930 --> 00:13:39,750
+لل vertex B زي ال summation لل vertex U طلع
+
+184
+00:13:39,750 --> 00:13:43,410
+باتنين، هاي المجموع كله على بعضه، هذا لمن؟ لل in،
+
+185
+00:13:43,410 --> 00:13:49,800
+هيساوي برضه ال summation لل outطيب الاتنين مجموحهم
+
+186
+00:13:49,800 --> 00:13:52,740
+بيعطيني ال total لل graph كله على بعضه معناته ال
+
+187
+00:13:52,740 --> 00:13:57,160
+total لل graph كله على بعضه يساوي 2 in أو 2 out
+
+188
+00:13:57,160 --> 00:14:01,720
+فإذا كل واحد منهم يساوي نص لأن بيساوي بعض الاتنين
+
+189
+00:14:01,720 --> 00:14:05,600
+فإذا كل واحد منهم يساوي نص ال degree أو ال total
+
+190
+00:14:05,600 --> 00:14:09,740
+degree طيب ال total degree قبل هيك احنا قلنا انه
+
+191
+00:14:09,740 --> 00:14:16,260
+بيساوي 2E طب نصه؟E E واحدة طيب خلينا نتأكد من
+
+192
+00:14:16,260 --> 00:14:19,220
+الكلام هذا فعلا الكلام هيك في الحالة تبعتنا هذا
+
+193
+00:14:19,220 --> 00:14:25,900
+صحيح ولا غير صحيح لحظوا هنا مجموحهم أربعة أو
+
+194
+00:14:25,900 --> 00:14:29,140
+تاخدوا مجموع من هنا برضه أيه أربعة ففي النهاية أنا
+
+195
+00:14:29,140 --> 00:14:32,360
+بتكلم عن أربعة هذه مجموعة ال degrees كلها على بعض
+
+196
+00:14:32,360 --> 00:14:37,510
+كل ال degrees مع بعضها نصهاإتنين يعني معنى ذلك أنه
+
+197
+00:14:37,510 --> 00:14:40,990
+المفروض أن في عندى اتنين links فعلا في عندى link
+
+198
+00:14:40,990 --> 00:14:48,350
+أول و link تاني E1 و E2 فعلا عندى E1 و E2 مجموح من
+
+199
+00:14:48,350 --> 00:14:53,770
+فقط اتنين هنا اتنينفالاتنين عبارة عن نص ال degree
+
+200
+00:14:53,770 --> 00:14:58,050
+ال total اللي هو كدهش هيكون؟ أربعة أو الاتنين هي
+
+201
+00:14:58,050 --> 00:15:03,790
+نفس ال in مجموع ال in degree أو ال out degree فهي
+
+202
+00:15:03,790 --> 00:15:07,030
+فعلا ال in degree هي اتنين وال out degree اتنين
+
+203
+00:15:10,810 --> 00:15:13,150
+طبعا هذه جزئية اللى كنا بنتكلم فيها عن ال
+
+204
+00:15:13,150 --> 00:15:17,450
+terminology طب ندخل الوجه شوية على بعض أنواع ال
+
+205
+00:15:17,450 --> 00:15:20,430
+graphs بعض أنواع ال graphs من ال graphs المهمة جدا
+
+206
+00:15:20,430 --> 00:15:22,830
+و اللي لها تطبيقات الحقيقة بتاعة تاخدوها يمكن
+
+207
+00:15:22,830 --> 00:15:26,610
+لاحقا في كذا مساق منها ال complete graphs هنتكلم
+
+208
+00:15:26,610 --> 00:15:28,930
+عن ال complete graphs هنتكلم عن ال cycles هنتكلم
+
+209
+00:15:28,930 --> 00:15:31,490
+عن ال wheels هنتكلم عن ال n cubes هنتكلم عن ال
+
+210
+00:15:31,490 --> 00:15:34,370
+bipartate و هنتكلم finally عن ال complete
+
+211
+00:15:34,370 --> 00:15:37,610
+bipartate graphs نبدأهم واحد واحد نبدأ بال
+
+212
+00:15:37,610 --> 00:15:43,430
+complete ال complete هيكون عندنان vertices او ن
+
+213
+00:15:43,430 --> 00:15:47,370
+nodes الـ n nodes هدولة كل node connected مع ال
+
+214
+00:15:47,370 --> 00:15:52,010
+other nodes كل node connected مع كل ال nodes
+
+215
+00:15:52,010 --> 00:15:57,810
+التانيين فهي معناها فهنا بتسميها kn انها دلني هي
+
+216
+00:15:57,810 --> 00:16:02,790
+جدية الشيعة عدد ال nodes عدد ال nodes فهنا ال node
+
+217
+00:16:02,790 --> 00:16:08,780
+واحدة فبسميها k1عندي two nodes بتسميها K2 عندي
+
+218
+00:16:08,780 --> 00:16:13,780
+three nodes بتسميها K3 في النهاية كل نقطة متصلة مع
+
+219
+00:16:13,780 --> 00:16:18,060
+مين؟ مع ال other points مع كل ال other points مع
+
+220
+00:16:18,060 --> 00:16:22,280
+every point مع every point تانين كويس و التاني نفس
+
+221
+00:16:22,280 --> 00:16:26,020
+الكلام و التالتة نفس الكلام هنا نفس القصة أن أربعة
+
+222
+00:16:26,020 --> 00:16:29,920
+معناه ذلك أن كل واحدة ال degree بتاعتها تلتة لأنه
+
+223
+00:16:29,920 --> 00:16:33,660
+متصلة مع التلتة اللي ضايقينه كل point هتكون متصلة
+
+224
+00:16:33,660 --> 00:16:37,870
+مع التلتة اللي ضايقينهمدام أربعة كل واحدة هتكون
+
+225
+00:16:37,870 --> 00:16:39,830
+متصلة مع التلاتة اللي ضايلة فكل واحدة degree
+
+226
+00:16:39,830 --> 00:16:43,770
+بتاعتها تلاتة كل واحدة degree بتاعتها تلاتة K خمسة
+
+227
+00:16:43,770 --> 00:16:46,830
+برضه خمسة nodes معناه ذلك أنه كل node degree
+
+228
+00:16:46,830 --> 00:16:50,030
+بتاعتها أربعة تمام أربعة و الكلام نفس الكلام
+
+229
+00:16:50,030 --> 00:16:55,270
+بنكمله طيب في ال K أو ال complete graphs جدش عدد
+
+230
+00:16:55,270 --> 00:16:59,790
+ال edges بتاعتنا جدش عدد ال edges اللي هنااللي
+
+231
+00:16:59,790 --> 00:17:04,090
+موجودين عندنا هيكونوا بساوة summation from 1 to n
+
+232
+00:17:04,090 --> 00:17:09,590
+-1 لل I وهذا طبعا بنحلها باستخدام ال Euler theorem
+
+233
+00:17:09,590 --> 00:17:15,090
+بتاعة Euler theorem بس ناخد بأنه n to minus one n
+
+234
+00:17:15,090 --> 00:17:20,850
+minus one القانون تبعنا لما كان summation to n كان
+
+235
+00:17:20,850 --> 00:17:27,940
+بساوة n في n plus 1 على 2 طب هنا minus oneبصير هنا
+
+236
+00:17:27,940 --> 00:17:32,000
+minus one وهنا minus one هذه صارت minus one هنا
+
+237
+00:17:32,000 --> 00:17:40,880
+وهذه صارت one zero صارت n في n minus one ال
+
+238
+00:17:40,880 --> 00:17:45,520
+degree
+
+239
+00:17:45,520 --> 00:17:50,260
+لكل واحدة منهم برضه سهل جدش عددهم نقص واحدال
+
+240
+00:17:50,260 --> 00:17:53,580
+degree للنقطة هذه عددهم أربعة نقص واحد فإذا ال
+
+241
+00:17:53,580 --> 00:17:55,500
+degree تلاتة هي تلاتة و ال degree هنا تلاتة و ال
+
+242
+00:17:55,500 --> 00:17:59,420
+degree هنا تلاتة ال degree لكل واحدة منهم تلاتة
+
+243
+00:17:59,420 --> 00:18:03,920
+طيب مجموحم اتناش اتناش من وين جبناها اتناش تلاتة
+
+244
+00:18:03,920 --> 00:18:08,000
+في أربعة تلاتة في أربعة جبناها من ال edges كم يمكن
+
+245
+00:18:08,000 --> 00:18:12,620
+نجبها من ال edges في اتنين صحيح مش احنا قلنا ان ال
+
+246
+00:18:12,620 --> 00:18:16,820
+degree للكل بيسوء اتنين في absolute Eبرضه هنا
+
+247
+00:18:16,820 --> 00:18:19,820
+اعطيناكوا إياها ال edges معنا ذلك مباشرة من هنا
+
+248
+00:18:19,820 --> 00:18:22,960
+بتقدروا تجيبوا عدد ال degrees ال total من هنا
+
+249
+00:18:22,960 --> 00:18:27,080
+مباشرة من خلاص ممكن عدد number of nuts مضروب بال
+
+250
+00:18:27,080 --> 00:18:30,120
+.. بالظبط ممكن تعملوا بنفس الفكرة عساس ان كل واحدة
+
+251
+00:18:30,120 --> 00:18:36,760
+إلها three degrees three في عددهم بالظبطOkay ال
+
+252
+00:18:36,760 --> 00:18:41,360
+cycles هذه واحدة من أنواع ال topologies اللي ممكن
+
+253
+00:18:41,360 --> 00:18:46,460
+تمر عليكم في الشبكات لل ring connection في ال ring
+
+254
+00:18:46,460 --> 00:18:50,660
+connection بتتوصل عادة بهذا الشكل ال BC بتكون كل
+
+255
+00:18:50,660 --> 00:18:54,580
+BC متوصل مع التاني كل BC بتكون متوصل مع التاني
+
+256
+00:18:54,580 --> 00:18:58,420
+فبتكون في النهاية عاملة ring بتكون عاملة شكل ring
+
+257
+00:18:58,420 --> 00:19:01,820
+طبعا عشان تكون شكل ring الأصل أنه بيبدأ من C تلاتة
+
+258
+00:19:01,820 --> 00:19:07,460
+C2 بعملش ring بعملش cycleC تلاتة بيعملش cycle طيب
+
+259
+00:19:07,460 --> 00:19:11,360
+في الآخر لازم يكون أكبر من أو يسوى تلاتة لأنه
+
+260
+00:19:11,360 --> 00:19:16,040
+اتنين بيعملش cycle تمام فال cycle on N vertices
+
+261
+00:19:16,040 --> 00:19:21,000
+بنسميها C من كلمة cycle بنسميها CNN عبارة عن
+
+262
+00:19:21,000 --> 00:19:25,240
+simple graph هذا ال graph بيحتوي على Nvertices
+
+263
+00:19:25,240 --> 00:19:29,940
+باعتبار ان احنا بسميه C A A N فال N هنا عدد ال
+
+264
+00:19:29,940 --> 00:19:34,080
+nodes معناه ذلك انه هيكون عندنا N nodes او N nodes
+
+265
+00:19:34,080 --> 00:19:39,720
+ال E ال connection ال connection اللي بينهم هتكون
+
+266
+00:19:39,720 --> 00:19:45,800
+بين كل نقطة و اللي جنبها بس خلاص فإذا V1 V2 stop
+
+267
+00:19:45,800 --> 00:19:54,250
+من V2 ل V3 transitivityمن V3 ل V4 من V4 ل V5 من V
+
+268
+00:19:54,250 --> 00:20:01,190
+N-1 to V N عشان احقق اعمل ال transitive closure
+
+269
+00:20:02,000 --> 00:20:08,120
+محتاج ايش تسوي؟ من V1 to N بس هنعكسها هتصير VN to
+
+270
+00:20:08,120 --> 00:20:11,960
+V1 VN to V1 هيك سكرنا مين ال loop تبعنا او سكرنا
+
+271
+00:20:11,960 --> 00:20:16,520
+ال cycle بتاعتنا فهيك اتسكرت علنا ال cycle okay
+
+272
+00:20:16,520 --> 00:20:20,340
+هاي مجموعة منهم وهي واضح انه هاد ال architecture
+
+273
+00:20:20,340 --> 00:20:23,320
+هاد او ال topology هاد ممكن تحتاجوها لاحقا في
+
+274
+00:20:23,320 --> 00:20:27,240
+الشبكات كنوع من انواع من انواع ال networks نوع من
+
+275
+00:20:27,240 --> 00:20:31,850
+انواع او ال topology لل networksOkay how many
+
+276
+00:20:31,850 --> 00:20:39,550
+edges are there in C N؟ قدش عدد ال edges؟ عندكم N
+
+277
+00:20:39,550 --> 00:20:43,430
+edges موجودة فعليا إذا كانت تلاتة في عندكم هيكون
+
+278
+00:20:43,430 --> 00:20:47,630
+تلاتة edges هنا أربع هيكون في عندكم أربع edges
+
+279
+00:20:47,630 --> 00:20:50,570
+خمسة هيكون في عندكم خمسة edges فهذه بتساوي ..
+
+280
+00:20:50,570 --> 00:20:53,530
+بتساوي N ال degree؟ نفس الشيء
+
+281
+00:20:57,330 --> 00:21:05,250
+total degree تبعكم اتنين في عدد ال edges ال wheels
+
+282
+00:21:05,250 --> 00:21:13,790
+مختلفة شوية عن ال cycle لما
+
+283
+00:21:13,790 --> 00:21:17,050
+اقول في wheel معينة عندي معناته في عندي عجلة يعني
+
+284
+00:21:17,050 --> 00:21:22,110
+العجلة تمشي شكل بالشكل هذا cycle و خلاص بدها
+
+285
+00:21:22,110 --> 00:21:26,220
+المحور تبعهامش بدها محور بدها نقطة الارتكاز
+
+286
+00:21:26,220 --> 00:21:30,340
+بتاعتها نقطة ارتكازها عبارة عن node عبارة عن node
+
+287
+00:21:30,340 --> 00:21:35,040
+لو افترض ان هدولة عددهم خمسة مثلا خمسة nodes وهي
+
+288
+00:21:35,040 --> 00:21:39,820
+متواصلين مع بعض ب ring يعني ك ring topology بالشكل
+
+289
+00:21:39,820 --> 00:21:44,560
+هذا او cycle C5
+
+290
+00:21:44,560 --> 00:21:48,880
+بالشكل هذا محتاجين center ال center هذا connected
+
+291
+00:21:48,880 --> 00:21:55,310
+مع Hأو مع every other node .. مع every other node
+
+292
+00:21:55,310 --> 00:21:58,810
+كويس؟ بالشكل هذا إيش اللي زودنا احنا هنا فعاليا؟
+
+293
+00:21:58,810 --> 00:22:04,010
+star برضه ممكن تمر عليكوا ك star connection ال
+
+294
+00:22:04,010 --> 00:22:08,230
+star connection وهذه واحدة من صورها ال .. ال .. ال
+
+295
+00:22:08,230 --> 00:22:11,270
+router ال router اللي بتشتغلوا عليه ال router هو
+
+296
+00:22:11,270 --> 00:22:15,570
+ماخد input و بعدين كده بيوزع starبوزي أستار بشكل
+
+297
+00:22:15,570 --> 00:22:19,110
+أستار بحيث أنه لو واحدة منهم صار لها أي .. أي فصل
+
+298
+00:22:19,110 --> 00:22:21,670
+بتأثرش على الفاجين بتأثرش على الفاجين طبعا اللي
+
+299
+00:22:21,670 --> 00:22:24,770
+أخدوا الشبكات عارفين الجزئيها دي إذا مااخدتهاش
+
+300
+00:22:24,770 --> 00:22:27,130
+الناس اللي مااخدو الشبكات حياخدوها بس القصد اللي
+
+301
+00:22:27,130 --> 00:22:29,450
+أنا بحاول وصلكه أنه ال topologies هذه انتوا هتمر
+
+302
+00:22:29,450 --> 00:22:34,210
+عليكم هتمر عليكم ك as graphs هتحتاجوها ففي عندكم
+
+303
+00:22:34,210 --> 00:22:37,150
+هنا صار هي ال ring و صار في عندكم ال star هدول هيك
+
+304
+00:22:37,150 --> 00:22:42,400
+مع بعض بنسميهمWheel أو شكل عجلة فمعنى ذلك ان هذه
+
+305
+00:22:42,400 --> 00:22:47,220
+هي ك Cycle هنضيف لها نقطة في النص و connected مع
+
+306
+00:22:47,220 --> 00:22:53,380
+ال all nodes اربعة نفس الكلام نقطة في النص و
+
+307
+00:22:53,380 --> 00:22:56,560
+هنوصلها مع الكل خمسة نفس الشيء ستة نفس الموضوع
+
+308
+00:22:56,560 --> 00:23:01,940
+سبعة و هكذاتمام؟ فبصير هيك شكلها أو كلهم بصيروا
+
+309
+00:23:01,940 --> 00:23:05,200
+عبارة عن .. كل واحدة منهم عبارة عن wheel أو كلهم
+
+310
+00:23:05,200 --> 00:23:08,120
+wheels في الحالة اللي وانا طيب جدش عدد ال edges
+
+311
+00:23:08,120 --> 00:23:12,340
+تبعتكم؟ ان في ان نقص واحد طب خلينا نشوف .. اقصوا
+
+312
+00:23:12,340 --> 00:23:16,580
+اقصوا اهدوا ال cycle جدش كان فيها؟ ان طيب ال .. ال
+
+313
+00:23:16,580 --> 00:23:23,180
+star لحالها؟ سؤالسؤال خالص ايه أصله هدوله؟ احنا
+
+314
+00:23:23,180 --> 00:23:26,620
+قلنا اللي في المحورية هدى بتتوصل مع كل واحدة منهم
+
+315
+00:23:26,620 --> 00:23:31,060
+طب هم ماجددش عددهم N معنى ذلك انه محتاجة N link
+
+316
+00:23:31,060 --> 00:23:35,500
+زيادة طب و هى أصلا ماجددش كان فيها ال cycle N صار
+
+317
+00:23:35,500 --> 00:23:40,000
+في عندي N زائد N اتنين N اتنين N مظبوط فصار في
+
+318
+00:23:40,000 --> 00:23:43,160
+عندي هنا N جاية من ال cycle و N جاية من ال star
+
+319
+00:23:43,160 --> 00:23:46,430
+اللى جواصار عندنا ال .. ال .. ال wheels كلهم على
+
+320
+00:23:46,430 --> 00:23:51,630
+بعض العدد ال inches بتاعتها بيساوي اتنين N اتنين N
+
+321
+00:23:51,630 --> 00:23:57,070
+طب عدد ال degrees اربعين اربعين تمام okay طب ال N
+
+322
+00:23:57,070 --> 00:24:01,470
+cubes او ال hyper cubes ال hyper cubes هذه ببساطة
+
+323
+00:24:01,470 --> 00:24:07,720
+كل اللي بنعمله انه بنسميها طبعا Qمن ال Q كلفظة ال
+
+324
+00:24:07,720 --> 00:24:17,840
+N لدرجة ال index لو كانت zero بتكون عبارة عن node
+
+325
+00:24:17,840 --> 00:24:23,220
+واحدة و ايش معناها zero هنا واحد و حاطين ال index
+
+326
+00:24:23,220 --> 00:24:27,140
+zero لان ال zero هذا يمثل جديش عدد الكبز اللي عملت
+
+327
+00:24:27,140 --> 00:24:33,790
+احنا لسه ماعملناش اي نسخ هنا ايش بيقولناالـ qn هي
+
+328
+00:24:33,790 --> 00:24:39,670
+عبارة عن قبي من qn-1 من اللي جابلها طب هذه اللي
+
+329
+00:24:39,670 --> 00:24:42,250
+جابلها ماكنش فيه جابلها هي أصغر عنصر ان يكون node
+
+330
+00:24:42,250 --> 00:24:46,270
+واحدة فهي مش ماخدة قبي من إشه، مدام مش ماخدة قبي
+
+331
+00:24:46,270 --> 00:24:50,020
+من إشه فهي zero قبل عند الانعرفت انها وجدت ليش ال
+
+332
+00:24:50,020 --> 00:24:54,400
+index zero لأن هنا zero copy هي نقطة و خلاص مافيش
+
+333
+00:24:54,400 --> 00:24:57,720
+اي connection ماربطناها مع اي شي طيب لما اقول q1
+
+334
+00:24:57,720 --> 00:25:01,840
+معناته بتعمل one copy one copy هذه بتعملها copy
+
+335
+00:25:01,840 --> 00:25:07,740
+زيادة بمعنى هذه النقطة الأصلية هنعملها copy و نوصل
+
+336
+00:25:07,740 --> 00:25:12,260
+بين كل نقطة و النقطة اللي سُنسخت منها بهذا الشكل
+
+337
+00:25:12,260 --> 00:25:22,250
+خلاص هذه q1 طيب q2نسخة من Q1 بتصير هاي هدا و Q1
+
+338
+00:25:22,250 --> 00:25:27,830
+نسخة منها طيب النقطة هذه مستنسخة من أي نقطة من هذه
+
+339
+00:25:27,830 --> 00:25:31,190
+بوصلهم مع بعض طيب هذه النقطة مستنسخة من مين النقطة
+
+340
+00:25:31,190 --> 00:25:36,250
+هذه بوصلهم مع بعض بس بعملش ال full connection يعني
+
+341
+00:25:36,250 --> 00:25:40,130
+مش بروح بوصل هذه في كل اللي موجود لأ كل واحدة في
+
+342
+00:25:40,130 --> 00:25:43,410
+النسخة في النقطة اللي توسخت منها بس
+
+343
+00:25:46,680 --> 00:25:53,460
+Q3 هذه الأصلية بعمل منها نسخة copy و بنوصل كل نقطة
+
+344
+00:25:53,460 --> 00:25:59,540
+بالنقطة اللي انت سخت منها فهي فعلا copies of Q and
+
+345
+00:25:59,540 --> 00:26:02,620
+minus one من اللي جابلها طب هذه لما بدنا نجيب Q4
+
+346
+00:26:02,620 --> 00:26:08,240
+هي الأصلية المكعب وهي نسخة من المكعب كل نقطة
+
+347
+00:26:08,240 --> 00:26:12,940
+بالنقطة اللي انت سخت منها فهي
+
+348
+00:26:12,940 --> 00:26:14,080
+بصير هذه الشكل Q
+
+349
+00:26:27,630 --> 00:26:31,490
+ممتاز مايعطيكم طبعا جديش عدد ال vertices لكل واحدة
+
+350
+00:26:31,490 --> 00:26:35,990
+لكل حالة منهم لكل حالة منهم هي number of vertices
+
+351
+00:26:35,990 --> 00:26:37,210
+two to the power
+
+352
+00:26:39,970 --> 00:26:45,750
+طيب هنا q0, q1, q2, q3 بتقدر تجيبوه بحيث انه لو
+
+353
+00:26:45,750 --> 00:26:50,610
+عوضتوا هنا ب0 و 1 فانتوا نود واحدة طيب لو عوضتوا
+
+354
+00:26:50,610 --> 00:26:55,590
+بالواحد بالإتنين بالإتنين هاي الأربعة هنا صار
+
+355
+00:26:55,590 --> 00:26:58,550
+تمانية صار ستة عشر اتنين و تلاتين و هكذا بتكملوا
+
+356
+00:26:58,550 --> 00:27:00,450
+عليها عدد ال edges
+
+357
+00:27:19,450 --> 00:27:35,470
+جربوها نجربها مصبوط
+
+358
+00:27:35,470 --> 00:27:39,810
+بتجربوا معايا و لا وان؟ بتجربوا معنا؟ أنا شوفتكوا
+
+359
+00:27:39,810 --> 00:27:43,930
+سكتوالحظة تكونوا سايفين ان انا بتجرب لحالي جربوها
+
+360
+00:27:43,930 --> 00:27:50,850
+مظبوطة
+
+361
+00:27:50,850 --> 00:27:55,430
+طيب هى مكنتش موجودة أساسا وليه الأمانة برضه صدقا
+
+362
+00:27:55,430 --> 00:28:00,110
+بشرحها عند الشباب واحد من الشباب طلعها واحد من
+
+363
+00:28:00,110 --> 00:28:02,130
+الشباب طلعنا ال relation بيقولي طب دكتورة دم هاد
+
+364
+00:28:02,130 --> 00:28:07,710
+ال relation بتنفع بتقول اه بتنفع صح فممكن n في
+
+365
+00:28:07,710 --> 00:28:09,730
+اتنين to the power of n minus one
+
+366
+00:28:14,540 --> 00:28:18,960
+كويس هذه شطرتكوا عاد أن كل اللي أخدتهوا في ال
+
+367
+00:28:18,960 --> 00:28:23,140
+discrete لو أنتوا بتتراجعوا على ال net ال .. ال IQ
+
+368
+00:28:23,140 --> 00:28:27,280
+test هتلاقيه أن كل اللي بتيجي في مسابقات الذكاء
+
+369
+00:28:27,280 --> 00:28:30,380
+العقلي و الأمور الأسئلة اللي بيجيبوها للأذكية و
+
+370
+00:28:30,380 --> 00:28:33,060
+للحاجات هذه و بيحسبوا منها المقياس كله أحنا أخدناه
+
+371
+00:28:33,060 --> 00:28:37,420
+في المساق يعني المساق هو كأنه مخصص لل IQلأن هو
+
+372
+00:28:37,420 --> 00:28:40,040
+المطلوب منكم انت لو بتدوروا على ال net كان لجاته
+
+373
+00:28:40,040 --> 00:28:43,420
+كتير اسئلة زي هذه بتقدروا تطلعوا منها relations و
+
+374
+00:28:43,420 --> 00:28:48,000
+بتقدروا تسبجوا حتى في المصار تبعنا فهذه موجودة
+
+375
+00:28:48,000 --> 00:28:53,620
+كتير في ال IQ في ال IQ test او ال intelligent test
+
+376
+00:28:53,620 --> 00:28:57,620
+بتلاقوا كتير اسئلة زي هذه جدش عدد ال edges تبعتها
+
+377
+00:28:57,620 --> 00:29:00,160
+جدش عدد ال nodes جدش عدد مش عارفين طب جيبلنا
+
+378
+00:29:00,160 --> 00:29:05,520
+relation ل ال index مع عدد ال .. كتير موجودة ..
+
+379
+00:29:05,520 --> 00:29:13,080
+كتير موجودةطيب جزء تاني الpy partate الpy
+
+380
+00:29:13,080 --> 00:29:15,780
+partate ببساطة جدا بيكون عند مجموعة ال vertices
+
+381
+00:29:15,780 --> 00:29:20,660
+بجسمهم نصين بجسمهم ايش فريقين كل فريق connected مع
+
+382
+00:29:20,660 --> 00:29:29,740
+each node of other part بس داخل ال part نفسه لأ
+
+383
+00:29:29,740 --> 00:29:32,780
+مافيش اي connection لاوجد اي connection لاوجد اي
+
+384
+00:29:32,780 --> 00:29:37,230
+connection فهتلاحظوا هناpart number one part
+
+385
+00:29:37,230 --> 00:29:42,610
+number two هنا هتوزع خمسة vertices و هنا هكون خمسة
+
+386
+00:29:42,610 --> 00:29:47,510
+vertices كويس كل node هنا connected او مسموح انه
+
+387
+00:29:47,510 --> 00:29:50,690
+يكون connected مع ال other numbers في ال part
+
+388
+00:29:50,690 --> 00:29:54,390
+التاني في ال part التاني مش في نفس ال part و العكس
+
+389
+00:29:54,390 --> 00:29:59,810
+صحيح فهذه V1 V2 في الحالة اللي عنا هنا مجدش عدد ال
+
+390
+00:29:59,810 --> 00:30:02,070
+vertices كله على بعض و هيكون ال union للاتنين مع
+
+391
+00:30:02,070 --> 00:30:08,390
+بعض عددال vertices هنا زاد عدد ال vertices هنا لما
+
+392
+00:30:08,390 --> 00:30:12,690
+بنتكلم عن فريقين كورة قدم فريق نفترض فيه 11 لاعب
+
+393
+00:30:12,690 --> 00:30:15,290
+نسبة الملعب وفريق تاني فيه 11 لاعب طب جدش عدد
+
+394
+00:30:15,290 --> 00:30:20,770
+اللاعبين على أرض الملعب 22 هدول union مع هدول جامع
+
+395
+00:30:20,770 --> 00:30:24,570
+مع هدول مافيش intersectionمش هتلاقوا لعب نزل بلعب
+
+396
+00:30:24,570 --> 00:30:28,110
+مرة مع حدول و مرة مع حدول صحيح؟ ماهو يا هنا يا هنا
+
+397
+00:30:28,110 --> 00:30:30,870
+ففي الحالة ال intersection between them ايش؟ five
+
+398
+00:30:30,870 --> 00:30:34,590
+.. five .. هيكون ال intersection هنا five فاحنا
+
+399
+00:30:34,590 --> 00:30:36,950
+فعليا كأننا معملنا two parts و ال two parts هدوة
+
+400
+00:30:36,950 --> 00:30:40,550
+لكل element في ال part الأول connected أو مسموح له
+
+401
+00:30:40,550 --> 00:30:43,010
+يكون connected مع ال part التاني مش مضرور يكون
+
+402
+00:30:43,010 --> 00:30:46,950
+connected الزامي يعني ولكن ال relation هنا بتحدد
+
+403
+00:30:46,950 --> 00:30:50,030
+انه هيكون connected او لا يعني زي هنا مثلا ال part
+
+404
+00:30:50,030 --> 00:30:52,310
+هذا مش متصل مع .. او ال element هذا مش متصل مع حد
+
+405
+00:30:53,030 --> 00:30:58,670
+لكن هو موجود ضمن ال V2 ضمن ال part التاني ضمن ال
+
+406
+00:30:58,670 --> 00:31:03,590
+part التاني okay لو قلنا لأ كل عنصر لازم يكون متصل
+
+407
+00:31:03,590 --> 00:31:07,590
+مع كل العناصر في ال part التاني فبنسميها complete
+
+408
+00:31:07,590 --> 00:31:12,330
+bipartate graph complete bipartate graph بمعنى كل
+
+409
+00:31:12,330 --> 00:31:17,350
+عنصر هي في ال part الأول connected مع كل عنصر في
+
+410
+00:31:17,350 --> 00:31:22,520
+ال part التانيفهذه نسميها full connection أو
+
+411
+00:31:22,520 --> 00:31:27,840
+complete bipartate graphs او كما قلنا complete او
+
+412
+00:31:27,840 --> 00:31:31,460
+full ففي الحالة هذه لو افترضنا انه عندنا في ال
+
+413
+00:31:31,460 --> 00:31:37,420
+part الاول عددهم M بمعنى ال cardinality لل set هذه
+
+414
+00:31:37,420 --> 00:31:43,880
+اللي هي ال M عددهم M وهنا ال cardinality N جدش عدد
+
+415
+00:31:43,880 --> 00:31:49,480
+ال vertices كله لل graphم زاد ان تمام طب جدش عدد
+
+416
+00:31:49,480 --> 00:31:54,400
+ال edges؟ ام في ان ام في ان تمام ام في ان فهيكون
+
+417
+00:31:54,400 --> 00:31:58,860
+هنا انه طبعا هذه برضه ال graph هذه لها لها كتير
+
+418
+00:31:58,860 --> 00:32:01,940
+applications الحقيقة يمكن من ال applications
+
+419
+00:32:01,940 --> 00:32:05,080
+بتاعتها أهمهم اللي هي ال neural network في في في
+
+420
+00:32:05,080 --> 00:32:08,020
+في ال field تبع ال AI في ال field تبع ال AI ال
+
+421
+00:32:08,020 --> 00:32:11,720
+neural network من أهم ال examples ده ال full
+
+422
+00:32:11,720 --> 00:32:16,400
+connection هذهاللي موجودة القصد انه كل شي بناخده
+
+423
+00:32:16,400 --> 00:32:19,700
+هو إله applications يمكن أنتوا يسعفكم للوقت ممكن
+
+424
+00:32:19,700 --> 00:32:22,200
+تلحقوها في مصداقات أخرى ويمكن ما تاخدوهاش يعني ال
+
+425
+00:32:22,200 --> 00:32:25,800
+New York Times ما تبقاش مر عليكوا بعد هيك ولكن لا
+
+426
+00:32:25,800 --> 00:32:31,260
+يمنع أن هي موجودة في ال AI و ال AI أحد عناصر أو
+
+427
+00:32:31,260 --> 00:32:36,100
+أحد ال fields بتاعة ال computer engineeringتمام ال
+
+428
+00:32:36,100 --> 00:32:38,380
+sub graphs ال sub graphs لما اقول والله في sub
+
+429
+00:32:38,380 --> 00:32:43,020
+graph او usual sub graph ل G لل graph G وال graph
+
+430
+00:32:43,020 --> 00:32:45,660
+G هذا متكون احنا قولنا انه تكوينه من ايش؟ من
+
+431
+00:32:45,660 --> 00:32:50,200
+مجموعة vertices ومجموعة edges مجموعة ال vertices
+
+432
+00:32:50,200 --> 00:32:53,940
+او ال nodes بنحطهم في set اسمها V مجموعة ال
+
+433
+00:32:53,940 --> 00:33:01,000
+lengths بنحطهم في E في set اسمها E ال sub graph لل
+
+434
+00:33:01,000 --> 00:33:07,050
+graph هذا هنسميه is a graph Hال H هيكون عبارة عن
+
+435
+00:33:07,050 --> 00:33:14,390
+مجموعة vertices مع مجموعة edges W و F بشرط ان W هي
+
+436
+00:33:14,390 --> 00:33:20,450
+subset من V هي جزء من V عشان يكون الجراف كله على
+
+437
+00:33:20,450 --> 00:33:24,910
+بعض هو جزء من الجراف هذا فلازم تكون اول شغلة ال W
+
+438
+00:33:24,910 --> 00:33:31,520
+subset من V و ال Fال links ال links لل sub graph
+
+439
+00:33:31,520 --> 00:33:34,300
+هو جزء من ال links اللي موجودة في ال graph الأصلي
+
+440
+00:33:34,300 --> 00:33:37,060
+ففي الحالة هدا نقول ال graph كله على بعض و هذا sub
+
+441
+00:33:37,060 --> 00:33:42,620
+graph من ال G فبتصير هنا ال H ال sub graph من ال G
+
+442
+00:33:42,620 --> 00:33:48,540
+من هنا لو أخدنا مجموعة منهم اقولكوا لو أخدنا هاي
+
+443
+00:33:48,540 --> 00:33:50,720
+الأول و التاني و التالت بيكفي لو أخدنا واحد اتنين
+
+444
+00:33:50,720 --> 00:33:54,020
+تلاتة و أخدنا ال connections بينهم يعني هاي واحد
+
+445
+00:33:54,020 --> 00:33:59,530
+اتنين تلاتةهذه subset منها خلاص هذه subset من ال G
+
+446
+00:33:59,530 --> 00:34:02,950
+في الحلقة هذه عندي هنا صار graph هو subset من ال
+
+447
+00:34:02,950 --> 00:34:06,630
+graph طب لو زودنا كمان واحد هنا وعملنا بهذا الشكل
+
+448
+00:34:06,630 --> 00:34:11,990
+بس برضه sub graph برضه sub graph ماتقولوش طب لأ
+
+449
+00:34:11,990 --> 00:34:15,270
+ماهو في هاي خط طب ماجهاش الخط مش المشكلة مش
+
+450
+00:34:15,270 --> 00:34:20,930
+المشكلة انا اللي بهمني انه كل node هنا كل node
+
+451
+00:34:20,930 --> 00:34:25,950
+belong to this graphبيولوجيك هي برضه هتكون belong
+
+452
+00:34:25,950 --> 00:34:29,590
+to this graph صحيح النود هذه موجودة النود هذه
+
+453
+00:34:29,590 --> 00:34:33,830
+موجودة النود هذه موجودة تمام ال links برضه مدام ال
+
+454
+00:34:33,830 --> 00:34:38,330
+link موجود هنا لازم يكون موجود هنا فكل link موجود
+
+455
+00:34:38,330 --> 00:34:42,870
+هنا موجود هنا خلاص العكس مش صحيح العكس غير صحيح ال
+
+456
+00:34:42,870 --> 00:34:45,330
+link اللي موجود هنا مش بالضرورة يكون موجود هنا هذه
+
+457
+00:34:45,330 --> 00:34:50,330
+subset هذه فئة جزئية من الفئة اللي هنا الفئة هذه
+
+458
+00:34:50,330 --> 00:34:55,110
+بنقيسها على ال nodesإنه ال notes اللي هنا جزء من
+
+459
+00:34:55,110 --> 00:34:58,290
+ال notes اللي هنا وبنقيصها كمان على مين على ال
+
+460
+00:34:58,290 --> 00:35:02,570
+connections على ال edges على ال links فكل link
+
+461
+00:35:02,570 --> 00:35:04,690
+موجود هنا المفروض إنه في الأصل كان موجود هنا
+
+462
+00:35:04,690 --> 00:35:12,330
+فبنقول إن هذا subset of g فهنا هناخد هاي subset
+
+463
+00:35:12,330 --> 00:35:16,910
+منها جزء منهامش بالضروري كلها، مش بالضروري كلها،
+
+464
+00:35:16,910 --> 00:35:20,250
+مدام جزء منها، كيف نقدر نقول إن هو جزء منها؟ بنمسك
+
+465
+00:35:20,250 --> 00:35:24,350
+ال vertices بتاعنا هل هما فعلا كل vertex موجودة
+
+466
+00:35:24,350 --> 00:35:27,970
+هنا موجودة هنا؟ موجودة طب هل كل link موجود هنا
+
+467
+00:35:27,970 --> 00:35:32,430
+فعلا موجود هنا؟ خلاص بإذن هذه ال H هي subset of G
+
+468
+00:35:36,900 --> 00:35:42,880
+Okay بالعكس ال union الاتحاد الاتحاد طبعا هيكون في
+
+469
+00:35:42,880 --> 00:35:45,700
+عندنا two graphs في عندنا graph number one graph
+
+470
+00:35:45,700 --> 00:35:50,060
+number two بدنا نجيب ال union او g1 union g2 of
+
+471
+00:35:50,060 --> 00:35:54,690
+two simple graphs g1 معرفينه على اساس ان هو v1اللي
+
+472
+00:35:54,690 --> 00:35:57,630
+هو عدد ال vertices بتاعونه أو ال set of vertices
+
+473
+00:35:57,630 --> 00:36:03,330
+بتاعونه وE1 اللي هو عدد ال edges بتاعونه طيب مع
+
+474
+00:36:03,330 --> 00:36:06,810
+مين هنعمل union؟ مع G2 اللي برضه له set of
+
+475
+00:36:06,810 --> 00:36:11,370
+vertices اسمها V2 ويله set of edges اسمها E2
+
+476
+00:36:11,370 --> 00:36:14,950
+simply هتكوني graph جديد لgraph جديد هذا ايش اللي
+
+477
+00:36:14,950 --> 00:36:18,790
+بيميزه؟ بيميزه ان ال vertices بتاعونه عبارة عن V1
+
+478
+00:36:18,790 --> 00:36:26,820
+union V2 و ال edges بتاعونه E1union اتنين فهنا هذي
+
+479
+00:36:26,820 --> 00:36:35,100
+هي ال V total وهنا ال E total للكل اذا رسمناهم
+
+480
+00:36:35,100 --> 00:36:38,660
+هدول مع هدول الاتنين وحطناهم مع بعض هتلاعنا ال
+
+481
+00:36:38,660 --> 00:36:41,840
+union تبعنا فهتلاقوه في الحالة اللي زي اللي عندنا
+
+482
+00:36:41,840 --> 00:36:46,500
+هنا هتكون بهذا الشكل الاتنينمع بعض يعني ارسموا هذا
+
+483
+00:36:46,500 --> 00:36:48,940
+الحال على ورقة شفاف و هذا الحال على ورقة شفاف و
+
+484
+00:36:48,940 --> 00:36:52,500
+اجعوهم مع بعض على بعض هيك ايش الشكل اللي هيطلع في
+
+485
+00:36:52,500 --> 00:36:55,720
+دهر الورقة الشفاف هو هذا ال union للكل مع بعضه
+
+486
+00:36:55,720 --> 00:36:57,300
+للكل مع بعضه
+
+487
+00:37:02,520 --> 00:37:07,820
+Okay هي خلصنا بعض أنواع .. بعض أنواع من مين من ال
+
+488
+00:37:07,820 --> 00:37:10,660
+graphs خلينا نشوف اللي هو كيف بقدر امثل ال graph و
+
+489
+00:37:10,660 --> 00:37:13,380
+احنا مثلناها قبل هيك ليش؟ لأنه احنا في النهاية
+
+490
+00:37:13,380 --> 00:37:16,140
+نتكلم عن ال graph ال graph عبارة عن إيش relation
+
+491
+00:37:16,140 --> 00:37:21,480
+أيام ال relation كيف كنا نمثل ال relation؟ كنا
+
+492
+00:37:21,480 --> 00:37:23,380
+نستخدم طرق تانية الشمعة
+
+493
+00:37:27,280 --> 00:37:32,500
+استخدمنا ال one zero matrix واستخدمنا ال directed
+
+494
+00:37:32,500 --> 00:37:35,520
+graph او ال diagraph متذكرين؟ طب احنا اصلا نشتغل
+
+495
+00:37:35,520 --> 00:37:39,340
+diagraph اساسا فمعنى ذلك التمثيل المتوقع انه بيسكن
+
+496
+00:37:39,340 --> 00:37:42,280
+باستخدام ال matrix استخدام matrix احنا فعليا
+
+497
+00:37:42,280 --> 00:37:46,720
+هنشتغل على ال matrix بطرق تانية واحدة ال adjacency
+
+498
+00:37:46,720 --> 00:37:50,840
+matrices و ال incidence matricesجابلهم هنتكلم بس
+
+499
+00:37:50,840 --> 00:37:54,620
+عن ال list هذه بسيطة جدا بنعمل قائمة بعدد ال
+
+500
+00:37:54,620 --> 00:37:57,660
+vertices وكل واحدة connected مع مين و بس فهذه
+
+501
+00:37:57,660 --> 00:38:02,120
+طريقة تمثيل ممكنة لل graph representations هناخد
+
+502
+00:38:02,120 --> 00:38:05,480
+تلت طرق بساطين جدا لإنه مرت أفكارهم علينا one zero
+
+503
+00:38:05,480 --> 00:38:07,980
+بحط one إذا كان ال relation موجودة zero إذا كان مش
+
+504
+00:38:07,980 --> 00:38:12,120
+موجودة فone بحطها إذا كان ال link موجود و zero إذا
+
+505
+00:38:12,120 --> 00:38:15,280
+ماكنش ال link موجود في الرسمة بس هنشوفها مراجعة
+
+506
+00:38:15,280 --> 00:38:17,560
+بالتفاصيل بعدين في جزئية تانية اللي هي ال graph
+
+507
+00:38:17,560 --> 00:38:21,310
+isomorphismIsomorphism اللي هي المشابهة هل هم
+
+508
+00:38:21,310 --> 00:38:23,950
+متنظرين ولا لأ الرسومات وهذه برضه من الحاجات اللي
+
+509
+00:38:23,950 --> 00:38:30,630
+كتير موجودة في ال IQ test او في ال intelligence
+
+510
+00:38:30,630 --> 00:38:33,650
+test
+
+511
+00:38:33,650 --> 00:38:37,530
+اللي بتعملوها عادة بيجيبوا الكراسمة معينة و بعدين
+
+512
+00:38:37,530 --> 00:38:40,030
+تحتها بيجيبوا مجموعة رسومات و بيقولوا هذا matching
+
+513
+00:38:40,030 --> 00:38:45,150
+مع مين ممكن يكون فيها مجموعة nodes بس ملوحين شوية
+
+514
+00:38:45,940 --> 00:38:49,540
+لففهم، عملهم، دورهم، محركهم تسعين درجة، مائة و
+
+515
+00:38:49,540 --> 00:38:53,660
+عشرين درجة، مغير، مظبط هنا الشطارة كيف تعرف أن هذا
+
+516
+00:38:53,660 --> 00:38:57,000
+هو مش شبه لهذا ال isomorphism هذا اللي هي التناظر
+
+517
+00:38:57,000 --> 00:39:00,740
+ممكن في النهاية الرسمة تكون مختلفة، شكلها تماما
+
+518
+00:39:00,740 --> 00:39:04,660
+مختلف، بس لأ هي نفس الرسمة بمعنى لو في two nodes
+
+519
+00:39:04,660 --> 00:39:08,560
+منهم، لفتوهم، هيطلع نفس الرسمة بنفس ال connections
+
+520
+00:39:08,560 --> 00:39:12,640
+بتاعتهم، هناخدها و هنتكلم عليهاإذا وصلنا إليها
+
+521
+00:39:12,640 --> 00:39:15,200
+هناخد بس شوية أفكار اللي هي عملية ال connections
+
+522
+00:39:15,200 --> 00:39:18,680
+عساس أنهي منها نحدد ال isomorphism موجودة أو لا
+
+523
+00:39:18,680 --> 00:39:23,280
+هنتكلم عن ال connection و بيكون خلصنا كل ما يخص ال
+
+524
+00:39:23,280 --> 00:39:31,400
+graph في شغلنا نبدأ بال representation أول شغل
+
+525
+00:39:31,400 --> 00:39:35,350
+اللي هي ال adjacency list بسيطة جداعندكوا graph
+
+526
+00:39:35,350 --> 00:39:39,470
+معين بتعمله representation مثله تمثيله مافيش أبساط
+
+527
+00:39:39,470 --> 00:39:45,450
+منه، ليش؟ جداش عدد ال notes تبعونه، رتبوهم عندكوا
+
+528
+00:39:45,450 --> 00:39:50,050
+A,B,C,D to F، فلس، A,B,C,D تمام، بنمسكهم هدى،
+
+529
+00:39:50,050 --> 00:39:52,810
+بنسميها vertex، ال column هدى بنسميه vertex في ال
+
+530
+00:39:52,810 --> 00:39:56,030
+list اللي عندنا ال list أو ال column التاني بنسميه
+
+531
+00:39:56,030 --> 00:40:01,830
+ال adjacent vertices كل اللي بنعمله، A هي إيه؟ هي
+
+532
+00:40:01,830 --> 00:40:07,070
+إيه؟ مجاورة مع مين؟ب و سي خلاص نكتب ب و سي انتهى
+
+533
+00:40:07,070 --> 00:40:16,050
+الكلام طيب ال b وين بي هذه بي لاحظوا مع a مع c مع
+
+534
+00:40:16,050 --> 00:40:23,590
+e مع f طيب ال d ايش
+
+535
+00:40:23,590 --> 00:40:27,830
+بتسميها هذه isolated isolated تمام isolated degree
+
+536
+00:40:27,830 --> 00:40:31,730
+بتاعة صفر فهذه مش متواصلة مع اي حد هذه zero فمدام
+
+537
+00:40:31,730 --> 00:40:38,490
+zeroزيرو فهي زيرو فعلا كويس سهل التوقع التمثيل
+
+538
+00:40:38,490 --> 00:40:42,070
+بالشكل هذا مافيش فيه اشي لاست لما تشوفوا adjacency
+
+539
+00:40:42,070 --> 00:40:45,770
+لاست لاست مافيش فيه اشي بس فتحطوا كل ال vertices
+
+540
+00:40:45,770 --> 00:40:52,370
+وكل واحدة مجاورة لمين وانتهى الكلام ال adjacency
+
+541
+00:40:52,370 --> 00:40:57,270
+لاست في حالة ال direct في حالة ال direct بنعملها
+
+542
+00:40:57,270 --> 00:41:02,550
+لل incident edges اذا في incident edges او لاكيف
+
+543
+00:41:02,550 --> 00:41:07,630
+يعني نفس الكلام بنحط مجموعة ال edges تبعوننا عفوا
+
+544
+00:41:07,630 --> 00:41:11,130
+ال vertices بتاعوننا اللي هو ال nodes و بنفترضهم
+
+545
+00:41:11,130 --> 00:41:14,970
+هدولة مين ال initial vertex هدولة ال initial
+
+546
+00:41:14,970 --> 00:41:19,730
+vertex بمعنى كل link طالع محسوب أما كل link داخل
+
+547
+00:41:19,730 --> 00:41:28,110
+لأ نمسك a و نمسكهم a هي ايه أكم link طالع بي على
+
+548
+00:41:28,110 --> 00:41:33,790
+بي و على دي و على ايه لحظوا فعلا بنحطهملحظوا هذا
+
+549
+00:41:33,790 --> 00:41:40,410
+ما حسبتش هذا بحسبش لإن أنا من الأول حاطبتها
+
+550
+00:41:40,410 --> 00:41:45,270
+initial vertex initial vertex مانحطهاش طيب لو
+
+551
+00:41:45,270 --> 00:41:51,670
+أخدنا B أخدنا B إيش اللي طالع منها؟ هاي واحد هاي
+
+552
+00:41:51,670 --> 00:41:57,030
+اتنين هدول؟ لأ هدول لأ طيب ففي الحالة هدا هيكون
+
+553
+00:41:57,030 --> 00:42:02,050
+عندي Bمن B طالع رايح لمين ل B؟ خلاص بنفط بي و رايح
+
+554
+00:42:02,050 --> 00:42:09,030
+التاني لمين ل D؟ هاي D طيب نمسك D؟
+
+555
+00:42:09,030 --> 00:42:14,490
+Zero فبتظل فاقيةرغم ان هي في الى three lengths بس
+
+556
+00:42:14,490 --> 00:42:18,030
+ال links كله in in degree كلهم in degree لأ مش
+
+557
+00:42:18,030 --> 00:42:20,070
+محسوبة ل in degree انا هنا بتعامل معها عساس ان هي
+
+558
+00:42:20,070 --> 00:42:23,030
+تكون هي ال initial ماتكونش هي ال terminal هي ال
+
+559
+00:42:23,030 --> 00:42:26,790
+terminal اه ليش؟ بدليل ان هي وصفتها هي هي E هي E
+
+560
+00:42:26,790 --> 00:42:31,060
+في كمان E تانية اه المفروض في E تانيةع دي .. دي ..
+
+561
+00:42:31,060 --> 00:42:33,060
+دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي
+
+562
+00:42:33,060 --> 00:42:34,680
+دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي
+
+563
+00:42:34,680 --> 00:42:39,200
+.. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي ..
+
+564
+00:42:39,200 --> 00:42:45,480
+دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي .. دي
+
+565
+00:42:45,480 --> 00:42:52,090
+دي .. دي .. دي .. دي .. دتمام هاي عملية التنفيذ في
+
+566
+00:42:52,090 --> 00:42:57,450
+حالة ال directed graph ناخد النوع التاني ال
+
+567
+00:42:57,450 --> 00:43:00,270
+adjacency matrices adjacency matrices اسمها
+
+568
+00:43:00,270 --> 00:43:02,670
+matrices خلاص معناه ان انا بتكلم عن matrix يعني في
+
+569
+00:43:02,670 --> 00:43:05,490
+النهاية هيكون في عندي رو و هيكون في عندي column
+
+570
+00:43:05,490 --> 00:43:08,610
+هاي ال matrix و هيكون في عندي رو و هيكون عندي
+
+571
+00:43:08,610 --> 00:43:14,820
+column و هيكون مجموعة عناصر I Jهجارة عن I J دائما
+
+572
+00:43:14,820 --> 00:43:22,180
+I هتكون لل ال raw ال raw هذا بنحط مين ال node هنحط
+
+573
+00:43:22,180 --> 00:43:24,580
+مجموعة ال nodes بتاعتنا كل ال nodes بتاعتكم
+
+574
+00:43:24,580 --> 00:43:31,140
+بترتبهم هنا كويس هنا ال adjacency معناته أنا بتكلم
+
+575
+00:43:31,140 --> 00:43:35,600
+عن ال node adjacent لمين ل node برضه فإذا برضه هنا
+
+576
+00:43:35,600 --> 00:43:40,850
+بنحط nodesبس احنا دايما نتطلع على المصطلح تبعنا
+
+577
+00:43:40,850 --> 00:43:43,810
+adjacency اه ال adjacency مع مين عادة ال adjacency
+
+578
+00:43:43,810 --> 00:43:48,330
+بنحط node مع node هل هم adjacent لبعض او لأ معنا
+
+579
+00:43:48,330 --> 00:43:51,290
+ذلك ان ال input بالنسبالي node و ال output هيكون
+
+580
+00:43:51,290 --> 00:43:54,450
+برضه node بنرطبهم هنا بنرطبهم هنا اذا والله هم
+
+581
+00:43:54,450 --> 00:43:58,410
+الاتنين adjacent لبعض بمعنى ان user link بينهم IJ
+
+582
+00:43:58,410 --> 00:44:07,100
+المقابلة لهم بنحطها واحدotherwise بنحطها zero خلاص
+
+583
+00:44:07,100 --> 00:44:13,380
+هاي طريقة التمثيل بتاعتنا مثلًا ناخد example بهذا
+
+584
+00:44:13,380 --> 00:44:19,620
+الشكل graph زي اللي احنا شايفينها هنا أكم
+
+585
+00:44:19,620 --> 00:44:25,080
+note في عندك؟ أربع هاي A,B,C وD ونفس الكلام هنا
+
+586
+00:44:25,080 --> 00:44:27,660
+برضه A,B,C وD
+
+587
+00:44:33,740 --> 00:44:40,220
+between a و a هل في أي self loop؟ لأ zero طيب هل
+
+588
+00:44:40,220 --> 00:44:45,440
+في relation between a و b؟ اه اه في طب a و c؟ اه
+
+589
+00:44:45,440 --> 00:44:54,310
+واحد a و d؟ one طيب بين b و aأه feeling طب بين b و
+
+590
+00:44:54,310 --> 00:45:00,470
+b نفسها طب b و c بي و دي فإذا فعلا a و d فقط و
+
+591
+00:45:00,470 --> 00:45:03,670
+بنكمل التمثيل طبعا طيب لأنه احنا بنتكلم عن
+
+592
+00:45:03,670 --> 00:45:10,570
+undirected لحظه لازم تكون symmetric بمعنى أن a,b
+
+593
+00:45:10,570 --> 00:45:20,530
+هي نفسها b,a صحيح ال b,a هي نفس a,b فلو اعملتوا ال
+
+594
+00:45:20,530 --> 00:45:23,390
+diagonal هنا هتلاقوا ان هما symmetric فانتين
+
+595
+00:45:23,390 --> 00:45:26,130
+هكونوا symmetric في الحالة بتاعتنا فهذه لازم
+
+596
+00:45:26,130 --> 00:45:28,230
+تاخدوا بالكم منها مدام ان انا بتكلم عن undirected
+
+597
+00:45:28,230 --> 00:45:31,710
+لازم تكون symmetric طيب اذا كانت نتكلم عن
+
+598
+00:45:31,710 --> 00:45:36,590
+multigraph، multigraph مانشتغلش على 01 matrix،
+
+599
+00:45:36,590 --> 00:45:40,840
+بنشتغل على natural matrixnatural matrix بمعنى انه
+
+600
+00:45:40,840 --> 00:45:44,700
+في عندنا عدد natural مستخدمه كده عدد العدد؟ هنا
+
+601
+00:45:44,700 --> 00:45:49,940
+بحكوا 1 عصر انه في relation لأ بحكوا 2 على عدد ال
+
+602
+00:45:49,940 --> 00:45:53,140
+paths الموجودة او عدد ال links الموجودة او عدد ال
+
+603
+00:45:53,140 --> 00:45:57,820
+links الموجودة for example لو
+
+604
+00:45:57,820 --> 00:46:03,320
+أخدنا شكل بهذا الشكل a,b,c,d برضه نفس الكلام هنعمل
+
+605
+00:46:03,320 --> 00:46:11,770
+a,b,c,d a,b,c,dالـ A و الـ A مافيش بينهم إشي طيب
+
+606
+00:46:11,770 --> 00:46:21,350
+خلينا نشوف ناخد مثلا ال C و ال D هاي C و D تلاتة
+
+607
+00:46:21,350 --> 00:46:23,710
+واحد اتنين تلاتة فبنكتبها تلاتة natural number
+
+608
+00:46:23,710 --> 00:46:27,910
+نشتغلش هنا zero one matrix لأ خلاص natural matrix
+
+609
+00:46:27,910 --> 00:46:30,830
+natural matrix ليش؟ لأنه بيصير بهمني أنا ال logic
+
+610
+00:46:30,830 --> 00:46:35,110
+بدي كده عدد ال links اللي موجودة بين ال two
+
+611
+00:46:35,110 --> 00:46:37,230
+vertices هدول اللي أنا بتكلم عنهم اللي هم ال C هنا
+
+612
+00:46:37,230 --> 00:46:44,320
+و Dأو D وC لأن نفس الكلام أنا ما زلت بشتغل
+
+613
+00:46:44,320 --> 00:46:47,600
+Undirected ما زلنا Undirected بمعنى أنه ما زلت
+
+614
+00:46:47,600 --> 00:46:53,360
+ملتزم بإيش Symmetric ما زلنا ملتزمين بدأ بتكلم عن
+
+615
+00:46:53,360 --> 00:46:56,280
+Undirected فهي لازم تطلع Symmetric اعملوا ال
+
+616
+00:46:56,280 --> 00:46:59,340
+diagonal تبعكم لو عكستوها هي هي هتبقى نفس ال
+
+617
+00:46:59,340 --> 00:47:03,400
+matrix نفس ال matrix على اعتبار أن احنا ما زلنا
+
+618
+00:47:03,400 --> 00:47:08,360
+Undirected okayالطريقة التالتة اللي هي ال
+
+619
+00:47:08,360 --> 00:47:11,880
+incidence matrix ال incidence matrix اه استنوا هي
+
+620
+00:47:11,880 --> 00:47:16,640
+matrix فهمنا بس incidence معناته يمكن يتغير
+
+621
+00:47:16,640 --> 00:47:20,040
+معاناها لو وجدت إشي إيش اللي هيتغير incidence هذه
+
+622
+00:47:20,040 --> 00:47:27,060
+بنطلقها على ال edge صحيح؟ مين اللي بيكون صادر عشان
+
+623
+00:47:27,060 --> 00:47:31,200
+يقول والله في إشي صادر في شعاع incident light مثلا
+
+624
+00:47:31,200 --> 00:47:36,780
+بدي يكون في عنده ال object و ال light نفسهمعناته
+
+625
+00:47:36,780 --> 00:47:41,000
+انا هنا بتكلم عن علاقة بين ال vertex و ال E مش بين
+
+626
+00:47:41,000 --> 00:47:44,380
+مش adjacency زي توي ال vertex مع ال vertex ثاني هم
+
+627
+00:47:44,380 --> 00:47:48,100
+متجاورة او لأ اختلف هنا ال relation اختلفت ال
+
+628
+00:47:48,100 --> 00:47:50,280
+relation اختلفت معناته انا لما بدي اجي امثل ال
+
+629
+00:47:50,280 --> 00:47:57,290
+matrix همثلها هنا ال vertices و هنا ال Eال edges
+
+630
+00:47:57,290 --> 00:48:01,530
+بتاعتنا ال edges بتاعتنا عشان نحدد هل وجد .. هل في
+
+631
+00:48:01,530 --> 00:48:08,430
+incidence between ال vertex و ال E ولا لأ هل ال E
+
+632
+00:48:08,430 --> 00:48:12,510
+هذه تعتبر incident من ال vertex هذه او لأ اذا
+
+633
+00:48:12,510 --> 00:48:17,790
+incident منها بحط قدامهم واحد فبنحطهم هنا E1 E2 E3
+
+634
+00:48:17,790 --> 00:48:22,050
+E4 to E جد ما يطلع اللي هي E مثلا اللي هي
+
+635
+00:48:22,050 --> 00:48:28,040
+cardinality بتاعتهاهنا نفس الكلام نضع V1 V2 to VN
+
+636
+00:48:28,040 --> 00:48:37,760
+نشوف VN مثلا هل منها صدر E1 يعني هم متصلين ات بعض
+
+637
+00:48:37,760 --> 00:48:44,780
+هل ال VN تعتبر ال initial تبع ال E1 ولا ال
+
+638
+00:48:44,780 --> 00:48:49,550
+terminalإذا فعلا هي .. خلّيني أتكلم في البداية عن
+
+639
+00:48:49,550 --> 00:48:54,690
+ال undirected إذا فعلا ال VN هذه إما ال initial أو
+
+640
+00:48:54,690 --> 00:48:59,130
+ال vertical أو ال terminal بتاعة E واحد بنحط هنا
+
+641
+00:48:59,130 --> 00:49:06,950
+واحد otherwise 0 طيب متوقع أن كل E إلها بداية و
+
+642
+00:49:06,950 --> 00:49:09,990
+إلها نهاية معنا ذلك أنه أتوقع أن ال column تبح هذا
+
+643
+00:49:09,990 --> 00:49:14,410
+لو أمسكه هلاجي فيه two onesهيكون هنا مثلا في كمان
+
+644
+00:49:14,410 --> 00:49:21,210
+one معناه ذلك ان ال E1 ده بيوصل لي V2 مع VN صح؟
+
+645
+00:49:21,210 --> 00:49:26,290
+نفترض ان الباقي zeros وين في ones؟ معناته E1
+
+646
+00:49:26,290 --> 00:49:32,410
+connected او بيعمل connection between V2 و V ..
+
+647
+00:49:32,410 --> 00:49:37,630
+نفترض أربعة و V4 تمام؟ بناء عليه هنشوفها logged
+
+648
+00:49:37,630 --> 00:49:42,940
+كيف ممكنان .. ان مثل ال .. برضه ال .. ال
+
+649
+00:49:42,940 --> 00:49:45,540
+undirected graph اللي موجود عندنا ال undirected
+
+650
+00:49:45,540 --> 00:49:47,100
+graph اللي موجود عندنا
+
+651
+00:49:50,550 --> 00:49:53,670
+جايين لها الوجد برضه لأ انت هنا بتصير بتشتغليش بس
+
+652
+00:49:53,670 --> 00:49:59,550
+zero one بتصير تشتغلي natural زي تقول اذا اكتر من
+
+653
+00:49:59,550 --> 00:50:03,010
+path او يعني عندك multi graph مش انت بتسأل اعملت
+
+654
+00:50:03,010 --> 00:50:05,930
+graph لأ اذا عملت graph بتصير نستخدمش واحد نستخدم
+
+655
+00:50:05,930 --> 00:50:11,270
+اكتر نستخدم اكتر او انت يمكن طريقة تمثيلك تختلف
+
+656
+00:50:11,270 --> 00:50:14,630
+ليش طريقة تمثيلك تختلف لأنه اذا بدك تفترض هنا في
+
+657
+00:50:14,630 --> 00:50:17,470
+واحد تاني ممكن تقولي ان هو هذا سبعة
+
+658
+00:50:20,930 --> 00:50:27,130
+بصير E سبعة فهنا متزودين لكمان column صح ال column
+
+659
+00:50:27,130 --> 00:50:31,430
+هذا متفق مع مع اتنين يعني هيكون زي هذا هيكون واحد
+
+660
+00:50:31,430 --> 00:50:39,830
+صفر صفر واحد بين A B C D و هنا طبعا قولنا واحد
+
+661
+00:50:39,830 --> 00:50:44,270
+اتنين تلاتة اربع خمسة ستة فهي صار سبعة معانا هى
+
+662
+00:50:44,270 --> 00:50:48,350
+صار معانا سبعة okay
+
+663
+00:50:50,000 --> 00:50:52,760
+في الحلقة دي صارت نقدر نعمل التنفيذ تبعنا بس ناخد
+
+664
+00:50:52,760 --> 00:50:58,360
+بالنا أن ال rows تبعتنا عبارة عن ال vertices أو ال
+
+665
+00:50:58,360 --> 00:51:02,280
+nodes ال columns تبعتنا عبارة عن ال edges تبعتنا
+
+666
+00:51:02,280 --> 00:51:06,880
+أو ال legs أو ال legs okay رسمناهم بنشوف عند ال a
+
+667
+00:51:06,880 --> 00:51:09,060
+one
+
+668
+00:51:11,150 --> 00:51:15,530
+عند ال a مع ال one هل هما ال a تعتبر أحد الأطراف
+
+669
+00:51:15,530 --> 00:51:19,670
+ال end points بتاعة one؟ مظبوط معناته one طب هل ال
+
+670
+00:51:19,670 --> 00:51:24,290
+a تعتبر برضه أحد ال end nodes بتاعة ال link اتنين؟
+
+671
+00:51:24,290 --> 00:51:30,070
+okay للتلاتة؟ لأ للاربعة؟ للخمسة؟ اه خمسة هي
+
+672
+00:51:30,070 --> 00:51:36,660
+الخمسة هي التلاتة وهي الخمسةستة بقيد كتير طيب
+
+673
+00:51:36,660 --> 00:51:40,760
+تعالوا نفحصها بطريقة مختلفة شوية احنا هنا امسكنا
+
+674
+00:51:40,760 --> 00:51:45,320
+row by row طب نمسكها column by column اتنين
+
+675
+00:51:45,320 --> 00:51:50,940
+connected بين ايش و ايش خلاص جدام ال a واحد و جدام
+
+676
+00:51:50,940 --> 00:51:54,480
+ال d واحد otherwise zeros لإن هو فعلا بيوصل اتنين
+
+677
+00:51:54,480 --> 00:52:00,280
+بقى طيب الستةself-loop معناته فقط مع نفسها مع ال C
+
+678
+00:52:00,280 --> 00:52:05,620
+هتلاقيه حتى هنا عبارة عن one واحد فقط بعرف ان هذا
+
+679
+00:52:05,620 --> 00:52:11,260
+self-loop أي اشي تاني بعرف انه وجد اربعة المفروض
+
+680
+00:52:11,260 --> 00:52:16,680
+بوصيه لي C مع دي طيب ستة او هذا واحد لحاله معناته
+
+681
+00:52:16,680 --> 00:52:20,360
+هذا self-loop مع ال C self-loop بنعرف ان هنا تتكلم
+
+682
+00:52:20,360 --> 00:52:23,460
+عن self-loop طيب لما يكون directed
+
+683
+00:52:26,380 --> 00:52:29,640
+بتتكلم هنا عن directed في الحالة هذه لأ بيصير
+
+684
+00:52:29,640 --> 00:52:38,600
+بتكون تمثلوا الشكل تبعكم فعليا ب two digits طيب زي
+
+685
+00:52:38,600 --> 00:52:43,260
+ما قلنا هنا ال incidence matrix اللي نقدر نمثلها
+
+686
+00:52:43,260 --> 00:52:49,480
+باستخدام اللي بنستعمل ال rowsvertices و ال columns
+
+687
+00:52:49,480 --> 00:52:55,120
+بنمثل فيهمين ال edges أو ال legs لو قلنا إنه بدنا
+
+688
+00:52:55,120 --> 00:52:58,000
+نشتغل على directed graph ال directed graph بصير
+
+689
+00:52:58,000 --> 00:53:02,540
+بدي two bits أنثلهم لكل E one بصير فعلا دي two
+
+690
+00:53:02,540 --> 00:53:07,040
+bits هنا في الحالة اللي عندنا هنا
+
+691
+00:53:16,280 --> 00:53:23,640
+فيه بيستخدموا تلاتة واحدة لل in واحدة لل out واحدة
+
+692
+00:53:23,640 --> 00:53:27,760
+لل self loop واحدة لل self loop وإن كان بنقدر
+
+693
+00:53:27,760 --> 00:53:31,500
+نمثلهم باتنين بس على اعتبار ان لو زهر عندكم ال in
+
+694
+00:53:31,500 --> 00:53:37,540
+one وال out one معناته self loop معناته هذا يعتبر
+
+695
+00:53:37,540 --> 00:53:43,750
+inلل بي و out لل بي برضه معناته منها إلها هذا
+
+696
+00:53:43,750 --> 00:53:47,610
+يعتبر self loop بتقدر تمثلها ولكن لأن عنوان الكتاب
+
+697
+00:53:47,610 --> 00:53:51,710
+كان بتتكلم عن two ones بيستخدمهم لل edges لل two
+
+698
+00:53:51,710 --> 00:53:54,270
+edges تبعوننا اللي هي ال in و ال out وفي one
+
+699
+00:53:54,270 --> 00:53:58,770
+مستخدم لها ال loop زي ما قلتلكوا أنا أتصور أنه لأ
+
+700
+00:53:58,770 --> 00:54:01,870
+باتنين بكافي جدا لأنه إذا كان اتفقوا one مع one
+
+701
+00:54:01,870 --> 00:54:04,670
+one one هذه معناته هذا self loop هذا بيحول في
+
+702
+00:54:04,670 --> 00:54:11,160
+الحالة هذه أصبح self loop تمامفبتقدروا تمثلوها بس
+
+703
+00:54:11,160 --> 00:54:14,880
+بتكونوا تزودوا عدد ال digits بتاعتكم عدد ال digits
+
+704
+00:54:14,880 --> 00:54:20,460
+بتاعتكم طيب ال isomorphism مدام عرفناها لوقت عملية
+
+705
+00:54:20,460 --> 00:54:25,480
+التمثيل بصير عملية ال isomorphism هذه المشابهة كيف
+
+706
+00:54:25,480 --> 00:54:29,560
+بدي أعرف أنهtwo graphs مش شبه بعض او لأ two graphs
+
+707
+00:54:29,560 --> 00:54:33,920
+عشان شبه بعض لازم في شواهد في الأول عناصر نتأكد
+
+708
+00:54:33,920 --> 00:54:37,080
+منها هل هي متساوية مع بعض ولا لأ قبل ما اقعد اقول
+
+709
+00:54:37,080 --> 00:54:40,040
+لأ طب انا بده اتخيل هذا لو اتحركت لو هذه لأ من غير
+
+710
+00:54:40,040 --> 00:54:43,920
+تخيلها بدون تخيلات او انه كيف لأ ال node هذي لو
+
+711
+00:54:43,920 --> 00:54:46,760
+حركناها هيك لأ لأ بدون اشيه كل اللي هتعملوه اول
+
+712
+00:54:46,760 --> 00:54:51,840
+شيء عدد ال nodes متساوي فبدنا نجمع نحط عشان اقول
+
+713
+00:54:51,840 --> 00:54:58,460
+G1 و G2 او G1 isomorphicto G2 مشابهة ومناظرة ل G2
+
+714
+00:54:58,460 --> 00:55:02,180
+بدنا نشوف أول شغلة هل ال cardinality ل ال vertices
+
+715
+00:55:02,180 --> 00:55:06,360
+بتساوية بمعنى عدد ال nodes متساويين نعم بنيجي نفحص
+
+716
+00:55:06,360 --> 00:55:08,980
+لها الأولى أو الله فيها خمسة nodes طب التانية فيها
+
+717
+00:55:08,980 --> 00:55:12,200
+ستة خلاص stop وقف مش بيشاووا بعض خلاص انتهى من غير
+
+718
+00:55:12,200 --> 00:55:15,100
+ما تدوروا على اشي تاني و الله يطلعوا يشاووا بعض
+
+719
+00:55:15,100 --> 00:55:19,180
+بدنا نشوف عدد ال lengths عدد ال lengths بتاعتهم هل
+
+720
+00:55:19,180 --> 00:55:23,600
+بيشاووا بيساووا بعض او لأ طيب طلعوا يساووا بعض ال
+
+721
+00:55:23,600 --> 00:55:29,800
+degreenumber of vertices with degree n اذا كان ال
+
+722
+00:55:29,800 --> 00:55:32,340
+degree واحد اذا كان ال degree واحد اذا كان ال
+
+723
+00:55:32,340 --> 00:55:34,600
+degree واحد اذا كان ال degree واحد اذا كان ال
+
+724
+00:55:34,600 --> 00:55:37,200
+degree واحد اذا كان ال degree واحد اذا كان ال
+
+725
+00:55:37,200 --> 00:55:43,350
+degree واحد اذا كان ال degree واحدطب أكم واحدة من
+
+726
+00:55:43,350 --> 00:55:46,410
+ال vertices طبعا ال degree بتاعتها بتساوي اتنين
+
+727
+00:55:46,410 --> 00:55:49,810
+خلصنا الاتنين التلاتة لعندي بتصلوا لأكبر degree
+
+728
+00:55:49,810 --> 00:55:52,370
+ممكنة في ال nodes اللي موجودة عندكم طبعا أنتوا
+
+729
+00:55:52,370 --> 00:55:54,610
+بتواصلوا هتشوفوا أكبر degree ممكنة ممكن تطلع اتنين
+
+730
+00:55:54,610 --> 00:55:57,750
+أو تلاتة أو أربع مثلا بتعملوا check على كل اللي
+
+731
+00:55:57,750 --> 00:56:01,850
+أقل منها جدش عدد ال degrees هنا وجدش عدد ال
+
+732
+00:56:01,850 --> 00:56:04,670
+degrees هنا لكل degree من ال degrees جدش عدد ال
+
+733
+00:56:04,670 --> 00:56:07,170
+nodes اللي بتحقق ال degree يعني إذا واحدة منهم
+
+734
+00:56:07,170 --> 00:56:10,190
+اختلفت خلص ال stop وقفوا مش هتوصل ال stopمستحيل
+
+735
+00:56:10,190 --> 00:56:14,130
+يظبطوا أن يكونوا مشابه بعض، زبطوا خير وبركة، طيب
+
+736
+00:56:14,130 --> 00:56:18,790
+فإذا عدد ال degree degree n is the same in both
+
+737
+00:56:18,790 --> 00:56:21,890
+graphs، هذا برضه شرط ضروري لازم يتحقق، طيب for
+
+738
+00:56:21,890 --> 00:56:27,590
+every prepared sub graph G of one graph there is a
+
+739
+00:56:27,590 --> 00:56:30,790
+prepared sub graph of the other graph is
+
+740
+00:56:30,790 --> 00:56:37,030
+isomorphic to G، فإذا كان فيsub graph طلعناه من G
+
+741
+00:56:37,030 --> 00:56:40,650
+مشابه هو نفسه بالظبط مشابهه بقدر اطلع نفس ال sub
+
+742
+00:56:40,650 --> 00:56:43,490
+graph من ال graph التاني بقى نفسه هذا عنصر برضه
+
+743
+00:56:43,490 --> 00:56:47,030
+بقدر امثل فيه ان والله الاتنين ممكن يكونوا متشابين
+
+744
+00:56:47,030 --> 00:56:49,730
+بس لازم يتحققوا جميع العناصر احنا طبعا لما نيجي
+
+745
+00:56:49,730 --> 00:56:53,310
+نحقق هنحقق العنصر الأول والتاني اللي بنشتر عليهم
+
+746
+00:56:53,310 --> 00:56:56,450
+لأن ال sub graphمافي احتمالات كتيرة ال sub graph
+
+747
+00:56:56,450 --> 00:56:58,850
+ال sub graph اللي هي كتير احتمالات انه ممكن نطلع
+
+748
+00:56:58,850 --> 00:57:01,710
+sub graph يطلع من هنا ل هنا فحنعمل check على
+
+749
+00:57:01,710 --> 00:57:04,370
+التنتين هدولة و منهم ان أكد هل الكلام صحيح او لا
+
+750
+00:57:04,370 --> 00:57:09,410
+طيب مثال ال isomorphism example ناخد isomorphism
+
+751
+00:57:09,410 --> 00:57:13,210
+example هل ال two graphs هدولة isomorphic كل واحدة
+
+752
+00:57:13,210 --> 00:57:18,640
+منهم للتاني او لأ is isomorphicاعملولنا إعادة
+
+753
+00:57:18,640 --> 00:57:22,340
+تسميات يعني قولولنا اديها دي وين مكانها هنا طبعا
+
+754
+00:57:22,340 --> 00:57:24,960
+هنا اتغيرت طبعا واضح ان هنا اتغيرت الشكل هذا بعيد
+
+755
+00:57:24,960 --> 00:57:27,840
+تماما بتحس انه مالوش علاقة بالشكل التاني بس خليني
+
+756
+00:57:27,840 --> 00:57:35,140
+أديهم واحدة واحدة عدد ال vertices جدش هنا عندى ستة
+
+757
+00:57:35,140 --> 00:57:40,880
+جدش هناك ستة هاي أول شرط تحقق شرط التاني ال edges
+
+758
+00:57:40,880 --> 00:57:46,870
+واحدتلاتة اربعة خمسة ستة سبعة تمانية تسعة طب هنا
+
+759
+00:57:46,870 --> 00:57:49,730
+واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية تسعة
+
+760
+00:57:49,730 --> 00:57:53,450
+okay هاي عدينا من التاني التالت الشرط التالت ال
+
+761
+00:57:53,450 --> 00:57:58,050
+degree طيب بدنا نشوف في degree zero هنا او هنا
+
+762
+00:57:58,050 --> 00:58:01,370
+مافيش degree zero مافيش اي isolated node طيب ال
+
+763
+00:58:01,370 --> 00:58:06,030
+degree one مافيش اي واحدة bended صحيح ولا واحدة
+
+764
+00:58:06,030 --> 00:58:09,810
+معلقة طيب ال .. ال isolated عفوا ال degree اتنين
+
+765
+00:58:19,690 --> 00:58:25,830
+خلّينا نقول هدي G1 أو هدي G2 خلّينا نشوف هنا لأ
+
+766
+00:58:25,830 --> 00:58:30,490
+هدي ال degree أكبر أكبر هاي واحدة و هاي اتنين صار
+
+767
+00:58:30,490 --> 00:58:34,530
+ال graph الأول فيه اتنين طيب هنا هاي في واحدة و
+
+768
+00:58:34,530 --> 00:58:38,570
+هاي اتنين في إيش غيرهم؟ طيب معناته هنا في two
+
+769
+00:58:38,570 --> 00:58:42,130
+vertices ال degree تقعدهم اتنين اتنين تشابهوا طيب
+
+770
+00:58:42,130 --> 00:58:47,030
+تلاتة إذا ال degree بتساوي تلاتة هاي في عندي واحدة
+
+771
+00:58:48,480 --> 00:58:55,440
+و هاي كمان واحدة في غيرهم؟ فش فإذا هاي اتنين طيب
+
+772
+00:58:55,440 --> 00:59:01,520
+هنا هاي في واحدة و هاي واحدة هاي في هنا واحدة و
+
+773
+00:59:01,520 --> 00:59:07,740
+هنا في واحدة تمام تنتين طيب degree أربعة هنا هاي
+
+774
+00:59:07,740 --> 00:59:12,300
+في واحدة و هاي واحدة طيب في الرسمة التانية
+
+775
+00:59:15,900 --> 00:59:20,280
+كويس هاي اتنين طيب degree خامسة مافيش لا هنا ولا
+
+776
+00:59:20,280 --> 00:59:22,700
+هنا خلاص هي أكبر degree كانت الأربع واضح أنه
+
+777
+00:59:22,700 --> 00:59:26,660
+معناته في isomorphism مبدأيا في isomorphism لضال
+
+778
+00:59:26,660 --> 00:59:33,980
+مدام اتفقنا أن في isomorphism بدنا ان
+
+779
+00:59:33,980 --> 00:59:38,440
+ننجل المسميات هذه لهناك طبعا هتلاحظوا أنه مدام كله
+
+780
+00:59:38,440 --> 00:59:40,860
+كان اتنين اتنين اتنين اتنين في إمكانية لحالين
+
+781
+00:59:40,860 --> 00:59:45,100
+حقيقةفى ممكنية هنا لحلين لأنه symmetric الشكل
+
+782
+00:59:45,100 --> 00:59:52,060
+الشكل symmetric ممكن نحط D مكان F و F مكان D ممكن
+
+783
+00:59:52,060 --> 00:59:56,320
+تظبط يعني الوقت احنا هنجرب حل منهم و بقى مش متذكر
+
+784
+00:59:56,320 --> 00:59:58,860
+انا الحل اللى رأى حطه هناك بس احنا خلانا نحل واحد
+
+785
+00:59:58,860 --> 01:00:02,080
+منهم الاتنين هيطلعوا صح لو اختلفوا خلانا نبدأ
+
+786
+01:00:02,080 --> 01:00:05,480
+الدرجة اتنين مين فى هنا ال degree بتاع اتم اتنين
+
+787
+01:00:05,480 --> 01:00:11,550
+دى خلانا ناخد دى نحطها دىدي connected مع واحدة
+
+788
+01:00:11,550 --> 01:00:15,570
+degree أربعة و واحدة degree تلاتة، صحيح؟ طيب، مين
+
+789
+01:00:15,570 --> 01:00:22,210
+ال degree أربعة؟ ال B و مين ال degree تلاتة؟ ال A،
+
+790
+01:00:22,210 --> 01:00:27,470
+كويس التانية اللي هي ال F، برضه نفس الكلام، مع
+
+791
+01:00:27,470 --> 01:00:30,890
+واحدة تلاتة و واحدة اتنين، مين التلاتة كانت؟ ال C
+
+792
+01:00:30,890 --> 01:00:38,170
+تلاتة و ال Eالـ C تلاتة تخضع تخضع تخضع تخضع تخضع
+
+793
+01:00:38,170 --> 01:00:39,050
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+794
+01:00:39,050 --> 01:00:39,950
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+795
+01:00:39,950 --> 01:00:41,650
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+796
+01:00:41,650 --> 01:00:41,830
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+797
+01:00:41,830 --> 01:00:49,950
+تخضع تخضع تخضع تخضع تخضع تخضع تخضع تخضع
+
+798
+01:00:49,950 --> 01:00:55,150
+تخضع تهذا حل موجود و ممكن نشوف احنا ايش اللي كنا
+
+799
+01:00:55,150 --> 01:00:58,310
+حالينه برضه كانت دي اه دي كنا بدنا أشتغلنا برضه في
+
+800
+01:00:58,310 --> 01:01:00,730
+دي ممكن ال F على فكرة تبدو من ال F و تطلع معاك و
+
+801
+01:01:00,730 --> 01:01:04,430
+ماشية في الحالة هذه ممكن تظبط حالتنا لأن هي
+
+802
+01:01:04,430 --> 01:01:07,390
+symmetric اصلا الرسمة الرسمة symmetric لما جينا
+
+803
+01:01:07,390 --> 01:01:09,450
+نطلعنا ع ال degrees رجيناهم كلهم اثنين اثنين اثنين
+
+804
+01:01:09,450 --> 01:01:15,450
+اثنين كلهم متشابهات طيب فهتلاحظوا انه قدرنا نعمل
+
+805
+01:01:15,450 --> 01:01:18,090
+renaming لمين لقى الرسم طبعا طيب هي دي
+
+806
+01:01:23,710 --> 01:01:28,810
+نشوف عدد ال nodes الأول هنا خمسة و هناك خمسة مش
+
+807
+01:01:28,810 --> 01:01:34,490
+الحال عدد ال edges تبعتنا نتصور هنا the same
+
+808
+01:01:34,490 --> 01:01:40,310
+vertices بمش الحال طيب عدد ال edges برضه نفس العدد
+
+809
+01:01:40,310 --> 01:01:47,640
+نمسك ال degrees لو أخدنا degreeبساوة اتنين زيرو في
+
+810
+01:01:47,640 --> 01:01:51,860
+زيرو فش زيرو في واحد فش واحد طب نبدأ معناته في
+
+811
+01:01:51,860 --> 01:01:54,300
+اتنين طبعا اللي جابلها زيرو واحد ده دولة زيرو
+
+812
+01:01:54,300 --> 01:01:59,440
+مافيش شيء نبدأ ديجري اتنين خلينا نقول جي وان و هدي
+
+813
+01:01:59,440 --> 01:02:03,680
+جي دو نبدأ
+
+814
+01:02:03,680 --> 01:02:08,540
+ديجري اتنين هنا في عندى واحدة هد تلاتة تلاتة تلاتة
+
+815
+01:02:08,540 --> 01:02:13,440
+تلاتة هنا في عندى فقط نود واحدة هنا واحد اتنين
+
+816
+01:02:13,440 --> 01:02:17,180
+تلاتة تلاتة تلاتة تلاتةstop خلاص واجف مافيش دلوقت
+
+817
+01:02:17,180 --> 01:02:21,700
+أكمل not isomorphic فإذا كل واحدة منهم not
+
+818
+01:02:21,700 --> 01:02:24,760
+isomorphic للتانية not isomorphic لمين للتانية
+
+819
+01:02:24,760 --> 01:02:29,460
+لأنه مبدأيا degree اتنين كان في هنا عندي واحد و
+
+820
+01:02:29,460 --> 01:02:36,680
+هنا تلاتة واحد versus three بسوش بعض بسوش بعض تمام
+
+821
+01:02:44,640 --> 01:02:49,620
+و مع ذلك خلّيني أقول و مع ذلك .. ممكن أتخلص كل يوم
+
+822
+01:02:49,620 --> 01:02:58,600
+.. و مع ذلك لاحظوا أنه ال .. مش دايما بتظبط، مش
+
+823
+01:02:58,600 --> 01:03:01,660
+دايما بس الشروط هاد اللي حالها بتظبط، هادي بنسميها
+
+824
+01:03:01,660 --> 01:03:04,640
+necessary condition but not sufficient condition
+
+825
+01:03:05,840 --> 01:03:10,260
+بمعنى شروط ضرورية لازم تتحقق بس مش كافية ليست
+
+826
+01:03:10,260 --> 01:03:15,160
+كافية ليش مش مش كافية عشان هسبقلكوا شوية شوفوا ليش
+
+827
+01:03:15,160 --> 01:03:19,540
+الشكل هذا خلينا
+
+828
+01:03:19,540 --> 01:03:22,920
+نسبق شوية عشان نقول والله لأ معناته في جزئية صغيرة
+
+829
+01:03:22,920 --> 01:03:24,920
+بدنا نعمل test عليها و بدنا نخلصنا
+
+830
+01:03:27,910 --> 01:03:36,770
+لحظة 123456 123456 123456 123456 123456 123456
+
+831
+01:03:36,770 --> 01:03:45,590
+123456 123456 123456 123456 123456 123456 123456
+
+832
+01:03:45,590 --> 01:03:45,790
+123456 123456 123456 123456 123456 123456 123456
+
+833
+01:03:45,790 --> 01:03:47,530
+123456 123456 123456 123456 123456 123456 123456
+
+834
+01:03:47,530 --> 01:03:47,730
+123456 123456 123456 123456 123456 123456 123456
+
+835
+01:03:47,730 --> 01:03:47,750
+123456 123456 123456 123456 123456 123456 123456
+
+836
+01:03:47,750 --> 01:03:47,770
+123456 123456 123456 123456 123456 123456 123456
+
+837
+01:03:47,770 --> 01:03:47,790
+123456 123456 123456 123456 123456 123456 123456
+
+838
+01:03:47,790 --> 01:03:54,250
+123456 123456 123456 123456
+
+839
+01:03:54,250 --> 01:03:58,460
+123معناة ان في اشي تاني لازم ناخد بالنا منه الشروط
+
+840
+01:03:58,460 --> 01:04:01,700
+اللي كنا بتتكلم عنها كانت ضرورية اه ضرورية بمعنى
+
+841
+01:04:01,700 --> 01:04:05,300
+انه لم .. لم تتحقق بقدر اطلع اطلع ال decision ان
+
+842
+01:04:05,300 --> 01:04:10,960
+هدول بيساويش بعض ولكن اذا تحققوا يمكن بقدر اقول
+
+843
+01:04:10,960 --> 01:04:14,000
+انه يمكن بيساوي بعضزي توي بقدر أقول إن هم أه يمكن
+
+844
+01:04:14,000 --> 01:04:17,260
+بيساوي بعض هنا هيتحققوا الشروط بس هدول هدول
+
+845
+01:04:17,260 --> 01:04:21,820
+بيساويش بعض هقول هذا ليست أزموفيكلا هذه إطلاقا طيب
+
+846
+01:04:21,820 --> 01:04:24,400
+ها إيش اللي بدنايا بدنا نشتغل شوية في ال
+
+847
+01:04:24,400 --> 01:04:27,660
+connectivity في ال connectivity هذه التواصلية
+
+848
+01:04:27,660 --> 01:04:31,120
+التواصلية الموضوع تبقى بسيط جدا من الأشكال اللي
+
+849
+01:04:31,120 --> 01:04:33,700
+عندنا هنا مين بقدر أقول إن ال graph ده connected
+
+850
+01:04:33,700 --> 01:04:37,350
+graphمين بقدر اقول منهم هدولة ال graph connected
+
+851
+01:04:37,350 --> 01:04:40,410
+graph ان كل ال points تبعته connected مع بعض
+
+852
+01:04:40,410 --> 01:04:45,790
+together فهدولة yes connected طب هده no واضح انه
+
+853
+01:04:45,790 --> 01:04:48,670
+في مفصول فهده مش connected بقدرش اقول ان هو
+
+854
+01:04:48,670 --> 01:04:53,290
+connected ال graph طب هده yes حتى لو بتطلع من C لل
+
+855
+01:04:53,290 --> 01:04:58,470
+E في path بمعنى كل نقطة مع اي نقطة تانية يوجد خط
+
+856
+01:04:58,470 --> 01:05:00,930
+بينهم يوجد path بينهم يوجد طريق بينهم يوجد
+
+857
+01:05:00,930 --> 01:05:06,140
+connection بينهمحتى لو مر ب other vertices الطيب
+
+858
+01:05:06,140 --> 01:05:12,500
+التالتة الرابعة لأ هدولة مش نقاط هدولة لو انهم
+
+859
+01:05:12,500 --> 01:05:16,260
+نقاط موجودة كان المفروض نحط node هنا بس هنا مافيش
+
+860
+01:05:16,260 --> 01:05:21,360
+node هنا لاوجد node فهد نوع هد منفصلين هدولة
+
+861
+01:05:21,360 --> 01:05:24,220
+بنسميهم component هدولة بنسميهم connected
+
+862
+01:05:24,220 --> 01:05:27,900
+components فإذا كل graph ممكن يكون يتكوّن من أكتر
+
+863
+01:05:27,900 --> 01:05:31,920
+من connected components واحدةأكتر than connected
+
+864
+01:05:31,920 --> 01:05:35,780
+components واحدة بمعنى أنه لو بالشكل هذا كله graph
+
+865
+01:05:35,780 --> 01:05:42,140
+واحد في أكم connected components أكم
+
+866
+01:05:42,140 --> 01:05:49,220
+connected components تلاتة ولا أربعة؟ هاي واحد،
+
+867
+01:05:49,220 --> 01:05:56,470
+هاي اتنين، هاي تلاتة، هاي أربعةفإذن واضح إنه في
+
+868
+01:05:56,470 --> 01:05:58,670
+عندنا ال components تبعتنا أو ال connected
+
+869
+01:05:58,670 --> 01:06:02,030
+components تبعتنا الجزء الأول هذا اللي هو a,b,c,d
+
+870
+01:06:02,030 --> 01:06:05,210
+هدول هي بيعملهم فقوس لحالهم هدول connected
+
+871
+01:06:05,210 --> 01:06:09,370
+component لحالهم طيب ال components تانية ال E
+
+872
+01:06:09,370 --> 01:06:14,820
+لحالها فما هي ال E لحالها و ال F ما زيهاهي ال F
+
+873
+01:06:14,820 --> 01:06:20,880
+برضه زيها طيب ال connected الأخيرة من I to J IGHJ
+
+874
+01:06:20,880 --> 01:06:24,200
+ففي عندي أربع components في الحالة .. في الحالة
+
+875
+01:06:24,200 --> 01:06:28,360
+هذه طيب في .. برضه لما يكون عندكوا بالشكل هذا
+
+876
+01:06:28,360 --> 01:06:34,840
+component ال G هذه بنسميها cut vertex بمعنى لو ان
+
+877
+01:06:34,840 --> 01:06:38,740
+عملنا removing هتفصل ال .. ال .. ال connected
+
+878
+01:06:38,740 --> 01:06:44,430
+component لأكتر من componentبتصير اكتر من two ..
+
+879
+01:06:44,430 --> 01:06:49,230
+يعني بتصير two او اكتر components فانت بتلاقي فيه
+
+880
+01:06:49,230 --> 01:06:54,930
+critical vertex لو انشالت بتفصل ال graph تبعكم
+
+881
+01:06:54,930 --> 01:06:58,390
+بيسميها cut vertex نفس الكلام فيه لل edges ال edge
+
+882
+01:06:58,390 --> 01:07:01,890
+لو كان .. بتفصل .. لو ال edge ده لو انفصلت لو غير
+
+883
+01:07:01,890 --> 01:07:06,110
+موجودة ال E .. ال D هتنفصل ال D هتفصل .. هتنفصل
+
+884
+01:07:06,110 --> 01:07:08,390
+لحالها طيب لو بهذا الشكل
+
+885
+01:07:11,500 --> 01:07:18,460
+مافيش هنا أي cut edge لأن أي واحد بنفصل مش هيأثر،
+
+886
+01:07:18,460 --> 01:07:22,040
+هتظل component واحدة بالنسبة لجزء هذا لحاله، هذا
+
+887
+01:07:22,040 --> 01:07:25,420
+هيك لحاله، أي واحدة منهم تنفصل، هتظل component
+
+888
+01:07:25,420 --> 01:07:31,000
+واحدة، صحيح؟ هي هي، okay و أي نقطة برضه هتنفصل،
+
+889
+01:07:31,000 --> 01:07:34,440
+باقى النقاط هتظل متصلة مع بعض، فإذا هنا مافيش لا
+
+890
+01:07:34,440 --> 01:07:40,130
+cut vertex ولا cut edge تمامفي هذا ال cut vertex
+
+891
+01:07:40,130 --> 01:07:42,770
+أو ال cut edge اللي هي بتعملنا separation او
+
+892
+01:07:42,770 --> 01:07:47,430
+separates one connected components او component
+
+893
+01:07:47,430 --> 01:07:53,370
+into two components if removed إذا كان انشالة
+
+894
+01:07:53,370 --> 01:07:57,310
+بتخلي ال one connected component تصير اكتر من one
+
+895
+01:07:57,310 --> 01:08:01,290
+او من اتنين او اكتر components اتنين او اكتر
+
+896
+01:08:01,290 --> 01:08:05,380
+componentsمصطلح تاني اللي هي ال weakly connected و
+
+897
+01:08:05,380 --> 01:08:07,960
+ال strongly connected weakly connected و ال
+
+898
+01:08:07,960 --> 01:08:11,680
+strongly connected عادة تستخدم في ال direct graph
+
+899
+01:08:11,680 --> 01:08:16,960
+في ال direct graph بمعنى إذا والله كل النقاط متصلة
+
+900
+01:08:16,960 --> 01:08:22,180
+مع بعض ولكن الاكتشاف بساعدنيش ان انا امشي بين اي
+
+901
+01:08:22,180 --> 01:08:26,340
+نقطة و التانية بنسميها weakly connected طيب إذا
+
+902
+01:08:26,340 --> 01:08:29,400
+واحدة منهم انفصلة تماما واضح ان هي not connected
+
+903
+01:08:29,400 --> 01:08:35,600
+أصلا بتكون connected أساساولكن إذا كان حتى بالأسهم
+
+904
+01:08:35,600 --> 01:08:38,960
+من أي نقطة لأي نقطة تانية بقدر أنشئ، من أي نقطة
+
+905
+01:08:38,960 --> 01:08:42,360
+لأي نقطة بقدر أروح، حسب الاتجاه، بنسميها strongly
+
+906
+01:08:42,360 --> 01:08:47,180
+connected هنا في الحالة اللي زي هذه، بدي أطلع من A
+
+907
+01:08:47,180 --> 01:08:47,940
+مثلا لل B
+
+908
+01:08:52,400 --> 01:08:56,080
+مافيش .. مضطر .. هو في connection ولكن اتجاهه مش
+
+909
+01:08:56,080 --> 01:09:00,060
+مظبوط اتجاهه بالعكس بنسميها انه لأ ماقدرش اقول ان
+
+910
+01:09:00,060 --> 01:09:02,800
+هو مافيش connection بس بقول weakly connected
+
+911
+01:09:02,800 --> 01:09:06,080
+بنسميها weakly connected طب حالة زي هذه بدي اروح
+
+912
+01:09:06,080 --> 01:09:09,860
+من A ل B طيب
+
+913
+01:09:09,860 --> 01:09:18,360
+بدي اروح من A ل C طب A ل D طب من B ل C طب
+
+914
+01:09:18,360 --> 01:09:25,230
+من ال .. ال B ل ال Dطب من دي لإيه؟ ففي طريق باشي
+
+915
+01:09:25,230 --> 01:09:28,550
+مع ال direct تبعنا مع الاتجاه تبعنا من أي نقطة و
+
+916
+01:09:28,550 --> 01:09:32,210
+أي نقطة تانيةفهنا بنسميها strongly connected
+
+917
+01:09:32,210 --> 01:09:35,950
+فواضحة تاني وجهة الفرق بين ال weakly connected و
+
+918
+01:09:35,950 --> 01:09:39,870
+ال strongly connected هذه في حالة انه as a
+
+919
+01:09:39,870 --> 01:09:44,250
+directed graph مافيش طريق ولكن لو نفسها تحولت ل
+
+920
+01:09:44,250 --> 01:09:48,050
+undirected بصير في طريق، بنسميها weakly، بنسميها
+
+921
+01:09:48,050 --> 01:09:51,730
+weakly، connection ولكن ضعيف، التانية لأ،
+
+922
+01:09:51,730 --> 01:09:56,510
+connection قوي، strongly connectedمعنى ذلك أنه
+
+923
+01:09:56,510 --> 01:09:59,330
+هنجد الحاجة التانية اللى بدى أشتغل عليها، بدنا
+
+924
+01:09:59,330 --> 01:10:03,890
+نشتغل على ال connection عشان نحدد هل هم isomorphic
+
+925
+01:10:03,890 --> 01:10:08,630
+ولا لا، إيش ال connection؟ إنه من أي نقطة عشان
+
+926
+01:10:08,630 --> 01:10:12,390
+أعمله و أرجع لنفس النقطة، جدش ال degree تبعتي، جدش
+
+927
+01:10:12,390 --> 01:10:16,630
+عدد ال points اللى أنا مرت عليهمجدش عدد ال points
+
+928
+01:10:16,630 --> 01:10:19,950
+اللي مرنا عليهم ال path تبعنا جدش حجمه جدش ال size
+
+929
+01:10:19,950 --> 01:10:24,010
+تبعه فهنا the number and size of connected
+
+930
+01:10:24,010 --> 01:10:27,950
+components connected components لما أقول والله بدي
+
+931
+01:10:27,950 --> 01:10:30,250
+أطلع من النقطة هذه و أرجع لتاني معناته ممكن أطلع
+
+932
+01:10:30,250 --> 01:10:36,250
+أشطر بهذا الشكلماجددش عدد ال .. اللي هي ال circle
+
+933
+01:10:36,250 --> 01:10:38,250
+تبعتنا او ال circuit بنتعمل circuit او .. او
+
+934
+01:10:38,250 --> 01:10:45,450
+circle ل individual terms او individual point
+
+935
+01:10:45,450 --> 01:10:51,050
+هتكون عندى واحد اتنين تلاتة اربعة اه معناه ذلك ان
+
+936
+01:10:51,050 --> 01:10:56,280
+في عندى نقطة ال connectivity بتاعتها اربعةأو ال
+
+937
+01:10:56,280 --> 01:10:59,300
+path تبعها أربعة طيب هل هنا هنا هنا نقطة فيها
+
+938
+01:10:59,300 --> 01:11:03,280
+أربعة في نقطة أربعة بس هل هي نفسها مرتبطة هنا
+
+939
+01:11:03,280 --> 01:11:08,040
+مرتبطة ممكن تكون مرتبطة بناء على ال condition اللي
+
+940
+01:11:08,040 --> 01:11:16,340
+احنا قلنا أكملوب هنا ال degree تبعته تلاتة مافيش
+
+941
+01:11:16,340 --> 01:11:19,660
+اي loop ال degree تبعته تلاتة صح طب هنا أكملوب في
+
+942
+01:11:19,660 --> 01:11:22,360
+ال degree تبعته تلاتة او يعني ال length تبعته
+
+943
+01:11:22,360 --> 01:11:24,900
+تلاتة ال size تبعته تلاتة فيه اتنين طب ليش مظهروش
+
+944
+01:11:24,900 --> 01:11:28,840
+هنامعناته مش .. مش .. مش isomorphic الاتنين
+
+945
+01:11:28,840 --> 01:11:34,880
+الاتنين مش isomorphic هي من النقطة هذه عشان
+
+946
+01:11:34,880 --> 01:11:38,520
+ارجعلها في عندي path واحد اتنين تلاتة هنا مافيش اي
+
+947
+01:11:38,520 --> 01:11:42,880
+نقطة برجعلها ب .. ب .. ب path ال size تبعه تلاتة
+
+948
+01:11:42,880 --> 01:11:49,440
+ويل فيه؟
+
+949
+01:11:49,440 --> 01:11:53,910
+مش هتلاقواخلاص معناته not isomorphic رغم ان هي
+
+950
+01:11:53,910 --> 01:11:57,030
+حققت الشروط السابقة الشروط اللي بدأنا فيها كلها
+
+951
+01:11:57,030 --> 01:12:01,110
+كانت متحققة بس واضح انه لأ مش isomorphic زودنا بس
+
+952
+01:12:01,110 --> 01:12:04,570
+جزئية ال connectivity هذه ال connectivity اللي
+
+953
+01:12:04,570 --> 01:12:08,050
+زودناها الجزية بتاعتنا انه عشان يكون في connection
+
+954
+01:12:08,050 --> 01:12:13,510
+بين النقطة و نفسها النقطة لنفسها connected جدش ال
+
+955
+01:12:13,510 --> 01:12:16,770
+size تبع ال length تبعنا جدش ال size تبعنا واضح ان
+
+956
+01:12:16,770 --> 01:12:20,890
+هنا في تلاتة طيب هنا لو اتكلمنا عن الأربعة مثلا
+
+957
+01:12:22,330 --> 01:12:27,610
+أكمبث هنا أربعة؟ واحد، واحد، واحد، واحد، واحد،
+
+958
+01:12:27,610 --> 01:12:29,810
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+959
+01:12:29,810 --> 01:12:30,850
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+960
+01:12:30,850 --> 01:12:32,850
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+961
+01:12:32,850 --> 01:12:35,930
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+962
+01:12:35,930 --> 01:12:37,470
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+963
+01:12:37,470 --> 01:12:40,370
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+964
+01:12:40,370 --> 01:12:41,070
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+965
+01:12:41,070 --> 01:12:49,090
+واحد، واحد، واحد
+
+966
+01:12:58,920 --> 01:13:03,140
+أحنا في الشرط
+
+967
+01:13:03,140 --> 01:13:06,700
+الأولان كنا بنقول ان عدد ال edges يساوي بعض بس هنا
+
+968
+01:13:06,700 --> 01:13:11,340
+لأ هنا صرنا بنحدد قداش طول مجموع ال edges عشان
+
+969
+01:13:11,340 --> 01:13:15,120
+ارجع لنفس النقطة عشان اعمل loop او اعمل circuit
+
+970
+01:13:16,090 --> 01:13:20,810
+عشان اعمل circuit جدش عدد ال edges اللي محتاجها
+
+971
+01:13:20,810 --> 01:13:24,770
+فواضح انه هنا كنت محتاج اعمل او اكمل loop بتلاتة
+
+972
+01:13:24,770 --> 01:13:27,330
+edges هنا ماكنش في إمكاني اعملها بتلاتة edges
+
+973
+01:13:27,330 --> 01:13:32,350
+فواضح انه هذه لأ مش مماثلة لها هذه بماثله انه كان
+
+974
+01:13:32,350 --> 01:13:35,190
+ممكن نفس ال characteristic اللي بقدر أطلحها من هنا
+
+975
+01:13:35,190 --> 01:13:38,130
+هي هي أطلحها من هنا بس هو هذا ماصارش فعليا هذا
+
+976
+01:13:38,130 --> 01:13:41,110
+ماحصلش معناه واضح ان هنا كان في تلاتة هناك ماكنش
+
+977
+01:13:41,110 --> 01:13:45,340
+في تلاتةفهيك بنقدر نقول أن هدول التنتين مش
+
+978
+01:13:45,340 --> 01:13:48,480
+isomorphism وبنان على هيك بنكون خلصنا ان شاء الله
+
+979
+01:13:48,480 --> 01:13:50,920
+محاضرتنا ل graphs و بنكون خلصنا مصاق ان شاء الله
+
+980
+01:13:50,920 --> 01:13:53,940
+طالع بنشوفكوا ان شاء الله في مصاقات أخرى و يعطيكوا
+
+981
+01:13:53,940 --> 01:13:55,860
+الصحة و العفو يا كل عاموا أنتوا بخير و ربنا يوفركم
+
+982
+01:13:55,860 --> 01:13:56,480
+في امتحاناتكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c95a9580ee333d0e9e20f1b7146a8240f2265f6f
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/CWKPgvl5zqA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4899, "start": 21.09, "end": 48.99, "text": "بسم الله الرحمن الرحيم الصلاة والسلام عليكم ورحمة الله وبركاته يا أبو حميد وسيدنا محمد وعلى أهلي وصحابي أجمعين نبدأ اليوم حاضرتنا من ال graph اللي بدأنا المرة اللي فاتت و المرة اللي فاتت أخدنا مجموعة أنواع هيك في قجلة يعني بس أخدنا إيش يعني .. لما نتكلم عن undirected graph أو simple graph إيش معناه؟ اتكلمنا عن ال .. ال multiple أو ال multigraph اتكلمنا عن ال pseudograph و اتكلمنا عن ال directed graph", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 35186, 5551, 3555, 2407, 11331, 2304, 25708, 46952, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 20292, 4032, 9381, 5016, 16758, 1829, 5551, 7435, 2304, 3615, 9957, 8717, 44510, 10721, 45595, 20498, 11331, 46958, 43500, 8315, 9154, 2423, 4295, 13672, 1829, 47525, 10721, 8315, 9673, 25720, 13672, 1829, 6156, 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هنتكلم عن .. عن ال .. شوية terminology خاصة بال graphs خاصة بإيش؟ بال graphs ال graphs هذه هنتكلم عن ال adjacent هنتكلم عن ال connects هنتكلم عن ال end points", "tokens": [2407, 2423, 4825, 4386, 1975, 2407, 2423, 12898, 4825, 4295, 1975, 2655, 4117, 19528, 8315, 18871, 33962, 2304, 3794, 3660, 16472, 36764, 24401, 4032, 5296, 19528, 25720, 13672, 1829, 6156, 9307, 2655, 1975, 2655, 4117, 19528, 8315, 4032, 49610, 5172, 8315, 43242, 16095, 5296, 3615, 41260, 19446, 4032, 36520, 8315, 5296, 3541, 6225, 8592, 25720, 1975, 2655, 1863, 9957, 4032, 12174, 12610, 8315, 16472, 9673, 25720, 25724, 995, 10632, 8032, 1863, 47283, 3215, 11296, 8032, 29399, 4117, 19528, 18871, 4386, 18871, 2423, 4386, 13412, 2407, 10632, 27575, 16490, 33546, 3660, 20666, 24877, 16490, 33546, 3660, 4724, 28814, 1829, 8592, 22807, 20666, 24877, 2423, 24877, 29538, 8032, 29399, 4117, 19528, 18871, 2423, 24441, 8032, 29399, 4117, 19528, 18871, 2423, 16967, 8032, 29399, 4117, 19528, 18871, 2423, 917, 2793], 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2085.33, "word": " هذه", "probability": 0.37255859375}, {"start": 2085.33, "end": 2085.87, "word": " subset", "probability": 0.970703125}, {"start": 2085.87, "end": 2086.51, "word": " هذه", "probability": 0.6142578125}, {"start": 2086.51, "end": 2087.33, "word": " فئة", "probability": 0.97900390625}, {"start": 2087.33, "end": 2088.01, "word": " جزئية", "probability": 0.9637451171875}, {"start": 2088.01, "end": 2088.31, "word": " من", "probability": 0.98974609375}, {"start": 2088.31, "end": 2088.87, "word": " الفئة", "probability": 0.9744466145833334}, {"start": 2088.87, "end": 2088.99, "word": " اللي", "probability": 0.942138671875}, {"start": 2088.99, "end": 2089.27, "word": " هنا", "probability": 0.98974609375}, {"start": 2089.27, "end": 2090.11, "word": " الفئة", "probability": 0.9742838541666666}, {"start": 2090.11, "end": 2090.33, "word": " هذه", "probability": 0.443359375}, {"start": 2090.33, "end": 2091.51, "word": " بنقيسها", "probability": 0.8023681640625}, {"start": 2091.51, "end": 2091.73, "word": " على", "probability": 0.90478515625}, {"start": 2091.73, "end": 2092.31, "word": " ال", "probability": 0.73095703125}, {"start": 2092.31, "end": 2092.63, "word": " nodes", "probability": 0.95751953125}], "temperature": 1.0}, {"id": 83, "seek": 211367, "start": 2093.11, "end": 2113.67, "text": "إنه ال notes اللي هنا جزء من ال notes اللي هنا وبنقيصها كمان على مين على ال connections على ال edges على ال links فكل link موجود هنا المفروض إنه في الأصل كان موجود هنا فبنقول إن هذا subset of g فهنا هناخد هاي subset منها جزء منها", "tokens": [28814, 1863, 3224, 2423, 5570, 13672, 1829, 34105, 10874, 11622, 38207, 9154, 2423, 5570, 13672, 1829, 34105, 46599, 1863, 4587, 1829, 9381, 11296, 9122, 2304, 7649, 15844, 3714, 9957, 15844, 2423, 9271, 15844, 2423, 8819, 15844, 2423, 6123, 6156, 28820, 2113, 3714, 29245, 23328, 34105, 9673, 5172, 32887, 11242, 36145, 3224, 8978, 16247, 36520, 25961, 3714, 29245, 23328, 34105, 6156, 3555, 1863, 39648, 36145, 23758, 25993, 295, 290, 6156, 3224, 8315, 8032, 1863, 47283, 3215, 8032, 47302, 25993, 9154, 11296, 10874, 11622, 38207, 9154, 11296], "avg_logprob": -0.19622092590082524, "compression_ratio": 1.9, "no_speech_prob": 2.205371856689453e-06, "words": [{"start": 2093.11, "end": 2093.53, "word": "إنه", "probability": 0.5651041666666666}, {"start": 2093.53, "end": 2093.79, "word": " ال", "probability": 0.7705078125}, {"start": 2093.79, "end": 2093.95, "word": " notes", "probability": 0.7841796875}, {"start": 2093.95, "end": 2094.11, "word": " اللي", "probability": 0.85205078125}, {"start": 2094.11, "end": 2094.33, "word": " هنا", "probability": 0.99072265625}, {"start": 2094.33, "end": 2094.99, "word": " جزء", "probability": 0.97998046875}, {"start": 2094.99, "end": 2095.11, "word": " من", "probability": 0.990234375}, {"start": 2095.11, "end": 2095.21, "word": " ال", "probability": 0.94140625}, {"start": 2095.21, "end": 2095.37, "word": " notes", "probability": 0.87841796875}, {"start": 2095.37, "end": 2095.53, "word": " اللي", "probability": 0.989501953125}, {"start": 2095.53, "end": 2095.77, "word": " هنا", "probability": 0.98779296875}, {"start": 2095.77, "end": 2096.95, "word": " وبنقيصها", "probability": 0.7805989583333334}, {"start": 2096.95, "end": 2097.19, "word": " كمان", "probability": 0.8806966145833334}, {"start": 2097.19, "end": 2097.35, "word": " على", "probability": 0.86474609375}, {"start": 2097.35, "end": 2097.67, "word": " مين", "probability": 0.6708984375}, {"start": 2097.67, "end": 2098.17, "word": " على", "probability": 0.54443359375}, {"start": 2098.17, "end": 2098.29, "word": " ال", "probability": 0.96826171875}, {"start": 2098.29, "end": 2098.77, "word": " connections", "probability": 0.96923828125}, {"start": 2098.77, "end": 2099.45, "word": " على", "probability": 0.8154296875}, {"start": 2099.45, "end": 2099.59, "word": " ال", "probability": 0.986328125}, {"start": 2099.59, "end": 2099.95, "word": " edges", "probability": 0.9287109375}, {"start": 2099.95, "end": 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"word": " موجود", "probability": 0.9816080729166666}, {"start": 2104.47, "end": 2104.69, "word": " هنا", "probability": 0.9931640625}, {"start": 2104.69, "end": 2105.31, "word": " فبنقول", "probability": 0.947265625}, {"start": 2105.31, "end": 2105.43, "word": " إن", "probability": 0.90478515625}, {"start": 2105.43, "end": 2105.61, "word": " هذا", "probability": 0.1099853515625}, {"start": 2105.61, "end": 2106.13, "word": " subset", "probability": 0.95849609375}, {"start": 2106.13, "end": 2106.55, "word": " of", "probability": 0.96533203125}, {"start": 2106.55, "end": 2108.05, "word": " g", "probability": 0.296630859375}, {"start": 2108.05, "end": 2110.57, "word": " فهنا", "probability": 0.8738606770833334}, {"start": 2110.57, "end": 2111.77, "word": " هناخد", "probability": 0.946044921875}, {"start": 2111.77, "end": 2111.97, "word": " هاي", "probability": 0.6201171875}, {"start": 2111.97, "end": 2112.33, "word": " subset", "probability": 0.98095703125}, {"start": 2112.33, "end": 2112.71, "word": " منها", "probability": 0.971435546875}, {"start": 2112.71, "end": 2113.35, "word": " جزء", "probability": 0.9832356770833334}, {"start": 2113.35, "end": 2113.67, "word": " منها", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 84, "seek": 213242, "start": 2114.17, "end": 2132.43, "text": "مش بالضروري كلها، مش بالضروري كلها، مدام جزء منها، كيف نقدر نقول إن هو جزء منها؟ بنمسك ال vertices بتاعنا هل هما فعلا كل vertex موجودة هنا موجودة هنا؟ موجودة طب هل كل link موجود هنا فعلا موجود هنا؟ خلاص بإذن هذه ال H هي subset of G", "tokens": [2304, 8592, 20666, 11242, 2288, 13063, 1829, 28242, 11296, 12399, 37893, 20666, 11242, 2288, 13063, 1829, 28242, 11296, 12399, 3714, 3215, 10943, 10874, 11622, 38207, 9154, 11296, 12399, 9122, 33911, 8717, 28543, 2288, 8717, 39648, 36145, 31439, 10874, 11622, 38207, 9154, 11296, 22807, 44945, 2304, 3794, 4117, 2423, 32053, 39894, 45761, 8315, 8032, 1211, 8032, 15042, 6156, 3615, 15040, 28242, 28162, 3714, 29245, 23328, 3660, 34105, 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"end": 2121.69, "word": " بتاعنا", "probability": 0.8831380208333334}, {"start": 2121.69, "end": 2122.15, "word": " هل", "probability": 0.775634765625}, {"start": 2122.15, "end": 2122.29, "word": " هما", "probability": 0.800537109375}, {"start": 2122.29, "end": 2122.63, "word": " فعلا", "probability": 0.9046223958333334}, {"start": 2122.63, "end": 2123.29, "word": " كل", "probability": 0.9296875}, {"start": 2123.29, "end": 2123.95, "word": " vertex", "probability": 0.91650390625}, {"start": 2123.95, "end": 2124.35, "word": " موجودة", "probability": 0.9847412109375}, {"start": 2124.35, "end": 2124.55, "word": " هنا", "probability": 0.99609375}, {"start": 2124.55, "end": 2125.33, "word": " موجودة", "probability": 0.8818359375}, {"start": 2125.33, "end": 2125.79, "word": " هنا؟", "probability": 0.90673828125}, {"start": 2125.79, "end": 2126.65, "word": " موجودة", "probability": 0.969970703125}, {"start": 2126.65, "end": 2126.91, "word": " طب", "probability": 0.678466796875}, {"start": 2126.91, "end": 2127.09, "word": " هل", "probability": 0.917724609375}, {"start": 2127.09, "end": 2127.27, "word": " كل", "probability": 0.99072265625}, {"start": 2127.27, "end": 2127.51, "word": " link", "probability": 0.96630859375}, {"start": 2127.51, "end": 2127.83, "word": " موجود", "probability": 0.9700520833333334}, {"start": 2127.83, "end": 2127.97, "word": " هنا", "probability": 0.9873046875}, {"start": 2127.97, "end": 2128.25, "word": " فعلا", "probability": 0.8068033854166666}, {"start": 2128.25, "end": 2128.53, "word": " موجود", "probability": 0.9041341145833334}, {"start": 2128.53, "end": 2129.39, "word": " هنا؟", "probability": 0.96875}, {"start": 2129.39, "end": 2129.59, "word": " خلاص", "probability": 0.9921875}, {"start": 2129.59, "end": 2129.91, "word": " بإذن", "probability": 0.7518310546875}, {"start": 2129.91, "end": 2130.15, "word": " هذه", "probability": 0.41650390625}, {"start": 2130.15, "end": 2130.37, "word": " ال", "probability": 0.92333984375}, {"start": 2130.37, "end": 2130.63, "word": " H", "probability": 0.7666015625}, {"start": 2130.63, "end": 2130.89, "word": " هي", "probability": 0.91259765625}, {"start": 2130.89, "end": 2131.21, "word": " subset", "probability": 0.96435546875}, {"start": 2131.21, "end": 2131.75, "word": " of", "probability": 0.98486328125}, {"start": 2131.75, "end": 2132.43, "word": " G", "probability": 0.94189453125}], "temperature": 1.0}, {"id": 85, "seek": 215371, "start": 2136.9, "end": 2153.72, "text": "Okay بالعكس ال union الاتحاد الاتحاد طبعا هيكون في عندنا two graphs في عندنا graph number one graph number two بدنا نجيب ال union او g1 union g2 of two simple graphs g1 معرفينه على اساس ان هو v1", "tokens": [8297, 20666, 3615, 4117, 3794, 2423, 11671, 2423, 9307, 5016, 18513, 2423, 9307, 5016, 18513, 23032, 3555, 3615, 995, 39896, 30544, 8978, 43242, 8315, 732, 24877, 8978, 43242, 8315, 4295, 1230, 472, 4295, 1230, 732, 47525, 8315, 8717, 7435, 1829, 3555, 2423, 11671, 1975, 2407, 290, 16, 11671, 290, 17, 295, 732, 2199, 24877, 290, 16, 20449, 28480, 9957, 3224, 15844, 24525, 32277, 16472, 31439, 371, 16], "avg_logprob": -0.23920036808532827, "compression_ratio": 1.5823529411764705, "no_speech_prob": 7.927417755126953e-06, "words": [{"start": 2136.9, "end": 2137.54, "word": "Okay", "probability": 0.1197509765625}, {"start": 2137.54, "end": 2138.18, "word": " بالعكس", "probability": 0.918212890625}, {"start": 2138.18, "end": 2138.44, "word": " ال", "probability": 0.9345703125}, {"start": 2138.44, "end": 2138.8, "word": " union", "probability": 0.9150390625}, {"start": 2138.8, "end": 2140.12, "word": " الاتحاد", "probability": 0.81414794921875}, {"start": 2140.12, "end": 2141.48, "word": " الاتحاد", "probability": 0.876708984375}, {"start": 2141.48, "end": 2142.4, "word": " طبعا", "probability": 0.8914794921875}, {"start": 2142.4, "end": 2142.72, "word": " هيكون", "probability": 0.76416015625}, {"start": 2142.72, "end": 2142.88, "word": " في", "probability": 0.73828125}, {"start": 2142.88, "end": 2143.2, "word": " عندنا", "probability": 0.86083984375}, {"start": 2143.2, "end": 2143.58, "word": " two", "probability": 0.71875}, {"start": 2143.58, "end": 2144.0, "word": " graphs", "probability": 0.91748046875}, {"start": 2144.0, "end": 2144.36, "word": " في", "probability": 0.408203125}, {"start": 2144.36, "end": 2144.56, "word": " عندنا", "probability": 0.935302734375}, {"start": 2144.56, "end": 2144.8, "word": " graph", "probability": 0.865234375}, {"start": 2144.8, "end": 2145.24, "word": " number", "probability": 0.93505859375}, {"start": 2145.24, "end": 2145.5, "word": " one", "probability": 0.8818359375}, {"start": 2145.5, "end": 2145.7, "word": " graph", "probability": 0.35009765625}, {"start": 2145.7, "end": 2145.94, "word": " number", "probability": 0.955078125}, {"start": 2145.94, "end": 2146.16, "word": " two", "probability": 0.89599609375}, {"start": 2146.16, "end": 2146.42, "word": " بدنا", "probability": 0.782470703125}, {"start": 2146.42, "end": 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"end": 3929.46, "text": "حتى لو مر ب other vertices الطيب التالتة الرابعة لأ هدولة مش نقاط هدولة لو انهم نقاط موجودة كان المفروض نحط node هنا بس هنا مافيش node هنا لاوجد node فهد نوع هد منفصلين هدولة بنسميهم component هدولة بنسميهم connected components فإذا كل graph ممكن يكون يتكوّن من أكتر من connected components واحدة", "tokens": [33753, 7578, 45164, 3714, 2288, 4724, 661, 32053, 41950, 1829, 3555, 16712, 6027, 2655, 3660, 34892, 16758, 27884, 5296, 10721, 8032, 3215, 12610, 3660, 37893, 8717, 4587, 41193, 8032, 3215, 12610, 3660, 45164, 16472, 16095, 8717, 4587, 41193, 3714, 29245, 23328, 3660, 25961, 9673, 5172, 32887, 11242, 8717, 5016, 9566, 9984, 34105, 4724, 3794, 34105, 19446, 41185, 8592, 9984, 34105, 20193, 29245, 3215, 9984, 6156, 3224, 3215, 8717, 45367, 8032, 3215, 9154, 5172, 36520, 9957, 8032, 3215, 12610, 3660, 44945, 38251, 1829, 16095, 6542, 8032, 3215, 12610, 3660, 44945, 38251, 1829, 16095, 4582, 6677, 6156, 28814, 15730, 28242, 4295, 3714, 43020, 7251, 30544, 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4436.48, "text": "فهيك بنقدر نقول أن هدول التنتين مش isomorphism وبنان على هيك بنكون خلصنا ان شاء الله محاضرتنا ل graphs و بنكون خلصنا مصاق ان شاء الله طالع بنشوفكوا ان شاء الله في مصاقات أخرى و يعطيكوا الصحة و العفو يا كل عاموا أنتوا بخير و ربنا يوفركم في امتحاناتكم", "tokens": [5172, 3224, 1829, 4117, 44945, 28543, 2288, 8717, 39648, 14739, 8032, 3215, 12610, 16712, 29399, 9957, 37893, 307, 32702, 1434, 46599, 1863, 7649, 15844, 39896, 4117, 44945, 30544, 16490, 1211, 9381, 8315, 16472, 13412, 16606, 21984, 3714, 5016, 46958, 43500, 8315, 5296, 24877, 4032, 44945, 30544, 16490, 1211, 9381, 8315, 3714, 9381, 995, 4587, 16472, 13412, 16606, 21984, 23032, 6027, 3615, 44945, 8592, 38688, 4117, 14407, 16472, 13412, 16606, 21984, 8978, 3714, 9381, 995, 4587, 9307, 5551, 34740, 7578, 4032, 37495, 9566, 1829, 4117, 14407, 31767, 5016, 3660, 4032, 18863, 5172, 2407, 35186, 28242, 6225, 10943, 14407, 14739, 2655, 14407, 4724, 9778, 13546, 4032, 12602, 3555, 8315, 7251, 38688, 2288, 24793, 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0.5927734375}, {"start": 4426.96, "end": 4427.12, "word": " هيك", "probability": 0.778564453125}, {"start": 4427.12, "end": 4427.34, "word": " بنكون", "probability": 0.923583984375}, {"start": 4427.34, "end": 4427.94, "word": " خلصنا", "probability": 0.9764404296875}, {"start": 4427.94, "end": 4428.22, "word": " ان", "probability": 0.492431640625}, {"start": 4428.22, "end": 4428.4, "word": " شاء", "probability": 0.943359375}, {"start": 4428.4, "end": 4428.48, "word": " الله", "probability": 0.9345703125}, {"start": 4428.48, "end": 4429.14, "word": " محاضرتنا", "probability": 0.9490234375}, {"start": 4429.14, "end": 4429.32, "word": " ل", "probability": 0.8076171875}, {"start": 4429.32, "end": 4429.68, "word": " graphs", "probability": 0.88623046875}, {"start": 4429.68, "end": 4429.8, "word": " و", "probability": 0.751953125}, {"start": 4429.8, "end": 4430.02, "word": " بنكون", "probability": 0.829833984375}, {"start": 4430.02, "end": 4430.36, "word": " خلصنا", "probability": 0.99072265625}, {"start": 4430.36, "end": 4430.68, "word": " مصاق", "probability": 0.6766357421875}, {"start": 4430.68, "end": 4430.76, "word": " ان", "probability": 0.8154296875}, {"start": 4430.76, "end": 4430.88, "word": " شاء", "probability": 0.98779296875}, {"start": 4430.88, "end": 4430.92, "word": " الله", "probability": 0.935546875}, {"start": 4430.92, "end": 4431.24, "word": " طالع", "probability": 0.86767578125}, {"start": 4431.24, "end": 4431.92, "word": " بنشوفكوا", "probability": 0.82451171875}, {"start": 4431.92, "end": 4431.96, "word": " ان", "probability": 0.6123046875}, {"start": 4431.96, "end": 4432.1, "word": " شاء", "probability": 0.99072265625}, {"start": 4432.1, "end": 4432.16, "word": " الله", "probability": 0.94091796875}, {"start": 4432.16, "end": 4432.28, "word": " في", "probability": 0.87939453125}, {"start": 4432.28, "end": 4432.68, "word": " مصاقات", "probability": 0.96875}, {"start": 4432.68, "end": 4433.3, "word": " أخرى", "probability": 0.9705403645833334}, {"start": 4433.3, "end": 4433.52, "word": " و", "probability": 0.97509765625}, {"start": 4433.52, "end": 4433.94, "word": " يعطيكوا", "probability": 0.7662109375}, {"start": 4433.94, "end": 4434.16, "word": " الصحة", "probability": 0.9791666666666666}, {"start": 4434.16, "end": 4434.2, "word": " و", "probability": 0.68017578125}, {"start": 4434.2, "end": 4434.38, "word": " العفو", "probability": 0.8243815104166666}, {"start": 4434.38, "end": 4434.48, "word": " يا", "probability": 0.4443359375}, {"start": 4434.48, "end": 4434.56, "word": " كل", "probability": 0.479248046875}, {"start": 4434.56, "end": 4434.76, "word": " عاموا", "probability": 0.6660563151041666}, {"start": 4434.76, "end": 4434.9, "word": " أنتوا", "probability": 0.7830403645833334}, {"start": 4434.9, "end": 4435.16, "word": " بخير", "probability": 0.9944661458333334}, {"start": 4435.16, "end": 4435.26, "word": " و", "probability": 0.953125}, {"start": 4435.26, "end": 4435.52, "word": " ربنا", "probability": 0.9694010416666666}, {"start": 4435.52, "end": 4435.86, "word": " يوفركم", "probability": 0.9322509765625}, {"start": 4435.86, "end": 4435.96, "word": " في", "probability": 0.85400390625}, {"start": 4435.96, "end": 4436.48, "word": " امتحاناتكم", "probability": 0.8680245535714286}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4437.0545, "duration_after_vad": 4266.066249999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cea024cddfa88fa2a4be0aff62016e27864d85a9
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_postprocess.srt
@@ -0,0 +1,3392 @@
+1
+00:00:20,960 --> 00:00:22,940
+طيب بسم الله الرحمن الرحيم والصلاة والسلام علي
+
+2
+00:00:22,940 --> 00:00:25,480
+أشرف الأنبياء والمسلمين سيدنا محمد وعليه عليه
+
+3
+00:00:25,480 --> 00:00:29,100
+وصحبه أجمعين المرة اللي فاتت كنا تتكلمنا عن ال
+
+4
+00:00:29,100 --> 00:00:34,580
+recursion و اليوم ان شاء الله بنكمل في نفس الموضوع
+
+5
+00:00:34,580 --> 00:00:40,710
+بإذن الله تعالىكنا اتكلمنا عن irrigation لأ as a
+
+6
+00:00:40,710 --> 00:00:43,890
+function اتكلمنا عن irrigation as a set و اتكلمنا
+
+7
+00:00:43,890 --> 00:00:47,450
+عنها as a string لو متذكرين اخر ما اتكلمنا عن ال
+
+8
+00:00:47,450 --> 00:00:52,230
+lambda و الشغل
+
+9
+00:00:54,300 --> 00:00:58,760
+ال Z ال ال big sigma و ال big sigma star و قولنا
+
+10
+00:00:58,760 --> 00:01:00,660
+ايش الفرق بين ال big sigma و ال big sigma star و
+
+11
+00:01:00,660 --> 00:01:03,800
+قولنا كنت .. كنت .. كنت بقولهم كويسة دلنا هنا ال
+
+12
+00:01:03,800 --> 00:01:07,420
+recursive algorithms .. recursive algorithms اللي
+
+13
+00:01:07,420 --> 00:01:09,680
+ضايلة في الجزء اللي عندنا عشان ننجل بعد هيك على
+
+14
+00:01:09,680 --> 00:01:14,610
+موضوعنا الفعل تاع اليوم نشوف ايشالفكرة في ال
+
+15
+00:01:14,610 --> 00:01:19,370
+recursive algorithms فعليا في ال algorithms نستفيد
+
+16
+00:01:19,370 --> 00:01:23,110
+من عملية ال recursion او عملية التكرار بحيث ان انا
+
+17
+00:01:23,110 --> 00:01:27,030
+ارجع اعيد نفس ال code هو هو اللي انا مازل موجود
+
+18
+00:01:27,030 --> 00:01:30,030
+فيه اصلا اللي انا اصلا موجود فيه ولكن لقيم جديدة
+
+19
+00:01:30,030 --> 00:01:35,060
+لقيم جديدة for example لو اخدنا مثلامثلًا، يحتاجون
+
+20
+00:01:35,060 --> 00:01:37,280
+إلى حساب أو عملية عملية عملية عملية عملية عملية
+
+21
+00:01:37,280 --> 00:01:42,460
+A�N A�N فبقدر أقول أن عملية عملية عملية عملية
+
+22
+00:01:42,460 --> 00:01:47,200
+عملية عملية A�N A لا تساوي صفر، الـ A هذه المفروض
+
+23
+00:01:47,200 --> 00:01:50,600
+أنها لا تساوي صفر، يكون لها قيمة حقيقية، قيمة
+
+24
+00:01:50,600 --> 00:01:53,500
+حقيقية، قيمة واضحة، ماتكونش بتساوي صفر، و الـ N
+
+25
+00:01:53,500 --> 00:01:59,700
+هذه إنتجر أو عدد طبيعي، عدد طبيعي، عدد طبيعي، عدد
+
+26
+00:01:59,700 --> 00:02:02,340
+طبيعي، عدد طبيعي، عدد طبيعي، عدد طبيعي، عدد طبيعي،
+
+27
+00:02:02,340 --> 00:02:06,570
+عدد طبيعي، عدد طبيعnatural number أقل قيمة فيها
+
+28
+00:02:06,570 --> 00:02:09,190
+zero يعني معناته أن ال zero belong to natural
+
+29
+00:02:09,190 --> 00:02:11,870
+number فممكن تكون zero والله إذا كان zero return
+
+30
+00:02:11,870 --> 00:02:17,570
+one و بنوقف بنوقف okay otherwise أو else return
+
+31
+00:02:17,570 --> 00:02:25,290
+لاحظوا إيش a في power a هي هي بس مش في n في n
+
+32
+00:02:25,290 --> 00:02:29,750
+minus one في n minus one كأن جبت relation between
+
+33
+00:02:29,750 --> 00:02:34,580
+a n و a n minus oneاللي أخدناها المرة اللي فاتت
+
+34
+00:02:34,580 --> 00:02:41,960
+لما قلنا a n بتساوي a n minus one بالظبط في a فهي
+
+35
+00:02:41,960 --> 00:02:47,600
+ال a كل اللي عملناه بس أننا بدنا نحسب لمين ل a to
+
+36
+00:02:47,600 --> 00:02:51,840
+the power n minus one بدل ما كنت بشغل a to the
+
+37
+00:02:51,840 --> 00:02:57,400
+power n فهيها حددناها n minus one طبعا هنا ال n
+
+38
+00:02:57,400 --> 00:03:02,370
+قلت واحدقلت القيمة واحد كويس هنرجع .. إيش هيعمل؟
+
+39
+00:03:02,370 --> 00:03:07,510
+هيرجع تاني لنفس ال procedure هو هو بس بمين؟ n-1
+
+40
+00:03:07,510 --> 00:03:12,530
+okay هل n هنا أصبحت zero لإن هي قلت واحد؟ جمت جلة
+
+41
+00:03:12,530 --> 00:03:18,150
+بواحد والله إذا كان zero return one لأ else return
+
+42
+00:03:18,150 --> 00:03:28,750
+كمان مرة هذه a مضروبة في a n-2 a
+
+43
+00:03:29,590 --> 00:03:38,630
+فى a n-3 لعند ما نصل هذى equal to zero هى stop
+
+44
+00:03:38,630 --> 00:03:42,850
+لأنه حيجف هنا خلاص حيجف هنا بس حيجف بعد ايش بعد ما
+
+45
+00:03:42,850 --> 00:03:48,510
+يكون ضرب كل ال a او ال a's اللى احنا جمعنا هى a a
+
+46
+00:03:48,510 --> 00:03:52,650
+a a والله لو عدد ال n هذى عددها اتنين هتلاقي انه
+
+47
+00:03:52,650 --> 00:03:56,760
+العملية هتتكرر مرتين عبارة عن a في aاللي حيحصل
+
+48
+00:03:56,760 --> 00:04:00,940
+فعلا انه هتكون a في a فهي فعلا ال a تربيع باعتبار
+
+49
+00:04:00,940 --> 00:04:04,500
+انه اتنين فانتوا فعلا جبتوا ال power عن طريق عملية
+
+50
+00:04:04,500 --> 00:04:11,320
+recursive او عن طريق recursive algorithm اكترار
+
+51
+00:04:11,320 --> 00:04:15,520
+ال algorithm نفسه اكترار ال algorithm نفسه كمان
+
+52
+00:04:15,520 --> 00:04:19,700
+مثالواضح جدا المثال هذا انه كان اصلا في عملية ال
+
+53
+00:04:19,700 --> 00:04:23,420
+recursion موجودة اللي هو ال Euclides algorithm لان
+
+54
+00:04:23,420 --> 00:04:25,400
+ال Euclides algorithm لما كنت بتحسبه ال greatest
+
+55
+00:04:25,400 --> 00:04:30,680
+common divisor كنت بتجيبه ال modular صحيح a mod b
+
+56
+00:04:31,620 --> 00:04:37,140
+إذا ال A أو الناتج ال modular لا يساوي 0، نستمر،
+
+57
+00:04:37,140 --> 00:04:39,520
+كنا بنكمل، كمان نعمل كمان modular تاني، كمان
+
+58
+00:04:39,520 --> 00:04:43,460
+modular تالت، كمان رابع، خمس، لعندنا الناتج الحاصل
+
+59
+00:04:43,460 --> 00:04:46,700
+ل ال modular، operation equal to 0، فبنقول إن ال
+
+60
+00:04:46,700 --> 00:04:50,660
+greatest common divisor إيش؟ ال element Bمتذكرينه؟
+
+61
+00:04:50,660 --> 00:04:54,280
+اذكرناها؟ كويس فمعنى ذلك ان في عملية تكرار هنا
+
+62
+00:04:54,280 --> 00:04:58,380
+لمين ل greatest common divisor operation اللى
+
+63
+00:04:58,380 --> 00:05:04,840
+بنعملها باستخدام ال modular او ال mod لterm أصغر
+
+64
+00:05:04,840 --> 00:05:07,920
+منهم طيب كيف نعمل الكلام هذا؟ لحظو ال procedure
+
+65
+00:05:07,920 --> 00:05:11,160
+greatest common divisor a,b belonging to natural
+
+66
+00:05:11,160 --> 00:05:15,620
+number ا و b بدنا نجيب greatest common divisor او
+
+67
+00:05:15,620 --> 00:05:19,660
+العامل المشترك الأكبرwe belong to natural number
+
+68
+00:05:19,660 --> 00:05:27,220
+if a is equal to zero و لاحظوا هنا عشان تظبط
+
+69
+00:05:27,220 --> 00:05:30,620
+العملية احنا مرتبينها بحيث انه ال element الأول هو
+
+70
+00:05:30,620 --> 00:05:34,920
+الأصغر هو الأصغر عشان ما نضطرش نعمل operation
+
+71
+00:05:34,920 --> 00:05:39,260
+إبافية في النص اللي هي عملية ال swap تذكرتوها؟ لأ
+
+72
+00:05:39,260 --> 00:05:41,560
+مش مضطرين نعمل swap كل اللي بعمله من الأساس برتبه
+
+73
+00:05:41,560 --> 00:05:44,180
+على أساس انه في الأول هو الأصغر و خلاص عشان ال
+
+74
+00:05:44,180 --> 00:05:50,310
+recursion يكون أسرع أو يكون أسهل okayA وB فلو اذا
+
+75
+00:05:50,310 --> 00:05:56,010
+A equal to 0 then return B ارجع القيمة B فلسنا طيب
+
+76
+00:05:56,010 --> 00:05:59,870
+otherwise لأ return لاحظوا greatest common divisor
+
+77
+00:05:59,870 --> 00:06:06,190
+بي مودلر او mod A فواضح ان هذا الterm الصغير هيأتي
+
+78
+00:06:06,190 --> 00:06:11,690
+في الأول فعلا Aكل اللي حنصير أنه هعيد التكرار نفسه
+
+79
+00:06:11,690 --> 00:06:17,450
+بس ال B هذه أصبحت هي مكان ال A مكانها ال A و ال A
+
+80
+00:06:17,450 --> 00:06:26,110
+القيمة الأصغر صار مكانها B mod A ال B mod A والله
+
+81
+00:06:26,110 --> 00:06:30,990
+إذا كان ال B mod A equal to 0 ارجع للقيمة ال B
+
+82
+00:06:30,990 --> 00:06:33,710
+اللي أهل وجد اتعرفت بيه اللي هي أصلا كانت مين؟ A
+
+83
+00:06:33,710 --> 00:06:41,760
+كانت إيه؟ A لأ لا تساوي 0الناتج اللى هو a لجديدة و
+
+84
+00:06:41,760 --> 00:06:45,480
+b لجديدة برضه هنرجع نعمل كمان modular كمان مرة
+
+85
+00:06:45,480 --> 00:06:50,080
+فهذه عملية التكرار اللى أخدتها سابقا لما كنتوا
+
+86
+00:06:50,080 --> 00:06:53,020
+جيبوا ال greatest common divisor باستخدام ال
+
+87
+00:06:53,020 --> 00:06:55,720
+modular operation باستخدام ال modular operation
+
+88
+00:06:55,720 --> 00:07:00,400
+okay طبعا في حالة زى هذه واضح أن هنا ال recursive
+
+89
+00:07:00,400 --> 00:07:05,460
+algorithm كتير أبسطأو أصغر .. كلها تلت أسطور ..
+
+90
+00:07:05,460 --> 00:07:08,680
+أصغر من أني لو بدي أعملها بالطريقة المطولة اللي
+
+91
+00:07:08,680 --> 00:07:10,740
+أخدناها سابقا .. بالطريقة المطولة اللي أخدناها
+
+92
+00:07:10,740 --> 00:07:13,940
+سابقا لإن أنا عارف هيك أن في recursion بيصير .. في
+
+93
+00:07:13,940 --> 00:07:16,780
+تكرار بيصير لعمليتي ال modular هنا .. تكرار
+
+94
+00:07:16,780 --> 00:07:21,200
+لعمليتي ال modular ف ال recursive algorithm الأمور
+
+95
+00:07:21,200 --> 00:07:23,860
+بتصير أسهل .. كلها تلت أسطور و خلاص مفهومة ..
+
+96
+00:07:23,860 --> 00:07:28,700
+مشكلتنا عندنا مشكلة واحدة .. لو ..ال بي سي ستبعتكم
+
+97
+00:07:28,700 --> 00:07:33,220
+not smart enough مش ذاكية او ال operation system
+
+98
+00:07:33,220 --> 00:07:36,460
+اللي انتوا شغالينه مش ذاكي كفاية انه يعرف انه شغال
+
+99
+00:07:36,460 --> 00:07:39,900
+في نفس ال algorithm ليش؟ لأنه في الحالة هدي جديش
+
+100
+00:07:39,900 --> 00:07:43,860
+عدد التكرارات هيروح يفتح نفس الملف كذا مرةفهيصير
+
+101
+00:07:43,860 --> 00:07:48,340
+بده stack أكبر، بده RAM أكبر، ال memory ساعته
+
+102
+00:07:48,340 --> 00:07:52,180
+هتستهلك لإنه هيفتحه كذا مرة، لو أخدنا الرقامين A
+
+103
+00:07:52,180 --> 00:07:55,400
+وB، أرقام كتير كبيرة، و نفترض إن ال greatest
+
+104
+00:07:55,400 --> 00:07:58,900
+common divisor بتبعهم واحد، معناه ذلك إنه هيتطر
+
+105
+00:07:58,900 --> 00:08:02,260
+يعمل operations كتيرة، في الحالة هذه عبل ما يصل
+
+106
+00:08:02,260 --> 00:08:05,020
+لمن؟ للواحد، لإن مافيش greatest common divisor
+
+107
+00:08:05,020 --> 00:08:10,160
+واضح من الأولفي الحالة هذه يعني يمكن يضطر يفتح ال
+
+108
+00:08:10,160 --> 00:08:15,560
+code خمستاشر عشرين مرة تلاتين مرة طب وين بده يحطهم
+
+109
+00:08:15,560 --> 00:08:18,860
+المفاتيح المفتوحة هذه الكتير؟ هيحطها في ال RAM في
+
+110
+00:08:18,860 --> 00:08:21,780
+ال stack تبعته ال stack مش حتى الساعة مش حتى
+
+111
+00:08:21,780 --> 00:08:24,760
+الساعةفهتلاقوا بعد فترة هذه المشكلة الوحيدة هنا
+
+112
+00:08:24,760 --> 00:08:29,180
+أنه هيحتاج stack أكبر وهذا بيبين إذا كانت ال
+
+113
+00:08:29,180 --> 00:08:32,600
+compiler تبعتكم is not smart enough عشان تعرف أنه
+
+114
+00:08:32,600 --> 00:08:35,620
+والله أنا بشتغل على نفس ال code فمافيش داعي أرجع
+
+115
+00:08:35,620 --> 00:08:38,940
+أفتحه كمان مرة مافيش داعي نرجع نفتحه كمان مرة حتى
+
+116
+00:08:38,940 --> 00:08:43,120
+لو أنا بعمل استدعاء له recalling لنفس ال greatest
+
+117
+00:08:43,120 --> 00:08:46,340
+common divisor code بس بده يعرف أنه أنا في نفس ال
+
+118
+00:08:46,340 --> 00:08:49,850
+code ما زلتكل اللي بده يضطر يشتغله يشتغل على أخر
+
+119
+00:08:49,850 --> 00:08:52,630
+نتاج أخر أرقام النتاج اللي في الأول بيخليهاش
+
+120
+00:08:52,630 --> 00:08:56,710
+موجودة في ال RAM خلاص بيشيلها بيحفظ حسب ال
+
+121
+00:08:56,710 --> 00:09:00,210
+algorithm ايش الأرقام اللي محتاجها فقط و ليس انه
+
+122
+00:09:00,210 --> 00:09:04,710
+يقعد كل مرة يفتح ال code من أول من أول و جديد okay
+
+123
+00:09:05,400 --> 00:09:08,200
+الـ Linear .. Linear Search أخدنا Linear Search
+
+124
+00:09:08,200 --> 00:09:11,360
+قبل هيك برضه بنقدر نعملها باستخدام ال recursive
+
+125
+00:09:11,360 --> 00:09:15,280
+operation أو ال .. ال .. as a recursive algorithm
+
+126
+00:09:15,280 --> 00:09:19,320
+ولكن هتكون هنا مالهاش كتير معنى ليش؟ لأنه ال
+
+127
+00:09:19,320 --> 00:09:23,400
+complexity أنا ماقدرتش أوفر فيها هناك وفرنا صارت
+
+128
+00:09:23,400 --> 00:09:26,060
+عندي تلت صفور فقط صار وفرنا في ال code هنا مش
+
+129
+00:09:26,060 --> 00:09:29,160
+هنقدر نوفر إشي لأنه هيك هيك هنشتغل Linear و هنشتغل
+
+130
+00:09:29,160 --> 00:09:32,680
+.. هنعمل scan على كل أو مسح على كل ال elements
+
+131
+00:09:32,680 --> 00:09:37,060
+اللي موجودة داخل ال ..الـ sequence اللي بندور فيه
+
+132
+00:09:37,060 --> 00:09:43,000
+خلّيني نشوف كيف بتم الموضوع متذكرين هل ال linear؟
+
+133
+00:09:43,000 --> 00:09:46,260
+linear search نبدأ من أول رقم و بنبدأ نقارن رقم
+
+134
+00:09:46,260 --> 00:09:48,980
+موجود هل هو موجود داخل ال sequence أو غير موجود ف
+
+135
+00:09:48,980 --> 00:09:53,260
+X رقم given من عندى بدنا نشوفه هل هو موجود في ال
+
+136
+00:09:53,260 --> 00:09:58,100
+sequence A أو غير موجود في ال sequence A فهيكون ال
+
+137
+00:09:58,100 --> 00:10:02,000
+procedure search A ممكن نكتبها linear search عشان
+
+138
+00:10:02,000 --> 00:10:05,540
+نميز إنه أنا بخطل على linearA هدا ال series اللى
+
+139
+00:10:05,540 --> 00:10:10,400
+بدنا ندور داخلها و ال series هدى هنعرفها ببداية و
+
+140
+00:10:10,400 --> 00:10:14,980
+نهاية ب start point و end point I و J هدولة
+
+141
+00:10:14,980 --> 00:10:20,530
+integers هدول هيكون عبارة عن إيش integersX ما زالت
+
+142
+00:10:20,530 --> 00:10:23,550
+هي داخل ال arguments بتاعتنا، فإذا هذه برضه موضوع
+
+143
+00:10:23,550 --> 00:10:26,450
+من الموضوعات اللي هي ال X، إيش ال item اللي بتكون
+
+144
+00:10:26,450 --> 00:10:29,890
+بدنا ندور عليه؟ فال item تبعنا item to be found
+
+145
+00:10:29,890 --> 00:10:34,530
+اللي بدنا ندور عليه، اللي هي نوجده، okay عرفنا ال
+
+146
+00:10:34,530 --> 00:10:37,900
+procedure بتاعتنا أو عرفناالـ arguments تبعت ال
+
+147
+00:10:37,900 --> 00:10:41,700
+algorithm تبعنا المطلوب طبعا منه عارفين أن الأقواص
+
+148
+00:10:41,700 --> 00:10:44,780
+هذه معناها مجرد comments هذه ال comments مش من
+
+149
+00:10:44,780 --> 00:10:48,600
+داخل أو مش من جزء ال algorithm نفسه find X in
+
+150
+00:10:48,600 --> 00:10:53,600
+series A at a location أكبر من أو يساوي I و أقل من
+
+151
+00:10:53,600 --> 00:10:56,320
+J فانا محددها والله إذا كان بتكون دوره في ال
+
+152
+00:10:56,320 --> 00:10:59,990
+series كله عملوها من صفرته Nإذا محتاجين كل ال
+
+153
+00:10:59,990 --> 00:11:05,010
+series تدوروا فيها فهنا بتبدأ من واحد من أول
+
+154
+00:11:05,010 --> 00:11:09,010
+location تقاش J حتكون اللي هي ال N فانتوا بتاخدوا
+
+155
+00:11:09,010 --> 00:11:13,850
+كل ال series بتاعتكم هنا in general هنقول من I to
+
+156
+00:11:13,850 --> 00:11:16,930
+J و بعدين بتخطوها زي ما بدكم حسب إيش اللي بيكون
+
+157
+00:11:16,930 --> 00:11:24,360
+مطلوب منكم okay if a I أول elementفإذا كان بدء من
+
+158
+00:11:24,360 --> 00:11:28,960
+واحد بحط a1 إذا كان الـ a1 أول واحد أو لا هنا بحطه
+
+159
+00:11:28,960 --> 00:11:33,660
+i عسى إنه يبقى variable لل subroutines اللي جاية
+
+160
+00:11:33,660 --> 00:11:37,540
+للsubroutines اللي هتجينا لجدام فai equal to إيش
+
+161
+00:11:37,540 --> 00:11:43,420
+to x if equal to x return i خلاص إذا صدفت إنه فعلا
+
+162
+00:11:43,420 --> 00:11:51,930
+أول عند ال element i هذا ال element الأخير jهنعمل
+
+163
+00:11:51,930 --> 00:11:56,110
+مقارنة ل X مع A I ال element اللي موجود في ال
+
+164
+00:11:56,110 --> 00:12:02,570
+location I هو نفسه بيسوي خلاص برجع كلمة I ان هو
+
+165
+00:12:02,570 --> 00:12:05,030
+موجود و ال location تبعه I
+
+166
+00:12:08,260 --> 00:12:16,300
+خلصنا منها نعود إلى I if I equal to J return 0 اذا
+
+167
+00:12:16,300 --> 00:12:20,920
+I في مرحلة من المراحل وصلت ان هي قيمتها نفسها J
+
+168
+00:12:20,920 --> 00:12:24,520
+معناته لايوجد elements بينهم انا واضح ان انا عملت
+
+169
+00:12:24,520 --> 00:12:30,130
+scan على كل درجة ان ال I وصلت ل J بناءعلى اللي حصل
+
+170
+00:12:30,130 --> 00:12:34,290
+تاني فهدي نوقفها شوية هنرجع لها كمان مرة عندنا
+
+171
+00:12:34,290 --> 00:12:38,990
+نوضح كيف فعلا ال I هتروح لل J هتروح بناء على ال
+
+172
+00:12:38,990 --> 00:12:41,350
+return اللي جاية بناء على ال return اللي جاية اذا
+
+173
+00:12:41,350 --> 00:12:44,210
+والله ال condition الأول لم يتحققcondition التاني
+
+174
+00:12:44,210 --> 00:12:48,150
+لم يتحقق ايش بدنا نعمل؟ معناته انا لأ ما زال في
+
+175
+00:12:48,150 --> 00:12:51,710
+elements موجودة ماعملتش فحص عليها وأول element
+
+176
+00:12:51,710 --> 00:12:56,770
+موجود لا يسوى x فإيش بدنا نعمل؟ return search كمان
+
+177
+00:12:56,770 --> 00:13:00,630
+مرة يعني انا عملت recalling لمين؟ لل code أنا بسمي
+
+178
+00:13:00,630 --> 00:13:03,390
+ال code search يعني instead of search إيش ال
+
+179
+00:13:03,390 --> 00:13:08,890
+elements سبعته؟ I plus 1 و J و X، X اللي هو بدور
+
+180
+00:13:08,890 --> 00:13:17,570
+عليه فأصبحت ال Iبنبدأ بمين؟ I زائد واحد جمعنا واحد
+
+181
+00:13:17,570 --> 00:13:22,990
+جمعنا عليها واحد وصارت هذه ال element التاني صارت
+
+182
+00:13:22,990 --> 00:13:26,590
+هي ال I بالنسبالنا بقارن كمان مرة خلصنا بدينا
+
+183
+00:13:26,590 --> 00:13:34,170
+بقارن برضه ايه؟ I هنا كانت واحد هنا أصبحت اتنين ال
+
+184
+00:13:34,170 --> 00:13:36,930
+location التاني أصبحت طيب بقارن X مع ال location
+
+185
+00:13:36,930 --> 00:13:44,330
+التاني لأ لاتساويو لسه ال I أقل من J على التالت،
+
+186
+00:13:44,330 --> 00:13:46,970
+على الرابع، على الخمس، على السادس، لما تصل إيش
+
+187
+00:13:46,970 --> 00:13:53,330
+بتساوي؟ J لما تصل بتساوي J بعد عدد تكرارات إيش
+
+188
+00:13:53,330 --> 00:13:58,830
+بتساوي عدد تكراراتها؟ J minus Iبنكون ال search هذا
+
+189
+00:13:58,830 --> 00:14:03,910
+عملنا له recalling j minus i مرة صحيح؟ قبل ما نصل
+
+190
+00:14:03,910 --> 00:14:07,030
+انه طلعوا بيساوي بعض والله طلعوا بيساوي بعض معناته
+
+191
+00:14:07,030 --> 00:14:11,010
+واضحة ان عملت search على الكل مش موجود ال X برجع
+
+192
+00:14:11,010 --> 00:14:13,990
+باش Zero و Zero احنا عرفناه من المرة اللي فاتت
+
+193
+00:14:13,990 --> 00:14:16,930
+Zero معناته انه غير موجود في مين؟ في ال series
+
+194
+00:14:16,930 --> 00:14:20,230
+بتاعتنا ال element X غير موجود في ال series اللي
+
+195
+00:14:20,230 --> 00:14:24,050
+موجودة عندنا في الحالة دي بنرجع ب X او بنرجع ب I
+
+196
+00:14:24,050 --> 00:14:29,720
+إذا لجينا إذا وجدناانت بتحقق واحدة من الاتنتين
+
+197
+00:14:29,720 --> 00:14:34,360
+هدول مش هنتطر نيجي لمين ل .. ل ال return هذه مش
+
+198
+00:14:34,360 --> 00:14:37,420
+هنتطر نرجع لل return الأخيرة انه يعملنا استدعاء
+
+199
+00:14:37,420 --> 00:14:44,240
+كمان مرة ل ال code بقيم جديدة okayطبعا واضح ان انا
+
+200
+00:14:44,240 --> 00:14:48,060
+هعمل scan على الكل فانا مستفدتش فائدة واضحة من
+
+201
+00:14:48,060 --> 00:14:50,620
+عملية ال recursive algorithm اللي احنا عملناها ال
+
+202
+00:14:50,620 --> 00:14:53,180
+recursive algorithm تبعنا ماكانش كتير في
+
+203
+00:14:53,180 --> 00:14:58,260
+improvement حقيقة ماكانش في تطوير على ال procedure
+
+204
+00:14:58,260 --> 00:15:02,100
+نفسها تحديث على الموضوع نفسه اللي ماتغيرش في حاجة
+
+205
+00:15:02,100 --> 00:15:05,160
+عدد السطور ماتوفرش كتير ال procedure نفسها
+
+206
+00:15:05,160 --> 00:15:09,160
+ماتغيرتش كتير ال procedure نفسها ماتغيرتشكتير انا
+
+207
+00:15:09,160 --> 00:15:11,760
+هيك هيك بدى ابحث على كل ال elements فاحنا فعلا
+
+208
+00:15:11,760 --> 00:15:14,580
+بحثنا على كل ال elements قبل ما نصل لقرار انه غير
+
+209
+00:15:14,580 --> 00:15:21,280
+موجود X طيب يمكن تكون برضه recursive algorithm
+
+210
+00:15:21,280 --> 00:15:24,900
+ممكن نستخدمه ل ال binary search ل ال binary search
+
+211
+00:15:24,900 --> 00:15:28,280
+و ال binary search بدنا نركز شوية فيه عشان نشوف
+
+212
+00:15:28,280 --> 00:15:32,680
+كيف استخدم عملية المين عملية ال binary search برضه
+
+213
+00:15:32,680 --> 00:15:33,920
+ال binary search متذكرينها
+
+214
+00:15:37,910 --> 00:15:42,570
+نفس الفكرة هي هي عندنا a .. a series .. series
+
+215
+00:15:42,570 --> 00:15:45,930
+اسمها a و بدنا ندور على element اسمه x فال element
+
+216
+00:15:45,930 --> 00:15:49,770
+اسمه x القالية بتاعتنا اسمها binary .. binary
+
+217
+00:15:49,770 --> 00:15:54,310
+قولنا قبلها ان انا باجي بعمل jump على ال mid point
+
+218
+00:15:54,310 --> 00:15:57,770
+و بنشوف ال element عند ال mid point او عند ال mid
+
+219
+00:15:57,770 --> 00:16:02,810
+location هل يساوي x او لأ و بنقارن اكبر منه او اقل
+
+220
+00:16:02,810 --> 00:16:07,560
+منه على اعتبار ان ال series اصلا orderedعلى اعتبار
+
+221
+00:16:07,560 --> 00:16:10,600
+ان هي اصلا معمولها sorting .. معمولها sorting ..
+
+222
+00:16:10,600 --> 00:16:15,520
+okay و
+
+223
+00:16:15,520 --> 00:16:19,400
+نفس الكلام همحطه من I to J in general .. in
+
+224
+00:16:19,400 --> 00:16:23,780
+general .. okay عندنا I .. ال .. ال A .. ال series
+
+225
+00:16:23,780 --> 00:16:27,400
+اللي بندور عليها .. ال series ها دي من I to J و
+
+226
+00:16:27,400 --> 00:16:29,820
+عندنا ال element X اللي بدور عليه .. اللي بندور
+
+227
+00:16:29,820 --> 00:16:33,560
+عليه .. okayالـ midpoint أول ما نحسب نحسب ال
+
+228
+00:16:33,560 --> 00:16:38,160
+midpoint الأولى زائد الأخيرة على اتنين بتنقض لها
+
+229
+00:16:38,160 --> 00:16:41,540
+floor لأنه أكيد ممكن تطلع كسر ممكن تطلع كسر و احنا
+
+230
+00:16:41,540 --> 00:16:44,460
+عارفين ان ال locations integers ال location
+
+231
+00:16:44,460 --> 00:16:48,700
+natural number حتى لأنه مش هتكون بال negative مش
+
+232
+00:16:48,700 --> 00:16:52,440
+هتكون بال negative okay خلصنا الله والله إذا كان X
+
+233
+00:16:52,440 --> 00:16:57,280
+equal to AM هي فعلا نفس القيمة عند ال AM هنا
+
+234
+00:16:58,320 --> 00:17:02,320
+بيساووا بعض enough خير و بركة معناته بنقدر نقول
+
+235
+00:17:02,320 --> 00:17:09,580
+بنجف و بنرجع بال location M انا وجدته خلاص stop
+
+236
+00:17:09,580 --> 00:17:13,180
+وين وجدته في ال location M طيب لأ ماوجدنهاش
+
+237
+00:17:13,180 --> 00:17:16,920
+ماوجدنهاش معناه ان في احتمالين اما ان ال X أكبر من
+
+238
+00:17:16,920 --> 00:17:22,020
+AM او انها أقل من AM ناخد الاحتمالين if X أقل من
+
+239
+00:17:22,020 --> 00:17:33,090
+AM and I أقل من Mفإذا إذا كانت ال X هذه فعليا أقل
+
+240
+00:17:33,090 --> 00:17:37,810
+من A M فإذا المفروض أنها تكون في المنطقة هذه صحيح؟
+
+241
+00:17:37,810 --> 00:17:42,250
+طب ممكن احنا فعلا تقلصنا لدرجة أن ال M هي نفس ال I
+
+242
+00:17:42,250 --> 00:17:48,010
+هل ممكن؟ أه ممكن، ممكن لأنه في المرحلة التانية،
+
+243
+00:17:48,010 --> 00:17:51,590
+هنجلل المسافة، هنجلل، هنجلل، ممكن يصلوا أن التنتين
+
+244
+00:17:51,590 --> 00:17:54,250
+هم نفس الرقم إذا والله نفس الرقم، stop، خلاص،
+
+245
+00:17:54,250 --> 00:17:57,390
+معناه أنا مالجيتهمشوصلنا وما راجعناش ال element
+
+246
+00:17:57,390 --> 00:18:05,230
+تبعتنا فحنشوف if then بتاعتنا إذا والله أقل من فهي
+
+247
+00:18:05,230 --> 00:18:11,630
+لاتساوي لاتساوي هي أقل من و I أقل من M يعني لسه في
+
+248
+00:18:11,630 --> 00:18:16,270
+مجموعة elements فيهم مازال في elements الأصل أني
+
+249
+00:18:16,270 --> 00:18:19,110
+أدور في ال elements هذه معناته لازم أكمل ال
+
+250
+00:18:19,110 --> 00:18:22,670
+procedure تبعتي بكملها بس بكملها بناء على إيش على
+
+251
+00:18:23,710 --> 00:18:27,210
+بناري سيرشوي نفسها كمان مرة بس بتعامل معاها
+
+252
+00:18:27,210 --> 00:18:31,090
+الموضوع على أساس أنه طبعا هذه لا تساوي لحظة هذه لا
+
+253
+00:18:31,090 --> 00:18:34,590
+تساوي فإذا بتعامل على ال element اللي جابلها أن
+
+254
+00:18:34,590 --> 00:18:41,170
+هذه هي ال A الجديدة عبارة عن I to J هاي J الجديدة
+
+255
+00:18:41,170 --> 00:18:47,070
+صارت ال J الجديدة عبارة عن M minus 1 العنصر اللي
+
+256
+00:18:47,070 --> 00:18:53,230
+جابلها على اعتبار أنه عند العنصر M لا تساويهي اصلا
+
+257
+00:18:53,230 --> 00:18:55,410
+انا كيف وصلت ل condition هذا، بناء على انه هذا لم
+
+258
+00:18:55,410 --> 00:18:58,690
+يتحقق، بناء على اساس ان ال condition الأول لم
+
+259
+00:18:58,690 --> 00:19:04,430
+يتحقق، ف condition التاني تحقق، بعرف انه ما زال
+
+260
+00:19:04,430 --> 00:19:08,750
+فيه مجموعة elements موجودة، بعرف ان J المفترضة
+
+261
+00:19:08,750 --> 00:19:15,350
+الجديدة هتكون M minus 1 و ليست Mوليست M فهنا أصلا
+
+262
+00:19:15,350 --> 00:19:18,650
+عندي A برجع بدخل نفس ال sequence هو هو و ال X اللي
+
+263
+00:19:18,650 --> 00:19:21,710
+بدور عنها هي هي و بدور when في interval من جدش
+
+264
+00:19:21,710 --> 00:19:34,390
+لجدش من I to M-1 عيدنا نفس الكلام لأ مش أقل منهx
+
+265
+00:19:34,390 --> 00:19:39,290
+ليست أقل من وليست تساوي فإذا الاحتمال التالت اللي
+
+266
+00:19:39,290 --> 00:19:42,110
+لازم حصله إذا ما تحققوش ال two conditions هدولة هو
+
+267
+00:19:42,110 --> 00:19:47,890
+else إنه هي لاتساوي .. لاتساوي وليست أقل من فأكيد
+
+268
+00:19:47,890 --> 00:19:53,930
+هتكون أكبر من فx أكبر من am طيب هاي ال condition
+
+269
+00:19:53,930 --> 00:19:54,790
+تبعنا x
+
+270
+00:19:59,960 --> 00:20:04,000
+هنا أكبر من AM فهي المفروض تكون موجودة في ال .. في
+
+271
+00:20:04,000 --> 00:20:07,900
+ال interval اللي على اليمين صح؟ في ال right side
+
+272
+00:20:07,900 --> 00:20:10,600
+okay في ال right side مدام هي موجودة في الجزء اللي
+
+273
+00:20:10,600 --> 00:20:15,320
+هنا هنا بقدر أعمل command search و بنحدد بناء عليه
+
+274
+00:20:15,320 --> 00:20:23,800
+I بتاعتنا بعد ال AM بعد ال location M فإذا تبدأ ال
+
+275
+00:20:23,800 --> 00:20:26,620
+I كأنها M plus 1
+
+276
+00:20:29,210 --> 00:20:33,770
+صح؟ تمام على اعتبار ان هذا لا يساوي فليش احطه في
+
+277
+00:20:33,770 --> 00:20:36,990
+ال interval هو لا يساوي خلاص ناخد اللي من بعده
+
+278
+00:20:36,990 --> 00:20:41,950
+ناخد من بعده فتصبح عنا إذا كانت ال am هي اللي أصغر
+
+279
+00:20:41,950 --> 00:20:53,600
+من x فx أكبر and m هذهأقل من j أقل من j يعني أن
+
+280
+00:20:53,600 --> 00:20:56,480
+يوجد بينهم مجموعة elements على الأقل element واحد
+
+281
+00:20:56,480 --> 00:21:01,200
+على الأقل element واحد وجد بينهم جدير أن أبحث عليه
+
+282
+00:21:01,200 --> 00:21:04,020
+من الأفضل أن أبحث عليه لا أستطيع أن أقول إن انتهيت
+
+283
+00:21:04,020 --> 00:21:08,840
+من ال search طبعي في الحالة هذه سنعود بمين؟ برضه
+
+284
+00:21:08,840 --> 00:21:14,280
+بنفس ال code ولكن ل series a ال x هي نفس ال
+
+285
+00:21:14,280 --> 00:21:20,490
+element اللي بدور عليه من أين؟m زائد واحد to j من
+
+286
+00:21:20,490 --> 00:21:24,930
+m زائد واحد to j بنرجع بنكرر نفس الموضوع هو هو
+
+287
+00:21:24,930 --> 00:21:31,150
+نفسنا بنكرر نفس الموضوع تماما okay else return
+
+288
+00:21:31,150 --> 00:21:36,910
+zero لاحظوا ال else هذه هذه ال else بتاعة ال F هذه
+
+289
+00:21:36,910 --> 00:21:42,090
+ال else هذه بتاعة ال F هذه ليش بقول الكلام هذا
+
+290
+00:21:42,090 --> 00:21:47,330
+بقول الكلام هذا عشان نقول انت حنجفنتطلع كمان شوية
+
+291
+00:21:47,330 --> 00:21:51,810
+هل وجدت ام تحبك بقدر اقول اني وقفت اذا كان وانا
+
+292
+00:21:51,810 --> 00:21:56,270
+بدور صدفت انه فعلا ال X طلعت بتساوي واحدة من ال
+
+293
+00:21:56,270 --> 00:22:00,530
+AM's سواء هنا او هنا مع انه التكرار ال recursion
+
+294
+00:22:00,530 --> 00:22:04,710
+اللي بعملها صدفت انه X equal to كذا فبرجع ابقيمتها
+
+295
+00:22:04,710 --> 00:22:09,410
+ابقيمته ال location نفسه وخلاص بوقف طب لأ نفترض ان
+
+296
+00:22:09,410 --> 00:22:14,030
+الأسوأ ال worst case انه X غير موجودة القصر ايش
+
+297
+00:22:14,030 --> 00:22:20,800
+بتصير؟X أقل من AM أو أكبر من AM هذي حضار تتحقق
+
+298
+00:22:20,800 --> 00:22:23,400
+معايا هذي الشيء اللي بوقفني و بوصلني في الآخر
+
+299
+00:22:23,400 --> 00:22:28,820
+واحدة من ال two conditions هذول اما ان ال I أقل من
+
+300
+00:22:28,820 --> 00:22:35,460
+M تمام و في الحالة اذا كان أقل ال I ليست أقل من M
+
+301
+00:22:35,460 --> 00:22:39,900
+نضرر انه ليست أقل من M ف automatically هذا لم
+
+302
+00:22:39,900 --> 00:22:45,420
+يتحقق في الحالة هذي else باجي بتأكد من هنابنتأكد
+
+303
+00:22:45,420 --> 00:22:49,760
+من هنا بتشوف ال M أقل من J فإذا هذا لن يقف ال
+
+304
+00:22:49,760 --> 00:22:59,100
+search إلا لما تصير ال I بتساوي J ال I هتساوي J في
+
+305
+00:22:59,100 --> 00:23:05,560
+الحالة هذه باتنين بنطبخوا على بعض تصبحالـ M أقل من
+
+306
+00:23:05,560 --> 00:23:10,240
+J لاتتحقق فالشرطين دول لازم يتحققوش مع بعض عشان
+
+307
+00:23:10,240 --> 00:23:15,820
+أجي لمن؟ لل else بتاعتها ففي الحالة هذه برجع صفر
+
+308
+00:23:15,820 --> 00:23:20,520
+تقلصت صار عندي عملية shrinking عندي لل duration
+
+309
+00:23:20,520 --> 00:23:25,120
+لدرجة أن وصلت الأثنين I و J بيسووا بعض ومع ذلك
+
+310
+00:23:25,120 --> 00:23:30,040
+ماوجدتش ال X فإذا X غير موجودة أصلا فإذا X غير
+
+311
+00:23:30,040 --> 00:23:38,120
+موجودة أساساOkay هذا في حالة ال recursive
+
+312
+00:23:38,120 --> 00:23:41,000
+algorithm لمين لل binary search أو recursive
+
+313
+00:23:41,000 --> 00:23:44,600
+binary search recursive binary search هذا الجزء
+
+314
+00:23:44,600 --> 00:23:47,240
+اللي كان ضايل عندنا في عملية ال recursion و اللي
+
+315
+00:23:47,240 --> 00:23:49,900
+كانت خاصة بال recursion algorithm أو recursive
+
+316
+00:23:49,900 --> 00:23:54,440
+algorithm قبل ما نبدأ
+
+317
+00:24:01,460 --> 00:24:05,540
+المرة اللى فاتت قبل كام محاضرة أخدنا ال basics لل
+
+318
+00:24:05,540 --> 00:24:09,700
+numbers للأرقام طب هالوقت بناخدها برضه ال basics
+
+319
+00:24:09,700 --> 00:24:14,260
+لمين لل counting للعدد أخدنا الأرقام تمام عرفنا
+
+320
+00:24:14,260 --> 00:24:17,500
+الأرقام وعرفنا إيش يعني أرقام وإيش يعني إيهوصرنا
+
+321
+00:24:17,500 --> 00:24:21,520
+ممتازين في الأرقام ويعرفنا الرقم ال even ويعرفنا
+
+322
+00:24:21,520 --> 00:24:25,920
+الرقم ال odd ويعرفنا الرقم ال prime ويعرفنا كيف
+
+323
+00:24:25,920 --> 00:24:28,240
+نتعامل مع الأرقام وكيف بقدر استخدمها في عملية ال
+
+324
+00:24:28,240 --> 00:24:31,120
+encryption كيف بستخدم الأرقام في عملية ال
+
+325
+00:24:31,120 --> 00:24:34,440
+encryption كيف ب .. بغير الأرقام باستخدام ال
+
+326
+00:24:34,440 --> 00:24:37,900
+modular وبن .. بنقول أن والله في رقم equivalent
+
+327
+00:24:37,900 --> 00:24:42,410
+لرقم تانيالكلام هذا كله خدناه .. صحيح؟ فالوقت بدنا
+
+328
+00:24:42,410 --> 00:24:45,930
+نتطور شوية كيف بقدر أعمل عملية ال counting .. العد
+
+329
+00:24:45,930 --> 00:24:50,570
+.. بدنا نعد .. إيش يعني عد؟ يعني تحسب .. يعني تجمع
+
+330
+00:24:50,570 --> 00:24:53,370
+تقول والله هدول عددهم خمسة .. هدول عددهم عشرة ..
+
+331
+00:24:53,370 --> 00:24:58,690
+هدول عددهم عشرين .. بدنا نبدأ نعدتمام؟ برضه بنفس
+
+332
+00:24:58,690 --> 00:25:02,250
+القالية هناك أخدنا شوية numbers و بس ابقوا حافظين
+
+333
+00:25:02,250 --> 00:25:04,190
+يعنى إيش ال numbers اللي احنا أخدناهم و كيف نتعامل
+
+334
+00:25:04,190 --> 00:25:06,090
+معاهم و كيف بنقول والله الرقامين دولة equivalent
+
+335
+00:25:06,090 --> 00:25:09,330
+لبعض أو مش equivalent لبعض كيف بستخدم ال numbers
+
+336
+00:25:09,330 --> 00:25:14,250
+في عملية ال encryption اليوم لأ بدنا نستعمل جداش
+
+337
+00:25:14,250 --> 00:25:20,400
+عددElements لحالة معينة بيحققولنا case معينة فبدنا
+
+338
+00:25:20,400 --> 00:25:25,560
+نعمل عدد counting بدنا نبدأ نعد كويس ف study of
+
+339
+00:25:25,560 --> 00:25:29,840
+the number of ways to put things together جداش ال
+
+340
+00:25:29,840 --> 00:25:32,860
+things اللي بقدر أجمحهم together على أساس إن هدولة
+
+341
+00:25:32,860 --> 00:25:37,220
+combination واحدة مع بعض هدولة case واحدة هدولة
+
+342
+00:25:37,220 --> 00:25:40,380
+task واحدة بيقدوا task واحدة فبقدر أقول جداش عددهم
+
+343
+00:25:40,380 --> 00:25:45,990
+اللي بيقدروا يحلولي task معينةفبنعمل عدد تعديق
+
+344
+00:25:45,990 --> 00:25:50,390
+تعديد عدد طيب الأعداد هذه for example طبعا هنشرح
+
+345
+00:25:50,390 --> 00:25:54,450
+كتير لسه في الكلام موضوع طويل لسه for example لو
+
+346
+00:25:54,450 --> 00:26:01,690
+قولنا في contest معينة مسابقة منافسة وداخل فيها
+
+347
+00:26:01,690 --> 00:26:07,350
+مائة شخص نفترض مائة شخص بجرم مائة شخص بجرم وجفنا
+
+348
+00:26:07,350 --> 00:26:11,050
+عند خط النهاية وجاعدين بنحط احتمالات possibilities
+
+349
+00:26:11,050 --> 00:26:17,020
+مين أول عشرة ممكن يصلوامن أول عشرة ممكن يصلوا من
+
+350
+00:26:17,020 --> 00:26:21,000
+المائة شخص اللي بتسابقوا فطبعا عندكوا كمية كبيرة
+
+351
+00:26:21,000 --> 00:26:23,580
+من الاحتمالات من ال possibilities من ال
+
+352
+00:26:23,580 --> 00:26:28,320
+possibilities قداش عددهم هنا counting عدد قداش عدد
+
+353
+00:26:28,320 --> 00:26:31,380
+الاحتمالات عدد انا قاعد باطلب منكوا عدد counting
+
+354
+00:26:31,380 --> 00:26:37,620
+عدولي كويس هذا exampleطبعا هالوقت احنا مش ماهلين
+
+355
+00:26:37,620 --> 00:26:41,000
+نحله إلا بس نخلص الموضوع تبعنا لما نخلص الموضوع
+
+356
+00:26:41,000 --> 00:26:44,800
+بنقدر نتكلم فيه هذا okay example تاني يعني أنا بس
+
+357
+00:26:44,800 --> 00:26:48,060
+بقولكوا في إيش ممكن نستخدم العد example تاني if a
+
+358
+00:26:48,060 --> 00:26:53,590
+password is six to eight letters or and digitsHow
+
+359
+00:26:53,590 --> 00:26:59,030
+many possibles can there be؟ قداش عدد ال passwords
+
+360
+00:26:59,030 --> 00:27:04,390
+اللي بقدر أعملها من ستة لتمانية letters or and
+
+361
+00:27:04,390 --> 00:27:08,210
+digits بمعنى اعملوا password كل واحدة بتعملها
+
+362
+00:27:08,210 --> 00:27:12,890
+password ال password هاللازم يكون عدد ال positions
+
+363
+00:27:12,890 --> 00:27:15,930
+تبعته عدد ال locations تبعته من ستة لتمانية يعني
+
+364
+00:27:15,930 --> 00:27:23,040
+يا ستة يا سبعة يا تمانية six or seven oreight or
+
+365
+00:27:23,040 --> 00:27:28,460
+مهمة جدا طيب في كل digit في كل location ايش
+
+366
+00:27:28,460 --> 00:27:32,820
+العناصر الممكنة اما انها تكون letters حروف او
+
+367
+00:27:32,820 --> 00:27:36,900
+digits او الاتنين مع بعض اللي هم ال combination في
+
+368
+00:27:36,900 --> 00:27:41,120
+ال six مع بعضتمام؟ طيب في الأخر قداش عدد ال
+
+369
+00:27:41,120 --> 00:27:44,200
+passwords الممكنة في الحالة هذه عدد ال passwords
+
+370
+00:27:44,200 --> 00:27:47,220
+الممكنة هذه المفروض من هنا لآخر ما نخلص موضوعنا
+
+371
+00:27:47,220 --> 00:27:49,620
+تكونوا جادرين تشتغلوا على الكلام هذا تكونوا جادرين
+
+372
+00:27:49,620 --> 00:27:52,000
+تحلوها بس أنا قاعد بقولكوا هي حاجات ل password
+
+373
+00:27:52,000 --> 00:27:54,340
+خاصة في شغلكوا بكرا بتكونوا تعملوا design ل
+
+374
+00:27:54,340 --> 00:27:59,140
+password معينة ل location لبرنامج بتكونوا تشتغلوه
+
+375
+00:27:59,140 --> 00:28:02,540
+او program كامل او software كاملة تبرمجوها بتكونوا
+
+376
+00:28:02,540 --> 00:28:05,140
+تعملوه ل password license عشان اللي بتعملوها
+
+377
+00:28:05,140 --> 00:28:10,530
+licenseجدّيش عدد ال users اللي انتوا متوقعين
+
+378
+00:28:10,530 --> 00:28:15,670
+يتبعوهم المنتج تبعكم بناء على جدّيش المتوقع تعملوا
+
+379
+00:28:15,670 --> 00:28:18,510
+عدد passwords لأن كل واحد بده ياخدله password صح
+
+380
+00:28:18,510 --> 00:28:23,430
+فهنا هذا شغلكوا اه بدنا نعرف ان اعد فبدنا نعرف ان
+
+381
+00:28:23,430 --> 00:28:27,670
+اعدOkay في two rules الحقيقة قبل ما نبدأ نشتغل في
+
+382
+00:28:27,670 --> 00:28:30,490
+عملية العدل ال two rules هدولة واحدة اللي هي عملية
+
+383
+00:28:30,490 --> 00:28:34,970
+ال summation و ال product أمتى الأرقام بجمعهم و
+
+384
+00:28:34,970 --> 00:28:38,130
+أمتى الأرقام بضربهم عشان أقول أمتى بجمعهم و أمتى
+
+385
+00:28:38,130 --> 00:28:42,250
+بضربهم بدنا نحط فرضية هنقول let M be the number of
+
+386
+00:28:42,250 --> 00:28:47,250
+ways to do task 1 and N the number of ways to do
+
+387
+00:28:47,250 --> 00:28:50,990
+task 2 لو افترضنا أن ال task الأولى بقدر أعملها ب
+
+388
+00:28:50,990 --> 00:28:57,530
+M طريقةبقدر أشتغل ال task الأولى بأما طريقة يعني
+
+389
+00:28:57,530 --> 00:29:01,430
+في لها خمسين طريقة بقدر أقدي فيها المهمة هذه okay
+
+390
+00:29:01,430 --> 00:29:05,490
+task تانية يمكن لها ستين طريقة بقدر أقدي فيها
+
+391
+00:29:05,490 --> 00:29:09,430
+المهمة طيب لما بدي أعمل اتنين مع بعض ال two tasks
+
+392
+00:29:09,430 --> 00:29:13,550
+مع بعض كيف بقدر أعدهم أنا عارف عدد هذي لحاله وعارف
+
+393
+00:29:13,550 --> 00:29:17,070
+عدد هذي كيف بعمل combination ال combination كيف
+
+394
+00:29:17,070 --> 00:29:22,150
+جمع ولا ضرب بيعتمد علىإيش ال combination اللي بده
+
+395
+00:29:22,150 --> 00:29:25,250
+أعمله بمعنى لو بده نشتغل على ال some rules اللي هي
+
+396
+00:29:25,250 --> 00:29:29,630
+الجامع هد معناها كالتاني ال task اللي بده تنعمل as
+
+397
+00:29:29,630 --> 00:29:33,390
+a total هي عبارة عن two either task one or task
+
+398
+00:29:33,390 --> 00:29:38,870
+two في الحالة هد بقول جامع بمعنى المثال تبع توي
+
+399
+00:29:38,870 --> 00:29:43,490
+لما كنا بنتكلم عن password من ستة لتمانية فإذا هل
+
+400
+00:29:43,490 --> 00:29:48,120
+انتوا بتقدروافي الحالة دي اما ستة او سبعة خليني
+
+401
+00:29:48,120 --> 00:29:50,620
+يعني عشان نبسطها اما ستة من ستة خليني اقول الى
+
+402
+00:29:50,620 --> 00:29:55,560
+سبعة اما ستة locations او سبعة locations فهل وجد
+
+403
+00:29:55,560 --> 00:29:58,200
+انت لما بدك تعمل ال password بتقدر تعمل الاتنين مع
+
+404
+00:29:58,200 --> 00:30:03,740
+بعض مادام بقدرش اعملهم سم اتنين ياصلي فإذا اما ستة
+
+405
+00:30:03,740 --> 00:30:10,040
+او سبعة ومنفصلين مادام منفصلين و او هيني بقول او
+
+406
+00:30:10,040 --> 00:30:15,630
+union union جمعجمع، معناه ذلك أنه جديش عدد
+
+407
+00:30:15,630 --> 00:30:19,890
+الاحتمالات لل passwords هذه بحيث انها تكون من ستة
+
+408
+00:30:19,890 --> 00:30:25,790
+لسبعة characters اما بشغل الحالة الأولى انها تكون
+
+409
+00:30:25,790 --> 00:30:29,670
+ستة وبشوف جديش عدد احتمالاتها، جديش عدد ال ways
+
+410
+00:30:29,670 --> 00:30:34,010
+اللي بقدر اعمل فيها password من ستة characters
+
+411
+00:30:34,010 --> 00:30:39,070
+وعدد الحالات اللي بعملها بسبعة characters ونجمع
+
+412
+00:30:39,070 --> 00:30:40,990
+لنقر
+
+413
+00:30:43,580 --> 00:30:46,760
+بقدرش اعمل اتين اتين مع بعض ما هو خلاص انت عملته
+
+414
+00:30:46,760 --> 00:30:49,840
+password واحدة ال password هدى يا ستة يا سبعة تنفع
+
+415
+00:30:49,840 --> 00:30:52,840
+تكون password حاجة تقبل ستة و سبعة characters مع
+
+416
+00:30:52,840 --> 00:30:57,300
+بعض؟ تنفعش فإذا في الحالة هدى either task one or
+
+417
+00:30:57,300 --> 00:31:02,340
+كلمة or على طول ل ال summation some rule okay the
+
+418
+00:31:02,340 --> 00:31:07,140
+product task the task do both task one and task
+
+419
+00:31:07,140 --> 00:31:14,640
+two simultaneously مع بعضبنعملهم مع بعض task 1 و
+
+420
+00:31:14,640 --> 00:31:20,060
+task 2 في مكانية انه يعملوا مع بعض زي برضه نفس ال
+
+421
+00:31:20,060 --> 00:31:23,020
+task بتاعتوي اللي احنا قولنا هناخدها لاحقا اللي هي
+
+422
+00:31:23,020 --> 00:31:28,160
+ال passwords هذه خلنا نبدأ ب 6 هي task 6 او 7
+
+423
+00:31:28,160 --> 00:31:33,020
+عرفنا او معناته هذه بحسب جدش ال ways اللي بقدر
+
+424
+00:31:33,020 --> 00:31:38,280
+اطبق يعني اجيب فيها عدد ال passwords ب6 digitsو
+
+425
+00:31:38,280 --> 00:31:41,100
+بجمع عليها جداش عدد ال passwords من سبعة digits
+
+426
+00:31:41,100 --> 00:31:45,120
+خليني نبدأ بالستة لإن بدي أحسب هذه لحالي الأول هذي
+
+427
+00:31:45,120 --> 00:31:47,880
+كمان كيف بدي أحسبها بدي أحسبها جالنا والله إما
+
+428
+00:31:47,880 --> 00:31:53,300
+letters أو digits أو digits بس هنا أو or digits
+
+429
+00:31:53,300 --> 00:31:58,660
+معنى ذلك إنه عندنا سبعة ستة
+
+430
+00:31:58,660 --> 00:32:06,070
+ستة هدولة كل واحد من هدول ممكن يكونالحرف .. أكم
+
+431
+00:32:06,070 --> 00:32:11,970
+حرف عندك؟ ستة و عشرين أكم رقم؟ عشرة من صفر لتسعة
+
+432
+00:32:11,970 --> 00:32:15,490
+ففي عندي عشرة بمعنى أن أنا في عندي أجدش عدد ال
+
+433
+00:32:15,490 --> 00:32:19,350
+possibilities لكل digit ستة و تلاتين طيب ل two
+
+434
+00:32:19,350 --> 00:32:25,970
+digits في ستة و تلاتين لأنه باخد أول عنصر هنا و
+
+435
+00:32:25,970 --> 00:32:28,610
+هيتكرر مع الستة و تلاتين اللي موجودين هنا تاني
+
+436
+00:32:28,610 --> 00:32:31,130
+عنصر برضه هيتكرر مع الستة و تلاتين تالت عنصر مع
+
+437
+00:32:31,130 --> 00:32:34,720
+الستة و تلاتين فلحظة أن انتوا بتعملواعملية ضرب
+
+438
+00:32:34,720 --> 00:32:40,140
+شبكة شبكة طيب تلاتة في ستة و تلاتين كمان أربعة
+
+439
+00:32:40,140 --> 00:32:42,840
+كمان ستة .. هاي ضرب ليش؟ لأن ال simultaneous اللي
+
+440
+00:32:42,840 --> 00:32:46,180
+بتضيق بده يحصل عليهم مع بعض عشان يكونوا الستة
+
+441
+00:32:46,180 --> 00:32:49,840
+digits عشان يكونوا الستة locations أو الستة
+
+442
+00:32:49,840 --> 00:32:52,580
+positions فهدول ال simultaneous اللي لازم كلهم
+
+443
+00:32:52,580 --> 00:32:55,840
+يكونوا موجودين مع مين مع بعض غير عملية انه والله
+
+444
+00:32:55,840 --> 00:32:58,540
+ستة أو سبعة ستة أو سبعة لأ احنا ماقدرش اعمل
+
+445
+00:32:58,540 --> 00:33:04,550
+password ستة هو نفسه سبعةتظبطش في هذه or واضحة هذه
+
+446
+00:33:04,550 --> 00:33:08,930
+and فانا بدي character لل location الأول و
+
+447
+00:33:08,930 --> 00:33:12,310
+character لل location التاني و character لل
+
+448
+00:33:12,310 --> 00:33:16,710
+location التالت عشان أكون الستة عشان و فإذا و أنا
+
+449
+00:33:16,710 --> 00:33:21,350
+بتكلم عن and فالأول and التاني and التالت and
+
+450
+00:33:21,350 --> 00:33:25,690
+الرابع and الخمس and السادس هي ستة positionsهذه
+
+451
+00:33:25,690 --> 00:33:28,790
+الستة positions في الحالة هذه بنقول عملية ضرب
+
+452
+00:33:28,790 --> 00:33:33,210
+product في الحالة بتاعتنا ف do both tasks one and
+
+453
+00:33:33,210 --> 00:33:38,890
+two ال task الأولى هتكون جداش عدد الطرق لل digit
+
+454
+00:33:38,890 --> 00:33:44,650
+الأولى لل location الأول andال task التانية لل
+
+455
+00:33:44,650 --> 00:33:49,710
+location التاني فما دام and للتانية طبعا and
+
+456
+00:33:49,710 --> 00:33:52,070
+التالتة and الرابع and الخمسة and السادسة and
+
+457
+00:33:52,070 --> 00:33:54,670
+السبعة بتعملوا generalization بعد ذلك للكلام
+
+458
+00:33:54,670 --> 00:34:03,070
+بتعمموا الموضوع بنعمم الموضوع تمام تفضلي السبعة أه
+
+459
+00:34:03,070 --> 00:34:06,370
+السبعة مختلفة هل وجد الرقم اللي هنطلعه هنا هيطلع
+
+460
+00:34:06,370 --> 00:34:11,030
+ستة و تلاتين to the power ستة هذا فقط لهذه الحالة
+
+461
+00:34:12,100 --> 00:34:19,240
+هنا زائد ستة و تلاتين و سبعة زائد
+
+462
+00:34:19,240 --> 00:34:22,360
+تمانية زي الحل نفسه اللي هو كان طالب أو تمانية من
+
+463
+00:34:22,360 --> 00:34:25,980
+ستة لتمانية كان عامل اللي ناياها زائد ستة و تلاتين
+
+464
+00:34:25,980 --> 00:34:32,300
+وتغار تمانية تمام theoretically الكلام هذا اللي هو
+
+465
+00:34:32,300 --> 00:34:35,440
+ال summation و الدرب كيف نقدر نعمله نعمله as a set
+
+466
+00:34:35,440 --> 00:34:40,370
+ايش يعني as a set ال 36 هدولةاللي هم كانوا خاصين
+
+467
+00:34:40,370 --> 00:34:43,010
+بال task number one ال task number one كان في عندى
+
+468
+00:34:43,010 --> 00:34:46,710
+36 ال 36 elements هدول هنتعامل معاهم ان هم 36
+
+469
+00:34:46,710 --> 00:34:52,550
+elements محطوطين فيه set اسمها ايه ال task التانية
+
+470
+00:34:52,550 --> 00:34:59,910
+set اسمها Bفبنحط ال possibilities أو ال ways اللي
+
+471
+00:34:59,910 --> 00:35:04,490
+بنقدر نعمل فيها ال task number one في ال set A و
+
+472
+00:35:04,490 --> 00:35:07,070
+ال task number two بنحطها في ال set اسمها B و
+
+473
+00:35:07,070 --> 00:35:09,990
+بنشوف إيش ال relation بين الانتين على أساس إن
+
+474
+00:35:09,990 --> 00:35:12,830
+هدولة في النهاية number of ways هدولة في النهاية
+
+475
+00:35:12,830 --> 00:35:16,950
+number of ways جدش عدد الطرق اللي بنخد فيها ال
+
+476
+00:35:16,950 --> 00:35:22,310
+task الأولى أو التانيةA is the set of ways to do
+
+477
+00:35:22,310 --> 00:35:26,730
+task one and B is the set of ways to do task
+
+478
+00:35:26,730 --> 00:35:32,030
+number two and if A and B are disjoint العند الآن
+
+479
+00:35:32,030 --> 00:35:35,550
+هنشغل على الصينية disjoint مختلفين عن بعض مش
+
+480
+00:35:35,550 --> 00:35:39,010
+معتمدين على بعض مش معتمدين على بعض مافيش
+
+481
+00:35:39,010 --> 00:35:43,070
+intersection between them يعني مافيش طريقة بتنفع
+
+482
+00:35:43,070 --> 00:35:47,840
+هنا و بتنفع هنامافيش طريقة تنفهن أو تنفهن مبدأيا
+
+483
+00:35:47,840 --> 00:35:50,180
+خلينا على المفهوم البسيط هذا و بعدين هنطوره شوي
+
+484
+00:35:50,180 --> 00:35:54,080
+شوي هنطوره شوي شوي في الحالة هذه the ways to do
+
+485
+00:35:54,080 --> 00:35:58,700
+either task one or or or معناته نتكلم عن summation
+
+486
+00:35:58,700 --> 00:36:04,680
+unionف a union b وفي الحالة دي ال cardinality جدش
+
+487
+00:36:04,680 --> 00:36:11,940
+عدد ال ways to do this task either task one or
+
+488
+00:36:11,940 --> 00:36:15,120
+task two تنتهي مع بعض هتكون عبارة عن cardinality ل
+
+489
+00:36:15,120 --> 00:36:18,420
+a union b هتكون عبارة عن cardinality جدش عدد ال
+
+490
+00:36:18,420 --> 00:36:22,980
+ways to do task one plus جدش عدد ال ways to do
+
+491
+00:36:22,980 --> 00:36:29,960
+task number two بجمحهم مع بعضجمع هنا زي هذه ستة
+
+492
+00:36:29,960 --> 00:36:33,840
+سبعة جدش عدد ال ways عشان أشتغل على ستة digits جدش
+
+493
+00:36:33,840 --> 00:36:36,440
+عدد ال ways عشان أشتغل على سبعة digits نجمعهم إذا
+
+494
+00:36:36,440 --> 00:36:42,600
+كان هيها either task one or or خلاص فصلنا انتهت
+
+495
+00:36:42,600 --> 00:36:47,260
+جمع جمع يعني بتاخد إيا ال a إيا ال b مش التنتين مع
+
+496
+00:36:47,260 --> 00:36:50,360
+بعض تمام بالظبط و احنا قولنا انه disjoint التنتين
+
+497
+00:36:51,740 --> 00:36:54,500
+Tintin was joined معناه ذلك أنهما مافيش شيء مشترك
+
+498
+00:36:54,500 --> 00:36:58,640
+بينهم فيا الأولى جداش عدد ال ways بتاعتها يا
+
+499
+00:36:58,640 --> 00:37:00,780
+التانية جداش عدد ال ways بتاعتها مجموعة Tintin
+
+500
+00:37:00,780 --> 00:37:03,760
+بيعطيه يا الأولى يا التانية جداش يا الأولى يا
+
+501
+00:37:03,760 --> 00:37:07,760
+التانية هدولة summation بتصير طيب ال ways to do
+
+502
+00:37:07,760 --> 00:37:13,020
+both task one and task two Cartesian product
+
+503
+00:37:13,020 --> 00:37:16,740
+Cartesian product فال cardinality بتاعتها كانت
+
+504
+00:37:16,740 --> 00:37:19,060
+عبارة عن ال cardinality أو عدد ال ways للأولى
+
+505
+00:37:19,850 --> 00:37:22,610
+مضروبة في عدد ال ways للتانية في عدد ال ways
+
+506
+00:37:22,610 --> 00:37:25,750
+للتانية زي الحالة اللي احنا اتكلمناها هنا زي
+
+507
+00:37:25,750 --> 00:37:30,150
+الحالة اللي هنا okay ناخد examples ناخد مجموعة
+
+508
+00:37:30,150 --> 00:37:33,730
+examples توضح المفاهيم بتاعتنا okay a student can
+
+509
+00:37:33,730 --> 00:37:38,130
+choose a computer project from one of three lists
+
+510
+00:37:38,130 --> 00:37:42,350
+عندكوا three lists في مساق من المساقات و الدكتور
+
+511
+00:37:42,350 --> 00:37:44,910
+حددلكوا مجموعة projects جالكوا كل واحدة منكم يا
+
+512
+00:37:44,910 --> 00:37:48,960
+بنات تختار تختارلها project تشتغل عليهطيب ال
+
+513
+00:37:48,960 --> 00:37:51,600
+project هذا قالكوا بس دي ربالكوا أنا موزعلكم إياه
+
+514
+00:37:51,600 --> 00:37:54,420
+three categories ال category الأولى يمكن تكون خاصة
+
+515
+00:37:54,420 --> 00:37:57,440
+بالناس اللي بيحبوا ال database المجموعة التانية
+
+516
+00:37:57,440 --> 00:37:59,600
+خاصة بالناس اللي بيحبوا البرمجة باستخدام ال Java
+
+517
+00:37:59,600 --> 00:38:02,740
+المجموعة التالتة يمكن خاصة بالناس اللي بيحبوا ال
+
+518
+00:38:02,740 --> 00:38:07,400
+networking وزعلكم إياهم وقالكم والله الأولى هذه
+
+519
+00:38:07,400 --> 00:38:10,680
+أنا في عندى 23 project إذا حابين تشتغلوا في ال
+
+520
+00:38:10,680 --> 00:38:12,940
+database حدا منكم بيحب يشتغل في ال database ياخد
+
+521
+00:38:12,940 --> 00:38:16,000
+واحدة من المشاريع هذه كويسة خمسة عشر للناس اللي
+
+522
+00:38:16,000 --> 00:38:19,360
+بيحبوا يشتغلوا بالبرمجةو في عنا 19 لناس اللي
+
+523
+00:38:19,360 --> 00:38:21,440
+بيحبوا مثلا يشتغلوا في ال networking في الشبكات
+
+524
+00:38:21,440 --> 00:38:25,460
+طيب عشان تختاروا جداش عندكوا عدد ال ways عشان
+
+525
+00:38:25,460 --> 00:38:29,660
+تختاروا فيها طبعا واضح انهم انفصلة ليش لأن انا
+
+526
+00:38:29,660 --> 00:38:33,320
+هختار واحد project واحد يا اما من category اول يا
+
+527
+00:38:33,320 --> 00:38:36,100
+من ال category التاني يا من ال category التالت مش
+
+528
+00:38:36,100 --> 00:38:39,800
+هاختار مشروع من الكل لأ هو طالب منك اختيار واحد
+
+529
+00:38:39,800 --> 00:38:43,660
+فاختيار كل واحد هيكون عبارة عن يا من 23 زائد 15
+
+530
+00:38:43,660 --> 00:38:46,400
+زائد 19 فانتوا بالنسبالكوا كلها projects واحدة
+
+531
+00:38:47,150 --> 00:38:49,830
+عددهم سبعة و خمسين project فانتوا فى عندكوا سبعة و
+
+532
+00:38:49,830 --> 00:38:52,970
+خمسين projects عشان تختاروا منها .. كل واحدة منكوا
+
+533
+00:38:52,970 --> 00:38:57,950
+تختار لها project من سبعة و خمسين project okay لو
+
+534
+00:38:57,950 --> 00:39:01,970
+عندكوا .. suppose statement label .. labels in
+
+535
+00:39:01,970 --> 00:39:05,930
+programming language must be a single letter or a
+
+536
+00:39:05,930 --> 00:39:10,090
+single decimal digit how many labels are there؟ لو
+
+537
+00:39:10,090 --> 00:39:12,890
+محتاجين تعملوا labeling ل .. خلنا نقول ل variables
+
+538
+00:39:13,860 --> 00:39:18,240
+في البرمجة وبتسموها باسم معين ال verb ساعتكم ففي
+
+539
+00:39:18,240 --> 00:39:20,660
+عندكم إمكانية إما أنكوا تسموها باستخدام single
+
+540
+00:39:20,660 --> 00:39:25,820
+letter حرف أو رقم .. او رقم طب كدش عندكوا عدد ال
+
+541
+00:39:25,820 --> 00:39:28,280
+ways اللي ممكن تسموه فيها أو تعملوا labeling فيها
+
+542
+00:39:28,280 --> 00:39:33,780
+ستة و عشرين زائد عشرة .. ستة و عشرين زائد عشرة
+
+543
+00:39:33,780 --> 00:39:38,180
+مافيش فيها .. عندكوا or معناته يا إما بستخدم
+
+544
+00:39:38,180 --> 00:39:42,540
+letter أو بستخدم digitيا لطريقة ديجالية، يا ستة و
+
+545
+00:39:42,540 --> 00:39:46,320
+عشرين، يا عشرة، معناه اتصار عندى ستة و تلاتين ways
+
+546
+00:39:46,320 --> 00:39:51,080
+بقدر امثل فيها، بعمل فيها عملية labeling okay how
+
+547
+00:39:51,080 --> 00:39:53,640
+many integers between one and one hundred
+
+548
+00:39:53,640 --> 00:39:58,380
+including ال one hundred are even or end with five
+
+549
+00:39:59,290 --> 00:40:04,050
+طيب كويس or معناته انا بتكلم عن two tasks فى task
+
+550
+00:40:04,050 --> 00:40:07,790
+أولى و فى task تانية بمسك ال task الأولى لحالها
+
+551
+00:40:07,790 --> 00:40:11,710
+جديش عدد الأرقام من واحد لمية طبعا مشمول معاهم
+
+552
+00:40:11,710 --> 00:40:17,090
+المية even حيكون عددهم خمسين مدام مشمولة لمية من
+
+553
+00:40:17,090 --> 00:40:21,830
+اتنين اربع ست تمانية عشر حيكون عددهم خمسين هذا ال
+
+554
+00:40:21,830 --> 00:40:28,170
+task الأولى task أولى ال task التانية end with
+
+555
+00:40:28,170 --> 00:40:35,650
+fiveقدش عدد الأرقام من واحد لمية بينتهي بخمسة
+
+556
+00:40:35,650 --> 00:40:39,950
+بمعنى الأحد تبعه خمسة خمسة، خمستاشر، خمسة وعشرين،
+
+557
+00:40:39,950 --> 00:40:42,090
+خمسة وثلاثين، خمسة واربعين، خمسة وخمسين، خمسة
+
+558
+00:40:42,090 --> 00:40:44,550
+وستين، خمسة وسبعين، خمسة و تمانين، خمسة وتسعين، في
+
+559
+00:40:44,550 --> 00:40:51,350
+عندنا عشرة طيب في intersection between them؟ ايش؟
+
+560
+00:40:51,350 --> 00:40:58,140
+خمستاشر15 even لاحظتي هنا أنا بتكلم عن even هدول
+
+561
+00:40:58,140 --> 00:41:04,960
+50 رقم even هدول عشر أرقام بتنتهي بخمسة فالخمسة
+
+562
+00:41:04,960 --> 00:41:10,940
+لايمكن تكون even فإذا this joint ومدين في or بجمع
+
+563
+00:41:10,940 --> 00:41:16,190
+وانا متطمن ان مافيش اي turn تاني محتاج اطرحهلأن
+
+564
+00:41:16,190 --> 00:41:18,890
+احنا عارفين إنه لازم إذا كان في intersection بدنا
+
+565
+00:41:18,890 --> 00:41:21,870
+نطرح قيمة ال intersection جاينة .. جاينة هتشرحها
+
+566
+00:41:21,870 --> 00:41:27,670
+فهنا هيطلع عددهم ستين ways لتمثيل ال task الأولى
+
+567
+00:41:27,670 --> 00:41:34,390
+or task التانية .. or task التانية فهي الستين okay
+
+568
+00:41:34,390 --> 00:41:38,550
+how many different pit strings of length seven are
+
+569
+00:41:38,550 --> 00:41:44,730
+there؟ جدش؟عدد ال strings اللي بقدر امثلها
+
+570
+00:41:44,730 --> 00:41:52,330
+باستخدام bit, string طوله او length طولها سبعة
+
+571
+00:41:52,330 --> 00:41:58,290
+جداش
+
+572
+00:41:58,290 --> 00:42:02,370
+عدد ال strings اللي بقدر امثلها عارفين ان هنا جداش
+
+573
+00:42:02,370 --> 00:42:09,400
+احتمالات هذه يا صفرية واحد اتنينطيب التانية برضه
+
+574
+00:42:09,400 --> 00:42:14,300
+اتنين تالتة اتنين خلاص معناه ذلك احنا عارفين انه
+
+575
+00:42:14,300 --> 00:42:18,800
+ضرب فواحد اتنين تلات اربع سبعة اتنين تلات اربع
+
+576
+00:42:18,800 --> 00:42:23,350
+سبعة خلاصمافيش فيها كتير مشاكل مافيش فيها كتير
+
+577
+00:42:23,350 --> 00:42:25,690
+مشاكل فانا بقدر اقول اه والله يجديش عدد ال strings
+
+578
+00:42:25,690 --> 00:42:28,710
+اللي ممكن نعملها combination او يجديش عدد ال
+
+579
+00:42:28,710 --> 00:42:32,290
+strings اللي بقدر اخدها من مجموعة digits عددهم
+
+580
+00:42:32,290 --> 00:42:36,810
+سبعة عددهم سبعة و هنا نتكلم عن bit digits او bit
+
+581
+00:42:36,810 --> 00:42:37,270
+string
+
+582
+00:42:41,030 --> 00:42:45,550
+Okay كمان مثال a license contains .. اه هنا بنتكلم
+
+583
+00:42:45,550 --> 00:42:47,950
+برضه عن license معناه أننا بنتحط code .. بنتحط
+
+584
+00:42:47,950 --> 00:42:50,750
+حاجة هيك زي ال code ال code هذا بتكون من إيه؟ a
+
+585
+00:42:50,750 --> 00:42:54,390
+sequence of three letters followed by three digits
+
+586
+00:43:05,780 --> 00:43:14,740
+three letters مطبوعين ايه؟ ب three digits اكامويز
+
+587
+00:43:14,740 --> 00:43:18,040
+بقدر امثل فيها ال string هدا او ال sequence هدا
+
+588
+00:43:18,040 --> 00:43:21,480
+هنا مطلوب جداش عدد ال license في الآخر المتاحة
+
+589
+00:43:21,480 --> 00:43:24,400
+اللي هو معناته جداش عدد ال sequences الموجودة اللي
+
+590
+00:43:24,400 --> 00:43:28,820
+بقدر امثلها بهذا الشكل هنا عندى زي ما قلنا هيكون
+
+591
+00:43:28,820 --> 00:43:33,600
+في عندى lettersال letters معناه ذلك ان الاحتمال
+
+592
+00:43:33,600 --> 00:43:43,600
+للأولى 26 تانية طيب هنا digits و
+
+593
+00:43:43,600 --> 00:43:48,060
+في النهاية كله ضرر على اعتبار ان كلهم في النهاية
+
+594
+00:43:48,060 --> 00:43:52,720
+هحنحطوه في sequence واحد together together بمعنى
+
+595
+00:43:52,720 --> 00:44:01,260
+محتاج اعمل ال task الأولى و ال task التانيةو ال
+
+596
+00:44:01,260 --> 00:44:07,460
+task التالتة and and and ال task الرابع and ال
+
+597
+00:44:07,460 --> 00:44:10,320
+task الخامس and ال task الساسع عشان انا اطلع ستة
+
+598
+00:44:10,320 --> 00:44:14,440
+locations مجسمين تلاتة letters و تلاتة digits فهذه
+
+599
+00:44:14,440 --> 00:44:17,520
+ال and ضرورية هنا ال and ضرورية و مادام and
+
+600
+00:44:17,520 --> 00:44:21,540
+مادامتها بتكلم عن multiplication بتكلم هنا عن
+
+601
+00:44:21,540 --> 00:44:29,930
+multiplication okay نرجع برضه لعملية ال labelingأه
+
+602
+00:44:29,930 --> 00:44:33,070
+يمكن برضه هاد السهلة لو كنا نعمل برضه عملية
+
+603
+00:44:33,070 --> 00:44:36,530
+labeling باستخدام ال basic language is either ال
+
+604
+00:44:36,530 --> 00:44:42,290
+label هذا أو المسمى هذا أحد حاجتين is either a
+
+605
+00:44:42,290 --> 00:44:49,910
+single letter or a letter followed by a digit فإذا
+
+606
+00:44:49,910 --> 00:44:54,430
+في عندى task أولى ال task الأولى كده عددهم؟ ستة
+
+607
+00:44:54,430 --> 00:44:57,970
+وعشرين انتهينا خالص ستة وعشرين okay
+
+608
+00:45:02,850 --> 00:45:06,790
+لأ في عندك ستة و عشرين followed by ten معناه انت
+
+609
+00:45:06,790 --> 00:45:12,850
+ستة و عشرين في عشرة علاقتهم مع بعض ضرب لأ في or
+
+610
+00:45:12,850 --> 00:45:19,090
+زائد فبتطلع هنا مائتين و سبتين زائد ستة و عشرين
+
+611
+00:45:19,090 --> 00:45:27,270
+ستة تمانية اتنينبطلع 286 زي ما قولنا بنعمل two
+
+612
+00:45:27,270 --> 00:45:31,190
+parts ست أولى الست الأولى هي single letter labels
+
+613
+00:45:31,190 --> 00:45:36,130
+الست التانية اللي هي single letters followed by a
+
+614
+00:45:36,130 --> 00:45:40,010
+digit و بنسميها D فطبعا ال total في الآخر هيكون
+
+615
+00:45:40,010 --> 00:45:43,950
+عبارة عن ال union لتنتين ال union لتنتين طب عشان
+
+616
+00:45:43,950 --> 00:45:46,290
+أجيب ال cardinality لل union لتنتين هجيب ال
+
+617
+00:45:46,290 --> 00:45:49,630
+cardinality الأولى زي ال cardinality للتانية زي ال
+
+618
+00:45:49,630 --> 00:45:55,540
+cardinality3 ثانية عشان تحصروا في الآخر على 286
+
+619
+00:45:55,540 --> 00:46:04,920
+286 okay كمان مثال مثال
+
+620
+00:46:04,920 --> 00:46:09,620
+كويس و related لتخصصكم هنا بنتكلم عن جداش عدد ال
+
+621
+00:46:09,620 --> 00:46:14,180
+IB addresses او ال internet protocol addresses ل
+
+622
+00:46:14,180 --> 00:46:19,600
+ال IB version 4 version 4 طبعا في نهولوجيا صار في
+
+623
+00:46:19,600 --> 00:46:23,960
+version 6صافي version 6 طوروا على ال version 4
+
+624
+00:46:23,960 --> 00:46:26,880
+احنا خلينا على ال version 4 ال version 4 هذا
+
+625
+00:46:26,880 --> 00:46:33,180
+عندكوا 32 digit 32 bit ال 32 bit هدول بدنا نمثل
+
+626
+00:46:33,180 --> 00:46:36,440
+فيهم ال ip addresses بتاعتنا بدنا نمثل فيهم ال ip
+
+627
+00:46:36,440 --> 00:46:39,080
+addresses طبعا عشان اتقولوا عن ال ip addresses
+
+628
+00:46:39,080 --> 00:46:44,060
+اولش انتم محتاجين ال network له ID و ال host له ID
+
+629
+00:46:44,060 --> 00:46:49,040
+لان في عدد hosts لكل network طيب قدش عدد ال
+
+630
+00:46:49,040 --> 00:46:53,880
+networksهيكون برضه multiplication بين الاتنين جداش
+
+631
+00:46:53,880 --> 00:47:01,100
+.. فضليه مثالنا
+
+632
+00:47:01,100 --> 00:47:05,800
+هيتكلم عن جداش عدد ال IP او ال internet protocol
+
+633
+00:47:05,800 --> 00:47:10,080
+addresses عنوين ال .. ال protocol .. لل internet
+
+634
+00:47:10,080 --> 00:47:14,710
+protocol او جداش عدد عنوين لل internetانت عنوانك
+
+635
+00:47:14,710 --> 00:47:19,530
+على الكمبيوتر تبعك بيبين as a IP address عند الناس
+
+636
+00:47:19,530 --> 00:47:22,850
+برا طيب انا برضه بيبين IP address انا في location
+
+637
+00:47:22,850 --> 00:47:25,710
+تاني بس الاتنين ممكن يكونوا مشتركين في ال location
+
+638
+00:47:25,710 --> 00:47:27,610
+.. في ال .. في ال network على فكرة اذا احنا ماخدين
+
+639
+00:47:27,610 --> 00:47:29,590
+من نفسنا من ال provider ماخدين من نفسنا .. ممكن
+
+640
+00:47:29,590 --> 00:47:33,310
+الشبكة نفسها بس ال host number بيختلف ال host
+
+641
+00:47:33,310 --> 00:47:36,770
+number ممكن يختلف او ال host ID بيختلف في النهاية
+
+642
+00:47:37,880 --> 00:47:47,040
+ال version 4 هذا جداش عدد ال ip addresses الممكنة
+
+643
+00:47:47,040 --> 00:47:51,580
+باستخدام ال version 4 هاي المطلوب طيب بدنا نعرف
+
+644
+00:47:51,580 --> 00:47:57,820
+شوية حقائق عن ال ip version 4 ال ip version 4 أولا
+
+645
+00:47:57,820 --> 00:48:02,380
+بتجسم لجمهد classes ال classes هدولة فعليا في a,b
+
+646
+00:48:02,380 --> 00:48:07,780
+,c في D وED و E في الكتاب موجودين انا اختصرتهم لان
+
+647
+00:48:07,780 --> 00:48:13,940
+مثلنا بس على جد ال ABC موجود D و هذا بيستخدم عادة
+
+648
+00:48:13,940 --> 00:48:18,800
+في ال broadcasting و موجود ال E مستخدم عادة لل
+
+649
+00:48:18,800 --> 00:48:23,340
+networking مش مطلوب انه في الشغل احنا هنشتغل بس
+
+650
+00:48:23,340 --> 00:48:29,040
+على ال class اللي نقدر نعمل فيها hosting او host
+
+651
+00:48:29,040 --> 00:48:34,820
+IDاستضافة ل .. ل users .. ل users بدنا نشوف قداش
+
+652
+00:48:34,820 --> 00:48:39,740
+عدد ال IP الممكنة باستخدام version 4 .. باستخدام
+
+653
+00:48:39,740 --> 00:48:42,540
+version 4 طيب ال facts اللي بدنا نعرفها كانت تالي
+
+654
+00:48:42,540 --> 00:48:47,780
+ان في عندي three types ال type أول اسمه class A ال
+
+655
+00:48:47,780 --> 00:48:52,060
+class A ده بيحتوي على سبعة bit للشبكة لل net ID
+
+656
+00:48:52,060 --> 00:48:56,640
+بنسميها net ID و غير مسموح ان يكون ones غير مسموح
+
+657
+00:48:56,640 --> 00:49:00,530
+ان تكون ones هذا فقط في class Aغير مسموح نكون ايش؟
+
+658
+00:49:00,530 --> 00:49:05,330
+one طيب عندنا اربع عشرين bit ل ال host ID ل ال
+
+659
+00:49:05,330 --> 00:49:10,890
+hosting okay class B address class B address has
+
+660
+00:49:10,890 --> 00:49:16,670
+fourteen bit ل ال network او لل net ID و sixteen ل
+
+661
+00:49:16,670 --> 00:49:22,930
+ال host ID class C has twenty one bit net ID و
+
+662
+00:49:22,930 --> 00:49:28,780
+eight bit ل ال host ID او لل hosting okayبنعرف
+
+663
+00:49:28,780 --> 00:49:31,900
+كمان معلومة ان ال three classes have distinct
+
+664
+00:49:31,900 --> 00:49:35,080
+headers طبيعي انا كيف بده اعرف ان انا في class A و
+
+665
+00:49:35,080 --> 00:49:38,560
+لا B و لا C كيف بده نعرف عن طريق ال header اول
+
+666
+00:49:38,560 --> 00:49:42,800
+bits هنستقبلها اول bits اللي بيميزها ال zero اللي
+
+667
+00:49:42,800 --> 00:49:47,810
+بيميزها ال zero ال zero هدأجة بعد أكم oneإذا جاء
+
+668
+00:49:47,810 --> 00:49:52,430
+مباشرة مافيش اي ones قدامه بعرف ان انا class A إذا
+
+669
+00:49:52,430 --> 00:49:55,950
+one بعدين ال zero انا class B و بشتغل بنانا عليه
+
+670
+00:49:55,950 --> 00:49:59,610
+بجسم مجموعة ال bits بعد هي بنانا عليه عشان أعرف
+
+671
+00:49:59,610 --> 00:50:03,980
+عنوان الشبكة الأول و بعدين بعرف عنوان ال hostبنان
+
+672
+00:50:03,980 --> 00:50:06,860
+على جداش عدد ال bits اللى لازم نعرف فيها العنوان
+
+673
+00:50:06,860 --> 00:50:09,560
+جداش عدد ال bits اللى بنعرف فيها العنوان لل
+
+674
+00:50:09,560 --> 00:50:15,000
+network و لمن و لل host لل network و لل host أو زي
+
+675
+00:50:15,000 --> 00:50:19,940
+class A، zero ببدأت zero مباشرة خلاص بجسم بعدها
+
+676
+00:50:19,940 --> 00:50:23,280
+كده على طول مباشرة سبعة و أربعة و أربعة و عشرين
+
+677
+00:50:23,280 --> 00:50:26,500
+بجسم سبعة و أربعة و عشرين السبعة دول بيحددوا ليه
+
+678
+00:50:26,500 --> 00:50:32,960
+أنا في أي network بتنعمل sub networksوالـ 24 بمثل
+
+679
+00:50:32,960 --> 00:50:37,540
+فيها ال hosts أو جدّيش عدد ال hosts لكل شبكة فيهم
+
+680
+00:50:37,540 --> 00:50:42,620
+جدّيش عدد ال hosts لكل شبكة okay class B هيكون في
+
+681
+00:50:42,620 --> 00:50:47,340
+عندي one و بعدين ال zero class C two ones بعدين
+
+682
+00:50:47,340 --> 00:50:51,520
+zero بعرف منهم كيف اجسم العدد البث اللي جاي يعني
+
+683
+00:50:51,520 --> 00:50:58,700
+عشان اعرف ال network ID و ال host ID تمامما
+
+684
+00:50:58,700 --> 00:51:02,760
+المطلوب في النهاية؟ لسه معلومة إضافية كمان انه في
+
+685
+00:51:02,760 --> 00:51:05,820
+ال host غير مسموح بال zeros و ال ones اللي هو ال
+
+686
+00:51:05,820 --> 00:51:08,960
+DC يعني لأن ال DC ممكن تكون عبارة عن noise في
+
+687
+00:51:08,960 --> 00:51:15,810
+النهاية أو nothing لو كانت zero فطبعاzero أو one
+
+688
+00:51:15,810 --> 00:51:23,150
+غير مسموح باستخدامها ل ال host ID هدول
+
+689
+00:51:23,150 --> 00:51:27,030
+مرفضين ل ال host zeros او ones لكل classes ل ال
+
+690
+00:51:27,030 --> 00:51:30,710
+three classes مرفضين مرفضين okay المطلوب انه يجداش
+
+691
+00:51:30,710 --> 00:51:37,110
+عدد ال IDs الممكنة ل ال version 4 طبعا واضح ال
+
+692
+00:51:37,110 --> 00:51:43,970
+version 4 في الحالة هذه اما هيكون class E اوclass
+
+693
+00:51:43,970 --> 00:51:50,990
+B أو class C واضحة انا بتصورها لوجهة بداية الرؤية
+
+694
+00:51:50,990 --> 00:51:59,130
+واضحة ان انا بتكلم عن number of class A plus
+
+695
+00:51:59,130 --> 00:52:04,010
+number number ID طبعا بتكلم عن ال ID ال ID عفوا ال
+
+696
+00:52:04,010 --> 00:52:11,430
+ID addresses class B plus number of
+
+697
+00:52:14,410 --> 00:52:20,710
+C نمسك الأول نمسك واحد واحد الأول لحظة من ال 32
+
+698
+00:52:20,710 --> 00:52:27,770
+bit هو في النهاية مشترك ال version ال IP version 4
+
+699
+00:52:27,770 --> 00:52:32,310
+مشترك أو بتفق أنه بيستخدم ال 32 bit واحدة منهم
+
+700
+00:52:32,310 --> 00:52:37,630
+راحت لمين للهدر؟ دل 31 ال 31 هم المجسدين سبعة و 24
+
+701
+00:52:37,630 --> 00:52:42,270
+سبعة نمسك السبعة في الأول طبعا لحظة أن ال sequence
+
+702
+00:52:42,270 --> 00:52:46,440
+في الأخر هيكون كلهم على بعضيعني أنا بقدرش أروح
+
+703
+00:52:46,440 --> 00:52:50,980
+أعرف الشبكة و أقول له اعرفني لأ كيف ده يعرفني هو
+
+704
+00:52:50,980 --> 00:52:53,700
+عارف الشبكة ال provider اللي أنا ماخد منه بس
+
+705
+00:52:53,700 --> 00:52:56,120
+ماعرفنيش أنا لإن أنا مش لحالي أفعل ال provider
+
+706
+00:52:56,120 --> 00:52:58,780
+يعني ال provider مش مقتنع ان انا لحالي في نفس
+
+707
+00:52:58,780 --> 00:53:02,660
+الوجد بقدرش أقول له أنا هاي رقم ايه اعرفني واصلني
+
+708
+00:53:02,660 --> 00:53:07,180
+طب ما هو مش عارف الشبكة ممكن يكون في واحد تاني في
+
+709
+00:53:07,180 --> 00:53:10,720
+شبكة تانية اللي له نفس الرقم رقم ال host بس على
+
+710
+00:53:10,720 --> 00:53:13,960
+شبكة تانية فلازم كله مع بعضه فهذا كله sequence
+
+711
+00:53:13,960 --> 00:53:18,160
+واحددعوني أخبركم إن سيكوانس واحد مع بعض هذا لازم
+
+712
+00:53:18,160 --> 00:53:21,700
+يظهر and هذا لازم يكون موجود لأن اتنين لازم يكونوا
+
+713
+00:53:21,700 --> 00:53:26,700
+and موجودة بينهم هذا and هذا كويس نمسك الأول الأول
+
+714
+00:53:26,700 --> 00:53:30,900
+اللي هو ال net عبارة عن سبعة سبعة digital أكم
+
+715
+00:53:30,900 --> 00:53:34,980
+احتمال إلها ستنقل
+
+716
+00:53:34,980 --> 00:53:39,960
+واحد بالظبط فهتكون اتنين تتبارد سبعة minus ال one
+
+717
+00:53:39,960 --> 00:53:47,460
+صحيح اللي هو إيه؟ال ones لاتساوي ones لاتساوي ones
+
+718
+00:53:47,460 --> 00:53:52,440
+طيب هدى هتنضرب فى مين؟ فى ال host فى ال host لدى
+
+719
+00:53:52,440 --> 00:53:57,720
+ايش؟ اثنين to the power ناقص اثنين ناقص اثنين شو
+
+720
+00:53:57,720 --> 00:54:03,320
+هما الاثنين؟ zeros or ones خلاص هدى لمين ل class
+
+721
+00:54:03,320 --> 00:54:11,120
+ايه؟هذه بتاعة class class B بتضربوهم بطلع برقم
+
+722
+00:54:11,120 --> 00:54:16,740
+اتنين اتنين مليون بليون تقريبا اتنين كسر بليون
+
+723
+00:54:16,740 --> 00:54:24,140
+كويس تجمع ولا تانية زائد class B اتنين و نص أربعة
+
+724
+00:54:24,140 --> 00:54:27,960
+عشر اتنين و نص اربعة عشر و ماجالش انه انه من نوع
+
+725
+00:54:27,960 --> 00:54:33,380
+ال ones فاتنين و نص اربعة عشر في ناقص اتنين تمام
+
+726
+00:54:33,380 --> 00:54:34,260
+التالتة
+
+727
+00:54:38,150 --> 00:54:44,810
+2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8
+
+728
+00:54:44,810 --> 00:54:52,190
+ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص
+
+729
+00:54:52,190 --> 00:54:53,410
+2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8
+
+730
+00:54:53,410 --> 00:54:54,430
+ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص
+
+731
+00:54:54,430 --> 00:55:03,180
+2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8هدول رقم
+
+732
+00:55:03,180 --> 00:55:06,820
+صغير كان يستدعي أنه فعلا تدخل و نعمل upgrading أو
+
+733
+00:55:06,820 --> 00:55:12,680
+يعملوا upgrading لمين ل version 6 في الآخر هذه
+
+734
+00:55:12,680 --> 00:55:17,100
+القالية تجمعوهم
+
+735
+00:55:17,100 --> 00:55:21,600
+عشان يطلع مجموع الأرقام class A class B class C
+
+736
+00:55:21,600 --> 00:55:27,180
+بتطلع لنا ال total 3.7 تقريبا billion IB addresses
+
+737
+00:55:29,170 --> 00:55:35,010
+واضح كيف حسبناهم؟ كيف عدناهم؟ طيب، كمان مرة، وين
+
+738
+00:55:35,010 --> 00:55:39,070
+المشكلة كانت عندك؟ في الجامعة ولا في الدراجة؟ نقص
+
+739
+00:55:39,070 --> 00:55:41,250
+واحد، نقص إثنين، نقص واحد، نقص إثنين، نقص واحد،
+
+740
+00:55:41,250 --> 00:55:43,670
+نقص إثنين، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+741
+00:55:43,670 --> 00:55:44,090
+نقص واحد، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+742
+00:55:44,090 --> 00:55:48,970
+نقص واحد، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+743
+00:55:48,970 --> 00:55:51,110
+نقص واحد، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+744
+00:55:51,110 --> 00:55:59,120
+نقص واحد، نقص واحد، نقص واحد، نيا ones يا zeros
+
+745
+00:55:59,120 --> 00:56:03,680
+ماعندكيش انت بتتكلم عن bit ال bit فيه احتمال غير
+
+746
+00:56:03,680 --> 00:56:09,080
+ال one و ال zero بس هو هنا بيحددلك بيقولك ان ال
+
+747
+00:56:09,080 --> 00:56:14,120
+class A بالنسبة له الشبكة ممنوعة تستخدم ال ones
+
+748
+00:56:15,320 --> 00:56:18,780
+يعني هنا شوية distractions جالك لازم تاخد بالك
+
+749
+00:56:18,780 --> 00:56:23,540
+منها انه في class A ما تستعمليش ال ones لل net ID
+
+750
+00:56:23,540 --> 00:56:27,200
+فال net ID أنا عارف ان هي سبعة صح فبقول جديش عدد
+
+751
+00:56:27,200 --> 00:56:31,980
+البدائي بتاعتها جديش عدد ال strings اللي ممكن
+
+752
+00:56:31,980 --> 00:56:35,780
+اطلعها من سبعة bits اتنين to the power سبعة بس
+
+753
+00:56:35,780 --> 00:56:39,260
+هيقول ليه استثني ال ones طب ال ones هي حالة واحدة
+
+754
+00:56:39,260 --> 00:56:39,840
+من الحالات
+
+755
+00:56:42,500 --> 00:56:46,600
+بالظبط لأ لأ ال ones اللي هي هي one to the power
+
+756
+00:56:46,600 --> 00:56:49,120
+of seven يعني one في ال locations السبعة في السبعة
+
+757
+00:56:49,120 --> 00:56:53,140
+locations هذه هي حالة واحدة تعتبر هي تعتبر حالة
+
+758
+00:56:53,140 --> 00:56:56,260
+واحدة من كل الحالات فبنعملها حالة بهذا الشكل و ب
+
+759
+00:56:56,260 --> 00:57:00,220
+stop بنوقف على هيك طيب لاحظوا أنه بالنسبة لل host
+
+760
+00:57:00,220 --> 00:57:04,300
+ميعطيني هنا ل three classes okay headers بعدين
+
+761
+00:57:04,300 --> 00:57:11,800
+جالني ال host IDones أو zeros not allowed مش مسموح
+
+762
+00:57:11,800 --> 00:57:14,840
+فيهم مش مسموح فيهم فautomatically هنا لما نقول
+
+763
+00:57:14,840 --> 00:57:18,320
+اتنين تتبارى اربعة و عشرين في عندي حالتين مش مسموح
+
+764
+00:57:18,320 --> 00:57:21,680
+فيهم اللي هم ال ones كله one one one one one و
+
+765
+00:57:21,680 --> 00:57:24,700
+zero zero zero zero ف minus two لإن هو دول
+
+766
+00:57:24,700 --> 00:57:30,920
+احتمالين يا ones يا zeros فبنطرح لاتنين طب مش فيه
+
+767
+00:57:30,920 --> 00:57:35,700
+اللي هو اللي موجود اللي هي دائما واحد صارت؟ okay
+
+768
+00:57:35,700 --> 00:57:39,650
+اختصرناها راحت خلصتلأن انت في عندك واحدة للهدر و
+
+769
+00:57:39,650 --> 00:57:43,210
+في عندك سبعة و جداش و اربع و عشرين سبعة و اربع و
+
+770
+00:57:43,210 --> 00:57:47,170
+عشرين واحد تلاتين زائد الهدر اتنين و تلاتين طيب
+
+771
+00:57:47,170 --> 00:57:52,210
+نمسك التانية في عندنا اربعتاش و ستاش تلاتين زائد
+
+772
+00:57:52,210 --> 00:57:57,190
+الاتنين تعونها هدولة ثابتين هدولة هي ماقدرش اقول
+
+773
+00:57:57,190 --> 00:58:01,150
+ان في احتمالات اغير لأ ده مش احتمالات هي ثابت
+
+774
+00:58:01,150 --> 00:58:04,490
+ماحطهاش في الحسبة لإن هدول ثابتين هدول الهدر تعون
+
+775
+00:58:04,490 --> 00:58:08,370
+هدول المميزين لكل classبحركهم مش هدول، مابقدرش
+
+776
+00:58:08,370 --> 00:58:18,490
+نحركهم okay
+
+777
+00:58:18,490 --> 00:58:23,230
+ال inclusion و ال exclusion هنا لما يكون في عندكوا
+
+778
+00:58:23,230 --> 00:58:31,000
+ال task Aعبارة عن M ways اتفقنا ان ال task A عبارة
+
+779
+00:58:31,000 --> 00:58:36,660
+عن M ways ال M ways هدولة في منهم K ways يمكن يطلع
+
+780
+00:58:36,660 --> 00:58:39,700
+بسوء ال M احتمال يطلع يمكن يكون بسوء قيمة ال M
+
+781
+00:58:39,700 --> 00:58:44,720
+كلها بس في K ways of doing task 1 are also
+
+782
+00:58:44,720 --> 00:58:48,860
+simultaneously accomplish task 2 بمعنى ان في
+
+783
+00:58:48,860 --> 00:58:52,020
+intersection between A و B ال intersection هذا
+
+784
+00:58:52,020 --> 00:58:59,250
+ممكن يكون كل Aإيه إحنا عارفين أن عددهم M؟ فمعنى
+
+785
+00:58:59,250 --> 00:59:02,450
+ذلك ال K في الحالة هذه اللي هي ال intersection بين
+
+786
+00:59:02,450 --> 00:59:07,130
+الأثنين بتساوي M في الحالة هذه ممكن تساوي أو ممكن
+
+787
+00:59:07,130 --> 00:59:13,590
+تكون أقل أقل إذا كان في جزء intersection فهنا
+
+788
+00:59:13,590 --> 00:59:20,750
+هتكون K وهنا هتكون M minus K هتكون الجزء المتبقي
+
+789
+00:59:20,750 --> 00:59:27,010
+جزء المتبقي كويسطبعا فإذا هنا بدأنا نشتغل لإن في و
+
+790
+00:59:27,010 --> 00:59:36,330
+الله كام طرح لعمل عملة واحدة تسكتوه تسكتوه
+
+791
+00:59:36,330 --> 00:59:41,670
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+792
+00:59:41,670 --> 00:59:41,690
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+793
+00:59:41,690 --> 00:59:41,710
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+794
+00:59:41,710 --> 00:59:44,790
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+795
+00:59:44,790 --> 00:59:54,210
+تسكتوه تسكتوه تسكتوه تسو جمعتها مرة مع ال cardinal
+
+796
+00:59:54,210 --> 00:59:58,430
+التي ل B طب مانفعش اكررها مرتين هي موجودة صارت
+
+797
+00:59:58,430 --> 01:00:01,590
+معايا مرتين فانا محتاج ايش أسوي اطرحها طب انا
+
+798
+01:00:01,590 --> 01:00:04,290
+عارفها اشي بالظبط اه عارفها هاد ال intersection
+
+799
+01:00:04,290 --> 01:00:07,730
+معناته لو اقدرت تحسب ال intersection between A و B
+
+800
+01:00:07,730 --> 01:00:12,550
+بتطرحها منها من مجموحهم من مجموحهم في الحالة هاد
+
+801
+01:00:12,550 --> 01:00:18,350
+بيصير عندنا then number of ways to accomplishdo
+
+802
+01:00:18,350 --> 01:00:23,090
+either task one or task two هتكون M plus N minus K
+
+803
+01:00:23,090 --> 01:00:27,530
+ال overlap
+
+804
+01:00:27,530 --> 01:00:31,310
+بينهم ال overlap بينهم في الحالة هذا ال
+
+805
+01:00:31,310 --> 01:00:34,010
+cardinality ل A union B هتساوي ال cardinality ل A
+
+806
+01:00:34,010 --> 01:00:38,150
+plus cardinality B minus cardinality intersection
+
+807
+01:00:38,150 --> 01:00:42,710
+ال intersection هذا الكلام not disjoint في حالة ان
+
+808
+01:00:42,710 --> 01:00:45,070
+هي not disjoint بمعنى يوجد intersection between
+
+809
+01:00:45,070 --> 01:00:45,370
+them
+
+810
+01:00:51,650 --> 01:00:55,550
+ببساطة جدا a plus b و خلاص ال cardinality ل a plus
+
+811
+01:00:55,550 --> 01:01:00,590
+ال cardinality ل 11 ناخد شوية examples عليها عشان
+
+812
+01:01:00,590 --> 01:01:05,190
+تتضحى
+
+813
+01:01:05,190 --> 01:01:10,250
+example how many pet strings of length 4 either
+
+814
+01:01:10,250 --> 01:01:13,970
+start with one or end with double zero
+
+815
+01:01:20,200 --> 01:01:24,880
+عندكوا string عبارة عن four length، ال four length
+
+816
+01:01:24,880 --> 01:01:32,800
+هدولة جدّاش عددهم بشرط بشرط أنه either start one
+
+817
+01:01:32,800 --> 01:01:40,700
+إما بيبدأوا بواحد أو بينتهوا orفبناخد الحالة
+
+818
+01:01:40,700 --> 01:01:43,580
+الأولى للحالة والثانية للحالة وما دام or بيجب أن
+
+819
+01:01:43,580 --> 01:01:47,740
+نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب
+
+820
+01:01:47,740 --> 01:01:47,940
+أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع
+
+821
+01:01:47,940 --> 01:01:49,040
+بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن
+
+822
+01:01:49,040 --> 01:01:51,660
+أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع
+
+823
+01:01:51,660 --> 01:02:06,880
+بيجب أن نجمع بيجب أن نجمع بيجب
+
+824
+01:02:06,880 --> 01:02:07,220
+أن ن
+
+825
+01:02:12,240 --> 01:02:16,400
+جدّاش عدد الـ strains اللي ممكن نعمل ال generation
+
+826
+01:02:16,400 --> 01:02:23,600
+هنا 2 ضغور 2 سوى 4 طيب ال summation لساوة 12 لأ
+
+827
+01:02:23,600 --> 01:02:29,180
+لأنه يوجد حالة أنا جمعتها هنا وجمعتها هنا كيف
+
+828
+01:02:29,180 --> 01:02:34,240
+أحسبها ال intersection لأ لأ لأ لأ إيش نطرح يعني
+
+829
+01:02:34,240 --> 01:02:38,660
+هيطلع أربعة اعملوا ال intersection إيش ال
+
+830
+01:02:38,660 --> 01:02:44,370
+intersection إنه الإتنين تحققوا مع بعضبمعنى ان ال
+
+831
+01:02:44,370 --> 01:02:51,190
+one تحققه و ال zero تحققه اكم ways لتمثيل ال
+
+832
+01:02:51,190 --> 01:02:55,330
+sequence بها اتنين اما هنا تكون صفر او واحد فهنا
+
+833
+01:02:55,330 --> 01:03:00,790
+تساوي اتنين صار عندنا تمانية زائد اربع ناقص اتنين
+
+834
+01:03:00,790 --> 01:03:04,170
+ساوي
+
+835
+01:03:04,170 --> 01:03:09,730
+عشرة ففي الحالة دايما اشتغلوا كتالي بنحسب ال ways
+
+836
+01:03:09,730 --> 01:03:16,050
+to do the task onethe number of ways to do task
+
+837
+01:03:16,050 --> 01:03:22,910
+two ونطرح منهم ال number of ways to do both task
+
+838
+01:03:22,910 --> 01:03:27,330
+one and task two both number one and two الاتنين
+
+839
+01:03:27,330 --> 01:03:31,610
+بدون يكونوا متحققين مع بعض four check حدد يعملكم
+
+840
+01:03:31,610 --> 01:03:34,230
+من أربعة كل احتمالات اللي بتبدأ ب one
+
+841
+01:03:46,540 --> 01:03:47,940
+1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
+
+842
+01:03:52,580 --> 01:03:55,740
+في مشترك اتنين بينهم فإذا بدنا نشطبهم الاتنين
+
+843
+01:03:55,740 --> 01:04:02,900
+هدولة عددهم اتنين شطبناهم فعلا عشرة عشرة العدد
+
+844
+01:04:02,900 --> 01:04:09,540
+الحالات الممكنة عشرة عدد الحالات الممكنة خلاص okay
+
+845
+01:04:09,540 --> 01:04:13,380
+انا
+
+846
+01:04:13,380 --> 01:04:18,500
+والله الشباب كانوا خلصوا اكتر من هيكطيب بكفى هيك
+
+847
+01:04:18,500 --> 01:04:21,820
+مرة جاية بنحاول نشد في يوم دول أكتر يالا أعطيكوا
+
+848
+01:04:21,820 --> 01:04:22,840
+العافية وبركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f756428c650de53a45a5c8772c3fae63d22bb500
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3614, "start": 20.96, "end": 36.14, "text": "طيب بسم الله الرحمن الرحيم والصلاة والسلام علي أشرف الأنبياء والمسلمين سيدنا محمد وعليه عليه وصحبه أجمعين المرة اللي فاتت كنا تتكلمنا عن ال recursion و اليوم ان شاء الله بنكمل في نفس الموضوع بإذن الله تعالى", "tokens": [9566, 1829, 3555, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 25894, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 2304, 3794, 19528, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 20292, 3224, 47356, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 9122, 8315, 6055, 2655, 4117, 19528, 8315, 18871, 2423, 20560, 313, 4032, 45595, 20498, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 8978, 8717, 36178, 9673, 2407, 11242, 45367, 4724, 28814, 8848, 1863, 21984, 37279, 6027, 7578], "avg_logprob": -0.1688144379055377, "compression_ratio": 1.8078817733990147, "no_speech_prob": 3.933906555175781e-06, "words": [{"start": 20.96, "end": 21.32, "word": "طيب", "probability": 0.779052734375}, {"start": 21.32, "end": 21.62, "word": " بسم", "probability": 0.712646484375}, {"start": 21.62, "end": 21.74, "word": " الله", "probability": 0.95947265625}, {"start": 21.74, "end": 22.0, "word": " الرحمن", "probability": 0.96826171875}, {"start": 22.0, "end": 22.26, "word": " الرحيم", "probability": 0.9920247395833334}, {"start": 22.26, "end": 22.46, "word": " والصلاة", "probability": 0.8387451171875}, {"start": 22.46, "end": 22.8, "word": " والسلام", "probability": 0.9007161458333334}, {"start": 22.8, "end": 22.94, "word": " علي", "probability": 0.41943359375}, {"start": 22.94, "end": 23.14, "word": " أشرف", "probability": 0.9373372395833334}, {"start": 23.14, "end": 23.46, "word": " الأنبياء", "probability": 0.98291015625}, {"start": 23.46, "end": 23.82, "word": " والمسلمين", "probability": 0.793505859375}, {"start": 23.82, "end": 24.14, "word": " سيدنا", "probability": 0.8580729166666666}, {"start": 24.14, "end": 24.66, "word": " محمد", "probability": 0.9912109375}, {"start": 24.66, "end": 25.36, "word": " وعليه", "probability": 0.7509765625}, {"start": 25.36, "end": 25.48, "word": " عليه", "probability": 0.17529296875}, {"start": 25.48, "end": 25.84, "word": " وصحبه", "probability": 0.90380859375}, {"start": 25.84, "end": 26.74, "word": " أجمعين", "probability": 0.9115234375}, {"start": 26.74, "end": 27.56, "word": " المرة", "probability": 0.95849609375}, {"start": 27.56, "end": 27.68, "word": " اللي", "probability": 0.861083984375}, {"start": 27.68, "end": 27.92, "word": " فاتت", "probability": 0.8605143229166666}, {"start": 27.92, "end": 28.16, "word": " كنا", "probability": 0.9140625}, {"start": 28.16, "end": 28.94, "word": " تتكلمنا", "probability": 0.7149658203125}, {"start": 28.94, "end": 29.04, "word": " عن", "probability": 0.9892578125}, {"start": 29.04, "end": 29.1, "word": " ال", "probability": 0.966796875}, {"start": 29.1, "end": 29.6, "word": " recursion", "probability": 0.97265625}, {"start": 29.6, "end": 30.22, "word": " و", "probability": 0.7685546875}, {"start": 30.22, "end": 31.96, "word": " اليوم", "probability": 0.87158203125}, {"start": 31.96, "end": 32.08, "word": " ان", "probability": 0.5849609375}, {"start": 32.08, "end": 32.26, "word": " شاء", "probability": 0.976806640625}, {"start": 32.26, "end": 32.34, "word": " الله", "probability": 0.962890625}, {"start": 32.34, "end": 33.16, "word": " بنكمل", "probability": 0.829345703125}, {"start": 33.16, "end": 33.6, "word": " في", "probability": 0.9111328125}, {"start": 33.6, "end": 33.98, "word": " نفس", "probability": 0.99755859375}, {"start": 33.98, "end": 34.58, "word": " الموضوع", "probability": 0.9990234375}, {"start": 34.58, "end": 35.56, "word": " بإذن", "probability": 0.9820556640625}, {"start": 35.56, "end": 35.7, "word": " الله", "probability": 0.93408203125}, {"start": 35.7, "end": 36.14, "word": " تعالى", "probability": 0.9894205729166666}], "temperature": 1.0}, {"id": 2, "seek": 5223, "start": 37.63, "end": 52.23, "text": "كنا اتكلمنا عن irrigation لأ as a function اتكلمنا عن irrigation as a set و اتكلمنا عنها as a string لو متذكرين اخر ما اتكلمنا عن ال lambda و الشغل", "tokens": [4117, 8315, 1975, 2655, 4117, 19528, 8315, 18871, 31753, 5296, 10721, 382, 257, 2445, 1975, 2655, 4117, 19528, 8315, 18871, 31753, 382, 257, 992, 4032, 1975, 2655, 4117, 19528, 8315, 18871, 11296, 382, 257, 6798, 45164, 44650, 8848, 37983, 9957, 1975, 34740, 19446, 1975, 2655, 4117, 19528, 8315, 18871, 2423, 13607, 4032, 25124, 17082, 1211], "avg_logprob": -0.17089844282184327, "compression_ratio": 1.6640625, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 37.63, "end": 38.33, "word": "كنا", "probability": 0.80029296875}, {"start": 38.33, "end": 38.77, "word": " اتكلمنا", "probability": 0.9123046875}, {"start": 38.77, "end": 38.97, "word": " عن", "probability": 0.99169921875}, {"start": 38.97, "end": 39.47, "word": " irrigation", "probability": 0.17578125}, {"start": 39.47, "end": 40.37, "word": " لأ", "probability": 0.734130859375}, {"start": 40.37, "end": 40.61, "word": " as", "probability": 0.9072265625}, {"start": 40.61, "end": 40.71, "word": " a", "probability": 0.986328125}, {"start": 40.71, "end": 41.13, "word": " function", "probability": 0.9765625}, {"start": 41.13, "end": 41.69, "word": " اتكلمنا", "probability": 0.85322265625}, {"start": 41.69, "end": 41.77, "word": " عن", "probability": 0.9638671875}, {"start": 41.77, "end": 42.05, "word": " irrigation", "probability": 0.92626953125}, {"start": 42.05, "end": 42.35, "word": " as", "probability": 0.98828125}, {"start": 42.35, "end": 42.65, "word": " a", "probability": 0.98486328125}, {"start": 42.65, "end": 43.09, "word": " set", "probability": 0.9833984375}, {"start": 43.09, "end": 43.45, "word": " و", "probability": 0.82373046875}, {"start": 43.45, "end": 43.89, "word": " اتكلمنا", "probability": 0.96123046875}, {"start": 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114.4, "word": " إنتجر", "probability": 0.6593017578125}, {"start": 114.4, "end": 115.0, "word": " أو", "probability": 0.880859375}, {"start": 115.0, "end": 116.16, "word": " عدد", "probability": 0.4912516276041667}, {"start": 116.16, "end": 116.5, "word": " طبيعي،", "probability": 0.7787109375}, {"start": 116.5, "end": 116.72, "word": " عدد", "probability": 0.9484049479166666}, {"start": 116.72, "end": 118.12, "word": " طبيعي،", "probability": 0.87041015625}, {"start": 118.12, "end": 119.4, "word": " عدد", "probability": 0.4959716796875}, {"start": 119.4, "end": 119.64, "word": " طبيعي،", "probability": 0.888671875}, {"start": 119.64, "end": 119.7, "word": " عدد", "probability": 0.83837890625}, {"start": 119.7, "end": 121.04, "word": " طبيعي،", "probability": 0.91767578125}, {"start": 121.04, "end": 121.64, "word": " عدد", "probability": 0.95166015625}, {"start": 121.64, "end": 121.64, "word": " طبيعي،", "probability": 0.95146484375}, {"start": 121.64, "end": 121.72, "word": " عدد", "probability": 0.9723307291666666}, {"start": 121.72, "end": 121.72, "word": " طبيعي،", "probability": 0.9671875}, {"start": 121.72, "end": 121.86, "word": " عدد", "probability": 0.9775390625}, {"start": 121.86, "end": 122.34, "word": " طبيعي،", "probability": 0.97265625}, {"start": 122.34, "end": 122.34, "word": " عدد", "probability": 0.98095703125}, {"start": 122.34, "end": 122.34, "word": " طبيعي،", "probability": 0.97412109375}, {"start": 122.34, "end": 122.34, "word": " عدد", "probability": 0.9840494791666666}, {"start": 122.34, "end": 122.76, "word": " طبيعي،", "probability": 0.9763671875}, {"start": 122.76, "end": 123.16, "word": " عدد", "probability": 0.9869791666666666}, {"start": 123.16, "end": 123.16, "word": " طبيع", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 6, "seek": 15255, "start": 123.49, "end": 152.55, "text": "natural number أقل قيمة فيها zero يعني معناته أن ال zero belong to natural number فممكن تكون zero والله إذا كان zero return one و بنوقف بنوقف 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الأكبر", "tokens": [2304, 2655, 8848, 37983, 9957, 3224, 22807, 1975, 8848, 37983, 8315, 11296, 22807, 9122, 45865, 3794, 6156, 2304, 3615, 1863, 7578, 29910, 23275, 16472, 8978, 6225, 42213, 10632, 6055, 37983, 9640, 34105, 32767, 9957, 5296, 6636, 2689, 25974, 284, 6916, 13672, 7578, 44945, 25957, 1211, 11296, 4724, 995, 14851, 9778, 3215, 10943, 2423, 31111, 1975, 2407, 2423, 1072, 5296, 7039, 5551, 9381, 17082, 2288, 9154, 16095, 23032, 1829, 3555, 9122, 33911, 8717, 25957, 1211, 2423, 28820, 10943, 23758, 22807, 5296, 5016, 19913, 2407, 2423, 10747, 6636, 2689, 25974, 284, 257, 11, 65, 22957, 281, 3303, 1230, 1975, 4032, 272, 47525, 8315, 8717, 7435, 1829, 3555, 6636, 2689, 25974, 284, 1975, 2407, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 4117, 26890], "avg_logprob": -0.21849385233687574, "compression_ratio": 1.695970695970696, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 289.62, "end": 290.66, "word": "متذكرينه؟", "probability": 0.8367047991071429}, 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"probability": 0.963134765625}, {"start": 309.42, "end": 309.98, "word": " a", "probability": 0.48974609375}, {"start": 309.98, "end": 310.36, "word": ",b", "probability": 0.5213623046875}, {"start": 310.36, "end": 310.7, "word": " belonging", "probability": 0.62890625}, {"start": 310.7, "end": 310.88, "word": " to", "probability": 0.97998046875}, {"start": 310.88, "end": 311.16, "word": " natural", "probability": 0.634765625}, {"start": 311.16, "end": 311.48, "word": " number", "probability": 0.94189453125}, {"start": 311.48, "end": 312.38, "word": " ا", "probability": 0.40185546875}, {"start": 312.38, "end": 312.58, "word": " و", "probability": 0.389404296875}, {"start": 312.58, "end": 312.78, "word": " b", "probability": 0.5751953125}, {"start": 312.78, "end": 313.04, "word": " بدنا", "probability": 0.57806396484375}, {"start": 313.04, "end": 313.24, "word": " نجيب", "probability": 0.995361328125}, {"start": 313.24, "end": 314.08, "word": " greatest", "probability": 0.72412109375}, {"start": 314.08, "end": 314.4, "word": " common", "probability": 0.9140625}, {"start": 314.4, "end": 314.96, "word": " divisor", "probability": 0.9677734375}, {"start": 314.96, "end": 315.62, "word": " او", "probability": 0.811279296875}, {"start": 315.62, "end": 316.1, "word": " العامل", "probability": 0.9124348958333334}, {"start": 316.1, "end": 316.5, "word": " المشترك", "probability": 0.98388671875}, {"start": 316.5, "end": 316.92, "word": " الأكبر", "probability": 0.8951822916666666}], "temperature": 1.0}, {"id": 14, "seek": 34700, "start": 317.94, "end": 347.0, "text": "we belong to natural number if a is equal to zero و لاحظوا هنا عشان تظبط العملية احنا مرتبينها بحيث انه ال element الأول هو الأصغر هو الأصغر عشان ما نضطرش نعمل operation إبافية في النص اللي هي عملية ال swap تذكرتوها؟ لأ مش مضطرين نعمل swap كل اللي بعمله من الأساس برتبه على أساس انه في الأول هو الأصغر و خلاص عشان ال recursion يكون أسرع أو يكون أسهل okay", "tokens": [826, 5784, 281, 3303, 1230, 498, 257, 307, 2681, 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0.696533203125}, {"start": 335.98, "end": 336.66, "word": " اللي", "probability": 0.91064453125}, {"start": 336.66, "end": 336.76, "word": " هي", "probability": 0.78369140625}, {"start": 336.76, "end": 337.06, "word": " عملية", "probability": 0.784912109375}, {"start": 337.06, "end": 337.2, "word": " ال", "probability": 0.72705078125}, {"start": 337.2, "end": 337.58, "word": " swap", "probability": 0.900390625}, {"start": 337.58, "end": 339.08, "word": " تذكرتوها؟", "probability": 0.7732631138392857}, {"start": 339.08, "end": 339.26, "word": " لأ", "probability": 0.954833984375}, {"start": 339.26, "end": 339.4, "word": " مش", "probability": 0.7548828125}, {"start": 339.4, "end": 339.72, "word": " مضطرين", "probability": 0.880078125}, {"start": 339.72, "end": 339.94, "word": " نعمل", "probability": 0.97705078125}, {"start": 339.94, "end": 340.14, "word": " swap", "probability": 0.93798828125}, {"start": 340.14, "end": 340.32, "word": " كل", "probability": 0.84619140625}, {"start": 340.32, "end": 340.42, "word": " اللي", "probability": 0.951171875}, {"start": 340.42, "end": 340.66, "word": " بعمله", "probability": 0.9646809895833334}, {"start": 340.66, "end": 340.82, "word": " من", "probability": 0.62548828125}, {"start": 340.82, "end": 341.14, "word": " الأساس", "probability": 0.9820963541666666}, {"start": 341.14, "end": 341.56, "word": " برتبه", "probability": 0.899169921875}, {"start": 341.56, "end": 341.66, "word": " على", "probability": 0.76171875}, {"start": 341.66, "end": 341.82, "word": " أساس", "probability": 0.90869140625}, {"start": 341.82, "end": 342.02, "word": " انه", "probability": 0.7030029296875}, {"start": 342.02, "end": 342.08, "word": " في", "probability": 0.7919921875}, {"start": 342.08, "end": 342.28, "word": " الأول", "probability": 0.978759765625}, {"start": 342.28, "end": 342.46, "word": " هو", "probability": 0.99072265625}, {"start": 342.46, "end": 342.78, "word": " الأصغر", "probability": 0.993408203125}, {"start": 342.78, "end": 342.86, "word": " و", "probability": 0.9072265625}, {"start": 342.86, "end": 343.1, "word": " خلاص", "probability": 0.9212239583333334}, {"start": 343.1, "end": 343.88, "word": " عشان", "probability": 0.9910481770833334}, {"start": 343.88, "end": 344.18, "word": " ال", "probability": 0.98388671875}, {"start": 344.18, "end": 344.94, "word": " recursion", "probability": 0.918212890625}, {"start": 344.94, "end": 345.4, "word": " يكون", "probability": 0.821044921875}, {"start": 345.4, "end": 345.78, "word": " أسرع", "probability": 0.981201171875}, {"start": 345.78, "end": 345.9, "word": " أو", "probability": 0.49072265625}, {"start": 345.9, "end": 346.04, "word": " يكون", "probability": 0.905517578125}, {"start": 346.04, "end": 346.4, "word": " أسهل", "probability": 0.98876953125}, {"start": 346.4, "end": 347.0, "word": " okay", "probability": 0.74853515625}], "temperature": 1.0}, {"id": 15, "seek": 36775, "start": 347.99, "end": 367.75, "text": "A وB فلو اذا A equal to 0 then return B ارجع القيمة B فلسنا طيب otherwise لأ return لاحظوا greatest common divisor بي مودلر او mod A فواضح ان هذا الterm الصغير هيأتي في الأول فعلا A", "tokens": [32, 4032, 33, 6156, 1211, 2407, 1975, 15730, 316, 2681, 281, 1958, 550, 2736, 363, 1975, 47341, 3615, 25062, 32640, 3660, 363, 6156, 1211, 3794, 8315, 23032, 1829, 3555, 5911, 5296, 10721, 2736, 20193, 5016, 19913, 14407, 6636, 2689, 25974, 284, 4724, 1829, 3714, 23328, 1211, 2288, 1975, 2407, 1072, 316, 6156, 2407, 46958, 5016, 16472, 23758, 2423, 7039, 31767, 17082, 13546, 39896, 10721, 31371, 8978, 16247, 12610, 6156, 3615, 15040, 316], "avg_logprob": -0.4456335518458118, "compression_ratio": 1.317948717948718, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 347.99, "end": 348.43, "word": "A", "probability": 0.1402587890625}, {"start": 348.43, "end": 349.47, "word": " وB", "probability": 0.4296875}, {"start": 349.47, "end": 350.07, "word": " فلو", "probability": 0.5296223958333334}, {"start": 350.07, "end": 350.31, "word": " اذا", "probability": 0.704833984375}, {"start": 350.31, "end": 350.91, "word": " A", "probability": 0.3828125}, {"start": 350.91, "end": 351.37, "word": " equal", "probability": 0.08978271484375}, {"start": 351.37, "end": 351.79, "word": " to", "probability": 0.93017578125}, {"start": 351.79, "end": 352.19, "word": " 0", "probability": 0.5458984375}, {"start": 352.19, "end": 352.79, "word": " then", "probability": 0.51953125}, {"start": 352.79, "end": 353.37, "word": " return", "probability": 0.8203125}, {"start": 353.37, "end": 353.69, "word": " B", "probability": 0.92626953125}, {"start": 353.69, "end": 354.29, "word": " ارجع", "probability": 0.6739095052083334}, {"start": 354.29, "end": 354.67, "word": " القيمة", "probability": 0.6997477213541666}, {"start": 354.67, "end": 354.79, "word": " B", "probability": 0.5205078125}, {"start": 354.79, "end": 355.31, "word": " فلسنا", "probability": 0.588104248046875}, {"start": 355.31, "end": 356.01, "word": " طيب", "probability": 0.90576171875}, {"start": 356.01, "end": 356.63, "word": " otherwise", "probability": 0.70458984375}, {"start": 356.63, "end": 356.95, "word": " لأ", "probability": 0.88623046875}, {"start": 356.95, "end": 357.39, "word": " return", "probability": 0.90380859375}, {"start": 357.39, "end": 358.17, "word": " لاحظوا", "probability": 0.7738037109375}, {"start": 358.17, "end": 358.79, "word": " greatest", "probability": 0.890625}, {"start": 358.79, "end": 359.13, "word": " common", "probability": 0.9580078125}, {"start": 359.13, "end": 359.87, "word": " divisor", "probability": 0.976806640625}, {"start": 359.87, "end": 361.53, "word": " بي", "probability": 0.4482421875}, {"start": 361.53, "end": 362.57, "word": " مودلر", "probability": 0.5994873046875}, {"start": 362.57, "end": 362.81, "word": " او", "probability": 0.869140625}, {"start": 362.81, "end": 363.23, "word": " mod", "probability": 0.423095703125}, {"start": 363.23, "end": 363.73, "word": " A", "probability": 0.69287109375}, {"start": 363.73, "end": 364.73, "word": " فواضح", "probability": 0.968505859375}, {"start": 364.73, "end": 364.85, "word": " ان", "probability": 0.875}, {"start": 364.85, "end": 365.05, "word": " هذا", "probability": 0.74658203125}, {"start": 365.05, "end": 365.31, "word": " الterm", "probability": 0.4443359375}, {"start": 365.31, "end": 365.79, "word": " الصغير", "probability": 0.9597981770833334}, {"start": 365.79, "end": 366.19, "word": " هيأتي", "probability": 0.4126790364583333}, {"start": 366.19, "end": 366.29, "word": " في", "probability": 0.91943359375}, {"start": 366.29, "end": 366.61, "word": " الأول", "probability": 0.8134765625}, {"start": 366.61, "end": 366.97, "word": " فعلا", "probability": 0.8468424479166666}, {"start": 366.97, "end": 367.75, "word": " A", "probability": 0.381591796875}], "temperature": 1.0}, {"id": 16, "seek": 39653, "start": 368.89, "end": 396.53, "text": "كل اللي حنصير أنه هعيد التكرار نفسه بس ال B هذه أصبحت هي مكان ال A مكانها ال A و ال A القيمة الأصغر صار مكانها B mod A ال B mod A والله إذا كان ال B mod A equal to 0 ارجع للقيمة ال B اللي أهل وجد اتعرفت بيه اللي هي أصلا كانت مين؟ A كانت إيه؟ A لأ لا تساوي 0", "tokens": [28820, 13672, 1829, 11331, 1863, 9381, 13546, 14739, 3224, 8032, 3615, 25708, 16712, 37983, 9640, 8717, 36178, 3224, 4724, 3794, 2423, 363, 29538, 5551, 9381, 3555, 33753, 39896, 3714, 41361, 2423, 316, 3714, 41361, 11296, 2423, 316, 4032, 2423, 316, 25062, 32640, 3660, 16247, 9381, 17082, 2288, 20328, 9640, 3714, 41361, 11296, 363, 1072, 316, 2423, 363, 1072, 316, 16070, 43761, 11933, 15730, 25961, 2423, 363, 1072, 316, 2681, 281, 1958, 1975, 47341, 3615, 24976, 4587, 32640, 3660, 2423, 363, 13672, 1829, 5551, 3224, 1211, 4032, 7435, 3215, 1975, 2655, 3615, 28480, 2655, 4724, 1829, 3224, 13672, 1829, 39896, 5551, 9381, 15040, 25961, 2655, 3714, 9957, 22807, 316, 25961, 2655, 11933, 1829, 3224, 22807, 316, 5296, 10721, 20193, 6055, 3794, 995, 45865, 1958], "avg_logprob": -0.23349294258702186, "compression_ratio": 1.8959276018099547, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 368.89, "end": 369.13, "word": "كل", "probability": 0.7958984375}, {"start": 369.13, "end": 369.23, "word": " اللي", "probability": 0.711669921875}, {"start": 369.23, "end": 369.69, "word": " حنصير", "probability": 0.82672119140625}, {"start": 369.69, "end": 370.13, "word": " أنه", "probability": 0.5814208984375}, {"start": 370.13, "end": 370.71, "word": " هعيد", "probability": 0.8033854166666666}, {"start": 370.71, "end": 371.15, "word": " التكرار", "probability": 0.76953125}, {"start": 371.15, "end": 371.69, "word": " نفسه", "probability": 0.9918619791666666}, {"start": 371.69, "end": 372.35, "word": " بس", "probability": 0.906494140625}, {"start": 372.35, "end": 373.33, "word": " ال", "probability": 0.9501953125}, {"start": 373.33, "end": 373.49, "word": " B", "probability": 0.357177734375}, {"start": 373.49, "end": 373.85, "word": " هذه", "probability": 0.47119140625}, {"start": 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الأصغر", "probability": 0.9873046875}, {"start": 378.19, "end": 378.43, "word": " صار", "probability": 0.828125}, {"start": 378.43, "end": 379.01, "word": " مكانها", "probability": 0.9908854166666666}, {"start": 379.01, "end": 380.15, "word": " B", "probability": 0.806640625}, {"start": 380.15, "end": 380.93, "word": " mod", "probability": 0.5244140625}, {"start": 380.93, "end": 383.01, "word": " A", "probability": 0.7763671875}, {"start": 383.01, "end": 384.73, "word": " ال", "probability": 0.5927734375}, {"start": 384.73, "end": 384.89, "word": " B", "probability": 0.9267578125}, {"start": 384.89, "end": 385.17, "word": " mod", "probability": 0.962890625}, {"start": 385.17, "end": 385.55, "word": " A", "probability": 0.974609375}, {"start": 385.55, "end": 386.11, "word": " والله", "probability": 0.845458984375}, {"start": 386.11, "end": 386.27, "word": " إذا", "probability": 0.937744140625}, {"start": 386.27, "end": 386.49, "word": " كان", "probability": 0.982421875}, {"start": 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"probability": 0.8787434895833334}, {"start": 391.51, "end": 391.61, "word": " وجد", "probability": 0.468994140625}, {"start": 391.61, "end": 392.15, "word": " اتعرفت", "probability": 0.93857421875}, {"start": 392.15, "end": 392.31, "word": " بيه", "probability": 0.8958333333333334}, {"start": 392.31, "end": 392.39, "word": " اللي", "probability": 0.93701171875}, {"start": 392.39, "end": 392.55, "word": " هي", "probability": 0.69580078125}, {"start": 392.55, "end": 392.83, "word": " أصلا", "probability": 0.8826497395833334}, {"start": 392.83, "end": 393.19, "word": " كانت", "probability": 0.900390625}, {"start": 393.19, "end": 393.53, "word": " مين؟", "probability": 0.5214029947916666}, {"start": 393.53, "end": 393.71, "word": " A", "probability": 0.7841796875}, {"start": 393.71, "end": 394.43, "word": " كانت", "probability": 0.8427734375}, {"start": 394.43, "end": 394.91, "word": " إيه؟", "probability": 0.72802734375}, {"start": 394.91, "end": 395.15, "word": " A", "probability": 0.9541015625}, {"start": 395.15, "end": 395.69, "word": " لأ", "probability": 0.87255859375}, {"start": 395.69, "end": 395.83, "word": " لا", "probability": 0.43359375}, {"start": 395.83, "end": 396.23, "word": " تساوي", "probability": 0.873046875}, {"start": 396.23, "end": 396.53, "word": " 0", "probability": 0.55126953125}], "temperature": 1.0}, {"id": 17, "seek": 42254, "start": 398.52, "end": 422.54, "text": "الناتج اللى هو a لجديدة و b لجديدة برضه هنرجع نعمل كمان modular كمان مرة فهذه عملية التكرار اللى أخدتها سابقا لما كنتوا جيبوا ال greatest common divisor باستخدام ال modular operation باستخدام ال modular operation okay طبعا في حالة زى هذه واضح أن هنا ال recursive algorithm كتير أبسط", "tokens": [6027, 8315, 2655, 7435, 13672, 7578, 31439, 257, 5296, 7435, 16254, 41891, 4032, 272, 5296, 7435, 16254, 41891, 4724, 43042, 3224, 8032, 1863, 47341, 3615, 8717, 25957, 1211, 9122, 2304, 7649, 31111, 9122, 2304, 7649, 3714, 25720, 6156, 3224, 24192, 6225, 42213, 10632, 16712, 37983, 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التكرار", "probability": 0.9440104166666666}, {"start": 407.1, "end": 407.66, "word": " اللى", "probability": 0.985107421875}, {"start": 407.66, "end": 408.58, "word": " أخدتها", "probability": 0.78369140625}, {"start": 408.58, "end": 409.14, "word": " سابقا", "probability": 0.9613037109375}, {"start": 409.14, "end": 409.7, "word": " لما", "probability": 0.83203125}, {"start": 409.7, "end": 410.08, "word": " كنتوا", "probability": 0.95947265625}, {"start": 410.08, "end": 410.34, "word": " جيبوا", "probability": 0.9041748046875}, {"start": 410.34, "end": 410.44, "word": " ال", "probability": 0.728515625}, {"start": 410.44, "end": 410.66, "word": " greatest", "probability": 0.81494140625}, {"start": 410.66, "end": 410.9, "word": " common", "probability": 0.93505859375}, {"start": 410.9, "end": 411.34, "word": " divisor", "probability": 0.98193359375}, {"start": 411.34, "end": 411.98, "word": " باستخدام", "probability": 0.9761555989583334}, {"start": 411.98, "end": 413.02, "word": " ال", "probability": 0.91015625}, {"start": 413.02, "end": 413.26, "word": " modular", "probability": 0.939453125}, {"start": 413.26, "end": 413.86, "word": " operation", "probability": 0.908203125}, {"start": 413.86, "end": 414.46, "word": " باستخدام", "probability": 0.887939453125}, {"start": 414.46, "end": 414.56, "word": " ال", "probability": 0.94970703125}, {"start": 414.56, "end": 414.88, "word": " modular", "probability": 0.98291015625}, {"start": 414.88, "end": 415.72, "word": " operation", "probability": 0.958984375}, {"start": 415.72, "end": 417.0, "word": " okay", "probability": 0.357421875}, {"start": 417.0, "end": 417.72, "word": " طبعا", "probability": 0.989501953125}, {"start": 417.72, "end": 417.84, "word": " في", "probability": 0.6533203125}, {"start": 417.84, "end": 418.08, "word": " حالة", "probability": 0.9925130208333334}, {"start": 418.08, "end": 418.22, "word": " زى", "probability": 0.900146484375}, {"start": 418.22, "end": 418.52, "word": " هذه", "probability": 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635.87, "text": "X ما زالت هي داخل ال arguments بتاعتنا، فإذا هذه برضه موضوع من الموضوعات اللي هي ال X، إيش ال item اللي بتكون بدنا ندور عليه؟ فال item تبعنا item to be found اللي بدنا ندور عليه، اللي هي نوجده، okay عرفنا ال procedure بتاعتنا أو عرفنا", "tokens": [55, 19446, 30767, 6027, 2655, 39896, 11778, 47283, 1211, 2423, 12869, 39894, 995, 34268, 8315, 12399, 6156, 28814, 15730, 29538, 4724, 43042, 3224, 3714, 2407, 11242, 45367, 9154, 9673, 2407, 11242, 45367, 9307, 13672, 1829, 39896, 2423, 1783, 12399, 11933, 1829, 8592, 2423, 3174, 13672, 1829, 39894, 30544, 47525, 8315, 8717, 3215, 13063, 47356, 22807, 6156, 6027, 3174, 6055, 3555, 3615, 8315, 3174, 281, 312, 1352, 13672, 1829, 47525, 8315, 8717, 3215, 13063, 47356, 12399, 13672, 1829, 39896, 8717, 29245, 3215, 3224, 12399, 1392, 6225, 28480, 8315, 2423, 10747, 39894, 995, 34268, 8315, 34051, 6225, 28480, 8315], "avg_logprob": -0.2627551029531323, "compression_ratio": 1.7453703703703705, "no_speech_prob": 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algorithm تبعنا المطلوب طبعا منه عارفين أن الأقواص هذه معناها مجرد comments هذه ال comments مش من داخل أو مش من جزء ال algorithm نفسه find X in series A at a location أكبر من أو يساوي I و أقل من J فانا محددها والله إذا كان بتكون دوره في ال series كله عملوها من صفرته N", "tokens": [6027, 39184, 12869, 6055, 3555, 34268, 2423, 9284, 6055, 3555, 3615, 8315, 9673, 9566, 1211, 37746, 23032, 3555, 3615, 995, 9154, 3224, 6225, 9640, 5172, 9957, 14739, 16247, 4587, 14407, 9381, 29538, 20449, 8315, 11296, 3714, 7435, 2288, 3215, 3053, 29538, 2423, 3053, 37893, 9154, 11778, 47283, 1211, 34051, 37893, 9154, 10874, 11622, 38207, 2423, 9284, 8717, 36178, 3224, 915, 1783, 294, 2638, 316, 412, 257, 4914, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 286, 4032, 5551, 4587, 1211, 9154, 508, 6156, 7649, 995, 3714, 24401, 3215, 11296, 16070, 43761, 11933, 15730, 25961, 39894, 30544, 11778, 13063, 3224, 8978, 2423, 2638, 28242, 3224, 6225, 42213, 2407, 11296, 9154, 20328, 5172, 43500, 3224, 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498, 257, 286, 5551, 12610, 4478], "avg_logprob": -0.2823222963248982, "compression_ratio": 1.651063829787234, "no_speech_prob": 0.0, "words": [{"start": 658.53, "end": 658.73, "word": "إذا", "probability": 0.79638671875}, {"start": 658.73, "end": 659.15, "word": " محتاجين", "probability": 0.9625244140625}, {"start": 659.15, "end": 659.53, "word": " كل", "probability": 0.91162109375}, {"start": 659.53, "end": 659.99, "word": " ال", "probability": 0.86669921875}, {"start": 659.99, "end": 660.21, "word": " series", "probability": 0.88330078125}, {"start": 660.21, "end": 660.63, "word": " تدوروا", "probability": 0.90478515625}, {"start": 660.63, "end": 660.97, "word": " فيها", "probability": 0.9765625}, {"start": 660.97, "end": 662.19, "word": " فهنا", "probability": 0.7477213541666666}, {"start": 662.19, "end": 662.69, "word": " بتبدأ", "probability": 0.8782552083333334}, {"start": 662.69, "end": 663.09, "word": " من", "probability": 0.98291015625}, {"start": 663.09, "end": 664.07, "word": " واحد", "probability": 0.74072265625}, {"start": 664.07, "end": 664.55, "word": " من", "probability": 0.8037109375}, {"start": 664.55, "end": 665.01, "word": " أول", "probability": 0.93896484375}, {"start": 665.01, "end": 665.71, "word": " location", "probability": 0.970703125}, {"start": 665.71, "end": 666.67, "word": " تقاش", "probability": 0.5562540690104166}, {"start": 666.67, "end": 667.13, "word": " J", "probability": 0.277587890625}, {"start": 667.13, "end": 667.65, "word": " حتكون", "probability": 0.5574544270833334}, {"start": 667.65, "end": 667.77, "word": " اللي", "probability": 0.94482421875}, {"start": 667.77, "end": 667.87, "word": " هي", "probability": 0.75146484375}, {"start": 667.87, "end": 668.01, "word": " ال", "probability": 0.6318359375}, {"start": 668.01, "end": 668.19, "word": " N", "probability": 0.60986328125}, {"start": 668.19, "end": 668.69, "word": " فانتوا", "probability": 0.851318359375}, {"start": 668.69, "end": 669.01, "word": " بتاخدوا", "probability": 0.94482421875}, {"start": 669.01, "end": 669.25, "word": " كل", "probability": 0.974609375}, {"start": 669.25, "end": 669.37, "word": " ال", "probability": 0.9736328125}, {"start": 669.37, "end": 669.57, "word": " series", "probability": 0.95654296875}, {"start": 669.57, "end": 670.01, "word": " بتاعتكم", "probability": 0.708740234375}, {"start": 670.01, "end": 671.11, "word": " هنا", "probability": 0.90625}, {"start": 671.11, "end": 671.71, "word": " in", "probability": 0.88525390625}, {"start": 671.71, "end": 672.31, "word": " general", "probability": 0.912109375}, {"start": 672.31, "end": 672.85, "word": " هنقول", "probability": 0.8414713541666666}, {"start": 672.85, "end": 673.15, "word": " من", "probability": 0.9755859375}, {"start": 673.15, "end": 673.47, "word": " I", "probability": 0.95751953125}, {"start": 673.47, "end": 673.85, "word": " to", "probability": 0.7373046875}, {"start": 673.85, "end": 674.45, "word": " J", "probability": 0.41259765625}, {"start": 674.45, "end": 674.75, "word": " و", "probability": 0.2188720703125}, {"start": 674.75, "end": 674.95, "word": " بعدين", "probability": 0.84912109375}, {"start": 674.95, "end": 675.33, "word": " بتخطوها", "probability": 0.82509765625}, {"start": 675.33, "end": 675.41, "word": " زي", "probability": 0.7305908203125}, {"start": 675.41, "end": 675.51, "word": " ما", "probability": 0.9580078125}, {"start": 675.51, "end": 675.79, "word": " بدكم", "probability": 0.7568359375}, {"start": 675.79, "end": 676.47, "word": " حسب", "probability": 0.94873046875}, {"start": 676.47, "end": 676.65, "word": " إيش", "probability": 0.7203776041666666}, {"start": 676.65, "end": 676.77, "word": " اللي", "probability": 0.971435546875}, {"start": 676.77, "end": 676.93, "word": " بيكون", "probability": 0.59521484375}, {"start": 676.93, "end": 677.37, "word": " مطلوب", "probability": 0.779296875}, {"start": 677.37, "end": 678.43, "word": " منكم", "probability": 0.937744140625}, {"start": 678.43, "end": 678.87, "word": " okay", "probability": 0.340087890625}, {"start": 678.87, "end": 679.93, "word": " if", "probability": 0.53173828125}, {"start": 679.93, "end": 681.11, "word": " a", "probability": 0.37353515625}, {"start": 681.11, "end": 681.63, "word": " I", "probability": 0.51171875}, {"start": 681.63, "end": 682.15, "word": " أول", "probability": 0.9033203125}, {"start": 682.15, "end": 682.47, "word": " element", "probability": 0.958984375}], "temperature": 1.0}, {"id": 30, "seek": 71036, "start": 683.52, "end": 710.36, "text": "فإذا كان بدء من واحد بحط a1 إذا كان الـ a1 أول واحد أو لا هنا بحطه i عسى إنه يبقى variable لل subroutines اللي جاية للsubroutines اللي هتجينا لجدام فai equal to إيش to x if equal to x return i خلاص إذا صدفت إنه فعلا أول عند ال element i هذا ال element الأخير j", "tokens": [5172, 28814, 15730, 25961, 47525, 38207, 9154, 36764, 24401, 4724, 5016, 9566, 257, 16, 11933, 15730, 25961, 2423, 39184, 257, 16, 5551, 12610, 36764, 24401, 34051, 20193, 34105, 4724, 5016, 9566, 3224, 741, 6225, 3794, 7578, 36145, 3224, 7251, 3555, 4587, 7578, 7006, 24976, 1422, 81, 346, 1652, 13672, 1829, 10874, 995, 10632, 24976, 30131, 81, 346, 1652, 13672, 1829, 8032, 2655, 7435, 1829, 8315, 5296, 7435, 3215, 10943, 6156, 1301, 2681, 281, 11933, 1829, 8592, 281, 2031, 498, 2681, 281, 2031, 2736, 741, 16490, 1211, 33546, 11933, 15730, 20328, 3215, 5172, 2655, 36145, 3224, 6156, 3615, 15040, 5551, 12610, 43242, 2423, 4478, 741, 23758, 2423, 4478, 16247, 9778, 13546, 361], "avg_logprob": -0.29827008502823965, "compression_ratio": 1.6623376623376624, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 683.52, "end": 683.86, "word": "فإذا", "probability": 0.80224609375}, {"start": 683.86, "end": 684.04, "word": " كان", "probability": 0.970703125}, {"start": 684.04, "end": 684.26, "word": " بدء", "probability": 0.80517578125}, {"start": 684.26, "end": 684.36, "word": " من", "probability": 0.98876953125}, {"start": 684.36, "end": 684.64, "word": " واحد", "probability": 0.847900390625}, {"start": 684.64, "end": 684.94, "word": " بحط", "probability": 0.7332356770833334}, {"start": 684.94, "end": 685.64, "word": " a1", "probability": 0.4202880859375}, {"start": 685.64, "end": 685.94, "word": " إذا", "probability": 0.762939453125}, {"start": 685.94, "end": 686.12, "word": " كان", "probability": 0.96728515625}, {"start": 686.12, "end": 686.46, "word": " الـ", "probability": 0.26727294921875}, {"start": 686.46, "end": 686.78, "word": " a1", "probability": 0.7744140625}, {"start": 686.78, "end": 687.28, "word": " أول", "probability": 0.83203125}, {"start": 687.28, "end": 687.62, "word": " واحد", "probability": 0.98291015625}, {"start": 687.62, "end": 687.74, "word": " أو", "probability": 0.72509765625}, {"start": 687.74, "end": 687.9, "word": " لا", "probability": 0.64306640625}, {"start": 687.9, "end": 688.52, "word": " هنا", "probability": 0.8134765625}, {"start": 688.52, "end": 688.96, "word": " بحطه", "probability": 0.75262451171875}, {"start": 688.96, "end": 689.1, "word": " i", "probability": 0.50537109375}, {"start": 689.1, "end": 689.3, "word": " عسى", "probability": 0.4998372395833333}, {"start": 689.3, "end": 689.6, "word": " إنه", "probability": 0.69970703125}, {"start": 689.6, "end": 689.96, "word": " يبقى", "probability": 0.80718994140625}, {"start": 689.96, "end": 690.84, "word": " variable", "probability": 0.87548828125}, {"start": 690.84, "end": 691.98, "word": " لل", "probability": 0.716796875}, {"start": 691.98, "end": 693.16, "word": " subroutines", "probability": 0.71258544921875}, {"start": 693.16, "end": 693.32, "word": " اللي", "probability": 0.947021484375}, {"start": 693.32, "end": 693.66, "word": " جاية", "probability": 0.8912760416666666}, {"start": 693.66, "end": 694.48, "word": " للsubroutines", "probability": 0.84912109375}, {"start": 694.48, "end": 694.64, "word": " اللي", "probability": 0.979736328125}, {"start": 694.64, "end": 695.04, "word": " هتجينا", "probability": 0.74453125}, {"start": 695.04, "end": 695.48, "word": " لجدام", "probability": 0.62579345703125}, {"start": 695.48, "end": 696.32, "word": " فai", "probability": 0.6021728515625}, {"start": 696.32, "end": 697.0, "word": " equal", "probability": 0.2298583984375}, {"start": 697.0, "end": 697.26, "word": " to", "probability": 0.96435546875}, {"start": 697.26, "end": 697.54, "word": " إيش", "probability": 0.7344156901041666}, {"start": 697.54, "end": 697.84, "word": " to", "probability": 0.388427734375}, {"start": 697.84, "end": 698.16, "word": " x", "probability": 0.75830078125}, {"start": 698.16, "end": 698.7, "word": " if", "probability": 0.7724609375}, {"start": 698.7, "end": 699.68, "word": " equal", "probability": 0.86767578125}, {"start": 699.68, "end": 699.86, "word": " to", "probability": 0.982421875}, {"start": 699.86, "end": 700.18, "word": " x", "probability": 0.96435546875}, {"start": 700.18, "end": 700.72, "word": " return", "probability": 0.77685546875}, {"start": 700.72, "end": 701.04, "word": " i", "probability": 0.8642578125}, {"start": 701.04, "end": 701.36, "word": " خلاص", "probability": 0.9244791666666666}, {"start": 701.36, "end": 702.32, "word": " إذا", "probability": 0.942626953125}, {"start": 702.32, "end": 702.9, "word": " صدفت", "probability": 0.730712890625}, {"start": 702.9, "end": 703.1, "word": " إنه", "probability": 0.755859375}, {"start": 703.1, "end": 703.42, "word": " فعلا", "probability": 0.86181640625}, {"start": 703.42, "end": 704.02, "word": " أول", "probability": 0.9443359375}, {"start": 704.02, "end": 706.04, "word": " عند", "probability": 0.9482421875}, {"start": 706.04, "end": 706.16, "word": " ال", "probability": 0.9248046875}, {"start": 706.16, "end": 706.4, "word": " element", "probability": 0.8671875}, {"start": 706.4, "end": 706.88, "word": " i", "probability": 0.720703125}, {"start": 706.88, "end": 709.22, "word": " هذا", "probability": 0.30908203125}, {"start": 709.22, "end": 709.34, "word": " ال", "probability": 0.9619140625}, {"start": 709.34, "end": 709.52, "word": " element", "probability": 0.87109375}, {"start": 709.52, "end": 709.94, "word": " الأخير", "probability": 0.8902994791666666}, {"start": 709.94, "end": 710.36, "word": " j", "probability": 0.79248046875}], "temperature": 1.0}, {"id": 31, "seek": 72503, "start": 711.45, "end": 725.03, "text": "هنعمل مقارنة ل X مع A I ال element اللي موجود في ال location I هو نفسه بيسوي خلاص برجع كلمة I ان هو موجود و ال location تبعه I", "tokens": [3224, 1863, 25957, 1211, 3714, 4587, 9640, 1863, 3660, 5296, 1783, 20449, 316, 286, 2423, 4478, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 4914, 286, 31439, 8717, 36178, 3224, 4724, 1829, 3794, 45865, 16490, 1211, 33546, 4724, 47341, 3615, 9122, 19528, 3660, 286, 16472, 31439, 3714, 29245, 23328, 4032, 2423, 4914, 6055, 3555, 3615, 3224, 286], "avg_logprob": -0.33470395155120314, "compression_ratio": 1.39568345323741, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 711.45, "end": 711.93, "word": "هنعمل", "probability": 0.7962646484375}, {"start": 711.93, "end": 712.41, "word": " مقارنة", "probability": 0.9765625}, {"start": 712.41, "end": 712.55, "word": " ل", "probability": 0.869140625}, {"start": 712.55, "end": 712.93, "word": " X", "probability": 0.55810546875}, {"start": 712.93, "end": 713.49, "word": " مع", "probability": 0.84326171875}, {"start": 713.49, "end": 714.03, "word": " A", "probability": 0.09423828125}, {"start": 714.03, "end": 714.75, "word": " I", "probability": 0.486572265625}, {"start": 714.75, "end": 715.19, "word": " ال", "probability": 0.365234375}, {"start": 715.19, "end": 715.47, "word": " element", "probability": 0.626953125}, {"start": 715.47, "end": 715.67, "word": " اللي", "probability": 0.782470703125}, {"start": 715.67, "end": 715.95, "word": " موجود", "probability": 0.9820963541666666}, {"start": 715.95, "end": 716.05, "word": " في", "probability": 0.93505859375}, {"start": 716.05, "end": 716.11, "word": " ال", "probability": 0.7607421875}, {"start": 716.11, "end": 716.39, "word": " location", "probability": 0.97802734375}, {"start": 716.39, "end": 716.73, "word": " I", "probability": 0.8134765625}, {"start": 716.73, "end": 719.15, "word": " هو", "probability": 0.5595703125}, {"start": 719.15, "end": 719.49, "word": " نفسه", "probability": 0.9617513020833334}, {"start": 719.49, "end": 719.87, "word": " بيسوي", "probability": 0.754638671875}, {"start": 719.87, "end": 720.69, "word": " خلاص", "probability": 0.814208984375}, {"start": 720.69, "end": 721.23, "word": " برجع", "probability": 0.92529296875}, {"start": 721.23, "end": 721.61, "word": " كلمة", "probability": 0.6494547526041666}, {"start": 721.61, "end": 721.85, "word": " I", "probability": 0.98193359375}, {"start": 721.85, "end": 722.41, "word": " ان", "probability": 0.306884765625}, {"start": 722.41, "end": 722.57, "word": " هو", "probability": 0.69677734375}, {"start": 722.57, "end": 723.25, "word": " موجود", "probability": 0.8211263020833334}, {"start": 723.25, "end": 723.61, "word": " و", "probability": 0.7607421875}, {"start": 723.61, "end": 723.77, "word": " ال", "probability": 0.12457275390625}, {"start": 723.77, "end": 724.07, "word": " location", "probability": 0.9765625}, {"start": 724.07, "end": 724.49, "word": " تبعه", "probability": 0.820556640625}, {"start": 724.49, "end": 725.03, "word": " I", "probability": 0.89501953125}], "temperature": 1.0}, {"id": 32, "seek": 74830, "start": 728.26, "end": 748.3, "text": "خلصنا منها نعود إلى I if I equal to J return 0 اذا I في مرحلة من المراحل وصلت ان هي قيمتها نفسها J معناته لايوجد elements بينهم انا واضح ان انا عملت scan على كل درجة ان ال I وصلت ل J بناء", "tokens": [9778, 1211, 9381, 8315, 9154, 11296, 8717, 3615, 23328, 30731, 286, 498, 286, 2681, 281, 508, 2736, 1958, 1975, 15730, 286, 8978, 3714, 2288, 5016, 37977, 9154, 9673, 23557, 5016, 1211, 4032, 36520, 2655, 16472, 39896, 12174, 32640, 2655, 11296, 8717, 36178, 11296, 508, 20449, 8315, 47395, 20193, 1829, 29245, 3215, 4959, 49374, 16095, 1975, 8315, 4032, 46958, 5016, 16472, 1975, 8315, 6225, 42213, 2655, 11049, 15844, 28242, 11778, 47341, 3660, 16472, 2423, 286, 4032, 36520, 2655, 5296, 508, 44945, 16606], "avg_logprob": -0.3342225715154555, "compression_ratio": 1.494949494949495, "no_speech_prob": 3.0994415283203125e-06, "words": [{"start": 728.26, "end": 728.74, "word": "خلصنا", "probability": 0.8946533203125}, {"start": 728.74, "end": 729.3, "word": " منها", "probability": 0.953125}, {"start": 729.3, "end": 730.88, "word": " نعود", "probability": 0.5649210611979166}, {"start": 730.88, "end": 731.06, "word": " إلى", "probability": 0.5888671875}, {"start": 731.06, "end": 731.18, "word": " I", "probability": 0.708984375}, {"start": 731.18, "end": 731.78, "word": " if", "probability": 0.2293701171875}, {"start": 731.78, "end": 732.8, "word": " I", "probability": 0.74072265625}, {"start": 732.8, "end": 733.2, "word": " equal", "probability": 0.405029296875}, {"start": 733.2, "end": 733.56, "word": " to", "probability": 0.9091796875}, {"start": 733.56, "end": 733.8, "word": " J", "probability": 0.55078125}, {"start": 733.8, "end": 734.28, "word": " return", "probability": 0.4306640625}, {"start": 734.28, "end": 734.66, "word": " 0", "probability": 0.58447265625}, {"start": 734.66, "end": 736.3, "word": " اذا", "probability": 0.44171142578125}, {"start": 736.3, "end": 737.44, "word": " I", "probability": 0.5849609375}, {"start": 737.44, "end": 737.84, "word": " في", "probability": 0.6572265625}, {"start": 737.84, "end": 738.2, "word": " مرحلة", "probability": 0.96533203125}, {"start": 738.2, "end": 738.3, "word": " من", "probability": 0.9736328125}, {"start": 738.3, "end": 738.88, "word": " المراحل", "probability": 0.9677734375}, {"start": 738.88, "end": 739.54, "word": " وصلت", "probability": 0.9811197916666666}, {"start": 739.54, "end": 739.72, "word": " ان", "probability": 0.345947265625}, {"start": 739.72, "end": 739.84, "word": " هي", "probability": 0.212646484375}, {"start": 739.84, "end": 740.22, "word": " قيمتها", "probability": 0.9788818359375}, {"start": 740.22, "end": 740.6, "word": " نفسها", "probability": 0.88525390625}, {"start": 740.6, "end": 740.92, "word": " J", "probability": 0.94287109375}, {"start": 740.92, "end": 742.06, "word": " معناته", "probability": 0.677734375}, {"start": 742.06, "end": 742.42, "word": " لايوجد", "probability": 0.8055419921875}, {"start": 742.42, "end": 742.68, "word": " elements", "probability": 0.7861328125}, {"start": 742.68, "end": 743.16, "word": " بينهم", "probability": 0.93994140625}, {"start": 743.16, "end": 743.62, "word": " انا", "probability": 0.7005615234375}, {"start": 743.62, "end": 744.06, "word": " واضح", "probability": 0.8170572916666666}, {"start": 744.06, "end": 744.18, "word": " ان", "probability": 0.89404296875}, {"start": 744.18, "end": 744.24, "word": " انا", "probability": 0.900146484375}, {"start": 744.24, "end": 744.52, "word": " عملت", "probability": 0.7958170572916666}, {"start": 744.52, "end": 744.76, "word": " scan", "probability": 0.416015625}, {"start": 744.76, "end": 744.94, "word": " على", "probability": 0.849609375}, {"start": 744.94, "end": 745.2, "word": " كل", "probability": 0.548828125}, {"start": 745.2, "end": 745.52, "word": " درجة", "probability": 0.9549153645833334}, {"start": 745.52, "end": 745.64, "word": " ان", "probability": 0.6259765625}, {"start": 745.64, "end": 745.76, "word": " ال", "probability": 0.382080078125}, {"start": 745.76, "end": 745.92, "word": " I", "probability": 0.7744140625}, {"start": 745.92, "end": 746.32, "word": " وصلت", "probability": 0.9765625}, {"start": 746.32, "end": 746.56, "word": " ل", "probability": 0.48486328125}, {"start": 746.56, "end": 747.44, "word": " J", "probability": 0.467041015625}, {"start": 747.44, "end": 748.3, "word": " بناء", "probability": 0.87939453125}], "temperature": 1.0}, {"id": 33, "seek": 76299, "start": 748.99, "end": 762.99, "text": "على اللي حصل تاني فهدي نوقفها شوية هنرجع لها كمان مرة عندنا نوضح كيف فعلا ال I هتروح لل J هتروح بناء على ال return اللي جاية بناء على ال return اللي جاية اذا والله ال condition الأول لم يتحقق", "tokens": [3615, 23942, 13672, 1829, 11331, 36520, 6055, 7649, 1829, 6156, 3224, 16254, 8717, 30543, 5172, 11296, 13412, 2407, 10632, 8032, 1863, 47341, 3615, 5296, 11296, 9122, 2304, 7649, 3714, 25720, 43242, 8315, 8717, 2407, 11242, 5016, 9122, 33911, 6156, 3615, 15040, 2423, 286, 8032, 2655, 32887, 5016, 24976, 508, 8032, 2655, 32887, 5016, 44945, 16606, 15844, 2423, 2736, 13672, 1829, 10874, 995, 10632, 44945, 16606, 15844, 2423, 2736, 13672, 1829, 10874, 995, 10632, 1975, 15730, 16070, 43761, 2423, 4188, 16247, 12610, 32767, 7251, 2655, 5016, 4587, 4587], "avg_logprob": -0.1910511345009912, "compression_ratio": 1.7679558011049723, "no_speech_prob": 4.380941390991211e-05, "words": [{"start": 748.99, "end": 749.49, "word": "على", "probability": 0.811279296875}, {"start": 749.49, "end": 749.87, "word": " اللي", "probability": 0.773681640625}, {"start": 749.87, "end": 750.13, "word": " حصل", "probability": 0.744140625}, {"start": 750.13, "end": 750.65, "word": " تاني", "probability": 0.7814127604166666}, {"start": 750.65, "end": 751.17, "word": " فهدي", "probability": 0.5669352213541666}, {"start": 751.17, "end": 751.85, "word": " نوقفها", "probability": 0.712646484375}, {"start": 751.85, "end": 752.27, "word": " شوية", "probability": 0.9007161458333334}, {"start": 752.27, "end": 752.95, "word": " هنرجع", "probability": 0.79931640625}, {"start": 752.95, "end": 753.11, "word": " لها", "probability": 0.684326171875}, {"start": 753.11, "end": 753.29, "word": " كمان", "probability": 0.87744140625}, {"start": 753.29, "end": 753.63, "word": " مرة", "probability": 0.985595703125}, {"start": 753.63, "end": 754.29, "word": " عندنا", "probability": 0.844970703125}, {"start": 754.29, "end": 754.77, "word": " نوضح", "probability": 0.9439697265625}, {"start": 754.77, "end": 755.13, "word": " كيف", "probability": 0.9765625}, {"start": 755.13, "end": 755.39, "word": " فعلا", "probability": 0.87109375}, {"start": 755.39, "end": 755.53, "word": " ال", "probability": 0.77880859375}, {"start": 755.53, "end": 755.63, "word": " I", "probability": 0.861328125}, {"start": 755.63, "end": 755.97, "word": " هتروح", "probability": 0.9486083984375}, {"start": 755.97, "end": 756.15, "word": " لل", "probability": 0.5361328125}, {"start": 756.15, "end": 756.71, "word": " J", "probability": 0.4599609375}, {"start": 756.71, "end": 757.63, "word": " هتروح", "probability": 0.9254150390625}, {"start": 757.63, "end": 757.89, "word": " بناء", "probability": 0.870361328125}, {"start": 757.89, "end": 758.15, "word": " على", "probability": 0.744140625}, {"start": 758.15, "end": 758.99, "word": " ال", "probability": 0.94580078125}, {"start": 758.99, "end": 759.31, "word": " return", "probability": 0.97412109375}, {"start": 759.31, "end": 759.55, "word": " اللي", "probability": 0.958984375}, {"start": 759.55, "end": 759.89, "word": " جاية", "probability": 0.9529622395833334}, {"start": 759.89, "end": 760.45, "word": " بناء", "probability": 0.869873046875}, {"start": 760.45, "end": 760.61, "word": " على", "probability": 0.87353515625}, {"start": 760.61, "end": 760.73, "word": " ال", "probability": 0.95458984375}, {"start": 760.73, "end": 760.97, "word": " return", "probability": 0.9794921875}, {"start": 760.97, "end": 761.09, "word": " اللي", "probability": 0.97119140625}, {"start": 761.09, "end": 761.23, "word": " جاية", "probability": 0.9822591145833334}, {"start": 761.23, "end": 761.35, "word": " اذا", "probability": 0.54571533203125}, {"start": 761.35, "end": 761.59, "word": " والله", "probability": 0.8974609375}, {"start": 761.59, "end": 761.79, "word": " ال", "probability": 0.9755859375}, {"start": 761.79, "end": 762.05, "word": " condition", "probability": 0.98046875}, {"start": 762.05, "end": 762.33, "word": " الأول", "probability": 0.916259765625}, {"start": 762.33, "end": 762.47, "word": " لم", "probability": 0.91748046875}, {"start": 762.47, "end": 762.99, "word": " يتحقق", "probability": 0.99111328125}], "temperature": 1.0}, {"id": 34, "seek": 79087, "start": 763.49, "end": 790.87, "text": "condition التاني لم يتحقق ايش بدنا نعمل؟ معناته انا لأ ما زال في elements موجودة ماعملتش فحص عليها وأول element موجود لا يسوى x فإيش بدنا نعمل؟ return search كمان مرة يعني انا عملت recalling لمين؟ لل code أنا بسمي ال code search يعني instead of search إيش ال elements سبعته؟ I plus 1 و J و X، X اللي هو بدور عليه فأصبحت ال I", "tokens": [18882, 849, 16712, 7649, 1829, 32767, 7251, 2655, 5016, 4587, 4587, 1975, 1829, 8592, 47525, 8315, 8717, 25957, 1211, 22807, 20449, 8315, 47395, 1975, 8315, 5296, 10721, 19446, 30767, 6027, 8978, 4959, 3714, 29245, 23328, 3660, 19446, 25957, 1211, 2655, 8592, 6156, 5016, 9381, 25894, 11296, 36725, 12610, 4478, 3714, 29245, 23328, 20193, 7251, 3794, 2407, 7578, 2031, 6156, 28814, 1829, 8592, 47525, 8315, 8717, 25957, 1211, 22807, 2736, 3164, 9122, 2304, 7649, 3714, 25720, 37495, 22653, 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771.35, "word": " وأول", "probability": 0.70068359375}, {"start": 771.35, "end": 771.71, "word": " element", "probability": 0.97900390625}, {"start": 771.71, "end": 772.27, "word": " موجود", "probability": 0.9752604166666666}, {"start": 772.27, "end": 772.57, "word": " لا", "probability": 0.5849609375}, {"start": 772.57, "end": 772.93, "word": " يسوى", "probability": 0.69354248046875}, {"start": 772.93, "end": 773.21, "word": " x", "probability": 0.59375}, {"start": 773.21, "end": 774.07, "word": " فإيش", "probability": 0.82342529296875}, {"start": 774.07, "end": 774.21, "word": " بدنا", "probability": 0.92529296875}, {"start": 774.21, "end": 774.69, "word": " نعمل؟", "probability": 0.954345703125}, {"start": 774.69, "end": 775.15, "word": " return", "probability": 0.8642578125}, {"start": 775.15, "end": 776.29, "word": " search", "probability": 0.56298828125}, {"start": 776.29, "end": 776.77, "word": " كمان", "probability": 0.9327799479166666}, {"start": 776.77, "end": 777.09, "word": 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"probability": 0.92822265625}, {"start": 781.27, "end": 781.83, "word": " يعني", "probability": 0.650634765625}, {"start": 781.83, "end": 782.13, "word": " instead", "probability": 0.264404296875}, {"start": 782.13, "end": 782.25, "word": " of", "probability": 0.86279296875}, {"start": 782.25, "end": 782.61, "word": " search", "probability": 0.8701171875}, {"start": 782.61, "end": 783.27, "word": " إيش", "probability": 0.7967936197916666}, {"start": 783.27, "end": 783.39, "word": " ال", "probability": 0.96533203125}, {"start": 783.39, "end": 783.65, "word": " elements", "probability": 0.83935546875}, {"start": 783.65, "end": 784.69, "word": " سبعته؟", "probability": 0.8180908203125}, {"start": 784.69, "end": 785.01, "word": " I", "probability": 0.5791015625}, {"start": 785.01, "end": 785.59, "word": " plus", "probability": 0.457763671875}, {"start": 785.59, "end": 786.19, "word": " 1", "probability": 0.464599609375}, {"start": 786.19, "end": 787.21, "word": " و", "probability": 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جمعنا واحد جمعنا عليها واحد وصارت هذه ال element التاني صارت هي ال I بالنسبالنا بقارن كمان مرة خلصنا بدينا بقارن برضه ايه؟ I هنا كانت واحد هنا أصبحت اتنين ال location التاني أصبحت طيب بقارن X مع ال location التاني لأ لاتساوي", "tokens": [3555, 1863, 44510, 10721, 4724, 2304, 9957, 22807, 286, 30767, 16373, 3215, 36764, 24401, 10874, 2304, 3615, 8315, 36764, 24401, 10874, 2304, 3615, 8315, 25894, 11296, 36764, 24401, 4032, 9381, 9640, 2655, 29538, 2423, 4478, 16712, 7649, 1829, 20328, 9640, 2655, 39896, 2423, 286, 20666, 1863, 35457, 6027, 8315, 4724, 4587, 9640, 1863, 9122, 2304, 7649, 3714, 25720, 16490, 1211, 9381, 8315, 47525, 1829, 8315, 4724, 4587, 9640, 1863, 4724, 43042, 3224, 1975, 1829, 3224, 22807, 286, 34105, 25961, 2655, 36764, 24401, 34105, 5551, 9381, 3555, 33753, 1975, 2655, 1863, 9957, 2423, 4914, 16712, 7649, 1829, 5551, 9381, 3555, 33753, 23032, 1829, 3555, 4724, 4587, 9640, 1863, 1783, 20449, 2423, 4914, 16712, 7649, 1829, 5296, 10721, 5296, 9307, 3794, 995, 45865], "avg_logprob": -0.1730276588045183, "compression_ratio": 1.990566037735849, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 792.97, "end": 793.55, "word": "بنبدأ", "probability": 0.79345703125}, {"start": 793.55, "end": 794.09, "word": " بمين؟", "probability": 0.64031982421875}, {"start": 794.09, "end": 794.57, "word": " I", "probability": 0.6748046875}, {"start": 794.57, "end": 795.83, "word": " زائد", "probability": 0.6440226236979166}, {"start": 795.83, "end": 796.31, "word": " واحد", "probability": 0.949951171875}, {"start": 796.31, "end": 796.87, "word": " جمعنا", "probability": 0.87451171875}, {"start": 796.87, "end": 797.57, "word": " واحد", "probability": 0.792236328125}, {"start": 797.57, "end": 798.67, "word": " جمعنا", "probability": 0.78204345703125}, {"start": 798.67, "end": 799.03, "word": " عليها", "probability": 0.98974609375}, {"start": 799.03, "end": 799.57, "word": " واحد", "probability": 0.982421875}, {"start": 799.57, "end": 799.93, "word": " وصارت", 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"probability": 0.9443359375}, {"start": 1238.03, "end": 1238.51, "word": " بعده", "probability": 0.71630859375}, {"start": 1238.51, "end": 1239.35, "word": " فتصبح", "probability": 0.962890625}, {"start": 1239.35, "end": 1239.73, "word": " عنا", "probability": 0.58837890625}, {"start": 1239.73, "end": 1240.19, "word": " إذا", "probability": 0.7420654296875}, {"start": 1240.19, "end": 1240.53, "word": " كانت", "probability": 0.885986328125}, {"start": 1240.53, "end": 1240.65, "word": " ال", "probability": 0.82763671875}, {"start": 1240.65, "end": 1240.89, "word": " am", "probability": 0.2161865234375}, {"start": 1240.89, "end": 1241.39, "word": " هي", "probability": 0.9287109375}, {"start": 1241.39, "end": 1241.59, "word": " اللي", "probability": 0.962890625}, {"start": 1241.59, "end": 1241.95, "word": " أصغر", "probability": 0.9478759765625}, {"start": 1241.95, "end": 1242.11, "word": " من", "probability": 0.9912109375}, {"start": 1242.11, "end": 1242.45, "word": " x", "probability": 0.87158203125}, {"start": 1242.45, "end": 1243.13, "word": " فx", "probability": 0.767578125}, {"start": 1243.13, "end": 1243.61, "word": " أكبر", "probability": 0.9656575520833334}, {"start": 1243.61, "end": 1244.93, "word": " and", "probability": 0.51708984375}, {"start": 1244.93, "end": 1246.73, "word": " m", "probability": 0.59130859375}, {"start": 1246.73, "end": 1247.83, "word": " هذه", "probability": 0.38671875}], "temperature": 1.0}, {"id": 53, "seek": 127598, "start": 1249.32, "end": 1275.98, "text": "أقل من j أقل من j يعني أن يوجد بينهم مجموعة elements على الأقل element واحد على الأقل element واحد وجد بينهم جدير أن أبحث عليه من الأفضل أن أبحث عليه لا أستطيع أن أقول إن انتهيت من ال search طبعي في الحالة هذه سنعود بمين؟ برضه بنفس ال code ولكن ل series a ال x هي نفس ال element اللي بدور عليه من أين؟", "tokens": [10721, 4587, 1211, 9154, 361, 5551, 4587, 1211, 9154, 361, 37495, 22653, 14739, 7251, 29245, 3215, 49374, 16095, 3714, 7435, 2304, 45367, 3660, 4959, 15844, 16247, 4587, 1211, 4478, 36764, 24401, 15844, 16247, 4587, 1211, 4478, 36764, 24401, 49610, 3215, 49374, 16095, 10874, 3215, 13546, 14739, 5551, 49628, 12984, 47356, 9154, 16247, 5172, 11242, 1211, 14739, 5551, 49628, 12984, 47356, 20193, 5551, 14851, 9566, 40228, 14739, 5551, 39648, 36145, 16472, 47395, 36081, 9154, 2423, 3164, 23032, 3555, 3615, 1829, 8978, 21542, 6027, 3660, 29538, 8608, 1863, 3615, 23328, 4724, 2304, 9957, 22807, 4724, 2288, 11242, 3224, 44945, 36178, 2423, 3089, 35525, 19452, 5296, 2638, 257, 2423, 2031, 39896, 8717, 36178, 2423, 4478, 13672, 1829, 47525, 13063, 47356, 9154, 5551, 9957, 22807], "avg_logprob": -0.32428277589258603, "compression_ratio": 2.0040983606557377, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1249.32, "end": 1249.78, "word": "أقل", "probability": 0.9171549479166666}, {"start": 1249.78, "end": 1250.02, "word": " من", "probability": 0.9853515625}, {"start": 1250.02, "end": 1250.6, "word": " j", "probability": 0.47021484375}, {"start": 1250.6, "end": 1251.66, "word": " أقل", "probability": 0.739013671875}, {"start": 1251.66, "end": 1252.12, "word": " من", "probability": 0.9873046875}, {"start": 1252.12, "end": 1252.92, "word": " j", "probability": 0.873046875}, {"start": 1252.92, "end": 1253.34, "word": " يعني", "probability": 0.738525390625}, {"start": 1253.34, "end": 1253.6, "word": " أن", "probability": 0.73681640625}, {"start": 1253.6, "end": 1254.02, "word": " يوجد", "probability": 0.82763671875}, {"start": 1254.02, "end": 1254.48, "word": " بينهم", "probability": 0.908203125}, {"start": 1254.48, "end": 1255.08, "word": " مجموعة", "probability": 0.85546875}, {"start": 1255.08, "end": 1255.38, "word": " elements", "probability": 0.5546875}, {"start": 1255.38, "end": 1255.54, "word": " على", "probability": 0.64794921875}, {"start": 1255.54, "end": 1255.8, "word": " الأقل", "probability": 0.986328125}, {"start": 1255.8, "end": 1256.08, "word": " element", "probability": 0.67138671875}, {"start": 1256.08, "end": 1256.48, "word": " واحد", "probability": 0.977294921875}, {"start": 1256.48, "end": 1257.04, "word": " على", "probability": 0.65478515625}, {"start": 1257.04, "end": 1257.36, "word": " الأقل", "probability": 0.9920247395833334}, {"start": 1257.36, "end": 1257.64, "word": " element", "probability": 0.94384765625}, {"start": 1257.64, "end": 1257.96, "word": " واحد", "probability": 0.982421875}, {"start": 1257.96, "end": 1258.2, "word": " وجد", "probability": 0.73486328125}, {"start": 1258.2, "end": 1258.64, "word": " بينهم", "probability": 0.83642578125}, {"start": 1258.64, "end": 1259.7, "word": " جدير", "probability": 0.6997884114583334}, {"start": 1259.7, "end": 1260.36, "word": " أن", "probability": 0.251708984375}, {"start": 1260.36, "end": 1260.86, "word": " أبحث", "probability": 0.8224283854166666}, {"start": 1260.86, "end": 1261.2, "word": " عليه", "probability": 0.802734375}, {"start": 1261.2, "end": 1262.1, "word": " من", "probability": 0.86669921875}, {"start": 1262.1, "end": 1262.44, "word": " الأفضل", "probability": 0.9844970703125}, {"start": 1262.44, "end": 1262.54, "word": " أن", "probability": 0.73046875}, {"start": 1262.54, "end": 1262.74, "word": " أبحث", "probability": 0.9423828125}, {"start": 1262.74, "end": 1262.92, "word": " عليه", "probability": 0.95751953125}, {"start": 1262.92, "end": 1263.02, "word": " لا", "probability": 0.1644287109375}, {"start": 1263.02, "end": 1263.2, "word": " أستطيع", "probability": 0.8056640625}, {"start": 1263.2, "end": 1263.34, "word": " أن", "probability": 0.72216796875}, {"start": 1263.34, "end": 1263.42, "word": " أقول", "probability": 0.959716796875}, {"start": 1263.42, "end": 1263.56, "word": " إن", "probability": 0.45458984375}, {"start": 1263.56, "end": 1264.02, "word": " انتهيت", "probability": 0.6255696614583334}, {"start": 1264.02, "end": 1264.32, "word": " من", "probability": 0.36474609375}, {"start": 1264.32, "end": 1264.32, "word": " ال", "probability": 0.1297607421875}, {"start": 1264.32, "end": 1264.8, "word": " search", "probability": 0.63232421875}, {"start": 1264.8, "end": 1265.14, "word": " طبعي", "probability": 0.662811279296875}, {"start": 1265.14, "end": 1265.78, "word": " في", "probability": 0.48388671875}, {"start": 1265.78, "end": 1266.46, "word": " الحالة", "probability": 0.92529296875}, {"start": 1266.46, "end": 1266.7, "word": " هذه", "probability": 0.83349609375}, {"start": 1266.7, "end": 1267.96, "word": " سنعود", "probability": 0.78759765625}, {"start": 1267.96, "end": 1268.5, "word": " بمين؟", "probability": 0.435699462890625}, {"start": 1268.5, "end": 1268.84, "word": " برضه", "probability": 0.6329345703125}, {"start": 1268.84, "end": 1269.12, "word": " بنفس", "probability": 0.947021484375}, {"start": 1269.12, "end": 1269.26, "word": " ال", "probability": 0.7099609375}, {"start": 1269.26, "end": 1269.44, "word": " code", "probability": 0.95751953125}, {"start": 1269.44, "end": 1270.54, "word": " ولكن", "probability": 0.756103515625}, {"start": 1270.54, "end": 1270.78, "word": " ل", "probability": 0.6181640625}, {"start": 1270.78, "end": 1271.54, "word": " series", "probability": 0.646484375}, {"start": 1271.54, "end": 1271.94, "word": " a", "probability": 0.425048828125}, {"start": 1271.94, "end": 1272.62, "word": " ال", "probability": 0.552734375}, {"start": 1272.62, "end": 1273.0, "word": " x", "probability": 0.68603515625}, {"start": 1273.0, "end": 1273.92, "word": " هي", "probability": 0.92041015625}, {"start": 1273.92, "end": 1274.16, "word": " نفس", "probability": 0.88916015625}, {"start": 1274.16, "end": 1274.28, "word": " ال", "probability": 0.49609375}, {"start": 1274.28, "end": 1274.5, "word": " element", "probability": 0.98583984375}, {"start": 1274.5, "end": 1274.66, "word": " اللي", "probability": 0.87451171875}, {"start": 1274.66, "end": 1274.9, "word": " بدور", "probability": 0.5443115234375}, {"start": 1274.9, "end": 1275.14, "word": " عليه", "probability": 0.98779296875}, {"start": 1275.14, "end": 1275.48, "word": " من", "probability": 0.57958984375}, {"start": 1275.48, "end": 1275.98, "word": " أين؟", "probability": 0.8865559895833334}], "temperature": 1.0}, {"id": 54, "seek": 130477, "start": 1276.71, "end": 1304.77, "text": "m زائد واحد to j من m زائد واحد to j بنرجع بنكرر نفس الموضوع هو هو نفسنا بنكرر نفس الموضوع تماما okay else return zero لاحظوا ال else هذه هذه ال else بتاعة ال F هذه ال else هذه بتاعة ال F هذه ليش بقول الكلام هذا بقول الكلام هذا عشان نقول انت حنجف", "tokens": [76, 30767, 16373, 3215, 36764, 24401, 281, 361, 9154, 275, 30767, 16373, 3215, 36764, 24401, 281, 361, 44945, 47341, 3615, 44945, 37983, 2288, 8717, 36178, 9673, 2407, 11242, 45367, 31439, 31439, 8717, 36178, 8315, 44945, 37983, 2288, 8717, 36178, 9673, 2407, 11242, 45367, 46811, 10943, 995, 1392, 1646, 2736, 4018, 20193, 5016, 19913, 14407, 2423, 1646, 29538, 29538, 2423, 1646, 39894, 995, 27884, 2423, 479, 29538, 2423, 1646, 29538, 39894, 995, 27884, 2423, 479, 29538, 32239, 8592, 4724, 39648, 2423, 28820, 10943, 23758, 4724, 39648, 2423, 28820, 10943, 23758, 6225, 8592, 7649, 8717, 39648, 16472, 2655, 11331, 1863, 7435, 5172], "avg_logprob": -0.21039604550541038, "compression_ratio": 2.128342245989305, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 1276.71, "end": 1277.01, "word": "m", "probability": 0.1900634765625}, {"start": 1277.01, "end": 1277.45, "word": " زائد", "probability": 0.4997202555338542}, {"start": 1277.45, "end": 1278.01, "word": " واحد", "probability": 0.925537109375}, {"start": 1278.01, "end": 1279.43, "word": " to", "probability": 0.54833984375}, {"start": 1279.43, "end": 1279.71, "word": " j", "probability": 0.91650390625}, {"start": 1279.71, "end": 1280.49, "word": " من", "probability": 0.54248046875}, {"start": 1280.49, "end": 1280.77, "word": " m", "probability": 0.66943359375}, {"start": 1280.77, "end": 1281.33, "word": " زائد", "probability": 0.931640625}, {"start": 1281.33, "end": 1281.71, "word": " واحد", "probability": 0.98828125}, {"start": 1281.71, "end": 1282.19, "word": " to", "probability": 0.88232421875}, {"start": 1282.19, "end": 1282.47, "word": " j", "probability": 0.93994140625}, {"start": 1282.47, "end": 1283.09, "word": " بنرجع", "probability": 0.7361653645833334}, {"start": 1283.09, "end": 1283.65, "word": " بنكرر", "probability": 0.84716796875}, {"start": 1283.65, "end": 1284.05, "word": " نفس", "probability": 0.994384765625}, {"start": 1284.05, "end": 1284.45, "word": " الموضوع", "probability": 0.9969482421875}, {"start": 1284.45, "end": 1284.63, "word": " هو", "probability": 0.64501953125}, {"start": 1284.63, "end": 1284.93, "word": " هو", "probability": 0.94140625}, {"start": 1284.93, "end": 1285.63, "word": " نفسنا", "probability": 0.6187744140625}, {"start": 1285.63, "end": 1286.51, "word": " بنكرر", "probability": 0.8427734375}, {"start": 1286.51, "end": 1286.79, "word": " نفس", "probability": 0.966552734375}, {"start": 1286.79, "end": 1287.21, "word": " الموضوع", "probability": 0.99560546875}, {"start": 1287.21, "end": 1288.13, "word": " تماما", "probability": 0.94140625}, {"start": 1288.13, "end": 1288.57, "word": " okay", "probability": 0.580078125}, {"start": 1288.57, "end": 1290.03, "word": " else", "probability": 0.81591796875}, {"start": 1290.03, "end": 1291.15, "word": " return", "probability": 0.9052734375}, {"start": 1291.15, "end": 1291.95, "word": " zero", "probability": 0.677734375}, {"start": 1291.95, "end": 1292.45, "word": " لاحظوا", "probability": 0.804443359375}, {"start": 1292.45, "end": 1292.53, "word": " ال", "probability": 0.97802734375}, {"start": 1292.53, "end": 1292.75, "word": " else", "probability": 0.9287109375}, {"start": 1292.75, "end": 1293.05, "word": " هذه", "probability": 0.54443359375}, {"start": 1293.05, "end": 1295.09, "word": " هذه", "probability": 0.462646484375}, {"start": 1295.09, "end": 1295.29, "word": " ال", "probability": 0.99169921875}, {"start": 1295.29, "end": 1295.67, "word": " else", "probability": 0.970703125}, {"start": 1295.67, "end": 1296.19, "word": " بتاعة", "probability": 0.955078125}, {"start": 1296.19, "end": 1296.35, "word": " ال", "probability": 0.82763671875}, {"start": 1296.35, "end": 1296.57, "word": " F", "probability": 0.59375}, {"start": 1296.57, "end": 1296.91, "word": " هذه", "probability": 0.73974609375}, {"start": 1296.91, "end": 1297.63, "word": " ال", "probability": 0.95751953125}, {"start": 1297.63, "end": 1297.91, "word": " else", "probability": 0.96533203125}, {"start": 1297.91, "end": 1298.27, "word": " هذه", "probability": 0.87158203125}, {"start": 1298.27, "end": 1298.59, "word": " بتاعة", "probability": 0.9637044270833334}, {"start": 1298.59, "end": 1298.73, "word": " ال", "probability": 0.935546875}, {"start": 1298.73, "end": 1298.93, "word": " F", "probability": 0.98095703125}, {"start": 1298.93, "end": 1299.81, "word": " هذه", "probability": 0.919921875}, {"start": 1299.81, "end": 1301.35, "word": " ليش", "probability": 0.9423828125}, {"start": 1301.35, "end": 1301.57, "word": " بقول", "probability": 0.986328125}, {"start": 1301.57, "end": 1301.89, "word": " الكلام", "probability": 0.9376627604166666}, {"start": 1301.89, "end": 1302.09, "word": " هذا", "probability": 0.86376953125}, {"start": 1302.09, "end": 1302.37, "word": " بقول", "probability": 0.7822265625}, {"start": 1302.37, "end": 1302.63, "word": " الكلام", "probability": 0.95849609375}, {"start": 1302.63, "end": 1302.77, "word": " هذا", "probability": 0.8779296875}, {"start": 1302.77, "end": 1302.97, "word": " عشان", "probability": 0.95703125}, {"start": 1302.97, "end": 1303.23, "word": " نقول", "probability": 0.799072265625}, {"start": 1303.23, "end": 1303.89, "word": " انت", "probability": 0.5845947265625}, {"start": 1303.89, "end": 1304.77, "word": " حنجف", "probability": 0.7919921875}], "temperature": 1.0}, {"id": 55, "seek": 133495, "start": 1306.31, "end": 1334.95, "text": "نتطلع كمان شوية هل وجدت ام تحبك بقدر اقول اني وقفت اذا كان وانا بدور صدفت انه فعلا ال X طلعت بتساوي واحدة من ال AM's سواء 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المائة شخص اللي بتسابقوا فطبعا عندكوا كمية كبيرة من الاحتمالات من ال possibilities من ال possibilities قداش عددهم هنا counting عدد قداش عدد الاحتمالات عدد انا قاعد باطلب منكوا عدد counting عدولي كويس هذا example", "tokens": [27842, 5551, 12610, 6225, 8592, 25720, 3714, 43020, 7251, 36520, 14407, 9154, 9673, 16373, 3660, 13412, 9778, 9381, 13672, 1829, 39894, 3794, 16758, 4587, 14407, 6156, 9566, 3555, 3615, 995, 43242, 4117, 14407, 9122, 2304, 10632, 9122, 3555, 48923, 9154, 42963, 33753, 2304, 6027, 9307, 9154, 2423, 12178, 9154, 2423, 12178, 12174, 3215, 33599, 6225, 3215, 3215, 16095, 34105, 13251, 6225, 3215, 3215, 12174, 3215, 33599, 6225, 3215, 3215, 42963, 33753, 2304, 6027, 9307, 6225, 3215, 3215, 1975, 8315, 12174, 995, 22488, 4724, 41193, 46152, 9154, 4117, 14407, 6225, 3215, 3215, 13251, 6225, 3215, 12610, 1829, 9122, 45865, 3794, 23758, 1365], "avg_logprob": -0.14606310748586468, "compression_ratio": 1.8689320388349515, "no_speech_prob": 2.980232238769531e-07, "words": 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نحله", "probability": 0.7520751953125}, {"start": 1598.4, "end": 1598.7, "word": " إلا", "probability": 0.74169921875}, {"start": 1598.7, "end": 1598.9, "word": " بس", "probability": 0.953369140625}, {"start": 1598.9, "end": 1599.38, "word": " نخلص", "probability": 0.8154296875}, {"start": 1599.38, "end": 1599.74, "word": " الموضوع", "probability": 0.9954833984375}, {"start": 1599.74, "end": 1600.14, "word": " تبعنا", "probability": 0.80780029296875}, {"start": 1600.14, "end": 1600.48, "word": " لما", "probability": 0.55804443359375}, {"start": 1600.48, "end": 1600.76, "word": " نخلص", "probability": 0.985107421875}, {"start": 1600.76, "end": 1601.0, "word": " الموضوع", "probability": 0.9932861328125}, {"start": 1601.0, "end": 1601.32, "word": " بنقدر", "probability": 0.7578938802083334}, {"start": 1601.32, "end": 1601.7, "word": " نتكلم", "probability": 0.9930419921875}, {"start": 1601.7, "end": 1601.9, "word": " فيه", "probability": 0.947509765625}, {"start": 1601.9, "end": 1602.12, "word": " هذا", "probability": 0.83203125}, {"start": 1602.12, "end": 1602.78, "word": " okay", "probability": 0.271728515625}, {"start": 1602.78, "end": 1603.8, "word": " example", "probability": 0.8359375}, {"start": 1603.8, "end": 1604.28, "word": " تاني", "probability": 0.9052734375}, {"start": 1604.28, "end": 1604.6, "word": " يعني", "probability": 0.883544921875}, {"start": 1604.6, "end": 1604.68, "word": " أنا", "probability": 0.7080078125}, {"start": 1604.68, "end": 1604.8, "word": " بس", "probability": 0.9814453125}, {"start": 1604.8, "end": 1605.2, "word": " بقولكوا", "probability": 0.8995361328125}, {"start": 1605.2, "end": 1605.52, "word": " في", "probability": 0.92041015625}, {"start": 1605.52, "end": 1605.7, "word": " إيش", "probability": 0.8660481770833334}, {"start": 1605.7, "end": 1605.94, "word": " ممكن", "probability": 0.9892578125}, {"start": 1605.94, "end": 1606.36, "word": " نستخدم", "probability": 0.9757080078125}, {"start": 1606.36, "end": 1606.7, "word": " العد", "probability": 0.971435546875}, {"start": 1606.7, "end": 1607.3, "word": " example", "probability": 0.1556396484375}, {"start": 1607.3, "end": 1607.66, "word": " تاني", "probability": 0.98828125}, {"start": 1607.66, "end": 1607.84, "word": " if", "probability": 0.8212890625}, {"start": 1607.84, "end": 1608.06, "word": " a", "probability": 0.81494140625}, {"start": 1608.06, "end": 1608.56, "word": " password", "probability": 0.94580078125}, {"start": 1608.56, "end": 1608.9, "word": " is", "probability": 0.9619140625}, {"start": 1608.9, "end": 1609.46, "word": " six", "probability": 0.63232421875}, {"start": 1609.46, "end": 1609.66, "word": " to", "probability": 0.97509765625}, {"start": 1609.66, "end": 1610.02, "word": " eight", "probability": 0.8828125}, {"start": 1610.02, "end": 1610.76, "word": " letters", "probability": 0.8193359375}, {"start": 1610.76, "end": 1611.22, "word": " or", "probability": 0.8857421875}, {"start": 1611.22, "end": 1611.74, "word": " and", "probability": 0.8310546875}, {"start": 1611.74, "end": 1612.36, "word": " digits", "probability": 0.94287109375}], "temperature": 1.0}, {"id": 68, "seek": 164091, "start": 1613.37, "end": 1640.91, "text": "How many possibles can there be؟ قداش عدد ال passwords اللي بقدر أعملها من ستة لتمانية letters or and digits بمعنى اعملوا password كل واحدة بتعملها password ال password هاللازم يكون عدد ال positions تبعته عدد ال locations تبعته من ستة لتمانية يعني يا ستة يا سبعة يا تمانية six or seven or", "tokens": [6462, 867, 1402, 14428, 393, 456, 312, 22807, 12174, 3215, 33599, 6225, 3215, 3215, 2423, 33149, 13672, 1829, 4724, 28543, 2288, 5551, 25957, 1211, 11296, 9154, 8608, 2655, 3660, 5296, 39237, 7649, 10632, 7825, 420, 293, 27011, 4724, 2304, 3615, 1863, 7578, 1975, 25957, 1211, 14407, 11524, 28242, 36764, 24401, 3660, 39894, 25957, 1211, 11296, 11524, 2423, 11524, 8032, 6027, 1211, 31377, 2304, 7251, 30544, 6225, 3215, 3215, 2423, 8432, 6055, 3555, 34268, 3224, 6225, 3215, 3215, 2423, 9253, 6055, 3555, 34268, 3224, 9154, 8608, 2655, 3660, 5296, 39237, 7649, 10632, 37495, 22653, 35186, 8608, 2655, 3660, 35186, 8608, 3555, 27884, 35186, 46811, 7649, 10632, 2309, 420, 3407, 420], "avg_logprob": -0.18650568452748387, "compression_ratio": 1.7896995708154506, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1613.37, "end": 1613.59, "word": "How", "probability": 0.281494140625}, {"start": 1613.59, "end": 1613.77, "word": " many", "probability": 0.8955078125}, {"start": 1613.77, "end": 1614.09, "word": " possibles", "probability": 0.529815673828125}, {"start": 1614.09, "end": 1614.33, "word": " can", "probability": 0.9140625}, {"start": 1614.33, "end": 1614.61, "word": " there", "probability": 0.84326171875}, {"start": 1614.61, "end": 1616.91, "word": " be؟", "probability": 0.7119140625}, {"start": 1616.91, "end": 1617.25, "word": " قداش", "probability": 0.5076497395833334}, {"start": 1617.25, "end": 1617.63, "word": " عدد", "probability": 0.9615885416666666}, {"start": 1617.63, "end": 1618.23, "word": " ال", "probability": 0.875}, {"start": 1618.23, "end": 1619.03, "word": " passwords", "probability": 0.55712890625}, {"start": 1619.03, "end": 1619.27, "word": " اللي", "probability": 0.9013671875}, {"start": 1619.27, "end": 1619.57, "word": " بقدر", "probability": 0.9827473958333334}, {"start": 1619.57, "end": 1620.05, "word": " أعملها", "probability": 0.87744140625}, {"start": 1620.05, "end": 1620.63, "word": " من", "probability": 0.95068359375}, {"start": 1620.63, "end": 1621.71, "word": " ستة", "probability": 0.805908203125}, {"start": 1621.71, "end": 1622.39, "word": " لتمانية", "probability": 0.8822021484375}, {"start": 1622.39, "end": 1623.13, "word": " letters", "probability": 0.68896484375}, {"start": 1623.13, "end": 1623.73, "word": " or", "probability": 0.8291015625}, {"start": 1623.73, "end": 1624.39, "word": " and", "probability": 0.90283203125}, {"start": 1624.39, "end": 1625.05, "word": " digits", "probability": 0.83056640625}, {"start": 1625.05, "end": 1626.45, "word": " بمعنى", "probability": 0.94326171875}, {"start": 1626.45, "end": 1627.23, "word": " اعملوا", "probability": 0.9249267578125}, {"start": 1627.23, "end": 1627.57, "word": " password", "probability": 0.9541015625}, {"start": 1627.57, "end": 1627.71, "word": " كل", "probability": 0.63134765625}, {"start": 1627.71, "end": 1627.91, "word": " واحدة", "probability": 0.8546549479166666}, {"start": 1627.91, "end": 1628.21, "word": " بتعملها", "probability": 0.7899169921875}, {"start": 1628.21, "end": 1628.63, "word": " password", "probability": 0.9775390625}, {"start": 1628.63, "end": 1628.79, "word": " ال", "probability": 0.78955078125}, {"start": 1628.79, "end": 1629.13, "word": " password", "probability": 0.94287109375}, {"start": 1629.13, "end": 1629.79, "word": " هاللازم", "probability": 0.766748046875}, {"start": 1629.79, "end": 1630.35, "word": " يكون", "probability": 0.99365234375}, {"start": 1630.35, "end": 1631.39, "word": " عدد", "probability": 0.9879557291666666}, {"start": 1631.39, "end": 1631.65, "word": " ال", "probability": 0.90478515625}, {"start": 1631.65, "end": 1632.89, "word": " positions", "probability": 0.697265625}, {"start": 1632.89, "end": 1633.39, "word": " تبعته", "probability": 0.791412353515625}, {"start": 1633.39, "end": 1633.61, "word": " عدد", "probability": 0.89013671875}, {"start": 1633.61, "end": 1633.67, "word": " ال", "probability": 0.92919921875}, {"start": 1633.67, "end": 1633.93, "word": " locations", "probability": 0.919921875}, {"start": 1633.93, "end": 1634.49, "word": " تبعته", "probability": 0.9620361328125}, {"start": 1634.49, "end": 1634.89, "word": " من", "probability": 0.984375}, {"start": 1634.89, "end": 1635.27, "word": " ستة", "probability": 0.9578450520833334}, {"start": 1635.27, "end": 1635.71, "word": " لتمانية", "probability": 0.951904296875}, {"start": 1635.71, "end": 1635.93, "word": " يعني", "probability": 0.897216796875}, {"start": 1635.93, "end": 1636.05, "word": " يا", "probability": 0.861328125}, {"start": 1636.05, "end": 1636.49, "word": " ستة", "probability": 0.9793294270833334}, {"start": 1636.49, "end": 1636.67, "word": " يا", "probability": 0.94287109375}, {"start": 1636.67, "end": 1637.07, "word": " سبعة", "probability": 0.98388671875}, {"start": 1637.07, "end": 1637.51, "word": " يا", "probability": 0.9150390625}, {"start": 1637.51, "end": 1638.11, "word": " تمانية", "probability": 0.9934895833333334}, {"start": 1638.11, "end": 1638.91, "word": " six", "probability": 0.7470703125}, {"start": 1638.91, "end": 1639.47, "word": " or", "probability": 0.9677734375}, {"start": 1639.47, "end": 1640.33, "word": " seven", "probability": 0.80126953125}, {"start": 1640.33, "end": 1640.91, "word": " or", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 69, "seek": 165766, "start": 1641.24, "end": 1657.66, "text": "eight or مهمة جدا طيب في كل digit في كل location ايش العناصر الممكنة اما انها تكون letters حروف او digits او الاتنين مع بعض اللي هم ال combination في ال six مع بعض", "tokens": [36309, 420, 3714, 16095, 3660, 10874, 28259, 23032, 1829, 3555, 8978, 28242, 14293, 8978, 28242, 4914, 1975, 1829, 8592, 18863, 1863, 33546, 2288, 9673, 43020, 3660, 1975, 15042, 16472, 11296, 6055, 30544, 7825, 11331, 32887, 5172, 1975, 2407, 27011, 1975, 2407, 2423, 9307, 1863, 9957, 20449, 45030, 11242, 13672, 1829, 8032, 2304, 2423, 6562, 8978, 2423, 2309, 20449, 45030, 11242], "avg_logprob": -0.21196209504956104, "compression_ratio": 1.5, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 1641.24, "end": 1641.88, "word": "eight", "probability": 0.6162109375}, {"start": 1641.88, "end": 1643.04, "word": " or", "probability": 0.325439453125}, {"start": 1643.04, "end": 1643.48, "word": " مهمة", "probability": 0.8401692708333334}, {"start": 1643.48, "end": 1643.78, "word": " جدا", "probability": 0.98388671875}, {"start": 1643.78, "end": 1644.64, "word": " طيب", "probability": 0.762939453125}, {"start": 1644.64, "end": 1645.34, "word": " في", "probability": 0.75634765625}, {"start": 1645.34, "end": 1645.54, "word": " كل", "probability": 0.98974609375}, {"start": 1645.54, "end": 1645.96, "word": " digit", "probability": 0.974609375}, {"start": 1645.96, "end": 1646.78, "word": " في", "probability": 0.7880859375}, {"start": 1646.78, "end": 1647.04, "word": " كل", "probability": 0.9912109375}, {"start": 1647.04, "end": 1647.88, "word": " location", "probability": 0.98388671875}, {"start": 1647.88, "end": 1648.46, "word": " ايش", "probability": 0.732177734375}, {"start": 1648.46, "end": 1649.46, "word": " العناصر", "probability": 0.9473876953125}, {"start": 1649.46, "end": 1650.34, "word": " الممكنة", "probability": 0.696044921875}, {"start": 1650.34, "end": 1650.88, "word": " اما", "probability": 0.731201171875}, {"start": 1650.88, "end": 1651.16, "word": " انها", "probability": 0.87939453125}, {"start": 1651.16, "end": 1651.34, "word": " تكون", "probability": 0.68408203125}, {"start": 1651.34, "end": 1651.66, "word": " letters", "probability": 0.7587890625}, {"start": 1651.66, "end": 1652.18, "word": " حروف", "probability": 0.9296875}, {"start": 1652.18, "end": 1652.82, "word": " او", "probability": 0.966064453125}, {"start": 1652.82, "end": 1653.56, "word": " digits", "probability": 0.927734375}, {"start": 1653.56, "end": 1654.48, "word": " او", "probability": 0.97998046875}, {"start": 1654.48, "end": 1655.58, "word": " الاتنين", "probability": 0.80859375}, {"start": 1655.58, "end": 1655.7, "word": " مع", "probability": 0.96630859375}, {"start": 1655.7, "end": 1655.94, "word": " بعض", "probability": 0.9951171875}, {"start": 1655.94, "end": 1656.04, "word": " اللي", "probability": 0.94677734375}, {"start": 1656.04, "end": 1656.16, "word": " هم", "probability": 0.804443359375}, {"start": 1656.16, "end": 1656.24, "word": " ال", "probability": 0.75048828125}, {"start": 1656.24, "end": 1656.64, "word": " combination", "probability": 0.96240234375}, {"start": 1656.64, "end": 1656.9, "word": " في", "probability": 0.9169921875}, {"start": 1656.9, "end": 1657.0, "word": " ال", "probability": 0.7392578125}, {"start": 1657.0, "end": 1657.18, "word": " six", "probability": 0.311767578125}, {"start": 1657.18, "end": 1657.36, "word": " مع", "probability": 0.9833984375}, {"start": 1657.36, "end": 1657.66, "word": " بعض", "probability": 0.997314453125}], "temperature": 1.0}, {"id": 70, "seek": 168554, "start": 1658.56, "end": 1685.54, "text": "تمام؟ طيب في الأخر قداش عدد ال passwords الممكنة في الحالة هذه عدد ال passwords الممكنة هذه المفروض من هنا لآخر ما نخلص موضوعنا تكونوا جادرين تشتغلوا على الكلام هذا تكونوا جادرين تحلوها بس أنا قاعد بقولكوا هي حاجات ل password خاصة في شغلكوا بكرا بتكونوا تعملوا design ل password معينة ل location لبرنامج بتكونوا تشتغلوه او program كامل او software كاملة تبرمجوها بتكونوا تعملوه ل password license عشان اللي بتعملوها license", "tokens": [39237, 10943, 22807, 23032, 1829, 3555, 8978, 16247, 34740, 12174, 3215, 33599, 6225, 3215, 3215, 2423, 33149, 9673, 43020, 3660, 8978, 21542, 6027, 3660, 29538, 6225, 3215, 3215, 2423, 33149, 9673, 43020, 3660, 29538, 9673, 5172, 32887, 11242, 9154, 34105, 5296, 148, 95, 34740, 19446, 8717, 9778, 1211, 9381, 3714, 2407, 11242, 45367, 8315, 6055, 30544, 14407, 10874, 18513, 2288, 9957, 6055, 8592, 2655, 17082, 1211, 14407, 15844, 2423, 28820, 10943, 23758, 6055, 30544, 14407, 10874, 18513, 2288, 9957, 6055, 5016, 1211, 2407, 11296, 4724, 3794, 41850, 12174, 995, 22488, 4724, 39648, 4117, 14407, 39896, 11331, 26108, 9307, 5296, 11524, 16490, 33546, 3660, 8978, 13412, 17082, 23275, 14407, 4724, 4117, 23557, 4724, 2655, 30544, 14407, 6055, 25957, 1211, 14407, 1715, 5296, 11524, 20449, 9957, 3660, 5296, 4914, 5296, 26890, 8315, 2304, 7435, 4724, 2655, 30544, 14407, 6055, 8592, 2655, 17082, 1211, 2407, 3224, 1975, 2407, 1461, 9122, 10943, 1211, 1975, 2407, 4722, 9122, 10943, 37977, 6055, 26890, 2304, 7435, 2407, 11296, 39894, 30544, 14407, 6055, 25957, 1211, 2407, 3224, 5296, 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"text": "بقدرش اعمل اتين اتين مع بعض ما هو خلاص انت عملته password واحدة ال password هدى يا ستة يا سبعة تنفع تكون password حاجة تقبل ستة و سبعة characters مع بعض؟ تنفعش فإذا في الحالة هدى either task one or كلمة or على طول ل ال summation some rule okay the product task the task do both task one and task two simultaneously مع بعض", "tokens": [3555, 28543, 2288, 8592, 1975, 25957, 1211, 1975, 2655, 9957, 1975, 2655, 9957, 20449, 45030, 11242, 19446, 31439, 16490, 1211, 33546, 16472, 2655, 6225, 42213, 47395, 11524, 36764, 24401, 3660, 2423, 11524, 8032, 3215, 7578, 35186, 8608, 2655, 3660, 35186, 8608, 3555, 27884, 6055, 1863, 5172, 3615, 6055, 30544, 11524, 11331, 26108, 3660, 6055, 4587, 36150, 8608, 2655, 3660, 4032, 8608, 3555, 27884, 4342, 20449, 45030, 11242, 22807, 6055, 1863, 5172, 3615, 8592, 6156, 28814, 15730, 8978, 21542, 6027, 3660, 8032, 3215, 7578, 2139, 5633, 472, 420, 9122, 19528, 3660, 420, 15844, 23032, 12610, 5296, 2423, 28811, 512, 4978, 1392, 264, 1674, 5633, 264, 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أرقام بتنتهي بخمسة فالخمسة لايمكن تكون even فإذا this joint ومدين في or بجمع وانا متطمن ان مافيش اي turn تاني محتاج اطرحه", "tokens": [5211, 754, 20193, 5016, 19913, 31371, 34105, 41850, 39894, 4117, 19528, 18871, 754, 8032, 3215, 12610, 2625, 12602, 4587, 2304, 754, 8032, 3215, 12610, 6225, 46309, 5551, 2288, 4587, 10943, 39894, 29399, 3224, 1829, 4724, 9778, 2304, 3794, 3660, 6156, 6027, 9778, 2304, 3794, 3660, 20193, 32640, 19452, 6055, 30544, 754, 6156, 28814, 15730, 341, 7225, 4032, 2304, 3215, 9957, 8978, 420, 4724, 7435, 2304, 3615, 4032, 7649, 995, 44650, 9566, 27842, 16472, 19446, 41185, 8592, 1975, 1829, 1261, 6055, 7649, 1829, 3714, 33753, 26108, 1975, 9566, 2288, 5016, 3224], "avg_logprob": -0.270089281129313, "compression_ratio": 1.538860103626943, "no_speech_prob": 1.3113021850585938e-06, "words": [{"start": 2452.7, "end": 2453.1, "word": "15", "probability": 0.2164306640625}, {"start": 2453.1, "end": 2453.48, "word": " even", "probability": 0.396240234375}, {"start": 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"start": 2475.93, "end": 2500.41, "text": "لأن احنا عارفين إنه لازم إذا كان في intersection بدنا نطرح قيمة ال intersection جاينة .. جاينة هتشرحها فهنا هيطلع عددهم ستين ways لتمثيل ال task الأولى or task التانية .. or task التانية فهي الستين okay how many different pit strings of length seven are there؟ جدش؟", "tokens": [1211, 33456, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 36145, 3224, 5296, 31377, 2304, 11933, 15730, 25961, 8978, 15236, 47525, 8315, 8717, 9566, 2288, 5016, 12174, 32640, 3660, 2423, 15236, 10874, 995, 9957, 3660, 4386, 10874, 995, 9957, 3660, 8032, 2655, 46309, 5016, 11296, 6156, 3224, 8315, 39896, 9566, 1211, 3615, 6225, 3215, 3215, 16095, 8608, 2655, 9957, 2098, 5296, 39237, 12984, 26895, 2423, 5633, 16247, 12610, 7578, 420, 5633, 16712, 7649, 10632, 4386, 420, 5633, 16712, 7649, 10632, 6156, 3224, 1829, 2423, 14851, 9957, 1392, 577, 867, 819, 10147, 13985, 295, 4641, 3407, 366, 456, 22807, 10874, 3215, 8592, 22807], "avg_logprob": -0.20557597630164204, 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في النهاية هحنحطوه في sequence واحد together together بمعنى محتاج اعمل ال task الأولى و ال task التانية", "tokens": [6027, 7825, 20449, 8315, 3224, 29910, 23275, 16472, 42963, 33753, 2304, 6027, 24976, 10721, 12610, 7578, 7551, 6055, 7649, 10632, 23032, 1829, 3555, 34105, 27011, 4032, 8978, 28239, 11296, 10632, 28242, 3224, 48812, 2288, 2288, 15844, 1975, 34268, 3555, 9640, 16472, 28242, 16095, 8978, 28239, 11296, 10632, 8032, 5016, 1863, 5016, 9566, 2407, 3224, 8978, 8310, 36764, 24401, 1214, 1214, 4724, 2304, 3615, 1863, 7578, 3714, 33753, 26108, 1975, 25957, 1211, 2423, 5633, 16247, 12610, 7578, 4032, 2423, 5633, 16712, 7649, 10632], "avg_logprob": -0.19879518251821218, "compression_ratio": 1.6700507614213198, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2611.66, "end": 2611.9, "word": "ال", "probability": 0.7568359375}, {"start": 2611.9, "end": 2612.2, "word": " letters", "probability": 0.630859375}, {"start": 2612.2, "end": 2612.86, "word": " معناه", "probability": 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letter followed by a digit فإذا في عندى task أولى ال task الأولى كده عددهم؟ ستة وعشرين انتهينا خالص ستة وعشرين okay", "tokens": [10721, 3224, 7251, 43020, 4724, 43042, 3224, 8032, 18513, 21136, 3224, 37977, 45164, 9122, 8315, 8717, 25957, 1211, 4724, 43042, 3224, 6225, 42213, 10632, 40244, 4724, 995, 14851, 9778, 3215, 10943, 2423, 3875, 2856, 307, 2139, 2423, 7645, 23758, 34051, 9673, 38251, 7578, 23758, 5551, 24401, 11331, 26108, 2655, 9957, 307, 2139, 257, 2167, 5063, 420, 257, 5063, 6263, 538, 257, 14293, 6156, 28814, 15730, 8978, 43242, 7578, 5633, 5551, 12610, 7578, 2423, 5633, 16247, 12610, 7578, 9122, 3215, 3224, 6225, 3215, 3215, 16095, 22807, 8608, 2655, 3660, 4032, 3615, 46309, 9957, 16472, 47395, 1829, 8315, 16490, 6027, 9381, 8608, 2655, 3660, 4032, 3615, 46309, 9957, 1392], "avg_logprob": -0.21296296544648982, "compression_ratio": 1.6491935483870968, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 2669.69, "end": 2669.93, "word": "أه", "probability": 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وعشرين", "probability": 0.8077392578125}, {"start": 2695.43, "end": 2695.83, "word": " انتهينا", "probability": 0.711090087890625}, {"start": 2695.83, "end": 2696.09, "word": " خالص", "probability": 0.8909505208333334}, {"start": 2696.09, "end": 2696.39, "word": " ستة", "probability": 0.8401692708333334}, {"start": 2696.39, "end": 2697.29, "word": " وعشرين", "probability": 0.9808349609375}, {"start": 2697.29, "end": 2697.97, "word": " okay", "probability": 0.759765625}], "temperature": 1.0}, {"id": 111, "seek": 272021, "start": 2702.85, "end": 2720.21, "text": "لأ في عندك ستة و عشرين followed by ten معناه انت ستة و عشرين في عشرة علاقتهم مع بعض ضرب لأ في or زائد فبتطلع هنا مائتين و سبتين زائد ستة و عشرين ستة تمانية اتنين", "tokens": [1211, 10721, 8978, 43242, 4117, 8608, 2655, 3660, 4032, 6225, 46309, 9957, 6263, 538, 2064, 20449, 8315, 3224, 16472, 2655, 8608, 2655, 3660, 4032, 6225, 46309, 9957, 8978, 6225, 8592, 25720, 11203, 995, 38149, 16095, 20449, 45030, 11242, 48812, 25513, 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"probability": 0.970703125}, {"start": 3629.73, "end": 3630.79, "word": " في", "probability": 0.51123046875}, {"start": 3630.79, "end": 3631.05, "word": " الحالة", "probability": 0.9384765625}, {"start": 3631.05, "end": 3631.19, "word": " هذا", "probability": 0.2161865234375}, {"start": 3631.19, "end": 3631.31, "word": " ال", "probability": 0.50830078125}, {"start": 3631.31, "end": 3631.81, "word": " cardinality", "probability": 0.8795572916666666}, {"start": 3631.81, "end": 3631.97, "word": " ل", "probability": 0.83642578125}, {"start": 3631.97, "end": 3632.15, "word": " A", "probability": 0.62939453125}, {"start": 3632.15, "end": 3632.51, "word": " union", "probability": 0.8837890625}, {"start": 3632.51, "end": 3632.77, "word": " B", "probability": 0.85107421875}, {"start": 3632.77, "end": 3633.13, "word": " هتساوي", "probability": 0.8521484375}, {"start": 3633.13, "end": 3633.23, "word": " ال", "probability": 0.52001953125}, {"start": 3633.23, "end": 3633.65, "word": " cardinality", 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الكلام", "probability": 0.9529622395833334}, {"start": 3640.01, "end": 3641.07, "word": " not", "probability": 0.93603515625}, {"start": 3641.07, "end": 3641.75, "word": " disjoint", "probability": 0.9345703125}, {"start": 3641.75, "end": 3642.41, "word": " في", "probability": 0.91162109375}, {"start": 3642.41, "end": 3642.63, "word": " حالة", "probability": 0.9754231770833334}, {"start": 3642.63, "end": 3642.71, "word": " ان", "probability": 0.62451171875}, {"start": 3642.71, "end": 3642.81, "word": " هي", "probability": 0.6025390625}, {"start": 3642.81, "end": 3642.99, "word": " not", "probability": 0.67431640625}, {"start": 3642.99, "end": 3643.41, "word": " disjoint", "probability": 0.94091796875}, {"start": 3643.41, "end": 3643.79, "word": " بمعنى", "probability": 0.88984375}, {"start": 3643.79, "end": 3644.19, "word": " يوجد", "probability": 0.9723307291666666}, {"start": 3644.19, "end": 3644.79, "word": " intersection", "probability": 0.89892578125}, {"start": 3644.79, "end": 3645.07, "word": " between", "probability": 0.9287109375}, {"start": 3645.07, "end": 3645.37, "word": " them", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 147, "seek": 367397, "start": 3651.65, "end": 3673.97, "text": "ببساطة جدا a plus b و خلاص ال cardinality ل a plus ال cardinality ل 11 ناخد شوية examples عليها عشان تتضحى example how many pet strings of length 4 either start with one or end with double zero", "tokens": [3555, 3555, 3794, 41193, 3660, 10874, 28259, 257, 1804, 272, 4032, 16490, 1211, 33546, 2423, 2920, 259, 1860, 5296, 257, 1804, 2423, 2920, 259, 1860, 5296, 2975, 8717, 47283, 3215, 13412, 2407, 10632, 5110, 25894, 11296, 6225, 8592, 7649, 6055, 2655, 11242, 5016, 7578, 1365, 577, 867, 3817, 13985, 295, 4641, 1017, 2139, 722, 365, 472, 420, 917, 365, 3834, 4018], "avg_logprob": -0.32963709965828925, "compression_ratio": 1.3505747126436782, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 3651.6499999999996, "end": 3652.45, "word": "ببساطة", 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"probability": 0.908203125}, {"start": 3672.83, "end": 3673.33, "word": " double", "probability": 0.82861328125}, {"start": 3673.33, "end": 3673.97, "word": " zero", "probability": 0.7470703125}], "temperature": 1.0}, {"id": 148, "seek": 369804, "start": 3680.2, "end": 3698.04, "text": "عندكوا string عبارة عن four length، ال four length هدولة جدّاش عددهم بشرط بشرط أنه either start one إما بيبدأوا بواحد أو بينتهوا or", "tokens": [3615, 41260, 4117, 14407, 6798, 6225, 3555, 9640, 3660, 18871, 1451, 4641, 12399, 2423, 1451, 4641, 8032, 3215, 12610, 3660, 10874, 3215, 11703, 33599, 6225, 3215, 3215, 16095, 4724, 46309, 9566, 4724, 46309, 9566, 14739, 3224, 2139, 722, 472, 11933, 15042, 4724, 1829, 44510, 10721, 14407, 4724, 14407, 24401, 34051, 4724, 9957, 47395, 14407, 420], "avg_logprob": -0.22753905771034105, "compression_ratio": 1.3310810810810811, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3680.2000000000003, "end": 3681.42, "word": "عندكوا", "probability": 0.866455078125}, {"start": 3681.42, "end": 3682.64, "word": " string", "probability": 0.432373046875}, {"start": 3682.64, "end": 3683.3, "word": " عبارة", "probability": 0.989013671875}, {"start": 3683.3, "end": 3683.42, "word": " عن", "probability": 0.998046875}, {"start": 3683.42, "end": 3683.6, "word": " four", "probability": 0.794921875}, {"start": 3683.6, "end": 3684.4, "word": " length،", "probability": 0.3753662109375}, {"start": 3684.4, "end": 3684.48, "word": " ال", "probability": 0.77587890625}, {"start": 3684.48, "end": 3684.68, "word": " four", "probability": 0.73828125}, {"start": 3684.68, "end": 3684.88, "word": " length", "probability": 0.74951171875}, {"start": 3684.88, "end": 3685.5, "word": " هدولة", "probability": 0.922607421875}, {"start": 3685.5, "end": 3687.44, "word": " جدّاش", "probability": 0.63262939453125}, {"start": 3687.44, "end": 3688.04, "word": " عددهم", "probability": 0.983154296875}, {"start": 3688.04, "end": 3689.08, "word": " بشرط", "probability": 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3699.34, "end": 3727.22, "text": "فبناخد الحالة الأولى للحالة والثانية للحالة وما دام or بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن ن", "tokens": [5172, 3555, 1863, 47283, 3215, 21542, 6027, 3660, 16247, 12610, 7578, 24976, 5016, 6027, 3660, 4032, 6027, 12984, 7649, 10632, 24976, 5016, 6027, 3660, 4032, 15042, 11778, 10943, 420, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 2304, 3615, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 2304, 3615, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 2304, 3615, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 2304, 3615, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 2304, 3615, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 2304, 3615, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 2304, 3615, 4724, 1829, 7435, 3555, 14739, 8717, 7435, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a319d90db0000e2c38a0bb9429578c54196d982a
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DD32SMqZgwk_raw.srt
@@ -0,0 +1,3404 @@
+1
+00:00:20,960 --> 00:00:22,940
+طيب بسم الله الرحمن الرحيم والصلاة والسلام علي
+
+2
+00:00:22,940 --> 00:00:25,480
+أشرف الأنبياء والمسلمين سيدنا محمد وعليه عليه
+
+3
+00:00:25,480 --> 00:00:29,100
+وصحبه أجمعين المرة اللي فاتت كنا تتكلمنا عن ال
+
+4
+00:00:29,100 --> 00:00:34,580
+recursion و اليوم ان شاء الله بنكمل في نفس الموضوع
+
+5
+00:00:34,580 --> 00:00:40,710
+بإذن الله تعالىكنا اتكلمنا عن irrigation لأ as a
+
+6
+00:00:40,710 --> 00:00:43,890
+function اتكلمنا عن irrigation as a set و اتكلمنا
+
+7
+00:00:43,890 --> 00:00:47,450
+عنها as a string لو متذكرين اخر ما اتكلمنا عن ال
+
+8
+00:00:47,450 --> 00:00:52,230
+lambda و الشغل
+
+9
+00:00:54,300 --> 00:00:58,760
+ال Z ال ال big sigma و ال big sigma star و قولنا
+
+10
+00:00:58,760 --> 00:01:00,660
+ايش الفرق بين ال big sigma و ال big sigma star و
+
+11
+00:01:00,660 --> 00:01:03,800
+قولنا كنت .. كنت .. كنت بقولهم كويسة دلنا هنا ال
+
+12
+00:01:03,800 --> 00:01:07,420
+recursive algorithms .. recursive algorithms اللي
+
+13
+00:01:07,420 --> 00:01:09,680
+ضايلة في الجزء اللي عندنا عشان ننجل بعد هيك على
+
+14
+00:01:09,680 --> 00:01:14,610
+موضوعنا الفعل تاع اليوم نشوف ايشالفكرة في ال
+
+15
+00:01:14,610 --> 00:01:19,370
+recursive algorithms فعليا في ال algorithms نستفيد
+
+16
+00:01:19,370 --> 00:01:23,110
+من عملية ال recursion او عملية التكرار بحيث ان انا
+
+17
+00:01:23,110 --> 00:01:27,030
+ارجع اعيد نفس ال code هو هو اللي انا مازل موجود
+
+18
+00:01:27,030 --> 00:01:30,030
+فيه اصلا اللي انا اصلا موجود فيه ولكن لقيم جديدة
+
+19
+00:01:30,030 --> 00:01:35,060
+لقيم جديدة for example لو اخدنا مثلامثلًا، يحتاجون
+
+20
+00:01:35,060 --> 00:01:37,280
+إلى حساب أو عملية عملية عملية عملية عملية عملية
+
+21
+00:01:37,280 --> 00:01:42,460
+A�N A�N فبقدر أقول أن عملية عملية عملية عملية
+
+22
+00:01:42,460 --> 00:01:47,200
+عملية عملية A�N A لا تساوي صفر، الـ A هذه المفروض
+
+23
+00:01:47,200 --> 00:01:50,600
+أنها لا تساوي صفر، يكون لها قيمة حقيقية، قيمة
+
+24
+00:01:50,600 --> 00:01:53,500
+حقيقية، قيمة واضحة، ماتكونش بتساوي صفر، و الـ N
+
+25
+00:01:53,500 --> 00:01:59,700
+هذه إنتجر أو عدد طبيعي، عدد طبيعي، عدد طبيعي، عدد
+
+26
+00:01:59,700 --> 00:02:02,340
+طبيعي، عدد طبيعي، عدد طبيعي، عدد طبيعي، عدد طبيعي،
+
+27
+00:02:02,340 --> 00:02:06,570
+عدد طبيعي، عدد طبيعnatural number أقل قيمة فيها
+
+28
+00:02:06,570 --> 00:02:09,190
+zero يعني معناته أن ال zero belong to natural
+
+29
+00:02:09,190 --> 00:02:11,870
+number فممكن تكون zero والله إذا كان zero return
+
+30
+00:02:11,870 --> 00:02:17,570
+one و بنوقف بنوقف okay otherwise أو else return
+
+31
+00:02:17,570 --> 00:02:25,290
+لاحظوا إيش a في power a هي هي بس مش في n في n
+
+32
+00:02:25,290 --> 00:02:29,750
+minus one في n minus one كأن جبت relation between
+
+33
+00:02:29,750 --> 00:02:34,580
+a n و a n minus oneاللي أخدناها المرة اللي فاتت
+
+34
+00:02:34,580 --> 00:02:41,960
+لما قلنا a n بتساوي a n minus one بالظبط في a فهي
+
+35
+00:02:41,960 --> 00:02:47,600
+ال a كل اللي عملناه بس أننا بدنا نحسب لمين ل a to
+
+36
+00:02:47,600 --> 00:02:51,840
+the power n minus one بدل ما كنت بشغل a to the
+
+37
+00:02:51,840 --> 00:02:57,400
+power n فهيها حددناها n minus one طبعا هنا ال n
+
+38
+00:02:57,400 --> 00:03:02,370
+قلت واحدقلت القيمة واحد كويس هنرجع .. إيش هيعمل؟
+
+39
+00:03:02,370 --> 00:03:07,510
+هيرجع تاني لنفس ال procedure هو هو بس بمين؟ n-1
+
+40
+00:03:07,510 --> 00:03:12,530
+okay هل n هنا أصبحت zero لإن هي قلت واحد؟ جمت جلة
+
+41
+00:03:12,530 --> 00:03:18,150
+بواحد والله إذا كان zero return one لأ else return
+
+42
+00:03:18,150 --> 00:03:28,750
+كمان مرة هذه a مضروبة في a n-2 a
+
+43
+00:03:29,590 --> 00:03:38,630
+فى a n-3 لعند ما نصل هذى equal to zero هى stop
+
+44
+00:03:38,630 --> 00:03:42,850
+لأنه حيجف هنا خلاص حيجف هنا بس حيجف بعد ايش بعد ما
+
+45
+00:03:42,850 --> 00:03:48,510
+يكون ضرب كل ال a او ال a's اللى احنا جمعنا هى a a
+
+46
+00:03:48,510 --> 00:03:52,650
+a a والله لو عدد ال n هذى عددها اتنين هتلاقي انه
+
+47
+00:03:52,650 --> 00:03:56,760
+العملية هتتكرر مرتين عبارة عن a في aاللي حيحصل
+
+48
+00:03:56,760 --> 00:04:00,940
+فعلا انه هتكون a في a فهي فعلا ال a تربيع باعتبار
+
+49
+00:04:00,940 --> 00:04:04,500
+انه اتنين فانتوا فعلا جبتوا ال power عن طريق عملية
+
+50
+00:04:04,500 --> 00:04:11,320
+recursive او عن طريق recursive algorithm اكترار
+
+51
+00:04:11,320 --> 00:04:15,520
+ال algorithm نفسه اكترار ال algorithm نفسه كمان
+
+52
+00:04:15,520 --> 00:04:19,700
+مثالواضح جدا المثال هذا انه كان اصلا في عملية ال
+
+53
+00:04:19,700 --> 00:04:23,420
+recursion موجودة اللي هو ال Euclides algorithm لان
+
+54
+00:04:23,420 --> 00:04:25,400
+ال Euclides algorithm لما كنت بتحسبه ال greatest
+
+55
+00:04:25,400 --> 00:04:30,680
+common divisor كنت بتجيبه ال modular صحيح a mod b
+
+56
+00:04:31,620 --> 00:04:37,140
+إذا ال A أو الناتج ال modular لا يساوي 0، نستمر،
+
+57
+00:04:37,140 --> 00:04:39,520
+كنا بنكمل، كمان نعمل كمان modular تاني، كمان
+
+58
+00:04:39,520 --> 00:04:43,460
+modular تالت، كمان رابع، خمس، لعندنا الناتج الحاصل
+
+59
+00:04:43,460 --> 00:04:46,700
+ل ال modular، operation equal to 0، فبنقول إن ال
+
+60
+00:04:46,700 --> 00:04:50,660
+greatest common divisor إيش؟ ال element Bمتذكرينه؟
+
+61
+00:04:50,660 --> 00:04:54,280
+اذكرناها؟ كويس فمعنى ذلك ان في عملية تكرار هنا
+
+62
+00:04:54,280 --> 00:04:58,380
+لمين ل greatest common divisor operation اللى
+
+63
+00:04:58,380 --> 00:05:04,840
+بنعملها باستخدام ال modular او ال mod لterm أصغر
+
+64
+00:05:04,840 --> 00:05:07,920
+منهم طيب كيف نعمل الكلام هذا؟ لحظو ال procedure
+
+65
+00:05:07,920 --> 00:05:11,160
+greatest common divisor a,b belonging to natural
+
+66
+00:05:11,160 --> 00:05:15,620
+number ا و b بدنا نجيب greatest common divisor او
+
+67
+00:05:15,620 --> 00:05:19,660
+العامل المشترك الأكبرwe belong to natural number
+
+68
+00:05:19,660 --> 00:05:27,220
+if a is equal to zero و لاحظوا هنا عشان تظبط
+
+69
+00:05:27,220 --> 00:05:30,620
+العملية احنا مرتبينها بحيث انه ال element الأول هو
+
+70
+00:05:30,620 --> 00:05:34,920
+الأصغر هو الأصغر عشان ما نضطرش نعمل operation
+
+71
+00:05:34,920 --> 00:05:39,260
+إبافية في النص اللي هي عملية ال swap تذكرتوها؟ لأ
+
+72
+00:05:39,260 --> 00:05:41,560
+مش مضطرين نعمل swap كل اللي بعمله من الأساس برتبه
+
+73
+00:05:41,560 --> 00:05:44,180
+على أساس انه في الأول هو الأصغر و خلاص عشان ال
+
+74
+00:05:44,180 --> 00:05:50,310
+recursion يكون أسرع أو يكون أسهل okayA وB فلو اذا
+
+75
+00:05:50,310 --> 00:05:56,010
+A equal to 0 then return B ارجع القيمة B فلسنا طيب
+
+76
+00:05:56,010 --> 00:05:59,870
+otherwise لأ return لاحظوا greatest common divisor
+
+77
+00:05:59,870 --> 00:06:06,190
+بي مودلر او mod A فواضح ان هذا الterm الصغير هيأتي
+
+78
+00:06:06,190 --> 00:06:11,690
+في الأول فعلا Aكل اللي حنصير أنه هعيد التكرار نفسه
+
+79
+00:06:11,690 --> 00:06:17,450
+بس ال B هذه أصبحت هي مكان ال A مكانها ال A و ال A
+
+80
+00:06:17,450 --> 00:06:26,110
+القيمة الأصغر صار مكانها B mod A ال B mod A والله
+
+81
+00:06:26,110 --> 00:06:30,990
+إذا كان ال B mod A equal to 0 ارجع للقيمة ال B
+
+82
+00:06:30,990 --> 00:06:33,710
+اللي أهل وجد اتعرفت بيه اللي هي أصلا كانت مين؟ A
+
+83
+00:06:33,710 --> 00:06:41,760
+كانت إيه؟ A لأ لا تساوي 0الناتج اللى هو a لجديدة و
+
+84
+00:06:41,760 --> 00:06:45,480
+b لجديدة برضه هنرجع نعمل كمان modular كمان مرة
+
+85
+00:06:45,480 --> 00:06:50,080
+فهذه عملية التكرار اللى أخدتها سابقا لما كنتوا
+
+86
+00:06:50,080 --> 00:06:53,020
+جيبوا ال greatest common divisor باستخدام ال
+
+87
+00:06:53,020 --> 00:06:55,720
+modular operation باستخدام ال modular operation
+
+88
+00:06:55,720 --> 00:07:00,400
+okay طبعا في حالة زى هذه واضح أن هنا ال recursive
+
+89
+00:07:00,400 --> 00:07:05,460
+algorithm كتير أبسطأو أصغر .. كلها تلت أسطور ..
+
+90
+00:07:05,460 --> 00:07:08,680
+أصغر من أني لو بدي أعملها بالطريقة المطولة اللي
+
+91
+00:07:08,680 --> 00:07:10,740
+أخدناها سابقا .. بالطريقة المطولة اللي أخدناها
+
+92
+00:07:10,740 --> 00:07:13,940
+سابقا لإن أنا عارف هيك أن في recursion بيصير .. في
+
+93
+00:07:13,940 --> 00:07:16,780
+تكرار بيصير لعمليتي ال modular هنا .. تكرار
+
+94
+00:07:16,780 --> 00:07:21,200
+لعمليتي ال modular ف ال recursive algorithm الأمور
+
+95
+00:07:21,200 --> 00:07:23,860
+بتصير أسهل .. كلها تلت أسطور و خلاص مفهومة ..
+
+96
+00:07:23,860 --> 00:07:28,700
+مشكلتنا عندنا مشكلة واحدة .. لو ..ال بي سي ستبعتكم
+
+97
+00:07:28,700 --> 00:07:33,220
+not smart enough مش ذاكية او ال operation system
+
+98
+00:07:33,220 --> 00:07:36,460
+اللي انتوا شغالينه مش ذاكي كفاية انه يعرف انه شغال
+
+99
+00:07:36,460 --> 00:07:39,900
+في نفس ال algorithm ليش؟ لأنه في الحالة هدي جديش
+
+100
+00:07:39,900 --> 00:07:43,860
+عدد التكرارات هيروح يفتح نفس الملف كذا مرةفهيصير
+
+101
+00:07:43,860 --> 00:07:48,340
+بده stack أكبر، بده RAM أكبر، ال memory ساعته
+
+102
+00:07:48,340 --> 00:07:52,180
+هتستهلك لإنه هيفتحه كذا مرة، لو أخدنا الرقامين A
+
+103
+00:07:52,180 --> 00:07:55,400
+وB، أرقام كتير كبيرة، و نفترض إن ال greatest
+
+104
+00:07:55,400 --> 00:07:58,900
+common divisor بتبعهم واحد، معناه ذلك إنه هيتطر
+
+105
+00:07:58,900 --> 00:08:02,260
+يعمل operations كتيرة، في الحالة هذه عبل ما يصل
+
+106
+00:08:02,260 --> 00:08:05,020
+لمن؟ للواحد، لإن مافيش greatest common divisor
+
+107
+00:08:05,020 --> 00:08:10,160
+واضح من الأولفي الحالة هذه يعني يمكن يضطر يفتح ال
+
+108
+00:08:10,160 --> 00:08:15,560
+code خمستاشر عشرين مرة تلاتين مرة طب وين بده يحطهم
+
+109
+00:08:15,560 --> 00:08:18,860
+المفاتيح المفتوحة هذه الكتير؟ هيحطها في ال RAM في
+
+110
+00:08:18,860 --> 00:08:21,780
+ال stack تبعته ال stack مش حتى الساعة مش حتى
+
+111
+00:08:21,780 --> 00:08:24,760
+الساعةفهتلاقوا بعد فترة هذه المشكلة الوحيدة هنا
+
+112
+00:08:24,760 --> 00:08:29,180
+أنه هيحتاج stack أكبر وهذا بيبين إذا كانت ال
+
+113
+00:08:29,180 --> 00:08:32,600
+compiler تبعتكم is not smart enough عشان تعرف أنه
+
+114
+00:08:32,600 --> 00:08:35,620
+والله أنا بشتغل على نفس ال code فمافيش داعي أرجع
+
+115
+00:08:35,620 --> 00:08:38,940
+أفتحه كمان مرة مافيش داعي نرجع نفتحه كمان مرة حتى
+
+116
+00:08:38,940 --> 00:08:43,120
+لو أنا بعمل استدعاء له recalling لنفس ال greatest
+
+117
+00:08:43,120 --> 00:08:46,340
+common divisor code بس بده يعرف أنه أنا في نفس ال
+
+118
+00:08:46,340 --> 00:08:49,850
+code ما زلتكل اللي بده يضطر يشتغله يشتغل على أخر
+
+119
+00:08:49,850 --> 00:08:52,630
+نتاج أخر أرقام النتاج اللي في الأول بيخليهاش
+
+120
+00:08:52,630 --> 00:08:56,710
+موجودة في ال RAM خلاص بيشيلها بيحفظ حسب ال
+
+121
+00:08:56,710 --> 00:09:00,210
+algorithm ايش الأرقام اللي محتاجها فقط و ليس انه
+
+122
+00:09:00,210 --> 00:09:04,710
+يقعد كل مرة يفتح ال code من أول من أول و جديد okay
+
+123
+00:09:05,400 --> 00:09:08,200
+الـ Linear .. Linear Search أخدنا Linear Search
+
+124
+00:09:08,200 --> 00:09:11,360
+قبل هيك برضه بنقدر نعملها باستخدام ال recursive
+
+125
+00:09:11,360 --> 00:09:15,280
+operation أو ال .. ال .. as a recursive algorithm
+
+126
+00:09:15,280 --> 00:09:19,320
+ولكن هتكون هنا مالهاش كتير معنى ليش؟ لأنه ال
+
+127
+00:09:19,320 --> 00:09:23,400
+complexity أنا ماقدرتش أوفر فيها هناك وفرنا صارت
+
+128
+00:09:23,400 --> 00:09:26,060
+عندي تلت صفور فقط صار وفرنا في ال code هنا مش
+
+129
+00:09:26,060 --> 00:09:29,160
+هنقدر نوفر إشي لأنه هيك هيك هنشتغل Linear و هنشتغل
+
+130
+00:09:29,160 --> 00:09:32,680
+.. هنعمل scan على كل أو مسح على كل ال elements
+
+131
+00:09:32,680 --> 00:09:37,060
+اللي موجودة داخل ال ..الـ sequence اللي بندور فيه
+
+132
+00:09:37,060 --> 00:09:43,000
+خلّيني نشوف كيف بتم الموضوع متذكرين هل ال linear؟
+
+133
+00:09:43,000 --> 00:09:46,260
+linear search نبدأ من أول رقم و بنبدأ نقارن رقم
+
+134
+00:09:46,260 --> 00:09:48,980
+موجود هل هو موجود داخل ال sequence أو غير موجود ف
+
+135
+00:09:48,980 --> 00:09:53,260
+X رقم given من عندى بدنا نشوفه هل هو موجود في ال
+
+136
+00:09:53,260 --> 00:09:58,100
+sequence A أو غير موجود في ال sequence A فهيكون ال
+
+137
+00:09:58,100 --> 00:10:02,000
+procedure search A ممكن نكتبها linear search عشان
+
+138
+00:10:02,000 --> 00:10:05,540
+نميز إنه أنا بخطل على linearA هدا ال series اللى
+
+139
+00:10:05,540 --> 00:10:10,400
+بدنا ندور داخلها و ال series هدى هنعرفها ببداية و
+
+140
+00:10:10,400 --> 00:10:14,980
+نهاية ب start point و end point I و J هدولة
+
+141
+00:10:14,980 --> 00:10:20,530
+integers هدول هيكون عبارة عن إيش integersX ما زالت
+
+142
+00:10:20,530 --> 00:10:23,550
+هي داخل ال arguments بتاعتنا، فإذا هذه برضه موضوع
+
+143
+00:10:23,550 --> 00:10:26,450
+من الموضوعات اللي هي ال X، إيش ال item اللي بتكون
+
+144
+00:10:26,450 --> 00:10:29,890
+بدنا ندور عليه؟ فال item تبعنا item to be found
+
+145
+00:10:29,890 --> 00:10:34,530
+اللي بدنا ندور عليه، اللي هي نوجده، okay عرفنا ال
+
+146
+00:10:34,530 --> 00:10:37,900
+procedure بتاعتنا أو عرفناالـ arguments تبعت ال
+
+147
+00:10:37,900 --> 00:10:41,700
+algorithm تبعنا المطلوب طبعا منه عارفين أن الأقواص
+
+148
+00:10:41,700 --> 00:10:44,780
+هذه معناها مجرد comments هذه ال comments مش من
+
+149
+00:10:44,780 --> 00:10:48,600
+داخل أو مش من جزء ال algorithm نفسه find X in
+
+150
+00:10:48,600 --> 00:10:53,600
+series A at a location أكبر من أو يساوي I و أقل من
+
+151
+00:10:53,600 --> 00:10:56,320
+J فانا محددها والله إذا كان بتكون دوره في ال
+
+152
+00:10:56,320 --> 00:10:59,990
+series كله عملوها من صفرته Nإذا محتاجين كل ال
+
+153
+00:10:59,990 --> 00:11:05,010
+series تدوروا فيها فهنا بتبدأ من واحد من أول
+
+154
+00:11:05,010 --> 00:11:09,010
+location تقاش J حتكون اللي هي ال N فانتوا بتاخدوا
+
+155
+00:11:09,010 --> 00:11:13,850
+كل ال series بتاعتكم هنا in general هنقول من I to
+
+156
+00:11:13,850 --> 00:11:16,930
+J و بعدين بتخطوها زي ما بدكم حسب إيش اللي بيكون
+
+157
+00:11:16,930 --> 00:11:24,360
+مطلوب منكم okay if a I أول elementفإذا كان بدء من
+
+158
+00:11:24,360 --> 00:11:28,960
+واحد بحط a1 إذا كان الـ a1 أول واحد أو لا هنا بحطه
+
+159
+00:11:28,960 --> 00:11:33,660
+i عسى إنه يبقى variable لل subroutines اللي جاية
+
+160
+00:11:33,660 --> 00:11:37,540
+للsubroutines اللي هتجينا لجدام فai equal to إيش
+
+161
+00:11:37,540 --> 00:11:43,420
+to x if equal to x return i خلاص إذا صدفت إنه فعلا
+
+162
+00:11:43,420 --> 00:11:51,930
+أول عند ال element i هذا ال element الأخير jهنعمل
+
+163
+00:11:51,930 --> 00:11:56,110
+مقارنة ل X مع A I ال element اللي موجود في ال
+
+164
+00:11:56,110 --> 00:12:02,570
+location I هو نفسه بيسوي خلاص برجع كلمة I ان هو
+
+165
+00:12:02,570 --> 00:12:05,030
+موجود و ال location تبعه I
+
+166
+00:12:08,260 --> 00:12:16,300
+خلصنا منها نعود إلى I if I equal to J return 0 اذا
+
+167
+00:12:16,300 --> 00:12:20,920
+I في مرحلة من المراحل وصلت ان هي قيمتها نفسها J
+
+168
+00:12:20,920 --> 00:12:24,520
+معناته لايوجد elements بينهم انا واضح ان انا عملت
+
+169
+00:12:24,520 --> 00:12:30,130
+scan على كل درجة ان ال I وصلت ل J بناءعلى اللي حصل
+
+170
+00:12:30,130 --> 00:12:34,290
+تاني فهدي نوقفها شوية هنرجع لها كمان مرة عندنا
+
+171
+00:12:34,290 --> 00:12:38,990
+نوضح كيف فعلا ال I هتروح لل J هتروح بناء على ال
+
+172
+00:12:38,990 --> 00:12:41,350
+return اللي جاية بناء على ال return اللي جاية اذا
+
+173
+00:12:41,350 --> 00:12:44,210
+والله ال condition الأول لم يتحققcondition التاني
+
+174
+00:12:44,210 --> 00:12:48,150
+لم يتحقق ايش بدنا نعمل؟ معناته انا لأ ما زال في
+
+175
+00:12:48,150 --> 00:12:51,710
+elements موجودة ماعملتش فحص عليها وأول element
+
+176
+00:12:51,710 --> 00:12:56,770
+موجود لا يسوى x فإيش بدنا نعمل؟ return search كمان
+
+177
+00:12:56,770 --> 00:13:00,630
+مرة يعني انا عملت recalling لمين؟ لل code أنا بسمي
+
+178
+00:13:00,630 --> 00:13:03,390
+ال code search يعني instead of search إيش ال
+
+179
+00:13:03,390 --> 00:13:08,890
+elements سبعته؟ I plus 1 و J و X، X اللي هو بدور
+
+180
+00:13:08,890 --> 00:13:17,570
+عليه فأصبحت ال Iبنبدأ بمين؟ I زائد واحد جمعنا واحد
+
+181
+00:13:17,570 --> 00:13:22,990
+جمعنا عليها واحد وصارت هذه ال element التاني صارت
+
+182
+00:13:22,990 --> 00:13:26,590
+هي ال I بالنسبالنا بقارن كمان مرة خلصنا بدينا
+
+183
+00:13:26,590 --> 00:13:34,170
+بقارن برضه ايه؟ I هنا كانت واحد هنا أصبحت اتنين ال
+
+184
+00:13:34,170 --> 00:13:36,930
+location التاني أصبحت طيب بقارن X مع ال location
+
+185
+00:13:36,930 --> 00:13:44,330
+التاني لأ لاتساويو لسه ال I أقل من J على التالت،
+
+186
+00:13:44,330 --> 00:13:46,970
+على الرابع، على الخمس، على السادس، لما تصل إيش
+
+187
+00:13:46,970 --> 00:13:53,330
+بتساوي؟ J لما تصل بتساوي J بعد عدد تكرارات إيش
+
+188
+00:13:53,330 --> 00:13:58,830
+بتساوي عدد تكراراتها؟ J minus Iبنكون ال search هذا
+
+189
+00:13:58,830 --> 00:14:03,910
+عملنا له recalling j minus i مرة صحيح؟ قبل ما نصل
+
+190
+00:14:03,910 --> 00:14:07,030
+انه طلعوا بيساوي بعض والله طلعوا بيساوي بعض معناته
+
+191
+00:14:07,030 --> 00:14:11,010
+واضحة ان عملت search على الكل مش موجود ال X برجع
+
+192
+00:14:11,010 --> 00:14:13,990
+باش Zero و Zero احنا عرفناه من المرة اللي فاتت
+
+193
+00:14:13,990 --> 00:14:16,930
+Zero معناته انه غير موجود في مين؟ في ال series
+
+194
+00:14:16,930 --> 00:14:20,230
+بتاعتنا ال element X غير موجود في ال series اللي
+
+195
+00:14:20,230 --> 00:14:24,050
+موجودة عندنا في الحالة دي بنرجع ب X او بنرجع ب I
+
+196
+00:14:24,050 --> 00:14:29,720
+إذا لجينا إذا وجدناانت بتحقق واحدة من الاتنتين
+
+197
+00:14:29,720 --> 00:14:34,360
+هدول مش هنتطر نيجي لمين ل .. ل ال return هذه مش
+
+198
+00:14:34,360 --> 00:14:37,420
+هنتطر نرجع لل return الأخيرة انه يعملنا استدعاء
+
+199
+00:14:37,420 --> 00:14:44,240
+كمان مرة ل ال code بقيم جديدة okayطبعا واضح ان انا
+
+200
+00:14:44,240 --> 00:14:48,060
+هعمل scan على الكل فانا مستفدتش فائدة واضحة من
+
+201
+00:14:48,060 --> 00:14:50,620
+عملية ال recursive algorithm اللي احنا عملناها ال
+
+202
+00:14:50,620 --> 00:14:53,180
+recursive algorithm تبعنا ماكانش كتير في
+
+203
+00:14:53,180 --> 00:14:58,260
+improvement حقيقة ماكانش في تطوير على ال procedure
+
+204
+00:14:58,260 --> 00:15:02,100
+نفسها تحديث على الموضوع نفسه اللي ماتغيرش في حاجة
+
+205
+00:15:02,100 --> 00:15:05,160
+عدد السطور ماتوفرش كتير ال procedure نفسها
+
+206
+00:15:05,160 --> 00:15:09,160
+ماتغيرتش كتير ال procedure نفسها ماتغيرتشكتير انا
+
+207
+00:15:09,160 --> 00:15:11,760
+هيك هيك بدى ابحث على كل ال elements فاحنا فعلا
+
+208
+00:15:11,760 --> 00:15:14,580
+بحثنا على كل ال elements قبل ما نصل لقرار انه غير
+
+209
+00:15:14,580 --> 00:15:21,280
+موجود X طيب يمكن تكون برضه recursive algorithm
+
+210
+00:15:21,280 --> 00:15:24,900
+ممكن نستخدمه ل ال binary search ل ال binary search
+
+211
+00:15:24,900 --> 00:15:28,280
+و ال binary search بدنا نركز شوية فيه عشان نشوف
+
+212
+00:15:28,280 --> 00:15:32,680
+كيف استخدم عملية المين عملية ال binary search برضه
+
+213
+00:15:32,680 --> 00:15:33,920
+ال binary search متذكرينها
+
+214
+00:15:37,910 --> 00:15:42,570
+نفس الفكرة هي هي عندنا a .. a series .. series
+
+215
+00:15:42,570 --> 00:15:45,930
+اسمها a و بدنا ندور على element اسمه x فال element
+
+216
+00:15:45,930 --> 00:15:49,770
+اسمه x القالية بتاعتنا اسمها binary .. binary
+
+217
+00:15:49,770 --> 00:15:54,310
+قولنا قبلها ان انا باجي بعمل jump على ال mid point
+
+218
+00:15:54,310 --> 00:15:57,770
+و بنشوف ال element عند ال mid point او عند ال mid
+
+219
+00:15:57,770 --> 00:16:02,810
+location هل يساوي x او لأ و بنقارن اكبر منه او اقل
+
+220
+00:16:02,810 --> 00:16:07,560
+منه على اعتبار ان ال series اصلا orderedعلى اعتبار
+
+221
+00:16:07,560 --> 00:16:10,600
+ان هي اصلا معمولها sorting .. معمولها sorting ..
+
+222
+00:16:10,600 --> 00:16:15,520
+okay و
+
+223
+00:16:15,520 --> 00:16:19,400
+نفس الكلام همحطه من I to J in general .. in
+
+224
+00:16:19,400 --> 00:16:23,780
+general .. okay عندنا I .. ال .. ال A .. ال series
+
+225
+00:16:23,780 --> 00:16:27,400
+اللي بندور عليها .. ال series ها دي من I to J و
+
+226
+00:16:27,400 --> 00:16:29,820
+عندنا ال element X اللي بدور عليه .. اللي بندور
+
+227
+00:16:29,820 --> 00:16:33,560
+عليه .. okayالـ midpoint أول ما نحسب نحسب ال
+
+228
+00:16:33,560 --> 00:16:38,160
+midpoint الأولى زائد الأخيرة على اتنين بتنقض لها
+
+229
+00:16:38,160 --> 00:16:41,540
+floor لأنه أكيد ممكن تطلع كسر ممكن تطلع كسر و احنا
+
+230
+00:16:41,540 --> 00:16:44,460
+عارفين ان ال locations integers ال location
+
+231
+00:16:44,460 --> 00:16:48,700
+natural number حتى لأنه مش هتكون بال negative مش
+
+232
+00:16:48,700 --> 00:16:52,440
+هتكون بال negative okay خلصنا الله والله إذا كان X
+
+233
+00:16:52,440 --> 00:16:57,280
+equal to AM هي فعلا نفس القيمة عند ال AM هنا
+
+234
+00:16:58,320 --> 00:17:02,320
+بيساووا بعض enough خير و بركة معناته بنقدر نقول
+
+235
+00:17:02,320 --> 00:17:09,580
+بنجف و بنرجع بال location M انا وجدته خلاص stop
+
+236
+00:17:09,580 --> 00:17:13,180
+وين وجدته في ال location M طيب لأ ماوجدنهاش
+
+237
+00:17:13,180 --> 00:17:16,920
+ماوجدنهاش معناه ان في احتمالين اما ان ال X أكبر من
+
+238
+00:17:16,920 --> 00:17:22,020
+AM او انها أقل من AM ناخد الاحتمالين if X أقل من
+
+239
+00:17:22,020 --> 00:17:33,090
+AM and I أقل من Mفإذا إذا كانت ال X هذه فعليا أقل
+
+240
+00:17:33,090 --> 00:17:37,810
+من A M فإذا المفروض أنها تكون في المنطقة هذه صحيح؟
+
+241
+00:17:37,810 --> 00:17:42,250
+طب ممكن احنا فعلا تقلصنا لدرجة أن ال M هي نفس ال I
+
+242
+00:17:42,250 --> 00:17:48,010
+هل ممكن؟ أه ممكن، ممكن لأنه في المرحلة التانية،
+
+243
+00:17:48,010 --> 00:17:51,590
+هنجلل المسافة، هنجلل، هنجلل، ممكن يصلوا أن التنتين
+
+244
+00:17:51,590 --> 00:17:54,250
+هم نفس الرقم إذا والله نفس الرقم، stop، خلاص،
+
+245
+00:17:54,250 --> 00:17:57,390
+معناه أنا مالجيتهمشوصلنا وما راجعناش ال element
+
+246
+00:17:57,390 --> 00:18:05,230
+تبعتنا فحنشوف if then بتاعتنا إذا والله أقل من فهي
+
+247
+00:18:05,230 --> 00:18:11,630
+لاتساوي لاتساوي هي أقل من و I أقل من M يعني لسه في
+
+248
+00:18:11,630 --> 00:18:16,270
+مجموعة elements فيهم مازال في elements الأصل أني
+
+249
+00:18:16,270 --> 00:18:19,110
+أدور في ال elements هذه معناته لازم أكمل ال
+
+250
+00:18:19,110 --> 00:18:22,670
+procedure تبعتي بكملها بس بكملها بناء على إيش على
+
+251
+00:18:23,710 --> 00:18:27,210
+بناري سيرشوي نفسها كمان مرة بس بتعامل معاها
+
+252
+00:18:27,210 --> 00:18:31,090
+الموضوع على أساس أنه طبعا هذه لا تساوي لحظة هذه لا
+
+253
+00:18:31,090 --> 00:18:34,590
+تساوي فإذا بتعامل على ال element اللي جابلها أن
+
+254
+00:18:34,590 --> 00:18:41,170
+هذه هي ال A الجديدة عبارة عن I to J هاي J الجديدة
+
+255
+00:18:41,170 --> 00:18:47,070
+صارت ال J الجديدة عبارة عن M minus 1 العنصر اللي
+
+256
+00:18:47,070 --> 00:18:53,230
+جابلها على اعتبار أنه عند العنصر M لا تساويهي اصلا
+
+257
+00:18:53,230 --> 00:18:55,410
+انا كيف وصلت ل condition هذا، بناء على انه هذا لم
+
+258
+00:18:55,410 --> 00:18:58,690
+يتحقق، بناء على اساس ان ال condition الأول لم
+
+259
+00:18:58,690 --> 00:19:04,430
+يتحقق، ف condition التاني تحقق، بعرف انه ما زال
+
+260
+00:19:04,430 --> 00:19:08,750
+فيه مجموعة elements موجودة، بعرف ان J المفترضة
+
+261
+00:19:08,750 --> 00:19:15,350
+الجديدة هتكون M minus 1 و ليست Mوليست M فهنا أصلا
+
+262
+00:19:15,350 --> 00:19:18,650
+عندي A برجع بدخل نفس ال sequence هو هو و ال X اللي
+
+263
+00:19:18,650 --> 00:19:21,710
+بدور عنها هي هي و بدور when في interval من جدش
+
+264
+00:19:21,710 --> 00:19:34,390
+لجدش من I to M-1 عيدنا نفس الكلام لأ مش أقل منهx
+
+265
+00:19:34,390 --> 00:19:39,290
+ليست أقل من وليست تساوي فإذا الاحتمال التالت اللي
+
+266
+00:19:39,290 --> 00:19:42,110
+لازم حصله إذا ما تحققوش ال two conditions هدولة هو
+
+267
+00:19:42,110 --> 00:19:47,890
+else إنه هي لاتساوي .. لاتساوي وليست أقل من فأكيد
+
+268
+00:19:47,890 --> 00:19:53,930
+هتكون أكبر من فx أكبر من am طيب هاي ال condition
+
+269
+00:19:53,930 --> 00:19:54,790
+تبعنا x
+
+270
+00:19:59,960 --> 00:20:04,000
+هنا أكبر من AM فهي المفروض تكون موجودة في ال .. في
+
+271
+00:20:04,000 --> 00:20:07,900
+ال interval اللي على اليمين صح؟ في ال right side
+
+272
+00:20:07,900 --> 00:20:10,600
+okay في ال right side مدام هي موجودة في الجزء اللي
+
+273
+00:20:10,600 --> 00:20:15,320
+هنا هنا بقدر أعمل command search و بنحدد بناء عليه
+
+274
+00:20:15,320 --> 00:20:23,800
+I بتاعتنا بعد ال AM بعد ال location M فإذا تبدأ ال
+
+275
+00:20:23,800 --> 00:20:26,620
+I كأنها M plus 1
+
+276
+00:20:29,210 --> 00:20:33,770
+صح؟ تمام على اعتبار ان هذا لا يساوي فليش احطه في
+
+277
+00:20:33,770 --> 00:20:36,990
+ال interval هو لا يساوي خلاص ناخد اللي من بعده
+
+278
+00:20:36,990 --> 00:20:41,950
+ناخد من بعده فتصبح عنا إذا كانت ال am هي اللي أصغر
+
+279
+00:20:41,950 --> 00:20:53,600
+من x فx أكبر and m هذهأقل من j أقل من j يعني أن
+
+280
+00:20:53,600 --> 00:20:56,480
+يوجد بينهم مجموعة elements على الأقل element واحد
+
+281
+00:20:56,480 --> 00:21:01,200
+على الأقل element واحد وجد بينهم جدير أن أبحث عليه
+
+282
+00:21:01,200 --> 00:21:04,020
+من الأفضل أن أبحث عليه لا أستطيع أن أقول إن انتهيت
+
+283
+00:21:04,020 --> 00:21:08,840
+من ال search طبعي في الحالة هذه سنعود بمين؟ برضه
+
+284
+00:21:08,840 --> 00:21:14,280
+بنفس ال code ولكن ل series a ال x هي نفس ال
+
+285
+00:21:14,280 --> 00:21:20,490
+element اللي بدور عليه من أين؟m زائد واحد to j من
+
+286
+00:21:20,490 --> 00:21:24,930
+m زائد واحد to j بنرجع بنكرر نفس الموضوع هو هو
+
+287
+00:21:24,930 --> 00:21:31,150
+نفسنا بنكرر نفس الموضوع تماما okay else return
+
+288
+00:21:31,150 --> 00:21:36,910
+zero لاحظوا ال else هذه هذه ال else بتاعة ال F هذه
+
+289
+00:21:36,910 --> 00:21:42,090
+ال else هذه بتاعة ال F هذه ليش بقول الكلام هذا
+
+290
+00:21:42,090 --> 00:21:47,330
+بقول الكلام هذا عشان نقول انت حنجفنتطلع كمان شوية
+
+291
+00:21:47,330 --> 00:21:51,810
+هل وجدت ام تحبك بقدر اقول اني وقفت اذا كان وانا
+
+292
+00:21:51,810 --> 00:21:56,270
+بدور صدفت انه فعلا ال X طلعت بتساوي واحدة من ال
+
+293
+00:21:56,270 --> 00:22:00,530
+AM's سواء هنا او هنا مع انه التكرار ال recursion
+
+294
+00:22:00,530 --> 00:22:04,710
+اللي بعملها صدفت انه X equal to كذا فبرجع ابقيمتها
+
+295
+00:22:04,710 --> 00:22:09,410
+ابقيمته ال location نفسه وخلاص بوقف طب لأ نفترض ان
+
+296
+00:22:09,410 --> 00:22:14,030
+الأسوأ ال worst case انه X غير موجودة القصر ايش
+
+297
+00:22:14,030 --> 00:22:20,800
+بتصير؟X أقل من AM أو أكبر من AM هذي حضار تتحقق
+
+298
+00:22:20,800 --> 00:22:23,400
+معايا هذي الشيء اللي بوقفني و بوصلني في الآخر
+
+299
+00:22:23,400 --> 00:22:28,820
+واحدة من ال two conditions هذول اما ان ال I أقل من
+
+300
+00:22:28,820 --> 00:22:35,460
+M تمام و في الحالة اذا كان أقل ال I ليست أقل من M
+
+301
+00:22:35,460 --> 00:22:39,900
+نضرر انه ليست أقل من M ف automatically هذا لم
+
+302
+00:22:39,900 --> 00:22:45,420
+يتحقق في الحالة هذي else باجي بتأكد من هنابنتأكد
+
+303
+00:22:45,420 --> 00:22:49,760
+من هنا بتشوف ال M أقل من J فإذا هذا لن يقف ال
+
+304
+00:22:49,760 --> 00:22:59,100
+search إلا لما تصير ال I بتساوي J ال I هتساوي J في
+
+305
+00:22:59,100 --> 00:23:05,560
+الحالة هذه باتنين بنطبخوا على بعض تصبحالـ M أقل من
+
+306
+00:23:05,560 --> 00:23:10,240
+J لاتتحقق فالشرطين دول لازم يتحققوش مع بعض عشان
+
+307
+00:23:10,240 --> 00:23:15,820
+أجي لمن؟ لل else بتاعتها ففي الحالة هذه برجع صفر
+
+308
+00:23:15,820 --> 00:23:20,520
+تقلصت صار عندي عملية shrinking عندي لل duration
+
+309
+00:23:20,520 --> 00:23:25,120
+لدرجة أن وصلت الأثنين I و J بيسووا بعض ومع ذلك
+
+310
+00:23:25,120 --> 00:23:30,040
+ماوجدتش ال X فإذا X غير موجودة أصلا فإذا X غير
+
+311
+00:23:30,040 --> 00:23:38,120
+موجودة أساساOkay هذا في حالة ال recursive
+
+312
+00:23:38,120 --> 00:23:41,000
+algorithm لمين لل binary search أو recursive
+
+313
+00:23:41,000 --> 00:23:44,600
+binary search recursive binary search هذا الجزء
+
+314
+00:23:44,600 --> 00:23:47,240
+اللي كان ضايل عندنا في عملية ال recursion و اللي
+
+315
+00:23:47,240 --> 00:23:49,900
+كانت خاصة بال recursion algorithm أو recursive
+
+316
+00:23:49,900 --> 00:23:54,440
+algorithm قبل ما نبدأ
+
+317
+00:24:01,460 --> 00:24:05,540
+المرة اللى فاتت قبل كام محاضرة أخدنا ال basics لل
+
+318
+00:24:05,540 --> 00:24:09,700
+numbers للأرقام طب هالوقت بناخدها برضه ال basics
+
+319
+00:24:09,700 --> 00:24:14,260
+لمين لل counting للعدد أخدنا الأرقام تمام عرفنا
+
+320
+00:24:14,260 --> 00:24:17,500
+الأرقام وعرفنا إيش يعني أرقام وإيش يعني إيهوصرنا
+
+321
+00:24:17,500 --> 00:24:21,520
+ممتازين في الأرقام ويعرفنا الرقم ال even ويعرفنا
+
+322
+00:24:21,520 --> 00:24:25,920
+الرقم ال odd ويعرفنا الرقم ال prime ويعرفنا كيف
+
+323
+00:24:25,920 --> 00:24:28,240
+نتعامل مع الأرقام وكيف بقدر استخدمها في عملية ال
+
+324
+00:24:28,240 --> 00:24:31,120
+encryption كيف بستخدم الأرقام في عملية ال
+
+325
+00:24:31,120 --> 00:24:34,440
+encryption كيف ب .. بغير الأرقام باستخدام ال
+
+326
+00:24:34,440 --> 00:24:37,900
+modular وبن .. بنقول أن والله في رقم equivalent
+
+327
+00:24:37,900 --> 00:24:42,410
+لرقم تانيالكلام هذا كله خدناه .. صحيح؟ فالوقت بدنا
+
+328
+00:24:42,410 --> 00:24:45,930
+نتطور شوية كيف بقدر أعمل عملية ال counting .. العد
+
+329
+00:24:45,930 --> 00:24:50,570
+.. بدنا نعد .. إيش يعني عد؟ يعني تحسب .. يعني تجمع
+
+330
+00:24:50,570 --> 00:24:53,370
+تقول والله هدول عددهم خمسة .. هدول عددهم عشرة ..
+
+331
+00:24:53,370 --> 00:24:58,690
+هدول عددهم عشرين .. بدنا نبدأ نعدتمام؟ برضه بنفس
+
+332
+00:24:58,690 --> 00:25:02,250
+القالية هناك أخدنا شوية numbers و بس ابقوا حافظين
+
+333
+00:25:02,250 --> 00:25:04,190
+يعنى إيش ال numbers اللي احنا أخدناهم و كيف نتعامل
+
+334
+00:25:04,190 --> 00:25:06,090
+معاهم و كيف بنقول والله الرقامين دولة equivalent
+
+335
+00:25:06,090 --> 00:25:09,330
+لبعض أو مش equivalent لبعض كيف بستخدم ال numbers
+
+336
+00:25:09,330 --> 00:25:14,250
+في عملية ال encryption اليوم لأ بدنا نستعمل جداش
+
+337
+00:25:14,250 --> 00:25:20,400
+عددElements لحالة معينة بيحققولنا case معينة فبدنا
+
+338
+00:25:20,400 --> 00:25:25,560
+نعمل عدد counting بدنا نبدأ نعد كويس ف study of
+
+339
+00:25:25,560 --> 00:25:29,840
+the number of ways to put things together جداش ال
+
+340
+00:25:29,840 --> 00:25:32,860
+things اللي بقدر أجمحهم together على أساس إن هدولة
+
+341
+00:25:32,860 --> 00:25:37,220
+combination واحدة مع بعض هدولة case واحدة هدولة
+
+342
+00:25:37,220 --> 00:25:40,380
+task واحدة بيقدوا task واحدة فبقدر أقول جداش عددهم
+
+343
+00:25:40,380 --> 00:25:45,990
+اللي بيقدروا يحلولي task معينةفبنعمل عدد تعديق
+
+344
+00:25:45,990 --> 00:25:50,390
+تعديد عدد طيب الأعداد هذه for example طبعا هنشرح
+
+345
+00:25:50,390 --> 00:25:54,450
+كتير لسه في الكلام موضوع طويل لسه for example لو
+
+346
+00:25:54,450 --> 00:26:01,690
+قولنا في contest معينة مسابقة منافسة وداخل فيها
+
+347
+00:26:01,690 --> 00:26:07,350
+مائة شخص نفترض مائة شخص بجرم مائة شخص بجرم وجفنا
+
+348
+00:26:07,350 --> 00:26:11,050
+عند خط النهاية وجاعدين بنحط احتمالات possibilities
+
+349
+00:26:11,050 --> 00:26:17,020
+مين أول عشرة ممكن يصلوامن أول عشرة ممكن يصلوا من
+
+350
+00:26:17,020 --> 00:26:21,000
+المائة شخص اللي بتسابقوا فطبعا عندكوا كمية كبيرة
+
+351
+00:26:21,000 --> 00:26:23,580
+من الاحتمالات من ال possibilities من ال
+
+352
+00:26:23,580 --> 00:26:28,320
+possibilities قداش عددهم هنا counting عدد قداش عدد
+
+353
+00:26:28,320 --> 00:26:31,380
+الاحتمالات عدد انا قاعد باطلب منكوا عدد counting
+
+354
+00:26:31,380 --> 00:26:37,620
+عدولي كويس هذا exampleطبعا هالوقت احنا مش ماهلين
+
+355
+00:26:37,620 --> 00:26:41,000
+نحله إلا بس نخلص الموضوع تبعنا لما نخلص الموضوع
+
+356
+00:26:41,000 --> 00:26:44,800
+بنقدر نتكلم فيه هذا okay example تاني يعني أنا بس
+
+357
+00:26:44,800 --> 00:26:48,060
+بقولكوا في إيش ممكن نستخدم العد example تاني if a
+
+358
+00:26:48,060 --> 00:26:53,590
+password is six to eight letters or and digitsHow
+
+359
+00:26:53,590 --> 00:26:59,030
+many possibles can there be؟ قداش عدد ال passwords
+
+360
+00:26:59,030 --> 00:27:04,390
+اللي بقدر أعملها من ستة لتمانية letters or and
+
+361
+00:27:04,390 --> 00:27:08,210
+digits بمعنى اعملوا password كل واحدة بتعملها
+
+362
+00:27:08,210 --> 00:27:12,890
+password ال password هاللازم يكون عدد ال positions
+
+363
+00:27:12,890 --> 00:27:15,930
+تبعته عدد ال locations تبعته من ستة لتمانية يعني
+
+364
+00:27:15,930 --> 00:27:23,040
+يا ستة يا سبعة يا تمانية six or seven oreight or
+
+365
+00:27:23,040 --> 00:27:28,460
+مهمة جدا طيب في كل digit في كل location ايش
+
+366
+00:27:28,460 --> 00:27:32,820
+العناصر الممكنة اما انها تكون letters حروف او
+
+367
+00:27:32,820 --> 00:27:36,900
+digits او الاتنين مع بعض اللي هم ال combination في
+
+368
+00:27:36,900 --> 00:27:41,120
+ال six مع بعضتمام؟ طيب في الأخر قداش عدد ال
+
+369
+00:27:41,120 --> 00:27:44,200
+passwords الممكنة في الحالة هذه عدد ال passwords
+
+370
+00:27:44,200 --> 00:27:47,220
+الممكنة هذه المفروض من هنا لآخر ما نخلص موضوعنا
+
+371
+00:27:47,220 --> 00:27:49,620
+تكونوا جادرين تشتغلوا على الكلام هذا تكونوا جادرين
+
+372
+00:27:49,620 --> 00:27:52,000
+تحلوها بس أنا قاعد بقولكوا هي حاجات ل password
+
+373
+00:27:52,000 --> 00:27:54,340
+خاصة في شغلكوا بكرا بتكونوا تعملوا design ل
+
+374
+00:27:54,340 --> 00:27:59,140
+password معينة ل location لبرنامج بتكونوا تشتغلوه
+
+375
+00:27:59,140 --> 00:28:02,540
+او program كامل او software كاملة تبرمجوها بتكونوا
+
+376
+00:28:02,540 --> 00:28:05,140
+تعملوه ل password license عشان اللي بتعملوها
+
+377
+00:28:05,140 --> 00:28:10,530
+licenseجدّيش عدد ال users اللي انتوا متوقعين
+
+378
+00:28:10,530 --> 00:28:15,670
+يتبعوهم المنتج تبعكم بناء على جدّيش المتوقع تعملوا
+
+379
+00:28:15,670 --> 00:28:18,510
+عدد passwords لأن كل واحد بده ياخدله password صح
+
+380
+00:28:18,510 --> 00:28:23,430
+فهنا هذا شغلكوا اه بدنا نعرف ان اعد فبدنا نعرف ان
+
+381
+00:28:23,430 --> 00:28:27,670
+اعدOkay في two rules الحقيقة قبل ما نبدأ نشتغل في
+
+382
+00:28:27,670 --> 00:28:30,490
+عملية العدل ال two rules هدولة واحدة اللي هي عملية
+
+383
+00:28:30,490 --> 00:28:34,970
+ال summation و ال product أمتى الأرقام بجمعهم و
+
+384
+00:28:34,970 --> 00:28:38,130
+أمتى الأرقام بضربهم عشان أقول أمتى بجمعهم و أمتى
+
+385
+00:28:38,130 --> 00:28:42,250
+بضربهم بدنا نحط فرضية هنقول let M be the number of
+
+386
+00:28:42,250 --> 00:28:47,250
+ways to do task 1 and N the number of ways to do
+
+387
+00:28:47,250 --> 00:28:50,990
+task 2 لو افترضنا أن ال task الأولى بقدر أعملها ب
+
+388
+00:28:50,990 --> 00:28:57,530
+M طريقةبقدر أشتغل ال task الأولى بأما طريقة يعني
+
+389
+00:28:57,530 --> 00:29:01,430
+في لها خمسين طريقة بقدر أقدي فيها المهمة هذه okay
+
+390
+00:29:01,430 --> 00:29:05,490
+task تانية يمكن لها ستين طريقة بقدر أقدي فيها
+
+391
+00:29:05,490 --> 00:29:09,430
+المهمة طيب لما بدي أعمل اتنين مع بعض ال two tasks
+
+392
+00:29:09,430 --> 00:29:13,550
+مع بعض كيف بقدر أعدهم أنا عارف عدد هذي لحاله وعارف
+
+393
+00:29:13,550 --> 00:29:17,070
+عدد هذي كيف بعمل combination ال combination كيف
+
+394
+00:29:17,070 --> 00:29:22,150
+جمع ولا ضرب بيعتمد علىإيش ال combination اللي بده
+
+395
+00:29:22,150 --> 00:29:25,250
+أعمله بمعنى لو بده نشتغل على ال some rules اللي هي
+
+396
+00:29:25,250 --> 00:29:29,630
+الجامع هد معناها كالتاني ال task اللي بده تنعمل as
+
+397
+00:29:29,630 --> 00:29:33,390
+a total هي عبارة عن two either task one or task
+
+398
+00:29:33,390 --> 00:29:38,870
+two في الحالة هد بقول جامع بمعنى المثال تبع توي
+
+399
+00:29:38,870 --> 00:29:43,490
+لما كنا بنتكلم عن password من ستة لتمانية فإذا هل
+
+400
+00:29:43,490 --> 00:29:48,120
+انتوا بتقدروافي الحالة دي اما ستة او سبعة خليني
+
+401
+00:29:48,120 --> 00:29:50,620
+يعني عشان نبسطها اما ستة من ستة خليني اقول الى
+
+402
+00:29:50,620 --> 00:29:55,560
+سبعة اما ستة locations او سبعة locations فهل وجد
+
+403
+00:29:55,560 --> 00:29:58,200
+انت لما بدك تعمل ال password بتقدر تعمل الاتنين مع
+
+404
+00:29:58,200 --> 00:30:03,740
+بعض مادام بقدرش اعملهم سم اتنين ياصلي فإذا اما ستة
+
+405
+00:30:03,740 --> 00:30:10,040
+او سبعة ومنفصلين مادام منفصلين و او هيني بقول او
+
+406
+00:30:10,040 --> 00:30:15,630
+union union جمعجمع، معناه ذلك أنه جديش عدد
+
+407
+00:30:15,630 --> 00:30:19,890
+الاحتمالات لل passwords هذه بحيث انها تكون من ستة
+
+408
+00:30:19,890 --> 00:30:25,790
+لسبعة characters اما بشغل الحالة الأولى انها تكون
+
+409
+00:30:25,790 --> 00:30:29,670
+ستة وبشوف جديش عدد احتمالاتها، جديش عدد ال ways
+
+410
+00:30:29,670 --> 00:30:34,010
+اللي بقدر اعمل فيها password من ستة characters
+
+411
+00:30:34,010 --> 00:30:39,070
+وعدد الحالات اللي بعملها بسبعة characters ونجمع
+
+412
+00:30:39,070 --> 00:30:40,990
+لنقر
+
+413
+00:30:43,580 --> 00:30:46,760
+بقدرش اعمل اتين اتين مع بعض ما هو خلاص انت عملته
+
+414
+00:30:46,760 --> 00:30:49,840
+password واحدة ال password هدى يا ستة يا سبعة تنفع
+
+415
+00:30:49,840 --> 00:30:52,840
+تكون password حاجة تقبل ستة و سبعة characters مع
+
+416
+00:30:52,840 --> 00:30:57,300
+بعض؟ تنفعش فإذا في الحالة هدى either task one or
+
+417
+00:30:57,300 --> 00:31:02,340
+كلمة or على طول ل ال summation some rule okay the
+
+418
+00:31:02,340 --> 00:31:07,140
+product task the task do both task one and task
+
+419
+00:31:07,140 --> 00:31:14,640
+two simultaneously مع بعضبنعملهم مع بعض task 1 و
+
+420
+00:31:14,640 --> 00:31:20,060
+task 2 في مكانية انه يعملوا مع بعض زي برضه نفس ال
+
+421
+00:31:20,060 --> 00:31:23,020
+task بتاعتوي اللي احنا قولنا هناخدها لاحقا اللي هي
+
+422
+00:31:23,020 --> 00:31:28,160
+ال passwords هذه خلنا نبدأ ب 6 هي task 6 او 7
+
+423
+00:31:28,160 --> 00:31:33,020
+عرفنا او معناته هذه بحسب جدش ال ways اللي بقدر
+
+424
+00:31:33,020 --> 00:31:38,280
+اطبق يعني اجيب فيها عدد ال passwords ب6 digitsو
+
+425
+00:31:38,280 --> 00:31:41,100
+بجمع عليها جداش عدد ال passwords من سبعة digits
+
+426
+00:31:41,100 --> 00:31:45,120
+خليني نبدأ بالستة لإن بدي أحسب هذه لحالي الأول هذي
+
+427
+00:31:45,120 --> 00:31:47,880
+كمان كيف بدي أحسبها بدي أحسبها جالنا والله إما
+
+428
+00:31:47,880 --> 00:31:53,300
+letters أو digits أو digits بس هنا أو or digits
+
+429
+00:31:53,300 --> 00:31:58,660
+معنى ذلك إنه عندنا سبعة ستة
+
+430
+00:31:58,660 --> 00:32:06,070
+ستة هدولة كل واحد من هدول ممكن يكونالحرف .. أكم
+
+431
+00:32:06,070 --> 00:32:11,970
+حرف عندك؟ ستة و عشرين أكم رقم؟ عشرة من صفر لتسعة
+
+432
+00:32:11,970 --> 00:32:15,490
+ففي عندي عشرة بمعنى أن أنا في عندي أجدش عدد ال
+
+433
+00:32:15,490 --> 00:32:19,350
+possibilities لكل digit ستة و تلاتين طيب ل two
+
+434
+00:32:19,350 --> 00:32:25,970
+digits في ستة و تلاتين لأنه باخد أول عنصر هنا و
+
+435
+00:32:25,970 --> 00:32:28,610
+هيتكرر مع الستة و تلاتين اللي موجودين هنا تاني
+
+436
+00:32:28,610 --> 00:32:31,130
+عنصر برضه هيتكرر مع الستة و تلاتين تالت عنصر مع
+
+437
+00:32:31,130 --> 00:32:34,720
+الستة و تلاتين فلحظة أن انتوا بتعملواعملية ضرب
+
+438
+00:32:34,720 --> 00:32:40,140
+شبكة شبكة طيب تلاتة في ستة و تلاتين كمان أربعة
+
+439
+00:32:40,140 --> 00:32:42,840
+كمان ستة .. هاي ضرب ليش؟ لأن ال simultaneous اللي
+
+440
+00:32:42,840 --> 00:32:46,180
+بتضيق بده يحصل عليهم مع بعض عشان يكونوا الستة
+
+441
+00:32:46,180 --> 00:32:49,840
+digits عشان يكونوا الستة locations أو الستة
+
+442
+00:32:49,840 --> 00:32:52,580
+positions فهدول ال simultaneous اللي لازم كلهم
+
+443
+00:32:52,580 --> 00:32:55,840
+يكونوا موجودين مع مين مع بعض غير عملية انه والله
+
+444
+00:32:55,840 --> 00:32:58,540
+ستة أو سبعة ستة أو سبعة لأ احنا ماقدرش اعمل
+
+445
+00:32:58,540 --> 00:33:04,550
+password ستة هو نفسه سبعةتظبطش في هذه or واضحة هذه
+
+446
+00:33:04,550 --> 00:33:08,930
+and فانا بدي character لل location الأول و
+
+447
+00:33:08,930 --> 00:33:12,310
+character لل location التاني و character لل
+
+448
+00:33:12,310 --> 00:33:16,710
+location التالت عشان أكون الستة عشان و فإذا و أنا
+
+449
+00:33:16,710 --> 00:33:21,350
+بتكلم عن and فالأول and التاني and التالت and
+
+450
+00:33:21,350 --> 00:33:25,690
+الرابع and الخمس and السادس هي ستة positionsهذه
+
+451
+00:33:25,690 --> 00:33:28,790
+الستة positions في الحالة هذه بنقول عملية ضرب
+
+452
+00:33:28,790 --> 00:33:33,210
+product في الحالة بتاعتنا ف do both tasks one and
+
+453
+00:33:33,210 --> 00:33:38,890
+two ال task الأولى هتكون جداش عدد الطرق لل digit
+
+454
+00:33:38,890 --> 00:33:44,650
+الأولى لل location الأول andال task التانية لل
+
+455
+00:33:44,650 --> 00:33:49,710
+location التاني فما دام and للتانية طبعا and
+
+456
+00:33:49,710 --> 00:33:52,070
+التالتة and الرابع and الخمسة and السادسة and
+
+457
+00:33:52,070 --> 00:33:54,670
+السبعة بتعملوا generalization بعد ذلك للكلام
+
+458
+00:33:54,670 --> 00:34:03,070
+بتعمموا الموضوع بنعمم الموضوع تمام تفضلي السبعة أه
+
+459
+00:34:03,070 --> 00:34:06,370
+السبعة مختلفة هل وجد الرقم اللي هنطلعه هنا هيطلع
+
+460
+00:34:06,370 --> 00:34:11,030
+ستة و تلاتين to the power ستة هذا فقط لهذه الحالة
+
+461
+00:34:12,100 --> 00:34:19,240
+هنا زائد ستة و تلاتين و سبعة زائد
+
+462
+00:34:19,240 --> 00:34:22,360
+تمانية زي الحل نفسه اللي هو كان طالب أو تمانية من
+
+463
+00:34:22,360 --> 00:34:25,980
+ستة لتمانية كان عامل اللي ناياها زائد ستة و تلاتين
+
+464
+00:34:25,980 --> 00:34:32,300
+وتغار تمانية تمام theoretically الكلام هذا اللي هو
+
+465
+00:34:32,300 --> 00:34:35,440
+ال summation و الدرب كيف نقدر نعمله نعمله as a set
+
+466
+00:34:35,440 --> 00:34:40,370
+ايش يعني as a set ال 36 هدولةاللي هم كانوا خاصين
+
+467
+00:34:40,370 --> 00:34:43,010
+بال task number one ال task number one كان في عندى
+
+468
+00:34:43,010 --> 00:34:46,710
+36 ال 36 elements هدول هنتعامل معاهم ان هم 36
+
+469
+00:34:46,710 --> 00:34:52,550
+elements محطوطين فيه set اسمها ايه ال task التانية
+
+470
+00:34:52,550 --> 00:34:59,910
+set اسمها Bفبنحط ال possibilities أو ال ways اللي
+
+471
+00:34:59,910 --> 00:35:04,490
+بنقدر نعمل فيها ال task number one في ال set A و
+
+472
+00:35:04,490 --> 00:35:07,070
+ال task number two بنحطها في ال set اسمها B و
+
+473
+00:35:07,070 --> 00:35:09,990
+بنشوف إيش ال relation بين الانتين على أساس إن
+
+474
+00:35:09,990 --> 00:35:12,830
+هدولة في النهاية number of ways هدولة في النهاية
+
+475
+00:35:12,830 --> 00:35:16,950
+number of ways جدش عدد الطرق اللي بنخد فيها ال
+
+476
+00:35:16,950 --> 00:35:22,310
+task الأولى أو التانيةA is the set of ways to do
+
+477
+00:35:22,310 --> 00:35:26,730
+task one and B is the set of ways to do task
+
+478
+00:35:26,730 --> 00:35:32,030
+number two and if A and B are disjoint العند الآن
+
+479
+00:35:32,030 --> 00:35:35,550
+هنشغل على الصينية disjoint مختلفين عن بعض مش
+
+480
+00:35:35,550 --> 00:35:39,010
+معتمدين على بعض مش معتمدين على بعض مافيش
+
+481
+00:35:39,010 --> 00:35:43,070
+intersection between them يعني مافيش طريقة بتنفع
+
+482
+00:35:43,070 --> 00:35:47,840
+هنا و بتنفع هنامافيش طريقة تنفهن أو تنفهن مبدأيا
+
+483
+00:35:47,840 --> 00:35:50,180
+خلينا على المفهوم البسيط هذا و بعدين هنطوره شوي
+
+484
+00:35:50,180 --> 00:35:54,080
+شوي هنطوره شوي شوي في الحالة هذه the ways to do
+
+485
+00:35:54,080 --> 00:35:58,700
+either task one or or or معناته نتكلم عن summation
+
+486
+00:35:58,700 --> 00:36:04,680
+unionف a union b وفي الحالة دي ال cardinality جدش
+
+487
+00:36:04,680 --> 00:36:11,940
+عدد ال ways to do this task either task one or
+
+488
+00:36:11,940 --> 00:36:15,120
+task two تنتهي مع بعض هتكون عبارة عن cardinality ل
+
+489
+00:36:15,120 --> 00:36:18,420
+a union b هتكون عبارة عن cardinality جدش عدد ال
+
+490
+00:36:18,420 --> 00:36:22,980
+ways to do task one plus جدش عدد ال ways to do
+
+491
+00:36:22,980 --> 00:36:29,960
+task number two بجمحهم مع بعضجمع هنا زي هذه ستة
+
+492
+00:36:29,960 --> 00:36:33,840
+سبعة جدش عدد ال ways عشان أشتغل على ستة digits جدش
+
+493
+00:36:33,840 --> 00:36:36,440
+عدد ال ways عشان أشتغل على سبعة digits نجمعهم إذا
+
+494
+00:36:36,440 --> 00:36:42,600
+كان هيها either task one or or خلاص فصلنا انتهت
+
+495
+00:36:42,600 --> 00:36:47,260
+جمع جمع يعني بتاخد إيا ال a إيا ال b مش التنتين مع
+
+496
+00:36:47,260 --> 00:36:50,360
+بعض تمام بالظبط و احنا قولنا انه disjoint التنتين
+
+497
+00:36:51,740 --> 00:36:54,500
+Tintin was joined معناه ذلك أنهما مافيش شيء مشترك
+
+498
+00:36:54,500 --> 00:36:58,640
+بينهم فيا الأولى جداش عدد ال ways بتاعتها يا
+
+499
+00:36:58,640 --> 00:37:00,780
+التانية جداش عدد ال ways بتاعتها مجموعة Tintin
+
+500
+00:37:00,780 --> 00:37:03,760
+بيعطيه يا الأولى يا التانية جداش يا الأولى يا
+
+501
+00:37:03,760 --> 00:37:07,760
+التانية هدولة summation بتصير طيب ال ways to do
+
+502
+00:37:07,760 --> 00:37:13,020
+both task one and task two Cartesian product
+
+503
+00:37:13,020 --> 00:37:16,740
+Cartesian product فال cardinality بتاعتها كانت
+
+504
+00:37:16,740 --> 00:37:19,060
+عبارة عن ال cardinality أو عدد ال ways للأولى
+
+505
+00:37:19,850 --> 00:37:22,610
+مضروبة في عدد ال ways للتانية في عدد ال ways
+
+506
+00:37:22,610 --> 00:37:25,750
+للتانية زي الحالة اللي احنا اتكلمناها هنا زي
+
+507
+00:37:25,750 --> 00:37:30,150
+الحالة اللي هنا okay ناخد examples ناخد مجموعة
+
+508
+00:37:30,150 --> 00:37:33,730
+examples توضح المفاهيم بتاعتنا okay a student can
+
+509
+00:37:33,730 --> 00:37:38,130
+choose a computer project from one of three lists
+
+510
+00:37:38,130 --> 00:37:42,350
+عندكوا three lists في مساق من المساقات و الدكتور
+
+511
+00:37:42,350 --> 00:37:44,910
+حددلكوا مجموعة projects جالكوا كل واحدة منكم يا
+
+512
+00:37:44,910 --> 00:37:48,960
+بنات تختار تختارلها project تشتغل عليهطيب ال
+
+513
+00:37:48,960 --> 00:37:51,600
+project هذا قالكوا بس دي ربالكوا أنا موزعلكم إياه
+
+514
+00:37:51,600 --> 00:37:54,420
+three categories ال category الأولى يمكن تكون خاصة
+
+515
+00:37:54,420 --> 00:37:57,440
+بالناس اللي بيحبوا ال database المجموعة التانية
+
+516
+00:37:57,440 --> 00:37:59,600
+خاصة بالناس اللي بيحبوا البرمجة باستخدام ال Java
+
+517
+00:37:59,600 --> 00:38:02,740
+المجموعة التالتة يمكن خاصة بالناس اللي بيحبوا ال
+
+518
+00:38:02,740 --> 00:38:07,400
+networking وزعلكم إياهم وقالكم والله الأولى هذه
+
+519
+00:38:07,400 --> 00:38:10,680
+أنا في عندى 23 project إذا حابين تشتغلوا في ال
+
+520
+00:38:10,680 --> 00:38:12,940
+database حدا منكم بيحب يشتغل في ال database ياخد
+
+521
+00:38:12,940 --> 00:38:16,000
+واحدة من المشاريع هذه كويسة خمسة عشر للناس اللي
+
+522
+00:38:16,000 --> 00:38:19,360
+بيحبوا يشتغلوا بالبرمجةو في عنا 19 لناس اللي
+
+523
+00:38:19,360 --> 00:38:21,440
+بيحبوا مثلا يشتغلوا في ال networking في الشبكات
+
+524
+00:38:21,440 --> 00:38:25,460
+طيب عشان تختاروا جداش عندكوا عدد ال ways عشان
+
+525
+00:38:25,460 --> 00:38:29,660
+تختاروا فيها طبعا واضح انهم انفصلة ليش لأن انا
+
+526
+00:38:29,660 --> 00:38:33,320
+هختار واحد project واحد يا اما من category اول يا
+
+527
+00:38:33,320 --> 00:38:36,100
+من ال category التاني يا من ال category التالت مش
+
+528
+00:38:36,100 --> 00:38:39,800
+هاختار مشروع من الكل لأ هو طالب منك اختيار واحد
+
+529
+00:38:39,800 --> 00:38:43,660
+فاختيار كل واحد هيكون عبارة عن يا من 23 زائد 15
+
+530
+00:38:43,660 --> 00:38:46,400
+زائد 19 فانتوا بالنسبالكوا كلها projects واحدة
+
+531
+00:38:47,150 --> 00:38:49,830
+عددهم سبعة و خمسين project فانتوا فى عندكوا سبعة و
+
+532
+00:38:49,830 --> 00:38:52,970
+خمسين projects عشان تختاروا منها .. كل واحدة منكوا
+
+533
+00:38:52,970 --> 00:38:57,950
+تختار لها project من سبعة و خمسين project okay لو
+
+534
+00:38:57,950 --> 00:39:01,970
+عندكوا .. suppose statement label .. labels in
+
+535
+00:39:01,970 --> 00:39:05,930
+programming language must be a single letter or a
+
+536
+00:39:05,930 --> 00:39:10,090
+single decimal digit how many labels are there؟ لو
+
+537
+00:39:10,090 --> 00:39:12,890
+محتاجين تعملوا labeling ل .. خلنا نقول ل variables
+
+538
+00:39:13,860 --> 00:39:18,240
+في البرمجة وبتسموها باسم معين ال verb ساعتكم ففي
+
+539
+00:39:18,240 --> 00:39:20,660
+عندكم إمكانية إما أنكوا تسموها باستخدام single
+
+540
+00:39:20,660 --> 00:39:25,820
+letter حرف أو رقم .. او رقم طب كدش عندكوا عدد ال
+
+541
+00:39:25,820 --> 00:39:28,280
+ways اللي ممكن تسموه فيها أو تعملوا labeling فيها
+
+542
+00:39:28,280 --> 00:39:33,780
+ستة و عشرين زائد عشرة .. ستة و عشرين زائد عشرة
+
+543
+00:39:33,780 --> 00:39:38,180
+مافيش فيها .. عندكوا or معناته يا إما بستخدم
+
+544
+00:39:38,180 --> 00:39:42,540
+letter أو بستخدم digitيا لطريقة ديجالية، يا ستة و
+
+545
+00:39:42,540 --> 00:39:46,320
+عشرين، يا عشرة، معناه اتصار عندى ستة و تلاتين ways
+
+546
+00:39:46,320 --> 00:39:51,080
+بقدر امثل فيها، بعمل فيها عملية labeling okay how
+
+547
+00:39:51,080 --> 00:39:53,640
+many integers between one and one hundred
+
+548
+00:39:53,640 --> 00:39:58,380
+including ال one hundred are even or end with five
+
+549
+00:39:59,290 --> 00:40:04,050
+طيب كويس or معناته انا بتكلم عن two tasks فى task
+
+550
+00:40:04,050 --> 00:40:07,790
+أولى و فى task تانية بمسك ال task الأولى لحالها
+
+551
+00:40:07,790 --> 00:40:11,710
+جديش عدد الأرقام من واحد لمية طبعا مشمول معاهم
+
+552
+00:40:11,710 --> 00:40:17,090
+المية even حيكون عددهم خمسين مدام مشمولة لمية من
+
+553
+00:40:17,090 --> 00:40:21,830
+اتنين اربع ست تمانية عشر حيكون عددهم خمسين هذا ال
+
+554
+00:40:21,830 --> 00:40:28,170
+task الأولى task أولى ال task التانية end with
+
+555
+00:40:28,170 --> 00:40:35,650
+fiveقدش عدد الأرقام من واحد لمية بينتهي بخمسة
+
+556
+00:40:35,650 --> 00:40:39,950
+بمعنى الأحد تبعه خمسة خمسة، خمستاشر، خمسة وعشرين،
+
+557
+00:40:39,950 --> 00:40:42,090
+خمسة وثلاثين، خمسة واربعين، خمسة وخمسين، خمسة
+
+558
+00:40:42,090 --> 00:40:44,550
+وستين، خمسة وسبعين، خمسة و تمانين، خمسة وتسعين، في
+
+559
+00:40:44,550 --> 00:40:51,350
+عندنا عشرة طيب في intersection between them؟ ايش؟
+
+560
+00:40:51,350 --> 00:40:58,140
+خمستاشر15 even لاحظتي هنا أنا بتكلم عن even هدول
+
+561
+00:40:58,140 --> 00:41:04,960
+50 رقم even هدول عشر أرقام بتنتهي بخمسة فالخمسة
+
+562
+00:41:04,960 --> 00:41:10,940
+لايمكن تكون even فإذا this joint ومدين في or بجمع
+
+563
+00:41:10,940 --> 00:41:16,190
+وانا متطمن ان مافيش اي turn تاني محتاج اطرحهلأن
+
+564
+00:41:16,190 --> 00:41:18,890
+احنا عارفين إنه لازم إذا كان في intersection بدنا
+
+565
+00:41:18,890 --> 00:41:21,870
+نطرح قيمة ال intersection جاينة .. جاينة هتشرحها
+
+566
+00:41:21,870 --> 00:41:27,670
+فهنا هيطلع عددهم ستين ways لتمثيل ال task الأولى
+
+567
+00:41:27,670 --> 00:41:34,390
+or task التانية .. or task التانية فهي الستين okay
+
+568
+00:41:34,390 --> 00:41:38,550
+how many different pit strings of length seven are
+
+569
+00:41:38,550 --> 00:41:44,730
+there؟ جدش؟عدد ال strings اللي بقدر امثلها
+
+570
+00:41:44,730 --> 00:41:52,330
+باستخدام bit, string طوله او length طولها سبعة
+
+571
+00:41:52,330 --> 00:41:58,290
+جداش
+
+572
+00:41:58,290 --> 00:42:02,370
+عدد ال strings اللي بقدر امثلها عارفين ان هنا جداش
+
+573
+00:42:02,370 --> 00:42:09,400
+احتمالات هذه يا صفرية واحد اتنينطيب التانية برضه
+
+574
+00:42:09,400 --> 00:42:14,300
+اتنين تالتة اتنين خلاص معناه ذلك احنا عارفين انه
+
+575
+00:42:14,300 --> 00:42:18,800
+ضرب فواحد اتنين تلات اربع سبعة اتنين تلات اربع
+
+576
+00:42:18,800 --> 00:42:23,350
+سبعة خلاصمافيش فيها كتير مشاكل مافيش فيها كتير
+
+577
+00:42:23,350 --> 00:42:25,690
+مشاكل فانا بقدر اقول اه والله يجديش عدد ال strings
+
+578
+00:42:25,690 --> 00:42:28,710
+اللي ممكن نعملها combination او يجديش عدد ال
+
+579
+00:42:28,710 --> 00:42:32,290
+strings اللي بقدر اخدها من مجموعة digits عددهم
+
+580
+00:42:32,290 --> 00:42:36,810
+سبعة عددهم سبعة و هنا نتكلم عن bit digits او bit
+
+581
+00:42:36,810 --> 00:42:37,270
+string
+
+582
+00:42:41,030 --> 00:42:45,550
+Okay كمان مثال a license contains .. اه هنا بنتكلم
+
+583
+00:42:45,550 --> 00:42:47,950
+برضه عن license معناه أننا بنتحط code .. بنتحط
+
+584
+00:42:47,950 --> 00:42:50,750
+حاجة هيك زي ال code ال code هذا بتكون من إيه؟ a
+
+585
+00:42:50,750 --> 00:42:54,390
+sequence of three letters followed by three digits
+
+586
+00:43:05,780 --> 00:43:14,740
+three letters مطبوعين ايه؟ ب three digits اكامويز
+
+587
+00:43:14,740 --> 00:43:18,040
+بقدر امثل فيها ال string هدا او ال sequence هدا
+
+588
+00:43:18,040 --> 00:43:21,480
+هنا مطلوب جداش عدد ال license في الآخر المتاحة
+
+589
+00:43:21,480 --> 00:43:24,400
+اللي هو معناته جداش عدد ال sequences الموجودة اللي
+
+590
+00:43:24,400 --> 00:43:28,820
+بقدر امثلها بهذا الشكل هنا عندى زي ما قلنا هيكون
+
+591
+00:43:28,820 --> 00:43:33,600
+في عندى lettersال letters معناه ذلك ان الاحتمال
+
+592
+00:43:33,600 --> 00:43:43,600
+للأولى 26 تانية طيب هنا digits و
+
+593
+00:43:43,600 --> 00:43:48,060
+في النهاية كله ضرر على اعتبار ان كلهم في النهاية
+
+594
+00:43:48,060 --> 00:43:52,720
+هحنحطوه في sequence واحد together together بمعنى
+
+595
+00:43:52,720 --> 00:44:01,260
+محتاج اعمل ال task الأولى و ال task التانيةو ال
+
+596
+00:44:01,260 --> 00:44:07,460
+task التالتة and and and ال task الرابع and ال
+
+597
+00:44:07,460 --> 00:44:10,320
+task الخامس and ال task الساسع عشان انا اطلع ستة
+
+598
+00:44:10,320 --> 00:44:14,440
+locations مجسمين تلاتة letters و تلاتة digits فهذه
+
+599
+00:44:14,440 --> 00:44:17,520
+ال and ضرورية هنا ال and ضرورية و مادام and
+
+600
+00:44:17,520 --> 00:44:21,540
+مادامتها بتكلم عن multiplication بتكلم هنا عن
+
+601
+00:44:21,540 --> 00:44:29,930
+multiplication okay نرجع برضه لعملية ال labelingأه
+
+602
+00:44:29,930 --> 00:44:33,070
+يمكن برضه هاد السهلة لو كنا نعمل برضه عملية
+
+603
+00:44:33,070 --> 00:44:36,530
+labeling باستخدام ال basic language is either ال
+
+604
+00:44:36,530 --> 00:44:42,290
+label هذا أو المسمى هذا أحد حاجتين is either a
+
+605
+00:44:42,290 --> 00:44:49,910
+single letter or a letter followed by a digit فإذا
+
+606
+00:44:49,910 --> 00:44:54,430
+في عندى task أولى ال task الأولى كده عددهم؟ ستة
+
+607
+00:44:54,430 --> 00:44:57,970
+وعشرين انتهينا خالص ستة وعشرين okay
+
+608
+00:45:02,850 --> 00:45:06,790
+لأ في عندك ستة و عشرين followed by ten معناه انت
+
+609
+00:45:06,790 --> 00:45:12,850
+ستة و عشرين في عشرة علاقتهم مع بعض ضرب لأ في or
+
+610
+00:45:12,850 --> 00:45:19,090
+زائد فبتطلع هنا مائتين و سبتين زائد ستة و عشرين
+
+611
+00:45:19,090 --> 00:45:27,270
+ستة تمانية اتنينبطلع 286 زي ما قولنا بنعمل two
+
+612
+00:45:27,270 --> 00:45:31,190
+parts ست أولى الست الأولى هي single letter labels
+
+613
+00:45:31,190 --> 00:45:36,130
+الست التانية اللي هي single letters followed by a
+
+614
+00:45:36,130 --> 00:45:40,010
+digit و بنسميها D فطبعا ال total في الآخر هيكون
+
+615
+00:45:40,010 --> 00:45:43,950
+عبارة عن ال union لتنتين ال union لتنتين طب عشان
+
+616
+00:45:43,950 --> 00:45:46,290
+أجيب ال cardinality لل union لتنتين هجيب ال
+
+617
+00:45:46,290 --> 00:45:49,630
+cardinality الأولى زي ال cardinality للتانية زي ال
+
+618
+00:45:49,630 --> 00:45:55,540
+cardinality3 ثانية عشان تحصروا في الآخر على 286
+
+619
+00:45:55,540 --> 00:46:04,920
+286 okay كمان مثال مثال
+
+620
+00:46:04,920 --> 00:46:09,620
+كويس و related لتخصصكم هنا بنتكلم عن جداش عدد ال
+
+621
+00:46:09,620 --> 00:46:14,180
+IB addresses او ال internet protocol addresses ل
+
+622
+00:46:14,180 --> 00:46:19,600
+ال IB version 4 version 4 طبعا في نهولوجيا صار في
+
+623
+00:46:19,600 --> 00:46:23,960
+version 6صافي version 6 طوروا على ال version 4
+
+624
+00:46:23,960 --> 00:46:26,880
+احنا خلينا على ال version 4 ال version 4 هذا
+
+625
+00:46:26,880 --> 00:46:33,180
+عندكوا 32 digit 32 bit ال 32 bit هدول بدنا نمثل
+
+626
+00:46:33,180 --> 00:46:36,440
+فيهم ال ip addresses بتاعتنا بدنا نمثل فيهم ال ip
+
+627
+00:46:36,440 --> 00:46:39,080
+addresses طبعا عشان اتقولوا عن ال ip addresses
+
+628
+00:46:39,080 --> 00:46:44,060
+اولش انتم محتاجين ال network له ID و ال host له ID
+
+629
+00:46:44,060 --> 00:46:49,040
+لان في عدد hosts لكل network طيب قدش عدد ال
+
+630
+00:46:49,040 --> 00:46:53,880
+networksهيكون برضه multiplication بين الاتنين جداش
+
+631
+00:46:53,880 --> 00:47:01,100
+.. فضليه مثالنا
+
+632
+00:47:01,100 --> 00:47:05,800
+هيتكلم عن جداش عدد ال IP او ال internet protocol
+
+633
+00:47:05,800 --> 00:47:10,080
+addresses عنوين ال .. ال protocol .. لل internet
+
+634
+00:47:10,080 --> 00:47:14,710
+protocol او جداش عدد عنوين لل internetانت عنوانك
+
+635
+00:47:14,710 --> 00:47:19,530
+على الكمبيوتر تبعك بيبين as a IP address عند الناس
+
+636
+00:47:19,530 --> 00:47:22,850
+برا طيب انا برضه بيبين IP address انا في location
+
+637
+00:47:22,850 --> 00:47:25,710
+تاني بس الاتنين ممكن يكونوا مشتركين في ال location
+
+638
+00:47:25,710 --> 00:47:27,610
+.. في ال .. في ال network على فكرة اذا احنا ماخدين
+
+639
+00:47:27,610 --> 00:47:29,590
+من نفسنا من ال provider ماخدين من نفسنا .. ممكن
+
+640
+00:47:29,590 --> 00:47:33,310
+الشبكة نفسها بس ال host number بيختلف ال host
+
+641
+00:47:33,310 --> 00:47:36,770
+number ممكن يختلف او ال host ID بيختلف في النهاية
+
+642
+00:47:37,880 --> 00:47:47,040
+ال version 4 هذا جداش عدد ال ip addresses الممكنة
+
+643
+00:47:47,040 --> 00:47:51,580
+باستخدام ال version 4 هاي المطلوب طيب بدنا نعرف
+
+644
+00:47:51,580 --> 00:47:57,820
+شوية حقائق عن ال ip version 4 ال ip version 4 أولا
+
+645
+00:47:57,820 --> 00:48:02,380
+بتجسم لجمهد classes ال classes هدولة فعليا في a,b
+
+646
+00:48:02,380 --> 00:48:07,780
+,c في D وED و E في الكتاب موجودين انا اختصرتهم لان
+
+647
+00:48:07,780 --> 00:48:13,940
+مثلنا بس على جد ال ABC موجود D و هذا بيستخدم عادة
+
+648
+00:48:13,940 --> 00:48:18,800
+في ال broadcasting و موجود ال E مستخدم عادة لل
+
+649
+00:48:18,800 --> 00:48:23,340
+networking مش مطلوب انه في الشغل احنا هنشتغل بس
+
+650
+00:48:23,340 --> 00:48:29,040
+على ال class اللي نقدر نعمل فيها hosting او host
+
+651
+00:48:29,040 --> 00:48:34,820
+IDاستضافة ل .. ل users .. ل users بدنا نشوف قداش
+
+652
+00:48:34,820 --> 00:48:39,740
+عدد ال IP الممكنة باستخدام version 4 .. باستخدام
+
+653
+00:48:39,740 --> 00:48:42,540
+version 4 طيب ال facts اللي بدنا نعرفها كانت تالي
+
+654
+00:48:42,540 --> 00:48:47,780
+ان في عندي three types ال type أول اسمه class A ال
+
+655
+00:48:47,780 --> 00:48:52,060
+class A ده بيحتوي على سبعة bit للشبكة لل net ID
+
+656
+00:48:52,060 --> 00:48:56,640
+بنسميها net ID و غير مسموح ان يكون ones غير مسموح
+
+657
+00:48:56,640 --> 00:49:00,530
+ان تكون ones هذا فقط في class Aغير مسموح نكون ايش؟
+
+658
+00:49:00,530 --> 00:49:05,330
+one طيب عندنا اربع عشرين bit ل ال host ID ل ال
+
+659
+00:49:05,330 --> 00:49:10,890
+hosting okay class B address class B address has
+
+660
+00:49:10,890 --> 00:49:16,670
+fourteen bit ل ال network او لل net ID و sixteen ل
+
+661
+00:49:16,670 --> 00:49:22,930
+ال host ID class C has twenty one bit net ID و
+
+662
+00:49:22,930 --> 00:49:28,780
+eight bit ل ال host ID او لل hosting okayبنعرف
+
+663
+00:49:28,780 --> 00:49:31,900
+كمان معلومة ان ال three classes have distinct
+
+664
+00:49:31,900 --> 00:49:35,080
+headers طبيعي انا كيف بده اعرف ان انا في class A و
+
+665
+00:49:35,080 --> 00:49:38,560
+لا B و لا C كيف بده نعرف عن طريق ال header اول
+
+666
+00:49:38,560 --> 00:49:42,800
+bits هنستقبلها اول bits اللي بيميزها ال zero اللي
+
+667
+00:49:42,800 --> 00:49:47,810
+بيميزها ال zero ال zero هدأجة بعد أكم oneإذا جاء
+
+668
+00:49:47,810 --> 00:49:52,430
+مباشرة مافيش اي ones قدامه بعرف ان انا class A إذا
+
+669
+00:49:52,430 --> 00:49:55,950
+one بعدين ال zero انا class B و بشتغل بنانا عليه
+
+670
+00:49:55,950 --> 00:49:59,610
+بجسم مجموعة ال bits بعد هي بنانا عليه عشان أعرف
+
+671
+00:49:59,610 --> 00:50:03,980
+عنوان الشبكة الأول و بعدين بعرف عنوان ال hostبنان
+
+672
+00:50:03,980 --> 00:50:06,860
+على جداش عدد ال bits اللى لازم نعرف فيها العنوان
+
+673
+00:50:06,860 --> 00:50:09,560
+جداش عدد ال bits اللى بنعرف فيها العنوان لل
+
+674
+00:50:09,560 --> 00:50:15,000
+network و لمن و لل host لل network و لل host أو زي
+
+675
+00:50:15,000 --> 00:50:19,940
+class A، zero ببدأت zero مباشرة خلاص بجسم بعدها
+
+676
+00:50:19,940 --> 00:50:23,280
+كده على طول مباشرة سبعة و أربعة و أربعة و عشرين
+
+677
+00:50:23,280 --> 00:50:26,500
+بجسم سبعة و أربعة و عشرين السبعة دول بيحددوا ليه
+
+678
+00:50:26,500 --> 00:50:32,960
+أنا في أي network بتنعمل sub networksوالـ 24 بمثل
+
+679
+00:50:32,960 --> 00:50:37,540
+فيها ال hosts أو جدّيش عدد ال hosts لكل شبكة فيهم
+
+680
+00:50:37,540 --> 00:50:42,620
+جدّيش عدد ال hosts لكل شبكة okay class B هيكون في
+
+681
+00:50:42,620 --> 00:50:47,340
+عندي one و بعدين ال zero class C two ones بعدين
+
+682
+00:50:47,340 --> 00:50:51,520
+zero بعرف منهم كيف اجسم العدد البث اللي جاي يعني
+
+683
+00:50:51,520 --> 00:50:58,700
+عشان اعرف ال network ID و ال host ID تمامما
+
+684
+00:50:58,700 --> 00:51:02,760
+المطلوب في النهاية؟ لسه معلومة إضافية كمان انه في
+
+685
+00:51:02,760 --> 00:51:05,820
+ال host غير مسموح بال zeros و ال ones اللي هو ال
+
+686
+00:51:05,820 --> 00:51:08,960
+DC يعني لأن ال DC ممكن تكون عبارة عن noise في
+
+687
+00:51:08,960 --> 00:51:15,810
+النهاية أو nothing لو كانت zero فطبعاzero أو one
+
+688
+00:51:15,810 --> 00:51:23,150
+غير مسموح باستخدامها ل ال host ID هدول
+
+689
+00:51:23,150 --> 00:51:27,030
+مرفضين ل ال host zeros او ones لكل classes ل ال
+
+690
+00:51:27,030 --> 00:51:30,710
+three classes مرفضين مرفضين okay المطلوب انه يجداش
+
+691
+00:51:30,710 --> 00:51:37,110
+عدد ال IDs الممكنة ل ال version 4 طبعا واضح ال
+
+692
+00:51:37,110 --> 00:51:43,970
+version 4 في الحالة هذه اما هيكون class E اوclass
+
+693
+00:51:43,970 --> 00:51:50,990
+B أو class C واضحة انا بتصورها لوجهة بداية الرؤية
+
+694
+00:51:50,990 --> 00:51:59,130
+واضحة ان انا بتكلم عن number of class A plus
+
+695
+00:51:59,130 --> 00:52:04,010
+number number ID طبعا بتكلم عن ال ID ال ID عفوا ال
+
+696
+00:52:04,010 --> 00:52:11,430
+ID addresses class B plus number of
+
+697
+00:52:14,410 --> 00:52:20,710
+C نمسك الأول نمسك واحد واحد الأول لحظة من ال 32
+
+698
+00:52:20,710 --> 00:52:27,770
+bit هو في النهاية مشترك ال version ال IP version 4
+
+699
+00:52:27,770 --> 00:52:32,310
+مشترك أو بتفق أنه بيستخدم ال 32 bit واحدة منهم
+
+700
+00:52:32,310 --> 00:52:37,630
+راحت لمين للهدر؟ دل 31 ال 31 هم المجسدين سبعة و 24
+
+701
+00:52:37,630 --> 00:52:42,270
+سبعة نمسك السبعة في الأول طبعا لحظة أن ال sequence
+
+702
+00:52:42,270 --> 00:52:46,440
+في الأخر هيكون كلهم على بعضيعني أنا بقدرش أروح
+
+703
+00:52:46,440 --> 00:52:50,980
+أعرف الشبكة و أقول له اعرفني لأ كيف ده يعرفني هو
+
+704
+00:52:50,980 --> 00:52:53,700
+عارف الشبكة ال provider اللي أنا ماخد منه بس
+
+705
+00:52:53,700 --> 00:52:56,120
+ماعرفنيش أنا لإن أنا مش لحالي أفعل ال provider
+
+706
+00:52:56,120 --> 00:52:58,780
+يعني ال provider مش مقتنع ان انا لحالي في نفس
+
+707
+00:52:58,780 --> 00:53:02,660
+الوجد بقدرش أقول له أنا هاي رقم ايه اعرفني واصلني
+
+708
+00:53:02,660 --> 00:53:07,180
+طب ما هو مش عارف الشبكة ممكن يكون في واحد تاني في
+
+709
+00:53:07,180 --> 00:53:10,720
+شبكة تانية اللي له نفس الرقم رقم ال host بس على
+
+710
+00:53:10,720 --> 00:53:13,960
+شبكة تانية فلازم كله مع بعضه فهذا كله sequence
+
+711
+00:53:13,960 --> 00:53:18,160
+واحددعوني أخبركم إن سيكوانس واحد مع بعض هذا لازم
+
+712
+00:53:18,160 --> 00:53:21,700
+يظهر and هذا لازم يكون موجود لأن اتنين لازم يكونوا
+
+713
+00:53:21,700 --> 00:53:26,700
+and موجودة بينهم هذا and هذا كويس نمسك الأول الأول
+
+714
+00:53:26,700 --> 00:53:30,900
+اللي هو ال net عبارة عن سبعة سبعة digital أكم
+
+715
+00:53:30,900 --> 00:53:34,980
+احتمال إلها ستنقل
+
+716
+00:53:34,980 --> 00:53:39,960
+واحد بالظبط فهتكون اتنين تتبارد سبعة minus ال one
+
+717
+00:53:39,960 --> 00:53:47,460
+صحيح اللي هو إيه؟ال ones لاتساوي ones لاتساوي ones
+
+718
+00:53:47,460 --> 00:53:52,440
+طيب هدى هتنضرب فى مين؟ فى ال host فى ال host لدى
+
+719
+00:53:52,440 --> 00:53:57,720
+ايش؟ اثنين to the power ناقص اثنين ناقص اثنين شو
+
+720
+00:53:57,720 --> 00:54:03,320
+هما الاثنين؟ zeros or ones خلاص هدى لمين ل class
+
+721
+00:54:03,320 --> 00:54:11,120
+ايه؟هذه بتاعة class class B بتضربوهم بطلع برقم
+
+722
+00:54:11,120 --> 00:54:16,740
+اتنين اتنين مليون بليون تقريبا اتنين كسر بليون
+
+723
+00:54:16,740 --> 00:54:24,140
+كويس تجمع ولا تانية زائد class B اتنين و نص أربعة
+
+724
+00:54:24,140 --> 00:54:27,960
+عشر اتنين و نص اربعة عشر و ماجالش انه انه من نوع
+
+725
+00:54:27,960 --> 00:54:33,380
+ال ones فاتنين و نص اربعة عشر في ناقص اتنين تمام
+
+726
+00:54:33,380 --> 00:54:34,260
+التالتة
+
+727
+00:54:38,150 --> 00:54:44,810
+2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8
+
+728
+00:54:44,810 --> 00:54:52,190
+ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص
+
+729
+00:54:52,190 --> 00:54:53,410
+2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8
+
+730
+00:54:53,410 --> 00:54:53,410
+ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص
+
+731
+00:54:53,410 --> 00:54:53,410
+2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8
+
+732
+00:54:53,410 --> 00:54:54,430
+ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص
+
+733
+00:54:54,430 --> 00:55:03,180
+2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8 ناقص 2 8هدول رقم
+
+734
+00:55:03,180 --> 00:55:06,820
+صغير كان يستدعي أنه فعلا تدخل و نعمل upgrading أو
+
+735
+00:55:06,820 --> 00:55:12,680
+يعملوا upgrading لمين ل version 6 في الآخر هذه
+
+736
+00:55:12,680 --> 00:55:17,100
+القالية تجمعوهم
+
+737
+00:55:17,100 --> 00:55:21,600
+عشان يطلع مجموع الأرقام class A class B class C
+
+738
+00:55:21,600 --> 00:55:27,180
+بتطلع لنا ال total 3.7 تقريبا billion IB addresses
+
+739
+00:55:29,170 --> 00:55:35,010
+واضح كيف حسبناهم؟ كيف عدناهم؟ طيب، كمان مرة، وين
+
+740
+00:55:35,010 --> 00:55:39,070
+المشكلة كانت عندك؟ في الجامعة ولا في الدراجة؟ نقص
+
+741
+00:55:39,070 --> 00:55:41,250
+واحد، نقص إثنين، نقص واحد، نقص إثنين، نقص واحد،
+
+742
+00:55:41,250 --> 00:55:43,670
+نقص إثنين، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+743
+00:55:43,670 --> 00:55:44,090
+نقص واحد، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+744
+00:55:44,090 --> 00:55:48,970
+نقص واحد، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+745
+00:55:48,970 --> 00:55:51,110
+نقص واحد، نقص واحد، نقص واحد، نقص واحد، نقص واحد،
+
+746
+00:55:51,110 --> 00:55:59,120
+نقص واحد، نقص واحد، نقص واحد، نيا ones يا zeros
+
+747
+00:55:59,120 --> 00:56:03,680
+ماعندكيش انت بتتكلم عن bit ال bit فيه احتمال غير
+
+748
+00:56:03,680 --> 00:56:09,080
+ال one و ال zero بس هو هنا بيحددلك بيقولك ان ال
+
+749
+00:56:09,080 --> 00:56:14,120
+class A بالنسبة له الشبكة ممنوعة تستخدم ال ones
+
+750
+00:56:15,320 --> 00:56:18,780
+يعني هنا شوية distractions جالك لازم تاخد بالك
+
+751
+00:56:18,780 --> 00:56:23,540
+منها انه في class A ما تستعمليش ال ones لل net ID
+
+752
+00:56:23,540 --> 00:56:27,200
+فال net ID أنا عارف ان هي سبعة صح فبقول جديش عدد
+
+753
+00:56:27,200 --> 00:56:31,980
+البدائي بتاعتها جديش عدد ال strings اللي ممكن
+
+754
+00:56:31,980 --> 00:56:35,780
+اطلعها من سبعة bits اتنين to the power سبعة بس
+
+755
+00:56:35,780 --> 00:56:39,260
+هيقول ليه استثني ال ones طب ال ones هي حالة واحدة
+
+756
+00:56:39,260 --> 00:56:39,840
+من الحالات
+
+757
+00:56:42,500 --> 00:56:46,600
+بالظبط لأ لأ ال ones اللي هي هي one to the power
+
+758
+00:56:46,600 --> 00:56:49,120
+of seven يعني one في ال locations السبعة في السبعة
+
+759
+00:56:49,120 --> 00:56:53,140
+locations هذه هي حالة واحدة تعتبر هي تعتبر حالة
+
+760
+00:56:53,140 --> 00:56:56,260
+واحدة من كل الحالات فبنعملها حالة بهذا الشكل و ب
+
+761
+00:56:56,260 --> 00:57:00,220
+stop بنوقف على هيك طيب لاحظوا أنه بالنسبة لل host
+
+762
+00:57:00,220 --> 00:57:04,300
+ميعطيني هنا ل three classes okay headers بعدين
+
+763
+00:57:04,300 --> 00:57:11,800
+جالني ال host IDones أو zeros not allowed مش مسموح
+
+764
+00:57:11,800 --> 00:57:14,840
+فيهم مش مسموح فيهم فautomatically هنا لما نقول
+
+765
+00:57:14,840 --> 00:57:18,320
+اتنين تتبارى اربعة و عشرين في عندي حالتين مش مسموح
+
+766
+00:57:18,320 --> 00:57:21,680
+فيهم اللي هم ال ones كله one one one one one و
+
+767
+00:57:21,680 --> 00:57:24,700
+zero zero zero zero ف minus two لإن هو دول
+
+768
+00:57:24,700 --> 00:57:30,920
+احتمالين يا ones يا zeros فبنطرح لاتنين طب مش فيه
+
+769
+00:57:30,920 --> 00:57:35,700
+اللي هو اللي موجود اللي هي دائما واحد صارت؟ okay
+
+770
+00:57:35,700 --> 00:57:39,650
+اختصرناها راحت خلصتلأن انت في عندك واحدة للهدر و
+
+771
+00:57:39,650 --> 00:57:43,210
+في عندك سبعة و جداش و اربع و عشرين سبعة و اربع و
+
+772
+00:57:43,210 --> 00:57:47,170
+عشرين واحد تلاتين زائد الهدر اتنين و تلاتين طيب
+
+773
+00:57:47,170 --> 00:57:52,210
+نمسك التانية في عندنا اربعتاش و ستاش تلاتين زائد
+
+774
+00:57:52,210 --> 00:57:57,190
+الاتنين تعونها هدولة ثابتين هدولة هي ماقدرش اقول
+
+775
+00:57:57,190 --> 00:58:01,150
+ان في احتمالات اغير لأ ده مش احتمالات هي ثابت
+
+776
+00:58:01,150 --> 00:58:04,490
+ماحطهاش في الحسبة لإن هدول ثابتين هدول الهدر تعون
+
+777
+00:58:04,490 --> 00:58:08,370
+هدول المميزين لكل classبحركهم مش هدول، مابقدرش
+
+778
+00:58:08,370 --> 00:58:18,490
+نحركهم okay
+
+779
+00:58:18,490 --> 00:58:23,230
+ال inclusion و ال exclusion هنا لما يكون في عندكوا
+
+780
+00:58:23,230 --> 00:58:31,000
+ال task Aعبارة عن M ways اتفقنا ان ال task A عبارة
+
+781
+00:58:31,000 --> 00:58:36,660
+عن M ways ال M ways هدولة في منهم K ways يمكن يطلع
+
+782
+00:58:36,660 --> 00:58:39,700
+بسوء ال M احتمال يطلع يمكن يكون بسوء قيمة ال M
+
+783
+00:58:39,700 --> 00:58:44,720
+كلها بس في K ways of doing task 1 are also
+
+784
+00:58:44,720 --> 00:58:48,860
+simultaneously accomplish task 2 بمعنى ان في
+
+785
+00:58:48,860 --> 00:58:52,020
+intersection between A و B ال intersection هذا
+
+786
+00:58:52,020 --> 00:58:59,250
+ممكن يكون كل Aإيه إحنا عارفين أن عددهم M؟ فمعنى
+
+787
+00:58:59,250 --> 00:59:02,450
+ذلك ال K في الحالة هذه اللي هي ال intersection بين
+
+788
+00:59:02,450 --> 00:59:07,130
+الأثنين بتساوي M في الحالة هذه ممكن تساوي أو ممكن
+
+789
+00:59:07,130 --> 00:59:13,590
+تكون أقل أقل إذا كان في جزء intersection فهنا
+
+790
+00:59:13,590 --> 00:59:20,750
+هتكون K وهنا هتكون M minus K هتكون الجزء المتبقي
+
+791
+00:59:20,750 --> 00:59:27,010
+جزء المتبقي كويسطبعا فإذا هنا بدأنا نشتغل لإن في و
+
+792
+00:59:27,010 --> 00:59:36,330
+الله كام طرح لعمل عملة واحدة تسكتوه تسكتوه
+
+793
+00:59:36,330 --> 00:59:41,670
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+794
+00:59:41,670 --> 00:59:41,690
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+795
+00:59:41,690 --> 00:59:41,710
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+796
+00:59:41,710 --> 00:59:44,790
+تسكتوه تسكتوه تسكتوه تسكتوه تسكتوه
+
+797
+00:59:44,790 --> 00:59:54,210
+تسكتوه تسكتوه تسكتوه تسو جمعتها مرة مع ال cardinal
+
+798
+00:59:54,210 --> 00:59:58,430
+التي ل B طب مانفعش اكررها مرتين هي موجودة صارت
+
+799
+00:59:58,430 --> 01:00:01,590
+معايا مرتين فانا محتاج ايش أسوي اطرحها طب انا
+
+800
+01:00:01,590 --> 01:00:04,290
+عارفها اشي بالظبط اه عارفها هاد ال intersection
+
+801
+01:00:04,290 --> 01:00:07,730
+معناته لو اقدرت تحسب ال intersection between A و B
+
+802
+01:00:07,730 --> 01:00:12,550
+بتطرحها منها من مجموحهم من مجموحهم في الحالة هاد
+
+803
+01:00:12,550 --> 01:00:18,350
+بيصير عندنا then number of ways to accomplishdo
+
+804
+01:00:18,350 --> 01:00:23,090
+either task one or task two هتكون M plus N minus K
+
+805
+01:00:23,090 --> 01:00:27,530
+ال overlap
+
+806
+01:00:27,530 --> 01:00:31,310
+بينهم ال overlap بينهم في الحالة هذا ال
+
+807
+01:00:31,310 --> 01:00:34,010
+cardinality ل A union B هتساوي ال cardinality ل A
+
+808
+01:00:34,010 --> 01:00:38,150
+plus cardinality B minus cardinality intersection
+
+809
+01:00:38,150 --> 01:00:42,710
+ال intersection هذا الكلام not disjoint في حالة ان
+
+810
+01:00:42,710 --> 01:00:45,070
+هي not disjoint بمعنى يوجد intersection between
+
+811
+01:00:45,070 --> 01:00:45,370
+them
+
+812
+01:00:51,650 --> 01:00:55,550
+ببساطة جدا a plus b و خلاص ال cardinality ل a plus
+
+813
+01:00:55,550 --> 01:01:00,590
+ال cardinality ل 11 ناخد شوية examples عليها عشان
+
+814
+01:01:00,590 --> 01:01:05,190
+تتضحى
+
+815
+01:01:05,190 --> 01:01:10,250
+example how many pet strings of length 4 either
+
+816
+01:01:10,250 --> 01:01:13,970
+start with one or end with double zero
+
+817
+01:01:20,200 --> 01:01:24,880
+عندكوا string عبارة عن four length، ال four length
+
+818
+01:01:24,880 --> 01:01:32,800
+هدولة جدّاش عددهم بشرط بشرط أنه either start one
+
+819
+01:01:32,800 --> 01:01:40,700
+إما بيبدأوا بواحد أو بينتهوا orفبناخد الحالة
+
+820
+01:01:40,700 --> 01:01:43,580
+الأولى للحالة والثانية للحالة وما دام or بيجب أن
+
+821
+01:01:43,580 --> 01:01:47,740
+نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب
+
+822
+01:01:47,740 --> 01:01:47,940
+أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع
+
+823
+01:01:47,940 --> 01:01:49,040
+بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن
+
+824
+01:01:49,040 --> 01:01:49,040
+نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب
+
+825
+01:01:49,040 --> 01:01:51,660
+أن نجمع بيجب أن نجمع بيجب أن نجمع بيجب أن نجمع
+
+826
+01:01:51,660 --> 01:02:06,880
+بيجب أن نجمع بيجب أن نجمع بيجب
+
+827
+01:02:06,880 --> 01:02:07,220
+أن ن
+
+828
+01:02:12,240 --> 01:02:16,400
+جدّاش عدد الـ strains اللي ممكن نعمل ال generation
+
+829
+01:02:16,400 --> 01:02:23,600
+هنا 2 ضغور 2 سوى 4 طيب ال summation لساوة 12 لأ
+
+830
+01:02:23,600 --> 01:02:29,180
+لأنه يوجد حالة أنا جمعتها هنا وجمعتها هنا كيف
+
+831
+01:02:29,180 --> 01:02:34,240
+أحسبها ال intersection لأ لأ لأ لأ إيش نطرح يعني
+
+832
+01:02:34,240 --> 01:02:38,660
+هيطلع أربعة اعملوا ال intersection إيش ال
+
+833
+01:02:38,660 --> 01:02:44,370
+intersection إنه الإتنين تحققوا مع بعضبمعنى ان ال
+
+834
+01:02:44,370 --> 01:02:51,190
+one تحققه و ال zero تحققه اكم ways لتمثيل ال
+
+835
+01:02:51,190 --> 01:02:55,330
+sequence بها اتنين اما هنا تكون صفر او واحد فهنا
+
+836
+01:02:55,330 --> 01:03:00,790
+تساوي اتنين صار عندنا تمانية زائد اربع ناقص اتنين
+
+837
+01:03:00,790 --> 01:03:04,170
+ساوي
+
+838
+01:03:04,170 --> 01:03:09,730
+عشرة ففي الحالة دايما اشتغلوا كتالي بنحسب ال ways
+
+839
+01:03:09,730 --> 01:03:16,050
+to do the task onethe number of ways to do task
+
+840
+01:03:16,050 --> 01:03:22,910
+two ونطرح منهم ال number of ways to do both task
+
+841
+01:03:22,910 --> 01:03:27,330
+one and task two both number one and two الاتنين
+
+842
+01:03:27,330 --> 01:03:31,610
+بدون يكونوا متحققين مع بعض four check حدد يعملكم
+
+843
+01:03:31,610 --> 01:03:34,230
+من أربعة كل احتمالات اللي بتبدأ ب one
+
+844
+01:03:46,540 --> 01:03:47,940
+1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
+
+845
+01:03:52,580 --> 01:03:55,740
+في مشترك اتنين بينهم فإذا بدنا نشطبهم الاتنين
+
+846
+01:03:55,740 --> 01:04:02,900
+هدولة عددهم اتنين شطبناهم فعلا عشرة عشرة العدد
+
+847
+01:04:02,900 --> 01:04:09,540
+الحالات الممكنة عشرة عدد الحالات الممكنة خلاص okay
+
+848
+01:04:09,540 --> 01:04:13,380
+انا
+
+849
+01:04:13,380 --> 01:04:18,500
+والله الشباب كانوا خلصوا اكتر من هيكطيب بكفى هيك
+
+850
+01:04:18,500 --> 01:04:21,820
+مرة جاية بنحاول نشد في يوم دول أكتر يالا أعطيكوا
+
+851
+01:04:21,820 --> 01:04:22,840
+العافية وبركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..547f9e44551e3ecb84bb2e6eebc2dddee0bf23cf
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc.srt
@@ -0,0 +1,1822 @@
+
+1
+00:00:20,970 --> 00:00:22,930
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,930 --> 00:00:25,310
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,310 --> 00:00:30,030
+أجمعين. بنكمل اليوم في الـ numbers theory، وصلنا يمكن
+
+4
+00:00:30,030 --> 00:00:36,470
+لـ الـ modulus و الـ modular system و الـ modular و
+
+5
+00:00:36,470 --> 00:00:43,700
+أخذنا آخر شكل اللي هي الـ spiral visualization، وكان
+
+6
+00:00:43,700 --> 00:00:49,720
+example mod 5، كان mod 5 as a example عشان نحدد
+
+7
+00:00:49,720 --> 00:00:53,960
+منه الـ .. الـ congruence أو الـ congruence theory
+
+8
+00:00:53,960 --> 00:00:59,760
+بتاعتنا، وقلنا أن ثلاثة congruent to ثمانية ..
+
+9
+00:00:59,760 --> 00:01:02,920
+congruent to ثلاثة عشر، والـ .. الـ .. الفيصل في
+
+10
+00:01:02,920 --> 00:01:07,480
+الموضوع كان أن الفرق بينهم .. بين الأرقام هي عبارة
+
+11
+00:01:07,480 --> 00:01:12,740
+عن الـ modulus أو مضروبة في some K مضروبة في some
+
+12
+00:01:12,740 --> 00:01:18,000
+integer K في some integer K. فلو قلنا ثلاثة وثمانية،
+
+13
+00:01:18,000 --> 00:01:21,540
+الفرق بينهم خمسة، أنا فعلاً بشتغل على modulus five.
+
+14
+00:01:21,540 --> 00:01:26,300
+بين الثلاثة والثمانية خمسة، بين الثلاثة والثلاثة عشر خمسة عشر، فهي عبارة
+
+15
+00:01:26,300 --> 00:01:30,220
+عن برضه some integer مضروب في مين؟ في الـ modulus
+
+16
+00:01:30,220 --> 00:01:34,460
+تبعنا اللي هو خمسة. الكلام هذا قلناه المرة اللي فاتت.
+
+17
+00:01:34,460 --> 00:01:43,830
+نكمل بعده ونشوف congruence theorems أو
+
+18
+00:01:43,830 --> 00:01:48,890
+facts. يمكن نقول let a, b belong to Z integer
+
+19
+00:01:48,890 --> 00:01:55,850
+numbers أو الـ modulers أو المعامل belong to
+
+20
+00:01:55,850 --> 00:02:01,300
+positive integer، to positive integer، then a
+
+21
+00:02:01,300 --> 00:02:06,400
+congruent to b mod m. هذا معناه there exist k، some
+
+22
+00:02:06,400 --> 00:02:12,440
+k، some integer، some integer، a equal to b plus km.
+
+23
+00:02:12,440 --> 00:02:17,500
+هي نفسها اللي طول الوقت قولناها a minus b، الفرق بينهم
+
+24
+00:02:17,500 --> 00:02:22,440
+عبارة عن some k مضروبة في الـ modulus، في الـ
+
+25
+00:02:22,440 --> 00:02:25,760
+modulus طبعاً. okay. فالفرق دائماً إذا كانوا فعلاً
+
+26
+00:02:25,760 --> 00:02:29,380
+congruent لبعض، إذا كانوا congruent لبعض، الأصل أن
+
+27
+00:02:29,380 --> 00:02:32,700
+الفرق بينهم دائماً بيساوي الـ modulus أو الـ modulus
+
+28
+00:02:32,700 --> 00:02:39,720
+في some integer k.  لـ
+
+29
+00:02:39,720 --> 00:02:44,220
+a, b, c, d belong to Z، و الـ modulus زي ما قلنا belong
+
+30
+00:02:44,220 --> 00:02:49,700
+to positive integer. then إذا كان a
+
+31
+00:02:49,700 --> 00:02:56,980
+congruent to b mod m، and c congruent to d mod m، then a
+
+32
+00:02:56,980 --> 00:03:07,260
+plus c congruent to b plus d. إذن بنضيف plus
+
+33
+00:03:07,260 --> 00:03:15,160
+أو ممكن أقول برضه then a مضروب في c congruent to
+
+34
+00:03:15,160 --> 00:03:20,780
+b مضروب في d، كله لازم يكون mod m، الـ modulus
+
+35
+00:03:20,780 --> 00:03:27,800
+دائماً يكون m ثابت. إذا a plus c congruent to b plus
+
+36
+00:03:27,800 --> 00:03:34,580
+d mod m، أو بقدر أقول a c congruent to b d modulus
+
+37
+00:03:34,580 --> 00:03:41,230
+أو mod m. طيب، Euclid's Algorithm .. Euclid's
+
+38
+00:03:41,230 --> 00:03:47,030
+Algorithm هو Algorithm عنده .. Euclid بده يجيب لنا
+
+39
+00:03:47,030 --> 00:03:49,910
+ويحسب لنا فيه الـ greatest common divisor .. الـ
+
+40
+00:03:49,910 --> 00:03:52,110
+greatest common divisor. إحنا قبل كده اشتغلنا على
+
+41
+00:03:52,110 --> 00:03:56,050
+greatest common divisor باستخدام باستخدام الـ prime
+
+42
+00:03:56,050 --> 00:03:59,950
+factorization، باستخدام الـ prime factors، الـ prime
+
+43
+00:03:59,950 --> 00:04:04,350
+factors. ممكن جداً تكون الأرقام كبيرة فما تقدرش
+
+44
+00:04:04,350 --> 00:04:08,730
+توصله، وبيظل Algorithm بديل عشان نجيب الـ greatest
+
+45
+00:04:08,730 --> 00:04:13,160
+common divisor، أو المعامل المشترك الأكبر، من القاسم
+
+46
+00:04:13,160 --> 00:04:15,620
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+47
+00:04:15,620 --> 00:04:16,180
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+48
+00:04:16,180 --> 00:04:16,620
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+49
+00:04:16,620 --> 00:04:17,380
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+50
+00:04:17,380 --> 00:04:18,020
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+51
+00:04:18,020 --> 00:04:18,040
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+52
+00:04:18,040 --> 00:04:23,060
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+53
+00:04:23,060 --> 00:04:27,980
+المشترك الأكبر، من القاسم المشترك الأكبر، من القاسم
+
+54
+00:04:27,980 --> 00:04:35,060
+المشترك الأكبر من القاسم. إذا الكبير موضل صغير لأن
+
+55
+00:04:35,060 --> 00:04:38,480
+الصغير موضل كبير، حيبقى نفس القيمة، مش هيتغير شيء، مش
+
+56
+00:04:38,480 --> 00:04:42,340
+هيتغير شيء. إحنا قلنا الـ modular operator هي عبارة
+
+57
+00:04:42,340 --> 00:04:47,200
+عن إيش؟ بيطلع لنا الـ remainder للقسمة بتاعتهم، أو الـ
+
+58
+00:04:47,200 --> 00:04:53,800
+division remainder، متبقي من القسمة، متبقي القسمة. كويس؟
+
+59
+00:04:53,800 --> 00:04:58,850
+دائماً متبقي القسمة هيكون أقل من مين؟ من الـ modulus. أقل
+
+60
+00:04:58,850 --> 00:05:03,970
+من الـ modulus. لما بنتكلم عن الساعة اثنا عشر، طبيعي كل
+
+61
+00:05:03,970 --> 00:05:07,810
+الساعات اللي بدي أقرأها بالنسبة لها الساعة اثنا عشر
+
+62
+00:05:07,810 --> 00:05:10,610
+هتكون أقل من الاثنا عشر، هتكون أقل من اثنا عشر، حتى عند
+
+63
+00:05:10,610 --> 00:05:15,900
+الاثنا عشر بنقول صفر. حتى عند الـ 12 بنقول صفر. ففي
+
+64
+00:05:15,900 --> 00:05:21,700
+الحالة هذه دائماً خارج أو الـ remainder للـ modular
+
+65
+00:05:21,700 --> 00:05:28,460
+operator بدي يكون أقل من مين؟ من الـ b. فإذا نفس الكلام هو
+
+66
+00:05:28,460 --> 00:05:34,520
+هو بقدر أرجع أكرر تاني على أساس أنه يساوي the
+
+67
+00:05:34,520 --> 00:05:38,680
+greatest common divisor لمين؟ لـ الـ b، لأنه صارت هي
+
+68
+00:05:38,680 --> 00:05:48,360
+الأكبر. هالوقت صارت أكبر. a mod b في الحالة التالية
+
+69
+00:05:48,360 --> 00:05:54,600
+طبعاً، حيُطلع في النهاية رقم. هذا حيُطلع رقم ناتج، الناتج
+
+70
+00:05:54,600 --> 00:05:58,980
+هذا، بنرجع نكرر نفس العملية تاني، لإمتى؟ لعند ما
+
+71
+00:05:58,980 --> 00:06:06,300
+النتيجة هذه equal to zero، لعند ما الناتج equal to
+
+72
+00:06:06,300 --> 00:06:11,800
+zero.  إن بيصير equal to zero، الرقم اللي ضايل هو هذا
+
+73
+00:06:11,800 --> 00:06:14,720
+الـ common .. الـ greatest common divisor، الرقم اللي
+
+74
+00:06:14,720 --> 00:06:19,300
+بيكون ضايل معه هو الـ greatest common divisor.  ناخد
+
+75
+00:06:19,300 --> 00:06:25,980
+مثال بيوضح .. بيوضح الصورة. لو مطلوب greatest
+
+76
+00:06:25,980 --> 00:06:31,640
+common divisor لـ 372 و 164.  اللي هي نفس الـ
+
+77
+00:06:31,640 --> 00:06:37,820
+greatest common divisor لـ 372 mod 164، الأكبر mod
+
+78
+00:06:37,820 --> 00:06:48,860
+الأصغر، والأصغر. طبعاً الناتج هنا هيكون أقل من 164.
+
+79
+00:06:48,860 --> 00:06:57,050
+Sure، أقل من 164 دائماً، لأن المتبقي من القسمة على 164
+
+80
+00:06:57,050 --> 00:07:02,530
+طبيعي بيكون أقل من 164. طبيعي. كويس؟ فحنشتغل على الـ
+
+81
+00:07:02,530 --> 00:07:05,810
+mod، الـ mod. جداش بيطلع؟ في الآخر بيطلع 44. فإذا
+
+82
+00:07:05,810 --> 00:07:09,630
+بتصير كأنه عندنا أربعة وأربعين ومئة
+
+83
+00:07:11,380 --> 00:07:15,900
+الكبير والصغير، كأنك اختزلت الـ greatest common
+
+84
+00:07:15,900 --> 00:07:22,620
+divisor لـ 372، 164 هو نفسه الـ greatest common
+
+85
+00:07:22,620 --> 00:07:30,800
+divisor لـ 164 و 44، هو نفسه، نفس القيمة. معنى ذلك كأنه
+
+86
+00:07:30,800 --> 00:07:34,060
+صار عندي مشكلة جديدة، problem جديدة، بس أخف شوية، أقل
+
+87
+00:07:34,060 --> 00:07:38,000
+درجة، كأنه بدور على greatest common divisor لـ 164
+
+88
+00:07:38,000 --> 00:07:44,660
+و 44. بنكرر نفس الكلام، 164 mod 44، الكلام ده بيطلع
+
+89
+00:07:44,660 --> 00:07:49,320
+32. معنى ذلك برضه الـ greatest common divisor لهذي
+
+90
+00:07:49,320 --> 00:07:53,100
+أو لهذي هو نفسه لهذي، لـ greatest common divisor لـ 44
+
+91
+00:07:53,100 --> 00:07:58,020
+و 32. كلهم اشتغلنا عليهم، حتلاقوا معاهم نفس الـ
+
+92
+00:07:58,020 --> 00:08:01,690
+greatest common divisor. ليش؟ لأنه ممكن السؤال يبدأ
+
+93
+00:08:01,690 --> 00:08:07,210
+من هنا. حتقول الـ greatest common divisor لـ 44، 32
+
+94
+00:08:07,210 --> 00:08:12,190
+حتطلع قيمة هي نفسها الـ greatest common divisor لـ
+
+95
+00:08:12,190 --> 00:08:21,710
+372، 164. طيب، هو نفسه لـ 32
+
+96
+00:08:21,710 --> 00:08:27,620
+و 12. برضه لهم نفس الـ greatest common divisor. طيب
+
+97
+00:08:27,620 --> 00:08:32,500
+ثمانية واثنا عشر. طيب، كويس. آخر شغل عند الثمانية و
+
+98
+00:08:32,500 --> 00:08:34,900
+اثنا عشر. هنا صار كأنه بده يتكلم عن الـ greatest common
+
+99
+00:08:34,900 --> 00:08:42,980
+divisor، ثمانية mod أربعة. ثمانية mod أربعة صفر. فش
+
+100
+00:08:42,980 --> 00:08:48,180
+متبقي. أنت فش متبقي. إيه اللي ضايل؟ أربعة.
+
+101
+00:08:48,180 --> 00:08:53,380
+فإذا الـ greatest common divisor هو أربعة. أكبر عامل
+
+102
+00:08:53,380 --> 00:09:00,560
+مشترك، عامل مشترك بينهم، أو قاسم مشترك أكبر لـ 372
+
+103
+00:09:00,560 --> 00:09:09,020
+و 164 هو الأربعة. طيب، أكبر عامل مشترك لـ 164 و 44 هي
+
+104
+00:09:09,020 --> 00:09:13,680
+الأربعة. أكبر عامل مشترك لـ 44 و 32 هي الأربعة. أكبر
+
+105
+00:09:13,680 --> 00:09:18,660
+عامل مشترك بين الأربعة و 8 هي الأربعة. لحظة! فكلهم
+
+106
+00:09:18,660 --> 00:09:24,100
+نفس نفس الناتج بيطلع. باستخدام الـ modular operator
+
+107
+00:09:24,100 --> 00:09:30,020
+باستخدام الـ modular operator. okay.
+
+108
+00:09:30,020 --> 00:09:34,740
+algorithm. نكتب algorithm للموضوع. الـ algorithm
+
+109
+00:09:34,740 --> 00:09:39,500
+procedure.  حنكتب procedure، وبدنا نحدد إيش اسمه؟
+
+110
+00:09:39,500 --> 00:09:42,480
+greatest common divisor. خلاص معروف أن الـ algorithm
+
+111
+00:09:42,480 --> 00:09:45,200
+اللي بدنا نعمله، أو الـ code اللي بدنا نكتبه لـ
+
+112
+00:09:45,200 --> 00:09:48,200
+greatest common divisor، الـ inputs تبعته عبارة عن
+
+113
+00:09:48,200 --> 00:09:50,360
+two numbers. بدي أجيب الـ greatest common divisor
+
+114
+00:09:50,360 --> 00:09:54,670
+لهم. بنجيب العامل القاسم الأكبر، أو القاسم المشترك
+
+115
+00:09:54,670 --> 00:09:58,050
+الأكبر. عبارة عن إيش؟ اسمهم positive integers.
+
+116
+00:09:58,050 --> 00:10:02,150
+positive integers. why؟ ب لا تساوي zero. لأنه عارفين
+
+117
+00:10:02,150 --> 00:10:05,010
+إذا سوت zero، خلاص بناخد الرقم الثاني على أساس أن
+
+118
+00:10:05,010 --> 00:10:08,390
+هو الـ common divisor، أو الـ greatest common divisor.
+
+119
+00:10:08,390 --> 00:10:12,350
+لا تساوي zero. هنستمر في الـ modular operation، الـ modular
+
+120
+00:10:12,350 --> 00:10:16,130
+operator تبعنا حيستمر، هيتكرر كمان مرة، طوال ما
+
+121
+00:10:16,130 --> 00:10:22,750
+هي لا تساوي صفر. begin. مش نعمل r؟ خلاص، r ما هي جايبين
+
+122
+00:10:22,750 --> 00:10:31,250
+إحنا من الـ a mod b، وهاد الـ r دائماً أقل من b، أقل
+
+123
+00:10:31,250 --> 00:10:35,610
+من b. فبنرتبهم. خلصنا العملية الـ mod operator،
+
+124
+00:10:35,610 --> 00:10:39,830
+بنرتبهم، الـ a بنحطها هي b، لأن هي الأكبر هالوقت.
+
+125
+00:10:39,830 --> 00:10:45,200
+حتصير هي الأكبر. الـ b هي حتصير الـ r، هي حتصير الـ
+
+126
+00:10:45,200 --> 00:10:48,300
+remainder للـ operator السابق، أو للـ operation
+
+127
+00:10:48,300 --> 00:10:51,360
+السابق. نعود إلى الـ operator الموجود، للـ operator
+
+128
+00:10:51,360 --> 00:10:57,080
+السابق. كويس؟ هنا و end.  نرجع نتأكد، هل الـ b الجديدة
+
+129
+00:10:57,080 --> 00:11:03,440
+تساوي صفر؟ إن بتساوي صفر، إذا الـ remainder equal to
+
+130
+00:11:03,440 --> 00:11:07,400
+zero، بتقول لنا الـ remainder لا يساوي zero، هنستمر. إن
+
+131
+00:11:07,400 --> 00:11:11,700
+بيساوي zero، زي حالة الـ 8 و 4، طول ما الـ 8 و 4 الـ r equal
+
+132
+00:11:11,700 --> 00:11:17,000
+to zero، stop. r equal to 0، يعني ب بتساوي 0، و r بتساوي
+
+133
+00:11:17,000 --> 00:11:25,260
+0، وحتجيب لنا قيمة a الأخيرة. فإذا return a، جيبلنا قيمة
+
+134
+00:11:25,260 --> 00:11:30,030
+a اللي طلعت في الآخر، بعد طبعاً ما إحنا رتبناهم بهذا
+
+135
+00:11:30,030 --> 00:11:33,830
+الشكل، أن الـ b حطيناها هي الـ a، والـ a هي صارت الـ b
+
+136
+00:11:33,830 --> 00:11:38,190
+فبناخد آخر term اللي هو greatest common divisor
+
+137
+00:11:38,190 --> 00:11:43,750
+عبارة عن الـ a اللي هنرجع فيه كنتيجة للـ greatest
+
+138
+00:11:43,750 --> 00:11:48,140
+common divisor operation. طيب، فهي automatically، فكل
+
+139
+00:11:48,140 --> 00:11:51,080
+مرة بنعمل sorting لها، بنرتب الأكبر في الأول، والأصغر
+
+140
+00:11:51,080 --> 00:11:54,660
+الأكبر دائماً في a، الأصغر دائماً في b، وبنرجع بنعيد
+
+141
+00:11:54,660 --> 00:11:59,980
+نفس الكلام. طيب، الـ algorithm سريع، الـ order تبعه أو
+
+142
+00:11:59,980 --> 00:12:06,650
+الـ big O logarithmic، عبارة عن logarithmic. مش حتفرق
+
+143
+00:12:06,650 --> 00:12:10,170
+a و b، لأنه في النهاية maximum منهم بس، في النهاية
+
+144
+00:12:10,170 --> 00:12:12,850
+هي logarithmic function، هيكون logarithmic function.
+
+145
+00:12:12,850 --> 00:12:15,470
+أو الـ growth .. الـ order of growth تبعنا
+
+146
+00:12:15,470 --> 00:12:19,450
+logarithmic. فالـ complexity logarithmic،
+
+147
+00:12:19,450 --> 00:12:22,870
+logarithmic تعتبر tractable ولا intractable؟
+
+148
+00:12:25,890 --> 00:12:29,930
+tractable، أقل من الـ .. الـ polynomial، أقل من الـ
+
+149
+00:12:29,930 --> 00:12:32,510
+polynomial، فهي tractable، بالعكس، أقل من الـ normal
+
+150
+00:12:32,510 --> 00:12:36,370
+حتى من الـ linear. أنا في إيش أنحدد من الـ .. بظبط
+
+151
+00:12:36,370 --> 00:12:39,630
+لأنك أنت في الآخر بتشتغلي أقل من الـ linear، الـ
+
+152
+00:12:39,630 --> 00:12:43,630
+linear. أنت عندك ثلاثمائة وسبعة وسبعين صحيح؟ و
+
+153
+00:12:43,630 --> 00:12:46,630
+مئة وأربعة وستين. هل أنت اشتغلت مئة وأربعة وستين ..
+
+154
+00:12:46,630 --> 00:12:49,110
+مرة واحدة؟ أخدت الأقل منهم. هل أنت اشتغلت مئة وأربعة و
+
+155
+00:12:49,110 --> 00:12:53,840
+ستين operator؟ كذا مرة .. iteration؟ لأ، طب هاد كده
+
+156
+00:12:53,840 --> 00:12:58,100
+كل مرة بناخد المتبقي .. المتبقي. فهي أقل حتى من الـ
+
+157
+00:12:58,100 --> 00:13:01,220
+164 كل مرة، فدائماً حتلاقيها الـ logarithmic في
+
+158
+00:13:01,220 --> 00:13:07,100
+الحلقة اللي بنشتغل فيها. كويس؟ الموضوع سهل، وهنمشي
+
+159
+00:13:07,100 --> 00:13:10,640
+فيه بسرعة، ويمكن يتقاطع مع امتحان كل يوم، اللي هو
+
+160
+00:13:10,640 --> 00:13:13,320
+عملية الـ systems، الـ other systems، عن الـ decimal
+
+161
+00:13:13,320 --> 00:13:15,580
+systems اللي إحنا بنتكلم عنها. فإحنا بنتكلم عن الـ
+
+162
+00:13:15,580 --> 00:13:20,300
+base في number systems. أنتو يمكن اللي عارفين الـ
+
+163
+00:13:20,300 --> 00:13:25,240
+decimal، الـ decimal عبارة عن عشرة، عشرة digits من
+
+164
+00:13:25,240 --> 00:13:29,810
+صفر لتسعة. وهذا اللي بنتعامل فيه، بحيث أن أنا كل
+
+165
+00:13:29,810 --> 00:13:33,710
+digit حتاخد قيمة من الأرقام، من الـ digits هذه، من
+
+166
+00:13:33,710 --> 00:13:39,410
+صفر لتسعة. فلو قلنا مثلاً ثلاثمائة وخمسة وستين،
+
+167
+00:13:39,410 --> 00:13:42,430
+ثلاثمائة وخمسة وستين، الأرقام اللي بناخدها هنا، خمسة
+
+168
+00:13:42,430 --> 00:13:46,350
+ستة، ثلاثة، خمسة، ستة، ثلاثة. هدول عمرهم ما هيزيدوا عن
+
+169
+00:13:46,350 --> 00:13:49,770
+مجموعة الـ digits اللي هي من صفر لتسعة، من صفر لتسعة.
+
+170
+00:13:49,770 --> 00:1
+
+223
+00:17:36,300 --> 00:17:40,500
+تشتغلوا فيه ولكن لا يمنع أنه على السريع لو بدنا نحول
+
+224
+00:17:40,500 --> 00:17:43,920
+الـ decimal لـ octal كل اللي بتعمله ما دام أنكم
+
+225
+00:17:43,920 --> 00:17:48,760
+تحولوا من decimal لحظة من decimal على طول بتدوروا
+
+226
+00:17:48,760 --> 00:17:52,420
+على .. على الـ reminders تبعونكم على الـ reminders
+
+227
+00:17:52,420 --> 00:17:54,660
+الـ reminders هدول هم اللي بيحددوا الرقم القادم
+
+228
+00:17:54,660 --> 00:17:59,390
+رقمنا اللي جاي فأنتوا بتعملوا الـ .. الـ caution الـ
+
+229
+00:17:59,390 --> 00:18:02,310
+caution كل مرة بتضاربوا تجسموها عشان تدوروا على الـ
+
+230
+00:18:02,310 --> 00:18:05,090
+reminders خلينا نشوف هنا لو بتحولوها لثماني
+
+231
+00:18:05,090 --> 00:18:08,590
+فبتجسموها ثمانية لو بتحولوها لستة عشر فبتجسموها
+
+232
+00:18:08,590 --> 00:18:12,930
+ستة عشر أيش الـ base اللي بتكويها بتحولوا بالنسبة لها
+
+233
+00:18:12,930 --> 00:18:16,990
+فهنا decimal بتكويها لأوكتال أوكتال بتجسموها ثمانية
+
+234
+00:18:16,990 --> 00:18:21,410
+خارج القسمة والمتبقي مهم جداً المتبقي هذا طيب خارج
+
+235
+00:18:21,410 --> 00:18:24,620
+القسمة برجع كمان مرة تجسموها على ثمانية ترجعوا
+
+236
+00:18:24,620 --> 00:18:28,660
+لعند امتى؟ لعند ما يصل خارج القسمة صفر لعند ما
+
+237
+00:18:28,660 --> 00:18:34,420
+يصل خارج القسمة صفر فقدركم تقسموا وفي كل قسمة
+
+238
+00:18:34,420 --> 00:18:38,260
+هيطلع طبعاً reminders هيظهر عندكم sequence of
+
+239
+00:18:38,260 --> 00:18:42,720
+reminders أول واحد هذا الـ least significant bit
+
+240
+00:18:42,720 --> 00:18:46,960
+والأخير الـ most significant bit فهيكون هذا one
+
+241
+00:18:46,960 --> 00:18:57,240
+سبعة صفر صفر ثلاثة هذا ثمانية في النظام الثماني،
+
+242
+00:18:57,240 --> 00:19:00,980
+كويس بهذا الشكل هي إنت وصلت صفر بتقفوا، إنت وصلت
+
+243
+00:19:00,980 --> 00:19:06,720
+صفر بتقفوا تمام، بالنسبة للهكسا نفس الموضوع هو هو،
+
+244
+00:19:06,720 --> 00:19:09,500
+برضه بتجسم على ستة عشر، بتجسم على ستة عشر، والمهم
+
+245
+00:19:09,500 --> 00:19:14,600
+عندكم هي الأرقام اللي بتظهر هنا فالأرقام هذه عبارة
+
+246
+00:19:14,600 --> 00:19:22,540
+شوي شوي ناخدها عشرة، أربعة عشر، ثلاثة، أحد عشر
+
+247
+00:19:22,540 --> 00:19:28,500
+اثنين نكتبها واحد، العشرة في الـhexa إيه؟ الأربعة عشر
+
+248
+00:19:28,500 --> 00:19:37,520
+إيه؟ ثلاثة خلاص هي ثلاثة عشر واثنين هذا ستة عشر
+
+249
+00:19:37,520 --> 00:19:43,160
+هذا هيك ستة عشر طيب بالنسبة لأبسط من هيك لما كنت
+
+250
+00:19:43,160 --> 00:19:49,450
+تشتغله من hexadecimal أو octal لـ binary أو العكس
+
+251
+00:19:49,450 --> 00:19:53,010
+لأن إحنا قلنا أصلاً الـ .. الـ octal و الـ hexadecimal
+
+252
+00:19:53,010 --> 00:19:55,350
+إحنا ماخدينهم من عدد الـ digits في الـ binary
+
+253
+00:19:55,350 --> 00:19:58,990
+عدد الـ digits في الـ binary فلو قلنا هي أن الـ
+
+254
+00:19:58,990 --> 00:20:02,630
+number هذا binary number بدنا نحوله لأوكتال أوكتال
+
+255
+00:20:02,630 --> 00:20:05,510
+إحنا عارفين ثلاثة فبنمسكهم ثلاثة ثلاثة كل three
+
+256
+00:20:05,510 --> 00:20:09,580
+digits group كل three digits group، الـ group
+
+257
+00:20:09,580 --> 00:20:13,520
+الأول أربعة، بنحط أربعة، الـ group الثاني سبعة، هاي
+
+258
+00:20:13,520 --> 00:20:19,620
+سبعة، ثالث، اثنين، هاي اثنين، سبعة، ثلاثة الكلام هو
+
+259
+00:20:19,620 --> 00:20:23,540
+.. هو وين؟ لكسر .. لكسر جسم الأربعة الـ groups ..
+
+260
+00:20:23,540 --> 00:20:27,040
+كل group فيه أربعة digits كل group فيه أربعة digits
+
+261
+00:20:27,040 --> 00:20:30,840
+الكلام هو .. هو نفس الـ .. هنا بدنا من أوكتال ..
+
+262
+00:20:30,840 --> 00:20:33,120
+أوكتال أنا عارف معناه كل رقم .. كل digit من هدول
+
+263
+00:20:33,120 --> 00:20:38,200
+بمثلها بـ three bits three bits حتى لو واحد بدنا
+
+264
+00:20:38,200 --> 00:20:42,740
+نعمله one صفر صفر لازم نكمله لـ three digits تبعه
+
+265
+00:20:42,740 --> 00:20:48,360
+لـ three digits تبعه كويس فهنا الخمسة هي الخمسة و
+
+266
+00:20:48,360 --> 00:20:53,420
+هاي الستة هاي الستة السابعة هاي السابعة تمام
+
+267
+00:20:53,420 --> 00:20:59,420
+الـhexa نفس الكلام الـ .. الموضوع بسيط وسهل مفيش فيه
+
+268
+00:20:59,420 --> 00:21:05,620
+تعقيدات وأخدناه مراراً وتكراراً أكيد okay نبدأ في
+
+269
+00:21:05,620 --> 00:21:08,400
+الـ .. في الـ .. الـ .. الـ codes وهذا اللي هو بهمنا
+
+270
+00:21:08,400 --> 00:21:13,960
+يمكن أكثر بدنا نبدأ نعمل أكواد أو pseudocodes لـ الـ
+
+271
+00:21:13,960 --> 00:21:16,840
+operations اللي ممكن نعملها على الـ binary numbers
+
+272
+00:21:17,840 --> 00:21:23,840
+أهمها عملية الجمع، adding عندكم two numbers، two
+
+273
+00:21:23,840 --> 00:21:28,860
+binary numbers وبدكم تجمعوهم فممكن نقول say مثلاً
+
+274
+00:21:28,860 --> 00:21:38,320
+أنه عندنا واحد صفر واحد وواحد
+
+275
+00:21:38,320 --> 00:21:38,880
+واحد واحد
+
+276
+00:21:42,010 --> 00:21:44,950
+طيب نشوف هنا إنكم procedure خلاص عارف أنه إحنا
+
+277
+00:21:44,950 --> 00:21:48,010
+دخلنا على أيش على code بدنا جايبين نكتب جايبين في
+
+278
+00:21:48,010 --> 00:21:51,330
+الـ pseudocode add آه معناه واضح أنه من الـ add
+
+279
+00:21:51,330 --> 00:21:55,150
+معناه هذا في عملية جمع ماذا تتبعت الـ M؟ Sequence
+
+280
+00:21:55,150 --> 00:22:08,170
+أول وثاني Sequence Sequence Sequence
+
+281
+00:22:08,170 --> 00:22:18,210
+Sequence Sequence
+
+282
+00:22:18,210 --> 00:22:18,230
+Sequence Sequence Sequence Sequence Sequence
+
+283
+00:22:18,230 --> 00:22:18,250
+Sequence Sequence Sequence Sequence Sequence
+
+284
+00:22:18,250 --> 00:22:18,270
+Sequence Sequence Sequence Sequence Sequence
+
+285
+00:22:18,270 --> 00:22:18,370
+Sequence Sequence Sequence Sequence Sequence
+
+286
+00:22:18,370 --> 00:22:18,510
+Sequence Sequence Sequence Sequence Sequence
+
+287
+00:22:18,510 --> 00:22:18,530
+Sequence Sequence Sequence Sequence Sequence
+
+288
+00:22:18,530 --> 00:22:20,550
+Sequence Sequence Sequence Sequence Sequence
+
+289
+00:22:20,550 --> 00:22:23,700
+Sequence Sequence Sequence العملية البسيطة كل مرة
+
+290
+00:22:23,700 --> 00:22:28,580
+بجمع مع الحمل طبعاً كويس فـ الـ carry نبدأ بـ zero
+
+291
+00:22:28,580 --> 00:22:31,800
+مافيش عشان فاضية لأن الـ memory كلها فاضية لأن الـ
+
+292
+00:22:31,800 --> 00:22:37,980
+registers كلها zeros كويس four bit index من zero
+
+293
+00:22:37,980 --> 00:22:43,880
+to n minus one to n minus one begin bit sum عبارة
+
+294
+00:22:43,880 --> 00:22:49,670
+عن a سنبدأ بالصفر ونمسك الـ code تبعنا هنبدأ بالـ
+
+295
+00:22:49,670 --> 00:22:54,790
+صفر فكأن نبدأ نجمع a 0 و b 0 مع الـ carry طيب هي الـ
+
+296
+00:22:54,790 --> 00:23:02,850
+a 0 وهي الـ b 0 والـ carry 0 فإذن نجد بتطلع 0 1 1
+
+297
+00:23:02,850 --> 00:23:07,030
+طيب نمسكهم شوي شوي هدول 0 و1 ونحط كل واحدة منهم
+
+298
+00:23:07,030 --> 00:23:14,340
+في الـ S بتاعتنا أو خلينا نجمعها تحديدا بنفس الشكل
+
+299
+00:23:14,340 --> 00:23:18,680
+واحد واحد بيساوي اثنين نكتب الاثنين الـ summation
+
+300
+00:23:18,680 --> 00:23:25,180
+bit index معناه الـ summation zero إحنا لسة under
+
+301
+00:23:25,180 --> 00:23:35,460
+zero فـ zero بتساوي الـ bit summation مود اثنين مود
+
+302
+00:23:35,460 --> 00:23:40,630
+اثنين صفر طيب الـ carry بدي اتغير هذه اللغة الـ bit
+
+303
+00:23:40,630 --> 00:23:45,210
+summation اللي هي اثنين على اثنين floor اثنين على
+
+304
+00:23:45,210 --> 00:23:49,810
+اثنين واحد floor واحد واحد carry صارت هنا أيش واحد
+
+305
+00:23:49,810 --> 00:23:54,490
+واحد okay
+
+306
+00:23:54,490 --> 00:24:02,430
+خلصنا الـ S0 الـ summation في الـ digit الأولى صار
+
+307
+00:24:02,430 --> 00:24:08,990
+هنا اثنين واحد أفضل واحد bit summation إيه الـ oneB
+
+308
+00:24:08,990 --> 00:24:14,350
+one زائد الـ carry A one B one زائد الـ carry صفر
+
+309
+00:24:14,350 --> 00:24:20,510
+واحد واحد زائد واحد بيساوي اثنين اثنين نفس الكلام
+
+310
+00:24:20,510 --> 00:24:26,850
+اثنين مود اثنين مود اثنين صفر zero فإذن الـ S one
+
+311
+00:24:26,850 --> 00:24:34,590
+zero carry one carry one okay اثنين
+
+312
+00:24:35,570 --> 00:24:38,630
+وهاذي اللي هي الـ N minus one آخر واحدة بدنا نتكلم
+
+313
+00:24:38,630 --> 00:24:43,090
+عن ثلاثة N minus one بتساوي اثنين فإذن عشان نحسب
+
+314
+00:24:43,090 --> 00:24:52,010
+الأخيرة A اثنين B اثنين وcarry واحد زائد واحد
+
+315
+00:24:52,010 --> 00:25:01,390
+زائد واحد ثلاثة فثلاثة هنا عشان نحسب الـ S اثنين مود
+
+316
+00:25:03,140 --> 00:25:09,140
+مود اثنين تساوي واحد كاري ثلاثة على اثنين واحد و
+
+317
+00:25:09,140 --> 00:25:14,420
+نصف floor واحد خلص
+
+318
+00:25:14,420 --> 00:25:22,660
+اللوب اللوب يتخلص هنا يتخلص بـ N-1 طيب بس في SM
+
+319
+00:25:22,660 --> 00:25:24,800
+ثلاثة
+
+320
+00:25:25,920 --> 00:25:29,020
+هو الـ carry إذا كان ضال معانا إيش في الحمل أو مضالش
+
+321
+00:25:29,020 --> 00:25:35,720
+إذا مضالش خلاص صفر ضل أفضل واحد بنزل الواحد بينزل
+
+322
+00:25:35,720 --> 00:25:40,040
+معناه الواحد فهل فعلاً يمثل هذا الرقم هذا خمسة زائد
+
+323
+00:25:40,040 --> 00:25:46,120
+سبعة اثنا عشر إيه اثنا عشر ثمانية وأربعة اثنا عشر فهي الـ
+
+324
+00:25:46,120 --> 00:25:48,620
+code في الآخر return الـ sequence تبع مين تبع الـ
+
+325
+00:25:48,620 --> 00:25:51,440
+summation الـ sequence تبع الـ summation من صفر to
+
+326
+00:25:51,440 --> 00:25:55,100
+end مش to end minus one مش to end minus one okay
+
+327
+00:25:55,100 --> 00:26:00,960
+هاي عملية الـ summation طيب عملية الطرح عندما تطرح
+
+328
+00:26:00,960 --> 00:26:05,130
+أرقام خليني أقول هاي الرقمين اللي طوالي إحنا
+
+329
+00:26:05,130 --> 00:26:11,570
+اشتغلناهم هدول بدنا نطرحهم من بعض بدنا نطرحهم من
+
+330
+00:26:11,570 --> 00:26:22,130
+بعض فخلينا نخففها شوية محتاجين
+
+331
+00:26:22,130 --> 00:26:26,030
+to complement طيب الـ .. الـ first complement كيف
+
+332
+00:26:26,030 --> 00:26:28,990
+كنتوا بتعملوه؟ أو أيش الهدف من الـ .. من الـ to
+
+333
+00:26:28,990 --> 00:26:34,880
+complement؟ بتحول للطرح بالسالب بتجيبوا الرقم
+
+334
+00:26:34,880 --> 00:26:39,080
+بالسالب وهذا الهدف أنه إحنا كل اللي بدنا إياه بدل ما
+
+335
+00:26:39,080 --> 00:26:45,920
+أقول a minus b بدي أقول a plus سالب b فالب تبعتهي
+
+336
+00:26:45,920 --> 00:26:51,360
+هذه بدي أجيبها الـ negative value بتاعتها في الـ
+
+337
+00:26:51,360 --> 00:26:55,940
+binary الـ complement المكمل سميها المكمل تبعها
+
+338
+00:26:55,940 --> 00:26:59,080
+المكمل تبعها بالنسبة لأكبر رقم في نفس عدد الـ
+
+339
+00:26:59,080 --> 00:27:04,570
+digits أخدتوها هي كنتوا صح؟ نسبة لأكبر رقم بنفس عدد
+
+340
+00:27:04,570 --> 00:27:07,750
+الـ digits جدش المكمل للرقم عشان يصل لأكبر رقم
+
+341
+00:27:07,750 --> 00:27:11,410
+فهذه هي الـ compliment تبعكم هذه هي compliment
+
+342
+00:27:11,410 --> 00:27:16,430
+كويسة عشان أجيبها بنجيبها بـ two operations بنجيب
+
+343
+00:27:16,430 --> 00:27:19,290
+الـ first complement ومنه بنجيب الـ second
+
+344
+00:27:19,290 --> 00:27:21,510
+complement الـ first complement إيش كنتوا بتعملوه؟
+
+345
+00:27:21,510 --> 00:27:27,090
+نعكس flip flip كل zero بنعمله one وكل one بنعمله
+
+346
+00:27:27,090 --> 00:27:31,540
+zero كل one بنعمله zero طيب الـ two's complement
+
+347
+00:27:31,540 --> 00:27:36,180
+نجمع نجمع زائد واحد زائد واحد بس ناخد بالنا إنكم
+
+348
+00:27:36,180 --> 00:27:43,020
+تضيفوا bit في الآخر ليش؟ إشارة إحنا by logic إحنا
+
+349
+00:27:43,020 --> 00:27:46,120
+بنختصر الموضوع بهذا الشكل بس هو فعلياً هنا في zero
+
+350
+00:27:46,120 --> 00:27:51,880
+الـ zero هذه تشير لإيش؟ للموجب إذا كانت واحد إذا
+
+351
+00:27:51,880 --> 00:27:55,340
+كان أنا محدد أنه أعطيكم الرقم بهذا الشكل وأقول
+
+352
+00:27:55,340 --> 00:28:01,250
+لكم لأ هذه three digits جدش الرقم positive خمسة
+
+353
+00:28:01,250 --> 00:28:07,870
+خمسة
+
+354
+00:28:07,870 --> 00:28:09,230
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+355
+00:28:09,230 --> 00:28:10,550
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+356
+00:28:10,550 --> 00:28:18,070
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+357
+00:28:18,070 --> 00:28:21,790
+خمسة خمسة خمسة
+
+358
+00:28:21,790 --> 00:28:29,830
+خمسة
+
+359
+00:28:31,160 --> 00:28:36,020
+اشتغلتوها قبلها طيب الـ subtraction of binary
+
+360
+00:28:36,020 --> 00:28:38,620
+numbers زي ما قلنا كل اللي بنعمله اللي بده يجيب
+
+361
+00:28:38,620 --> 00:28:41,820
+الـ minus للـ a فبيجيب الـ first complement أو الـ
+
+362
+00:28:41,820 --> 00:28:48,960
+complement للـ a plus واحد طيب الـ procedure بنعمل
+
+363
+00:28:48,960 --> 00:28:54,310
+subtract أو الـ sequence a والـ sequence b .. الـ
+
+364
+00:28:54,310 --> 00:28:57,410
+sequence b هنا complement .. جبنا له الـ binary
+
+365
+00:28:57,410 --> 00:29:03,290
+two's complement .. represents of integers b و a
+
+366
+00:29:03,290 --> 00:29:07,430
+كيف نعملها .. add .. نعمل adding عادية .. نعمل
+
+367
+00:29:07,430 --> 00:29:17,330
+عملية adding .. هيها .. لمين .. لـ a مع addB
+
+368
+00:29:17,330 --> 00:29:23,010
+complement واحد فالـ B complement بعكس وجمعنا واحد
+
+369
+00:29:23,010 --> 00:29:32,710
+فالـ term هذا صار كأنه minus B جمعناه مع A فأصبحت
+
+370
+00:29:32,710 --> 00:29:40,250
+كأنه A minus B كأنها A plus minus B أو بجمعها مع
+
+371
+00:29:40,250 --> 00:29:44,730
+minus B فظهرت كأنها سالفة في الحالة اللي عندكم هنا
+
+372
+00:29:44,730 --> 00:29:45,030
+fold
+
+373
+00:29:49,000 --> 00:29:54,300
+one صفر one المقروء هذا هيكون عبارة عن صفر يعكسه
+
+374
+00:29:54,300 --> 00:30:02,880
+plus واحد one one zero one تمام one one zero one
+
+375
+00:30:02,880 --> 00:30:10,920
+فهذه صارت أنه نجمعها على one zero one one جدش
+
+376
+00:30:10,920 --> 00:30:16,880
+واحد واحد
+
+377
+00:30:19,300 --> 00:30:24,300
+طيب خليني أمسككم حاجة حاجة الرقم اللي بدنا نطرح
+
+378
+00:30:24,300 --> 00:30:28,520
+منه كم digit؟ أربعة هل يعقل أن الناتج يكون أكبر
+
+379
+00:30:28,520 --> 00:30:35,740
+من أربعة digit؟ طب هذا أيش الرقم؟ overflow فهدا
+
+380
+00:30:35,740 --> 00:30:41,020
+إيش بنسويله؟ بنشيله بنشيله خلاص بدنا إياه ليش؟ لأنه
+
+381
+00:30:41,020 --> 00:30:46,780
+هذا زيادة عن الرقم الكبير في الطريقة طب لا يمكن
+
+382
+00:30:46,780 --> 00:30:52,020
+الرقم الكبير في الطرح يطلعنا رقم أكبر منه، كويس
+
+383
+00:30:52,020 --> 00:30:56,760
+فهنا بنقف لعند الحالة هذه طيب في الحالة هذه هيك
+
+384
+00:30:56,760 --> 00:31:00,700
+خلصنا شغل، نجد إحنا الرقمين اللي كنا شغالينهم
+
+385
+00:31:00,700 --> 00:31:09,400
+أساساً كانت عشرة نقص جدش، كان نقص خمسة عشان نشوف
+
+386
+00:31:09,400 --> 00:31:10,680
+الناتج مظبوط آه مظبوط
+
+387
+00:31:15,170 --> 00:31:19,190
+تخيلوا من الـ overflow تاخدوا بالكم وأكبر من n على
+
+388
+00:31:19,190 --> 00:31:23,850
+طول هذا overflow وببساطة جداً بشيله و خلاص طيب
+
+389
+00:31:23,850 --> 00:31:26,550
+multiplication برضه مرت عليكم عملية الـ
+
+390
+00:31:26,550 --> 00:31:31,130
+multiplication لـ الـ binary كيف تضربوه تحولوها لـ
+
+391
+00:31:31,130 --> 00:31:35,290
+summation تحولوها لـ summation بعدد أصفار تذكرونها
+
+392
+00:31:35,290 --> 00:31:40,570
+طيب كويس خلينا برضه ناخد رقمين وخلينا ناخد مثلاً
+
+393
+00:31:40,570 --> 00:31:45,740
+هاي رقمين هذه الرقمين ونبدأ نشوف الـ procedure
+
+394
+00:31:45,740 --> 00:31:51,380
+multiply two sequence أو two binary نوحهم two
+
+395
+00:31:51,380 --> 00:31:54,360
+sequence هدول binary representation of a and b
+
+396
+00:31:54,360 --> 00:32:01,820
+belonging to natural number product الـ product
+
+397
+00:32:01,820 --> 00:32:07,780
+بتاعتنا في zero أول ما بدأنا لسة مفيش أي شيء ضفناه
+
+398
+00:32:07
+
+445
+00:36:06,480 --> 00:36:09,700
+هذا الـ N بتاعتنا فحسبنا الـ N بتاعتنا هذا .. لحظوا
+
+446
+00:36:09,700 --> 00:36:16,340
+هذا الـ A term هذا هيك الـ A فهي A over D A over D
+
+447
+00:36:16,340 --> 00:36:19,060
+عشانها لوجة الـ D و الـ A هي .. هي بنشتغل فيهم كتير
+
+448
+00:36:19,060 --> 00:36:21,220
+فانتوا تكونوا عارفين مين الـ A و مين الـ D من الـ B
+
+449
+00:36:21,220 --> 00:36:25,930
+الـ D اللي هي الـ divisor طبعا الـ divisor. Okay، هنبدأ
+
+450
+00:36:25,930 --> 00:36:32,730
+for I .. لحظة هنا N minus one down في .. هنا الـ
+
+451
+00:36:32,730 --> 00:36:39,210
+counter عكسي for loop من الأكبر للأقل فهنا نعملهاش
+
+452
+00:36:39,210 --> 00:36:42,270
+زي اللي فاتت و بنسيبها N minus one to و خلاص لأ
+
+453
+00:36:42,270 --> 00:36:45,670
+down to فبعرف ان انتوا جاسبكوا من الأكبر في
+
+454
+00:36:45,670 --> 00:36:48,390
+الأصغر ماحدش يكتبليها to كذا و يقولي انا هنا
+
+455
+00:36:48,390 --> 00:36:52,400
+كاتبلك من الأكبر لأصغر هقوله لأ غلط الـ structure
+
+456
+00:36:52,400 --> 00:36:56,840
+الصح ده بقى هـ down to فبعملها من الأكبر للأقل طيب
+
+457
+00:36:56,840 --> 00:37:02,380
+هنا هنعملها من n minus one to zero ونبدأ if a أكبر
+
+458
+00:37:02,380 --> 00:37:08,220
+من d و i zeros طيب معناه ذلك ان احنا هنا صرنا
+
+459
+00:37:08,220 --> 00:37:12,920
+نقسم على واحد اتنين تلاتة اربعة خمسة احنا بنشتغل
+
+460
+00:37:12,920 --> 00:37:18,080
+على امتعتنا خمسة معناه ذلك هنا باربعة بنبدأ باربعة
+
+461
+00:37:18,080 --> 00:37:19,420
+بتصير الـ D
+
+462
+00:37:22,480 --> 00:37:26,540
+أربعة أربعة أربعة
+
+463
+00:37:26,540 --> 00:37:29,080
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+464
+00:37:29,080 --> 00:37:29,540
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+465
+00:37:29,540 --> 00:37:32,360
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+466
+00:37:32,360 --> 00:37:35,940
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+467
+00:37:35,940 --> 00:37:35,960
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+468
+00:37:35,960 --> 00:37:36,400
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+469
+00:37:36,400 --> 00:37:49,080
+أربعة أربعة أربعة أربعة أربعة أ
+
+470
+00:37:49,970 --> 00:37:56,510
+خرج القسمة zero بنرجح هنا لمين؟ تلاتة تلاتة و بنشيل
+
+471
+00:37:56,510 --> 00:38:10,210
+صفر صار دي و تلت أصفر دي
+
+472
+00:38:10,210 --> 00:38:14,670
+و تلت أصفر و بنجرب هل a أكبر من الدي الجديدة
+
+473
+00:38:14,670 --> 00:38:18,440
+بالتلت أصفر؟ لأ واضح انه لأ معناته الـ quotient
+
+474
+00:38:18,440 --> 00:38:27,320
+بتاعتنا برضه zero quotient zero هي طيب اتنين هي
+
+475
+00:38:27,320 --> 00:38:36,580
+الـ D مع صفر يعنى A أكبر من أو يساوي D اه أكبر من
+
+476
+00:38:36,580 --> 00:38:41,340
+أو يساوي هي then
+
+477
+00:38:41,340 --> 00:38:45,080
+معناته بتنزل على then أول شي quotient equal to one
+
+478
+00:38:46,770 --> 00:38:52,230
+والـ إيه الجديدة مطروحهم من بعض، هنطرحهم من بعض،
+
+479
+00:38:52,230 --> 00:38:56,490
+طيب عشان نطرحهم من بعض إيش بدنا نعمل؟ to
+
+480
+00:38:56,490 --> 00:39:00,390
+complement، to complement، لذا انتوا مش هتقدروا
+
+481
+00:39:00,390 --> 00:39:03,270
+بسرعة قصرية تترحوها وإن كان المفروض إنه بيطلع
+
+482
+00:39:03,270 --> 00:39:09,370
+مظبوط، هي صفر واحد صفر واحد صفر طيب خلينا ناخد
+
+483
+00:39:09,370 --> 00:39:16,070
+هذه، هذه الأصل هتكون إيش؟ one one صفر one صفر
+
+484
+00:39:18,490 --> 00:39:24,850
+one تعكسوها زائد واحد عشان
+
+485
+00:39:24,850 --> 00:39:31,650
+تجيب الـ two's complement طيب هاي صفر صفر واحد واحد
+
+486
+00:39:31,650 --> 00:39:36,630
+صفر واحد okay هذه بتجمع مع مين؟ مع الـ term هذا واحد
+
+487
+00:39:36,630 --> 00:39:42,670
+واحد واحد واحد صفر هنجمحها مع صفر صفر واحد واحد
+
+488
+00:39:42,670 --> 00:39:43,750
+صفر واحد
+
+489
+00:39:47,570 --> 00:39:51,070
+هو أصلا هيك هيك هيروح هيروح، ماتجلوش، هيروح هيروح،
+
+490
+00:39:51,070 --> 00:39:53,190
+لإن احنا ندوس إلى واحد، اتنين، تلاتة، أربعة، خمسة،
+
+491
+00:39:53,190 --> 00:39:56,110
+بس، هيك هيك هدى حاطير حاطير هالوقت مع الجامعة
+
+492
+00:39:56,110 --> 00:40:02,930
+يعنى، طيب، صفر، واحد، زيرو، واحد، واحد، واحد،
+
+493
+00:40:02,930 --> 00:40:09,770
+واحد، واحد، واحد، زيرو، و هنا زيرو، واحد، واحد،
+
+494
+00:40:09,770 --> 00:40:13,650
+اتنين، تلاتة، أربعة، خمسة، stop، overflow، خلاص هي
+
+495
+00:40:13,650 --> 00:40:14,150
+الرقم طبعا
+
+496
+00:40:16,950 --> 00:40:22,190
+هي الرقم تبعكم خلصنا okay هاي خارج القسمة تبعتنا
+
+497
+00:40:22,190 --> 00:40:25,170
+هاد الـ a اللي جديدة هال وجدت الـ a اللي بنشتغل
+
+498
+00:40:25,170 --> 00:40:34,190
+عليها طيب خلصنا بنيجي للمين؟ للواحد عند الواحد بهذا
+
+499
+00:40:34,190 --> 00:40:43,170
+الشكل هاي D زائد 1 صفر أكبر من أو تساوي الـ D اه
+
+500
+00:40:43,170 --> 00:40:45,150
+تساوي الـ D بيساوي بعض
+
+501
+00:40:49,060 --> 00:40:56,480
+كويس و بنحط واحد و بنحط واحد بعدين بيساوي بعض فإذا
+
+502
+00:40:56,480 --> 00:41:04,980
+Qi بيصير واحد هاي واحد Qi هي Qi هاي واحد تمام و
+
+503
+00:41:04,980 --> 00:41:11,380
+الـ a الجديدة طلعت zeros بعد هيك خلصنا الـ loop صفر
+
+504
+00:41:15,030 --> 00:41:22,630
+إيه؟ أكبر من دي؟ طبعا هتصير دي لحالها الـ a الجديدة لأن دي
+
+505
+00:41:22,630 --> 00:41:27,830
+zero صفر مافيش أصفر طب أكبر من؟ لأ مش أكبر منه
+
+506
+00:41:27,830 --> 00:41:34,690
+فإذا else دي zero خلصنا؟
+
+507
+00:41:34,690 --> 00:41:40,910
+هاي أخر رقم خلاص الناتج؟ هاي الناتج ستة في خمسة هي
+
+508
+00:41:40,910 --> 00:41:46,450
+الثلاثين ستة في خمسة هاي الثلاثين الثلاثين ففي
+
+509
+00:41:46,450 --> 00:41:52,270
+الآخر بترجع بمين؟ هيضل عندكم الـ a الأخيرة بعد ما
+
+510
+00:41:52,270 --> 00:41:56,170
+وصلتوا للصفر آخر a بتضل هذا المفروض الـ R الـ
+
+511
+00:41:56,170 --> 00:41:59,410
+remainder اللي ضلت لأنه ممكن تكون .. ما تكونش zeros
+
+512
+00:41:59,410 --> 00:42:03,070
+يعني ممكن تكون مثلا one half بهذا الشكل هي أقل من
+
+513
+00:42:03,070 --> 00:42:07,010
+هذا بس إلها قيمة فتحسبوها على أساس إن هي بتصير الـ
+
+514
+00:42:07,010 --> 00:42:12,780
+R هي المتبقي من خارج القسمة المطولة المتبقي من خارج
+
+515
+00:42:12,780 --> 00:42:19,280
+القسمة المطولة طبعا الـ return Q هي Q والـ R هي R في
+
+516
+00:42:19,280 --> 00:42:21,640
+الحالة اللي عندنا Zero لأنه بيكبروا القسمة على بعض
+
+517
+00:42:21,640 --> 00:42:24,660
+ثلاثين على خمسة فعلا بيكبر القسمة ممكن تكون أرقام
+
+518
+00:42:24,660 --> 00:42:29,000
+تكبرش القسمة لأ
+
+519
+00:42:29,000 --> 00:42:31,840
+احنا هنا بكفي بس ان نجيب الـ quotient و الـ
+
+520
+00:42:31,840 --> 00:42:37,430
+remainder و خلاص كأنك بتقول ايه لو قولنا مثلا واحد
+
+521
+00:42:37,430 --> 00:42:43,550
+ثلاثين على خمسة هتساوي ستة واحد على خمسة
+
+522
+00:42:47,280 --> 00:42:49,980
+الـ quotient و الـ remainder quotient و الـ remainder
+
+523
+00:42:49,980 --> 00:42:55,380
+بهذا الشكل و خلاص okay فهي الـ division هي عملية الـ
+
+524
+00:42:55,380 --> 00:42:59,420
+division الـ .. نسيبكوا المرة الجاية هنتكلم عن
+
+525
+00:42:59,420 --> 00:43:04,600
+موضوع حلو جدا الموضوع .. المرة الجاية اللي انتوا
+
+526
+00:43:04,600 --> 00:43:09,860
+هتشتغلوه بس نعطيكوا تعريف عليه هنشتغل على الـ
+
+527
+00:43:09,860 --> 00:43:12,680
+cryptography تشفير
+
+528
+00:43:16,350 --> 00:43:19,650
+إذا بدناش محاضرة خلنا نكمل، برضه هتكون هيك مقتضبة
+
+529
+00:43:19,650 --> 00:43:25,950
+صفيرة طيب فالمرة الجاية هنتكلم بس هنحاول بعجلة
+
+530
+00:43:25,950 --> 00:43:29,590
+يعني المرة الجاية تكون أصغر من هيك هنتكلم عن الـ
+
+531
+00:43:29,590 --> 00:43:35,430
+cryptography عن التشفير و بعدين هنتكلم عن حاجة مهمة
+
+532
+00:43:35,430 --> 00:43:38,930
+جدا تستعملوها كتير في شغلكم اللي هو تعمل
+
+533
+00:43:38,930 --> 00:43:43,580
+generation لـ random values لقيم راندوم ليه؟ انتوا
+
+534
+00:43:43,580 --> 00:43:46,400
+بتقولوا و الله نطلع راندوم ليه مجموعة قيم كيف
+
+535
+00:43:46,400 --> 00:43:49,420
+نطلعها راندوم ليه هذه؟ هي فعليا المفروض ان انا اذا
+
+536
+00:43:49,420 --> 00:43:52,440
+بدي اعمل generation كمان مرة لنفس الـ random هذه
+
+537
+00:43:52,440 --> 00:43:56,500
+المفروض اطلع نفس الـ sequence كيف بدي نعمل؟
+
+538
+00:43:56,500 --> 00:43:59,180
+فحناخدها المرة الجاية ان شاء الله برضه باستخدام الـ
+
+539
+00:43:59,180 --> 00:44:02,490
+modular operation و هنتكلم فيها عن الـ pseudo random
+
+540
+00:44:02,490 --> 00:44:09,270
+numbers او ارقام شبه عشوائية هي هتشوفوا انتوا
+
+541
+00:44:09,270 --> 00:44:13,550
+عشوائية فهتتخيل ان والله الأرقام مش مرتبة و مستحيل
+
+542
+00:44:13,550 --> 00:44:15,930
+اعرف اجيبهم من بعض لانه ممكن يكون الـ sequence كتير
+
+543
+00:44:15,930 --> 00:44:18,770
+جدا ألاف الأرقام ورا بعض بس ألاف الأرقام ورا بعض
+
+544
+00:44:18,770 --> 00:44:22,690
+هدولة اللي عملهم generation عملهم بمن code محدد
+
+545
+00:44:23,010 --> 00:44:26,170
+بقدر يرجع يعملهم generation كمان مرة .. بقدر يرجع
+
+546
+00:44:26,170 --> 00:44:28,750
+يعملهم generation كمان مرة .. هذه بتفيدنا جدا في
+
+547
+00:44:28,750 --> 00:44:32,670
+عملية الـ cryptography اللي هي عملية التشفير .. في
+
+548
+00:44:32,670 --> 00:44:35,430
+عملية التشفير لإنه بكل بساطة ممكن sequence معين
+
+549
+00:44:35,430 --> 00:44:39,090
+تضربوه في الـ sequence of random هدولة فيطلع معلومة
+
+550
+00:44:39,090 --> 00:44:42,850
+مختلفة و تبعتوها اللي هيشوفها مش فاهم منها حاجة ..
+
+551
+00:44:42,850 --> 00:44:45,470
+اللي هيشوفها مش هيكون فاهم منها حاجة فبنخلي الكلام
+
+552
+00:44:45,470 --> 00:44:49,770
+هذا للمرة الجاية ان شاء الله تعالى و بنبدأ بموضوع
+
+553
+00:44:49,770 --> 00:44:51,690
+ان شاء الله تعالى .. يعطيكوا العافية و ربنا يوفقك
+
+554
+00:44:51,690 --> 00:44:52,130
+و ربنا يوفقك
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b951192264cbeb976eaa1544fbba16fbe9887db9
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc_postprocess.srt
@@ -0,0 +1,2216 @@
+1
+00:00:20,970 --> 00:00:22,930
+بسم الله الرحمن الرحيم الصلاة والسلام علي أشرف
+
+2
+00:00:22,930 --> 00:00:25,310
+الأنبياء والأبساطري سيدنا محمد وعلي أليه وصحبه
+
+3
+00:00:25,310 --> 00:00:30,030
+أجمعين بنكمل اليوم في ال numbers theory وصلنا يمكن
+
+4
+00:00:30,030 --> 00:00:36,470
+ل ال modulus و ال modular system و ال modular و
+
+5
+00:00:36,470 --> 00:00:43,700
+أخدنا أخر شكل اللي هي ال spiral visualizationوكان
+
+6
+00:00:43,700 --> 00:00:49,720
+example mod 5 كان mod 5 as a example عساس انه نحدد
+
+7
+00:00:49,720 --> 00:00:53,960
+منه ال .. ال congruence او ال congruence ال theory
+
+8
+00:00:53,960 --> 00:00:59,760
+بتاعتنا و قولنا انه تلاتة congruent to تمانية ..
+
+9
+00:00:59,760 --> 00:01:02,920
+congruent to تلاتاشر و ال .. ال .. الفيصل في
+
+10
+00:01:02,920 --> 00:01:07,480
+الموضوع كان ان الفرق بينهم .. بين الأرقام هي عبارة
+
+11
+00:01:07,480 --> 00:01:12,740
+عن ال modulus اومضروبة في sum K مضروبة في sum
+
+12
+00:01:12,740 --> 00:01:18,000
+integer K في sum integer K فلو قلنا تلاتة و تمانية
+
+13
+00:01:18,000 --> 00:01:21,540
+الفرق بينهم خمسة انا فعلا بشتغل على modulus five
+
+14
+00:01:21,540 --> 00:01:26,300
+بين التلاتة و التمنتاش خمستاشف خمستاشف فهي عبارة
+
+15
+00:01:26,300 --> 00:01:30,220
+عن برضه sum integer مضروب في مين في ال modulus
+
+16
+00:01:30,220 --> 00:01:34,460
+تبعنا اللي هو خمسة كلام هذا قلناه المرة اللي فاتت
+
+17
+00:01:34,460 --> 00:01:43,830
+نكمل بعده و نشوفconcurrence theorems او
+
+18
+00:01:43,830 --> 00:01:48,890
+facts يمكن نقول let a,b belong to z integer
+
+19
+00:01:48,890 --> 00:01:55,850
+numbers ام ال modelers أو المعامل belong to
+
+20
+00:01:55,850 --> 00:02:01,300
+integerpositive integer to positive integer then a
+
+21
+00:02:01,300 --> 00:02:06,400
+congruent to b mod m هدى معناه there exist k some
+
+22
+00:02:06,400 --> 00:02:12,440
+k some integer some integer a equal to b plus km
+
+23
+00:02:12,440 --> 00:02:17,500
+هى نفسها اللى طوى قولناها a minus b الفرق بينهم
+
+24
+00:02:17,500 --> 00:02:22,440
+عبارة عن some k مضروبة فيهاش في ال modulusفي ال
+
+25
+00:02:22,440 --> 00:02:25,760
+modulus طبعا okay فالفرق دائما اذا كانوا فعلا
+
+26
+00:02:25,760 --> 00:02:29,380
+coherent لبعض اذا كانوا congruent لبعض الاصل ان
+
+27
+00:02:29,380 --> 00:02:32,700
+الفرق بينهم دائما بيساوي ال modulus او ال modulus
+
+28
+00:02:32,700 --> 00:02:39,720
+في some integer k لت
+
+29
+00:02:39,720 --> 00:02:44,220
+a,b,c,d belong to z و ال modulus زي ما قلنا belong
+
+30
+00:02:44,220 --> 00:02:49,700
+to integer positive integer then اذا اذا كان a
+
+31
+00:02:49,700 --> 00:02:56,980
+congruent to bm and c congruent to d mod m then a
+
+32
+00:02:56,980 --> 00:03:07,260
+plus c congruent to mean b plus d فإذن بنفع plus
+
+33
+00:03:07,260 --> 00:03:15,160
+أو ممكن أقول برضه then a مضروب في cconcurrent to
+
+34
+00:03:15,160 --> 00:03:20,780
+mean B مضروب في D كله لازم يكون mod M الموديلس
+
+35
+00:03:20,780 --> 00:03:27,800
+دائما يكون M ثابت اذا A plus C congruent to B plus
+
+36
+00:03:27,800 --> 00:03:34,580
+D mod M او بقدر اقول A C congruent to B D موديلس
+
+37
+00:03:34,580 --> 00:03:41,230
+أو mod Mطيب, Euclid's Algorithm .. Euclid's
+
+38
+00:03:41,230 --> 00:03:47,030
+Algorithm هو Algorithm عنده .. Euclid بده يجيب لنا
+
+39
+00:03:47,030 --> 00:03:49,910
+و يحسب لنا فيه ال greatest common divisor .. ال
+
+40
+00:03:49,910 --> 00:03:52,110
+greatest common divisor احنا قبل كده اشتغلنا على
+
+41
+00:03:52,110 --> 00:03:56,050
+greatest common divisor باستخدامباستخدام ال prime
+
+42
+00:03:56,050 --> 00:03:59,950
+factorization باستخدام ال prime factors ال prime
+
+43
+00:03:59,950 --> 00:04:04,350
+factors ممكن جدا تكون الأرقام كبيرة فما تقدروش
+
+44
+00:04:04,350 --> 00:04:08,730
+تصلولها وبتظل algorithm بديل عشان نجيب ال greatest
+
+45
+00:04:08,730 --> 00:04:13,160
+common divisorأو المعامل المشترك الأكبر من القاسم
+
+46
+00:04:13,160 --> 00:04:15,620
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+47
+00:04:15,620 --> 00:04:16,180
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+48
+00:04:16,180 --> 00:04:16,620
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+49
+00:04:16,620 --> 00:04:17,380
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+50
+00:04:17,380 --> 00:04:18,020
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+51
+00:04:18,020 --> 00:04:18,040
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+52
+00:04:18,040 --> 00:04:23,060
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+53
+00:04:23,060 --> 00:04:27,980
+المشترك الأكبر من القاسم المشترك الأكبر من القاسم
+
+54
+00:04:27,980 --> 00:04:35,060
+المشترك الأكبر من القفإذا الكبير موضل صغير لأن
+
+55
+00:04:35,060 --> 00:04:38,480
+الصغير موضل كبير حيبقى نفس القيمة مش هيتغير اشي مش
+
+56
+00:04:38,480 --> 00:04:42,340
+هيتغير اشي احنا قولنا الموضلار operator هي عبارة
+
+57
+00:04:42,340 --> 00:04:47,200
+عن ايش بيطلعنا ال remainder للقسم بتاعتهم أو ال
+
+58
+00:04:47,200 --> 00:04:53,800
+division remainder متبقى من القسم متبقى القسم كويس
+
+59
+00:04:53,800 --> 00:04:58,850
+دائما متبقى القسم هيكون اقل من مين من الموضلاتأقل
+
+60
+00:04:58,850 --> 00:05:03,970
+من ال modulus لما بنتكلم عن الساعة اتناش طبيعي كل
+
+61
+00:05:03,970 --> 00:05:07,810
+الساعات اللى بدي أقرأها بالنسبة لها الساعة اتناش
+
+62
+00:05:07,810 --> 00:05:10,610
+هتكون أقل من الاتناش، هتكون أقل من اتناش، حتى عند
+
+63
+00:05:10,610 --> 00:05:15,900
+الاتناش بيقول صفرحتى عند ال 12 بنقول صفر ففي
+
+64
+00:05:15,900 --> 00:05:21,700
+الحالة هذه دائما خارج او ال remainder ل المدلر
+
+65
+00:05:21,700 --> 00:05:28,460
+operator بدي أقل من مين من ال B فإذا نفس الكلام هو
+
+66
+00:05:28,460 --> 00:05:34,520
+هو بقدر أرجع رتبه تاني على أساس أنه يساوي the
+
+67
+00:05:34,520 --> 00:05:38,680
+greatest common divisor لمين ل ال B لأنه صارت هي
+
+68
+00:05:38,680 --> 00:05:48,360
+الأكبر هالوجد صارت أكبرA mod B في الحالة التالية
+
+69
+00:05:48,360 --> 00:05:54,600
+طبعا حيطلع في نهاية رقم هذا حيطلع رقم ناتج الناتج
+
+70
+00:05:54,600 --> 00:05:58,980
+هذا بنرجع نكرر نفس العملية تانية لإمتى لعند ما
+
+71
+00:05:58,980 --> 00:06:06,300
+الناتج هذا equal to zero لعند ما الناتج equal to
+
+72
+00:06:06,300 --> 00:06:11,800
+zeroانت بيصير equal to zero الرقم اللي ضايل هو هذا
+
+73
+00:06:11,800 --> 00:06:14,720
+ال common .. ال greatest common divisor الرقم اللي
+
+74
+00:06:14,720 --> 00:06:19,300
+بيكون ضايل معاه هو ال greatest common divisor ناخد
+
+75
+00:06:19,300 --> 00:06:25,980
+مثال بيوضح .. بيوضح الصورة لو مطلوب greatest
+
+76
+00:06:25,980 --> 00:06:31,640
+common divisor ل 372 و 164Automatic اللي هي نفس ال
+
+77
+00:06:31,640 --> 00:06:37,820
+greatest common divisor لأ 372 mod 164 الأكبر mod
+
+78
+00:06:37,820 --> 00:06:48,860
+الأصغر و الأصغر طبعا الناتج هنا هيكون أقل من 164
+
+79
+00:06:48,860 --> 00:06:57,050
+sureأقل من 164 دائما لأن المتبقي من القسم على 164
+
+80
+00:06:57,050 --> 00:07:02,530
+طبيعي بيكون أقل من 164 طبيعي كويسة فحنشتغل على ال
+
+81
+00:07:02,530 --> 00:07:05,810
+mood ال mood جداش بيطلع في الآخر بيطلع 44 فإذا
+
+82
+00:07:05,810 --> 00:07:09,630
+تصير كأنه عندنا اربعة وأربعين ومية
+
+83
+00:07:11,380 --> 00:07:15,900
+الكبير والصغير كأنك اختزلت ال greatest common
+
+84
+00:07:15,900 --> 00:07:22,620
+divisor ل 372 164 هو نفسه ال greatest common
+
+85
+00:07:22,620 --> 00:07:30,800
+divisor ل 164 و 44 هو نفسه نفس القيمةمعنى ذلك كأنه
+
+86
+00:07:30,800 --> 00:07:34,060
+صار عندى مشكلة جديدة problem جديدة بس أخف شوية أقل
+
+87
+00:07:34,060 --> 00:07:38,000
+درجتها كأنه بدور على greatest common divisor ل 164
+
+88
+00:07:38,000 --> 00:07:44,660
+و 44 بنكرر نفس الكلام 164 mod 44 الكلام ده بطلعت
+
+89
+00:07:44,660 --> 00:07:49,320
+32 معنى ذلك برضه ال greatest common divisor لهدي
+
+90
+00:07:49,320 --> 00:07:53,100
+أو لهدي هو نفسه لهي ل greatest common divisor ل 44
+
+91
+00:07:53,100 --> 00:07:58,020
+و 32 كلهم اشتغلوا عليهم هتلاقوا معاهم نفس ال
+
+92
+00:07:58,020 --> 00:08:01,690
+greatest common divisorليش؟ لأنه ممكن السؤال يبدأ
+
+93
+00:08:01,690 --> 00:08:07,210
+من هنا هتقول ال greatest common divisor ل 44.32
+
+94
+00:08:07,210 --> 00:08:12,190
+هتلعق قيمة هي نفسها ال greatest common divisor ل
+
+95
+00:08:12,190 --> 00:08:21,710
+372.164 طيب هو نفسه ل 32
+
+96
+00:08:21,710 --> 00:08:27,620
+.12 برضه يلهم نفس ال greatest common divisorتعون
+
+97
+00:08:27,620 --> 00:08:32,500
+تمانية و اتناش طيب كويس اخر شغل عند التمانية و
+
+98
+00:08:32,500 --> 00:08:34,900
+اتناش هنا صار كأنه بده اتكلم عن ال greatest common
+
+99
+00:08:34,900 --> 00:08:42,980
+divisor تمانية مد اربعة تمانية مد اربعة سفر فش
+
+100
+00:08:42,980 --> 00:08:48,180
+متبقي انت فش متبقي ايه جافو ايش اللي ضال اربعة
+
+101
+00:08:48,180 --> 00:08:53,380
+فإذا ال greatest common divisor هو اربعة اكبر عامل
+
+102
+00:08:53,380 --> 00:09:00,560
+مشتركعامل قسم مشترك بينهم أو قسم مشترك أكبر ل 372
+
+103
+00:09:00,560 --> 00:09:09,020
+164 هو الأربعة طيب أكبر عامل مشترك ل 164 و 44 هي
+
+104
+00:09:09,020 --> 00:09:13,680
+الأربعة أكبر عامل مشترك ل 44 و 32 هي الأربعة أكبر
+
+105
+00:09:13,680 --> 00:09:18,660
+عامل مشترك بين الأربعة و 8 هي الأربعة لحظة فكلهم
+
+106
+00:09:18,660 --> 00:09:24,100
+نفس نفس الناتج بيطلعباستخدام ال modular operator
+
+107
+00:09:24,100 --> 00:09:30,020
+باستخدام ال modular operator okay
+
+108
+00:09:30,020 --> 00:09:34,740
+algorithm نكتب algorithm للموضوع ال algorithm
+
+109
+00:09:34,740 --> 00:09:39,500
+procedure هنكتب procedure و بدنا نحدد ايش اسمه
+
+110
+00:09:39,500 --> 00:09:42,480
+greatest common divisor خلاص معروف ان ال algorithm
+
+111
+00:09:42,480 --> 00:09:45,200
+اللى بدنا نعمل او ال code اللى بدنا نكتبه ل
+
+112
+00:09:45,200 --> 00:09:48,200
+greatest common divisor ال inputs تبعته عبارة عن
+
+113
+00:09:48,200 --> 00:09:50,360
+two numbers بدى اجيب ال greatest common divisor
+
+114
+00:09:50,360 --> 00:09:54,670
+لهمبنجيب العامل القسمة الأكبر أو القاسم المشترك
+
+115
+00:09:54,670 --> 00:09:58,050
+الأكبر عبارة عن ايه اسمهم positive integers
+
+116
+00:09:58,050 --> 00:10:02,150
+positive integers why ب لا تساوي zero لأنه عارفين
+
+117
+00:10:02,150 --> 00:10:05,010
+إذا سوت zero خلاص بناخد الرقم التاني على أساس أن
+
+118
+00:10:05,010 --> 00:10:08,390
+هو ال common divisor أو ال greatest common divisor
+
+119
+00:10:08,390 --> 00:10:12,350
+لا تساوي zero هنستمر في المدرر ال operation المدرر
+
+120
+00:10:12,350 --> 00:10:16,130
+ال operator تبعنا هيستمر هيتكرر كمان مرة طوال ما
+
+121
+00:10:16,130 --> 00:10:22,750
+هي لا تساوي صفر beginمش نعمل R خلاص R ما هي جايبين
+
+122
+00:10:22,750 --> 00:10:31,250
+احنا من ال A mod B و هاد ال R دائما اقل من B اقل
+
+123
+00:10:31,250 --> 00:10:35,610
+من B فبنرتبهم خلصنا العملية ال mod of ال operator
+
+124
+00:10:35,610 --> 00:10:39,830
+بنرتبهم ال A بنحطها هي B لأن هي الأكبر هالوجه
+
+125
+00:10:39,830 --> 00:10:45,200
+هتصير هي الأكبر ال B هي هتصير ال R هي هتصيرالـ
+
+126
+00:10:45,200 --> 00:10:48,300
+remainder لل operator السابق أو لل operation
+
+127
+00:10:48,300 --> 00:10:51,360
+السابق نعود إلى ال operator الموجود لل operator
+
+128
+00:10:51,360 --> 00:10:57,080
+السابق كويسة هنا و end نرجع نتأكد هل البيل جديدة
+
+129
+00:10:57,080 --> 00:11:03,440
+تسوى صفر انت هتسوى صفر اذا ال remainder equal to
+
+130
+00:11:03,440 --> 00:11:07,400
+zero تقولنا ال remainder لا يسوى zero هنستمر انت
+
+131
+00:11:07,400 --> 00:11:11,700
+بيسوى zero زي حالة ال 8 و 4 تول 8 و 4 ال R equal
+
+132
+00:11:11,700 --> 00:11:17,000
+to zero stopR equal to 0 يعني بي بتسوي 0 وR بتسوي
+
+133
+00:11:17,000 --> 00:11:25,260
+0 و هتلي قيمة a الأخيرة فإذا return a جيبلنا قيمة
+
+134
+00:11:25,260 --> 00:11:30,030
+a اللي دلت في الآخر بعد طبعا ما احنارتبناهم بهذا
+
+135
+00:11:30,030 --> 00:11:33,830
+الشكل ان ال B حطناها هي ال A و ال A هي صارت ال B
+
+136
+00:11:33,830 --> 00:11:38,190
+فبناخد اخر term اللي هو greatest common divisor
+
+137
+00:11:38,190 --> 00:11:43,750
+عبارة عن ال A اللي هنرجع فيه كنتج لل greatest
+
+138
+00:11:43,750 --> 00:11:48,140
+common divisor operationطيب فهي automatically فكل
+
+139
+00:11:48,140 --> 00:11:51,080
+مرة بنعمل sorting لها بنرتب الأكبر فرق و الأصغر
+
+140
+00:11:51,080 --> 00:11:54,660
+الأكبر دايما في A الأصغر دايما في B و بنرجع بنعيد
+
+141
+00:11:54,660 --> 00:11:59,980
+نفس الكلام طيب ال algorithm سريع ال order تبعه أو
+
+142
+00:11:59,980 --> 00:12:06,650
+ال big O logarithmicعبارة عن logarithmic مش هتفرج
+
+143
+00:12:06,650 --> 00:12:10,170
+a و b لإنه في النهاية maximum منهم بس في النهاية
+
+144
+00:12:10,170 --> 00:12:12,850
+هي logarithmic function هيكون logarithmic function
+
+145
+00:12:12,850 --> 00:12:15,470
+أو ال growth .. ال order of growth تبعتنا
+
+146
+00:12:15,470 --> 00:12:19,450
+logarithmic فال complexity logarithmic،
+
+147
+00:12:19,450 --> 00:12:22,870
+logarithmic تعتبر tractable ولا intractable؟
+
+148
+00:12:25,890 --> 00:12:29,930
+attractable أقل من ال .. ال polynomial أقل من ال
+
+149
+00:12:29,930 --> 00:12:32,510
+polynomial فهي attractable بالعكس أقل من ال normal
+
+150
+00:12:32,510 --> 00:12:36,370
+حتى من ال linear أنا في إيش انحدد من ال .. بظبط
+
+151
+00:12:36,370 --> 00:12:39,630
+لإنك أنت في الآخر بتشتغلي أقل من ال linear ال
+
+152
+00:12:39,630 --> 00:12:43,630
+linear أنت عندك تلاتمية و تلاتة و سبعين صحيح؟ و
+
+153
+00:12:43,630 --> 00:12:46,630
+مية أربعة و ستين هل أنت اشتغلت مية أربعة و ستين ..
+
+154
+00:12:46,630 --> 00:12:49,110
+لو جدت أخد الأقل منهم هل أنت اشتغلت مية أربعة و
+
+155
+00:12:49,110 --> 00:12:53,840
+ستين operator؟كذا مرة .. iteration؟ لأ طب ها كدهش
+
+156
+00:12:53,840 --> 00:12:58,100
+كل مرة ناخد المتبقي .. المتبقي فهي أقل حتى من ال
+
+157
+00:12:58,100 --> 00:13:01,220
+164 كل مرة فدائما هتلاقيها ال logarithmic في
+
+158
+00:13:01,220 --> 00:13:07,100
+الحلقةاللي بنشتغل فيها، كويس الموضوع سهل و هنمشي
+
+159
+00:13:07,100 --> 00:13:10,640
+فيه بسرعة و يمكن يتقاطع مع امتحان كل يوم اللي هو
+
+160
+00:13:10,640 --> 00:13:13,320
+عملية ال systems ال other systems عن ال decimal
+
+161
+00:13:13,320 --> 00:13:15,580
+systems اللي احنا بتكلم عنها فاحنا بتكلم عن ال
+
+162
+00:13:15,580 --> 00:13:20,300
+base بي numbers systems انتوا يمكن اللي عارفين ال
+
+163
+00:13:20,300 --> 00:13:25,240
+decimal ال decimal عبارة عن عشرة عشرة digits من
+
+164
+00:13:25,240 --> 00:13:29,810
+صفر لتسعة وهذا اللي بنتعامل فيها بحيث ان اناكل
+
+165
+00:13:29,810 --> 00:13:33,710
+digit هتاخد قيمة من الأرقام من ال digits هذه من
+
+166
+00:13:33,710 --> 00:13:39,410
+صفر أو جسع فلو قلنا مثلا تلاتمية خمسة وستين
+
+167
+00:13:39,410 --> 00:13:42,430
+تلاتمية خمسة وستين الأرقام اللي بناخدها هنا خمسة
+
+168
+00:13:42,430 --> 00:13:46,350
+ستة تلاتة خمسة ستة تلاتة هدولة عمره ما هيزيدوا عن
+
+169
+00:13:46,350 --> 00:13:49,770
+مجموعة ال digits اللي هي من صفر لتسعة من صفر لتسعة
+
+170
+00:13:49,770 --> 00:13:53,730
+ماحدش هييجي يقولي والله في عند رقم مية سبعة عشرة
+
+171
+00:13:55,560 --> 00:13:59,220
+مالهاش معنات عشر هذه معناته صفر والواحد بييجي معه
+
+172
+00:13:59,220 --> 00:14:02,360
+فبتصير مية و تمانين مافيش إمكانية إن إحنا نحن نحط
+
+173
+00:14:02,360 --> 00:14:06,300
+أرقام أكبر من ال digits اللي مسموحة في ال system
+
+174
+00:14:06,300 --> 00:14:09,420
+ال system تبعنا base عشرة فهم عشرة digits هم
+
+175
+00:14:09,420 --> 00:14:14,340
+المسموحين من صفر لتسعة كويسة في الحالة بتاعتنا هذه
+
+176
+00:14:14,340 --> 00:14:21,900
+هدب يرتب على أساس أنه a node a واحد a اتنينالرقم
+
+177
+00:14:21,900 --> 00:14:27,960
+الأول عشان اجيب جداش قيمتهم بنضربه في الأحد مدام
+
+178
+00:14:27,960 --> 00:14:31,240
+صفر فبنضربه ال base بتاعتنا جداش decimal عشرة
+
+179
+00:14:31,240 --> 00:14:36,270
+فبتكلم عن عشر قطبور zero مضروبة في خمسةهذه الأحد
+
+180
+00:14:36,270 --> 00:14:40,910
+كما كنا بنعرفها العشرات ten to the power واحد نضرب
+
+181
+00:14:40,910 --> 00:14:44,590
+في الرقم ال digit ما جاتوش قيمتها الأخيرة ما جاتوش
+
+182
+00:14:44,590 --> 00:14:48,030
+ال digit بتاعتنا تلاتة في ten to the power اتنين
+
+183
+00:14:48,030 --> 00:14:51,870
+طيب ناخد بالنا الشغلة ال order تبعنا ما جاتوش عدد
+
+184
+00:14:51,870 --> 00:14:56,990
+ال digits بتاعتنا تلاتة فال orders from zero to n
+
+185
+00:14:56,990 --> 00:14:58,370
+minus one
+
+186
+00:15:04,700 --> 00:15:08,320
+لأن هاد هنشتغلها لغة في ال algorithms لما ال four
+
+187
+00:15:08,320 --> 00:15:10,940
+loops تبعتنا ناخدها من صفر to n minus one احنا
+
+188
+00:15:10,940 --> 00:15:14,580
+عارفين ليش to n minus one لإن هي عددهم تلاتة معنا
+
+189
+00:15:14,580 --> 00:15:17,940
+ذلك انهم هيكونوا من صفر لاثنين هي ال three digit
+
+190
+00:15:17,940 --> 00:15:20,800
+ساعونة هي ال three digit ساعونة فاحنا هنكون غطناهم
+
+191
+00:15:20,800 --> 00:15:25,740
+فعلا هنكون فعلا غطناهم كويس ابنجمعهم summation
+
+192
+00:15:25,740 --> 00:15:28,800
+فبنقدر
+
+193
+00:15:28,800 --> 00:15:35,070
+نقول والله هاد خمسة هاد سبتين هاد تلاتميةبنجمعه
+
+194
+00:15:35,070 --> 00:15:40,870
+وهذه هي آلية الـالجمع ان احنا لا نعرف قيمة الرقم
+
+195
+00:15:40,870 --> 00:15:45,330
+كله الرقم اللي بتكون من مجموعة digits مجموعة
+
+196
+00:15:45,330 --> 00:15:48,810
+digits في system معين ال system ده اشي اللي بيميزه
+
+197
+00:15:48,810 --> 00:15:51,810
+عن غيره ال base تبعته ال base تبعته هنا عشرة
+
+198
+00:15:51,810 --> 00:15:55,890
+فبتسأل على عشرة to the power zero to the power
+
+199
+00:15:55,890 --> 00:15:58,650
+واحد to the power اتنين طيب لو اتغيرت العشرة
+
+200
+00:15:58,650 --> 00:16:01,230
+لاتنين فبتصير اتنين to the power zero اتنين to the
+
+201
+00:16:01,230 --> 00:16:03,290
+power واحد اتنين to the power اتنين نتكلم عن
+
+202
+00:16:03,290 --> 00:16:09,100
+binaries لو الأكترتمانية لو ال hexadecimal ستة عشر
+
+203
+00:16:09,100 --> 00:16:12,760
+فبتصير ستة عشر زفر ستة عشر واحد ستة عشر اتنين تدبر
+
+204
+00:16:12,760 --> 00:16:20,300
+واحد تدبر اتنين تدبر تلاتة و هكذا و هكذا مجموعة
+
+205
+00:16:21,280 --> 00:16:25,740
+systems او particular bases of interest اللي بتقدر
+
+206
+00:16:25,740 --> 00:16:27,680
+تهتموا فيها اللي انتوا هتهتموا فيها و هنقولها لوضع
+
+207
+00:16:27,680 --> 00:16:32,000
+كمان ليش هو ما يمكن اكتر three اكتر مجموعة systems
+
+208
+00:16:32,000 --> 00:16:34,640
+نتعامل معها ال decimal هذه الطبيعية اللي احنا
+
+209
+00:16:34,640 --> 00:16:37,380
+بنشتغل فيها أساسا اللي هي ال digits بتاعتنا من صفر
+
+210
+00:16:37,380 --> 00:16:40,840
+لتسعة و في عندكوا المهمة جدا ال binary او ال
+
+211
+00:16:40,840 --> 00:16:44,940
+binary digits فهذه مجموعة bits مجموعة ال bits و
+
+212
+00:16:44,940 --> 00:16:49,540
+هذا اللي بتعامل فيها الجهاز او ال pc ال computerفي
+
+213
+00:16:49,540 --> 00:16:52,240
+معظم ال operations تبعته في معظم ال operations
+
+214
+00:16:52,240 --> 00:16:56,700
+تبعته الاقتال ثماني و الثماني هذا هتكون نسبة ل ال
+
+215
+00:16:56,700 --> 00:17:02,000
+binary عشان ناخد three digits و بنتعامل معها كرقم
+
+216
+00:17:02,000 --> 00:17:05,340
+ف three digits يداش maximum number بيقولنا سبعة
+
+217
+00:17:05,340 --> 00:17:11,260
+ساقية الصفرتمانية، فإذا أنا بتكلم من صفر لسبعة،
+
+218
+00:17:11,260 --> 00:17:17,920
+يعني تمانية اكتل، طيب الستعش أربعة digits، نتعامل
+
+219
+00:17:17,920 --> 00:17:21,820
+مع أربعة digits لتسهيل الرقم، لتسهيل حسبة الرقم
+
+220
+00:17:21,820 --> 00:17:28,540
+بدل ما يكون عدد ال bits تبعته كبير، طيب ال
+
+221
+00:17:28,540 --> 00:17:32,860
+converting to base Bبرضه انتوا ماخدين الكلام هذا
+
+222
+00:17:32,860 --> 00:17:36,300
+احنا متأكد يعنى ماخدين الموضوع هذا و عارفين كيف
+
+223
+00:17:36,300 --> 00:17:40,500
+تشتغلوا فيه ولكن لا يمنع انه ع السريع لو بدنا نحول
+
+224
+00:17:40,500 --> 00:17:43,920
+ال decimal ل octal كل اللي بتعمله مدام انكوا
+
+225
+00:17:43,920 --> 00:17:48,760
+تحولوا من decimal لحظة من decimal على طول بتدوروا
+
+226
+00:17:48,760 --> 00:17:52,420
+على .. على ال reminders تبعونكم على ال reminders
+
+227
+00:17:52,420 --> 00:17:54,660
+ال reminders هدول هم اللي بيحددوا الرقم القادم
+
+228
+00:17:54,660 --> 00:17:59,390
+رقمنا اللي جاي فانتوا بتعملوا ال .. ال cautionال
+
+229
+00:17:59,390 --> 00:18:02,310
+caution كل مرة بتضاربوا تجسموها عشان تدوروا على ال
+
+230
+00:18:02,310 --> 00:18:05,090
+reminders خلينا نشوف هنا لو بتحولوها لثماني
+
+231
+00:18:05,090 --> 00:18:08,590
+فبتجسموها تمانية لو بتحولوها لستعاش فبتجسموها
+
+232
+00:18:08,590 --> 00:18:12,930
+ستعاش ايش ال base اللي بتكويها بتحولوا بالنسبالها
+
+233
+00:18:12,930 --> 00:18:16,990
+فهنا decimal بتكويها ل أبتال أبتال بتجسموها تمانية
+
+234
+00:18:16,990 --> 00:18:21,410
+خارج القسمة والمتبقي مهم جدا المتبقي هذا طيب خارج
+
+235
+00:18:21,410 --> 00:18:24,620
+القسمة بترجع كمان مرة تجسموها على تمانيةترجعوا
+
+236
+00:18:24,620 --> 00:18:28,660
+لعند امتى؟ لعند ما يصل لخارج القسمة صفر لعند ما
+
+237
+00:18:28,660 --> 00:18:34,420
+يصل لخارج القسمة صفر فقدركم تقسموا و في كل قسمة
+
+238
+00:18:34,420 --> 00:18:38,260
+هيتطلع طبعا reminders هيظهر عنكم sequence of
+
+239
+00:18:38,260 --> 00:18:42,720
+reminders أول واحد هذا ال least significant pet
+
+240
+00:18:42,720 --> 00:18:46,960
+والأخير ال most significant pet فهيكون هذه one
+
+241
+00:18:46,960 --> 00:18:57,240
+سبعة صفر صفر تلاتةهذا ثماني في النظام الثماني،
+
+242
+00:18:57,240 --> 00:19:00,980
+كويس بهذا الشكل هي إنت وصلت صفر بتجفوا، إنت وصلت
+
+243
+00:19:00,980 --> 00:19:06,720
+صفر هتجفوا تمام، بالنسبة للهكسا نفس الموضوع هو هو،
+
+244
+00:19:06,720 --> 00:19:09,500
+برضه بتجسم على ست عشر، بتجسم على ست عشر، والمهم
+
+245
+00:19:09,500 --> 00:19:14,600
+عندكم هي الأرقام اللي بتظهر هنا فالأرقام هذه عبارة
+
+246
+00:19:14,600 --> 00:19:22,540
+شوي شوي ناخدها عشرة، اربعة عشر، تلاتة، احداشرو
+
+247
+00:19:22,540 --> 00:19:28,500
+اتنين نبسكوا واحدة العشرة في الhexa ايه؟ الاربعتعش
+
+248
+00:19:28,500 --> 00:19:37,520
+ايه؟ تلاتة خلاص هي تلاتة داشت و اتنين هذا ستة عشر
+
+249
+00:19:37,520 --> 00:19:43,160
+هذا هيك ستة عشر طيب بالنسبة الأبسط من هيكة لما كنت
+
+250
+00:19:43,160 --> 00:19:49,450
+تشتغله من hexadecimal أو أكتال ل binary أو العكس
+
+251
+00:19:49,450 --> 00:19:53,010
+لإن إحنا قولنا أصلا ال .. الأكتال و ال hexadecimal
+
+252
+00:19:53,010 --> 00:19:55,350
+إحنا ماخدينهم من جداش عدد ال digits في ال binary
+
+253
+00:19:55,350 --> 00:19:58,990
+جداش عدد ال digits في ال binary فلو قولنا هي إن ال
+
+254
+00:19:58,990 --> 00:20:02,630
+number هذا binary number بدنا نحاوله لأكتال أكتال
+
+255
+00:20:02,630 --> 00:20:05,510
+إحنا عارفين تلاتة فبنمسكهم تلاتة تلاتة كل three
+
+256
+00:20:05,510 --> 00:20:09,580
+digits groupكل three digits ال group، ال group
+
+257
+00:20:09,580 --> 00:20:13,520
+الأول أربعة، بنحط أربعة، ال group التاني سبعة، هاي
+
+258
+00:20:13,520 --> 00:20:19,620
+سبعة، تالت، اتنين، هاي اتنين، سبعة، تلاتةالكلام هو
+
+259
+00:20:19,620 --> 00:20:23,540
+.. هو وين؟ لكسر .. لكسر جسم الأربعات ال groups ..
+
+260
+00:20:23,540 --> 00:20:27,040
+كل group فيه أربع digits كل group فيه أربع digits
+
+261
+00:20:27,040 --> 00:20:30,840
+الكلام هو .. هو نفس ال .. هنا بدنا من أكتال ..
+
+262
+00:20:30,840 --> 00:20:33,120
+أكتال أنا عارف معناته كل رقم .. كل digit من هدولة
+
+263
+00:20:33,120 --> 00:20:38,200
+بمثلها ب three bits three bits حتى لو واحد بدنا
+
+264
+00:20:38,200 --> 00:20:42,740
+نعمله one صفر صفر لازم نتكمله ل three digits تعونه
+
+265
+00:20:42,740 --> 00:20:48,360
+ل three digits تعونه كويس فهنا الخمسة هي الخمسةو
+
+266
+00:20:48,360 --> 00:20:53,420
+هاي الستة هاي الستة السابعة هاي السابعة تمام
+
+267
+00:20:53,420 --> 00:20:59,420
+الhexa نفس الكلام ال .. الموضوع بسيط وسهل مفيش فيه
+
+268
+00:20:59,420 --> 00:21:05,620
+تعقيدات و أخدته مرارا و تقرارا أكيد okay نبدأ في
+
+269
+00:21:05,620 --> 00:21:08,400
+ال .. في ال .. ال .. ال codes و هذا اللي هو بهمنا
+
+270
+00:21:08,400 --> 00:21:13,960
+يمكن أكتر بدنا نبدأ نعمل أكواد أو pseudocodes ل ال
+
+271
+00:21:13,960 --> 00:21:16,840
+operations اللي ممكن نعملها على ال binary numbers
+
+272
+00:21:17,840 --> 00:21:23,840
+أهمها عملية الجمع, adding عندكوا two numbers, two
+
+273
+00:21:23,840 --> 00:21:28,860
+binary numbers و بدكوا تجمعوهم فممكن نقول say مثلا
+
+274
+00:21:28,860 --> 00:21:38,320
+إنه عندنا واحد صفر واحد و واحد
+
+275
+00:21:38,320 --> 00:21:38,880
+واحد واحد
+
+276
+00:21:42,010 --> 00:21:44,950
+طيب انشوف هنا في انكم procedure خلاص عارف انه احنا
+
+277
+00:21:44,950 --> 00:21:48,010
+دخلنا على اياش على code بدنا جايدين نكتب جايدين في
+
+278
+00:21:48,010 --> 00:21:51,330
+ال pseudocode add اه معناته واضح انه من ال add
+
+279
+00:21:51,330 --> 00:21:55,150
+معناته هذا في عملية جمعماذا تتبعت ال M؟ Sequence
+
+280
+00:21:55,150 --> 00:22:08,170
+أول و تاني Sequence Sequence Sequence
+
+281
+00:22:08,170 --> 00:22:18,210
+Sequence Sequence
+
+282
+00:22:18,210 --> 00:22:18,230
+Sequence Sequence Sequence Sequence Sequence
+
+283
+00:22:18,230 --> 00:22:18,250
+Sequence Sequence Sequence Sequence Sequence
+
+284
+00:22:18,250 --> 00:22:18,270
+Sequence Sequence Sequence Sequence Sequence
+
+285
+00:22:18,270 --> 00:22:18,370
+Sequence Sequence Sequence Sequence Sequence
+
+286
+00:22:18,370 --> 00:22:18,510
+Sequence Sequence Sequence Sequence Sequence
+
+287
+00:22:18,510 --> 00:22:18,530
+Sequence Sequence Sequence Sequence Sequence
+
+288
+00:22:18,530 --> 00:22:20,550
+Sequence Sequence Sequence Sequence Sequence
+
+289
+00:22:20,550 --> 00:22:23,700
+Sequence Sequence Sequenceالعملية البسيطة كل مرة
+
+290
+00:22:23,700 --> 00:22:28,580
+بجمع مع الحمل طبعا كويس ف ال carry نبدأ ب zero
+
+291
+00:22:28,580 --> 00:22:31,800
+مافيش عشان فاضية لإن ال memory كلها فاضية لإن ال
+
+292
+00:22:31,800 --> 00:22:37,980
+registers كلها zeros كويس four bit index من zero
+
+293
+00:22:37,980 --> 00:22:43,880
+to n minus one to n minus one begin bit sum عبارة
+
+294
+00:22:43,880 --> 00:22:49,670
+عن a سنبدأ بالصفرو نمسك ال code تبعنا هنبدأ بال
+
+295
+00:22:49,670 --> 00:22:54,790
+صفر فكأن نبدأ نجمع a 0 و b 0 مع ال carry طيب هى ال
+
+296
+00:22:54,790 --> 00:23:02,850
+a 0 و هى ال b 0 و ال carry 0 فإذا نجدش بتطلع 0 1 1
+
+297
+00:23:02,850 --> 00:23:07,030
+طيب نمسكهم شوي شوي هدول 0 و 1 و نحط كل واحدة منهم
+
+298
+00:23:07,030 --> 00:23:14,340
+ف ال S بتاعتنااو خلينا نجمعها تحديدا بنفس الشكل
+
+299
+00:23:14,340 --> 00:23:18,680
+واحد واحد بساوي اتنين نبسك الاتنين ال summation
+
+300
+00:23:18,680 --> 00:23:25,180
+bit index معناته ال summation zero احنا لسه under
+
+301
+00:23:25,180 --> 00:23:35,460
+zero ف zero بتساوي ال bit summation مود اتنين مود
+
+302
+00:23:35,460 --> 00:23:40,630
+اتنين صفر طيب ال carryبدي اتغير هذه اللغة ال bit
+
+303
+00:23:40,630 --> 00:23:45,210
+summation اللي هي اتنين على اتنين floor اتنين على
+
+304
+00:23:45,210 --> 00:23:49,810
+اتنين واحد floor واحد واحد carry صارت هنا ايش واحد
+
+305
+00:23:49,810 --> 00:23:54,490
+واحد okay
+
+306
+00:23:54,490 --> 00:24:02,430
+خلصنا ال S0 ال summation في ال digit الاولى صار
+
+307
+00:24:02,430 --> 00:24:08,990
+هنا اتنين واحد افضل واحد bit summation ايه ال oneB
+
+308
+00:24:08,990 --> 00:24:14,350
+one زائد ال carry A one B one زائد ال carry صفر
+
+309
+00:24:14,350 --> 00:24:20,510
+واحد واحد زائد واحد بيساوي اتنين اتنين نفس الكلام
+
+310
+00:24:20,510 --> 00:24:26,850
+اتنين مدت اتنين مدت اتنين صفر zero فإذا ال S one
+
+311
+00:24:26,850 --> 00:24:34,590
+zero carry one carry one okay اتنين
+
+312
+00:24:35,570 --> 00:24:38,630
+وها دي اللي هي ال N minus one أخر واحدة بدنا نتكلم
+
+313
+00:24:38,630 --> 00:24:43,090
+عن تلاتة N minus one بتساوي اتنين فإذن عشان نحسب
+
+314
+00:24:43,090 --> 00:24:52,010
+الأخيرة A اتنين B اتنين we carry واحد زائد واحد
+
+315
+00:24:52,010 --> 00:25:01,390
+زائد واحد تلاتة فتلاتة هنا عشان نحسب ال S اتنين مد
+
+316
+00:25:03,140 --> 00:25:09,140
+مدة اتنين تسوي واحد كاري تلاتة على اتنين واحد و
+
+317
+00:25:09,140 --> 00:25:14,420
+نصف floor واحد خلص
+
+318
+00:25:14,420 --> 00:25:22,660
+اللوب اللوب يتخلص هنا يتخلص ب N-1 طيب بس في SM
+
+319
+00:25:22,660 --> 00:25:24,800
+تلاتة
+
+320
+00:25:25,920 --> 00:25:29,020
+هو ال carry إذا كان ضال معانا إش في الحمل أو مضالش
+
+321
+00:25:29,020 --> 00:25:35,720
+إذا مضالش خلاص صفر ضل أفضل واحد بنزل الواحدبينزل
+
+322
+00:25:35,720 --> 00:25:40,040
+معناه الواحد فهل فعلا يمثل هذا الرقم هذا خمسة زائد
+
+323
+00:25:40,040 --> 00:25:46,120
+سبعة اتناش ايه اتناش تمانية واربعة اتناش فهي ال
+
+324
+00:25:46,120 --> 00:25:48,620
+code في الاخر return ال sequence تبع مين تبع ال
+
+325
+00:25:48,620 --> 00:25:51,440
+summation ال sequence تبع ال summation من صفر to
+
+326
+00:25:51,440 --> 00:25:55,100
+end مش to end minus one مش to end minus one okay
+
+327
+00:25:55,100 --> 00:26:00,960
+هاي عملية ال summation طيب عملية الطرح عندما تطرح
+
+328
+00:26:00,960 --> 00:26:05,130
+أرقام خليني أقول هايالرقامين اللي طوي احنا
+
+329
+00:26:05,130 --> 00:26:11,570
+اشتغلناهم هدولة بدنا نطرحهم من بعض بدنا نطرحهم من
+
+330
+00:26:11,570 --> 00:26:22,130
+بعض فخلينا نخففها شوية محتاجين
+
+331
+00:26:22,130 --> 00:26:26,030
+toast compliment طيب ال .. ال first compliment كيف
+
+332
+00:26:26,030 --> 00:26:28,990
+كنتوا بتعملوه؟ او ايش الهدف من ال .. من ال toast
+
+333
+00:26:28,990 --> 00:26:34,880
+compliment؟بتحول للتالب بالسالب بتجيبوا الرقم
+
+334
+00:26:34,880 --> 00:26:39,080
+بالسالب وهذا الهدف انه احنا كل اللي بدنايا بدل ما
+
+335
+00:26:39,080 --> 00:26:45,920
+اقول a minus b بدي اقول a plus سالب بي فالب تبعتي
+
+336
+00:26:45,920 --> 00:26:51,360
+هذي بدي اجيبها ال negative value بتاعتها في ال
+
+337
+00:26:51,360 --> 00:26:55,940
+binary ال complement المكمل سميها المكمل تبعها
+
+338
+00:26:55,940 --> 00:26:59,080
+المكمل تبعها بالنسبة لأكبر رقم في نفس عدد ال
+
+339
+00:26:59,080 --> 00:27:04,570
+digitsخدتوها هي كنتوا صح؟ نسبة لأكبر رقم بنفس عدد
+
+340
+00:27:04,570 --> 00:27:07,750
+ال digits جداش المكمل للرقم عشان يصل لأكبر رقم
+
+341
+00:27:07,750 --> 00:27:11,410
+فهذه هي ال compliment تبعكم هذه هي compliment
+
+342
+00:27:11,410 --> 00:27:16,430
+كويسة عشان أجيبها بنجيبها ال two operations بنجيب
+
+343
+00:27:16,430 --> 00:27:19,290
+ال first compliment ومنه بنجيب ال second
+
+344
+00:27:19,290 --> 00:27:21,510
+compliment ال first compliment إيش كنتوا بتعمله؟
+
+345
+00:27:21,510 --> 00:27:27,090
+نعكس flip flip كل zero بنعمله one وكل one بنعمله
+
+346
+00:27:27,090 --> 00:27:31,540
+zero كل one بنعمله zeroطيب ال two's complement
+
+347
+00:27:31,540 --> 00:27:36,180
+نجمع نجمع زائد واحد زائد واحد بس ناخد بالنا إنك
+
+348
+00:27:36,180 --> 00:27:43,020
+تضيف bit في الآخر ليش؟ إشارة احنا by logic احنا
+
+349
+00:27:43,020 --> 00:27:46,120
+بنختصر الموضوع بهذا الشكل بس هو فعليا هنا في zero
+
+350
+00:27:46,120 --> 00:27:51,880
+ال zero هذه تشير لإيش؟ للموجب إذا كانت واحد إذا
+
+351
+00:27:51,880 --> 00:27:55,340
+كان أنا محدد أنه أعطيكوا الرقم بهذا الشكل و أقول
+
+352
+00:27:55,340 --> 00:28:01,250
+لكوا لأ هذه three digits جدش الرقم positiveخمسة
+
+353
+00:28:01,250 --> 00:28:07,870
+خمسة
+
+354
+00:28:07,870 --> 00:28:09,230
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+355
+00:28:09,230 --> 00:28:10,550
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+356
+00:28:10,550 --> 00:28:18,070
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+357
+00:28:18,070 --> 00:28:21,790
+خمسة خمسة خمسة
+
+358
+00:28:21,790 --> 00:28:29,830
+خمسة
+
+359
+00:28:31,160 --> 00:28:36,020
+أشتغلتوها قبلها طيب ال subtraction of binary
+
+360
+00:28:36,020 --> 00:28:38,620
+numbers زي ما قولنا كل اللي بنعمله اللي بده يجيب
+
+361
+00:28:38,620 --> 00:28:41,820
+ال minus لل a فبجيب ال first complement أو ال
+
+362
+00:28:41,820 --> 00:28:48,960
+complement لل a plus واحد طيب ال procedure بنعمل
+
+363
+00:28:48,960 --> 00:28:54,310
+subtractأو ال sequence a و ال sequence b .. ال
+
+364
+00:28:54,310 --> 00:28:57,410
+sequence b هنا complement .. جيبنا له ال binary
+
+365
+00:28:57,410 --> 00:29:03,290
+two's complement .. represents of integers b و a
+
+366
+00:29:03,290 --> 00:29:07,430
+كيف نعملها .. add .. نعمل adding عادية .. نعمل
+
+367
+00:29:07,430 --> 00:29:17,330
+عملية adding .. هيها .. لمين .. ل a مع addB
+
+368
+00:29:17,330 --> 00:29:23,010
+complement واحد فال B complement بعكس وجمعنا واحد
+
+369
+00:29:23,010 --> 00:29:32,710
+فال term هذا صار كأنه minus B جمعناه مع A فأصبحت
+
+370
+00:29:32,710 --> 00:29:40,250
+كأنه A minus B كأنها A plus minus B أو بجمعها مع
+
+371
+00:29:40,250 --> 00:29:44,730
+minus B فظهرت كأنها سالفة في الحالة اللي عندكم هنا
+
+372
+00:29:44,730 --> 00:29:45,030
+fold
+
+373
+00:29:49,000 --> 00:29:54,300
+one صفر one المقروح هذا هكون عبارة عن صفر يعكسه
+
+374
+00:29:54,300 --> 00:30:02,880
+plus واحد one one zero one تمام one one zero one
+
+375
+00:30:02,880 --> 00:30:10,920
+فهذه صارت إنه نجمحها على one zero one one جداش
+
+376
+00:30:10,920 --> 00:30:16,880
+واحد واحد
+
+377
+00:30:19,300 --> 00:30:24,300
+طيب خلّيني أمسككم حاجة حاجة الرقم اللي بدنا نطرح
+
+378
+00:30:24,300 --> 00:30:28,520
+منه أكام digit؟ أربعة هل يُعقل إن النتج يكون أكبر
+
+379
+00:30:28,520 --> 00:30:35,740
+من أربعة digit؟ طب هد إيش الرقم؟ overflow فهد
+
+380
+00:30:35,740 --> 00:30:41,020
+إيش بنسويله؟ بسكيت بنبسه خلاص بدناه شيء ليش؟ لأنه
+
+381
+00:30:41,020 --> 00:30:46,780
+هد زيادة عن الرقم الكبير في الطريقةطب لا يمكن
+
+382
+00:30:46,780 --> 00:30:52,020
+الرقم الكبير في الطريح يطلعنا رقم أكبر منه، كويس
+
+383
+00:30:52,020 --> 00:30:56,760
+فهنا بنقف لعند الحالة هذه طيب في الحالة هذه هيك
+
+384
+00:30:56,760 --> 00:31:00,700
+خلصنا شغل، نجدش احنا الرقامين اللي كنا شغلينهم
+
+385
+00:31:00,700 --> 00:31:09,400
+أساسا كانت عشرة نقص جديش، كان نقص خمسة عشان نشوف
+
+386
+00:31:09,400 --> 00:31:10,680
+الناتج مظبوط أه مظبوط
+
+387
+00:31:15,170 --> 00:31:19,190
+تخيلوا من ال overflow تاخدوا بالك و أكبر من n على
+
+388
+00:31:19,190 --> 00:31:23,850
+طول هذا overflow وببساطة جدا بشيله و خلاص طيب
+
+389
+00:31:23,850 --> 00:31:26,550
+multiplication برضه مرت عليكوا عملية ال
+
+390
+00:31:26,550 --> 00:31:31,130
+multiplication ل ال binary كيف تضربوه تحولوها ل
+
+391
+00:31:31,130 --> 00:31:35,290
+summation تحولوها ل summation بعدد أسفار تذكرينها
+
+392
+00:31:35,290 --> 00:31:40,570
+طيب كويس خلونا برضه ناخدنا رقمين و خلونا ناخد مثلا
+
+393
+00:31:40,570 --> 00:31:45,740
+هاي رقمينهذه الرقمين ونبدأ نشوف ال procedure
+
+394
+00:31:45,740 --> 00:31:51,380
+multiply two sequence او two binary نوحهم two
+
+395
+00:31:51,380 --> 00:31:54,360
+sequence هدولة binary representation of a and b
+
+396
+00:31:54,360 --> 00:32:01,820
+belonging to natural number product الدرب product
+
+397
+00:32:01,820 --> 00:32:07,780
+بتاعتنا في zeroأول ما بدأنا لسه مافيش أي إشي ضفناه
+
+398
+00:32:07,780 --> 00:32:12,360
+مافيش أي حاجة طيب four I من zero لأ لأ لأ لأ لأ لأ
+
+399
+00:32:12,360 --> 00:32:14,500
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+400
+00:32:14,500 --> 00:32:17,560
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+401
+00:32:17,560 --> 00:32:17,740
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+402
+00:32:17,740 --> 00:32:26,620
+لأ لأ لأ لأ
+
+403
+00:32:29,130 --> 00:32:33,750
+لو يسوى واحد، صفر، فإذا و لا مسمونا بنفس الحاجة
+
+404
+00:32:33,750 --> 00:32:37,190
+بالصيفة زي ما هي ال product بتظهر صفر و خليها صفر
+
+405
+00:32:37,190 --> 00:32:46,870
+طيب الحلقة التانية هنا I ب one ب واحد ب واحد اه
+
+406
+00:32:46,870 --> 00:32:51,890
+خلينا نشوف معناته ال product بتساوي ال product
+
+407
+00:32:51,890 --> 00:33:01,220
+القديمة مع ايه؟ بعدد أصفر ال Iجدش ال I بتاعتنا
+
+408
+00:33:01,220 --> 00:33:07,320
+واحد معنى ذلك أنه زائد هي product القديمة صفر زائد
+
+409
+00:33:07,320 --> 00:33:13,320
+one صفر one أكم صفر عندنا كمان صفر I بتساوي واحد
+
+410
+00:33:13,320 --> 00:33:17,900
+فبضيف عدد أصفر ضفنا صفر واحد لإن ال I عندك إيه
+
+411
+00:33:17,900 --> 00:33:26,000
+بواحد كويسة خلصناها عند اتنين ب اتنين واحد فإذا
+
+412
+00:33:26,000 --> 00:33:31,340
+product بتساوي product تبعنا هيهفإذن بتساوي one
+
+413
+00:33:31,340 --> 00:33:37,880
+صفر one صفر زائد زائد أيش زائد برضه ال a بعدد أصفر
+
+414
+00:33:37,880 --> 00:33:46,600
+كده؟ اثنين صفرين فإذن one صفر one و صفرين زائد
+
+415
+00:33:47,410 --> 00:33:52,010
+خلصنا زائد، لأ خلصنا، إذا في زائد بتكملوا زائد،
+
+416
+00:33:52,010 --> 00:33:55,890
+إذا في كمان زائد بتكملوا زائد، خلصنا خلاص، stop
+
+417
+00:33:55,890 --> 00:33:59,290
+تعالوا نجمع الأرقام اللي بتكون حوش عندنا في ال
+
+418
+00:33:59,290 --> 00:34:10,170
+program 101010 و هنا 0101 011111
+
+419
+00:34:10,780 --> 00:34:16,100
+طيب الرقم هد قداش؟ تلاتين لإن هد واحد اتنين تلاتة
+
+420
+00:34:16,100 --> 00:34:20,320
+أربعة خمسة خمسة الماكسما متباحة واحد و تلاتين ناجس
+
+421
+00:34:20,320 --> 00:34:23,520
+واحد الخانة اللي ضايلة فتلاتين هنا بتتكلم عن
+
+422
+00:34:23,520 --> 00:34:26,720
+تلاتين هم هد قداش هنا كانوا؟ خمسة في ستة مظبوط
+
+423
+00:34:26,720 --> 00:34:32,980
+خمسة في ستة مظبوط تمام خدنا بالنا من ال zeros عدد
+
+424
+00:34:32,980 --> 00:34:36,440
+ال zeros اللي بتضفوها حسب هل الرقم واحد في ال B
+
+425
+00:34:36,440 --> 00:34:42,770
+ولا لأ حسب الرقم واحد او لأOkay ال binary division
+
+426
+00:34:42,770 --> 00:34:47,130
+with remainder القسمة أخدتوا القسمة أخدتواها ممتاز
+
+427
+00:34:47,130 --> 00:34:51,750
+معناته الأمور برضه سلسة طيب خلينا ناخد نفس الأرقام
+
+428
+00:34:51,750 --> 00:34:55,450
+هيك معروفة زي اللي احنا أخدناها هنا واحد واحد واحد
+
+429
+00:34:55,450 --> 00:35:03,990
+واحد صفر على الخمسة على الخمسة ماشي على الخمسة
+
+430
+00:35:03,990 --> 00:35:07,470
+ونبدأ
+
+431
+00:35:07,470 --> 00:35:13,730
+في ال code تبعناهمدام with remainder معناه ذلك إنه
+
+432
+00:35:13,730 --> 00:35:18,650
+واضح إن أنا هشغل على ال modular operation محتاجين
+
+433
+00:35:18,650 --> 00:35:21,510
+ال modular operator فإذا ال procedure .. ال
+
+434
+00:35:21,510 --> 00:35:24,190
+procedure هذا إيش اللي هنحسبه منه؟ هنحسب فعليا ال
+
+435
+00:35:24,190 --> 00:35:27,650
+modular، مدام هحتاج remainder، و سوف نشتغل على
+
+436
+00:35:27,650 --> 00:35:30,570
+division، هي العملية الأساسية أو ال code الأساسي
+
+437
+00:35:30,570 --> 00:35:36,130
+division، لإيش a, d belong to z positiveللمجموعة
+
+438
+00:35:36,130 --> 00:35:42,170
+positive integers في الحالة بتاعتنا محتاجين جداش
+
+439
+00:35:42,170 --> 00:35:47,350
+عدد ال digits عشان احسب عدد ال digits في ال
+
+440
+00:35:47,350 --> 00:35:50,650
+problem بتاعتنا بنشوف n انها دي المفروض ال maximum
+
+441
+00:35:50,650 --> 00:35:55,050
+لانه بدنا ننسب ل n-1 جداش قيمتها maximum length of
+
+442
+00:35:55,540 --> 00:36:00,240
+A in bits أو length of D in bits مين الأكبر منهم
+
+443
+00:36:00,240 --> 00:36:03,060
+بيقول أن هذا هو ال size تبع ال problem تبعي اللي
+
+444
+00:36:03,060 --> 00:36:06,480
+بنشتغل فيه هي ال D .. هي ال .. ال .. ال N بتاعتنا
+
+445
+00:36:06,480 --> 00:36:09,700
+هذا ال N بتاعتنا فحسبنا ال N بتاعتنا هذا .. لحظوا
+
+446
+00:36:09,700 --> 00:36:16,340
+هذا ال A term هذا هيك ال A فهي A over D A over D
+
+447
+00:36:16,340 --> 00:36:19,060
+عشانها لوجة ال D و ال A هي .. هي بنشتغل فيهم كتير
+
+448
+00:36:19,060 --> 00:36:21,220
+فانتوا تكونوا عارفين مين ال A و مين ال D من ال B
+
+449
+00:36:21,220 --> 00:36:25,930
+ال D اللي هي ال divisor طبعا ال divisorOkay هنبدأ
+
+450
+00:36:25,930 --> 00:36:32,730
+for I .. لحظة هنا N minus one down في .. هنا ال
+
+451
+00:36:32,730 --> 00:36:39,210
+counter عكسي for loop من الأكبر للأقل فهنا نعملهاش
+
+452
+00:36:39,210 --> 00:36:42,270
+زي اللي فاتت و بنسيبها N minus one two و خلاص لأ
+
+453
+00:36:42,270 --> 00:36:45,670
+down two فبعرف ان انتوا جاسبكوا من الأكبر في
+
+454
+00:36:45,670 --> 00:36:48,390
+الأصغر ماحدش يكتبليها two كذا و يقولي انا هنا
+
+455
+00:36:48,390 --> 00:36:52,400
+كاتبلك من الأكبر لأصغر هقوله لأ غلطالـ structure
+
+456
+00:36:52,400 --> 00:36:56,840
+الصح ده بقى ه down to فبعملها من الأكبر للأقل طيب
+
+457
+00:36:56,840 --> 00:37:02,380
+هنا هنعملها من n minus one to zero ونبدأ if a أكبر
+
+458
+00:37:02,380 --> 00:37:08,220
+من d و i zeros طيب معناه ذلك ان احنا هنا صيرنا
+
+459
+00:37:08,220 --> 00:37:12,920
+نقسم على واحد اتنين تلاتة اربعة خمسة احنا بنشتغل
+
+460
+00:37:12,920 --> 00:37:18,080
+على امتعتنا خمسة معناه ذلك هنا باربعة بنبدأ اربعة
+
+461
+00:37:18,080 --> 00:37:19,420
+بتصير ال D
+
+462
+00:37:22,480 --> 00:37:26,540
+أربعة أربعة أربعة
+
+463
+00:37:26,540 --> 00:37:29,080
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+464
+00:37:29,080 --> 00:37:29,540
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+465
+00:37:29,540 --> 00:37:32,360
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+466
+00:37:32,360 --> 00:37:35,940
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+467
+00:37:35,940 --> 00:37:35,960
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+468
+00:37:35,960 --> 00:37:36,400
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+469
+00:37:36,400 --> 00:37:49,080
+أربعة أربعة أربعة أربعة أربعة أ
+
+470
+00:37:49,970 --> 00:37:56,510
+خرج القسم zero بنرجح هنا لمين؟ تلاتة تلاتة و بنشيل
+
+471
+00:37:56,510 --> 00:38:10,210
+صفر صار دي و تلت أصفر دي
+
+472
+00:38:10,210 --> 00:38:14,670
+و تلت أصفر و بنجرب هل ايه أكبر من الدي الجديدة
+
+473
+00:38:14,670 --> 00:38:18,440
+بالتلت أصفر؟لأ واضح انه لأ معناته ال quotient
+
+474
+00:38:18,440 --> 00:38:27,320
+بتاعتنا برضه zero quotient zero هى طيب اتنين هى
+
+475
+00:38:27,320 --> 00:38:36,580
+ال D مع صفر يعنى A أكبر من أو يساوي D اه أكبر من
+
+476
+00:38:36,580 --> 00:38:41,340
+أو يساوي هى then
+
+477
+00:38:41,340 --> 00:38:45,080
+معناته بتنزل على then أول شي quotient equal to one
+
+478
+00:38:46,770 --> 00:38:52,230
+وال إيه الجديدة مطروحهم من بعض، هنترحهم من بعض،
+
+479
+00:38:52,230 --> 00:38:56,490
+طيب عشان نترحهم من بعض إيش بدنا نعمل؟ to
+
+480
+00:38:56,490 --> 00:39:00,390
+complement، to complement، لذا انتوا مش هتقدروا
+
+481
+00:39:00,390 --> 00:39:03,270
+بسرعة قصرية تترحوها وإن كان المفروض إنه بيطلع
+
+482
+00:39:03,270 --> 00:39:09,370
+مظبوط، هي صفر واحد صفر واحد صفر طيب خلينا ناخد
+
+483
+00:39:09,370 --> 00:39:16,070
+هذه، هذه الأصل هتكون إيش؟ one one صفر one صفر
+
+484
+00:39:18,490 --> 00:39:24,850
+one تعكسوها زائد واحد عشان
+
+485
+00:39:24,850 --> 00:39:31,650
+تجيب ال two's complement طيب هاي صفر صفر واحد واحد
+
+486
+00:39:31,650 --> 00:39:36,630
+صفر واحد okay هذه بتجمع مع مين مع ال term هذا واحد
+
+487
+00:39:36,630 --> 00:39:42,670
+واحد واحد واحد صفر هنجمحها مع صفر صفر واحد واحد
+
+488
+00:39:42,670 --> 00:39:43,750
+صفر واحد
+
+489
+00:39:47,570 --> 00:39:51,070
+هو أصلا هيك هيك هيروح هيروح، ماتجلوش، هيروح هيروح،
+
+490
+00:39:51,070 --> 00:39:53,190
+لإن احنا ندوس إلى واحد، اتنين، تلاتة، أربعة، خمسة،
+
+491
+00:39:53,190 --> 00:39:56,110
+بس، هيك هيك هدى حاطير حاطير هالوقت مع الجامعة
+
+492
+00:39:56,110 --> 00:40:02,930
+يعنى، طيب، صفر، واحد، زيرو، واحد، واحد، واحد،
+
+493
+00:40:02,930 --> 00:40:09,770
+واحد، واحد، واحد، زيرو، و هنا زيرو، واحد، واحد،
+
+494
+00:40:09,770 --> 00:40:13,650
+اتنين، تلاتة، أربعة، خمسة، stop، overflow، خلاص هي
+
+495
+00:40:13,650 --> 00:40:14,150
+الرقم طبعا
+
+496
+00:40:16,950 --> 00:40:22,190
+هي الرقم تبعكم خلصنا okay هاي خارج القسمة تبعتنا
+
+497
+00:40:22,190 --> 00:40:25,170
+هاد ال a اللي جديدة هال وجدت ال a اللي بنشتغل
+
+498
+00:40:25,170 --> 00:40:34,190
+عليها طيب خلصنا بنيجي للمين للواحد عند الواحد بهذا
+
+499
+00:40:34,190 --> 00:40:43,170
+الشكل هاي D زائد 1 صفر اكبر من او تساوي ال D اه
+
+500
+00:40:43,170 --> 00:40:45,150
+تساوي ال D بيساوي بعض
+
+501
+00:40:49,060 --> 00:40:56,480
+كويس و بنحط واحد و بنحط واحد بعدين بيساوي بعض فإذا
+
+502
+00:40:56,480 --> 00:41:04,980
+Qi بيصير واحد هاي واحد Qi هي Qi هاي واحد تمام و
+
+503
+00:41:04,980 --> 00:41:11,380
+الأن جديدة طلعت zeros بعد هيك خلصنا ال loop صفر
+
+504
+00:41:15,030 --> 00:41:22,630
+إيه؟ أكبر من دي؟ طبعا هتصير دي لحالها الوجد لأن دي
+
+505
+00:41:22,630 --> 00:41:27,830
+zero صفر مافيش أصفر طب أكبر من؟ لأ مش أكبر منه
+
+506
+00:41:27,830 --> 00:41:34,690
+فإذا else دي zero خلصنا؟
+
+507
+00:41:34,690 --> 00:41:40,910
+هاي أخر رقم خلاص الناتج؟ هاي الناتج ستة في خمسة هي
+
+508
+00:41:40,910 --> 00:41:46,450
+التلاتين ستة في خمسة هاي التلاتينالتلاتين ففي
+
+509
+00:41:46,450 --> 00:41:52,270
+الآخر بترجع بمين؟ هيضل عندكم ال a الأخيرة بعد ما
+
+510
+00:41:52,270 --> 00:41:56,170
+وصلتوا للصفر آخر a بتضل هذا المفروض ال R ال
+
+511
+00:41:56,170 --> 00:41:59,410
+remainder اللي ضلت لأنه ممكن تكون ..ما تكونش zeros
+
+512
+00:41:59,410 --> 00:42:03,070
+يعني ممكن تكون مثلا one half بهذا الشكل هي أقل من
+
+513
+00:42:03,070 --> 00:42:07,010
+هذا بس إلها قيمة فتحسبوها على أساس إن هي بتصير ال
+
+514
+00:42:07,010 --> 00:42:12,780
+Rهي المتبقي من خارج القسمة المطولة المتبقي من خارج
+
+515
+00:42:12,780 --> 00:42:19,280
+القسمة المطولة طبعا ال return Q هي Q وال R هي R في
+
+516
+00:42:19,280 --> 00:42:21,640
+الحالة اللي عندنا Zero لأنه بيكبروا القسمة على بعض
+
+517
+00:42:21,640 --> 00:42:24,660
+تلاتين على خمسة فعلا بيكبر القسمة ممكن تكون أرقام
+
+518
+00:42:24,660 --> 00:42:29,000
+تكبرش القسمة لأ
+
+519
+00:42:29,000 --> 00:42:31,840
+احنا هنا بكفي بس ان نجيب ال quotient و ال
+
+520
+00:42:31,840 --> 00:42:37,430
+remainder و خلاصكأنك بتقول ايه لو قولنا مثلا واحد
+
+521
+00:42:37,430 --> 00:42:43,550
+تلاتين على خمسة هتساوي ستة واحد على خمسة
+
+522
+00:42:47,280 --> 00:42:49,980
+ال quotient و ال remainder quotient و ال remainder
+
+523
+00:42:49,980 --> 00:42:55,380
+بهذا الشكل و خلاص okay فهي ال division هى عملية ال
+
+524
+00:42:55,380 --> 00:42:59,420
+division ال .. نسيبكوا المرة الجاية هنتكلم عن
+
+525
+00:42:59,420 --> 00:43:04,600
+موضوع حلو جدا الموضوع .. المرة الجاية اللى انتوا
+
+526
+00:43:04,600 --> 00:43:09,860
+هتشتغلوه بس نعطيكوا تعريف عليه هنشتغل على ال
+
+527
+00:43:09,860 --> 00:43:12,680
+cryptography تشفير
+
+528
+00:43:16,350 --> 00:43:19,650
+إذا بدناش محاضرة خلنا نكمل، برضه هتكون هيك مقتضبة
+
+529
+00:43:19,650 --> 00:43:25,950
+صفيرة طيب فالمرة الجاية هنتكلم بس هنحاول بعجلة
+
+530
+00:43:25,950 --> 00:43:29,590
+يعني المرة الجاية تكون أصغر من هيك هنتكلم عن ال
+
+531
+00:43:29,590 --> 00:43:35,430
+cartography عن التشفير و بعدين هنتكلم عن حاجة مهمة
+
+532
+00:43:35,430 --> 00:43:38,930
+جدا تستعملوها كتير في شغلكم اللي هو تعمل
+
+533
+00:43:38,930 --> 00:43:43,580
+generation ل random valuesلقيم راندوم ليه؟ انتوا
+
+534
+00:43:43,580 --> 00:43:46,400
+بتقولوا و الله نطلع راندوم ليه مجموعة قيم كيف
+
+535
+00:43:46,400 --> 00:43:49,420
+نطلعها راندوم ليه هذه؟ هي فعليا المفروض ان انا اذا
+
+536
+00:43:49,420 --> 00:43:52,440
+بدي اعمل generation كمان مرة لنفس ال random هذه
+
+537
+00:43:52,440 --> 00:43:56,500
+المفروض اطلع نفس ال sequence كيف بدي نعمل؟
+
+538
+00:43:56,500 --> 00:43:59,180
+فحناخدها المرة الجاية ان شاء الله برضه باستخدام ال
+
+539
+00:43:59,180 --> 00:44:02,490
+modular operationو هنتكلم فيها عن ال pseudo random
+
+540
+00:44:02,490 --> 00:44:09,270
+numbers او ارقام شبه عشوائية هي هتشوفوا انتوا
+
+541
+00:44:09,270 --> 00:44:13,550
+عشوائية فهتتخيل ان والله الأرقام مش مرتبة و مستحيل
+
+542
+00:44:13,550 --> 00:44:15,930
+اعرف اجيبهم من بعض لانه ممكن يكون ال sequence كتير
+
+543
+00:44:15,930 --> 00:44:18,770
+جدا ألاف الأرقام ورا بعض بس ألاف الأرقام ورا بعض
+
+544
+00:44:18,770 --> 00:44:22,690
+هدولة اللي عملهم generation عملهم بمن code محدد
+
+545
+00:44:23,010 --> 00:44:26,170
+بقدر يرجع يعملهم generation كمان مرة .. بقدر يرجع
+
+546
+00:44:26,170 --> 00:44:28,750
+يعملهم generation كمان مرة .. هذه بتفيدنا جدا في
+
+547
+00:44:28,750 --> 00:44:32,670
+عملية ال cryptography اللي هي عملية التشفير .. في
+
+548
+00:44:32,670 --> 00:44:35,430
+عملية التشفير لإنه بكل بساطة ممكن sequence معين
+
+549
+00:44:35,430 --> 00:44:39,090
+تضربوه في ال sequence of random هدولة فيطلع معلومة
+
+550
+00:44:39,090 --> 00:44:42,850
+مختلفة و تبعتوها اللي هيشوفها مش فاهم منها حاجة ..
+
+551
+00:44:42,850 --> 00:44:45,470
+اللي هيشوفها مش هيكون فاهم منها حاجة فبنخلي الكلام
+
+552
+00:44:45,470 --> 00:44:49,770
+هذا للمرة الجاية ان شاء الله تعالى و بنبدأ بموضوع
+
+553
+00:44:49,770 --> 00:44:51,690
+ان شاء الله تعالى .. يعطيكوا العافية و ربنا يوفقك
+
+554
+00:44:51,690 --> 00:44:52,130
+و ربنا يوفقك
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f47034c3ff8ee3a0fbdc8a1b6fe69236ebbe50fb
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/DvOmNMSO6nc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4213, "start": 20.97, "end": 42.13, "text": "بسم الله الرحمن الرحيم الصلاة والسلام علي أشرف الأنبياء والأبساطري سيدنا محمد وعلي أليه وصحبه أجمعين بنكمل اليوم في ال numbers theory وصلنا يمكن ل ال modulus و ال modular system و ال modular و أخدنا أخر شكل اللي هي ال spiral visualization", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 16070, 3794, 37440, 25894, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 10721, 3555, 3794, 41193, 16572, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 20292, 5551, 20292, 3224, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 44945, 24793, 1211, 45595, 20498, 8978, 2423, 3547, 5261, 4032, 36520, 8315, 7251, 43020, 5296, 2423, 42287, 4032, 2423, 31111, 1185, 4032, 2423, 31111, 4032, 5551, 9778, 3215, 8315, 5551, 34740, 13412, 28820, 13672, 1829, 39896, 2423, 25165, 25801], "avg_logprob": -0.19041894883899899, "compression_ratio": 1.6816143497757847, 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Euclid's Algorithm هو Algorithm عنده .. Euclid بده يجيب لنا و يحسب لنا فيه ال greatest common divisor .. ال greatest common divisor احنا قبل كده اشتغلنا على greatest common divisor باستخدام", "tokens": [9566, 1829, 3555, 11, 462, 1311, 75, 327, 311, 35014, 6819, 76, 4386, 462, 1311, 75, 327, 311, 35014, 6819, 76, 31439, 35014, 6819, 76, 43242, 3224, 4386, 462, 1311, 75, 327, 47525, 3224, 7251, 7435, 1829, 3555, 5296, 8315, 4032, 7251, 5016, 35457, 5296, 8315, 8978, 3224, 2423, 6636, 2689, 25974, 284, 4386, 2423, 6636, 2689, 25974, 284, 1975, 5016, 8315, 12174, 36150, 9122, 3215, 3224, 1975, 8592, 2655, 17082, 1211, 8315, 15844, 6636, 2689, 25974, 284, 4724, 995, 14851, 9778, 3215, 10943], "avg_logprob": -0.2667279397740084, "compression_ratio": 1.7160493827160495, "no_speech_prob": 0.0, "words": [{"start": 218.39, "end": 219.07, "word": "طيب,", "probability": 0.84521484375}, {"start": 219.41, "end": 220.01, "word": " Euclid's", "probability": 0.73759765625}, {"start": 220.01, "end": 220.79, "word": " Algorithm", 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بديل عشان نجيب ال greatest common divisor", "tokens": [3555, 995, 14851, 9778, 3215, 10943, 2423, 5835, 5952, 2144, 4724, 995, 14851, 9778, 3215, 10943, 2423, 5835, 6771, 2423, 5835, 6771, 3714, 43020, 10874, 28259, 6055, 30544, 16247, 2288, 4587, 10943, 9122, 3555, 48923, 6156, 15042, 6055, 28543, 2288, 2407, 8592, 6055, 36520, 12610, 11296, 46599, 2655, 19913, 1211, 9284, 4724, 16254, 1211, 6225, 8592, 7649, 8717, 7435, 1829, 3555, 2423, 6636, 2689, 25974, 284], "avg_logprob": -0.2824160323214175, "compression_ratio": 1.532544378698225, "no_speech_prob": 0.0, "words": [{"start": 235.07, "end": 235.59, "word": "باستخدام", "probability": 0.8567708333333334}, {"start": 235.59, "end": 235.71, "word": " ال", "probability": 0.87744140625}, {"start": 235.71, "end": 236.05, "word": " prime", "probability": 0.26953125}, {"start": 236.05, "end": 237.27, "word": " factorization", "probability": 0.68603515625}, {"start": 237.27, "end": 237.95, "word": " باستخدام", "probability": 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"text": "أو المعامل المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من القاسم المشترك الأكبر من الق", "tokens": [10721, 2407, 9673, 3615, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 4117, 26890, 9154, 25062, 32277, 2304, 9673, 8592, 2655, 31747, 16247, 4117, 26890, 9154, 25062, 32277, 2304, 9673, 8592, 2655, 31747, 16247, 4117, 26890, 9154, 25062, 32277, 2304, 9673, 8592, 2655, 31747, 16247, 4117, 26890, 9154, 25062, 32277, 2304, 9673, 8592, 2655, 31747, 16247, 4117, 26890, 9154, 25062, 32277, 2304, 9673, 8592, 2655, 31747, 16247, 4117, 26890, 9154, 25062, 32277, 2304, 9673, 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"end": 1134.8, "word": " ثماني", "probability": 0.875732421875}, {"start": 1134.8, "end": 1136.24, "word": " في", "probability": 0.47412109375}, {"start": 1136.24, "end": 1136.72, "word": " النظام", "probability": 0.9876302083333334}, {"start": 1136.72, "end": 1137.24, "word": " الثماني،", "probability": 0.7867635091145834}, {"start": 1137.24, "end": 1138.02, "word": " كويس", "probability": 0.9386393229166666}, {"start": 1138.02, "end": 1138.42, "word": " بهذا", "probability": 0.7061767578125}, {"start": 1138.42, "end": 1138.76, "word": " الشكل", "probability": 0.99267578125}, {"start": 1138.76, "end": 1138.96, "word": " هي", "probability": 0.5546875}, {"start": 1138.96, "end": 1139.18, "word": " إنت", "probability": 0.703857421875}, {"start": 1139.18, "end": 1139.5, "word": " وصلت", "probability": 0.9230143229166666}, {"start": 1139.5, "end": 1139.74, "word": " صفر", "probability": 0.9443359375}, {"start": 1139.74, "end": 1140.46, "word": " بتجفوا،", "probability": 0.8302734375}, 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"probability": 0.9927978515625}, {"start": 1150.68, "end": 1150.8, "word": " اللي", "probability": 0.935546875}, {"start": 1150.8, "end": 1151.14, "word": " بتظهر", "probability": 0.98193359375}, {"start": 1151.14, "end": 1151.34, "word": " هنا", "probability": 0.9921875}, {"start": 1151.34, "end": 1153.76, "word": " فالأرقام", "probability": 0.9244791666666666}, {"start": 1153.76, "end": 1153.98, "word": " هذه", "probability": 0.60546875}, {"start": 1153.98, "end": 1154.6, "word": " عبارة", "probability": 0.995361328125}, {"start": 1154.6, "end": 1154.94, "word": " شوي", "probability": 0.793701171875}, {"start": 1154.94, "end": 1155.08, "word": " شوي", "probability": 0.940185546875}, {"start": 1155.08, "end": 1155.44, "word": " ناخدها", "probability": 0.8345947265625}, {"start": 1155.44, "end": 1156.82, "word": " عشرة،", "probability": 0.77392578125}, {"start": 1156.82, "end": 1157.12, "word": " اربعة", "probability": 0.67919921875}, {"start": 1157.12, "end": 1158.7, "word": " عشر،", 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"word": " hexa", "probability": 0.6993408203125}], "temperature": 1.0}, {"id": 51, "seek": 120634, "start": 1186.33, "end": 1206.35, "text": "decimal أو أكتال ل binary أو العكس لإن إحنا قولنا أصلا ال .. الأكتال و ال hexadecimal إحنا ماخدينهم من جداش عدد ال digits في ال binary جداش عدد ال digits في ال binary فلو قولنا هي إن ال number هذا binary number بدنا نحاوله لأكتال أكتال إحنا عارفين تلاتة فبنمسكهم تلاتة تلاتة كل three digits group", "tokens": [42821, 10650, 34051, 5551, 4117, 2655, 6027, 5296, 17434, 34051, 18863, 4117, 3794, 5296, 28814, 1863, 11933, 5016, 8315, 12174, 12610, 8315, 5551, 9381, 15040, 2423, 4386, 16247, 4117, 2655, 6027, 4032, 2423, 23291, 762, 66, 10650, 11933, 5016, 8315, 3714, 47283, 3215, 9957, 16095, 9154, 10874, 3215, 33599, 6225, 3215, 3215, 2423, 27011, 8978, 2423, 17434, 10874, 3215, 33599, 6225, 3215, 3215, 2423, 27011, 8978, 2423, 17434, 6156, 1211, 2407, 12174, 12610, 8315, 39896, 36145, 2423, 1230, 23758, 17434, 1230, 47525, 8315, 8717, 5016, 995, 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1281.08, "word": " adding", "probability": 0.939453125}, {"start": 1281.08, "end": 1282.46, "word": " عندكوا", "probability": 0.7630208333333334}, {"start": 1282.46, "end": 1282.6, "word": " two", "probability": 0.91845703125}, {"start": 1282.6, "end": 1283.56, "word": " numbers,", "probability": 0.80126953125}, {"start": 1283.68, "end": 1283.84, "word": " two", "probability": 0.92431640625}, {"start": 1283.84, "end": 1284.22, "word": " binary", "probability": 0.8720703125}, {"start": 1284.22, "end": 1284.68, "word": " numbers", "probability": 0.89794921875}, {"start": 1284.68, "end": 1284.92, "word": " و", "probability": 0.4375}, {"start": 1284.92, "end": 1285.06, "word": " بدكوا", "probability": 0.600830078125}, {"start": 1285.06, "end": 1285.72, "word": " تجمعوهم", "probability": 0.948974609375}, {"start": 1285.72, "end": 1286.54, "word": " فممكن", "probability": 0.8984375}, {"start": 1286.54, "end": 1287.0, "word": " نقول", "probability": 0.979248046875}, {"start": 1287.0, "end": 1288.4, "word": " say", "probability": 0.912109375}, {"start": 1288.4, "end": 1288.86, "word": " مثلا", "probability": 0.979248046875}, {"start": 1288.86, "end": 1289.26, "word": " إنه", "probability": 0.6536865234375}, {"start": 1289.26, "end": 1289.8, "word": " عندنا", "probability": 0.810302734375}, {"start": 1289.8, "end": 1290.64, "word": " واحد", "probability": 0.6275634765625}, {"start": 1290.64, "end": 1290.96, "word": " صفر", "probability": 0.91845703125}, {"start": 1290.96, "end": 1291.4, "word": " واحد", "probability": 0.990234375}, {"start": 1291.4, "end": 1291.8, "word": " و", "probability": 0.79345703125}, {"start": 1291.8, "end": 1298.32, "word": " واحد", "probability": 0.7724609375}, {"start": 1298.32, "end": 1298.54, "word": " واحد", "probability": 0.950927734375}, {"start": 1298.54, "end": 1298.88, "word": " واحد", "probability": 0.98828125}], "temperature": 1.0}, {"id": 56, "seek": 131249, "start": 1302.01, "end": 1312.49, "text": "طيب انشوف هنا في انكم procedure خلاص عارف انه احنا دخلنا على اياش على code بدنا جايدين نكتب جايدين في ال pseudocode add اه معناته واضح انه من ال add معناته هذا في عملية جمع", "tokens": [9566, 1829, 3555, 16472, 8592, 38688, 34105, 8978, 16472, 24793, 10747, 16490, 1211, 33546, 6225, 9640, 5172, 16472, 3224, 1975, 5016, 8315, 11778, 9778, 1211, 8315, 15844, 1975, 1829, 33599, 15844, 3089, 47525, 8315, 10874, 995, 25708, 9957, 8717, 4117, 2655, 3555, 10874, 995, 25708, 9957, 8978, 2423, 25505, 532, 905, 1429, 909, 1975, 3224, 20449, 8315, 47395, 4032, 46958, 5016, 16472, 3224, 9154, 2423, 909, 20449, 8315, 47395, 23758, 8978, 6225, 42213, 10632, 10874, 2304, 3615], "avg_logprob": -0.24318909759704882, "compression_ratio": 1.6826347305389222, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1302.01, "end": 1302.33, "word": "طيب", "probability": 0.8419596354166666}, {"start": 1302.33, "end": 1302.67, "word": " انشوف", "probability": 0.69482421875}, {"start": 1302.67, "end": 1302.83, "word": " هنا", 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"text": "بدي اتغير هذه اللغة ال bit summation اللي هي اتنين على اتنين floor اتنين على اتنين واحد floor واحد واحد carry صارت هنا ايش واحد واحد okay خلصنا ال S0 ال summation في ال digit الاولى صار هنا اتنين واحد افضل واحد bit summation ايه ال one", "tokens": [3555, 16254, 1975, 2655, 17082, 13546, 29538, 13672, 17082, 3660, 2423, 857, 28811, 13672, 1829, 39896, 1975, 2655, 1863, 9957, 15844, 1975, 2655, 1863, 9957, 4123, 1975, 2655, 1863, 9957, 15844, 1975, 2655, 1863, 9957, 36764, 24401, 4123, 36764, 24401, 36764, 24401, 3985, 20328, 9640, 2655, 34105, 1975, 1829, 8592, 36764, 24401, 36764, 24401, 1392, 16490, 1211, 9381, 8315, 2423, 318, 15, 2423, 28811, 8978, 2423, 14293, 42963, 12610, 7578, 20328, 9640, 34105, 1975, 2655, 1863, 9957, 36764, 24401, 1975, 5172, 11242, 1211, 36764, 24401, 857, 28811, 1975, 1829, 3224, 2423, 472], "avg_logprob": -0.28091399259464717, "compression_ratio": 1.989010989010989, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1418.97, "end": 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يتخلص هنا يتخلص ب N-1 طيب بس في SM تلاتة", "tokens": [2304, 41891, 1975, 2655, 1863, 9957, 6055, 3794, 45865, 36764, 24401, 9122, 9640, 1829, 6055, 1211, 9307, 3660, 15844, 1975, 2655, 1863, 9957, 36764, 24401, 4032, 8717, 9381, 5172, 4123, 36764, 24401, 16490, 1211, 9381, 13672, 37746, 13672, 37746, 7251, 2655, 9778, 1211, 9381, 34105, 7251, 2655, 9778, 1211, 9381, 4724, 426, 12, 16, 23032, 1829, 3555, 4724, 3794, 8978, 13115, 6055, 1211, 9307, 3660], "avg_logprob": -0.32007574583544873, "compression_ratio": 1.573643410852713, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 1503.14, "end": 1504.04, "word": "مدة", "probability": 0.541015625}, {"start": 1504.04, "end": 1504.4, "word": " اتنين", "probability": 0.8603515625}, {"start": 1504.4, "end": 1504.98, "word": " تسوي", "probability": 0.6649576822916666}, {"start": 1504.98, "end": 1505.42, "word": " واحد", "probability": 0.98388671875}, {"start": 1505.42, "end": 1507.38, "word": " كاري", "probability": 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2649.11, "word": " هتشوفوا", "probability": 0.828173828125}, {"start": 2649.11, "end": 2649.27, "word": " انتوا", "probability": 0.8629557291666666}, {"start": 2649.27, "end": 2649.79, "word": " عشوائية", "probability": 0.99345703125}, {"start": 2649.79, "end": 2651.11, "word": " فهتتخيل", "probability": 0.7641194661458334}, {"start": 2651.11, "end": 2651.23, "word": " ان", "probability": 0.84326171875}, {"start": 2651.23, "end": 2651.55, "word": " والله", "probability": 0.7213134765625}, {"start": 2651.55, "end": 2652.03, "word": " الأرقام", "probability": 0.8953857421875}, {"start": 2652.03, "end": 2652.19, "word": " مش", "probability": 0.986328125}, {"start": 2652.19, "end": 2652.69, "word": " مرتبة", "probability": 0.9580078125}, {"start": 2652.69, "end": 2653.13, "word": " و", "probability": 0.98046875}, {"start": 2653.13, "end": 2653.55, "word": " مستحيل", "probability": 0.9478759765625}, {"start": 2653.55, "end": 2653.79, "word": " اعرف", "probability": 0.8987630208333334}, {"start": 2653.79, "end": 2654.21, "word": " اجيبهم", "probability": 0.9228515625}, {"start": 2654.21, "end": 2654.37, "word": " من", "probability": 0.98828125}, {"start": 2654.37, "end": 2654.63, "word": " بعض", "probability": 0.996337890625}, {"start": 2654.63, "end": 2654.89, "word": " لانه", "probability": 0.6982421875}, {"start": 2654.89, "end": 2655.07, "word": " ممكن", "probability": 0.940185546875}, {"start": 2655.07, "end": 2655.25, "word": " يكون", "probability": 0.989990234375}, {"start": 2655.25, "end": 2655.35, "word": " ال", "probability": 0.3193359375}, {"start": 2655.35, "end": 2655.63, "word": " sequence", "probability": 0.97412109375}, {"start": 2655.63, "end": 2655.93, "word": " كتير", "probability": 0.9718424479166666}, {"start": 2655.93, "end": 2656.17, "word": " جدا", "probability": 0.97265625}, {"start": 2656.17, "end": 2656.57, "word": " ألاف", "probability": 0.6861979166666666}, {"start": 2656.57, "end": 2656.95, "word": " الأرقام", "probability": 0.988037109375}, {"start": 2656.95, "end": 2657.13, "word": " ورا", "probability": 0.7666015625}, {"start": 2657.13, "end": 2657.39, "word": " بعض", "probability": 0.9921875}, {"start": 2657.39, "end": 2657.87, "word": " بس", "probability": 0.8935546875}, {"start": 2657.87, "end": 2658.09, "word": " ألاف", "probability": 0.9173177083333334}, {"start": 2658.09, "end": 2658.43, "word": " الأرقام", "probability": 0.993896484375}, {"start": 2658.43, "end": 2658.59, "word": " ورا", "probability": 0.885986328125}, {"start": 2658.59, "end": 2658.77, "word": " بعض", "probability": 0.9892578125}, {"start": 2658.77, "end": 2659.47, "word": " هدولة", "probability": 0.8428955078125}, {"start": 2659.47, "end": 2659.63, "word": " اللي", "probability": 0.92724609375}, {"start": 2659.63, "end": 2659.93, "word": " عملهم", "probability": 0.9376627604166666}, {"start": 2659.93, "end": 2660.53, "word": " generation", "probability": 0.9306640625}, {"start": 2660.53, "end": 2661.37, "word": " عملهم", "probability": 0.9796549479166666}, {"start": 2661.37, "end": 2661.61, "word": " بمن", "probability": 0.675048828125}, {"start": 2661.61, "end": 2661.99, "word": " code", "probability": 0.626953125}, {"start": 2661.99, "end": 2662.69, "word": " محدد", "probability": 0.9967447916666666}], "temperature": 1.0}, {"id": 108, "seek": 269213, "start": 2663.01, "end": 2692.13, "text": "بقدر يرجع يعملهم generation كمان مرة .. بقدر يرجع يعملهم generation كمان مرة .. هذه بتفيدنا جدا في عملية ال cryptography اللي هي عملية التشفير .. في عملية التشفير لإنه بكل بساطة ممكن sequence معين تضربوه في ال sequence of random هدولة فيطلع معلومة مختلفة و تبعتوها اللي هيشوفها مش فاهم منها حاجة .. اللي هيشوفها مش هيكون فاهم منها حاجة فبنخلي الكلام هذا للمرة الجاية ان شاء الله تعالى و بنبدأ بموضوع ان شاء الله تعالى .. يعطيكوا العافية و ربنا يوفقك و ربنا يوفقك", "tokens": [3555, 28543, 2288, 7251, 47341, 3615, 7251, 25957, 1211, 16095, 5125, 9122, 2304, 7649, 3714, 25720, 4386, 4724, 28543, 2288, 7251, 47341, 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11242, 45367, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 4386, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 4032, 12602, 3555, 8315, 7251, 38688, 4587, 4117, 4032, 12602, 3555, 8315, 7251, 38688, 4587, 4117], "avg_logprob": -0.154186320473563, "compression_ratio": 2.247093023255814, "no_speech_prob": 1.4662742614746094e-05, "words": [{"start": 2663.01, "end": 2663.51, "word": "بقدر", "probability": 0.8987630208333334}, {"start": 2663.51, "end": 2663.87, "word": " يرجع", "probability": 0.9698893229166666}, {"start": 2663.87, "end": 2664.25, "word": " يعملهم", "probability": 0.9405517578125}, {"start": 2664.25, "end": 2664.61, "word": " generation", "probability": 0.93701171875}, {"start": 2664.61, "end": 2664.93, "word": " كمان", "probability": 0.9710286458333334}, {"start": 2664.93, "end": 2665.17, "word": " مرة", "probability": 0.979736328125}, {"start": 2665.17, "end": 2665.57, "word": " ..", "probability": 0.486328125}, {"start": 2665.57, "end": 2665.89, "word": " بقدر", "probability": 0.9034830729166666}, {"start": 2665.89, "end": 2666.17, "word": " يرجع", "probability": 0.9889322916666666}, {"start": 2666.17, "end": 2666.47, "word": " يعملهم", "probability": 0.987060546875}, {"start": 2666.47, "end": 2666.77, "word": " generation", "probability": 0.9697265625}, {"start": 2666.77, "end": 2667.05, "word": " كمان", "probability": 0.9931640625}, {"start": 2667.05, "end": 2667.29, "word": " مرة", "probability": 0.985595703125}, {"start": 2667.29, "end": 2667.59, "word": " ..", "probability": 0.65380859375}, {"start": 2667.59, "end": 2667.75, "word": " هذه", "probability": 0.1851806640625}, {"start": 2667.75, "end": 2668.25, "word": " بتفيدنا", "probability": 0.9515380859375}, {"start": 2668.25, "end": 2668.57, "word": " جدا", "probability": 0.987548828125}, {"start": 2668.57, "end": 2668.75, "word": " في", "probability": 0.7705078125}, {"start": 2668.75, "end": 2669.05, "word": " عملية", "probability": 0.9817708333333334}, {"start": 2669.05, "end": 2669.23, "word": " ال", "probability": 0.6708984375}, {"start": 2669.23, "end": 2669.77, "word": " cryptography", "probability": 0.656982421875}, {"start": 2669.77, "end": 2670.99, "word": " اللي", "probability": 0.8583984375}, {"start": 2670.99, "end": 2671.11, "word": " هي", "probability": 0.92236328125}, {"start": 2671.11, "end": 2671.39, "word": " عملية", "probability": 0.9793294270833334}, {"start": 2671.39, "end": 2672.13, "word": " التشفير", "probability": 0.9591064453125}, {"start": 2672.13, "end": 2672.55, "word": " ..", "probability": 0.86865234375}, {"start": 2672.55, "end": 2672.67, "word": " في", "probability": 0.197998046875}, {"start": 2672.67, "end": 2672.95, "word": " عملية", "probability": 0.9677734375}, {"start": 2672.95, "end": 2673.47, "word": " التشفير", "probability": 0.99072265625}, {"start": 2673.47, "end": 2673.73, "word": " لإنه", "probability": 0.7694091796875}, {"start": 2673.73, "end": 2673.99, "word": " بكل", "probability": 0.978759765625}, {"start": 2673.99, "end": 2674.31, "word": " بساطة", "probability": 0.982666015625}, {"start": 2674.31, "end": 2674.61, "word": " ممكن", "probability": 0.957763671875}, {"start": 2674.61, "end": 2674.99, "word": " sequence", "probability": 0.85546875}, {"start": 2674.99, "end": 2675.43, "word": " معين", "probability": 0.981689453125}, {"start": 2675.43, "end": 2676.13, "word": " تضربوه", "probability": 0.91171875}, {"start": 2676.13, "end": 2676.21, "word": " في", "probability": 0.9384765625}, {"start": 2676.21, "end": 2676.33, "word": " ال", "probability": 0.93896484375}, {"start": 2676.33, "end": 2676.63, "word": " sequence", "probability": 0.96484375}, {"start": 2676.63, "end": 2676.83, "word": " of", "probability": 0.93505859375}, {"start": 2676.83, "end": 2677.13, "word": " random", "probability": 0.74560546875}, {"start": 2677.13, "end": 2677.65, "word": " هدولة", "probability": 0.83740234375}, {"start": 2677.65, "end": 2678.77, "word": " فيطلع", "probability": 0.78447265625}, {"start": 2678.77, "end": 2679.09, "word": " معلومة", "probability": 0.9815673828125}, {"start": 2679.09, "end": 2679.61, "word": " مختلفة", "probability": 0.989990234375}, {"start": 2679.61, "end": 2679.89, "word": " و", "probability": 0.69189453125}, {"start": 2679.89, "end": 2680.43, "word": " تبعتوها", "probability": 0.97958984375}, {"start": 2680.43, "end": 2680.89, "word": " اللي", "probability": 0.899658203125}, {"start": 2680.89, "end": 2681.29, "word": " هيشوفها", "probability": 0.88330078125}, {"start": 2681.29, "end": 2681.43, "word": " مش", "probability": 0.9814453125}, {"start": 2681.43, "end": 2681.85, "word": " فاهم", "probability": 0.8499348958333334}, {"start": 2681.85, "end": 2682.05, "word": " منها", "probability": 0.9560546875}, {"start": 2682.05, "end": 2682.63, "word": " حاجة", "probability": 0.9952799479166666}, {"start": 2682.63, "end": 2682.85, "word": " ..", "probability": 0.685546875}, {"start": 2682.85, "end": 2682.95, "word": " اللي", "probability": 0.988525390625}, {"start": 2682.95, "end": 2683.27, "word": " هيشوفها", "probability": 0.9649658203125}, {"start": 2683.27, "end": 2683.39, "word": " مش", "probability": 0.990234375}, {"start": 2683.39, "end": 2683.61, "word": " هيكون", "probability": 0.89501953125}, {"start": 2683.61, "end": 2683.83, "word": " فاهم", "probability": 0.97314453125}, {"start": 2683.83, "end": 2684.11, "word": " منها", "probability": 0.99365234375}, {"start": 2684.11, "end": 2684.65, "word": " حاجة", "probability": 0.9832356770833334}, {"start": 2684.65, "end": 2685.19, "word": " فبنخلي", "probability": 0.677587890625}, {"start": 2685.19, "end": 2685.47, "word": " الكلام", "probability": 0.9697265625}, {"start": 2685.47, "end": 2685.65, "word": " هذا", "probability": 0.87109375}, {"start": 2685.65, "end": 2685.97, "word": " للمرة", "probability": 0.9599609375}, {"start": 2685.97, "end": 2686.17, "word": " الجاية", "probability": 0.8904622395833334}, {"start": 2686.17, "end": 2686.31, "word": " ان", "probability": 0.576171875}, {"start": 2686.31, "end": 2686.43, "word": " شاء", "probability": 0.91259765625}, {"start": 2686.43, "end": 2686.53, "word": " الله", "probability": 0.9443359375}, {"start": 2686.53, "end": 2686.85, "word": " تعالى", "probability": 0.9422200520833334}, {"start": 2686.85, "end": 2686.97, "word": " و", "probability": 0.86181640625}, {"start": 2686.97, "end": 2687.73, "word": " بنبدأ", "probability": 0.8323567708333334}, {"start": 2687.73, "end": 2689.77, "word": " بموضوع", "probability": 0.8505859375}, {"start": 2689.77, "end": 2689.91, "word": " ان", "probability": 0.7353515625}, {"start": 2689.91, "end": 2690.09, "word": " شاء", "probability": 0.9599609375}, {"start": 2690.09, "end": 2690.15, "word": " الله", "probability": 0.9541015625}, {"start": 2690.15, "end": 2690.35, "word": " تعالى", "probability": 0.7744954427083334}, {"start": 2690.35, "end": 2690.43, "word": " ..", "probability": 0.384033203125}, {"start": 2690.43, "end": 2690.63, "word": " يعطيكوا", "probability": 0.8455078125}, {"start": 2690.63, "end": 2690.97, "word": " العافية", "probability": 0.8753255208333334}, {"start": 2690.97, "end": 2691.13, "word": " و", "probability": 0.8095703125}, {"start": 2691.13, "end": 2691.33, "word": " ربنا", "probability": 0.8946940104166666}, {"start": 2691.33, "end": 2691.69, "word": " يوفقك", "probability": 0.775390625}, {"start": 2691.69, "end": 2691.71, "word": " و", "probability": 0.572265625}, {"start": 2691.71, "end": 2691.85, "word": " ربنا", "probability": 0.9091796875}, {"start": 2691.85, "end": 2692.13, "word": " يوفقك", "probability": 0.6700439453125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2693.14325, "duration_after_vad": 2587.2987499999886}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U.srt
new file mode 100644
index 0000000000000000000000000000000000000000..47d1ce8f5957bf5dab2a6c0884fe6b99720ed0a9
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U.srt
@@ -0,0 +1,2657 @@
+1
+00:00:20,960 --> 00:00:22,980
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:22,980 --> 00:00:25,680
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,680 --> 00:00:29,980
+أجمعين. نفتح اليوم لقائنا إن شاء الله، محاضرتنا
+
+4
+00:00:29,980 --> 00:00:36,260
+استكمالا لما سبق الحديث عنه بموضوع الـ algorithms
+
+5
+00:00:36,260 --> 00:00:40,600
+المرة اللي فاتت، بدأنا بالـ algorithms، واتكلمنا أنه
+
+6
+00:00:40,600 --> 00:00:43,540
+في عندنا language وسميناها informal programming
+
+7
+00:00:43,540 --> 00:00:47,720
+language.  الـ language بتختلف عن الـ real languages الـ
+
+8
+00:00:47,720 --> 00:00:50,520
+real languages هذه. المفروض تكون كل مبرمج عنده
+
+9
+00:00:50,520 --> 00:00:54,520
+واحدة على الأقل متقنها جيدا، بصورة كتير كويسة عشان
+
+10
+00:00:54,520 --> 00:00:58,840
+يشتغل، يبرمج فيها. أما الـ pseudocode language اللي
+
+11
+00:00:58,840 --> 00:01:02,810
+اتكلمنا عنها المرة السابقة، as informal لغة هذه
+
+12
+00:01:02,810 --> 00:01:09,590
+للكتابة، للبحث المكتوب، هذه للتعارف بين المبرمجين
+
+13
+00:01:09,590 --> 00:01:12,510
+وبعضهم على أساس إنه يعرفوا كيف الـ sequence اللي
+
+14
+00:01:12,510 --> 00:01:15,710
+انعمل فيه الـ code، كيف الـ algorithm انعمل كـ steps
+
+15
+00:01:15,710 --> 00:01:19,830
+كخطوات، كـ procedures. تمام؟ المرة اللي فاتت، بدأ أنا
+
+16
+00:01:19,830 --> 00:01:23,630
+قولنا أنه الـ .. الـ pseudocode بيتكون من مجموعة
+
+17
+00:01:23,630 --> 00:01:27,430
+عناصر، أهمها عناصر المهمين كتير اللي هم الـ
+
+18
+00:01:27,430 --> 00:01:31,770
+declaration، الإعلان أو افتتاح الـ .. الـ code أنه
+
+19
+00:01:31,770 --> 00:01:35,830
+والله يا قارئ في code، بدنا بدناش نتعامل عليه الـ
+
+20
+00:01:35,830 --> 00:01:42,310
+declaration. هنتكلم عنه في مجموعة other comments
+
+21
+00:01:42,310 --> 00:01:46,140
+هذه. اسمها statements. كل الـ statement إلها task
+
+22
+00:01:46,140 --> 00:01:50,080
+محددة، إلها وظيفة محددة، هنمسكهم لواحدة واحدة
+
+23
+00:01:50,080 --> 00:01:53,780
+الـ tasks هذه، ونتعامل معها، وأتوقع في منهم حاجات
+
+24
+00:01:53,780 --> 00:01:56,420
+حتى باقية ممكن أخدتوها في البرمجة، مرت عليكم في
+
+25
+00:01:56,420 --> 00:02:00,920
+برمجة قبل هيك، فالجزء اليوم هيكون كتير فيه جزء شغل
+
+26
+00:02:00,920 --> 00:02:07,900
+برمجة، ولكن زي ما قولنا هو informal language. طيب،
+
+27
+00:02:07,900 --> 00:02:13,220
+نبدأ على بركة الله في الـ pseudocode. نتكلم عن
+
+28
+00:02:13,220 --> 00:02:18,340
+declaration ابتدائنا، وبعدين إن نعرج على مجموعة
+
+29
+00:02:18,340 --> 00:02:21,830
+statements. نحن نعرفها إيش بالظبط، كيف تشتغل، عشان
+
+30
+00:02:21,830 --> 00:02:25,350
+نبدأ نكتب أكواد من أنفسنا. عادة نبدأ نكتب code، كل
+
+31
+00:02:25,350 --> 00:02:29,650
+شغل بناخدها، نكون قادرين إن احنا نعملها code، أو
+
+32
+00:02:29,650 --> 00:02:34,470
+على الأقل نوصف الـ steps بتاعت الـ code بتاعتها
+
+33
+00:02:34,470 --> 00:02:38,910
+فابتداء بالـ procedure، وبنعمل الـ procedure name
+
+34
+00:02:38,910 --> 00:02:44,550
+وبين قوسين بنعمل مجموعة الـ arguments. نقطتين هذه
+
+35
+00:02:44,550 --> 00:02:47,610
+standard، لازم تتعاملوا معها بهذا الشكل، الـ standard
+
+36
+00:02:47,610 --> 00:02:51,530
+وبتحطوا الـ type تبع الـ arguments. نمسكهم حاجة حاجة
+
+37
+00:02:51,530 --> 00:02:56,670
+الـ procedure بنحطها بشكل bold. تعريفا إن والله في
+
+38
+00:02:56,670 --> 00:03:00,550
+code بدأنا فيه، تعريفا إن والله في code بدأنا نشتغل
+
+39
+00:03:00,550 --> 00:03:06,350
+عليه. طيب الـ code هذا بنحط له اسم، بنستعمله اسم، الاسم
+
+40
+00:03:07,380 --> 00:03:10,620
+و هذا الكلام يفضل تعمله في معظم الشغل، كل البرمجة
+
+41
+00:03:10,620 --> 00:03:14,840
+بتاعتكم، دايما اسم الـ code يكون معبر عن الـ task
+
+42
+00:03:14,840 --> 00:03:17,960
+بتاعة الـ code، يكون معبر عن الـ task بتاع الـ code
+
+43
+00:03:17,960 --> 00:03:21,200
+بيريحكوا بعدين لما تعملوا الـ code، وترجعوا له بعد
+
+44
+00:03:21,200 --> 00:03:24,080
+شهرين، بعد تلت شهور، بعد خمس شهور، تكونوا على الأقل
+
+45
+00:03:24,080 --> 00:03:28,160
+عارفين لإيش الـ code هذا. الحاجة التانية، الـ code جدعا
+
+46
+00:03:28,160 --> 00:03:34,960
+بتحطوا له اسم معبر عنه. قد تحتاجوا الـ code كـ function
+
+47
+00:03:36,170 --> 00:03:41,890
+أو subroutine، أو code تستعملوه في code، في code
+
+48
+00:03:41,890 --> 00:03:46,970
+ثاني، تعملوا له استدعاء،  يتنفذ شغله، ويرجعه، فبده
+
+49
+00:03:46,970 --> 00:03:51,030
+يكون له معنى. طيب زي ما قولنا procedure، هذي ثابتة
+
+50
+00:03:51,030 --> 00:03:54,570
+بتكتبوها بهذا الشكل، الـ procedure name، أنتو بتحطوا
+
+51
+00:03:54,570 --> 00:03:58,590
+اسم من عندكم، بس يعبر عن الـ task بتاعة الـ code اللي
+
+52
+00:03:58,590 --> 00:04:02,970
+مش بده يعمل بالظبط. طيب argument، مجموعة الـ inputs
+
+53
+00:04:04,430 --> 00:04:07,230
+إيش هي الـ inputs اللي بتكون تشتغلوا عليها؟ يعني
+
+54
+00:04:07,230 --> 00:04:10,950
+إيش الـ input تبع الـ code؟ بتكون تحددوهم هنا، بعدين
+
+55
+00:04:10,950 --> 00:04:16,310
+نقطتين، تحددوا الـ type تبعهم، إيش نوعهم؟ إيش نوعهم؟
+
+56
+00:04:16,310 --> 00:04:20,570
+كويس. فهذه كل الجزئية، مجرد عملية declaration، هي
+
+57
+00:04:20,570 --> 00:04:26,290
+إعلان إن والله الـ text اللي جاي هو code، هو هذا مش
+
+58
+00:04:26,290 --> 00:04:29,110
+paragraph عادي، هذا code، بدنا ناخد بالنا منه. For
+
+59
+00:04:29,110 --> 00:04:33,840
+example: procedure هي، خلاص بعرف إن أنا داخل على إيش
+
+60
+00:04:33,840 --> 00:04:37,680
+على code، maximum. لاحظوا الاسم، يعطيني حق معناه
+
+61
+00:04:37,680 --> 00:04:42,100
+واضح إنه بدور على maximum، الـ task maximum، بدور على
+
+62
+00:04:42,100 --> 00:04:45,000
+قيمة maximum، من إيش؟ من مجموعة inputs، الشيء الـ
+
+63
+00:04:45,000 --> 00:04:49,600
+inputs عبارة عن list L. بعرف إن الـ list اللي
+
+64
+00:04:49,600 --> 00:04:52,860
+اسمها L فيها مجموعة عناصر، بدي أطلع الـ maximum
+
+65
+00:04:52,860 --> 00:04:57,100
+value منهم. فبيعطيني indication لإيش. طيب إيش نوعهم
+
+66
+00:04:57,100 --> 00:05:00,780
+الـ elements داخل الـ list هذه، أو الـ list إيش نوعها؟
+
+67
+00:05:00,780 --> 00:05:03,680
+list of integers. بعرف إن أنا بتكلم عن integers
+
+68
+00:05:03,680 --> 00:05:07,820
+بناء على ذلك، بكون عامل حساباتي في الـ code إن أنا
+
+69
+00:05:07,820 --> 00:05:10,580
+بتعامل مع integers، بتعاملش مع real numbers مثلا
+
+70
+00:05:10,580 --> 00:05:14,960
+تمام. وبعدين بعد هيك، خلاص هذه عملية الـ declaration
+
+71
+00:05:14,960 --> 00:05:20,280
+أعلنّا عن إنه الـ text اللي جاي code، فبتعامل معه مع
+
+72
+00:05:20,280 --> 00:05:23,060
+مجموعة الـ statements اللي جاية على أساس إن هي
+
+73
+00:05:23,060 --> 00:05:28,540
+acquired، إنه هذا code برمجي، كويس. أول statement
+
+74
+00:05:28,540 --> 00:05:32,500
+هنتعامل معها، اللي هي تعريف الـ variable، كيف نكتب
+
+75
+00:05:32,500 --> 00:05:35,840
+variable، ونعمل له expression معين، نعمله تعريف،
+
+76
+00:05:35,840 --> 00:05:41,660
+نعمل له معادلة، نعمله formulation، فبدكتب variable، لا
+
+77
+00:05:41,660 --> 00:05:44,600
+نضع علامة يساوي، في نقطتين، قبل علامة يساوي، وبعدين
+
+78
+00:05:44,600 --> 00:05:47,200
+علامة يساوي، فالـ variable هدأش بيساوي expression
+
+79
+00:05:47,200 --> 00:05:51,780
+ممكن نضع، إما معادلة، أو لأن احنا بنتكلم عن informal
+
+80
+00:05:51,780 --> 00:05:54,980
+language، إذا كان المعادلة ممكن تكون طويلة، وأنتم
+
+81
+00:05:54,980 --> 00:05:58,600
+مش عارفينها بالظبط، ممكن تكتبوا جملة، بس تكون مختصرة
+
+82
+00:05:58,600 --> 00:06:02,540
+جدا، وتعبر عن الـ variable هدأش بالشو بالظبط. زي
+
+83
+00:06:02,540 --> 00:06:07,440
+ممكن نقول v بتساوي تلاتة x plus سبعة، equation
+
+84
+00:06:07,440 --> 00:06:14,180
+مافيش مشكلة، خلاص. بناء على قيمة X التي سابقة موجودة
+
+85
+00:06:14,180 --> 00:06:17,360
+في الكود، سأعوض فيها هنا، لكي أحصل على قيمة V. لا
+
+86
+00:06:17,360 --> 00:06:20,780
+مشكلة فيها، تشوف قيمة X، لو X مثلا باتنين، معناته
+
+87
+00:06:20,780 --> 00:06:26,880
+تتغير V إلى 13، نحولها إلى 13، لكي 6 زائد 7، نحصل
+
+88
+00:06:26,880 --> 00:06:30,540
+عليها. طيب وباعتبار زي ما قلنا أننا نتعامل مع
+
+89
+00:06:33,730 --> 00:06:37,770
+ممكن أكتبها بهذا الشكل X، بس لازم أحافظ على إيه؟
+
+90
+00:06:37,770 --> 00:06:41,730
+على يساوي، بهذا الشكل. قصة the largest integer in
+
+91
+00:06:41,730 --> 00:06:45,890
+the last cell، ممكن أكتبها بهذا الشكل، ممكن تكون
+
+92
+00:06:45,890 --> 00:06:50,330
+الجزء هذا بدي أجيب من subroutine ثانية موجودة من
+
+93
+00:06:50,330 --> 00:06:54,470
+function موجودة، استدعيها، أجيب الـ maximum، أو the
+
+94
+00:06:54,470 --> 00:06:57,710
+largest integer، موجودة هنا، فبعرفه على أساس إن هذا
+
+95
+00:06:57,710 --> 00:07:01,340
+X بتساوي كذا. لأنه زي ما قلنا، أنتو مش هتكتبوها ده
+
+96
+00:07:01,340 --> 00:07:05,400
+لا في Java، ولا أنتو، مجرد بس بدي أعمل وصف، كيف بدي
+
+97
+00:07:05,400 --> 00:07:08,800
+أفكر في كتابة الـ code، كيف بنفكر في كتابة الـ code،
+
+98
+00:07:08,800 --> 00:07:14,350
+كيف بنكتب الـ code، تمام. مدام informal statement، زي
+
+99
+00:07:14,350 --> 00:07:18,310
+ما قلنا، ممكن نكتبها كتابة، بس في أضيق الظروف جدعا
+
+100
+00:07:18,310 --> 00:07:22,370
+تقدر تحط الـ formulation، بيكون أفضل. ما قدرناش بتكون
+
+101
+00:07:22,370 --> 00:07:26,110
+مختصرة جدا، إنه نكتبش paragraph كامل، يعني مش هنكتب
+
+102
+00:07:26,110 --> 00:07:30,070
+paragraph، نقول x بتساوي كذا، لما يكون كذا، وأنا مش
+
+103
+00:07:30,070 --> 00:07:34,430
+عارف إيش بتساوي كذا. لأ، هذه بتكتبوها بس في حالات
+
+104
+00:07:34,430 --> 00:07:38,670
+مختصرة جدا، زي لما تكون تعملوا code، تقولوا أو
+
+105
+00:07:38,670 --> 00:07:43,290
+تشتغلوا، وبعدين تكتبوا swap x and y. swap x and y
+
+106
+00:07:43,290 --> 00:07:47,530
+بدي x و y تكونوا محتاجين أثناء الشغل، وهنحتاج آخر
+
+107
+00:07:47,530 --> 00:07:52,730
+المحاضرة، في آخر المحاضرة هنشتغل على code محتاجين
+
+108
+00:07:52,730 --> 00:07:57,470
+نعمل swap. فممكن وإحنا بنشتغل أكون عرفت x و y، و
+
+109
+00:07:57,470 --> 00:08:02,030
+أقول الله، إذا كان x أكبر من y، swap x و y، عشان إن
+
+110
+00:08:02,030 --> 00:08:06,790
+أنا دايما بدي x هي القيمة الكبيرة. فممكن نكتبها بهذا
+
+111
+00:08:06,790 --> 00:08:08,750
+الشكل. طبعا أنتو عارفين إنه في الـ .. في الـ real
+
+112
+00:08:08,750 --> 00:08:11,290
+programming language، هذه لها شغلة بتكون تعملوها
+
+113
+00:08:11,290 --> 00:08:15,770
+condition، أول، بناء على الـ condition بتقولوا، بتحط
+
+114
+00:08:15,770 --> 00:08:19,250
+هذه في temporary variable، وهذه مكان هذه، وبعدين
+
+115
+00:08:19,250 --> 00:08:23,050
+بتحولوا عليها. يعني في لها جزئية بتكونوا عارفينها
+
+116
+00:08:23,050 --> 00:08:26,430
+احنا هنا لأ، بغض النظر عن إيش الجزئية البرمجية
+
+117
+00:08:26,430 --> 00:08:29,930
+هنقول والله الهدف من الـ code تبعنا، أو في الجزئية
+
+118
+00:08:29,930 --> 00:08:34,370
+هدف الـ line هذا، إننا نعمل swap x مع y، هذي تيجي
+
+119
+00:08:34,370 --> 00:08:39,550
+مكان هذه، وهذي تيجي مكان هذه. Okay. في الـ real
+
+120
+00:08:39,550 --> 00:08:42,230
+programming، طبعا الكلام غير مسموح في الـ real
+
+121
+00:08:42,230 --> 00:08:45,990
+programming اللي بتكلم عن C++، أو بتكلم عن الـ Java
+
+122
+00:08:45,990 --> 00:08:50,390
+مش مسموح الكلام بهذا الشكل. طيب مش معناه هيك إنه
+
+123
+00:08:50,390 --> 00:08:55,250
+نروح نقول .. نعمل مجموعة lines، وبعدين نقول do so
+
+124
+00:08:55,250 --> 00:08:59,870
+and so on، أو إلى آخره مثلا، أو استمر في ذلك، أو .. لأ
+
+125
+00:08:59,870 --> 00:09:02,910
+لازم يكون الوصف واضح. مش معناه إن هي informal
+
+126
+00:09:02,910 --> 00:09:06,970
+ما تكونش واضحة، لازم نعمل breakdown للـ algorithm
+
+127
+00:09:06,970 --> 00:09:13,590
+تبعنا بـ steps، خطوات توضح .. توضح بالظبط الـ code، أو
+
+128
+00:09:13,590 --> 00:09:17,490
+الـ algorithm كيف ماشي. خطوات الـ algorithm مهمة جدا
+
+129
+00:09:17,490 --> 00:09:23,990
+okay. الـ statement الثانية begin and end، تستخدم
+
+130
+00:09:23,990 --> 00:09:27,530
+لاحقا مع مجموعة statements ثانية، مجموعة الـ
+
+131
+00:09:27,530 --> 00:09:30,790
+statements، عادة اللي هنشتغل فيها، خصوصا اللي بتكون
+
+132
+00:09:30,790 --> 00:09:36,090
+في الـ loops، سواء الـ for loop، أو الـ while loop، الـ
+
+133
+00:09:36,090 --> 00:09:38,790
+for loop، أو الـ while loop، بتعاملوا مع الـ statement
+
+134
+00:09:38,790 --> 00:09:44,010
+اللي وراها مباشرة بس، وخلاص بنفذ، بيعمل execution للـ
+
+135
+00:09:44,010 --> 00:09:46,190
+statement اللي وراها، وبعدين برجع للـ loop ثاني
+
+136
+00:09:46,190 --> 00:09:50,030
+احنا ممكن جدا نكون محتاجين نعمل أكثر من statement
+
+137
+00:09:51,060 --> 00:09:53,940
+هنحتاج في أكواد كتير، أن نكون أكثر من الـ statement
+
+138
+00:09:53,940 --> 00:09:56,740
+واحدة. طب في الحالة دي إيش هنعمل؟ عادي بنكتب كل الـ
+
+139
+00:09:56,740 --> 00:10:00,620
+statements، نبدأها بـ begin، وننهيها بـ end، فبعرف إن
+
+140
+00:10:00,620 --> 00:10:04,680
+بين begin و end، هدول كلهم بتعاملوا كإنهم statement
+
+141
+00:10:04,680 --> 00:10:10,100
+واحدة، كإنهم group واحد. بنفعش أنفذ واحدة وأسيب
+
+142
+00:10:10,100 --> 00:10:14,420
+الباقي، أرجع للـ for تبعتي، كله هيتنفذ بعد الـ end
+
+143
+00:10:14,420 --> 00:10:20,130
+برجع للـ loop، للـ for أول .. أو حتى في الـ if then
+
+144
+00:10:20,130 --> 00:10:24,630
+في الـ if then، then ممكن تتعامل مع أول line بس معها
+
+145
+00:10:24,630 --> 00:10:28,690
+لأ، أنا بديها تتعامل مع three statements، بحط begin
+
+146
+00:10:28,690 --> 00:10:32,310
+end للتلاتة، للتلاتة statements، بعرف إن كل هدولة
+
+147
+00:10:32,310 --> 00:10:36,430
+هيتنفذوا إذا تحققت .. إذا تحقق الـ condition تبع الـ
+
+148
+00:10:36,430 --> 00:10:40,950
+if، فبحقق الـ three statements، أو بنفذ الـ three ..
+
+149
+00:10:40,950 --> 00:10:45,080
+الـ three statements بتاعة then، بتاعة then. كويس. زي
+
+150
+00:10:45,080 --> 00:10:49,680
+ما قولنا، هذه ممكن نستعملها لحقيقة إن كل مجموعة
+
+151
+00:10:49,680 --> 00:10:53,120
+sequence من الـ statements، نتعامل معها، إذا إيش
+
+152
+00:10:53,120 --> 00:10:56,560
+single statement، أو group واحد، كله لازم يتنفذ مع
+
+153
+00:10:56,560 --> 00:11:00,960
+بعض، الـ execution لازم لكل مع بعض. okay، هذه ممكن
+
+154
+00:11:00,960 --> 00:11:04,300
+نستخدمها أكثر شيء. يعني ممكن تيجي بعد الـ procedure
+
+155
+00:11:04,300 --> 00:11:09,060
+في الـ declaration، غالبا تيجي مع الـ if then، لأن if
+
+156
+00:11:09,060 --> 00:11:14,460
+then else، بعد الـ then هيكون فيه مجموعة statements، و
+
+157
+00:11:14,460 --> 00:11:17,240
+بعد الـ else هيكون فيه مجموعة statements. هو بيتعامل
+
+158
+00:11:17,240 --> 00:11:19,720
+معاها إن هي statement واحدة. لأ، أنا بدي مجموعة
+
+159
+00:11:19,720 --> 00:11:23,760
+statements، فبدي أحدد الـ block تبعي هذا، نقول begin
+
+160
+00:11:23,760 --> 00:11:26,660
+end. فكل اللي between begin and end، هدول بتعامل
+
+161
+00:11:26,660 --> 00:11:29,040
+معاهم كأنهم statement واحدة، حتى لو كانوا multiple lines
+
+162
+00:11:29,040 --> 00:11:32,790
+حتى لو كانوا multiple statements، كلهم multiple statements
+
+163
+00:11:32,790 --> 00:11:38,530
+بتعامل معاهم as a one statement، للـ loop، سواء for
+
+164
+00:11:38,530 --> 00:11:42,850
+أو while، سواء for أو while. هنتكلم لغة عن مجموعة
+
+165
+00:11:42,850 --> 00:11:49,270
+examples، هتوضح الـ statement هذه. بالرغم إن أنا
+
+166
+00:11:49,270 --> 00:11:55,350
+بتعامل مع informal language، بس لازم أكون التعبير
+
+167
+00:11:55,350 --> 00:12:01,300
+تبعتي مختصر. لازم تكون مختصرة، ولازم تكون واضحة. طيب
+
+168
+00:12:01,300 --> 00:12:07,360
+في الآخر ممكن زي توضيح أكتب V تساوي تلاتة X مثلا
+
+169
+00:12:07,360 --> 00:12:15,680
+زائد سبعة. طيب بده أوضح بس للقارئ، إنه الشيء V أنا
+
+170
+00:12:15,680 --> 00:12:19,500
+إيش قصدي فيه الـ V؟ فبقى بدي
+
+223
+00:16:11,490 --> 00:16:15,910
+إلا في حالة واحدة فقط، إن الـ condition تبعكم false
+
+224
+00:16:15,910 --> 00:16:20,570
+الـ truth value .. الـ truth value تبعته false، okay
+
+225
+00:16:20,570 --> 00:16:24,330
+الـ while، الـ while بدينا .. بدينا هلوجد .. هناخد
+
+226
+00:16:24,330 --> 00:16:27,570
+جملتين اللي هم علاقة بالـ loop، اللي هم علاقة بالـ
+
+227
+00:16:27,570 --> 00:16:30,070
+loop، فبس بتاخدوا بالكم في الـ while وأنتوا
+
+228
+00:16:30,070 --> 00:16:32,930
+بتكتبواها، خلوكوا حذرين جدا إنه ماتصلوش لعملية
+
+229
+00:16:32,930 --> 00:16:38,530
+cycling أو عملية إنه forever، يضمن إن الـ code يظل
+
+230
+00:16:38,530 --> 00:16:41,370
+شغال forever، إيش يعني forever؟ معناته أنا ماعنديش
+
+231
+00:16:41,370 --> 00:16:45,170
+.. الـ condition تبعي مش عامله .. مش عامل control
+
+232
+00:16:45,170 --> 00:16:50,870
+عليه، مافيش إمكانية يعمله أو يصير له broken، إنه
+
+233
+00:16:50,870 --> 00:16:54,410
+ينكسر، هيظل مستمر شغال، طيب إيش هو بالظبط هذا الـ
+
+234
+00:16:54,410 --> 00:17:00,050
+while؟ while condition statement، فإذا بكتب while
+
+235
+00:17:00,050 --> 00:17:04,890
+بهذا الشكل، وبحط condition، طول
+
+236
+00:17:04,890 --> 00:17:08,780
+ما الـ condition true، نفذ الـ statement، طيب، هينفذ
+
+237
+00:17:08,780 --> 00:17:12,840
+الـ statement و هيرجع لمين؟ للـ condition، هينفذ الـ
+
+238
+00:17:12,840 --> 00:17:17,460
+statement و هيرجع لمين؟ للـ condition، متحقق، هيرجع
+
+239
+00:17:17,460 --> 00:17:19,660
+ينفذ الـ statement و يرجع لـ condition، statement
+
+240
+00:17:19,660 --> 00:17:24,240
+يرجع لـ condition، فإذا الـ statement هذه مافيش فيها
+
+241
+00:17:25,730 --> 00:17:30,410
+فانكشن أو مافيش فيها variable معين ممكن يوقفنا الـ
+
+242
+00:17:30,410 --> 00:17:34,690
+condition، هتظل forever، شغالة، هتظل ماشي على طول،
+
+243
+00:17:34,690 --> 00:17:40,870
+هيظل على طول، هتفاجأ إن والله الـ code مستمرة، تيجي
+
+244
+00:17:40,870 --> 00:17:43,770
+الكهربا وتقطع الكهربا، والـ code شغال عندكم، والـ
+
+245
+00:17:43,770 --> 00:17:47,670
+code مش راضي يخلص، تمام، فناخد بالنا وإحنا بنشتغل
+
+246
+00:17:47,670 --> 00:17:50,730
+الحقيقة في الـ while هذه أو في الـ for loop كله يعني
+
+247
+00:17:50,730 --> 00:17:53,950
+في الـ loops سواء الـ for loop أو .. بس يمكن الـ for
+
+248
+00:17:53,950 --> 00:17:57,170
+loop الأمور فيها control أكثر، هنتكلم عليها، الـ
+
+249
+00:17:57,170 --> 00:18:00,650
+while، طيب أولا في الـ condition بدنا نعمل evaluate
+
+250
+00:18:00,650 --> 00:18:03,550
+the propositional expression، بدنا نعمل evaluate لـ
+
+251
+00:18:03,550 --> 00:18:08,960
+.. لمين؟ للـ V، أنتو فيه عندكم proposition، V أكبر من
+
+252
+00:18:08,960 --> 00:18:14,100
+خمسة، فأول شغل هنعملها إنه نقدر قيمة V، عرفناها، نقدر
+
+253
+00:18:14,100 --> 00:18:17,060
+قيمة الـ truth value تبع الـ proposition هذه، لأنه
+
+254
+00:18:17,060 --> 00:18:21,340
+بناء عليها هنفذ الـ statement أو لأ، هنعمل execution
+
+255
+00:18:21,340 --> 00:18:26,760
+للـ statement أو مش هنعمل، فالـ condition true، نفذنا
+
+256
+00:18:26,760 --> 00:18:30,800
+false، خلاص بنسيبه وبكمل باقي الـ code، بنسيب يعني
+
+257
+00:18:30,800 --> 00:18:34,930
+الجملة، هدف يكون خلصناها، كسرناها، ونكمل الـ code
+
+258
+00:18:34,930 --> 00:18:43,230
+تبعنا، طيب فهذا هيظل شغال زي ما قلنا forever، إذا
+
+259
+00:18:43,230 --> 00:18:49,170
+كان ما تحققش إن الـ condition false، فاللي ممكن
+
+260
+00:18:49,170 --> 00:18:53,530
+يوقفنا الـ loop هذا، إن الـ condition تبعنا الـ truth
+
+261
+00:18:53,530 --> 00:18:57,090
+value تبعته false، وفي وقفة بنشوف الـ statement
+
+262
+00:18:57,090 --> 00:19:02,220
+اللي ورا، طيب الـ while هذه اللحظة، معناته هي مرتبطة
+
+263
+00:19:02,220 --> 00:19:06,820
+بيها بالـ condition، زي if then اللي إحنا اتحركنا
+
+264
+00:19:06,820 --> 00:19:15,900
+فيها، دي if yes وبرجع if yes if yes if yes، أيه أنتم
+
+265
+00:19:15,900 --> 00:19:22,400
+بتصير false بعد قد إيش؟ مش عارف، يعني ممكن code تضطر
+
+266
+00:19:22,400 --> 00:19:26,440
+بعد عشرة steps، يمكن code ثاني بعد مائة steps، code
+
+267
+00:19:26,440 --> 00:19:31,580
+ثالث يمكن بعد ألف steps، فهدا تقدرش تحددوها، الـ y في
+
+268
+00:19:31,580 --> 00:19:38,600
+الآخر، تماثل if then، بس أنا مش عارف قد إيش عدد المرات
+
+269
+00:19:38,600 --> 00:19:41,360
+التكرار اللي هيشتغلها، فهدا تماثل بالظبط كأني بقول
+
+270
+00:19:41,360 --> 00:19:50,200
+if condition if condition، ألاحظوا إيش هنا begin، كل
+
+271
+00:19:50,200 --> 00:19:55,880
+هذا بدها تتنفذ مرة واحدة، لمين؟ للـ if condition، كأنه
+
+272
+00:19:55,880 --> 00:19:56,980
+كل هذا لمين؟ للـ then
+
+273
+00:20:00,580 --> 00:20:04,140
+كويس، إيش الـ condition اللي بدنا نطبقه؟ الـ condition
+
+274
+00:20:04,140 --> 00:20:10,060
+true، هنقول إن الـ condition هنا true، statement هي
+
+275
+00:20:10,060 --> 00:20:13,480
+هو أساسا الـ condition بده statement له، هي الـ
+
+276
+00:20:13,480 --> 00:20:16,540
+statement، اتحققت، بعد الـ statement، if condition
+
+277
+00:20:16,540 --> 00:20:21,920
+برضه while، هي هنا condition، اتحقق، statement هي الـ
+
+278
+00:20:21,920 --> 00:20:25,940
+statement، بعد الـ statement، if، معناه ترجع برضه للـ
+
+279
+00:20:25,940 --> 00:20:30,070
+condition، إذا true، برضه كمان مرة، ارجع اعمل
+
+280
+00:20:30,070 --> 00:20:33,670
+statement، طيب
+
+281
+00:20:33,670 --> 00:20:37,450
+إذا true، كمان مرة، كمان مرة، كمان مرة، قد إيش عدد
+
+282
+00:20:37,450 --> 00:20:42,750
+التكرارات؟ بيحددها مين؟ الـ statement هذه، الـ
+
+283
+00:20:42,750 --> 00:20:45,910
+statement هذه، امتى هتجبر الـ condition إنه يصير
+
+284
+00:20:45,910 --> 00:20:51,610
+false؟ امتى هيصير false؟ فإحنا هنا نقدر نمثل if
+
+285
+00:20:51,610 --> 00:20:55,840
+then، بس واضح إنه if then هتكون مرهقة جدا، واضح إن
+
+286
+00:20:55,840 --> 00:20:58,760
+الـ while، حلّ المشكلة هذه، بدل ما أضطر أعمل if
+
+287
+00:20:58,760 --> 00:21:02,720
+then وأنا مش عارف قد إيش هيستمر، مش عارف قد إيش هيستمر
+
+288
+00:21:02,720 --> 00:21:07,800
+صحيح؟ ممكن زي ما قلت لكم يستمر ألف iteration أو
+
+289
+00:21:07,800 --> 00:21:12,100
+ألف step، يعني يضطر يعمل، فواضح إن الـ while سهّلت لنا
+
+290
+00:21:12,100 --> 00:21:15,000
+الموضوع هذا، بس زي ما قلت لكم بدنا نكون حريصين في الـ
+
+291
+00:21:15,000 --> 00:21:18,680
+statement، كيف أكتبها بحيث إنه أنا امتى بدي يجي في
+
+292
+00:21:18,680 --> 00:21:25,030
+الـ .. أو نعمل .. نكسر الـ loop هذه أو نطلع من الـ
+
+293
+00:21:25,030 --> 00:21:30,850
+while loop، طيب في loop ثانية اللي هي الـ for loop
+
+294
+00:21:30,850 --> 00:21:37,370
+الـ for loop، يمكن عليها control أفضل شوية، ليش؟ لأنه
+
+295
+00:21:37,370 --> 00:21:41,510
+بحدد variable، بحطه الـ initial value و final value
+
+296
+00:21:41,510 --> 00:21:46,190
+فببدأ الـ loop تبعته أو مجموعة الـ loops تبعته من
+
+297
+00:21:46,190 --> 00:21:49,670
+ابتداء من الـ initial value وكل مرة بيزيد واحد
+
+298
+00:21:49,670 --> 00:21:54,170
+automatically، طبعا كل مرة بيزيد واحد على الـ initial
+
+299
+00:21:54,170 --> 00:21:58,650
+value، اللي وراها إثنين، تلاتة، initial زاد إثنين،
+
+300
+00:21:58,650 --> 00:22:00,950
+initial زاد تلاتة، initial زاد أربعة، لما يصل للـ
+
+301
+00:22:00,950 --> 00:22:05,550
+final، خلاص بنفذ عند الـ variable بيساوي الـ final
+
+302
+00:22:05,550 --> 00:22:12,010
+value، وبـ stop، بطلع برا الـ for loop، خلاص خلص، بطلع
+
+303
+00:22:12,010 --> 00:22:16,210
+خارج الـ for loop، فهنا محددة بتكون، يعني وأنتوا
+
+304
+00:22:16,210 --> 00:22:18,410
+بتشتغلوا وأنتوا محددينها، أنتم عارفين كم
+
+305
+00:22:18,410 --> 00:22:23,110
+iteration هتعمل أو كم loop هيتلف، عدد الـ
+
+306
+00:22:23,110 --> 00:22:26,050
+statements، كم مرة هيتنفذ، أنتم عارفين، أنتم
+
+307
+00:22:26,050 --> 00:22:28,630
+عارفين من وين؟ من الفرق بين الـ final والـ initial
+
+308
+00:22:28,630 --> 00:22:31,710
+values، من الفرق بين الـ final والـ initial value
+
+309
+00:22:31,710 --> 00:22:36,010
+فعارفين بالظبط كم مرة الـ loop هيتنفذ أو يعمله
+
+310
+00:22:36,010 --> 00:22:41,110
+execution، فالـ initial value عبارة عن integer
+
+311
+00:22:41,110 --> 00:22:45,070
+expression، هيكون عبارة عن integer، الـ final برضه
+
+312
+00:22:45,070 --> 00:22:48,790
+another integer expression، بس طبعا لازم يكون قيمته
+
+313
+00:22:48,790 --> 00:22:55,000
+أكبر من الـ integer الـ initial، أكبر من الـ initial value
+
+314
+00:22:55,000 --> 00:22:58,540
+اللي اتكلمنا عنه، okay، لحظة، أنتم بنعمل execute
+
+315
+00:22:58,540 --> 00:23:01,800
+لمين؟ لمجموعة الـ statement، للـ statement بتاعتنا
+
+316
+00:23:01,800 --> 00:23:04,400
+اللي ممكن تكون زي ما قلنا أكثر من الـ statement، لو
+
+317
+00:23:04,400 --> 00:23:08,320
+حطينا لها begin end، ممكن تكون أكثر من الـ statement
+
+318
+00:23:08,320 --> 00:23:12,900
+طيب، execute statement first with variable equal to
+
+319
+00:23:12,900 --> 00:23:19,440
+initial value، بعدين initial value زائد واحد، initial
+
+320
+00:23:19,440 --> 00:23:22,800
+value زائد إثنين، زائد تلاتة، زائد أربعة، زائد خمسة،
+
+321
+00:23:22,800 --> 00:23:27,020
+لعند ما نصل في النهاية لـ الـ variable بيساوي الـ
+
+322
+00:23:27,020 --> 00:23:31,020
+final، وبعد هيك خلاص بيطلع برا الـ loop، automatic
+
+323
+00:23:31,020 --> 00:23:35,340
+بيطلع لحاله برا الـ loop، automatic، بيطلع لحد، طيب
+
+324
+00:23:35,340 --> 00:23:40,240
+هذه الحقيقة هي while، بس عليها control، أنا عارف امتى
+
+325
+00:23:40,240 --> 00:23:44,020
+هتخلص، هي function while بالظبط، بس أنا عارف امتى
+
+326
+00:23:44,020 --> 00:23:50,140
+هتخلص، امتى هتخلص؟ هتخلص كالتالي، هي عبارة عن begin
+
+327
+00:23:50,140 --> 00:23:52,840
+and end، إيش في داخل الـ begin والـ end، كلها دول
+
+328
+00:23:52,840 --> 00:23:56,620
+بتنفذ مع بعض، variable بيساوي الـ initial value، okay
+
+329
+00:23:56,620 --> 00:24:01,660
+while variable أقل من final، طول ما هو أقل من أو
+
+330
+00:24:01,660 --> 00:24:06,260
+يساوي الـ final، معناته هذا بتبقى متحقق، أول مرة، ما
+
+331
+00:24:06,260 --> 00:24:08,840
+هيبدأ، initial value، الـ initial value أقل من الـ
+
+332
+00:24:08,840 --> 00:24:13,140
+final، begin، statement، تحقق الـ statement، وبعدين
+
+333
+00:24:13,140 --> 00:24:16,330
+إيش عمل له؟ variable بيساوي الـ variable زائد واحد
+
+334
+00:24:16,330 --> 00:24:19,570
+هي الـ control اللي كنت بقول لكم عليه، لازم تكون مع
+
+335
+00:24:19,570 --> 00:24:22,830
+الـ statement عشان الـ while، لازم يكون فيه control
+
+336
+00:24:22,830 --> 00:24:25,830
+إنتم الـ y ده يطلع من الـ y، كويس، فهي عملنا الـ
+
+337
+00:24:25,830 --> 00:24:29,070
+variable بتساوي الـ variable زائد واحد، وend، خلصناها
+
+338
+00:24:29,070 --> 00:24:33,250
+دي، هالواجهة بيجي هنا variable، قيمتها إيش؟ زائد
+
+339
+00:24:33,250 --> 00:24:37,410
+واحد، الـ variable زائد واحد أقل من أو تساوي final،
+
+340
+00:24:37,410 --> 00:24:41,330
+true، حقق كمان مرة، بس صارت زائد إثنين، هيك لأنه كمان
+
+341
+00:24:41,330 --> 00:24:45,430
+واحد، زيادة، كمان إثنين، تلاتة، أربعة، خمسة، عشرة، عشرين،
+
+342
+00:24:45,760 --> 00:24:49,700
+أنت بتصير أكبر من الـ final، اللحظة لما بتساوي final
+
+343
+00:24:49,700 --> 00:24:55,740
+عملت execution، الحقيقة للـ statement، فهي حققت لي الـ
+
+344
+00:24:55,740 --> 00:24:58,980
+function، عند الـ final value، حققتها، لأن هي حسبت الـ
+
+345
+00:24:58,980 --> 00:25:02,720
+statement، بعد هيك هتصير زائد واحد، صارت كأنها final
+
+346
+00:25:02,720 --> 00:25:08,710
+زائد واحد، and، نفذ لأ، ما نفذش، اطلع، ما حققش الـ
+
+347
+00:25:08,710 --> 00:25:13,450
+statement عندك، بعد الـ final، هو آخر قيمة حققتها للـ
+
+348
+00:25:13,450 --> 00:25:17,510
+statement، في حال كانت الـ variable بتساوي final، و
+
+349
+00:25:17,510 --> 00:25:23,110
+stop، ووقف هنا، فهذه هيك كأنه بقول for loop، من
+
+350
+00:25:23,110 --> 00:25:27,130
+initial value to final value، بدل ما أكتب كم سطر
+
+351
+00:25:27,130 --> 00:25:29,770
+هنا عندي، بدل ما أكتب تمام سطور، بكتبها سطر واحد
+
+352
+00:25:29,770 --> 00:25:32,490
+بكتبها بسطر واحد فقط
+
+353
+00:25:35,690 --> 00:25:43,510
+procedure of argument، function
+
+354
+00:25:43,510 --> 00:25:46,730
+هنا بتتعامل مع function، إيش يعني function؟ الـ function
+
+355
+00:25:46,730 --> 00:25:49,570
+هذا بتتعامل مع إن هي code ثاني مكتوب، بدي أعمله
+
+356
+00:25:49,570 --> 00:25:55,630
+استدعاء، code آخر موجود، وأنتم شغالين عليه قبل هيك
+
+357
+00:25:55,630 --> 00:25:59,190
+وبرمجته، طب ليش أرجع أكتبه كمان مرة؟ ليش نرجع
+
+358
+00:25:59,190 --> 00:26:02,170
+نكتبه كمان مرة؟ إذا أنتم بتعملوا مشروع تخرج أو
+
+359
+00:26:02,170 --> 00:26:07,890
+شيء وعملتوا كذا أكواد، nested codes مع بعض، خلصنا
+
+360
+00:26:07,890 --> 00:26:11,710
+code معين، فبتعملهم أجزاء، أحيانا جزء خلصنا، بتخلوه
+
+361
+00:26:11,710 --> 00:26:14,560
+على جنب، كل ما تشوف تكتبوا الجزء الثاني، بتعملوا لهذا
+
+362
+00:26:14,560 --> 00:26:18,300
+إيش؟ استدعاء، وبتنفذوا منه، خلاص، استدعاء، مش مضطرين
+
+363
+00:26:18,300 --> 00:26:23,620
+مش مضطرين ترجعوا تكتبوا نفس الـ code كمان مرة، ففي
+
+364
+00:26:23,620 --> 00:26:27,240
+الحالة هذه مضطرين نشتغل أو هنحتاج نشتغل على حاجة
+
+365
+00:26:27,240 --> 00:26:32,000
+اسمها procedure argument، بنحط له الـ input، فبكتب لو
+
+366
+00:26:32,000 --> 00:26:36,620
+مثلا أنتم عاملين الـ maximum، الـ maximum algorithm
+
+367
+00:26:36,620 --> 00:26:41,880
+جابل هيك، فممكن أقول max، حسب إحنا إيش كنا بسميناه
+
+368
+00:26:41,880 --> 00:26:45,000
+لأن طبعا هنا الـ function هتكون بالاسم تبع الـ code
+
+369
+00:26:45,000 --> 00:26:47,860
+نفسه، إيش إحنا كنا بسميناه؟ عشان إيش قلت لكم أول ما
+
+370
+00:26:47,860 --> 00:26:52,420
+بدأنا، الاسم لازم يكون يعبر عن الـ function نفسه، عن
+
+371
+00:26:52,420 --> 00:26:56,400
+الـ functionality، عن الـ task بتاعة الـ code، الـ code
+
+372
+00:26:56,400 --> 00:26:59,860
+إيش بيعمل؟ لازم الاسم يكون يعبر عن الموضوع ده
+
+373
+00:26:59,860 --> 00:27:05,380
+فبنقول max، وبنحط مثلا list، قائمة، معنى ذلك إيش
+
+374
+00:27:05,380 --> 00:27:09,700
+بتسوي؟ طبعا هتكون الـ code تبعنا شغال، begin مثلا، و
+
+375
+00:27:09,700 --> 00:27:16,240
+end، و statements عادي هنا، بس في النص محتاج بس الـ
+
+376
+00:27:16,240 --> 00:27:19,040
+maximum value في الـ list هذه، لأن محتاجها مثلا في
+
+377
+00:27:19,040 --> 00:27:22,240
+process صغيرة بدنا نعملها، محتاجينها في process
+
+378
+00:27:22,240 --> 00:27:28,030
+بدنا نعملها، إيه بتكتب بهذا الشكل، maxof L، بروح الـ
+
+379
+00:27:28,030 --> 00:27:30,670
+list اللي أصلا متعرفة داخل البرنامج كانت، أو ممكن
+
+380
+00:27:30,670 --> 00:27:34,550
+أنا من الأساس أعرفها as a argument، زي ما عملناها
+
+381
+00:27:34,550 --> 00:27:40,690
+في الـ declaration، a1, a2 to an، مثلا بعرف إن الـ
+
+382
+00:27:40,690 --> 00:27:46,330
+sequence هذا بسحبه من البرنامج تبعي، بوديه للـ
+
+383
+00:27:46,330 --> 00:27:52,960
+function max، بحسب له وبرجع لي النتيجة، برجع لنا
+
+384
+00:27:52,960 --> 00:27:57,080
+النتيجة، النتيجة بشتغل عليها، النتيجة بنشتغل عليها
+
+385
+00:27:57,080 --> 00:28:00,640
+طيب هذه اسمها function، ممكن نسميها procedure بهذا
+
+386
+00:28:00,640 --> 00:28:04,440
+الشكل أو function، لأن واضح إنها بتشتغل كـ function
+
+387
+00:28:04,440 --> 00:28:07,580
+بعطيها الـ input عشان ترجع لي output، بعطيها input
+
+388
+00:28:07,580 --> 00:28:10,980
+عشان ترجع لي output، بعض الـ languages، أحيانا الـ
+
+389
+00:28:10,980 --> 00:28:15,700
+languages بيسموها sub routines، في sub programs أو
+
+390
+00:28:15,
+
+445
+00:32:13,050 --> 00:32:16,450
+كأنها موجودة على طول هيخلص السطر هذا ويرجع لمين؟ لل
+
+446
+00:32:16,450 --> 00:32:21,250
+four تبعته الـ four I بتساوي تلاتة بده يقارن مع
+
+447
+00:32:21,250 --> 00:32:26,390
+عنصر تلاتة I بتساوي أربعة خمسة ستة سبعة N بيقارن
+
+448
+00:32:26,390 --> 00:32:31,090
+آخر عنصر مع الـ V اللي قيمتها بتتغير باستمرار كل
+
+449
+00:32:31,090 --> 00:32:33,790
+ما لاقَت رقم أكبر منها كل ما لاقَت رقم أكبر منها
+
+450
+00:32:33,790 --> 00:32:39,140
+بتخزنه بتاخده هو قيمتها، كويسة في الآخر لما خلصنا
+
+451
+00:32:39,140 --> 00:32:44,780
+هنا وخلصت الـ loop يعني كأنه عمل search على كل الـ
+
+452
+00:32:44,780 --> 00:32:49,980
+elements هنا to n طيب آخر قيمة جابها لـ V هي أكبر
+
+453
+00:32:49,980 --> 00:32:55,440
+قيمة مدام عمل search عليهم كلهم و خلصت الـ list الـ
+
+454
+00:32:55,440 --> 00:32:59,000
+list of elements خلصت، معناه ذلك أن آخر قيمة خزنت لـ
+
+455
+00:32:59,000 --> 00:33:03,740
+V هي المفروض أكبر قيمة داخل الـ list، صحيح؟ فـ return
+
+456
+00:33:03,740 --> 00:33:07,920
+رجع ليه بقيمة V إزاي بالظبط؟ كأنكم بتعملوا brand V؟
+
+457
+00:33:08,530 --> 00:33:14,830
+طباعة النقاشية قيمة V فنكتبها return ارجع V فكأنه
+
+458
+00:33:14,830 --> 00:33:22,030
+طلع قيمة V اللي هي the largest integer in the list
+
+459
+00:33:22,030 --> 00:33:27,130
+okay another example task الـ tasks بتاعتنا هلأ جت من
+
+460
+00:33:27,130 --> 00:33:31,130
+الـ tasks المهمة واللي لسه بيشتغلوا عليها كتير
+
+461
+00:33:31,130 --> 00:33:34,050
+يعني فيها شغل كتير وفيها تطورات كتير وفيها شغل
+
+462
+00:33:34,050 --> 00:33:38,170
+كتير بيشتغلوا، ما زالوا اللي هي الـ searching أو الـ
+
+463
+00:33:38,170 --> 00:33:41,030
+problem of searching أو الـ search أنا بدور على
+
+464
+00:33:41,030 --> 00:33:44,170
+element داخل الـ sequence في element بدور عليه داخل
+
+465
+00:33:44,170 --> 00:33:46,310
+الـ sequence، بس بدنا نحدد هنا أن أنا بتكلم عن
+
+466
+00:33:46,310 --> 00:33:52,910
+ordered list زي افترضوا أنه عملنا امتحان النصفي
+
+467
+00:33:53,660 --> 00:33:57,040
+خلصنا امتحان النصفي وطلعت فينا شوية درجات، الدرجات
+
+468
+00:33:57,040 --> 00:34:03,160
+هي دي بدنا نشوف كم درجة جد أو خليني نقول اللي
+
+469
+00:34:03,160 --> 00:34:07,560
+نجحوا، كيف درجاتهم؟ كم طالب نجح؟ كم طالب رسب؟ كم
+
+470
+00:34:07,560 --> 00:34:12,600
+شيء، فبنعملها logic search على الـ threshold بتاعة
+
+471
+00:34:12,600 --> 00:34:15,460
+النجاح، على الستين، عشان نشوف كم فيه أكثر منها و
+
+472
+00:34:15,460 --> 00:34:20,150
+كم فيه أقل منها، كأنه عندنا مثلاً نفترض واحد جاب
+
+473
+00:34:20,150 --> 00:34:22,410
+واحد، واحد جاب اثنين، واحد جاب عشرة، واحد جاب
+
+474
+00:34:22,410 --> 00:34:28,590
+عشرين، واحد جاب مثلاً خمسة وعشرين، جاب أربعين، خمسة
+
+475
+00:34:28,590 --> 00:34:37,050
+وخمسين، ستين، سبعين، تسعة وسبعين، ثمانين، هاي
+
+476
+00:34:37,050 --> 00:34:41,550
+تسعين، يلا ما تسعلوش، اثنين وتسعين، تسعة وتسعين،
+
+477
+00:34:41,550 --> 00:34:47,340
+حاضر، تسعة وتسعين، كويس، نفترض أن احنا بهذا الشكل فيه
+
+478
+00:34:47,340 --> 00:34:52,020
+مجموعة درجات، طبعاً هخزنهم عندي وين؟ على الـ Excel
+
+479
+00:34:52,020 --> 00:34:58,020
+حاجة، عند الـ column تبعت الدرجة وأعمله sorting، ايش
+
+480
+00:34:58,020 --> 00:35:02,380
+يعني أعمله sorting يعني أعمله ترتيب، تساعدني، فمعناه
+
+481
+00:35:02,380 --> 00:35:05,700
+ده اللي هرّتبه لهم بهذا الشكل، تساعدني، ordered، فصارت
+
+482
+00:35:05,700 --> 00:35:09,380
+ايش؟ ordered list، الـ ordered list ده بتدور على
+
+483
+00:35:09,380 --> 00:35:18,410
+الرقم 60 موجود ولا لأ؟ نختار نبحث عن رقم ستين إذا
+
+484
+00:35:18,410 --> 00:35:23,910
+موجود بده الـ location تبعه، بدنا الـ location والله
+
+485
+00:35:23,910 --> 00:35:28,530
+الـ location فعلياً، إذا عرفت الـ location وأنا عارف
+
+486
+00:35:28,530 --> 00:35:31,670
+كم العدد الإجمالي للطلاب اللي دخلوا الامتحان؟
+
+487
+00:35:31,670 --> 00:35:37,610
+بنقدر كم فيه أكبر وكم فيه أقل، بس احنا هالواجهة
+
+488
+00:35:37,610 --> 00:35:43,930
+هي task، نرجع نتعامل مع الموضوع بصفته الحالية عندنا
+
+489
+00:35:43,930 --> 00:35:50,010
+قائمة مرتبة وبدنا ندور على رقم داخلها، هل موجود
+
+490
+00:35:50,010 --> 00:35:53,650
+ولا لأ؟ فإذا أنا عندي الـ input تبعتي القائمة نفسها
+
+491
+00:35:53,650 --> 00:35:58,310
+الـ list نفسها زائد الـ input اللي بدور عليه، I know
+
+492
+00:35:58,310 --> 00:36:01,170
+element، ما أنا ممكن كل ما بغير الـ element هتتغير
+
+493
+00:36:01,170 --> 00:36:04,610
+النتائج اللي بتطلع، بدنا مثلاً خليني أقول الـ 60، خليني
+
+494
+00:36:04,610 --> 00:36:09,570
+على الـ 60 .. 60، نفترض في عندنا sequence أو مجموعة
+
+495
+00:36:09,570 --> 00:36:13,930
+أرقام بهذا الشكل وبدنا ندور، مرتبة كمان مرة هنا
+
+496
+00:36:13,930 --> 00:36:18,690
+بقولها مرتبة وبندور على الستين فيها، طيب في عندنا
+
+497
+00:36:18,690 --> 00:36:24,390
+حقيقة نوعين لشغل لأن احنا أساساً اتفقنا أنه بدنا
+
+498
+00:36:24,390 --> 00:36:27,810
+ندور على X هل هي موجودة ولا لأ؟ واَيش النتيجة اللي
+
+499
+00:36:27,810 --> 00:36:32,620
+بدي إياها؟ مش بدي الـ X، بدي الـ location تبع X بالظبط
+
+500
+00:36:32,620 --> 00:36:35,740
+الموقع تبعها، في agitation، موقعها الخامسة، العاشرة، الـ
+
+501
+00:36:35,740 --> 00:36:37,660
+element العشرين، الـ element الثلاثين في الـ sequence
+
+502
+00:36:37,660 --> 00:36:42,900
+في الـ last وين بالظبط؟ فبنحدد الـ location تبعها، طيب
+
+503
+00:36:42,900 --> 00:36:47,460
+الـ problem الحقيقة محتاجة efficient algorithm لأن
+
+504
+00:36:47,460 --> 00:36:50,800
+في algorithms كتيرة بتشتغل الموضوع هذا، هناخد منها
+
+505
+00:36:50,800 --> 00:36:55,480
+نوعين، في نوع أول واحد بنسميه linear ولاحقاً هناخد
+
+506
+00:36:55,480 --> 00:36:58,700
+binary، فنبدأ بالـ linear search، الـ linear search
+
+507
+00:36:58,700 --> 00:37:04,550
+بنشتغل عليه كتالي: أن أنا بمسك الـ 60 اللي بدي أدور
+
+508
+00:37:04,550 --> 00:37:10,530
+عليها وبقارنها مع الأولى، مع الثانية، مع الثالثة، مع
+
+509
+00:37:10,530 --> 00:37:14,090
+الرابعة، مع الخامسة، مع السادسة، مع السابعة .. امتى
+
+510
+00:37:14,090 --> 00:37:19,510
+بوقف؟ امتى بنوقف؟ لما وقفنا خلاص لإنه مش هتكون
+
+511
+00:37:19,510 --> 00:37:23,630
+مع الباقيين، احنا مرتبينهم، الباقيين ومرتّبينهم بحيث
+
+512
+00:37:23,630 --> 00:37:28,850
+أن هم distinct integers بمعنى ايش؟ أنه ما فيش قيمتين
+
+513
+00:37:28,850 --> 00:37:34,800
+زي بعض، معنى ذلك أنه مدام وصلت لها خلاص، وجهتنا الـ
+
+514
+00:37:34,800 --> 00:37:38,300
+location تبعها، بدي ايه؟ بس الـ location تبعها، بدنا
+
+515
+00:37:38,300 --> 00:37:42,480
+ايه؟ بتكون وجدنا شغلنا و stop على هيك، طيب بس بتظهر
+
+516
+00:37:42,480 --> 00:37:46,380
+المشكلة أنه احنا عادة الرقم X اللي بدور عليه أنا
+
+517
+00:37:46,380 --> 00:37:50,520
+مش عارف هو موجود وين داخل الـ list، يمكن يكون آخر
+
+518
+00:37:50,520 --> 00:37:54,790
+element، ممكن يكون آخر element موجود، ممكن يكون أول
+
+519
+00:37:54,790 --> 00:37:57,790
+element، معنى ذلك أن الـ search هيكون سريع جداً أو
+
+520
+00:37:57,790 --> 00:38:00,050
+يكون آخر element، معنى ذلك أن الـ search هيكون بطيء
+
+521
+00:38:00,050 --> 00:38:05,270
+جداً، عبل ما يخلص يعمل scan عليهم كلهم، لو عندنا ..
+
+522
+00:38:05,270 --> 00:38:10,770
+تخيلوا لو في البلدية أو في .. في أي مكان في قائمة
+
+523
+00:38:10,770 --> 00:38:15,590
+بأسماء المواطنين وبدنا ندور على اسم معين، نتكلم عن
+
+524
+00:38:15,590 --> 00:38:19,590
+ملايين، والاسم بدنا نعمله linear وأنا مش عارف
+
+525
+00:38:19,590 --> 00:38:23,970
+الاسم هذا موجود في الـ database، أول اسم ولا آخر اسم؟
+
+526
+00:38:23,970 --> 00:38:28,090
+يمكن آخر اسم وعندك مدينة فيها اثنين مليون أو مكان
+
+527
+00:38:28,090 --> 00:38:30,890
+فيه اثنين مليون بني آدم، معنى ذلك أنك تعملوا اثنين
+
+528
+00:38:30,890 --> 00:38:35,670
+مليون مقارنة، أكبر ولا لأ؟ ولا مش هو هو؟ ولا مش هو هو؟
+
+529
+00:38:35,670 --> 00:38:39,430
+ولا مش هو هو؟ ولا مش هو هو؟ الـ code هيكون كتير طويل
+
+530
+00:38:39,430 --> 00:38:43,950
+كتير طويل، طيب خلينا نتكلم عن sequence بسيط من واحد
+
+531
+00:38:43,950 --> 00:38:46,430
+لـ  واحد، distinct integers
+
+532
+00:38:51,110 --> 00:38:55,190
+ايش هنشتغل؟ كانت تالي procedure linear search، واضح
+
+533
+00:38:55,190 --> 00:38:58,190
+أن أنا وضحته من الأول، ما أقدرش أقول search لحاله لأنه
+
+534
+00:38:58,190 --> 00:39:01,570
+في أنواع من الـ search، أنواع اللي أنتوَ شغالينه
+
+535
+00:39:01,570 --> 00:39:05,290
+فواضح كويس جداً لو كان واضحاً linear search فبعرف
+
+536
+00:39:05,290 --> 00:39:08,370
+أنه linear، أقواس عشان نحط الـ input ساعتنا، الـ
+
+537
+00:39:08,370 --> 00:39:11,790
+arguments، أول input اللي هو الـ X اللي أنا بدي أعمل
+
+538
+00:39:11,790 --> 00:39:15,590
+search عليه، بدور عليه، وهذا integer، الـ input الثاني
+
+539
+00:39:15,590 --> 00:39:19,330
+القائمة اللي بدي أدور فيها، okay، بدي أدور على ستين
+
+540
+00:39:19,330 --> 00:39:24,440
+وين؟ في ملف الـ Excel تبع درجات الـ discrete، خلاص
+
+541
+00:39:24,440 --> 00:39:28,780
+افهمناها، معناته هي الملف هي الـ list تبعتي، هي الـ
+
+542
+00:39:28,780 --> 00:39:34,520
+list بتاعتنا، فإذا بدي الـ input x integer و a1 a2
+
+543
+00:39:34,520 --> 00:39:40,160
+a3 أو الـ list distinct integers، برضه مجموعة
+
+544
+00:39:40,160 --> 00:39:45,000
+integers متباينة، متميزة، مميزة، ما فيش رقمين زي بعض
+
+545
+00:39:46,240 --> 00:39:49,060
+نبدأ بـ I بتساوي واحد، فخلاص أنا هنا محدد أن الـ
+
+546
+00:39:49,060 --> 00:39:52,560
+index الأولى، بدي أبدأ أقارن مع مين؟ مع أول element
+
+547
+00:39:52,560 --> 00:39:56,560
+أول element، الـ location تبعته واحد، فـ I بتساوي واحد
+
+548
+00:39:56,560 --> 00:40:01,980
+الـ location الأول، طيب while نبدأ I أقل من أو تساوي
+
+549
+00:40:01,980 --> 00:40:08,460
+and مدام I أقل من آخر عنصر، معناته أنا لسه داخل الـ
+
+550
+00:40:08,460 --> 00:40:13,760
+list، ما زلت بقارن في أرقام داخل الـ list، ما قارنتهاش
+
+551
+00:40:14,340 --> 00:40:22,440
+لازم أكملّهم، فهذا أول شرط، and x لا تساوي a i لأن
+
+552
+00:40:22,440 --> 00:40:25,980
+إذا ساوتها خلاص، ما فيش داعي أكمل باقي الـ search، إذا
+
+553
+00:40:25,980 --> 00:40:30,120
+ساوتها ما فيش داعي أكمل، واحنا بندور وطلعت هنا، بدور
+
+554
+00:40:30,120 --> 00:40:34,200
+على رقم واحد مثلاً، جينا
+
+555
+00:40:34,200 --> 00:40:38,880
+هنا واحد، ساوت، إذا ساوت خلاص stop، ليش تدور في
+
+556
+00:40:38,880 --> 00:40:42,120
+الباقي؟ طب ما أنتوَ عارفين أن هي ordered و distinct
+
+557
+00:40:43,180 --> 00:40:46,840
+عارفين أن هي ordered يعني مرتبة، اللي .. اللي بعد
+
+558
+00:40:46,840 --> 00:40:51,480
+الواحد هتكون أكبر من الواحد، و distinct، مميزة، اللي
+
+559
+00:40:51,480 --> 00:40:56,340
+وراها لا يمكن يكون واحد برضه، فخلاص stop، وقف، الـ I
+
+560
+00:40:56,340 --> 00:41:00,480
+هي اللي بدي إياها، طيب otherwise، أنه لأ والله، لا تساوي
+
+561
+00:41:00,480 --> 00:41:07,040
+معنى ذلك أنه صار عندنا اشتغل، اشتغل، فلاحظوا I داخل
+
+562
+00:41:07,040 --> 00:41:11,520
+الـ list لسه أقل من أو تساوي and
+
+563
+00:41:13,670 --> 00:41:16,450
+فإذا الـ condition هذا أن أنا ما زلت ما خلصتش كل
+
+564
+00:41:16,450 --> 00:41:19,910
+العناصر، هي الهدف منه، أنا ما زلت ما خلصتش كل
+
+565
+00:41:19,910 --> 00:41:22,370
+العناصر، بس في condition ثاني ممكن يطلعني من الـ ..
+
+566
+00:41:22,370 --> 00:41:26,570
+من مين؟ من الـ while، شوية أن أنا لاقيت العنصر، okay
+
+567
+00:41:26,570 --> 00:41:28,770
+أنا ما خلصتش كل العناصر، بس أنا لاقيت اللي بدور
+
+568
+00:41:28,770 --> 00:41:33,910
+عليه، خلاص، يعني ايه؟ لاقيته، شكل
+
+569
+00:41:35,460 --> 00:41:39,120
+هتقول والله طب ماشي، هل وجد؟ بدنا نعمل خطة؟ يلا
+
+570
+00:41:39,120 --> 00:41:42,500
+توزعوا البنات، كل واحدة متر في متر تدور فيه، طب اه
+
+571
+00:41:42,500 --> 00:41:45,020
+لا، استنوا، لاقيتوا، طب ايه هو معنى بقى الـ procedure
+
+572
+00:41:45,020 --> 00:41:48,380
+اللي سبقتكم؟ ملاش، ما خلاص لاقينا، فمعنى ذلك مدام
+
+573
+00:41:48,380 --> 00:41:55,160
+أنا لاقيته، stop، العنصر اللي بدور عليه لاقيته، وقف
+
+574
+00:41:55,160 --> 00:42:01,610
+فإذا هذا داخل أن أنا خلصت الـ list أو لأ؟ أو أن أنا
+
+575
+00:42:01,610 --> 00:42:06,550
+لاقيت العنصر، فـ two conditions لازم يكونوا واخدين
+
+576
+00:42:06,550 --> 00:42:08,890
+بالنا منهم، إما أن أنا خلصت كل الـ sequence وما لاقيتش
+
+577
+00:42:08,890 --> 00:42:14,350
+العنصر فـ وقف عشان ما يضلش forever، أو أن أنا لاقيته
+
+578
+00:42:14,350 --> 00:42:17,310
+العنصر، فخلاص ما عادش باقي الـ search تبعي، باقي الـ
+
+579
+00:42:17,310 --> 00:42:21,550
+search بيصير ماضي، على الوقت اللي باقي، في الحالة هذه
+
+580
+00:42:21,550 --> 00:42:26,390
+إذا لأ، أنا ما زلت داخل الـ list، ما خلصتش وما لاقيتش
+
+581
+00:42:26,390 --> 00:42:33,880
+العنصر، لا يساوي، لأ يساوي، مدام لأ يساوي، أحقق الـ
+
+582
+00:42:33,880 --> 00:42:36,900
+statement بتاعة الـ I، I بتساوي I زائد واحد، شوف
+
+583
+00:42:36,900 --> 00:42:42,960
+العنصر الثاني، العنصر الثاني برضه لسه أقل من N، أقل
+
+584
+00:42:42,960 --> 00:42:49,980
+من الـ N و X لا تساوي، شوف الثالث، I بتصير مثلاً اثنين
+
+585
+00:42:49,980 --> 00:42:54,940
+زائد واحد، ثلاثة، الرابع، الخامس، العاشر، العشرين، طيب
+
+586
+00:42:54,940 --> 00:42:57,220
+وصلنا لـ I = N
+
+587
+00:42:59,760 --> 00:43:05,400
+معناته أنا قاعد بقارن آخر عنصر، I بتساوي N، جينا
+
+588
+00:43:05,400 --> 00:43:12,000
+هنا I بتساوي N زائد واحد، why لأ؟ هذه false، قصرنا
+
+589
+00:43:12,000 --> 00:43:20,740
+الـ why بتاعتنا بالحالة هذه، I أقل من أو تساوي N،
+
+590
+00:43:20,740 --> 00:43:27,720
+لأ، فعلياً اللي قصر الـ why تبعتي، N زائد واحد، صحيح؟
+
+591
+00:43:27,720 --> 00:43:29,860
+احنا وصلنا .. أن هي logic، الحالة اللي مفترضها أن
+
+592
+00:43:29,860 --> 00:43:33,600
+أنا وصلت لآخر الـ sequence، وصلنا لآخر الـ sequence
+
+593
+00:43:33,600 --> 00:43:39,220
+طيب ومش .. ومش العنصر هذا اللي قصر الـ while، ومش
+
+594
+00:43:39,220 --> 00:43:42,480
+الـ condition الثاني، الـ condition الأول، معنى ذلك
+
+595
+00:43:42,480 --> 00:43:44,800
+مدام الـ condition الأول اللي قصر الـ while، معناته
+
+596
+00:43:44,800 --> 00:43:49,880
+أكيد الـ I بتساوي N زائد 1، كيف تتنكسر هذه؟ كيف أنتَ
+
+597
+00:43:49,880 --> 00:43:54,470
+.. أنت بتصير false، بالظبط، N زائد واحد، مدام صارت N
+
+598
+00:43:54,470 --> 00:43:59,730
+زائد واحد، معناته هنا برضه false، في الحالة هذه else
+
+599
+00:43:59,730 --> 00:44:03,630
+location zero، معناته أن العنصر غير موجود، أنا فهمتهم
+
+600
+00:44:03,630 --> 00:44:07,870
+كلهم، وصلت لآخر element، ما لاقيتش العنصر، ما لاقيتش
+
+601
+00:44:07,870 --> 00:44:11,030
+العنصر
+
+602
+00:44:11,030 --> 00:44:19,930
+طيب أثناء الشغل، ما وصلناش لسه لـ .. للـ ايش؟ للـ N زائد
+
+603
+00:44:19,930 --> 00:44:25,820
+واحد، واحنا هنا بندور على 60
+
+604
+00:44:25,820 --> 00:44:34,360
+وجينا الـ 60، عند الـ 60، وجينا الـ 60، I عند 59 تمام
+
+605
+00:44:34,360 --> 00:44:40,860
+قارنّا، ما فيش، لا 59 لا تساوي، جينا هنا صارت 60، باجي
+
+606
+00:44:40,860 --> 00:44:47,260
+بقارن هنا الـ 60، لسه أقام .. أعفون .. هذه الـ
+
+607
+00:44:47,260 --> 00:44:49,860
+location مش عارف كم عددها، الـ location كان سبعة
+
+608
+00:44:49,860 --> 00:44:53,000
+خليني أقول سبعة، من .. من كم؟ واحد، اثنين،
+
+609
+00:44:53,0
+
+667
+00:50:18,880 --> 00:50:22,920
+أقل معناته لا يمكن أن تكون في الجزء الأكبر، صار عندنا
+
+668
+00:50:22,920 --> 00:50:26,500
+interval جديدة، نفس الكلام، نص الـ interval جديدة
+
+669
+00:50:26,500 --> 00:50:31,860
+خلينا نقول أقل الـ .. عفواً، x أكبر معناته لا يمكن
+
+670
+00:50:31,860 --> 00:50:34,500
+أن تكون في الجهة الأقل، اللي هي في الـ left، في الـ left
+
+671
+00:50:34,500 --> 00:50:40,090
+side، نفس الكلام، نرجع نكرره لعند ما في الآخر تلاقوا
+
+672
+00:50:40,090 --> 00:50:44,610
+حال كنتوا بتقارنوا بعنصر واحد، طالع العنصر هذا
+
+673
+00:50:44,610 --> 00:50:47,950
+بنقارن.. بنقارنه مباشرةً، هل هو بيساوي أو لا، إذا
+
+674
+00:50:47,950 --> 00:50:52,430
+بيساوي معناته هو، لا يساوي، معناته برضه بنرجع بالـ
+
+675
+00:50:52,430 --> 00:50:55,890
+location zero زي ما شفنا آخر الكود، كتبنا location
+
+676
+00:50:55,890 --> 00:50:58,950
+zero، هنا نفس الكلام، إذا ما طلعش بيساوي، بكون
+
+677
+00:50:58,950 --> 00:51:03,890
+location zero، هنحصر في الآخر على عنصر واحد، نحصر
+
+678
+00:51:03,890 --> 00:51:07,580
+كل الموضوع ده في عنصر واحد، العنصر الواحد ده إما
+
+679
+00:51:07,580 --> 00:51:11,500
+بيساوي أو غير موجود، إما بيساوي أو غير موجود، طب
+
+680
+00:51:11,500 --> 00:51:17,560
+كويسة، هيك وضحنا الفكرة، خلينا نكتب الـ algorithm أو
+
+681
+00:51:17,560 --> 00:51:23,640
+الـ code تبعها، وضحنا الفكرة، نكتب الـ code برضه كتالي:
+
+682
+00:51:23,640 --> 00:51:28,420
+procedure، اه يا جماعة، احنا بدأنا في code، بدأنا في
+
+683
+00:51:28,420 --> 00:51:34,310
+code procedure اسمه.. أنا مش عارف، خلاص هيك واضحة بشكل
+
+684
+00:51:34,310 --> 00:51:37,410
+هذا، أنا مش عارف، يمكن كونه just كو linear، linear، و
+
+685
+00:51:37,410 --> 00:51:43,130
+أتي.. أتبع معاكم، طب أنا مش في بالي binary، أنا بدأت
+
+686
+00:51:43,130 --> 00:51:46,270
+معاكم، أخطط عن إنه linear، لجيت إنه صار في عندي
+
+687
+00:51:46,270 --> 00:51:49,410
+مشكلة، أنا مش عارف أتبع الـ code، وحصفون ليه، يمكن في
+
+688
+00:51:49,410 --> 00:51:52,210
+عشر دقائق وأنا مش عارف إيش اللي بتكتبوه، و
+
+689
+00:51:52,210 --> 00:51:54,990
+يمكن في الآخر أروح نعمل غلط، و.. لأ لأ، شكل الـ code مش
+
+690
+00:51:54,990 --> 00:51:59,850
+نافع، بدو يكون واضح، المسمى binary search، خلاص عرفت
+
+691
+00:51:59,850 --> 00:52:03,810
+أن أنتم بتتكلموا عن إيش، binary search، إيش الـ
+
+692
+00:52:03,810 --> 00:52:07,070
+arguments بتاعتنا، الـ X اللي بدور عليها، و هي integer
+
+693
+00:52:07,070 --> 00:52:12,250
+و الـ sequence أو الـ list اللي بده يدور فيها على X
+
+694
+00:52:12,250 --> 00:52:14,870
+اللي بده يدور فيها على مين؟ على X، وهي distinct
+
+695
+00:52:14,870 --> 00:52:19,950
+integers، طيب، هنبدأ الـ sequence تبعنا واضح من إيش؟
+
+696
+00:52:19,950 --> 00:52:26,510
+من واحد to.. أنا الواحد هتكون هي الـ I اللي هي بداية
+
+697
+00:52:26,510 --> 00:52:30,030
+الـ sequence، أو الـ left end note of the search
+
+698
+00:52:30,030 --> 00:52:36,810
+interval، والآن الـ right point، حددنا البداية و
+
+699
+00:52:36,810 --> 00:52:40,310
+النهاية، حددنا البداية و النهاية، البداية و
+
+700
+00:52:40,310 --> 00:52:44,890
+النهاية، هدول محتاجينهم عشان نحسب الـ mid point،
+
+701
+00:52:44,890 --> 00:52:49,590
+النقطة اللي في النص، في نص الـ sequence، طيب، نبدأ
+
+702
+00:52:49,590 --> 00:52:57,850
+while I أقل من J، طول ما I أقل من J، الطبيعي، معناته
+
+703
+00:52:57,850 --> 00:53:00,470
+في interval بينهم، في مجموعة elements داخل الـ
+
+704
+00:53:00,470 --> 00:53:02,590
+interval، مدام في elements داخل الـ interval، لازم
+
+705
+00:53:02,590 --> 00:53:06,810
+أن تكون I أقل من J، اه لحظة، في عندي أكتر من statement
+
+706
+00:53:06,810 --> 00:53:10,410
+عندنا أكتر من statement محتاجين نعملها، فمحتاج
+
+707
+00:53:10,410 --> 00:53:14,570
+begin و end، هاي الـ begin و هاي الـ end على نفس
+
+708
+00:53:14,570 --> 00:53:19,830
+المستوى، محتاجين ننفذ في كل قيمة للـ while، للـ
+
+709
+00:53:19,830 --> 00:53:23,150
+condition هذا، محتاجين ننفذ اتنين statements هدول
+
+710
+00:53:23,150 --> 00:53:28,700
+مع بعض، لا نكتفي بـ statement واحد و نرجع في begin و
+
+711
+00:53:28,700 --> 00:53:35,600
+end، طيب نحسب إيش الـ midpoint، الـ M = I + J over two،
+
+712
+00:53:35,600 --> 00:53:39,660
+floor، حسبنا النقطة اللي في النص، تمام، النقطة اللي
+
+713
+00:53:39,660 --> 00:53:45,280
+في النص هذه، وجدنا أنّه M أقل من X، M < X، M أكبر منها
+
+714
+00:53:45,280 --> 00:53:51,560
+معناته اللي يمكن أن يكون في الـ left، هي
+
+715
+00:53:51,560 --> 00:53:59,150
+الـ I، J، وهنا الـ A[M]، حسب اشتغالنا على الـ M، وهذه الـ X
+
+716
+00:53:59,150 --> 00:54:06,230
+اللي بدور عليها، وجدنا أن X أكبر من A[M]،
+
+717
+00:54:06,230 --> 00:54:15,370
+لا يمكن أن يكون هنا X، صحيح، لأنه أكبر، X أكبر، okay، في
+
+718
+00:54:15,370 --> 00:54:22,630
+الحالة دي، I automatically هتيجي وين؟ M + 1، أنا
+
+719
+00:54:22,630 --> 00:54:27,190
+ماقلت أو يساوي، احنا مش حاطين هنا أو يساوي، عارفين
+
+720
+00:54:27,190 --> 00:54:31,190
+لو حاطين أو يساوي، بقول لكم اه، بـ automatically الـ I
+
+721
+00:54:31,190 --> 00:54:37,870
+بيصير الـ M الجديدة، أما لأ، هي M + 1، ليش؟ لأنه
+
+722
+00:54:37,870 --> 00:54:43,970
+أكبر، X أكبر من A[M]، معناته لا يمكن أن أحط أبدأ من A[M]
+
+723
+00:54:43,970 --> 00:54:49,610
+لأن A[M] أصلاً فعلاً مش محققة الـ condition، هي ليست X،
+
+724
+00:54:51,350 --> 00:54:57,010
+فهنا بنقول إنه إيش؟ M + 1، فهي إذا X أكبر من
+
+725
+00:54:57,010 --> 00:55:02,710
+A[M]، then I = M + 1، زائد واحد، لأن الـ condition
+
+726
+00:55:02,710 --> 00:55:09,690
+مافيه يساوي، طيب otherwise أو else، J = M، إذا
+
+727
+00:55:09,690 --> 00:55:16,190
+والله لأ العكس، إيش العكس؟ أو يساوي، أو يساوي، هي اللي
+
+728
+00:55:16,190 --> 00:55:18,310
+هتخلينا نقول إن هنا M
+
+729
+00:55:20,490 --> 00:55:27,990
+هنا بتقول M، فإذا كانت هنا أقل أو يساوي، عكس الأكبر
+
+730
+00:55:27,990 --> 00:55:32,890
+من، أقل أو يساوي، طيب، فإذا ممكن أن تكون تساوي، ففي الحالة
+
+731
+00:55:32,890 --> 00:55:36,610
+هذه، الـ J هتيجي مكان الـ M، لأنه في احتمال أنها تكون
+
+732
+00:55:36,610 --> 00:55:40,090
+بتساويه، ما هي هتكون حققت الشرط، إذا كان الـ X بتساوي
+
+733
+00:55:40,090 --> 00:55:46,270
+الـ A[M]، هتكون حققته فعلاً، فبنحط J = M،
+
+734
+00:55:48,000 --> 00:55:51,980
+واضحة؟ واضحة؟ لماذا هنا M + 1، ولماذا هنا M؟
+
+735
+00:55:51,980 --> 00:55:55,700
+كويسة،
+
+736
+00:55:55,700 --> 00:56:00,160
+ونخلص الجزء هذا، تيجي هنا طبعاً هتكون اتغيرت قيم I
+
+737
+00:56:00,160 --> 00:56:03,420
+أو J، يا الـ I يا الـ J هتكون اتغيرت بناءً على الـ
+
+738
+00:56:03,420 --> 00:56:08,860
+condition هذا، صح؟ كويسة، بنحقق، بنشوف كمان مرة،
+
+739
+00:56:08,860 --> 00:56:16,300
+لسه I أقل من J، مازالت، بنحسب mid point جديدة، و بنرجع
+
+740
+00:56:16,300 --> 00:56:22,180
+نقارنها، و بنستمر لعند ما نصل في الآخر أن الـ J هذا
+
+741
+00:56:22,180 --> 00:56:28,520
+بتساوي M، والـ I هتيجي عند القيمة اللي قدامها،
+
+742
+00:56:28,520 --> 00:56:31,920
+جايتها بالظبط، صار بينهم إيش؟ نقطة، يعني وصلنا لـ
+
+743
+00:56:31,920 --> 00:56:35,200
+أنّه.. بنتكلم عن element واحد فقط، الـ interval
+
+744
+00:56:35,200 --> 00:56:42,880
+فصارت هنا I = M + 1، M زائد واحد، هتيجي
+
+745
+00:56:42,880 --> 00:56:48,500
+مشابهة لمين؟ للـ J، هتطلع تساوي J، إذا كان في الآخر
+
+746
+00:56:48,500 --> 00:56:54,920
+element واحد، إذا ظل element واحد، نتيجة إن الـ I
+
+747
+00:56:54,920 --> 00:57:00,660
+زاد واحد، فالـ element الواحد هذا اللي هو أصلاً
+
+748
+00:57:00,660 --> 00:57:05,980
+موجود بينهم، خلى الـ I والـ J يساووا بعض، هيخلي الـ I و
+
+749
+00:57:05,980 --> 00:57:15,180
+J يساووا بعض، في الحالة هذه، الـ while إيش صار فيه؟ خلاص
+
+750
+00:57:15,180 --> 00:57:23,260
+وقف، هيوقف، وهيطلع هنا، بوقف عند آخر I موجودة، عند
+
+751
+00:57:23,260 --> 00:57:27,180
+آخر I موجودة، الـ I الأخيرة هذه، احنا اتفقنا إنه مش
+
+752
+00:57:27,180 --> 00:57:30,720
+ه يصير الكلام هذا إلا لما يظل عنصر واحد في الآخر، بس
+
+753
+00:57:30,720 --> 00:57:35,860
+عنصر وحيد فقط، هو العنصر الوحيد، مدام ظهر عنصر
+
+754
+00:57:35,860 --> 00:57:41,550
+وحيد، نتيجة إنه في عندنا هنا الـ J قربت لـ M، والـ I
+
+755
+00:57:41,550 --> 00:57:47,210
+قربت لـ M + 1، هنطبقوا على بعض عند عنصر واحد،
+
+756
+00:57:47,210 --> 00:57:51,050
+في الآخر، كله هتظل اللوب هتشغل لما تصف عندي على
+
+757
+00:57:51,050 --> 00:57:57,150
+عنصر واحد، اللي هو في الـ location I، خلصنا،
+
+758
+00:57:57,150 --> 00:58:01,290
+بعمل check سريعة، إما إن الـ X بتساوي هي الـ element
+
+759
+00:58:01,290 --> 00:58:07,170
+الأخير اللي ظل، برجع بالـ location تبعه، إلا برجع في
+
+760
+00:58:07,170 --> 00:58:11,570
+Zero، معناته أصلاً الرقم غير موجود، يعني العنصر نفسه
+
+761
+00:58:11,570 --> 00:58:14,350
+اللي أنا بدور عليه هو أصلاً غير.. غير موجود في
+
+762
+00:58:14,350 --> 00:58:20,610
+الحالة هذه، تمام، برضه من الأكواد المهمة للـ search،
+
+763
+00:58:20,610 --> 00:58:27,270
+طيب، مفهوم الـ code هذا واضح؟ طيب، خلاص، حسب لكم هنا
+
+764
+00:58:27,270 --> 00:58:29,790
+exercise، كنت بدي أشرح لكم اللي هو summation،
+
+765
+00:58:29,790 --> 00:58:35,930
+summation، عندكم sequence، مذاكرين الـ summation؟
+
+766
+00:58:38,250 --> 00:58:42,790
+صحيح؟ هنا عندنا summation لـ sequence من I =
+
+767
+00:58:42,790 --> 00:58:49,370
+1 to N، ببساطة
+
+768
+00:58:49,370 --> 00:58:52,670
+جداً، الـ procedure، بنسميه بالاسم تبعه، حطينا الـ
+
+769
+00:58:52,670 --> 00:58:55,650
+argument، ساعتنا الـ input اللي هي الـ sequence نفسه،
+
+770
+00:58:55,650 --> 00:59:00,160
+اللي بدنا نجمعه، integers، بنحط summation = صفر،
+
+771
+00:59:00,160 --> 00:59:03,200
+لسه ما بدنا نجمع إشي، فالـ summation، الأساس
+
+772
+00:59:03,200 --> 00:59:09,240
+بنسميها zero، الـ zero هذه، ببدأ إبلوب من واحد to n،
+
+773
+00:59:09,240 --> 00:59:14,860
+من واحد to N، كويس، ممكن حد يبدأ من إيش؟ أيه، واحد،
+
+774
+00:59:14,860 --> 00:59:24,840
+ويبدأ من اتنين ممكن؟ ممكن، لحظة، أنا بدأ أوصلكم إنه
+
+775
+00:59:24,840 --> 00:59:29,180
+مش بالضروري كلكم تكتبوا نفس الـ code، كل واحد ممكن
+
+776
+00:59:29,180 --> 00:59:35,400
+يعمل code غير الثاني، يعني كل.. كويس،
+
+777
+00:59:35,400 --> 00:59:40,020
+الـ I بدأ من واحد، لو أنا هيك بالشكل هذا، الـ S =
+
+778
+00:59:40,020 --> 00:59:44,100
+صفر، الـ summation zero، طبعاً، إذا بدأ بدأ من اتنين،
+
+779
+00:59:44,100 --> 00:59:50,060
+معناته الـ S بدأ.. بدأها بـ A[1]، القصد
+
+780
+00:59:50,060 --> 00:59:53,500
+إنه كل واحد ممكن يكتب الـ code بطريقته، وكل واحد
+
+781
+00:59:53,500 --> 00:59:57,000
+عنده طريقة تفكيره غير الثاني، وهذا ميزة الحقيقة في
+
+782
+00:59:57,000 --> 01:00:00,340
+البرمجة، أحلى إيش في البرمجة إنه.. إنه احنا مش
+
+783
+01:00:00,340 --> 01:00:03,040
+مجبورين كلنا نفكر بنفس الطريقة، مش مجبورين كلنا
+
+784
+01:00:03,040 --> 01:00:07,180
+نفكر بنفس الطريقة، okay، الـ I من 1 to N، أخذنا الـ
+
+785
+01:00:07,180 --> 01:00:10,640
+sequence كله، بعدين S = S + A[I]، الـ element
+
+786
+01:00:10,640 --> 01:00:13,700
+اللي لعندنا، فباجمع، بعمل accumulation،
+
+787
+01:00:13,700 --> 01:00:17,800
+accumulator، فباجمع، accumulator بيجمع القيم
+
+788
+01:00:17,800 --> 01:00:23,160
+هذه، قيمة فارغة، كل ما أمرج على element ببدأ أحطه، كل
+
+789
+01:00:23,160 --> 01:00:26,000
+ما أمرج على element بحطه، بحطه، بحطه، بحطه، لما في
+
+790
+01:00:26,000 --> 01:00:30,980
+الآخر بجمع قيمهم، فإنا أعطيت summation للكل، أعطينا
+
+791
+01:00:30,980 --> 01:00:36,840
+summation للكل، جزء آخر اللي هو عملية الـ sorting،
+
+792
+01:00:36,840 --> 01:00:41,700
+احنا اتفقنا إنه ordered list، صح؟ طب إذا كانت ليست
+
+793
+01:00:41,700 --> 01:00:45,720
+ordered، unordered list، إيش بتكون تسويه؟ أنت بتكون
+
+794
+01:00:45,720 --> 01:00:51,940
+ترتبها، يعني بتكون ترتبها، أنك تحاول تعمل sorting
+
+795
+01:00:51,940 --> 01:00:55,020
+algorithm، هذه برضه إلها algorithm، إن أنا أرتب الـ
+
+796
+01:00:55,020 --> 01:01:00,300
+list تبعنا، مش هقول الأكواد، بس هقول الفكرة وخلصنا،
+
+797
+01:01:00,300 --> 01:01:05,570
+في فكرتين، هنسيب واحدة منهم، في bubble sort وفي الـ
+
+798
+01:01:05,570 --> 01:01:08,310
+insertion sort، الـ insertion sort هناخدها للمرة
+
+799
+01:01:08,310 --> 01:01:13,270
+الجاية، الـ bubble، ع السريع، اسمها مختلف عن المعنى
+
+800
+01:01:13,270 --> 01:01:16,290
+الحقيقي تبعها، المعنى الحقيقي التالي، وأنتوا
+
+801
+01:01:16,290 --> 01:01:21,770
+بتأخذوا حاجة، أبدأ من أعلى أو من أول element، الـ
+
+802
+01:01:21,770 --> 01:01:25,930
+element الأول هذا، بشوفه أكبر من الثاني أو لا، إذا
+
+803
+01:01:25,930 --> 01:01:34,690
+أكبر، بعمل swap، ببدأ، وبعدين الثاني والثالث،لاحظوا
+
+804
+01:01:34,690 --> 01:01:38,530
+هنا لأ، الثلاثين مش أكبر من واحد، الثلاثين، فبسيبها، طيب،
+
+805
+01:01:38,530 --> 01:01:42,450
+واحد، والثلاثين، وواحد، اه، أكبر، ببدل، هاي هما اجوا هنا،
+
+806
+01:01:42,450 --> 01:01:47,050
+تبدلوا، طيب، هنا صارت واحد، والثلاثين، ما احنا قلنا هيك
+
+807
+01:01:47,050 --> 01:01:51,490
+بدلنا، صار هنا تمام، واحد، وثلاثين، واتنين، وثلاثين،
+
+808
+01:01:51,490 --> 01:01:56,390
+لأ، بنسيبهم، طيب، اتنين، وثلاثين، وثلاثه، وثلاثين،
+
+809
+01:01:56,390 --> 01:02:03,540
+بنسيبهم، ثلاثة، وثلاثين، واتنين، اه، ببدل، صار هنا في
+
+810
+01:02:03,540 --> 01:02:07,300
+ثلاثة، وثلاثين، ثلاثة، وثلاثين، أربعة، وثلاثين، لأ،
+
+811
+01:02:07,300 --> 01:02:11,780
+بتظل ثلاثة، وثلاثين، طيب، أربعة، وثلاثين، هنا ثلاثة، و
+
+812
+01:02:11,780 --> 01:02:15,620
+ثلاثين، أربعة، وثلاثين، أربعة، وثلاثين، مع الثلاثه، اه،
+
+813
+01:02:15,620 --> 01:02:20,740
+تنزل تحت، طيب، لاحظوا شغلة مهمة، إن الأربعة، وثلاثين
+
+814
+01:02:20,740 --> 01:02:26,560
+هذه، لما نزلت تحت، هي أكبر قيمة موجودة، أفضل شغلة
+
+815
+01:02:26,560 --> 01:02:28,720
+عشان التوضع، افترضوا هنا في ثلاثة مئة،
+
+816
+01:02:31,830 --> 01:02:37,330
+300 مع الـ 31 هتبدل، و 300 مع الـ 1 هتبدل، 300 مع الـ
+
+817
+01:02:37,330 --> 01:02:40,790
+32 هتبدل، هتبدل، هتبدل، لما تصفف في الآخر في القاع تحت،
+
+818
+01:02:40,790 --> 01:02:47,530
+صح، هتصفف في القاع، طيب، المرة الجاية لما أخلص هدول مش
+
+819
+01:02:47,530 --> 01:02:54,910
+هضطر أبدل 1، 2، 3، 4، 5، 6، 7، هبدل 6 بس، الأخيرة سيبوها،
+
+820
+01:02:54,910 --> 01:03:01,070
+وفروا، وجدنا وفروا عملية حسابها، لأنها لحالها ترتبت،
+
+821
+01:03:01,070 --> 01:03:04,790
+بالظبط، طيب، فبنخلص، بتيجي في الآخر برضه هنا،
+
+822
+01:03:04,790 --> 01:03:07,730
+خلصناها، خلاص، هذه برضه هتثبت، فلاحظوا هنا
+
+823
+01:03:07,730 --> 01:03:13,730
+بتختزلوا عنصر، عنصرين، ثلاثة، أربعة، خمسة، فكل مرة
+
+824
+01:03:13,730 --> 01:03:18,400
+الـ code تبعكم، الـ width اللي بترتبها، أجل بتصير الـ
+
+825
+01:03:18,400 --> 01:03:22,380
+interval اللي بترتبها بتقل، اللي محتاجين ترتبوها،
+
+826
+01:03:22,380 --> 01:03:25,400
+طيب، لاحظوا إن أنتم اشتغلتوا على الأرقام الكبيرة،
+
+827
+01:03:25,400 --> 01:03:29,660
+صح؟ بس لاحظوا الصغيرة إيش صار فيها؟ كأنا قاعدة
+
+828
+01:03:29,660 --> 01:03:33,980
+بتطلع زي الـ bubble فوق، قاعات اله
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bb5bdbefe353b51e6a57b16d5c5478d5d6cc1053
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U_postprocess.srt
@@ -0,0 +1,3368 @@
+1
+00:00:20,960 --> 00:00:22,980
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:22,980 --> 00:00:25,680
+الأنبياء والمسلمين سيدنا محمد وعلى أيدي وصحيح
+
+3
+00:00:25,680 --> 00:00:29,980
+أجمعين نفتح اليوم لقائنا ان شاء الله محاضرتنا
+
+4
+00:00:29,980 --> 00:00:36,260
+استكمالا لما سبق الحديث عنه بموضوع ال algorithms
+
+5
+00:00:36,260 --> 00:00:40,600
+المرة اللي فاتة بدأنا بال algorithms واتكلمنا أنه
+
+6
+00:00:40,600 --> 00:00:43,540
+في عندنا language وسميناها informal programming
+
+7
+00:00:43,540 --> 00:00:47,720
+languagelanguage بتختلف عن ال real languages ال
+
+8
+00:00:47,720 --> 00:00:50,520
+real languages هذه المفروض تكون كل مبرمج عنده
+
+9
+00:00:50,520 --> 00:00:54,520
+واحدة على الأقل متقنها جيدا بصورة كتير كويسة عشان
+
+10
+00:00:54,520 --> 00:00:58,840
+يشتغل يبرمج فيها أما ال pseudocode language اللي
+
+11
+00:00:58,840 --> 00:01:02,810
+اتكلمنا عنها المرة السادسة as informalلغة هذه
+
+12
+00:01:02,810 --> 00:01:09,590
+للكتابة للبحث المكتوب هذه للتعارف بين المبرمجين
+
+13
+00:01:09,590 --> 00:01:12,510
+وبعضهم على أساس إنه يعرفوا كيف ال sequence اللي
+
+14
+00:01:12,510 --> 00:01:15,710
+انعمل فيه ال code كيف ال algorithm انعمل ك steps
+
+15
+00:01:15,710 --> 00:01:19,830
+كخطوات ك proceduresتمام؟ المرة اللي فاتت بدأ أنا
+
+16
+00:01:19,830 --> 00:01:23,630
+قولنا أنه ال .. ال pseudocode بيتكون من مجموعة
+
+17
+00:01:23,630 --> 00:01:27,430
+عناصر أهمها أنصر المهمين كتير اللي هم ال
+
+18
+00:01:27,430 --> 00:01:31,770
+declaration الإعلان أو افتتاح ال .. ال code أنه
+
+19
+00:01:31,770 --> 00:01:35,830
+والله يا قارئ في code بدنا بدناش نتعامل عليه ال
+
+20
+00:01:35,830 --> 00:01:42,310
+declaration هنتكلم عنه في مجموعة other comments
+
+21
+00:01:42,310 --> 00:01:46,140
+هذه اسمها statementsكل ال statement إلها task
+
+22
+00:01:46,140 --> 00:01:50,080
+محددة، إلها وظيفة محددة، هنمسكهم لوجة واحدة واحدة
+
+23
+00:01:50,080 --> 00:01:53,780
+ال tasks هذه و نتعامل معها، و أتوقع في منهم حاجات
+
+24
+00:01:53,780 --> 00:01:56,420
+حتى باقي ممكن أخدتوها في البرمجة، مرت عليكم في
+
+25
+00:01:56,420 --> 00:02:00,920
+برمجة قبل هيك، فالجزء اليوم هيكون كتير فيه جزء شغل
+
+26
+00:02:00,920 --> 00:02:07,900
+برمجة، ولكن زي ما قولنا هو informal language طيب،
+
+27
+00:02:07,900 --> 00:02:13,220
+نبدأ على بركة الله في ال pseudocodeنتكلم عن
+
+28
+00:02:13,220 --> 00:02:18,340
+declaration ابتدائنا و بعدين ان نعرج على مجموعة
+
+29
+00:02:18,340 --> 00:02:21,830
+statementsنحن نعرفها إيش بالظبط كيف تشتغل عشان
+
+30
+00:02:21,830 --> 00:02:25,350
+نبدأ نكتب أكواد من أنفسها عادة نبدأ نكتب code كل
+
+31
+00:02:25,350 --> 00:02:29,650
+شغل بناخدها نكون قادرين إن احنا نعمللها code أو
+
+32
+00:02:29,650 --> 00:02:34,470
+على الأقل نوصف ال steps بتاعت ال code تبعتها
+
+33
+00:02:34,470 --> 00:02:38,910
+فابتداء بال procedure و بنعمل ال procedure name
+
+34
+00:02:38,910 --> 00:02:44,550
+وبينقصين بنعمل مجموعة ال argumentsنقطين هذه
+
+35
+00:02:44,550 --> 00:02:47,610
+standard لازم تتعاملوا معها بهذا الشكل ال standard
+
+36
+00:02:47,610 --> 00:02:51,530
+و بتحطوا ال type تبع ال arguments نمسكهم حاجة حاجة
+
+37
+00:02:51,530 --> 00:02:56,670
+ال procedure بنحطها بشكل bold تعريفا ان والله في
+
+38
+00:02:56,670 --> 00:03:00,550
+code بدأنا فيه تعريفا ان والله في code بدأنا نشتغل
+
+39
+00:03:00,550 --> 00:03:06,350
+عليه طيب ال code هذا بنحطله اسم بنستعمله اسم الاسم
+
+40
+00:03:07,380 --> 00:03:10,620
+و هذا الكلام يفضل تعمله في معظم الشغل كل البرمجة
+
+41
+00:03:10,620 --> 00:03:14,840
+بتاعتكم دايما اسم ال code يكون معبر عن ال task
+
+42
+00:03:14,840 --> 00:03:17,960
+بتاعة ال code يكون معبر عن ال task بتاع ال code
+
+43
+00:03:17,960 --> 00:03:21,200
+بريحكوا بعدين لما تعملوا ال code و ترجعوله بعد
+
+44
+00:03:21,200 --> 00:03:24,080
+شهرين بعد تلت شهور بعد خمس شهور تكون على الأقل
+
+45
+00:03:24,080 --> 00:03:28,160
+يعرفين لإيش ال code هذا الحاجة التانية ال code جدش
+
+46
+00:03:28,160 --> 00:03:34,960
+بتحطوله اسم معبر عنه قد تحتاجوا ال code ك function
+
+47
+00:03:36,170 --> 00:03:41,890
+أو subroutine أو code تستعملوه في code في code
+
+48
+00:03:41,890 --> 00:03:46,970
+تاني تعملوله استدعاء اتنفذوا شغله و اترجعوه فبده
+
+49
+00:03:46,970 --> 00:03:51,030
+يكون له معنى طيب زي ما قولنا procedure هذي ثابتة
+
+50
+00:03:51,030 --> 00:03:54,570
+بتكتبوها بهذا الشكل ال procedure name انتوا بتحطوا
+
+51
+00:03:54,570 --> 00:03:58,590
+اسم من عندكم بس يعبر عن ال task بتاعة ال code اللي
+
+52
+00:03:58,590 --> 00:04:02,970
+مش بده يعمل بالظبط طيب argument مجموعة ال inputs
+
+53
+00:04:04,430 --> 00:04:07,230
+إيش هي ال inputs اللي بتكون تشتغلوا عليها؟ يعني
+
+54
+00:04:07,230 --> 00:04:10,950
+إيش ال input تبع ال code بتكون تحددوهم هنا بعدين
+
+55
+00:04:10,950 --> 00:04:16,310
+نقطين تحددوا ال type تبعهم إيش نوعهم؟ إيش نوعهم؟
+
+56
+00:04:16,310 --> 00:04:20,570
+كويس فهذه كل الجزئية مجرد عملية declaration هي
+
+57
+00:04:20,570 --> 00:04:26,290
+إعلان إن والله ال text اللي جاي هو code هو هذا مش
+
+58
+00:04:26,290 --> 00:04:29,110
+paragraph عادي هذا code بدنا ناخد بالنا منه for
+
+59
+00:04:29,110 --> 00:04:33,840
+exampleprocedure هي خلاص بعرف ان انا داخل على ايش
+
+60
+00:04:33,840 --> 00:04:37,680
+على code maximum لاحظوا الاسم يعطيني حق معناته
+
+61
+00:04:37,680 --> 00:04:42,100
+واضح انه بدور على maximum ال task maximum بدور على
+
+62
+00:04:42,100 --> 00:04:45,000
+قيمة maximum من ايش؟ من مجموعة inputs الشيء ال
+
+63
+00:04:45,000 --> 00:04:49,600
+inputs عبارة عن lastlist L بعرف إن ال list اللي
+
+64
+00:04:49,600 --> 00:04:52,860
+اسمها L فيها مجموعة عناصر بدي أطلع ال maximum
+
+65
+00:04:52,860 --> 00:04:57,100
+value منهم فبيعطيني indication لإيش طيب إيش نوعهم
+
+66
+00:04:57,100 --> 00:05:00,780
+ال elements داخل ال list هذه أو ال list إيش نوعها
+
+67
+00:05:00,780 --> 00:05:03,680
+list of integers بعرف إن أنا بتكلم عن integers
+
+68
+00:05:03,680 --> 00:05:07,820
+بناء على ذلك بكون عامل حساباتي في ال code إن أنا
+
+69
+00:05:07,820 --> 00:05:10,580
+بتعامل مع integers بتعاملش مع real numbers مثلا
+
+70
+00:05:10,580 --> 00:05:14,960
+تمام وبعدين بعد هيك خلاص هذه عملية ال declaration
+
+71
+00:05:14,960 --> 00:05:20,280
+أعلننا عنإنه ال text اللي جاي code فبتعامل معه مع
+
+72
+00:05:20,280 --> 00:05:23,060
+مجموعة ال statements اللي جاية على أساس إن هي
+
+73
+00:05:23,060 --> 00:05:28,540
+acquired إنه هذا code برمجي، كويس أول statement
+
+74
+00:05:28,540 --> 00:05:32,500
+هنتعامل معها اللي هي تعريف ال variable كيف نكتب
+
+75
+00:05:32,500 --> 00:05:35,840
+variable و نعمله expression معين، نعمله تعريف،
+
+76
+00:05:35,840 --> 00:05:41,660
+نعمله معادلة، نعمله formulation، فبدكتبvariable لا
+
+77
+00:05:41,660 --> 00:05:44,600
+نضع علامة يساوي في نقطين قبل علامة يساوي و بعدين
+
+78
+00:05:44,600 --> 00:05:47,200
+علامة يساوي فال variable هدأش بيساوي expression
+
+79
+00:05:47,200 --> 00:05:51,780
+ممكن نضع اما معادلة او لان احنا بنتكلم عن informal
+
+80
+00:05:51,780 --> 00:05:54,980
+language اذا كان المعادلة ممكن تكون طويلة و انتم
+
+81
+00:05:54,980 --> 00:05:58,600
+مش عارفينها بالظبط ممكن تكتبوا جملة بس تكون مختصرة
+
+82
+00:05:58,600 --> 00:06:02,540
+جدا و تعبر عن ال variable هدأش بالشو بالظبط زي
+
+83
+00:06:02,540 --> 00:06:07,440
+ممكن نقول v بتساوي تلاتة x plus سبعة equation
+
+84
+00:06:07,440 --> 00:06:14,180
+مافيش مشكلة خلاص بناء على قيمةX التي سابقة موجودة
+
+85
+00:06:14,180 --> 00:06:17,360
+في الكود سأعوض فيها هنا لكي أحصل على قيمة V لا
+
+86
+00:06:17,360 --> 00:06:20,780
+مشكلة فيها تشوف قيمة X لو X مثلا باتنين معناته
+
+87
+00:06:20,780 --> 00:06:26,880
+تتغير V إلى 13 نحولها إلى 13 لكي 6 زائد 7 نحصل
+
+88
+00:06:26,880 --> 00:06:30,540
+عليها طيب و باعتبار زي ما قلنا أننا نتعامل مع
+
+89
+00:06:33,730 --> 00:06:37,770
+ممكن اكتبها بهذا الشكل X بس لازم احافظ على ايه؟
+
+90
+00:06:37,770 --> 00:06:41,730
+على يساوي بهذا الشكل بقصة the largest integer in
+
+91
+00:06:41,730 --> 00:06:45,890
+the last cell ممكن اكتبها بهذا الشكل ممكن تكون
+
+92
+00:06:45,890 --> 00:06:50,330
+الجزء هذا بدي اجيبه من subroutine تانية موجودة من
+
+93
+00:06:50,330 --> 00:06:54,470
+function موجودة استدعيها اجيب ال maximum او the
+
+94
+00:06:54,470 --> 00:06:57,710
+largest integer موجودة هنا فبعرفه على اساس ان هذا
+
+95
+00:06:57,710 --> 00:07:01,340
+X بتساوي كذالأنه زي ما قلنا أنتوا مش هتكتبوها ده
+
+96
+00:07:01,340 --> 00:07:05,400
+لا في Java ولا أنتوا مجرد بس بدي أعمل وصف كيف بدي
+
+97
+00:07:05,400 --> 00:07:08,800
+أفكر في كتابة ال code، كيف بنفكر في كتابة ال code،
+
+98
+00:07:08,800 --> 00:07:14,350
+كيف بنكتب ال code، تماممدام informal statement زي
+
+99
+00:07:14,350 --> 00:07:18,310
+ما قلنا ممكن نكتبها كتابة بس في أضيق الظروف جدش
+
+100
+00:07:18,310 --> 00:07:22,370
+تقدر تحطه ال formulation بيكون أفضل ماجدرناش بتكون
+
+101
+00:07:22,370 --> 00:07:26,110
+مختصرة جدا بإنه نكتبش paragraph كامل يعني مش هنكتب
+
+102
+00:07:26,110 --> 00:07:30,070
+paragraph نقول x بتسوي كذا لما يكون كذا و أنا مش
+
+103
+00:07:30,070 --> 00:07:34,430
+عارف أيش بتسوي كذا لأ هذه بتكتبوها بس في حالات
+
+104
+00:07:34,430 --> 00:07:38,670
+مختصرة جدا زي لما تكون تعملوا code تقولوا او
+
+105
+00:07:38,670 --> 00:07:43,290
+تشتغلوا و بعدين تكتبوا swap x and yswap x and y
+
+106
+00:07:43,290 --> 00:07:47,530
+بدّي x و y تكونوا محتاجين أثناء الشغل و هنحتاج أخر
+
+107
+00:07:47,530 --> 00:07:52,730
+المحاضرة في أخر المحاضرة هنشتغل على code محتاجين
+
+108
+00:07:52,730 --> 00:07:57,470
+نعمل swap فممكن و احنا بنشتغل أكون عرفت x و y و
+
+109
+00:07:57,470 --> 00:08:02,030
+أقول الله إذا كان x أكبر من y swap x و y عساس إن
+
+110
+00:08:02,030 --> 00:08:06,790
+أنا دايما بدي x هي القيمة الكبيرةفممكن نكتبها بهذا
+
+111
+00:08:06,790 --> 00:08:08,750
+الشكل طبعا انتوا عارفين انه في ال .. في ال real
+
+112
+00:08:08,750 --> 00:08:11,290
+programming language هذه لها شغلة بتكون تعملولها
+
+113
+00:08:11,290 --> 00:08:15,770
+condition أول بناء على ال condition بتقولوا بتحط
+
+114
+00:08:15,770 --> 00:08:19,250
+هذه في temporary variable و هذه مكان هذه و بعدين
+
+115
+00:08:19,250 --> 00:08:23,050
+بتحولوا عليها يعني في لها جزئية بتكونوا عارفينها
+
+116
+00:08:23,050 --> 00:08:26,430
+احنا هنا لأ بغض النظر عن ايش الجزئية البرمجية
+
+117
+00:08:26,430 --> 00:08:29,930
+هنقول والله الهدف من ال code تبعنا او في الجزئية
+
+118
+00:08:29,930 --> 00:08:34,370
+هدف ال line هذا اننا نعمل swap x مع y هذي تيجي
+
+119
+00:08:34,370 --> 00:08:39,550
+مكان هذه و هذي تيجي مكان هذهOkay في ال real
+
+120
+00:08:39,550 --> 00:08:42,230
+programming طبعا الكلام غير مسموح في ال real
+
+121
+00:08:42,230 --> 00:08:45,990
+programming اللي بتكلم عن C++ او بتكلم عن ال Java
+
+122
+00:08:45,990 --> 00:08:50,390
+مش مسموح الكلام بهذا الشكل طيب مش معناه هيك انه
+
+123
+00:08:50,390 --> 00:08:55,250
+نروح نقول .. نعمل مجموعة lines و بعدين نقول do so
+
+124
+00:08:55,250 --> 00:08:59,870
+and soأو إلى أخره مثلا أو استمر في ذلك أو .. لأ
+
+125
+00:08:59,870 --> 00:09:02,910
+لازم يكون الوصف واضح مش معناه ان هي informal
+
+126
+00:09:02,910 --> 00:09:06,970
+ماتكونش واضحة لازم نعمل breakdown لل algorithm
+
+127
+00:09:06,970 --> 00:09:13,590
+تبعنا ب steps خطوات توضح .. توضح بالظبط ال code أو
+
+128
+00:09:13,590 --> 00:09:17,490
+ال algorithm كيف ماشي خطوات ال algorithm مهمة جدا
+
+129
+00:09:17,490 --> 00:09:23,990
+okay ال statement التانيةbegin and end تستخدم
+
+130
+00:09:23,990 --> 00:09:27,530
+لاحقا مع مجموعة statements تانية مجموعة ال
+
+131
+00:09:27,530 --> 00:09:30,790
+statements عادة اللي هنشتغل فيها خصوصا اللي بتكون
+
+132
+00:09:30,790 --> 00:09:36,090
+في ال loops سواء ال for loop او ال while loop ال
+
+133
+00:09:36,090 --> 00:09:38,790
+for loop او ال while loop بتعاملوا مع ال statement
+
+134
+00:09:38,790 --> 00:09:44,010
+اللي وراها مباشرة بس وخلاص بنفذ بيعمل execution لل
+
+135
+00:09:44,010 --> 00:09:46,190
+statement اللي وراها و بعدين برجع لل loop تاني
+
+136
+00:09:46,190 --> 00:09:50,030
+احنا ممكن جدا نكون محتاجين نعمل اكتر من statement
+
+137
+00:09:51,060 --> 00:09:53,940
+هنحتاج في أكوالي كتير أن نكون أكتر من ال statement
+
+138
+00:09:53,940 --> 00:09:56,740
+واحدة طب في الحالة دي اش هنعمل عادي بنكتب كل ال
+
+139
+00:09:56,740 --> 00:10:00,620
+statements نبدأها ب begin و ننهيها ب end فبعرف ان
+
+140
+00:10:00,620 --> 00:10:04,680
+بين begin و end هدول كلهم بتعاملوا كإنهم statement
+
+141
+00:10:04,680 --> 00:10:10,100
+واحدة كإنهم ال group واحد بنفعش أنفذ واحدة و أسيب
+
+142
+00:10:10,100 --> 00:10:14,420
+الباقي أرجع لل four تبعتي كله هيتنفذ بعد ال end
+
+143
+00:10:14,420 --> 00:10:20,130
+برجع لل loop لل four أول .. او حتى في ال if then
+
+144
+00:10:20,130 --> 00:10:24,630
+في ال if then then ممكن تتعامل مع اول line بس معها
+
+145
+00:10:24,630 --> 00:10:28,690
+لأ انا بديها تتعامل مع three statements بحط begin
+
+146
+00:10:28,690 --> 00:10:32,310
+end للتلاتة للتلاتة statements بعرف ان كل هدولة
+
+147
+00:10:32,310 --> 00:10:36,430
+هيتنفذوا اذا تحققت .. اذا تحقق ال condition تبع ال
+
+148
+00:10:36,430 --> 00:10:40,950
+if فبحقق ال three statements او بنفذ ال three ..
+
+149
+00:10:40,950 --> 00:10:45,080
+ال three statements بتاعة then بتاعة thenكويس زي
+
+150
+00:10:45,080 --> 00:10:49,680
+ما قولنا هذه ممكن نستعملها لحقيقة ان كل مجموعة
+
+151
+00:10:49,680 --> 00:10:53,120
+sequence من ال statements نتعامل معها اذا ايش
+
+152
+00:10:53,120 --> 00:10:56,560
+single statement او group واحد كله لازم يتنفذ مع
+
+153
+00:10:56,560 --> 00:11:00,960
+بعض ال execution لازم لكل مع بعض okay هذه ممكن
+
+154
+00:11:00,960 --> 00:11:04,300
+نستخدمها اكتر شئ يعني ممكن تيجي بعد ال procedure
+
+155
+00:11:04,300 --> 00:11:09,060
+في ال declaration غالبا تيجي مع ال if then لان if
+
+156
+00:11:09,060 --> 00:11:14,460
+thenelse بعد ال then هيكون فيه مجموعة statements و
+
+157
+00:11:14,460 --> 00:11:17,240
+بعد ال else هيكون فيه مجموعة statements هو بتعامل
+
+158
+00:11:17,240 --> 00:11:19,720
+معاها أن هي statement واحدة لأ أنا بدي مجموعة
+
+159
+00:11:19,720 --> 00:11:23,760
+statements فبدي أحدد ال block تبعي هذا نقول begin
+
+160
+00:11:23,760 --> 00:11:26,660
+end فكل اللي between begin and end هدول بتعامل
+
+161
+00:11:26,660 --> 00:11:29,040
+معاهم كأنهم statement واحدة حتى لو كانوا meet line
+
+162
+00:11:29,040 --> 00:11:32,790
+حتى لو كانوا meet statementكلهم meet statements
+
+163
+00:11:32,790 --> 00:11:38,530
+بتعامل معاهم as a one statement ل ال loop سواء for
+
+164
+00:11:38,530 --> 00:11:42,850
+أو while سواء for أو while هنتكلم لغة عن مجموعة
+
+165
+00:11:42,850 --> 00:11:49,270
+examples هتوضح ال statement هذه بالرغم أن أنا
+
+166
+00:11:49,270 --> 00:11:55,350
+بتعامل مع informal language بس لازم أكون التعبير
+
+167
+00:11:55,350 --> 00:12:01,300
+تبعتي مختصرالازم تكون مختصرة و لازم تكون واضحة طيب
+
+168
+00:12:01,300 --> 00:12:07,360
+في الآخر ممكن زي تويه اكتب V تساوي تلاتة X مثلا
+
+169
+00:12:07,360 --> 00:12:15,680
+زائد سبعة طيب بده اوضح بس للقارق انه الشية Vأنا
+
+170
+00:12:15,680 --> 00:12:19,500
+إيش جذب فيه ال V فبقى بدي أعمله comment ال comment
+
+171
+00:12:19,500 --> 00:12:24,100
+هدى بنحطها بالأقواس المجاعة ده هدى اللى كنا
+
+172
+00:12:24,100 --> 00:12:28,980
+نستخدمها زمان لمين للست كنا نستعملها للست فهدى أي
+
+173
+00:12:28,980 --> 00:12:32,800
+جملة بتنكتب داخلها بعرف أنه هدى ليس من نسيج ال
+
+174
+00:12:32,800 --> 00:12:40,400
+code هدى فقط لتوضيح للقارئ توضيح للقارئ .. توضيح
+
+175
+00:12:40,400 --> 00:12:43,200
+إلي أنا كمان لإن ممكن أكتب ال code و بعد شهرين لما
+
+176
+00:12:43,200 --> 00:12:47,720
+أرجعلهبعد شهرين لما ارجعله هرجعله انا ايامها انا
+
+177
+00:12:47,720 --> 00:12:51,960
+لما حطيت V ايش كان جصد فيها حطوه احيانا خصوصا اذا
+
+178
+00:12:51,960 --> 00:12:55,840
+ال code تبعكوا كبير هتقولوا اه V انا ماكنتش فاكر
+
+179
+00:12:55,840 --> 00:12:59,260
+انا ايش كنت بدي منها فكويس ان هي بقوات زي هذه
+
+180
+00:12:59,260 --> 00:13:02,920
+تكتبوا اللي بدكوا يعنى بتعملوها انتوا اظن بتعملوا
+
+181
+00:13:02,920 --> 00:13:08,540
+double slash فبتغير حتى لون الكتابة بعرف بالظبط
+
+182
+00:13:08,540 --> 00:13:13,540
+انه هذا مش من ال codeهد بتنفذش هد مجرد command
+
+183
+00:13:13,540 --> 00:13:17,480
+ملاحظات بكتبها إما لنفسي أو للي بده يقرأ إذا بدي
+
+184
+00:13:17,480 --> 00:13:20,540
+أعطي ال code هد لحده يقرأ و يكمل عليه فأقوله أنا
+
+185
+00:13:20,540 --> 00:13:26,360
+والله ال V هد نفترض مثلا the largest value in the
+
+186
+00:13:26,360 --> 00:13:33,180
+list so far حتى الآن خلاص بعرف أنه أه دي أه دي أه
+
+187
+00:13:33,180 --> 00:13:35,540
+صح اتذكرت هد كانت المفروض بتعبر عن ال maximum
+
+188
+00:13:35,540 --> 00:13:39,000
+value بتسهل عليا في المتابعة لاحقا بتسهل علينا في
+
+189
+00:13:39,000 --> 00:13:45,730
+إيش في المتابعةتمام أحيانا بيسموها remark في بعض
+
+190
+00:13:45,730 --> 00:13:49,070
+ال languages أحيانا بيسموها remark ومهمة جدا هذه
+
+191
+00:13:49,070 --> 00:13:54,470
+مهمة جدا رغم أنها لا يتم تنفيذها ولكن هذه هي اللي
+
+192
+00:13:54,470 --> 00:13:59,130
+بتوضحلكم ال code تبعكم انتوا كيف كتبته كيف انتوا
+
+193
+00:13:59,130 --> 00:14:03,450
+كتبته زائد لو حد بده يقرأ بعد كل code و بده يكمل
+
+194
+00:14:03,450 --> 00:14:07,500
+عليه لما تكون group الكويس ان كل خطوةأو الخطوات
+
+195
+00:14:07,500 --> 00:14:11,120
+المفصلية حقيقة تكونوا عاملين .. اه انتوا طبعا
+
+196
+00:14:11,120 --> 00:14:13,300
+هتعملوا double slash احنا طبعا عندنا في ال
+
+197
+00:14:13,300 --> 00:14:17,400
+language بتاعتنا هنا بال .. بالأقواص المجاعة ده
+
+198
+00:14:17,400 --> 00:14:20,120
+لإنها ده بالkernel تمام؟ عندكوا بتعملوا double
+
+199
+00:14:20,120 --> 00:14:24,840
+slash و بتكتبوا بعد كل سطر أو جاند كل سطر إيش
+
+200
+00:14:24,840 --> 00:14:28,520
+قصدوا فيه حتى بتضل إلكوا انتوا حتى بتضل إلكوا
+
+201
+00:14:28,520 --> 00:14:33,000
+انتواتمام نبدأ في ال statement اللي وراها ال if
+
+202
+00:14:33,000 --> 00:14:38,200
+then if condition then statement if condition إذا
+
+203
+00:14:38,200 --> 00:14:41,260
+تحقق ال propositional expression هدا لإن ال
+
+204
+00:14:41,260 --> 00:14:43,980
+condition هدا هيكون عبارة عن proposition ال
+
+205
+00:14:43,980 --> 00:14:47,620
+proposition إما إله يعني في جيب الأحوال إله truth
+
+206
+00:14:47,620 --> 00:14:54,240
+value إذا كانت true نفذ ال statement إذا كانت
+
+207
+00:14:54,240 --> 00:14:59,830
+false سيبهاخلاص سيفه و أكمل .. أكمل ال code طيب
+
+208
+00:14:59,830 --> 00:15:03,270
+فهذه ال .. ال condition تبعنا ال condition زي ما
+
+209
+00:15:03,270 --> 00:15:05,530
+قولنا propositional expression هي عبارة عن
+
+210
+00:15:05,530 --> 00:15:09,390
+proposition أو proposition في الآخر ممكن أقول V
+
+211
+00:15:09,390 --> 00:15:14,550
+أكبر من خمسة بهذا الشكل و أنتوا عادة في ال flow
+
+212
+00:15:14,550 --> 00:15:22,570
+chart بتحبوه بهذا الشكل ال condition yes or noفهذه
+
+213
+00:15:22,570 --> 00:15:27,230
+yes معناه اننا بتكلم عن true لل condition او false
+
+214
+00:15:27,230 --> 00:15:33,870
+لل condition في حالة ال no فهذه then وهذه else
+
+215
+00:15:33,870 --> 00:15:38,980
+وهذا ال condition تبعنا اللي هو Fبهذا الشكل هي ال
+
+216
+00:15:38,980 --> 00:15:42,840
+if then هي شكلها لما .. و انت بترسمه flow chart
+
+217
+00:15:42,840 --> 00:15:49,300
+معاكم flow chart طيب form تانية و غالبا افضل حتى
+
+218
+00:15:49,300 --> 00:15:52,300
+تكون دايما احنا اللي عارفين ال form هذا اللي هو if
+
+219
+00:15:52,300 --> 00:15:56,920
+condition then statement one else statement two
+
+220
+00:15:56,920 --> 00:16:03,150
+اذا والله ال condition trueبننفذ ال statements
+
+221
+00:16:03,150 --> 00:16:07,010
+اللي بعد them، false بننفذ ال statements اللي بعد
+
+222
+00:16:07,010 --> 00:16:11,490
+else فمعنى ذلك أن ال statement two لا يمكن تنفيذه
+
+223
+00:16:11,490 --> 00:16:15,910
+إلا في حالة واحدة فقطإن ال condition تبعكم false
+
+224
+00:16:15,910 --> 00:16:20,570
+ال truth value .. ال truth value تبعته false okay
+
+225
+00:16:20,570 --> 00:16:24,330
+ال while ال while بدينا .. بدينا هلوجد .. هناخد
+
+226
+00:16:24,330 --> 00:16:27,570
+جملتين اللي هم علاقة بال loop اللي هم علاقة بال
+
+227
+00:16:27,570 --> 00:16:30,070
+loop فبس بتاخدوا بالكم في ال while و أنتوا
+
+228
+00:16:30,070 --> 00:16:32,930
+بتكتبواها خلوكوا حذرين جدا إنه ماتصلوش لعملية
+
+229
+00:16:32,930 --> 00:16:38,530
+cycling أو عملية إنه forever يضمنإن ال code يظل
+
+230
+00:16:38,530 --> 00:16:41,370
+شغال forever إيش يعني forever؟ معناته أنا ماعنديش
+
+231
+00:16:41,370 --> 00:16:45,170
+.. ال condition تبعي مش عامله .. مش عامل control
+
+232
+00:16:45,170 --> 00:16:50,870
+عليه مافيش إمكاني يعمله أو يصيرله broken إنه
+
+233
+00:16:50,870 --> 00:16:54,410
+ينكسر، هيظل مستمر شغال طيب إيش هو بالظبط هذا ال
+
+234
+00:16:54,410 --> 00:17:00,050
+while؟ while condition statement فإذا بكتب while
+
+235
+00:17:00,050 --> 00:17:04,890
+بهذا الشكل و بحط condition طول
+
+236
+00:17:04,890 --> 00:17:08,780
+ما ال condition trueنفذ ال statement، طيب، هينفذ
+
+237
+00:17:08,780 --> 00:17:12,840
+ال statement و هيرجع لمين؟ لل condition، هينفذ ال
+
+238
+00:17:12,840 --> 00:17:17,460
+statement و هيرجع لمين؟ لل condition، متحقق، هيرجع
+
+239
+00:17:17,460 --> 00:17:19,660
+ينفذ ال statement و يرجع ل condition، statement
+
+240
+00:17:19,660 --> 00:17:24,240
+يرجع ل condition، فإذا ال statement هذه مافيش فيها
+
+241
+00:17:25,730 --> 00:17:30,410
+فانكشن أو مافيش فيها variable معين ممكن يواجفنا ال
+
+242
+00:17:30,410 --> 00:17:34,690
+condition هتظل forever شجعها، هتظل ماشي على طول،
+
+243
+00:17:34,690 --> 00:17:40,870
+هيظل على طول، هتفاجأه إن والله ال code مستمرهتيجي
+
+244
+00:17:40,870 --> 00:17:43,770
+الكهربا و تقطع الكهربا و ال code شغال عندكم و ال
+
+245
+00:17:43,770 --> 00:17:47,670
+code مش راضي يخلص تمام فناخد بالنا و احنا بنشتغل
+
+246
+00:17:47,670 --> 00:17:50,730
+الحقيقة في ال while هذه او في ال for loop كله يعني
+
+247
+00:17:50,730 --> 00:17:53,950
+في ال loops سواء ال for loop او .. بس يمكن ال for
+
+248
+00:17:53,950 --> 00:17:57,170
+loop الأمور فيها control اكتر هنتكلم عليها ال
+
+249
+00:17:57,170 --> 00:18:00,650
+while طيب اولا في ال condition بدنا نعمل evaluate
+
+250
+00:18:00,650 --> 00:18:03,550
+the propositional expression بدنا نعمل evaluate ل
+
+251
+00:18:03,550 --> 00:18:08,960
+.. لمين؟لل V انتوا فيه عندكم proposition V أكبر من
+
+252
+00:18:08,960 --> 00:18:14,100
+خمسة فأول شغل هنعملها انه نقدر جدش V عرفناها نقدر
+
+253
+00:18:14,100 --> 00:18:17,060
+جدش ال truth value تبع ال proposition هذه لأنه
+
+254
+00:18:17,060 --> 00:18:21,340
+بناء عليها هنفذ ال statement او لأ هنعمل execution
+
+255
+00:18:21,340 --> 00:18:26,760
+لل statement او مش هنعمل فال condition true نفذنا
+
+256
+00:18:26,760 --> 00:18:30,800
+false خلاص بسيبه و بكمل باقي ال code بنسيب يعني
+
+257
+00:18:30,800 --> 00:18:34,930
+الجملة هدف بيكون خلصناهاكسرناها و نكمل ال code
+
+258
+00:18:34,930 --> 00:18:43,230
+تبعنا طيب فهذا هيظل شغال زي ما قلنا forever إذا
+
+259
+00:18:43,230 --> 00:18:49,170
+كان ماتحققتش ان ال condition false فاللي ممكن
+
+260
+00:18:49,170 --> 00:18:53,530
+يوقفلنا ال loop هذا ان ال condition تبعنا ال truth
+
+261
+00:18:53,530 --> 00:18:57,090
+value تبعته false و في وقفه بنشوف ال statement
+
+262
+00:18:57,090 --> 00:19:02,220
+اللي ورا طيب ال while هذهلحظة، معناته هي مرتبطة
+
+263
+00:19:02,220 --> 00:19:06,820
+بيها بال condition زي if then اللي احنا اتحركنا
+
+264
+00:19:06,820 --> 00:19:15,900
+فيها دي if yes وبرجع if yes if yes if yes ايه انت
+
+265
+00:19:15,900 --> 00:19:22,400
+بتصير false بعد قداش مش عارف يعني ممكن code تضطر
+
+266
+00:19:22,400 --> 00:19:26,440
+بعد عشرة steps يمكن code تاني بعد مائة steps code
+
+267
+00:19:26,440 --> 00:19:31,580
+تالت يمكن بعد الف stepsفهد تقدرش تحددوها ال y في
+
+268
+00:19:31,580 --> 00:19:38,600
+الآخر تماثل if then بس أنا مش عارف جداش عدد المرات
+
+269
+00:19:38,600 --> 00:19:41,360
+التكرار اللي هيشتغلها فهد تماثل بالظبط كأني بقول
+
+270
+00:19:41,360 --> 00:19:50,200
+if condition if condition ألحظوا إيش هنا begin كل
+
+271
+00:19:50,200 --> 00:19:55,880
+هد بدها تتنفذ مرة واحدة لمين لل if condition كأنه
+
+272
+00:19:55,880 --> 00:19:56,980
+كل هد لمين ل then
+
+273
+00:20:00,580 --> 00:20:04,140
+كويس إيش ال condition اللي بدنا نطبقه ال condition
+
+274
+00:20:04,140 --> 00:20:10,060
+true هنقول إن ال condition هنا true statement هى
+
+275
+00:20:10,060 --> 00:20:13,480
+هو الأساسا ال condition بده statement له هى ال
+
+276
+00:20:13,480 --> 00:20:16,540
+statement اتحققت بعد ال statement if condition
+
+277
+00:20:16,540 --> 00:20:21,920
+برضه while هى هنا condition اتحقق statement هى ال
+
+278
+00:20:21,920 --> 00:20:25,940
+statement بعد ال statement if معناه ترجع برضه لل
+
+279
+00:20:25,940 --> 00:20:30,070
+condition إذا trueبرضه كمان مرة ارجع اعمل
+
+280
+00:20:30,070 --> 00:20:33,670
+statement طيب
+
+281
+00:20:33,670 --> 00:20:37,450
+اذا true كمان مرة كمان مرة كمان مرة جدش عدد
+
+282
+00:20:37,450 --> 00:20:42,750
+التكرارات بيحددها مين ال statement هذى ال
+
+283
+00:20:42,750 --> 00:20:45,910
+statement هذى امتى هتجبر ال condition انه يصير
+
+284
+00:20:45,910 --> 00:20:51,610
+false امتى هيصير false فاحنا هنا نقدر نمطلق if
+
+285
+00:20:51,610 --> 00:20:55,840
+then بس واضح انه if then هتكون مرهقة جدافواضح ان
+
+286
+00:20:55,840 --> 00:20:58,760
+ال while حللنا المشكلة هذه بدل ما اضطر اعمل if
+
+287
+00:20:58,760 --> 00:21:02,720
+then وانا مش عارف جدش هيستمر مش عارف جدش هيستمر
+
+288
+00:21:02,720 --> 00:21:07,800
+صحيح؟ ممكن زي ما قلتلكوا يستمر الف iteration او
+
+289
+00:21:07,800 --> 00:21:12,100
+الف step يعني يضطر يعمل فواضح ان ال while سهرتنا
+
+290
+00:21:12,100 --> 00:21:15,000
+الموضوع هذا بس زي ما قلت لك بدنا نكون حارسين في ال
+
+291
+00:21:15,000 --> 00:21:18,680
+statement كيف اكتبها بحيث انه انا امتى بدي يجي في
+
+292
+00:21:18,680 --> 00:21:25,030
+ال .. او نعمل .. نكسر ال loop هذهأو نطلع من ال
+
+293
+00:21:25,030 --> 00:21:30,850
+while loop طيب في loop تانية اللي هي ال for loop
+
+294
+00:21:30,850 --> 00:21:37,370
+ال for loop يمكن عليها control أفضل شوية ليش؟ لأنه
+
+295
+00:21:37,370 --> 00:21:41,510
+بحدد variable بحطه ال initial value و final value
+
+296
+00:21:41,510 --> 00:21:46,190
+فببدأ ال loop تبعته او مجموعة ال loops تبعته من
+
+297
+00:21:46,190 --> 00:21:49,670
+ابتداء من ال initial value و كل مرة بيزود واحد
+
+298
+00:21:49,670 --> 00:21:54,170
+automaticallyطبعا كل مرة بيزود واحد ع ال initial
+
+299
+00:21:54,170 --> 00:21:58,650
+value اللي وراها اتنين تلاتة initial زاد اتنين
+
+300
+00:21:58,650 --> 00:22:00,950
+initial زاد تلاتة initial زاد اربع لما يصل لل
+
+301
+00:22:00,950 --> 00:22:05,550
+finalخلاص بنفذ عند ال variable بساوي ال final
+
+302
+00:22:05,550 --> 00:22:12,010
+value و ب stop بطلع برا ال for loop خلاص خلص بطلع
+
+303
+00:22:12,010 --> 00:22:16,210
+خارج ال for loop فهنا محددة بتكون يعني و أنتوا
+
+304
+00:22:16,210 --> 00:22:18,410
+بتشتغلوا و أنتوا محددينها أنتوا عارفين أكم
+
+305
+00:22:18,410 --> 00:22:23,110
+iteration هتعمل أو أكم loop هيتلف عدد ال
+
+306
+00:22:23,110 --> 00:22:26,050
+statements أكم مرة هيتنفذ أنتوا عارفين انتوا
+
+307
+00:22:26,050 --> 00:22:28,630
+عارفين من وين من الفرق بين ال final و ال initial
+
+308
+00:22:28,630 --> 00:22:31,710
+valuesمن الفرق بين ال final و ال initial value
+
+309
+00:22:31,710 --> 00:22:36,010
+فعارفين بالظبط كم مرة ال loop هيتنفذ أو يعمله
+
+310
+00:22:36,010 --> 00:22:41,110
+execution ف ال initial value عبارة عن integer
+
+311
+00:22:41,110 --> 00:22:45,070
+expression هكون عبارة عن integer ال final برضه
+
+312
+00:22:45,070 --> 00:22:48,790
+another integer expression بس طبعا لازم يكون قيمته
+
+313
+00:22:48,790 --> 00:22:55,000
+أكبر منالانتجر ال initial أكبر من ال initial value
+
+314
+00:22:55,000 --> 00:22:58,540
+اللي اتكلمنا عنه okay لحظة انتوا بنعمل execute
+
+315
+00:22:58,540 --> 00:23:01,800
+لمين لمجموعة ال statement لل statement بتاعتنا
+
+316
+00:23:01,800 --> 00:23:04,400
+اللي ممكن تكون زي ما قولنا أكتر من ال statement لو
+
+317
+00:23:04,400 --> 00:23:08,320
+حطينا لها begin end ممكن تكون أكتر من ال statement
+
+318
+00:23:08,320 --> 00:23:12,900
+طيب execute statement first with variable equal to
+
+319
+00:23:12,900 --> 00:23:19,440
+initial value بعدين initial value زائد واحدinitial
+
+320
+00:23:19,440 --> 00:23:22,800
+value زائد اتنين زائد تلاتة زائد اربعة زائد خمسة
+
+321
+00:23:22,800 --> 00:23:27,020
+لعند ما نصل في النهاية ل ال variable بساوي ال
+
+322
+00:23:27,020 --> 00:23:31,020
+final و بعد هيك خلاص بيطلع برا ال loop automatic
+
+323
+00:23:31,020 --> 00:23:35,340
+بيطلع لحاله برا ال loop automatic بيطلع لحد طيب
+
+324
+00:23:35,340 --> 00:23:40,240
+هذه حقيقة هي while بس عليها control أنا عارف امتى
+
+325
+00:23:40,240 --> 00:23:44,020
+هتخلص هي function while بالظبط بس أنا عارف امتى
+
+326
+00:23:44,020 --> 00:23:50,140
+هتخلص امتى هتخلص هتخلصكالتالي هي عبارة عن begin
+
+327
+00:23:50,140 --> 00:23:52,840
+and end ايش في داخل ال begin و ال end كلها دول
+
+328
+00:23:52,840 --> 00:23:56,620
+بتنفذ مع بعض variable بيساوي ال initial value okay
+
+329
+00:23:56,620 --> 00:24:01,660
+while variable اقل من final طول ما هو اقل من او
+
+330
+00:24:01,660 --> 00:24:06,260
+يساوي ال final معناته هذا بتبقى متحقق اول مرة ما
+
+331
+00:24:06,260 --> 00:24:08,840
+هيبدأ initial value ال initial value اقل من ال
+
+332
+00:24:08,840 --> 00:24:13,140
+final begin statement تحقق ال statement و بعدين
+
+333
+00:24:13,140 --> 00:24:16,330
+ايش عمل ليهvariable بيساوي ال variable زائد واحد
+
+334
+00:24:16,330 --> 00:24:19,570
+هي ال control اللي كنت بقولكوا عليه لازم تكون مع
+
+335
+00:24:19,570 --> 00:24:22,830
+ال statement عشان ال whileلازم يكون فيه control
+
+336
+00:24:22,830 --> 00:24:25,830
+انت ال y ده يطلع من ال y كويس فهي عملنا ال
+
+337
+00:24:25,830 --> 00:24:29,070
+variable بتسوي ال variable زائد واحد و end خلصناها
+
+338
+00:24:29,070 --> 00:24:33,250
+دي هالواجهة بيجي هنا variable قيمتها إيش؟ زائد
+
+339
+00:24:33,250 --> 00:24:37,410
+واحد ال variable زائد واحد أقل من أو تسوي final
+
+340
+00:24:37,410 --> 00:24:41,330
+true حقق كمان مرة بس صارت زائد اتنين هيك لأنه كمان
+
+341
+00:24:41,330 --> 00:24:45,430
+واحد زيادة كمان اتنين تلاتة اربع خمسة عشرة عشرين
+
+342
+00:24:45,760 --> 00:24:49,700
+أنت بتصير أكبر من ال final لحظة لما بتسوي final
+
+343
+00:24:49,700 --> 00:24:55,740
+عملت execution الحقيقة لل statement فهي حققت لي ال
+
+344
+00:24:55,740 --> 00:24:58,980
+function عند ال final value حققتها لأن هي حسبت ال
+
+345
+00:24:58,980 --> 00:25:02,720
+statement بعد هيك هتصير زائد واحد صارت كأنها final
+
+346
+00:25:02,720 --> 00:25:08,710
+زائد واحدand نفذ لأ ما نفذش اطلع ماحققش ال
+
+347
+00:25:08,710 --> 00:25:13,450
+statement عندك بعد ال final هو اخر قيمة حققها لل
+
+348
+00:25:13,450 --> 00:25:17,510
+statement في حال كانت ال variable بتساوي final و
+
+349
+00:25:17,510 --> 00:25:23,110
+stop وجف هنا فهذه هيك كأنه بقول for loop من
+
+350
+00:25:23,110 --> 00:25:27,130
+initial value to final value بدل ما اكتب اكم سطر
+
+351
+00:25:27,130 --> 00:25:29,770
+هنا عندى بدل ما اكتب تمام سطور بكتبها سطر واحد
+
+352
+00:25:29,770 --> 00:25:32,490
+بكتبها بسطر واحد فقط
+
+353
+00:25:35,690 --> 00:25:43,510
+procedure of argument فانكشن
+
+354
+00:25:43,510 --> 00:25:46,730
+هنا بتتعامل مع فانكشن، إيش يعني فانكشن؟ الفانكشن
+
+355
+00:25:46,730 --> 00:25:49,570
+هذا بتتعامل مع أن هي code تاني مكتوب، بدي أعمله
+
+356
+00:25:49,570 --> 00:25:55,630
+استدعاءcode أخر موجود و أنتوا شغالين عليه قبل هيك
+
+357
+00:25:55,630 --> 00:25:59,190
+و برمجته طب ليش أرجع أكتبه كمان مرة؟ ليش نرجع
+
+358
+00:25:59,190 --> 00:26:02,170
+نكتبه كمان مرة؟ إذا أنتوا بتعملوا مشروع تخرج أو
+
+359
+00:26:02,170 --> 00:26:07,890
+إشي و عملتوا كذا أكواد nested codes مع بعض خلصنا
+
+360
+00:26:07,890 --> 00:26:11,710
+code معين فبتعملهم أجزاء أحيانا جزء خلصنا بتخلوه
+
+361
+00:26:11,710 --> 00:26:14,560
+على جنبكلما تشوف تكتبوا الجزء التاني بتعملوا لهذا
+
+362
+00:26:14,560 --> 00:26:18,300
+إيش استدعاء و بتنفذوا منه خلاص استدعاء مش مضطرين
+
+363
+00:26:18,300 --> 00:26:23,620
+مش مضطرين ترجعوا تكتبوا نفس ال code كمان مرة ففي
+
+364
+00:26:23,620 --> 00:26:27,240
+الحالة هذه مضطرين نشتغل أو هنحتاج نشتغل على حاجة
+
+365
+00:26:27,240 --> 00:26:32,000
+اسمها procedure argument بنحطله ال input فبكتب لو
+
+366
+00:26:32,000 --> 00:26:36,620
+مثلا انتوا عاملين ال maximum ال maximum algorithm
+
+367
+00:26:36,620 --> 00:26:41,880
+جابل هيك فممكن أقول maxحسب احنا ايش كنا بسميناه
+
+368
+00:26:41,880 --> 00:26:45,000
+لان طبعا هنا ال function هتكون بالاسم تبع ال code
+
+369
+00:26:45,000 --> 00:26:47,860
+نفسه ايش احنا كنا بسميناه عشان ايش قلتلكم اول ما
+
+370
+00:26:47,860 --> 00:26:52,420
+بدأنا الاسم لازم يكون يعبر عن ال function نفسه عن
+
+371
+00:26:52,420 --> 00:26:56,400
+ال functionality عن ال task بتاعة ال code ال code
+
+372
+00:26:56,400 --> 00:26:59,860
+ايش بيعمل لازم الاسم يكون يعبر عن الموضوع ده
+
+373
+00:26:59,860 --> 00:27:05,380
+فبنقول max و بنحط مثلا list قائمة معنا ذلك ايش
+
+374
+00:27:05,380 --> 00:27:09,700
+بتسوي طبعا هتكون ال code تبعنا شغالbegin مثلا و
+
+375
+00:27:09,700 --> 00:27:16,240
+end و statements عادي هنا بس فى النص محتاج بس ال
+
+376
+00:27:16,240 --> 00:27:19,040
+maximum value فى ال list هذه لإن محتاجها مثلا فى
+
+377
+00:27:19,040 --> 00:27:22,240
+process صغيرة بدنا نعملها محتاجينها فى process
+
+378
+00:27:22,240 --> 00:27:28,030
+بدنا نعملها ايه بتكتب بهذا الشكل maxof L بروح ال
+
+379
+00:27:28,030 --> 00:27:30,670
+list اللي اصلا متعرفة داخل البرنامج كانت او ممكن
+
+380
+00:27:30,670 --> 00:27:34,550
+انا من الاساس اعرفها as a argument زي ما عملناها
+
+381
+00:27:34,550 --> 00:27:40,690
+في ال declaration a1, a2 to an مثلا بعرف ان ال
+
+382
+00:27:40,690 --> 00:27:46,330
+sequence هذا بسحبه من البرنامج تبعي بوديه لل
+
+383
+00:27:46,330 --> 00:27:52,960
+functionmax بحسب ليه و برجعلي النتيجة برجعلنا
+
+384
+00:27:52,960 --> 00:27:57,080
+النتيجة النتيجة بشتغل عليها النتيجة بنشتغل عليها
+
+385
+00:27:57,080 --> 00:28:00,640
+طيب هذه اسمها function ممكن نسميها procedure بهذا
+
+386
+00:28:00,640 --> 00:28:04,440
+الشكل او function لان واضح انها بتشتغل ك function
+
+387
+00:28:04,440 --> 00:28:07,580
+بعطيها ال input عشان ترجعلي output بعطيها input
+
+388
+00:28:07,580 --> 00:28:10,980
+عشان ترجعلي output بعض ال languages أحيان ال
+
+389
+00:28:10,980 --> 00:28:15,700
+languages بيسموها sub routines في sub programs او
+
+390
+00:28:15,700 --> 00:28:20,110
+methods او methodsهتلاقوا مش عارف انتوا في ال Java
+
+391
+00:28:20,110 --> 00:28:24,270
+إيش بتسموها method method method فإذا هي فعلا في
+
+392
+00:28:24,270 --> 00:28:27,250
+واحدة من المصاميات هدولة كل language بتستخدم مصطلح
+
+393
+00:28:27,250 --> 00:28:31,930
+من المصطلحات فعلا okay نبدأ خلصنا هيك مجموعة ال
+
+394
+00:28:31,930 --> 00:28:37,190
+statements اللي محتاجينها في ال code عشان نكتب
+
+395
+00:28:37,190 --> 00:28:40,770
+algorithm عنا عشان نكتب algorithm هلوجد هنبدأ بال
+
+396
+00:28:40,770 --> 00:28:45,450
+applications نبدأ ناخد تطبيقاتنبدأ نشتغل على
+
+397
+00:28:45,450 --> 00:28:49,530
+التطبيقات التطبيق الأول ال max أو ال maximum
+
+398
+00:28:49,530 --> 00:28:53,370
+procedure in pseudocode عندكوا sequence و بدنا ال
+
+399
+00:28:53,370 --> 00:28:56,390
+maximum value بدنا ال maximum value تخلي ال
+
+400
+00:28:56,390 --> 00:28:58,510
+sequence قولناها احنا المرة المحاضرة اللي فاتت
+
+401
+00:28:58,510 --> 00:29:01,590
+المحاضرة اللي فاتت الكودة كتبناها بس كتبناها as a
+
+402
+00:29:01,590 --> 00:29:06,250
+language كتابة كلاب كلمنا كلام قولنا بفترض
+
+403
+00:29:06,250 --> 00:29:12,550
+temporary variableوبحطه إن ال maximum value هي أول
+
+404
+00:29:12,550 --> 00:29:17,910
+element وبعدين بنقارن أول element أو V سمنها مع
+
+405
+00:29:17,910 --> 00:29:21,970
+التانية مع ال element التاني إذا ال element التاني
+
+406
+00:29:21,970 --> 00:29:25,770
+أكبر بنحط قيمة V تساوي ال element التاني بعدين
+
+407
+00:29:25,770 --> 00:29:28,450
+بنجرب التالت الرابع الخامس السادس لعد ما نخلص كل
+
+408
+00:29:28,450 --> 00:29:33,730
+ال list بتاعتنا طيب نكتبها لوجة code pseudocode
+
+409
+00:29:33,730 --> 00:29:39,110
+واضح فده طبعا هنبدأ بالإعلانprocedure خلاص معناته
+
+410
+00:29:39,110 --> 00:29:42,570
+فيه إجراء، فيه code بده يكتب، فيه procedure
+
+411
+00:29:42,570 --> 00:29:46,870
+محتاجينه يكتبوه يعبر عن إيش؟ max خلاص بعرف إنه
+
+412
+00:29:46,870 --> 00:29:50,700
+والله يعبر عن حاجةmax معناته انا بدور على maximum
+
+413
+00:29:50,700 --> 00:29:57,080
+إيش ال input تبعتنا؟ sequence a1 a2 to an to an أو
+
+414
+00:29:57,080 --> 00:30:01,500
+series على أساس إنه عندنا finite elements موجودين
+
+415
+00:30:01,500 --> 00:30:06,640
+طيب إيش نوعهم؟ ناخد بالنا نقطين و بنحط إيش نوعهم؟
+
+416
+00:30:06,640 --> 00:30:11,300
+integers نوعهم integers فخلاص حددناهاالخطوة الأولى
+
+417
+00:30:11,300 --> 00:30:16,540
+قلنا variable نفترض أنه يساوي أول element وحتى
+
+418
+00:30:16,540 --> 00:30:20,620
+الآن أول element هو الأكبر بالنسبالنا أنا بدي أعمل
+
+419
+00:30:20,620 --> 00:30:23,960
+بحث بدأت لسه من أول element هو الأكبر حتى اللحظة
+
+420
+00:30:23,960 --> 00:30:27,160
+بالنسبالي أنا ماشوفتش لسه إيش حد تاني هو أكبر رقم
+
+421
+00:30:27,160 --> 00:30:33,260
+لعنده الآن فنفترض أنه هذا a1 ال V من جتين ساوي a1
+
+422
+00:30:33,260 --> 00:30:37,220
+في هذه ال largest element so far حتى اللحظة هو
+
+423
+00:30:37,220 --> 00:30:43,000
+أكبر رقم عنديحتى الآن ال V هو أكبر رقم خلصنا من
+
+424
+00:30:43,000 --> 00:30:47,940
+أول element هالوقت بدنا ندور على من؟ من 2 to n من
+
+425
+00:30:47,940 --> 00:30:51,520
+ال element التاني لنهاية ال list فكل هدول بنعملهم
+
+426
+00:30:51,520 --> 00:30:56,500
+four من اتنين لأن الواحد خلاص أخدنا من اتنين to
+
+427
+00:30:56,500 --> 00:31:02,260
+each to n ف go through rest of elements بنمر على
+
+428
+00:31:02,260 --> 00:31:04,240
+باقي ال elements
+
+429
+00:31:06,870 --> 00:31:09,650
+F مرّيني على بقية ال elements فطبعا هنبدأ ب I
+
+430
+00:31:09,650 --> 00:31:16,990
+بتساوي 2 اتنين معناته أتنين أكبر من V والله إذا
+
+431
+00:31:16,990 --> 00:31:20,690
+أكبر من V المفروض V تاخد قيمتها معناته V بتساوي ال
+
+432
+00:31:20,690 --> 00:31:25,170
+AI اللي هي 2فكأني بدور على الأكبر بين الرقامين،
+
+433
+00:31:25,170 --> 00:31:27,530
+كأننا بنعمل و بندور على إيش على الأكبر بين
+
+434
+00:31:27,530 --> 00:31:31,410
+الرقامين، هدول لحظه أقواس، يعني كل هدول هيك مجرد
+
+435
+00:31:31,410 --> 00:31:35,150
+لل .. لل .. للتوضيح مش أكتر، هي ال code بس، التلات
+
+436
+00:31:35,150 --> 00:31:39,690
+سطور هدولة و هدا، هيهم، هي كل ال code تبعكم، هده
+
+437
+00:31:39,690 --> 00:31:46,030
+لمجرد لحظه فيه أقواس، هد مش code، هد للتوضيحكويسة
+
+438
+00:31:46,030 --> 00:31:50,870
+إذا والله أكبر خلاص بنحط قيمة V بتسويها طيب لاحظوا
+
+439
+00:31:50,870 --> 00:31:54,430
+ال for loop بياخد أول statement وراها بس هاي ال
+
+440
+00:31:54,430 --> 00:31:57,830
+statement سطر واحد بعدك هيرجع لمين لل loop نفسها
+
+441
+00:31:57,830 --> 00:32:01,390
+هيرجع لل loop نفسها أنا لا حطيت begin ولا end ولا
+
+442
+00:32:01,390 --> 00:32:05,770
+غيره معناته خد ال statement واحدة بعدك هاي السطر
+
+443
+00:32:05,770 --> 00:32:09,150
+بياخد one statement فقط هاي ال one statement
+
+444
+00:32:09,150 --> 00:32:13,050
+بتاعته بعدها لو في هنا مجموعة ال statementsولا
+
+445
+00:32:13,050 --> 00:32:16,450
+كأنها موجودة على طول هيخلص السطر هذا ويرجع لمين لل
+
+446
+00:32:16,450 --> 00:32:21,250
+four تبعته ال four I بتساوي تلاتة بده يقارن مع
+
+447
+00:32:21,250 --> 00:32:26,390
+عنصر تلاتة I بتساوي أربعة خمسة ستة سبعة N بيقارن
+
+448
+00:32:26,390 --> 00:32:31,090
+AN آخر عنصر مع ال V اللي جاعة بتتغير باستمرار كل
+
+449
+00:32:31,090 --> 00:32:33,790
+ما لجت رقم أكبر منها كل ما لجت رقم أكبر منها
+
+450
+00:32:33,790 --> 00:32:39,140
+بتخزنه بتاخده هو قيمتها كويسةفي الآخر لما خلصنا
+
+451
+00:32:39,140 --> 00:32:44,780
+هنا و خلصت ال loop يعني كأنه عمل search على كل ال
+
+452
+00:32:44,780 --> 00:32:49,980
+elements هنا to n طيب أخر قيمة جابها ل V هي أكبر
+
+453
+00:32:49,980 --> 00:32:55,440
+قيمة مدام عمل search عليهم كلهم و خلصت ال list ال
+
+454
+00:32:55,440 --> 00:32:59,000
+list of elements خلصت معناه ذلك أن أخر قيمة خزنت ل
+
+455
+00:32:59,000 --> 00:33:03,740
+V هي المفروض أكبر قيمة داخل ال list صحيح ف return
+
+456
+00:33:03,740 --> 00:33:07,920
+رجع ليه بقيمة V إزاي بالظبط كأنكم بتعملوا brand V؟
+
+457
+00:33:08,530 --> 00:33:14,830
+إطباع النقاشية قيمة V فنكتبها return ارجع V فكأنه
+
+458
+00:33:14,830 --> 00:33:22,030
+طلع قيمة V اللي هي the largest integer in the list
+
+459
+00:33:22,030 --> 00:33:27,130
+okay another example taskال tasks بتاعتنا هلوجت من
+
+460
+00:33:27,130 --> 00:33:31,130
+ال tasks المهمة و اللي لسه بيشتغلوا عليها كتير
+
+461
+00:33:31,130 --> 00:33:34,050
+يعني فيها شغل كتير و فيها تطورات كتير و فيها شغل
+
+462
+00:33:34,050 --> 00:33:38,170
+كتير بيشتغلوا ما زالوا اللي هي ال searching او ال
+
+463
+00:33:38,170 --> 00:33:41,030
+problem of searching او ال search انا بدور على
+
+464
+00:33:41,030 --> 00:33:44,170
+element داخل ال sequence في element بدور عليه داخل
+
+465
+00:33:44,170 --> 00:33:46,310
+ال sequence بس بدنا نحدد هنا ان انا بتكلم عن
+
+466
+00:33:46,310 --> 00:33:52,910
+ordered list زي افترضوا انه عملنا امتحان النصفي
+
+467
+00:33:53,660 --> 00:33:57,040
+خلصنا امتحان النصفة و طلعت فينا شوية درجات الدرجات
+
+468
+00:33:57,040 --> 00:34:03,160
+هي دي بدنا نشوف اكم درجة جد او خليني نقول اللي
+
+469
+00:34:03,160 --> 00:34:07,560
+نجحين كيف درجاتهم اكم طالب نجح اكم طالب رسب اكم
+
+470
+00:34:07,560 --> 00:34:12,600
+اشي فبنعملها logic search على ال threshold بتاعة
+
+471
+00:34:12,600 --> 00:34:15,460
+النجاح على الستين عشان نشوف جدش فيه اكتر منها و
+
+472
+00:34:15,460 --> 00:34:20,150
+جدش فيه اقل منهاكأنه عندنا مثلا نفترض واحد جاب
+
+473
+00:34:20,150 --> 00:34:22,410
+واحد، واحد جاب اتنين، واحد جاب عشرة، واحد جاب
+
+474
+00:34:22,410 --> 00:34:28,590
+عشرين، واحد جاب مثلا خمسة وعشرين، جاب أربعين، خمسة
+
+475
+00:34:28,590 --> 00:34:37,050
+وخمسين، ستين، سبعين، تسعة وسبعين، تمانين، هاي
+
+476
+00:34:37,050 --> 00:34:41,550
+تسعين، يلا ما تسعلوش، اتنين وتسعين، تسعة وتسعين،
+
+477
+00:34:41,550 --> 00:34:47,340
+حاضر، تسعة وتسعينكويس نفترض ان احنا بهذا الشكل فيه
+
+478
+00:34:47,340 --> 00:34:52,020
+مجموعة درجات طبعا هخزنهم عندي وين على ال Excel
+
+479
+00:34:52,020 --> 00:34:58,020
+حاجة عند ال column تبعت الدرجة و اعمله sorting ايش
+
+480
+00:34:58,020 --> 00:35:02,380
+يعني اعمله sorting يعني اعمله كرتيب تساعدى فمعناه
+
+481
+00:35:02,380 --> 00:35:05,700
+ده اللي هرتب لهم بهذا الشكل تساعدى ordered فصارت
+
+482
+00:35:05,700 --> 00:35:09,380
+ايش ordered list ال ordered list ده بتدور على
+
+483
+00:35:09,380 --> 00:35:18,410
+الرقم 60 موجود ولا لأنختار نبحث عن رقم ستين إذا
+
+484
+00:35:18,410 --> 00:35:23,910
+موجود بده ال location تبعه بدنا ال location والله
+
+485
+00:35:23,910 --> 00:35:28,530
+ال location فعليا إذا عرفت ال location وانا عارف
+
+486
+00:35:28,530 --> 00:35:31,670
+جدش العدد الإجمالي للطلاب اللي دخلوا الامتحان
+
+487
+00:35:31,670 --> 00:35:37,610
+بنقدر جدش فيه أكبر و جدش فيه أقل بس احنا هالواجهة
+
+488
+00:35:37,610 --> 00:35:43,930
+هي taskنرجع نتعامل مع الموضوع بصفته الحالية عندنا
+
+489
+00:35:43,930 --> 00:35:50,010
+قائمة مرتبة و بدنا ندور على رقم داخلها هل موجود
+
+490
+00:35:50,010 --> 00:35:53,650
+ولا لأ فإذا انا عندي ال input تبعتي القائمة نفسها
+
+491
+00:35:53,650 --> 00:35:58,310
+ال less نفسها زائد ال input اللي بدور عليه I know
+
+492
+00:35:58,310 --> 00:36:01,170
+element ما أنا ممكن كل ما بغير ال element هتتغير
+
+493
+00:36:01,170 --> 00:36:04,610
+النتاج اللي بتطلع بدنا مثلا خليني أقول ال 60 خليني
+
+494
+00:36:04,610 --> 00:36:09,570
+على ال 60 .. 60نفترض في عندنا sequence أو مجموعة
+
+495
+00:36:09,570 --> 00:36:13,930
+أرقام بهذا الشكل و بدنا ندور مرتبة كمان مرة هنا
+
+496
+00:36:13,930 --> 00:36:18,690
+بقولها مرتبة و بندور على الستين فيها طيب في عندنا
+
+497
+00:36:18,690 --> 00:36:24,390
+حقيقة نوعين لشغل لإن احنا أساسا اتفقنا أنه بدنا
+
+498
+00:36:24,390 --> 00:36:27,810
+ندور على X هل هي موجودة ولا لا و إيش النتيجة اللي
+
+499
+00:36:27,810 --> 00:36:32,620
+بديها مش بدي الله X بدي ال location تبع Xبالظبط
+
+500
+00:36:32,620 --> 00:36:35,740
+الموقع تبعها في agitation موقعها الخامسة العشرة ال
+
+501
+00:36:35,740 --> 00:36:37,660
+element العشرين ال element التلاتين في ال sequence
+
+502
+00:36:37,660 --> 00:36:42,900
+في ال last وين بالظبط فبنحدد ال location تبعها طيب
+
+503
+00:36:42,900 --> 00:36:47,460
+ال problem الحقيقة محتاجة efficient algorithm لأن
+
+504
+00:36:47,460 --> 00:36:50,800
+في algorithms كتيرة بتشتغل الموضوع هذا هناخد منها
+
+505
+00:36:50,800 --> 00:36:55,480
+نوعين في نوع أول واحد بنسميه linear ولاحقا هناخد
+
+506
+00:36:55,480 --> 00:36:58,700
+binary فنبدأ بال linear search ال linear search
+
+507
+00:36:58,700 --> 00:37:04,550
+بنشتغل عليه كتالة إن أنا بمسك ال 60اللي بدي أدور
+
+508
+00:37:04,550 --> 00:37:10,530
+عليها و بقارنها مع الأولى مع التانية مع التالتة مع
+
+509
+00:37:10,530 --> 00:37:14,090
+الرابعة مع الخمسة مع السادسة مع السابعة .. امتى
+
+510
+00:37:14,090 --> 00:37:19,510
+بصلي بوقف امتى بنصلي لها وقفنا خلاص لإنه مش هتكون
+
+511
+00:37:19,510 --> 00:37:23,630
+مع الباجئين احنا مرتبينهم الباجئين و مرتبينهم بحيث
+
+512
+00:37:23,630 --> 00:37:28,850
+ان هم distinct integers بمعنى إيش انه مافيش قيمتين
+
+513
+00:37:28,850 --> 00:37:34,800
+زي بعضمعنى ذلك أنه مدام وصلت لها خلاص وجهتنا ال
+
+514
+00:37:34,800 --> 00:37:38,300
+location تبعها بدي ايه بس ال location تبعها بدنا
+
+515
+00:37:38,300 --> 00:37:42,480
+ايه بتكون وجفنا شغلنا و stop على هيك طيب بس بتظهر
+
+516
+00:37:42,480 --> 00:37:46,380
+المشكلة أنه احنا عادة الرقم X اللي بدور عليه انا
+
+517
+00:37:46,380 --> 00:37:50,520
+مش عارف هو موجود وين داخل ال list يمكن يكون اخر
+
+518
+00:37:50,520 --> 00:37:54,790
+element ممكن يكون اخر element موجودممكن يكون اول
+
+519
+00:37:54,790 --> 00:37:57,790
+element معناه ذلك ان ال search هيكون سريع جدا او
+
+520
+00:37:57,790 --> 00:38:00,050
+يكون اخر element معناه ذلك ان ال search هيكون بطيق
+
+521
+00:38:00,050 --> 00:38:05,270
+جدا عبل ما يخلص يعمل scan عليهم كلهم لو عندنا ..
+
+522
+00:38:05,270 --> 00:38:10,770
+تخيلوا لو في البلدية او في .. في اي مكان في قائمة
+
+523
+00:38:10,770 --> 00:38:15,590
+باسماء المواطنين و بدنا ندور على اسم معين نتكلم عن
+
+524
+00:38:15,590 --> 00:38:19,590
+ملايين و الاسم بدنا نعمله linear و انا مش عارف
+
+525
+00:38:19,590 --> 00:38:23,970
+الاسم هذا موجود في ال databaseأول اسم و لا اخر اسم
+
+526
+00:38:23,970 --> 00:38:28,090
+يمكن اخر اسم و عندك مدينة فيها اتنين مليون او مكان
+
+527
+00:38:28,090 --> 00:38:30,890
+فيه اتنين مليون بني ادم معناه ذلك انك تعملوا اتنين
+
+528
+00:38:30,890 --> 00:38:35,670
+مليون مقارنة اكبر ولا لا ولا مش هو هو ولا مش هو هو
+
+529
+00:38:35,670 --> 00:38:39,430
+ولا مش هو هو ولا مش هو ال code هيكون كتير طويل
+
+530
+00:38:39,430 --> 00:38:43,950
+كتير طويل طيب خلينا نتكلم عن sequence بسيط من واحد
+
+531
+00:38:43,950 --> 00:38:46,430
+تقن واحد distinct integers
+
+532
+00:38:51,110 --> 00:38:55,190
+إيش هنشتغل؟ كانت تالي procedure linear search واضح
+
+533
+00:38:55,190 --> 00:38:58,190
+إن أنا وضحته من الأول بقدرش أقول search لحاله لأنه
+
+534
+00:38:58,190 --> 00:39:01,570
+في أنواع من ال search أنواع اللي أنتوا شغالينه
+
+535
+00:39:01,570 --> 00:39:05,290
+فواضح كويس جدا لو كان واضحا linear search فبعرف
+
+536
+00:39:05,290 --> 00:39:08,370
+إنه linear أقواس عشان نحط ال input ساعتنا ال
+
+537
+00:39:08,370 --> 00:39:11,790
+arguments أول input اللي هو ال X اللي أنا بدي أعمل
+
+538
+00:39:11,790 --> 00:39:15,590
+search عليه بدور عليه وهذا integer ال input التاني
+
+539
+00:39:15,590 --> 00:39:19,330
+القائمة اللي بدي أدور فيها okay بدي أدور على ستين
+
+540
+00:39:19,330 --> 00:39:24,440
+وين؟في ملف ال Excel تبع درجات ال discrete خلاص
+
+541
+00:39:24,440 --> 00:39:28,780
+افهمناها معناته هي الملف هي ال list تبعتي هي ال
+
+542
+00:39:28,780 --> 00:39:34,520
+list بتاعتنا فإذا بدي ال input x integer و a1 a2
+
+543
+00:39:34,520 --> 00:39:40,160
+a3 او ال list distinct integers برضه مجموعة
+
+544
+00:39:40,160 --> 00:39:45,000
+integers متباينة متميزة مميزة مافيش رقمين زي بعض
+
+545
+00:39:46,240 --> 00:39:49,060
+نبدأ ب I بتساوي واحد فخلاص أنا هنا محدد ان ال
+
+546
+00:39:49,060 --> 00:39:52,560
+index الأولى بدي أبدأ أقارن مع مين مع أول element
+
+547
+00:39:52,560 --> 00:39:56,560
+أول element ال location تبعته واحد ف I بتساوي واحد
+
+548
+00:39:56,560 --> 00:40:01,980
+ال location الأول طيب while نبدأ I أقل من أو تساوي
+
+549
+00:40:01,980 --> 00:40:08,460
+and مدام I أقل من آخر عنصر معناته أنا لسه داخل ال
+
+550
+00:40:08,460 --> 00:40:13,760
+list مازلت بقارن في أرقام داخل ال list مقارنتهاش
+
+551
+00:40:14,340 --> 00:40:22,440
+لازم أكملهم فهذا أول شرط and x لا تساوي a i لأن
+
+552
+00:40:22,440 --> 00:40:25,980
+إذا سوتها خلاص مافيش داعي أكمل باقي السعر إذا
+
+553
+00:40:25,980 --> 00:40:30,120
+سوتها مافيش داعي أكمل و احنا بندور و طلعت هنا بدور
+
+554
+00:40:30,120 --> 00:40:34,200
+على رقم واحد مثلا جينا
+
+555
+00:40:34,200 --> 00:40:38,880
+هنا واحد ساوى إذا ساوى خلاص stop ليش تدور في
+
+556
+00:40:38,880 --> 00:40:42,120
+الباقي طب ما أنتوا عارفين إن هي order و distinct
+
+557
+00:40:43,180 --> 00:40:46,840
+عارفين إن هي ordered يعني امرتبة اللي .. اللي بعد
+
+558
+00:40:46,840 --> 00:40:51,480
+الواحد هتكون أكبر من الواحد و distinct مميزة اللي
+
+559
+00:40:51,480 --> 00:40:56,340
+وراها لا يمكن يكون واحد برضه فخلاص stop وقف ال I
+
+560
+00:40:56,340 --> 00:41:00,480
+هي اللي بديها طيب otherwise إنه لأ و الله لا تساوي
+
+561
+00:41:00,480 --> 00:41:07,040
+معناه ذلك إنه صار عندنا اشتغل اشتغل فلاحظوا I داخل
+
+562
+00:41:07,040 --> 00:41:11,520
+ال list لسه أقل من أو تساوي and
+
+563
+00:41:13,670 --> 00:41:16,450
+فإذا ال condition هذا إن أنا ما زلت ما خلصتش كل
+
+564
+00:41:16,450 --> 00:41:19,910
+العناصر، هي الهدف منه، أنا ما زلت ما خلصتش كل
+
+565
+00:41:19,910 --> 00:41:22,370
+العناصر، بس في condition تاني ممكن يطلعني من ال ..
+
+566
+00:41:22,370 --> 00:41:26,570
+من مين؟ من ال while شوة إن أنا لاجي العنصر، okay
+
+567
+00:41:26,570 --> 00:41:28,770
+أنا ماخلصتش كل العناصر، بس أنا لاجيت اللي بدور
+
+568
+00:41:28,770 --> 00:41:33,910
+عليه، خلاص، يعني ايه؟ وجعته شكل
+
+569
+00:41:35,460 --> 00:41:39,120
+هتقول و الله طب ماشي هل وجد بدنا نعمل خطة؟ يلا
+
+570
+00:41:39,120 --> 00:41:42,500
+توزعوا البنات كل واحدة متر في متر اتدور فيه طب اه
+
+571
+00:41:42,500 --> 00:41:45,020
+لا استنوا لجيتوا طب ايه هو معنى بقى ال procedure
+
+572
+00:41:45,020 --> 00:41:48,380
+اللي سابعتكم؟ ملاش ما خلاص لجينا فمعنى ذلك مدام
+
+573
+00:41:48,380 --> 00:41:55,160
+انا لجيته stop العنصر اللي بدور عليه لجيته وقف
+
+574
+00:41:55,160 --> 00:42:01,610
+فإذا هذا داخل إن أنا خلصت ال list أو لأأو إن أنا
+
+575
+00:42:01,610 --> 00:42:06,550
+لجيته العنصر ف two conditions لازم يكون ماخدين
+
+576
+00:42:06,550 --> 00:42:08,890
+بالنا منهم إما إن أنا خلصت كل ال sequence وما لجتش
+
+577
+00:42:08,890 --> 00:42:14,350
+العنصر فوجف عشان ماضلش forever أو إن أنا لجيته
+
+578
+00:42:14,350 --> 00:42:17,310
+العنصر فخلاص ماعنى باجر ال search تبعي باجي ال
+
+579
+00:42:17,310 --> 00:42:21,550
+search بيصير ماضي ع الوقت اللي باجي في الحالة هذه
+
+580
+00:42:21,550 --> 00:42:26,390
+إذا لأ أنا مازل داخل ال list مخلصتش وما لجتش
+
+581
+00:42:26,390 --> 00:42:33,880
+العنصر لا يساويلأ يساوي مادام لأ يساوي احقق ال
+
+582
+00:42:33,880 --> 00:42:36,900
+statement بتاعة ال Y I بتساوي I زائد واحد شوف
+
+583
+00:42:36,900 --> 00:42:42,960
+العنصر التاني العنصر التاني برضه لسه أقل من N أقل
+
+584
+00:42:42,960 --> 00:42:49,980
+من ال N و X لاتساوي شوف التالت I بتصير مثلا اتنين
+
+585
+00:42:49,980 --> 00:42:54,940
+زائد واحد تلاتة الرابع الخامس العشر العشرين طيب
+
+586
+00:42:54,940 --> 00:42:57,220
+وصلنا ل I N
+
+587
+00:42:59,760 --> 00:43:05,400
+معناته انا قاعد بقارن اخر عنصر ان بتساوي ان جينا
+
+588
+00:43:05,400 --> 00:43:12,000
+هنا اي بتساوي ان زائد واحد why لأ هذه false قصرنا
+
+589
+00:43:12,000 --> 00:43:20,740
+ال why بتاعتنا بالحالة هذه اي اقل من او تساوي ان
+
+590
+00:43:20,740 --> 00:43:27,720
+لأ فعليا اللي قصر ال why تبعتي ان زائد واحدصحيح؟
+
+591
+00:43:27,720 --> 00:43:29,860
+احنا وصلنا .. انها logic الحالة اللي مفترضها ان
+
+592
+00:43:29,860 --> 00:43:33,600
+انا وصلت لآخر ال sequence وصلنا لآخر ال sequence
+
+593
+00:43:33,600 --> 00:43:39,220
+طيب و مش .. و مش العنصر هذا اللي قسر ال while و مش
+
+594
+00:43:39,220 --> 00:43:42,480
+ال condition التاني ال condition الأول معناه ذلك
+
+595
+00:43:42,480 --> 00:43:44,800
+مدام ال condition الأول اللي قسر ال while معناته
+
+596
+00:43:44,800 --> 00:43:49,880
+أكيد ال I بتساوي N زائد 1 كيف تتنكسر هذه؟ كيف أنت
+
+597
+00:43:49,880 --> 00:43:54,470
+.. أنت بتصير falseبالظبط n زائد واحد مدام صارت n
+
+598
+00:43:54,470 --> 00:43:59,730
+زائد واحد معناته هنا برضه false في الحالة هذه else
+
+599
+00:43:59,730 --> 00:44:03,630
+location zero معناته أن العنصر غير موجود أنا لفتهم
+
+600
+00:44:03,630 --> 00:44:07,870
+كلهم وصلت لآخر element مش لاجي العنصر مش لاجين
+
+601
+00:44:07,870 --> 00:44:11,030
+العنصر
+
+602
+00:44:11,030 --> 00:44:19,930
+طيب أثناء الشغل ماوصلناش لسه ل .. لل إيش لل n زائد
+
+603
+00:44:19,930 --> 00:44:25,820
+واحدو احنا هنا بندور 60
+
+604
+00:44:25,820 --> 00:44:34,360
+وجينا ال 60 عند ال 60 وجينا ال 60 I عند 59 تمام
+
+605
+00:44:34,360 --> 00:44:40,860
+قارننا مافيش لا 59 لا تساوي جينا هنا صارت 60 باجي
+
+606
+00:44:40,860 --> 00:44:47,260
+بقارن هنا ال 60لسة أقام .. أعفون .. هذه ال
+
+607
+00:44:47,260 --> 00:44:49,860
+location مش عارف جديش عددها ال location كان سبعة
+
+608
+00:44:49,860 --> 00:44:53,000
+خليني أقول سبعة من .. من جديش .. واحد، اتنين،
+
+609
+00:44:53,000 --> 00:44:56,040
+تلاتة، أربعة، خمسة، ستة، سبعة، تمانية العنصر رقم
+
+610
+00:44:56,040 --> 00:45:00,600
+تمانية هذه ال I من واحد لتمانية من جديش تسعة، عشر،
+
+611
+00:45:00,600 --> 00:45:02,940
+أحداشر، اتناشر، تلاتاشر، اربعتاشر خليني أقول من
+
+612
+00:45:02,940 --> 00:45:08,200
+أربعتاشر إجينا هنا على تمانية
+
+613
+00:45:10,700 --> 00:45:15,040
+Okay هي مزارة أقل من مين؟ من ال 14 Okay فليكن ولكن
+
+614
+00:45:15,040 --> 00:45:23,180
+X اللي هي 60 تساوي ايه 8؟ 1 2 3 4 .. لأنه بتساوي
+
+615
+00:45:23,180 --> 00:45:27,040
+60 تحقق
+
+616
+00:45:27,040 --> 00:45:34,380
+الشرط تحقق معناته عدم المسواة false هذا لا يساوي
+
+617
+00:45:34,380 --> 00:45:40,530
+معناته أصبحت هذا falseهي اللي اتحقق هنا أنه يساوي
+
+618
+00:45:40,530 --> 00:45:46,570
+فعدم المساوية صارت هي false في الحالة دي ال while
+
+619
+00:45:46,570 --> 00:45:53,910
+خلاص وقف باجي بنجل هنا I أقل من N صح I أقل من N
+
+620
+00:45:53,910 --> 00:45:58,810
+فإيش برجع location I طيب كويس في الحالة دي أخر آية
+
+621
+00:45:58,810 --> 00:46:03,430
+وصلت لها إيش كانت تمانية تمانية هيرجع لبمين بال
+
+622
+00:46:03,430 --> 00:46:08,570
+location بقيمة ال location اللي هي Iاللي هي تمانية
+
+623
+00:46:08,570 --> 00:46:13,610
+يعني كأنه مدام طلعلي رقد تمانية يعني كأنه العنصر
+
+624
+00:46:13,610 --> 00:46:18,070
+موجود وموجود في ال location التامن في ال list إذا
+
+625
+00:46:18,070 --> 00:46:22,510
+رجعلي صفر غير موجود في كل ال sequence لأن هذا لن
+
+626
+00:46:22,510 --> 00:46:26,290
+يتحقق إلا إذا كانت هنا وصلنا ل N زائد واحد N زائد
+
+627
+00:46:26,290 --> 00:46:31,030
+واحد هنا مش هيتحقق ال condition else رجعلي في zero
+
+628
+00:46:31,750 --> 00:46:36,850
+معناته عمل search على كل ال sequence بدون ما يصل
+
+629
+00:46:36,850 --> 00:46:41,430
+للرقم فإذا الرقم أصلا غير موجود في هيك حالة في هيك
+
+630
+00:46:41,430 --> 00:46:46,210
+حالة فهياخدنا الحالتين إما إنه يعمل search على كل
+
+631
+00:46:46,210 --> 00:46:52,290
+ال last أو إنه لأ لجأ لهنصر لجأ لهنصر ال binary
+
+632
+00:46:52,290 --> 00:46:57,100
+search ال binary searchمميزة برضه ال binary search
+
+633
+00:46:57,100 --> 00:47:02,480
+في البحث على أساس انه من واحد لجدش لتسعة وتسعين
+
+634
+00:47:02,480 --> 00:47:08,120
+فاحنا هنا بنحطهم بنرتبهم هاي ال واحد العنصر واحد
+
+635
+00:47:08,120 --> 00:47:16,260
+بدي عند العنصر a واحد فال index تبعتنا وهد ال a i
+
+636
+00:47:17,770 --> 00:47:24,450
+اتنين تلاتة اربعة خمسة ستة لاربعتاج اذا احنا
+
+637
+00:47:24,450 --> 00:47:27,610
+بنتكلم عن الحالة اللي احنا بنشتغل عليها هنا طبعا
+
+638
+00:47:27,610 --> 00:47:33,290
+هنا هيكون اتنين عشرة عشرين بهذا الشكل هنرتبهم بهذا
+
+639
+00:47:33,290 --> 00:47:37,030
+الشكل طيب لما اجي اعمل search هعمل search مش
+
+640
+00:47:37,030 --> 00:47:44,700
+linear binary معناته ثنائي بجسمال space تبع هذا
+
+641
+00:47:44,700 --> 00:47:51,880
+كله او ال list تبعته ل نصين بنجي هنا و بنقسم نصين
+
+642
+00:47:51,880 --> 00:47:57,600
+و باخد M ال mid point او ال mid location ال
+
+643
+00:47:57,600 --> 00:48:00,160
+location اللي في المص طيب ال location اللي في المص
+
+644
+00:48:00,160 --> 00:48:05,740
+هذا بقارن القيمة اللي عنده مع ال X اللي بدور عليها
+
+645
+00:48:05,740 --> 00:48:10,860
+بنقارن القيمة اللي موجودة هنا يعني بمعنى بقارن
+
+646
+00:48:10,860 --> 00:48:12,340
+القيمة A M
+
+647
+00:48:16,360 --> 00:48:25,540
+ام لجينا ان X أكبر من ام معناته لا يمكن X تكون في
+
+648
+00:48:25,540 --> 00:48:28,560
+الجزء اللي هنا لان كل الجزء اللي هنا ordered أقل
+
+649
+00:48:28,560 --> 00:48:34,100
+من ام طب X أكبر لسه من ام معناته لا يمكن يكون في
+
+650
+00:48:34,100 --> 00:48:38,780
+الجزء هذا اوتوماتيك هيك صارت تعريفنا لو قلنا ان
+
+651
+00:48:38,780 --> 00:48:47,980
+هذه بدية من I to J صارتم لأ مش هي ال I الجديدة M
+
+652
+00:48:47,980 --> 00:48:55,840
+زائد واحد هي ال I الجديدة وبنبدأ ال algorithm مرة
+
+653
+00:48:55,840 --> 00:49:02,000
+تانية ليش I زائد واحد لإنه X أكبر من M من AM
+
+654
+00:49:02,000 --> 00:49:06,980
+معناته عند ال location M لأ مش موجود العنصرغير
+
+655
+00:49:06,980 --> 00:49:11,320
+موجود طيب نعمل بحث نبدأ من M زائد واحد من بعده
+
+656
+00:49:11,320 --> 00:49:16,340
+نبدأ من بعده ليش هضيع وقت فيه ففي الحالة هذه بنبدأ
+
+657
+00:49:16,340 --> 00:49:24,320
+code جديد هايو أو بنعمل loop اللي عملناه على I J
+
+658
+00:49:24,320 --> 00:49:28,980
+الأولى بنعمله على I J التانية برضه في نص ال
+
+659
+00:49:28,980 --> 00:49:32,600
+interval بتاعتهم في نص ال interval بسيطة I زائد J
+
+660
+00:49:32,600 --> 00:49:36,020
+على اتنين طيب ممكن يطلع كسر
+
+661
+00:49:39,510 --> 00:49:46,070
+floor floor خلاص اعملوله floor خدوا أقلب واحد يعني
+
+662
+00:49:46,070 --> 00:49:52,170
+بلاش منها ال fractions بلاش منها القصور تمام في
+
+663
+00:49:52,170 --> 00:49:56,470
+الحالة هذه هذا
+
+664
+00:49:56,470 --> 00:50:02,550
+الجزء كله لا يمكن تكون X موجودة فيه لأن X أكبر من
+
+665
+00:50:02,550 --> 00:50:09,820
+أكبر رقم فيه هو مرتب و هو مرتبطيب عند نص ال
+
+666
+00:50:09,820 --> 00:50:18,880
+interval جديدة هنقول x أقل لا يمكن تكون أكبر مدام
+
+667
+00:50:18,880 --> 00:50:22,920
+أقل معناته لا يمكن تكون في الجزء الأكبر صار عندنا
+
+668
+00:50:22,920 --> 00:50:26,500
+interval جديدة نفس الكلام نص ال interval جديدة
+
+669
+00:50:26,500 --> 00:50:31,860
+خلينا نقول أقل ال .. عفوا x أكبر معناته لا يمكن
+
+670
+00:50:31,860 --> 00:50:34,500
+تكون في الجهة الأقل اللي هي في ال left في ال left
+
+671
+00:50:34,500 --> 00:50:40,090
+sideنفس الكلام نرجع نكرره لعند ما في الآخر تلاقيوا
+
+672
+00:50:40,090 --> 00:50:44,610
+حال كنتوا بتقارنوا بعنصر واحد طالع العنصر هذا
+
+673
+00:50:44,610 --> 00:50:47,950
+بنقارن .. بنقارنه مباشرة، هل هو بيساوي أو لا، إذا
+
+674
+00:50:47,950 --> 00:50:52,430
+بيساوي معناته هو، لا يساوي، معناته برضه بنرجع بال
+
+675
+00:50:52,430 --> 00:50:55,890
+location zero زي ما توا أخر الكود، كتبنا location
+
+676
+00:50:55,890 --> 00:50:58,950
+zero، هنا نفس الكلام، إذا ما طلعش بيساوي، بكون
+
+677
+00:50:58,950 --> 00:51:03,890
+location zero هنحصر في الآخر على عنصر واحد، نحصر
+
+678
+00:51:03,890 --> 00:51:07,580
+كل الموضوع ده في عنصر واحدانصر الواحد ده ده اما
+
+679
+00:51:07,580 --> 00:51:11,500
+بيساوي او غير موجود اما بيساوي او غير موجود طب
+
+680
+00:51:11,500 --> 00:51:17,560
+كويسة هيك وضحنا الفكرة خلينا نكتب ال algorithm او
+
+681
+00:51:17,560 --> 00:51:23,640
+ال code تبعها وضحنا الفكرة نكتب ال code برضه كتالي
+
+682
+00:51:23,640 --> 00:51:28,420
+procedure اه يا جماعة احنا بدأنا في code بدأنا في
+
+683
+00:51:28,420 --> 00:51:34,310
+code procedure اسمهأنا مش عارف خلاص هيك واضحة بشكل
+
+684
+00:51:34,310 --> 00:51:37,410
+هذا أنا مش عارف يمكن كونه just كو linear linear و
+
+685
+00:51:37,410 --> 00:51:43,130
+أتي أتبع معاكم طب أنا مش في بالي binary أنا بدأت
+
+686
+00:51:43,130 --> 00:51:46,270
+معاكم أخطط عن انه linear لجيت انه صار في عندي
+
+687
+00:51:46,270 --> 00:51:49,410
+مشكلة أنا مش عارف أتبع ال code و حصفون ليه يمكن في
+
+688
+00:51:49,410 --> 00:51:52,210
+عشر دقائق و أنا مش عارف انتوا إيش اللي بتكتبوه و
+
+689
+00:51:52,210 --> 00:51:54,990
+يمكن في الآخر أروح نعمل غلط و لأ لأ شكل ال code مش
+
+690
+00:51:54,990 --> 00:51:59,850
+نافع بدو يكون واضح المسمة binary search خلاص عرفت
+
+691
+00:51:59,850 --> 00:52:03,810
+أن انتوا بتتكلموا عن إيشبناري سيرجي ايش ال
+
+692
+00:52:03,810 --> 00:52:07,070
+arguments بتاعتنا ال X اللي بدور عليها وهد integer
+
+693
+00:52:07,070 --> 00:52:12,250
+و ال sequence او ال list اللي بده ادور فيها على X
+
+694
+00:52:12,250 --> 00:52:14,870
+اللي بده ادور فيها على مين على X و هد distinct
+
+695
+00:52:14,870 --> 00:52:19,950
+integers طيب هنبدأ ال sequence تبعنا واضح من ايش
+
+696
+00:52:19,950 --> 00:52:26,510
+من واحد to أنا الواحد هتكون هي ال I اللي هي بداية
+
+697
+00:52:26,510 --> 00:52:30,030
+ال sequence او ال left end note of the search
+
+698
+00:52:30,030 --> 00:52:36,810
+intervalوالان ال right point حددنا البداية و
+
+699
+00:52:36,810 --> 00:52:40,310
+النهاية الحددنا البداية و النهاية البداية و
+
+700
+00:52:40,310 --> 00:52:44,890
+النهاية هدولا محتاجينهم عشان نحسب ال mid point
+
+701
+00:52:44,890 --> 00:52:49,590
+النقطة اللي في النص في نص ال sequence طيب نبدأ
+
+702
+00:52:49,590 --> 00:52:57,850
+while I أقل من J طول ما I أقل من J الطبيعيمعناته
+
+703
+00:52:57,850 --> 00:53:00,470
+في interval بينهم في مجموعة elements داخل ال
+
+704
+00:53:00,470 --> 00:53:02,590
+interval مدان في elements داخل ال interval لازم
+
+705
+00:53:02,590 --> 00:53:06,810
+تكون I أقل من J أه لحظة في عندي أكتر من statement
+
+706
+00:53:06,810 --> 00:53:10,410
+عندنا أكتر من statement محتاجين نعملها فمحتاج
+
+707
+00:53:10,410 --> 00:53:14,570
+begin و end هاي ال begin و هاي ال end على نفس
+
+708
+00:53:14,570 --> 00:53:19,830
+المستوى محتاجين ننفذ في كل قيمة لل while لل
+
+709
+00:53:19,830 --> 00:53:23,150
+condition هدا محتاجين ننفذ اتنين statements هدول
+
+710
+00:53:23,150 --> 00:53:28,700
+مع بعض لا اكتفي ب statement واحد و ارجعفى begin و
+
+711
+00:53:28,700 --> 00:53:35,600
+end طيب نحسب ايش ال midpoint ال M I زي J over two
+
+712
+00:53:35,600 --> 00:53:39,660
+floor حسبنا النقطة اللى فى النص تمام النقطة اللى
+
+713
+00:53:39,660 --> 00:53:45,280
+فى النص هذه وجدنا انهى اقل من X M X M اكبر منها
+
+714
+00:53:45,280 --> 00:53:51,560
+معناته اللى يمكن يكون فى ال left هد
+
+715
+00:53:51,560 --> 00:53:59,150
+ال I J و هنا ال A Mحسب إشتغالنا على الام وهذه ال X
+
+716
+00:53:59,150 --> 00:54:06,230
+اللي بدور عليها وجدنا أن X أكبر من AM
+
+717
+00:54:06,230 --> 00:54:15,370
+لا يمكن يكون هنا X صحيح لأنه أكبر X أكبر okay في
+
+718
+00:54:15,370 --> 00:54:22,630
+الحالة دي I automatic هتيجي وين M زائد واحد أنا
+
+719
+00:54:22,630 --> 00:54:27,190
+ماقلتش أو يساويأحنا مش حاطين هنا او يساوي عارفين
+
+720
+00:54:27,190 --> 00:54:31,190
+لو حاطين او يساوي بقولكوا اه ب automatic ال I
+
+721
+00:54:31,190 --> 00:54:37,870
+بيصير ال M لجديدة أما لأ هي M زائد واحد ليش لأنه
+
+722
+00:54:37,870 --> 00:54:43,970
+أكبر X أكبر من AM معناته لا يمكن أحط أبدأ من AM
+
+723
+00:54:43,970 --> 00:54:49,610
+لأن AM أصلا فعلا مش محققة ال condition هي ليست X
+
+724
+00:54:51,350 --> 00:54:57,010
+فهنا بنقول انه ايش M زائد واحد فهي اذا X أكبر من
+
+725
+00:54:57,010 --> 00:55:02,710
+ايه M then I زائد واحد زائد واحد لأن ال condition
+
+726
+00:55:02,710 --> 00:55:09,690
+مافيه يساوي طيب otherwise او else J بتساوي M اذا
+
+727
+00:55:09,690 --> 00:55:16,190
+والله لأ العكس ايش العكس او يساوي او يساوي هي اللي
+
+728
+00:55:16,190 --> 00:55:18,310
+هتخلينا نقول ان هنا M
+
+729
+00:55:20,490 --> 00:55:27,990
+هنا بتقول M فإذا كانت هنا أقل أو يساوي عكس الأكبر
+
+730
+00:55:27,990 --> 00:55:32,890
+من أقل أو يساوي طيب فإذا ممكن تكون تساوي ففي الحال
+
+731
+00:55:32,890 --> 00:55:36,610
+هاد ال J هتيجي مكان ال M لأنه في احتمال أنها تكون
+
+732
+00:55:36,610 --> 00:55:40,090
+بتسويها ما هي هتكون حققت الشرط إذا كان ال X بتساوي
+
+733
+00:55:40,090 --> 00:55:46,270
+ال AM هتكون حققته فعلا فبنحط J بتساوي M
+
+734
+00:55:48,000 --> 00:55:51,980
+واضحة؟ واضحة لماذا هنا M زائد واحد ولماذا هنا M؟
+
+735
+00:55:51,980 --> 00:55:55,700
+كويسة
+
+736
+00:55:55,700 --> 00:56:00,160
+ونخلص الجزء هذا تيجي هنا طبعا هتكون اتغيرت قيم I
+
+737
+00:56:00,160 --> 00:56:03,420
+أو J يا ال I يا ال J هتكون اتغيرت بناء ال
+
+738
+00:56:03,420 --> 00:56:08,860
+condition هذا، صح؟ كويسة بنحقق، بنشوف كمان مرة،
+
+739
+00:56:08,860 --> 00:56:16,300
+لسه I أقل من Jمازالت بنحسب مد point جديدة و بنرجع
+
+740
+00:56:16,300 --> 00:56:22,180
+نقرنها و بنستمر لعد ما نصل في الآخر أن ال j هذا
+
+741
+00:56:22,180 --> 00:56:28,520
+بتساوي m و ال I هتيجي عند القيمة اللي جدامها
+
+742
+00:56:28,520 --> 00:56:31,920
+جابلها بالظبط صار بينهم إيه نقطة يعني وصلناها
+
+743
+00:56:31,920 --> 00:56:35,200
+أنهية .. بنتكلم عن element واحد فقط ال interval
+
+744
+00:56:35,200 --> 00:56:42,880
+فصارت هنا I بتساوي M زائد واحدmزاد واحد هتيجي
+
+745
+00:56:42,880 --> 00:56:48,500
+مشابه لمين لل j هتطلع تساوي j إذا كان دل في الآخر
+
+746
+00:56:48,500 --> 00:56:54,920
+element واحد إذا دل element واحد نتيجة إن ال I
+
+747
+00:56:54,920 --> 00:57:00,660
+مزاد واحد فال element الواحد هذا اللي هو أصلا
+
+748
+00:57:00,660 --> 00:57:05,980
+موجود بينهم خلى ال I و ال J بسووا بعض هيخلى ال I و
+
+749
+00:57:05,980 --> 00:57:15,180
+J بسوا بعض في الحالة هذهال while إيش صار فيه؟ خلاص
+
+750
+00:57:15,180 --> 00:57:23,260
+وقف، هيوقف و هيطلع هنا بوقف عند آخر I موجودة، عند
+
+751
+00:57:23,260 --> 00:57:27,180
+آخر I موجودة ال I الأخيرة هذه إحنا اتفقنا إنه مش
+
+752
+00:57:27,180 --> 00:57:30,720
+هصير الكلام هذا إلا لما يظل عنصر واحد في الآخر، بس
+
+753
+00:57:30,720 --> 00:57:35,860
+عنصر وحيد فقط هو العنصر الوحيد، مدام ظهر عنصر
+
+754
+00:57:35,860 --> 00:57:41,550
+وحيد، نتيجة إنه في عند هنا ال J بقربها ل Mو ال I
+
+755
+00:57:41,550 --> 00:57:47,210
+بقربها ل M plus واحد هنطبقوا على بعض عند أنصر واحد
+
+756
+00:57:47,210 --> 00:57:51,050
+في الآخر كله هتظل اللوب هتشغل لما تصف عندي على
+
+757
+00:57:51,050 --> 00:57:57,150
+أنصر واحد اللي هو في ال location I خلصنا
+
+758
+00:57:57,150 --> 00:58:01,290
+بعمل check سريعة إما إن ال X بتساوي هي ال element
+
+759
+00:58:01,290 --> 00:58:07,170
+الأخير اللي ظال برجع بال location تبعه إلا برجع في
+
+760
+00:58:07,170 --> 00:58:11,570
+Zero معناته أصلا الرقم غير موجوديعني العنصر نفسه
+
+761
+00:58:11,570 --> 00:58:14,350
+اللي أنا بدور عليه هو أصلا غير .. غير موجود في
+
+762
+00:58:14,350 --> 00:58:20,610
+الحالة هذه تمام برضه من الأكواد المهمة لل search
+
+763
+00:58:20,610 --> 00:58:27,270
+طيب مفهوم ال code هذا واضح؟ طيب خلاص حسبلكم في هنا
+
+764
+00:58:27,270 --> 00:58:29,790
+exercise كنت بدي أشرحلكم اللي هو summation
+
+765
+00:58:29,790 --> 00:58:35,930
+summation عندكوا sequence مذاكرين ال summation؟
+
+766
+00:58:38,250 --> 00:58:42,790
+صحيح؟ هنا عندنا summation لـ sequence من I بتساوي
+
+767
+00:58:42,790 --> 00:58:49,370
+1 to N ببساطة
+
+768
+00:58:49,370 --> 00:58:52,670
+جدا ال procedure بتسموه بالاسم تبعه حطينا ال
+
+769
+00:58:52,670 --> 00:58:55,650
+argument ساعتنا ال input اللي هي ال sequence نفسه
+
+770
+00:58:55,650 --> 00:59:00,160
+اللي بدنا نجمه integersبنحط summation بساوة صفر
+
+771
+00:59:00,160 --> 00:59:03,200
+لسه ما بدنا عشان نجمح إشي فال summation الأسهد
+
+772
+00:59:03,200 --> 00:59:09,240
+بيسميها zero ال zero هذي ببدأ إبلوب من واحد to n
+
+773
+00:59:09,240 --> 00:59:14,860
+من واحد to ن كويس ممكن حد يبدأ من إيه؟ ايه واحد
+
+774
+00:59:14,860 --> 00:59:24,840
+ويبدأ من اتنين ممكن؟ ممكن لحظة أنا بدأ أوصلكوا إنه
+
+775
+00:59:24,840 --> 00:59:29,180
+مش بالضروري كلكوا تكتبوا نفس ال codeكل واحد ممكن
+
+776
+00:59:29,180 --> 00:59:35,400
+يعمل code غير التاني يعني كل .. كويس
+
+777
+00:59:35,400 --> 00:59:40,020
+ال I بدأ من واحد لو أنا هيك بالشكل هذا ال S بتساوي
+
+778
+00:59:40,020 --> 00:59:44,100
+صفر ال summation zero طبعا إذا بدأ بدأ من اتنين
+
+779
+00:59:44,100 --> 00:59:50,060
+معناته ال S بدأ بدأها ب A واحد القصد
+
+780
+00:59:50,060 --> 00:59:53,500
+إنه كل واحد ممكن يكتب ال code بطريقته وكل واحد
+
+781
+00:59:53,500 --> 00:59:57,000
+عنده طريقة تفكيره غير التاني وهذا ميزة الحقيقة في
+
+782
+00:59:57,000 --> 01:00:00,340
+البرمجةأحلى إيش في البرمجة أنه .. أنه احنا مش
+
+783
+01:00:00,340 --> 01:00:03,040
+مجبورين كلنا نفكر بنفس الطريقة، مش مجبورين كلنا
+
+784
+01:00:03,040 --> 01:00:07,180
+نفكر بنفس الطريقة، okay ال I من 1 تقن، أخدنا ال
+
+785
+01:00:07,180 --> 01:00:10,640
+sequence كله، بعدين S بتسوي S زائد AI، ال element
+
+786
+01:00:10,640 --> 01:00:13,700
+اللي لنا عنده، فجاعت بجبّع، بعمل accumulation،
+
+787
+01:00:13,700 --> 01:00:17,800
+accumulator و جاعت بجمبعaccumulator بيجمع الاسس
+
+788
+01:00:17,800 --> 01:00:23,160
+هذه قيس فاضي كل مابمرج على element بدأ بحطه كل
+
+789
+01:00:23,160 --> 01:00:26,000
+مابمرج على element بحطه بحطه بحطه بحطه لما في
+
+790
+01:00:26,000 --> 01:00:30,980
+الآخر بجمع قيمهم فانا اعطيت summation للكل اعطينا
+
+791
+01:00:30,980 --> 01:00:36,840
+summation للكل جزء اخر اللي هو عملية ال sorting
+
+792
+01:00:36,840 --> 01:00:41,700
+احنا اتفقنا انه ordered list صح؟ طب إيجادكوا مش
+
+793
+01:00:41,700 --> 01:00:45,720
+ordered, unordered listإيش بتكون تسويه؟ أنت بتكون
+
+794
+01:00:45,720 --> 01:00:51,940
+ترتبوها كي بتكون ترتبوها أنك تحاول تعمل sorting
+
+795
+01:00:51,940 --> 01:00:55,020
+algorithm هذه برضه إلها algorithm إن أنا أرتب ال
+
+796
+01:00:55,020 --> 01:01:00,300
+list تبعتنا مش هقول الأكواد بس هقول الفكرة و خلصنا
+
+797
+01:01:00,300 --> 01:01:05,570
+في فكرتين هنسيب واحدة منهمفي bubble sort وفي ال
+
+798
+01:01:05,570 --> 01:01:08,310
+insertion sort ال insertion sort هناخدها للمرة
+
+799
+01:01:08,310 --> 01:01:13,270
+الجاية ال bubble ع السريع اسمها مختلف عن المعنى
+
+800
+01:01:13,270 --> 01:01:16,290
+الحقيقي تبعها المعنى الحقيقي التالي و أنتوا
+
+801
+01:01:16,290 --> 01:01:21,770
+بتبرجوا حاجة أبدأ من أعلى أو من أول element ال
+
+802
+01:01:21,770 --> 01:01:25,930
+element الأول هذا بشوفه أكبر من التاني و لا لأ إذا
+
+803
+01:01:25,930 --> 01:01:34,690
+أكبر بعمل swap ببدأ و بعدين التاني و التالتلحظوا
+
+804
+01:01:34,690 --> 01:01:38,530
+هنا لأ التلاتين مش اكبر من واحد تلاتين فبسيبها طيب
+
+805
+01:01:38,530 --> 01:01:42,450
+واحد و تلاتين و واحد اه اكبر ببدل هاي هم اجوا هنا
+
+806
+01:01:42,450 --> 01:01:47,050
+تبدلوا طيب هنا صارت واحد و تلاتين ماحنا قولنا هيك
+
+807
+01:01:47,050 --> 01:01:51,490
+بدلنا صار هنا تمام واحد و تلاتين و اتنين و تلاتين
+
+808
+01:01:51,490 --> 01:01:56,390
+لأ بنسيبهم طيب اتنين و تلاتين و تلاتة و تلاتين
+
+809
+01:01:56,390 --> 01:02:03,540
+بنسيبهم تلاتة و تلاتين و اتنين اه بنبدلصار هنا في
+
+810
+01:02:03,540 --> 01:02:07,300
+تلاتة و تلاتين تلاتة و تلاتين اربعة و تلاتين لأ
+
+811
+01:02:07,300 --> 01:02:11,780
+بتظل تلاتة و تلاتين طيب اربعة و تلاتين هنا تلاتة و
+
+812
+01:02:11,780 --> 01:02:15,620
+تلاتين اربعة و تلاتين اربعة و تلاتين مع التلاتة اه
+
+813
+01:02:15,620 --> 01:02:20,740
+تنزل تحت طيب لاحظوا شغلة مهمة ان الاربعة و تلاتين
+
+814
+01:02:20,740 --> 01:02:26,560
+هذه لما نزلت تحت هي اكبر قيمة موجودة افضل شغلة
+
+815
+01:02:26,560 --> 01:02:28,720
+عشان التوضع افترضوا هنا في تلات مية
+
+816
+01:02:31,830 --> 01:02:37,330
+300 مع ال 31 هتبدل و 300 مع ال 1 هتبدل 300 مع ال
+
+817
+01:02:37,330 --> 01:02:40,790
+32 هتبدل هتبدل هتبدل لما تصفف الأخر في القاع تحت
+
+818
+01:02:40,790 --> 01:02:47,530
+صح هتصفف القاع طيب المرة الجاية لما أخلص هدول مش
+
+819
+01:02:47,530 --> 01:02:54,910
+هضطر أبدل 1 2 3 4 5 6 7 هبدل 6 بس الأخيرة سيبوها
+
+820
+01:02:54,910 --> 01:03:01,070
+وفروا وجتها وفروا عملية حسبتهالأنها لحالها ترتبت،
+
+821
+01:03:01,070 --> 01:03:04,790
+بالظبط، طيب، فبنخلص، ابتيجي في الآخر برضه هنا،
+
+822
+01:03:04,790 --> 01:03:07,730
+خلصناها، خلاص، هذه برضه هتثبت، فلاحظوا هنا
+
+823
+01:03:07,730 --> 01:03:13,730
+بتختزلوا عنصر، عنصرين، تلاتة، أربعة، خمسة، فكل مرة
+
+824
+01:03:13,730 --> 01:03:18,400
+ال code تبعكوا ال width اللي بترتبوها أجل بتصيرال
+
+825
+01:03:18,400 --> 01:03:22,380
+interval اللي بترتبوها بتقل اللي محتاجين ترتبوها
+
+826
+01:03:22,380 --> 01:03:25,400
+طيب لاحظوا أن انتوا اشتغلتوا على الأرقام الكبيرة
+
+827
+01:03:25,400 --> 01:03:29,660
+صح؟ بس لاحظوا الصغيرة إيش صار فيها كأنا قاعدة
+
+828
+01:03:29,660 --> 01:03:33,980
+بتطلع زي ال bubble فوق قاعات الهواء وهذه إيشت منها
+
+829
+01:03:33,980 --> 01:03:38,880
+المسمة فالمسمة هو جاي عكسي يعني شوية إحنا هنا فوق
+
+830
+01:03:38,880 --> 01:03:42,820
+قاعات الهواء بتطلع ف bubble قاعدة هي اللي بتطلع
+
+831
+01:03:42,820 --> 01:03:48,160
+بتصعد لفوق كل مرة لما كلها تجمع فوقرغم أن ال code
+
+832
+01:03:48,160 --> 01:03:54,420
+أصلا اشتغلناه على القيم الأكبر بحاول
+
+833
+01:03:54,420 --> 01:03:57,620
+أن أنزلها لتحت بس automatically مادام الكبير بنزل
+
+834
+01:03:57,620 --> 01:04:01,520
+لتحت لازم الأصغير يطلع لفوق لازم الأصغير يطلع لفوق
+
+835
+01:04:01,520 --> 01:04:07,560
+لو الميه مش تجيله كان الفقاعة اللي هو دلت تحتبس
+
+836
+01:04:07,560 --> 01:04:10,240
+لأن الماية دي لما تنزل تحت ففوقعت الهواء لازم تطلع
+
+837
+01:04:10,240 --> 01:04:15,760
+وهذه الناحية العكسية للمعادلات زي اصطلاحا التيار
+
+838
+01:04:15,760 --> 01:04:19,420
+الكهربا بكيف بمشي خدتوه صح؟ انتوا عارفين انه
+
+839
+01:04:19,420 --> 01:04:23,600
+اصطلاحا غير ال actual طيب بكفي لهنا المرة الجاية
+
+840
+01:04:23,600 --> 01:04:25,900
+بناخد ال code تبعها و بناخد ال insertion ان شاء
+
+841
+01:04:25,900 --> 01:04:28,740
+الله و نبدأ في موضوع جديد بإبن الله تعالى استكمال
+
+842
+01:04:28,740 --> 01:04:30,220
+ال algorithms تبعكوا يعطيكوا العصر
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..833aa0fff3b7866fd918654e8e9f80d1d7011164
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Lei8GE0Qn7U_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4414, "start": 20.96, "end": 44.14, "text": "بسم الله الرحمن الرحيم والصلاة والسلام على أشرف الأنبياء والمسلمين سيدنا محمد وعلى أيدي وصحيح أجمعين نفتح اليوم لقائنا ان شاء الله محاضرتنا استكمالا لما سبق الحديث عنه بموضوع ال algorithms المرة اللي فاتة بدأنا بال algorithms واتكلمنا أنه في عندنا language وسميناها informal programming language", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 2304, 3794, 19528, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 36632, 16254, 4032, 9381, 5016, 1829, 5016, 5551, 7435, 2304, 3615, 9957, 8717, 5172, 2655, 5016, 45595, 20498, 5296, 4587, 16373, 8315, 16472, 13412, 16606, 21984, 3714, 5016, 46958, 43500, 8315, 44713, 24793, 6027, 995, 5296, 15042, 8608, 3555, 4587, 21542, 16254, 12984, 18871, 3224, 4724, 2304, 2407, 11242, 45367, 2423, 14642, 9673, 25720, 13672, 1829, 6156, 9307, 3660, 47525, 10721, 8315, 20666, 14642, 4032, 9307, 4117, 19528, 8315, 14739, 3224, 8978, 43242, 8315, 2856, 4032, 38251, 1829, 8315, 11296, 24342, 9410, 2856], "avg_logprob": -0.15740265758311162, "compression_ratio": 1.8148148148148149, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 20.96, "end": 21.22, "word": "بسم", "probability": 0.908203125}, {"start": 21.22, "end": 21.34, "word": " الله", "probability": 0.96826171875}, {"start": 21.34, "end": 21.6, "word": " الرحمن", "probability": 0.9560546875}, {"start": 21.6, "end": 21.92, "word": " الرحيم", "probability": 0.9894205729166666}, {"start": 21.92, "end": 22.24, "word": " والصلاة", "probability": 0.854736328125}, {"start": 22.24, "end": 22.64, "word": " والسلام", "probability": 0.9344075520833334}, {"start": 22.64, "end": 22.78, "word": " على", "probability": 0.277587890625}, {"start": 22.78, "end": 22.98, "word": " أشرف", "probability": 0.9083658854166666}, {"start": 22.98, "end": 23.3, "word": " الأنبياء", 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statements اللي بعد else فمعنى ذلك أن ال statement two لا يمكن تنفيذه إلا في حالة واحدة فقط", "tokens": [3555, 1863, 1863, 5172, 8848, 2423, 12363, 13672, 1829, 39182, 552, 12399, 7908, 44945, 1863, 5172, 8848, 2423, 12363, 13672, 1829, 39182, 1646, 6156, 2304, 3615, 1863, 7578, 29910, 23275, 14739, 2423, 5629, 732, 20193, 7251, 43020, 6055, 1863, 41185, 24192, 11933, 15040, 8978, 11331, 6027, 3660, 36764, 24401, 3660, 6156, 47432], "avg_logprob": -0.21373820417332198, "compression_ratio": 1.586466165413534, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 961.87, "end": 962.45, "word": "بننفذ", "probability": 0.71502685546875}, {"start": 962.45, "end": 962.59, "word": " ال", "probability": 0.74267578125}, {"start": 962.59, "end": 963.15, "word": " statements", "probability": 0.96875}, {"start": 963.15, "end": 963.45, "word": " اللي", "probability": 0.946533203125}, {"start": 963.45, "end": 963.61, "word": " بعد", "probability": 0.9580078125}, {"start": 963.61, "end": 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عبارة عن integer expression هكون عبارة عن integer ال final برضه another integer expression بس طبعا لازم يكون قيمته أكبر من", "tokens": [27842, 27188, 2288, 4587, 49374, 2423, 2572, 4032, 2423, 5883, 2158, 6156, 3615, 9640, 5172, 9957, 20666, 19913, 3555, 9566, 9122, 2304, 3714, 25720, 2423, 6367, 8032, 36081, 1863, 5172, 8848, 34051, 7251, 25957, 43761, 15058, 6156, 2423, 5883, 2158, 6225, 3555, 9640, 3660, 18871, 24922, 6114, 8032, 30544, 6225, 3555, 9640, 3660, 18871, 24922, 2423, 2572, 4724, 43042, 3224, 1071, 24922, 6114, 4724, 3794, 23032, 3555, 3615, 995, 5296, 31377, 2304, 7251, 30544, 12174, 32640, 47395, 5551, 4117, 26890, 9154], "avg_logprob": -0.23628049416512978, "compression_ratio": 1.715736040609137, "no_speech_prob": 6.735324859619141e-06, "words": [{"start": 1349.95, "end": 1350.19, "word": "من", "probability": 0.473388671875}, {"start": 1350.19, "end": 1350.51, "word": " الفرق", "probability": 0.9671223958333334}, {"start": 1350.51, "end": 1350.71, "word": " بين", 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برمجته طب ليش أرجع أكتبه كمان مرة؟ ليش نرجع نكتبه كمان مرة؟ إذا أنتوا بتعملوا مشروع تخرج أو إشي و عملتوا كذا أكواد nested codes مع بعض خلصنا code معين فبتعملهم أجزاء أحيانا جزء خلصنا بتخلوه على جنبك", "tokens": [22332, 5551, 34740, 3714, 29245, 23328, 4032, 14739, 2655, 14407, 13412, 17082, 6027, 9957, 47356, 12174, 36150, 39896, 4117, 4032, 4724, 2288, 2304, 7435, 47395, 23032, 3555, 32239, 8592, 5551, 47341, 3615, 5551, 4117, 2655, 3555, 3224, 9122, 2304, 7649, 3714, 25720, 22807, 32239, 8592, 8717, 47341, 3615, 8717, 4117, 2655, 3555, 3224, 9122, 2304, 7649, 3714, 25720, 22807, 11933, 15730, 14739, 2655, 14407, 39894, 25957, 1211, 14407, 37893, 32887, 3615, 6055, 34740, 7435, 34051, 11933, 8592, 1829, 4032, 6225, 42213, 2655, 14407, 9122, 15730, 5551, 4117, 14407, 3215, 15646, 292, 14211, 20449, 45030, 11242, 16490, 1211, 9381, 8315, 3089, 20449, 9957, 6156, 3555, 2655, 25957, 1211, 16095, 5551, 7435, 11622, 16606, 5551, 5016, 1829, 7649, 995, 10874, 11622, 38207, 16490, 1211, 9381, 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ال", "probability": 0.88623046875}, {"start": 1690.98, "end": 1692.0, "word": " languages", "probability": 0.74853515625}, {"start": 1692.0, "end": 1692.56, "word": " بيسموها", "probability": 0.9365234375}, {"start": 1692.56, "end": 1693.08, "word": " sub", "probability": 0.94921875}, {"start": 1693.08, "end": 1693.48, "word": " routines", "probability": 0.40380859375}, {"start": 1693.48, "end": 1694.28, "word": " في", "probability": 0.912109375}, {"start": 1694.28, "end": 1694.82, "word": " sub", "probability": 0.80810546875}, {"start": 1694.82, "end": 1695.38, "word": " programs", "probability": 0.736328125}, {"start": 1695.38, "end": 1695.7, "word": " او", "probability": 0.81640625}, {"start": 1695.7, "end": 1696.22, "word": " methods", "probability": 0.7724609375}, {"start": 1696.22, "end": 1696.82, "word": " او", "probability": 0.92822265625}, {"start": 1696.82, "end": 1697.3, "word": " methods", "probability": 0.86669921875}], "temperature": 1.0}, {"id": 71, "seek": 172335, "start": 1698.43, "end": 1723.35, "text": "هتلاقوا مش عارف انتوا في ال Java إيش بتسموها method method method فإذا هي فعلا في واحدة من المصاميات هدولة كل language بتستخدم مصطلح من المصطلحات فعلا okay نبدأ خلصنا هيك مجموعة ال statements اللي محتاجينها في ال code عشان نكتب algorithm عنا عشان نكتب algorithm هلوجد هنبدأ بال applications نبدأ ناخد تطبيقات", "tokens": [3224, 2655, 15040, 4587, 14407, 37893, 6225, 9640, 5172, 16472, 2655, 14407, 8978, 2423, 10745, 11933, 1829, 8592, 39894, 38251, 2407, 11296, 3170, 3170, 3170, 6156, 28814, 15730, 39896, 6156, 3615, 15040, 8978, 36764, 24401, 3660, 9154, 9673, 9381, 10943, 1829, 9307, 8032, 3215, 12610, 3660, 28242, 2856, 39894, 14851, 9778, 40448, 3714, 9381, 9566, 1211, 5016, 9154, 9673, 9381, 9566, 1211, 5016, 9307, 6156, 3615, 15040, 1392, 8717, 44510, 10721, 16490, 1211, 9381, 8315, 39896, 4117, 3714, 7435, 2304, 2407, 27884, 2423, 12363, 13672, 1829, 3714, 33753, 26108, 9957, 11296, 8978, 2423, 3089, 6225, 8592, 7649, 8717, 4117, 2655, 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1711.83, "word": " مجموعة", "probability": 0.93505859375}, {"start": 1711.83, "end": 1711.93, "word": " ال", "probability": 0.9306640625}, {"start": 1711.93, "end": 1712.49, "word": " statements", "probability": 0.95361328125}, {"start": 1712.49, "end": 1712.73, "word": " اللي", "probability": 0.976318359375}, {"start": 1712.73, "end": 1713.51, "word": " محتاجينها", "probability": 0.99052734375}, {"start": 1713.51, "end": 1714.35, "word": " في", "probability": 0.98583984375}, {"start": 1714.35, "end": 1714.79, "word": " ال", "probability": 0.68017578125}, {"start": 1714.79, "end": 1715.11, "word": " code", "probability": 0.37451171875}, {"start": 1715.11, "end": 1716.87, "word": " عشان", "probability": 0.8023274739583334}, {"start": 1716.87, "end": 1717.19, "word": " نكتب", "probability": 0.99658203125}, {"start": 1717.19, "end": 1717.69, "word": " algorithm", "probability": 0.88525390625}, {"start": 1717.69, "end": 1718.91, "word": " عنا", "probability": 0.7529296875}, {"start": 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procedure in pseudocode عندكوا sequence و بدنا ال maximum value بدنا ال maximum value تخلي ال sequence قولناها احنا المرة المحاضرة اللي فاتت المحاضرة اللي فاتت الكودة كتبناها بس كتبناها as a language كتابة كلاب كلمنا كلام قولنا بفترض temporary variable", "tokens": [1863, 44510, 10721, 8717, 8592, 2655, 17082, 1211, 15844, 16712, 9566, 21292, 4587, 9307, 16712, 9566, 21292, 4587, 16247, 12610, 2423, 11469, 34051, 2423, 6674, 10747, 294, 25505, 532, 905, 1429, 43242, 4117, 14407, 8310, 4032, 47525, 8315, 2423, 6674, 2158, 47525, 8315, 2423, 6674, 2158, 6055, 9778, 20292, 2423, 8310, 12174, 12610, 8315, 11296, 1975, 5016, 8315, 9673, 25720, 9673, 5016, 46958, 25720, 13672, 1829, 6156, 9307, 2655, 9673, 5016, 46958, 25720, 13672, 1829, 6156, 9307, 2655, 33251, 23328, 3660, 9122, 2655, 3555, 8315, 11296, 4724, 3794, 9122, 2655, 3555, 8315, 11296, 382, 257, 2856, 9122, 2655, 16758, 3660, 9122, 15040, 3555, 9122, 19528, 8315, 28242, 10943, 12174, 12610, 8315, 4724, 5172, 2655, 43042, 13413, 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{"start": 1738.51, "end": 1739.39, "word": " المحاضرة", "probability": 0.95361328125}, {"start": 1739.39, "end": 1739.49, "word": " اللي", "probability": 0.976318359375}, {"start": 1739.49, "end": 1739.71, "word": " فاتت", "probability": 0.9890950520833334}, {"start": 1739.71, "end": 1740.03, "word": " الكودة", "probability": 0.808837890625}, {"start": 1740.03, "end": 1740.49, "word": " كتبناها", "probability": 0.9693359375}, {"start": 1740.49, "end": 1740.59, "word": " بس", "probability": 0.8505859375}, {"start": 1740.59, "end": 1741.07, "word": " كتبناها", "probability": 0.97578125}, {"start": 1741.07, "end": 1741.51, "word": " as", "probability": 0.8857421875}, {"start": 1741.51, "end": 1741.59, "word": " a", "probability": 0.9580078125}, {"start": 1741.59, "end": 1741.97, "word": " language", "probability": 0.89892578125}, {"start": 1741.97, "end": 1743.03, "word": " كتابة", "probability": 0.8583984375}, {"start": 1743.03, "end": 1743.65, "word": " كلاب", "probability": 0.6101888020833334}, {"start": 1743.65, "end": 1744.47, "word": " كلمنا", "probability": 0.7344563802083334}, {"start": 1744.47, "end": 1744.73, "word": " كلام", "probability": 0.7396240234375}, {"start": 1744.73, "end": 1745.25, "word": " قولنا", "probability": 0.9287109375}, {"start": 1745.25, "end": 1746.25, "word": " بفترض", "probability": 0.953857421875}, {"start": 1746.25, "end": 1747.29, "word": " temporary", "probability": 0.86083984375}, {"start": 1747.29, "end": 1748.43, "word": " variable", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 73, "seek": 177645, "start": 1749.19, "end": 1776.45, "text": "وبحطه إن ال maximum value هي أول element وبعدين بنقارن أول element أو V سمنها مع التانية مع ال element التاني إذا ال element التاني أكبر بنحط قيمة V تساوي ال element التاني بعدين بنجرب التالت الرابع الخامس السادس لعد ما نخلص كل ال list بتاعتنا طيب نكتبها لوجة code pseudocode واضح فده طبعا هنبدأ بالإعلان", "tokens": [37746, 5016, 9566, 3224, 36145, 2423, 6674, 2158, 39896, 5551, 12610, 4478, 46599, 22488, 9957, 44945, 4587, 9640, 1863, 5551, 12610, 4478, 34051, 691, 8608, 27842, 11296, 20449, 16712, 7649, 10632, 20449, 2423, 4478, 16712, 7649, 1829, 11933, 15730, 2423, 4478, 16712, 7649, 1829, 5551, 4117, 26890, 44945, 5016, 9566, 12174, 32640, 3660, 691, 6055, 3794, 995, 45865, 2423, 4478, 16712, 7649, 1829, 39182, 9957, 44945, 7435, 25513, 16712, 6027, 2655, 34892, 16758, 3615, 33962, 10943, 3794, 21136, 18513, 3794, 5296, 22488, 19446, 8717, 9778, 1211, 9381, 28242, 2423, 1329, 39894, 995, 34268, 8315, 23032, 1829, 3555, 8717, 4117, 2655, 3555, 11296, 45164, 7435, 3660, 3089, 25505, 532, 905, 1429, 4032, 46958, 5016, 6156, 3215, 3224, 23032, 3555, 3615, 995, 8032, 1863, 44510, 10721, 20666, 28814, 30241, 7649], "avg_logprob": -0.1655765503875969, "compression_ratio": 1.8549618320610688, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 1749.19, "end": 1749.99, "word": "وبحطه", "probability": 0.69561767578125}, {"start": 1749.99, "end": 1750.49, "word": " إن", "probability": 0.2318115234375}, {"start": 1750.49, "end": 1750.83, "word": " ال", "probability": 0.60546875}, {"start": 1750.83, "end": 1751.29, "word": " maximum", "probability": 0.89794921875}, {"start": 1751.29, "end": 1751.99, "word": " value", "probability": 0.98681640625}, {"start": 1751.99, "end": 1752.21, "word": " هي", "probability": 0.87109375}, {"start": 1752.21, "end": 1752.55, "word": " أول", "probability": 0.94189453125}, {"start": 1752.55, "end": 1752.93, "word": " element", "probability": 0.9482421875}, {"start": 1752.93, "end": 1753.99, "word": " وبعدين", "probability": 0.8021647135416666}, {"start": 1753.99, "end": 1754.45, "word": " بنقارن", "probability": 0.9752197265625}, {"start": 1754.45, "end": 1754.67, "word": " أول", "probability": 0.890380859375}, {"start": 1754.67, "end": 1755.05, "word": " element", "probability": 0.9794921875}, {"start": 1755.05, "end": 1755.63, "word": " أو", "probability": 0.6826171875}, {"start": 1755.63, "end": 1756.31, "word": " V", "probability": 0.56640625}, {"start": 1756.31, "end": 1757.53, "word": " سمنها", "probability": 0.6390787760416666}, {"start": 1757.53, "end": 1757.91, "word": " مع", "probability": 0.97705078125}, {"start": 1757.91, "end": 1758.47, "word": " التانية", "probability": 0.9611002604166666}, {"start": 1758.47, "end": 1758.77, "word": " مع", "probability": 0.70654296875}, {"start": 1758.77, "end": 1758.89, "word": " ال", "probability": 0.96630859375}, {"start": 1758.89, "end": 1759.13, "word": " element", "probability": 0.95947265625}, {"start": 1759.13, "end": 1759.59, "word": " التاني", "probability": 0.9295247395833334}, {"start": 1759.59, "end": 1760.67, "word": " إذا", "probability": 0.91357421875}, {"start": 1760.67, "end": 1761.35, "word": " ال", "probability": 0.97412109375}, {"start": 1761.35, "end": 1761.63, "word": " element", "probability": 0.98291015625}, {"start": 1761.63, "end": 1761.97, "word": " التاني", "probability": 0.9471028645833334}, {"start": 1761.97, "end": 1762.33, "word": " أكبر", "probability": 0.9853515625}, {"start": 1762.33, "end": 1762.77, "word": " بنحط", "probability": 0.9178059895833334}, {"start": 1762.77, "end": 1763.35, "word": " قيمة", "probability": 0.9944661458333334}, {"start": 1763.35, "end": 1764.05, "word": " V", "probability": 0.95556640625}, {"start": 1764.05, "end": 1764.57, "word": " تساوي", "probability": 0.790771484375}, {"start": 1764.57, "end": 1764.65, "word": " ال", "probability": 0.96630859375}, {"start": 1764.65, "end": 1764.87, "word": " element", "probability": 0.97900390625}, {"start": 1764.87, "end": 1765.31, "word": " التاني", "probability": 0.9820963541666666}, {"start": 1765.31, "end": 1765.77, "word": " بعدين", "probability": 0.772216796875}, {"start": 1765.77, "end": 1766.09, "word": " بنجرب", "probability": 0.96044921875}, {"start": 1766.09, "end": 1766.51, "word": " التالت", "probability": 0.9708658854166666}, {"start": 1766.51, "end": 1766.87, "word": " الرابع", "probability": 0.92041015625}, {"start": 1766.87, "end": 1767.21, "word": " الخامس", "probability": 0.90283203125}, {"start": 1767.21, "end": 1767.47, "word": " السادس", "probability": 0.6913045247395834}, {"start": 1767.47, "end": 1767.65, "word": " لعد", "probability": 0.531982421875}, {"start": 1767.65, "end": 1767.71, "word": " ما", "probability": 0.9033203125}, {"start": 1767.71, "end": 1768.11, "word": " نخلص", "probability": 0.9678955078125}, {"start": 1768.11, "end": 1768.45, "word": " كل", "probability": 0.9619140625}, {"start": 1768.45, "end": 1769.07, "word": " ال", "probability": 0.83740234375}, {"start": 1769.07, "end": 1769.45, "word": " list", "probability": 0.958984375}, {"start": 1769.45, "end": 1770.25, "word": " بتاعتنا", "probability": 0.86376953125}, {"start": 1770.25, "end": 1771.35, "word": " طيب", "probability": 0.91650390625}, {"start": 1771.35, "end": 1771.85, "word": " نكتبها", "probability": 0.89208984375}, {"start": 1771.85, "end": 1772.09, "word": " لوجة", "probability": 0.68310546875}, {"start": 1772.09, "end": 1772.47, "word": " code", "probability": 0.92333984375}, {"start": 1772.47, "end": 1773.73, "word": " pseudocode", "probability": 0.779998779296875}, {"start": 1773.73, "end": 1774.23, "word": " واضح", "probability": 0.9728190104166666}, {"start": 1774.23, "end": 1775.01, "word": " فده", "probability": 0.8896484375}, {"start": 1775.01, "end": 1775.47, "word": " طبعا", "probability": 0.9854736328125}, {"start": 1775.47, "end": 1775.91, "word": " هنبدأ", "probability": 0.941162109375}, {"start": 1775.91, "end": 1776.45, "word": " بالإعلان", "probability": 0.9840087890625}], "temperature": 1.0}, {"id": 74, "seek": 178833, "start": 1777.39, "end": 1788.33, "text": "procedure خلاص معناته فيه إجراء، فيه code بده يكتب، فيه procedure محتاجينه يكتبوه يعبر عن إيش؟ max خلاص بعرف إنه والله يعبر عن حاجة", "tokens": [4318, 1232, 540, 16490, 1211, 33546, 20449, 8315, 47395, 8978, 3224, 11933, 7435, 2288, 16606, 12399, 8978, 3224, 3089, 47525, 3224, 7251, 4117, 2655, 3555, 12399, 8978, 3224, 10747, 3714, 33753, 26108, 9957, 3224, 7251, 4117, 2655, 3555, 2407, 3224, 37495, 26890, 18871, 11933, 1829, 8592, 22807, 11469, 16490, 1211, 33546, 45030, 28480, 36145, 3224, 16070, 43761, 37495, 26890, 18871, 11331, 26108, 3660], "avg_logprob": -0.2100830131676048, "compression_ratio": 1.5177304964539007, "no_speech_prob": 1.5497207641601562e-06, "words": [{"start": 1777.39, "end": 1778.11, "word": "procedure", "probability": 0.7970377604166666}, {"start": 1778.11, "end": 1778.79, "word": " خلاص", "probability": 0.9288736979166666}, {"start": 1778.79, "end": 1779.11, "word": " معناته", "probability": 0.8331705729166666}, {"start": 1779.11, "end": 1779.29, "word": " فيه", "probability": 0.5699462890625}, {"start": 1779.29, "end": 1780.33, "word": " إجراء،", "probability": 0.845947265625}, {"start": 1780.33, "end": 1780.69, "word": " فيه", "probability": 0.766845703125}, {"start": 1780.69, "end": 1780.89, "word": " code", "probability": 0.87109375}, {"start": 1780.89, "end": 1781.17, "word": " بده", "probability": 0.695556640625}, {"start": 1781.17, "end": 1781.57, "word": " يكتب،", "probability": 0.803662109375}, {"start": 1781.57, "end": 1782.13, "word": " فيه", "probability": 0.9521484375}, {"start": 1782.13, "end": 1782.57, "word": " procedure", "probability": 0.9423828125}, {"start": 1782.57, "end": 1783.09, "word": " محتاجينه", "probability": 0.89228515625}, {"start": 1783.09, "end": 1783.85, "word": " يكتبوه", "probability": 0.8907063802083334}, {"start": 1783.85, "end": 1784.47, "word": " يعبر", "probability": 0.657470703125}, {"start": 1784.47, "end": 1784.63, "word": " عن", "probability": 0.98828125}, {"start": 1784.63, "end": 1785.37, "word": " إيش؟", "probability": 0.89892578125}, {"start": 1785.37, "end": 1785.89, "word": " max", "probability": 0.63671875}, {"start": 1785.89, "end": 1786.29, "word": " خلاص", "probability": 0.8177083333333334}, {"start": 1786.29, "end": 1786.65, "word": " بعرف", "probability": 0.866455078125}, {"start": 1786.65, "end": 1786.87, "word": " إنه", "probability": 0.701904296875}, {"start": 1786.87, "end": 1787.17, "word": " والله", "probability": 0.6627197265625}, {"start": 1787.17, "end": 1787.77, "word": " يعبر", "probability": 0.948974609375}, {"start": 1787.77, "end": 1787.93, "word": " عن", "probability": 0.9833984375}, {"start": 1787.93, "end": 1788.33, "word": " حاجة", "probability": 0.99853515625}], "temperature": 1.0}, {"id": 75, "seek": 180956, "start": 1789.04, "end": 1809.56, "text": "max معناته انا بدور على maximum إيش ال input تبعتنا؟ sequence a1 a2 to an to an أو series على أساس إنه عندنا finite elements موجودين طيب إيش نوعهم؟ ناخد بالنا نقطين و بنحط إيش نوعهم؟ integers نوعهم integers فخلاص حددناها", "tokens": [41167, 20449, 8315, 47395, 1975, 8315, 47525, 13063, 15844, 6674, 11933, 1829, 8592, 2423, 4846, 6055, 3555, 34268, 8315, 22807, 8310, 257, 16, 257, 17, 281, 364, 281, 364, 34051, 2638, 15844, 5551, 3794, 32277, 36145, 3224, 43242, 8315, 19362, 4959, 3714, 29245, 23328, 9957, 23032, 1829, 3555, 11933, 1829, 8592, 8717, 45367, 16095, 22807, 8717, 47283, 3215, 20666, 8315, 8717, 47432, 9957, 4032, 44945, 5016, 9566, 11933, 1829, 8592, 8717, 45367, 16095, 22807, 41674, 8717, 45367, 16095, 41674, 6156, 9778, 1211, 33546, 11331, 3215, 3215, 8315, 11296], "avg_logprob": -0.19346909710530485, "compression_ratio": 1.5231481481481481, "no_speech_prob": 0.0, "words": [{"start": 1789.04, "end": 1789.42, "word": "max", "probability": 0.765625}, {"start": 1789.42, "end": 1789.74, "word": " معناته", "probability": 0.826171875}, {"start": 1789.74, "end": 1789.88, "word": " انا", "probability": 0.5836181640625}, {"start": 1789.88, "end": 1790.12, "word": " بدور", "probability": 0.857666015625}, {"start": 1790.12, "end": 1790.28, "word": " على", "probability": 0.6708984375}, {"start": 1790.28, "end": 1790.7, "word": " maximum", "probability": 0.8037109375}, {"start": 1790.7, "end": 1791.54, "word": " إيش", "probability": 0.6884358723958334}, {"start": 1791.54, "end": 1791.66, "word": " ال", "probability": 0.974609375}, {"start": 1791.66, "end": 1791.86, "word": " input", "probability": 0.87646484375}, {"start": 1791.86, "end": 1792.86, "word": " تبعتنا؟", "probability": 0.8306640625}, {"start": 1792.86, "end": 1793.86, "word": " sequence", "probability": 0.8525390625}, {"start": 1793.86, "end": 1794.58, "word": " a1", "probability": 0.608642578125}, {"start": 1794.58, "end": 1794.92, "word": " a2", "probability": 0.724853515625}, {"start": 1794.92, "end": 1795.1, "word": " to", "probability": 0.748046875}, {"start": 1795.1, "end": 1795.42, "word": " an", "probability": 0.66064453125}, {"start": 1795.42, "end": 1796.16, "word": " to", "probability": 0.25390625}, {"start": 1796.16, "end": 1796.8, "word": " an", "probability": 0.63916015625}, {"start": 1796.8, "end": 1797.08, "word": " أو", "probability": 0.7861328125}, {"start": 1797.08, "end": 1797.52, "word": " series", "probability": 0.89208984375}, {"start": 1797.52, "end": 1797.96, "word": " على", "probability": 0.38525390625}, {"start": 1797.96, "end": 1798.12, "word": " أساس", "probability": 0.79541015625}, {"start": 1798.12, "end": 1798.3, "word": " إنه", "probability": 0.705078125}, {"start": 1798.3, "end": 1799.14, "word": " عندنا", "probability": 0.943115234375}, {"start": 1799.14, "end": 1799.7, "word": " finite", "probability": 0.93994140625}, {"start": 1799.7, "end": 1800.64, "word": " elements", "probability": 0.90771484375}, {"start": 1800.64, "end": 1801.5, "word": " موجودين", "probability": 0.970703125}, {"start": 1801.5, "end": 1802.72, "word": " طيب", "probability": 0.9368489583333334}, {"start": 1802.72, "end": 1802.98, "word": " إيش", "probability": 0.9552408854166666}, {"start": 1802.98, "end": 1803.52, "word": " نوعهم؟", "probability": 0.9207763671875}, {"start": 1803.52, "end": 1803.78, "word": " ناخد", "probability": 0.9386393229166666}, {"start": 1803.78, "end": 1804.06, "word": " بالنا", "probability": 0.91162109375}, {"start": 1804.06, "end": 1804.54, "word": " نقطين", "probability": 0.7646484375}, {"start": 1804.54, "end": 1805.28, "word": " و", "probability": 0.82421875}, {"start": 1805.28, "end": 1805.74, "word": " بنحط", "probability": 0.89111328125}, {"start": 1805.74, "end": 1806.02, "word": " إيش", "probability": 0.9684244791666666}, {"start": 1806.02, "end": 1806.64, "word": " نوعهم؟", "probability": 0.9578857421875}, {"start": 1806.64, "end": 1807.08, "word": " integers", "probability": 0.90576171875}, {"start": 1807.08, "end": 1808.06, "word": " نوعهم", "probability": 0.9392903645833334}, {"start": 1808.06, "end": 1808.5, "word": " integers", "probability": 0.978515625}, {"start": 1808.5, "end": 1808.96, "word": " فخلاص", "probability": 0.9219970703125}, {"start": 1808.96, "end": 1809.56, "word": " حددناها", "probability": 0.9884765625}], "temperature": 1.0}, {"id": 76, "seek": 183802, "start": 1810.5, "end": 1838.02, "text": "الخطوة الأولى قلنا variable نفترض أنه يساوي أول element وحتى الآن أول element هو الأكبر بالنسبالنا أنا بدي أعمل بحث بدأت لسه من أول element هو الأكبر حتى اللحظة بالنسبالي أنا ماشوفتش لسه إيش حد تاني هو أكبر رقم لعنده الآن فنفترض أنه هذا a1 ال V من جتين ساوي a1 في هذه ال largest element so far حتى اللحظة هو أكبر رقم عندي", "tokens": [6027, 9778, 9566, 2407, 3660, 16247, 12610, 7578, 12174, 1211, 8315, 7006, 8717, 5172, 2655, 43042, 14739, 3224, 7251, 3794, 995, 45865, 5551, 12610, 4478, 4032, 33753, 7578, 6024, 48506, 5551, 12610, 4478, 31439, 16247, 4117, 26890, 20666, 1863, 35457, 6027, 8315, 41850, 4724, 16254, 5551, 25957, 1211, 4724, 5016, 12984, 47525, 10721, 2655, 5296, 3794, 3224, 9154, 5551, 12610, 4478, 31439, 16247, 4117, 26890, 11331, 49975, 13672, 5016, 19913, 3660, 20666, 1863, 35457, 6027, 1829, 41850, 19446, 8592, 38688, 2655, 8592, 5296, 3794, 3224, 11933, 1829, 8592, 11331, 3215, 6055, 7649, 1829, 31439, 5551, 4117, 26890, 12602, 4587, 2304, 5296, 3615, 41260, 3224, 6024, 48506, 6156, 1863, 5172, 2655, 43042, 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location والله ال location فعليا إذا عرفت ال location وانا عارف جدش العدد الإجمالي للطلاب اللي دخلوا الامتحان بنقدر جدش فيه أكبر و جدش فيه أقل بس احنا هالواجهة هي task", "tokens": [1863, 46456, 9640, 8717, 49628, 12984, 18871, 12602, 4587, 2304, 8608, 2655, 9957, 11933, 15730, 3714, 29245, 23328, 47525, 3224, 2423, 4914, 6055, 3555, 3615, 3224, 47525, 8315, 2423, 4914, 16070, 43761, 2423, 4914, 6156, 3615, 20292, 995, 11933, 15730, 6225, 28480, 2655, 2423, 4914, 4032, 7649, 995, 6225, 9640, 5172, 10874, 3215, 8592, 18863, 3215, 3215, 33688, 7435, 2304, 6027, 1829, 24976, 9566, 15040, 3555, 13672, 1829, 11778, 9778, 1211, 14407, 2423, 10943, 2655, 5016, 7649, 44945, 28543, 2288, 10874, 3215, 8592, 8978, 3224, 5551, 4117, 26890, 4032, 10874, 3215, 8592, 8978, 3224, 5551, 4587, 1211, 4724, 3794, 1975, 5016, 8315, 8032, 6027, 2407, 26108, 3224, 3660, 39896, 5633], "avg_logprob": -0.21677927927927929, "compression_ratio": 1.8047619047619048, "no_speech_prob": 1.1920928955078125e-07, 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3507.27, "end": 3507.85, "word": " exercise", "probability": 0.85009765625}, {"start": 3507.85, "end": 3508.07, "word": " كنت", "probability": 0.95361328125}, {"start": 3508.07, "end": 3508.31, "word": " بدي", "probability": 0.652099609375}, {"start": 3508.31, "end": 3508.73, "word": " أشرحلكم", "probability": 0.79404296875}, {"start": 3508.73, "end": 3508.87, "word": " اللي", "probability": 0.93115234375}, {"start": 3508.87, "end": 3509.13, "word": " هو", "probability": 0.98974609375}, {"start": 3509.13, "end": 3509.79, "word": " summation", "probability": 0.6337890625}, {"start": 3509.79, "end": 3511.53, "word": " summation", "probability": 0.289306640625}, {"start": 3511.53, "end": 3513.39, "word": " عندكوا", "probability": 0.8330078125}, {"start": 3513.39, "end": 3513.93, "word": " sequence", "probability": 0.98828125}, {"start": 3513.93, "end": 3515.13, "word": " مذاكرين", "probability": 0.61663818359375}, {"start": 3515.13, "end": 3515.23, "word": " ال", "probability": 0.93798828125}, {"start": 3515.23, "end": 3515.93, "word": " summation؟", "probability": 0.91015625}], "temperature": 1.0}, {"id": 139, "seek": 353763, "start": 3518.25, "end": 3537.63, "text": "صحيح؟ هنا عندنا summation لـ sequence من I بتساوي 1 to N ببساطة جدا ال procedure بتسموه بالاسم تبعه حطينا ال argument ساعتنا ال input اللي هي ال sequence نفسه اللي بدنا نجمه integers", "tokens": [9381, 5016, 1829, 5016, 22807, 34105, 43242, 8315, 28811, 5296, 39184, 8310, 9154, 286, 39894, 3794, 995, 45865, 502, 281, 426, 4724, 3555, 3794, 41193, 3660, 10874, 28259, 2423, 10747, 39894, 38251, 2407, 3224, 20666, 32277, 2304, 6055, 3555, 3615, 3224, 11331, 9566, 1829, 8315, 2423, 6770, 8608, 995, 34268, 8315, 2423, 4846, 13672, 1829, 39896, 2423, 8310, 8717, 36178, 3224, 13672, 1829, 47525, 8315, 8717, 7435, 2304, 3224, 41674], "avg_logprob": -0.27288731135113137, "compression_ratio": 1.4491978609625669, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 3518.25, "end": 3519.03, "word": 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" input", "probability": 0.947265625}, {"start": 3534.41, "end": 3534.57, "word": " اللي", "probability": 0.84814453125}, {"start": 3534.57, "end": 3534.71, "word": " هي", "probability": 0.85302734375}, {"start": 3534.71, "end": 3534.85, "word": " ال", "probability": 0.90771484375}, {"start": 3534.85, "end": 3535.27, "word": " sequence", "probability": 0.97802734375}, {"start": 3535.27, "end": 3535.65, "word": " نفسه", "probability": 0.9710286458333334}, {"start": 3535.65, "end": 3535.71, "word": " اللي", "probability": 0.952880859375}, {"start": 3535.71, "end": 3535.89, "word": " بدنا", "probability": 0.715576171875}, {"start": 3535.89, "end": 3536.27, "word": " نجمه", "probability": 0.8778076171875}, {"start": 3536.27, "end": 3537.63, "word": " integers", "probability": 0.339111328125}], "temperature": 1.0}, {"id": 140, "seek": 356734, "start": 3538.64, "end": 3567.34, "text": "بنحط summation بساوة صفر لسه ما بدنا عشان نجمح إشي فال summation الأسهد بيسميها zero ال zero هذي ببدأ إبلوب 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الكبير", "probability": 0.7740885416666666}, {"start": 3837.32, "end": 3837.62, "word": " بنزل", "probability": 0.87109375}, {"start": 3837.62, "end": 3837.86, "word": " لتحت", "probability": 0.9720052083333334}, {"start": 3837.86, "end": 3838.12, "word": " لازم", "probability": 0.9676106770833334}, {"start": 3838.12, "end": 3838.4, "word": " الأصغير", "probability": 0.7998046875}, {"start": 3838.4, "end": 3838.6, "word": " يطلع", "probability": 0.9705810546875}, {"start": 3838.6, "end": 3838.96, "word": " لفوق", "probability": 0.9029947916666666}, {"start": 3838.96, "end": 3839.7, "word": " لازم", "probability": 0.629638671875}, {"start": 3839.7, "end": 3840.06, "word": " الأصغير", "probability": 0.9794921875}, {"start": 3840.06, "end": 3840.88, "word": " يطلع", "probability": 0.9942626953125}, {"start": 3840.88, "end": 3841.52, "word": " لفوق", "probability": 0.96142578125}, {"start": 3841.52, "end": 3841.9, "word": " لو", "probability": 0.73974609375}, {"start": 3841.9, "end": 3843.4, "word": " الميه", "probability": 0.6668294270833334}, {"start": 3843.4, "end": 3844.34, "word": " مش", "probability": 0.94580078125}, {"start": 3844.34, "end": 3844.86, "word": " تجيله", "probability": 0.7042236328125}, {"start": 3844.86, "end": 3845.34, "word": " كان", "probability": 0.8359375}, {"start": 3845.34, "end": 3845.84, "word": " الفقاعة", "probability": 0.712860107421875}, {"start": 3845.84, "end": 3845.96, "word": " اللي", "probability": 0.699462890625}, {"start": 3845.96, "end": 3846.04, "word": " هو", "probability": 0.9794921875}, {"start": 3846.04, "end": 3846.32, "word": " دلت", "probability": 0.7176920572916666}, {"start": 3846.32, "end": 3846.62, "word": " تحت", "probability": 0.974609375}], "temperature": 1.0}, {"id": 152, "seek": 387022, "start": 3847.3, "end": 3870.22, "text": "بس لأن الماية دي لما تنزل تحت ففوقعت الهواء لازم تطلع وهذه الناحية العكسية للمعادلات زي اصطلاحا التيار الكهربا بكيف بمشي خدتوه صح؟ انتوا عارفين انه اصطلاحا غير ال actual طيب بكفي لهنا المرة الجاية بناخد ال code تبعها و بناخد ال insertion ان شاء الله و نبدأ في موضوع جديد بإبن الله تعالى استكمال ال algorithms تبعكوا يعطيكوا العصر", "tokens": [3555, 3794, 5296, 33456, 2423, 15042, 10632, 11778, 1829, 5296, 15042, 6055, 1863, 11622, 1211, 6055, 33753, 6156, 5172, 30543, 34268, 2423, 3224, 2407, 16606, 5296, 31377, 2304, 6055, 9566, 1211, 3615, 37037, 24192, 2423, 8315, 5016, 10632, 18863, 4117, 3794, 10632, 5296, 19528, 3615, 18513, 1211, 9307, 30767, 1829, 1975, 9381, 9566, 15040, 5016, 995, 38392, 9640, 33251, 3224, 25513, 995, 4724, 4117, 33911, 4724, 2304, 8592, 1829, 16490, 3215, 2655, 2407, 3224, 20328, 5016, 22807, 16472, 2655, 14407, 6225, 9640, 5172, 9957, 16472, 3224, 1975, 9381, 9566, 15040, 5016, 995, 32771, 13546, 2423, 3539, 23032, 1829, 3555, 4724, 4117, 41185, 5296, 3224, 8315, 9673, 25720, 25724, 995, 10632, 44945, 47283, 3215, 2423, 3089, 6055, 3555, 3615, 11296, 4032, 44945, 47283, 3215, 2423, 8969, 313, 16472, 13412, 16606, 21984, 4032, 8717, 44510, 10721, 8978, 3714, 2407, 11242, 45367, 10874, 16254, 3215, 4724, 28814, 3555, 1863, 21984, 37279, 6027, 7578, 44713, 24793, 6027, 2423, 14642, 6055, 3555, 3615, 4117, 14407, 37495, 9566, 1829, 4117, 14407, 18863, 9381, 2288], "avg_logprob": -0.21745562130177515, "compression_ratio": 1.8566775244299674, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 3847.3, "end": 3847.56, "word": "بس", "probability": 0.812744140625}, {"start": 3847.56, "end": 3847.7, "word": " لأن", "probability": 0.567138671875}, {"start": 3847.7, "end": 3847.96, "word": " الماية", "probability": 0.6124267578125}, {"start": 3847.96, "end": 3848.08, "word": " دي", "probability": 0.755859375}, {"start": 3848.08, "end": 3848.2, "word": " لما", "probability": 0.84326171875}, {"start": 3848.2, "end": 3848.6, "word": " تنزل", "probability": 0.791748046875}, {"start": 3848.6, "end": 3848.8, "word": " تحت", "probability": 0.956787109375}, {"start": 3848.8, "end": 3849.42, "word": " ففوقعت", "probability": 0.669921875}, {"start": 3849.42, "end": 3849.66, "word": " الهواء", "probability": 0.76519775390625}, {"start": 3849.66, "end": 3849.84, "word": " لازم", "probability": 0.99267578125}, {"start": 3849.84, "end": 3850.24, "word": " تطلع", "probability": 0.99072265625}, {"start": 3850.24, "end": 3851.14, "word": " وهذه", "probability": 0.517822265625}, {"start": 3851.14, "end": 3851.9, "word": " الناحية", "probability": 0.843994140625}, {"start": 3851.9, "end": 3852.72, "word": " العكسية", "probability": 0.990478515625}, {"start": 3852.72, "end": 3854.22, "word": " للمعادلات", "probability": 0.9498697916666666}, {"start": 3854.22, "end": 3854.52, "word": " زي", "probability": 0.802490234375}, {"start": 3854.52, "end": 3855.38, "word": " اصطلاحا", "probability": 0.839599609375}, {"start": 3855.38, "end": 3855.76, "word": " التيار", "probability": 0.546539306640625}, {"start": 3855.76, "end": 3856.04, "word": " الكهربا", "probability": 0.890869140625}, {"start": 3856.04, "end": 3856.26, "word": " بكيف", "probability": 0.9153645833333334}, {"start": 3856.26, "end": 3856.64, "word": " بمشي", "probability": 0.908935546875}, {"start": 3856.64, "end": 3858.08, "word": " خدتوه", "probability": 0.631494140625}, {"start": 3858.08, "end": 3858.82, "word": " صح؟", "probability": 0.8263346354166666}, {"start": 3858.82, "end": 3859.02, "word": " انتوا", "probability": 0.7728678385416666}, {"start": 3859.02, "end": 3859.26, "word": " عارفين", "probability": 0.9664306640625}, {"start": 3859.26, "end": 3859.42, "word": " انه", "probability": 0.720458984375}, {"start": 3859.42, "end": 3859.9, "word": " اصطلاحا", "probability": 0.927978515625}, {"start": 3859.9, "end": 3860.12, "word": " غير", "probability": 0.991943359375}, {"start": 3860.12, "end": 3860.58, "word": " ال", "probability": 0.97119140625}, {"start": 3860.58, "end": 3860.92, "word": " actual", "probability": 0.60107421875}, {"start": 3860.92, "end": 3861.6, "word": " طيب", "probability": 0.8365885416666666}, {"start": 3861.6, "end": 3862.3, "word": " بكفي", "probability": 0.6663411458333334}, {"start": 3862.3, "end": 3863.0, "word": " لهنا", "probability": 0.7303059895833334}, {"start": 3863.0, "end": 3863.38, "word": " المرة", "probability": 0.88427734375}, {"start": 3863.38, "end": 3863.6, "word": " الجاية", "probability": 0.8639322916666666}, {"start": 3863.6, "end": 3863.94, "word": " بناخد", "probability": 0.95751953125}, {"start": 3863.94, "end": 3864.06, "word": " ال", "probability": 0.87841796875}, {"start": 3864.06, "end": 3864.24, "word": " code", "probability": 0.951171875}, {"start": 3864.24, "end": 3864.66, "word": " تبعها", "probability": 0.910888671875}, {"start": 3864.66, "end": 3864.8, "word": " و", "probability": 0.5615234375}, {"start": 3864.8, "end": 3865.06, "word": " بناخد", "probability": 0.9235026041666666}, {"start": 3865.06, "end": 3865.16, "word": " ال", "probability": 0.98193359375}, {"start": 3865.16, "end": 3865.62, "word": " insertion", "probability": 0.977783203125}, {"start": 3865.62, "end": 3865.74, "word": " ان", "probability": 0.767578125}, {"start": 3865.74, "end": 3865.9, "word": " شاء", "probability": 0.973388671875}, {"start": 3865.9, "end": 3865.96, "word": " الله", "probability": 0.94921875}, {"start": 3865.96, "end": 3866.1, "word": " و", "probability": 0.93701171875}, {"start": 3866.1, "end": 3866.6, "word": " نبدأ", "probability": 0.8756510416666666}, {"start": 3866.6, "end": 3866.98, "word": " في", "probability": 0.87548828125}, {"start": 3866.98, "end": 3867.26, "word": " موضوع", "probability": 0.98681640625}, {"start": 3867.26, "end": 3867.58, "word": " جديد", "probability": 0.9915364583333334}, {"start": 3867.58, "end": 3867.84, "word": " بإبن", "probability": 0.831787109375}, {"start": 3867.84, "end": 3868.0, "word": " الله", "probability": 0.94873046875}, {"start": 3868.0, "end": 3868.28, "word": " تعالى", "probability": 0.9010416666666666}, {"start": 3868.28, "end": 3868.74, "word": " استكمال", "probability": 0.9573567708333334}, {"start": 3868.74, "end": 3868.88, "word": " ال", "probability": 0.8681640625}, {"start": 3868.88, "end": 3869.36, "word": " algorithms", "probability": 0.86865234375}, {"start": 3869.36, "end": 3869.7, "word": " تبعكوا", "probability": 0.6283203125}, {"start": 3869.7, "end": 3869.96, "word": " يعطيكوا", "probability": 0.82060546875}, {"start": 3869.96, "end": 3870.22, "word": " العصر", "probability": 0.7046712239583334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3870.8825, "duration_after_vad": 3749.721249999984}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/OU1auPtwyf4.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/OU1auPtwyf4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0d37285ef9158a04b60ab90c9521ad93fe91c193
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/OU1auPtwyf4.srt
@@ -0,0 +1,2723 @@
+
+1
+00:00:20,940 --> 00:00:23,080
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:23,080 --> 00:00:25,800
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,800 --> 00:00:30,460
+أجمعين. طيب، اليوم بعد ما خلصنا الـ sequence اليوم
+
+4
+00:00:30,460 --> 00:00:35,340
+هنبدأ مع الـ summation استكمالا لموضوع الـ sequence
+
+5
+00:00:35,340 --> 00:00:39,580
+والـ strings لما بدأنا نتكلم عن الـ strings لما
+
+6
+00:00:39,580 --> 00:00:44,460
+يكون عندنا string أو series وبدنا نجمع الحدود
+
+7
+00:00:44,460 --> 00:00:48,460
+داخل الـ series هذه، فهنا بندخل في عملية summation
+
+8
+00:00:49,150 --> 00:00:52,010
+عملية الـ summation هذه هنتكلم عنها اليوم إن شاء
+
+9
+00:00:52,010 --> 00:00:55,150
+الله، فبنعملها نتكلم عنها على أساس أن لو عندنا
+
+10
+00:00:55,150 --> 00:01:01,550
+series from a to n أو للـ elements a, n والـ n هذه
+
+11
+00:01:01,550 --> 00:01:06,430
+اللي موجودة عندنا هنا متحكم فيها two limits limit
+
+12
+00:01:06,430 --> 00:01:12,560
+أولى J أكبر من أو يساوي صفر، فإذا ممكن تكون صفر أو
+
+13
+00:01:12,560 --> 00:01:18,520
+ممكن تكون أكبر من صفر، هذه الـ lower bound بتاعتنا
+
+14
+00:01:18,520 --> 00:01:22,460
+أو الـ lower limit بتاعتنا، أو الـ upper limit الـ
+
+15
+00:01:22,460 --> 00:01:26,560
+upper limit to K، وK طبعا الطبيعي جدا لازم تكون
+
+16
+00:01:26,560 --> 00:01:31,060
+أكبر من J أو تساوي J، فأنا بتعامل مع element واحد
+
+17
+00:01:31,060 --> 00:01:34,300
+في هذه الحالة، نتعامل في الحالة هذه مع element واحد
+
+18
+00:01:34,300 --> 00:01:39,870
+فقط اللي هو نفسه الـ J، كويس؟ إذا فعلا حددنا العناصر
+
+19
+00:01:39,870 --> 00:01:44,030
+هذه الـ sequence تبعنا، حددنا الـ lower bound، حددنا
+
+20
+00:01:44,030 --> 00:01:49,790
+الـ upper bound، فإذا الـ summation a n from j to k
+
+21
+00:01:49,790 --> 00:01:55,690
+نكتبها بالشكل التالي: summation a i from i equal to
+
+22
+00:01:55,690 --> 00:02:03,750
+j to k هذه عبارة عن a j plus a j plus واحد plus a
+
+23
+00:02:03,750 --> 00:02:04,570
+j plus two
+
+24
+00:02:10,840 --> 00:02:16,540
+يكون أخذنا كل الـ elements from j to k، كويس؟ الـ I
+
+25
+00:02:16,540 --> 00:02:21,000
+هذه الـ index لمن؟ للـ summation هذه، بتسميها الـ
+
+26
+00:02:21,000 --> 00:02:28,940
+index للـ summation. بعض الـ summations
+
+27
+00:02:28,940 --> 00:02:33,550
+ممكن تكون infinite series. لـ infinite series بنعمل
+
+28
+00:02:33,550 --> 00:02:37,970
+summation، فهتكون عبارة عن summation from I equal
+
+29
+00:02:37,970 --> 00:02:44,450
+to J to infinity، هتكون infinite series AI، فهتكون
+
+30
+00:02:44,450 --> 00:02:45,630
+الـ element
+
+31
+00:02:55,330 --> 00:02:59,050
+فهيظل مجموعة الـ limits تاعتنا to infinity، ففي عندي
+
+32
+00:02:59,050 --> 00:03:02,730
+infinite series.
+
+33
+00:03:04,410 --> 00:03:07,090
+هذه شكل من الأشكال أنَّها ممكن تكون summation عبارة
+
+34
+00:03:07,090 --> 00:03:10,650
+عن infinite series. طيب، ممكن تكون عبارة عن function
+
+35
+00:03:10,650 --> 00:03:16,710
+some functions over all members of a set X capital
+
+36
+00:03:16,710 --> 00:03:20,610
+X. X1, X2, X3. بنحدد الـ set بتاعتنا، الـ set بتاعتنا ده
+
+37
+00:03:20,610 --> 00:03:24,590
+هي الـ domain للـ function، هي domain الـ function
+
+38
+00:03:24,590 --> 00:03:29,910
+يعني هيكون عبارة عن summation F of X. طيب، إيش الـ
+
+39
+00:03:29,910 --> 00:03:34,560
+Xات المحتملة؟ ده هي الـ domain، الأرقام كلها المجمعة
+
+40
+00:03:34,560 --> 00:03:37,740
+هذه بنحطها في الـ domain، فهتكون هي الـ X، القيم اللي
+
+41
+00:03:37,740 --> 00:03:40,600
+ممكن آخذ منها قيم X أو الـ elements اللي باخذ منها
+
+42
+00:03:40,600 --> 00:03:45,240
+قيم X، فبنقول X belong to capital X أو set X.
+
+43
+00:03:48,150 --> 00:03:51,770
+element by element، وبنعوض في f of x وبنجمع
+
+44
+00:03:51,770 --> 00:03:57,490
+فبتصير f of x one plus f of x two plus f of x
+
+45
+00:03:57,490 --> 00:04:00,630
+three، لعد ما نخلص كل الـ elements اللي موجودة في
+
+46
+00:04:00,630 --> 00:04:06,810
+set x. ممكن برضه الـ summation نعملها لمين؟ للـ
+
+47
+00:04:06,810 --> 00:04:12,130
+predicate. إذا كان الـ x اللي هي set x عبارة عن set
+
+48
+00:04:12,130 --> 00:04:19,410
+of elements x such that p of x. معنى ذلك أن الـ set
+
+49
+00:04:19,410 --> 00:04:24,590
+لكل قيم x اللي تحقق الـ function P of X اللي تحقق
+
+50
+00:04:24,590 --> 00:04:26,950
+هذه الـ predicate، أيام اتكلمنا عن الـ predicate
+
+51
+00:04:26,950 --> 00:04:30,050
+فمعنى ذلك أنه ممكن نقول أن هي الـ summation لكل
+
+52
+00:04:30,050 --> 00:04:34,250
+element بيحقق الـ predicate P of X، بنقول F of X
+
+53
+00:04:34,250 --> 00:04:36,890
+معنى ذلك أن F of X واحد، وF of X اتنين، وF of X
+
+54
+00:04:36,890 --> 00:04:39,770
+ثلاثة. X واحد، وX اتنين، وX ثلاثة، هدول هم اللي
+
+55
+00:04:39,770 --> 00:04:46,200
+بيحققوا الـ predicate P of X.. P of X.. أي element
+
+56
+00:04:46,200 --> 00:04:49,940
+لا يحقق الـ predicate بنحطه مع الجمع.. بنحطه الـ
+
+57
+00:04:49,940 --> 00:04:54,820
+functional value مع الجمع..
+
+58
+00:04:56,540 --> 00:05:00,040
+Simple summation example، يعني حاجة بسيطة جدا هنا
+
+59
+00:05:00,040 --> 00:05:02,140
+لو عملنا summation، أنا عارف أن أنتم ماخدين الـ
+
+60
+00:05:02,140 --> 00:05:08,200
+summation قبل هيك. I from two to four I تربيع plus
+
+61
+00:05:08,200 --> 00:05:11,600
+واحد، فاحنا مجرد تعويض، بنعوض بالـ I مرة بتنين، مرة
+
+62
+00:05:11,600 --> 00:05:15,100
+بتلاتة، مرة بأربعة، مرة بخمسة؟ لأ، خمسة لأ، لإنه طلعنا
+
+63
+00:05:15,100 --> 00:05:15,420
+برا.
+
+64
+00:05:22,460 --> 00:05:26,400
+بنجمع الأرقام بتاعتنا عشان نطلع ناتج الـ summation
+
+65
+00:05:26,400 --> 00:05:34,280
+كلام بسيط، وكلام مر عليكم كتير قبل هيك. more
+
+66
+00:05:34,280 --> 00:05:37,660
+summation examples. لو أخذنا infinite series with a
+
+67
+00:05:37,660 --> 00:05:42,950
+finite sum، بقي finite summation. فإذا هنا في ممكن
+
+68
+00:05:42,950 --> 00:05:45,770
+يكون عندكوا infinite series، وأخذناها يمكن المرة
+
+69
+00:05:45,770 --> 00:05:48,490
+اللي فاتت، سألتكوا عليها المرة اللي فاتت، لو كان
+
+70
+00:05:48,490 --> 00:05:52,510
+عندنا مثلا summation from I equal to zero to
+
+71
+00:05:52,510 --> 00:05:57,130
+infinity لإيش؟ لـ two to the power minus I. I مرة
+
+72
+00:05:57,130 --> 00:06:02,290
+بتكون صفر، فهيكون هنا الـ element تبعنا بواحد، مرة
+
+73
+00:06:02,290 --> 00:06:07,750
+هتكون بواحد، هيكون نص، نص،
+
+74
+00:06:10,290 --> 00:06:19,110
+مرة هتكون بربع، تمن، واحد على ستاشر وهكذا to
+
+75
+00:06:19,110 --> 00:06:24,710
+infinity. طيب، الواحد قديش ضايل للثنين؟ ضايل واحد،
+
+76
+00:06:24,710 --> 00:06:30,250
+أعطاني نصه. طيب قديش ضايل؟ نص، أعطاني نص النص، كل مرة
+
+77
+00:06:30,250 --> 00:06:35,330
+هيضل يعطينا نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+78
+00:06:35,330 --> 00:06:35,890
+نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+79
+00:06:35,890 --> 00:06:40,470
+نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+80
+00:06:40,470 --> 00:06:42,350
+نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+81
+00:06:42,350 --> 00:06:51,690
+نص، نص، نص، نص، نص، نص،
+
+82
+00:06:51,690 --> 00:06:56,920
+نص. كيف؟ ممكن يقول لنا summation x تربيع ويحدد أنَّنا
+
+83
+00:06:56,920 --> 00:07:01,920
+إيش الـ x تبعتنا؟ الـ x is prime، فلاحظوا predicate هي
+
+84
+00:07:01,920 --> 00:07:10,120
+x is prime، تمام، and x أقل من عشرة، فواضح أن أنا
+
+85
+00:07:10,120 --> 00:07:14,920
+بتكلم عن أربعة elements: اتنين، تلاتة، خمسة، سبعة. خلاص. 2،
+
+86
+00:07:14,920 --> 00:07:18,980
+3، 5، 7، هدول بيحققوا لي الـ predicate وبيحققوا لي الـ
+
+87
+00:07:18,980 --> 00:07:22,700
+condition x أقل من عشرة، فإذا واضح إن أنا بحطها هنا
+
+88
+00:07:22,700 --> 00:07:28,000
+اتنين مرة، تلاتة مرة، خمسة مرة، وسبعة مرة، بنضرب
+
+89
+00:07:28,000 --> 00:07:33,620
+بنعمل الـ functional value لكل واحدة منهم وبنجمع الـ
+
+90
+00:07:33,620 --> 00:07:35,580
+summation كلها، كويس؟
+
+91
+00:07:38,110 --> 00:07:43,630
+هنتكلم عن شوية summation manipulations أو مهارات
+
+92
+00:07:43,630 --> 00:07:47,030
+ممكن نستعملها لعملية الـ summation، لما بيجيكوا
+
+93
+00:07:47,030 --> 00:07:50,450
+summation، في شوية مهارات ممكن نسهل على حالنا
+
+94
+00:07:50,450 --> 00:07:53,870
+حسابها.. نسهل على حالنا حسابها. أول إشي الـ
+
+95
+00:07:53,870 --> 00:07:57,240
+constant. لو كان عندك constant داخل الـ function، داخل
+
+96
+00:07:57,240 --> 00:08:00,500
+الـ summation، اللي أسهل أنه أضربه برا، بدل ما كل
+
+97
+00:08:00,500 --> 00:08:03,700
+term أضربه في الـ summation، في الـ constant كل term
+
+98
+00:08:03,700 --> 00:08:05,860
+أضربه في الـ constant، طب ما أطلعه مرة، وأحسب كل الـ
+
+99
+00:08:05,860 --> 00:08:09,640
+summation تبعك، وأضرب مرة واحدة، نضرب الـ constant
+
+100
+00:08:09,640 --> 00:08:14,000
+هذا مرة واحدة فقط، فهذه الـ distributive law.
+
+101
+00:08:15,380 --> 00:08:19,280
+Summation لـ two functions. لو جدتوا الـ two
+
+102
+00:08:19,280 --> 00:08:22,060
+functions هدول واضحين وواضحين، بيبين أن هذه
+
+103
+00:08:22,060 --> 00:08:24,080
+function غير هذه، بقدر أفصلهم اتنين اتنين، كل واحدة
+
+104
+00:08:24,080 --> 00:08:29,240
+summation، إذا كان الـ index تبعهم نفسهم، اتفضلي.
+
+105
+00:08:31,510 --> 00:08:35,750
+آه، التوضيح هنا للـ summation، لأن أنتي وزعتي لحظة
+
+106
+00:08:35,750 --> 00:08:42,870
+خليكي معايا، لو جينا C F of X واحد زائد C F of X
+
+107
+00:08:42,870 --> 00:08:52,650
+اتنين زائد C F of X تلاتة، مش هي نفس C F of X واحد
+
+108
+00:08:52,650 --> 00:09:00,120
+plus F of X اتنين plus F of X تلاتة. طب أنتي هنا إيش
+
+109
+00:09:00,120 --> 00:09:02,240
+عملتي في هذا؟ بِـ .. بِـ .. بِـ ..
+
+110
+00:09:02,240 --> 00:09:02,640
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+111
+00:09:02,640 --> 00:09:02,740
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+112
+00:09:02,740 --> 00:09:02,920
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+113
+00:09:02,920 --> 00:09:04,420
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+114
+00:09:04,420 --> 00:09:06,640
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+115
+00:09:06,640 --> 00:09:07,500
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+116
+00:09:07,500 --> 00:09:09,320
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+117
+00:09:09,320 --> 00:09:12,000
+بِـ .. بِـ .. بِـ .. بِـ ..
+
+118
+00:09:13,730 --> 00:09:19,610
+Okay. نفس الكلام زي ما قلنا، نرجع للـ .. للـ .. للـ .. للـ ..
+
+119
+00:09:19,610 --> 00:09:19,650
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+120
+00:09:19,650 --> 00:09:19,790
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+121
+00:09:19,790 --> 00:09:20,070
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+122
+00:09:20,070 --> 00:09:22,170
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+123
+00:09:22,170 --> 00:09:29,430
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+124
+00:09:29,430 --> 00:09:32,210
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+125
+00:09:32,210 --> 00:09:32,770
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+126
+00:09:32,770 --> 00:09:34,370
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+127
+00:09:43,920 --> 00:09:49,040
+الـ index بتاع الـ summation. فلو قلنا I equal to J
+
+128
+00:09:49,040 --> 00:09:55,260
+from J to K لـ F of I، ممكن أعمل shift، أزود هنا N، و
+
+129
+00:09:55,260 --> 00:09:58,640
+أزود هنا N، وأطرح من هنا الـ N عشان أعدِّل التأثير
+
+130
+00:09:58,640 --> 00:10:05,290
+فلو عوضته، هيطلع نفس الـ terms. لو عوضته هيطلع نفس الـ
+
+131
+00:10:05,290 --> 00:10:09,370
+limits بتاعتنا هما هما. فعدد الـ elements اللي بدنا
+
+132
+00:10:09,370 --> 00:10:13,650
+نجمعهم هو هو، عدد أو مجموع في النهاية هو هو، لأنه
+
+133
+00:10:13,650 --> 00:10:19,450
+لحظة، لو عوضته في الـ term ده هنا، هيطلع J هي نفسها J
+
+134
+00:10:19,450 --> 00:10:22,610
+فأنا بأؤكد: أول element هو هو نفس الـ element، عملنا
+
+135
+00:10:22,610 --> 00:10:27,170
+عملية shift، بتفيدنا أحيانا في بعض الـ problems، زي ما
+
+136
+00:10:27,170 --> 00:10:31,830
+هنشوف لاحقا، هناخد أمثلة من الـ problems، هتفيدنا الحاجات
+
+137
+00:10:31,830 --> 00:10:36,650
+دي، كويس؟ عملية الـ splitting، الفصل، عملية الـ
+
+138
+00:10:36,650 --> 00:10:39,990
+splitting، إن أنا ممكن أقول إن الـ summation from j
+
+139
+00:10:39,990 --> 00:10:44,910
+to k، f of i، f of i ممكن أفصلها لـ two summations
+
+140
+00:10:44,910 --> 00:10:48,970
+two summations، بدهم limit، الـ limit اللي بدي
+
+141
+00:10:48,970 --> 00:10:54,410
+أختاره لازم يكون بينهم. زي أقول والله أن عندي مجموعة
+
+142
+00:10:54,410 --> 00:10:57,270
+الـ sequence فيها.. الـ sequence تبعي أو الـ series
+
+143
+00:10:57,270 --> 00:11:01,750
+تبعتي، فيها مجموعة elements، من element من صفر، من
+
+144
+00:11:01,750 --> 00:11:05,890
+واحد لمئة، طبيعي، ممكن أعمله two series، من واحد
+
+145
+00:11:05,890 --> 00:11:10,790
+لخمسين، من واحد لتسعة وأربعين، من واحد لتسعة وتسعين،
+
+146
+00:11:10,790 --> 00:11:15,350
+بس ما أقدرش أقول من واحد لأقل لمئة، واحد، لازم يكون الـ
+
+147
+00:11:15,350 --> 00:11:22,770
+M اللي بتضيف هذه، من J to K، between J وK، فإذا ممكن
+
+148
+00:11:22,770 --> 00:11:26,270
+نفرضها، نشتغل في الحالة هذه على أساس إن في عندنا
+
+149
+00:11:26,270 --> 00:11:33,320
+two summations، واحدة من J to M، والتانية من M plus واحد
+
+150
+00:11:33,320 --> 00:11:37,560
+لـ K، الـ element اللي وراه مباشرة. لـ K، ف أنا بكون حظرت على I
+
+151
+00:11:37,560 --> 00:11:45,050
+لـ J to K، زي ما قلنا، الـ M دي لازم تكون بينهم. طيب، الـ
+
+152
+00:11:45,050 --> 00:11:48,890
+reversal.. الـ reversal نفس، يعني شوية مختلفة عن الـ
+
+153
+00:11:48,890 --> 00:11:52,850
+shift، shift معكوس.. shift معكوس، بحيث أن أنا بشيف
+
+154
+00:11:52,850 --> 00:11:56,630
+الـ summation لآخر element في الأول، وببدأ للي
+
+155
+00:11:56,630 --> 00:11:59,910
+قابله، للي قابله، لعند ما أصل لأول.. لأول element
+
+156
+00:11:59,910 --> 00:12:08,550
+from j to k بنخليها من صفر، هنا بتصير من صفر، فإذا
+
+157
+00:12:08,550 --> 00:12:15,470
+أنا طرحت j، وبنطرح فوق j، وهنا بنعكس، هي كانت I
+
+158
+00:12:15,470 --> 00:12:19,690
+صارت minus I، ف أنا عملت الـ reverse هنا، عملت عملية
+
+159
+00:12:19,690 --> 00:12:24,830
+الـ inverse، عكسنا عملية الـ summation، بحيث أن أنا
+
+160
+00:12:24,830 --> 00:12:29,130
+آخذ آخر element في الأول. طبعا لو جيت عوضته، هتلاقي
+
+161
+00:12:29,130 --> 00:12:34,550
+أن هو عكسوا بعض، هنا صفر، f of k، آخر element كان
+
+162
+00:12:34,550 --> 00:12:34,990
+موجود
+
+163
+00:12:37,870 --> 00:12:41,990
+كان موجود، لو عكسته وحطيته هذا مكان الـ I، هتلاحظ
+
+164
+00:12:41,990 --> 00:12:46,970
+أن الـ K مع الـ K، الـ J أول element، مجرد عكسناهم،
+
+165
+00:12:46,970 --> 00:12:49,590
+صرنا بناخد الـ summation مش من أول term لآخر term،
+
+166
+00:12:49,590 --> 00:12:53,690
+من آخر term لأول term. طيب، الـ grouping، الـ
+
+167
+00:12:53,690 --> 00:12:58,490
+grouping هذه بتفيدنا، مناسبة جدا لما يكون في عندكوا
+
+168
+00:12:58,490 --> 00:13:05,170
+الـ limits تبعتنا من 0 to 2k، لو أنتم عارفين أن
+
+169
+00:13:05,170 --> 00:13:10,490
+أنتم عندكوا عدد
+
+223
+00:17:07,740 --> 00:17:13,300
+summation from one to n للأرقام بتاعتنا اللي هي هو
+
+224
+00:17:13,300 --> 00:17:17,200
+من واحد لـعشرة، لو افترضنا أنها عشرة يعني، طيب
+
+225
+00:17:17,200 --> 00:17:22,340
+automatically هذه مباشرة هتسوي خمسة وخمسين، خمسة و
+
+226
+00:17:22,340 --> 00:17:29,200
+خمسين، كيف خمسة وخمسين؟ الـ n اللي مطلوبة وضُربت في
+
+227
+00:17:29,200 --> 00:17:35,260
+n زائد واحد على اتنين، وجسمه على اتنين، فإذا عشرة
+
+228
+00:17:35,260 --> 00:17:39,260
+في أحد عشر، وجسمه على اتنين، طيب العشرة على اتنين
+
+229
+00:17:39,260 --> 00:17:43,700
+خمسة، خمسة في أحد عشر، خلاص خمسة وخمسين، اجمعوه على
+
+230
+00:17:43,700 --> 00:17:45,980
+الأقل، الحسبة لو بتجمعوه على الأقل الحسبة لسه يدوق
+
+231
+00:17:45,980 --> 00:17:50,300
+وبتكون الحبطة واحد، زي اتنين يدوق، فإذا نرجع واضح
+
+232
+00:17:50,300 --> 00:17:55,100
+أن احنا في إنها الوجب نتكلم عن summation from I to
+
+233
+00:17:55,100 --> 00:17:59,950
+N، لإيش؟ للـ I، للـ I هذه اللي هو الـ counter اللي بده
+
+234
+00:17:59,950 --> 00:18:04,310
+يعد من واحد لعشرة مثلاً، فكل اللي بنعمله عشرة في
+
+235
+00:18:04,310 --> 00:18:07,290
+الرقم اللي وراه.. أو الرقم اللي بتكون.. كله..
+
+236
+00:18:07,290 --> 00:18:10,210
+تجمعه مع كل الأعداد اللي أقل منه، هو نفس الرقم
+
+237
+00:18:10,210 --> 00:18:13,590
+تضربه في الرقم اللي أعلى منه، وبتجسمه على.. على
+
+238
+00:18:13,590 --> 00:18:17,070
+اتنين، لو بتتكلموا عن عشرين مثلاً، عشرين على اتنين
+
+239
+00:18:17,070 --> 00:18:20,970
+عشرة، عشرة في واحد وعشرين، مائة وعشرة، خلاص مائة و
+
+240
+00:18:20,970 --> 00:18:25,660
+عشَرَة، قعدوا اجمعوا على الحاسب، واحد زي اتنين زي تلاتة
+
+241
+00:18:25,660 --> 00:18:28,780
+زي أربعة، لعندما تصلوا لـ زي التسعة عشر، زي اتنين
+
+242
+00:18:28,780 --> 00:18:33,860
+وعشرة، اتنين وعشرة، اعملوها اليوم لكي تجربوها، مروا
+
+243
+00:18:33,860 --> 00:18:38,680
+حالكم عليها، طيب كيف جابها؟ من وين جابها الكلام هذا؟
+
+244
+00:18:38,680 --> 00:18:42,120
+عمل أنه والله فعلاً أنا مع ناتو بدي أفرض أن فعلاً الـ
+
+245
+00:18:42,120 --> 00:18:45,100
+summation بيكون عند كيف واحد زي اتنين زي تلاتة زي
+
+246
+00:18:45,100 --> 00:18:48,920
+اتنين to n over two لعند الـ element اللي في النص
+
+247
+00:18:50,200 --> 00:18:55,900
+plus n over two plus one لعندما يصل لآخر two terms
+
+248
+00:18:55,900 --> 00:19:01,160
+اللي هي n ناقص واحد و n، هدول أول element مع آخر
+
+249
+00:19:01,160 --> 00:19:07,420
+element، مجموعهم n زائد واحد، طيب الـ element اللي
+
+250
+00:19:07,420 --> 00:19:14,100
+اتبعد، واللي قبله برضه n ناقص زائد واحد، كلهم
+
+251
+00:19:14,100 --> 00:19:22,080
+هتلاقيهم بمتماثلين، بيجمعوا مع بعضهم زائد واحد، طيب
+
+252
+00:19:22,080 --> 00:19:28,060
+كداش اتكررت الـ n زائد واحد هذه؟ بعدد n، نصف عدد n
+
+253
+00:19:28,060 --> 00:19:31,940
+نصف عدد n هي عدد تكراراتهم، هي نقف هنا، هي عدد
+
+254
+00:19:31,940 --> 00:19:37,720
+تكراراتهم n over two، n over two في n زائد واحد، n
+
+255
+00:19:37,720 --> 00:19:42,980
+over two في n زائد واحد هي نفسها n في n زائد واحد
+
+256
+00:19:42,980 --> 00:19:43,400
+على، تمام
+
+257
+00:19:47,360 --> 00:19:50,740
+فمعادلة سهلة وبسيطة، ويمكن استخدامها بسهولة يعني
+
+258
+00:19:50,740 --> 00:19:54,280
+الـ
+
+259
+00:19:54,280 --> 00:19:59,200
+geometric progression أو المتتالية الحسابية
+
+260
+00:19:59,200 --> 00:20:03,040
+الهندسية، عفواً الهندسية، اللي فاتت الحسابية، احنا
+
+261
+00:20:03,040 --> 00:20:05,940
+بنتكلم عن الهندسية، فالمتتالية الهندسية بتاعتنا الـ
+
+262
+00:20:05,940 --> 00:20:11,780
+geometric أو الهندسية فعلاً عبارة عن إيش؟ A في R to
+
+263
+00:20:11,780 --> 00:20:16,550
+the power I Element، وطبعاً هنا الـ summation ده
+
+264
+00:20:16,550 --> 00:20:21,570
+ماببدأش من الصفر، ماببدأش من الصفر، ده ماببدأش بـ a
+
+265
+00:20:21,570 --> 00:20:24,010
+لحالة في الأول، a لحالة في الأول، معناته مضروبة في
+
+266
+00:20:24,010 --> 00:20:31,310
+واحد في r to the power zero، بعدين a في r to the
+
+267
+00:20:31,310 --> 00:20:35,770
+power واحد، r to the power اتنين، تلاتة، أربعة، to the
+
+268
+00:20:35,770 --> 00:20:42,270
+power k لعند ما نصل لـ الـ element k أو الـ element k
+
+269
+00:20:42,270 --> 00:20:46,640
+زائد واحد، حقيقةً لأن هنا بدأنا بواحد، اتنين، تلاتة، طيب
+
+270
+00:20:46,640 --> 00:20:53,000
+a و r belong to R هي real numbers
+
+271
+00:20:53,000 --> 00:20:58,760
+أو الـ coefficient بتاعة المتتالية الهندسية بتاعتنا
+
+272
+00:20:58,760 --> 00:21:03,620
+okay، فالـ summation تبعنا هيكون from zero to k لـ a
+
+273
+00:21:03,620 --> 00:21:14,550
+ri، هذا برضه لهالها formula جاهزة، كيف نجيبها؟
+
+274
+00:21:14,550 --> 00:21:18,630
+هنجيبها بالإثبات من مجموعة الـ rules اللي توا
+
+275
+00:21:18,630 --> 00:21:20,930
+خدناها، مجموعة الـ rules اللي توا خدناها، هنستعمل
+
+276
+00:21:20,930 --> 00:21:25,630
+شوية منهم، أساس أن نجيب الـ summation هذه، طيب هذه الـ
+
+277
+00:21:25,630 --> 00:21:30,030
+summation، أول حاجة هنعملها هنضرب الطرفين في R، هنا
+
+278
+00:21:30,030 --> 00:21:34,390
+في R وهنا في R، طيب الـ R اللي انضربت هنا بقدر
+
+279
+00:21:34,390 --> 00:21:38,270
+ببساطة جداً أدخلها جوا وأجمعها مع R to the bar
+
+280
+00:21:39,350 --> 00:21:46,430
+فهتصير r to the power of i زائد واحد، اللي هي هنا
+
+281
+00:21:46,430 --> 00:21:51,450
+وصلنا
+
+282
+00:21:51,450 --> 00:21:54,430
+للحالة التالتة هنا، بعد هي كيف نعمل عملية الـ shift
+
+283
+00:21:54,430 --> 00:22:01,490
+نعمل قبلها، خلصنا هنا عند r one زائد i أو i زائد
+
+284
+00:22:01,490 --> 00:22:05,110
+one، مش هتفرق كتير، هنا بيظل في عندنا إيش بدنا نسوي؟
+
+285
+00:22:05,110 --> 00:22:11,750
+بدنا نعمل shift، تبدأ هنا من واحد، ليش من واحد؟ عشان
+
+286
+00:22:11,750 --> 00:22:15,990
+بده أوصل الـ form تبعي اللي هو زائد واحد هنا، يتناسب
+
+287
+00:22:15,990 --> 00:22:20,330
+مع الـ upper، الـ upper ماعنديش end عند هنا، صارت end
+
+288
+00:22:20,330 --> 00:22:23,990
+زائد واحد، عشان نوصلها للـ upper ونقول والله هي دي
+
+289
+00:22:23,990 --> 00:22:26,790
+ممكن تكون form متناسقة مع بعضها، فمحتاجين نعمل
+
+290
+00:22:26,790 --> 00:22:31,070
+shift، عشان نعمل shift، هزود هنا زائد واحد وهزود
+
+291
+00:22:31,070 --> 00:22:36,600
+هنا زائد واحد، وإيش عمل هنا؟ ناقص، هنا بدنا نعمل
+
+292
+00:22:36,600 --> 00:22:41,300
+ناقص واحد، عشان تأثيرهم يروح مع بعضهم كويس، عملنا
+
+293
+00:22:41,300 --> 00:22:48,420
+الكلام هذا، لحظة رجعتوا لنفس الـ term اللي هو إيه؟ r
+
+294
+00:22:48,420 --> 00:22:52,760
+to the power i، بس الـ form تبعنا صار من one to n
+
+295
+00:22:52,760 --> 00:22:59,560
+زائد واحد to n زائد واحد، هذا كله إيش بيساوي؟ بيساوي R
+
+296
+00:22:59,560 --> 00:23:04,320
+في الـ summation، طب نلاحظ أن هذا لا يساوي الـ
+
+297
+00:23:04,320 --> 00:23:09,520
+summation، الـ term هذا لا يساوي الـ summation، ليش؟
+
+298
+00:23:09,520 --> 00:23:15,780
+لأن هذا بدأ من 0 to N، هنا بدأ من 1 to N زائد 1، هذه
+
+299
+00:23:15,780 --> 00:23:19,100
+مختلفة، فإذا هذه لا تساوي الـ summation، الـ term اللي
+
+300
+00:23:19,100 --> 00:23:22,380
+وصلناه هنا لا يساوي الـ summation، الـ summation
+
+301
+00:23:22,380 --> 00:23:28,800
+تبعنا هو فعلياً من وين بدأ؟ من 0 to N، فإذا أنا هذا
+
+302
+00:23:28,800 --> 00:23:34,180
+بدي إياه أوصله لـ n، عشان أوصله لـ n محتاجين نعمل
+
+303
+00:23:34,180 --> 00:23:40,360
+عملية splitting من zero أو من واحد to n ومن n زائد
+
+304
+00:23:40,360 --> 00:23:44,320
+واحد to n زائد واحد، فالـ term تبعنا بيظل n، أنا
+
+305
+00:23:44,320 --> 00:23:46,880
+هالواجهة، كل الفكرة أن هذا الـ term هذا، عشان واحنا
+
+306
+00:23:46,880 --> 00:23:49,900
+مش هيل، ما تقولوش، عشان اللي بنعمله احنا بدنا نوصل الـ
+
+307
+00:23:49,900 --> 00:23:55,810
+term هذا أنه يكون نفس الـ summation، عشان يرجع للـ
+
+308
+00:23:55,810 --> 00:24:02,690
+summation هذه، الـ N لفوق، الـ N زائد واحد بده أحولها
+
+309
+00:24:02,690 --> 00:24:06,350
+لـ N، في عندي قانون جاهز اللي هو الـ splitting، الـ
+
+310
+00:24:06,350 --> 00:24:09,130
+splitting، بقدر أعمل الـ summation تبعي من واحد
+
+311
+00:24:09,130 --> 00:24:11,950
+هنشوف في الـ logic كيف نحلها، الواحد الواحد ده اللي
+
+312
+00:24:11,950 --> 00:24:15,410
+ضايلة، بنشوف كيف نظبطها، بس ناخد حاجة حاجة، نظبط الـ N
+
+313
+00:24:15,410 --> 00:24:21,600
+زائد واحد، فهنقول هي من واحد to N زائد n زائد واحد to
+
+314
+00:24:21,600 --> 00:24:25,740
+n زائد واحد، يعني term زيادة اللي هو الـ n زائد واحد
+
+315
+00:24:25,740 --> 00:24:28,540
+اللي كان موجود، هذا الـ summation عبارة عن term واحد
+
+316
+00:24:28,540 --> 00:24:34,480
+بس اللي هو n زائد واحد، نعود مباشرة في الـ n زائد واحد
+
+317
+00:24:34,480 --> 00:24:40,760
+بيصير ar to the power of n زائد واحد، خلاص كويس، هاي
+
+318
+00:24:40,760 --> 00:24:43,140
+الـ summation اللي ضال، الـ summation اللي ضال فيها
+
+319
+00:24:43,140 --> 00:24:50,690
+عند الـ zero، عشان أقول إن هذا هو الـ S، عندي مشكلة،
+
+320
+00:24:50,690 --> 00:24:55,150
+الشيء أن هذا الـ summation تبعك ده من zero، طب إيش
+
+321
+00:24:55,150 --> 00:24:59,630
+نسوي؟ أنا إيش ناقص عليا؟ إيش الـ term اللي ناقص
+
+322
+00:24:59,630 --> 00:25:03,550
+عليا؟ ناقص عليا term واحد بس اللي هو عند التعويض I
+
+323
+00:25:03,550 --> 00:25:08,830
+بتساوي zero اللي هو A تماماً، A في R to the power
+
+324
+00:25:08,830 --> 00:25:15,550
+zero، طب مابجمعه ومابطرحه، صحيح؟ لو جمعناها وطرحناها
+
+325
+00:25:15,550 --> 00:25:19,910
+بمشي الحل ونشوف، بعدين كله طبعاً في الآخر هيجمع
+
+326
+00:25:19,910 --> 00:25:22,790
+بمجموعة elements موجودة، الـ elements ده هي اللي
+
+327
+00:25:22,790 --> 00:25:25,250
+هتعطيني الـ form اللي مطلوب، الـ form اللي يجب أن
+
+328
+00:25:25,250 --> 00:25:29,730
+أنا أحسبها عشان
+
+329
+00:25:29,730 --> 00:25:34,690
+نصل زي ما قلنا للحالة ها دي، ها دي وصلناها، فـإيش
+
+330
+00:25:34,690 --> 00:25:39,110
+مشكلة؟ بس ضلت إيش؟ أنا بديها هنا من zero، نبدأها من 0
+
+331
+00:25:39,110 --> 00:25:49,270
+فهنزود ar⁰ ونطرح ar⁰ هذه مع الـ term تبعها مع الـ
+
+332
+00:25:49,270 --> 00:25:56,170
+summation تبعها، وهذه هتبقى تنجمع مع الـ ar n زائد
+
+333
+00:25:56,170 --> 00:25:59,490
+one اللي كانت أصلاً موجودة، اللي كانت أساساً موجودة
+
+334
+00:25:59,490 --> 00:26:03,990
+صار هذه بقدر أعملها summation from i تساوي 0 to 0
+
+335
+00:26:03,990 --> 00:26:09,170
+معينة أن هي element، وبنحط بدلالـ zero، هذا مانحطه
+
+336
+00:26:09,170 --> 00:26:18,470
+I عشان أعمل عكس splitting، لحظة من صفر to zero وهنا
+
+337
+00:26:18,470 --> 00:26:21,750
+هنا من واحد to end، بقدر أقول من صفر to end، مدام
+
+338
+00:26:21,750 --> 00:26:28,430
+نفس الـ function هي هي، فإذا صارت من مباشرة من صفر
+
+339
+00:26:28,430 --> 00:26:32,430
+to what؟ to end، صفر to end، ولحظة هذه
+
+340
+00:26:32,430 --> 00:26:37,560
+automatically صارت هي الـ summation نفسها، هي الـ summation هذه
+
+341
+00:26:37,560 --> 00:26:41,080
+المفروض R في الـ summation، فهذه بقدر الوجب آخذها عن
+
+342
+00:26:41,080 --> 00:26:47,520
+ناحية ثانية، بنخلص من الـ summation، احنا بدنا نلغي كلمة
+
+343
+00:26:47,520 --> 00:26:51,100
+الـ summation، بدي terms بدون summation، terms أقدر أعود
+
+344
+00:26:51,100 --> 00:26:55,600
+مباشرة فيها، أرقام يعني قيـ formula، أعود مباشرة
+
+345
+00:26:55,600 --> 00:26:59,180
+فيها، okay، هذه مناسبة أرقام بأعود فيها على طول، قُلّي
+
+346
+00:26:59,180 --> 00:27:03,060
+بس جدّيش قيمة الـ N؟ بأعوّض بـ N زائد واحد، جدّيش قيمة الـ
+
+347
+00:27:03,060 --> 00:27:06,140
+R بأعوّض فيها، A بأعوّض فيها، بس الـ summation هو
+
+348
+00:27:06,140 --> 00:27:08,720
+المشكلة، فهذه الـ summation ممكن أجي أعكسه عن ناحية
+
+349
+00:27:08,720 --> 00:27:12,140
+ثانية، وعشان هيك كنا بندور أنه الـ summation اللي
+
+350
+00:27:12,140 --> 00:27:15,620
+ظهر عندنا بدنا نظبطه بنفس الـ summation تبعنا عشان
+
+351
+00:27:15,620 --> 00:27:21,200
+نقدر نجمعهم مع بعض، نقدر نجمعهم مع بعض، كويس، فصارت
+
+352
+00:27:21,200 --> 00:27:25,120
+هنا عبارة عن summation وهنا بناخد الـ A مشترك لأن
+
+353
+00:27:25,120 --> 00:27:32,050
+في عندكوا A وفي A، لأن هذه أصلاً كانت ar⁰، ar⁰
+
+354
+00:27:32,050 --> 00:27:45,350
+بواحد، خدوا الـ a مشترك، بتصير هذه واحد، فهي okay، صارت
+
+355
+00:27:45,350 --> 00:27:54,110
+r، كل هذا الـ term هيك بيساوي r، فئة صحيح
+
+356
+00:27:54,110 --> 00:28:05,810
+تمام، لو هذه راحت عن ناحية ثانية، تمام، بتصير هنا ناقص
+
+357
+00:28:05,810 --> 00:28:10,330
+S، طيب
+
+358
+00:28:10,330 --> 00:28:17,950
+أخذنا الـ S مشترك، بنقدر
+
+359
+00:28:17,950 --> 00:28:28,990
+نقولها لغة S بتساوي الـ term هذا، هيه على r-1، جبنا الـ
+
+360
+00:28:28,990 --> 00:28:36,710
+summation على r-1، فهي المعادلة المفروضة، بتصحيحها
+
+361
+00:28:36,710 --> 00:28:42,410
+معادلة مافيش فيها summation، يعني مجرد تعويض مباشر
+
+362
+00:28:42,410 --> 00:28:47,450
+بتصير بس بتظل تعويض مباشر، اعطيني جدّيش الـ n بدك
+
+363
+00:28:47,450 --> 00:28:52,080
+تجمعهم لـ أي term، بنعود في المعادلة، هي جدّيش الـ
+
+364
+00:28:52,080 --> 00:28:55,040
+coefficients تبعتها أصلاً، إيش الـ parameters بتاعة
+
+365
+00:28:55,040 --> 00:29:02,740
+المتتالية الهندسية؟ هذه بنحطها a و r وبنعود، بطلع الـ
+
+366
+00:29:02,740 --> 00:29:05,060
+summation اللي بندور عليه
+
+367
+00:29:20,940 --> 00:29:27,480
+فبطلع الـ summation بيساوي a في R to the power n
+
+368
+00:29:27,480 --> 00:29:33,260
+زائد واحد ناقص واحد على R ناقص واحد، هذا إمتى؟ هذا
+
+369
+00:29:33,260 --> 00:29:39,140
+إمتى الكلام؟ لما تكون R لا تساوي واحد، لأن لو ساوت
+
+370
+00:29:39,140 --> 00:29:43,080
+واحد ففي
+
+371
+00:29:43,080 --> 00:29:47,000
+حالة بتساوي واحد، احنا هنحسبها لحالها، إذا حالة بتساوي
+
+372
+00:29:47,000 --> 00:29:49,760
+واحد فـ automatically بنعود فيها مباشرة، لأن هو عبارة عن
+
+373
+00:29:51,450 --> 00:29:54,870
+term لحاله أو two terms فعلياً، إذا عوضنا بواحد
+
+374
+00:29:54,870 --> 00:30:05,730
+فهيطلع a constant، هنا لو عوضنا r هذه بواحد، واحد
+
+375
+00:30:05,730 --> 00:30:11,690
+power أي شيء بواحد خلاص هتبقى واحد، والـ a constant
+
+376
+00:30:11,690 --> 00:30:21,620
+ثابتة، فهتساوي a في الـ summation من صفر to n، طيب كم
+
+377
+00:30:21,620 --> 00:30:26,980
+مرة تتكرر الـ element هذا؟ من صفر to N، N مرة، لو
+
+378
+00:30:26,980 --> 00:30:30,360
+أنا بجمع من واحد، لو أنا شغال من واحد to N، عندي N
+
+379
+00:30:30,360 --> 00:30:37,780
+مرة زائد الصفر، N زائد واحد، N زائد واحد، فهذا عبارة عن
+
+380
+00:30:37,780 --> 00:30:43,640
+N زائد واحد في الـ constant، على اعتبار أن الـ
+
+381
+00:30:43,640 --> 00:30:46,060
+constant هو كان جوا، بنقدر نطلعه برا مدام constant
+
+382
+00:30:46,950 --> 00:30:53,630
+فبتطلع n زائد واحد في إيه؟ في a، فإذا عندنا two
+
+383
+00:30:53,630 --> 00:30:58,970
+conditions لـ geometric progression، إذا كانت r لا
+
+384
+00:30:58,970 --> 00:31:05,050
+تساوي واحد، الـ summation بيساوي a، افتحوا أقواس، r n
+
+385
+00:31:05,050 --> 00:31:09,090
+زائد واحد ناقص واحد على r ناقص واحد، طيب تساوي
+
+386
+00:31:09,090 --> 00:31:15,810
+واحد، هتساوي n زائد واحد في a، كويس؟ خلاص فهذه بتكون
+
+387
+00:31:15,810 --> 00:31:22,150
+هي إثباتها أو
+
+445
+00:35:08,190 --> 00:35:15,600
+بيقول a في n plus واحد خلصناOkay؟ كويسة الـ .. الـ
+
+446
+00:35:15,600 --> 00:35:19,420
+Euler's track
+
+447
+00:35:19,420 --> 00:35:24,960
+أو اللي هو خاصة بالـ summation الحسابية اللي هي
+
+448
+00:35:24,960 --> 00:35:29,540
+المتطابقة الحسابية كانت بهذا الشكل زي ما قولنا n في
+
+449
+00:35:29,540 --> 00:35:34,000
+اللي بعدها n plus واحد كله على اتنين كله على اتنين
+
+450
+00:35:34,000 --> 00:35:40,250
+في الـ quadratic n في n plus واحد لحظة في اتنين n
+
+451
+00:35:40,250 --> 00:35:45,410
+plus واحد على ستة فهتزيده
+
+452
+00:35:45,410 --> 00:35:51,950
+كمان term و تجيسمه على ستة هذا ليش للتربيعية طيب
+
+453
+00:35:51,950 --> 00:35:58,870
+التكعيبية أسهل تكعيبية تربيع تربيع تربيع تربيع n
+
+454
+00:35:58,870 --> 00:36:05,130
+تربيع n plus واحد تربيع على اتنين تربيع أسهل حتى في
+
+455
+00:36:05,130 --> 00:36:11,410
+حفظها Euler's rule
+
+456
+00:36:11,410 --> 00:36:16,110
+و بتربعوها بتربعوا الـ terms بتاعتها بتربعوا n
+
+457
+00:36:16,110 --> 00:36:23,270
+تربيع n plus one تربيع على أربعة على أربعة من
+
+458
+00:36:23,270 --> 00:36:26,290
+المجموعات اللي أخدناها مجموعة الـ rules اللي
+
+459
+00:36:26,290 --> 00:36:33,470
+أخدناها بدنا نعمل summation لـ k تربيع quadratic
+
+460
+00:36:33,470 --> 00:36:39,150
+form معادلة تربيعية الـ quadratic form هذه from k
+
+461
+00:36:39,150 --> 00:36:46,070
+equal to fifty to one hundred هذا إيش بدنا نسويه؟
+
+462
+00:36:46,070 --> 00:36:50,830
+أول شي؟ splitting بدنا نفكر في عملية الـ splitting
+
+463
+00:36:50,830 --> 00:36:52,750
+ليش؟ لأن احنا عارفين أن الـ summation
+
+464
+00:36:57,880 --> 00:37:06,960
+لو قلنا k بتساوي من واحد لـ k مية k تربيع بنقدر
+
+465
+00:37:06,960 --> 00:37:15,860
+نحسبها صحيح احنا عارفين مسبقا أن هذا n تربيع في n
+
+466
+00:37:15,860 --> 00:37:20,420
+plus واحد لكوادرتيك اللي هو جزء التربيع في اتنين n
+
+467
+00:37:20,420 --> 00:37:26,710
+plus واحد على ستة كويسة هذي بتقسمها بيقول هذي
+
+468
+00:37:26,710 --> 00:37:35,850
+بتساوي summation k واحد لـ 99 لأن
+
+469
+00:37:35,850 --> 00:37:39,110
+الخمسين بتديها في الـ term الثاني و الخمسين ما تقدرش
+
+470
+00:37:39,110 --> 00:37:42,210
+نكررها فانا محتاجة في الـ term الثاني الـ term اللي
+
+471
+00:37:42,210 --> 00:37:46,410
+احنا محتاجين نحسب زائد summation من k بتساوي خمسين
+
+472
+00:37:46,410 --> 00:37:51,500
+لمئة الـ term هذا أو خلينا نقول لـ الـ term هذا
+
+473
+00:37:51,500 --> 00:37:55,700
+بناخده عن ناحية تانية بنطرحه فبصير هذا الـ term إيش
+
+474
+00:37:55,700 --> 00:38:01,720
+بساوي بساوي summation من k بتساوي مئة من k
+
+475
+00:38:01,720 --> 00:38:09,180
+بتساوي واحد لمئة واحد لمئة ناقص summation من k
+
+476
+00:38:09,180 --> 00:38:14,640
+بتساوي واحد لـ تسعة و أربعين فا أنا محتاج أجيب الـ
+
+477
+00:38:14,640 --> 00:38:21,100
+two terms هدولة القانون هي مرة بنعوض بمئة في مئة
+
+478
+00:38:21,100 --> 00:38:27,440
+و واحد في مئتين و واحد على ستة و مرة بنعوض تسعة
+
+479
+00:38:27,440 --> 00:38:32,860
+و أربعين في خمسين في مئة بتطلع تسعة و تسعين تسعة
+
+480
+00:38:32,860 --> 00:38:36,480
+و تسعين على ستة بنحسب الـ term و بنحسب الـ term و
+
+481
+00:38:36,480 --> 00:38:39,900
+بنطرحهم من بعض نطرح الـ term الثاني من الـ term
+
+482
+00:38:39,900 --> 00:38:46,100
+الأول هو ده فعلا اللي حاسبه فبنقدر نجيب من خمسين
+
+483
+00:38:46,100 --> 00:38:48,040
+لمئة خمسين لمئة
+
+484
+00:38:57,070 --> 00:39:00,330
+فهيك بنكون أخدنا مجموعة summations أو مجموعة
+
+485
+00:39:00,330 --> 00:39:05,590
+notations الـ summation للـ limits و الـ limits
+
+486
+00:39:05,590 --> 00:39:08,570
+ساعتنا من i to k و قلنا أن ما بقدر أعمل summation
+
+487
+00:39:08,570 --> 00:39:12,530
+to infinite series و قلنا بنتكلم عن الـ summation
+
+488
+00:39:12,530 --> 00:39:15,790
+في حالة أن احنا نتكلم عن function و بنتكلم عن الـ
+
+489
+00:39:15,790 --> 00:39:21,370
+predicate برضه أخدناها أخدنا شوية formulas بنقدر
+
+490
+00:39:21,370 --> 00:39:25,090
+نشتغلها و بنقدر نستنتجها زي ما اتكلمنا عنها طيب الـ
+
+491
+00:39:25,090 --> 00:39:28,250
+cardinalities الـ cardinalities احنا خدناها أنا
+
+492
+00:39:28,250 --> 00:39:30,610
+عارف أن احنا خدناها و كانت أمرها لما خدناها كانت
+
+493
+00:39:30,610 --> 00:39:37,050
+سهلة ليش؟ لأن كنا بنتعامل مع finite set أو finite
+
+494
+00:39:37,050 --> 00:39:40,870
+series فكانت سهلة بقى بعدهم بأي طريقة كانت و بنجيب
+
+495
+00:39:40,870 --> 00:39:43,150
+الـ cardinality و انتهينا و خلاص انتهى الموضوع
+
+496
+00:39:43,150 --> 00:39:47,000
+مافيش أي مشاكل و تمام تمام  احنا هنا بدنا نتعامل
+
+497
+00:39:47,000 --> 00:39:50,640
+.. نشمل الموضوع أكبر، نخليه أكثر شمولية، نتعامل مع
+
+498
+00:39:50,640 --> 00:39:54,360
+الـ infinite sets الـ infinite sets كيف بقدر أجيب الـ
+
+499
+00:39:54,360 --> 00:39:57,890
+cardinality بتاعتها؟ أو إيش الـ infinite sets اللي
+
+500
+00:39:57,890 --> 00:40:00,610
+بقدر أقول أن هي بقدر أجيب لها cardinality أو بقدر
+
+501
+00:40:00,610 --> 00:40:04,550
+على الأقل أوصف cardinality بتاعتها إنه معدودة بقدر
+
+502
+00:40:04,550 --> 00:40:08,830
+أحسبها حتى لو ما حسبتش exactly برقم بس بقدر أقول
+
+503
+00:40:08,830 --> 00:40:14,350
+أن هي محسوبة countable قابلة للعد أو أن هي لأ غير
+
+504
+00:40:14,350 --> 00:40:17,690
+محسوبة إمتى بنقدر نقول الكلام هذا؟ عشان نقول الكلام
+
+505
+00:40:17,690 --> 00:40:22,400
+هذا هناخد شوية مفاهيم نثبت الموضوع ده عشان نثبته
+
+506
+00:40:22,400 --> 00:40:26,740
+محتاجين نرجع شوية لـ cardinality نفسها إيش يعني
+
+507
+00:40:26,740 --> 00:40:31,020
+cardinality فلو قولنا لو في عندنا two sets A and B
+
+508
+00:40:31,020 --> 00:40:36,120
+بنقدر نقول A و B have the same cardinality إمتى و
+
+509
+00:40:36,120 --> 00:40:38,780
+بنكتبها كالتالي cardinality A equal to cardinality B
+
+510
+00:40:38,780 --> 00:40:42,820
+if and only if there exists a bijection between
+
+511
+00:40:42,820 --> 00:40:47,070
+them إذا كان فعلا الـ relation بينهم الـ function
+
+512
+00:40:47,070 --> 00:40:51,530
+بينهم bijection bijection إيش يعني one to one و on
+
+513
+00:40:51,530 --> 00:40:54,790
+to one one to one و on to one كويسة إذا قدرنا نثبت
+
+514
+00:40:54,790 --> 00:40:58,170
+الكلامة لأن والله فعلا العلاقة كـ function بين
+
+515
+00:40:58,170 --> 00:41:01,430
+الاثنين هدولة بين الـ two sets هدولة bijection فإذا
+
+516
+00:41:01,430 --> 00:41:06,070
+الـ two sets هدولة أكيد لهم نفس الـ cardinality لهم
+
+517
+00:41:06,070 --> 00:41:10,190
+نفس الـ cardinality تمام هذه تعريف مميز نقدر نشتغل
+
+518
+00:41:10,190 --> 00:41:16,550
+من خلاله فإذا لو قلنا a على أساس أن هاي عندكم a وهي
+
+519
+00:41:16,550 --> 00:41:20,670
+b لو عملتوا relation بينهم الـ function هذي is a
+
+520
+00:41:20,670 --> 00:41:23,670
+bijection إذا أكيد هدول الـ two cardinalities
+
+521
+00:41:23,670 --> 00:41:28,330
+بتاعتهم بيساووا بعض تمام a و b are finite ما فيش
+
+522
+00:41:28,330 --> 00:41:33,470
+مشكلة finite معناه سهل يعني معدود معناته محدد بدون
+
+523
+00:41:33,470 --> 00:41:36,410
+finite محدد بقدر أعده بنقدر نعده الأمور ما فيش
+
+524
+00:41:36,410 --> 00:41:40,110
+هيكون فيها مشكلة في الحالة بتاعتنا بنقدر نقول if
+
+525
+00:41:40,110 --> 00:41:43,790
+and only if a and b have the same number of
+
+526
+00:41:43,790 --> 00:41:46,810
+elements و الـ number of elements هذه كنا دائما
+
+527
+00:41:46,810 --> 00:41:50,030
+بنعرفها أن element belong to mean natural number
+
+528
+00:41:50,030 --> 00:41:56,950
+طيب معننى ذلك إذا قدرنا نقول أن الـ set بتاعتنا
+
+529
+00:41:56,950 --> 00:42:01,510
+بقدر أمثلها مع الـ natural number بـ function و
+
+530
+00:42:01,510 --> 00:42:06,240
+بتعطيني bijection function معناته هي مساوية للـ
+
+531
+00:42:06,240 --> 00:42:10,420
+natural number هي infinite احنا متعقدين تماما أن
+
+532
+00:42:10,420 --> 00:42:14,960
+هي infinite لأن الـ finite مجرد للشرح بس احنا بدنا
+
+533
+00:42:14,960 --> 00:42:20,080
+نتعامل لو وجدت مع الـ infinite set infinite set لو
+
+534
+00:42:20,080 --> 00:42:23,380
+قدرت أثبت أن هي bijection مع الـ natural number
+
+535
+00:42:23,380 --> 00:42:27,280
+okay أنا مش هقول أن أنا exactly هاي عددها بس بقدر
+
+536
+00:42:27,280 --> 00:42:31,810
+أقول أن هي countable قابلة للعد ليش؟  لأن بيشكشن
+
+537
+00:42:31,810 --> 00:42:34,750
+مع الـ natural number معناته كل element في الـ
+
+538
+00:42:34,750 --> 00:42:38,730
+natural number يقابله element في الـ set اللي أنا
+
+539
+00:42:38,730 --> 00:42:42,570
+بدور عليه الـ cardinality، صح؟ هو بيشكشن يعني كل
+
+540
+00:42:42,570 --> 00:42:45,370
+element موجود هنا مقابله element هنا، طيب الـ
+
+541
+00:42:45,370 --> 00:42:51,190
+natural number عارفين أن هي a numeral أو أرقام
+
+542
+00:42:51,190 --> 00:42:57,040
+معدودة، عد can be numerate يمكن تعددها أو بقدر
+
+543
+00:42:57,040 --> 00:43:01,840
+أعدها بنقدر نعدها واحد اتنين تلاتة أربعة  لمليون
+
+544
+00:43:01,840 --> 00:43:05,320
+بنقدر نعدها و عملنا bijection معها بـ set معين
+
+545
+00:43:05,320 --> 00:43:09,020
+معناته حتى الـ set هذي بنقدر نعدها حتى الـ set الـ
+
+546
+00:43:09,020 --> 00:43:13,220
+bijection مع الـ natural number قابلة للعد اللي
+
+547
+00:43:13,220 --> 00:43:16,820
+عندنا بنكتفي أن هي قابلة للعد بنعرف أن الـ cardinal
+
+548
+00:43:16,820 --> 00:43:22,190
+بتاعتها okay قابلة للعد فهي countable set countable
+
+549
+00:43:22,190 --> 00:43:25,310
+نقدر نقول أن الـ cardinality بتاعتها countable ممكن
+
+550
+00:43:25,310 --> 00:43:29,430
+نعدها طيب في طبعا sets هنلاقي أن هي uncountable
+
+551
+00:43:29,430 --> 00:43:33,130
+لا يمكن عدها و هناخد examples عنها هنتكلم عنها في الـ
+
+552
+00:43:33,130 --> 00:43:38,670
+countable vs uncountable الـ
+
+553
+00:43:38,670 --> 00:43:42,290
+countable زي ما قلنا مبدئيا هي countable إذا كانت
+
+554
+00:43:42,290 --> 00:43:47,730
+finite هذا متفق عليه فـ الـ finite معناته بقدر أعدها
+
+555
+00:43:47,730 --> 00:43:51,150
+countable خلصنا أو if
+
+556
+00:43:53,690 --> 00:43:56,530
+cardinality of S equal to cardinality of natural
+
+557
+00:43:56,530 --> 00:43:59,110
+number فهي ممكن تكون finite ولكن الـ cardinality
+
+558
+00:43:59,110 --> 00:44:03,870
+بتاعتها مساوية للـ cardinality للـ natural number طب
+
+559
+00:44:03,870 --> 00:44:05,870
+عشان أقول أن هي فعلا cardinality مع الـ natural
+
+560
+00:44:05,870 --> 00:44:08,270
+number لازم أتحقق مع الـ natural number function
+
+561
+00:44:08,270 --> 00:44:12,370
+bijection function bijection function إذا فعلا
+
+562
+00:44:12,370 --> 00:44:15,750
+بتحقق bijection function مع natural number بقول
+
+563
+00:44:15,750 --> 00:44:19,790
+إذا كان .. فإذا أن هذه الـ cardinality بيساووا بعض و
+
+564
+00:44:19,790 --> 00:44:24,780
+هنا بنقول أن الـ S is countable Okay, else أو
+
+565
+00:44:24,780 --> 00:44:29,040
+otherwise هي uncountable بنقول عنها إيش؟
+
+566
+00:44:29,040 --> 00:44:32,640
+uncountable طيب countable زي ما قولنا we can
+
+567
+00:44:32,640 --> 00:44:38,600
+numerate بقدر أعدها، يمكن أعدها أنا في النهاية كيف
+
+568
+00:44:38,600 --> 00:44:44,060
+بعدها؟ لحظة واحد، اتنين، تلاتة، أربعة، natural
+
+569
+00:44:44,060 --> 00:44:47,760
+number، صح؟ فإذا اتفقت مع الـ natural number في
+
+570
+00:44:47,760 --> 00:44:52,000
+العد فهي بقدر أعدها لأن أنا أصلا بعد عن طريق الـ
+
+571
+00:44:52,000 --> 00:44:56,690
+natural number صح احنا أساسا بنعد كيف؟ عن طريق الـ
+
+572
+00:44:56,690 --> 00:45:01,270
+natural number احنا بنكرر أرقام الـ sequence أو
+
+573
+00:45:01,270 --> 00:45:05,190
+اللي اللي هي بتاعة الـ natural number صفر واحد
+
+574
+00:45:05,190 --> 00:45:09,510
+اتنين تلاتة أربعة هي العد تبعنا في حد بعد بطريقة
+
+575
+00:45:09,510 --> 00:45:14,060
+ثانية natural number فإذا كان بقدر أقول أن الـ set دي
+
+576
+00:45:14,060 --> 00:45:18,720
+الـ cardinality بتاعتها مساوية للـ cardinality للـ
+
+577
+00:45:18,720 --> 00:45:21,720
+natural number فإذن هي معدودة بنقدر نعدها على
+
+578
+00:45:21,720 --> 00:45:26,480
+الأقل على الأقل بنقدر نعدها okay sequentially list
+
+579
+00:45:26,480 --> 00:45:27,140
+بالشكل
+
+580
+00:45:30,240 --> 00:45:33,940
+متعاقب، مجموعة elements متعاقبة في S مشابهة لـ
+
+581
+00:45:33,940 --> 00:45:37,440
+elements الـ natural number طيب، بنقدر نعملها
+
+582
+00:45:37,440 --> 00:45:43,600
+enumeration عملية العد، نقدر نعدها examples لها الـ
+
+583
+00:45:43,600 --> 00:45:47,300
+natural number و الـ integers لأن الـ integers برضه
+
+584
+00:45:47,300 --> 00:45:51,440
+واحد اتنين تلاتة أربعة ما فيش فيها fractions ما فيش
+
+585
+00:45:51,440 --> 00:45:55,140
+فيها fractions خلاص هي معدودة الـ units بتاعتها
+
+586
+00:45:55,140 --> 00:46:00,380
+ثابتة طيب في المقابل لو اتكلمنا عن الـ real number
+
+587
+00:46:00,380 --> 00:46:04,400
+طيب عشان أوضح لكم أكثر تخيلوا أن ما بديش أتكلم عن كل
+
+588
+00:46:04,400 --> 00:46:10,800
+الـ real number بدي أتكلم بس من صفر لواحد بس إذا
+
+589
+00:46:10,800 --> 00:46:13,520
+قدرنا نعد من صفر لواحد بدي أقول لكم real number
+
+590
+00:46:13,520 --> 00:46:17,470
+معدود مع أنه real number بس من صفر لواحد خلينا
+
+591
+00:46:17,470 --> 00:46:21,550
+نشوفها نشوفها طيب خلينا نشوف كم element داخل من
+
+592
+00:46:21,550 --> 00:46:31,830
+صفر لواحد ممكن يكون صفر نص ثلث ربع خمس ست لأ غلط
+
+593
+00:46:31,830 --> 00:46:37,770
+لسه في بينهم هدولة ممكن أقول لكم 2.1 1
+
+594
+00:46:37,770 --> 00:46:41,900
+على 2.1 طب لأ واحد هيقول لي لأ في جبينها
+
+595
+00:46:41,900 --> 00:46:47,340
+1 على 2 فاصلة زيرو زيرو زيرو زيرو زيرو واحد
+
+596
+00:46:47,340 --> 00:46:53,440
+فأنا هيك بديها و هيطلع فعلا رقم مختلف، مضبوط؟ طيب
+
+597
+00:46:53,440 --> 00:46:57,040
+صار عندنا عدد لانهائي من الـ elements هنا لأ و غير
+
+598
+00:46:57,040 --> 00:47:01,760
+معدود كمان، لا يتفق مع الـ natural number لو احنا
+
+599
+00:47:01,760 --> 00:47:07,640
+ضلينا على جد نص ثلث .. ربع .. خمس .. ست كان مشيت مع
+
+600
+00:47:07,640 --> 00:47:10,840
+الـ natural number باعتبار أن الـ denominator تبعنا
+
+601
+00:47:10,840 --> 00:47:14,920
+المقام متفق مع الـ natural مع عملية العدل بس احنا
+
+602
+00:47:14,920 --> 00:47:22,140
+فجأنا أن لأ في أكثر بين كل رقم و رقم في عدد لانهائي
+
+603
+00:47:22,140 --> 00:47:28,080
+من الأرقام بين كل رقم اه و هنا .. هـ .. صفر ..
+
+604
+00:47:28,080 --> 00:47:32,260
+اتنين بين كل رقم و رقم في برضه عدد لانهائي من
+
+605
+00:47:32,260 --> 00:47:39,080
+الأرقام معناته تشبكت تشبكت و هنا واضح أن بين الصفر
+
+606
+00:47:39,080 --> 00:47:43,000
+و الواحد لسه ما طلعناش عن الواحد ماقدرش أعدهم فكيف
+
+607
+00:47:43,000 --> 00:47:45,760
+بدي أعد الـ real numbers كلهم فواضح أن هنا
+
+608
+00:47:45,760 --> 00:47:49,880
+uncountable واضح تماما uncountable الـ real numbers
+
+609
+00:47:49,880 --> 00:47:54,160
+نفس الكلام لو الـ real number to the power 2 أو الـ
+
+610
+00:47:54,160 --> 00:47:58,000
+power of natural number عارفين الـ power نتكلم عن
+
+611
+00:47:58,000 --> 00:48:02,140
+set نتكلم عن set لو عندكم two elements الـ power
+
+612
+00:48:02,140 --> 00:48:07,100
+جداً هتطلع أربعة متذكرين؟ طيب لو عندكم three
+
+613
+00:48:07,100 --> 00:48:12,700
+elements ثمانية لو عندكم four elements طب لو
+
+614
+00:48:12,700 --> 00:48:17,220
+عندكم natural number infinity اتنين to the power
+
+615
+00:48:17,220 --> 00:48:22,440
+infinity stop لا تتفق بأي حال من الأحوال مع الـ
+
+616
+00:48:22,440 --> 00:48:25,930
+natural number نفسه لا يمكن أن نقول أن هي
+
+617
+00:48:25,930 --> 00:48:29,730
+bijection مع الـ natural number نفسها، تمام؟ فواضح
+
+618
+00:48:29,730 --> 00:48:33,830
+أن احنا في الحالة هذه بيجوش مع بعض، بيجوش مع بعض
+
+619
+00:48:33,830 --> 00:48:39,630
+طيب، فإذا الـ
+
+667
+00:52:02,610 --> 00:52:07,720
+تستخدموها لحل المعادلات الـ linear equations  أخذتوها
+
+668
+00:52:07,720 --> 00:52:14,080
+قبل هيك كيف بتحلوا باستخدام الـ matrix؟ بتكون عندكوا
+
+669
+00:52:14,080 --> 00:52:19,140
+مجموعات equations، عدد من الـ variables، ومتوفر
+
+670
+00:52:19,140 --> 00:52:22,340
+عندكوا نفس العدد من الـ equations، بتقدروا تحلوا
+
+671
+00:52:22,340 --> 00:52:29,960
+المثال أنكوا تقولوا مثلاً، say، نفترض x1 أو 3x1 زائد
+
+672
+00:52:29,960 --> 00:52:38,760
+2x2 فرضا بتساوي عشرة، خلينا نقول 2x1 ناقص
+
+673
+00:52:38,760 --> 00:52:41,960
+x2
+
+674
+00:52:41,960 --> 00:52:45,780
+بتساوي 6
+
+675
+00:52:45,780 --> 00:52:50,180
+أي معادلات هذه؟ كيف كنتوا بتحلوها؟ طبعاً أنا عارف أن
+
+676
+00:52:50,180 --> 00:52:53,680
+أنتوا أبسط شغلة أنكوا تقولوا: بدنا نضرب، نضرب هنا في
+
+677
+00:52:53,680 --> 00:52:57,160
+اثنين، ونجمع، ونخلص. طيب افرضوا عندكوا عشرة
+
+678
+00:52:57,160 --> 00:53:02,890
+variables في عشر معادلات، يعني معنا ذلك خطوة خطوة
+
+679
+00:53:02,890 --> 00:53:05,650
+عشان تعملوا cancellation لـ variable by variable، مش
+
+680
+00:53:05,650 --> 00:53:08,050
+هي كده، تعملوا إنتوا تاوي لما قلتوا بدنا نختزل هدول
+
+681
+00:53:08,050 --> 00:53:10,830
+إنتوا ضيعتوا variable فكل operation بتكون ضايع
+
+682
+00:53:10,830 --> 00:53:14,110
+variable، عشان يظل variable واحد في الآخر بتقوله
+
+683
+00:53:14,110 --> 00:53:19,410
+قداش بيساوي، وترجعه بالعكس، بالعكس واحد تجيبه من
+
+684
+00:53:19,410 --> 00:53:24,630
+الثاني. طب لو عندكوا عشر معادلات، صعبة
+
+685
+00:53:24,630 --> 00:53:29,140
+الأمور. طيب، اللي أسهل من هيك أنكم تحلّوها بـ
+
+686
+00:53:29,140 --> 00:53:34,060
+matrix، بتكون قوله: والله في عندنا تلاتة، اثنين، اثنين
+
+687
+00:53:34,060 --> 00:53:39,740
+ناقص واحد في x1، x2. طبعاً لو ضربتوا هذول في
+
+688
+00:53:39,740 --> 00:53:45,820
+هذول، هتطلع نفس المعادلة، بتساوي عشرة، في ستة. بتاخدوا
+
+689
+00:53:45,820 --> 00:53:48,200
+هذه على ناحية ثانية، كيف تاخدوها على ناحية
+
+690
+00:53:48,200 --> 00:53:54,160
+ثانية؟ inverse، فبتحسبوها، بتجيبوا لها هنا الـ
+
+691
+00:53:54,160 --> 00:53:56,900
+inverse تبعها، فواضح أنه بتضرب في الـ inverse، خلاص
+
+692
+00:53:56,900 --> 00:54:02,100
+بتروح، وهنا برضه هتضربوها في مين؟ في الـ inverse
+
+693
+00:54:02,100 --> 00:54:09,500
+تبعكوا هنا، عشان تساوي مين؟ x1، x2. طبعاً هيكون 2 في
+
+694
+00:54:09,500 --> 00:54:17,140
+2، 2 في 2، هيطلع element، و2x2 هيطلع element، هتطلع
+
+695
+00:54:17,140 --> 00:54:22,040
+عبارة عن column، الـ column هذا مساوي لـ x1 وx2، هذا
+
+696
+00:54:22,040 --> 00:54:24,540
+الطريقة اللي إنتوا اشتغلتوها سابقاً، فهي application
+
+697
+00:54:24,540 --> 00:54:26,960
+هي واحدة من التطبيقات اللي إنتوا بتشتغلوا عليها
+
+698
+00:54:26,960 --> 00:54:29,960
+فعلياً. طيب، الـ computer graphics والـ image
+
+699
+00:54:29,960 --> 00:54:35,280
+processing، ليش؟ لعندي الآن الـ image processing كل
+
+700
+00:54:35,280 --> 00:54:38,200
+علم الـ image processing بيتعامل مع الصورة أن هي
+
+701
+00:54:38,200 --> 00:54:44,460
+pixels، dots. طب إنتوا معناته dots مع dots هي matrix
+
+702
+00:54:44,460 --> 00:54:49,420
+فإذا إنتوا مثل بـ matrix، التلفزيون عندكم عبارة عن
+
+703
+00:54:49,420 --> 00:54:54,400
+dots، pixels مربعة، بس صغيرة جداً، كل ما صغرت كتير، كل
+
+704
+00:54:54,400 --> 00:54:58,340
+ما الـ resolution كانت أعلى، بمعنى أنه في الآخر
+
+705
+00:54:58,340 --> 00:55:02,760
+هيطلع عندكم pixels
+
+706
+00:55:05,170 --> 00:55:07,670
+بهذا الشكل، هو ده العلم فعلاً، كل الـ signal
+
+707
+00:55:07,670 --> 00:55:10,210
+processing بهذا الشكل. لو اتكلمنا عن الـ image، الـ
+
+708
+00:55:10,210 --> 00:55:14,510
+image هيك تمثل، الـ image تمثل بهذا الشكل، تمثل بهذا
+
+709
+00:55:14,510 --> 00:55:19,110
+الشكل، على أساس أنه لو قلنا مثلاً الرقم، الرقم اثنين
+
+710
+00:55:19,110 --> 00:55:23,250
+لو بدنا نقول الرقم اثنين، ممكن نمثله بهذا الشكل، هيك
+
+711
+00:55:23,250 --> 00:55:30,150
+فلاحظوا، فهقول
+
+712
+00:55:30,150 --> 00:55:38,220
+الـ element 1 و2 قيمته بـ1، طب الـ element 1 و1
+
+713
+00:55:38,220 --> 00:55:42,460
+قيمته صفر. هذا لو بدنا نشتغل عليها الـ image، على أساس أن
+
+714
+00:55:42,460 --> 00:55:46,900
+هي أبيض وأسود، لونها أبيض وأسود. طيب ممكن ما تكونش
+
+715
+00:55:46,900 --> 00:55:50,260
+من صفر لواحد بس، يا صفر يا واحد، ممكن تكون من صفر لـ
+
+716
+00:55:50,260 --> 00:55:54,020
+255، لو بدنا نشتغل على grey level على الصورة اللي
+
+717
+00:55:54,020 --> 00:55:59,380
+هي ملونة، تدريج رمادي من صفر لـ 255، فممكن يكون الـ
+
+718
+00:55:59,380 --> 00:56:05,060
+255 الغامق، الصفر الفاتح، وبينهم تدرجات اللون الـ
+
+719
+00:56:05,060 --> 00:56:09,670
+grey level هذا الرمادي. طيب، بدنا نشتغل ملونة، بيكون في
+
+720
+00:56:09,670 --> 00:56:16,530
+عندنا لكل صورة تلاتة matrices، واحدة لـ الـ red، واحدة
+
+721
+00:56:16,530 --> 00:56:21,490
+لـ الـ blue، واحدة لـ الـ green، تمام. هايهم، وبرضه
+
+722
+00:56:21,490 --> 00:56:25,350
+بنمثلهم بين 0 و255، بين 0 و255، لكل
+
+723
+00:56:25,350 --> 00:56:27,610
+واحدة منهم. الـ degradations هدول مع بعض، بنحطهم مع
+
+724
+00:56:27,610 --> 00:56:32,330
+بعض، بيعطينا dimension ثلاثي للنقطة الواحدة، بقدر
+
+725
+00:56:32,330 --> 00:56:37,630
+اجيب منها اللون. هذه الصور، فواضح أن أنا بتعامل في
+
+726
+00:56:37,630 --> 00:56:41,940
+النهاية بـ matrix، بنتعامل معها as a matrix، الـ signal
+
+727
+00:56:41,940 --> 00:56:43,860
+processing. بدام أنا بتعامل مع الصورة نفسها كـ
+
+728
+00:56:43,860 --> 00:56:46,720
+matrix، فإذا كل process اللي بنقدر، أو المعالجة اللي
+
+729
+00:56:46,720 --> 00:56:50,040
+بنعملها عليها، إحنا بنعمل معالجة على matrix، فإذا
+
+730
+00:56:50,040 --> 00:56:56,520
+هذا الـ field كله معتمد على الـ matrices، كويس. الـ
+
+731
+00:56:56,520 --> 00:56:59,000
+models of computational science زي ما قلنا
+
+732
+00:56:59,000 --> 00:57:03,840
+الحسابات الهندسية والعلمية كلها بتعتمد على الـ
+
+733
+00:57:03,840 --> 00:57:07,540
+matrix، كلها بتعتمد على الـ matrix. لما نقول مثلاً، حتى
+
+734
+00:57:07,540 --> 00:57:09,940
+لما تشتغلوا على الـ derivative، لما بتعملوا الـ
+
+735
+00:57:09,940 --> 00:57:12,900
+derivative الأول والـ derivative الثاني، لما يكون
+
+736
+00:57:12,900 --> 00:57:17,290
+عندكوا dimensions للـ function، أكتر يعني several
+
+737
+00:57:17,290 --> 00:57:20,070
+variables، أكتر من one variable، إنتوا هتضطروا
+
+738
+00:57:20,070 --> 00:57:23,190
+تحتاجوا لـ matrices تشتغلوا فيها، في الآخر هتحتاجوا
+
+739
+00:57:23,190 --> 00:57:26,610
+العمليات بتاعتكوا كلها هتشتغلوا على matrices. طيب،
+
+740
+00:57:26,610 --> 00:57:29,530
+الـ quantum mechanics، برضه الـ quantum mechanics أو
+
+741
+00:57:29,530 --> 00:57:33,150
+ميكانيكا الكم، هذه من العلوم اللي كتير فيها شغل و
+
+742
+00:57:33,150 --> 00:57:39,340
+حديثة جداً، شغل كتير لها في الـ matrices، وخدوا على
+
+743
+00:57:39,340 --> 00:57:42,580
+غرار ذلك كتير جداً، مدام إنتوا هتشتغلوا، وفعلاً كل
+
+744
+00:57:42,580 --> 00:57:47,360
+شغلكوا هيكون صلب، شغلكوا كله في الـ... على الـ
+
+745
+00:57:47,360 --> 00:57:50,780
+digital، معناته هتشتغلوا مع discrete، معناته
+
+746
+00:57:50,780 --> 00:57:52,900
+هتتعاملوا مع كل المصطلحات اللي إحنا بنحكيها في الـ
+
+747
+00:57:52,900 --> 00:57:57,680
+course هذا، وأهمها الـ matrix، أهمها الـ matrix. طيب،
+
+748
+00:57:57,680 --> 00:58:02,620
+امتى؟ بقول أن الـ two matrices هدول بيساووا بعض، إذا
+
+749
+00:58:02,620 --> 00:58:07,140
+كان عدد الصفوف، أو الـ dimension، يعني الـ dimension
+
+750
+00:58:07,140 --> 00:58:08,940
+هنا بيساوي الـ dimension هنا، عدد الصفوف هنا بيساوي
+
+751
+00:58:08,940 --> 00:58:10,720
+عدد الصفوف هنا، عدد الـ columns هنا بيساوي عدد الـ
+
+752
+00:58:10,720 --> 00:58:16,180
+columns هنا، زائد كل عنصر في نفس الـ location بيساوي
+
+753
+00:58:16,180 --> 00:58:21,640
+بعض، كل عنصرين في نفس الـ location بيساووا بعض. فهذه
+
+754
+00:58:21,640 --> 00:58:27,910
+برضه مش فيها مشكلة، مش محتاجة نأخرها. لو نتكلم عن
+
+755
+00:58:27,910 --> 00:58:31,570
+matrices، بيان الشكل اثنين في اثنين، اثنين في اثنين، هاي
+
+756
+00:58:31,570 --> 00:58:34,870
+أول شرط. طيب، بعدين خلينا نشوف واحد واحد، هل بيساوي
+
+757
+00:58:34,870 --> 00:58:38,730
+واحد واحد هنا؟ اه. طيب، اثنين واحد بيساوي اثنين واحد
+
+758
+00:58:38,730 --> 00:58:42,670
+هنا؟ اه. طيب، واحد اثنين، اه، اثنين اثنين، طب كويس
+
+759
+00:58:42,670 --> 00:58:49,330
+بيساوي بعض. طيب، بالشكل هذا لأ، لأن أول شرط اختلف عدد
+
+760
+00:58:49,330 --> 00:58:51,670
+الصفوف، اه، عدد الصفوف، بس عدد الأعمدة لأ، مش عدد
+
+761
+00:58:51,670 --> 00:58:59,090
+الأعمدة، لا يساوي، لا يساوي، فهنا a لا تساوي b. طيب، في
+
+762
+00:58:59,090 --> 00:59:01,130
+الـ matrix لما تكون، بتتكلم عن الـ matrix لحظة، و
+
+763
+00:59:01,130 --> 00:59:07,790
+بنحطها bold بهذا الشكل، a بتساوي bracket، ما نستخدمش
+
+764
+00:59:07,790 --> 00:59:15,730
+الـ curly هذه، ليست تمام، وما نستخدمش الإحداثيات الـ
+
+765
+00:59:15,730 --> 00:59:19,610
+Cartesian، النقاط اللي كنا بنشتغل فيها على النقاط
+
+766
+00:59:19,610 --> 00:59:22,110
+اللي هي ممكن تكون اثنين أو تكون ثلاثة أو تكون في
+
+767
+00:59:22,110 --> 00:59:25,910
+النهاية بس نقاط إحداثيات هذه، بنشتغل على bracket
+
+768
+00:59:27,190 --> 00:59:31,890
+اللي هي تمثل لنا matrix، بتعرف أن هي تمثل الـ matrix
+
+769
+00:59:31,890 --> 00:59:39,490
+ففي الحالة هذه، A، i وj، الـ i الصفوف بتحطّوها
+
+770
+00:59:39,490 --> 00:59:43,770
+في الأول، j الأعمدة. الصفوف في الغالب بنمثلها من
+
+771
+00:59:43,770 --> 00:59:50,510
+واحد to M، الأعمدة من واحد to N، وعادة عشان نوصف الـ
+
+772
+00:59:50,510 --> 00:59:55,230
+matrix هذه بنوصفها i في j، فإحنا بنقول هنا قداش عدد
+
+773
+00:59:55,230 --> 01:00:01,190
+الـ i، سميتهم M، طب قداش عدد الصفوف الأعمدة؟ N، فبنقول
+
+774
+01:00:01,190 --> 01:00:06,770
+هذه M في N matrix، عدد الصفوف في عدد الأعمدة، الصفوف
+
+775
+01:00:06,770 --> 01:00:11,570
+الأول، الـ rows الأول في عدد الأعمدة ثاني، وتمثل بهذا
+
+776
+01:00:11,570 --> 01:00:16,030
+الشكل، العنصر اللي هنا 2 و1، على أساس أنه هو في الـ
+
+777
+01:00:16,030 --> 01:00:22,850
+row الثانية، الـ column الأول. طيب هنا لأ، هذه الـ row
+
+778
+01:00:22,850 --> 01:00:28,010
+الأول، والـ column الثاني، فصار نقدر نميزها من الـ
+
+779
+01:00:28,010 --> 01:00:30,970
+indices بتاعتها، أو الـ index واحد واثنين، هدول
+
+780
+01:00:30,970 --> 01:00:37,330
+تبعونهم. طيب، الـ index لو عندنا الـ matrix M في M
+
+781
+01:00:37,330 --> 01:00:40,490
+matrix، وبنمثلها زي ما قلنا، على هيئة brackets
+
+782
+01:00:40,490 --> 01:00:47,030
+لمجموعة elements، مجموعة الـ elements هذه A من i j، i
+
+783
+01:00:47,030 --> 01:00:55,520
+زي ما قلنا من واحد to M، j من واحد to N. هذه الـ
+
+784
+01:00:55,520 --> 01:01:04,300
+elements عبارة عن members of a set S، فبنقدر نعرفها
+
+785
+01:01:04,300 --> 01:01:09,700
+في الحالة بتاعتنا، على أساس أنها function، if function
+
+786
+01:01:09,700 --> 01:01:12,660
+لأ، الـ matrix A، from natural number to natural
+
+787
+01:01:12,660 --> 01:01:20,150
+number، أو from N to N، N في N. هذه الصفوف وهذه
+
+788
+01:01:20,150 --> 01:01:26,670
+الأعمدة، صفوف، أعمدة، employs أو لـ set S، فإذا
+
+789
+01:01:26,670 --> 01:01:34,050
+الصفوف، أو الـ domain تبعنا من N في N، to set from N
+
+790
+01:01:34,050 --> 01:01:37,970
+to N، to set، هذا الناتج، الـ output تبعنا، الـ set للـ
+
+791
+01:01:37,970 --> 01:01:43,770
+elements اللي هتكون موجودة، الـ input تبعها من الـ
+
+792
+01:01:43,770 --> 01:01:48,280
+natural number تبع الصفوف، مضروبة في الـ natural
+
+793
+01:01:48,280 --> 01:01:50,420
+number بتاعة الأعمدة، دي كلها هيك، هوية واحدة مع
+
+794
+01:01:50,420 --> 01:01:53,920
+بعض، فصارت N تربيع، كأنها N تربيع، ما هي فعلاً N تربيع
+
+795
+01:01:53,920 --> 01:02:00,480
+لأن إنت بتتكلم عن شيء مربع، كذا في كذا، وصفها هيك
+
+796
+01:02:00,480 --> 01:02:05,300
+وصفها، صفوف في أعمدة، هيك الوصف تبعها، صفوف في عدد
+
+797
+01:02:05,300 --> 01:02:10,160
+الأعمدة، في عدد صفوف في عدد أعمدة، فـ such that for i
+
+798
+01:02:10,160 --> 01:02:15,720
+أقل من M، باعتبار أن إحنا حددنا الـ i from one to N، و
+
+799
+01:02:15,720 --> 01:02:21,120
+j أقل من N، فإذا F للـ matrix، الـ function للـ matrix
+
+800
+01:02:21,120 --> 01:02:26,720
+عبارة عن i j، function في مين؟ في الـ location هنا
+
+801
+01:02:26,720 --> 01:02:28,880
+واضح أنه هي function في الـ location، لأن إحنا فعلاً
+
+802
+01:02:28,880 --> 01:02:34,360
+الـ element A i j كيف بعرفه؟ بعرفه بناءً على الـ
+
+803
+01:02:34,360 --> 01:02:37,540
+location تبعه، فإذا هي فعلاً كـ function، هي function
+
+804
+01:02:37,540 --> 01:02:41,300
+في الـ location، الـ location أنهي location؟ الـ rows
+
+805
+01:02:41,300 --> 01:02:48,520
+والـ columns، فببدأ بالـ row، بقول والله الـ row i، الـ
+
+806
+01:02:48,520 --> 01:02:54,080
+column j، بعرف في الحالة هذه الـ element اللي يقع في
+
+807
+01:02:54,080 --> 01:02:58,520
+هذا الـ location، يقع في هذا الـ location، كويس
+
+808
+01:03:00,000 --> 01:03:03,040
+ممكن نعرف الموضوع على أساس أنه هي هذه، هيك الـ domain
+
+809
+01:03:03,040 --> 01:03:07,380
+over which AI is defined، فإذا عرفنا الـ domain
+
+810
+01:03:07,380 --> 01:03:13,160
+تبعنا، عرفنا الـ domain، بنقدر نعرف الـ type of
+
+811
+01:03:13,160 --> 01:03:18,660
+infinite or and multidimensional matrices can be
+
+812
+01:03:18,660 --> 01:03:20,880
+obtained. طبعاً إحنا مش هنتعامل مع الـ
+
+813
+01:03:20,880 --> 01:03:23,980
+multidimensional matrices، إحنا هنتعامل بس مع اللي
+
+814
+01:03:23,980 --> 01:03:30,080
+هي ثنائية الأبعاد، اللي هي الصفوف، الأعمدة بس، هنتعامل
+
+815
+01:03:30,080 --> 01:03:34,000
+مع صفوف، وفئة أعمدة فقط، مش هنتعامل معها أكثر من هنا
+
+816
+01:03:34,000 --> 01:03:38,240
+مجموعة rows مع مجموعة columns
+
+817
+01:03:41,290 --> 01:03:44,810
+كيف كنتوا بتجمعوا الـ matrices؟ كل عنصر مع عنصر
+
+818
+01:03:44,810 --> 01:03:50,430
+المقابل له، فإذا i وj لازم تكون متفقين مع i وj
+
+819
+01:03:50,430 --> 01:03:55,710
+المقابلة لهم في الـ matrix الثانية، فمش فيها مشكلة، A
+
+820
+01:03:55,710 --> 01:04:01,900
+plus A plus B عبارة عن، هي هي، متفقين في A<sub>ij</sub>، A<sub>ij</sub>، هذا الـ
+
+821
+01:04:01,900 --> 01:04:04,260
+element من الـ matrix الأولى، وهذا الـ element من الـ
+
+822
+01:04:04,260 --> 01:04:09,880
+matrix الثانية، عشان يعطوني matrix جديدة. فهنا 2 مع
+
+823
+01:04:09,880 --> 01:04:18,760
+الـ 1، 6 مع التلاتة، صفر مع ناقص 1، 2 و11 وناقص 8
+
+824
+01:04:18,760 --> 01:04:23,920
+مع 3، بنجمع، بيطلع معانا matrix جديدة، مش فيه مشكلة
+
+825
+01:04:23,920 --> 01:04:28,360
+مرة عليكوا أكيد كتير، multiplication، multiplication
+
+826
+01:04:28,360 --> 01:04:34,550
+برضه مرت علينا، كيف كنتوا تشتغلوا فيها؟ A في B بتساوي
+
+827
+01:04:34,550 --> 01:04:38,630
+C، الـ C ده عبارة عن إيش؟ ما هو يحتوي على مجموعة
+
+828
+01:04:38,630 --> 01:04:43,210
+elements، يحتوي على مجموعة elements، الـ elements هذه
+
+829
+01:04:43,210 --> 01:04:51,990
+خلينا نقول لـ i وj، هنقول الـ index لنا L from 1 to
+
+830
+01:04:51,990 --> 01:04:59,470
+K، عبارة عن إيش؟ A<sub>i</sub> الأول
+
+831
+01:04:59,470 --> 01:05:09,550
+عدد الصفوف، وL الـ counter تبعنا، j العنصر الثاني، عدد
+
+832
+01:05:09,5
+
+889
+01:09:52,940 --> 01:09:57,020
+واحدة ما تنفعش بنتيجة الشرط اللي احنا قلناه أن عدد
+
+890
+01:09:57,020 --> 01:09:59,420
+الـ columns في الأولى لازم يساوي عدد الـ rows في
+
+891
+01:09:59,420 --> 01:10:04,720
+التانية، لازم يكون عدد الـ rows في الثانية، okay خلاص
+
+892
+01:10:04,720 --> 01:10:08,280
+بسيب لكم المثال تقرأوه لأنفسكم، هو في المثال عشان
+
+893
+01:10:08,280 --> 01:10:12,220
+بعدين نبدأ في الموضوع، يعني يلا، أعطيكم العافية و
+
+894
+01:10:12,220 --> 01:10:12,940
+أنا أُبارك الله فيكم
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/OU1auPtwyf4_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/OU1auPtwyf4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..05325fde8fd0e6cc1dff1d81b5e0351799524350
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/OU1auPtwyf4_raw.srt
@@ -0,0 +1,3600 @@
+1
+00:00:20,940 --> 00:00:23,080
+بسم الله الرحمن الرحيم والصلاة و السلام علي أشرف
+
+2
+00:00:23,080 --> 00:00:25,800
+الأنبياء والمرسلين سيدنا محمد وعلى أقل هو صاحبي
+
+3
+00:00:25,800 --> 00:00:30,460
+أجمعين طيب اليوم بعد ما خلصنا ال sequence اليوم
+
+4
+00:00:30,460 --> 00:00:35,340
+هنبدأ مع ال summation استكمالا لموضوع ال sequence
+
+5
+00:00:35,340 --> 00:00:39,580
+و ال strings لما بدأنا نتكلم عن ال strings لما
+
+6
+00:00:39,580 --> 00:00:44,460
+يكون عندنا string أو series و بدنا نجمع الحدود
+
+7
+00:00:44,460 --> 00:00:48,460
+داخل ال series هذه فهنا بندخل في عملية summation
+
+8
+00:00:49,150 --> 00:00:52,010
+عملية ال summation هذه هنتكلم عنها اليوم ان شاء
+
+9
+00:00:52,010 --> 00:00:55,150
+الله فبنعملها نتكلم عنها على اساس ان لو عندنا
+
+10
+00:00:55,150 --> 00:01:01,550
+series from a to n او لل elements a,n و ال n هذه
+
+11
+00:01:01,550 --> 00:01:06,430
+اللي موجودة عندنا هنا متحكم فيها two limits limit
+
+12
+00:01:06,430 --> 00:01:12,560
+أولىJ أكبر من أو يساوي صفر فإذا ممكن تكون صفر أو
+
+13
+00:01:12,560 --> 00:01:18,520
+ممكن تكون أكبر من صفر هذي ال lower bound بتاعتنا
+
+14
+00:01:18,520 --> 00:01:22,460
+أو ال lower limit بتاعتنا أو ال upper limit ال
+
+15
+00:01:22,460 --> 00:01:26,560
+upper limit to K و K طبعا الطبيعي جدا لازم تكون
+
+16
+00:01:26,560 --> 00:01:31,060
+أكبر من J أو تساوي J فانا بتعامل مع element واحد
+
+17
+00:01:31,060 --> 00:01:34,300
+في هذه الحالة نتعامل في الحالة هذه مع element واحد
+
+18
+00:01:34,300 --> 00:01:39,870
+فقط اللي هو نفسه ال Jكويس إذا فعلا حددنا العناصر
+
+19
+00:01:39,870 --> 00:01:44,030
+هذه ال sequence تبعنا حددنا ال lower bound حددنا
+
+20
+00:01:44,030 --> 00:01:49,790
+ال upper bound فإذا ال summation a n from j to k
+
+21
+00:01:49,790 --> 00:01:55,690
+نكتبها بالشكل التالي summation a i from i equal to
+
+22
+00:01:55,690 --> 00:02:03,750
+j to k هذه عبارة عن a j plus a j plus واحد plus a
+
+23
+00:02:03,750 --> 00:02:04,570
+j plus two
+
+24
+00:02:10,840 --> 00:02:16,540
+يكون اخدنا كل ال elements from j to k كويس ال I
+
+25
+00:02:16,540 --> 00:02:21,000
+هذه ال index لمن؟ لل summation هذه بتسميها ال
+
+26
+00:02:21,000 --> 00:02:28,940
+index لل summation بعض ال summations
+
+27
+00:02:28,940 --> 00:02:33,550
+ممكن تكون infinite seriesلـ infinite series بنعمل
+
+28
+00:02:33,550 --> 00:02:37,970
+summation فهتكون عبارة عن summation from I equal
+
+29
+00:02:37,970 --> 00:02:44,450
+to J to infinity هتكون infinite series AI فهتكون
+
+30
+00:02:44,450 --> 00:02:45,630
+ال element
+
+31
+00:02:55,330 --> 00:02:59,050
+فهيظل مجموعة ال limits تاعتنا to infinity ففي عندي
+
+32
+00:02:59,050 --> 00:03:02,730
+infinite series
+
+33
+00:03:04,410 --> 00:03:07,090
+هذه شكل من الأشكال انها ممكن تكون summation عبارة
+
+34
+00:03:07,090 --> 00:03:10,650
+عن infinite series طيب ممكن تكون عبارة عن function
+
+35
+00:03:10,650 --> 00:03:16,710
+some functions over all members of a set X capital
+
+36
+00:03:16,710 --> 00:03:20,610
+X X1 X2 X3 بنحدد ال set بتاعتنا ال set بتاعتنا ده
+
+37
+00:03:20,610 --> 00:03:24,590
+هي ال domain لل function هي domain ال function
+
+38
+00:03:24,590 --> 00:03:29,910
+يعني هيكون عبارة عن summation F of X طيب ايش ال
+
+39
+00:03:29,910 --> 00:03:34,560
+Xات المحتملة ده هي ال domainالأرقام كلها المجمعة
+
+40
+00:03:34,560 --> 00:03:37,740
+هذه بنحطها في ال domain فهتكون هي ال X القيم اللي
+
+41
+00:03:37,740 --> 00:03:40,600
+ممكن أخد منها قيم X أو ال elements اللي باخد منها
+
+42
+00:03:40,600 --> 00:03:45,240
+قيم X فبنقول X belong to capital X أو set X
+
+43
+00:03:48,150 --> 00:03:51,770
+element by element و بنعود في f of x و بنجمع
+
+44
+00:03:51,770 --> 00:03:57,490
+فبتصير f of x one plus f of x two plus f of x
+
+45
+00:03:57,490 --> 00:04:00,630
+three لعد ما نخلص كل ال elements اللي موجودة في
+
+46
+00:04:00,630 --> 00:04:06,810
+set x ممكن برضه ال summation نعملها لمين لل
+
+47
+00:04:06,810 --> 00:04:12,130
+predicate إذا كان ال x اللي هي set x عبارة عن set
+
+48
+00:04:12,130 --> 00:04:19,410
+of elements x such that p of xمعنى ذلك أن ال set
+
+49
+00:04:19,410 --> 00:04:24,590
+لكل قيم x اللي تحقق ال function P of X اللي تحقق
+
+50
+00:04:24,590 --> 00:04:26,950
+هذه ال predicate أيام اتكلمنا عن ال predicate
+
+51
+00:04:26,950 --> 00:04:30,050
+فمعنى ذلك أنه ممكن نقول ان هي ال summation لكل
+
+52
+00:04:30,050 --> 00:04:34,250
+element بيحقق ال predicate P of X بنقول F of X
+
+53
+00:04:34,250 --> 00:04:36,890
+معنى ذلك أن F of X واحد و F of X اتنين و F of X
+
+54
+00:04:36,890 --> 00:04:39,770
+ثلاثة X واحد و X اتنين و X ثلاثة هدول هم اللي
+
+55
+00:04:39,770 --> 00:04:46,200
+بيحققوا ال predicateP of X .. P of X .. أي element
+
+56
+00:04:46,200 --> 00:04:49,940
+لا يحقق ال predicate بنحطه مع الجمع .. بنحطه ال
+
+57
+00:04:49,940 --> 00:04:54,820
+functional value مع الجمع ..
+
+58
+00:04:56,540 --> 00:05:00,040
+Simple summation example يعني حاجة بسيطة جدا هنا
+
+59
+00:05:00,040 --> 00:05:02,140
+لو عملنا summation انا عارف ان انتوا ماخدين ال
+
+60
+00:05:02,140 --> 00:05:08,200
+summation قبل هيك I from two to four I تربية plus
+
+61
+00:05:08,200 --> 00:05:11,600
+واحد فاحنا مجرد تعويض بنعوض بال I مرة بتنين مرة
+
+62
+00:05:11,600 --> 00:05:15,100
+بتلاتة مرة باربعة مرة بخمسة لأ خمسة لأ لإنه طلعنا
+
+63
+00:05:15,100 --> 00:05:15,420
+برا
+
+64
+00:05:22,460 --> 00:05:26,400
+بنجمع الأرقام بتاعتنا عشان نطلع ناتج ال summation
+
+65
+00:05:26,400 --> 00:05:34,280
+كلام بسيط و كلام مر عليكم كتير قبل هيك more
+
+66
+00:05:34,280 --> 00:05:37,660
+summation examples لو أخدنا infinite series with a
+
+67
+00:05:37,660 --> 00:05:42,950
+finite sumبقى finite summation فإذا هنا في ممكن
+
+68
+00:05:42,950 --> 00:05:45,770
+يكون عندكوا infinite series واخدناها يمكن المرة
+
+69
+00:05:45,770 --> 00:05:48,490
+اللي فاتت سألتكوا عليها المرة اللي فاتت لو كان
+
+70
+00:05:48,490 --> 00:05:52,510
+عندنا مثلا summation from I equal to zero to
+
+71
+00:05:52,510 --> 00:05:57,130
+infinity لإيش ل two to the power minus I I مرة
+
+72
+00:05:57,130 --> 00:06:02,290
+بتكون صفر فهيكون هنا ال element تبعنا بواحد مرة
+
+73
+00:06:02,290 --> 00:06:07,750
+هتكون بواحد هيكون نص نص
+
+74
+00:06:10,290 --> 00:06:19,110
+مرة هتكون بتنين ربع تمن واحد على ستاش و هكذا to
+
+75
+00:06:19,110 --> 00:06:24,710
+infinity طيب الواحد قدش ضايله للتنين؟ ضايله واحد،
+
+76
+00:06:24,710 --> 00:06:30,250
+أطاني نصهطيب جدش ضايل؟ نص، هطاني نص النص، كل مرة
+
+77
+00:06:30,250 --> 00:06:35,330
+هيضل يعطينا نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+78
+00:06:35,330 --> 00:06:35,890
+نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+79
+00:06:35,890 --> 00:06:40,470
+نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+80
+00:06:40,470 --> 00:06:42,350
+نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+81
+00:06:42,350 --> 00:06:42,350
+نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص، نص،
+
+82
+00:06:42,350 --> 00:06:51,690
+نص، نص، نص، نص، نص، نص،
+
+83
+00:06:51,690 --> 00:06:56,920
+نص،كيف؟ ممكن يقولنا summation x تربيع ويحدد اننا
+
+84
+00:06:56,920 --> 00:07:01,920
+ايش ال x تبعتنا ال x is prime فلاحظوا predicate هي
+
+85
+00:07:01,920 --> 00:07:10,120
+x is prime تمام and x اقل من عشرة فواضح ان انا
+
+86
+00:07:10,120 --> 00:07:14,920
+بتكلم عن اربع elements اتنين تلاتة خمسة سبعة خلاص2
+
+87
+00:07:14,920 --> 00:07:18,980
+3 5 7 هدولة بيحققولي ال predicate و بيحققولي ال
+
+88
+00:07:18,980 --> 00:07:22,700
+condition x أقل من عشرة فإذا واضح إن أنا بحطها هنا
+
+89
+00:07:22,700 --> 00:07:28,000
+اتنين مرة تلاتة مرة خمسة مرة و سبعة مرة بنضرب
+
+90
+00:07:28,000 --> 00:07:33,620
+بنعمل ال functional value لكل واحدة منهم وبنجمع ال
+
+91
+00:07:33,620 --> 00:07:35,580
+summation كلها كويس
+
+92
+00:07:38,110 --> 00:07:43,630
+هنتكلم عن شوية summation, manipulations أو مهارات
+
+93
+00:07:43,630 --> 00:07:47,030
+ممكن نستعدلها لعملية ال summation لما بيجيكوا
+
+94
+00:07:47,030 --> 00:07:50,450
+summation في شوية مهارات ممكن نسهل على حالنا
+
+95
+00:07:50,450 --> 00:07:53,870
+حسابها .. نسهل على حالنا حسابها أول إشي ال
+
+96
+00:07:53,870 --> 00:07:57,240
+constantلو كان عندك constant داخل ال function داخل
+
+97
+00:07:57,240 --> 00:08:00,500
+ال summation اللي أسهل أنه أضربه برا بدل ما كل
+
+98
+00:08:00,500 --> 00:08:03,700
+term أضربه في ال summation في ال constant كل term
+
+99
+00:08:03,700 --> 00:08:05,860
+أضربه في ال constant طب ما بطلعه مرة و بحسب كل ال
+
+100
+00:08:05,860 --> 00:08:09,640
+summation تبعك و بضرب مرة واحدة نضرب ال constant
+
+101
+00:08:09,640 --> 00:08:14,000
+هذا مرة واحدة فقط فهذه ال distributive law
+
+102
+00:08:15,380 --> 00:08:19,280
+Summation ل two functions لو جدتوا ال two
+
+103
+00:08:19,280 --> 00:08:22,060
+functions هدولة واضحى وواضحين بيبين ان هدى
+
+104
+00:08:22,060 --> 00:08:24,080
+function غير هدى بقدر افصلهم اتنين تنين كل واحدة
+
+105
+00:08:24,080 --> 00:08:29,240
+summation اذا كان ال index تبعهم نفسهم اتفضلي
+
+106
+00:08:31,510 --> 00:08:35,750
+أه التوزيح هنا لل summation لأ أنتي وزعتي لحظة
+
+107
+00:08:35,750 --> 00:08:42,870
+خليكي معايا لو جلنا C F of X واحد زائد C F of X
+
+108
+00:08:42,870 --> 00:08:52,650
+اتنين زائد C F of X تلاتة مش هي نفس C F of X واحد
+
+109
+00:08:52,650 --> 00:09:00,120
+plus F of X اتنين plus F of X تلاتةطب انت هنا إيش
+
+110
+00:09:00,120 --> 00:09:02,240
+عملت في هذا؟ بزارة ال .. بزارة ال .. بزارة ال ..
+
+111
+00:09:02,240 --> 00:09:02,640
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+112
+00:09:02,640 --> 00:09:02,740
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+113
+00:09:02,740 --> 00:09:02,920
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+114
+00:09:02,920 --> 00:09:04,420
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+115
+00:09:04,420 --> 00:09:06,640
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+116
+00:09:06,640 --> 00:09:07,500
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+117
+00:09:07,500 --> 00:09:09,320
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+118
+00:09:09,320 --> 00:09:12,000
+بزارة ال .. بزارة ال .. بزارة ال .. بزارة ال ..
+
+119
+00:09:13,730 --> 00:09:19,610
+Okay نفس الكلام زي ما قلنا نرجع لل ال ال ال ال ال
+
+120
+00:09:19,610 --> 00:09:19,650
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+121
+00:09:19,650 --> 00:09:19,790
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+122
+00:09:19,790 --> 00:09:20,070
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+123
+00:09:20,070 --> 00:09:22,170
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+124
+00:09:22,170 --> 00:09:29,430
+ال ال ال ال ال ال ال ال ال ال ال ال
+
+125
+00:09:29,430 --> 00:09:29,430
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+126
+00:09:29,430 --> 00:09:32,210
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+127
+00:09:32,210 --> 00:09:32,770
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+128
+00:09:32,770 --> 00:09:32,770
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+129
+00:09:32,770 --> 00:09:32,770
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+130
+00:09:32,770 --> 00:09:34,370
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+131
+00:09:34,370 --> 00:09:34,370
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+132
+00:09:34,370 --> 00:09:34,370
+ال ال ال ال
+
+133
+00:09:43,920 --> 00:09:49,040
+الـ index بتاع ال summation فلو قلنا I equal to J
+
+134
+00:09:49,040 --> 00:09:55,260
+from J to K ل F of I ممكن اعمل shift ازود هنا N و
+
+135
+00:09:55,260 --> 00:09:58,640
+ازود هنا N و اطرح من هنا ال N عشان اعاد للتأثير
+
+136
+00:09:58,640 --> 00:10:05,290
+فلو عوضته هيطلع نفس ال termsلو عوضته هيطلع نفس ال
+
+137
+00:10:05,290 --> 00:10:09,370
+limits بتاعنا هما هما فعدد ال elements اللي بدنا
+
+138
+00:10:09,370 --> 00:10:13,650
+نجمحهم هو هو عدد او مجموع في النهاية هو هو لأنه
+
+139
+00:10:13,650 --> 00:10:19,450
+لحظة لو عوضته في ال term ده هنا هيطلع J هي نفسها J
+
+140
+00:10:19,450 --> 00:10:22,610
+فانا بادر اول element هو هو نفس ال element عملنا
+
+141
+00:10:22,610 --> 00:10:27,170
+عملية shift بتفيدنا احيانا في بعض ال problemsزي ما
+
+142
+00:10:27,170 --> 00:10:31,830
+هنشوف لاحقا، هناخد أكام من البرو، هتفيدنا الحاجات
+
+143
+00:10:31,830 --> 00:10:36,650
+دي كويس، عملية ال splitting، الفصل عملية ال
+
+144
+00:10:36,650 --> 00:10:39,990
+splitting إن أنا ممكن أقول إن ال summation from j
+
+145
+00:10:39,990 --> 00:10:44,910
+to k, f of i, f of i ممكن أفصلها ل two summations
+
+146
+00:10:44,910 --> 00:10:48,970
+two summations بدهم limit، ال limit اللي بدي
+
+147
+00:10:48,970 --> 00:10:54,410
+أختاره لازم يكون بينهمزي اقول والله ان عندي مجموعة
+
+148
+00:10:54,410 --> 00:10:57,270
+ال sequence فيها .. ال sequence تبعي او ال series
+
+149
+00:10:57,270 --> 00:11:01,750
+تبعتي فيها مجموعة elements meet element من صفر من
+
+150
+00:11:01,750 --> 00:11:05,890
+واحد لمية طبيعي ممكن اعمله two series من واحد
+
+151
+00:11:05,890 --> 00:11:10,790
+لخمسينمن واحد لتسعة وأربعين من واحد لتسعة وتسعين
+
+152
+00:11:10,790 --> 00:11:15,350
+بس مقدرش أقول من واحد لأقل لمية واحد لازم يكون ال
+
+153
+00:11:15,350 --> 00:11:22,770
+M اللي بتضيف هذه من J to K between J وK فإذا ممكن
+
+154
+00:11:22,770 --> 00:11:26,270
+نفرضها نشتغل في الحالة هذه على أساس إن في عندنا
+
+155
+00:11:26,270 --> 00:11:33,320
+two summations واحدة منوالتانية من M plus واحد ال
+
+156
+00:11:33,320 --> 00:11:37,560
+element اللي وراه مباشرة 2K فانا بكون حظرت على I
+
+157
+00:11:37,560 --> 00:11:45,050
+AJ 2K زي ما قولنا ال M دي لازم تكون بينهمطيب ال
+
+158
+00:11:45,050 --> 00:11:48,890
+reversal .. ال reversal نفس يعني شوية مختلفة عن ال
+
+159
+00:11:48,890 --> 00:11:52,850
+shift shift معكوس .. shift معكوس بحيث أن أنا بشيب
+
+160
+00:11:52,850 --> 00:11:56,630
+ال summation لآخر element في الأول و ببدأ للي
+
+161
+00:11:56,630 --> 00:11:59,910
+جابله للي جابله لعند ما أصل لأول .. لأول element
+
+162
+00:11:59,910 --> 00:12:08,550
+from j to k بنخليها من صفر هنا بتصير من صفر فإذا
+
+163
+00:12:08,550 --> 00:12:15,470
+أنا طرحت j و بنطرح فوق jو هنا بنعكس هيها كانت I
+
+164
+00:12:15,470 --> 00:12:19,690
+صارت minus I فانا عملت ال reverse هنا عملت عملية
+
+165
+00:12:19,690 --> 00:12:24,830
+ال inverse عكسنا عملية ال summation بحيث ان انا
+
+166
+00:12:24,830 --> 00:12:29,130
+اخد اخر element في الاول طبعا لو وجهك عوضته هتلاقي
+
+167
+00:12:29,130 --> 00:12:34,550
+ان هو عكسوا بعض هنا صفر f of k اخر element كان
+
+168
+00:12:34,550 --> 00:12:34,990
+موجود
+
+169
+00:12:37,870 --> 00:12:41,990
+كان موجود، لو عكسته و حطيته هذا مكان ال I، هتلاحظ
+
+170
+00:12:41,990 --> 00:12:46,970
+ان ال K مع ال K، ال J أول element، مجرد عكسناهم،
+
+171
+00:12:46,970 --> 00:12:49,590
+صرنا بناخد ال summation مش من أول term لآخر term،
+
+172
+00:12:49,590 --> 00:12:53,690
+من آخر term لأول term طيب، ال grouping، ال
+
+173
+00:12:53,690 --> 00:12:58,490
+grouping هذه بتنفعومناسبة جدا لما يكون في عندكوا
+
+174
+00:12:58,490 --> 00:13:05,170
+ال limits تبعتنا من 0 to 2k لو انتوا عارفين ان
+
+175
+00:13:05,170 --> 00:13:10,490
+انتوا عندكوا عدد زوجي فإذا بقدر اعملهم اجسم ع 2
+
+176
+00:13:10,490 --> 00:13:13,910
+مبدئيا مدان بقدر اجسم ع 2 يعني بقدر اعملهم two
+
+177
+00:13:13,910 --> 00:13:19,750
+groups اقولكوا لو بتقدر تحصلوا على ان عدد ال
+
+178
+00:13:19,750 --> 00:13:23,210
+elements هدولة بتقدروا تجسموها تلاتة اجسموها تلاتة
+
+179
+00:13:23,210 --> 00:13:27,400
+تعملوا three groupsبحيث ان انا بعمل العملية مرة
+
+180
+00:13:27,400 --> 00:13:31,180
+واحدة و بحسبها لل three groups في نفس العملية
+
+181
+00:13:31,180 --> 00:13:35,200
+الحسابية خلّينا
+
+182
+00:13:35,200 --> 00:13:39,360
+نقول من صفر ل two K بنخليها من صفر ل K واحدة بس
+
+183
+00:13:39,360 --> 00:13:46,040
+لنص ال upper limit بتاعتنا و بنحط هنا ال two
+
+184
+00:13:46,040 --> 00:13:50,120
+conditions تعوننا اللي هم ال element اللي اختزلته
+
+185
+00:13:50,120 --> 00:13:53,680
+بتصير بدل ما هي function واحدة two functions واحدة
+
+186
+00:13:53,680 --> 00:14:01,520
+evenو واحدة odd ال even two I ال odd two I plus
+
+187
+00:14:01,520 --> 00:14:07,140
+one فهنا أخدت ال two elements اللي كانوا هنا أساسا
+
+188
+00:14:07,140 --> 00:14:15,280
+two أنا في جميع أحوال جمعت عدد two K elements بس
+
+189
+00:14:15,280 --> 00:14:18,460
+في كل iteration في كل مرحلة جمعت اتنين اتنين
+
+190
+00:14:18,460 --> 00:14:24,260
+جمعتهم اتنينات يعني بدل ما اجمع واحد واحدمئة مرة
+
+191
+00:14:24,260 --> 00:14:29,860
+جمعتهم اتنين اتنين خمسين مرة كويس فعملية ال
+
+192
+00:14:29,860 --> 00:14:33,120
+grouping هذه ممكن نعملها فبتلاقي ال summation
+
+193
+00:14:33,120 --> 00:14:38,200
+limit بتبعته جدل بس في المقابل بدنا نزود عدد ال
+
+194
+00:14:38,200 --> 00:14:41,500
+functions جوا يعني عدد ال functions لإنه بدنا ناخد
+
+195
+00:14:41,500 --> 00:14:45,120
+كل ال terms اللي أنا عملت جامب عنهم انتوا لما
+
+196
+00:14:45,120 --> 00:14:48,580
+بتجسموا على اتنين بتعملوا jump ابجدش ال factor
+
+197
+00:14:48,580 --> 00:14:50,740
+اللي انتوا جسمته عليه فضلا
+
+198
+00:14:54,810 --> 00:15:02,990
+تقدر هنا بالظبط زائد f2i plus 2 اذا كان هنا تلاتة
+
+199
+00:15:02,990 --> 00:15:06,030
+يعني انت عارف انه هيقبل على تلاتة عارف انه هيقبل
+
+200
+00:15:06,030 --> 00:15:09,070
+على تلاتة لو مثلا عندنا عدد limit سبعتنا عندنا
+
+201
+00:15:09,070 --> 00:15:14,730
+عشرة تقدر تعمل grouping بتنين خمسة خمسة صحيح فانت
+
+202
+00:15:14,730 --> 00:15:19,010
+بتعمليها من صفر بتصير لخمسة بدل لعشرة وعارف ان انت
+
+203
+00:15:19,010 --> 00:15:22,350
+هتعملي two groups بدل جسم بتاع التاني طب بس العشرة
+
+204
+00:15:22,350 --> 00:15:26,090
+بتقدر تقسمها على تلاتةلأ فبتقدرش هنا تعمل group،
+
+205
+00:15:26,090 --> 00:15:33,010
+بتقدرش هنا تعمل group okay
+
+206
+00:15:33,010 --> 00:15:36,070
+نبدأ ناخد شوية examples، نبدأ ناخد شوية examples
+
+207
+00:15:36,070 --> 00:15:39,650
+أول examples هناخده embrace your friends
+
+208
+00:15:42,110 --> 00:15:44,150
+هتطلعوا من المحاضرة تبدأوا تشتغلوها على طول مع
+
+209
+00:15:44,150 --> 00:15:48,530
+صاحباتكم مع أخواتكم مش عارف مع أخوتكم تقولوله
+
+210
+00:15:48,530 --> 00:15:53,850
+اعطيني أي رقم من two digits يعني من واحد لتسعة
+
+211
+00:15:53,850 --> 00:15:57,950
+وتسعين هحسبلكوا كل الأرقام مجموعه مع كل الأرقام
+
+212
+00:15:57,950 --> 00:16:01,230
+اللي أقل منه يعني لو جولنا عشرة مثلا هجمعلكوا عشر
+
+213
+00:16:01,230 --> 00:16:03,810
+زي التسعة زي التمانية زي السبعة زي الستة زي الخمسة
+
+214
+00:16:03,810 --> 00:16:07,270
+لعندي الواحد بدون لوورجة و جلم و بدون إشي و قبل ما
+
+215
+00:16:07,270 --> 00:16:12,310
+أنت تفكر تفتح القلع الحاسبة تبعتكجربوها، اعملوها،
+
+216
+00:16:12,310 --> 00:16:16,190
+طبعا أول ما بدت الموضوع هذا بدأ على أساس أنه
+
+217
+00:16:16,190 --> 00:16:21,770
+Leonhard Euler بدأ هو عمره اتناشر سنة، كان عمره
+
+218
+00:16:21,770 --> 00:16:24,650
+اتناشر سنة في الصف، اعطتهم المعلمة بتاعتهم مسألة
+
+219
+00:16:24,650 --> 00:16:29,570
+بهذا الشكل، فعلى طول الإجابة رفع إيده، الجواب كذا،
+
+220
+00:16:29,570 --> 00:16:33,210
+طبعا ماحدش لحج بس يتكلم ولا حد لحج أساسا يقرأ إيش
+
+221
+00:16:33,210 --> 00:16:36,830
+اللي مكتوب على الصبورةكيف مش كيف الراجل عمل لها
+
+222
+00:16:36,830 --> 00:16:41,410
+معادلة و عمل لها closed form formula او formula
+
+223
+00:16:41,410 --> 00:16:46,530
+جاهزة موفقة و منتهية و حلها و خلص okay كان عمره
+
+224
+00:16:46,530 --> 00:16:49,270
+اتناشر سنة في وقتها .. كان عمره في وقتها اتناشر
+
+225
+00:16:49,270 --> 00:16:54,350
+سنة طيب ايش الفكرة فيها اننا اللي بتحولها لرياضيات
+
+226
+00:16:54,350 --> 00:16:59,100
+هتكون عبارة عن summation from one to nو n هذا هو
+
+227
+00:16:59,100 --> 00:17:03,220
+الرقم اللي احنا بتتكلم عنه انه جمعلنا من واحد
+
+228
+00:17:03,220 --> 00:17:07,740
+لعشرة عشرة هتكون هي الاش ال n تبعتنا فهي عبارة عن
+
+229
+00:17:07,740 --> 00:17:13,300
+summation from one to n للأرقام بتاعتنا اللي هي هو
+
+230
+00:17:13,300 --> 00:17:17,200
+من واحد لاش لعشرة لو افترضنا انه عشرة يعني طيب
+
+231
+00:17:17,200 --> 00:17:22,340
+automatically هذه مباشرة هتسوي خمسة و خمسين خمسة و
+
+232
+00:17:22,340 --> 00:17:29,200
+خمسين كيف خمسة و خمسين ال nاللي مطلوبة و ضربوها في
+
+233
+00:17:29,200 --> 00:17:35,260
+n plus واحد على اتنين و جسمه على اتنين فإذا عشرة
+
+234
+00:17:35,260 --> 00:17:39,260
+في احداش و جسمه على اتنين طيب العشرة على اتنين
+
+235
+00:17:39,260 --> 00:17:43,700
+خمسة خمسة في احداش خلاص خمسة و خمسين اجمعوه على
+
+236
+00:17:43,700 --> 00:17:45,980
+الاقل الحسبة لو بتجمعوه على الاقل الحسبة لسه يدوق
+
+237
+00:17:45,980 --> 00:17:50,300
+و بتكون الحبطة واحد زي اتنين يدوق فإذا نرجع واضح
+
+238
+00:17:50,300 --> 00:17:55,100
+إن احنا في انها الوجب تتكلم عن summation from I to
+
+239
+00:17:55,100 --> 00:17:59,950
+Nلإيش؟ لل I لل I هذي اللي هو ال counter اللي بده
+
+240
+00:17:59,950 --> 00:18:04,310
+يعد من واحد لعشرة مثلا فكل اللي بنعمله عشرة في
+
+241
+00:18:04,310 --> 00:18:07,290
+الرقم اللي وراه .. او الرقم اللي بتكون .. كله ..
+
+242
+00:18:07,290 --> 00:18:10,210
+تجمعه مع كل الأعداد اللي أقل منه هو نفس الرقم
+
+243
+00:18:10,210 --> 00:18:13,590
+تضربه في الرقم اللي أعلى منه و بتجسمه على .. على
+
+244
+00:18:13,590 --> 00:18:17,070
+اتنين لو بتتكلموا عن عشرين مثلا عشرين على اتنين
+
+245
+00:18:17,070 --> 00:18:20,970
+عشرة عشرة في واحد و عشرين متن و عشرة خلاص متن و
+
+246
+00:18:20,970 --> 00:18:25,660
+عشراقعدوا اجمعوا على الحاسب احد زي اتنين زي تلاتة
+
+247
+00:18:25,660 --> 00:18:28,780
+زي اربعة لعندما تصلوا لها زي التسعتاش زي اتنين
+
+248
+00:18:28,780 --> 00:18:33,860
+وعشرة اتنين وعشرة اعملوها اليوم لكي تجربوها مروا
+
+249
+00:18:33,860 --> 00:18:38,680
+حالكوا عليها طيب كيف جابها من وين جابها الكلام هذا
+
+250
+00:18:38,680 --> 00:18:42,120
+عمل انه والله فعلا انا مع ناتو بدي افرض ان فعلا ال
+
+251
+00:18:42,120 --> 00:18:45,100
+summation بيكون عند كيف واحد زي اتنين زي تلاتة زي
+
+252
+00:18:45,100 --> 00:18:48,920
+اتنين to n over two لعند ال element اللي في النص
+
+253
+00:18:50,200 --> 00:18:55,900
+plus n over two plus one لعندما يصل لآخر two terms
+
+254
+00:18:55,900 --> 00:19:01,160
+اللي هي n minus one و n هدولة أول element مع آخر
+
+255
+00:19:01,160 --> 00:19:07,420
+element مجموحهم n plus one طيب ال element اللي
+
+256
+00:19:07,420 --> 00:19:14,100
+اتبعد و اللي جبل برضه n minus plus واحد كلهم
+
+257
+00:19:14,100 --> 00:19:22,080
+هتلاقيهم بمتماثلين بيجمعوا مع بعضن plus واحد طيب
+
+258
+00:19:22,080 --> 00:19:28,060
+كداش اتكررت ال n plus واحد هذه بعدد n نصف عدد n
+
+259
+00:19:28,060 --> 00:19:31,940
+نصف عدد ن هى عدد تكراراتهم هى نقف هنا هى عدد
+
+260
+00:19:31,940 --> 00:19:37,720
+تكراراتهم n over two n over two في n plus واحد n
+
+261
+00:19:37,720 --> 00:19:42,980
+over two في n plus واحد هى نفسها n في n plus واحد
+
+262
+00:19:42,980 --> 00:19:43,400
+على تمام
+
+263
+00:19:47,360 --> 00:19:50,740
+فمعادلة سهلة و بسيطة و يمكن استخدامها بسهولة يعنى
+
+264
+00:19:50,740 --> 00:19:54,280
+ال
+
+265
+00:19:54,280 --> 00:19:59,200
+geometric progression أو المتتالية الحسابية
+
+266
+00:19:59,200 --> 00:20:03,040
+الهندسية عفوا الهندسية اللى فاتت الحسابية احنا
+
+267
+00:20:03,040 --> 00:20:05,940
+بنتكلم عن الهندسية فالمتتالة الهندسية بتاعتنا ال
+
+268
+00:20:05,940 --> 00:20:11,780
+geometric او الهندسية فعلا عبارة عن ايش A في R to
+
+269
+00:20:11,780 --> 00:20:16,550
+the power IElement وطبعا هنا ال summation ده
+
+270
+00:20:16,550 --> 00:20:21,570
+ماببدأ من الصفر ماببدأ من الصفر ده ماببدأ ب a
+
+271
+00:20:21,570 --> 00:20:24,010
+لحالة في الأول a لحالة في الأول معناته مضربة في
+
+272
+00:20:24,010 --> 00:20:31,310
+واحد في r to the power zero بعدين a في r to the
+
+273
+00:20:31,310 --> 00:20:35,770
+power واحد r to the power اتنين تلاتة اربعة to the
+
+274
+00:20:35,770 --> 00:20:42,270
+power k لعند ما نصل ل ال element k او ال element k
+
+275
+00:20:42,270 --> 00:20:46,640
+plus واحد حقيقةلأن هنا بدنا بواحد اتنين تلاتة طيب
+
+276
+00:20:46,640 --> 00:20:53,000
+a و r belong to R هي real numbers
+
+277
+00:20:53,000 --> 00:20:58,760
+او ال coefficient بتاعة المتتالية الهندسية بتاعتنا
+
+278
+00:20:58,760 --> 00:21:03,620
+okay فال summation تبعنا هيكون from zero to k ل a
+
+279
+00:21:03,620 --> 00:21:14,550
+ri هذا برضه لهالها formula جاهزة كيف نجيبها؟
+
+280
+00:21:14,550 --> 00:21:18,630
+هنجيبها بالإثبات من مجموعة ال rules اللي توا
+
+281
+00:21:18,630 --> 00:21:20,930
+خدناها مجموعة ال rules اللي توا خدناها هنستعمل
+
+282
+00:21:20,930 --> 00:21:25,630
+شوية منهم عساس ان نجيب ال summation هذه طيب هذه ال
+
+283
+00:21:25,630 --> 00:21:30,030
+summation أول حاجة هنعملها هنضرب الطرفين في R هنا
+
+284
+00:21:30,030 --> 00:21:34,390
+في R و هنا في R طيب ال R اللي انضربت هنا بقدر
+
+285
+00:21:34,390 --> 00:21:38,270
+ببساطة جدا أدخلها جوا و أجمحها مع R to the bar
+
+286
+00:21:39,350 --> 00:21:46,430
+فهتصير r to the power of i plus one اللي هي هنا
+
+287
+00:21:46,430 --> 00:21:51,450
+وصلنا
+
+288
+00:21:51,450 --> 00:21:54,430
+للحالة التالتة هنا بعد هي كيف نعمل عملية ال shift
+
+289
+00:21:54,430 --> 00:22:01,490
+نعمل قبلها خلصنا هنا عند r one plus i او اي plus
+
+290
+00:22:01,490 --> 00:22:05,110
+one مش هتفرق كتيرهنا بيظل في عنا إيش بدنا نسوي؟
+
+291
+00:22:05,110 --> 00:22:11,750
+بدنا نعمل shift تبدأ هنا من واحد ليش من واحد؟ عشان
+
+292
+00:22:11,750 --> 00:22:15,990
+بده أوصل ال form تبعي اللي هو plus واحد هنا يتناسب
+
+293
+00:22:15,990 --> 00:22:20,330
+مع ال upper ال upper ماعنديش end عند هنا صارت end
+
+294
+00:22:20,330 --> 00:22:23,990
+plus واحد عشان نوصلها لل upper ونقول والله هي دي
+
+295
+00:22:23,990 --> 00:22:26,790
+ممكن تكون form متناسقة مع بعضها فمحتاجين نعمل
+
+296
+00:22:26,790 --> 00:22:31,070
+shift عشان نعمل shift هزود هنا plus واحد و هزود
+
+297
+00:22:31,070 --> 00:22:36,600
+هنا plus واحدو إيش عمل هنا؟ minus هنا بدنا نعمل
+
+298
+00:22:36,600 --> 00:22:41,300
+minus one عشان تأثيرهم يروح مع بعضهم كويس اعملنا
+
+299
+00:22:41,300 --> 00:22:48,420
+الكلام هذا لحظة رجعتوا لنفس ال term اللي هو ايه؟ r
+
+300
+00:22:48,420 --> 00:22:52,760
+to the power i بس ال form تبعنا صار من one to n
+
+301
+00:22:52,760 --> 00:22:59,560
+plus one to n plus one هذا كله إيش بيساوي؟ بيساويR
+
+302
+00:22:59,560 --> 00:23:04,320
+في الـ summation طب نلاحظ أن هذا لا يساوي ال
+
+303
+00:23:04,320 --> 00:23:09,520
+summation ال term هذا لا يساوي ال summation ليش؟
+
+304
+00:23:09,520 --> 00:23:15,780
+لأن هذا بدأ من 0 to N هنا بدأ من 1 to N plus 1 هذه
+
+305
+00:23:15,780 --> 00:23:19,100
+مختلفة فإذا هذه لا تساوي ال summation ال term اللي
+
+306
+00:23:19,100 --> 00:23:22,380
+وصلناه هنا لا يساوي ال summation ال summation
+
+307
+00:23:22,380 --> 00:23:28,800
+تبعنا هو فعليا من وين بدأ من 0 to Nفإذا أنا هذا
+
+308
+00:23:28,800 --> 00:23:34,180
+بدي إياها أوصلها ل n عشان أوصلها ل n محتاجين نعمل
+
+309
+00:23:34,180 --> 00:23:40,360
+عملية splitting من zero أو من واحد to n ومن n plus
+
+310
+00:23:40,360 --> 00:23:44,320
+واحد to n plus واحد فال term تبعنا بيظل n أنا
+
+311
+00:23:44,320 --> 00:23:46,880
+هالواجهة كل الفكرة أن هذا ال term هذا عشان و احنا
+
+312
+00:23:46,880 --> 00:23:49,900
+مشهيل ما تقولوش عشان اللي بنعمله احنا بدنا نوصل ال
+
+313
+00:23:49,900 --> 00:23:55,810
+term هذا انه يكون نفس ال summationعشان يرجع لل
+
+314
+00:23:55,810 --> 00:24:02,690
+summation هذه ال N لفوق ال N plus واحد بده احولها
+
+315
+00:24:02,690 --> 00:24:06,350
+ل N فى عندى قانون جاهز اللى هو ال splitting ال
+
+316
+00:24:06,350 --> 00:24:09,130
+splitting بقدر اعمل ال summation تبعى من واحد
+
+317
+00:24:09,130 --> 00:24:11,950
+هنشوف في ال logic كيف نحلها الواحد الواحد ده اللى
+
+318
+00:24:11,950 --> 00:24:15,410
+ضايلة بنشوف كيف نظبطها بس ناخد حاجة حاجة نظبط ال N
+
+319
+00:24:15,410 --> 00:24:21,600
+plus واحد فهنقول هي من واحد to Nplus n plus one to
+
+320
+00:24:21,600 --> 00:24:25,740
+n plus one يعني term زيادة اللي هو ال n plus one
+
+321
+00:24:25,740 --> 00:24:28,540
+اللي كان موجود هذا ال summation عبارة عن term واحد
+
+322
+00:24:28,540 --> 00:24:34,480
+بس اللي هو n plus one نعود مباشرة في ال n plus one
+
+323
+00:24:34,480 --> 00:24:40,760
+بيصير ar to the power of n plus one خلاص كويس هاي
+
+324
+00:24:40,760 --> 00:24:43,140
+ال summation اللي ضال ال summation اللي ضال فيها
+
+325
+00:24:43,140 --> 00:24:50,690
+عند ال zero عشان أقول إن هذا هو ال Sعندي مشكلة،
+
+326
+00:24:50,690 --> 00:24:55,150
+الشيء أن هذا ال summation تبعك ده من zero طب إيش
+
+327
+00:24:55,150 --> 00:24:59,630
+نسوي؟ أنا إيش ناجس عليا؟ إيش ال term اللي بنجس
+
+328
+00:24:59,630 --> 00:25:03,550
+عليا؟ ناجس عليا term واحد بس اللي هو عند التعويض I
+
+329
+00:25:03,550 --> 00:25:08,830
+بتسوي zero اللي هو A تمامًا A في R to the power
+
+330
+00:25:08,830 --> 00:25:15,550
+zero طب مابجمعه و باطرحه صحيح؟لو جمعناها و طرحناها
+
+331
+00:25:15,550 --> 00:25:19,910
+بمش الحل و نشوف بعدين كله طبعا في الآخر هيجمع
+
+332
+00:25:19,910 --> 00:25:22,790
+بمجموعة elements موجودة ال elements ده هي اللي
+
+333
+00:25:22,790 --> 00:25:25,250
+هتعطيني ال form اللي مطلوب ال form اللي بيجب ان
+
+334
+00:25:25,250 --> 00:25:29,730
+انا احسبها عشان
+
+335
+00:25:29,730 --> 00:25:34,690
+نصل زي ما قلنا ل الحالة ها دي ها دي وصلناها فيش
+
+336
+00:25:34,690 --> 00:25:39,110
+مشكلة بس ضلت ايش انا بديها هنا من zeroنبدأها من 0
+
+337
+00:25:39,110 --> 00:25:49,270
+فهنزود ar⁰ ونطرح ar⁰ هذه مع ال term تبعها مع ال
+
+338
+00:25:49,270 --> 00:25:56,170
+summation تبعها وهذه هتبقى تنجمع مع ال ar n plus
+
+339
+00:25:56,170 --> 00:25:59,490
+one اللي كانت أصلا موجودة اللي كانت أساسا موجودة
+
+340
+00:25:59,490 --> 00:26:03,990
+صار هذه بقدر اعملها summation from i تساوي 0 to 0
+
+341
+00:26:03,990 --> 00:26:09,170
+معينة ان هي element و بنحط بدلالـ zero هذا مانحطه
+
+342
+00:26:09,170 --> 00:26:18,470
+I عشان اعمل عكس splitting لحظة من صفر to zero و
+
+343
+00:26:18,470 --> 00:26:21,750
+هنا من واحد to end بقدر اقول من صفر to end مدام
+
+344
+00:26:21,750 --> 00:26:28,430
+نفس ال function هي هي فإذا صارت من مباشرة من صفر
+
+345
+00:26:28,430 --> 00:26:32,430
+to what؟ to end صفر to end و لحظة هذه
+
+346
+00:26:32,430 --> 00:26:37,560
+automatically صارت هيالصممشن نفسه هي الصممشن هذه
+
+347
+00:26:37,560 --> 00:26:41,080
+المفروض R في الصممشن فهذه بقدر الوجب تاخدها عن
+
+348
+00:26:41,080 --> 00:26:47,520
+ناحية تانية بنخلص من الصممشن احنا بدنا نلغى كلمة
+
+349
+00:26:47,520 --> 00:26:51,100
+الصممشن بدى terms بدون صممشن terms اقدر اعود
+
+350
+00:26:51,100 --> 00:26:55,600
+مباشرة فيها ارقام يعني قيا او formula اعود مباشرة
+
+351
+00:26:55,600 --> 00:26:59,180
+فيها okay هذه مناسبة ارقام باعود فيها على طولقللي
+
+352
+00:26:59,180 --> 00:27:03,060
+بس جديش قيمة ال N بعوض ب N plus واحد جديش قيمة ال
+
+353
+00:27:03,060 --> 00:27:06,140
+R بنعوض فيها A بنعوض فيها بس ال summation هو
+
+354
+00:27:06,140 --> 00:27:08,720
+المشكلة فهذه ال summation ممكن أجي أعكسه عن ناحية
+
+355
+00:27:08,720 --> 00:27:12,140
+تانية وعشان هيك كنا بندور أنه ال summation اللي
+
+356
+00:27:12,140 --> 00:27:15,620
+ظهر عندنا بدنا نظبطه بنفس ال summation تبعنا عشان
+
+357
+00:27:15,620 --> 00:27:21,200
+نقدر نجمحهم مع بعض نقدر نجمحهم مع بعض كويس فصارت
+
+358
+00:27:21,200 --> 00:27:25,120
+هنا عبارة عن summation و هنا بناخد ال A مشترك لإن
+
+359
+00:27:25,120 --> 00:27:32,050
+في عندكوا A وفيه Aلأن هذه أصلاً كانت ar²⁰ ar²⁰
+
+360
+00:27:32,050 --> 00:27:45,350
+بواحد خدوا ال a مشترك بتصير هذه واحد فهي okay صارت
+
+361
+00:27:45,350 --> 00:27:54,110
+r كل هذا ال term هيك بيساوي r فئة صحيح
+
+362
+00:27:54,110 --> 00:28:05,810
+تمام لو هذه راحت عن ناحية تانيةتمام بتصير هنا ناقص
+
+363
+00:28:05,810 --> 00:28:10,330
+S طيب
+
+364
+00:28:10,330 --> 00:28:17,950
+أخدنا ال S مشترك بنقدر
+
+365
+00:28:17,950 --> 00:28:28,990
+نقولها لغة S بتساوي ال term هذا هيهعلى r-1 جبنا ال
+
+366
+00:28:28,990 --> 00:28:36,710
+summation على r-1 فهي المعادلة المفروضة بتصحيحها
+
+367
+00:28:36,710 --> 00:28:42,410
+معادلة مافيش فيها summation يعني مجرد تعويض مباشر
+
+368
+00:28:42,410 --> 00:28:47,450
+بتصير بس بتظل تعويض مباشر اعطيني جدش ال n بدك
+
+369
+00:28:47,450 --> 00:28:52,080
+تجمحهم ل أي termبنعود في المعادلة هى جدش ال
+
+370
+00:28:52,080 --> 00:28:55,040
+coefficients تبعتها اصلا ايش ال parameters بتاعة
+
+371
+00:28:55,040 --> 00:29:02,740
+المتتالي الهندسى هدى بنحطها a و r و بنعود بطلع ال
+
+372
+00:29:02,740 --> 00:29:05,060
+summation اللى بندور عليه
+
+373
+00:29:20,940 --> 00:29:27,480
+فبطلع ال summation بساوي a في R to the power n
+
+374
+00:29:27,480 --> 00:29:33,260
+plus one minus one على R minus one هذا امتى .. هذا
+
+375
+00:29:33,260 --> 00:29:39,140
+امتى الكلام لما تكون R لاتساوي واحد لان لو سوى
+
+376
+00:29:39,140 --> 00:29:43,080
+واحد ففي
+
+377
+00:29:43,080 --> 00:29:47,000
+حال بتساوي واحد احنا هنحسبها لحالها اذا حال بتساوي
+
+378
+00:29:47,000 --> 00:29:49,760
+واحد ف automatic بنعود فيها مباشرة لان هو عبارة عن
+
+379
+00:29:51,450 --> 00:29:54,870
+ترم لحاله او two terms فعليا اذا عوضنا بواحد
+
+380
+00:29:54,870 --> 00:30:05,730
+فهيطلع a constant هنا لو عوضنا r هذه بواحد واحد
+
+381
+00:30:05,730 --> 00:30:11,690
+power اي اشي بواحد خلاص هتبقى واحد وال a constant
+
+382
+00:30:11,690 --> 00:30:21,620
+ثابتة فهتساوي a في ال summation من صفر to nطيب كم
+
+383
+00:30:21,620 --> 00:30:26,980
+مرة ماتكرر ال element هذا؟ من صفر to N N مرة لو
+
+384
+00:30:26,980 --> 00:30:30,360
+انا بجمع من واحد لو انا شغال من واحد to N هعندي N
+
+385
+00:30:30,360 --> 00:30:37,780
+مرة زائد الصفر N plus one N plus one فهذا عبارة عن
+
+386
+00:30:37,780 --> 00:30:43,640
+N plus one في ال constant على اعتبار ان ال
+
+387
+00:30:43,640 --> 00:30:46,060
+constant هو كان جوا بنقدر نطلع برا مدام constant
+
+388
+00:30:46,950 --> 00:30:53,630
+فبتطلع n plus one في إيه؟ في a فإذا عندنا two
+
+389
+00:30:53,630 --> 00:30:58,970
+conditions لجيومتريك ال progression إذا كانت r لا
+
+390
+00:30:58,970 --> 00:31:05,050
+تساوي واحد ال summation بيساوي a افتحوا أقواص r n
+
+391
+00:31:05,050 --> 00:31:09,090
+plus واحد minus واحد على r minus واحد طيب تساوي
+
+392
+00:31:09,090 --> 00:31:15,810
+واحد هتساوي n plus واحد في aكويس؟ خلاص فهذه بتكون
+
+393
+00:31:15,810 --> 00:31:22,150
+هي أثباتها أو طريقة الحساب ال summation للمتتالية
+
+394
+00:31:22,150 --> 00:31:26,510
+الهندسية طيب nested summations .. nested
+
+395
+00:31:26,510 --> 00:31:29,970
+summations أو ال summations المتشابكة لما يكون في
+
+396
+00:31:29,970 --> 00:31:32,890
+عندكوا أكتر من summation فهذه مش شابهة تماما
+
+397
+00:31:32,890 --> 00:31:35,770
+لعملية ال integration لما يكون عندكوا أكتر من
+
+398
+00:31:35,770 --> 00:31:38,650
+integration ماعرفش مرت عليكم سابقا او لأ في واحدة
+
+399
+00:31:38,650 --> 00:31:42,750
+من ال .. الرياضيات اللي أخدتوهاأو لأ ممكن يكون
+
+400
+00:31:42,750 --> 00:31:46,250
+عندكوا أكتر من integration أكتر من integration أو
+
+401
+00:31:46,250 --> 00:31:51,570
+تكامل .. تكامل في اتجاهين مثلا واحد ممكن يكون
+
+402
+00:31:51,570 --> 00:31:56,510
+تكامل dx و dy فممكن يكون أكتر من واحد حيمر عليكوا
+
+403
+00:31:56,510 --> 00:32:00,570
+مدى ما مرش معناته حيمر مثلا ب جيب لازم يكون
+
+404
+00:32:00,570 --> 00:32:03,250
+أخدتهوا مانفعش إذا ماخدتهوش حركة معناته بيكون في
+
+405
+00:32:03,250 --> 00:32:05,790
+بساق لسه هتاخدوه بيتكون المعادلة التفضلية
+
+406
+00:32:05,790 --> 00:32:10,460
+ماخدتهوهاش لسهناخد ال summation هلأ، لو افترضنا
+
+407
+00:32:10,460 --> 00:32:13,160
+نفس الفكرة هي هي، ليش؟ لأن ال integration .. احنا
+
+408
+00:32:13,160 --> 00:32:15,140
+نتعامل مع ال integration لما نكون نشتغل على
+
+409
+00:32:15,140 --> 00:32:18,640
+continuous function او continuous signal لما
+
+410
+00:32:18,640 --> 00:32:22,250
+بنشتغل في ال discrete، مافيش integrationال
+
+411
+00:32:22,250 --> 00:32:26,030
+integration بنعوض عنه أو بنستعيد عنه بال summation
+
+412
+00:32:26,030 --> 00:32:29,970
+عشانك احنا مش بتتكلم هنا عن ال summation لأنه خاصة
+
+413
+00:32:29,970 --> 00:32:33,230
+بال discrete elements بكرا لما تاخدوا ان شاء الله
+
+414
+00:32:33,230 --> 00:32:35,990
+كمان مصاق اللي هو ال DSP او ال digital signal
+
+415
+00:32:35,990 --> 00:32:39,350
+processing و تتعاملوا مع ال digital ال digital مش
+
+416
+00:32:39,350 --> 00:32:43,590
+هتعملوا integration هتعملوا summation هتشتغلوا مع
+
+417
+00:32:43,590 --> 00:32:47,030
+summation بهذا الشكل فلو كانت actually هي عبارة عن
+
+418
+00:32:47,030 --> 00:32:50,050
+integration هتحولهم ل two summation عشان تشتغلوا
+
+419
+00:32:50,050 --> 00:32:54,260
+فيهم discreteعشان تشتغلوا as a discrete signal
+
+420
+00:32:54,260 --> 00:32:58,240
+كويس فعشان هيك ناخدهم الآن عشان نلمحهد لشغلكوا
+
+421
+00:32:58,240 --> 00:33:02,420
+لاحقا لحظة حيكون في عندكوا double summation
+
+422
+00:33:02,420 --> 00:33:09,220
+وعندكوا هاي ال variable بتاعة كل واحدة منهم هذه J
+
+423
+00:33:09,220 --> 00:33:14,320
+فال variable هي موجود و I هي موجود كويس first ليه
+
+424
+00:33:14,320 --> 00:33:19,060
+بنبدأهم واحدة واحدة بنبدأ بالداخلية في الأولداخلية
+
+425
+00:33:19,060 --> 00:33:25,620
+من واحد لتلاتة و I J طيب هي variable في إيش؟ J فال
+
+426
+00:33:25,620 --> 00:33:30,000
+I بالنسبالها constant بقدر أطلحها برا طلعناها برا
+
+427
+00:33:30,790 --> 00:33:34,770
+لأن ال summation هو لجيه فقط جيه ال I مش فارغة ال
+
+428
+00:33:34,770 --> 00:33:39,210
+I constant كويس بنشتغل عليها على الجيه فبنعوض واحد
+
+429
+00:33:39,210 --> 00:33:42,030
+زي اتنين زي التلاتة خلاص هو هي ال limit سبعتنا
+
+430
+00:33:42,030 --> 00:33:45,950
+واحد زي اتنين زي التلاتة ستة فبصير عندنا ستة I
+
+431
+00:33:45,950 --> 00:33:49,870
+الستة constant بقدر أطلعها برضه برا بدل ما نضربها
+
+432
+00:33:49,870 --> 00:33:53,290
+في ال three terms في ال four terms تبعتنا four
+
+433
+00:33:53,290 --> 00:33:56,930
+terms كل واحد أضربه في ستة لأ بنطلعها برا بنجمعه و
+
+434
+00:33:56,930 --> 00:34:01,860
+بعدين نضرب برا واحدة في ستةجمعنا من واحد لاربعة
+
+435
+00:34:01,860 --> 00:34:06,620
+هاي في عندكم ستة زي اربع عشرة و بعدين نضروف في مين
+
+436
+00:34:06,620 --> 00:34:09,720
+في ال constant اللي طلعنا برا بطلع المجموع هنا
+
+437
+00:34:09,720 --> 00:34:13,280
+ستين بطلع عندكم مجموع ستين فهنا الحاجة اللي بدنا
+
+438
+00:34:13,280 --> 00:34:17,860
+نحددها مين ال free و مين ال bound variables هنا
+
+439
+00:34:17,860 --> 00:34:23,280
+كان عندنا ال free ال Iقدرت اتحرك فيها و طلع برا ال
+
+440
+00:34:23,280 --> 00:34:26,760
+j كانت ال bound فبتظل موجودة داخل ال summation و
+
+441
+00:34:26,760 --> 00:34:29,360
+ماقدرش أتحرك فيها لأن هذه هي ال function اللي بدنا
+
+442
+00:34:29,360 --> 00:34:32,240
+نشتغل عليها داخل ال summation في ال summation
+
+443
+00:34:32,240 --> 00:34:37,460
+بتاعنا، كويس مشابه تماما ل ال quantifiers لما
+
+444
+00:34:37,460 --> 00:34:40,160
+اتكلمنا عن ال quantifiers فاكرين و لما اتكلمتوا في
+
+445
+00:34:40,160 --> 00:34:42,840
+ال integration او في ال integrals زي ما انتوا
+
+446
+00:34:42,840 --> 00:34:44,240
+بتقولوا مااخدتوهاش ان شاء الله بتاخدوها
+
+447
+00:34:47,390 --> 00:34:54,230
+هيك أنلخص مجموعة shortcut expressions الجيومتريك
+
+448
+00:34:54,230 --> 00:34:58,310
+أخدناها، اتكلمنا عنها في حال r لا تساوي واحد فكانت
+
+449
+00:34:58,310 --> 00:35:02,790
+تساوي هي ال a في r to the power n plus واحد minus
+
+450
+00:35:02,790 --> 00:35:08,190
+واحد على r minus واحد طيب إذا كان r تساوي واحد كنا
+
+451
+00:35:08,190 --> 00:35:15,600
+بيقول a في n plus واحد خلصناOkay؟ كويسة ال .. ال
+
+452
+00:35:15,600 --> 00:35:19,420
+oilers track
+
+453
+00:35:19,420 --> 00:35:24,960
+أو اللي هو خاصة بال summation الحسابية اللي هي
+
+454
+00:35:24,960 --> 00:35:29,540
+المتطالب الحسابية كانت بهذا الشكل زي ما قولنا n في
+
+455
+00:35:29,540 --> 00:35:34,000
+اللي بعدها n plus واحد كله على اتنين كله على اتنين
+
+456
+00:35:34,000 --> 00:35:40,250
+في ال quadratic n في n plus واحد لحظةفي اتنين N
+
+457
+00:35:40,250 --> 00:35:45,410
+plus واحد على ستة فهتزيده
+
+458
+00:35:45,410 --> 00:35:51,950
+كمان term و تجيسمه على ستة هذا ليش للتربيعية طيب
+
+459
+00:35:51,950 --> 00:35:58,870
+التكعيبية اسهل تكعيبية تربيع تربيع تربيع تربيع N
+
+460
+00:35:58,870 --> 00:36:05,130
+تربيع N plus واحد تربيع على اتنين تربيعأسهل حتى في
+
+461
+00:36:05,130 --> 00:36:11,410
+حفظها اويلارز رول
+
+462
+00:36:11,410 --> 00:36:16,110
+و بتربقوها بتربقوا ال terms بتاعتها بتربقوا n
+
+463
+00:36:16,110 --> 00:36:23,270
+تربيع n plus one تربيع على أربعة على أربعة من
+
+464
+00:36:23,270 --> 00:36:26,290
+المجموعات اللي أخدناها مجموعة ال rules اللي
+
+465
+00:36:26,290 --> 00:36:33,470
+أخدناها بدنا نعمل summation ل k تربيعQuadratic
+
+466
+00:36:33,470 --> 00:36:39,150
+form معادلة تربيعية ال quadratic form هذه from k
+
+467
+00:36:39,150 --> 00:36:46,070
+equal to fifty to one hundred هذا إيش بدنا نسويه
+
+468
+00:36:46,070 --> 00:36:50,830
+أول شي؟ splitting بدنا نفكر في عملية ال splitting
+
+469
+00:36:50,830 --> 00:36:52,750
+ليش؟ لإن احنا عارفين إن ال summation
+
+470
+00:36:57,880 --> 00:37:06,960
+لو قلنا k بتساوي من واحد ل k مية k تربيع بنقدر
+
+471
+00:37:06,960 --> 00:37:15,860
+نحسبها صحيح احنا عارفين مسبقا ان هذا n تربيع في n
+
+472
+00:37:15,860 --> 00:37:20,420
+plus واحد لكوادرتي اللي هو جزء التربيع في اتنين n
+
+473
+00:37:20,420 --> 00:37:26,710
+plus واحد على ستةكويسة هذي بتقسمها بيقول هذي
+
+474
+00:37:26,710 --> 00:37:35,850
+بتساوي summation K واحد لجداش تسعة واربعين لأن
+
+475
+00:37:35,850 --> 00:37:39,110
+الخمسين بتديها في ال term التاني و الخمسين ماتقدرش
+
+476
+00:37:39,110 --> 00:37:42,210
+نكررها فانا محتاجة في ال term التاني ال term اللي
+
+477
+00:37:42,210 --> 00:37:46,410
+احنا محتاجين نحسب زائد summation من K بتساوي خمسين
+
+478
+00:37:46,410 --> 00:37:51,500
+لميةال term هذا أو خلينا نقول لأ ال term هذا
+
+479
+00:37:51,500 --> 00:37:55,700
+بناخده عن ناحية تانية بنطرحه فبصير هذا ال term ايش
+
+480
+00:37:55,700 --> 00:38:01,720
+بساوي بساوي summation من كيه بتساوي مية من كيه
+
+481
+00:38:01,720 --> 00:38:09,180
+بتساوي واحد لمية واحد لمية ناقص summation من كيه
+
+482
+00:38:09,180 --> 00:38:14,640
+بتساوي واحد لتسعة واربعين فازا انا محتاج اجيب ال
+
+483
+00:38:14,640 --> 00:38:21,100
+two terms هدولة القانون هيه مرة بنعوض بميةمية في
+
+484
+00:38:21,100 --> 00:38:27,440
+مية و واحد في متين و واحد على ستة و مرة بنعوض تسعة
+
+485
+00:38:27,440 --> 00:38:32,860
+و اربعين في خمسين في جداش بتطلع تسعة و تسعين تسعة
+
+486
+00:38:32,860 --> 00:38:36,480
+و تسعين على ستة بنحسب ال term و بنحسب ال term و
+
+487
+00:38:36,480 --> 00:38:39,900
+بنطرحهم من بعض نطرح ال term التاني من ال term
+
+488
+00:38:39,900 --> 00:38:46,100
+الأول هو ده فعلا اللي حاسبه فبنقدر نجيب من خمسين
+
+489
+00:38:46,100 --> 00:38:48,040
+لمية خمسين لمية
+
+490
+00:38:57,070 --> 00:39:00,330
+فهيكي بنكون أخدنا مجموعة summations أو مجموعة
+
+491
+00:39:00,330 --> 00:39:05,590
+notations ال summation لل limits و ال limits
+
+492
+00:39:05,590 --> 00:39:08,570
+ساعتنا من I to K و قلنا إن ما بقدر أعمل summation
+
+493
+00:39:08,570 --> 00:39:12,530
+to infinite series و قلنا بنتكلم عن ال summation
+
+494
+00:39:12,530 --> 00:39:15,790
+في حالة إن احنا نتكلم عن function و بنتكلم عن ال
+
+495
+00:39:15,790 --> 00:39:21,370
+predicate برضه أخدناها أخدنا شوية formulas بنقدر
+
+496
+00:39:21,370 --> 00:39:25,090
+نشتغلها و بنقدر نستنتجها زي ما اتكلمنا عنهاطيب ال
+
+497
+00:39:25,090 --> 00:39:28,250
+cardinalities ال cardinalities إحنا خدناها أنا
+
+498
+00:39:28,250 --> 00:39:30,610
+عارف إن إحنا خدناها و كانت أمرها لما خدناها كانت
+
+499
+00:39:30,610 --> 00:39:37,050
+سهلة ليش؟ لإن كنا بنتعامل مع finite set أو finite
+
+500
+00:39:37,050 --> 00:39:40,870
+series فكانت سهلة بقى بعدهم بأي طريقة كانت و بنجيب
+
+501
+00:39:40,870 --> 00:39:43,150
+ال cardinality و انتهينا و خلاص انتهي الموضوع
+
+502
+00:39:43,150 --> 00:39:47,000
+مافيش أي مشاكل و تمام تماملأ إحنا هنا بدنا نتعامل
+
+503
+00:39:47,000 --> 00:39:50,640
+.. نشمل الموضوع أكبر، نخليه أكتر شمولية، نتعامل مع
+
+504
+00:39:50,640 --> 00:39:54,360
+ال infinite sets ال infinite sets كيف بقدر أجيب ال
+
+505
+00:39:54,360 --> 00:39:57,890
+cardinality بتاعتها؟أو إيش ال infinite sets اللي
+
+506
+00:39:57,890 --> 00:40:00,610
+بقدر أقول إن هي بقدر أجيب لها cardinality أو بقدر
+
+507
+00:40:00,610 --> 00:40:04,550
+على الأقل أوصف cardinality بتاعتها إنه معدودة بقدر
+
+508
+00:40:04,550 --> 00:40:08,830
+أحسبها حتى لو ما حسبتاش exactly برقم بس بقدر أقول
+
+509
+00:40:08,830 --> 00:40:14,350
+إن هي محسوبة countable قابلة للعد أو إن هي لأ غير
+
+510
+00:40:14,350 --> 00:40:17,690
+محسوبة إمتى بنقدر نقول كلام هذا؟ عشان نقول كلام
+
+511
+00:40:17,690 --> 00:40:22,400
+هذا هناخد شوية مفاهيمونثبت الموضوع ده عشان نثبته
+
+512
+00:40:22,400 --> 00:40:26,740
+محتاجين نرجع شوية ل cardinality نفسها إيش يعني
+
+513
+00:40:26,740 --> 00:40:31,020
+cardinality فلو قولنا لو في عندنا two sets A and B
+
+514
+00:40:31,020 --> 00:40:36,120
+بنقدر نقول A و B have the same cardinality أمتى و
+
+515
+00:40:36,120 --> 00:40:38,780
+بنكتبها كتالة cardinality A equal to cardinality B
+
+516
+00:40:38,780 --> 00:40:42,820
+if and only if there exists a bijection between
+
+517
+00:40:42,820 --> 00:40:47,070
+themإذا كان فعلا ال relation بينهم ال function
+
+518
+00:40:47,070 --> 00:40:51,530
+بينهم bijection bijection إيش يعني one to one و on
+
+519
+00:40:51,530 --> 00:40:54,790
+to one one to one و on to one كويسة إذا قدرنا نثبت
+
+520
+00:40:54,790 --> 00:40:58,170
+الكلامة لأن والله فعلا العلاقة ك function بين
+
+521
+00:40:58,170 --> 00:41:01,430
+التنتين هدولة بين ال two sets هدولة bijection فإذا
+
+522
+00:41:01,430 --> 00:41:06,070
+ال two sets هدولة أكيد لهم نفس ال cardinality لهم
+
+523
+00:41:06,070 --> 00:41:10,190
+نفس ال cardinality تمام هذه تعريف مميز نقدر نشتغل
+
+524
+00:41:10,190 --> 00:41:16,550
+من خلاله فإذا لو قلنا aعلى أساس إن هاي عندكم a وهي
+
+525
+00:41:16,550 --> 00:41:20,670
+بي لو عملتوا relation بينهم ال function هدى is a
+
+526
+00:41:20,670 --> 00:41:23,670
+bijection إذا أكيد هدول ال two cardinalities
+
+527
+00:41:23,670 --> 00:41:28,330
+بتاعتهم بيسووا بعض تمام a و b are finite مافيش
+
+528
+00:41:28,330 --> 00:41:33,470
+مشكلة finite معناه سهل يعني معدود معناته محدد بدون
+
+529
+00:41:33,470 --> 00:41:36,410
+finite محدد بقدر أعده بنقدر نعده الأمور مافيش
+
+530
+00:41:36,410 --> 00:41:40,110
+هيكون فيها مشكلة في الحالة بتاعتنا بنقدر نقول if
+
+531
+00:41:40,110 --> 00:41:43,790
+and only if a and b have the samenumber of
+
+532
+00:41:43,790 --> 00:41:46,810
+elements و ال number of elements هذه كنا دائما
+
+533
+00:41:46,810 --> 00:41:50,030
+بنعرفها ان element belong to mean natural number
+
+534
+00:41:50,030 --> 00:41:56,950
+طيب ماعنى ذلك إذا قدرنا نقول ان ال set بتاعتنا
+
+535
+00:41:56,950 --> 00:42:01,510
+بقدر امثلها مع ال natural number ب function و
+
+536
+00:42:01,510 --> 00:42:06,240
+بتعطيني bijection functionمعناته هي مساوية لل
+
+537
+00:42:06,240 --> 00:42:10,420
+natural number هي infinite احنا متعقدين تماما ان
+
+538
+00:42:10,420 --> 00:42:14,960
+هي infinite لان ال finite مجرد للشرح بس احنا بدنا
+
+539
+00:42:14,960 --> 00:42:20,080
+نتعامل لو وجدت مع ال infinite set infinite set لو
+
+540
+00:42:20,080 --> 00:42:23,380
+كدرت اثبت ان هي bijection مع ال natural number
+
+541
+00:42:23,380 --> 00:42:27,280
+okay انا مش هقول ان انا exactly هاي عددها بس بقدر
+
+542
+00:42:27,280 --> 00:42:31,810
+اقول ان هي countable قابلة للعدل ليش؟مدان بيشكشن
+
+543
+00:42:31,810 --> 00:42:34,750
+مع ال natural number معناته كل element في ال
+
+544
+00:42:34,750 --> 00:42:38,730
+natural number يقابله element في السبت اللي أنا
+
+545
+00:42:38,730 --> 00:42:42,570
+بدوره على ال cardinality، صح؟ هو بيشكشن يعني كل
+
+546
+00:42:42,570 --> 00:42:45,370
+element موجود هنا مقابله element هنا، طيب ال
+
+547
+00:42:45,370 --> 00:42:51,190
+natural number عارفين إن هي a numeral أو أرقام
+
+548
+00:42:51,190 --> 00:42:57,040
+معدودة، عدcan be numerate يمكن تعددها او بقدر
+
+549
+00:42:57,040 --> 00:43:01,840
+اعدها بنقدر نعدها واحد اتنين تلاتة اربعة مدينة
+
+550
+00:43:01,840 --> 00:43:05,320
+بنقدر نعدها وعملنا bijection معها ب set معين
+
+551
+00:43:05,320 --> 00:43:09,020
+معناته حتى ال set هذي بنقدر نعدها حتى ال set ال
+
+552
+00:43:09,020 --> 00:43:13,220
+bijection مع ال natural number قابلة للعد اللي
+
+553
+00:43:13,220 --> 00:43:16,820
+عندنا بنكتفي ان هي قابلة للعد بنعرف ان ال cardinal
+
+554
+00:43:16,820 --> 00:43:22,190
+بتاعتها okay قابلة للعد فهي countableset countable
+
+555
+00:43:22,190 --> 00:43:25,310
+نقدر نقول ان ال cardinality بتاعتها countable ممكن
+
+556
+00:43:25,310 --> 00:43:29,430
+عدها طيب في طبعا sets هنلاقي ان هي uncountable
+
+557
+00:43:29,430 --> 00:43:33,130
+لايمكن عدها و هناخد examples عنها هنتكلم عنها ف ال
+
+558
+00:43:33,130 --> 00:43:38,670
+countable vs uncountable ال
+
+559
+00:43:38,670 --> 00:43:42,290
+countable زي ما قلنا مبدئية هى countable اذا كانت
+
+560
+00:43:42,290 --> 00:43:47,730
+finite هذا متفق عليهف ال night معناته بقدر اعدها
+
+561
+00:43:47,730 --> 00:43:51,150
+countable خلصنا او if
+
+562
+00:43:53,690 --> 00:43:56,530
+cardinality of S equal to cardinality of natural
+
+563
+00:43:56,530 --> 00:43:59,110
+number فهي ممكن تكون finite ولكن ال cardinality
+
+564
+00:43:59,110 --> 00:44:03,870
+بتاعتها مساوية لل cardinality لل natural number طب
+
+565
+00:44:03,870 --> 00:44:05,870
+عشان اقول ان هي فعلا cardinality مع ال natural
+
+566
+00:44:05,870 --> 00:44:08,270
+number لازم اتحقق مع ال natural number function
+
+567
+00:44:08,270 --> 00:44:12,370
+bijection function bijection function اذا فعلا
+
+568
+00:44:12,370 --> 00:44:15,750
+بتحقق bijection function مع natural number بقول
+
+569
+00:44:15,750 --> 00:44:19,790
+اذا كان .. فإذا ان هذه ال cardinality بيسوا بعض و
+
+570
+00:44:19,790 --> 00:44:24,780
+هنا بنقول ان ال S is countableOkay, else أو
+
+571
+00:44:24,780 --> 00:44:29,040
+otherwise هي uncountable بنقول عنها إيش؟
+
+572
+00:44:29,040 --> 00:44:32,640
+uncountable طيب countable زى ما قولنا we can
+
+573
+00:44:32,640 --> 00:44:38,600
+numerate بقدر أعدها، يمكن أعدها أنا في النهاية كيف
+
+574
+00:44:38,600 --> 00:44:44,060
+بعد؟ لحظة واحد، اتنين، تلاتة، اربعة، natural
+
+575
+00:44:44,060 --> 00:44:47,760
+number، صح؟ فإذا اتفقت مع ال natural number في
+
+576
+00:44:47,760 --> 00:44:52,000
+العد فهي بقدر أعدها لأن أنا أصلا بعد عن طريق ال
+
+577
+00:44:52,000 --> 00:44:56,690
+natural numberصح احنا أساسا بنعد كيف؟ عن طريق ال
+
+578
+00:44:56,690 --> 00:45:01,270
+natural number احنا بنكرر أرقام ال sequence أو
+
+579
+00:45:01,270 --> 00:45:05,190
+اللى اللى هى بتاعة ال natural number صفر واحد
+
+580
+00:45:05,190 --> 00:45:09,510
+اتنين ثلاثة أربعة هى العد تبعنا فى حد بعد بطريقة
+
+581
+00:45:09,510 --> 00:45:14,060
+تانيةnatural number فإذا كان بقدر أقول إنك الستها
+
+582
+00:45:14,060 --> 00:45:18,720
+دي ال cardinality بتاعتها مساوية لل cardinality لل
+
+583
+00:45:18,720 --> 00:45:21,720
+natural number فإذن هي معدودة بنقدر نعدها على
+
+584
+00:45:21,720 --> 00:45:26,480
+الأقل على الأقل بنقدر نعدها okay sequentially list
+
+585
+00:45:26,480 --> 00:45:27,140
+بالشكل
+
+586
+00:45:30,240 --> 00:45:33,940
+متعاقب، مجموعة elements متعاقبة في S مشابهة لـ
+
+587
+00:45:33,940 --> 00:45:37,440
+elements الـ natural number طيب، بنقدر نعملها
+
+588
+00:45:37,440 --> 00:45:43,600
+enumeration عملية العد، نقدر نعدها examples لها ال
+
+589
+00:45:43,600 --> 00:45:47,300
+natural number و ال integers لأن ال integers برضه
+
+590
+00:45:47,300 --> 00:45:51,440
+واحد اتنين تلاتة اربعة مافيش فيها fractionsمافيش
+
+591
+00:45:51,440 --> 00:45:55,140
+فيها fractions خلاص هي معدودة ال units بتاعتها
+
+592
+00:45:55,140 --> 00:46:00,380
+ثابتة طيب في المقابل لو اتكلمنا عن ال real number
+
+593
+00:46:00,380 --> 00:46:04,400
+طيب عشان اوضحكوا اكتر تخيلوا ان مابديش اتكلم عن كل
+
+594
+00:46:04,400 --> 00:46:10,800
+ال real number بدي اتكلم بس من صفر لواحد بس اذا
+
+595
+00:46:10,800 --> 00:46:13,520
+قدرنا نعد من صفر لواحد بدي اقولكوا real number
+
+596
+00:46:13,520 --> 00:46:17,470
+معدودمع انه real number بس من صفر ل واحد خلينا
+
+597
+00:46:17,470 --> 00:46:21,550
+نشوفها نشوفها طيب خلينا نشوف اكم element داخل من
+
+598
+00:46:21,550 --> 00:46:31,830
+صفر ل واحد ممكن يكون صفر نص تلت ربع خمس ست لأ غلط
+
+599
+00:46:31,830 --> 00:46:37,770
+لسه في بينهم هدولة ممكن اقولك اتنين فاصل واحد واحد
+
+600
+00:46:37,770 --> 00:46:41,900
+على اتنين فاصل واحدطب لأ واحد هيقول لي لأ في جبلها
+
+601
+00:46:41,900 --> 00:46:47,340
+واحد على اتنين فاصلة زيرو زيرو زيرو زيرو زيرو واحد
+
+602
+00:46:47,340 --> 00:46:53,440
+فانا هيك بديها و هيطلع فعلا رقم مختلف، مصبوط؟ طيب
+
+603
+00:46:53,440 --> 00:46:57,040
+صار عندنا عدد لنهائي من ال elements هنا لأ و غير
+
+604
+00:46:57,040 --> 00:47:01,760
+معدود كمان، لا يتفق مع ال natural number لو احنا
+
+605
+00:47:01,760 --> 00:47:07,640
+ضلينا على جد نصتلت .. ربع .. خمس .. ست كان مشيت مع
+
+606
+00:47:07,640 --> 00:47:10,840
+ال natural number باعتبار ان ال denominator تبعنا
+
+607
+00:47:10,840 --> 00:47:14,920
+المقام متفق مع ال natural مع عملية العدل بس احنا
+
+608
+00:47:14,920 --> 00:47:22,140
+فجأنا ان لأ في اكتر بين كل رقم و رقم في عدد لانهاء
+
+609
+00:47:22,140 --> 00:47:28,080
+من الأرقام بين كل رقم اه و هنا .. ه .. صفر ..
+
+610
+00:47:28,080 --> 00:47:32,260
+اتنين بين كل رقم و رقم في برضه عدد لانهاء من
+
+611
+00:47:32,260 --> 00:47:39,080
+الأرقاممعناته تشبكت تشبكت و هنا واضح انه بين الصفر
+
+612
+00:47:39,080 --> 00:47:43,000
+و الواحد لسه ما طلعناش عن الواحد ماقدرش أعدهم فكيف
+
+613
+00:47:43,000 --> 00:47:45,760
+بدي أعد ال real numbers كلهم فواضح ان هنا
+
+614
+00:47:45,760 --> 00:47:49,880
+uncountable واضح تماما uncountable ال real numbers
+
+615
+00:47:49,880 --> 00:47:54,160
+نفس الكلام لو ال real number to the power 2 او ال
+
+616
+00:47:54,160 --> 00:47:58,000
+power of natural number عارفين ال power نتكلم عن
+
+617
+00:47:58,000 --> 00:48:02,140
+set نتكلم عن set لو عندكوا two elements ال power
+
+618
+00:48:02,140 --> 00:48:07,100
+جدش هتطلعلناهأربعة متذكرين؟ طيب لو عندكوا three
+
+619
+00:48:07,100 --> 00:48:12,700
+elements تمانية لو عندكوا four elements طب لو
+
+620
+00:48:12,700 --> 00:48:17,220
+عندكوا natural number infinity اتنين to the power
+
+621
+00:48:17,220 --> 00:48:22,440
+infinity stop لا تتفق بأي حال من الأحوال مع ال
+
+622
+00:48:22,440 --> 00:48:25,930
+natural number نفسهالا يمكن أن نقول إن هي
+
+623
+00:48:25,930 --> 00:48:29,730
+bijection مع ال natural number نفسها، تمام؟ فواضح
+
+624
+00:48:29,730 --> 00:48:33,830
+إن إحنا في الحالة هذه بيجوش مع بعض، بيجوش مع بعض
+
+625
+00:48:33,830 --> 00:48:39,630
+طيب، فإذا ال Z countable، okay اتفقنا على أساس إنه
+
+626
+00:48:39,630 --> 00:48:46,090
+بنقدر نحطها زوج مترابط مع ال natural numberبنقدر
+
+627
+00:48:46,090 --> 00:48:48,730
+نحطها كزوج مترابط مع ال natural number تبدأ من أول
+
+628
+00:48:48,730 --> 00:48:51,230
+limit و تبقى to infinity الاتنين يمشوا مع بعض to
+
+629
+00:48:51,230 --> 00:48:54,470
+infinity الاتنين يمشوا مع بعض to infinity ب ..
+
+630
+00:48:54,470 --> 00:48:59,270
+بيرز
+
+631
+00:48:59,270 --> 00:49:02,970
+متشابهة مع بعض طيب الأول كان تقول زي ما قلنا هيوم
+
+632
+00:49:02,970 --> 00:49:06,230
+أعطيناها من صفر لواحد وكمان ايش الواحد غير مشمول
+
+633
+00:49:06,230 --> 00:49:09,930
+يعني حتى كمان الواحد غير مشمول يعني احنا لسه
+
+634
+00:49:09,930 --> 00:49:14,410
+موصلناش للواحد و لا يمكن نعدهامن صفر لسه موصلناش
+
+635
+00:49:14,410 --> 00:49:21,790
+للواحد هدى بالظبط هدى
+
+636
+00:49:21,790 --> 00:49:28,290
+غير مشمولة طيب فإذا واضح من صفر لأقل من واحد هدى R
+
+637
+00:49:28,290 --> 00:49:31,370
+belonging to real number من صفر لأقل من واحد is
+
+638
+00:49:31,370 --> 00:49:35,290
+uncountable إذا كان جزء بسيط من ال real numbers
+
+639
+00:49:35,290 --> 00:49:38,770
+uncountable كيف بده هتكون كلها فواضح إن كلها
+
+640
+00:49:38,770 --> 00:49:39,790
+uncountable
+
+641
+00:49:43,330 --> 00:49:46,790
+هذا الجزء اللى كان بدنا نكمله مع ال cardinality
+
+642
+00:49:46,790 --> 00:49:51,610
+بتاعتنا، كويس هذا
+
+643
+00:49:51,610 --> 00:49:56,150
+هي ال summation اللى أكيد مرت عليكم سابقا الموضوع
+
+644
+00:49:56,150 --> 00:49:59,150
+خفيف و أتوقع مر عليكم سابقا في الموضوع اللى أخف
+
+645
+00:49:59,150 --> 00:50:03,930
+منه و لذيذ اللى هي ال matrices matrix نتعامل مع
+
+646
+00:50:03,930 --> 00:50:09,630
+matrix لسه وقت كتيرال matrix هذه ببساطة جدا هي
+
+647
+00:50:09,630 --> 00:50:14,210
+rectangular array هي مجموعة elements محطوطة في شكل
+
+648
+00:50:14,210 --> 00:50:20,610
+رباعي تتكون من مجموعة صفوف ومجموعة أعمدة مجموعة
+
+649
+00:50:20,610 --> 00:50:26,210
+صفوف ومجموعة أعمدة تحتوي تقاطع الصفوف مع الأعمدة
+
+650
+00:50:26,210 --> 00:50:30,570
+على أرقامحاجات مرّى عليكم سابقا، حاجات مرّى عليكم
+
+651
+00:50:30,570 --> 00:50:34,810
+سابقا، مش محتاجين نضيع فيها وجهة لاحقا، تمام؟
+
+652
+00:50:34,810 --> 00:50:38,410
+فلاحظوا هنا matrix مش هذا الشكل، فيها مجموعة rows
+
+653
+00:50:38,410 --> 00:50:43,830
+و columns، بنقول عنها إيش تعريفها، ال dimension
+
+654
+00:50:43,830 --> 00:50:49,320
+تبعهابنحط الصفوف في الأول و بنقول فيه عدد الأعمدة
+
+655
+00:50:49,320 --> 00:50:52,900
+عدد الصفوف اندي عندي واحد اتنين تلاتة عدد الأعمدة
+
+656
+00:50:52,900 --> 00:50:56,840
+واحد اتنين فبنقول تلاتة في اتنين matrix matrix
+
+657
+00:50:56,840 --> 00:51:04,950
+تلاتة في اتنين matrix نعرف ان هي تحتوي على threeصف
+
+658
+00:51:04,950 --> 00:51:11,490
+أو rows في two columns ممكن تكون عبارة عن n في n
+
+659
+00:51:11,490 --> 00:51:17,610
+matrix فهذه بنسميها square matrix مربعة، بتكون
+
+660
+00:51:17,610 --> 00:51:22,270
+مربعة ال order تبعها n applications
+
+661
+00:51:23,500 --> 00:51:26,740
+ليش محتاجينها؟ لأ احنا محتاجينها جدا لان قلتلكوا
+
+662
+00:51:26,740 --> 00:51:29,000
+قبل هات في ال signal processing بكرا و انتوا
+
+663
+00:51:29,000 --> 00:51:30,860
+بتشتغلوا في signal processing هتتعاملوا مع ال
+
+664
+00:51:30,860 --> 00:51:34,600
+digital مع digital signal processing و هو ده ال
+
+665
+00:51:34,600 --> 00:51:37,620
+field تبعكوا اللي انتوا هتشتغلوا فيه مش هتتعاملوا
+
+666
+00:51:37,620 --> 00:51:41,270
+معاكم في المصر، رايحوا حالكممش هتتعاملوا مع
+
+667
+00:51:41,270 --> 00:51:43,850
+continuous functions هتتعاملوا كل شغلكوا مع
+
+668
+00:51:43,850 --> 00:51:46,970
+discrete discrete بمعنى ان انتوا هتتعاملوا مع
+
+669
+00:51:46,970 --> 00:51:50,810
+integers او whatever يعني ممكن ماتكونش integers
+
+670
+00:51:50,810 --> 00:51:55,350
+real numbers ولكن هتكون محطوطة ك discrete ال
+
+671
+00:51:55,350 --> 00:51:59,030
+elements بتاعتكوا هتكون discrete من اهم ال tools
+
+672
+00:51:59,030 --> 00:52:02,610
+اللي هتحتاجوها هي ال matrix ال matrix هذا ممكن
+
+673
+00:52:02,610 --> 00:52:07,720
+تستخدموها لحل المعادلات ال linear equationsأخدتوها
+
+674
+00:52:07,720 --> 00:52:14,080
+قبل هيك كيف بتحلوا باستخدام ال matrix بتكون عندكوا
+
+675
+00:52:14,080 --> 00:52:19,140
+مجموعات equations عدد من ال variables و متوفر
+
+676
+00:52:19,140 --> 00:52:22,340
+عندكوا نفس العدد من ال equations بتقدروا تحلوا
+
+677
+00:52:22,340 --> 00:52:29,960
+المثلة انكوا تقولوا مثلا say نفترض x1 او 3x1 زائد
+
+678
+00:52:29,960 --> 00:52:38,760
+2x2 فرضا بتساوي عشرةخلينا نقول اتنين اكس واحد ناجس
+
+679
+00:52:38,760 --> 00:52:41,960
+اكس
+
+680
+00:52:41,960 --> 00:52:45,780
+اتنين ستة
+
+681
+00:52:45,780 --> 00:52:50,180
+اي معادلات هذه كيف كنتوا بتحلوها طبعا انا عارف ان
+
+682
+00:52:50,180 --> 00:52:53,680
+انتوا أبسط شغلة انكوا تقولوا بدنا نضرب نضرب هنا في
+
+683
+00:52:53,680 --> 00:52:57,160
+اتنين و نجمع و نخلص طيب افرضوا عندكوا عشرة
+
+684
+00:52:57,160 --> 00:53:02,890
+variables في عشر معادلاتيعني معنا ذلك خطوة خطوة
+
+685
+00:53:02,890 --> 00:53:05,650
+عشان تعملوا cancellation ل variable by variable مش
+
+686
+00:53:05,650 --> 00:53:08,050
+هي كده تعمله انتوا تاوي لما قلتوا بدنا نختزل هدولة
+
+687
+00:53:08,050 --> 00:53:10,830
+انتوا ضيعتوا variable فكل operation بتكون ضايع
+
+688
+00:53:10,830 --> 00:53:14,110
+variable عشان يظل variable واحد في الآخر بتقوله
+
+689
+00:53:14,110 --> 00:53:19,410
+قداش بالساوي و ترجعه بالعكس بالعكس واحد تجيبه من
+
+690
+00:53:19,410 --> 00:53:24,630
+التاني طب لو عندكوا عشر معادلة صعبة
+
+691
+00:53:24,630 --> 00:53:29,140
+الأمور طيب اللي أسهل من هيك انكم تحلوها بمينبال
+
+692
+00:53:29,140 --> 00:53:34,060
+matrix بتكون قوله والله في عندنا تلاتة اتنين اتنين
+
+693
+00:53:34,060 --> 00:53:39,740
+minus one في x واحد x اتنين طبعا لو ضربتوا هد في
+
+694
+00:53:39,740 --> 00:53:45,820
+هد هتطلعي نفس المعادلة بتساوي عشرة في ستةبتاخدوا
+
+695
+00:53:45,820 --> 00:53:48,200
+هذه على ناحية التانية كيف تاخدوها على ناحية
+
+696
+00:53:48,200 --> 00:53:54,160
+التانية؟ inverse فبتحسبوها بتجيبولها هنا ال
+
+697
+00:53:54,160 --> 00:53:56,900
+inverse تبعها فواضح انه بتضرب في ال inverse خلاص
+
+698
+00:53:56,900 --> 00:54:02,100
+بتروح و هنا برضه هتضربوها في مين؟ في ال inverse
+
+699
+00:54:02,100 --> 00:54:09,500
+تبعتكوا هنا عشان تساوي مين؟ X1 X2 طبعا هيكون 2 في
+
+700
+00:54:09,500 --> 00:54:17,140
+2 2 في 2 هيطلع elementو 2x2 هيطلع element هتطلع
+
+701
+00:54:17,140 --> 00:54:22,040
+عبارة عن column ال column هذا مساوي ل X1 و X2 هذا
+
+702
+00:54:22,040 --> 00:54:24,540
+الطريقة اللي انتوا اشتغلتوها سابقا فهي application
+
+703
+00:54:24,540 --> 00:54:26,960
+هي واحدة من التطبيقات اللي انتوا بتشتغلوا عليها
+
+704
+00:54:26,960 --> 00:54:29,960
+فعليا طيب ال computer graphics و ال image
+
+705
+00:54:29,960 --> 00:54:35,280
+processing ليش؟ لعندي الآن ال image processing كل
+
+706
+00:54:35,280 --> 00:54:38,200
+علم ال image processing بتعامل مع الصورة ان هي
+
+707
+00:54:38,200 --> 00:54:44,460
+pixelsDots طب انتوا معناته dots مع dots هي matrix
+
+708
+00:54:44,460 --> 00:54:49,420
+فإذا انتوا مثل ب matrix التلفزيون عندكم عبارة عن
+
+709
+00:54:49,420 --> 00:54:54,400
+dots بيكسل مربعة بس صغيرة جدا كل ما صغرت كتير كل
+
+710
+00:54:54,400 --> 00:54:58,340
+ما ال resolution كانت أعلى بمعنى انه في الآخر
+
+711
+00:54:58,340 --> 00:55:02,760
+هيطلع عندكم بيكسل
+
+712
+00:55:05,170 --> 00:55:07,670
+بهذا الشكل هو ده العلم فعلا كل ال signal
+
+713
+00:55:07,670 --> 00:55:10,210
+processing بهذا الشكل لو اتكلمنا عن ال image ال
+
+714
+00:55:10,210 --> 00:55:14,510
+image هيك تمثل ال image تمثل بهذا الشكل تمثل بهذا
+
+715
+00:55:14,510 --> 00:55:19,110
+الشكل على أساس انه لو قلنا مثلا الرقم الرقم اتنين
+
+716
+00:55:19,110 --> 00:55:23,250
+لو بدنا نقول الرقم اتنين ممكن نمثله بهذا الشكل هيك
+
+717
+00:55:23,250 --> 00:55:30,150
+فلاحظوا فهقول
+
+718
+00:55:30,150 --> 00:55:38,220
+ال element1 و 2 قيمته ب 1 طب ال element 1 و 1
+
+719
+00:55:38,220 --> 00:55:42,460
+قيمته صفرهذا لو بدنا نشتغل عليها ال image عساس ان
+
+720
+00:55:42,460 --> 00:55:46,900
+هي أبيض و أسود لونها أبيض و أسود طيب ممكن ما تكونش
+
+721
+00:55:46,900 --> 00:55:50,260
+من صفر ل واحد بس يا صفر يا واحد ممكن تكون من صفر ل
+
+722
+00:55:50,260 --> 00:55:54,020
+255 لو بدنا نشتغل علي grey level على الصورة اللي
+
+723
+00:55:54,020 --> 00:55:59,380
+هي ملونة تدريج رمادي من صفر ل 255 فممكن يكون ال
+
+724
+00:55:59,380 --> 00:56:05,060
+255 الغامق الصفر الفاتح و بينهم تدرجات اللون ال
+
+725
+00:56:05,060 --> 00:56:09,670
+grey level هذا الرمادي طيب بدنا نشتغل ملونهيكون في
+
+726
+00:56:09,670 --> 00:56:16,530
+عندنا لكل صورة تلاتة matrices واحدة ل ال red واحدة
+
+727
+00:56:16,530 --> 00:56:21,490
+ل ال blue واحدة ل ال green تمام هايهم و برضه
+
+728
+00:56:21,490 --> 00:56:25,350
+بنمثلهم بين خمسة و خمسين بين خمسة و خمسين لكل
+
+729
+00:56:25,350 --> 00:56:27,610
+واحدة منهم ال degradations هدول مع بعض بنحطهم مع
+
+730
+00:56:27,610 --> 00:56:32,330
+بعض بيعطينا dimension ثلاثي للنقطة الواحدة بقدر
+
+731
+00:56:32,330 --> 00:56:37,630
+اجيب منها اللون هذه الصور فواضح ان انا بتعامل في
+
+732
+00:56:37,630 --> 00:56:41,940
+النهاية ب matrixبنتعامل معها as a matrix ال signal
+
+733
+00:56:41,940 --> 00:56:43,860
+processing بدام أنا بتعامل مع الصورة نفسها ك
+
+734
+00:56:43,860 --> 00:56:46,720
+matrix فإذا كل process اللي بنقدر أو المعالجة اللي
+
+735
+00:56:46,720 --> 00:56:50,040
+بنعملها عليها احنا بنعمل معالجة على matrix فإذا
+
+736
+00:56:50,040 --> 00:56:56,520
+هذا ال field كله معتمد على ال matrices، كويسالـ
+
+737
+00:56:56,520 --> 00:56:59,000
+models of computational science زي ما قلنا
+
+738
+00:56:59,000 --> 00:57:03,840
+الحسابات الهندسية والعلمية كلها بتعتمد على ال
+
+739
+00:57:03,840 --> 00:57:07,540
+matrix كلها بتعتمد على ال matrix لما نقول مثلا حتى
+
+740
+00:57:07,540 --> 00:57:09,940
+لما تشتغلوا على ال derivative لما بتعملوا ال
+
+741
+00:57:09,940 --> 00:57:12,900
+derivative الأول وال derivative التاني لما يكون
+
+742
+00:57:12,900 --> 00:57:17,290
+عندكوا ضيمين لل functionأكتر يعني several
+
+743
+00:57:17,290 --> 00:57:20,070
+variables أكتر من one variable أنتوا هتضطروا
+
+744
+00:57:20,070 --> 00:57:23,190
+تحتاجوا ل matrices تشتغلوا فيها في الآخر هتحتاجوا
+
+745
+00:57:23,190 --> 00:57:26,610
+العمليات بتاعتكوا كلها هتشتغلوا على matrices طيب
+
+746
+00:57:26,610 --> 00:57:29,530
+ال quantum mechanics برضه ال quantum mechanics أو
+
+747
+00:57:29,530 --> 00:57:33,150
+ميكانيكا الكام هذه من العلوم اللي كتير فيها شغل و
+
+748
+00:57:33,150 --> 00:57:39,340
+حديثة جدا شغل كتير لها في ال matricesو خدوا على
+
+749
+00:57:39,340 --> 00:57:42,580
+غرار ذلك كتير جدا، مدام انتوا هتشتغلوا و فعلا كل
+
+750
+00:57:42,580 --> 00:57:47,360
+شغلكوا هيكون صلب شغلكوا كله في ال .. على ال
+
+751
+00:57:47,360 --> 00:57:50,780
+digital معناته هتشتغلوا مع discrete، معناته
+
+752
+00:57:50,780 --> 00:57:52,900
+هتتعاملوا مع كل المصطلحات اللي احنا بتحكيها في ال
+
+753
+00:57:52,900 --> 00:57:57,680
+course هذا، و اهمها ال matrix، اهمها ال matrix طيب
+
+754
+00:57:57,680 --> 00:58:02,620
+امتى؟بقول ان ال two matrices هدولة بيسوا بعض اذا
+
+755
+00:58:02,620 --> 00:58:07,140
+كان عدد الصفوف او ال dimension يعني ال dimension
+
+756
+00:58:07,140 --> 00:58:08,940
+هنا بيسوا ال dimension هنا عدد الصفوف هنا بيسوا
+
+757
+00:58:08,940 --> 00:58:10,720
+عدد الصفوف هنا عدد ال columns هنا بيسوا عدد ال
+
+758
+00:58:10,720 --> 00:58:16,180
+columns هنا زائد كل عنصر في نفس ال location بيسوا
+
+759
+00:58:16,180 --> 00:58:21,640
+بعض كل عنصرين في نفس ال location بيسوا بعض فهذه
+
+760
+00:58:21,640 --> 00:58:27,910
+برضه مش فيها مشكلة مش محتاجة نأخرها لو نتكلم عنتو
+
+761
+00:58:27,910 --> 00:58:31,570
+مترسس بيان الشكل اتنين في اتنين اتنين في اتنين هاي
+
+762
+00:58:31,570 --> 00:58:34,870
+اول شرط طيب بعدين خلينا نشوف واحد واحد هل بيساوي
+
+763
+00:58:34,870 --> 00:58:38,730
+واحد واحد هنا اه طيب اتنين واحد بيساوي اتنين واحد
+
+764
+00:58:38,730 --> 00:58:42,670
+هنا اه طيب واحد اتنين اه اتنين اتنين طب كويس
+
+765
+00:58:42,670 --> 00:58:49,330
+بيساوي بعض طيب بالشكل هذا لأ لأن اول شرط اختلف عدد
+
+766
+00:58:49,330 --> 00:58:51,670
+الصفوف اه عدد الصفوف بس عدد الاعمدة لأ مش عدد
+
+767
+00:58:51,670 --> 00:58:59,090
+الاعمدة لا يساوي لأ يساوي فهنا a لا تساوي bطيب في
+
+768
+00:58:59,090 --> 00:59:01,130
+ال matrix لما تكون تتكلم عن ال matrix لحظة و
+
+769
+00:59:01,130 --> 00:59:07,790
+بنحطها bold بهذا الشكل a بتساوي bracket مستعملاش
+
+770
+00:59:07,790 --> 00:59:15,730
+ال curly هذه لست تمام و مستعملاش الإحدافيات ال
+
+771
+00:59:15,730 --> 00:59:19,610
+Cartesian النقاط اللي كنا بنشتغل فيها على النقاط
+
+772
+00:59:19,610 --> 00:59:22,110
+اللي هي ممكن تكون اتنين او تكون تلاتة او تكون في
+
+773
+00:59:22,110 --> 00:59:25,910
+النهاية بس نقاط إحدافيات هذه بنشتغل على bracket
+
+774
+00:59:27,190 --> 00:59:31,890
+اللي هي تمثل لنا matrix بتعرف ان هي تمثل ال matrix
+
+775
+00:59:31,890 --> 00:59:39,490
+ففي الحالة هذه A I و J ال I الصفر الصفوف بتنحطيها
+
+776
+00:59:39,490 --> 00:59:43,770
+في الأول J الأعمدة الصفوف في الغالب بنمثلها من
+
+777
+00:59:43,770 --> 00:59:50,510
+واحد to M الأعمدة من واحد to N و عادة عشان نوصف ال
+
+778
+00:59:50,510 --> 00:59:55,230
+matrix هذه بنوصفها I في J فاحنا بنقول هنا جدش عدد
+
+779
+00:59:55,230 --> 01:00:01,190
+ال I سبعتهم Mطب كداش عدد الصفوف الأعمدة؟ N فبنقول
+
+780
+01:00:01,190 --> 01:00:06,770
+هذه M في N Matrix عدد الصفوف في عدد الأعمدة الصفوف
+
+781
+01:00:06,770 --> 01:00:11,570
+الأول ال rows الأول في عدد الأعمدة تاني وتمثل بهذا
+
+782
+01:00:11,570 --> 01:00:16,030
+الشكل العنصر اللي هنا 2 و 1 على أساس ان هو في ال
+
+783
+01:00:16,030 --> 01:00:22,850
+row التانية ال column الأولطيب هنا لأ هذه ال role
+
+784
+01:00:22,850 --> 01:00:28,010
+أول و ال column التاني فصار نقدر نميزها من ال
+
+785
+01:00:28,010 --> 01:00:30,970
+indices بتاعتهم او ال index واحد و اتنين هدولة
+
+786
+01:00:30,970 --> 01:00:37,330
+تعونهم طيب ال index لو عندنا ال matrix M في M
+
+787
+01:00:37,330 --> 01:00:40,490
+matrix و بنمثلها زي ما قلنا على سيسنية brackets
+
+788
+01:00:40,490 --> 01:00:47,030
+لمجموعة elements مجموعة ال elements هذه A من I J I
+
+789
+01:00:47,030 --> 01:00:55,520
+زي ما قلنا من واحد to MJ من واحد to N هذه الـ
+
+790
+01:00:55,520 --> 01:01:04,300
+elements عبارة عن members of asset S فبنقدر نعرفها
+
+791
+01:01:04,300 --> 01:01:09,700
+في الحالة بتاعتنا عساس ان هي function if function
+
+792
+01:01:09,700 --> 01:01:12,660
+لأ ال matrix A from natural number to natural
+
+793
+01:01:12,660 --> 01:01:20,150
+number او from N to N N في Nهذه الصفوف وهذه
+
+794
+01:01:20,150 --> 01:01:26,670
+الأعمدة صفوف الأعمدة employs أو لـ set us فإذا
+
+795
+01:01:26,670 --> 01:01:34,050
+الصفوف أو ال domain تبعنا من n في n to set from n
+
+796
+01:01:34,050 --> 01:01:37,970
+to n to set هذا الناتج ال output تبعنا ال set لل
+
+797
+01:01:37,970 --> 01:01:43,770
+elements اللي هتكون موجودة ال input تبعها من ال
+
+798
+01:01:43,770 --> 01:01:48,280
+natural number تبع الصفوفمضروبة في ال natural
+
+799
+01:01:48,280 --> 01:01:50,420
+number بتاعة الأعمدها دي كلها هيك هوية واحدة مع
+
+800
+01:01:50,420 --> 01:01:53,920
+بعض فصارت n تربيه كأنها n تربيه ما هي فعلا n تربيه
+
+801
+01:01:53,920 --> 01:02:00,480
+لإن انت بتتكلم عن شيء مربع كذا في كذا وصفها هيك
+
+802
+01:02:00,480 --> 01:02:05,300
+وصفها صفوف في أعمدة هيك الوصف تبعها صفوف في عدد
+
+803
+01:02:05,300 --> 01:02:10,160
+الأعمد في عدد صفوف في عدد أعمدة فsuch that for I
+
+804
+01:02:10,160 --> 01:02:15,720
+أقل من M باعتبار أن احنا حددنا ال I from one to nو
+
+805
+01:02:15,720 --> 01:02:21,120
+J أقل من N فإذا F لل matrix ال function لل matrix
+
+806
+01:02:21,120 --> 01:02:26,720
+عبارة عن I J function في مين؟ في ال location هنا
+
+807
+01:02:26,720 --> 01:02:28,880
+واضح أنه هي function في ال location لأن احنا فعلا
+
+808
+01:02:28,880 --> 01:02:34,360
+ال element A I J كيف بعرفه؟ بعرفه بناء على ال
+
+809
+01:02:34,360 --> 01:02:37,540
+location تبعه فإذا هي فعلا ك function هي function
+
+810
+01:02:37,540 --> 01:02:41,300
+في ال location ال location أنهي location؟ ال rows
+
+811
+01:02:41,300 --> 01:02:48,520
+و ال columns فببدأ بال rowبقول والله ال row I ال
+
+812
+01:02:48,520 --> 01:02:54,080
+column J بعرف في الحالة هذه ال element اللي يقع في
+
+813
+01:02:54,080 --> 01:02:58,520
+هذا ال location يقع في هذا ال location كويس
+
+814
+01:03:00,000 --> 01:03:03,040
+ممكن نعرف الموضوع على أساس ان هي هذه هيك ال domain
+
+815
+01:03:03,040 --> 01:03:07,380
+over which AI is defined فإذا عرفنا ال domain
+
+816
+01:03:07,380 --> 01:03:13,160
+تبعنا، تعرف ال domain، بنقدر نعرف ال type of
+
+817
+01:03:13,160 --> 01:03:18,660
+infinite or and multidimensional matrices can be
+
+818
+01:03:18,660 --> 01:03:20,880
+obtained طبعا احنا مش هنتعامل مع ال
+
+819
+01:03:20,880 --> 01:03:23,980
+multidimensional matrices، احنا هنتعامل بس مع اللي
+
+820
+01:03:23,980 --> 01:03:30,080
+هي تنفذالاتنين اللي هي الصفوف الأعمدة بس هنتعامل
+
+821
+01:03:30,080 --> 01:03:34,000
+مع صفوف فئة أعمدة فقط مش هنتعامل معها أكتر من هنا
+
+822
+01:03:34,000 --> 01:03:38,240
+مجموعة rows مع مصموم مجموعة columns
+
+823
+01:03:41,290 --> 01:03:44,810
+كيف كنتوا بتجمعوا ال matrices؟ كل عنصر مع عنصر
+
+824
+01:03:44,810 --> 01:03:50,430
+المقابل له فإذا I و J لازم تكون متفقين مع I و J
+
+825
+01:03:50,430 --> 01:03:55,710
+المقابلة لهم في ال matrix التانية فمش فيها مشكلة A
+
+826
+01:03:55,710 --> 01:04:01,900
+plus A plus B عبارة عن هيها متفقين في AJ AJهذا ال
+
+827
+01:04:01,900 --> 01:04:04,260
+element من ال matrix الأولى وهذا ال element من ال
+
+828
+01:04:04,260 --> 01:04:09,880
+matrix التانى عشان يعطونى matrix إضافية فهنا 2 مع
+
+829
+01:04:09,880 --> 01:04:18,760
+ال 11 6 مع التلاتة صفر مع minus 12 و 11 و minus 8
+
+830
+01:04:18,760 --> 01:04:23,920
+مع 3 بنجمع بطلع معانا matrix لجديدة مش فى مشكلة
+
+831
+01:04:23,920 --> 01:04:28,360
+مرة عليكوا أكيد كتير multiplication multiplication
+
+832
+01:04:28,360 --> 01:04:34,550
+برضه مرت علينا كيف كنتوا تشتغلوا فيهاA في B بساوي
+
+833
+01:04:34,550 --> 01:04:38,630
+C الـ C ده عبارة عن إيش؟ ما هو يحتوي على مجموعة
+
+834
+01:04:38,630 --> 01:04:43,210
+elements يحتوي على مجموعة elements ال elements هذه
+
+835
+01:04:43,210 --> 01:04:51,990
+خلينا نقول ل I و J هنقول ال index لنا L from 1 to
+
+836
+01:04:51,990 --> 01:04:59,470
+K عبارة عن إيش A I الأول
+
+837
+01:04:59,470 --> 01:05:09,550
+عدد الصفوفو L ال counter تبعنا J العنصر التاني عدد
+
+838
+01:05:09,550 --> 01:05:16,610
+الأعمدة للتاني فإذا عدد الأعمدة له في الحالة هذه
+
+839
+01:05:16,610 --> 01:05:23,070
+هتكون بهذا الشكل كأنكم تضربوا كل
+
+840
+01:05:23,070 --> 01:05:30,970
+صف في مية في عمود كل صف في عمود كويس الصف هذا هو
+
+841
+01:05:30,970 --> 01:05:36,450
+اللي هو الأولهنا I بتساوي واحد فهنا هيكون عندكم I
+
+842
+01:05:36,450 --> 01:05:40,930
+واحد على
+
+843
+01:05:40,930 --> 01:05:45,790
+اعتبار انه نفترض نشملها لوجبت على واحد واحد بدنا
+
+844
+01:05:45,790 --> 01:05:48,830
+نجيب C واحد واحد جدلا خليني اقول بدنا نجيب C واحد
+
+845
+01:05:48,830 --> 01:05:52,110
+واحد فازا انا بتعامل مع واحد هنا و واحد هنا عشان
+
+846
+01:05:52,110 --> 01:05:54,830
+بس نوضحها يعني انا بدي اي element بدي ال element
+
+847
+01:05:54,830 --> 01:06:00,530
+الأول هاي ال C بدي ال element الأول فيهابدنا ال
+
+848
+01:06:00,530 --> 01:06:04,110
+element الأول فلاحظوا ال element الأول هنا هو
+
+849
+01:06:04,110 --> 01:06:10,030
+تقاطع ال row الأول مع ال column الأول ف ال row من
+
+850
+01:06:10,030 --> 01:06:13,930
+ال matrix الأولى مع ال column من ال matrix التانية
+
+851
+01:06:13,930 --> 01:06:17,650
+فهي ال row للأولى مع ال matrix التانية طيب هاي
+
+852
+01:06:17,650 --> 01:06:21,990
+واحد و واحد هنبدأ ايه ال elements بتاعة ال row
+
+853
+01:06:21,990 --> 01:06:26,720
+الأولى وهي ثابت عن نصارى ثالث ثابتة بواحدفإذا من
+
+854
+01:06:26,720 --> 01:06:33,200
+واحد to K، K بس تنتج منها إيش؟ إن هذه عدد ال
+
+855
+01:06:33,200 --> 01:06:38,380
+columns للماتريكس الأولى، عدد ال columns للماتريكس
+
+856
+01:06:38,380 --> 01:06:42,200
+الأولى، و لازم تكون برضه عدد ال rows للماتريكس
+
+857
+01:06:42,200 --> 01:06:47,360
+التانيةمدام نفس ال counter هو و هو مستخدم عدد هي
+
+858
+01:06:47,360 --> 01:06:52,980
+ال columns للأولى هو نفسه عدد ال rows للتانية فإذا
+
+859
+01:06:52,980 --> 01:06:57,320
+عشان أضرب مصففتين لازم يتفق فيهم العدد هذا اللي هو
+
+860
+01:06:57,320 --> 01:07:03,080
+إيه عدد صفوف الأولى يساوي عدد أعمدة التانية صحيح
+
+861
+01:07:03,080 --> 01:07:08,260
+عدد أعمدة الأولى يساوي عدد صفوف التانية عدد أعمدة
+
+862
+01:07:08,260 --> 01:07:13,390
+الأولىيساوي عدد صفوف التانية بحيث لما أمسك كل
+
+863
+01:07:13,390 --> 01:07:16,410
+element أضربه في ال element المقابل كل element في
+
+864
+01:07:16,410 --> 01:07:23,250
+ال element المقابل يطلع لعدد متساوي ونجمع
+
+865
+01:07:23,250 --> 01:07:27,470
+أو أنت في الآخرة summation ضربنا كل element مع ال
+
+866
+01:07:27,470 --> 01:07:30,550
+element المقابل كل element مع ال element المقابل
+
+867
+01:07:30,550 --> 01:07:34,370
+كل element مع ال element المقابل قاعدين نضرب a11
+
+868
+01:07:34,370 --> 01:07:48,040
+في b11 هذا مع هذاطلعنا term summation زائد هتصير
+
+869
+01:07:48,040 --> 01:07:53,260
+هنا ال بتنين واحد و اتنين هيه مضروف في مين؟ في
+
+870
+01:07:53,260 --> 01:08:00,180
+اتنين و واحد في هذا هي كمان term صار زائد احنا
+
+871
+01:08:00,180 --> 01:08:05,600
+summation برضه ال تلاتة صار بتعمل مع واحد و تلاتة
+
+872
+01:08:05,600 --> 01:08:12,020
+مع تلاتة و واحدواحد و اربعة اربعة و واحد خلصناهم
+
+873
+01:08:12,020 --> 01:08:15,220
+كلهم ال K معناه ذلك ان انا خلصت كل ال columns او
+
+874
+01:08:15,220 --> 01:08:19,520
+كل ال rows لبتاني بنكون خلصنا ال summation تبعنا
+
+875
+01:08:19,520 --> 01:08:25,640
+جمعناهم و حطينا قيمتهم هنا هاي اول element انا
+
+876
+01:08:25,640 --> 01:08:28,420
+عارف انه مرت عليكم بس انا كنت معاني اشرح ال
+
+877
+01:08:28,420 --> 01:08:31,560
+formula بتاعتنا بس معنيين اشرح ال formula بتاعتنا
+
+878
+01:08:36,370 --> 01:08:42,590
+فهذه عملية الدار
+
+879
+01:08:42,590 --> 01:08:47,170
+بتاعتنا وزي ما قلنا كمان مرة لازم تتفق عدد ال
+
+880
+01:08:47,170 --> 01:08:49,610
+columns في الأولى مع عدد ال rows في التانية
+
+881
+01:08:49,610 --> 01:08:54,890
+والناتج هيكون عبارة عن matrix ايش بتساوي؟ بتساوي
+
+882
+01:08:54,890 --> 01:08:58,130
+عدد ال rows في الأولى في عدد ال columns للتانية
+
+883
+01:09:00,820 --> 01:09:04,740
+عدد ال rows في الأولى في عدد ال columns في التانية
+
+884
+01:09:04,740 --> 01:09:11,760
+C اللى هتطلع الناتج لازم يكون عدد ال rows بتاعة A
+
+885
+01:09:11,760 --> 01:09:18,310
+في عدد ال column بتاعة Bصحيح؟ هذيك اللي لازم
+
+886
+01:09:18,310 --> 01:09:21,490
+يتفقوا مع بعض، عدد ال column تحت الأولى مع عدد ال
+
+887
+01:09:21,490 --> 01:09:25,410
+rows تحت التانية لازم يكونوا متساويين عشان عملية
+
+888
+01:09:25,410 --> 01:09:28,370
+الضرب تظبط عشان تظبط عملية الضرب و يكون فعلا في
+
+889
+01:09:28,370 --> 01:09:31,290
+ناتج لعملية ضربه otherwise مافيش ناتج لعملية
+
+890
+01:09:31,290 --> 01:09:35,230
+الضرب، بتوقف، مش هيكون مافيش إمكانية ضربه طبعا في
+
+891
+01:09:35,230 --> 01:09:37,810
+الأخر بس الملاحظة الأخيرة أن عملية الضرب هنا غير
+
+892
+01:09:37,810 --> 01:09:43,610
+تبدولية بمعنى A B لاتساوية
+
+893
+01:09:45,960 --> 01:09:49,200
+لاتساو بي في ايه؟ لاتساو بي في ايه؟ ممكن واحدة
+
+894
+01:09:49,200 --> 01:09:52,940
+منهم تكون تظبط و تانية تظبطش ممكن جدا واحدة تنفع
+
+895
+01:09:52,940 --> 01:09:57,020
+واحدة ماتنفعش بنتيجة الشرط اللي احنا قلناه ان عدد
+
+896
+01:09:57,020 --> 01:09:59,420
+ال columns في الأولى لازم يسوى عدد ال rows في
+
+897
+01:09:59,420 --> 01:10:04,720
+التانية لازم يكون عدد ال rows في التانية okay خلاص
+
+898
+01:10:04,720 --> 01:10:08,280
+بسيب لكوا المثال قرأهوا لحالكوا هي في المثال عشان
+
+899
+01:10:08,280 --> 01:10:12,220
+بعدين نبدأ في الموضوع يعني يالا أعطيكوا العافية و
+
+900
+01:10:12,220 --> 01:10:12,940
+أنا أتبارك الله فيك
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio.srt
new file mode 100644
index 0000000000000000000000000000000000000000..068a890c9da7f8e546859ca871bb7e902ef65da0
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio.srt
@@ -0,0 +1,2630 @@
+1
+00:00:21,550 --> 00:00:23,590
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,590 --> 00:00:25,850
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,850 --> 00:00:29,590
+أجمعين. استكمالا لمحاضرتنا الأولى التي كنا اتكلمنا
+
+4
+00:00:29,590 --> 00:00:32,670
+فيها كـ introduction للـ discrete ككل، discrete
+
+5
+00:00:32,670 --> 00:00:37,510
+mathematics كمُصَاق كامل، واتكلمنا:  إيش... في إيش
+
+6
+00:00:37,510 --> 00:00:40,230
+هيفيدنا، إيش هناخد منه، في إيش هيخدمنا، كيف
+
+7
+00:00:40,230 --> 00:00:44,070
+هيخدمكم في مجال تخصصكم في الـ computer engineering.
+
+8
+00:00:44,070 --> 00:00:47,510
+اليوم هنبدأ مع أول محاضرات المصاق التي هي
+
+9
+00:00:47,510 --> 00:00:51,710
+foundations of logic أو introduction to logic. هنبدأ
+
+10
+00:00:51,710 --> 00:00:55,290
+بتعريف بسيط: mathematical logic is a tool for
+
+11
+00:00:55,290 --> 00:00:57,990
+working with complicated compound statements.
+
+12
+00:00:57,990 --> 00:01:02,490
+هنتعامل مع اللي هي logic. احنا لو هتحدد شغلنا ليه
+
+13
+00:01:02,490 --> 00:01:04,530
+على الـ logic في محاضرتنا اليوم، الـ mathematical
+
+14
+00:01:04,530 --> 00:01:09,310
+logic هي فعليا نشتغل فيها على مجموعة statements
+
+15
+00:01:09,310 --> 00:01:13,650
+بندمجها مع بعض بحيث أن يصير عندنا complicated
+
+16
+00:01:13,650 --> 00:01:20,600
+compound statements، statements مركبة معقدة كبيرة،
+
+17
+00:01:20,600 --> 00:01:22,600
+الكبيرة هذه المركبة أو المعقدة من إيش بدها
+
+18
+00:01:22,600 --> 00:01:26,580
+تيجي؟ هتيجي فعليا من مجموعة statements صغيرة في الـ
+
+19
+00:01:26,580 --> 00:01:29,800
+language... في اللغة. عادة اللغة بتيجي من إيش؟ شوية
+
+20
+00:01:29,800 --> 00:01:34,280
+حروف، بنكون منها كلمات، كلمة جنب كلمة بتعطينا معنى.
+
+21
+00:01:34,280 --> 00:01:37,580
+المعنى. إذا اتكون عندنا معنى، إحنا هنا هنستعملها...
+
+22
+00:01:37,580 --> 00:01:41,120
+هنقول عنها proposition. عندنا المعنى هذا خلاص
+
+23
+00:01:41,120 --> 00:01:45,910
+بيعطيني معلومة، المعلومة دي أقدر أحكم عنها كـ... بـ
+
+24
+00:01:45,910 --> 00:01:50,270
+truth value: false or true. اتكلمنا كتير عن... عن
+
+25
+00:01:50,270 --> 00:01:56,310
+قصة false و true المرة اللي فاتت، تمام. فبيظل عندنا
+
+26
+00:01:56,310 --> 00:02:00,410
+أنه كيف نكونهم مع بعض، هدول الأجزاء، كيف نكونهم مع
+
+27
+00:02:00,410 --> 00:02:04,490
+بعض. هناخدهم من خلال مجموعة operators. هنتكلم اليوم
+
+28
+00:02:04,490 --> 00:02:08,050
+عنهم إن شاء الله تعالى. بس فعليا عشان أتكلم عن الـ
+
+29
+00:02:08,050 --> 00:02:10,230
+mathematical logic هي بتتكون من إيش؟ أول حاجة
+
+30
+00:02:10,230 --> 00:02:13,730
+language. بكون أن الـ language... الـ language هذا بدي
+
+31
+00:02:13,730 --> 00:02:19,070
+أترجمه لإيش؟ لمجموعة رياضيات... مجموعة رياضيات عن
+
+32
+00:02:19,070 --> 00:02:22,950
+طريق symbols معينة، notations معينة، أقدر أعمل prove
+
+33
+00:02:22,950 --> 00:02:27,650
+لها. ففعليا محتاج language for expressing them.
+
+34
+00:02:27,650 --> 00:02:31,890
+للتعبير عن الـ statements بتاعتي. بعدين محتاج
+
+35
+00:02:31,890 --> 00:02:33,170
+concise notation.
+
+36
+00:02:36,430 --> 00:02:41,530
+علامات مختصرة، أو symbols، أو symbols عشان نعبر
+
+37
+00:02:41,530 --> 00:02:46,130
+عنها رياضيا. ما نقدرش... بدنا نثبت شغلة مكتوبة في
+
+38
+00:02:46,130 --> 00:02:48,650
+one paragraph. اقعد كل شوية أقول one paragraph
+
+39
+00:02:48,650 --> 00:02:52,250
+معايا عشان أثبت، و هل بيساوي true or false. فلأ
+
+40
+00:02:52,250 --> 00:02:58,080
+بنعبر عنه بإيش؟ بـ symbol واحد. أي شغلة بتصير سهلة
+
+41
+00:02:58,080 --> 00:03:03,800
+أنها P equal to كذا، و بتعمل بعدين مع P و Q هدول
+
+42
+00:03:03,800 --> 00:03:07,380
+لما نثبت ونخلص بنشوف P و Q اللي أثبتناهم بيعبروا
+
+43
+00:03:07,380 --> 00:03:10,050
+عن إيش في الـ language. تمام. فمحتاجين concise
+
+44
+00:03:10,050 --> 00:03:14,270
+notation for writing them. بعدين الـ methodology for
+
+45
+00:03:14,270 --> 00:03:18,330
+objectively reasoning about their truth table
+
+46
+00:03:18,330 --> 00:03:24,190
+تبعهم، اللي هي الـ truth or falsity. ففعليا
+
+47
+00:03:24,190 --> 00:03:27,590
+بصير بدي إيش الطريقة اللي هستعملها لإثبات بطريقة
+
+48
+00:03:27,590 --> 00:03:33,030
+منطقية، بطريقة معقولة، إثبات مدى صحة أو عدم صحة الـ
+
+49
+00:03:33,030 --> 00:03:38,130
+statement بتاعتي. بالطريقة هذه هي الشغل تبع المصاق، هي
+
+50
+00:03:38,130 --> 00:03:40,430
+شغل المصاق. إيش الـ methodology اللي بدنا نستخدمها؟
+
+51
+00:03:40,430 --> 00:03:46,250
+الحقيقة هذا الـ branch كبير وله علاقة بالـ formal
+
+52
+00:03:46,250 --> 00:03:51,390
+proofs، في الـ formal proofs. طيب فعليا الـ
+
+53
+00:03:51,390 --> 00:03:54,790
+foundations of logic، هنتكلم هناخد overview عليها.
+
+54
+00:03:54,790 --> 00:03:59,590
+هنتكلم عن الـ propositional logic بتفاصيلها شوية،
+
+55
+00:03:59,590 --> 00:04:01,990
+شوية. هنتكلم عن تفاصيلها. بعدين هنقول شوية شوية على
+
+56
+00:04:01,990 --> 00:04:07,570
+الـ predicate logic برضه بتفاصيلها، وهنحكي في وقتها
+
+57
+00:04:07,570 --> 00:04:11,230
+عنها. اليوم ابصرينا وبنحكي بس عن الجزئية هذه اللي
+
+58
+00:04:11,230 --> 00:04:16,430
+هي جزئية للـ proposition logic، propositional logic
+
+59
+00:04:16,430 --> 00:04:20,870
+هي فعليا برضه عبارة عن compound statements built
+
+60
+00:04:20,870 --> 00:04:25,210
+from similar statements. زي ما قلنا أنا بتكلم عن
+
+61
+00:04:25,210 --> 00:04:28,550
+statement كبيرة، تعبير كبير، بس هو جا من مجموعة
+
+62
+00:04:28,550 --> 00:04:33,010
+تعبير صغيرة. طيب كيف ركبناهم؟ التعبير الصغيرة هذه عن
+
+63
+00:04:33,010 --> 00:04:38,290
+طريق operators، عن طريق روابط. الروابط هي شغلنا اليوم.
+
+64
+00:04:38,290 --> 00:04:43,630
+اليوم هنتكلم كتير عن جزء الروابط. الروابط في الـ...
+
+65
+00:04:43,630 --> 00:04:48,270
+في الـ numbers عادة، اللي هي الجمع، الطرح، القسمة لأن
+
+66
+00:04:48,270 --> 00:04:51,790
+هذا بيربط لنا رقم مع رقم فبيطلع لنا ناتج جديد. لما يقول
+
+67
+00:04:51,790 --> 00:04:55,670
+واحد زائد خمسة، زائد هذه علامة الزائد، هذه هي
+
+68
+00:04:55,670 --> 00:05:00,170
+operator، operator للـ numbers. طيب الـ operators اللي
+
+69
+00:05:00,170 --> 00:05:03,750
+إحنا هنشتغل عليها لأ، هتكون علاقة بالـ logic. فهذه
+
+70
+00:05:03,750 --> 00:05:08,630
+Boolean connectives أو Boolean algebra بيشتغل في
+
+71
+00:05:08,630 --> 00:05:11,130
+الجزئية هذه، و هذه اللي هنشتغل عليه إن شاء الله
+
+72
+00:05:11,130 --> 00:05:13,490
+تعالى. وهتكون مرة عليكم قبل هيك، بس يمكن زي ما
+
+73
+00:05:13,490 --> 00:05:17,490
+قلنا، ناخدها بتسميات جديدة، بس أنتم كلها عارفينها:
+
+74
+00:05:17,490 --> 00:05:20,490
+الـ and، والـ or، والـ x or. هنرجع كلها اليوم، نقيتها.
+
+75
+00:05:20,490 --> 00:05:23,410
+هنرجع كلها اليوم، نقيتها. الكلام ده الحقيقة بيفيدنا
+
+76
+00:05:23,410 --> 00:05:26,310
+في كتير مجالات، أهمها يمكن اللي هو في الـ digital
+
+77
+00:05:26,310 --> 00:05:29,310
+electronics circuits، والأمور اللي زي هذه. يعني
+
+78
+00:05:29,310 --> 00:05:32,970
+أنتم لو في السنة الجاية، المفروض إن شاء الله
+
+79
+00:05:32,970 --> 00:05:36,390
+بتاخدوا الـ digital electronics، هتاخدوا فيها كتير
+
+80
+00:05:36,390 --> 00:05:39,450
+عن الـ logic gates. هتتكلموا كتير كتير كتير فيها، في
+
+81
+00:05:39,450 --> 00:05:42,830
+الـ logic gates. okay. في الـ conditions الحقيقة في
+
+82
+00:05:42,830 --> 00:05:45,610
+التعبير عن الـ conditions في البرنامج لما تقولوا if
+
+83
+00:05:45,610 --> 00:05:48,910
+then. جزئية الـ if then، هذه اللي بتعملوها في البرنامج.
+
+84
+00:05:48,910 --> 00:05:53,500
+أعتقد أنكم ما لحقتوش تاخدوا برمجة، ما لحقتوش يمكن
+
+85
+00:05:53,500 --> 00:05:56,900
+تاخدوا برمجة كتير، بس عادة في الـ flow chart بتحطوا
+
+86
+00:05:56,900 --> 00:06:01,700
+حاجة بالشكل هذا، زي condition. نفترض مثلا x أكبر من
+
+87
+00:06:01,700 --> 00:06:06,520
+خمسة، فأنتوا حاطين condition لحظة، وبتحطوله yes or
+
+88
+00:06:06,520 --> 00:06:11,260
+no. بناء عليه إيش بتكون تعملوا الـ action، سواء تحقق
+
+89
+00:06:11,260 --> 00:06:14,200
+أو ما تحققش. تحقق أو ما تحققش، يعني أنتم بتتكلموا عن
+
+90
+00:06:14,200 --> 00:06:20,410
+true or false في condition، وهذا هل هو true or false.
+
+91
+00:06:20,410 --> 00:06:27,190
+بناء عليه بدنا نعمل action قادم. تمام. الجزئية هذه
+
+92
+00:06:27,190 --> 00:06:30,710
+مستخدمة في الـ conditions، زي ما قلنا في الـ... الـ
+
+93
+00:06:30,710 --> 00:06:34,290
+conditions in program، في الـ queries to databases.
+
+94
+00:06:34,290 --> 00:06:38,610
+في، عادة في البحث في الـ database لما بتعملوا بحث
+
+95
+00:06:38,610 --> 00:06:41,770
+على الـ database، نفترض الـ database على الجامعة.
+
+96
+00:06:41,770 --> 00:06:45,470
+بتكتبوا رقمكم الجامعي وبتعملوا enter، فهو بفحص
+
+97
+00:06:46,230 --> 00:06:51,790
+الأرقام كلها، أمتى بتصير فيه quality الـ equal، أن
+
+98
+00:06:51,790 --> 00:06:55,230
+الرقم تبعكم equal لـ folder موجود عنده، بفتح الـ folder.
+
+99
+00:06:55,230 --> 00:06:59,230
+folder، فبتشوفوا صفحتكم، إيش مسجلين، إيش مش مسجلين.
+
+100
+00:06:59,230 --> 00:07:02,130
+علاماتكم، إيش الموثقات اللي خلصتوها، إيش اللي ما
+
+101
+00:07:02,130 --> 00:07:04,530
+خلصتوهاش، إيش اللي نازل، إيش اللي مش نازل. الأمور دي
+
+102
+00:07:04,530 --> 00:07:09,590
+كلها بتنعمل برضه عن طريق logic gates أو logic
+
+103
+00:07:09,590 --> 00:07:12,960
+concepts. الـ search engines، نفس الكلام، لأنكم
+
+104
+00:07:12,960 --> 00:07:18,880
+بتقارنوا، بتعملوا comparison، فيه شروط اتحققت، بجيب
+
+105
+00:07:18,880 --> 00:07:21,460
+الصفحة اللي اتحققت فيها الشروط. الشروط ده بناء على
+
+106
+00:07:21,460 --> 00:07:23,940
+إيش؟ على keywords أنتم بتكتبوها على الـ search
+
+107
+00:07:23,940 --> 00:07:27,900
+engine. فبناء عليه، إذا اتحققت داخل الصفحة الـ web
+
+108
+00:07:27,900 --> 00:07:32,080
+page، بجيب الـ web page. فبتلاقوا مجموعة من الـ
+
+109
+00:07:32,080 --> 00:07:36,130
+web pages موجودة عندكم. okay. نبدأ بأول جزئية اللي هي
+
+110
+00:07:36,130 --> 00:07:39,810
+الـ proposition. الـ proposition، الإعلان، أو أنا
+
+111
+00:07:39,810 --> 00:07:43,930
+بحط لكم جملة إعلامية، declarative sentence، جملة
+
+112
+00:07:43,930 --> 00:07:49,310
+إعلامية لحالة معينة، لإشي معين، بنقدر نعرف إن هي
+
+113
+00:07:49,310 --> 00:07:54,010
+فقرة، أصغر فقرة ممكنة في اللغة، بحيث أن هي بتعطيكم
+
+114
+00:07:54,010 --> 00:07:58,510
+معنى، والمعنى هذا بقدر أحكم عليه true or false.
+
+115
+00:07:58,510 --> 00:08:03,490
+يعني إيه الـ truth، truth value؟ كويس. عادة بنستعمل
+
+116
+00:08:03,490 --> 00:08:09,310
+lowercase أو small letter بشكل هذا. غالبا بنستعمل
+
+117
+00:08:09,310 --> 00:08:13,010
+الـ P، Q، و R في الغالب هم الدارجين في الكتاب اللي
+
+118
+00:08:13,010 --> 00:08:16,210
+هنستعمله، في الكتاب اللي هتستعمله، هذه اللي بتعبر
+
+119
+00:08:16,210 --> 00:08:19,530
+على الـ statements، على مجموعة الـ statements with
+
+120
+00:08:19,530 --> 00:08:24,810
+definite meaning. بمعنى محدد. ومعنى محدد يعني أنا
+
+121
+00:08:24,810 --> 00:08:27,830
+بقدر أحكم عليه. هيا نكررها كذا مرة، بقدر أحكم عليه
+
+122
+00:08:27,830 --> 00:08:32,610
+قد إيش القيمة بتاعته. كويس. having a truth value
+
+123
+00:08:32,610 --> 00:08:37,230
+that's either true or false. إلها قيمة هذه أو هذه.
+
+124
+00:08:37,230 --> 00:08:39,870
+طبعا لا يمكن يكونوا اتنين في نفس الوقت، مش مجازة.
+
+125
+00:08:39,870 --> 00:08:43,590
+طبعا أعطيكم جملة true و false في نفس اللحظة، لا
+
+126
+00:08:43,590 --> 00:08:48,290
+يمكن. هذه بقت proposition، أو neither، لا هي هيك ولا
+
+127
+00:08:48,290 --> 00:08:52,350
+هيك، خائشة، لا هي صح ولا هي غلط، متصبتش، متنفعش، أو
+
+128
+00:08:52,350 --> 00:08:55,470
+somewhere in between. لما أقول somewhere in between،
+
+129
+00:08:55,470 --> 00:08:57,810
+دخلتنا في حاجة جديدة، مش... مش مجالنا، هذه اللي هي
+
+130
+00:08:57,810 --> 00:09:01,550
+probability. دخلنا في جزئية... احتمال. والله أربعين
+
+131
+00:09:01,550 --> 00:09:06,530
+في المية true، وستين في المية false، in between، لأ.
+
+132
+00:09:06,530 --> 00:09:09,690
+هذه دخلنا في إشي تاني. فهذه ما تحطهاش في proposition.
+
+133
+00:09:09,690 --> 00:09:12,490
+اللي هناخده اليوم، أو اللي هنتكلم عنه اليوم، هنتكلم
+
+134
+00:09:12,490 --> 00:09:17,300
+اليوم بأبسط صورة، بأبسط صورة من الصورة بتاعته. طيب، من
+
+135
+00:09:17,300 --> 00:09:19,400
+خلال الكلمتين اللي قلناها، خلّيني آخد شوية examples
+
+136
+00:09:19,400 --> 00:09:23,140
+ونشوف إيش يعني proposition، إيش يعني proposition.
+
+137
+00:09:23,140 --> 00:09:29,200
+فلو قلنا: it's raining. false، okay. إلها قيمة، ممكن لو
+
+138
+00:09:29,200 --> 00:09:31,240
+الدنيا بتشتي بتصير true، بس في النهاية هي جملة، و
+
+139
+00:09:31,240 --> 00:09:34,920
+إلها قيمة، وكاملة، خلاص، بتعطيني معنى. فإذا حسب الـ
+
+140
+00:09:34,920 --> 00:09:38,300
+situation، بقدر أقول إن هي يا true يا false. هذه
+
+141
+00:09:38,300 --> 00:09:44,040
+proposition: القدس is the capital of Palestine.
+
+142
+00:09:44,040 --> 00:09:50,100
+القدس عاصمة فلسطين. true، true، فعلا. فإذا هذه برضه
+
+143
+00:09:50,100 --> 00:09:53,840
+proposition. فإذا هذه proposition. okay. one plus two
+
+144
+00:09:53,840 --> 00:09:57,280
+equal to three. أقول لكم one plus two equal to five،
+
+145
+00:09:57,280 --> 00:10:03,420
+false. ولكن proposition. لحظة، proposition، القيمة
+
+146
+00:10:03,420 --> 00:10:06,740
+بتاعتها false، okay. مش... مش مشكلة، بس في النهاية
+
+147
+00:10:06,740 --> 00:10:12,620
+proposition. okay. في المقابل، في حالات، نعطيكم شوية
+
+148
+00:10:12,620 --> 00:10:15,660
+حالات، هي are not propositions.
+
+149
+00:10:18,320 --> 00:10:22,410
+Who's there؟ question. طب إيش أقول له هذا؟ أقول له صح
+
+150
+00:10:22,410 --> 00:10:25,670
+ولا غلط؟ مش عارف. يعني عن إيش بيحكي. الـ questions
+
+151
+00:10:25,670 --> 00:10:28,350
+بتنحطش مع الـ proposition. فهذه مش proposition.
+
+152
+00:10:28,350 --> 00:10:30,530
+أحيانا وأنتوا بتعملوا chatting، أحيانا بتعملوا
+
+153
+00:10:30,530 --> 00:10:33,750
+هههههه، لالا لالا، حاجات يعني بتنكتبها لغاية
+
+154
+00:10:33,750 --> 00:10:36,670
+صارت كتير، عبارة في الـ chatting، وفي الـ forums، وفي
+
+155
+00:10:36,670 --> 00:10:40,190
+الحاجات هذه. كويس. زي لالا لالا، هذه meaningless.
+
+156
+00:10:40,190 --> 00:10:45,310
+مالهاش معنى. مالهاش معنى، لا يمكن أبدا تفرضوها أنها
+
+157
+00:10:45,310 --> 00:10:48,850
+proposition، تشتغلوا عليها. هذه بدون معنى. طيب، just
+
+158
+00:10:48,850 --> 00:10:54,500
+do it. أوامر... أوامر برضه مالهاش معايا... يمكن ما بديش
+
+159
+00:10:54,500 --> 00:10:57,620
+أنفذ الأوامر... يمكن ما بديش... بيديش أنفذه... بالنسبالي
+
+160
+00:10:57,620 --> 00:11:01,880
+false، واحد تاني بده ينفذه... بس في الآخر الأوامر مش
+
+161
+00:11:01,880 --> 00:11:05,520
+محسوبة كـ proposition. الـ... الـ... الـ... الـ... الـ
+
+162
+00:11:05,520 --> 00:11:09,600
+fake، أو اللي هي الجمل الغامضة. yeah, I sorta don't
+
+163
+00:11:09,600 --> 00:11:13,940
+know whatever... طب ماشي، فهمنا منها... ما فهمناش إشي...
+
+164
+00:11:13,940 --> 00:11:17,280
+الجملة بدا مغامضة، ومش فاهم منها حاجة، على طول
+
+165
+00:11:18,220 --> 00:11:21,940
+هذه not proposition. بقدرش أقول عنها proposition، أو
+
+166
+00:11:21,940 --> 00:11:25,780
+جملة ناقصة. بمعنى أنا بقدرش أقول هذه true or false.
+
+167
+00:11:25,780 --> 00:11:31,820
+زي one plus two stop. طيب كمل لي أنا، one plus two، مش
+
+168
+00:11:31,820 --> 00:11:34,380
+عارف أقول لك صح ولا غلط. اعطيني يا بتقولي تلاتة،
+
+169
+00:11:34,380 --> 00:11:37,480
+فبقول لك true، وبتصير proposition. يا بتقولي ألف، و
+
+170
+00:11:37,480 --> 00:11:41,840
+بقول لك false، و proposition. بس في النهاية لازم يكون
+
+171
+00:11:41,840 --> 00:11:45,140
+لها قيمة، أنا جادة بحكم عليها true ولا false.
+
+172
+00:11:45
+
+223
+00:15:31,710 --> 00:15:34,770
+اللي بعده اللي هي الـ by conditional operator if
+
+224
+00:15:34,770 --> 00:15:41,500
+and only if، مش if then، if and only if إذا وإذا فقط،
+
+225
+00:15:41,500 --> 00:15:44,280
+تمام؟ هنشوف الفرق بين التنتين، في فرق كبير بين
+
+226
+00:15:44,280 --> 00:15:48,020
+التنتين، فمدام if and only if فهي ماخدة implication
+
+227
+00:15:48,020 --> 00:15:56,100
+في الاتجاهين من a to b ومن b to a، كويس نبدأ ..
+
+228
+00:15:56,100 --> 00:16:00,260
+إيش هقول لكم؟ نبدأ نراجع لأن إحنا فعلا هنراجع شوية
+
+229
+00:16:00,260 --> 00:16:02,860
+الـ operators هدول، الـ negation، بداية نبدأ بالـ
+
+230
+00:16:02,860 --> 00:16:06,740
+negation أو الـ not، فببساطة جداً ماخدينها جابل هيك
+
+231
+00:16:06,740 --> 00:16:11,910
+لو قلنا P equal to I have brown hair، لما بدي أعملها
+
+232
+00:16:11,910 --> 00:16:17,770
+negation، لما أقول negation P بتصير I don't have brown hair، و
+
+233
+00:16:17,770 --> 00:16:22,710
+بنتكمل كل اللي عملته، عملية نفي، عملية نفي اللي هي
+
+234
+00:16:22,710 --> 00:16:26,310
+الـ negation بتاعتنا، طيب الـ truth table بتبعها
+
+235
+00:16:26,310 --> 00:16:33,050
+بالشكل اللي إحنا شايفينه T F F T، بهذا الشكل، كويس
+
+236
+00:16:33,050 --> 00:16:37,650
+الـ conjunction أو اللي أنتو زي ما قولنا .. أنتو
+
+237
+00:16:37,650 --> 00:16:40,810
+حافظينها طول عمركم، اللي بتقولوها الـ and أو الـ و
+
+238
+00:16:40,810 --> 00:16:44,730
+إحنا هنسميها conjunction، اللي هي الاتحاد أو توحيد
+
+239
+00:16:44,730 --> 00:16:48,850
+أو دمج .. دمج، فهذه بتشتغل على two propositions
+
+240
+00:16:48,850 --> 00:16:55,170
+بالنسبة لنا، وهيكون الرمز بتاعها زي زي ما قولنا
+
+241
+00:16:55,170 --> 00:16:59,780
+الـ ۸ الهندية جايه من الـ A كأنها من الـ A، فهي
+
+242
+00:16:59,780 --> 00:17:02,740
+العلامة أو الـ symbol اللي إحنا هنستعمله، فلو قولنا
+
+243
+00:17:02,740 --> 00:17:09,620
+if P equal to I will have chicken for lunch، زي أنا
+
+244
+00:17:09,620 --> 00:17:15,140
+والله عندي فعلاً دجاج للغداء، وQ equal to I will
+
+245
+00:17:15,140 --> 00:17:21,320
+have cheese for dinner، وجبنة للعشاء، لو قولنا P
+
+246
+00:17:21,320 --> 00:17:25,960
+conjunction Q، إيش بتصير؟ I will .. التنتين إحنا
+
+247
+00:17:25,960 --> 00:17:29,300
+هنربطهم بإيش؟ بـ and، I will have chicken for lunch
+
+248
+00:17:29,300 --> 00:17:33,860
+and، الـ and هذه هي الـ conjunction هذه، and I will
+
+249
+00:17:33,860 --> 00:17:37,180
+have .. فإحنا نزلناهم زي ما هم، ربطناهم ربط، عمل
+
+250
+00:17:37,180 --> 00:17:40,580
+إيه اللي اتربط؟ فصارت إيش؟ statement واحدة، صارت
+
+251
+00:17:40,580 --> 00:17:44,820
+sentence واحدة، صارت جملة واحدة، خلاص بنكتبها ورا
+
+252
+00:17:44,820 --> 00:17:46,760
+بعض، و هو ده فعلاً حتى الـ language اللي كنت تعمل
+
+253
+00:17:46,760 --> 00:17:50,340
+ما حدش بيكتب جملة جملة، بنكتب جملة وبنربطهم في بعض
+
+254
+00:17:50,340 --> 00:17:54,560
+عشان نعمل paragraph، عشان نعمل مجموعة
+
+255
+00:17:54,560 --> 00:17:57,420
+paragraphs، بتطلع لي chapter، مجموعة chapters
+
+256
+00:17:57,420 --> 00:18:01,440
+بتطلع لي كتاب وهكذا، فإحنا بنكون من حاجات بسيطة
+
+257
+00:18:01,440 --> 00:18:05,400
+بنكون حاجات complicated، ونفس الكلام هنا، عملية
+
+258
+00:18:05,400 --> 00:18:12,720
+الربط باستخدام الـ conjunction، الـ truth table للـ
+
+259
+00:18:12,720 --> 00:18:16,580
+conjunction، مرة ثانية جابل هيك، الحالة الوحيدة اللي
+
+260
+00:18:16,580 --> 00:18:21,320
+ممكن يكون فيها true، إن كل proposition
+
+261
+00:18:24,000 --> 00:18:29,240
+فـ for all propositions are true, then the result is
+
+262
+00:18:29,240 --> 00:18:33,020
+true، لازم كلهم يكونوا true عشان فعلاً أضمن أنه الكل
+
+263
+00:18:33,020 --> 00:18:36,560
+true، لو عندنا two propositions، two propositions
+
+264
+00:18:36,560 --> 00:18:39,840
+فعلياً هيكون كام احتمال عندكم، أو كام احتمال ممكن هيكون
+
+265
+00:18:39,840 --> 00:18:44,500
+أربعة، جاي منين؟ من two to the power n، two to the
+
+266
+00:18:44,500 --> 00:18:47,440
+power n، لأن أنا بتكلم عن binary، الـ binary معناته
+
+267
+00:18:47,440 --> 00:18:49,480
+ثنائي، شو الثنائي عندنا؟
+
+268
+00:18:52,650 --> 00:18:57,310
+احتمال الـ output، إنتوا يا true يا false، فإذا
+
+269
+00:18:57,310 --> 00:19:01,310
+ثنائي، وعشان هيك دائماً نشتغل على الاتنين، على
+
+270
+00:19:01,310 --> 00:19:04,170
+الاتنين لإنه ما عنديش يا .. إيش الـ .. الـ .. الـ ..
+
+271
+00:19:04,170 --> 00:19:07,910
+الـ symbols اللي بدي أعوضها هنا false or true؟ في
+
+272
+00:19:07,910 --> 00:19:11,190
+شيء ثاني غيرهم؟ لأ، فأنا بتكلم عن binary فعلاً، عشان
+
+273
+00:19:11,190 --> 00:19:14,710
+هيك فيه أنا إثنين بيمثلوا لي، يدوني عدد الـ rows اللي
+
+274
+00:19:14,710 --> 00:19:18,750
+ممكن أحتاجهم في العملية بتاعتي، طيب also negation
+
+275
+00:19:18,750 --> 00:19:23,210
+and conjunction operations together are sufficient
+
+276
+00:19:23,210 --> 00:19:28,970
+to express any poly and truth table، حقيقة الـ
+
+277
+00:19:28,970 --> 00:19:33,050
+negation مع الـ and أو الـ conjunction، كافية أنها
+
+278
+00:19:33,050 --> 00:19:37,510
+تعبر عن كمية كبيرة جداً، إذا ما كانش معظم،  حقيقة الـ
+
+279
+00:19:37,510 --> 00:19:41,550
+poly and truth table، أو معظم الـ operators اللي
+
+280
+00:19:41,550 --> 00:19:46,210
+ممكن نستخدمها، الـ operators اللي ممكن نستعملها، طيب
+
+281
+00:19:46,210 --> 00:19:50,170
+الـ disjunction، الـ disjunction اللي هي الـ or، كنتوا
+
+282
+00:19:50,170 --> 00:19:57,730
+تستعملوها، مكانها or جاية، ممكن تكون هذه من عملية
+
+283
+00:19:57,730 --> 00:20:01,130
+الجمع
+
+284
+00:20:01,130 --> 00:20:05,950
+أو الـ ax بتاعتنا، فالسؤال اللي كان هيحصل، ليش؟ لأنه أي
+
+285
+00:20:05,950 --> 00:20:11,890
+واحدة من الـ propositions true، النتيجة true، فإذا
+
+286
+00:20:11,890 --> 00:20:14,690
+يكفي أن تكون واحدة، صار عندنا زودنا احتمالات لـ true
+
+287
+00:20:14,690 --> 00:20:18,670
+في النتيجة، بنزود هيك عدد احتمالات لـ true، ليش؟ لأن
+
+288
+00:20:18,670 --> 00:20:22,370
+أي واحدة كافية أنها تكون .. أنها تخلي الناتج true
+
+289
+00:20:22,370 --> 00:20:25,930
+هنشوف طبعاً الـ truth table بتاعها، لو قولنا مثلاً for
+
+290
+00:20:25,930 --> 00:20:32,130
+example P equal to my car has a bad engine، سيارة
+
+291
+00:20:32,130 --> 00:20:35,670
+ماتورها .. يبدو أن ماتورها مثلاً مش .. مش كويس، في
+
+292
+00:20:35,670 --> 00:20:41,490
+أطلان أو .. أو خربان، أو Q my car has a bad
+
+293
+00:20:41,490 --> 00:20:45,960
+carburetor، الـ carburetor برضه ممكن يكون هو العطلان
+
+294
+00:20:45,960 --> 00:20:49,580
+فأنا ممكن أروح لميكانيكي والسيارة معايا إيش مالها
+
+295
+00:20:49,580 --> 00:20:52,440
+يقول الله ما عارف، شوف يمكن يكون الـ motor أو
+
+296
+00:20:52,440 --> 00:20:58,140
+carburetor، أو لحظة، ويمكن يطلع الاتنين مع بعض، يمكن
+
+297
+00:20:58,140 --> 00:21:00,980
+لما يفحص يلاقي إن الاتنين مع بعض، فهنا صارت الـ أو
+
+298
+00:21:00,980 --> 00:21:06,260
+بتشمل الـ both cases أو الـ both propositions
+
+299
+00:21:08,580 --> 00:21:16,300
+لو قلنا بـ disjunction q، either اما
+
+300
+00:21:16,300 --> 00:21:21,560
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+301
+00:21:21,560 --> 00:21:21,640
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+302
+00:21:21,640 --> 00:21:21,760
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+303
+00:21:21,760 --> 00:21:22,600
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+304
+00:21:22,600 --> 00:21:23,300
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+305
+00:21:23,300 --> 00:21:23,320
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+306
+00:21:23,320 --> 00:21:33,400
+اما اما
+
+307
+00:21:33,400 --> 00:21:38,720
+ما لازم تنقل two propositions، أو خليني أقول all
+
+308
+00:21:38,720 --> 00:21:42,700
+propositions are true عشان أقول إن النتيجة true
+
+309
+00:21:42,700 --> 00:21:48,620
+هنا لأ، just one true is enough، just one
+
+310
+00:21:48,620 --> 00:21:56,900
+proposition is true enough to get true result، okay
+
+311
+00:21:56,900 --> 00:22:02,600
+ففي الحالة هذه بنقدر نقول إن or both are أيضاً true
+
+312
+00:22:03,180 --> 00:22:06,940
+يعني ممكن يكون الشغلتين برضه .. التنتين true زي ما
+
+313
+00:22:06,940 --> 00:22:11,340
+قلنا، ممكن تكون الـ motor و الـ carburetor ييجي يفحص
+
+314
+00:22:11,340 --> 00:22:15,240
+ويلقى إنه الاتنين خربانين، مش بس واحد، هذه أحياناً
+
+315
+00:22:15,240 --> 00:22:20,440
+الـ operator هذه بنسميها inclusive or، in غير الـ
+
+316
+00:22:20,440 --> 00:22:24,040
+exclusive or اللي هي الـ xor، in معناته إيش الـ in
+
+317
+00:22:24,040 --> 00:22:27,660
+هذه؟ في حاجة included، الشيء الـ included اللي فعلياً
+
+318
+00:22:27,660 --> 00:22:33,190
+إحنا بنتكلم عنها both cases، both cases هنا included
+
+319
+00:22:33,190 --> 00:22:38,530
+مع الـ truth table كـ true، فعشان هي ممكن نسميها
+
+320
+00:22:38,530 --> 00:22:45,210
+inclusive or، عشان هي بتضمن معانا الـ both cases
+
+321
+00:22:45,210 --> 00:22:49,700
+الأخيرة في الـ xor، هذه الوحيدة اللي بتختلف، هتلاقوها
+
+322
+00:22:49,700 --> 00:22:52,660
+نفس الـ or ولكن الجزء الأخير اللي هيختلف، و
+
+323
+00:22:52,660 --> 00:22:57,420
+هنتكلم logically عن الـ difference between الـ or و
+
+324
+00:22:57,420 --> 00:23:01,120
+الـ xor، لما نيجي ناخد الـ xor، طيب نفس الكلام ممكن
+
+325
+00:23:01,120 --> 00:23:06,480
+negation مع الـ disjunction في جملة واحدة ممكن
+
+326
+00:23:06,480 --> 00:23:11,480
+يكونوا مع بعض عادي، universally ممكن يكونوا متعرف
+
+327
+00:23:11,480 --> 00:23:16,460
+عليها أو متوقع إنهم ممكن يكونوا مع بعض، طيب صرنا
+
+328
+00:23:16,460 --> 00:23:21,300
+ماخدين هنا كذا operator، طب هذا هيطرح لنا سؤال إنه طب
+
+329
+00:23:21,300 --> 00:23:24,020
+ما ممكن يكون في عندنا nested propositional
+
+330
+00:23:24,020 --> 00:23:27,420
+expressions، nested اللي هو متشابك، اللي يجي أكثر
+
+331
+00:23:27,420 --> 00:23:32,060
+من operator، طب لمين الأولوية، الـ priority لمين، الـ
+
+332
+00:23:32,060 --> 00:23:34,660
+priority، الحقيقة عادةً إن إحنا وإحنا بنشتغل لأنه
+
+333
+00:23:34,660 --> 00:23:37,680
+طوّلنا اتكلمنا إن أول شغل عندنا بدنا language
+
+334
+00:23:37,680 --> 00:23:40,760
+expression، فالـ language هي اللي بتحكمنا، الـ
+
+335
+00:23:40,760 --> 00:23:42,660
+language هي اللي بتحكمنا عشان يكونوا بتكتبوا في الـ
+
+336
+00:23:42,660 --> 00:23:45,560
+language بتاعتكم، لازم تاخدوا بالكم إن الكلمة، الكلمة
+
+337
+00:23:45,560 --> 00:23:50,100
+أهمها الكلمة، الكلمة دي وين بتحطوها بتغير المعنى
+
+338
+00:23:50,100 --> 00:23:53,060
+بتغير المعنى، بتخليني أنا كمان لما بدي أجي أترجمها
+
+339
+00:23:53,060 --> 00:23:58,320
+لرياضيات بتغير كل الشغل معايا، ناخد example نوضح
+
+340
+00:23:58,320 --> 00:24:03,900
+فيه، الصورة، I just saw my old friend, and
+
+341
+00:24:03,900 --> 00:24:10,060
+either he's grown or I have shrunk، أنا شفت صديقي
+
+342
+00:24:10,060 --> 00:24:16,210
+القديم، أو الصديق القديم، وكأنه يا إما هو grew زيادة
+
+343
+00:24:16,210 --> 00:24:19,190
+عن اللزوم، كبر زيادة عن اللزوم، أو أنا اتقلصت، أو
+
+344
+00:24:19,190 --> 00:24:25,870
+ضعفت، shrank، اللي هو اتقلص، أو أنا ضعفت، شكلي، هذه
+
+345
+00:24:25,870 --> 00:24:29,470
+الجملة، طيب لما نيجي نعبر عنها باستخدام الـ
+
+346
+00:24:29,470 --> 00:24:35,930
+propositions، هنقول إن هذه proposition لحالها، okay
+
+347
+00:24:35,930 --> 00:24:44,330
+هعطيها F، التانية هنا he's grown proposition، طيب I
+
+348
+00:24:44,330 --> 00:24:47,290
+have shrunk proposition، حاطيها الـ S، وهنا حاطيها
+
+349
+00:24:47,290 --> 00:24:54,190
+الـ G، هتصير إيش؟ F and افتح أقواس اه، ليش فتحنا
+
+350
+00:24:54,190 --> 00:25:00,390
+الأقواس هنا، هنشوفه، G disjunction S، لإنه في كلمة
+
+351
+00:25:00,390 --> 00:25:05,590
+كلمة هذه خلتني أعرف إن الجزء هذا شيء والجزء هذا
+
+352
+00:25:05,590 --> 00:25:10,240
+شيء ثاني، الكلمة دي لو اتغير مكانها هتغير طريقة
+
+353
+00:25:10,240 --> 00:25:15,080
+الترجمة بتاعتي، لو اتغير مكانها طبيع كل شيء هيتغير
+
+354
+00:25:15,080 --> 00:25:18,720
+عندنا، طيب خلينا ناخد الشكل اللي موجود عندنا هنا
+
+355
+00:25:18,720 --> 00:25:25,120
+كلمة وفي and، معناها to end، either، خلاص عرفت إنه
+
+356
+00:25:25,120 --> 00:25:29,740
+إيش فيه؟ فيه or، يعني الـ or وين ما كانت عشان أحدد
+
+357
+00:25:29,740 --> 00:25:31,620
+اللي قبلها proposition واللي بعدها proposition
+
+358
+00:25:31,620 --> 00:25:37,730
+ثانية، هي الـ or، فاللي قبلها هي هذه proposition واللي
+
+359
+00:25:37,730 --> 00:25:41,370
+بعدها proposition ثانية، وفي هي disjunction between
+
+360
+00:25:41,370 --> 00:25:48,050
+them، طيب لو كتبناها بهذا الشكل، حقيقة هذه something
+
+361
+00:25:48,670 --> 00:25:53,030
+meaning ثاني مختلف تماماً، هنا بيعطيكوا معنى مختلف
+
+362
+00:25:53,030 --> 00:25:57,310
+تماماً عن المعنى الحقيقي للجملة زي ما هي مكتوبة
+
+363
+00:25:57,310 --> 00:26:01,410
+قدامنا، لما بتكتب بهذا الشكل، المعنى بيصير كأنه أنا
+
+364
+00:26:01,410 --> 00:26:09,190
+شفت صاحبي وهو كبر أو نما، خلاص، فإذا أنا حكمت عليه
+
+365
+00:26:09,190 --> 00:26:12,270
+إن هي true، لازم يكون نما، طب خلينا نشوف الفرق بين
+
+366
+00:26:12,270 --> 00:26:14,270
+التنتين، اللي هي فيه فرق شاسع بين التنتين، هذه
+
+367
+00:26:14,270 --> 00:26:20,700
+معناها عشان كل الجملة هنا تكون true، يا اما هذه true أو
+
+368
+00:26:20,700 --> 00:26:27,480
+هذه كلها true، صحيح؟ طيب في الحالة هذه، إذا أو ممكن
+
+369
+00:26:27,480 --> 00:26:31,460
+إني التنتين هدول يكونوا false وأكتفي إن هذه true
+
+370
+00:26:31,460 --> 00:26:36,240
+وخلاص، وأقول إني ما شوفتش صاحبي من أصله، طب لأ
+
+371
+00:26:36,240 --> 00:26:40,100
+أنا شفت صاحبي، المعنى اتغير، أنا شفت صاحبي، كيف
+
+372
+00:26:40,100 --> 00:26:46,240
+ما شفتش صاحبي، لحظة، هذه كلها عشان تكون true، أنتو
+
+373
+00:26:46,240 --> 00:26:50,150
+هنا بتتكلموا عن disjunction، يكفي إن واحدة منهم تكون
+
+374
+00:26:50,150 --> 00:26:54,050
+true، طب ممكن تكون هذه الـ true، أكون أنا فعلاً يمكن
+
+375
+00:26:54,050 --> 00:26:57,110
+سافرت أو شيء أو حاجة، مع المعبر ومع السفر ومع
+
+376
+00:26:57,110 --> 00:27:01,890
+الرحلة، الواحد يضعف وزنه شوية، يخف وزنه، شيء صار، شيء مرض
+
+377
+00:27:01,890 --> 00:27:06,430
+حاسس حاله هيك هزيل شوية، ممكن مش عارف، يعني بتصير
+
+378
+00:27:06,430 --> 00:27:09,890
+true، فتلاقي إن هو هذه خلاص بطل الـ هبوط بمعنى إن لو
+
+379
+00:27:09,890 --> 00:27:16,480
+أنا ما شفتش، طب كيف عرفت إن هو he is grown؟ فلاحظوا
+
+380
+00:27:16,480 --> 00:27:20,140
+إن المعنى اتغير تماماً غير التانية هناك، التانية
+
+381
+00:27:20,140 --> 00:27:24,560
+هناك إيش مالها؟ and
+
+382
+00:27:24,560 --> 00:27:28,360
+أو conjunction، conjunction عشان كلها تكون true
+
+383
+00:27:28,360 --> 00:27:33,700
+لازم الجزء هذا true وهذا true، الزمن صح، الزمن لازم
+
+384
+00:27:33,700 --> 00:27:37,080
+تكون هذا true وهذا true، طيب مدام الزمن هذا true
+
+385
+00:27:37,080 --> 00:27:44,520
+خلاص، فإذا أنا شفت صاحبي، خلاص true، طيب هنا عشان
+
+386
+00:27:44,520 --> 00:27:49,150
+تكون هذه true، واحدة منهم كافية، إنه ممكن فعلاً يا إما
+
+387
+00:27:49,150 --> 00:27:55,990
+هو كبر هيك مرة واحدة، يعني شيء حاجة، أو أنا أضعفت
+
+388
+00:27:55,990 --> 00:28:01,910
+لأي سبب كان، فصارت المعنى بهذا الشكل، ينطبق تماماً مع
+
+389
+00:28:01,910 --> 00:28:05,450
+الجملة اللي أنا فهمتها، فانطبق تماماً مع الجملة اللي
+
+390
+00:28:05,450 --> 00:28:10,750
+فهمناها، غير إيش الجملة التانية، غير الجملة التانية
+
+391
+00:28:10,750 --> 00:28:11,890
+تمام
+
+392
+00:28:14,960 --> 00:28:18,800
+اللي أصعب طبعاً، كنتوا كتبتوا بالشكل هذا بدون أقواس، و
+
+393
+00:28:18,800 --> 00:28:22,140
+بدون priority لأي حاجة، خلاص conjunction
+
+445
+00:32:03,840 --> 00:32:09,340
+مدام مافيش أي negation، مافيش أي شيء مغيره، فاللون was
+
+446
+00:32:09,340 --> 00:32:15,880
+with this morning and it didn't rain last night،
+
+447
+00:32:15,880 --> 00:32:19,320
+طيب، الأخيرة احنا ما .. ما تكلمناش لسه عليها
+
+448
+00:32:19,320 --> 00:32:24,870
+الأخيرة، negation هي الـ  لحظة negation هي الـ
+
+449
+00:32:24,870 --> 00:32:28,290
+was موجودة، فإذا الفعل المساعد موجود، أعمله not بس
+
+450
+00:32:28,290 --> 00:32:32,430
+في الآخر، وخلصناه كويسة. هذه الـ negation بتاعتنا بس
+
+451
+00:32:32,430 --> 00:32:36,710
+خدوا بالكم، الـ operator اللي عندنا are، يعني بدنا
+
+452
+00:32:36,710 --> 00:32:43,690
+نبدأ بإيش؟ either، تمام. فبتضيف either في الحالة
+
+453
+00:32:43,690 --> 00:32:51,770
+اللي عندنا هنا، في الصوت بيقطع، بدنا نحط are، تمام.
+
+454
+00:32:54,090 --> 00:32:58,770
+الـ XOR، الـ operator الثالثة، الرابعة، الـ operator
+
+455
+00:32:58,770 --> 00:33:03,070
+الرابعة هي الـ XOR operator، هذه binary exclusive OR
+
+456
+00:33:03,070 --> 00:33:06,250
+operator، اتكلمنا عنها برضه، combines two
+
+457
+00:33:06,250 --> 00:33:10,610
+propositions، بالنسبة لنا عشان تعطينا logical أو
+
+458
+00:33:10,610 --> 00:33:16,190
+logic XOR، أو X junction، أو X junction، for example
+
+459
+00:33:16,190 --> 00:33:22,580
+في، I will earn an A in this course، إن شاء الله، أنا
+
+460
+00:33:22,580 --> 00:33:28,480
+هجيب A في الـ course هذا، okay، proposition Q، I will
+
+461
+00:33:28,480 --> 00:33:33,760
+drop this course، لا قدر الله، كويس، فهي عندنا two
+
+462
+00:33:33,760 --> 00:33:41,160
+propositions، لما أجي أقول P أو P X or Q، هذه منطقيا
+
+463
+00:33:41,160 --> 00:33:43,900
+أن هي تكون X or، لأنه لا يمكن الاثنين يجوا مع بعض.
+
+464
+00:33:43,900 --> 00:33:50,440
+فإذا true true، مش منطقية، إن الاثنين يكونوا true، مش
+
+465
+00:33:50,440 --> 00:33:54,240
+منطقية، فهنا الأنسب والأفضل لجملتين بالشكل هذا، أن
+
+466
+00:33:54,240 --> 00:33:58,900
+أنا أستعمل x or، I will either earn an A for this
+
+467
+00:33:58,900 --> 00:34:07,030
+course or I will drop it، but not both، طبيعي، كيف بدي
+
+468
+00:34:07,030 --> 00:34:10,050
+.. يعني أنا كيف رصّبت، وكيف جبت A في نفس الوقت؟
+
+469
+00:34:10,050 --> 00:34:14,010
+بتجيش، فإذا هذا by logic، أحيانا أنتم بدكم حسب
+
+470
+00:34:14,010 --> 00:34:18,310
+فهمكم للـ .. للجملة as a language، بدكم تفهموا إيش
+
+471
+00:34:18,310 --> 00:34:21,690
+لازم تستعملوا إيش؟ بدكم تستعملوا، هل في احتمال أنه
+
+472
+00:34:21,690 --> 00:34:26,990
+والله ممكن ناخد الـ .. الـ both، أنه الـ .. يعني الـ
+
+473
+00:34:26,990 --> 00:34:32,930
+both are true ممكن، فإذا إذا ممكن or اللي هي
+
+474
+00:34:32,930 --> 00:34:37,410
+disjunction، إذا مش ممكن الـ X junction، أو الـ X or
+
+475
+00:34:37,410 --> 00:34:40,710
+الـ
+
+476
+00:34:40,710 --> 00:34:44,250
+truth table تبعها هو نفس الـ or، الـ truth table نفس
+
+477
+00:34:44,250 --> 00:34:50,370
+الـ or، باختلاف من الـ both are true، هذه هتكون false.
+
+478
+00:34:50,370 --> 00:35:01,020
+كويسة، X بدل N، لو الـ E X هذه، فإذا أنا بتكلم عن مين؟
+
+479
+00:35:01,020 --> 00:35:03,700
+عن الـ or العادية، الـ disjunction العادية، الـ
+
+480
+00:35:03,700 --> 00:35:06,980
+disjunction اللي احنا اتكلمنا عنها، ولكن هنا x، فإذا
+
+481
+00:35:06,980 --> 00:35:15,560
+excludes the possibility that both p and q are true.
+
+482
+00:35:15,560 --> 00:35:22,000
+ما يجوش مع الـ x or بيجوش مع بعض، ليش؟ لأنه في
+
+483
+00:35:22,000 --> 00:35:25,970
+expression بتعبر عن الموضوع هذا، هناخده لاحقا، في
+
+484
+00:35:25,970 --> 00:35:28,890
+operator خاصة بالجزئية فيها دي، لا يمكن ييجوا مع
+
+485
+00:35:28,890 --> 00:35:33,670
+بعض، الاثنين هدول في جملة مع بعض، أو ورا بعض، يعني
+
+486
+00:35:33,670 --> 00:35:41,050
+مباشرة، okay، for example، نوضح الـ or والـ xor، or و
+
+487
+00:35:41,050 --> 00:35:44,430
+xor، لو أخدنا مثلا في الـ English، طبعا معتمدة تماما
+
+488
+00:35:44,430 --> 00:35:47,230
+على الـ English، أنتم كيف فاهمين اللغة؟ أنتم كيف
+
+489
+00:35:47,230 --> 00:35:50,770
+فاهمين اللغة بتاعتكم، عشان ترجموها لمجموعة symbols؟
+
+490
+00:35:51,750 --> 00:35:59,750
+لو قلنا وسام is a singer or وسام is a writer، هذه
+
+491
+00:35:59,750 --> 00:36:03,910
+المفروض or ولا x or؟ or، لأنه ممكن يكون الاثنين.
+
+492
+00:36:03,910 --> 00:36:07,510
+ممكن يكون بيغني وبيكتب في نفس الوقت، فليكن ممكن
+
+493
+00:36:07,510 --> 00:36:13,430
+يكون فعلا بيغني وبيكتب في نفس الوقت، الجملة
+
+494
+00:36:13,430 --> 00:36:18,410
+الثانية، وسام is a man or وسام is a woman، لأن كلمة
+
+495
+00:36:18,410 --> 00:36:22,980
+وسام ممكن تحتمل، صح؟ يعني الاسم ممكن يحتمل، فأنا لو
+
+496
+00:36:22,980 --> 00:36:27,980
+كنت قرأته وسام، حد مثلا بعت لي email وبيقول لي والله
+
+497
+00:36:27,980 --> 00:36:31,240
+أنا بتسجل في الـ course بس مش عارف كيف أدخل على الـ model
+
+498
+00:36:31,240 --> 00:36:36,340
+وسام، طب ممكن يكون male أو female، طب هذه man ولا
+
+499
+00:36:36,340 --> 00:36:40,160
+woman ممكن، ففي الحالة هذه، okay، ممكن نكتبها الجملة بس
+
+500
+00:36:40,160 --> 00:36:44,200
+ما أقدرش أقول أن هي or، يعني لما أجي أترجمها، فهذه لازم
+
+501
+00:36:44,200 --> 00:36:48,800
+تكون x or، لازم تكون x or، تمام.
+
+502
+00:36:52,070 --> 00:36:55,930
+Okay، الجزء اللي بعده هو الـ implication، هذا جديد
+
+503
+00:36:55,930 --> 00:36:59,270
+.. جديد يمكن شوية مفاهيم عليكم شوية، كويس، الـ
+
+504
+00:36:59,270 --> 00:37:01,930
+implication .. implication مفيدة جدا في الـ if then
+
+505
+00:37:01,930 --> 00:37:05,150
+في البرمجة، وأنتم بتتكلموا عن برمجة، مفيدة
+
+506
+00:37:05,150 --> 00:37:09,710
+أهميتها لما تيجوا تتكلموا في البرنامج بتاعكم if
+
+507
+00:37:09,710 --> 00:37:14,570
+then، بمعنى أنه إذا تحقق الـ condition، الشرط، حقق
+
+508
+00:37:14,570 --> 00:37:20,430
+للنتيجة، تمام. أو if، أنتم عادة بتكتبوها، نكتب أن هي
+
+509
+00:37:20,430 --> 00:37:25,130
+كود صغير، لو قلنا if x أكبر، نفترض مثلا من five
+
+510
+00:37:25,130 --> 00:37:31,070
+نحط له هنا statement معينة، أو خلينا نحط احنا من هنا
+
+511
+00:37:31,070 --> 00:37:40,250
+أي statement، خلينا نقول print فرضا.
+
+512
+00:37:40,250 --> 00:37:41,710
+طيب، else
+
+513
+00:37:44,850 --> 00:37:53,910
+نفترض brand and، خلينا نقول حاجة بهذا الشكل، طيب.
+
+514
+00:37:53,910 --> 00:38:01,290
+فإذا أنا صرت مرتبط بمين؟ بالشرط، إذا تحقق الشرط، حقق
+
+515
+00:38:01,290 --> 00:38:07,290
+ليه النتيجة، مظبوط. إذا تحقق الشرط، حقق ليه النتيجة، هي
+
+516
+00:38:07,290 --> 00:38:09,250
+المفهوم الأساس اللي هناخده من الـ implication
+
+517
+00:38:09,250 --> 00:38:15,930
+ما يتحققش، else، إيش الـ condition اللي هنعمله؟ كويس.
+
+518
+00:38:15,930 --> 00:38:22,730
+خلينا، الـ example اللي هتكون عندنا هنا، فـ if P is
+
+519
+00:38:22,730 --> 00:38:28,810
+true، then Q is true، but if P is not true، then Q
+
+520
+00:38:28,810 --> 00:38:34,130
+could be either true or false، بمعنى، Okay، أنا ..
+
+521
+00:38:34,130 --> 00:38:37,290
+يعني ربطه بـ condition معين، بس لو ما اتحققش، أنا
+
+522
+00:38:37,290 --> 00:38:41,710
+ماليش علاقة فيه، أنا ماليش علاقة فيه، بصير أنا ماليش
+
+523
+00:38:41,710 --> 00:38:46,670
+دعوة، زي واحد بيقول لابنه مثلا، والله أنا لو نجحت
+
+524
+00:38:46,670 --> 00:38:51,650
+هأشتري لك بسكليت، تمام؟ طيب، ما نجحش، ماهو ممكن يكون
+
+525
+00:38:51,650 --> 00:38:54,990
+حرام أشتري له البسكليت، أنا ماليش علاقة فيك بس
+
+526
+00:38:54,990 --> 00:38:58,490
+الشرط، إذا والله is it true، نجحت، الـ condition
+
+527
+00:38:58,490 --> 00:39:02,110
+اتحقق، النتيجة لازم تتحقق، معناته أنا حسب وعدي اللي
+
+528
+00:39:02,110 --> 00:39:05,910
+أجبته لك، طيب، ما اتحققش، أنا بس اللي ماليش دعوة، بس أنت
+
+529
+00:39:05,910 --> 00:39:09,130
+جبت من برا، أنا ماليش علاقة، فإذا ممكن false وممكن
+
+530
+00:39:09,130 --> 00:39:13,550
+true، لحظة، ببساطة، هاي .. هاي معنى الـ implication
+
+531
+00:39:13,550 --> 00:39:18,510
+أنه إذا اتحقق شرط، بيضمن لي الشرط، يعني necessary
+
+532
+00:39:18,510 --> 00:39:23,730
+ضرورية، ضرورية تحقق الشرط عشان تصير النتيجة، ولكن
+
+533
+00:39:23,730 --> 00:39:26,370
+ممكن تصير النتيجة بدون الشرط، هذه الـ necessary
+
+534
+00:39:26,370 --> 00:39:30,090
+condition، بنسميها necessary condition، في فرق بين
+
+535
+00:39:30,090 --> 00:39:32,430
+necessary condition و sufficient condition، فاحنا
+
+536
+00:39:32,430 --> 00:39:35,110
+هنا متكلم عن جزئية necessary condition، شرط ضروري
+
+537
+00:39:35,110 --> 00:39:40,650
+ولكن مش ملزم، لحظة، مش ملزم كتير، خلينا نشوف example
+
+538
+00:39:40,650 --> 00:39:47,490
+عليها، let P equal to you study hard، أن أنت درست
+
+539
+00:39:47,490 --> 00:39:52,870
+كويس، درست بصورة جيدة، Q equal to you will get a
+
+540
+00:39:52,870 --> 00:40:00,860
+good grade، تمام. لما أقول P implies q، كأني بقول if
+
+541
+00:40:00,860 --> 00:40:05,420
+you study hard، then you will get a good grade، طيب.
+
+542
+00:40:05,420 --> 00:40:10,160
+else، يعني لو أنا ما درستش كويس، it could go either
+
+543
+00:40:10,160 --> 00:40:15,060
+way، ممكن ينجح، يكون والله لسه متذكرين شوية حاجات من
+
+544
+00:40:15,060 --> 00:40:18,300
+اللي قالها الدكتور في وقت المحاضرة قبل شهر، زمان قد
+
+545
+00:40:18,300 --> 00:40:21,580
+يكون، يعني لفت الامتحان، ما درسناش كويس، ولكن صدفة
+
+546
+00:40:21,580 --> 00:40:25,660
+أنه الامتحان إجا معظم من حاجات أنا لسه متذكرها، بمش
+
+547
+00:40:25,660 --> 00:40:33,600
+الحال، بس الأصل أن مدام درست، إذا درست hard بصورة
+
+548
+00:40:33,600 --> 00:40:37,320
+قوية، بصورة جيدة، كويس، وفاهم صح، الأصل أنه إيش يصير؟
+
+549
+00:40:37,320 --> 00:40:43,700
+أنه النتيجة تتحقق، اللي هي get a good grade، تمام.
+
+550
+00:40:43,700 --> 00:40:48,940
+فبيصير عندنا هنا الـ truth table بتاعنا، الحالة
+
+551
+00:40:48,940 --> 00:40:50,980
+الوحيدة اللي ممكن تكون false، وهنشرحها لو جيت
+
+552
+00:40:50,980 --> 00:40:57,330
+واحدة واحدة، اللي هي TF، اتحقق الـ condition، بس
+
+553
+00:40:57,330 --> 00:41:01,350
+ما صارتش النتيجة، طب ليش؟ ما حققناش الـ condition، ليش
+
+554
+00:41:01,350 --> 00:41:03,910
+ما حصلناش على نتيجة؟ هذه الحالة الوحيدة الـ false
+
+555
+00:41:03,910 --> 00:41:06,530
+اللي أصلا غير منطقية، الأصل أنها تكون فعلا false.
+
+556
+00:41:06,530 --> 00:41:13,590
+الولد نجح، طب ليش ما جبتهوش البسكليت؟ صح، ماهي منطقي
+
+557
+00:41:13,590 --> 00:41:16,930
+معناته هيفوق عليا، وهيعمل لي جثة، لأنه فعلا false.
+
+558
+00:41:16,930 --> 00:41:22,010
+الوضع خطأ، الأصل أن هذه الحالة الوحيدة اللي تكون
+
+559
+00:41:22,010 --> 00:41:27,630
+فيها false، أما ما اتحققش الشرط، ما حصلناش على نتيجة، ما
+
+560
+00:41:27,630 --> 00:41:32,750
+هو طبيعي، ما درسش، ما نجحش، طيب، ما درسش ونجح،
+
+561
+00:41:32,750 --> 00:41:35,590
+برضه ممكن الامتحان إجا سهل، يعني بتصير هنا
+
+562
+00:41:35,590 --> 00:41:37,690
+conditions تانية، ممكن تتحكم في الموضوع، ممكن
+
+563
+00:41:37,690 --> 00:41:43,810
+الامتحان طالع سهل، الطالب أو الطالبة كانوا متذكرين
+
+564
+00:41:43,810 --> 00:41:48,610
+بعض معلومات من المحاضرات نفسها من زمان، بس ليلة
+
+565
+00:41:48,610 --> 00:41:53,300
+امتحان، ما صادفوا أنه ما درسوش كويس، true ممكنة، طيب.
+
+566
+00:41:53,300 --> 00:41:58,200
+true و false، درست كويس لكن ما نجحش، هذه الوحيدة
+
+567
+00:41:58,200 --> 00:42:01,760
+اللي فيها مشكلة، طب أنت درست، طب مدام درست، معناته
+
+568
+00:42:01,760 --> 00:42:04,320
+كان فيه مشكلة في الدراسة من أصلها، يعني معناته مش
+
+569
+00:42:04,320 --> 00:42:07,020
+hard، ما كانتش hard، فهذه الحالة الوحيدة اللي نقدر
+
+570
+00:42:07,020 --> 00:42:14,020
+نقول عنها false، طيب، درس نجح، منطقي، true، منطقية جدا
+
+571
+00:42:14,020 --> 00:42:14,860
+تكون true.
+
+572
+00:42:18,220 --> 00:42:22,280
+for example، بناء على الشكل اللي احنا حاطينه هذا، لو
+
+573
+00:42:22,280 --> 00:42:28,720
+قلنا مثلا one equal to zero، employees pigs can
+
+574
+00:42:28,720 --> 00:42:33,640
+fly، اللي لو قلنا واحد بيساوي صفر، بيضمن إن
+
+575
+00:42:33,640 --> 00:42:37,980
+الخنزير بيعرف يطير، طبعا أنتم هتلاحظوا أن هي ..
+
+576
+00:42:37,980 --> 00:42:41,700
+إيش الكلام اللي مالوش أي علاقة ببعضه؟ هي true، هي
+
+577
+00:42:41,700 --> 00:42:45,240
+true، لأن الـ condition مش حقيقي أصلا، فالنتيجة مش
+
+578
+00:42:45,240 --> 00:42:51,000
+حقيقية، فكجملة logically منطقية، هي كلها غلط في غلط.
+
+579
+00:42:51,000 --> 00:42:54,820
+فمنطق أن البداية غلط، والنهاية غلط، بتاعتها false،
+
+580
+00:42:54,820 --> 00:43:00,280
+false، فهذه بتعبر عن إيش؟ false، false، is it true؟
+
+581
+00:43:00,280 --> 00:43:03,380
+ناخد
+
+582
+00:43:03,380 --> 00:43:08,680
+مجموعة examples، ونشوف هتعرفوا إيه معانا، هي false
+
+583
+00:43:08,680 --> 00:43:13,980
+ولا true، ولا إيش بالظبط، لو قلنا if this lecture
+
+584
+00:43:13,980 --> 00:43:20,040
+ends، إذا المحاضرة انتهت، then the sun will rise
+
+585
+00:43:20,040 --> 00:43:24,420
+tomorrow، طب هي انتهت؟ طب أنا هنا بتكلم معاكم
+
+586
+00:43:24,420 --> 00:43:28,820
+ما انتهتش، فإذا إنها دي false، بداية false، طيب خلينا
+
+587
+00:43:28,820 --> 00:43:29,500
+نرجع شوية.
+
+588
+00:43:33,240 --> 00:43:36,440
+ناخد الجزء بتاعنا هذا، اللي هي false, false, false,
+
+589
+00:43:36,660 --> 00:43:42,040
+true, true, false، الوحيدة كانت اللي فيها مشكلة.
+
+590
+00:43:42,040 --> 00:43:49,880
+خلينا نشوف أن احنا بدأنا بـ false أصلا، صح؟ أنا
+
+591
+00:43:49,880 --> 00:43:53,400
+ما انتهتش المحاضرة، المحاضرة لسه ما انتهتش، باقي لها نص
+
+592
+00:43:53,400 --> 00:43:56,060
+ساعة، زمان، كويس، فإذا أنا بتكلم عن جزء هذا
+
+593
+00:44:01,270 --> 00:44:06,750
+صح؟ طب في الحالتين true، بغض النظر عن مين؟ عن
+
+594
+00:44:06,750 --> 00:44:10,630
+النتيجة، بغض النظر عن إيش النتيجة اللي بتطلع .. عن
+
+595
+00:44:10,630 --> 00:44:13,570
+الـ .. عن الـ Q statement أو الـ Q proposition بتاعتنا
+
+596
+00:44:13,570 --> 00:44:16,810
+هي في الآخر، الـ implication كله على بعضه هيكون true
+
+597
+00:44:16,810 --> 00:44:22,150
+لأنه بدأنا بخطأ، بدنا بـ .. بـ .. بـ .. false، احنا ما
+
+598
+00:44:22,150 --> 00:44:24,670
+انتهى .. ما انتهتش المحاضرة، then the .. the ..
+
+599
+00:44:24,670 --> 00:44:29,810
+the sun will rise tomorrow، okay، ممكن تكون true، بس
+
+600
+00:44:29,810 --> 00:44:35,710
+في النهاية برضه كلها على بعض is true، كويس، if
+
+601
+00:44:35,710 --> 00:44:42,150
+Tuesday is a day of the week، true، تمام، then I am a
+
+602
+00:44:42,150 --> 00:44:47,210
+penguin، a penguin، اللي هو البطريق، false، طب صارت في
+
+603
+00:44:47,210 --> 00:44:52,810
+كلها true false، كلها false، صحيح، كلها صارت إيش؟ false.
+
+604
+00:44:52,810 --> 00:44:58,230
+طيب، if one plus one equal to six، then Obama is a
+
+605
+00:44:58,230 --> 00:45:01,310
+president، طب ما هو فعلا Obama is a president، بس مش
+
+606
+00:45:01,310 --> 00:45:04,110
+عشان هيك، هقول أن هي true، لأن هذه false أصلا، فـ
+
+607
+00:45:04,110 --> 00:45:08,510
+false، حكمت على الموضوع، خلصنا، false، سواء النتيجة
+
+608
+00:45:08,510 --> 00:45:12,490
+كانت false أو true، هو منطقي، منطق الـ implication
+
+609
+00:45:12,490 --> 00:45:15,290
+بتاعنا، الـ implication بتاعنا منطقي، فإذن هذه المفروض
+
+610
+00:45:15,290 --> 00:45:21,470
+أن هي true، طيب، if the moon is made of a green
+
+611
+00:45:21,470 --> 00:45:22,210
+cheese.
+
+612
+00:45:24,600 --> 00:45:28,200
+إذا كان مصنوع .. القمر مصنوع من .. من جبنة خضراء،
+
+613
+00:45:28,200 --> 00:45:32,500
+then I am richer than Bill Gates، عارف
+
+667
+00:49:43,310 --> 00:49:48,050
+implication في employees q معناته أنا غيرتهم مع
+
+668
+00:49:48,050 --> 00:49:54,150
+بعض، عكستهم. خليت النتيجة في الأول والشرط في الثاني.
+
+669
+00:49:54,150 --> 00:49:57,970
+طبعا هتعطي نتائج مختلفة تماما، بس إيش علاقتهم مع
+
+670
+00:49:57,970 --> 00:50:02,570
+بعض؟ هي converse لل implication الأصلي، طبعا أكيد.
+
+671
+00:50:02,570 --> 00:50:06,820
+النتائج هتكون طبعا مختلفة، شيء طبيعي.
+
+672
+00:50:06,820 --> 00:50:12,040
+كويس. أما الـ inverse تبعها، إنه نفسها بس بعملها
+
+673
+00:50:12,040 --> 00:50:17,540
+لمين؟ للـ negation للـ P و للـ negation للـ Q.
+
+674
+00:50:17,540 --> 00:50:21,060
+فبيصير عندنا expression ثاني. طيب، الـ contrapositive
+
+675
+00:50:21,060 --> 00:50:27,300
+بنجمع في بعض. لحظة، هعمل الـ converse مع الـ inverse
+
+676
+00:50:27,300 --> 00:50:31,820
+مع بعض. جِبنا الاتنين، فهي مسارة الـ Q في الأول،
+
+677
+00:50:33,040 --> 00:50:37,400
+وعملنا negation لكل واحدة قبلها. طيب، واحدة من الـ
+
+678
+00:50:37,400 --> 00:50:43,080
+three operators الجديدة هدول، أو الـ three terms
+
+679
+00:50:43,080 --> 00:50:48,360
+هدول فعليا مساوية، أو بتعطيني the same truth table
+
+680
+00:50:48,360 --> 00:50:55,060
+of implication. واحدة منهم هتعطي نفس النتائج لمين؟
+
+681
+00:50:55,060 --> 01:00:00,660
+للـ implication. يا ترى مين منهم؟ تانية
+
+682
+01:00:02,780 --> 01:00:05,640
+الثالثة. منطقة الثالثة. أنتم عاملين inverse مع
+
+683
+01:00:05,640 --> 01:00:09,940
+converse. يعني عكسين، عكس عكسين. العكس في المنطق أنه
+
+684
+01:00:09,940 --> 01:00:13,120
+هتكون هي الأقرب لأنها تكون مساوية في الـ
+
+685
+01:00:13,120 --> 01:00:16,860
+contrapositive. في الغالب هي فعلا، وهذا حقيقة هي
+
+686
+01:00:16,860 --> 01:00:20,080
+اللي هتكون متساوية، أو مساوية للـ implication عشان
+
+687
+01:00:20,080 --> 01:00:23,780
+نثبت الكلام هذا، ممكن نستعمل truth table. نستخدم في
+
+688
+01:00:23,780 --> 01:00:26,040
+الموضوع هذا ونجرب، هل فعلا متساوية أو لا.
+
+689
+01:00:29,200 --> 01:00:35,140
+هي مجموعة الاحتمالات الممكنة. negation Q
+
+690
+01:00:35,140 --> 01:00:40,120
+محتاجينها عشان نحسب الـ contrapositive. negation P
+
+691
+01:00:40,120 --> 01:00:42,980
+محتاجينها عشان نحسب برضه الـ contrapositive. مجرد
+
+692
+01:00:42,980 --> 01:00:49,200
+عكس. يعني خدوا هذا الجزء، عكسوه هنا. راحظوا، تمام؟
+
+693
+01:00:49,200 --> 01:00:56,340
+الجزء الثاني P، عكسوه هنا، وبدأوا يحسبوا الـ
+
+694
+01:00:56,340 --> 01:01:00,660
+implication والـ contrapositive. الـ implication
+
+695
+01:01:00,660 --> 01:01:03,800
+بيحسبها من الـ two columns هدول. الحالة الوحيدة اللي
+
+696
+01:01:03,800 --> 01:01:12,400
+هي false، هي true، و false otherwise. truth table. طيب،
+
+697
+01:01:12,400 --> 01:01:15,800
+الحالة الثانية في الـ contrapositive، بدأت تطلع الـ
+
+698
+01:01:15,800 --> 01:01:18,940
+two columns هدول، وبنفس الترتيب هذا. negation Q في
+
+699
+01:01:18,940 --> 01:01:23,740
+الأول، و negation P في الثانية. برضه الحالة الوحيدة
+
+700
+01:01:23,740 --> 01:01:28,440
+اللي هي true. ففي الـ column هذا
+
+701
+01:01:28,440 --> 01:01:32,160
+مساوي للـ column هذا. فإذا فعلا الـ implication equal
+
+702
+01:01:32,160 --> 01:01:39,900
+to، أو equivalent لـ الـ contrapositive تبعها. طيب،
+
+703
+01:01:39,900 --> 01:01:43,520
+دلّنا على الـ biconditional operator. الـ
+
+704
+01:01:43,520 --> 01:01:46,840
+biconditional operator. هنا بنتكلم عن implication
+
+705
+01:01:46,840 --> 01:01:54,260
+في الاتجاهين. المعنى اللغوي تبعها if and only if. إذا
+
+706
+01:01:54,260 --> 01:01:59,980
+وإذا فقط. طيب كنت إيش بقول؟ بقول: إذا درستوا هتاخدوا
+
+707
+01:01:59,980 --> 01:02:06,520
+معدل جيد، معدل كويس. يعني القصد فيها: إذا ما درستوش
+
+708
+01:02:06,520 --> 01:02:10,440
+سِبته، ماليش علاقة. لكن لما أقول لكم: ديروا بالكم، إذا
+
+709
+01:02:10,440 --> 01:02:14,540
+درستوا، وإذا درستوا فقط، هتاخدوا معدل جيد. معناته إذا
+
+710
+01:02:14,540 --> 01:02:19,050
+ما درستوش، مش هتاخدوا. ما سِبتهش لحالها، هيك بظروفها هي.
+
+711
+01:02:19,050 --> 01:02:21,610
+الفكرة أنه ما نسيبهاش بظروفها. فـ if and only if
+
+712
+01:02:21,610 --> 01:02:28,530
+بتختلف في جزئية الـ false. إذا ما اتحققش، مش هيتحقق
+
+713
+01:02:28,530 --> 01:02:32,970
+النتيجة. انتهى. مش هيتحقق النتيجة. خلينا نشوف if and
+
+714
+01:02:32,970 --> 01:02:37,870
+only if هذه، كيف ممكن نستعملها. لو قلنا: P is Obama
+
+715
+01:02:37,870 --> 01:02:43,230
+wins the 2012 election. Obama فاز في انتخابات 2012
+
+716
+01:02:43,230 --> 01:02:48,560
+اللي كانت تجديدها. Q equal to Obama will be
+
+717
+01:02:48,560 --> 01:02:55,940
+president for all of 2014. قعد طول 2014 وهيكمل
+
+718
+01:02:55,940 --> 01:03:01,520
+إلى 2016. كويس. فإذا هنا لاحظوا: أوباما، مدام نجح في
+
+719
+01:03:01,520 --> 01:03:05,580
+2012، هو أكيد لازم يكون الرئيس في 2014، لأنه لسه ما
+
+720
+01:03:05,580 --> 01:03:08,760
+انتهت الفترة الرئاسية تبعته. ما انتهت الفترة
+
+721
+01:03:08,760 --> 01:03:12,840
+الرئاسية. فـ by logic، لما واحد يقول لي: والله في 2012
+
+722
+01:03:12,840 --> 01:03:17,360
+أوباما فاز في الانتخابات، واحنا هلوجك في 2014 من
+
+723
+01:03:17,360 --> 01:03:20,860
+غير ما أعرف أخباره، ومن غير by logic، آه هي أمريكا
+
+724
+01:03:20,860 --> 01:03:23,320
+جديش الفترة الرئيسية؟ آه، أربع سنين. آه، يعني معناته
+
+725
+01:03:23,320 --> 01:03:26,240
+لسه أوباما. يعني خلاص، ائيك لحاله، وقلتُها مع أن أنا
+
+726
+01:03:26,240 --> 01:03:28,620
+مش عارف أخباره. فأنا أفترض، ولا بعرف. آه، معناته هو هو
+
+727
+01:03:28,620 --> 01:03:33,700
+لسه موجود. آه، صح، هو موجود. كويس. فلما بقول P by
+
+728
+01:03:33,700 --> 01:03:39,760
+conditional Q، كأني بقول: if، و فقط إذا، كسب أوباما
+
+729
+01:03:39,760 --> 01:03:47,720
+الانتصار 2012، أوباما سيكون الرئيس للجميع في 2014.
+
+730
+01:03:52,470 --> 01:03:57,730
+الـ truth table للـ biconditional، زي ما قلنا هي
+
+731
+01:03:57,730 --> 01:04:02,350
+مشابهة تقريبا لمين؟ ل... ال... هي الحقيقة مشابهة
+
+732
+01:04:02,350 --> 01:04:05,610
+لكذا واحدة فيهم، وهنرجع لها لو جيت بكذا شغلة. أول ما
+
+733
+01:04:05,610 --> 01:04:08,890
+هنربطها، هنبدأ نربطها مع الـ... الـ implication.
+
+734
+01:04:08,890 --> 01:04:11,790
+مع الـ implication. لما آجي أربطها مع الـ implication،
+
+735
+01:04:11,790 --> 01:04:15,510
+هي احنا هنا شرطنا الوحيد فيها، أنه لازم الـ
+
+736
+01:04:15,510 --> 01:04:21,110
+condition في الاتجاهين. if and only if. فإذا if a
+
+737
+01:04:21,110 --> 01:04:29,680
+false. Okay, false. طيب، false true. لأ، لأ. هنا كنا
+
+738
+01:04:29,680 --> 01:04:33,220
+سايبينها بظروفها. ممكن يكون متذكر شغلها هنا. قلنا
+
+739
+01:04:33,220 --> 01:04:37,760
+if and only if. إذا ما اتحققش، ما فيش. فإذا فعلا
+
+740
+01:04:37,760 --> 01:04:41,870
+ما اتحققش، ما فيش false. هذه الحالة الوحيدة يمكن أن
+
+741
+01:04:41,870 --> 01:04:44,950
+هناك كانت true في الـ implication. هناك كانت true
+
+742
+01:04:44,950 --> 01:04:50,590
+نتيجة هنا. only if اللي ضفناها. لأ، استفدت إيه؟ الـ
+
+743
+01:04:50,590 --> 01:04:54,190
+error ده. طيب، true و false. احنا من أول متفقين أن هي
+
+744
+01:04:54,190 --> 01:04:58,430
+أصلا false. طيب، true true. اتحقق شرط الـ condition
+
+745
+01:04:58,430 --> 01:05:01,520
+الطبيعي. لازم يتحقق النتيجة. تحقق الـ condition
+
+746
+01:05:01,520 --> 01:05:06,140
+الطبيعي جدا، لازم تتحقق نتيجته. فهذه true. مش مشكلة
+
+747
+01:05:06,140 --> 01:05:10,620
+في هذا الموضوع. الفرق الوحيد كان في الـ row ده. Okay.
+
+748
+01:05:10,620 --> 01:05:15,780
+هذه. هيك ربطناها مع مين؟ مع الـ implication. طيب، نيجي
+
+749
+01:05:15,780 --> 01:05:21,160
+نربطها شوية هيك مع الـ XOR. إيش الفرق بينها وبين الـ
+
+750
+01:05:21,160 --> 01:05:24,960
+XOR؟ إيش
+
+751
+01:05:24,960 --> 01:05:30,990
+الفرق بينها وبين الـ XOR؟ هنا لاحظوا: لأ، عكس، العكس
+
+752
+01:05:30,990 --> 01:05:35,790
+العكس. لحظة، هذه العكس تماما. هنا كانت هنا true وهنا
+
+753
+01:05:35,790 --> 01:05:40,130
+false. صحيح. لأ، هنا بالعكس تماما. وعشان إيه قلت لكم
+
+754
+01:05:40,130 --> 01:05:45,570
+بتجيش. كنا نعمل negation مع XOR، لأن في operator
+
+755
+01:05:45,570 --> 01:05:49,050
+بيعبّر عن الموضوع هذا، اللي هي biconditional. هي فعلا
+
+756
+01:05:49,050 --> 01:05:55,360
+بتعطيكم العكس. العكس لمين؟ للـ X OR، أو الـ opposite of
+
+757
+01:05:55,360 --> 01:06:01,560
+X OR، طبعا. تمام، كويس. فلاحظوا إيش أخذنا إحنا؟ الوجد
+
+758
+01:06:01,560 --> 01:06:07,060
+فعلا؟ أخذنا كذا شغلة. بدأنا مع الـ negation، وهنا
+
+759
+01:06:07,060 --> 01:06:10,080
+بدنا نعمل negation. هاي في عندكم زي كأنه revision
+
+760
+01:06:10,080 --> 01:06:15,640
+لكل الـ operators اللي أخذناهم. negation للـ P، false
+
+761
+01:06:15,640 --> 01:06:18,200
+بتصير true، false بتصير true، true بتصير false، و
+
+762
+01:06:18,200 --> 01:06:22,780
+هكذا. كويس. الـ conjunction اللي أنتم كنتوا عارفينها
+
+763
+01:06:22,780 --> 01:06:26,740
+and. conjunction. الحالة الوحيدة كلّه false باستثناء
+
+764
+01:06:26,740 --> 01:06:33,460
+true true بتعطي true. الـ disjunction، كلّه true
+
+765
+01:06:33,460 --> 01:06:39,100
+باستثناء false false بتعطي false. الـ X OR. X OR
+
+766
+01:06:39,100 --> 01:06:45,940
+يختلفوا true، متشابهين false. كويس.
+
+767
+01:06:47,630 --> 01:06:51,430
+وناخد بالنا دائما نفرّق بينها، خصوصا لما بتكلم عن
+
+768
+01:06:51,430 --> 01:06:56,610
+الـ language. نفرّق بينها وبين الـ OR مهم جدا من خلال
+
+769
+01:06:56,610 --> 01:07:01,870
+الـ context للـ language. من خلال سياق الجمل تعرفوا
+
+770
+01:07:01,870 --> 01:07:05,730
+أنتم المفروض تتعاملوا مع OR، أو ترجموها OR ولا XOR.
+
+771
+01:07:05,730 --> 01:07:09,670
+مهم جدا. كويس. الـ implication، حكينا عن الـ
+
+772
+01:07:09,670 --> 01:07:11,830
+implication. اتكلمنا عن الـ implication، وبعدين
+
+773
+01:07:11,830 --> 01:07:16,250
+اتكلمنا عن الـ biconditional. عن الـ biconditional.
+
+774
+01:07:18,080 --> 01:07:21,740
+الـ notations بتاعتهم... الـ notations بتاعتهم...
+
+775
+01:07:21,740 --> 01:07:27,380
+لاحظوا الـ propositional logic، كيف شكلهم... هدول الـ
+
+776
+01:07:27,380 --> 01:07:30,360
+notations اللي إحنا اتعلمناهم اليوم... أخذناهم
+
+777
+01:07:30,360 --> 01:07:33,880
+اليوم... polynomial اللي أنتم كنتوا تاخدوهم سابقا
+
+778
+01:07:33,880 --> 01:07:38,060
+...كيف كنتوا تكتبوهم سابقا، أو يمكن تكتبوهم في الـ
+
+779
+01:07:38,060 --> 01:07:41,160
+logic design... في الـ logic design... في الـ logic
+
+780
+01:07:41,160 --> 01:07:46,200
+design، بتشتغلوا على هدول... بتعملوهم. الـ hat اللي
+
+781
+01:07:46,200 --> 01:07:48,720
+فوق هذه. فخلاص بعرف الـ... البار عارف أن اللي فوق
+
+782
+01:07:48,720 --> 01:07:51,340
+اللي هنا، بعرف أنه هذه إيش؟ negation، أو اللي هي الـ
+
+783
+01:07:51,340 --> 01:07:56,440
+inverse، أو الـ inverter. كويس. هنا بالشكل هذا، هي كده
+
+784
+01:07:56,440 --> 01:08:00,440
+كأنهم مضروبين، ضرب في بعض. فهي and. plus بيعملوا
+
+785
+01:08:00,440 --> 01:08:04,640
+بينهم plus. فأنتم بتعرفوا أنه OR. الـ X OR هي هي الـ
+
+786
+01:08:04,640 --> 01:08:07,060
+implication، والـ if and only if. ما كنتوش مش هتاخدوهم
+
+787
+01:08:07,060 --> 01:08:10,020
+ما بتاخدوهمش. يعني فعليا كنتوا في الرياضيات هنا
+
+788
+01:08:10,020 --> 01:08:14,740
+بتاخدوهم. كويس. في الـ Java، باستخدام الـ Java، و
+
+789
+01:08:14,740 --> 01:08:18,180
+باستخدام، سواء إن أنتم بتتكلموا عن bit-wise أو word-
+
+790
+01:08:18,180 --> 01:08:23,160
+wise vector، ولا scalar value. بتختلف طبعا أحيانا.
+
+791
+01:08:23,160 --> 01:08:26,080
+فممكن اللي بتبقى، اللي هيبرمج بالـ C أو بالـ Java،
+
+792
+01:08:26,080 --> 01:08:31,160
+هيلاقي أنه برضه مضمونة، موجودة في البرمجة. بتقدروا
+
+793
+01:08:31,160 --> 01:08:33,940
+تبرمجوهم باستخدام أحد الـ symbols هدول، اللي هم هدول
+
+794
+01:08:33,940 --> 01:08:36,580
+الروابط. باستخدامكم... باستخدامها. وهدول الروابط
+
+795
+01:08:36,580 --> 01:08:40,020
+باستخدام، إذا كان بتتكلموا عن الـ bit-wise. كويس. الـ
+
+796
+01:08:40,020 --> 01:08:43,680
+logic gates، هدول اللي كنتوا بتاخدوهم في الـ circuits.
+
+797
+01:08:44,300 --> 01:08:46,880
+وأنتم بتتكلموا عن الـ circuits، كنتوا تعبروا عنهم
+
+798
+01:08:46,880 --> 01:08:50,000
+بالـ symbols اللي موجودة هنا. inverter، كنتوا بتعملوه
+
+799
+01:08:50,000 --> 01:08:57,400
+بالشكل هذا. الـ AND، الـ OR، والـ XOR، والـ XOR، وطبعا من
+
+800
+01:08:57,400 --> 01:08:59,920
+الأشكال دول، كنتوا بتشكلوا حاجات كتير تانية. يعني
+
+801
+01:08:59,920 --> 01:09:04,320
+ممكن على طول الـ... الـ circle هذه تحطوها هنا...
+
+802
+01:09:04,320 --> 01:09:08,320
+تحطوها هنا. فبتجيبوا gates جديدة. كنتوا تجيبوا
+
+803
+01:09:08,320 --> 01:09:11,760
+gates جديدة بالظبط، تصير عكسها. فبتصير بدل OR بتصير
+
+804
+01:09:11,760 --> 01:09:18,140
+NOR. بس بدل أن تصير NAND، وهكذا. تمام.
+
+805
+01:09:18,140 --> 01:09:25,710
+طيب، بكفي هنا. كويس. هيك المرة الجاية، هنبدأ مع جزئية
+
+806
+01:09:25,710 --> 01:09:28,610
+الـ... الـ... الـ... الـ bit، أو الـ bits and bit
+
+807
+01:09:28,610 --> 01:09:33,490
+operations. النظرية بتقول إن إحنا هنتعامل مع الـ zero
+
+808
+01:09:33,490 --> 01:09:36,630
+مرة تانية، على أساس أنه هو false، وهنتعامل مع الـ one
+
+809
+01:09:36,630 --> 01:09:40,250
+على أساس أنه هو true. وبعدين أكتر من slide ضايقين، و
+
+810
+01:09:40,250 --> 01:09:42,450
+بعدين ننتقل على موضوعنا الجاي إن شاء الله تعالى.
+
+811
+01:09:42,450 --> 01:09:46,850
+ابتداء من الأسبوع القادم بإذن الله تعالى. يعطيكم
+
+812
+01:09:46,850 --> 01:09:47,130
+العفو.
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..22c1277e4e32f0b1d8f524b8681c74b8dd59f3c8
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_postprocess.srt
@@ -0,0 +1,3248 @@
+1
+00:00:21,550 --> 00:00:23,590
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,590 --> 00:00:25,850
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبها
+
+3
+00:00:25,850 --> 00:00:29,590
+أجمعين استكمالا لمحاضرتنا الأولى اللى كنا اتكلمنا
+
+4
+00:00:29,590 --> 00:00:32,670
+فيها ك introduction لال discrete ككل discrete
+
+5
+00:00:32,670 --> 00:00:37,510
+mathematics كمصاق كامل واتكلمنا إيش .. في إيش
+
+6
+00:00:37,510 --> 00:00:40,230
+هيفيدنا، إيش هناخد منه، في إيش هيخدمنا، كيف
+
+7
+00:00:40,230 --> 00:00:44,070
+هيخدمكوا في مجال تخصصكم في ال computer engineering
+
+8
+00:00:44,070 --> 00:00:47,510
+اليوم هنبدأ مع أول محاضرات المصاق اللى هي
+
+9
+00:00:47,510 --> 00:00:51,710
+foundations of logic أو introduction to logicهنبدأ
+
+10
+00:00:51,710 --> 00:00:55,290
+بتعريف بسيطة ال mathematical logic is a tool for
+
+11
+00:00:55,290 --> 00:00:57,990
+working with complicated compound statements
+
+12
+00:00:57,990 --> 00:01:02,490
+هنتعامل مع اللي هي logic احنا لو هتحدد شغلنا علاش
+
+13
+00:01:02,490 --> 00:01:04,530
+على ال logic في محاضرتنا اليوم ال mathematical
+
+14
+00:01:04,530 --> 00:01:09,310
+logic هي فعليا نشتغل فيها على مجموعة statements
+
+15
+00:01:09,310 --> 00:01:13,650
+بندمشها مع بعض بحيث انه يصير عندنا complicated
+
+16
+00:01:13,650 --> 00:01:20,600
+compound statements statements مركبة معقدةالكبيرة
+
+17
+00:01:20,600 --> 00:01:22,600
+.. الكبيرة هذه المركبة أو المعقدة من إيش بدها
+
+18
+00:01:22,600 --> 00:01:26,580
+تيجي؟ هتيجي فعليا من مجموعة statements صغيرة في ال
+
+19
+00:01:26,580 --> 00:01:29,800
+language .. في اللغة عادة اللغة بتيجي من إيش؟ شوية
+
+20
+00:01:29,800 --> 00:01:34,280
+حروف بنكون منها كلمات كلمة جنب كلمة بتعطينا معنى
+
+21
+00:01:34,280 --> 00:01:37,580
+المعنى إذا اتكون عندنا معنى إحنا هنا هنستعملها ..
+
+22
+00:01:37,580 --> 00:01:41,120
+هنقول عنها proposition عندنا المعنى هذا خلاص
+
+23
+00:01:41,120 --> 00:01:45,910
+بيعطيني معلومةالمعلومة دي مقدر احكم عنها ك .. ب
+
+24
+00:01:45,910 --> 00:01:50,270
+truth value false or true اتكلمنا كتير عن .. عن
+
+25
+00:01:50,270 --> 00:01:56,310
+قصة false و true المرة اللي فاتت تمام فبيظل عندنا
+
+26
+00:01:56,310 --> 00:02:00,410
+انه كيف نكونهم مع بعض هدول الأجزاء كيف نكونهم مع
+
+27
+00:02:00,410 --> 00:02:04,490
+بعض هناخدهم من خلال مجموعة operators هنتكلم اليوم
+
+28
+00:02:04,490 --> 00:02:08,050
+عنهم ان شاء الله تعالى بس فعليا عشان اتكلم عن ال
+
+29
+00:02:08,050 --> 00:02:10,230
+mathematical logic هي بتتكون من ايش؟ اول حاجة
+
+30
+00:02:10,230 --> 00:02:13,730
+languageبكون ان ال language .. ال language هذا بدي
+
+31
+00:02:13,730 --> 00:02:19,070
+أترجمها لإيش؟ لمجموعة رياضيات .. مجموعة رياضيات عن
+
+32
+00:02:19,070 --> 00:02:22,950
+طريق symbols معينة notations معينة أقدر أعمل prove
+
+33
+00:02:22,950 --> 00:02:27,650
+لها ففعليا محتاج language for expressing them
+
+34
+00:02:27,650 --> 00:02:31,890
+للتعبير عن ال statements بتاعتي بعدين محتاج
+
+35
+00:02:31,890 --> 00:02:33,170
+concise notation
+
+36
+00:02:36,430 --> 00:02:41,530
+علامات مختصرة او symbols او symbols عساس انه نعبر
+
+37
+00:02:41,530 --> 00:02:46,130
+عنها رياضيا مانقدرش .. بدنا نثبت شغلة مكتوبة في
+
+38
+00:02:46,130 --> 00:02:48,650
+one paragraph اقعد كل شوية اقول one paragraph
+
+39
+00:02:48,650 --> 00:02:52,250
+معايا عشان أثبت و هل بيساوي true or false فلأ
+
+40
+00:02:52,250 --> 00:02:58,080
+بنعبر عنه بإيش؟ ب symbol واحدأي شغلة بتصير سهلة
+
+41
+00:02:58,080 --> 00:03:03,800
+أنها P equal to كذا و بتعمل بعدين مع P و Q هدولة
+
+42
+00:03:03,800 --> 00:03:07,380
+لما نثبت و نخلص بنشوف P و Q اللي أثبتناهم بيعبروا
+
+43
+00:03:07,380 --> 00:03:10,050
+عن إيش في ال languageتمام فمحتاجين concise
+
+44
+00:03:10,050 --> 00:03:14,270
+notation for writing them بعدين ال methodology for
+
+45
+00:03:14,270 --> 00:03:18,330
+objectively reasoning about their truth table
+
+46
+00:03:18,330 --> 00:03:24,190
+تبعنا اللي هي ال truth or falsity ففعليا
+
+47
+00:03:24,190 --> 00:03:27,590
+بصير بدى إيش الطريقة اللى هستعملها لإثبات بطريقة
+
+48
+00:03:27,590 --> 00:03:33,030
+منطقية بطريقة معقولة إثبات مدى صحة أو عدم صحة ال
+
+49
+00:03:33,030 --> 00:03:38,130
+statement تبعتيبالطريقة هذه هي الشغل تبع المصحق هي
+
+50
+00:03:38,130 --> 00:03:40,430
+شغل المصحق إيش ال methodology اللى بدنا نستخدمها
+
+51
+00:03:40,430 --> 00:03:46,250
+الحقيقة هذا ال branch كبير ويله علاقة بال formal
+
+52
+00:03:46,250 --> 00:03:51,390
+proofs في ال formal proofs طيب فعليا ال
+
+53
+00:03:51,390 --> 00:03:54,790
+foundations of logic هنتكلم هناخد overview عليها
+
+54
+00:03:54,790 --> 00:03:59,590
+هنتكلم عن ال propositional logic بتفاصيلها شوية
+
+55
+00:03:59,590 --> 00:04:01,990
+شوية هنتكلم عن تفاصيلها بعدين هنقول شوية شوية على
+
+56
+00:04:01,990 --> 00:04:07,570
+ال predicate logicبرضه بتفاصيلها و هنحكي في وقتها
+
+57
+00:04:07,570 --> 00:04:11,230
+عنها اليوم ابصرينا و بنحكي بس عن الجزئية هذه اللي
+
+58
+00:04:11,230 --> 00:04:16,430
+هي جزئية ل proposition logic propositional logic
+
+59
+00:04:16,430 --> 00:04:20,870
+هي فعليا برضه عبارة عن compound statements built
+
+60
+00:04:20,870 --> 00:04:25,210
+from similar statements زي ما قلنا انا بتكلم عن
+
+61
+00:04:25,210 --> 00:04:28,550
+statement كبيرة تعبير كبير بس هو جا من مجموعة
+
+62
+00:04:28,550 --> 00:04:33,010
+تعبير صغيرة طيب كيف ركبناهم التعبير الصغيرة هذه عن
+
+63
+00:04:33,010 --> 00:04:38,290
+طريق operatorsعن طريق روابط الروابط هي شغلنا اليوم
+
+64
+00:04:38,290 --> 00:04:43,630
+اليوم هنتكلم كتير عن جزء الروابط الروابط في ال ..
+
+65
+00:04:43,630 --> 00:04:48,270
+في ال numbers عادة اللي هي الجمع الطرح القسمة لأن
+
+66
+00:04:48,270 --> 00:04:51,790
+هذا بتربطنا رقم مع رقم فبيطلعنا ناتج جديد لما يقول
+
+67
+00:04:51,790 --> 00:04:55,670
+واحد زائد خمسة زائد هذه علامة الزائد هذه هي
+
+68
+00:04:55,670 --> 00:05:00,170
+operatoroperator لل numbers طيب ال operators اللي
+
+69
+00:05:00,170 --> 00:05:03,750
+احنا هنشتغل عليها لأ هتكون علاقة بال logic فهده
+
+70
+00:05:03,750 --> 00:05:08,630
+Boolean connectives أو Boolean algebra بيشتغل في
+
+71
+00:05:08,630 --> 00:05:11,130
+الجزئية هده و هده اللي هنشتغل عليه ان شاء الله
+
+72
+00:05:11,130 --> 00:05:13,490
+تعالى و هتكون مرة عليكوا قبل هيكي بس يمكن زي ما
+
+73
+00:05:13,490 --> 00:05:17,490
+قلنا ناخدها بتسميات جديدة بس انتوا كلها عارفينها
+
+74
+00:05:17,490 --> 00:05:20,490
+ال and و ال or و ال x or هنرجع كلها اليوم انقيتها
+
+75
+00:05:20,490 --> 00:05:23,410
+هنرجع كلها اليوم انقيتها الكلام ده الحقيقة بيفيدنا
+
+76
+00:05:23,410 --> 00:05:26,310
+في كتير مجالات اهمها يمكن اللي هوفي ال digital
+
+77
+00:05:26,310 --> 00:05:29,310
+electronics circuits و الأمور اللي زي هذه يعني
+
+78
+00:05:29,310 --> 00:05:32,970
+انتوا لو في السنة الجاية المفروض ان شاء الله
+
+79
+00:05:32,970 --> 00:05:36,390
+بتاخدوا ال digital electronics هتاخدوا فيها كتير
+
+80
+00:05:36,390 --> 00:05:39,450
+عن ال logic gates هتتكلموا كتير كتير كتير فيها في
+
+81
+00:05:39,450 --> 00:05:42,830
+ال logic gates okay في ال conditions الحقيقة في
+
+82
+00:05:42,830 --> 00:05:45,610
+التعبير عن ال conditions في البرنامج لما تقولوا if
+
+83
+00:05:45,610 --> 00:05:48,910
+then جزيتي ال if then هد اللي بتعملوها في البرنامج
+
+84
+00:05:48,910 --> 00:05:53,500
+أعتقد انكسا ما لاحتوش تاخدوا برمجةمالاحقتوش يمكن
+
+85
+00:05:53,500 --> 00:05:56,900
+تاخدوا برمجة كتير بس عادة في ال flow chart بتحطوا
+
+86
+00:05:56,900 --> 00:06:01,700
+حاجة بالشكل هذا زي condition نفترض مثلا x أكبر من
+
+87
+00:06:01,700 --> 00:06:06,520
+خمسة فانتوا حاطين condition لحظه و بتحطوله yes or
+
+88
+00:06:06,520 --> 00:06:11,260
+no بناء عليه إيش بتكون تعملوا ال action سواء اتحقق
+
+89
+00:06:11,260 --> 00:06:14,200
+أو ماتحققش اتحقق أو ماتحققش يعني انتوا بتتكلم عن
+
+90
+00:06:14,200 --> 00:06:20,410
+true or falseفي condition وهدا هل هو true or false
+
+91
+00:06:20,410 --> 00:06:27,190
+بناء عليه بدنا نعمل action قادم تمام الجزئية هذه
+
+92
+00:06:27,190 --> 00:06:30,710
+مستخدمة في ال conditions زى ما قلنا في ال .. ال
+
+93
+00:06:30,710 --> 00:06:34,290
+conditions in program في ال queries to databases
+
+94
+00:06:34,290 --> 00:06:38,610
+في عادة في البحث في ال database لما بتعملوا بحث
+
+95
+00:06:38,610 --> 00:06:41,770
+على ال database نفترض ال database على الجامعة
+
+96
+00:06:41,770 --> 00:06:45,470
+بتكتبوا رقمكوا الجامعي و بتعملوا enter فهو بفحص
+
+97
+00:06:46,230 --> 00:06:51,790
+الارقام كلها امتى بتصير فيه quality ال equal ان
+
+98
+00:06:51,790 --> 00:06:55,230
+الرقم تبعكو equal ل folder موجود عنده بفتح الكل
+
+99
+00:06:55,230 --> 00:06:59,230
+folder فبتشوفوا صفحتكم ايش مسجلين ايش مش مسجلين
+
+100
+00:06:59,230 --> 00:07:02,130
+علاماتكم ايش الموثيقات اللي خلصتوها ايش اللي ما
+
+101
+00:07:02,130 --> 00:07:04,530
+خلصتوهاش ايش اللي نازل ايش اللي مش نازل الأمور دي
+
+102
+00:07:04,530 --> 00:07:09,590
+كلها بتنعمل برضه عن طريق logic gates او logic
+
+103
+00:07:09,590 --> 00:07:12,960
+conceptsالـ search engines نفس الكلام لأنكم
+
+104
+00:07:12,960 --> 00:07:18,880
+بتقارنه بتعملوا comparison فيه شروط اتحققت بجيب
+
+105
+00:07:18,880 --> 00:07:21,460
+الصفحة اللي اتحققت فيها الشروط الشروط ده بناء على
+
+106
+00:07:21,460 --> 00:07:23,940
+ايش؟ على keywords انتوا بتكتبوها على ال search
+
+107
+00:07:23,940 --> 00:07:27,900
+engine فبناء عليه اذا اتحققت داخل الصفحة ال web
+
+108
+00:07:27,900 --> 00:07:32,080
+page بجيب ال qn1 ال web page فبتلاقوا مجموعة من ال
+
+109
+00:07:32,080 --> 00:07:36,130
+web pages موجودة عندكم okayنبدأ بأول جزئية اللي هي
+
+110
+00:07:36,130 --> 00:07:39,810
+ال proposition ال proposition الإعلان أو أنا
+
+111
+00:07:39,810 --> 00:07:43,930
+بحطلكوا جملة إعلامية declarative sentence جملة
+
+112
+00:07:43,930 --> 00:07:49,310
+إعلامية لحالة معينة، لإشي معين، بنقدر نعرف إن هي
+
+113
+00:07:49,310 --> 00:07:54,010
+فقرةأصغر فقرة ممكنة في اللغة بحيث ان هي بتعطيكوا
+
+114
+00:07:54,010 --> 00:07:58,510
+معنى و المعنى هذا بقدر احكم عليه true or false
+
+115
+00:07:58,510 --> 00:08:03,490
+يعني ايه ال truth truth value كويس عادة بنستعمل
+
+116
+00:08:03,490 --> 00:08:09,310
+lowercase او small letter بشكل هذا غالبا بنستعمل
+
+117
+00:08:09,310 --> 00:08:13,010
+ال P Q و R في الغالب هم الدارجين في الكتاب اللي
+
+118
+00:08:13,010 --> 00:08:16,210
+هنستعمله في الكتاب اللي هتستعمله هذه اللي هي بتعبر
+
+119
+00:08:16,210 --> 00:08:19,530
+على ال statements على مجموعة ال statementswith
+
+120
+00:08:19,530 --> 00:08:24,810
+definite meaning بمعنى محدد ومعنى محدد يعني انا
+
+121
+00:08:24,810 --> 00:08:27,830
+بقدر احكم عليه هيا نكررها كذا مرة بقدر احكم عليه
+
+122
+00:08:27,830 --> 00:08:32,610
+قد ايش القيمة تبعته كويس having a truth value
+
+123
+00:08:32,610 --> 00:08:37,230
+that's either true or false إله قيمة هذه أو هذه
+
+124
+00:08:37,230 --> 00:08:39,870
+طبعا لا يمكن يكونوا اتنين في نفس الوجد مش ماجولة
+
+125
+00:08:39,870 --> 00:08:43,590
+طبعا أعطيكوا جملة true و false في نفس اللحظة لا
+
+126
+00:08:43,590 --> 00:08:48,290
+يمكن هذه بطلت proposition أو neitherلا هي هيك ولا
+
+127
+00:08:48,290 --> 00:08:52,350
+هيك، خائش، لا هي صح ولا هي غلط، متصبتش، متنفعش أو
+
+128
+00:08:52,350 --> 00:08:55,470
+somewhere in between لما أقول somewhere in between
+
+129
+00:08:55,470 --> 00:08:57,810
+دخلتنا في حاجة جديدة مش مش مجالنا هذه اللي هي
+
+130
+00:08:57,810 --> 00:09:01,550
+probability دخلنا في جزية .. احتمال والله اربعين
+
+131
+00:09:01,550 --> 00:09:06,530
+في المية true وستين في المية false in between لأ
+
+132
+00:09:06,530 --> 00:09:09,690
+هذه دخلنا في إشي تاني فهذه ماتحطهاش في proposition
+
+133
+00:09:09,690 --> 00:09:12,490
+اللي هناخده اليوم أو اللي هنتكلم عنه اليوم هنتكلم
+
+134
+00:09:12,490 --> 00:09:17,300
+اليوم بأبسط صوره بأبسط صورة من الصورة تبعته طيبمن
+
+135
+00:09:17,300 --> 00:09:19,400
+خلال الكلمتين اللي قلناها خلّيني أخد شوية examples
+
+136
+00:09:19,400 --> 00:09:23,140
+و نشوف إيش يعني proposition إيش يعني proposition
+
+137
+00:09:23,140 --> 00:09:29,200
+فلو قلنا it's raining false okay إلها قيمة ممكن لو
+
+138
+00:09:29,200 --> 00:09:31,240
+الدنيا بتشتي بتصير true بس في النهاية هي جملة و
+
+139
+00:09:31,240 --> 00:09:34,920
+إلها قيمة و كام لخلاص يعطتني معنى فإذا حسب ال
+
+140
+00:09:34,920 --> 00:09:38,300
+situation بقدر أقول إن هي يا true يا false هذه
+
+141
+00:09:38,300 --> 00:09:44,040
+proposition القدس is the capital of Palestine
+
+142
+00:09:44,040 --> 00:09:50,100
+الجدس عاصمة فلسطينtrue true فعلا فإذا هذه برضه
+
+143
+00:09:50,100 --> 00:09:53,840
+proposition فإذا هذه proposition okay one plus two
+
+144
+00:09:53,840 --> 00:09:57,280
+equal to three أقولكوا one plus two equal to five
+
+145
+00:09:57,280 --> 00:10:03,420
+false ولكن proposition لحظة proposition القيمة
+
+146
+00:10:03,420 --> 00:10:06,740
+تبعته false okay مش مشكلة بس في النهاية
+
+147
+00:10:06,740 --> 00:10:12,620
+proposition okay في المقابل في حالات نعطيكوا شوية
+
+148
+00:10:12,620 --> 00:10:15,660
+حالات هي are not propositions
+
+149
+00:10:18,320 --> 00:10:22,410
+Who's there؟question طب إيش أقوله هذا؟ أقوله صح
+
+150
+00:10:22,410 --> 00:10:25,670
+ولا غلط؟ مش عارف يعني عن إيش بيحكي ال questions
+
+151
+00:10:25,670 --> 00:10:28,350
+بتنحطش مع ال proposition فهذه مش proposition
+
+152
+00:10:28,350 --> 00:10:30,530
+أحيانًا و أنتوا بتعملوا chatting أحيانًا بتعملوا
+
+153
+00:10:30,530 --> 00:10:33,750
+هههههه لالا لالا للا حاجات يعني بتنكتبها لغاية
+
+154
+00:10:33,750 --> 00:10:36,670
+صارت كتير عبارة في ال chatting و في ال forums و في
+
+155
+00:10:36,670 --> 00:10:40,190
+الحاجات هذه كويس زي لالا لالا هذه meaningless
+
+156
+00:10:40,190 --> 00:10:45,310
+مالهاش معنى مالهاش معنى لا يمكن أبدا تفرضوها أن هي
+
+157
+00:10:45,310 --> 00:10:48,850
+proposition تشتغلوا عليها هذه بدون معنى طيب just
+
+158
+00:10:48,850 --> 00:10:54,500
+do itأوامر ..أوامر برضه مالهاش معايا ..يمكن بديش
+
+159
+00:10:54,500 --> 00:10:57,620
+أنفذ الأوامر ..يمكن بديش ..بيديش أنفذه ..بالنسبالي
+
+160
+00:10:57,620 --> 00:11:01,880
+false واحد تاني بده ينفذه ..بس في الآخر الأوامر مش
+
+161
+00:11:01,880 --> 00:11:05,520
+محسوبة ك proposition ال .. ال .. ال .. ال .. ال
+
+162
+00:11:05,520 --> 00:11:09,600
+fake أو اللي هي الجمال الغامضة yeah I sorta don't
+
+163
+00:11:09,600 --> 00:11:13,940
+know whatever ..طب ماشي فهمنا منها ..مافهمناش أشي
+
+164
+00:11:13,940 --> 00:11:17,280
+.. الجملة بدا مغامضة و مش فاهم منها حاجة على طول
+
+165
+00:11:18,220 --> 00:11:21,940
+هذه not proposition بقدرش أقول عنها proposition أو
+
+166
+00:11:21,940 --> 00:11:25,780
+جملة ناقصة بمعنى أنا بقدرش أقول هذه true or false
+
+167
+00:11:25,780 --> 00:11:31,820
+زي one plus two stop طيب كمللي انا one plus two مش
+
+168
+00:11:31,820 --> 00:11:34,380
+عارف أقولك صح ولا غلط اعطيني يا بتقولي تلاتة
+
+169
+00:11:34,380 --> 00:11:37,480
+فبقولك true و بتصير proposition يا بتقولي الف و
+
+170
+00:11:37,480 --> 00:11:41,840
+بقولك false و proposition بس في النهاية لازم يكون
+
+171
+00:11:41,840 --> 00:11:45,140
+لها قيمة انا لا جادة بحكم عليها true ولا false
+
+172
+00:11:45,140 --> 00:11:52,120
+فإذا هذه not propositionOkay ال operators اتفجناها
+
+173
+00:11:52,120 --> 00:11:54,820
+لوجة انه إيش معنى proposition هي عبارة عن جملة
+
+174
+00:11:54,820 --> 00:11:59,140
+إلها معنى و بقدر أعطيها قيمة نقدر نعطيها قيمة أو
+
+175
+00:11:59,140 --> 00:12:03,240
+يعني أحد القيمتين اللي هي true أو false ال
+
+176
+00:12:03,240 --> 00:12:05,780
+operators زي ما قلنا في ال numbers لما بتكلم عن
+
+177
+00:12:05,780 --> 00:12:07,860
+numbers ال operators بالنسبالنا اللي هي زي
+
+178
+00:12:09,000 --> 00:12:14,000
+positive, plus, minus جمع, طريح, قسمة, ضرب كل هذه
+
+179
+00:12:14,000 --> 00:12:19,420
+تربط لنا two numbers مع بعض عشان يعطوني نتيجة
+
+180
+00:12:19,420 --> 00:12:28,600
+تالتة نتيجة إضافية ممكن تكون unary
+
+181
+00:12:28,600 --> 00:12:34,120
+أو عبارة عن أحدية الoperand بمعنى محتاج معامل واحد
+
+182
+00:12:34,120 --> 00:12:39,130
+معها زي ال minusمحتاجة رقم واحد بس مش محتاجة اكتر
+
+183
+00:12:39,130 --> 00:12:42,870
+من هيك رقم واحد يكفي فبعرف ان هذا بالنسبالها عكست
+
+184
+00:12:42,870 --> 00:12:47,130
+الرقم عكست الرقم حوالين ال zero يعني صار بدل ان هو
+
+185
+00:12:47,130 --> 00:12:51,350
+اعلى من zero بتلاتة لأقل من zero بتلاتة كويس او
+
+186
+00:12:51,350 --> 00:12:56,850
+تكون binary فهذه بتاخد two operands او two معاملين
+
+187
+00:12:56,850 --> 00:13:01,670
+يعني زي الدرب الجمع القسمة الطرح كل هدولة بياخدوا
+
+188
+00:13:01,670 --> 00:13:08,280
+ارقامثلاثية أو بياخدوا يعني binary operators في
+
+189
+00:13:08,280 --> 00:13:11,560
+الحالة اللي عندنا كويس في عندنا برضه ال
+
+190
+00:13:11,560 --> 00:13:15,980
+propositions او propositional نفس الفكرة زي ما
+
+191
+00:13:15,980 --> 00:13:18,060
+اتكلمنا عن ال numbers بقدر اتكلم عن ال
+
+192
+00:13:18,060 --> 00:13:21,200
+propositions ولكن في ال propositions بنشتغل على ال
+
+193
+00:13:21,200 --> 00:13:24,700
+boolean operators اللي برضه انتوا ممكن مرت عليكم
+
+194
+00:13:24,700 --> 00:13:28,560
+سابقا ال and و ال or و ال nor كل هدولة هم هم هم
+
+195
+00:13:28,560 --> 00:13:32,900
+الروابط بتاعتنااللي مقابلين لمين للجمع والطرح
+
+196
+00:13:32,900 --> 00:13:37,980
+والضرب والقسمة كويس بدل الأرقام فبنصير نتعامل مع
+
+197
+00:13:37,980 --> 00:13:42,780
+ال propositions بدل الأرقام إيش ال propositions
+
+198
+00:13:42,780 --> 00:13:47,100
+اللي حقيقة هنتعامل معها هنتعامل مع مجموعة من ال
+
+199
+00:13:47,100 --> 00:13:49,940
+operators أول operator اللي بتتعامل مع ال
+
+200
+00:13:49,940 --> 00:13:52,600
+propositions ال negation operator اللي أنتوا كنتوا
+
+201
+00:13:52,600 --> 00:13:57,580
+بتسميها ال not أو ال inverter كانت inverter فهذه
+
+202
+00:13:57,580 --> 00:14:02,660
+العكسزي ال minus في ال numbers ال conjunction
+
+203
+00:14:02,660 --> 00:14:07,560
+operator انتوا كنتوا تعرفوها and ال conjunction او
+
+204
+00:14:07,560 --> 00:14:12,680
+الدمج او الدمج اذا صار الدمج بالنسبالي true ماصارش
+
+205
+00:14:12,680 --> 00:14:17,320
+دمج فالس فهي معناها فإذا لازم يكون كل part لحاله
+
+206
+00:14:17,320 --> 00:14:20,900
+true و true يندمجوا مع بعض فإذا صارت ال true مدمجة
+
+207
+00:14:20,900 --> 00:14:24,880
+من هنا و من هنا دمج اتنتج بيصير trueهنتكلم عنها
+
+208
+00:14:24,880 --> 00:14:29,120
+بالتفصيل disjunction operator هذه مقابلة كانت لل
+
+209
+00:14:29,120 --> 00:14:33,380
+or انتوا كنتوا عارفينها ب or فبرضه binary و
+
+210
+00:14:33,380 --> 00:14:36,480
+العلامة بتاعتها هتكون بهذا الشكل عاملة زي السبعة
+
+211
+00:14:36,480 --> 00:14:42,600
+هندي ال and سبعة تمانية هندي بهذا الشكل كويس ال
+
+212
+00:14:42,600 --> 00:14:48,420
+exclusive or او ال x or برضه binary circle مع plus
+
+213
+00:14:48,420 --> 00:14:52,380
+العلامة بتاعتها او ال symbol اللي هنستعملها ايا
+
+214
+00:14:52,720 --> 00:14:56,080
+الحاجات الإضافية اللى هتكون مرت عليكم ويمكن تكون
+
+215
+00:14:56,080 --> 00:15:00,560
+جديدة ال implication operator أول مرة هتتعاملوا
+
+216
+00:15:00,560 --> 00:15:03,980
+معها إضافة للمجموعة ال operators اللى موجودة
+
+217
+00:15:03,980 --> 00:15:09,080
+implies اللى هي يعني كأنه a implies b لو صار a
+
+218
+00:15:09,080 --> 00:15:12,940
+بيضمن لنا حدوث b هذه كتير هتستعملوها انتوا لازم
+
+219
+00:15:12,940 --> 00:15:16,000
+تفهموها كويس لأن هذه بتستخدموها في ال if then
+
+220
+00:15:16,850 --> 00:15:19,970
+هتستخدم نفس المعنى في ال if then في البرمجة في
+
+221
+00:15:19,970 --> 00:15:26,770
+البرمجة كويس وهي ال symbol بتاعتها if then if a
+
+222
+00:15:26,770 --> 00:15:31,710
+then b كويس ال condition اللي بعده او ال operator
+
+223
+00:15:31,710 --> 00:15:34,770
+اللي بعده اللي هي ال by conditional operator if
+
+224
+00:15:34,770 --> 00:15:41,500
+and only if مش if then if and only ifإذا وإذا فقط،
+
+225
+00:15:41,500 --> 00:15:44,280
+تمام؟ هنشوف الفرق بين التنتين، في فرق كبير بين
+
+226
+00:15:44,280 --> 00:15:48,020
+التنتين فمدام if and only if فهي ماخدة implication
+
+227
+00:15:48,020 --> 00:15:56,100
+في الاتجاهين من a to b و من b to a، كويس نبدأ ..
+
+228
+00:15:56,100 --> 00:16:00,260
+إيش هقولكن؟ نبدأ نراجع لإن احنا فعلا هنراجع شوية
+
+229
+00:16:00,260 --> 00:16:02,860
+ال operators هدولة ال negation، بداية نبدأ بال
+
+230
+00:16:02,860 --> 00:16:06,740
+negation أو ال not فببساطة جدا ماخدينها جابل هيك
+
+231
+00:16:06,740 --> 00:16:11,910
+لو قلنا P equal to I have brownhere لما بدي أعملها
+
+232
+00:16:11,910 --> 00:16:17,770
+negation لما أقول negation P بتصير I don't و
+
+233
+00:16:17,770 --> 00:16:22,710
+بنتكمل كل اللي عملته عملية نفي عملية نفي اللي هي
+
+234
+00:16:22,710 --> 00:16:26,310
+ال negation بتاعتنا طيب ال truth table بتبعها
+
+235
+00:16:26,310 --> 00:16:33,050
+بالشكل اللي احنا شايفينه T F F T بهذا الشكل كويس
+
+236
+00:16:33,050 --> 00:16:37,650
+ال conjunctionأو اللي انتوا زي ما قولنا .. انتوا
+
+237
+00:16:37,650 --> 00:16:40,810
+حافظينها طول عمركم اللي بتقولوها ال and أو ال و
+
+238
+00:16:40,810 --> 00:16:44,730
+احنا هنسميها conjunction اللي هي الاتحاد او توحي
+
+239
+00:16:44,730 --> 00:16:48,850
+او دمج .. دمج فهذه بتشتغل على two propositions
+
+240
+00:16:48,850 --> 00:16:55,170
+بالنسبالنا و هيكون العلمة بتاعتها زي زي ما قولنا
+
+241
+00:16:55,170 --> 00:16:59,780
+التمانية الهنديجاية من ال A كأنها من ال A فهي
+
+242
+00:16:59,780 --> 00:17:02,740
+العلامة أو ال symbol اللي احنا هنستعمله فلو قولنا
+
+243
+00:17:02,740 --> 00:17:09,620
+if P equal to I will have chicken for lunch زي انا
+
+244
+00:17:09,620 --> 00:17:15,140
+والله عندي فعلا دجاج للغدا و Q equal to I will
+
+245
+00:17:15,140 --> 00:17:21,320
+have cheese for dinner و جبنة للعشاء لو قولنا P
+
+246
+00:17:21,320 --> 00:17:25,960
+conjunction Q إيش بتصير؟I will .. التنتين احنا
+
+247
+00:17:25,960 --> 00:17:29,300
+هنربطهم بإيش؟ ب end I will have chicken for lunch
+
+248
+00:17:29,300 --> 00:17:33,860
+and ال end هذه هي ال conjunction هذه and I will
+
+249
+00:17:33,860 --> 00:17:37,180
+have .. فاحنا نزلناهم زي ما هم .. ربطناهم ربط عمل
+
+250
+00:17:37,180 --> 00:17:40,580
+أيه اتربط؟ فصارت إيش؟ statement واحدة صارت
+
+251
+00:17:40,580 --> 00:17:44,820
+sentence واحدة صارت جملة واحدة خلاص بنكتبها ورا
+
+252
+00:17:44,820 --> 00:17:46,760
+بعض و هو دي فعلا حتى ال language اللي كنتي تعمل
+
+253
+00:17:46,760 --> 00:17:50,340
+ماحدش بكتب جملة جملة بنكتب جملة و بنربطهم في بعض
+
+254
+00:17:50,340 --> 00:17:54,560
+عشان نعمل paragraph عشان نعمل paragraphمجموعة
+
+255
+00:17:54,560 --> 00:17:57,420
+paragraphs بتطلعولي chapter مجموعة chapters
+
+256
+00:17:57,420 --> 00:18:01,440
+بتطلعولي كتاب و هكذا فاحنا بنكون من حاجات بسيطة
+
+257
+00:18:01,440 --> 00:18:05,400
+بنكون حاجات complicated و نفس الكلام هنا عملية
+
+258
+00:18:05,400 --> 00:18:12,720
+الربط باستخدام ال conjunction ال truth table لل
+
+259
+00:18:12,720 --> 00:18:16,580
+conjunction مرة علينة جبل هيكة الحالة الوحيدة اللي
+
+260
+00:18:16,580 --> 00:18:21,320
+ممكن يكون فيها true ان كل proposition
+
+261
+00:18:24,000 --> 00:18:29,240
+فfor all propositions are true then the result is
+
+262
+00:18:29,240 --> 00:18:33,020
+true لازم كلهم يكونوا true عشان فعلا أضمن أنه الكل
+
+263
+00:18:33,020 --> 00:18:36,560
+true لو عندنا two propositions two propositions
+
+264
+00:18:36,560 --> 00:18:39,840
+فعليا هيكون أكمروه عندكم أو أكم احتمال ممكن هيكون
+
+265
+00:18:39,840 --> 00:18:44,500
+أربعة جاي من مين؟ من two to the power n two to the
+
+266
+00:18:44,500 --> 00:18:47,440
+power n لأن أنا بتكلم عن binary ال binary معناته
+
+267
+00:18:47,440 --> 00:18:49,480
+ثنائي شو الثنائي عندنا؟
+
+268
+00:18:52,650 --> 00:18:57,310
+احتمالة ال output انتوا يا true يا false فإذا
+
+269
+00:18:57,310 --> 00:19:01,310
+ثنائي وعشان هيك دايما نشتغل على الاتنين على
+
+270
+00:19:01,310 --> 00:19:04,170
+الاتنين لإنه ماعنديش يا .. ايش ال .. ال .. ال ..
+
+271
+00:19:04,170 --> 00:19:07,910
+ال symbols اللي بدي أعوضها هنا false or true؟ في
+
+272
+00:19:07,910 --> 00:19:11,190
+إشي تاني غيرهم؟ لأ فانا بتكلم عن binary فعلا عشان
+
+273
+00:19:11,190 --> 00:19:14,710
+هيك فيه انا اتنين بيمثلولي يديش عدد الروز اللي
+
+274
+00:19:14,710 --> 00:19:18,750
+ممكن أحتاجهم في العملية تبعتي طيب also negation
+
+275
+00:19:18,750 --> 00:19:23,210
+andconjunction operations together are sufficient
+
+276
+00:19:23,210 --> 00:19:28,970
+to express any poly and truth table حقيقة ال
+
+277
+00:19:28,970 --> 00:19:33,050
+negation مع ال and أو ال conjunction كافي أنها
+
+278
+00:19:33,050 --> 00:19:37,510
+تعبر عن كمية كبيرة جدا إذا ما كانش معظم الحقيقة ال
+
+279
+00:19:37,510 --> 00:19:41,550
+poly and truth table أو معظم ال operators اللي
+
+280
+00:19:41,550 --> 00:19:46,210
+ممكن نستخدمها ال operators اللي ممكن نستعملها طيب
+
+281
+00:19:46,210 --> 00:19:50,170
+ال disjunctionالـ disjunction اللي هي ال or كنتوا
+
+282
+00:19:50,170 --> 00:19:57,730
+تستعملوها مكانها or جاية ممكن تكون هذه من عملية
+
+283
+00:19:57,730 --> 00:20:01,130
+الفأس
+
+284
+00:20:01,130 --> 00:20:05,950
+او ال ax تبعتنا فالسؤال اللي كان هحدث ليش لأنه أي
+
+285
+00:20:05,950 --> 00:20:11,890
+واحدة من ال proposition true النتيجة true فإذا
+
+286
+00:20:11,890 --> 00:20:14,690
+يكفي أن تكون واحدة صار عندنا زودنا احتمالات ل true
+
+287
+00:20:14,690 --> 00:20:18,670
+في النتيجةبنزود هيك عدد احتمالات ل true ليش؟ لأن
+
+288
+00:20:18,670 --> 00:20:22,370
+أي واحدة كافية أنها تكون .. أنها تخلي الناتج true
+
+289
+00:20:22,370 --> 00:20:25,930
+هنشوف طبعا ال 3 ثامل تبعها لو قولنا مثلا for
+
+290
+00:20:25,930 --> 00:20:32,130
+example P equal to my car has a bad engine سيارة
+
+291
+00:20:32,130 --> 00:20:35,670
+ماتورها .. يبدو أن ماتورها مثلا مش .. مش كويس في
+
+292
+00:20:35,670 --> 00:20:41,490
+أطلان أو .. أو خربان او Q my car has a bad
+
+293
+00:20:41,490 --> 00:20:45,960
+carburetorال carburetor برضه ممكن يكون هو العطلان
+
+294
+00:20:45,960 --> 00:20:49,580
+فانا ممكن اروح لميكانيكى والسيارة معايا ايش مالها
+
+295
+00:20:49,580 --> 00:20:52,440
+يقول الله مش عارف شوف يمكن يكون ال motor او
+
+296
+00:20:52,440 --> 00:20:58,140
+carburetor او لحظة ويمكن يطلع الاتنين مع بعض يمكن
+
+297
+00:20:58,140 --> 00:21:00,980
+لما يفحص يلاجئ انه الاتنين مع بعض فهنا صارت ال او
+
+298
+00:21:00,980 --> 00:21:06,260
+بتشمل ال both cases او ال both propositions
+
+299
+00:21:08,580 --> 00:21:16,300
+لو قلنا بـ disjunction q either اما
+
+300
+00:21:16,300 --> 00:21:21,560
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+301
+00:21:21,560 --> 00:21:21,640
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+302
+00:21:21,640 --> 00:21:21,760
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+303
+00:21:21,760 --> 00:21:22,600
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+304
+00:21:22,600 --> 00:21:23,300
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+305
+00:21:23,300 --> 00:21:23,320
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+306
+00:21:23,320 --> 00:21:33,400
+اما اما
+
+307
+00:21:33,400 --> 00:21:38,720
+املازم تنقل two propositions أو خلّيني أقول all
+
+308
+00:21:38,720 --> 00:21:42,700
+propositions are true عشان أقول إن النتيجة true
+
+309
+00:21:42,700 --> 00:21:48,620
+هنا لأ just one true is enough just one
+
+310
+00:21:48,620 --> 00:21:56,900
+proposition is true enough to get true result okay
+
+311
+00:21:56,900 --> 00:22:02,600
+ففي الحالة هذه بنقدر نقول إن or both are أيضا true
+
+312
+00:22:03,180 --> 00:22:06,940
+يعني ممكن يكون الشغلتين برضه .. التنتين true زي ما
+
+313
+00:22:06,940 --> 00:22:11,340
+قلنا ممكن تكون ال motor و ال carburetor ييجي يفحص
+
+314
+00:22:11,340 --> 00:22:15,240
+و يلاقي انه الاتنين خربانين مش بس واحد هذه أحيانا
+
+315
+00:22:15,240 --> 00:22:20,440
+ال operator هذه بنسميها inclusive or in غير ال
+
+316
+00:22:20,440 --> 00:22:24,040
+exclusive or اللي هي ال xor in معناته ايش ال in
+
+317
+00:22:24,040 --> 00:22:27,660
+هذه؟ في حاجة included الشيء ال included اللي فعليا
+
+318
+00:22:27,660 --> 00:22:33,190
+احنا بنتكلم عنها path casePoth case هنا included
+
+319
+00:22:33,190 --> 00:22:38,530
+مع ال truth table ك true فعشان هي ممكن نسميها
+
+320
+00:22:38,530 --> 00:22:45,210
+inclusive or عساس ان هي تضمن معانا ال both cases
+
+321
+00:22:45,210 --> 00:22:49,700
+الأخيرة في ال X or هذه الوحيدة اللي بتختلفهتلاقوها
+
+322
+00:22:49,700 --> 00:22:52,660
+نفس ال or ولكن الجزء الأخير اللي هيختلف و
+
+323
+00:22:52,660 --> 00:22:57,420
+هنتكلمologically عن ال difference between ال or و
+
+324
+00:22:57,420 --> 00:23:01,120
+ال x or لما نيجي ناخد ال x or طيب نفس الكلام ممكن
+
+325
+00:23:01,120 --> 00:23:06,480
+negation مع ال disjunction في جملة واحدة ممكن
+
+326
+00:23:06,480 --> 00:23:11,480
+يكونوا مع بعض عادي universally ممكن يكونوا متعرف
+
+327
+00:23:11,480 --> 00:23:16,460
+عليها او متوقع انها ممكن يكونوا مع بعض طيب صرنا
+
+328
+00:23:16,460 --> 00:23:21,300
+ماخدين هنا كذاoperator طب هذا هيترحلنا سؤال انه طب
+
+329
+00:23:21,300 --> 00:23:24,020
+ما ممكن يكون في عندنا nested propositional
+
+330
+00:23:24,020 --> 00:23:27,420
+expressions nested اللي هو متشابك اللي لاجي أكتر
+
+331
+00:23:27,420 --> 00:23:32,060
+من operator طب لمين الأولوية ال priority لمين ال
+
+332
+00:23:32,060 --> 00:23:34,660
+priority الحقيقة عادة ان احنا و احنا بنشتغل لأنه
+
+333
+00:23:34,660 --> 00:23:37,680
+طو اتكلمنا انه اول شغل عندنا بدنا language
+
+334
+00:23:37,680 --> 00:23:40,760
+expression فال language هي اللي بتحكمنا ال
+
+335
+00:23:40,760 --> 00:23:42,660
+language هي اللي بتحكمنا عشان يكونوا بتكتبوا في ال
+
+336
+00:23:42,660 --> 00:23:45,560
+language تبعتكم لازم تاخدوا بالكم ان الرابط الرابط
+
+337
+00:23:45,560 --> 00:23:50,100
+أهمها الكومةالكمهة دي وين بتحطوها بتغير المعنى
+
+338
+00:23:50,100 --> 00:23:53,060
+بتغير المعنى بتخليني أنا كمان لما بدي أجي أترجمها
+
+339
+00:23:53,060 --> 00:23:58,320
+لرياضيات بتغير كل الشغل معايا ناخد example نوضح
+
+340
+00:23:58,320 --> 00:24:03,900
+فيه الرؤية الصورة I just saw my old friend, and
+
+341
+00:24:03,900 --> 00:24:10,060
+either his ground or I have shrank أنا شفت أزمير
+
+342
+00:24:10,060 --> 00:24:16,210
+القديم أو الصديق القديمو كأنه يا اما هو far زيادة
+
+343
+00:24:16,210 --> 00:24:19,190
+عن اللزوم كبر زيادة عن اللزوم او انا اتقلصت او
+
+344
+00:24:19,190 --> 00:24:25,870
+ضعفت شرانك اللي هو اتقلص او انا ضعفت شكلي هذه
+
+345
+00:24:25,870 --> 00:24:29,470
+الجملة طيب لما نيجي نعبر عنها باستخدام ال
+
+346
+00:24:29,470 --> 00:24:35,930
+propositions هنقول ان هذه proposition لحالها okay
+
+347
+00:24:35,930 --> 00:24:44,330
+هعطيها F التانية هنا his groundproposition طيب I
+
+348
+00:24:44,330 --> 00:24:47,290
+have shrunk proposition حاطيها ال S و هنا حاطيها
+
+349
+00:24:47,290 --> 00:24:54,190
+ال G هتصير ايش؟ F and افتح عقواس اه ليش فتحنا
+
+350
+00:24:54,190 --> 00:25:00,390
+العقواس هنا هنشوفه G disjunction S لإنه في كومة
+
+351
+00:25:00,390 --> 00:25:05,590
+كومة هذه خلتني أعرف إن الجزء هذا إشي و الجزء هذا
+
+352
+00:25:05,590 --> 00:25:10,240
+إشي تانيالكومة دي لو اتغير مكانها هتغير طريقة
+
+353
+00:25:10,240 --> 00:25:15,080
+الترجمة تبعتي لو اتغير مكانها طبيعي كل شي هيتغير
+
+354
+00:25:15,080 --> 00:25:18,720
+عندنا طيب خلينا ناخد الشكل اللي موجود عندنا هنا
+
+355
+00:25:18,720 --> 00:25:25,120
+كومة و في end معناه to end either خلاص عرفت انه
+
+356
+00:25:25,120 --> 00:25:29,740
+إيش فيه فيه or يعني ال or وين ماكانها عشان أحدد
+
+357
+00:25:29,740 --> 00:25:31,620
+اللي جابلها proposition و اللي بعتها proposition
+
+358
+00:25:31,620 --> 00:25:37,730
+تانيهي ال or فاللي قبلها هيه هذا proposition واللي
+
+359
+00:25:37,730 --> 00:25:41,370
+بعدها proposition تاني وفيه هي disjunction between
+
+360
+00:25:41,370 --> 00:25:48,050
+them طيب لو كتبناها بهذا الشكل حقيقة هذه something
+
+361
+00:25:48,670 --> 00:25:53,030
+meaning تاني مختلف تماما هنا بيعطيكوا معنى مختلف
+
+362
+00:25:53,030 --> 00:25:57,310
+تماما عن المعنى الحقيقي للجملة زي ما هي مكتوبة
+
+363
+00:25:57,310 --> 00:26:01,410
+قدامنا لما بتكتب بهذا الشكل المعنى بيصير كأنه أنا
+
+364
+00:26:01,410 --> 00:26:09,190
+شوفت صاحبي و هو كبر أو نمى خلاص فإذا انا حكمت عليه
+
+365
+00:26:09,190 --> 00:26:12,270
+ان هي true لازم يكون نمى طب خلينا نشوف الفرق بين
+
+366
+00:26:12,270 --> 00:26:14,270
+التنتين اللي هي فيه فرق شاسع بين التنتين هذه
+
+367
+00:26:14,270 --> 00:26:20,700
+معناها عشان كل الجملة هنا تكون trueاما هذه true او
+
+368
+00:26:20,700 --> 00:26:27,480
+هذه كلها true صحيح؟ طيب في الحالة هذه اذا او ممكن
+
+369
+00:26:27,480 --> 00:26:31,460
+انا اتنتين هدولة يكونوا false و اكتفي ان هذه true
+
+370
+00:26:31,460 --> 00:26:36,240
+وخلاص و اقول ان انا ماشوفتش صاحبي من اصله طب لأ
+
+371
+00:26:36,240 --> 00:26:40,100
+انا شوفت صاحبي المعنى اتغير انا شوفت صاحبي كيف
+
+372
+00:26:40,100 --> 00:26:46,240
+ماشوفت صاحبي لحظة هذه كلها عشان تكون true انتوا
+
+373
+00:26:46,240 --> 00:26:50,150
+هنا بتتكلموا عن disjunctionيكفي ان واحدة منهم تكون
+
+374
+00:26:50,150 --> 00:26:54,050
+true طب ممكن تكون هذه ال true اكون انا فعلا يمكن
+
+375
+00:26:54,050 --> 00:26:57,110
+سافرت او اشي او حاجة مع المعبر و مع السفر و مع
+
+376
+00:26:57,110 --> 00:27:01,890
+الهدى الواحد ضعف وزنه شوية خف وزنه اشي صار اشي مرض
+
+377
+00:27:01,890 --> 00:27:06,430
+حاسس حاله هيك هزيل شوية ممكن مش عارف يعني بتصير
+
+378
+00:27:06,430 --> 00:27:09,890
+true فتلاقي ان هو هذه خلاص بطل الهبط بمعنى ان لو
+
+379
+00:27:09,890 --> 00:27:16,480
+انا ماشوفتش طب كيف عرفت ان هو he is groundفلاحظوا
+
+380
+00:27:16,480 --> 00:27:20,140
+أن المعنى اتغير تماما غير التانية هناك التانية
+
+381
+00:27:20,140 --> 00:27:24,560
+هناك إيش مالها and
+
+382
+00:27:24,560 --> 00:27:28,360
+أو conjunction conjunction عشان كلها تكون true
+
+383
+00:27:28,360 --> 00:27:33,700
+لازم الجزء هذا true و هذا true الزمن صح الزمن لازم
+
+384
+00:27:33,700 --> 00:27:37,080
+تكون هذا true و هذا true طيب مدام الزمن هذا true
+
+385
+00:27:37,080 --> 00:27:44,520
+خلاص فإذا أنا شفت صاحبي خلاص true طيب هنا عشان
+
+386
+00:27:44,520 --> 00:27:49,150
+تكون هذه trueواحدة منهم كافية أنه ممكن فعلا يا إما
+
+387
+00:27:49,150 --> 00:27:55,990
+هو كبر هيك مرة واحدة يعني إشي حاجة أو أنا أضعفت
+
+388
+00:27:55,990 --> 00:28:01,910
+لأي سبب كان فصارت المعنى بالشكل هذا ينطبق تماما مع
+
+389
+00:28:01,910 --> 00:28:05,450
+الجملة اللي أنا فهمتها فانطبق تماما مع الجملة اللي
+
+390
+00:28:05,450 --> 00:28:10,750
+فهمناها غير إيش الجملة التانية غير الجملة التانية
+
+391
+00:28:10,750 --> 00:28:11,890
+تمام
+
+392
+00:28:14,960 --> 00:28:18,800
+اللي أصعب طبعا كنتوا كتبوا بالشكل هذا بدون أقواص و
+
+393
+00:28:18,800 --> 00:28:22,140
+بدون priority لأي حاجة خلاص conjunction
+
+394
+00:28:22,140 --> 00:28:25,620
+conjunction كويس اللي كتبناهم لأ نفعش لإنه هيك زي
+
+395
+00:28:25,620 --> 00:28:31,120
+بالظبط كنتوا كتبوا كتابة بدون أي كومة بدون أي نقاط
+
+396
+00:28:31,120 --> 00:28:36,340
+بدون أي روابط بدون أي شيء اكتبوا خلاص ابتسألوا
+
+397
+00:28:36,340 --> 00:28:40,000
+السؤال بدون علامة استفهام ابنعمل الجملة ملحومين
+
+398
+00:28:40,000 --> 00:28:43,760
+ببعض طب تعالوا اقرأوا بعدها انتوا مش هتفهم الشي
+
+399
+00:28:43,760 --> 00:28:46,210
+اللي كنتوا كاتبينهلو غيبتولكوا شهر زمان و شهرتوا و
+
+400
+00:28:46,210 --> 00:28:49,710
+كتبتوا .. قرأتوا اللي كتبتوا مش هتفهموا انتوا إيه
+
+401
+00:28:49,710 --> 00:28:54,250
+.. إيش إيش كنتوا بتكتبوا فبتصير ambiguous words
+
+402
+00:28:54,250 --> 00:28:57,610
+بالنسبالك أو ambiguous proposition غامضة، غير
+
+403
+00:28:57,610 --> 00:29:02,740
+مفهومة، غير واضحةطيب عادة ال priority في ال .. إذا
+
+404
+00:29:02,740 --> 00:29:06,160
+كان صار بالشكل هذا أنها عادة بتكون لمين؟ في الغالب
+
+405
+00:29:06,160 --> 00:29:09,680
+ل ال negation ال negation لها ال priority عن مين؟
+
+406
+00:29:09,680 --> 00:29:12,120
+عن ال and و ال or أو ال conjunction و ال
+
+407
+00:29:12,120 --> 00:29:14,740
+disjunction .. disjunction و ال conjunction
+
+408
+00:29:14,740 --> 00:29:18,100
+فالتنتين هذول كيف بدي أعرف ال priority بتاعة واحدة
+
+409
+00:29:18,100 --> 00:29:22,040
+عن التانية من صياق الجملة؟ من الجملة نفسها؟ و كيف
+
+410
+00:29:22,040 --> 00:29:25,400
+أنا فهمت الجملة؟ عشان أعرف أعبر عنها بطريقة صحية؟
+
+411
+00:29:25,400 --> 00:29:28,330
+لأهذه المفروض جابل هذه وهذه جابل هذه وين الأقواص
+
+412
+00:29:28,330 --> 00:29:31,770
+اللي نحط بالظبط بس احنا راوية ان نتكلم عن ايهاش ال
+
+413
+00:29:31,770 --> 00:29:35,570
+negation ال negation اللي لها priority عن ال ال
+
+414
+00:29:35,570 --> 00:29:39,330
+other operators فلو قولنا بالشكل هذا okay مقبولة
+
+415
+00:29:39,330 --> 00:29:43,050
+هذا بالنسبالنا مقبولة انه بدون أقواص انا فاهم ان
+
+416
+00:29:43,050 --> 00:29:48,050
+ال negation لها أولوية فهي كأنه بالظبط بالشكل هذا
+
+417
+00:29:48,050 --> 00:29:51,090
+لا
+
+418
+00:29:51,090 --> 00:29:57,140
+يمكن تكون هيكلأن الأولوية لمن؟ بالظبط الأولوية ل
+
+419
+00:29:57,140 --> 00:30:01,640
+indication طيب أعتقد برضه إحنا كان في عندنا
+
+420
+00:30:01,640 --> 00:30:03,780
+الأولوية حتى في الأرقام يعني أنتوا لو كنتوا
+
+421
+00:30:03,780 --> 00:30:13,760
+بتكتبوا في برنامج معين أو إشي معين لو نفترض x ضرب
+
+422
+00:30:13,760 --> 00:30:16,700
+y plus z
+
+423
+00:30:19,380 --> 00:30:22,160
+هي فيه priority الحقيقة في البرامج تضارب له
+
+424
+00:30:22,160 --> 00:30:26,420
+priority تضاربه القسمة عن الجامعه والطرحه صحيح
+
+425
+00:30:26,420 --> 00:30:29,920
+فنفس الكلام هنا بالنسبة لان نيجاشن بس إلها
+
+426
+00:30:29,920 --> 00:30:35,960
+priority عن ال conjunction و ال disjunction طيب
+
+427
+00:30:35,960 --> 00:30:39,780
+بناء على الكلام هذا خلينا نشوف شوية جمل و نترجمها
+
+428
+00:30:39,780 --> 00:30:44,520
+مع بعض و نشوف كيف ممكن نعبر عنها خلينا نقول انه
+
+429
+00:30:44,520 --> 00:30:51,630
+let Pit rained last night شتية الليلة الماضية أو
+
+430
+00:30:51,630 --> 00:30:58,130
+يعني صار في شتة الليلة الماضية the sprinklers came
+
+431
+00:30:58,130 --> 00:31:01,530
+on last night sprinklers اللي هي الرشاشات الميه
+
+432
+00:31:01,530 --> 00:31:03,510
+اللي بتكون مزروعة في الأرض هذه محتوطة في الأرض
+
+433
+00:31:03,510 --> 00:31:08,650
+وبترش ميه فخليني أقول إن هي إجت الليلة الماضية
+
+434
+00:31:08,650 --> 00:31:13,950
+برضه ر equal to the lawn was wet this morning
+
+435
+00:31:13,950 --> 00:31:19,050
+العشباليوم الصبح كان مبلول، كويس، هي في عندنا
+
+436
+00:31:19,050 --> 00:31:23,550
+three .. three proposition بدنا نعمل translation
+
+437
+00:31:23,550 --> 00:31:27,890
+لمين؟ لمجموعة symbols بالشكل اللي احنا شايفينه،
+
+438
+00:31:27,890 --> 00:31:33,850
+negation فيه، بدنا
+
+439
+00:31:33,850 --> 00:31:38,630
+نعكس هذهdidn't didn't بالظبط ليش؟ لأن مافيش عندنا
+
+440
+00:31:38,630 --> 00:31:42,150
+هنا الفعل المساعد محتاجين فعل مساعد نعمل فيه عملية
+
+441
+00:31:42,150 --> 00:31:48,310
+النفع فهنا هنضيف بس didn't rain last night okay
+
+442
+00:31:48,310 --> 00:31:53,830
+التانية are conjunction negation بيه ال negation
+
+443
+00:31:53,830 --> 00:31:57,810
+بيه هي موجودة فهيها مافيش عندنا مشكلة فيها and
+
+444
+00:31:57,810 --> 00:32:03,840
+بنحط قدامها and بتظل are نزلوا areوانت هينا منها،
+
+445
+00:32:03,840 --> 00:32:09,340
+مدام مافيش اي negation مافيش أيش مغيره، فاللون was
+
+446
+00:32:09,340 --> 00:32:15,880
+with this morning and it didn't rain last night،
+
+447
+00:32:15,880 --> 00:32:19,320
+طيب، الأخيرة احنا ما .. مااتكلمناش لسه على
+
+448
+00:32:19,320 --> 00:32:24,870
+الأخيرة، negation areأه لحظة negation are هي ال
+
+449
+00:32:24,870 --> 00:32:28,290
+was موجودة فإذا الفعل المساعد موجود اعمله not بس
+
+450
+00:32:28,290 --> 00:32:32,430
+في الآخر و خلصناه كويسة هذا ال negation تبعتنا بس
+
+451
+00:32:32,430 --> 00:32:36,710
+خدوا بالك ال operator اللي عندنا are يعني بدنا
+
+452
+00:32:36,710 --> 00:32:43,690
+نبدأ بإيش either تمام فبتفضطه either في الحالة
+
+453
+00:32:43,690 --> 00:32:51,770
+اللي عندنا هنا في الصوت بقطع بدنا نحط are تمام
+
+454
+00:32:54,090 --> 00:32:58,770
+ال XOR ال operator التالتة الرابعة ال operator
+
+455
+00:32:58,770 --> 00:33:03,070
+الرابعة هي ال XOR operator هذه binary exclusive OR
+
+456
+00:33:03,070 --> 00:33:06,250
+operator اتكلمنا عنها برضه combines two
+
+457
+00:33:06,250 --> 00:33:10,610
+propositions بالنسبالنا عشان تعطينا logical او
+
+458
+00:33:10,610 --> 00:33:16,190
+logic XOR او X junction او X junction for example
+
+459
+00:33:16,190 --> 00:33:22,580
+في I will earn an A in this course ان شاء اللهأنا
+
+460
+00:33:22,580 --> 00:33:28,480
+هجيب A في ال course هذا okay proposition Q I will
+
+461
+00:33:28,480 --> 00:33:33,760
+drop this course لا قدر الله كويس فهي عندنا two
+
+462
+00:33:33,760 --> 00:33:41,160
+propositions لما أجي أقول P أو P X or Q هذه منطقيا
+
+463
+00:33:41,160 --> 00:33:43,900
+ان هي تكون X or لأنه لايمكن التنين يجوا مع بعض
+
+464
+00:33:43,900 --> 00:33:50,440
+فإذا true true مش منطقيةإن الإتنين يكونوا true مش
+
+465
+00:33:50,440 --> 00:33:54,240
+منطقية فهنا الأنسب والأفضل لجملتين بالشكل هذا إن
+
+466
+00:33:54,240 --> 00:33:58,900
+أنا أستعمل x or I will either earn an A for this
+
+467
+00:33:58,900 --> 00:34:07,030
+course or I will drop it but not bothطبيعي كيف بدى
+
+468
+00:34:07,030 --> 00:34:10,050
+.. يعني انا كيف رصبت و كيف جبت ايه في نفس الوقت
+
+469
+00:34:10,050 --> 00:34:14,010
+بتجيش فإذا هدى by logic أحيانا انتوا بدكوا حسب
+
+470
+00:34:14,010 --> 00:34:18,310
+فهمكوا لل .. للجملة as a language بدكوا تفهموا إيش
+
+471
+00:34:18,310 --> 00:34:21,690
+لازم تستعملوا إيش بدكوا تستعملوا هل في احتمال أنه
+
+472
+00:34:21,690 --> 00:34:26,990
+والله ممكن ناخد ال .. ال both أنه ال .. يعني ال
+
+473
+00:34:26,990 --> 00:34:32,930
+both are true ممكن فإذا إذا ممكن orاللي هي
+
+474
+00:34:32,930 --> 00:34:37,410
+disjunction إذا مش ممكن ال X junction أو ال X or
+
+475
+00:34:37,410 --> 00:34:40,710
+ال
+
+476
+00:34:40,710 --> 00:34:44,250
+truth table تبعها هو نفس ال or ال truth table نفس
+
+477
+00:34:44,250 --> 00:34:50,370
+ال or باختلاف من ال both are true هذه هتكون false
+
+478
+00:34:50,370 --> 00:35:01,020
+كويسة X بدل N لو ال E X هذيفإذا أنا بتكلم عن مين؟
+
+479
+00:35:01,020 --> 00:35:03,700
+عن ال or العادية ال disjunction العادية ال
+
+480
+00:35:03,700 --> 00:35:06,980
+disjunction اللي احنا اتكلمنا عنها ولكن هنا x فإذا
+
+481
+00:35:06,980 --> 00:35:15,560
+executes possibility that both p and q are true
+
+482
+00:35:15,560 --> 00:35:22,000
+نجاش مع ال x or بيجوش مع بعض ليش؟ لأنه في
+
+483
+00:35:22,000 --> 00:35:25,970
+expression بعبر عن الموضوع هذا، هناخده لاحقافي
+
+484
+00:35:25,970 --> 00:35:28,890
+operator خاصة بالجزئية فيها دي لا يمكن ييجوا مع
+
+485
+00:35:28,890 --> 00:35:33,670
+بعض التنتين هدولة في جملة مع بعض أو ورا بعض يعني
+
+486
+00:35:33,670 --> 00:35:41,050
+مباشرة okay for example نوضح ال or و ال xor or و
+
+487
+00:35:41,050 --> 00:35:44,430
+xor لو أخدنا مثلا في ال English طبعا معتمدة تماما
+
+488
+00:35:44,430 --> 00:35:47,230
+على ال English انتوا كيف فاهمين اللغة انتوا كيف
+
+489
+00:35:47,230 --> 00:35:50,770
+فاهمين اللغة بتاعتكم عشان ترجموها لمجموعة symbols
+
+490
+00:35:51,750 --> 00:35:59,750
+لو قلنا وسام is a singer or وسام is a writer هذه
+
+491
+00:35:59,750 --> 00:36:03,910
+المفروض or ولا x or؟ or لأنه ممكن يكون الأثنين
+
+492
+00:36:03,910 --> 00:36:07,510
+ممكن يكون بيغني و بيكتب في نفس الوجد فليكن ممكن
+
+493
+00:36:07,510 --> 00:36:13,430
+يكون فعلا بيغني و بيكتب في نفس الوجد الجملة
+
+494
+00:36:13,430 --> 00:36:18,410
+التانية وسام is a man or وسام is a woman لأن كلمة
+
+495
+00:36:18,410 --> 00:36:22,980
+وسام ممكن تحتمل صح؟يعني الاسم ممكن يحتمل فانا لو
+
+496
+00:36:22,980 --> 00:36:27,980
+كنت قرأته وسام حد مثلا بعتلي email وبيقولي والله
+
+497
+00:36:27,980 --> 00:36:31,240
+انا بتسجل المصاق بس مش عارف كيف ادخل على ال model
+
+498
+00:36:31,240 --> 00:36:36,340
+وسام طب ممكن يكون male او female طب هذي man ولا و
+
+499
+00:36:36,340 --> 00:36:40,160
+man ممكن ففي الحالة هذي okay ممكن نكتبها الجملة بس
+
+500
+00:36:40,160 --> 00:36:44,200
+مقدرش اقول انها or يعني لما أجي أترجمها فهذه لازم
+
+501
+00:36:44,200 --> 00:36:48,800
+تكون x or لازم تكون x or تمام
+
+502
+00:36:52,070 --> 00:36:55,930
+Okay الجزء اللي بعده هو ال implication هذا الجديد
+
+503
+00:36:55,930 --> 00:36:59,270
+.. جديد يمكن شوية مفاهيم عنكم شوية، كويس ال
+
+504
+00:36:59,270 --> 00:37:01,930
+implication .. implication مفيدة جدا في ال if then
+
+505
+00:37:01,930 --> 00:37:05,150
+في البرمجة و أنتم بتتكلموا عن برمجة مفيدة
+
+506
+00:37:05,150 --> 00:37:09,710
+الأهميتها لما تيجوا تتكلموا في البرنامج تبعكم if
+
+507
+00:37:09,710 --> 00:37:14,570
+then بمعنى إنه إذا تحقق ال condition الشرط حقق
+
+508
+00:37:14,570 --> 00:37:20,430
+للنتيجةتمام او if انتوا عادة بتكتبوها نكتب انها
+
+509
+00:37:20,430 --> 00:37:25,130
+كود صغير لو قولنا if x أكبر نفترض مثلا من five
+
+510
+00:37:25,130 --> 00:37:31,070
+نحطله هنا statement معينة او خلينا نحط احنا من هنا
+
+511
+00:37:31,070 --> 00:37:40,250
+اي statement خلينا نقول print فرضا
+
+512
+00:37:40,250 --> 00:37:41,710
+طيب else
+
+513
+00:37:44,850 --> 00:37:53,910
+نفترض brand and خلينا نقول حاجة بهذا الشكل طيب
+
+514
+00:37:53,910 --> 00:38:01,290
+فإذا أنا صرت مرتبط بمين بالشرط إذا تحقق الشرط حقق
+
+515
+00:38:01,290 --> 00:38:07,290
+ليه النتيجة مظبوط إذا تحقق الشرط حقق ليه النتيجةهي
+
+516
+00:38:07,290 --> 00:38:09,250
+المفهوم الأساس اللى هناخده من ال implication
+
+517
+00:38:09,250 --> 00:38:15,930
+ماتحققش else إيش ال condition اللى هنعمله؟ كويس
+
+518
+00:38:15,930 --> 00:38:22,730
+خلينا ما ال example اللى هتكون عندنا هنا ف if P is
+
+519
+00:38:22,730 --> 00:38:28,810
+true then Q is true but if P is not true then Q
+
+520
+00:38:28,810 --> 00:38:34,130
+could be either true or false بمعنىOkay انا ..
+
+521
+00:38:34,130 --> 00:38:37,290
+يعني ربطه ب condition معين بس لو مااتحققش انا
+
+522
+00:38:37,290 --> 00:38:41,710
+ماليش علاقة فيه انا ماليش علاقة فيه بصير انا ماليش
+
+523
+00:38:41,710 --> 00:38:46,670
+دعوة زي واحد بيقول لابنه مثلا والله انا لو انجحت
+
+524
+00:38:46,670 --> 00:38:51,650
+هشريلك بسكاليت تمام؟ طيب مانجحش ماهو ممكن يكون
+
+525
+00:38:51,650 --> 00:38:54,990
+حتاني اشتر على البسكاليت انا ماليش علاقة فيك بس
+
+526
+00:38:54,990 --> 00:38:58,490
+الشرط اذا والله is it true انجحت ال condition
+
+527
+00:38:58,490 --> 00:39:02,110
+اتحققالنتيجة لازم تتحقق معناته انا حسب وعدي اللي
+
+528
+00:39:02,110 --> 00:39:05,910
+اتجبلك طيب ماتحققش انا بس اللي ماليش دعوة بس انت
+
+529
+00:39:05,910 --> 00:39:09,130
+جبت من برا انا ماليش علاقة فإذا ممكن false و ممكن
+
+530
+00:39:09,130 --> 00:39:13,550
+true لحظة ببساطة هاي .. هاي معنى ال implication
+
+531
+00:39:13,550 --> 00:39:18,510
+انه إذا اتحقق شرط بيضمنلي الشرطت يعني necessary
+
+532
+00:39:18,510 --> 00:39:23,730
+ضرورية ضرورية تحقق الشرط عشان تصير النتيجة ولكن
+
+533
+00:39:23,730 --> 00:39:26,370
+ممكن تصير النتيجة بدون الشرط هذه ال necessary
+
+534
+00:39:26,370 --> 00:39:30,090
+condition بنسميها necessary conditionفى فرق بين
+
+535
+00:39:30,090 --> 00:39:32,430
+necessary condition و sufficient condition فاحنا
+
+536
+00:39:32,430 --> 00:39:35,110
+هنا متكلم عن جزئية necessary condition شرط ضرورى
+
+537
+00:39:35,110 --> 00:39:40,650
+ولكن مش ملزم لحظة مش ملزم كتير خلينى نشوف example
+
+538
+00:39:40,650 --> 00:39:47,490
+عليها let P equal to you study hard ان انت درستي
+
+539
+00:39:47,490 --> 00:39:52,870
+كويس درستي بصورة جيدة Q equal to you will get a
+
+540
+00:39:52,870 --> 00:40:00,860
+good grade تمام لما اقول Pimplies q كأني بقول if
+
+541
+00:40:00,860 --> 00:40:05,420
+you study hard then you will get a good grade طيب
+
+542
+00:40:05,420 --> 00:40:10,160
+else يعني لو أنا مادرستش كويس it could go either
+
+543
+00:40:10,160 --> 00:40:15,060
+way ممكن ينجح يكون والله لسه متذكرين شوية حاجات من
+
+544
+00:40:15,060 --> 00:40:18,300
+اللي جالها الدكتور في وقت المحاضرة قبل شهر زمان قد
+
+545
+00:40:18,300 --> 00:40:21,580
+يكون يعني لفت الامتحان مادرستناش كويس ولكن صدفت
+
+546
+00:40:21,580 --> 00:40:25,660
+أنه الامتحان إجا معظم من حاجات أنا لسه متذكرها بمش
+
+547
+00:40:25,660 --> 00:40:33,600
+الحال بسالاصل ان مدام ذكرت اذا ذكرت hard بصورة
+
+548
+00:40:33,600 --> 00:40:37,320
+قوية بصورة جيدة كويس و فاهم صح الاصل انه ايش يصير
+
+549
+00:40:37,320 --> 00:40:43,700
+انه نتيجة تتحقق اللي هي get a good grade تمام
+
+550
+00:40:43,700 --> 00:40:48,940
+فبصير عندنا هنا ال truth table تبعنا الحالة
+
+551
+00:40:48,940 --> 00:40:50,980
+الوحيدة اللي ممكن تكون false و هنشرحها لو جيت
+
+552
+00:40:50,980 --> 00:40:57,330
+واحدة واحدة اللي هي TF اتحقق ال conditionبس
+
+553
+00:40:57,330 --> 00:41:01,350
+ماصارتش النتيجة طب ليش؟ مانحققت ال condition ليش
+
+554
+00:41:01,350 --> 00:41:03,910
+ماحصلناش عن نتيجة؟ هذه الحالة الوحيدة ال false
+
+555
+00:41:03,910 --> 00:41:06,530
+اللي أصلا غير منطقية الأصل أنها تكون فعلا false
+
+556
+00:41:06,530 --> 00:41:13,590
+الولد نجح طب ليش ماجبتلهوش البسكليت؟ صح ماهي منطقي
+
+557
+00:41:13,590 --> 00:41:16,930
+معناته حيفوق عليا و هعملنا جثة لأنه فعلا false
+
+558
+00:41:16,930 --> 00:41:22,010
+الوضع خطأ الأصل أنه هذه الحالة الوحيدة اللي تكون
+
+559
+00:41:22,010 --> 00:41:27,630
+فيها falseأما مااتحققش الشرط ماحصلناش عن نتيجة، ما
+
+560
+00:41:27,630 --> 00:41:32,750
+هو طبيعي، مادرستش، مانجحتش طيب، مادرستش و انجحت،
+
+561
+00:41:32,750 --> 00:41:35,590
+برضه ممكن الامتحان إجا سهل، يعني بتصير هنا
+
+562
+00:41:35,590 --> 00:41:37,690
+conditions تانية، ممكن تتحكم في الموضوع، ممكن
+
+563
+00:41:37,690 --> 00:41:43,810
+الامتحان طالع سهل، الطالب أو الطالبة كانوا متذكرين
+
+564
+00:41:43,810 --> 00:41:48,610
+بعض معلومات من المحاضرات نفسها من زمان، بس ليلة
+
+565
+00:41:48,610 --> 00:41:53,300
+امتحان ماصادفتوا انه مادرسوش كويس، true ممكنةطيب
+
+566
+00:41:53,300 --> 00:41:58,200
+true و false درسي كويس لكن ما نجحش هذه الوحيدة
+
+567
+00:41:58,200 --> 00:42:01,760
+اللي فيها مشكلة طب أنت درست طب مدام درست معناته
+
+568
+00:42:01,760 --> 00:42:04,320
+كان فيه مشكلة في الدراسة من أصله يعني معناته مش
+
+569
+00:42:04,320 --> 00:42:07,020
+hard ماكنتش hard فهذه الحالة الوحيدة اللي نقدر
+
+570
+00:42:07,020 --> 00:42:14,020
+نقول عنها false طيب درس نجح منطقي true منطقية جدا
+
+571
+00:42:14,020 --> 00:42:14,860
+تكون true
+
+572
+00:42:18,220 --> 00:42:22,280
+for example بناء على الشكل اللي احنا حاطينه هذا لو
+
+573
+00:42:22,280 --> 00:42:28,720
+قولنا مثلا one equal to zero employees pigs can
+
+574
+00:42:28,720 --> 00:42:33,640
+fly اللي لو قولنا واحد بيساوي صفر بيضمن لإن
+
+575
+00:42:33,640 --> 00:42:37,980
+الخنزير بتعرف يطير طبعا انتوا هتلاحظوا ان هي ..
+
+576
+00:42:37,980 --> 00:42:41,700
+ايش الكلام اللي مالوش أي علاقة ببعضه؟ هي trueهي
+
+577
+00:42:41,700 --> 00:42:45,240
+true لأن ال condition مش حقيقي أصلا فالنتيجة مش
+
+578
+00:42:45,240 --> 00:42:51,000
+حقيقية فكجملة logically منطقية هي كلها غلط في غلط
+
+579
+00:42:51,000 --> 00:42:54,820
+فمنطق أن البداية غلط و النهاية غلط بتاعتها false
+
+580
+00:42:54,820 --> 00:43:00,280
+false فهذه بتعبر عن إيش false false is it true
+
+581
+00:43:00,280 --> 00:43:03,380
+ناخد
+
+582
+00:43:03,380 --> 00:43:08,680
+مجموعة examples و نشوف هتعرفوا إيهمعانا هى false
+
+583
+00:43:08,680 --> 00:43:13,980
+ولا true ولا اش بالظبط لو قلنا if this lecture
+
+584
+00:43:13,980 --> 00:43:20,040
+ends اذا المحاضرة انتهت then the sun will rise
+
+585
+00:43:20,040 --> 00:43:24,420
+tomorrow طب هى انتهت؟ طب أنا هنا بتكلم معاكم
+
+586
+00:43:24,420 --> 00:43:28,820
+ماانتهتش فإذا انها دى false بدية false طيب خلينا
+
+587
+00:43:28,820 --> 00:43:29,500
+نرجع شوية
+
+588
+00:43:33,240 --> 00:43:36,440
+ناخد الجزء تبعنا هذا اللي هي false, false, false,
+
+589
+00:43:36,660 --> 00:43:42,040
+true, true, false الوحيدة كانت اللي فيها مشكلة
+
+590
+00:43:42,040 --> 00:43:49,880
+خلينا نشوف ان احنا بدين ب false اصلا صح؟ انا
+
+591
+00:43:49,880 --> 00:43:53,400
+ماانتهتش المحاضرة المحاضرة لسه ماانتهتش ضايلها نص
+
+592
+00:43:53,400 --> 00:43:56,060
+ساعة زمان كويس فإذا انا بتكلم عن جزء هذا
+
+593
+00:44:01,270 --> 00:44:06,750
+صح؟ طب في الحالتين true بغض النظر عن مين عن
+
+594
+00:44:06,750 --> 00:44:10,630
+النتيجة بغض النظر عن إيش النتيجة اللي بتطلع .. عن
+
+595
+00:44:10,630 --> 00:44:13,570
+ال .. عن ال Q statement أو ال Q proposition تبعنا
+
+596
+00:44:13,570 --> 00:44:16,810
+هي في الآخر ال implication كله على بعضه هيكون true
+
+597
+00:44:16,810 --> 00:44:22,150
+لإنه بدنا خطأ بدنا ب .. ب .. ب .. false احنا ما
+
+598
+00:44:22,150 --> 00:44:24,670
+انتهى .. ما انتهتش السلم حاضرة then the .. the ..
+
+599
+00:44:24,670 --> 00:44:29,810
+the sun will rise tomorrow okay ممكن تكون trueبس
+
+600
+00:44:29,810 --> 00:44:35,710
+فى النهاية برضه كلها على بعض is true كويس if
+
+601
+00:44:35,710 --> 00:44:42,150
+Tuesday is a day of the week true تمام then I am a
+
+602
+00:44:42,150 --> 00:44:47,210
+penguin a penguin اللى هو البطريق false طب صارت فى
+
+603
+00:44:47,210 --> 00:44:52,810
+ك true false كلها false صحيح كلها صارت ايش false
+
+604
+00:44:52,810 --> 00:44:58,230
+طيبif one plus one equal to six then Obama is a
+
+605
+00:44:58,230 --> 00:45:01,310
+president طب ما هو فعلا Obama is a president بس مش
+
+606
+00:45:01,310 --> 00:45:04,110
+عشان هيك هقول إن هي true لأن هذي false أصلا ف
+
+607
+00:45:04,110 --> 00:45:08,510
+false حكمت على الموضوع خلصنا false سواء النتيجة
+
+608
+00:45:08,510 --> 00:45:12,490
+كانت false or true هو منطقي منطق ال implication
+
+609
+00:45:12,490 --> 00:45:15,290
+تبعنا ال implication تبعنا منطقي فإذن هذي المفروض
+
+610
+00:45:15,290 --> 00:45:21,470
+إن هي true طيب if the moon is made of a green
+
+611
+00:45:21,470 --> 00:45:22,210
+cheese
+
+612
+00:45:24,600 --> 00:45:28,200
+إذا كان مصنوع .. الجمر مصنوع من .. من جبنة خضرة
+
+613
+00:45:28,200 --> 00:45:32,500
+then I am richer than Bill Gates عارفين Bill
+
+614
+00:45:32,500 --> 00:45:38,420
+Gates؟ okay يعني لا هذه صح ولا هذه صح واضح false
+
+615
+00:45:38,420 --> 00:45:43,920
+employees false فإذا كلها هتكون true كلها هتكون
+
+616
+00:45:43,920 --> 00:45:48,180
+true تمام
+
+617
+00:45:48,180 --> 00:45:54,380
+شوية expressionsبتعبّر لنا عن عملية ال implication
+
+618
+00:45:54,380 --> 00:45:59,420
+اللي احنا بنحكي عنها أنه ممكن نقول implies P
+
+619
+00:45:59,420 --> 00:46:04,640
+implies Q فإذا P تضمن Q فهذا هو الشرط هي النتيجة
+
+620
+00:46:04,640 --> 00:46:10,640
+في شرط أو السابقة اللي المفروض تتحقق فتحقق للنتيجة
+
+621
+00:46:10,640 --> 00:46:20,160
+أو ممكن تكون if P then Q if P بدون thenضمن كومة
+
+622
+00:46:20,160 --> 00:46:25,840
+then Q برضه تستعمل فانتوا لو اجدكوا اي جملة فيها
+
+623
+00:46:25,840 --> 00:46:29,560
+عبارة من العبارات هدولة بس بتعرف وين انو جزء ال P
+
+624
+00:46:29,560 --> 00:46:33,520
+وانو جزء ال Q عشان ما يتلخبطش معاكم الجدول لانوا
+
+625
+00:46:33,520 --> 00:46:36,380
+ديروا بالك لو لخبط ال P مع ال Q تلخبطت معاكم
+
+626
+00:46:36,380 --> 00:46:41,500
+هتضيعوا في الجزئية هذه لان هذه هتصير تيجي مكان هذه
+
+627
+00:46:41,500 --> 00:46:44,180
+و هذه هتيجي مكان هذه فهتلاقي انه الاصل اللي بتصير
+
+628
+00:46:44,180 --> 00:46:47,460
+هذه هي ال false وهذه صارت ال trueفاطلح بطن النتائج
+
+629
+00:46:47,460 --> 00:46:50,420
+معاكم عشان هي مهم جدا تعرفوا انتوا في اي
+
+630
+00:46:50,420 --> 00:46:53,780
+expression من هدولة تشتغلوا ال expression الصح
+
+631
+00:46:53,780 --> 00:46:58,040
+تتعاملوا معاه عشان تضمنوا مين ال P و مين ال Q لازم
+
+632
+00:46:58,040 --> 00:47:03,060
+تستخرجوهم بعناية مين ال condition و مين النتيجة
+
+633
+00:47:03,060 --> 00:47:06,980
+عشان تعرفوا الناتج لل implication operator كلها
+
+634
+00:47:06,980 --> 00:47:10,200
+على وقت فضلي بس المهم بالنسبالي انه مثلا حتر و كتر
+
+635
+00:47:10,200 --> 00:47:16,550
+و مصطلما و P و 7صح أنا بحكيلك هنا لو إجتك ال
+
+636
+00:47:16,550 --> 00:47:20,570
+statement تبعتك إجتك language ممكن أعطيكيها
+
+637
+00:47:20,570 --> 00:47:25,570
+language أو تعطي language و أنت اللي اتطلعي بالظبط
+
+638
+00:47:25,570 --> 00:47:29,030
+أه مهم جدا تعرفيه حسب ال exceptions اللي احنا
+
+639
+00:47:29,030 --> 00:47:31,330
+حاطينهم اللي وجد هنا ال exceptions إذا كان
+
+640
+00:47:31,330 --> 00:47:34,570
+employees معناته اللي جابلها هي ال P و اللي بعدها
+
+641
+00:47:34,570 --> 00:47:40,250
+هي ال Q لأنها هي PPploys Q فإذا P تضمن Q واضحة P
+
+642
+00:47:40,250 --> 00:47:43,850
+تضمن Q فإذا الأولى هي الشرط التاني هي النتيجة كويس
+
+643
+00:47:43,850 --> 00:47:51,690
+when عندما P ضمن then Q فهنا على طول اللى بتيجي
+
+644
+00:47:51,690 --> 00:47:55,370
+قبل الكومة بعد ال when قبل الكومة هذه هي ال P
+
+645
+00:47:55,370 --> 00:48:06,260
+whenever كلما كلما حدثت P then Q تمام Q if PQ
+
+646
+00:48:06,260 --> 00:48:14,380
+تتحقق إذا في تمام وين بالعكس هي Q وين بتكون تطلع
+
+647
+00:48:14,380 --> 00:48:18,140
+على وجه ال وين اللي هنا كان في كومة فكانت بتفصل
+
+648
+00:48:18,140 --> 00:48:23,460
+كانت عند حدوث بي كومة افصل إيش بيصير طب هنا لأ هنا
+
+649
+00:48:23,460 --> 00:48:28,280
+جملة واحدة Q وين بي فالقصد اللي كنتوا تاخدوا بالكم
+
+650
+00:48:28,280 --> 00:48:30,940
+من ال expressions هذه أنية واحدة اللي هتتحقق معاكم
+
+651
+00:48:30,940 --> 00:48:33,900
+بتعرفوا منها تطلعوا هذه في الآخر هتكون عبارة عن
+
+652
+00:48:33,900 --> 00:48:39,510
+إيشهذه هتكون جملة مكتوبة هنا جملة وهنا جملة فانتوا
+
+653
+00:48:39,510 --> 00:48:42,510
+هتلاقيوا جملة كاملة بتكونوا تعرفوا if ومافيش اي
+
+654
+00:48:42,510 --> 00:48:45,550
+comma بينهم معناته الجزء اللي في الأول بتاخدوها و
+
+655
+00:48:45,550 --> 00:48:50,130
+بتقولوا q equal to كذا فبتكونوا ضمنين انه ايش
+
+656
+00:48:50,130 --> 00:48:53,910
+الحالة بتاعتها بتحطوها كنتيجة مش بنحطها condition
+
+657
+00:48:53,910 --> 00:48:58,870
+هنا في الأولتمام؟ هاي الهدف من شوية الجمل هدولة
+
+658
+00:48:58,870 --> 00:49:02,390
+طبعا في أكتر من هيك بس يعني بزيادة حتى بزيادة كتير
+
+659
+00:49:02,390 --> 00:49:06,150
+المجوهات الجمل اللي موجودة عندكم أو ال expressions
+
+660
+00:49:06,150 --> 00:49:09,450
+اللي موجودة عندكم زي أخر واحدة مثلا q is employed
+
+661
+00:49:09,450 --> 00:49:16,810
+by p يعني قدمنا المفقود بيها عن الفعل يعني صارت
+
+662
+00:49:16,810 --> 00:49:24,540
+okay هي مضمونةمن B by P في ال implication في شوية
+
+663
+00:49:24,540 --> 00:49:30,620
+تعبير أو في شوية مصطلحات تستخدم مع ال implication
+
+664
+00:49:30,620 --> 00:49:34,060
+أولها
+
+665
+00:49:34,060 --> 00:49:40,690
+ال converse و ال inverse و ال contrapositiveال
+
+666
+00:49:40,690 --> 00:49:43,310
+converse لما أقول في عملت converse ل ال
+
+667
+00:49:43,310 --> 00:49:48,050
+implication في employees q معناته أنا غيرتهم مع
+
+668
+00:49:48,050 --> 00:49:54,150
+بعض عكستهم خليت النتيجة في الأول و الشرط في التاني
+
+669
+00:49:54,150 --> 00:49:57,970
+طبعا هتعطي نتائج مختلفة تماما بس إيش علاقتهم مع
+
+670
+00:49:57,970 --> 00:50:02,570
+بعض هي converse لل implication الأصلي طبعا أكيد
+
+671
+00:50:02,570 --> 00:50:06,820
+نتائج مختلفةالنتائج هتكون طبعا مختلفة، إشي طبيعي
+
+672
+00:50:06,820 --> 00:50:12,040
+كويس أما ال inverse تبعها إنه نفسها بس بعملها
+
+673
+00:50:12,040 --> 00:50:17,540
+لمين؟ لل negation negation ال P employs negation Q
+
+674
+00:50:17,540 --> 00:50:21,060
+فبصير عندنا expression تاني طيب ال contrapositive
+
+675
+00:50:21,060 --> 00:50:27,300
+تنتين في بعض لحظة هعمل ال converse مع ال inverse
+
+676
+00:50:27,300 --> 00:50:31,820
+تنتين مع بعض جلبنا التنتين فهي مسارة ال Q في الأول
+
+677
+00:50:33,040 --> 00:50:37,400
+وعملنا negation لكل واحدة قبلها طيب واحدة من ال
+
+678
+00:50:37,400 --> 00:50:43,080
+three operators الجديدة هدولة او ال three terms
+
+679
+00:50:43,080 --> 00:50:48,360
+هدولة فعليا مساوية او بتعطيني the same truth table
+
+680
+00:50:48,360 --> 00:50:55,060
+of implication واحدة منهم هتعطي نفس النتائج لمين
+
+681
+00:50:55,060 --> 00:51:00,660
+لل implication يا ترى مين منهم تانية
+
+682
+00:51:02,780 --> 00:51:05,640
+التالتة منطقة التالتة انتوا عاملين inverse مع
+
+683
+00:51:05,640 --> 00:51:09,940
+coinverse يعني عكسين عكس عكسين العكس فالمنطق انه
+
+684
+00:51:09,940 --> 00:51:13,120
+هتكون هي الأقرب انها تكون مساوية فال
+
+685
+00:51:13,120 --> 00:51:16,860
+contrapositive في الغالب هي فعلا وهذا حقيقة هي
+
+686
+00:51:16,860 --> 00:51:20,080
+اللي هتكون متساوية او مساوية لل implication عشان
+
+687
+00:51:20,080 --> 00:51:23,780
+نثبت الكلام هذا ممكن نستعمل truth table نستخدم في
+
+688
+00:51:23,780 --> 00:51:26,040
+الموضوع هذا ونجرب هل فعلا متساوية او لا
+
+689
+00:51:29,200 --> 00:51:35,140
+هي مجموعة الاحتمالات الممكنة لهم نيجيشن q
+
+690
+00:51:35,140 --> 00:51:40,120
+محتاجينها عشان نحسب الcontra positive نيجيشن P
+
+691
+00:51:40,120 --> 00:51:42,980
+محتاجينها عشان نحسب برضه الcontra positive مجرد
+
+692
+00:51:42,980 --> 00:51:49,200
+عكس يعني خدوا هذا الجزء عكسوه هنا راحظوا تمام
+
+693
+00:51:49,200 --> 00:51:56,340
+الجزء التاني P عكسوه هناوبدأوا يحسبوا ال
+
+694
+00:51:56,340 --> 00:52:00,660
+implication و ال contrapositive ال implication
+
+695
+00:52:00,660 --> 00:52:03,800
+بيحسبها من ال two columns هدول الحالة الوحيدة اللي
+
+696
+00:52:03,800 --> 00:52:12,400
+false هي true و false otherwise truth طيب
+
+697
+00:52:12,400 --> 00:52:15,800
+الحالة التانية في ال contrapositive بداش تطلع ال
+
+698
+00:52:15,800 --> 00:52:18,940
+two columns هدولة و بنفس الترتيب هذا negation q في
+
+699
+00:52:18,940 --> 00:52:23,740
+الأول و negation p في التانيةبرضه الحالة الوحيدة
+
+700
+00:52:23,740 --> 00:52:28,440
+اللي هي true فالس فالس هتلاقي ان ال column هذا
+
+701
+00:52:28,440 --> 00:52:32,160
+مساوي لل column هذا فإذا فعلا ال implication equal
+
+702
+00:52:32,160 --> 00:52:39,900
+to او equivalent ل ال contrapositive تبعها طيب
+
+703
+00:52:39,900 --> 00:52:43,520
+دلنا لعنا ال biconditional operator ال
+
+704
+00:52:43,520 --> 00:52:46,840
+biconditional operator هنا بنتكلم عن implication
+
+705
+00:52:46,840 --> 00:52:54,260
+في الاتجاهينالمعنى اللغوي تبعها if and only if إذا
+
+706
+00:52:54,260 --> 00:52:59,980
+وإذا فقط تقوى كنت إيش بقول بقول إذا درستوا هتاخدوا
+
+707
+00:52:59,980 --> 00:53:06,520
+معدل جيد معدل كويس يعني القصد فيها إذا ما درستوش
+
+708
+00:53:06,520 --> 00:53:10,440
+سبتها ماليش علاقة لكن لما أقولكوا ديروا بالكم إذا
+
+709
+00:53:10,440 --> 00:53:14,540
+درستوا وإذا درستوا فقط هتاخدوا معدل جيد معناته إذا
+
+710
+00:53:14,540 --> 00:53:19,050
+ما درستوش مش هتاخدواماسبنهاش لحالها هيك بظروفها هي
+
+711
+00:53:19,050 --> 00:53:21,610
+الفكرة انه ماانتثبتش بظروفها ف if and only if
+
+712
+00:53:21,610 --> 00:53:28,530
+بتختلف في جزئية ال false إذا مااتحققش مش هيتحقق
+
+713
+00:53:28,530 --> 00:53:32,970
+النتيجة انتهى مش هيتحقق النتيجة خلينا نشوف if and
+
+714
+00:53:32,970 --> 00:53:37,870
+only if هذه كيف ممكن نستعملها لو قولنا P is Obama
+
+715
+00:53:37,870 --> 00:53:43,230
+wins the 2012 election Obama فاز في انتخابات 2012
+
+716
+00:53:43,230 --> 00:53:48,560
+اللي كانت التجديد تبعهQ equal to Obama will be
+
+717
+00:53:48,560 --> 00:53:55,940
+president for all of 2014 قعد إن طول 2014 و هيكمل
+
+718
+00:53:55,940 --> 00:54:01,520
+إن 2016 كويس فإذا هنا لاحظوا أوباما مدام نجح في
+
+719
+00:54:01,520 --> 00:54:05,580
+2012 هو أكيد لازم يكون الرئيس في 2014 لأنه لسه ما
+
+720
+00:54:05,580 --> 00:54:08,760
+انتهتش الفترة الرئاسية تبعته ما انتهتش الفترة
+
+721
+00:54:08,760 --> 00:54:12,840
+الرئاسية ف by logic لما واحد يقولي والله في 2012
+
+722
+00:54:12,840 --> 00:54:17,360
+أوباما فاز في الانتخاباتو احنا هلوجت في 2014 من
+
+723
+00:54:17,360 --> 00:54:20,860
+غير ماعرف اخبار و من غير by logic اه هي امريكا
+
+724
+00:54:20,860 --> 00:54:23,320
+جديش الفترة الرئيسية اه اربع سنة اه يعني معناته
+
+725
+00:54:23,320 --> 00:54:26,240
+لسه أوباما يعني خلاص ايك لحاله و قلتها مع ان انا
+
+726
+00:54:26,240 --> 00:54:28,620
+مش عارف اخباره فانا افترض ولا بعرف اه معناته هو هو
+
+727
+00:54:28,620 --> 00:54:33,700
+لسه موجود اه صح هو موجود كويس فلما بقول P by
+
+728
+00:54:33,700 --> 00:54:39,760
+conditional Q كأني بقول ifو فقط إذا قتل أوباما
+
+729
+00:54:39,760 --> 00:54:47,720
+الانتصار 2012 أوباما سيكون الرئيس للجميع في 2014
+
+730
+00:54:52,470 --> 00:54:57,730
+ال truth table لل by conditional زي ما قلنا هي
+
+731
+00:54:57,730 --> 00:55:02,350
+مشابهة تقريبا لمين ل .. ال .. هي الحقيقة مشابهة
+
+732
+00:55:02,350 --> 00:55:05,610
+لكذا واحدة فيهم و هنربطها لو جدت بكذا شغلة أول ما
+
+733
+00:55:05,610 --> 00:55:08,890
+هنربطها هبدنا نربطها مع ال by ال .. ال implication
+
+734
+00:55:08,890 --> 00:55:11,790
+مع ال implication لما أجى أربطها مع ال implication
+
+735
+00:55:11,790 --> 00:55:15,510
+هي احنا هنا شرطنا الوحيد فيها أنه لازم ال
+
+736
+00:55:15,510 --> 00:55:21,110
+condition في الاتجاهين if and only if فإذا if a
+
+737
+00:55:21,110 --> 00:55:29,680
+falseOkay false طيب false true لأ لأ هنا كنا
+
+738
+00:55:29,680 --> 00:55:33,220
+سايبينها بظروفها ممكن يكون متذكر شغلها هنا قولنا
+
+739
+00:55:33,220 --> 00:55:37,760
+if and only if إذا ما اتحققش مافيش فإذا فعلا
+
+740
+00:55:37,760 --> 00:55:41,870
+مااتحققشمافيش false هذه الحالة الوحيدة يمكن ان
+
+741
+00:55:41,870 --> 00:55:44,950
+هناك كانت true في ال implication هناك كانت true
+
+742
+00:55:44,950 --> 00:55:50,590
+نتيجة هنا only if اللي ضفناها لأ استفنت ليه ال
+
+743
+00:55:50,590 --> 00:55:54,190
+error ده طيب true و false احنا من اول متفقين ان هي
+
+744
+00:55:54,190 --> 00:55:58,430
+اصلا false طيب true true اتحقق لشريح ال condition
+
+745
+00:55:58,430 --> 00:56:01,520
+الطبيعي لازم يتحقق النتيجةتحقق ال condition
+
+746
+00:56:01,520 --> 00:56:06,140
+الطبيعي جدا لازم تتحقق نتيجته فهذه true مش مشكلة
+
+747
+00:56:06,140 --> 00:56:10,620
+في هذا الموضوع الفرق الوحيد كان في الروح ده okay
+
+748
+00:56:10,620 --> 00:56:15,780
+هذه هيك ربطناها مع مين؟ مع ال implication طيب نيجي
+
+749
+00:56:15,780 --> 00:56:21,160
+نربطها شوية هيك مع ال XOR ايش الفرق بينها و بين ال
+
+750
+00:56:21,160 --> 00:56:24,960
+XOR ايش
+
+751
+00:56:24,960 --> 00:56:30,990
+الفرق بينها و بين ال XOR هنا لاحظوليلأ عكس العكس
+
+752
+00:56:30,990 --> 00:56:35,790
+العكس لحظه هذه العكس تماما هنا كانت هنا true وهنا
+
+753
+00:56:35,790 --> 00:56:40,130
+false صحيح لأ هنا بالعكس تماما و عشان ايه قلتلكم
+
+754
+00:56:40,130 --> 00:56:45,570
+بتجيش كنا نعمل negation مع xor لأن في operator
+
+755
+00:56:45,570 --> 00:56:49,050
+بعبر عن الموضوع هذا اللي هي by conditional هي فعلا
+
+756
+00:56:49,050 --> 00:56:55,360
+بتعطيكوا العكسالعكس لمن؟ لل x or أو ال opposite of
+
+757
+00:56:55,360 --> 00:57:01,560
+x or طبعا، تمام، كويس فلاحظوا إيش أخدنا احنا الوجد
+
+758
+00:57:01,560 --> 00:57:07,060
+فعلا؟ أخدنا كذا شغلة بدأنا مع ال negation وهنا
+
+759
+00:57:07,060 --> 00:57:10,080
+بدنا نعمل negation هاي في عندكوا زي كأنه revision
+
+760
+00:57:10,080 --> 00:57:15,640
+لكل ال operators اللي أخدناهم negation لل P، false
+
+761
+00:57:15,640 --> 00:57:18,200
+بتصير true، false بتصير true، true بتصير false و
+
+762
+00:57:18,200 --> 00:57:22,780
+هكذا، كويس ال conjunctionاللي انتوا كنتوا عارفينها
+
+763
+00:57:22,780 --> 00:57:26,740
+and conjunction الحالة الوحيدة كله false باستثناء
+
+764
+00:57:26,740 --> 00:57:33,460
+true true بتعطي true ال disjunction كله true
+
+765
+00:57:33,460 --> 00:57:39,100
+باستثناء false false بتعطي false ال X or X or
+
+766
+00:57:39,100 --> 00:57:45,940
+اختلفوا true متشابهين false كويس
+
+767
+00:57:47,630 --> 00:57:51,430
+و ناخد بالنا دائما نفرق بينها خصوصا لما بتكلم عن
+
+768
+00:57:51,430 --> 00:57:56,610
+ال language افرق بينها و بين ال or مهم جدا من خلال
+
+769
+00:57:56,610 --> 00:58:01,870
+ال context لل language من خلال سياق الجمل تعرفوا
+
+770
+00:58:01,870 --> 00:58:05,730
+انتوا المفروض تتعاملوا مع or او ترجموها or ولا xor
+
+771
+00:58:05,730 --> 00:58:09,670
+مهم جدا كويس ال implication حكينا عن ال
+
+772
+00:58:09,670 --> 00:58:11,830
+implication اتكلمنا عن ال implication و بعدين
+
+773
+00:58:11,830 --> 00:58:16,250
+اتكلمنا عن ال by conditional عن ال by conditional
+
+774
+00:58:18,080 --> 00:58:21,740
+ال notations بتاعتهم .. ال notations بتاعتهم ..
+
+775
+00:58:21,740 --> 00:58:27,380
+لاحظوا ال propositional logic كيف شكلهم .. هدول ال
+
+776
+00:58:27,380 --> 00:58:30,360
+notations اللي احنا اتعلمناهم اليوم .. أخدناهم
+
+777
+00:58:30,360 --> 00:58:33,880
+اليوم .. polynomial اللي انتوا كنتوا تاخدوهم سابقا
+
+778
+00:58:33,880 --> 00:58:38,060
+.. كيف كنتوا تكتبوهم سابقا أو يمكن تكتبوهم في ال
+
+779
+00:58:38,060 --> 00:58:41,160
+logic design .. في ال logic design .. في ال logic
+
+780
+00:58:41,160 --> 00:58:46,200
+design بتشتغلوا على هدول .. بتعملوهمالـ hat اللي
+
+781
+00:58:46,200 --> 00:58:48,720
+فوق هذه فخلاص بعرف ال .. البار عارف ان اللي فوق
+
+782
+00:58:48,720 --> 00:58:51,340
+اللي هنا بعرف انه هذي إيش negation أو اللي هي ال
+
+783
+00:58:51,340 --> 00:58:56,440
+inverse أو ال inverter كويس هنا بالشكل هذا هي كده
+
+784
+00:58:56,440 --> 00:59:00,440
+كأنهم مضروين ضارب في بعض فهي and plus بيعملوا
+
+785
+00:59:00,440 --> 00:59:04,640
+بينهم plus فانتوا بتعرفوا انه or ال x or هي هي ال
+
+786
+00:59:04,640 --> 00:59:07,060
+implication وال if and only if ماكنتوا مش هتاخدوهم
+
+787
+00:59:07,060 --> 00:59:10,020
+مابتاخدوهمش يعني فعليا كنتوا في الرياضية هنا
+
+788
+00:59:10,020 --> 00:59:14,740
+بتاخدوهم كويس في ال java باستخدام ال javaو
+
+789
+00:59:14,740 --> 00:59:18,180
+باستخدام سواء ان انت بتتكلم عن bit-wise او word
+
+790
+00:59:18,180 --> 00:59:23,160
+-wise vector ولا scalar value بتختلف طبعا احيانا
+
+791
+00:59:23,160 --> 00:59:26,080
+فممكن اللي بتبقى اللي هيبرمج بال C او بال Java
+
+792
+00:59:26,080 --> 00:59:31,160
+هيلاقي انه برضه مضمونة موجودة في البرمجة بتقدروا
+
+793
+00:59:31,160 --> 00:59:33,940
+تبرمجوهم باستخدام احد ال symbols هدوة اللي هم هدول
+
+794
+00:59:33,940 --> 00:59:36,580
+الروابط باستخدامكوا باستخدامها وهد الروابط
+
+795
+00:59:36,580 --> 00:59:40,020
+باستخدام اذا كان بتتكلم عن ال bit-wise كويس ال
+
+796
+00:59:40,020 --> 00:59:43,680
+logic gates هد اللي كنتوا بتاخدوهم في ال circuits
+
+797
+00:59:44,300 --> 00:59:46,880
+وانتوا بتتكلموا عن ال circuits كنتوا تعبروا عنهم
+
+798
+00:59:46,880 --> 00:59:50,000
+بال symbols اللي موجودة هنا inverter كنتوا بتعملوه
+
+799
+00:59:50,000 --> 00:59:57,400
+بالشكل هذا ال and ال r و ال xr و ال xr و طبعا من
+
+800
+00:59:57,400 --> 00:59:59,920
+الأشكال دول كنتوا بتشكلوا حاجات كتير تانية يعني
+
+801
+00:59:59,920 --> 01:00:04,320
+ممكن على طول ال .. ال circle هذه تحطوها هنا ..
+
+802
+01:00:04,320 --> 01:00:08,320
+تحطوها هنا ف بتجيبوا gates جديدة كنتوا تجيبوا
+
+803
+01:00:08,320 --> 01:00:11,760
+gates جديدة بالظبط تصير عكسها فبتصير بدل or بتصير
+
+804
+01:00:11,760 --> 01:00:18,140
+norبس بدل ان بصير ناد و هكذا تمام
+
+805
+01:00:18,140 --> 01:00:25,710
+طيب بكفل هنا كويس هيك المرة الجايةهبنبدأ مع جزئية
+
+806
+01:00:25,710 --> 01:00:28,610
+ال .. ال .. ال .. ال bit أو ال bits and bit
+
+807
+01:00:28,610 --> 01:00:33,490
+operations النظرية تلعد ان احنا هنتعامل مع ال zero
+
+808
+01:00:33,490 --> 01:00:36,630
+مرة تانية على اساس ان هو false و هنتعامل مع ال one
+
+809
+01:00:36,630 --> 01:00:40,250
+على اساس ان هو true و بعدين اكتر من slide ضايقين و
+
+810
+01:00:40,250 --> 01:00:42,450
+بعدين ننجل على موضوعنا الجاي ان شاء الله تعالى
+
+811
+01:00:42,450 --> 01:00:46,850
+ابتداء من الأسبوع القادم بإذن الله تعالى يعطيكوا
+
+812
+01:00:46,850 --> 01:00:47,130
+العفو
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6ec9c103b3702f812115e72b202e4ee24d886e24
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4969, "start": 21.55, "end": 49.69, "text": "بسم الله الرحمن الرحيم الصلاة والسلام على أشرف الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبها أجمعين استكمالا لمحاضرتنا الأولى اللى كنا اتكلمنا فيها ك introduction لال discrete ككل discrete mathematics كمصاق كامل واتكلمنا إيش .. في إيش هيفيدنا، إيش هناخد منه، في إيش هيخدمنا، كيف هيخدمكوا في مجال تخصصكم في ال computer engineering اليوم هنبدأ مع أول محاضرات المصاق اللى هي foundations of logic أو introduction to logic", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 29973, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 11296, 5551, 7435, 2304, 3615, 9957, 44713, 24793, 6027, 995, 32767, 5016, 46958, 43500, 8315, 16247, 12610, 7578, 13672, 7578, 9122, 8315, 1975, 2655, 4117, 19528, 8315, 8978, 11296, 9122, 9339, 5296, 6027, 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لالا لالا للا حاجات يعني بتنكتبها لغاية صارت كتير عبارة في ال chatting و في ال forums و في الحاجات هذه كويس زي لالا لالا هذه meaningless مالهاش معنى مالهاش معنى لا يمكن أبدا تفرضوها أن هي proposition تشتغلوا عليها هذه بدون معنى طيب just do it", "tokens": [20343, 313, 23032, 3555, 11933, 1829, 8592, 5551, 39648, 3224, 23758, 22807, 5551, 39648, 3224, 20328, 5016, 49429, 32771, 1211, 9566, 22807, 37893, 6225, 9640, 5172, 37495, 22653, 18871, 11933, 1829, 8592, 4724, 1829, 5016, 4117, 1829, 2423, 1651, 39894, 1863, 5016, 9566, 8592, 20449, 2423, 24830, 6156, 3224, 24192, 37893, 24830, 5551, 5016, 1829, 7649, 14111, 995, 4032, 14739, 2655, 14407, 39894, 25957, 1211, 14407, 24654, 5551, 5016, 1829, 7649, 14111, 995, 39894, 25957, 1211, 14407, 8032, 3224, 3224, 3224, 3224, 3224, 5296, 6027, 995, 5296, 6027, 995, 5296, 15040, 11331, 26108, 9307, 37495, 22653, 39894, 1863, 4117, 2655, 3555, 11296, 5296, 17082, 995, 10632, 20328, 9640, 2655, 9122, 2655, 13546, 6225, 3555, 9640, 3660, 8978, 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ال negation بتاعتنا طيب ال truth table بتبعها بالشكل اللي احنا شايفينه T F F T بهذا الشكل كويس ال conjunction", "tokens": [6703, 5296, 15042, 4724, 16254, 5551, 25957, 1211, 11296, 2485, 399, 5296, 15042, 5551, 39648, 2485, 399, 430, 39894, 9381, 13546, 286, 500, 380, 4032, 4724, 29399, 24793, 1211, 28242, 13672, 1829, 6225, 42213, 47395, 6225, 42213, 10632, 8717, 41185, 6225, 42213, 10632, 8717, 41185, 13672, 1829, 39896, 2423, 2485, 399, 39894, 995, 34268, 8315, 23032, 1829, 3555, 2423, 3494, 3199, 39894, 3555, 3615, 11296, 20666, 8592, 28820, 13672, 1829, 1975, 5016, 8315, 13412, 995, 33911, 9957, 3224, 314, 479, 479, 314, 4724, 3224, 15730, 25124, 28820, 9122, 45865, 3794, 2423, 27482], "avg_logprob": -0.18632392729482344, "compression_ratio": 1.6813725490196079, "no_speech_prob": 2.1457672119140625e-06, "words": [{"start": 970.01, "end": 970.35, "word": "here", "probability": 0.049468994140625}, {"start": 970.35, "end": 971.47, "word": " لما", "probability": 0.931396484375}, 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عندنا؟", "probability": 0.9734700520833334}], "temperature": 1.0}, {"id": 44, "seek": 115901, "start": 1132.65, "end": 1159.01, "text": "احتمالة ال output انتوا يا true يا false فإذا ثنائي وعشان هيك دايما نشتغل على الاتنين على الاتنين لإنه ماعنديش يا .. ايش ال .. ال .. ال .. ال symbols اللي بدي أعوضها هنا false or true؟ في إشي تاني غيرهم؟ لأ فانا بتكلم عن binary فعلا عشان هيك فيه انا اتنين بيمثلولي يديش عدد الروز اللي ممكن أحتاجهم في العملية تبعتي طيب also negation and", "tokens": [995, 33753, 2304, 6027, 3660, 2423, 5598, 16472, 2655, 14407, 35186, 2074, 35186, 7908, 6156, 28814, 15730, 38637, 1863, 16373, 1829, 4032, 3615, 8592, 7649, 39896, 4117, 11778, 47302, 15042, 8717, 8592, 2655, 17082, 1211, 15844, 2423, 9307, 1863, 9957, 15844, 2423, 9307, 1863, 9957, 5296, 28814, 1863, 3224, 19446, 3615, 1863, 16254, 8592, 35186, 4386, 1975, 1829, 8592, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 16944, 13672, 1829, 4724, 16254, 5551, 3615, 2407, 11242, 11296, 34105, 7908, 420, 2074, 22807, 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او ال ax تبعتنا فالسؤال اللي كان هحدث ليش لأنه أي واحدة من ال proposition true النتيجة true فإذا يكفي أن تكون واحدة صار عندنا زودنا احتمالات ل true في النتيجة", "tokens": [6027, 39184, 717, 10010, 882, 13672, 1829, 39896, 2423, 420, 9122, 29399, 14407, 6055, 14851, 25957, 1211, 2407, 11296, 3714, 41361, 11296, 420, 10874, 995, 10632, 3714, 43020, 6055, 30544, 29538, 9154, 6225, 42213, 10632, 27188, 10721, 3794, 1975, 2407, 2423, 6360, 6055, 3555, 34268, 8315, 6156, 6027, 3794, 33604, 6027, 13672, 1829, 25961, 8032, 24401, 12984, 32239, 8592, 5296, 33456, 3224, 36632, 36764, 24401, 3660, 9154, 2423, 24830, 2074, 28239, 31371, 7435, 3660, 2074, 6156, 28814, 15730, 7251, 4117, 41185, 14739, 6055, 30544, 36764, 24401, 3660, 20328, 9640, 43242, 8315, 30767, 23328, 8315, 1975, 33753, 2304, 6027, 9307, 5296, 2074, 8978, 28239, 31371, 7435, 3660], "avg_logprob": -0.18676986594066441, "compression_ratio": 1.7860262008733625, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1187.63, 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didn't rain last night okay التانية are conjunction negation بيه ال negation بيه هي موجودة فهيها مافيش عندنا مشكلة فيها and بنحط قدامها and بتظل are نزلوا are", "tokens": [38169, 77, 380, 994, 380, 20666, 19913, 3555, 9566, 32239, 8592, 22807, 5296, 33456, 19446, 41185, 8592, 43242, 8315, 34105, 27188, 30241, 9673, 3794, 995, 22488, 3714, 33753, 26108, 9957, 6156, 30241, 47524, 995, 22488, 8717, 25957, 1211, 8978, 3224, 6225, 42213, 10632, 28239, 5172, 3615, 6156, 3224, 8315, 8032, 1863, 11242, 33911, 4724, 3794, 994, 380, 4830, 1036, 1818, 1392, 16712, 7649, 10632, 366, 27482, 2485, 399, 4724, 1829, 3224, 2423, 2485, 399, 4724, 1829, 3224, 39896, 3714, 29245, 23328, 3660, 6156, 3224, 1829, 11296, 19446, 41185, 8592, 43242, 8315, 37893, 28820, 3660, 8978, 11296, 293, 44945, 5016, 9566, 12174, 3215, 10943, 11296, 293, 39894, 19913, 1211, 366, 8717, 11622, 1211, 14407, 366], "avg_logprob": -0.16847826812578284, "compression_ratio": 1.7563025210084033, "no_speech_prob": 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جزئية necessary condition شرط ضرورى ولكن مش ملزم لحظة مش ملزم كتير خلينى نشوف example عليها let P equal to you study hard ان انت درستي كويس درستي بصورة جيدة Q equal to you will get a good grade تمام لما اقول P", "tokens": [5172, 7578, 6156, 2288, 4587, 49374, 4818, 4188, 4032, 11563, 4188, 6156, 39319, 8315, 34105, 44650, 4117, 19528, 18871, 10874, 11622, 19986, 10632, 4818, 4188, 13412, 2288, 9566, 48812, 2288, 13063, 7578, 35525, 19452, 37893, 3714, 1211, 11622, 2304, 5296, 5016, 19913, 3660, 37893, 3714, 1211, 11622, 2304, 9122, 2655, 13546, 16490, 1211, 9957, 7578, 8717, 8592, 38688, 1365, 25894, 11296, 718, 430, 2681, 281, 291, 2979, 1152, 16472, 16472, 2655, 11778, 2288, 14851, 1829, 9122, 45865, 3794, 11778, 2288, 14851, 1829, 4724, 9381, 13063, 3660, 10874, 25708, 3660, 1249, 2681, 281, 291, 486, 483, 257, 665, 7204, 46811, 10943, 5296, 15042, 1975, 39648, 430], "avg_logprob": -0.15713443382168715, "compression_ratio": 1.5714285714285714, "no_speech_prob": 4.76837158203125e-07, 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2423, 4386, 2423, 4386, 2423, 857, 34051, 2423, 9239, 293, 857, 7705, 28239, 19913, 2288, 10632, 6055, 1211, 22488, 16472, 1975, 5016, 8315, 8032, 29399, 3615, 10943, 1211, 20449, 2423, 4018, 3714, 25720, 6055, 7649, 10632, 15844, 24525, 32277, 16472, 31439, 7908, 4032, 8032, 29399, 3615, 10943, 1211, 20449, 2423, 472, 15844, 24525, 32277, 16472, 31439, 2074, 4032, 39182, 9957, 1975, 4117, 2655, 2288, 9154, 4137, 48812, 47302, 4587, 9957, 4032, 39182, 9957, 8717, 1863, 7435, 1211, 15844, 3714, 2407, 11242, 45367, 8315, 25724, 47302, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 48127, 2655, 3215, 16606, 9154, 16247, 35457, 45367, 25062, 18513, 2304, 4724, 28814, 8848, 1863, 21984, 37279, 6027, 7578, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407], "avg_logprob": -0.18643465626871947, "compression_ratio": 1.946768060836502, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 3623.97, "end": 3624.53, "word": "هبنبدأ", "probability": 0.728271484375}, {"start": 3624.53, "end": 3624.79, "word": " مع", "probability": 0.91162109375}, {"start": 3624.79, "end": 3625.71, "word": " جزئية", "probability": 0.9676513671875}, {"start": 3625.71, "end": 3626.09, "word": " ال", "probability": 0.95361328125}, {"start": 3626.09, "end": 3626.09, "word": " ..", "probability": 0.332275390625}, {"start": 3626.09, "end": 3626.45, "word": " ال", "probability": 0.93701171875}, {"start": 3626.45, "end": 3626.45, "word": " ..", "probability": 0.8583984375}, {"start": 3626.45, "end": 3626.87, "word": " ال", "probability": 0.958984375}, {"start": 3626.87, "end": 3626.97, "word": " ..", "probability": 0.337158203125}, {"start": 3626.97, "end": 3626.97, "word": " ال", "probability": 0.845703125}, {"start": 3626.97, "end": 3627.13, "word": " bit", "probability": 0.53173828125}, {"start": 3627.13, "end": 3627.77, "word": " أو", "probability": 0.6416015625}, {"start": 3627.77, "end": 3627.91, "word": " ال", "probability": 0.92626953125}, {"start": 3627.91, "end": 3628.11, "word": " bits", "probability": 0.87060546875}, {"start": 3628.11, "end": 3628.31, "word": " and", "probability": 0.9541015625}, {"start": 3628.31, "end": 3628.61, "word": " bit", "probability": 0.79345703125}, {"start": 3628.61, "end": 3629.47, "word": " operations", "probability": 0.94775390625}, {"start": 3629.47, "end": 3631.07, "word": " النظرية", "probability": 0.8681640625}, {"start": 3631.07, "end": 3631.47, "word": " تلعد", "probability": 0.5320638020833334}, {"start": 3631.47, "end": 3632.39, "word": " ان", "probability": 0.400146484375}, {"start": 3632.39, "end": 3632.55, "word": " احنا", "probability": 0.9640299479166666}, {"start": 3632.55, "end": 3633.03, "word": " هنتعامل", "probability": 0.96728515625}, {"start": 3633.03, "end": 3633.17, "word": " مع", "probability": 0.9921875}, {"start": 3633.17, "end": 3633.31, "word": " ال", "probability": 0.93896484375}, {"start": 3633.31, "end": 3633.49, "word": " zero", "probability": 0.72021484375}, {"start": 3633.49, "end": 3633.71, "word": " مرة", "probability": 0.91650390625}, {"start": 3633.71, "end": 3633.93, "word": " تانية", "probability": 0.9801432291666666}, {"start": 3633.93, "end": 3634.07, "word": " على", "probability": 0.86328125}, {"start": 3634.07, "end": 3634.23, "word": " اساس", "probability": 0.78369140625}, {"start": 3634.23, "end": 3634.35, "word": " ان", "probability": 0.802734375}, {"start": 3634.35, "end": 3634.57, "word": " هو", "probability": 0.92236328125}, {"start": 3634.57, "end": 3635.37, "word": " false", "probability": 0.9208984375}, {"start": 3635.37, "end": 3635.49, "word": " و", "probability": 0.90234375}, {"start": 3635.49, "end": 3635.93, "word": " هنتعامل", "probability": 0.973828125}, {"start": 3635.93, "end": 3636.15, "word": " مع", "probability": 0.9892578125}, {"start": 3636.15, "end": 3636.41, "word": " ال", "probability": 0.9951171875}, {"start": 3636.41, "end": 3636.63, "word": " one", "probability": 0.9658203125}, {"start": 3636.63, "end": 3636.79, "word": " على", "probability": 0.8974609375}, {"start": 3636.79, "end": 3636.99, "word": " اساس", "probability": 0.951904296875}, {"start": 3636.99, "end": 3637.13, "word": " ان", "probability": 0.736328125}, {"start": 3637.13, "end": 3637.41, "word": " هو", "probability": 0.95068359375}, {"start": 3637.41, "end": 3638.05, "word": " true", "probability": 0.994140625}, {"start": 3638.05, "end": 3638.49, "word": " و", "probability": 0.77490234375}, {"start": 3638.49, "end": 3638.93, "word": " بعدين", "probability": 0.934814453125}, {"start": 3638.93, "end": 3639.43, "word": " اكتر", "probability": 0.62017822265625}, {"start": 3639.43, "end": 3639.51, "word": " من", "probability": 0.9931640625}, {"start": 3639.51, "end": 3639.83, "word": " slide", "probability": 0.49462890625}, {"start": 3639.83, "end": 3640.17, "word": " ضايقين", "probability": 0.7908935546875}, {"start": 3640.17, "end": 3640.25, "word": " و", "probability": 0.88232421875}, {"start": 3640.25, "end": 3640.45, "word": " بعدين", "probability": 0.962646484375}, {"start": 3640.45, "end": 3640.75, "word": " ننجل", "probability": 0.8681640625}, {"start": 3640.75, "end": 3640.89, "word": " على", "probability": 0.6650390625}, {"start": 3640.89, "end": 3641.31, "word": " موضوعنا", "probability": 0.97705078125}, {"start": 3641.31, "end": 3641.61, "word": " الجاي", "probability": 0.638427734375}, {"start": 3641.61, "end": 3641.95, "word": " ان", "probability": 0.8662109375}, {"start": 3641.95, "end": 3642.09, "word": " شاء", "probability": 0.96630859375}, {"start": 3642.09, "end": 3642.15, "word": " الله", "probability": 0.931640625}, {"start": 3642.15, "end": 3642.45, "word": " تعالى", "probability": 0.98583984375}, {"start": 3642.45, "end": 3642.77, "word": " ابتداء", "probability": 0.78778076171875}, {"start": 3642.77, "end": 3642.95, "word": " من", "probability": 0.970703125}, {"start": 3642.95, "end": 3644.53, "word": " الأسبوع", "probability": 0.8512369791666666}, {"start": 3644.53, "end": 3645.33, "word": " القادم", "probability": 0.9952799479166666}, {"start": 3645.33, "end": 3645.63, "word": " بإذن", "probability": 0.9720458984375}, {"start": 3645.63, "end": 3645.93, "word": " الله", "probability": 0.947265625}, {"start": 3645.93, "end": 3646.53, "word": " تعالى", "probability": 0.98876953125}, {"start": 3646.53, "end": 3646.85, "word": " يعطيكوا", "probability": 0.750732421875}, {"start": 3646.85, "end": 3647.13, "word": " العفو", "probability": 0.9033203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3647.855, "duration_after_vad": 3535.00562499998}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..78388acdd23921971649cbaf984defb8f8763e57
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Qi_QYuS3bio_raw.srt
@@ -0,0 +1,3256 @@
+1
+00:00:21,550 --> 00:00:23,590
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,590 --> 00:00:25,850
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبها
+
+3
+00:00:25,850 --> 00:00:29,590
+أجمعين استكمالا لمحاضرتنا الأولى اللى كنا اتكلمنا
+
+4
+00:00:29,590 --> 00:00:32,670
+فيها ك introduction لال discrete ككل discrete
+
+5
+00:00:32,670 --> 00:00:37,510
+mathematics كمصاق كامل واتكلمنا إيش .. في إيش
+
+6
+00:00:37,510 --> 00:00:40,230
+هيفيدنا، إيش هناخد منه، في إيش هيخدمنا، كيف
+
+7
+00:00:40,230 --> 00:00:44,070
+هيخدمكوا في مجال تخصصكم في ال computer engineering
+
+8
+00:00:44,070 --> 00:00:47,510
+اليوم هنبدأ مع أول محاضرات المصاق اللى هي
+
+9
+00:00:47,510 --> 00:00:51,710
+foundations of logic أو introduction to logicهنبدأ
+
+10
+00:00:51,710 --> 00:00:55,290
+بتعريف بسيطة ال mathematical logic is a tool for
+
+11
+00:00:55,290 --> 00:00:57,990
+working with complicated compound statements
+
+12
+00:00:57,990 --> 00:01:02,490
+هنتعامل مع اللي هي logic احنا لو هتحدد شغلنا علاش
+
+13
+00:01:02,490 --> 00:01:04,530
+على ال logic في محاضرتنا اليوم ال mathematical
+
+14
+00:01:04,530 --> 00:01:09,310
+logic هي فعليا نشتغل فيها على مجموعة statements
+
+15
+00:01:09,310 --> 00:01:13,650
+بندمشها مع بعض بحيث انه يصير عندنا complicated
+
+16
+00:01:13,650 --> 00:01:20,600
+compound statements statements مركبة معقدةالكبيرة
+
+17
+00:01:20,600 --> 00:01:22,600
+.. الكبيرة هذه المركبة أو المعقدة من إيش بدها
+
+18
+00:01:22,600 --> 00:01:26,580
+تيجي؟ هتيجي فعليا من مجموعة statements صغيرة في ال
+
+19
+00:01:26,580 --> 00:01:29,800
+language .. في اللغة عادة اللغة بتيجي من إيش؟ شوية
+
+20
+00:01:29,800 --> 00:01:34,280
+حروف بنكون منها كلمات كلمة جنب كلمة بتعطينا معنى
+
+21
+00:01:34,280 --> 00:01:37,580
+المعنى إذا اتكون عندنا معنى إحنا هنا هنستعملها ..
+
+22
+00:01:37,580 --> 00:01:41,120
+هنقول عنها proposition عندنا المعنى هذا خلاص
+
+23
+00:01:41,120 --> 00:01:45,910
+بيعطيني معلومةالمعلومة دي مقدر احكم عنها ك .. ب
+
+24
+00:01:45,910 --> 00:01:50,270
+truth value false or true اتكلمنا كتير عن .. عن
+
+25
+00:01:50,270 --> 00:01:56,310
+قصة false و true المرة اللي فاتت تمام فبيظل عندنا
+
+26
+00:01:56,310 --> 00:02:00,410
+انه كيف نكونهم مع بعض هدول الأجزاء كيف نكونهم مع
+
+27
+00:02:00,410 --> 00:02:04,490
+بعض هناخدهم من خلال مجموعة operators هنتكلم اليوم
+
+28
+00:02:04,490 --> 00:02:08,050
+عنهم ان شاء الله تعالى بس فعليا عشان اتكلم عن ال
+
+29
+00:02:08,050 --> 00:02:10,230
+mathematical logic هي بتتكون من ايش؟ اول حاجة
+
+30
+00:02:10,230 --> 00:02:13,730
+languageبكون ان ال language .. ال language هذا بدي
+
+31
+00:02:13,730 --> 00:02:19,070
+أترجمها لإيش؟ لمجموعة رياضيات .. مجموعة رياضيات عن
+
+32
+00:02:19,070 --> 00:02:22,950
+طريق symbols معينة notations معينة أقدر أعمل prove
+
+33
+00:02:22,950 --> 00:02:27,650
+لها ففعليا محتاج language for expressing them
+
+34
+00:02:27,650 --> 00:02:31,890
+للتعبير عن ال statements بتاعتي بعدين محتاج
+
+35
+00:02:31,890 --> 00:02:33,170
+concise notation
+
+36
+00:02:36,430 --> 00:02:41,530
+علامات مختصرة او symbols او symbols عساس انه نعبر
+
+37
+00:02:41,530 --> 00:02:46,130
+عنها رياضيا مانقدرش .. بدنا نثبت شغلة مكتوبة في
+
+38
+00:02:46,130 --> 00:02:48,650
+one paragraph اقعد كل شوية اقول one paragraph
+
+39
+00:02:48,650 --> 00:02:52,250
+معايا عشان أثبت و هل بيساوي true or false فلأ
+
+40
+00:02:52,250 --> 00:02:58,080
+بنعبر عنه بإيش؟ ب symbol واحدأي شغلة بتصير سهلة
+
+41
+00:02:58,080 --> 00:03:03,800
+أنها P equal to كذا و بتعمل بعدين مع P و Q هدولة
+
+42
+00:03:03,800 --> 00:03:07,380
+لما نثبت و نخلص بنشوف P و Q اللي أثبتناهم بيعبروا
+
+43
+00:03:07,380 --> 00:03:10,050
+عن إيش في ال languageتمام فمحتاجين concise
+
+44
+00:03:10,050 --> 00:03:14,270
+notation for writing them بعدين ال methodology for
+
+45
+00:03:14,270 --> 00:03:18,330
+objectively reasoning about their truth table
+
+46
+00:03:18,330 --> 00:03:24,190
+تبعنا اللي هي ال truth or falsity ففعليا
+
+47
+00:03:24,190 --> 00:03:27,590
+بصير بدى إيش الطريقة اللى هستعملها لإثبات بطريقة
+
+48
+00:03:27,590 --> 00:03:33,030
+منطقية بطريقة معقولة إثبات مدى صحة أو عدم صحة ال
+
+49
+00:03:33,030 --> 00:03:38,130
+statement تبعتيبالطريقة هذه هي الشغل تبع المصحق هي
+
+50
+00:03:38,130 --> 00:03:40,430
+شغل المصحق إيش ال methodology اللى بدنا نستخدمها
+
+51
+00:03:40,430 --> 00:03:46,250
+الحقيقة هذا ال branch كبير ويله علاقة بال formal
+
+52
+00:03:46,250 --> 00:03:51,390
+proofs في ال formal proofs طيب فعليا ال
+
+53
+00:03:51,390 --> 00:03:54,790
+foundations of logic هنتكلم هناخد overview عليها
+
+54
+00:03:54,790 --> 00:03:59,590
+هنتكلم عن ال propositional logic بتفاصيلها شوية
+
+55
+00:03:59,590 --> 00:04:01,990
+شوية هنتكلم عن تفاصيلها بعدين هنقول شوية شوية على
+
+56
+00:04:01,990 --> 00:04:07,570
+ال predicate logicبرضه بتفاصيلها و هنحكي في وقتها
+
+57
+00:04:07,570 --> 00:04:11,230
+عنها اليوم ابصرينا و بنحكي بس عن الجزئية هذه اللي
+
+58
+00:04:11,230 --> 00:04:16,430
+هي جزئية ل proposition logic propositional logic
+
+59
+00:04:16,430 --> 00:04:20,870
+هي فعليا برضه عبارة عن compound statements built
+
+60
+00:04:20,870 --> 00:04:25,210
+from similar statements زي ما قلنا انا بتكلم عن
+
+61
+00:04:25,210 --> 00:04:28,550
+statement كبيرة تعبير كبير بس هو جا من مجموعة
+
+62
+00:04:28,550 --> 00:04:33,010
+تعبير صغيرة طيب كيف ركبناهم التعبير الصغيرة هذه عن
+
+63
+00:04:33,010 --> 00:04:38,290
+طريق operatorsعن طريق روابط الروابط هي شغلنا اليوم
+
+64
+00:04:38,290 --> 00:04:43,630
+اليوم هنتكلم كتير عن جزء الروابط الروابط في ال ..
+
+65
+00:04:43,630 --> 00:04:48,270
+في ال numbers عادة اللي هي الجمع الطرح القسمة لأن
+
+66
+00:04:48,270 --> 00:04:51,790
+هذا بتربطنا رقم مع رقم فبيطلعنا ناتج جديد لما يقول
+
+67
+00:04:51,790 --> 00:04:55,670
+واحد زائد خمسة زائد هذه علامة الزائد هذه هي
+
+68
+00:04:55,670 --> 00:05:00,170
+operatoroperator لل numbers طيب ال operators اللي
+
+69
+00:05:00,170 --> 00:05:03,750
+احنا هنشتغل عليها لأ هتكون علاقة بال logic فهده
+
+70
+00:05:03,750 --> 00:05:08,630
+Boolean connectives أو Boolean algebra بيشتغل في
+
+71
+00:05:08,630 --> 00:05:11,130
+الجزئية هده و هده اللي هنشتغل عليه ان شاء الله
+
+72
+00:05:11,130 --> 00:05:13,490
+تعالى و هتكون مرة عليكوا قبل هيكي بس يمكن زي ما
+
+73
+00:05:13,490 --> 00:05:17,490
+قلنا ناخدها بتسميات جديدة بس انتوا كلها عارفينها
+
+74
+00:05:17,490 --> 00:05:20,490
+ال and و ال or و ال x or هنرجع كلها اليوم انقيتها
+
+75
+00:05:20,490 --> 00:05:23,410
+هنرجع كلها اليوم انقيتها الكلام ده الحقيقة بيفيدنا
+
+76
+00:05:23,410 --> 00:05:26,310
+في كتير مجالات اهمها يمكن اللي هوفي ال digital
+
+77
+00:05:26,310 --> 00:05:29,310
+electronics circuits و الأمور اللي زي هذه يعني
+
+78
+00:05:29,310 --> 00:05:32,970
+انتوا لو في السنة الجاية المفروض ان شاء الله
+
+79
+00:05:32,970 --> 00:05:36,390
+بتاخدوا ال digital electronics هتاخدوا فيها كتير
+
+80
+00:05:36,390 --> 00:05:39,450
+عن ال logic gates هتتكلموا كتير كتير كتير فيها في
+
+81
+00:05:39,450 --> 00:05:42,830
+ال logic gates okay في ال conditions الحقيقة في
+
+82
+00:05:42,830 --> 00:05:45,610
+التعبير عن ال conditions في البرنامج لما تقولوا if
+
+83
+00:05:45,610 --> 00:05:48,910
+then جزيتي ال if then هد اللي بتعملوها في البرنامج
+
+84
+00:05:48,910 --> 00:05:53,500
+أعتقد انكسا ما لاحتوش تاخدوا برمجةمالاحقتوش يمكن
+
+85
+00:05:53,500 --> 00:05:56,900
+تاخدوا برمجة كتير بس عادة في ال flow chart بتحطوا
+
+86
+00:05:56,900 --> 00:06:01,700
+حاجة بالشكل هذا زي condition نفترض مثلا x أكبر من
+
+87
+00:06:01,700 --> 00:06:06,520
+خمسة فانتوا حاطين condition لحظه و بتحطوله yes or
+
+88
+00:06:06,520 --> 00:06:11,260
+no بناء عليه إيش بتكون تعملوا ال action سواء اتحقق
+
+89
+00:06:11,260 --> 00:06:14,200
+أو ماتحققش اتحقق أو ماتحققش يعني انتوا بتتكلم عن
+
+90
+00:06:14,200 --> 00:06:20,410
+true or falseفي condition وهدا هل هو true or false
+
+91
+00:06:20,410 --> 00:06:27,190
+بناء عليه بدنا نعمل action قادم تمام الجزئية هذه
+
+92
+00:06:27,190 --> 00:06:30,710
+مستخدمة في ال conditions زى ما قلنا في ال .. ال
+
+93
+00:06:30,710 --> 00:06:34,290
+conditions in program في ال queries to databases
+
+94
+00:06:34,290 --> 00:06:38,610
+في عادة في البحث في ال database لما بتعملوا بحث
+
+95
+00:06:38,610 --> 00:06:41,770
+على ال database نفترض ال database على الجامعة
+
+96
+00:06:41,770 --> 00:06:45,470
+بتكتبوا رقمكوا الجامعي و بتعملوا enter فهو بفحص
+
+97
+00:06:46,230 --> 00:06:51,790
+الارقام كلها امتى بتصير فيه quality ال equal ان
+
+98
+00:06:51,790 --> 00:06:55,230
+الرقم تبعكو equal ل folder موجود عنده بفتح الكل
+
+99
+00:06:55,230 --> 00:06:59,230
+folder فبتشوفوا صفحتكم ايش مسجلين ايش مش مسجلين
+
+100
+00:06:59,230 --> 00:07:02,130
+علاماتكم ايش الموثيقات اللي خلصتوها ايش اللي ما
+
+101
+00:07:02,130 --> 00:07:04,530
+خلصتوهاش ايش اللي نازل ايش اللي مش نازل الأمور دي
+
+102
+00:07:04,530 --> 00:07:09,590
+كلها بتنعمل برضه عن طريق logic gates او logic
+
+103
+00:07:09,590 --> 00:07:12,960
+conceptsالـ search engines نفس الكلام لأنكم
+
+104
+00:07:12,960 --> 00:07:18,880
+بتقارنه بتعملوا comparison فيه شروط اتحققت بجيب
+
+105
+00:07:18,880 --> 00:07:21,460
+الصفحة اللي اتحققت فيها الشروط الشروط ده بناء على
+
+106
+00:07:21,460 --> 00:07:23,940
+ايش؟ على keywords انتوا بتكتبوها على ال search
+
+107
+00:07:23,940 --> 00:07:27,900
+engine فبناء عليه اذا اتحققت داخل الصفحة ال web
+
+108
+00:07:27,900 --> 00:07:32,080
+page بجيب ال qn1 ال web page فبتلاقوا مجموعة من ال
+
+109
+00:07:32,080 --> 00:07:36,130
+web pages موجودة عندكم okayنبدأ بأول جزئية اللي هي
+
+110
+00:07:36,130 --> 00:07:39,810
+ال proposition ال proposition الإعلان أو أنا
+
+111
+00:07:39,810 --> 00:07:43,930
+بحطلكوا جملة إعلامية declarative sentence جملة
+
+112
+00:07:43,930 --> 00:07:49,310
+إعلامية لحالة معينة، لإشي معين، بنقدر نعرف إن هي
+
+113
+00:07:49,310 --> 00:07:54,010
+فقرةأصغر فقرة ممكنة في اللغة بحيث ان هي بتعطيكوا
+
+114
+00:07:54,010 --> 00:07:58,510
+معنى و المعنى هذا بقدر احكم عليه true or false
+
+115
+00:07:58,510 --> 00:08:03,490
+يعني ايه ال truth truth value كويس عادة بنستعمل
+
+116
+00:08:03,490 --> 00:08:09,310
+lowercase او small letter بشكل هذا غالبا بنستعمل
+
+117
+00:08:09,310 --> 00:08:13,010
+ال P Q و R في الغالب هم الدارجين في الكتاب اللي
+
+118
+00:08:13,010 --> 00:08:16,210
+هنستعمله في الكتاب اللي هتستعمله هذه اللي هي بتعبر
+
+119
+00:08:16,210 --> 00:08:19,530
+على ال statements على مجموعة ال statementswith
+
+120
+00:08:19,530 --> 00:08:24,810
+definite meaning بمعنى محدد ومعنى محدد يعني انا
+
+121
+00:08:24,810 --> 00:08:27,830
+بقدر احكم عليه هيا نكررها كذا مرة بقدر احكم عليه
+
+122
+00:08:27,830 --> 00:08:32,610
+قد ايش القيمة تبعته كويس having a truth value
+
+123
+00:08:32,610 --> 00:08:37,230
+that's either true or false إله قيمة هذه أو هذه
+
+124
+00:08:37,230 --> 00:08:39,870
+طبعا لا يمكن يكونوا اتنين في نفس الوجد مش ماجولة
+
+125
+00:08:39,870 --> 00:08:43,590
+طبعا أعطيكوا جملة true و false في نفس اللحظة لا
+
+126
+00:08:43,590 --> 00:08:48,290
+يمكن هذه بطلت proposition أو neitherلا هي هيك ولا
+
+127
+00:08:48,290 --> 00:08:52,350
+هيك، خائش، لا هي صح ولا هي غلط، متصبتش، متنفعش أو
+
+128
+00:08:52,350 --> 00:08:55,470
+somewhere in between لما أقول somewhere in between
+
+129
+00:08:55,470 --> 00:08:57,810
+دخلتنا في حاجة جديدة مش مش مجالنا هذه اللي هي
+
+130
+00:08:57,810 --> 00:09:01,550
+probability دخلنا في جزية .. احتمال والله اربعين
+
+131
+00:09:01,550 --> 00:09:06,530
+في المية true وستين في المية false in between لأ
+
+132
+00:09:06,530 --> 00:09:09,690
+هذه دخلنا في إشي تاني فهذه ماتحطهاش في proposition
+
+133
+00:09:09,690 --> 00:09:12,490
+اللي هناخده اليوم أو اللي هنتكلم عنه اليوم هنتكلم
+
+134
+00:09:12,490 --> 00:09:17,300
+اليوم بأبسط صوره بأبسط صورة من الصورة تبعته طيبمن
+
+135
+00:09:17,300 --> 00:09:19,400
+خلال الكلمتين اللي قلناها خلّيني أخد شوية examples
+
+136
+00:09:19,400 --> 00:09:23,140
+و نشوف إيش يعني proposition إيش يعني proposition
+
+137
+00:09:23,140 --> 00:09:29,200
+فلو قلنا it's raining false okay إلها قيمة ممكن لو
+
+138
+00:09:29,200 --> 00:09:31,240
+الدنيا بتشتي بتصير true بس في النهاية هي جملة و
+
+139
+00:09:31,240 --> 00:09:34,920
+إلها قيمة و كام لخلاص يعطتني معنى فإذا حسب ال
+
+140
+00:09:34,920 --> 00:09:38,300
+situation بقدر أقول إن هي يا true يا false هذه
+
+141
+00:09:38,300 --> 00:09:44,040
+proposition القدس is the capital of Palestine
+
+142
+00:09:44,040 --> 00:09:50,100
+الجدس عاصمة فلسطينtrue true فعلا فإذا هذه برضه
+
+143
+00:09:50,100 --> 00:09:53,840
+proposition فإذا هذه proposition okay one plus two
+
+144
+00:09:53,840 --> 00:09:57,280
+equal to three أقولكوا one plus two equal to five
+
+145
+00:09:57,280 --> 00:10:03,420
+false ولكن proposition لحظة proposition القيمة
+
+146
+00:10:03,420 --> 00:10:06,740
+تبعته false okay مش مشكلة بس في النهاية
+
+147
+00:10:06,740 --> 00:10:12,620
+proposition okay في المقابل في حالات نعطيكوا شوية
+
+148
+00:10:12,620 --> 00:10:15,660
+حالات هي are not propositions
+
+149
+00:10:18,320 --> 00:10:22,410
+Who's there؟question طب إيش أقوله هذا؟ أقوله صح
+
+150
+00:10:22,410 --> 00:10:25,670
+ولا غلط؟ مش عارف يعني عن إيش بيحكي ال questions
+
+151
+00:10:25,670 --> 00:10:28,350
+بتنحطش مع ال proposition فهذه مش proposition
+
+152
+00:10:28,350 --> 00:10:30,530
+أحيانًا و أنتوا بتعملوا chatting أحيانًا بتعملوا
+
+153
+00:10:30,530 --> 00:10:33,750
+هههههه لالا لالا للا حاجات يعني بتنكتبها لغاية
+
+154
+00:10:33,750 --> 00:10:36,670
+صارت كتير عبارة في ال chatting و في ال forums و في
+
+155
+00:10:36,670 --> 00:10:40,190
+الحاجات هذه كويس زي لالا لالا هذه meaningless
+
+156
+00:10:40,190 --> 00:10:45,310
+مالهاش معنى مالهاش معنى لا يمكن أبدا تفرضوها أن هي
+
+157
+00:10:45,310 --> 00:10:48,850
+proposition تشتغلوا عليها هذه بدون معنى طيب just
+
+158
+00:10:48,850 --> 00:10:54,500
+do itأوامر ..أوامر برضه مالهاش معايا ..يمكن بديش
+
+159
+00:10:54,500 --> 00:10:57,620
+أنفذ الأوامر ..يمكن بديش ..بيديش أنفذه ..بالنسبالي
+
+160
+00:10:57,620 --> 00:11:01,880
+false واحد تاني بده ينفذه ..بس في الآخر الأوامر مش
+
+161
+00:11:01,880 --> 00:11:05,520
+محسوبة ك proposition ال .. ال .. ال .. ال .. ال
+
+162
+00:11:05,520 --> 00:11:09,600
+fake أو اللي هي الجمال الغامضة yeah I sorta don't
+
+163
+00:11:09,600 --> 00:11:13,940
+know whatever ..طب ماشي فهمنا منها ..مافهمناش أشي
+
+164
+00:11:13,940 --> 00:11:17,280
+.. الجملة بدا مغامضة و مش فاهم منها حاجة على طول
+
+165
+00:11:18,220 --> 00:11:21,940
+هذه not proposition بقدرش أقول عنها proposition أو
+
+166
+00:11:21,940 --> 00:11:25,780
+جملة ناقصة بمعنى أنا بقدرش أقول هذه true or false
+
+167
+00:11:25,780 --> 00:11:31,820
+زي one plus two stop طيب كمللي انا one plus two مش
+
+168
+00:11:31,820 --> 00:11:34,380
+عارف أقولك صح ولا غلط اعطيني يا بتقولي تلاتة
+
+169
+00:11:34,380 --> 00:11:37,480
+فبقولك true و بتصير proposition يا بتقولي الف و
+
+170
+00:11:37,480 --> 00:11:41,840
+بقولك false و proposition بس في النهاية لازم يكون
+
+171
+00:11:41,840 --> 00:11:45,140
+لها قيمة انا لا جادة بحكم عليها true ولا false
+
+172
+00:11:45,140 --> 00:11:52,120
+فإذا هذه not propositionOkay ال operators اتفجناها
+
+173
+00:11:52,120 --> 00:11:54,820
+لوجة انه إيش معنى proposition هي عبارة عن جملة
+
+174
+00:11:54,820 --> 00:11:59,140
+إلها معنى و بقدر أعطيها قيمة نقدر نعطيها قيمة أو
+
+175
+00:11:59,140 --> 00:12:03,240
+يعني أحد القيمتين اللي هي true أو false ال
+
+176
+00:12:03,240 --> 00:12:05,780
+operators زي ما قلنا في ال numbers لما بتكلم عن
+
+177
+00:12:05,780 --> 00:12:07,860
+numbers ال operators بالنسبالنا اللي هي زي
+
+178
+00:12:09,000 --> 00:12:14,000
+positive, plus, minus جمع, طريح, قسمة, ضرب كل هذه
+
+179
+00:12:14,000 --> 00:12:19,420
+تربط لنا two numbers مع بعض عشان يعطوني نتيجة
+
+180
+00:12:19,420 --> 00:12:28,600
+تالتة نتيجة إضافية ممكن تكون unary
+
+181
+00:12:28,600 --> 00:12:34,120
+أو عبارة عن أحدية الoperand بمعنى محتاج معامل واحد
+
+182
+00:12:34,120 --> 00:12:39,130
+معها زي ال minusمحتاجة رقم واحد بس مش محتاجة اكتر
+
+183
+00:12:39,130 --> 00:12:42,870
+من هيك رقم واحد يكفي فبعرف ان هذا بالنسبالها عكست
+
+184
+00:12:42,870 --> 00:12:47,130
+الرقم عكست الرقم حوالين ال zero يعني صار بدل ان هو
+
+185
+00:12:47,130 --> 00:12:51,350
+اعلى من zero بتلاتة لأقل من zero بتلاتة كويس او
+
+186
+00:12:51,350 --> 00:12:56,850
+تكون binary فهذه بتاخد two operands او two معاملين
+
+187
+00:12:56,850 --> 00:13:01,670
+يعني زي الدرب الجمع القسمة الطرح كل هدولة بياخدوا
+
+188
+00:13:01,670 --> 00:13:08,280
+ارقامثلاثية أو بياخدوا يعني binary operators في
+
+189
+00:13:08,280 --> 00:13:11,560
+الحالة اللي عندنا كويس في عندنا برضه ال
+
+190
+00:13:11,560 --> 00:13:15,980
+propositions او propositional نفس الفكرة زي ما
+
+191
+00:13:15,980 --> 00:13:18,060
+اتكلمنا عن ال numbers بقدر اتكلم عن ال
+
+192
+00:13:18,060 --> 00:13:21,200
+propositions ولكن في ال propositions بنشتغل على ال
+
+193
+00:13:21,200 --> 00:13:24,700
+boolean operators اللي برضه انتوا ممكن مرت عليكم
+
+194
+00:13:24,700 --> 00:13:28,560
+سابقا ال and و ال or و ال nor كل هدولة هم هم هم
+
+195
+00:13:28,560 --> 00:13:32,900
+الروابط بتاعتنااللي مقابلين لمين للجمع والطرح
+
+196
+00:13:32,900 --> 00:13:37,980
+والضرب والقسمة كويس بدل الأرقام فبنصير نتعامل مع
+
+197
+00:13:37,980 --> 00:13:42,780
+ال propositions بدل الأرقام إيش ال propositions
+
+198
+00:13:42,780 --> 00:13:47,100
+اللي حقيقة هنتعامل معها هنتعامل مع مجموعة من ال
+
+199
+00:13:47,100 --> 00:13:49,940
+operators أول operator اللي بتتعامل مع ال
+
+200
+00:13:49,940 --> 00:13:52,600
+propositions ال negation operator اللي أنتوا كنتوا
+
+201
+00:13:52,600 --> 00:13:57,580
+بتسميها ال not أو ال inverter كانت inverter فهذه
+
+202
+00:13:57,580 --> 00:14:02,660
+العكسزي ال minus في ال numbers ال conjunction
+
+203
+00:14:02,660 --> 00:14:07,560
+operator انتوا كنتوا تعرفوها and ال conjunction او
+
+204
+00:14:07,560 --> 00:14:12,680
+الدمج او الدمج اذا صار الدمج بالنسبالي true ماصارش
+
+205
+00:14:12,680 --> 00:14:17,320
+دمج فالس فهي معناها فإذا لازم يكون كل part لحاله
+
+206
+00:14:17,320 --> 00:14:20,900
+true و true يندمجوا مع بعض فإذا صارت ال true مدمجة
+
+207
+00:14:20,900 --> 00:14:24,880
+من هنا و من هنا دمج اتنتج بيصير trueهنتكلم عنها
+
+208
+00:14:24,880 --> 00:14:29,120
+بالتفصيل disjunction operator هذه مقابلة كانت لل
+
+209
+00:14:29,120 --> 00:14:33,380
+or انتوا كنتوا عارفينها ب or فبرضه binary و
+
+210
+00:14:33,380 --> 00:14:36,480
+العلامة بتاعتها هتكون بهذا الشكل عاملة زي السبعة
+
+211
+00:14:36,480 --> 00:14:42,600
+هندي ال and سبعة تمانية هندي بهذا الشكل كويس ال
+
+212
+00:14:42,600 --> 00:14:48,420
+exclusive or او ال x or برضه binary circle مع plus
+
+213
+00:14:48,420 --> 00:14:52,380
+العلامة بتاعتها او ال symbol اللي هنستعملها ايا
+
+214
+00:14:52,720 --> 00:14:56,080
+الحاجات الإضافية اللى هتكون مرت عليكم ويمكن تكون
+
+215
+00:14:56,080 --> 00:15:00,560
+جديدة ال implication operator أول مرة هتتعاملوا
+
+216
+00:15:00,560 --> 00:15:03,980
+معها إضافة للمجموعة ال operators اللى موجودة
+
+217
+00:15:03,980 --> 00:15:09,080
+implies اللى هي يعني كأنه a implies b لو صار a
+
+218
+00:15:09,080 --> 00:15:12,940
+بيضمن لنا حدوث b هذه كتير هتستعملوها انتوا لازم
+
+219
+00:15:12,940 --> 00:15:16,000
+تفهموها كويس لأن هذه بتستخدموها في ال if then
+
+220
+00:15:16,850 --> 00:15:19,970
+هتستخدم نفس المعنى في ال if then في البرمجة في
+
+221
+00:15:19,970 --> 00:15:26,770
+البرمجة كويس وهي ال symbol بتاعتها if then if a
+
+222
+00:15:26,770 --> 00:15:31,710
+then b كويس ال condition اللي بعده او ال operator
+
+223
+00:15:31,710 --> 00:15:34,770
+اللي بعده اللي هي ال by conditional operator if
+
+224
+00:15:34,770 --> 00:15:41,500
+and only if مش if then if and only ifإذا وإذا فقط،
+
+225
+00:15:41,500 --> 00:15:44,280
+تمام؟ هنشوف الفرق بين التنتين، في فرق كبير بين
+
+226
+00:15:44,280 --> 00:15:48,020
+التنتين فمدام if and only if فهي ماخدة implication
+
+227
+00:15:48,020 --> 00:15:56,100
+في الاتجاهين من a to b و من b to a، كويس نبدأ ..
+
+228
+00:15:56,100 --> 00:16:00,260
+إيش هقولكن؟ نبدأ نراجع لإن احنا فعلا هنراجع شوية
+
+229
+00:16:00,260 --> 00:16:02,860
+ال operators هدولة ال negation، بداية نبدأ بال
+
+230
+00:16:02,860 --> 00:16:06,740
+negation أو ال not فببساطة جدا ماخدينها جابل هيك
+
+231
+00:16:06,740 --> 00:16:11,910
+لو قلنا P equal to I have brownhere لما بدي أعملها
+
+232
+00:16:11,910 --> 00:16:17,770
+negation لما أقول negation P بتصير I don't و
+
+233
+00:16:17,770 --> 00:16:22,710
+بنتكمل كل اللي عملته عملية نفي عملية نفي اللي هي
+
+234
+00:16:22,710 --> 00:16:26,310
+ال negation بتاعتنا طيب ال truth table بتبعها
+
+235
+00:16:26,310 --> 00:16:33,050
+بالشكل اللي احنا شايفينه T F F T بهذا الشكل كويس
+
+236
+00:16:33,050 --> 00:16:37,650
+ال conjunctionأو اللي انتوا زي ما قولنا .. انتوا
+
+237
+00:16:37,650 --> 00:16:40,810
+حافظينها طول عمركم اللي بتقولوها ال and أو ال و
+
+238
+00:16:40,810 --> 00:16:44,730
+احنا هنسميها conjunction اللي هي الاتحاد او توحي
+
+239
+00:16:44,730 --> 00:16:48,850
+او دمج .. دمج فهذه بتشتغل على two propositions
+
+240
+00:16:48,850 --> 00:16:55,170
+بالنسبالنا و هيكون العلمة بتاعتها زي زي ما قولنا
+
+241
+00:16:55,170 --> 00:16:59,780
+التمانية الهنديجاية من ال A كأنها من ال A فهي
+
+242
+00:16:59,780 --> 00:17:02,740
+العلامة أو ال symbol اللي احنا هنستعمله فلو قولنا
+
+243
+00:17:02,740 --> 00:17:09,620
+if P equal to I will have chicken for lunch زي انا
+
+244
+00:17:09,620 --> 00:17:15,140
+والله عندي فعلا دجاج للغدا و Q equal to I will
+
+245
+00:17:15,140 --> 00:17:21,320
+have cheese for dinner و جبنة للعشاء لو قولنا P
+
+246
+00:17:21,320 --> 00:17:25,960
+conjunction Q إيش بتصير؟I will .. التنتين احنا
+
+247
+00:17:25,960 --> 00:17:29,300
+هنربطهم بإيش؟ ب end I will have chicken for lunch
+
+248
+00:17:29,300 --> 00:17:33,860
+and ال end هذه هي ال conjunction هذه and I will
+
+249
+00:17:33,860 --> 00:17:37,180
+have .. فاحنا نزلناهم زي ما هم .. ربطناهم ربط عمل
+
+250
+00:17:37,180 --> 00:17:40,580
+أيه اتربط؟ فصارت إيش؟ statement واحدة صارت
+
+251
+00:17:40,580 --> 00:17:44,820
+sentence واحدة صارت جملة واحدة خلاص بنكتبها ورا
+
+252
+00:17:44,820 --> 00:17:46,760
+بعض و هو دي فعلا حتى ال language اللي كنتي تعمل
+
+253
+00:17:46,760 --> 00:17:50,340
+ماحدش بكتب جملة جملة بنكتب جملة و بنربطهم في بعض
+
+254
+00:17:50,340 --> 00:17:54,560
+عشان نعمل paragraph عشان نعمل paragraphمجموعة
+
+255
+00:17:54,560 --> 00:17:57,420
+paragraphs بتطلعولي chapter مجموعة chapters
+
+256
+00:17:57,420 --> 00:18:01,440
+بتطلعولي كتاب و هكذا فاحنا بنكون من حاجات بسيطة
+
+257
+00:18:01,440 --> 00:18:05,400
+بنكون حاجات complicated و نفس الكلام هنا عملية
+
+258
+00:18:05,400 --> 00:18:12,720
+الربط باستخدام ال conjunction ال truth table لل
+
+259
+00:18:12,720 --> 00:18:16,580
+conjunction مرة علينة جبل هيكة الحالة الوحيدة اللي
+
+260
+00:18:16,580 --> 00:18:21,320
+ممكن يكون فيها true ان كل proposition
+
+261
+00:18:24,000 --> 00:18:29,240
+فfor all propositions are true then the result is
+
+262
+00:18:29,240 --> 00:18:33,020
+true لازم كلهم يكونوا true عشان فعلا أضمن أنه الكل
+
+263
+00:18:33,020 --> 00:18:36,560
+true لو عندنا two propositions two propositions
+
+264
+00:18:36,560 --> 00:18:39,840
+فعليا هيكون أكمروه عندكم أو أكم احتمال ممكن هيكون
+
+265
+00:18:39,840 --> 00:18:44,500
+أربعة جاي من مين؟ من two to the power n two to the
+
+266
+00:18:44,500 --> 00:18:47,440
+power n لأن أنا بتكلم عن binary ال binary معناته
+
+267
+00:18:47,440 --> 00:18:49,480
+ثنائي شو الثنائي عندنا؟
+
+268
+00:18:52,650 --> 00:18:57,310
+احتمالة ال output انتوا يا true يا false فإذا
+
+269
+00:18:57,310 --> 00:19:01,310
+ثنائي وعشان هيك دايما نشتغل على الاتنين على
+
+270
+00:19:01,310 --> 00:19:04,170
+الاتنين لإنه ماعنديش يا .. ايش ال .. ال .. ال ..
+
+271
+00:19:04,170 --> 00:19:07,910
+ال symbols اللي بدي أعوضها هنا false or true؟ في
+
+272
+00:19:07,910 --> 00:19:11,190
+إشي تاني غيرهم؟ لأ فانا بتكلم عن binary فعلا عشان
+
+273
+00:19:11,190 --> 00:19:14,710
+هيك فيه انا اتنين بيمثلولي يديش عدد الروز اللي
+
+274
+00:19:14,710 --> 00:19:18,750
+ممكن أحتاجهم في العملية تبعتي طيب also negation
+
+275
+00:19:18,750 --> 00:19:23,210
+andconjunction operations together are sufficient
+
+276
+00:19:23,210 --> 00:19:28,970
+to express any poly and truth table حقيقة ال
+
+277
+00:19:28,970 --> 00:19:33,050
+negation مع ال and أو ال conjunction كافي أنها
+
+278
+00:19:33,050 --> 00:19:37,510
+تعبر عن كمية كبيرة جدا إذا ما كانش معظم الحقيقة ال
+
+279
+00:19:37,510 --> 00:19:41,550
+poly and truth table أو معظم ال operators اللي
+
+280
+00:19:41,550 --> 00:19:46,210
+ممكن نستخدمها ال operators اللي ممكن نستعملها طيب
+
+281
+00:19:46,210 --> 00:19:50,170
+ال disjunctionالـ disjunction اللي هي ال or كنتوا
+
+282
+00:19:50,170 --> 00:19:57,730
+تستعملوها مكانها or جاية ممكن تكون هذه من عملية
+
+283
+00:19:57,730 --> 00:20:01,130
+الفأس
+
+284
+00:20:01,130 --> 00:20:05,950
+او ال ax تبعتنا فالسؤال اللي كان هحدث ليش لأنه أي
+
+285
+00:20:05,950 --> 00:20:11,890
+واحدة من ال proposition true النتيجة true فإذا
+
+286
+00:20:11,890 --> 00:20:14,690
+يكفي أن تكون واحدة صار عندنا زودنا احتمالات ل true
+
+287
+00:20:14,690 --> 00:20:18,670
+في النتيجةبنزود هيك عدد احتمالات ل true ليش؟ لأن
+
+288
+00:20:18,670 --> 00:20:22,370
+أي واحدة كافية أنها تكون .. أنها تخلي الناتج true
+
+289
+00:20:22,370 --> 00:20:25,930
+هنشوف طبعا ال 3 ثامل تبعها لو قولنا مثلا for
+
+290
+00:20:25,930 --> 00:20:32,130
+example P equal to my car has a bad engine سيارة
+
+291
+00:20:32,130 --> 00:20:35,670
+ماتورها .. يبدو أن ماتورها مثلا مش .. مش كويس في
+
+292
+00:20:35,670 --> 00:20:41,490
+أطلان أو .. أو خربان او Q my car has a bad
+
+293
+00:20:41,490 --> 00:20:45,960
+carburetorال carburetor برضه ممكن يكون هو العطلان
+
+294
+00:20:45,960 --> 00:20:49,580
+فانا ممكن اروح لميكانيكى والسيارة معايا ايش مالها
+
+295
+00:20:49,580 --> 00:20:52,440
+يقول الله مش عارف شوف يمكن يكون ال motor او
+
+296
+00:20:52,440 --> 00:20:58,140
+carburetor او لحظة ويمكن يطلع الاتنين مع بعض يمكن
+
+297
+00:20:58,140 --> 00:21:00,980
+لما يفحص يلاجئ انه الاتنين مع بعض فهنا صارت ال او
+
+298
+00:21:00,980 --> 00:21:06,260
+بتشمل ال both cases او ال both propositions
+
+299
+00:21:08,580 --> 00:21:16,300
+لو قلنا بـ disjunction q either اما
+
+300
+00:21:16,300 --> 00:21:21,560
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+301
+00:21:21,560 --> 00:21:21,560
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+302
+00:21:21,560 --> 00:21:21,640
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+303
+00:21:21,640 --> 00:21:21,760
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+304
+00:21:21,760 --> 00:21:22,600
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+305
+00:21:22,600 --> 00:21:23,300
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+306
+00:21:23,300 --> 00:21:23,300
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+307
+00:21:23,300 --> 00:21:23,320
+اما اما اما اما اما اما اما اما اما اما اما اما
+
+308
+00:21:23,320 --> 00:21:33,400
+اما اما
+
+309
+00:21:33,400 --> 00:21:38,720
+املازم تنقل two propositions أو خلّيني أقول all
+
+310
+00:21:38,720 --> 00:21:42,700
+propositions are true عشان أقول إن النتيجة true
+
+311
+00:21:42,700 --> 00:21:48,620
+هنا لأ just one true is enough just one
+
+312
+00:21:48,620 --> 00:21:56,900
+proposition is true enough to get true result okay
+
+313
+00:21:56,900 --> 00:22:02,600
+ففي الحالة هذه بنقدر نقول إن or both are أيضا true
+
+314
+00:22:03,180 --> 00:22:06,940
+يعني ممكن يكون الشغلتين برضه .. التنتين true زي ما
+
+315
+00:22:06,940 --> 00:22:11,340
+قلنا ممكن تكون ال motor و ال carburetor ييجي يفحص
+
+316
+00:22:11,340 --> 00:22:15,240
+و يلاقي انه الاتنين خربانين مش بس واحد هذه أحيانا
+
+317
+00:22:15,240 --> 00:22:20,440
+ال operator هذه بنسميها inclusive or in غير ال
+
+318
+00:22:20,440 --> 00:22:24,040
+exclusive or اللي هي ال xor in معناته ايش ال in
+
+319
+00:22:24,040 --> 00:22:27,660
+هذه؟ في حاجة included الشيء ال included اللي فعليا
+
+320
+00:22:27,660 --> 00:22:33,190
+احنا بنتكلم عنها path casePoth case هنا included
+
+321
+00:22:33,190 --> 00:22:38,530
+مع ال truth table ك true فعشان هي ممكن نسميها
+
+322
+00:22:38,530 --> 00:22:45,210
+inclusive or عساس ان هي تضمن معانا ال both cases
+
+323
+00:22:45,210 --> 00:22:49,700
+الأخيرة في ال X or هذه الوحيدة اللي بتختلفهتلاقوها
+
+324
+00:22:49,700 --> 00:22:52,660
+نفس ال or ولكن الجزء الأخير اللي هيختلف و
+
+325
+00:22:52,660 --> 00:22:57,420
+هنتكلمologically عن ال difference between ال or و
+
+326
+00:22:57,420 --> 00:23:01,120
+ال x or لما نيجي ناخد ال x or طيب نفس الكلام ممكن
+
+327
+00:23:01,120 --> 00:23:06,480
+negation مع ال disjunction في جملة واحدة ممكن
+
+328
+00:23:06,480 --> 00:23:11,480
+يكونوا مع بعض عادي universally ممكن يكونوا متعرف
+
+329
+00:23:11,480 --> 00:23:16,460
+عليها او متوقع انها ممكن يكونوا مع بعض طيب صرنا
+
+330
+00:23:16,460 --> 00:23:21,300
+ماخدين هنا كذاoperator طب هذا هيترحلنا سؤال انه طب
+
+331
+00:23:21,300 --> 00:23:24,020
+ما ممكن يكون في عندنا nested propositional
+
+332
+00:23:24,020 --> 00:23:27,420
+expressions nested اللي هو متشابك اللي لاجي أكتر
+
+333
+00:23:27,420 --> 00:23:32,060
+من operator طب لمين الأولوية ال priority لمين ال
+
+334
+00:23:32,060 --> 00:23:34,660
+priority الحقيقة عادة ان احنا و احنا بنشتغل لأنه
+
+335
+00:23:34,660 --> 00:23:37,680
+طو اتكلمنا انه اول شغل عندنا بدنا language
+
+336
+00:23:37,680 --> 00:23:40,760
+expression فال language هي اللي بتحكمنا ال
+
+337
+00:23:40,760 --> 00:23:42,660
+language هي اللي بتحكمنا عشان يكونوا بتكتبوا في ال
+
+338
+00:23:42,660 --> 00:23:45,560
+language تبعتكم لازم تاخدوا بالكم ان الرابط الرابط
+
+339
+00:23:45,560 --> 00:23:50,100
+أهمها الكومةالكمهة دي وين بتحطوها بتغير المعنى
+
+340
+00:23:50,100 --> 00:23:53,060
+بتغير المعنى بتخليني أنا كمان لما بدي أجي أترجمها
+
+341
+00:23:53,060 --> 00:23:58,320
+لرياضيات بتغير كل الشغل معايا ناخد example نوضح
+
+342
+00:23:58,320 --> 00:24:03,900
+فيه الرؤية الصورة I just saw my old friend, and
+
+343
+00:24:03,900 --> 00:24:10,060
+either his ground or I have shrank أنا شفت أزمير
+
+344
+00:24:10,060 --> 00:24:16,210
+القديم أو الصديق القديمو كأنه يا اما هو far زيادة
+
+345
+00:24:16,210 --> 00:24:19,190
+عن اللزوم كبر زيادة عن اللزوم او انا اتقلصت او
+
+346
+00:24:19,190 --> 00:24:25,870
+ضعفت شرانك اللي هو اتقلص او انا ضعفت شكلي هذه
+
+347
+00:24:25,870 --> 00:24:29,470
+الجملة طيب لما نيجي نعبر عنها باستخدام ال
+
+348
+00:24:29,470 --> 00:24:35,930
+propositions هنقول ان هذه proposition لحالها okay
+
+349
+00:24:35,930 --> 00:24:44,330
+هعطيها F التانية هنا his groundproposition طيب I
+
+350
+00:24:44,330 --> 00:24:47,290
+have shrunk proposition حاطيها ال S و هنا حاطيها
+
+351
+00:24:47,290 --> 00:24:54,190
+ال G هتصير ايش؟ F and افتح عقواس اه ليش فتحنا
+
+352
+00:24:54,190 --> 00:25:00,390
+العقواس هنا هنشوفه G disjunction S لإنه في كومة
+
+353
+00:25:00,390 --> 00:25:05,590
+كومة هذه خلتني أعرف إن الجزء هذا إشي و الجزء هذا
+
+354
+00:25:05,590 --> 00:25:10,240
+إشي تانيالكومة دي لو اتغير مكانها هتغير طريقة
+
+355
+00:25:10,240 --> 00:25:15,080
+الترجمة تبعتي لو اتغير مكانها طبيعي كل شي هيتغير
+
+356
+00:25:15,080 --> 00:25:18,720
+عندنا طيب خلينا ناخد الشكل اللي موجود عندنا هنا
+
+357
+00:25:18,720 --> 00:25:25,120
+كومة و في end معناه to end either خلاص عرفت انه
+
+358
+00:25:25,120 --> 00:25:29,740
+إيش فيه فيه or يعني ال or وين ماكانها عشان أحدد
+
+359
+00:25:29,740 --> 00:25:31,620
+اللي جابلها proposition و اللي بعتها proposition
+
+360
+00:25:31,620 --> 00:25:37,730
+تانيهي ال or فاللي قبلها هيه هذا proposition واللي
+
+361
+00:25:37,730 --> 00:25:41,370
+بعدها proposition تاني وفيه هي disjunction between
+
+362
+00:25:41,370 --> 00:25:48,050
+them طيب لو كتبناها بهذا الشكل حقيقة هذه something
+
+363
+00:25:48,670 --> 00:25:53,030
+meaning تاني مختلف تماما هنا بيعطيكوا معنى مختلف
+
+364
+00:25:53,030 --> 00:25:57,310
+تماما عن المعنى الحقيقي للجملة زي ما هي مكتوبة
+
+365
+00:25:57,310 --> 00:26:01,410
+قدامنا لما بتكتب بهذا الشكل المعنى بيصير كأنه أنا
+
+366
+00:26:01,410 --> 00:26:09,190
+شوفت صاحبي و هو كبر أو نمى خلاص فإذا انا حكمت عليه
+
+367
+00:26:09,190 --> 00:26:12,270
+ان هي true لازم يكون نمى طب خلينا نشوف الفرق بين
+
+368
+00:26:12,270 --> 00:26:14,270
+التنتين اللي هي فيه فرق شاسع بين التنتين هذه
+
+369
+00:26:14,270 --> 00:26:20,700
+معناها عشان كل الجملة هنا تكون trueاما هذه true او
+
+370
+00:26:20,700 --> 00:26:27,480
+هذه كلها true صحيح؟ طيب في الحالة هذه اذا او ممكن
+
+371
+00:26:27,480 --> 00:26:31,460
+انا اتنتين هدولة يكونوا false و اكتفي ان هذه true
+
+372
+00:26:31,460 --> 00:26:36,240
+وخلاص و اقول ان انا ماشوفتش صاحبي من اصله طب لأ
+
+373
+00:26:36,240 --> 00:26:40,100
+انا شوفت صاحبي المعنى اتغير انا شوفت صاحبي كيف
+
+374
+00:26:40,100 --> 00:26:46,240
+ماشوفت صاحبي لحظة هذه كلها عشان تكون true انتوا
+
+375
+00:26:46,240 --> 00:26:50,150
+هنا بتتكلموا عن disjunctionيكفي ان واحدة منهم تكون
+
+376
+00:26:50,150 --> 00:26:54,050
+true طب ممكن تكون هذه ال true اكون انا فعلا يمكن
+
+377
+00:26:54,050 --> 00:26:57,110
+سافرت او اشي او حاجة مع المعبر و مع السفر و مع
+
+378
+00:26:57,110 --> 00:27:01,890
+الهدى الواحد ضعف وزنه شوية خف وزنه اشي صار اشي مرض
+
+379
+00:27:01,890 --> 00:27:06,430
+حاسس حاله هيك هزيل شوية ممكن مش عارف يعني بتصير
+
+380
+00:27:06,430 --> 00:27:09,890
+true فتلاقي ان هو هذه خلاص بطل الهبط بمعنى ان لو
+
+381
+00:27:09,890 --> 00:27:16,480
+انا ماشوفتش طب كيف عرفت ان هو he is groundفلاحظوا
+
+382
+00:27:16,480 --> 00:27:20,140
+أن المعنى اتغير تماما غير التانية هناك التانية
+
+383
+00:27:20,140 --> 00:27:24,560
+هناك إيش مالها and
+
+384
+00:27:24,560 --> 00:27:28,360
+أو conjunction conjunction عشان كلها تكون true
+
+385
+00:27:28,360 --> 00:27:33,700
+لازم الجزء هذا true و هذا true الزمن صح الزمن لازم
+
+386
+00:27:33,700 --> 00:27:37,080
+تكون هذا true و هذا true طيب مدام الزمن هذا true
+
+387
+00:27:37,080 --> 00:27:44,520
+خلاص فإذا أنا شفت صاحبي خلاص true طيب هنا عشان
+
+388
+00:27:44,520 --> 00:27:49,150
+تكون هذه trueواحدة منهم كافية أنه ممكن فعلا يا إما
+
+389
+00:27:49,150 --> 00:27:55,990
+هو كبر هيك مرة واحدة يعني إشي حاجة أو أنا أضعفت
+
+390
+00:27:55,990 --> 00:28:01,910
+لأي سبب كان فصارت المعنى بالشكل هذا ينطبق تماما مع
+
+391
+00:28:01,910 --> 00:28:05,450
+الجملة اللي أنا فهمتها فانطبق تماما مع الجملة اللي
+
+392
+00:28:05,450 --> 00:28:10,750
+فهمناها غير إيش الجملة التانية غير الجملة التانية
+
+393
+00:28:10,750 --> 00:28:11,890
+تمام
+
+394
+00:28:14,960 --> 00:28:18,800
+اللي أصعب طبعا كنتوا كتبوا بالشكل هذا بدون أقواص و
+
+395
+00:28:18,800 --> 00:28:22,140
+بدون priority لأي حاجة خلاص conjunction
+
+396
+00:28:22,140 --> 00:28:25,620
+conjunction كويس اللي كتبناهم لأ نفعش لإنه هيك زي
+
+397
+00:28:25,620 --> 00:28:31,120
+بالظبط كنتوا كتبوا كتابة بدون أي كومة بدون أي نقاط
+
+398
+00:28:31,120 --> 00:28:36,340
+بدون أي روابط بدون أي شيء اكتبوا خلاص ابتسألوا
+
+399
+00:28:36,340 --> 00:28:40,000
+السؤال بدون علامة استفهام ابنعمل الجملة ملحومين
+
+400
+00:28:40,000 --> 00:28:43,760
+ببعض طب تعالوا اقرأوا بعدها انتوا مش هتفهم الشي
+
+401
+00:28:43,760 --> 00:28:46,210
+اللي كنتوا كاتبينهلو غيبتولكوا شهر زمان و شهرتوا و
+
+402
+00:28:46,210 --> 00:28:49,710
+كتبتوا .. قرأتوا اللي كتبتوا مش هتفهموا انتوا إيه
+
+403
+00:28:49,710 --> 00:28:54,250
+.. إيش إيش كنتوا بتكتبوا فبتصير ambiguous words
+
+404
+00:28:54,250 --> 00:28:57,610
+بالنسبالك أو ambiguous proposition غامضة، غير
+
+405
+00:28:57,610 --> 00:29:02,740
+مفهومة، غير واضحةطيب عادة ال priority في ال .. إذا
+
+406
+00:29:02,740 --> 00:29:06,160
+كان صار بالشكل هذا أنها عادة بتكون لمين؟ في الغالب
+
+407
+00:29:06,160 --> 00:29:09,680
+ل ال negation ال negation لها ال priority عن مين؟
+
+408
+00:29:09,680 --> 00:29:12,120
+عن ال and و ال or أو ال conjunction و ال
+
+409
+00:29:12,120 --> 00:29:14,740
+disjunction .. disjunction و ال conjunction
+
+410
+00:29:14,740 --> 00:29:18,100
+فالتنتين هذول كيف بدي أعرف ال priority بتاعة واحدة
+
+411
+00:29:18,100 --> 00:29:22,040
+عن التانية من صياق الجملة؟ من الجملة نفسها؟ و كيف
+
+412
+00:29:22,040 --> 00:29:25,400
+أنا فهمت الجملة؟ عشان أعرف أعبر عنها بطريقة صحية؟
+
+413
+00:29:25,400 --> 00:29:28,330
+لأهذه المفروض جابل هذه وهذه جابل هذه وين الأقواص
+
+414
+00:29:28,330 --> 00:29:31,770
+اللي نحط بالظبط بس احنا راوية ان نتكلم عن ايهاش ال
+
+415
+00:29:31,770 --> 00:29:35,570
+negation ال negation اللي لها priority عن ال ال
+
+416
+00:29:35,570 --> 00:29:39,330
+other operators فلو قولنا بالشكل هذا okay مقبولة
+
+417
+00:29:39,330 --> 00:29:43,050
+هذا بالنسبالنا مقبولة انه بدون أقواص انا فاهم ان
+
+418
+00:29:43,050 --> 00:29:48,050
+ال negation لها أولوية فهي كأنه بالظبط بالشكل هذا
+
+419
+00:29:48,050 --> 00:29:51,090
+لا
+
+420
+00:29:51,090 --> 00:29:57,140
+يمكن تكون هيكلأن الأولوية لمن؟ بالظبط الأولوية ل
+
+421
+00:29:57,140 --> 00:30:01,640
+indication طيب أعتقد برضه إحنا كان في عندنا
+
+422
+00:30:01,640 --> 00:30:03,780
+الأولوية حتى في الأرقام يعني أنتوا لو كنتوا
+
+423
+00:30:03,780 --> 00:30:13,760
+بتكتبوا في برنامج معين أو إشي معين لو نفترض x ضرب
+
+424
+00:30:13,760 --> 00:30:16,700
+y plus z
+
+425
+00:30:19,380 --> 00:30:22,160
+هي فيه priority الحقيقة في البرامج تضارب له
+
+426
+00:30:22,160 --> 00:30:26,420
+priority تضاربه القسمة عن الجامعه والطرحه صحيح
+
+427
+00:30:26,420 --> 00:30:29,920
+فنفس الكلام هنا بالنسبة لان نيجاشن بس إلها
+
+428
+00:30:29,920 --> 00:30:35,960
+priority عن ال conjunction و ال disjunction طيب
+
+429
+00:30:35,960 --> 00:30:39,780
+بناء على الكلام هذا خلينا نشوف شوية جمل و نترجمها
+
+430
+00:30:39,780 --> 00:30:44,520
+مع بعض و نشوف كيف ممكن نعبر عنها خلينا نقول انه
+
+431
+00:30:44,520 --> 00:30:51,630
+let Pit rained last night شتية الليلة الماضية أو
+
+432
+00:30:51,630 --> 00:30:58,130
+يعني صار في شتة الليلة الماضية the sprinklers came
+
+433
+00:30:58,130 --> 00:31:01,530
+on last night sprinklers اللي هي الرشاشات الميه
+
+434
+00:31:01,530 --> 00:31:03,510
+اللي بتكون مزروعة في الأرض هذه محتوطة في الأرض
+
+435
+00:31:03,510 --> 00:31:08,650
+وبترش ميه فخليني أقول إن هي إجت الليلة الماضية
+
+436
+00:31:08,650 --> 00:31:13,950
+برضه ر equal to the lawn was wet this morning
+
+437
+00:31:13,950 --> 00:31:19,050
+العشباليوم الصبح كان مبلول، كويس، هي في عندنا
+
+438
+00:31:19,050 --> 00:31:23,550
+three .. three proposition بدنا نعمل translation
+
+439
+00:31:23,550 --> 00:31:27,890
+لمين؟ لمجموعة symbols بالشكل اللي احنا شايفينه،
+
+440
+00:31:27,890 --> 00:31:33,850
+negation فيه، بدنا
+
+441
+00:31:33,850 --> 00:31:38,630
+نعكس هذهdidn't didn't بالظبط ليش؟ لأن مافيش عندنا
+
+442
+00:31:38,630 --> 00:31:42,150
+هنا الفعل المساعد محتاجين فعل مساعد نعمل فيه عملية
+
+443
+00:31:42,150 --> 00:31:48,310
+النفع فهنا هنضيف بس didn't rain last night okay
+
+444
+00:31:48,310 --> 00:31:53,830
+التانية are conjunction negation بيه ال negation
+
+445
+00:31:53,830 --> 00:31:57,810
+بيه هي موجودة فهيها مافيش عندنا مشكلة فيها and
+
+446
+00:31:57,810 --> 00:32:03,840
+بنحط قدامها and بتظل are نزلوا areوانت هينا منها،
+
+447
+00:32:03,840 --> 00:32:09,340
+مدام مافيش اي negation مافيش أيش مغيره، فاللون was
+
+448
+00:32:09,340 --> 00:32:15,880
+with this morning and it didn't rain last night،
+
+449
+00:32:15,880 --> 00:32:19,320
+طيب، الأخيرة احنا ما .. مااتكلمناش لسه على
+
+450
+00:32:19,320 --> 00:32:24,870
+الأخيرة، negation areأه لحظة negation are هي ال
+
+451
+00:32:24,870 --> 00:32:28,290
+was موجودة فإذا الفعل المساعد موجود اعمله not بس
+
+452
+00:32:28,290 --> 00:32:32,430
+في الآخر و خلصناه كويسة هذا ال negation تبعتنا بس
+
+453
+00:32:32,430 --> 00:32:36,710
+خدوا بالك ال operator اللي عندنا are يعني بدنا
+
+454
+00:32:36,710 --> 00:32:43,690
+نبدأ بإيش either تمام فبتفضطه either في الحالة
+
+455
+00:32:43,690 --> 00:32:51,770
+اللي عندنا هنا في الصوت بقطع بدنا نحط are تمام
+
+456
+00:32:54,090 --> 00:32:58,770
+ال XOR ال operator التالتة الرابعة ال operator
+
+457
+00:32:58,770 --> 00:33:03,070
+الرابعة هي ال XOR operator هذه binary exclusive OR
+
+458
+00:33:03,070 --> 00:33:06,250
+operator اتكلمنا عنها برضه combines two
+
+459
+00:33:06,250 --> 00:33:10,610
+propositions بالنسبالنا عشان تعطينا logical او
+
+460
+00:33:10,610 --> 00:33:16,190
+logic XOR او X junction او X junction for example
+
+461
+00:33:16,190 --> 00:33:22,580
+في I will earn an A in this course ان شاء اللهأنا
+
+462
+00:33:22,580 --> 00:33:28,480
+هجيب A في ال course هذا okay proposition Q I will
+
+463
+00:33:28,480 --> 00:33:33,760
+drop this course لا قدر الله كويس فهي عندنا two
+
+464
+00:33:33,760 --> 00:33:41,160
+propositions لما أجي أقول P أو P X or Q هذه منطقيا
+
+465
+00:33:41,160 --> 00:33:43,900
+ان هي تكون X or لأنه لايمكن التنين يجوا مع بعض
+
+466
+00:33:43,900 --> 00:33:50,440
+فإذا true true مش منطقيةإن الإتنين يكونوا true مش
+
+467
+00:33:50,440 --> 00:33:54,240
+منطقية فهنا الأنسب والأفضل لجملتين بالشكل هذا إن
+
+468
+00:33:54,240 --> 00:33:58,900
+أنا أستعمل x or I will either earn an A for this
+
+469
+00:33:58,900 --> 00:34:07,030
+course or I will drop it but not bothطبيعي كيف بدى
+
+470
+00:34:07,030 --> 00:34:10,050
+.. يعني انا كيف رصبت و كيف جبت ايه في نفس الوقت
+
+471
+00:34:10,050 --> 00:34:14,010
+بتجيش فإذا هدى by logic أحيانا انتوا بدكوا حسب
+
+472
+00:34:14,010 --> 00:34:18,310
+فهمكوا لل .. للجملة as a language بدكوا تفهموا إيش
+
+473
+00:34:18,310 --> 00:34:21,690
+لازم تستعملوا إيش بدكوا تستعملوا هل في احتمال أنه
+
+474
+00:34:21,690 --> 00:34:26,990
+والله ممكن ناخد ال .. ال both أنه ال .. يعني ال
+
+475
+00:34:26,990 --> 00:34:32,930
+both are true ممكن فإذا إذا ممكن orاللي هي
+
+476
+00:34:32,930 --> 00:34:37,410
+disjunction إذا مش ممكن ال X junction أو ال X or
+
+477
+00:34:37,410 --> 00:34:40,710
+ال
+
+478
+00:34:40,710 --> 00:34:44,250
+truth table تبعها هو نفس ال or ال truth table نفس
+
+479
+00:34:44,250 --> 00:34:50,370
+ال or باختلاف من ال both are true هذه هتكون false
+
+480
+00:34:50,370 --> 00:35:01,020
+كويسة X بدل N لو ال E X هذيفإذا أنا بتكلم عن مين؟
+
+481
+00:35:01,020 --> 00:35:03,700
+عن ال or العادية ال disjunction العادية ال
+
+482
+00:35:03,700 --> 00:35:06,980
+disjunction اللي احنا اتكلمنا عنها ولكن هنا x فإذا
+
+483
+00:35:06,980 --> 00:35:15,560
+executes possibility that both p and q are true
+
+484
+00:35:15,560 --> 00:35:22,000
+نجاش مع ال x or بيجوش مع بعض ليش؟ لأنه في
+
+485
+00:35:22,000 --> 00:35:25,970
+expression بعبر عن الموضوع هذا، هناخده لاحقافي
+
+486
+00:35:25,970 --> 00:35:28,890
+operator خاصة بالجزئية فيها دي لا يمكن ييجوا مع
+
+487
+00:35:28,890 --> 00:35:33,670
+بعض التنتين هدولة في جملة مع بعض أو ورا بعض يعني
+
+488
+00:35:33,670 --> 00:35:41,050
+مباشرة okay for example نوضح ال or و ال xor or و
+
+489
+00:35:41,050 --> 00:35:44,430
+xor لو أخدنا مثلا في ال English طبعا معتمدة تماما
+
+490
+00:35:44,430 --> 00:35:47,230
+على ال English انتوا كيف فاهمين اللغة انتوا كيف
+
+491
+00:35:47,230 --> 00:35:50,770
+فاهمين اللغة بتاعتكم عشان ترجموها لمجموعة symbols
+
+492
+00:35:51,750 --> 00:35:59,750
+لو قلنا وسام is a singer or وسام is a writer هذه
+
+493
+00:35:59,750 --> 00:36:03,910
+المفروض or ولا x or؟ or لأنه ممكن يكون الأثنين
+
+494
+00:36:03,910 --> 00:36:07,510
+ممكن يكون بيغني و بيكتب في نفس الوجد فليكن ممكن
+
+495
+00:36:07,510 --> 00:36:13,430
+يكون فعلا بيغني و بيكتب في نفس الوجد الجملة
+
+496
+00:36:13,430 --> 00:36:18,410
+التانية وسام is a man or وسام is a woman لأن كلمة
+
+497
+00:36:18,410 --> 00:36:22,980
+وسام ممكن تحتمل صح؟يعني الاسم ممكن يحتمل فانا لو
+
+498
+00:36:22,980 --> 00:36:27,980
+كنت قرأته وسام حد مثلا بعتلي email وبيقولي والله
+
+499
+00:36:27,980 --> 00:36:31,240
+انا بتسجل المصاق بس مش عارف كيف ادخل على ال model
+
+500
+00:36:31,240 --> 00:36:36,340
+وسام طب ممكن يكون male او female طب هذي man ولا و
+
+501
+00:36:36,340 --> 00:36:40,160
+man ممكن ففي الحالة هذي okay ممكن نكتبها الجملة بس
+
+502
+00:36:40,160 --> 00:36:44,200
+مقدرش اقول انها or يعني لما أجي أترجمها فهذه لازم
+
+503
+00:36:44,200 --> 00:36:48,800
+تكون x or لازم تكون x or تمام
+
+504
+00:36:52,070 --> 00:36:55,930
+Okay الجزء اللي بعده هو ال implication هذا الجديد
+
+505
+00:36:55,930 --> 00:36:59,270
+.. جديد يمكن شوية مفاهيم عنكم شوية، كويس ال
+
+506
+00:36:59,270 --> 00:37:01,930
+implication .. implication مفيدة جدا في ال if then
+
+507
+00:37:01,930 --> 00:37:05,150
+في البرمجة و أنتم بتتكلموا عن برمجة مفيدة
+
+508
+00:37:05,150 --> 00:37:09,710
+الأهميتها لما تيجوا تتكلموا في البرنامج تبعكم if
+
+509
+00:37:09,710 --> 00:37:14,570
+then بمعنى إنه إذا تحقق ال condition الشرط حقق
+
+510
+00:37:14,570 --> 00:37:20,430
+للنتيجةتمام او if انتوا عادة بتكتبوها نكتب انها
+
+511
+00:37:20,430 --> 00:37:25,130
+كود صغير لو قولنا if x أكبر نفترض مثلا من five
+
+512
+00:37:25,130 --> 00:37:31,070
+نحطله هنا statement معينة او خلينا نحط احنا من هنا
+
+513
+00:37:31,070 --> 00:37:40,250
+اي statement خلينا نقول print فرضا
+
+514
+00:37:40,250 --> 00:37:41,710
+طيب else
+
+515
+00:37:44,850 --> 00:37:53,910
+نفترض brand and خلينا نقول حاجة بهذا الشكل طيب
+
+516
+00:37:53,910 --> 00:38:01,290
+فإذا أنا صرت مرتبط بمين بالشرط إذا تحقق الشرط حقق
+
+517
+00:38:01,290 --> 00:38:07,290
+ليه النتيجة مظبوط إذا تحقق الشرط حقق ليه النتيجةهي
+
+518
+00:38:07,290 --> 00:38:09,250
+المفهوم الأساس اللى هناخده من ال implication
+
+519
+00:38:09,250 --> 00:38:15,930
+ماتحققش else إيش ال condition اللى هنعمله؟ كويس
+
+520
+00:38:15,930 --> 00:38:22,730
+خلينا ما ال example اللى هتكون عندنا هنا ف if P is
+
+521
+00:38:22,730 --> 00:38:28,810
+true then Q is true but if P is not true then Q
+
+522
+00:38:28,810 --> 00:38:34,130
+could be either true or false بمعنىOkay انا ..
+
+523
+00:38:34,130 --> 00:38:37,290
+يعني ربطه ب condition معين بس لو مااتحققش انا
+
+524
+00:38:37,290 --> 00:38:41,710
+ماليش علاقة فيه انا ماليش علاقة فيه بصير انا ماليش
+
+525
+00:38:41,710 --> 00:38:46,670
+دعوة زي واحد بيقول لابنه مثلا والله انا لو انجحت
+
+526
+00:38:46,670 --> 00:38:51,650
+هشريلك بسكاليت تمام؟ طيب مانجحش ماهو ممكن يكون
+
+527
+00:38:51,650 --> 00:38:54,990
+حتاني اشتر على البسكاليت انا ماليش علاقة فيك بس
+
+528
+00:38:54,990 --> 00:38:58,490
+الشرط اذا والله is it true انجحت ال condition
+
+529
+00:38:58,490 --> 00:39:02,110
+اتحققالنتيجة لازم تتحقق معناته انا حسب وعدي اللي
+
+530
+00:39:02,110 --> 00:39:05,910
+اتجبلك طيب ماتحققش انا بس اللي ماليش دعوة بس انت
+
+531
+00:39:05,910 --> 00:39:09,130
+جبت من برا انا ماليش علاقة فإذا ممكن false و ممكن
+
+532
+00:39:09,130 --> 00:39:13,550
+true لحظة ببساطة هاي .. هاي معنى ال implication
+
+533
+00:39:13,550 --> 00:39:18,510
+انه إذا اتحقق شرط بيضمنلي الشرطت يعني necessary
+
+534
+00:39:18,510 --> 00:39:23,730
+ضرورية ضرورية تحقق الشرط عشان تصير النتيجة ولكن
+
+535
+00:39:23,730 --> 00:39:26,370
+ممكن تصير النتيجة بدون الشرط هذه ال necessary
+
+536
+00:39:26,370 --> 00:39:30,090
+condition بنسميها necessary conditionفى فرق بين
+
+537
+00:39:30,090 --> 00:39:32,430
+necessary condition و sufficient condition فاحنا
+
+538
+00:39:32,430 --> 00:39:35,110
+هنا متكلم عن جزئية necessary condition شرط ضرورى
+
+539
+00:39:35,110 --> 00:39:40,650
+ولكن مش ملزم لحظة مش ملزم كتير خلينى نشوف example
+
+540
+00:39:40,650 --> 00:39:47,490
+عليها let P equal to you study hard ان انت درستي
+
+541
+00:39:47,490 --> 00:39:52,870
+كويس درستي بصورة جيدة Q equal to you will get a
+
+542
+00:39:52,870 --> 00:40:00,860
+good grade تمام لما اقول Pimplies q كأني بقول if
+
+543
+00:40:00,860 --> 00:40:05,420
+you study hard then you will get a good grade طيب
+
+544
+00:40:05,420 --> 00:40:10,160
+else يعني لو أنا مادرستش كويس it could go either
+
+545
+00:40:10,160 --> 00:40:15,060
+way ممكن ينجح يكون والله لسه متذكرين شوية حاجات من
+
+546
+00:40:15,060 --> 00:40:18,300
+اللي جالها الدكتور في وقت المحاضرة قبل شهر زمان قد
+
+547
+00:40:18,300 --> 00:40:21,580
+يكون يعني لفت الامتحان مادرستناش كويس ولكن صدفت
+
+548
+00:40:21,580 --> 00:40:25,660
+أنه الامتحان إجا معظم من حاجات أنا لسه متذكرها بمش
+
+549
+00:40:25,660 --> 00:40:33,600
+الحال بسالاصل ان مدام ذكرت اذا ذكرت hard بصورة
+
+550
+00:40:33,600 --> 00:40:37,320
+قوية بصورة جيدة كويس و فاهم صح الاصل انه ايش يصير
+
+551
+00:40:37,320 --> 00:40:43,700
+انه نتيجة تتحقق اللي هي get a good grade تمام
+
+552
+00:40:43,700 --> 00:40:48,940
+فبصير عندنا هنا ال truth table تبعنا الحالة
+
+553
+00:40:48,940 --> 00:40:50,980
+الوحيدة اللي ممكن تكون false و هنشرحها لو جيت
+
+554
+00:40:50,980 --> 00:40:57,330
+واحدة واحدة اللي هي TF اتحقق ال conditionبس
+
+555
+00:40:57,330 --> 00:41:01,350
+ماصارتش النتيجة طب ليش؟ مانحققت ال condition ليش
+
+556
+00:41:01,350 --> 00:41:03,910
+ماحصلناش عن نتيجة؟ هذه الحالة الوحيدة ال false
+
+557
+00:41:03,910 --> 00:41:06,530
+اللي أصلا غير منطقية الأصل أنها تكون فعلا false
+
+558
+00:41:06,530 --> 00:41:13,590
+الولد نجح طب ليش ماجبتلهوش البسكليت؟ صح ماهي منطقي
+
+559
+00:41:13,590 --> 00:41:16,930
+معناته حيفوق عليا و هعملنا جثة لأنه فعلا false
+
+560
+00:41:16,930 --> 00:41:22,010
+الوضع خطأ الأصل أنه هذه الحالة الوحيدة اللي تكون
+
+561
+00:41:22,010 --> 00:41:27,630
+فيها falseأما مااتحققش الشرط ماحصلناش عن نتيجة، ما
+
+562
+00:41:27,630 --> 00:41:32,750
+هو طبيعي، مادرستش، مانجحتش طيب، مادرستش و انجحت،
+
+563
+00:41:32,750 --> 00:41:35,590
+برضه ممكن الامتحان إجا سهل، يعني بتصير هنا
+
+564
+00:41:35,590 --> 00:41:37,690
+conditions تانية، ممكن تتحكم في الموضوع، ممكن
+
+565
+00:41:37,690 --> 00:41:43,810
+الامتحان طالع سهل، الطالب أو الطالبة كانوا متذكرين
+
+566
+00:41:43,810 --> 00:41:48,610
+بعض معلومات من المحاضرات نفسها من زمان، بس ليلة
+
+567
+00:41:48,610 --> 00:41:53,300
+امتحان ماصادفتوا انه مادرسوش كويس، true ممكنةطيب
+
+568
+00:41:53,300 --> 00:41:58,200
+true و false درسي كويس لكن ما نجحش هذه الوحيدة
+
+569
+00:41:58,200 --> 00:42:01,760
+اللي فيها مشكلة طب أنت درست طب مدام درست معناته
+
+570
+00:42:01,760 --> 00:42:04,320
+كان فيه مشكلة في الدراسة من أصله يعني معناته مش
+
+571
+00:42:04,320 --> 00:42:07,020
+hard ماكنتش hard فهذه الحالة الوحيدة اللي نقدر
+
+572
+00:42:07,020 --> 00:42:14,020
+نقول عنها false طيب درس نجح منطقي true منطقية جدا
+
+573
+00:42:14,020 --> 00:42:14,860
+تكون true
+
+574
+00:42:18,220 --> 00:42:22,280
+for example بناء على الشكل اللي احنا حاطينه هذا لو
+
+575
+00:42:22,280 --> 00:42:28,720
+قولنا مثلا one equal to zero employees pigs can
+
+576
+00:42:28,720 --> 00:42:33,640
+fly اللي لو قولنا واحد بيساوي صفر بيضمن لإن
+
+577
+00:42:33,640 --> 00:42:37,980
+الخنزير بتعرف يطير طبعا انتوا هتلاحظوا ان هي ..
+
+578
+00:42:37,980 --> 00:42:41,700
+ايش الكلام اللي مالوش أي علاقة ببعضه؟ هي trueهي
+
+579
+00:42:41,700 --> 00:42:45,240
+true لأن ال condition مش حقيقي أصلا فالنتيجة مش
+
+580
+00:42:45,240 --> 00:42:51,000
+حقيقية فكجملة logically منطقية هي كلها غلط في غلط
+
+581
+00:42:51,000 --> 00:42:54,820
+فمنطق أن البداية غلط و النهاية غلط بتاعتها false
+
+582
+00:42:54,820 --> 00:43:00,280
+false فهذه بتعبر عن إيش false false is it true
+
+583
+00:43:00,280 --> 00:43:03,380
+ناخد
+
+584
+00:43:03,380 --> 00:43:08,680
+مجموعة examples و نشوف هتعرفوا إيهمعانا هى false
+
+585
+00:43:08,680 --> 00:43:13,980
+ولا true ولا اش بالظبط لو قلنا if this lecture
+
+586
+00:43:13,980 --> 00:43:20,040
+ends اذا المحاضرة انتهت then the sun will rise
+
+587
+00:43:20,040 --> 00:43:24,420
+tomorrow طب هى انتهت؟ طب أنا هنا بتكلم معاكم
+
+588
+00:43:24,420 --> 00:43:28,820
+ماانتهتش فإذا انها دى false بدية false طيب خلينا
+
+589
+00:43:28,820 --> 00:43:29,500
+نرجع شوية
+
+590
+00:43:33,240 --> 00:43:36,440
+ناخد الجزء تبعنا هذا اللي هي false, false, false,
+
+591
+00:43:36,660 --> 00:43:42,040
+true, true, false الوحيدة كانت اللي فيها مشكلة
+
+592
+00:43:42,040 --> 00:43:49,880
+خلينا نشوف ان احنا بدين ب false اصلا صح؟ انا
+
+593
+00:43:49,880 --> 00:43:53,400
+ماانتهتش المحاضرة المحاضرة لسه ماانتهتش ضايلها نص
+
+594
+00:43:53,400 --> 00:43:56,060
+ساعة زمان كويس فإذا انا بتكلم عن جزء هذا
+
+595
+00:44:01,270 --> 00:44:06,750
+صح؟ طب في الحالتين true بغض النظر عن مين عن
+
+596
+00:44:06,750 --> 00:44:10,630
+النتيجة بغض النظر عن إيش النتيجة اللي بتطلع .. عن
+
+597
+00:44:10,630 --> 00:44:13,570
+ال .. عن ال Q statement أو ال Q proposition تبعنا
+
+598
+00:44:13,570 --> 00:44:16,810
+هي في الآخر ال implication كله على بعضه هيكون true
+
+599
+00:44:16,810 --> 00:44:22,150
+لإنه بدنا خطأ بدنا ب .. ب .. ب .. false احنا ما
+
+600
+00:44:22,150 --> 00:44:24,670
+انتهى .. ما انتهتش السلم حاضرة then the .. the ..
+
+601
+00:44:24,670 --> 00:44:29,810
+the sun will rise tomorrow okay ممكن تكون trueبس
+
+602
+00:44:29,810 --> 00:44:35,710
+فى النهاية برضه كلها على بعض is true كويس if
+
+603
+00:44:35,710 --> 00:44:42,150
+Tuesday is a day of the week true تمام then I am a
+
+604
+00:44:42,150 --> 00:44:47,210
+penguin a penguin اللى هو البطريق false طب صارت فى
+
+605
+00:44:47,210 --> 00:44:52,810
+ك true false كلها false صحيح كلها صارت ايش false
+
+606
+00:44:52,810 --> 00:44:58,230
+طيبif one plus one equal to six then Obama is a
+
+607
+00:44:58,230 --> 00:45:01,310
+president طب ما هو فعلا Obama is a president بس مش
+
+608
+00:45:01,310 --> 00:45:04,110
+عشان هيك هقول إن هي true لأن هذي false أصلا ف
+
+609
+00:45:04,110 --> 00:45:08,510
+false حكمت على الموضوع خلصنا false سواء النتيجة
+
+610
+00:45:08,510 --> 00:45:12,490
+كانت false or true هو منطقي منطق ال implication
+
+611
+00:45:12,490 --> 00:45:15,290
+تبعنا ال implication تبعنا منطقي فإذن هذي المفروض
+
+612
+00:45:15,290 --> 00:45:21,470
+إن هي true طيب if the moon is made of a green
+
+613
+00:45:21,470 --> 00:45:22,210
+cheese
+
+614
+00:45:24,600 --> 00:45:28,200
+إذا كان مصنوع .. الجمر مصنوع من .. من جبنة خضرة
+
+615
+00:45:28,200 --> 00:45:32,500
+then I am richer than Bill Gates عارفين Bill
+
+616
+00:45:32,500 --> 00:45:38,420
+Gates؟ okay يعني لا هذه صح ولا هذه صح واضح false
+
+617
+00:45:38,420 --> 00:45:43,920
+employees false فإذا كلها هتكون true كلها هتكون
+
+618
+00:45:43,920 --> 00:45:48,180
+true تمام
+
+619
+00:45:48,180 --> 00:45:54,380
+شوية expressionsبتعبّر لنا عن عملية ال implication
+
+620
+00:45:54,380 --> 00:45:59,420
+اللي احنا بنحكي عنها أنه ممكن نقول implies P
+
+621
+00:45:59,420 --> 00:46:04,640
+implies Q فإذا P تضمن Q فهذا هو الشرط هي النتيجة
+
+622
+00:46:04,640 --> 00:46:10,640
+في شرط أو السابقة اللي المفروض تتحقق فتحقق للنتيجة
+
+623
+00:46:10,640 --> 00:46:20,160
+أو ممكن تكون if P then Q if P بدون thenضمن كومة
+
+624
+00:46:20,160 --> 00:46:25,840
+then Q برضه تستعمل فانتوا لو اجدكوا اي جملة فيها
+
+625
+00:46:25,840 --> 00:46:29,560
+عبارة من العبارات هدولة بس بتعرف وين انو جزء ال P
+
+626
+00:46:29,560 --> 00:46:33,520
+وانو جزء ال Q عشان ما يتلخبطش معاكم الجدول لانوا
+
+627
+00:46:33,520 --> 00:46:36,380
+ديروا بالك لو لخبط ال P مع ال Q تلخبطت معاكم
+
+628
+00:46:36,380 --> 00:46:41,500
+هتضيعوا في الجزئية هذه لان هذه هتصير تيجي مكان هذه
+
+629
+00:46:41,500 --> 00:46:44,180
+و هذه هتيجي مكان هذه فهتلاقي انه الاصل اللي بتصير
+
+630
+00:46:44,180 --> 00:46:47,460
+هذه هي ال false وهذه صارت ال trueفاطلح بطن النتائج
+
+631
+00:46:47,460 --> 00:46:50,420
+معاكم عشان هي مهم جدا تعرفوا انتوا في اي
+
+632
+00:46:50,420 --> 00:46:53,780
+expression من هدولة تشتغلوا ال expression الصح
+
+633
+00:46:53,780 --> 00:46:58,040
+تتعاملوا معاه عشان تضمنوا مين ال P و مين ال Q لازم
+
+634
+00:46:58,040 --> 00:47:03,060
+تستخرجوهم بعناية مين ال condition و مين النتيجة
+
+635
+00:47:03,060 --> 00:47:06,980
+عشان تعرفوا الناتج لل implication operator كلها
+
+636
+00:47:06,980 --> 00:47:10,200
+على وقت فضلي بس المهم بالنسبالي انه مثلا حتر و كتر
+
+637
+00:47:10,200 --> 00:47:16,550
+و مصطلما و P و 7صح أنا بحكيلك هنا لو إجتك ال
+
+638
+00:47:16,550 --> 00:47:20,570
+statement تبعتك إجتك language ممكن أعطيكيها
+
+639
+00:47:20,570 --> 00:47:25,570
+language أو تعطي language و أنت اللي اتطلعي بالظبط
+
+640
+00:47:25,570 --> 00:47:29,030
+أه مهم جدا تعرفيه حسب ال exceptions اللي احنا
+
+641
+00:47:29,030 --> 00:47:31,330
+حاطينهم اللي وجد هنا ال exceptions إذا كان
+
+642
+00:47:31,330 --> 00:47:34,570
+employees معناته اللي جابلها هي ال P و اللي بعدها
+
+643
+00:47:34,570 --> 00:47:40,250
+هي ال Q لأنها هي PPploys Q فإذا P تضمن Q واضحة P
+
+644
+00:47:40,250 --> 00:47:43,850
+تضمن Q فإذا الأولى هي الشرط التاني هي النتيجة كويس
+
+645
+00:47:43,850 --> 00:47:51,690
+when عندما P ضمن then Q فهنا على طول اللى بتيجي
+
+646
+00:47:51,690 --> 00:47:55,370
+قبل الكومة بعد ال when قبل الكومة هذه هي ال P
+
+647
+00:47:55,370 --> 00:48:06,260
+whenever كلما كلما حدثت P then Q تمام Q if PQ
+
+648
+00:48:06,260 --> 00:48:14,380
+تتحقق إذا في تمام وين بالعكس هي Q وين بتكون تطلع
+
+649
+00:48:14,380 --> 00:48:18,140
+على وجه ال وين اللي هنا كان في كومة فكانت بتفصل
+
+650
+00:48:18,140 --> 00:48:23,460
+كانت عند حدوث بي كومة افصل إيش بيصير طب هنا لأ هنا
+
+651
+00:48:23,460 --> 00:48:28,280
+جملة واحدة Q وين بي فالقصد اللي كنتوا تاخدوا بالكم
+
+652
+00:48:28,280 --> 00:48:30,940
+من ال expressions هذه أنية واحدة اللي هتتحقق معاكم
+
+653
+00:48:30,940 --> 00:48:33,900
+بتعرفوا منها تطلعوا هذه في الآخر هتكون عبارة عن
+
+654
+00:48:33,900 --> 00:48:39,510
+إيشهذه هتكون جملة مكتوبة هنا جملة وهنا جملة فانتوا
+
+655
+00:48:39,510 --> 00:48:42,510
+هتلاقيوا جملة كاملة بتكونوا تعرفوا if ومافيش اي
+
+656
+00:48:42,510 --> 00:48:45,550
+comma بينهم معناته الجزء اللي في الأول بتاخدوها و
+
+657
+00:48:45,550 --> 00:48:50,130
+بتقولوا q equal to كذا فبتكونوا ضمنين انه ايش
+
+658
+00:48:50,130 --> 00:48:53,910
+الحالة بتاعتها بتحطوها كنتيجة مش بنحطها condition
+
+659
+00:48:53,910 --> 00:48:58,870
+هنا في الأولتمام؟ هاي الهدف من شوية الجمل هدولة
+
+660
+00:48:58,870 --> 00:49:02,390
+طبعا في أكتر من هيك بس يعني بزيادة حتى بزيادة كتير
+
+661
+00:49:02,390 --> 00:49:06,150
+المجوهات الجمل اللي موجودة عندكم أو ال expressions
+
+662
+00:49:06,150 --> 00:49:09,450
+اللي موجودة عندكم زي أخر واحدة مثلا q is employed
+
+663
+00:49:09,450 --> 00:49:16,810
+by p يعني قدمنا المفقود بيها عن الفعل يعني صارت
+
+664
+00:49:16,810 --> 00:49:24,540
+okay هي مضمونةمن B by P في ال implication في شوية
+
+665
+00:49:24,540 --> 00:49:30,620
+تعبير أو في شوية مصطلحات تستخدم مع ال implication
+
+666
+00:49:30,620 --> 00:49:34,060
+أولها
+
+667
+00:49:34,060 --> 00:49:40,690
+ال converse و ال inverse و ال contrapositiveال
+
+668
+00:49:40,690 --> 00:49:43,310
+converse لما أقول في عملت converse ل ال
+
+669
+00:49:43,310 --> 00:49:48,050
+implication في employees q معناته أنا غيرتهم مع
+
+670
+00:49:48,050 --> 00:49:54,150
+بعض عكستهم خليت النتيجة في الأول و الشرط في التاني
+
+671
+00:49:54,150 --> 00:49:57,970
+طبعا هتعطي نتائج مختلفة تماما بس إيش علاقتهم مع
+
+672
+00:49:57,970 --> 00:50:02,570
+بعض هي converse لل implication الأصلي طبعا أكيد
+
+673
+00:50:02,570 --> 00:50:06,820
+نتائج مختلفةالنتائج هتكون طبعا مختلفة، إشي طبيعي
+
+674
+00:50:06,820 --> 00:50:12,040
+كويس أما ال inverse تبعها إنه نفسها بس بعملها
+
+675
+00:50:12,040 --> 00:50:17,540
+لمين؟ لل negation negation ال P employs negation Q
+
+676
+00:50:17,540 --> 00:50:21,060
+فبصير عندنا expression تاني طيب ال contrapositive
+
+677
+00:50:21,060 --> 00:50:27,300
+تنتين في بعض لحظة هعمل ال converse مع ال inverse
+
+678
+00:50:27,300 --> 00:50:31,820
+تنتين مع بعض جلبنا التنتين فهي مسارة ال Q في الأول
+
+679
+00:50:33,040 --> 00:50:37,400
+وعملنا negation لكل واحدة قبلها طيب واحدة من ال
+
+680
+00:50:37,400 --> 00:50:43,080
+three operators الجديدة هدولة او ال three terms
+
+681
+00:50:43,080 --> 00:50:48,360
+هدولة فعليا مساوية او بتعطيني the same truth table
+
+682
+00:50:48,360 --> 00:50:55,060
+of implication واحدة منهم هتعطي نفس النتائج لمين
+
+683
+00:50:55,060 --> 00:51:00,660
+لل implication يا ترى مين منهم تانية
+
+684
+00:51:02,780 --> 00:51:05,640
+التالتة منطقة التالتة انتوا عاملين inverse مع
+
+685
+00:51:05,640 --> 00:51:09,940
+coinverse يعني عكسين عكس عكسين العكس فالمنطق انه
+
+686
+00:51:09,940 --> 00:51:13,120
+هتكون هي الأقرب انها تكون مساوية فال
+
+687
+00:51:13,120 --> 00:51:16,860
+contrapositive في الغالب هي فعلا وهذا حقيقة هي
+
+688
+00:51:16,860 --> 00:51:20,080
+اللي هتكون متساوية او مساوية لل implication عشان
+
+689
+00:51:20,080 --> 00:51:23,780
+نثبت الكلام هذا ممكن نستعمل truth table نستخدم في
+
+690
+00:51:23,780 --> 00:51:26,040
+الموضوع هذا ونجرب هل فعلا متساوية او لا
+
+691
+00:51:29,200 --> 00:51:35,140
+هي مجموعة الاحتمالات الممكنة لهم نيجيشن q
+
+692
+00:51:35,140 --> 00:51:40,120
+محتاجينها عشان نحسب الcontra positive نيجيشن P
+
+693
+00:51:40,120 --> 00:51:42,980
+محتاجينها عشان نحسب برضه الcontra positive مجرد
+
+694
+00:51:42,980 --> 00:51:49,200
+عكس يعني خدوا هذا الجزء عكسوه هنا راحظوا تمام
+
+695
+00:51:49,200 --> 00:51:56,340
+الجزء التاني P عكسوه هناوبدأوا يحسبوا ال
+
+696
+00:51:56,340 --> 00:52:00,660
+implication و ال contrapositive ال implication
+
+697
+00:52:00,660 --> 00:52:03,800
+بيحسبها من ال two columns هدول الحالة الوحيدة اللي
+
+698
+00:52:03,800 --> 00:52:12,400
+false هي true و false otherwise truth طيب
+
+699
+00:52:12,400 --> 00:52:15,800
+الحالة التانية في ال contrapositive بداش تطلع ال
+
+700
+00:52:15,800 --> 00:52:18,940
+two columns هدولة و بنفس الترتيب هذا negation q في
+
+701
+00:52:18,940 --> 00:52:23,740
+الأول و negation p في التانيةبرضه الحالة الوحيدة
+
+702
+00:52:23,740 --> 00:52:28,440
+اللي هي true فالس فالس هتلاقي ان ال column هذا
+
+703
+00:52:28,440 --> 00:52:32,160
+مساوي لل column هذا فإذا فعلا ال implication equal
+
+704
+00:52:32,160 --> 00:52:39,900
+to او equivalent ل ال contrapositive تبعها طيب
+
+705
+00:52:39,900 --> 00:52:43,520
+دلنا لعنا ال biconditional operator ال
+
+706
+00:52:43,520 --> 00:52:46,840
+biconditional operator هنا بنتكلم عن implication
+
+707
+00:52:46,840 --> 00:52:54,260
+في الاتجاهينالمعنى اللغوي تبعها if and only if إذا
+
+708
+00:52:54,260 --> 00:52:59,980
+وإذا فقط تقوى كنت إيش بقول بقول إذا درستوا هتاخدوا
+
+709
+00:52:59,980 --> 00:53:06,520
+معدل جيد معدل كويس يعني القصد فيها إذا ما درستوش
+
+710
+00:53:06,520 --> 00:53:10,440
+سبتها ماليش علاقة لكن لما أقولكوا ديروا بالكم إذا
+
+711
+00:53:10,440 --> 00:53:14,540
+درستوا وإذا درستوا فقط هتاخدوا معدل جيد معناته إذا
+
+712
+00:53:14,540 --> 00:53:19,050
+ما درستوش مش هتاخدواماسبنهاش لحالها هيك بظروفها هي
+
+713
+00:53:19,050 --> 00:53:21,610
+الفكرة انه ماانتثبتش بظروفها ف if and only if
+
+714
+00:53:21,610 --> 00:53:28,530
+بتختلف في جزئية ال false إذا مااتحققش مش هيتحقق
+
+715
+00:53:28,530 --> 00:53:32,970
+النتيجة انتهى مش هيتحقق النتيجة خلينا نشوف if and
+
+716
+00:53:32,970 --> 00:53:37,870
+only if هذه كيف ممكن نستعملها لو قولنا P is Obama
+
+717
+00:53:37,870 --> 00:53:43,230
+wins the 2012 election Obama فاز في انتخابات 2012
+
+718
+00:53:43,230 --> 00:53:48,560
+اللي كانت التجديد تبعهQ equal to Obama will be
+
+719
+00:53:48,560 --> 00:53:55,940
+president for all of 2014 قعد إن طول 2014 و هيكمل
+
+720
+00:53:55,940 --> 00:54:01,520
+إن 2016 كويس فإذا هنا لاحظوا أوباما مدام نجح في
+
+721
+00:54:01,520 --> 00:54:05,580
+2012 هو أكيد لازم يكون الرئيس في 2014 لأنه لسه ما
+
+722
+00:54:05,580 --> 00:54:08,760
+انتهتش الفترة الرئاسية تبعته ما انتهتش الفترة
+
+723
+00:54:08,760 --> 00:54:12,840
+الرئاسية ف by logic لما واحد يقولي والله في 2012
+
+724
+00:54:12,840 --> 00:54:17,360
+أوباما فاز في الانتخاباتو احنا هلوجت في 2014 من
+
+725
+00:54:17,360 --> 00:54:20,860
+غير ماعرف اخبار و من غير by logic اه هي امريكا
+
+726
+00:54:20,860 --> 00:54:23,320
+جديش الفترة الرئيسية اه اربع سنة اه يعني معناته
+
+727
+00:54:23,320 --> 00:54:26,240
+لسه أوباما يعني خلاص ايك لحاله و قلتها مع ان انا
+
+728
+00:54:26,240 --> 00:54:28,620
+مش عارف اخباره فانا افترض ولا بعرف اه معناته هو هو
+
+729
+00:54:28,620 --> 00:54:33,700
+لسه موجود اه صح هو موجود كويس فلما بقول P by
+
+730
+00:54:33,700 --> 00:54:39,760
+conditional Q كأني بقول ifو فقط إذا قتل أوباما
+
+731
+00:54:39,760 --> 00:54:47,720
+الانتصار 2012 أوباما سيكون الرئيس للجميع في 2014
+
+732
+00:54:52,470 --> 00:54:57,730
+ال truth table لل by conditional زي ما قلنا هي
+
+733
+00:54:57,730 --> 00:55:02,350
+مشابهة تقريبا لمين ل .. ال .. هي الحقيقة مشابهة
+
+734
+00:55:02,350 --> 00:55:05,610
+لكذا واحدة فيهم و هنربطها لو جدت بكذا شغلة أول ما
+
+735
+00:55:05,610 --> 00:55:08,890
+هنربطها هبدنا نربطها مع ال by ال .. ال implication
+
+736
+00:55:08,890 --> 00:55:11,790
+مع ال implication لما أجى أربطها مع ال implication
+
+737
+00:55:11,790 --> 00:55:15,510
+هي احنا هنا شرطنا الوحيد فيها أنه لازم ال
+
+738
+00:55:15,510 --> 00:55:21,110
+condition في الاتجاهين if and only if فإذا if a
+
+739
+00:55:21,110 --> 00:55:29,680
+falseOkay false طيب false true لأ لأ هنا كنا
+
+740
+00:55:29,680 --> 00:55:33,220
+سايبينها بظروفها ممكن يكون متذكر شغلها هنا قولنا
+
+741
+00:55:33,220 --> 00:55:37,760
+if and only if إذا ما اتحققش مافيش فإذا فعلا
+
+742
+00:55:37,760 --> 00:55:41,870
+مااتحققشمافيش false هذه الحالة الوحيدة يمكن ان
+
+743
+00:55:41,870 --> 00:55:44,950
+هناك كانت true في ال implication هناك كانت true
+
+744
+00:55:44,950 --> 00:55:50,590
+نتيجة هنا only if اللي ضفناها لأ استفنت ليه ال
+
+745
+00:55:50,590 --> 00:55:54,190
+error ده طيب true و false احنا من اول متفقين ان هي
+
+746
+00:55:54,190 --> 00:55:58,430
+اصلا false طيب true true اتحقق لشريح ال condition
+
+747
+00:55:58,430 --> 00:56:01,520
+الطبيعي لازم يتحقق النتيجةتحقق ال condition
+
+748
+00:56:01,520 --> 00:56:06,140
+الطبيعي جدا لازم تتحقق نتيجته فهذه true مش مشكلة
+
+749
+00:56:06,140 --> 00:56:10,620
+في هذا الموضوع الفرق الوحيد كان في الروح ده okay
+
+750
+00:56:10,620 --> 00:56:15,780
+هذه هيك ربطناها مع مين؟ مع ال implication طيب نيجي
+
+751
+00:56:15,780 --> 00:56:21,160
+نربطها شوية هيك مع ال XOR ايش الفرق بينها و بين ال
+
+752
+00:56:21,160 --> 00:56:24,960
+XOR ايش
+
+753
+00:56:24,960 --> 00:56:30,990
+الفرق بينها و بين ال XOR هنا لاحظوليلأ عكس العكس
+
+754
+00:56:30,990 --> 00:56:35,790
+العكس لحظه هذه العكس تماما هنا كانت هنا true وهنا
+
+755
+00:56:35,790 --> 00:56:40,130
+false صحيح لأ هنا بالعكس تماما و عشان ايه قلتلكم
+
+756
+00:56:40,130 --> 00:56:45,570
+بتجيش كنا نعمل negation مع xor لأن في operator
+
+757
+00:56:45,570 --> 00:56:49,050
+بعبر عن الموضوع هذا اللي هي by conditional هي فعلا
+
+758
+00:56:49,050 --> 00:56:55,360
+بتعطيكوا العكسالعكس لمن؟ لل x or أو ال opposite of
+
+759
+00:56:55,360 --> 00:57:01,560
+x or طبعا، تمام، كويس فلاحظوا إيش أخدنا احنا الوجد
+
+760
+00:57:01,560 --> 00:57:07,060
+فعلا؟ أخدنا كذا شغلة بدأنا مع ال negation وهنا
+
+761
+00:57:07,060 --> 00:57:10,080
+بدنا نعمل negation هاي في عندكوا زي كأنه revision
+
+762
+00:57:10,080 --> 00:57:15,640
+لكل ال operators اللي أخدناهم negation لل P، false
+
+763
+00:57:15,640 --> 00:57:18,200
+بتصير true، false بتصير true، true بتصير false و
+
+764
+00:57:18,200 --> 00:57:22,780
+هكذا، كويس ال conjunctionاللي انتوا كنتوا عارفينها
+
+765
+00:57:22,780 --> 00:57:26,740
+and conjunction الحالة الوحيدة كله false باستثناء
+
+766
+00:57:26,740 --> 00:57:33,460
+true true بتعطي true ال disjunction كله true
+
+767
+00:57:33,460 --> 00:57:39,100
+باستثناء false false بتعطي false ال X or X or
+
+768
+00:57:39,100 --> 00:57:45,940
+اختلفوا true متشابهين false كويس
+
+769
+00:57:47,630 --> 00:57:51,430
+و ناخد بالنا دائما نفرق بينها خصوصا لما بتكلم عن
+
+770
+00:57:51,430 --> 00:57:56,610
+ال language افرق بينها و بين ال or مهم جدا من خلال
+
+771
+00:57:56,610 --> 00:58:01,870
+ال context لل language من خلال سياق الجمل تعرفوا
+
+772
+00:58:01,870 --> 00:58:05,730
+انتوا المفروض تتعاملوا مع or او ترجموها or ولا xor
+
+773
+00:58:05,730 --> 00:58:09,670
+مهم جدا كويس ال implication حكينا عن ال
+
+774
+00:58:09,670 --> 00:58:11,830
+implication اتكلمنا عن ال implication و بعدين
+
+775
+00:58:11,830 --> 00:58:16,250
+اتكلمنا عن ال by conditional عن ال by conditional
+
+776
+00:58:18,080 --> 00:58:21,740
+ال notations بتاعتهم .. ال notations بتاعتهم ..
+
+777
+00:58:21,740 --> 00:58:27,380
+لاحظوا ال propositional logic كيف شكلهم .. هدول ال
+
+778
+00:58:27,380 --> 00:58:30,360
+notations اللي احنا اتعلمناهم اليوم .. أخدناهم
+
+779
+00:58:30,360 --> 00:58:33,880
+اليوم .. polynomial اللي انتوا كنتوا تاخدوهم سابقا
+
+780
+00:58:33,880 --> 00:58:38,060
+.. كيف كنتوا تكتبوهم سابقا أو يمكن تكتبوهم في ال
+
+781
+00:58:38,060 --> 00:58:41,160
+logic design .. في ال logic design .. في ال logic
+
+782
+00:58:41,160 --> 00:58:46,200
+design بتشتغلوا على هدول .. بتعملوهمالـ hat اللي
+
+783
+00:58:46,200 --> 00:58:48,720
+فوق هذه فخلاص بعرف ال .. البار عارف ان اللي فوق
+
+784
+00:58:48,720 --> 00:58:51,340
+اللي هنا بعرف انه هذي إيش negation أو اللي هي ال
+
+785
+00:58:51,340 --> 00:58:56,440
+inverse أو ال inverter كويس هنا بالشكل هذا هي كده
+
+786
+00:58:56,440 --> 00:59:00,440
+كأنهم مضروين ضارب في بعض فهي and plus بيعملوا
+
+787
+00:59:00,440 --> 00:59:04,640
+بينهم plus فانتوا بتعرفوا انه or ال x or هي هي ال
+
+788
+00:59:04,640 --> 00:59:07,060
+implication وال if and only if ماكنتوا مش هتاخدوهم
+
+789
+00:59:07,060 --> 00:59:10,020
+مابتاخدوهمش يعني فعليا كنتوا في الرياضية هنا
+
+790
+00:59:10,020 --> 00:59:14,740
+بتاخدوهم كويس في ال java باستخدام ال javaو
+
+791
+00:59:14,740 --> 00:59:18,180
+باستخدام سواء ان انت بتتكلم عن bit-wise او word
+
+792
+00:59:18,180 --> 00:59:23,160
+-wise vector ولا scalar value بتختلف طبعا احيانا
+
+793
+00:59:23,160 --> 00:59:26,080
+فممكن اللي بتبقى اللي هيبرمج بال C او بال Java
+
+794
+00:59:26,080 --> 00:59:31,160
+هيلاقي انه برضه مضمونة موجودة في البرمجة بتقدروا
+
+795
+00:59:31,160 --> 00:59:33,940
+تبرمجوهم باستخدام احد ال symbols هدوة اللي هم هدول
+
+796
+00:59:33,940 --> 00:59:36,580
+الروابط باستخدامكوا باستخدامها وهد الروابط
+
+797
+00:59:36,580 --> 00:59:40,020
+باستخدام اذا كان بتتكلم عن ال bit-wise كويس ال
+
+798
+00:59:40,020 --> 00:59:43,680
+logic gates هد اللي كنتوا بتاخدوهم في ال circuits
+
+799
+00:59:44,300 --> 00:59:46,880
+وانتوا بتتكلموا عن ال circuits كنتوا تعبروا عنهم
+
+800
+00:59:46,880 --> 00:59:50,000
+بال symbols اللي موجودة هنا inverter كنتوا بتعملوه
+
+801
+00:59:50,000 --> 00:59:57,400
+بالشكل هذا ال and ال r و ال xr و ال xr و طبعا من
+
+802
+00:59:57,400 --> 00:59:59,920
+الأشكال دول كنتوا بتشكلوا حاجات كتير تانية يعني
+
+803
+00:59:59,920 --> 01:00:04,320
+ممكن على طول ال .. ال circle هذه تحطوها هنا ..
+
+804
+01:00:04,320 --> 01:00:08,320
+تحطوها هنا ف بتجيبوا gates جديدة كنتوا تجيبوا
+
+805
+01:00:08,320 --> 01:00:11,760
+gates جديدة بالظبط تصير عكسها فبتصير بدل or بتصير
+
+806
+01:00:11,760 --> 01:00:18,140
+norبس بدل ان بصير ناد و هكذا تمام
+
+807
+01:00:18,140 --> 01:00:25,710
+طيب بكفل هنا كويس هيك المرة الجايةهبنبدأ مع جزئية
+
+808
+01:00:25,710 --> 01:00:28,610
+ال .. ال .. ال .. ال bit أو ال bits and bit
+
+809
+01:00:28,610 --> 01:00:33,490
+operations النظرية تلعد ان احنا هنتعامل مع ال zero
+
+810
+01:00:33,490 --> 01:00:36,630
+مرة تانية على اساس ان هو false و هنتعامل مع ال one
+
+811
+01:00:36,630 --> 01:00:40,250
+على اساس ان هو true و بعدين اكتر من slide ضايقين و
+
+812
+01:00:40,250 --> 01:00:42,450
+بعدين ننجل على موضوعنا الجاي ان شاء الله تعالى
+
+813
+01:00:42,450 --> 01:00:46,850
+ابتداء من الأسبوع القادم بإذن الله تعالى يعطيكوا
+
+814
+01:00:46,850 --> 01:00:47,130
+العفو
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e99a28f523ff0100c7a009d552d2e03b02d18984
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao.srt
@@ -0,0 +1,2593 @@
+1
+00:00:20,670 --> 00:00:22,530
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,530 --> 00:00:24,870
+الأنبياء والمرسلين سيدنا محمد وعليه وصحبه أجمعين
+
+3
+00:00:24,870 --> 00:00:27,310
+نتكمل في الموضوع  الـcomplex اللي كنا اتكلمنا فيه
+
+4
+00:00:27,310 --> 00:00:30,970
+آخر مرة، آخر مرة اتكلمنا عن مجموعة الـ order of
+
+5
+00:00:30,970 --> 00:00:39,180
+growth وعملنا خطّ على أقل من مئة أو يعني order
+
+6
+00:00:39,180 --> 00:00:44,300
+polynomial فأقل، order polynomial فأقل، قولنا أن هذه
+
+7
+00:00:44,300 --> 00:00:49,100
+بنسميها tractable بمعنى قابلة للحل، بمعنى أن الـ
+
+8
+00:00:49,100 --> 00:00:53,890
+algorithm ده قابل للحل، أكبر أو أعلى من Polynomial
+
+9
+00:00:53,890 --> 00:00:56,550
+exponential أو factorial أو n to the power of n
+
+10
+00:00:56,550 --> 00:01:02,290
+كنا بنقول أن هذه intractable أو invisible بمعنى
+
+11
+00:01:02,290 --> 00:01:09,870
+غير قابلة للحل، نظريًا غير قابلة للحل، فبنسميها
+
+12
+00:01:09,870 --> 00:01:14,010
+invisible أو intractable، رغم ذلك في بعض functions
+
+13
+00:01:14,010 --> 00:01:19,500
+أحيانًا بتشتغل أو بتكون شاذة عن القاعدة، زي حالة بهذا
+
+14
+00:01:19,500 --> 00:01:22,580
+الشكل، n to the power مليون، n to the power
+
+15
+00:01:22,580 --> 00:01:27,240
+مليون، هذه نقدر نصنفها مع الـ polynomial، تصنف مع الـ
+
+16
+00:01:27,240 --> 00:01:30,960
+polynomial، ومع ذلك فهي technically tractable
+
+17
+00:01:30,960 --> 00:01:35,900
+polynomial فأقل، tractable، فرغم ذلك طريقة حلها
+
+18
+00:01:35,900 --> 00:01:41,570
+هتكون صعبة جدًا، لأنه كلما زادت عدد n بتزيد بصورة
+
+19
+00:01:41,570 --> 00:01:45,570
+كبيرة جدًا، الـ time بيزيد بصورة كتير كبيرة، الـ order
+
+20
+00:01:45,570 --> 00:01:49,690
+of growth تبعنا، الـ order هنا of growth، في المقابل
+
+21
+00:01:49,690 --> 00:01:54,510
+عندكوا exponential، exponential function، n to the
+
+22
+00:01:54,510 --> 00:01:57,750
+power الـ variable، n to the power الـ variable، هيها
+
+23
+00:01:57,750 --> 00:02:03,710
+log، log، log n، يعني لو اتكلمنا هنا عن الـ n هذه
+
+24
+00:02:03,710 --> 00:02:08,800
+خلينا نقول 10 to the power مليون، تخيلوا مش هى
+
+25
+00:02:08,800 --> 00:02:15,920
+المليون، تنتظر مليون، في الحالة هذه log، تنتظر مليون
+
+26
+00:02:15,920 --> 00:02:27,440
+مليون، log المليون ستة، log الستة تقلصت جدًا، فهنا صار
+
+27
+00:02:27,440 --> 00:02:31,180
+في simplification كبير جدًا، لمين؟ للـ problem تبعتكم
+
+28
+00:02:31,180 --> 00:02:35,320
+رغم أن هي technically intractable، رغم أن هي فعليًا
+
+29
+00:02:35,320 --> 00:02:40,320
+تصنف على أساس أن هي intractable أو invisible order
+
+30
+00:02:40,320 --> 00:02:48,020
+for example، ناخد مجموعة orders أو مجموعة functions
+
+31
+00:02:48,390 --> 00:02:52,650
+ونحسبهم بالنسبة للـ pc تبعنا، وكيف الـ response
+
+32
+00:02:52,650 --> 00:02:55,230
+أصلًا تبع الـ pc اللي احنا بنشتغل عليه عادة، الـ
+
+33
+00:02:55,230 --> 00:02:58,970
+response تبعنا للـ operator الواحدة بيكون محتاج في
+
+34
+00:02:58,970 --> 00:03:02,950
+حدود one nanosecond، في حدود one nanosecond، والـ
+
+35
+00:03:02,950 --> 00:03:06,490
+one nanosecond دي عادة تمثل الـ response في الغالب
+
+36
+00:03:06,490 --> 00:03:11,950
+تبع الـ transistor أو الـ silicon semiconductor، رقم
+
+37
+00:03:12,740 --> 00:03:17,120
+قريب جدًا من الـ transistor أو من الـ response للـ
+
+38
+00:03:17,120 --> 00:03:23,280
+silicon، كويس، فهنشتغل عليه، وعندنا الآن هنا عدد الـ
+
+39
+00:03:23,280 --> 00:03:26,440
+inputs للـ operator اللي هنشتغل عليه، فعندنا مجموعة
+
+40
+00:03:26,440 --> 00:03:30,280
+operators، بدنا نحسب قد ايش هنحتاج time لكل operator
+
+41
+00:03:30,280 --> 00:03:33,460
+منهم، لكل operator من الـ operators اللي هنا، أو الـ
+
+42
+00:03:33,460 --> 00:03:38,560
+operations function بتاعتنا، هنبدأ بـ N بتساوي عشرة، نـ
+
+43
+00:03:38,560 --> 00:03:43,760
+بتساوي عشرة، احنا نتكلم عن digits، عن bit، طيب الـ bit
+
+44
+00:03:43,760 --> 00:03:47,720
+أكم byte أو بالعكس، الـ byte أكم bit؟ ثمانية، معناه
+
+45
+00:03:47,720 --> 00:03:54,000
+ذلك أن عشرة bits قد ايش بقى أكم byte؟ واحد وربع، واحد
+
+46
+00:03:54,000 --> 00:03:58,040
+وربع، واحد هي ثمانية، بيضل اتنين وربع، فـ one point
+
+47
+00:03:58,040 --> 00:04:04,780
+two five bytes، 10 to the power of 6 أو مليون bit
+
+48
+00:04:04,780 --> 00:04:09,060
+هتكون 125 كيلو بايت، 125 كيلو بايت، فاحنا نتكلم
+
+49
+00:04:09,060 --> 00:04:12,180
+بأرقام معقولة، يعني أرقام مش كتير كبيرة، ومع ذلك
+
+50
+00:04:12,180 --> 00:04:14,400
+بدنا نشوف في log الـ response كيف بتطلع معانا للـ
+
+51
+00:04:14,400 --> 00:04:16,320
+time لكل operation من الـ operations اللي موجودة
+
+52
+00:04:16,320 --> 00:04:22,240
+عندنا، هنبدأ بالأقل اللي هو الـ logarithmic للـ base
+
+53
+00:04:22,240 --> 00:04:26,940
+2 أو الـ binary، هذه عشان تحسبوها فعليًا، وتطلعوا
+
+54
+00:04:26,940 --> 00:04:31,820
+الرقم هذا، بتكونوا تتكلموا عن log 10، طبعًا الـ log 10
+
+55
+00:04:31,820 --> 00:04:33,740
+على الـ calculator اللي عندكم، يمكن مش كل الـ
+
+56
+00:04:33,740 --> 00:04:36,280
+calculators بتطلع لكم إياها للأساس 2، فا
+
+57
+00:04:36,280 --> 00:04:40,920
+automatically بتجي اسمه على log 2، فصارت هذه توازي
+
+58
+00:04:40,920 --> 00:04:47,800
+log أساس 2 للـ 10، كويس، إذًا الـ calculator تبعتكم
+
+59
+00:04:47,800 --> 00:04:50,560
+بتوفر لكم إنكم تختاروه، أو أنتم تعملوا selection
+
+60
+00:04:50,560 --> 00:04:54,840
+للـ base تبعتكم بالضبط للـ log، ممكن تجسّموا على الـ
+
+61
+00:04:54,840 --> 00:04:57,340
+log اللي أنتم محتاجينه، فبتكون كأنكم هو الـ
+
+62
+00:04:57,340 --> 00:04:59,880
+reference تبعتكم، أصلًا كأنه هو الـ base تبعتكم
+
+63
+00:04:59,880 --> 00:05:05,060
+فحسبوها، بتطلع 3.3، بالنسبة للمليون هتطلع في حدود 20
+
+64
+00:05:05,060 --> 00:05:09,260
+nanosecond، في حدود 20، ما زالت مقبولة بالنسبة للـ
+
+65
+00:05:09,260 --> 00:05:14,550
+time كـ response، الـ linear واضح، عشرة، عشرة، linear،
+
+66
+00:05:14,550 --> 00:05:19,730
+مليون، مليون، فمليون nano يعني one millisecond، one
+
+67
+00:05:19,730 --> 00:05:24,610
+millisecond، الـ linear في لغة رياضية، اضربوا الاتنين
+
+68
+00:05:24,610 --> 00:05:28,570
+في بعض، ما هي اتنين هي الـ N، فهي الـ log، لو ضربتم في
+
+69
+00:05:28,570 --> 00:05:31,930
+بعض، بتطلع كم الـ response اللي هنحتاجه؟ برضه ما زال
+
+70
+00:05:31,930 --> 00:05:37,330
+مقبول، طيب عند الـ polynomial، والدرجة تربيع...
+
+71
+00:05:37,330 --> 00:05:41,930
+الدرجة تربيع، n تربيع، في حدود، إذا كان عندنا عشرة
+
+72
+00:05:41,930 --> 00:05:45,410
+input، الـ input بتاعتنا عددهم عشرة، هيكون في عندنا
+
+73
+00:05:45,410 --> 00:05:48,650
+مئة nanosecond، إذا كان عندنا مليون، هيصل في حدود
+
+74
+00:05:48,650 --> 00:05:58,800
+ستّ عشر minute وأربعين second، 11 جيجا و 40 ثانية، في
+
+75
+00:05:58,800 --> 00:06:01,000
+حدود، يعني ربع الساعة الزمن... في حدود ربع الساعة
+
+76
+00:06:01,000 --> 00:06:03,220
+الزمن، أكثر شوية... في حدود ربع الساعة الزمن اللي
+
+77
+00:06:03,220 --> 00:06:05,760
+عندي، لأن ما زالت نسبيًا مقبولة، إذا كان الـ code
+
+78
+00:06:05,760 --> 00:06:09,800
+بالسهل، يعني أن أنا أولًا ممكن أسقّل عليه هذه، حتى لأن
+
+79
+00:06:09,800 --> 00:06:13,500
+polynomial، طيب أكبر من الـ polynomial، exponential،
+
+80
+00:06:14,350 --> 00:06:20,550
+exponential، عقَد عشرة، فـ 2 to the power عشرة ألف
+
+81
+00:06:20,550 --> 00:06:22,990
+و أربعة وعشرين، هذا أنتم عارفينه من أيام كنتوا بتاخدوا
+
+82
+00:06:22,990 --> 00:06:27,770
+الـ binary، صحيح، ألف وأربعة وعشرين nano، فبتصير واحد
+
+83
+00:06:27,770 --> 00:06:33,550
+فاصلة صفر، أربعة وعشرين micro، كويس، هنا مليون، 2 to
+
+84
+00:06:33,550 --> 00:06:37,210
+the power مليون، بتطلع 10 to the power تلاتمية
+
+85
+00:06:37,210 --> 00:06:46,390
+وواحد ألف وأربعة ونصف، هذا الـ power، جيجا year، يونات
+
+86
+00:06:46,390 --> 00:06:53,310
+بتاعتك، جيجا year، جيجا سنة، بتكون تستنوا عليها جيجا
+
+87
+00:06:53,310 --> 00:06:56,830
+سنة قبل ما يطلع لكم نتائج، فطبعًا واضح لأن الـ
+
+88
+00:06:56,830 --> 00:06:59,430
+exponential على طول هنا بتقدر تصنفها أن هي إيش؟
+
+89
+00:06:59,430 --> 00:07:03,850
+intractable، غير ممكنة، غير قابلة للحل، لأن بالشكل
+
+90
+00:07:03,850 --> 00:07:06,950
+هذا طبعًا غير قابل للحل، تقولوا والله استنالك جيجا
+
+91
+00:07:06,950 --> 00:07:11,580
+year، بدّيش أقول تنتظر كذا، بكفي جيجا year واحدة، لما
+
+92
+00:07:11,580 --> 00:07:14,300
+أقول لكم، الله، اه، استنّوا، بس اه، خلاص هاي الـ... عملت
+
+93
+00:07:14,300 --> 00:07:18,260
+execution للبرنامج تبعكم، بس استنوا جيجا، مالهاش
+
+94
+00:07:18,260 --> 00:07:21,520
+منطق أبداً، فواضح أن احنا بدأنا ندخل في إيش؟ في الـ
+
+95
+00:07:21,520 --> 00:07:25,900
+intractable problem، intractable problem، طيب في
+
+96
+00:07:25,900 --> 00:07:29,770
+الآن factorial، طبعًا ما زلنا احنا بنتكلم عن الـ n
+
+97
+00:07:29,770 --> 00:07:32,730
+الصغيرة، مافيش مشكلة، بس احنا بطلنا نتعامل مع الـ n
+
+98
+00:07:32,730 --> 00:07:35,170
+الصغيرة، مع الـ inputs اللي عددهم صغير، احنا أصبحنا
+
+99
+00:07:35,170 --> 00:07:37,930
+نتعامل مع inputs عددهم كبير، database بتكون تتعامل
+
+100
+00:07:37,930 --> 00:07:41,250
+وبتتصرفوا مع database فيها عدد كبير جدًا من الـ
+
+101
+00:07:41,250 --> 00:07:46,650
+inputs، فيها عدد كبير جدًا من الـ inputs، فهذه رقم مش
+
+102
+00:07:46,650 --> 00:07:49,770
+هتقدر تحسبه، بالأقل الحسبة مش هتقدر تحسبه، بالأقل
+
+103
+00:07:49,770 --> 00:07:54,830
+الحسبة، لأن هذه بتتكلموا عن مليون factorial،
+
+104
+00:07:56,950 --> 00:07:59,790
+مليون، اضربه في كل الرقم اللي تحته، اللي أقل من
+
+105
+00:07:59,790 --> 00:08:02,870
+المليون، مش هيطلع ولا في أي حاسبة ولا كمبيوتر هيطلع
+
+106
+00:08:02,870 --> 00:08:08,610
+الكل، ناتج كله هيجيب invalid، كله هيطلع invalid، أتوقع
+
+107
+00:08:08,610 --> 00:08:10,910
+حتى الـ computer،  ساعد كل رقم هذا مش هيطلع، الكل يعني
+
+108
+00:08:11,470 --> 00:08:15,190
+حتى الرقم هذا مش هيطلع معاكم، هذا الرقم يدوب
+
+109
+00:08:15,190 --> 00:08:18,350
+بالحاسوب، حاسوب زي ما يقولوا قوي، كويس، الـ browser
+
+110
+00:08:18,350 --> 00:08:21,430
+بتاعته عالي، عشان نطلع الرقم، عشان يطلع لنا الرقم هذا
+
+111
+00:08:21,430 --> 00:08:24,790
+فعليًا، calculator ساعتكم مش هيطلع هذا، وأنتم
+
+112
+00:08:24,790 --> 00:08:28,330
+بتحسبوه، جربوه، إذا أنتم طبقوها مليون، هتلاقوا
+
+113
+00:08:28,330 --> 00:08:32,450
+invalid، هنا نفس الكلام، مليون factorial مش هيطلع
+
+114
+00:08:32,450 --> 00:08:41,040
+شيء، okay، and solve the problem، في ال... ألف وتسعمائة
+
+115
+00:08:41,040 --> 00:08:46,440
+وثلاثين، تورينج، واحد اسمه تورينج، اكتشف أو وجد أن
+
+116
+00:08:46,440 --> 00:08:50,820
+والله في إشكالية، أن في بعض مشاكل... بعض problems
+
+117
+00:08:50,820 --> 00:08:55,260
+أو algorithms غير قابلة للحل، لا يمكن حلها، لا
+
+118
+00:08:55,260 --> 00:09:00,140
+يمكن حلها، طيب عشان يقول أن هي لا يمكن حلها، أو غير
+
+119
+00:09:00,140 --> 00:09:05,130
+قابل أنه حتى يعمل decision، الحل صح أو خطأ، غير قادر
+
+120
+00:09:05,130 --> 00:09:10,710
+أنه يعطي yes or no question، حتى الـ problems عنده
+
+121
+00:09:10,710 --> 00:09:14,450
+مافيش إمكانية لحلها، فهي unsolved problem، أو
+
+122
+00:09:14,450 --> 00:09:21,210
+uncomputable functions، هذه من أهم مشاكلنا اللي هي
+
+123
+00:09:21,210 --> 00:09:25,170
+الـ halting problem، الـ halting problem هي أنه إما
+
+124
+00:09:25,170 --> 00:09:29,170
+الـ algorithm finally هيجيب، مش هيطلع شيء في النهاية،
+
+125
+00:09:29,170 --> 00:09:34,100
+الـ algorithm هيجيب أو continue forever، أو الـ code
+
+126
+00:09:34,100 --> 00:09:37,060
+يظل يستمر على طول، يعني اللي أنتم بتتكلموا عنه هذا
+
+127
+00:09:37,060 --> 00:09:40,540
+for جيجا year، هذه أنتم بالنسبة لكم forever، هيظل
+
+128
+00:09:40,540 --> 00:09:45,040
+شغال، هيك معناته خلص، الجهاز، اقطعوه على جنب، و
+
+129
+00:09:45,040 --> 00:09:48,560
+انسوه، مافيش جهاز، هذا إذا أنتم مصرين، بتكون نتيجة
+
+130
+00:09:48,560 --> 00:09:52,020
+مش هيطلع النتائج في النهاية، مش هيطلع النتائج، فهذه
+
+131
+00:09:52,020 --> 00:09:58,630
+إما finally halt، stop، في النهاية هيجيب، أو to
+
+132
+00:09:58,630 --> 00:10:02,150
+infinite loop، هيظل ماشي to infinity، في الآخر، هذه
+
+133
+00:10:02,150 --> 00:10:05,410
+المسميات كلها بتندرج مع unsolved problem، unsolved
+
+134
+00:10:05,410 --> 00:10:09,550
+problem، كويسة، الموضوع ده دخلنا في جزئية ثانية، أنه
+
+135
+00:10:09,550 --> 00:10:13,030
+مدام في unsolved problem أو unsolved algorithms،
+
+136
+00:10:13,030 --> 00:10:17,670
+فاحنا عارفين الـ P، الـ P هذه كانت كل الـ problems
+
+137
+00:10:17,670 --> 00:10:21,210
+اللي كنا بنسميها tractable، حطيناها داخل set
+
+138
+00:10:21,210 --> 00:10:28,520
+سميناها بالـ P، بالـ P، capital P، هذه كلها عبارة عن
+
+139
+00:10:28,520 --> 00:10:30,800
+الـ problems اللي هي الـ order تبعها polynomial
+
+140
+00:10:30,800 --> 00:10:36,180
+فأقل، polynomial فأقل، تمام، خلصنا من الـ P، الآن
+
+141
+00:10:36,180 --> 00:10:42,560
+هندى، بنتكلم هنا عن set of problems for which there
+
+142
+00:10:42,560 --> 00:10:45,260
+exists a tractable algorithm for checking
+
+143
+00:10:45,260 --> 00:10:50,460
+solutions to see if they are correct، معناه ذلك أنه
+
+144
+00:10:50,460 --> 00:10:54,860
+هذي لكل الـ algorithms اللي أمكن حلها، اللي أمكن
+
+145
+00:10:54,860 --> 00:10:58,580
+حلّها، اللي بنقدر نقول أن والله algorithms ممكن حلها،
+
+146
+00:10:59,790 --> 00:11:03,610
+في إمكانية لحلها، طبعًا واضح أن العلاقة بين الاتنين أنه
+
+147
+00:11:03,610 --> 00:11:08,530
+by logic هيكون أن الـ P subset of NP، لأن الـ P
+
+148
+00:11:08,530 --> 00:11:11,350
+tractable... tractable، عفواً، intractable، هي
+
+149
+00:11:11,350 --> 00:11:15,610
+polynomial فأقل، معناته قابلة للحل، معناه ذلك أنه
+
+150
+00:11:15,610 --> 00:11:20,810
+ممكن جدًا يجيء حل داخل الـ algorithms اللي تم حلها
+
+151
+00:11:20,810 --> 00:11:24,830
+فعلاً، اللي تم حلها فعلاً، أو يمكن إيجاد حل... نجد
+
+152
+00:11:24,830 --> 00:11:30,250
+حل، هذا الكلام نظريًا، كان هذا نظريًا، ولكن unproven
+
+153
+00:11:30,250 --> 00:11:34,350
+projector... conjecture، عفواً... conjecture في الـ
+
+154
+00:11:34,350 --> 00:11:37,630
+computer science، في العلوم، علم الحاسوب، في ما زالت
+
+155
+00:11:37,630 --> 00:11:41,930
+بعض الحدث أو بعض البديهيات الغير مثبتة، بعض
+
+156
+00:11:41,930 --> 00:11:48,530
+البديهيات الغير مثبتة، تقول لنا لأ، أنه  P is a subset
+
+157
+00:11:48,530 --> 00:11:54,030
+or prepare subset NP، بمعنى أنه يوجد... يوجد في
+
+158
+00:11:54,030 --> 00:11:58,340
+الحلول الممكنة، أو يوجد في المسائل اللي تم حلها، بعض
+
+159
+00:11:58,340 --> 00:12:02,480
+الـ problems، الـ intractable، intractable، ولكن أمكن
+
+160
+00:12:02,480 --> 00:12:06,980
+نحلها، حتى الآن مافيش أي إثبات للموضوع هذا، بمعنى
+
+161
+00:12:06,980 --> 00:12:12,240
+أنه استثنى الـ P equal to NP، استثنى أنه فقط ما
+
+162
+00:12:12,240 --> 00:12:17,760
+يمكن نحله هو الـ intractable، بس إذا قلنا subset أو
+
+163
+00:12:17,760 --> 00:12:21,040
+يساوي، هو استثنى أن هي تساوي، معناته كأنه بيقول لنا أن
+
+164
+00:12:21,040 --> 00:12:26,440
+لأ، حسب الحدث تبعنا، الحدث أن، لأ، مشكلة intractable
+
+165
+00:12:26,440 --> 00:12:30,380
+أمكن نحلها، في حاجات أما كانت حالها مش tractable،
+
+166
+00:12:30,380 --> 00:12:34,920
+ظلّت المشكلة حتى الآن قائمة، حتى الآن المشكلة  دل
+
+167
+00:12:34,920 --> 00:12:38,620
+وقت قائمة، محدش أثبتها، فالعند الآن هي unproven
+
+168
+00:12:38,620 --> 00:12:42,700
+conjecture، هي ما زالت حتى الآن حدث أو بديهية غير
+
+169
+00:12:42,700 --> 00:12:48,540
+مثبتة، وتم الإعلان عنها كبديهية غير مثبتة في سنة
+
+170
+00:12:48,540 --> 00:12:54,950
+2000، وانحطّت ضمن سبع بديهيات، ضمن السبع بديهيات، السبع
+
+171
+00:12:
+
+223
+00:15:57,620 --> 00:16:03,340
+نشتغل على الـ divides, factor, multiple, العوامل
+
+224
+00:16:03,340 --> 00:16:10,300
+المشتركة، العامل أو القاسم المشترك، والمضاعف
+
+225
+00:16:10,300 --> 00:16:17,090
+المضاعف للرقم. طيب، لو افترضنا a و b integers، و a لا
+
+226
+00:16:17,090 --> 00:16:20,650
+تساوي صفر؛ لأنه هذا سنضعه في denominator، في مقام
+
+227
+00:16:20,650 --> 00:16:24,790
+سنضعه في المقام،  الـ a. فما دام سنضعه في المقام، لازم
+
+228
+00:16:24,790 --> 00:16:27,130
+ما تكونش بتساوي صفر؛ لأنه سيطلع لنا
+
+229
+00:16:27,130 --> 00:16:32,150
+undefined value. كأنّي أُريد أن أقول b
+
+230
+00:16:32,150 --> 00:16:38,010
+على a. فـ a هذه لازم لا تساوي صفر، لازم لا تساوي صفر.
+
+231
+00:16:38,010 --> 00:16:45,630
+كويس. a divides b، هكذا نكتبها،  divides به، لأن فعلاً
+
+232
+00:16:45,630 --> 00:16:50,370
+a هو الذي قسم به، كانت قيمة كبيرة، a قسمها
+
+233
+00:16:50,370 --> 00:16:55,630
+قسمها إلى مجموعة groups، مثلاً لو قلنا اثنا عشر على ثلاثة
+
+234
+00:16:55,630 --> 00:16:59,750
+كأنّ الثلاثة ستقسم الاثني عشر إلى three groups، كل group
+
+235
+00:16:59,750 --> 00:17:05,410
+فيه أربعة، اللي هو خارج القسمة، اللي هو أربعة. فهنا
+
+236
+00:17:05,410 --> 00:17:09,850
+بنقولها: أيش؟ a divides b، a يقسم b، هذه معناها a
+
+237
+00:17:09,850 --> 00:17:14,190
+divides b، there exists c. كيف تعريفها؟ there exists
+
+238
+00:17:14,190 --> 00:17:19,550
+c، برضه integer، بحيث إنّ c هو خارج القسمة، c في a
+
+239
+00:17:19,550 --> 00:17:24,070
+يساوي الـ b. معناته، إذاً فعلاً there exists c، يوجد
+
+240
+00:17:24,070 --> 00:17:29,150
+integer، لو ضربناه في a يطلع b، معناته a divides b
+
+241
+00:17:29,150 --> 00:17:35,020
+is true. خارج القسمة integer. أنا أعرف أنّه ممكن يطلع
+
+242
+00:17:35,020 --> 00:17:39,900
+fraction، بس إحنا خلينا لسه فيه... فيه شرط ابتدائي، أنّه
+
+243
+00:17:39,900 --> 00:17:44,370
+لازم تكون integer. إذا integer، نقول true. فإذا كان
+
+244
+00:17:44,370 --> 00:17:48,890
+والله، عندنا بالشكل هذا: ثلاثة divides minus twelve.
+
+245
+00:17:48,890 --> 00:17:53,690
+هذا يطلع integer، ولا لا يطلع integer؟ integer معناته
+
+246
+00:17:53,690 --> 00:18:00,410
+true. طيب، three divides seven؟ لأ، false. فإذا if and
+
+247
+00:18:00,410 --> 00:18:08,470
+only if a divides b، then we say a is a factor of
+
+248
+00:18:08,470 --> 00:18:17,070
+أو a divisor. أما بتسمّيه factor، هو أحد معاملات b، هو
+
+249
+00:18:17,070 --> 00:18:23,150
+أحد معاملات b. فعلاً، لأنّ 12 تساوي 3 في 4، فهي
+
+250
+00:18:23,150 --> 00:18:27,030
+واحدة من معاملات الـ 12، هي واحدة من معاملات a أو
+
+251
+00:18:27,030 --> 00:18:35,410
+divisor، قاسم لـ الـ b، قاسم of b، و الـ b نسمّيها
+
+252
+00:18:35,410 --> 00:18:41,220
+multiple، مضاعفات. الثلاثة مضاعفات الـ a، من مضاعفات a.
+
+253
+00:18:41,220 --> 00:18:44,680
+جديش متكررة الـ a؟ هي خارج القسمة، متكررة أربع مرات
+
+254
+00:18:44,680 --> 00:18:51,420
+عشان تعطينا المضاعف اثنا عشر، أو المضاعف b، وهذه كانت
+
+255
+00:18:51,420 --> 00:18:59,180
+كويس. هنا، for example، لو قلنا b is even، بقدر
+
+256
+00:18:59,180 --> 00:19:03,860
+أعرف أنّ two divides b. إذا فعلاً two divides b is
+
+257
+00:19:03,860 --> 00:19:10,000
+true، معناته الـ b دائماً even، دائماً even. إذا two
+
+258
+00:19:10,000 --> 00:19:15,180
+divides b is true، فإذا دائماً even. طيب، الـ zero even؟
+
+259
+00:19:15,180 --> 00:19:23,980
+بناءً على النظرية هذه، zero، هل هي belong to Z؟ اه.
+
+260
+00:19:23,980 --> 00:19:29,680
+خلاص، معناته إذا even. فإذا even. طيب، الـ minus four
+
+261
+00:19:32,120 --> 00:19:37,800
+two divides minus four، قد ايش الناتج؟ الـ minus two
+
+262
+00:19:37,800 --> 00:19:43,560
+belong to z، إذن برضه true. إذن true، فإذن even.
+
+263
+00:19:43,560 --> 00:19:48,860
+فمعناها دي even. طيب، شوية facts، facts relation أو
+
+264
+00:19:48,860 --> 00:19:57,460
+على الـ divides relation، a divides zero، true، لأنّه
+
+265
+00:19:57,460 --> 00:20:00,240
+سيطلع zero، الناتج هنا zero، و الـ zero إحنا عارفين
+
+266
+00:20:00,240 --> 00:20:04,100
+أنّه هو belong to z. فإحنا عارفين أنّ هو a و b و c
+
+267
+00:20:04,100 --> 00:20:07,700
+اللّي سنشتغل فيهم، هدول كلهم integers، كلهم integers.
+
+268
+00:20:07,700 --> 00:20:12,780
+فـ integer divides zero، سيطلع zero، و الـ zero
+
+269
+00:20:12,780 --> 00:20:22,360
+integer. طيب، a divides b and a divides c، لو بنقدر
+
+270
+00:20:22,360 --> 00:20:30,360
+نقول أنّ a تقسم b، و يعطينا true، يعطينا true.
+
+271
+00:20:30,360 --> 00:20:33,700
+معناته ممكن يكون خارج قسمة، يعني خارج قسمة خلّاني
+
+272
+00:20:33,700 --> 00:20:40,380
+أقول s، و الـ s هذه integer، هذه integer، و and
+
+273
+00:20:43,550 --> 00:20:49,250
+over a، بمعنى a divides c، برضه خارج قسمة، معناته هذه
+
+274
+00:20:49,250 --> 00:20:52,710
+true and true. إذا فعلاً تحقق الشرط ده، معناته خلّنا
+
+275
+00:20:52,710 --> 00:20:56,650
+نقول إنّه لها t، و t هذه برضه integer، لها خارج قسمة
+
+276
+00:20:56,650 --> 00:21:01,970
+integer. إذا تحقق الاثنين هدول، then a divides b
+
+277
+00:21:01,970 --> 00:21:06,930
+plus c صحيح.
+
+278
+00:21:06,930 --> 00:21:15,290
+فإذا لو قلنا b plus c، من هنا عارفين أنّ b تساوي a
+
+279
+00:21:15,290 --> 00:21:30,290
+في s، c تساوي a في t، نجمعهم، هيساوي a في s زائد a
+
+280
+00:21:30,290 --> 00:21:38,290
+في t، نأخذ common a، s زائد t. طيب، هي معناته في عامل
+
+281
+00:21:38,290 --> 00:21:42,890
+مشترك، معناته بتُقسَم. معناته في إمكانية للقسمة، في
+
+282
+00:21:42,890 --> 00:21:46,650
+إمكانية للقسمة. ما دام طلعت الـ a أصلاً عامل مشترك
+
+283
+00:21:46,650 --> 00:21:51,830
+common، common، معناته برضه بتُقسَم على a، أو a نقدر
+
+284
+00:21:51,830 --> 00:21:58,770
+نقول أنّ a divides b plus c. فهي هذه، مثبتة، إثبات للـ
+
+285
+00:21:58,770 --> 00:22:02,350
+proof، الـ proof اللي هي الحالة الثانية، proof، الحالة
+
+286
+00:22:02,350 --> 00:22:09,850
+الثانية، تمام. a divides b، then a divides b في أي
+
+287
+00:22:09,850 --> 00:22:15,590
+integer، لأنّ هنا صارت multiple of b، ما دام أصلاً b
+
+288
+00:22:15,590 --> 00:22:20,270
+تُقبل القسمة على a، b مضروبة في أي integer، برضه
+
+289
+00:22:20,270 --> 00:22:25,130
+الناتج سيقبل القسمة على a، برضه سيقبل القسمة على a.
+
+290
+00:22:25,130 --> 00:22:30,690
+okay.
+
+291
+00:22:30,690 --> 00:22:37,370
+a divides b and b divides c، then a divides c.
+
+292
+00:22:41,820 --> 00:22:50,580
+زي لو قلنا اثنا عشر على ثلاثة، true، true، لأنّه يعطينا
+
+293
+00:22:50,580 --> 00:22:57,960
+قيمة. طيب، أربعة وعشرون على اثنا عشر، true، then أربعة و
+
+294
+00:22:57,960 --> 00:23:02,300
+عشرون لازم تكون تقبل القسمة على ثلاثة، لازم تقبل
+
+295
+00:23:02,300 --> 00:23:08,140
+القسمة على ثلاثة. فهي برضه النظرية رقم أربعة، أو الـ
+
+296
+00:23:08,140 --> 00:23:13,820
+fact number four، إذا a divides b and b divides c،
+
+297
+00:23:13,820 --> 00:23:18,080
+أكيد a divides c.
+
+298
+00:23:18,080 --> 00:23:24,600
+طيب، هذه خلّصنا جزئية اللي هي عملية الضرب، عملية الضرب.
+
+299
+00:23:25,470 --> 00:23:28,590
+Okay. نتكلم عن الـ primes، الـ primes، عارفين إحنا
+
+300
+00:23:28,590 --> 00:23:32,290
+سابقاً، الـ primes، كنا سابقاً عارفينها، الـ prime هو رقم
+
+301
+00:23:32,290 --> 00:23:36,270
+لا يقبل القسمة إلا على نفسه أو على الواحد. بمعنى
+
+302
+00:23:36,270 --> 00:23:40,270
+ما له factors، ما له factors، ما له أي رقمين ممكن
+
+303
+00:23:40,270 --> 00:23:43,610
+أضربهما في بعض ويُطلعا، ما له مجموعة factors، الـ
+
+304
+00:23:43,610 --> 00:23:47,530
+factors الوحيدة تبعته اللي هو نفسه والواحد الصحيح.
+
+305
+00:23:47,530 --> 00:23:52,450
+والواحد الصحيح. فإذا بنقدر نقول integer p، أو prime
+
+306
+00:23:52,450 --> 00:23:56,210
+أكبر من واحد، هذا ما نسمّيه، الـ p is prime if and
+
+307
+00:23:56,210 --> 00:24:00,210
+only if it's not the product of any two integers
+
+308
+00:24:00,210 --> 00:24:07,070
+هو مش ناتج من ضرب two integers أكبر من واحد، الواحد
+
+309
+00:24:07,070 --> 00:24:09,750
+هو الحالة الوحيدة اللي ممكن تنفع، ليش؟ لأنّه مضروبة
+
+310
+00:24:09,750 --> 00:24:17,360
+في نفسها، الـ p هيكون عبارة عن الـ p في واحد فقط، أو ما
+
+311
+00:24:17,360 --> 00:24:21,020
+لا يمكن أن يُنتج أو نقدر نلتقطه، نجيبه من two integers
+
+312
+00:24:21,020 --> 00:24:25,240
+مضروبين في بعض، باستثناء الواحد. طيب، فبنقول p أكبر من
+
+313
+00:24:25,240 --> 00:24:28,900
+واحد، فإذا الـ... الـ... الـ primes تبعتنا بتبدأ من
+
+314
+00:24:28,900 --> 00:24:35,700
+اثنين، اثنين، ثلاثة، خمسة، سبعة، أحد عشر، بتكمل أكبر
+
+315
+00:24:35,700 --> 00:24:40,980
+من واحد، and there is no exist، لا يوجد a و b، لا
+
+316
+00:24:40,980 --> 00:24:46,610
+يوجد أي رقمين belong to natural number، والرقمين
+
+317
+00:24:46,610 --> 00:24:52,670
+لازم يكونوا أكبر من واحد، حصل ضربهم يساوي الـ b، لا
+
+318
+00:24:52,670 --> 00:24:58,390
+يوجد a و b، حصل ضربهم يعطي b.
+
+319
+00:25:02,650 --> 00:25:06,450
+Okay. الحالة الوحيدة زي ما قلنا، أما اللي هي الـ
+
+320
+00:25:06,450 --> 00:25:11,230
+prime نفسه والواحد، الواحد والـ p itself نفسها، بس
+
+321
+00:25:11,230 --> 00:25:16,510
+و هذه لا تُدرج ضمن التعريف؛ لأنّ إحنا استثنينا هنا a
+
+322
+00:25:16,510 --> 00:25:21,870
+أكبر من واحد، و p أكبر من واحد، فلا يساوي واحد. some
+
+323
+00:25:21,870 --> 00:25:26,390
+primes، اثنين، ثلاثة، خمسة، سبعة، أحد عشر، ثلاثة عشر، الـ 17
+
+324
+00:25:26,390 --> 00:25:31,290
+بتكمل. طيب، الـ non-prime، إذا كان رقم non-prime،
+
+325
+00:25:31,290 --> 00:25:34,790
+نسمّيه composite، composite. إيش يعني؟ يعني ممكن
+
+326
+00:25:34,790 --> 00:25:38,210
+تأليفه من رقمين آخرين. يعني ممكن نقول إنّه هو
+
+327
+00:25:38,210 --> 00:25:42,250
+composed by multiplying two integers greater than
+
+328
+00:25:42,250 --> 00:25:47,710
+one. فإذا بقدر أنتجه من حاصل ضرب رقمين آخرين، هذا
+
+329
+00:25:47,710 --> 00:25:51,430
+بنقول إنّه non-prime. هذا إيش؟ non-prime. إذا
+
+330
+00:25:51,430 --> 00:25:55,130
+ما قدرناش، بكون اسمه prime على طول، بكون اسمه الـ
+
+331
+00:25:55,130 --> 00:25:55,330
+prime.
+
+332
+00:25:58,850 --> 00:26:04,870
+طيب، fundamental theorem of arithmetic، every
+
+333
+00:26:04,870 --> 00:26:09,110
+integer greater than one، كل رقم integer أكبر من
+
+334
+00:26:09,110 --> 00:26:13,430
+one can be written uniquely as a prime or as the
+
+335
+00:26:13,430 --> 00:26:18,630
+product of two or more primes. فإذا كل رقم أكبر من
+
+336
+00:26:19,940 --> 00:26:23,820
+من واحد... كل رقم... ما فيش استثناء... كل رقم أكبر من
+
+337
+00:26:23,820 --> 00:26:29,760
+واحد بنقدر نمثّله إمّا بـ prime إذا هو نفسه prime، أو
+
+338
+00:26:29,760 --> 00:26:34,600
+two primes مضروبين في بعض أو أكثر... ممكن يكون
+
+339
+00:26:34,600 --> 00:26:36,220
+ثلاثة primes مضروبين في بعض... أربعة primes
+
+340
+00:26:36,220 --> 00:26:39,500
+مضروبين في بعض... بس جميع الأرقام ممكن نعملها
+
+341
+00:26:39,500 --> 00:26:43,520
+مجموعة primes مضروبين في بعض، مجموعة الـ primes
+
+342
+00:26:43,520 --> 00:26:46,940
+تُمثّل بمجموعة الـ primes مضروبين في بعض، زي ما
+
+343
+00:26:46,940 --> 00:26:50,440
+قلنا، product of two or more primes where the prime
+
+344
+00:26:50,440 --> 00:26:54,280
+factors are written in order of non-decreasing
+
+345
+00:26:54,280 --> 00:26:58,000
+size. دائماً نبدأ الـ analysis تبعتنا بالـ primes
+
+346
+00:26:58,000 --> 00:27:01,600
+الأقل. نبدأ بالـ primes الأقل. إيش يعني نبدأ
+
+347
+00:27:01,600 --> 00:27:05,960
+بالـ primes الأقل؟ يعني لو بدنا نجيب الـ factors الـ
+
+348
+00:27:05,960 --> 00:27:10,180
+prime factors تبعت، نأخذ رقم كبير، ألفي
+
+349
+00:27:12,480 --> 00:27:17,580
+نبدأ بأقل الـ prime، إيش؟ الاثنين، أقل الـ prime، نبدأ
+
+350
+00:27:17,580 --> 00:27:20,880
+بالاثنين. هل يقبل القسمة على اثنين؟ اه، يقبل القسمة على اثنين.
+
+351
+00:27:20,880 --> 00:27:25,800
+قد ايش بيظل؟ ألف. طيب، الألف بتقبل القسمة على اثنين؟ اه.
+
+352
+00:27:25,800 --> 00:27:35,590
+تُقبل القسمة على اثنين، طيب، تصير خمسمائة، على اثنين، مئتان وخمسون، على اثنين، مئة
+
+353
+00:27:35,590 --> 00:27:38,410
+وخمسة وعشرين. اه، مئة وخمسة وعشرون لا تُقبل على اثنين،
+
+354
+00:27:38,410 --> 00:27:41,330
+مئة وخمسة وعشرون لا تُقبل على اثنين، يظل مئة وخمسة
+
+355
+00:27:41,330 --> 00:27:44,970
+وعشرون. بدنا برضه نشوف الرقم اللي وراء الاثنين،
+
+356
+00:27:44,970 --> 00:27:48,470
+الثلاثة. هل تُقبل القسمة على ثلاثة؟ لأ، لأنّه عندك
+
+357
+00:27:48,470 --> 00:27:50,910
+ثلاثة، خمسة، ثمانية. ثمانية لا تُقبل على ثلاثة،
+
+358
+00:27:50,910 --> 00:27:53,290
+ثمانية لا تُقبل على ثلاثة، فهذا الرقم كله لا يُقبل
+
+359
+00:27:53,290 --> 00:27:56,590
+على ثلاثة. طيب، بعد الثلاثة، في الخمسة، الخمسة
+
+360
+00:27:56,590 --> 00:28:02,230
+تُقبل على خمسة، اه، تُقبل على خمسة، في خمسة، يظل
+
+361
+00:28:02,230 --> 00:28:06,310
+خمسة وعشرين، خمسة، الخمسة نفسها prime، بتنزل زي ما
+
+362
+00:28:06,310 --> 00:28:10,750
+هي. فلاحظوا أنّ إحنا عملناها analysis باستخدام
+
+363
+00:28:10,750 --> 00:28:15,210
+مجموعة of primes. نقدر نقول أنّ هي عبارة عن اثنين
+
+364
+00:28:15,210 --> 00:28:20,770
+أربعة to the power أربعة في خمسة to the power ثلاثة
+
+365
+00:28:20,770 --> 00:28:24,550
+نقدر
+
+366
+00:28:24,550 --> 00:28:28,350
+نعملها analysis، كل رقم موجود بتقدر تعمله بهذا
+
+367
+00:28:28,350 --> 00:28:33,170
+الشكل، بتقدر تعمله بهذا الشكل. طيب، ألفيّن وواحد...
+
+368
+00:28:33,170 --> 00:28:36,910
+لاحظوا... اثنين... واحد، ثلاثة تُقبل القسمة على ثلاثة؟
+
+369
+00:28:36,910 --> 00:28:40,810
+على اثنين؟ لأ، لأنّها أصلاً odd، odd.
+
+370
+00:28:40,810 --> 00:28:44,950
+على ثلاثة تُقبل... تُقبل. سبعة، ثلاثة خارج القسمة، هل
+
+371
+00:28:44,950 --> 00:28:47,450
+يُقبل القسمة على ثلاثة؟ هيكون، مش سيقبل القسمة على
+
+372
+00:28:47,450 --> 00:28:51,830
+ثلاثة، نجرب على خمسة؟ نجرب على سبعة؟ على أحد
+
+373
+00:28:51,830 --> 00:28:55,790
+...على أحد عشر...لا. تسعة؟ لأ، تسعة لأ... تسعة بتقدر
+
+374
+00:28:55,790 --> 00:28:59,690
+تقولي ثلاثة في ثلاثة، أحد عشر...ثلاثة عشر... سبعة عشر...
+
+375
+00:28:59,690 --> 00:29:02,750
+...ثلاثة وعشرون. عند ثلاثة وعشرون، أو بتقبل على
+
+376
+00:29:02,750 --> 00:29:05,290
+ثلاثة وعشرون، خارج القسمة بتطلع تسعة وعشرون، هي
+
+377
+00:29:05,290 --> 00:29:09,810
+تسعة وعشرون هي نفسها a prime، هي نفسها a prime.
+
+378
+00:29:09,810 --> 00:29:13,570
+فهيكون ثلاثة، بهذا الشكل. طيب، ألفيّن واثنين، واضح
+
+379
+00:29:13,570 --> 00:29:16,690
+أنّها أصلاً even، فتُقبل مباشرة القسمة على اثنين، و
+
+380
+00:29:16,690 --> 00:29:18,650
+نبدأ نعمل لها analysis، دائماً نبتدي analysis من
+
+381
+00:29:18,650 --> 00:29:24,510
+الأقل، من الأقل، أقل، اثنين. خلصنا اثنين، عند السبعة،
+
+382
+00:29:24,510 --> 00:29:29,980
+خلصنا السبعة، الناتج مش سيقبل القسمة على سبعة، نجربش
+
+383
+00:29:29,980 --> 00:29:33,960
+على اثنين؛ لأنّه لو أصلاً من الأول بيقبل على اثنين،
+
+384
+00:29:33,960 --> 00:29:36,860
+كان بتطلعها من الأساس من اثنين، فما نغلّب هالحركة.
+
+385
+00:29:36,860 --> 00:29:39,840
+نبدأ ونرجع، ونبدأ من اثنين وثلاثة وخمسة، خلاص من
+
+386
+00:29:39,840 --> 00:29:42,360
+بعد السبعة، ما يُقسَم على الناتج وما يُقسَم على
+
+387
+00:29:42,360 --> 00:29:46,240
+السبعة، هذا من بعده، من أحد عشر، طبعاً؟ طيب، ألفيّن و
+
+388
+00:29:46,240 --> 00:29:53,100
+ثلاثة هي نفسها prime، ألفيّن وثلاثة prime،
+
+445
+00:34:35,270 --> 00:34:44,740
+صفر such that There exists only one Q and R that
+
+446
+00:34:44,740 --> 00:34:45,560
+belong to Z
+
+447
+00:35:00,830 --> 00:35:04,470
+أقل من D إذا أكبر من D، حصر القسمة لسه ما خلصتش
+
+448
+00:35:04,470 --> 00:35:07,730
+القسمة المطولة لما زالت ما خلصتش، فلازم نحدد برضه إنه
+
+449
+00:35:07,730 --> 00:35:11,590
+R، عشان أقول إن هذه القيمة هذه فعلا هي R
+
+450
+00:35:11,590 --> 00:35:17,990
+إذا كانت أقل من D، و A = QD + R
+
+451
+00:35:20,760 --> 00:35:27,820
+من هذه الحالة بنقدر برضه نجيب R و Q
+
+452
+00:35:27,820 --> 00:35:30,700
+بنقدر نجيبهم برضه في الحالة اللي احنا بنشتغل
+
+453
+00:35:30,700 --> 00:35:34,720
+عليها، طبعا بالنسبة لـ Q لأن هي خارج القسمة أصلا
+
+454
+00:35:34,720 --> 00:35:39,380
+خارج القسمة، بس بدنا نستثني الـ R، خارج القسمة بدون
+
+455
+00:35:39,380 --> 00:35:45,680
+استثناء الـ R، فـ Q بقدر أقول إنها تساوي A ÷ D
+
+456
+00:35:45,680 --> 00:35:47,720
+floor
+
+457
+00:35:49,470 --> 00:35:53,530
+على الـ D اللي
+
+458
+00:35:53,530 --> 00:36:00,910
+هي الـ divisor، floor تمام، فـ floor على طول جربتلنا
+
+459
+00:36:00,910 --> 00:36:06,170
+الـ R قربتها للصفر، جربتها للصفر فخلاص خارج القسم
+
+460
+00:36:06,170 --> 00:36:11,570
+بقدر أجيبه مرتاح، خارج القسمة و floor بجيبلنا الـ
+
+461
+00:36:11,570 --> 00:36:15,710
+quotient term
+
+462
+00:36:15,710 --> 00:36:23,650
+أو الـ quotient Q، طيب الـ R عشان نحسب R بنحسبه
+
+463
+00:36:23,650 --> 00:36:32,550
+R هتكون عبارة عن إيش؟ الفرق بين A و D في Q، فإذا A
+
+464
+00:36:32,550 --> 00:36:39,810
+- D في Q، لو مطلوب منكوا تجيبوا الـ quotient
+
+465
+00:36:39,810 --> 00:36:45,690
+مباشرة و الـ R أو الـ remainder بشكل مباشر، فهي القسمة
+
+466
+00:36:45,690 --> 00:36:49,910
+المطولة فعليا بتنعمل بهذا الشكل
+
+467
+00:36:49,910 --> 00:36:53,750
+لاحقا هناخد algorithm للقسمة المطولة، كيف تبدأ الـ
+
+468
+00:36:53,750 --> 00:36:57,490
+greatest
+
+469
+00:36:57,490 --> 00:37:02,850
+common divisor أو العامل المشترك الأكبر
+
+470
+00:37:02,850 --> 00:37:07,020
+القيمتين هدول بتجيبوا
+
+471
+00:37:07,020 --> 00:37:12,120
+العامل المشترك الأكبر، بمعنى إيش؟ الرقم اللي كلا
+
+472
+00:37:12,120 --> 00:37:15,680
+الرقمين بيقسموا عليه، و أكبر رقم ممكن الإتنين يقسموا
+
+473
+00:37:15,680 --> 00:37:19,780
+عليه، أكبر رقم ممكن الإتنين يقسموا عليه، ببساطة جدا
+
+474
+00:37:19,780 --> 00:37:24,220
+بنسميها greatest common divisor أو GCD
+
+475
+00:37:24,220 --> 00:37:27,060
+لـ A و B، فالإتنين هدول بدنا نجيب
+
+476
+00:37:27,060 --> 00:37:31,370
+العامل المشترك الأكبر لهم، للـ A و B مع بعض
+
+477
+00:37:31,370 --> 00:37:35,670
+a و b، وطبعا مافيش واحد منهم صفر
+
+478
+00:37:35,670 --> 00:37:40,130
+اللي هو الـ greatest common
+
+479
+00:37:40,130 --> 00:37:44,270
+divisor، هذا هو الأكبر
+
+480
+00:37:44,270 --> 00:37:49,630
+رقم موجب، integer d that is divisor
+
+481
+00:37:49,630 --> 00:37:53,810
+both a and b
+
+482
+00:37:53,810 --> 00:37:58,460
+و أكبر
+
+483
+00:37:58,460 --> 00:38:02,060
+رقم ممكن يكون  لـ A و لـ B مع بعض
+
+484
+00:38:02,060 --> 00:38:06,880
+نكتبها D، greatest common divisor A و B عبارة عن
+
+485
+00:38:06,880 --> 00:38:15,640
+هو أكبر رقم بحيث  ان D  لـ A و D
+
+486
+00:38:15,640 --> 00:38:22,260
+لـ B، فعلا بيقسم، ممكن يقسم A و ممكن يقسم B و
+
+487
+00:38:22,260 --> 00:38:26,650
+الرقم الأكبر منهم، for example
+
+488
+00:38:26,650 --> 00:38:30,410
+common divisor 24, 36، نمسكهم
+
+489
+00:38:30,410 --> 00:38:35,530
+بالطريقة المملة شوية، وبعدين بنشوف إيش الطرق
+
+490
+00:38:35,530 --> 00:38:38,710
+الأفضل، خلينا نشوف الـ 24، إيش الأرقام اللي
+
+491
+00:38:38,710 --> 00:38:41,690
+ممكن تقسم على 24
+
+492
+00:38:41,690 --> 00:38:51,090
+1, 2, 3, 4, 6, 8, 12, 24
+
+493
+00:38:51,090 --> 00:38:59,670
+طيب، هذه بتاعة الـ 24، الـ 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
+
+494
+00:38:59,670 --> 00:39:05,270
+طيب هذه بتاعة الـ 24
+
+495
+00:39:05,270 --> 00:39:10,330
+الـ 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
+
+496
+00:39:12,270 --> 00:39:30,650
+1,2,3,4,6, 8, 9,12,18, 24, 36  قول
+
+497
+00:39:30,650 --> 00:39:35,830
+عند الـ 36، كويس، هل يمكن أن نشوف من المعاملات هدول
+
+498
+00:39:35,830 --> 00:39:40,700
+من الـ divisor الأكبر مشترك بينهم
+
+499
+00:39:40,700 --> 00:39:45,680
+مشترك بينهم 12، فإذا الـ greatest common divisor
+
+500
+00:39:45,680 --> 00:39:50,640
+لـ 24، 36، هو 12
+
+501
+00:39:50,640 --> 00:39:58,780
+لـ 24 و لـ 36
+
+502
+00:39:58,780 --> 00:40:01,380
+الطريقة العقيمة شوية، لأن ممكن تدفع في
+
+503
+00:40:01,380 --> 00:40:03,740
+الأرقام الصغيرة، اللي جد هيك، بس إذا كانت كبيرة
+
+504
+00:40:03,740 --> 00:40:07,950
+الأرقام، طبعا الموضوع بصير أصعب من هيك، مش هنقدر
+
+505
+00:40:07,950 --> 00:40:14,550
+نشتغل بهذا الشكل، فـ الـ greatest is twelve، طيب بدنا
+
+506
+00:40:14,550 --> 00:40:20,170
+طريقة رياضية شوية، نقدر نجيب فيها
+
+507
+00:40:20,170 --> 00:40:23,670
+الحل، الطريقة أحسن من هيك، بدنا
+
+508
+00:40:23,670 --> 00:40:28,950
+نرجع لمين؟ لـ الـ prime factors، الـ prime factors ممكن
+
+509
+00:40:28,950 --> 00:40:32,640
+يحلولنا الموضوع، لو قلنا الـ A والـ B، بدنا نجيب الـ
+
+510
+00:40:32,640 --> 00:40:35,920
+للإتنين، فبنجيب
+
+511
+00:40:35,920 --> 00:40:39,180
+الـ A و بنجيب الـ primes تبعته، كل الـ prime ممكن
+
+512
+00:40:39,180 --> 00:40:43,500
+تتكرر، زي ما توي شفنا في الـ 2000 كان فيه اتنين
+
+513
+00:40:43,500 --> 00:40:46,640
+to the power أربعة، فبنحط اتنين to the power أربعة
+
+514
+00:40:46,640 --> 00:40:50,640
+خمسة to the power اتنين، وهكذا بنحط جميع الـ primes
+
+515
+00:40:50,640 --> 00:40:56,680
+تبعت A، و بنحط الـ primes تبعت B، وبنشوف الـ
+
+516
+00:40:56,680 --> 00:41:02,300
+prime اللي اتكرر من هنا وهنا، بناخد الـ power الأقل
+
+517
+00:41:02,300 --> 00:41:06,540
+له، فإذا لما بقول greatest common divisor لـ a و b
+
+518
+00:41:06,540 --> 00:41:12,120
+بأخد الـ prime الأول و
+
+519
+00:41:12,120 --> 00:41:15,940
+بشوف الـ power في الحالة الأولى والحالة التانية
+
+520
+00:41:15,940 --> 00:41:20,480
+الأقل بأخدها، الـ prime التاني
+
+521
+00:41:23,490 --> 00:41:30,810
+الاقل بناخدها، سواء a<sup>2</sup> أو b<sup>2</sup>، الاقل منهم بنختارها
+
+522
+00:41:30,810 --> 00:41:34,670
+لعند ما نخلص جميع الـ factors أو الـ prime factors
+
+523
+00:41:34,670 --> 00:41:37,970
+بتاعتنا، بنضرب في الآخر الرقم اللي ظهر، فالرقم هذا
+
+524
+00:41:37,970 --> 00:41:44,670
+هيطلع الـ common divisor، ناخد مثل، محتاجين نعمل الـ
+
+525
+00:41:44,670 --> 00:41:54,370
+greatest common divisor لـ 84، 96
+
+526
+00:41:54,370 --> 00:41:56,710
+الـ 84، 96، طبعا لحظة، اقسموا
+
+527
+00:41:56,710 --> 00:42:00,330
+على اتنين، ما جسمش على اتنين، انقلوا على تلاتة، ما
+
+528
+00:42:00,330 --> 00:42:03,650
+جسمش على تلاتة، انقلوا على خمسة، انقلوا على سبعة،
+
+529
+00:42:03,650 --> 00:42:06,450
+تاخدوهم تساعدوا، خلاص مدام انتم ماشيين تساعدوا
+
+530
+00:42:06,450 --> 00:42:11,790
+ترجعوش تنزلوا تاني، تمام، فهنا
+
+531
+00:42:11,790 --> 00:42:15,590
+هيطلع 2<sup>2</sup> × 3 × 7، 2<sup>5</sup> × 3
+
+532
+00:42:15,590 --> 00:42:20,070
+2<sup>2</sup>، 3<sup>1</sup>
+
+533
+00:42:20,070 --> 00:42:22,390
+3<sup>1</sup>، 7<sup>1</sup>
+
+534
+00:42:22,390 --> 00:42:26,830
+3<sup>1</sup>
+
+535
+00:42:26,830 --> 00:42:31,910
+3<sup>1</sup>
+
+536
+00:42:31,910 --> 00:42:33,130
+
+537
+00:42:33,130 --> 00:42:33,290
+
+538
+00:42:33,290 --> 00:42:36,470
+
+539
+00:42:36,470 --> 00:42:39,990
+
+540
+00:42:39,990 --> 00:42:45,900
+فأقل 2<sup>2</sup>
+
+541
+00:42:45,900 --> 00:42:52,440
+3<sup>1</sup>، 7<sup>0</sup>
+
+542
+00:42:52,440 --> 00:42:58,600
+فهذه بواحد وهذه بتلاتة وهذه
+
+543
+00:42:58,600 --> 00:43:01,280
+باربعة و عشرين
+
+544
+00:43:02,330 --> 00:43:06,910
+فـ هـيطلع عندكوا الـ greatest common divisor لـ 84 و
+
+545
+00:43:06,910 --> 00:43:14,090
+96 = 12
+
+546
+00:43:14,090 --> 00:43:17,930
+و 96 أكبر من الـ 12
+
+547
+00:43:22,460 --> 00:43:26,960
+طيب الـ primes، احنا اتفقنا الـ primes هو في النهاية
+
+548
+00:43:26,960 --> 00:43:30,960
+مجموعة أرقام، كل رقم منهم لا يقبل القسمة إلا على
+
+549
+00:43:30,960 --> 00:43:36,980
+نفسه أو على الواحد، رغم ذلك بنقدر
+
+550
+00:43:36,980 --> 00:43:40,580
+نقول إنه كل رقمين مع بعض ممكن يكونوا relatively
+
+551
+00:43:40,580 --> 00:43:46,200
+primes، relatively primes يعني بالنسبة لبعض هم
+
+552
+00:43:46,200 --> 00:43:49,990
+شايفين بعض، أمتى بقدر أقول
+
+553
+00:43:49,990 --> 00:43:53,890
+الكلام هذا؟ أو بنسميها co-prime، كل واحد منهم بصير
+
+554
+00:43:53,890 --> 00:43:57,830
+co-prime للتاني أو relatively prime
+
+555
+00:43:57,830 --> 00:44:02,310
+بقدرش أقول والله الخمسة
+
+556
+00:44:02,310 --> 00:44:06,610
+لأ، مادام relative بالنسبة
+
+557
+00:44:06,610 --> 00:44:11,630
+لمين؟ لازم أتكلم عن رقمين، أمتى ببسكت؟ بقول
+
+558
+00:44:11,630 --> 00:44:14,650
+الخمسة prime؟ okay، لأنها أصلا prime، لكن أقول
+
+559
+00:44:14,650 --> 00:44:18,310
+والله العشرة relative prime؟ لأ، هي لحالها مش
+
+560
+00:44:18,310 --> 00:44:23,770
+relative prime، لأنه أفرض إنه عشرة مع اتنين، لأ، فيه
+
+561
+00:44:23,770 --> 00:44:27,290
+عوامل مشتركة بينهم
+
+562
+00:44:27,290 --> 00:44:29,350
+مقدر أقول إنها relative prime لما أحط معاها رقم
+
+563
+00:44:29,350 --> 00:44:34,170
+تاني، و الـ greatest common divisor اللي لهم واحد
+
+564
+00:44:34,170 --> 00:44:37,270
+العامل المشترك الأكبر
+
+565
+00:44:37,270 --> 00:44:41,570
+تبعهم واحد، يعني لا يوجد أي عوامل مشتركة
+
+566
+00:44:41,570 --> 00:44:47,420
+عوامل مشتركة بينهم، زي مثال هنا
+
+567
+00:44:47,420 --> 00:44:54,420
+الـ 21 و العشرة، لا يوجد أي عامل مشترك بينهم
+
+568
+00:44:54,420 --> 00:45:00,180
+عامل مشترك بينهم، كيف؟ الـ 21 عبارة عن 3 × 7
+
+569
+00:45:00,180 --> 00:45:04,760
+هنشوف في الآخر إيش بتسوي
+
+570
+00:45:04,760 --> 00:45:09,960
+هنا، طيب العشرة عبارة عن 2 × 5
+
+571
+00:45:09,960 --> 00:45:13,180
+2<sup>0</sup>، 3<sup>1</sup>، 5<sup>0</sup>
+
+572
+00:45:13,180 --> 00:45:17,540
+و 7<sup>1</sup>، هنا 2<sup>1</sup>، 3<sup>0</sup>، 5<sup>1</sup>
+
+573
+00:45:17,540 --> 00:45:20,660
+و 7<sup>0</sup>
+
+574
+00:45:20,660 --> 00:45:23,840
+بناخد الـ greatest
+
+575
+00:45:23,840 --> 00:45:26,160
+بينهم الأقل دايما
+
+576
+00:45:26,160 --> 00:45:30,560
+2<sup>0</sup>، 3<sup>0</sup>، 5<sup>0</sup>، 7<sup>0</sup> = 1
+
+577
+00:45:30,560 --> 00:45:35,980
+فإذا الـ
+
+578
+00:45:35,980 --> 00:45:41,980
+greatest common divisor للعشرة و الواحد و عشرين
+
+579
+00:45:41,980 --> 00:45:46,680
+هيساوي واحد، في هذه الحالة بقدر أقول أن
+
+580
+00:45:46,680 --> 00:45:52,840
+الأتنين relative prime مع بعض
+
+581
+00:45:52,840 --> 00:45:57,900
+كل واحد لحاله لأ،
+
+582
+00:45:57,900 --> 00:46:02,500
+هو مش prime لحاله، بس مع بعض co-
+
+583
+00:46:02,500 --> 00:46:07,140
+-prime مع بعض، فإذا الـ ... بنسميها
+
+584
+00:46:07,140 --> 00:46:11,680
+relatively prime  if and only if their
+
+585
+00:46:11,680 --> 00:46:16,690
+greatest common divisor = 1
+
+586
+00:46:16,690 --> 00:46:21,050
+لا الـ 21 prime ولا العشرة prime، بس
+
+587
+00:46:21,050 --> 00:46:24,810
+الأتنين مع بعض، كل واحد شايف التاني prime
+
+588
+00:46:24,810 --> 00:46:27,350
+لأن مافيش أي عامل مشترك بينهم
+
+589
+00:46:27,350 --> 00:46:31,600
+no
+
+590
+00:46:31,600 --> 00:46:35,720
+common factors > 1
+
+591
+00:46:35,720 --> 00:46:41,480
+ممكن نحطهم في set A، set of integers
+
+592
+00:46:41,480 --> 00:46:48,900
+A1, A2, A3, A4 بحيث إن كل pairwise
+
+593
+00:46:48,900 --> 00:46:55,770
+بينهم، كل two elements داخل الـ set co-prime مع بعض
+
+594
+00:46:55,770 --> 00:46:59,830
+مع بعض، أو relative prime مع بعض
+
+595
+00:46:59,830 --> 00:47:05,870
+فهنا بنسميها set of
+
+596
+00:47:05,870 --> 00:47:09,950
+co-prime أو relative prime، في حالتنا، في
+
+597
+00:47:09,950 --> 00:47:13,770
+الحالة، إذا كان كل عنصرين مع بعض بنعمل الـ
+
+598
+00:47:13,770 --> 00:47:17,030
+analysis بتاعهم، بيطلعوا co-prime مع بعض
+
+599
+00:47:17,030 --> 00:47:19,110
+أو relative prime
+
+600
+00:47:20,550 --> 00:47:25,330
+فبنقول إن الـ set كلها relatively prime
+
+601
+00:47:25,330 --> 00:47:31,410
+أخدنا الـ greatest common divisor، طب فيه حاجة تانية
+
+602
+00:47:31,410 --> 00:47:37,070
+least common multiple، المضاعف
+
+603
+00:47:37,070 --> 00:47:42,930
+المشترك الأصغر اللي بقدر أقول إنه
+
+604
+00:47:46,490 --> 00:47:53,130
+الـ A و الـ B بيقدروا يقسموا
+
+605
+00:47:53,130 --> 00:47:57,770
+الـ A و الـ B بيقدروا يقسموا
+
+606
+00:47:57,770 --> 00:47:58,350
+
+607
+00:47:58,350 --> 00:48:05,730
+
+608
+00:48:05,730 --> 00:48:07,470
+
+609
+00:48:07,470 --> 00:48:09,950
+
+610
+00:48:09,950 --> 00:48:15,870
+
+611
+00:48:15,950 --> 00:48:22,510
+ممكنة، أقل قيمة ممكنة عشان تحقق هذا الشرط
+
+612
+00:48:22,510 --> 00:48:28,350
+لـ A و لـ B
+
+613
+00:48:28,350 --> 00:48:35,210
+هنا نفس الفكرة، بدنا نجيب الـ least common multiple
+
+614
+00:48:35,210 --> 00:48:41,170
+للستة و العشرة، نمسكهم واحدة واحدة، ممكن برضه بالطريقة
+
+615
+00:48:41,170 --> 00:48:43,370
+الفدائية، نشوف هو إيش يعني، عشان نفهم بس إيش يعني
+
+616
+00:48:43,370 --> 00:48:48,900
+multiple هنا، عشان أقول multiple للستة ممكن تكون
+
+617
+00:48:48,900 --> 00:48:54,440
+الستة، 12، 18، 24، 30، 36، 42
+
+618
+00:48:54,440 --> 00:49:01,680
+
+619
+00:49:01,680 --> 00:49:07,820
+كويس، العشرة: 10، 20، 30، 40
+
+620
+00:49:07,820 --> 00:49:12,700
+
+621
+00:49:15,430 --> 00:49:21,830
+أقل مضاعف مشترك، لاحظوا أن الـ 30 ممكن تكون 30 كمان هنا
+
+622
+00:49:21,830 --> 00:49:24,610
+
+623
+00:49:24,610 --> 00:49:27,450
+
+624
+00:49:27,450 --> 00:49:30,490
+
+625
+00:49:30,490 --> 00:49:33,510
+
+626
+00:49:33,510 --> 00:49:36,970
+
+627
+00:49:36,970 --> 00:49:42,270
+
+628
+00:49:42,270 --> 00:49:46,450
+الـ least common multiple، هذه الطريقة
+
+629
+00:49:46,450 -->
+
+667
+00:52:53,600 --> 00:52:58,420
+بتاعتكم طيب لما تصلوا للـ .. للساعة 24 هتلاقوا
+
+668
+00:52:58,420 --> 00:53:02,560
+الساعة صارت أنكم صفر،صح؟ بتلاقوا ساعاتكم لو أنتم
+
+669
+00:53:02,560 --> 00:53:06,780
+مظبطين ساعاتكم الرقمية طبعا الرقمية على الـ 24
+
+670
+00:53:06,780 --> 00:53:09,620
+system أو الـ 24 system لأنه هيكون عندكم فيه
+
+671
+00:53:09,620 --> 00:53:12,680
+إمكانية 24 system أو 12 system هتلاقوا أنه برجع
+
+672
+00:53:12,680 --> 00:53:17,460
+صفر، ترجع لـ zero كويس، فعندكم هنا اليوم بيصير هو الـ
+
+673
+00:53:17,460 --> 00:53:19,840
+modulus، الـ modulus بتاعكم إن أنتم بتشتغلوا عليه هو
+
+674
+00:53:19,840 --> 00:53:24,140
+24، فلما نيجي نتكلم هنا عن الـ mod operator هو ده
+
+675
+00:53:24,140 --> 00:53:27,210
+اللي بنشتغل عليه، بدنا نشوف إيش .. إيش معناه هذا؟
+
+676
+00:53:27,210 --> 00:53:30,250
+معناه إن أنتم بتعملوا division remainder، إيش
+
+677
+00:53:30,250 --> 00:53:36,070
+المتبقي؟ إيش المتبقي؟ يعني لما نقول الساعة الـ
+
+678
+00:53:36,070 --> 00:53:41,810
+بدأنا فيها أربعة عشر ساعة، أربعة عشر، إيش معناها؟
+
+679
+00:53:41,810 --> 00:53:44,910
+أربعة عشر على الموديلوس اللي إحنا شغالين عليه إحنا
+
+680
+00:53:44,910 --> 00:53:48,010
+إيش الموديلوس اللي باقي؟ إثنا عشر، إثنا عشر، نجسمهم على بعض
+
+681
+00:53:48,010 --> 00:53:55,260
+واحد، إثنا عشر، اتنين، اتنين، أقل من الـ 12، صح؟ معناته
+
+682
+00:53:55,260 --> 00:53:58,440
+الساعة اتنين، لاحظوا إحنا معناته بنشتغل على مين؟
+
+683
+00:53:58,440 --> 00:54:01,540
+على الـ remainder، بنشتغل على الـ remainder، هذا هو
+
+684
+00:54:01,540 --> 00:54:05,660
+الـ equivalent للأربعة عشر، هذا الـ equivalent لمين؟
+
+685
+00:54:05,660 --> 00:54:09,480
+للأربعة عشر، فلو قلنا، فإحنا هنسميها أحيانا division
+
+686
+00:54:09,480 --> 00:54:15,450
+remainder operator، متبقي القسمة أو عملية متبقي
+
+687
+00:54:15,450 --> 00:54:20,510
+القسمة، طيب لو قلنا a و d عبارة عن z أو integers أو
+
+688
+00:54:20,510 --> 00:54:25,150
+integers، والـ d أكبر من واحد، أكبر من واحد، عشان إن
+
+689
+00:54:25,150 --> 00:54:28,870
+يكون فيه إمكانية للـ modulus، ما تكونش أنا بتكلم عن
+
+690
+00:54:28,870 --> 00:54:33,250
+واحد، واحد، معناته هتبقى باستمرار أربعة عشر على واحد
+
+691
+00:54:33,250 --> 00:54:37,250
+بواحد، بأربعة عشر، عفوا خمسة عشر على واحد، خمسة عشر، مش
+
+692
+00:54:37,250 --> 00:54:39,990
+هتفرق كتير، يعني أنا مش عامل modulus هنا، مش عاملين
+
+693
+00:54:39,990 --> 00:54:54,390
+modulus then a مد يولو دي ا مد دي ا مد يولو
+
+694
+00:54:54,390 --> 00:54:58,710
+دي ا مد يولو دي ا مد يولو دي ا مد يولو دي ا مد
+
+695
+00:54:58,710 --> 00:54:59,910
+يولو دي ا مد يولو دي ا مد يولو دي ا مد
+
+696
+00:54:59,910 --> 00:55:00,110
+يولو دي ا مد يولو دي ا مد يولو دي ا مد يولو دي
+
+697
+00:55:00,110 --> 00:55:00,150
+ا مد يولو دي ا مد يولو دي ا مد يولو دي ا مد يولو
+
+698
+00:55:00,150 --> 00:55:00,250
+دي ا مد يولو دي ا مد يولو دي ا مد يولو دي ا
+
+699
+00:55:00,250 --> 00:55:07,740
+مد يولو دي ا مد يولو دي ا مد يولو دي ا مد إذا A
+
+700
+00:55:07,740 --> 00:55:12,440
+مد D بساوي R، لا أعلم إذا كان مرّ عليكم هذا سابقا
+
+701
+00:55:12,440 --> 00:55:17,560
+المد، لازم مرّ عليكم، مرّ، طيب كويس كتير، كويس، فالـ
+
+702
+00:55:17,560 --> 00:55:24,200
+algorithm with dividend A and divisor D، بمعنى
+
+703
+00:55:24,200 --> 00:55:30,880
+remainder، لما A is divided by D، لما نقول A مقسمة
+
+704
+00:55:30,880 --> 00:55:38,020
+باستخدام D، فـ D divides A، الـ R اللي بتطلع هي ناتج
+
+705
+00:55:38,020 --> 00:55:42,580
+الـ module بتاعنا، ناتج الـ module أو الـ modular
+
+706
+00:55:42,580 --> 00:55:44,860
+operator
+
+707
+00:55:45,640 --> 00:55:49,120
+هذه طبعا ممكن تستخدم في بعض .. في بعض لغات البرمجة
+
+708
+00:55:49,120 --> 00:55:52,820
+تستخدم أحيانا علامة النسبة المئوية، هذه .. هذه
+
+709
+00:55:52,820 --> 00:55:57,160
+بتعطي المعنى للـ mod .. أو للـ modular operator ..
+
+710
+00:55:57,160 --> 00:56:05,380
+للمودولار operator، okay، المودولار congruence
+
+711
+00:56:05,380 --> 00:56:11,120
+المودولار congruence اللي هي المكافئة، المكافئة، زي
+
+712
+00:56:11,120 --> 00:56:17,670
+ما هنا أربعة عشر مكافئ اتنين بالنسبة للموديلار 12
+
+713
+00:56:17,670 --> 00:56:24,450
+بالنسبة للموديلار 12، اتنين وأربعة عشر، كل واحدة منهم
+
+714
+00:56:24,450 --> 00:56:28,170
+congruence أو congruent للتانية، فالـ congruence أو
+
+715
+00:56:28,170 --> 00:56:32,170
+الموديلار congruence هي المشابهة أو المناظرة أو
+
+716
+00:56:32,170 --> 00:56:38,570
+المكافئة تحت الموديلوس M، لو حددنا الموديلوس طبعا
+
+717
+00:56:38,570 --> 00:56:42,730
+الموديلوس هنا اللي هو نشتغل عليه كموديلو ..
+
+718
+00:56:42,730 --> 00:56:48,790
+كموديلو بتاعتنا إثنا عشر، طيب أربعة عشر موديلوس أو
+
+719
+00:56:48,790 --> 00:56:52,190
+موديلو إثنا عشر بيساوي اتنين، فالاثنين هنا مكافئة
+
+720
+00:56:52,190 --> 00:56:58,330
+لمين؟ للأربعة عشر، اتنين مكافئة أو congruent للأربعة عشر
+
+721
+00:56:58,330 --> 00:57:04,170
+فهنقول Z positive، هي الـ natural أو الـ n belonging
+
+722
+00:57:04,170 --> 00:57:08,750
+to z، شرط إن الـ n أكبر من صفر، أكبر من صفر، فإحنا في
+
+723
+00:57:08,750 --> 00:57:11,230
+النهاية النتائج بتاعتنا بتكون كلها بالـ positive
+
+724
+00:57:11,230 --> 00:57:14,210
+لاحقا هنتكلم عن الـ negative، إيش ممكن يغير معانا في
+
+725
+00:57:14,210 --> 00:57:16,450
+الشغل، لأنه ممكن يغير في الشغل الحقيقة في الـ
+
+726
+00:57:16,450 --> 00:57:21,030
+negative في الـ modular بيعطينا نتائج أحيانا مختلفة
+
+727
+00:57:21,030 --> 00:57:25,490
+شوية، هنتكلم عنها لاحقا، هنتكلم عنها لاحقا، then a is
+
+728
+00:57:25,490 --> 00:57:32,940
+congruent to b modulo m، بنكتبها كده، congruent
+
+729
+00:57:32,940 --> 00:57:37,220
+مكافئة،  علامة المكافئة، هي مش تساوي، لإن فعليا اتنين
+
+730
+00:57:37,220 --> 00:57:42,920
+لا تساوي أربعة عشر، ولكن هي مكافئة لها باستخدام مدولس
+
+731
+00:57:42,920 --> 00:57:46,560
+هذا تحديدا باستخدام مدولس إثنا عشر، على مدولس تاني لأ
+
+732
+00:57:46,560 --> 00:57:51,100
+لا تكافئها، لو مدولس خمسة، لو مدولس ثلاثمية وستين لأ
+
+733
+00:57:51,100 --> 00:57:57,220
+لا تكافئها، بس إحنا في الحالة هذه مكافئة للـ B mod M
+
+734
+00:57:57,220 --> 00:58:01,320
+if and only if، هذا الكلام يقوله صحيح إن فعلا A
+
+735
+00:58:01,320 --> 00:58:07,340
+congruent B is if and only if M divides الفرق
+
+736
+00:58:07,340 --> 00:58:11,550
+بينهم، طب خلينا نشوف الفرق بينهم، فعلا الفرق بينهم
+
+737
+00:58:11,550 --> 00:58:17,670
+إثنا عشر، آه صح، بيقسم على بعضه، إثنا عشر، بيقسم الفرق بينهم
+
+738
+00:58:17,670 --> 00:58:22,950
+أو بتقدر تقسم الفرق بينهم، لو قلنا ستة وعشرين
+
+739
+00:58:22,950 --> 00:58:29,230
+congruent
+
+740
+00:58:29,230 --> 00:58:32,990
+to two، برضه congruent لأتنين، ليش؟ لأن الفرق بينهم
+
+741
+00:58:32,990 --> 00:58:37,190
+كده أربعة وعشرين، فالإثنا عشر divides أربعة وعشرين
+
+742
+00:58:38,350 --> 00:58:43,510
+مظبوط، مادام بتعطينا تقسيم صحيح، فإذا الاثنين هدول
+
+743
+00:58:43,510 --> 00:58:47,450
+فعلا congruence أو لبعض، أو كل واحدة منهم congruent
+
+744
+00:58:47,450 --> 00:58:52,570
+للتانية، مكافئة، شبيهة، مناظرة، whatever،
+
+745
+00:58:52,570 --> 00:58:57,510
+equivalent لبعض في الحالة بتاعتنا، طيب، في الآخر A
+
+746
+00:58:57,510 --> 00:59:03,720
+minus B mod M، المفروض يساوي صفر، لأنه المفروض هذا
+
+747
+00:59:03,720 --> 00:59:07,680
+يمثل عدد مضاعفات الموديلوس بتاعكم، الموديلوس بتاعكم
+
+748
+00:59:07,680 --> 00:59:13,200
+أربعة وعشرين .. ناقص اتنين، أربعة وعشرين، طيب
+
+749
+00:59:13,200 --> 00:59:19,620
+أربعة وعشرين mod صفر، إثنا عشر، إحنا بدنا نشتغل  الهنا
+
+750
+00:59:19,620 --> 00:59:22,280
+عاملين على الـ remainder اللي بيظل، لو قلنا أربعة
+
+751
+00:59:22,280 --> 00:59:27,540
+وعشرين على إثنا عشر، اتنين، أربعة وعشرين، صفر، آه
+
+752
+00:59:27,540 --> 00:59:35,350
+remainder Zero، remainder 0، ففعلا الفرق لازم يساوي
+
+753
+00:59:35,350 --> 00:59:40,390
+لنا 0 بالنسبة للـ mod 12، إذا كان الفرق هذا ناتج
+
+754
+00:59:40,390 --> 00:59:45,350
+من two elements، الـ two elements هدول أكيد هيكونوا
+
+755
+00:59:45,350 --> 00:59:51,910
+congruent لبعض، مكافئين لبعض، بحيث إنه أنتج لنا إما
+
+756
+00:59:51,910 --> 00:59:57,910
+الـ modulus أو مضاعفاته، الفرق بينهم يساوي الموديلوس
+
+757
+00:59:57,910 --> 01:00:02,270
+أو مضاعفاته، الإثنا عشر أو مضاعفاته، فالفرق بينهم إما
+
+758
+01:00:02,270 --> 01:00:06,890
+إثنا عشر أو أربعة وعشرين، ستة وثلاثين، المهم مضاعفاته
+
+759
+01:00:06,890 --> 01:00:12,190
+مهم مضاعفاته، طيب زي ما قلنا بنستخدم علامة المكافئة
+
+760
+01:00:12,190 --> 01:00:16,390
+هذه، عشان إن هي is defined as، ممكن تعريفها كـ اتنين
+
+761
+01:00:16,390 --> 01:00:22,880
+فالـ أربعة عشر ممكن نعرفها كـ اتنين بالنسبة للساعة ..
+
+762
+01:00:22,880 --> 01:00:25,540
+بالنسبة للساعة فبدنا نكون ناسبين إحنا بالنسبة لمين؟
+
+763
+01:00:25,540 --> 01:00:29,960
+فهي الـ mod كذا، بالنسبة لمين؟ .. بالنسبة لمين؟
+
+764
+01:00:29,960 --> 01:00:32,880
+الأربعة عشر مش بالمطلق دايما بتساوي اتنين أو تكافئ
+
+765
+01:00:32,880 --> 01:00:36,460
+اتنين، إنما بالنسبة للساعة تكافئ اتنين لما أنتم
+
+766
+01:00:36,460 --> 01:00:41,580
+تيجوا تدوروا على البرنامج الـ .. الكالندر بتاعكم، و
+
+767
+01:00:41,580 --> 01:00:45,060
+تلاقوا دخلتوا على صفحتكم وموعد المحاضرة الساعة
+
+768
+01:00:45,060 --> 01:00:47,820
+أربعة عشر، فأنتم عارفين إن الساعة إثنا عشر .. الساعة
+
+769
+01:00:47,820 --> 01:00:50,580
+اتنين، تيجوا على الساعة الثانية لتكونوا موجودين حتى
+
+770
+01:00:50,580 --> 01:00:55,160
+لو أنتم مظبطين ساعتكم عقارب الساعة ومافيش فيها
+
+771
+01:00:55,160 --> 01:00:58,900
+أربعة وعشرين، فأنتم بتشتغلوا على الإثنا عشر أكيد
+
+772
+01:00:58,900 --> 01:01:01,300
+هتيجوا على الثانية لأنه صرتوا حافظينها، بس مش
+
+773
+01:01:01,300 --> 01:01:04,660
+بالضروري إن كل أربعة عشر هتشوفوها هتكون بالنسبة لكم
+
+774
+01:01:04,660 --> 01:01:07,280
+equivalent لاتنين، لأ لأ
+
+775
+01:01:10,860 --> 01:01:15,140
+خلصنا .. خلصنا .. هاي الكلام، الدوائر اللي إحنا
+
+776
+01:01:15,140 --> 01:01:18,180
+عملناها، إما ثلاثين وسبعين أو إثنا عشر، هنا عملناها
+
+777
+01:01:18,180 --> 01:01:23,660
+mod خمسة، عملناها هنا mod خمسة، فـ .. أو modulo five
+
+778
+01:01:23,660 --> 01:01:27,760
+فـ example modulo five، كإنكم بتبدأ مدان modulo
+
+779
+01:01:27,760 --> 01:01:33,220
+five too small، خمس أضلاع بهذا الشكل، على أساس إن كل
+
+780
+01:01:33,220 --> 01:01:36,500
+واحدة منهم رقم، وبعد ما يخلصوا الخمسة تكونوا
+
+781
+01:01:36,500 --> 01:01:40,060
+رجعتوا مرة ثانية لنفس الـ congruent، لنفس الـ
+
+782
+01:01:40,060 --> 01:01:43,160
+congruent أو لنفس الضلع، أول ضلع هيكون اللي هو الـ
+
+783
+01:01:43,160 --> 01:01:48,980
+zero، one، two، three، four، طب equivalent خمسة، خمسة
+
+784
+01:01:48,980 --> 01:01:52,140
+equivalent للـ zero، أصلا خمسة equivalent للـ zero زي
+
+785
+01:01:52,140 --> 01:01:54,360
+ما تقولوا إثنا عشر، إثنا عشر معايا equivalent للـ zero
+
+786
+01:01:55,270 --> 01:01:57,430
+الإثنا عشر، أنتم هتكونوا رفيتوا ورجعتوا ثاني عند الـ zero
+
+787
+01:01:57,430 --> 01:02:03,310
+عند الـ zero، كويس، فـ zero، واحد، اتنين، ثلاثة، أربعة
+
+788
+01:02:03,310 --> 01:02:09,170
+الخمسة congruent لـ zero، congruent لـ عشرة، congruent
+
+789
+01:02:09,170 --> 01:02:15,930
+لـ fifteen، لخمسة عشر، لكله، طيب، الثمانية congruent لمين؟
+
+790
+01:02:15,930 --> 01:02:19,920
+لثلاثة،عشرة، الكلام هذا بيقول إن ده ده ده ده ده ده
+
+791
+01:02:19,920 --> 01:02:20,560
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+792
+01:02:20,560 --> 01:02:21,580
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+793
+01:02:21,580 --> 01:02:25,140
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+794
+01:02:25,140 --> 01:02:25,200
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+795
+01:02:25,200 --> 01:02:25,800
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+796
+01:02:25,800 --> 01:02:34,640
+ده ده ده ده
+
+797
+01:02:34,640 --> 01:02:38,240
+ده ده ده ده ده ده ده ده ده ده ده
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4f37d6af0629403c228cb85c01f390fa311c2048
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao_postprocess.srt
@@ -0,0 +1,3188 @@
+1
+00:00:20,670 --> 00:00:22,530
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,530 --> 00:00:24,870
+الأنبياء والمرسلين سيدنا محمد وعليه وصحبه أجمعين
+
+3
+00:00:24,870 --> 00:00:27,310
+نتكمل في الموضوع ال complexic اللي كنا اتكلمنا فيه
+
+4
+00:00:27,310 --> 00:00:30,970
+أخر مرة أخر مرة اتكلمنا عن مجموعة ال order of
+
+5
+00:00:30,970 --> 00:00:39,180
+growth وعملنا خطعلى أقل مئة أو يعني order
+
+6
+00:00:39,180 --> 00:00:44,300
+polynomial فأقل order polynomial فأقل قولنا أن هذه
+
+7
+00:00:44,300 --> 00:00:49,100
+بنسميها tractable بمعنى قابلة للحل بمعنى أن ال
+
+8
+00:00:49,100 --> 00:00:53,890
+algorithm ده قابل للحل أكبر أو أعلى منPolynomial
+
+9
+00:00:53,890 --> 00:00:56,550
+exponential of factorial أو n to the power of n
+
+10
+00:00:56,550 --> 00:01:02,290
+كنا بنقول إن هذه intractable أو invisible بمعنى
+
+11
+00:01:02,290 --> 00:01:09,870
+غير قابلة للحل نظريا نظريا غير قابلة للحل فبنسميها
+
+12
+00:01:09,870 --> 00:01:14,010
+invisible أو tractable رغم ذلك في بعض functions
+
+13
+00:01:14,010 --> 00:01:19,500
+أحيانا بتشت أو بتكون شاذة عن القاعدةزي حالة بهذا
+
+14
+00:01:19,500 --> 00:01:22,580
+الشكل and to the power مليون and to the power
+
+15
+00:01:22,580 --> 00:01:27,240
+مليون هذه نقدر نصنفها مع ال polynomial تصنف مع ال
+
+16
+00:01:27,240 --> 00:01:30,960
+polynomial و مع ذلك فهي technically tractable
+
+17
+00:01:30,960 --> 00:01:35,900
+polynomial فأقل attractable فرغم ذلك طريقة حلها
+
+18
+00:01:35,900 --> 00:01:41,570
+هتكون صعبة جدا لأنهكلما زادت عدد n بتزيد بصورة
+
+19
+00:01:41,570 --> 00:01:45,570
+كبيرة جدا ال time بيزيد بصورة كتير كبيرة ال order
+
+20
+00:01:45,570 --> 00:01:49,690
+of growth تبعنا ال order هنا of growth في المقابل
+
+21
+00:01:49,690 --> 00:01:54,510
+عندكوا exponential exponential function n to the
+
+22
+00:01:54,510 --> 00:01:57,750
+power ال variable n to the power ال variable هيها
+
+23
+00:01:57,750 --> 00:02:03,710
+log log log n يعني لو اتكلمنا هنا عن ال n هذه
+
+24
+00:02:03,710 --> 00:02:08,800
+خلينا نقول 10 to the power مليونتخيلوا مش هي
+
+25
+00:02:08,800 --> 00:02:15,920
+المليون تنتظر مليون في الحالة هذه log تنتظر مليون
+
+26
+00:02:15,920 --> 00:02:27,440
+مليون log المليون ستة log الستة تقلصت جدافهنا صار
+
+27
+00:02:27,440 --> 00:02:31,180
+في simplification كبير جدا لمين لproblem تبعتكم
+
+28
+00:02:31,180 --> 00:02:35,320
+رغم ان هي technically intractable رغم ان هي فعليا
+
+29
+00:02:35,320 --> 00:02:40,320
+تصنف على اساس ان هي intractable او invisible order
+
+30
+00:02:40,320 --> 00:02:48,020
+for example ناخد مجموعة orders او مجموعة functions
+
+31
+00:02:48,390 --> 00:02:52,650
+و نحسبهم بالنسبة ل ال pc تبعنا و كيف ال response
+
+32
+00:02:52,650 --> 00:02:55,230
+أصلا تبع ال pc اللي احنا بنشتغل عادة عليه ال
+
+33
+00:02:55,230 --> 00:02:58,970
+response تبعنا لل operator الواحدة بيكون محتاج في
+
+34
+00:02:58,970 --> 00:03:02,950
+حدود one nanosecond في حدود one nanosecond و ال
+
+35
+00:03:02,950 --> 00:03:06,490
+one nanosecond دي عادة تمثل ال response في الغالب
+
+36
+00:03:06,490 --> 00:03:11,950
+تبع ال transistor او ال silicon semiconductor فرقم
+
+37
+00:03:12,740 --> 00:03:17,120
+قريب جدا من ال transistor او من ال response لل
+
+38
+00:03:17,120 --> 00:03:23,280
+silicon كويس فهنشتغل عليه وعندنا الان هنا عدد ال
+
+39
+00:03:23,280 --> 00:03:26,440
+inputs ل ال operator اللي هنشتغل عليه فعنا مجموعة
+
+40
+00:03:26,440 --> 00:03:30,280
+operators بدنا نحسب جداش هنحتاج time لكل operator
+
+41
+00:03:30,280 --> 00:03:33,460
+منهم لكل operator من ال operators اللي هنا او ال
+
+42
+00:03:33,460 --> 00:03:38,560
+operations function بتاعتناهنبدأ ب N بتساوي عشرة ن
+
+43
+00:03:38,560 --> 00:03:43,760
+بتساوي عشرة احنا نتكلم عن digits عن bit طيب ال bit
+
+44
+00:03:43,760 --> 00:03:47,720
+اكم bite او بالعكس ال bite اكم bit تمانية معناه
+
+45
+00:03:47,720 --> 00:03:54,000
+ذلك ان عشرة bits جدش بقى اكم bite واحد وربع واحد
+
+46
+00:03:54,000 --> 00:03:58,040
+وربع واحد هي تمانية بيضل اتنين وربع ف one point
+
+47
+00:03:58,040 --> 00:04:04,780
+two five bites10 to the power of 6 او مليون بيت
+
+48
+00:04:04,780 --> 00:04:09,060
+هتكون 125 كيلو بايت 125 كيلو بايت فاحنا نتكلم
+
+49
+00:04:09,060 --> 00:04:12,180
+بأرقام معقولة يعني أرقام مش كتير كبيرة و مع ذلك
+
+50
+00:04:12,180 --> 00:04:14,400
+بدنا نشوف في log ال response كيف بتطلع معانا لل
+
+51
+00:04:14,400 --> 00:04:16,320
+time لكل operation من ال operations اللي موجودة
+
+52
+00:04:16,320 --> 00:04:22,240
+عندنا هنبدأ بالأقل اللي هو ال logarithmic لل base
+
+53
+00:04:22,240 --> 00:04:26,940
+2 او ال binary هذه عشان تحسبوها فعليا و تطلعوا
+
+54
+00:04:26,940 --> 00:04:31,820
+الرقم هذا بتكونوا تتكلموا عن log 10طبعا ال log 10
+
+55
+00:04:31,820 --> 00:04:33,740
+على ال calculator اللي عندكم يمكن مش كل ال
+
+56
+00:04:33,740 --> 00:04:36,280
+calculators بتطلعلكوا إياها للأساس 2 فا
+
+57
+00:04:36,280 --> 00:04:40,920
+automatically بتجي اسمه على log 2 فصارت هذه توازي
+
+58
+00:04:40,920 --> 00:04:47,800
+log أساس 2 لل 10كويس إذا ال calculator تبعتكم
+
+59
+00:04:47,800 --> 00:04:50,560
+بتوفر الكمش إنكوا تختاره أو أنتوا تعملوا selection
+
+60
+00:04:50,560 --> 00:04:54,840
+ل ال base تبعتكم بالظبط لل log ممكن تجسموا على ال
+
+61
+00:04:54,840 --> 00:04:57,340
+log اللي أنتوا محتاجينه فبتكون كأنكوا هو ال
+
+62
+00:04:57,340 --> 00:04:59,880
+reference تبعتكوا أصلا كأنه هو ال base تبعتكم
+
+63
+00:04:59,880 --> 00:05:05,060
+فحسبوها بتطلع 3.3 بالنسبة للمليون هتطلع في حدود 20
+
+64
+00:05:05,060 --> 00:05:09,260
+nano second في حدود 20 ما زالت مقبولة بالنسبة لل
+
+65
+00:05:09,260 --> 00:05:14,550
+time ك responseاللينيار واضح عشرة عشرة لينيار
+
+66
+00:05:14,550 --> 00:05:19,730
+مليون مليون فمليون نانو يعني one millisecond one
+
+67
+00:05:19,730 --> 00:05:24,610
+millisecond ال linear في لغة ريثميك اضربوا الاتنين
+
+68
+00:05:24,610 --> 00:05:28,570
+في بعض ما هي اتنين هي ال N فهي ال log لو ضربتم في
+
+69
+00:05:28,570 --> 00:05:31,930
+بعض بتطلع كم ال response اللي هنحتاجهبرضه ما زال
+
+70
+00:05:31,930 --> 00:05:37,330
+مقبول طيب عند ال polynomial و الدرجة تربيع ..
+
+71
+00:05:37,330 --> 00:05:41,930
+الدرجة تربيع and تربيع في حدود إذا كان عندنا عشرة
+
+72
+00:05:41,930 --> 00:05:45,410
+input ال input بتاعتنا عددهم عشرة هيكون في عندنا
+
+73
+00:05:45,410 --> 00:05:48,650
+ميت nano second إذا كان عندنا مليون هيصل في حدود
+
+74
+00:05:48,650 --> 00:05:58,800
+ستاشر minute و أربعين second11 جيجا و 40 ثانية في
+
+75
+00:05:58,800 --> 00:06:01,000
+حدود يعني ربع الساعة الزمن .. في حدود ربع الساعة
+
+76
+00:06:01,000 --> 00:06:03,220
+الزمن اكتر شوية .. في حدود ربع الساعة الزمن اللي
+
+77
+00:06:03,220 --> 00:06:05,760
+عندي لان ما زالت نسبيا مقبولة اذا كان ال code
+
+78
+00:06:05,760 --> 00:06:09,800
+بالسهل يعني ان انا اولا ممكن اسقل عليه هذه حتى لان
+
+79
+00:06:09,800 --> 00:06:13,500
+polynomial طب اكبر من ال polynomial exponential
+
+80
+00:06:14,350 --> 00:06:20,550
+Exponential عقده عشرة فتنين to the power عشرة الف
+
+81
+00:06:20,550 --> 00:06:22,990
+واربع عشرين هذا انتوا عارفين من ايام كنتوا بتاخدوا
+
+82
+00:06:22,990 --> 00:06:27,770
+ال binary صحيح الف واربع عشرين nano فبتصير واحد
+
+83
+00:06:27,770 --> 00:06:33,550
+فاصلة صفر اربع عشرين micro كويس هنا مليون تنين to
+
+84
+00:06:33,550 --> 00:06:37,210
+the power مليون بتطلع عشرة to the power تلاتمية
+
+85
+00:06:37,210 --> 00:06:46,390
+واحد الف واربعة ونص هذا ال power جيجا yearاليونات
+
+86
+00:06:46,390 --> 00:06:53,310
+بتاعتك جيجا يير جيجا سنة بتكون تستنوا عليها جيجا
+
+87
+00:06:53,310 --> 00:06:56,830
+سنة قبل ما يطلعوا لكوا نتائج فطبعا ماضح لإن ال
+
+88
+00:06:56,830 --> 00:06:59,430
+exponential على طول هنا بتقدر تصنفها ان هي إيش
+
+89
+00:06:59,430 --> 00:07:03,850
+intractable غير ممكنة غير قابلة للحل لأن بالشكل
+
+90
+00:07:03,850 --> 00:07:06,950
+هذا طبعا غير قابل للحل تقولي والله أستنالك جيجا
+
+91
+00:07:06,950 --> 00:07:11,580
+يير بديش أقول تنتظر كذا بكفي جيجا يير واحدةلما
+
+92
+00:07:11,580 --> 00:07:14,300
+اقولكم الله اه استنولكم بس اه خلاص هاي ال .. اعملت
+
+93
+00:07:14,300 --> 00:07:18,260
+execution للبرنامج تبعكم بس استنوني يجيّر، مالهاش
+
+94
+00:07:18,260 --> 00:07:21,520
+منطق أبدا، فواضح ان احنا بدأنا ندخل في إيش؟ في ال
+
+95
+00:07:21,520 --> 00:07:25,900
+interactable problem، interactable problem، طيب في
+
+96
+00:07:25,900 --> 00:07:29,770
+الانfactorial طبعا ما زلنا احنا بتتكلم عن ال n
+
+97
+00:07:29,770 --> 00:07:32,730
+صغيرة مافيش مشكلة بس احنا بطلنا نتعامل مع ال n
+
+98
+00:07:32,730 --> 00:07:35,170
+الصغيرة مع ال inputs اللي عدده صغير احنا أصبحنا
+
+99
+00:07:35,170 --> 00:07:37,930
+نتعامل مع inputs عددهم كبير database بتكون تتعامل
+
+100
+00:07:37,930 --> 00:07:41,250
+و بتتصرفوا مع database فيها عدد كبير جدا من ال
+
+101
+00:07:41,250 --> 00:07:46,650
+inputs فيها عدد كبير جدا من ال inputs فهذه رقم مش
+
+102
+00:07:46,650 --> 00:07:49,770
+هتقدر تحسبه بالأقل الحسبة مش هتقدر تحسبه بالأقل
+
+103
+00:07:49,770 --> 00:07:54,830
+الحسبة لإن هذي بتتكلموا عن مليون factorial
+
+104
+00:07:56,950 --> 00:07:59,790
+مليون اضربه في كل الرقم اللى تحته اللى اقل من
+
+105
+00:07:59,790 --> 00:08:02,870
+المليون مش هطلع ولا في اي حاسبة ولا كمبيوتر هطلع
+
+106
+00:08:02,870 --> 00:08:08,610
+الكل ناتج كله هيجف invalid كله هطلع invalid اتوقع
+
+107
+00:08:08,610 --> 00:08:10,910
+حتى ال computer ساعد كل رقم هذا مش هطلع الكل يعنى
+
+108
+00:08:11,470 --> 00:08:15,190
+حتى الرقم هذا مش هيطلع معاكم هذا الرقم يدوب
+
+109
+00:08:15,190 --> 00:08:18,350
+بالحاسوب حاسوب زي ما يقولوا جوي كويس ال browser
+
+110
+00:08:18,350 --> 00:08:21,430
+بتبعته عالي عشان نطلع الرقم عشان نطلعنا الرقم هذا
+
+111
+00:08:21,430 --> 00:08:24,790
+فعال calculator ساعتكم مش هيطلع هذا و انتوا
+
+112
+00:08:24,790 --> 00:08:28,330
+بتحسبوه جربوه اذا انتوا طبقوها مليون هتلاقوا
+
+113
+00:08:28,330 --> 00:08:32,450
+invalid هنا نفس الكلام مليون factorial مش هيطلع
+
+114
+00:08:32,450 --> 00:08:41,040
+اشي okay and solve the problemفي ال .. الف تسعمائة
+
+115
+00:08:41,040 --> 00:08:46,440
+و تلاتين turning واحد اسمه turning اكتشف او وجد ان
+
+116
+00:08:46,440 --> 00:08:50,820
+والله في اشكالية ان في بعض مشاكل .. بعض problems
+
+117
+00:08:50,820 --> 00:08:55,260
+او algorithms غير قابلة للحل، لا يمكن حلها، لا
+
+118
+00:08:55,260 --> 00:09:00,140
+يمكن حلها طيب عشان يقول ان هي لا يمكن حلها او غير
+
+119
+00:09:00,140 --> 00:09:05,130
+قابل انه حتى يعمل decision الحل صح او خطأغير قادر
+
+120
+00:09:05,130 --> 00:09:10,710
+إنه يعطي yes or no question حتى ال problems عنده
+
+121
+00:09:10,710 --> 00:09:14,450
+مافيش إمكانية لحلها فهي unsolved problem أو
+
+122
+00:09:14,450 --> 00:09:21,210
+uncomputable functions هذه من أهم مشاكلنا اللي هي
+
+123
+00:09:21,210 --> 00:09:25,170
+ال halting problem ال halting problem هي إنه إما
+
+124
+00:09:25,170 --> 00:09:29,170
+ال algorithm finally هيجف مش هيطلع إشي في النهاية
+
+125
+00:09:29,170 --> 00:09:34,100
+ال algorithm هيجف أو continue foreverأو ال code
+
+126
+00:09:34,100 --> 00:09:37,060
+يظل يستمر على طول يعني اللي انتوا بتتكلموا عنه هذا
+
+127
+00:09:37,060 --> 00:09:40,540
+for جيجا يير هذه انتوا بالنسبالكوا forever هيظل
+
+128
+00:09:40,540 --> 00:09:45,040
+شغال هيك معناته ضل خلاص الجهاز قطوه على جنب و
+
+129
+00:09:45,040 --> 00:09:48,560
+انسوه مافيش جهاز هذا اذا انتوا مصرين بتكون نتيجة
+
+130
+00:09:48,560 --> 00:09:52,020
+مش هيطلع النتائج في النهاية مش هيطلع النتائج فهذه
+
+131
+00:09:52,020 --> 00:09:58,630
+اما finally halt stop في النهاية حيجف اوto
+
+132
+00:09:58,630 --> 00:10:02,150
+infinite loop هيظل match to infinity في الآخر هذه
+
+133
+00:10:02,150 --> 00:10:05,410
+المتسمية كلها بتندرج مع unsolved problem unsolved
+
+134
+00:10:05,410 --> 00:10:09,550
+problem كويسة الموضوع ده دخلنا في جزئية تانية انه
+
+135
+00:10:09,550 --> 00:10:13,030
+مدام في unsolved problem او unsolved algorithms
+
+136
+00:10:13,030 --> 00:10:17,670
+فاحنا عارفين ال P ال P هذه كانت كل ال problems
+
+137
+00:10:17,670 --> 00:10:21,210
+اللي كنا بتسميها tractable حطيناها داخل set
+
+138
+00:10:21,210 --> 00:10:28,520
+سميناهابال P، بال P، capital P، هذه كلها عبارة عن
+
+139
+00:10:28,520 --> 00:10:30,800
+ال problems اللي هي ال order تبعها polynomial
+
+140
+00:10:30,800 --> 00:10:36,180
+فأقل، polynomial فأقل، تمام خلصنا من ال Vالأنبي
+
+141
+00:10:36,180 --> 00:10:42,560
+هدى بنتكلم هنا عن set of problems for which there
+
+142
+00:10:42,560 --> 00:10:45,260
+exists a tractable algorithm for checking
+
+143
+00:10:45,260 --> 00:10:50,460
+solutions to see if they are correct معناه ذلك انه
+
+144
+00:10:50,460 --> 00:10:54,860
+هدى لكل ال algorithms اللى أمكن حلها اللى أمكن
+
+145
+00:10:54,860 --> 00:10:58,580
+حلها اللى بنقدر نقول ان والله algorithms ممكن حلها
+
+146
+00:10:59,790 --> 00:11:03,610
+في إمكانية لحلها طبعا واضح ان العلاقة بالاتنين انه
+
+147
+00:11:03,610 --> 00:11:08,530
+by logic هيكي ان ال P subset of and P لأن ال P
+
+148
+00:11:08,530 --> 00:11:11,350
+interactable .. attractable عفوا interactable هي
+
+149
+00:11:11,350 --> 00:11:15,610
+polynomial فأقل معناته قابلة للحل معناه ذلك انه
+
+150
+00:11:15,610 --> 00:11:20,810
+ممكن جدا يجي لحل داخل ال algorithms اللي تم حلها
+
+151
+00:11:20,810 --> 00:11:24,830
+فعلا اللي تم حلها فعلا او يمكن ايجاد لحل .. نجد
+
+152
+00:11:24,830 --> 00:11:30,250
+لحل هذا الكلام نظرياكان هذا نظريا ولكن unproven
+
+153
+00:11:30,250 --> 00:11:34,350
+projector .. conjecture عفوا .. conjecture في ال
+
+154
+00:11:34,350 --> 00:11:37,630
+computer science في العلوم علم الحسوب في ما زالت
+
+155
+00:11:37,630 --> 00:11:41,930
+بعض الحدث أو بعض البديهيات الغير مثبتة بعض
+
+156
+00:11:41,930 --> 00:11:48,530
+البديهيات الغير مثبتة تقولنا لأ انه prepare في set
+
+157
+00:11:48,530 --> 00:11:54,030
+او prepare subset and b بمعنى انه يوجد .. يوجد في
+
+158
+00:11:54,030 --> 00:11:58,340
+الحلول الممكنة او يوجد في المسائل اللي تم حلهابعض
+
+159
+00:11:58,340 --> 00:12:02,480
+ال problems ال interactable interactable ولكن أمكن
+
+160
+00:12:02,480 --> 00:12:06,980
+نحلها حتى الآن مافيش اي اثبات للموضوع هذا بمعنى
+
+161
+00:12:06,980 --> 00:12:12,240
+انه استثنى ال b equal to and استثنى انه فقط ما
+
+162
+00:12:12,240 --> 00:12:17,760
+يمكن نحله هو ال interactable بس اذا قلنا subset او
+
+163
+00:12:17,760 --> 00:12:21,040
+يساوي هو استثنى ان هي تساوي معناته كأنه بيقولنا ان
+
+164
+00:12:21,040 --> 00:12:26,440
+لأ حسب الحادث تبعنا حادثا ان لأ مشكلة interactable
+
+165
+00:12:26,440 --> 00:12:30,380
+أمكن نحلهافي حاجات أما كانت حالها مش tractable،
+
+166
+00:12:30,380 --> 00:12:34,920
+ضالت المشكلة حتى الآن قائمة، حتى الآن المشكلة دل
+
+167
+00:12:34,920 --> 00:12:38,620
+قائمة ماحدش أثبتها، فالعند الآن هي unproven
+
+168
+00:12:38,620 --> 00:12:42,700
+conjecture هي ما زالت حتى الآن حدث أو بديهية غير
+
+169
+00:12:42,700 --> 00:12:48,540
+مثبتة و تم الإعلان عنها كبديهية غير مثبتة في سنة
+
+170
+00:12:48,540 --> 00:12:54,950
+2000 وانحطت ضمن سبع بديهياتضمن السبع بدهيات، السبع
+
+171
+00:12:54,950 --> 00:12:58,170
+بدهيات هدولة اللي بيقدر يثبت أي واحدة منهم في
+
+172
+00:12:58,170 --> 00:13:01,570
+جائزة مليون دولار، وحتى الآن قائمة، حتى الآن
+
+173
+00:13:01,570 --> 00:13:04,810
+قائمة، ما تمش حل إلا واحدة منهم من السبع خلال
+
+174
+00:13:04,810 --> 00:13:08,840
+الاربتاشر سنة اللي فاتوا حلت بس واحدةواللي حلها
+
+175
+00:13:08,840 --> 00:13:12,160
+ماخدش الفروس يعني مارضيش ياخدهم هو جالب مابتيش
+
+176
+00:13:12,160 --> 00:13:15,520
+إياهم المليون دولار بس لعند الآن هذي من المشاكل
+
+177
+00:13:15,520 --> 00:13:18,380
+اللي لمته حل لأن هو حل واحدة سبعة غير التانية هذي
+
+178
+00:13:18,380 --> 00:13:23,360
+مازالت موجودة ضمن ستة انه اثبتوا .. اثبتولنا ال
+
+179
+00:13:23,360 --> 00:13:26,140
+relation هذي انه مستثنى ال interactable ال
+
+180
+00:13:26,140 --> 00:13:30,060
+interactable مستثنى من ال solve the problem لعند
+
+181
+00:13:30,060 --> 00:13:34,060
+الآن هذي غير محلولة فاللي هيحلها هيصبح في يوم
+
+182
+00:13:34,060 --> 00:13:38,770
+الليلة مشهورفي يوم الليلة، زائد كمان مليون دولار،
+
+183
+00:13:38,770 --> 00:13:43,030
+لو دورته عن نت، لو دورته عن نت هتلاقوا اسم المؤسسة
+
+184
+00:13:43,820 --> 00:13:47,100
+اسم المؤسسة و العنوان اللي تتوجهوله إذا كانت تعرف
+
+185
+00:13:47,100 --> 00:13:50,140
+تثبتوا حاجة منهم و بالمرة بتشوفوا كمان ال 6
+
+186
+00:13:50,140 --> 00:13:53,100
+problems التانين إذا كانت بتقدروا تحلوا إشي منهم
+
+187
+00:13:53,100 --> 00:13:56,040
+يعني علماء العالم كلهم اللي عنده الان لهم 14 سنة و
+
+188
+00:13:56,040 --> 00:13:58,740
+بيشتغلوا فيهم و ماوصلوش لا إشي بالعافية واحدة
+
+189
+00:13:58,740 --> 00:14:01,400
+انحلت واحدة انحلت و صاحبة مارضوش ياخدوا الفلوس
+
+190
+00:14:01,400 --> 00:14:05,340
+كمان عشان نبدأ الوجد في ال basic numbers ال basic
+
+191
+00:14:05,340 --> 00:14:08,260
+numbers ببساطة جدا هنرجع للأرقام القديمة اللي
+
+192
+00:14:08,260 --> 00:14:11,860
+اتخدتوها في ابتدائي و عاداليهنبدأ للأرقام القديمة
+
+193
+00:14:11,860 --> 00:14:15,960
+اللي أخدتها في ابتدائي و إعدادي و أتوقع أن كلنا of
+
+194
+00:14:15,960 --> 00:14:20,040
+course كلنا بنعرف ال integers كلنا عارفين إيش يعني
+
+195
+00:14:20,040 --> 00:14:22,760
+ال integers و كلنا عارفين إيش يعني أرقام و كلنا
+
+196
+00:14:22,760 --> 00:14:25,700
+عارفين كيف بتعامل مع ال integers لأن كل شغلنا
+
+197
+00:14:25,700 --> 00:14:28,880
+هالواجهة هنتكلم عن integers هنتكلم عن integers
+
+198
+00:14:28,880 --> 00:14:33,960
+كويسة فال integers هذه كل اللي هنضيفه في شغلنا بس
+
+199
+00:14:33,960 --> 00:14:37,460
+كل اللي هنضيفه في شغلنا أنه هنتعلم شوية specific
+
+200
+00:14:37,460 --> 00:14:41,440
+notations و terminologyالعمليات الحسابية اللي
+
+201
+00:14:41,440 --> 00:14:44,760
+كنتوا تعملوها ضرب قسمة جمع ضرب القسمة هو اللي
+
+202
+00:14:44,760 --> 00:14:47,640
+هنشتغل عليه اصلا احنا هنشتغل اكتر منه هنشتغل في
+
+203
+00:14:47,640 --> 00:14:50,440
+البداية هلوجد كتعريفات للجمع و القسمة و الحاجات
+
+204
+00:14:50,440 --> 00:14:53,560
+البسيطة اللي احنا هناخدها مع شوية terminology
+
+205
+00:14:53,560 --> 00:14:56,740
+إضافية هي اللي هتتعلموها على الكمبيوتر على ال pc
+
+206
+00:14:56,740 --> 00:15:00,580
+ليش؟ لأن الهدف الأساسي مش ان انا اعرف كيف اقسم
+
+207
+00:15:00,580 --> 00:15:05,080
+انتوا لأ انتوا لوجد مهندسين حسوب مهندس حسوب كويس
+
+208
+00:15:05,080 --> 00:15:07,840
+انا بعرف اقسم لحالي بس بتكتبوا code بتخلوا
+
+209
+00:15:07,840 --> 00:15:11,640
+الكمبيوتر يفهم يقسم لحفمعنى ذلك لازم تكونوا فاهمين
+
+210
+00:15:11,640 --> 00:15:16,160
+عملية القسمة بقالية معينة بنفع تحولوها لاحقا ل
+
+211
+00:15:16,160 --> 00:15:20,240
+code عرفتوا إيش الفرجة الوجد اللي هنعمله؟ هنتكلم
+
+212
+00:15:20,240 --> 00:15:24,400
+في حاجات أنتوا عارفينها نقسم رقمين على بعض مش
+
+213
+00:15:24,400 --> 00:15:26,920
+محتاجة شغل كتير بس احنا هنقعدلنا فيها كمان slide
+
+214
+00:15:26,920 --> 00:15:30,860
+هالوجد و احنا بتتكلم إن كيف أقسم رقمين على بعضكويس
+
+215
+00:15:30,860 --> 00:15:32,740
+وإيش أسمي الرقم هذا وإيش أسمي الرقم هذا وكيف
+
+216
+00:15:32,740 --> 00:15:36,960
+نعملهم وكيف نسويهم وكيف أطلع القسم المشترك الأكبر
+
+217
+00:15:36,960 --> 00:15:40,580
+وكيف نطلع الكلام أنتوا أخدتهوا سابقا أنا عارف ولكن
+
+218
+00:15:40,580 --> 00:15:44,680
+احنا بدنا ناخده قالية أنه ممكن أكتب code للكمبيوتر
+
+219
+00:15:44,680 --> 00:15:47,140
+ومش انا اللي بده أحلها مش احنا اللي بدنا نحلها
+
+220
+00:15:47,140 --> 00:15:49,760
+كمهم ان انتوا كنتوا كتبوا code تخلوا ال pc هو اللي
+
+221
+00:15:49,760 --> 00:15:53,980
+يفهمهاتمام فهي الفرق الوحيد في الشغل احنا هنقول بس
+
+222
+00:15:53,980 --> 00:15:57,620
+ناخد الموضوع بوجهة نظر مختلفة شوية خلينا نقول
+
+223
+00:15:57,620 --> 00:16:03,340
+نشتغل على ال divides factor multiple العوامل
+
+224
+00:16:03,340 --> 00:16:10,300
+المشتركة العامل او القاسم المشترك و المضاعف
+
+225
+00:16:10,300 --> 00:16:17,090
+المضاعفة للرقم طيب لو افترضنا a و b integersو a لا
+
+226
+00:16:17,090 --> 00:16:20,650
+تساوي صفر لأنه هذا بناحطه في denominator في مقام
+
+227
+00:16:20,650 --> 00:16:24,790
+لحنحطه في المقام ال a فمدام هتنحطه في المقام لازم
+
+228
+00:16:24,790 --> 00:16:27,130
+ما تكونش بتساوي صفر لأنه هيطلعلك .. هيطلعلنا
+
+229
+00:16:27,130 --> 00:16:32,150
+undefined value undefined value كأني بده أقول b
+
+230
+00:16:32,150 --> 00:16:38,010
+على a فa هذه لازم لا تساوي صفر لازم لا تساوي صفر
+
+231
+00:16:38,010 --> 00:16:45,630
+كويسة a divides b هيك بنكتبهاdivides بيه لأن فعلا
+
+232
+00:16:45,630 --> 00:16:50,370
+a هو اللي قسم بيه بيه كانت قيمة كبيرة a قسمها
+
+233
+00:16:50,370 --> 00:16:55,630
+قسمها لمجموعة groups مثلا لو قلنا اتناش على تلاتة
+
+234
+00:16:55,630 --> 00:16:59,750
+كأن التلاتة هتجسم لاتناش ل three groups كل group
+
+235
+00:16:59,750 --> 00:17:05,410
+قدش فيه خارج القسمة اللي هو اربعةاللي هو أربع فهنا
+
+236
+00:17:05,410 --> 00:17:09,850
+بنقولها إيش a divides b a يقسم b هذي معناها a
+
+237
+00:17:09,850 --> 00:17:14,190
+divides b there exists c كيف تعريفها there exists
+
+238
+00:17:14,190 --> 00:17:19,550
+c برضه integer بحيث إنه c هو خارج القسمة c في a
+
+239
+00:17:19,550 --> 00:17:24,070
+يساوي ال b معناته إذا فعلا there exists c يوجد
+
+240
+00:17:24,070 --> 00:17:29,150
+integer لو ضربناه في a بطلع b معناته a divides b
+
+241
+00:17:29,150 --> 00:17:35,020
+is true خارج قسمة integerأنا عارف إنه ممكن يطلع
+
+242
+00:17:35,020 --> 00:17:39,900
+fraction بس احنا خلّينا لسه فيه .. فيه ابتدائي إنه
+
+243
+00:17:39,900 --> 00:17:44,370
+لازم تكون integer إذا integer بنقولtrue فإذا كان
+
+244
+00:17:44,370 --> 00:17:48,890
+والله عندنا بالشكل هذا تلاتة divides minus twelve
+
+245
+00:17:48,890 --> 00:17:53,690
+هذا بيطلع integer ولا بيطلعش integer انتجر معناته
+
+246
+00:17:53,690 --> 00:18:00,410
+true طيب three divides seven لأ false فإذا if and
+
+247
+00:18:00,410 --> 00:18:08,470
+only if a divides b then we say a is a factor of
+
+248
+00:18:08,470 --> 00:18:17,070
+or a divisorاما بتسميه factor هو احد معاملات B هو
+
+249
+00:18:17,070 --> 00:18:23,150
+احد معاملات B فعلا لانه لحظة 12 بتساوي 3 في 4 فهي
+
+250
+00:18:23,150 --> 00:18:27,030
+واحدة من معاملات ال 12 هي واحدة من معاملات A او
+
+251
+00:18:27,030 --> 00:18:35,410
+divisor قاسم قاسم ل ال B قاسم of B و ال B بنسميها
+
+252
+00:18:35,410 --> 00:18:41,220
+multiple مضاعفاتالتلاتة مضاعفات ال a من مضاعفات a
+
+253
+00:18:41,220 --> 00:18:44,680
+جديش متكررة ال a هي خارج القسمة متكررة أربع مرات
+
+254
+00:18:44,680 --> 00:18:51,420
+عشان تعطينا المضاعف اتناش أو المضاعف بي وهذه كانت
+
+255
+00:18:51,420 --> 00:18:59,180
+C كويس هنا for example لو قولنا بي is even بقدر
+
+256
+00:18:59,180 --> 00:19:03,860
+أعرفها two divides بي إذا فعلا two divides بي is
+
+257
+00:19:03,860 --> 00:19:10,000
+trueمعناته ال B دائما even دائما even إذا two
+
+258
+00:19:10,000 --> 00:19:15,180
+divides B is true فإذا دائما even طيب ال zero even
+
+259
+00:19:15,180 --> 00:19:23,980
+بناء على النظرية هذه zero هل هي belong to Z؟ أه
+
+260
+00:19:23,980 --> 00:19:29,680
+خلاص معناته إذا even فإذا even طيب ال minus four
+
+261
+00:19:32,120 --> 00:19:37,800
+to divides minus four قدش الناتج ال minus two
+
+262
+00:19:37,800 --> 00:19:43,560
+belong to z فإذن برضه true إذن true فإذن even
+
+263
+00:19:43,560 --> 00:19:48,860
+فمعناه دي even طيب شوية facts facts relation أو
+
+264
+00:19:48,860 --> 00:19:57,460
+على ال divides relation a divides zero trueلأنه
+
+265
+00:19:57,460 --> 00:20:00,240
+هيتطلع zero النتج هنا zero و ال zero احنا عارفين
+
+266
+00:20:00,240 --> 00:20:04,100
+ان هو belong to z فاحنا عارفين ان هو a و b و c
+
+267
+00:20:04,100 --> 00:20:07,700
+اللي هنشتغل فيهم هدول كلهم integers كلهم integers
+
+268
+00:20:07,700 --> 00:20:12,780
+ف integer divides zero هيطلع zero و ال zero
+
+269
+00:20:12,780 --> 00:20:22,360
+integer طيب a divides b and a divides c لو بنقدر
+
+270
+00:20:22,360 --> 00:20:30,360
+نقول ان a تقسم bو بيعطيك بيعطينا true بيعطينا true
+
+271
+00:20:30,360 --> 00:20:33,700
+معناته ممكن يكون خارج قسمة يعني خارج قسمة خلاني
+
+272
+00:20:33,700 --> 00:20:40,380
+أقول S و ال S هذه integer هذه integer و and
+
+273
+00:20:43,550 --> 00:20:49,250
+over a بمعنى a divides c برضه خارج قسمة معناته هذه
+
+274
+00:20:49,250 --> 00:20:52,710
+true and true إذا فعلا تحقق الشرطة ده معناته خلنا
+
+275
+00:20:52,710 --> 00:20:56,650
+نقول إنه إلها T وT هذه برضه integer إلها خارج قسمة
+
+276
+00:20:56,650 --> 00:21:01,970
+integer إذا تحققوا الإتنين هدولة then a divides b
+
+277
+00:21:01,970 --> 00:21:06,930
+زائر c صحيح
+
+278
+00:21:06,930 --> 00:21:15,290
+فإذا لو قلنا b plus c من هناعارفين أن P بتساوي A
+
+279
+00:21:15,290 --> 00:21:30,290
+في S، C تساوي A في T، نجمعهم، هيساوي A في S زائد A
+
+280
+00:21:30,290 --> 00:21:38,290
+في T ناخد common A S زائد T طيب، هي معناته في عمل
+
+281
+00:21:38,290 --> 00:21:42,890
+مشترك، معناته بتجسبمعناته في إمكانية للقسمة في
+
+282
+00:21:42,890 --> 00:21:46,650
+إمكانية للقسمة مدام طلعت ال a أصلا عامل مشترك
+
+283
+00:21:46,650 --> 00:21:51,830
+common common معناته برضه بتقسم على a أو a نقدر
+
+284
+00:21:51,830 --> 00:21:58,770
+نقول أن a divides b plus c فهي هذه مثبتة إثبات لل
+
+285
+00:21:58,770 --> 00:22:02,350
+proof ال proof اللي هي الحالة التانية proof الحالة
+
+286
+00:22:02,350 --> 00:22:09,850
+التانية تمام a divides b thenA Divides B في أي
+
+287
+00:22:09,850 --> 00:22:15,590
+integer لأن هنا صارت multiple of B مدام أصلا B
+
+288
+00:22:15,590 --> 00:22:20,270
+تقبل القسم على A B مضروبة في أي integer برضه
+
+289
+00:22:20,270 --> 00:22:25,130
+الناتج هيقبل القسم على A برضه هيقبل القسم على A
+
+290
+00:22:25,130 --> 00:22:30,690
+okay
+
+291
+00:22:30,690 --> 00:22:37,370
+A Divides B and B Divides C then A Divides C
+
+292
+00:22:41,820 --> 00:22:50,580
+زي لو قلنا اتناش على تلاتة true true لأنه هيعطينا
+
+293
+00:22:50,580 --> 00:22:57,960
+قيمة طيب اربعة و عشرين على اتناش true then اربعة و
+
+294
+00:22:57,960 --> 00:23:02,300
+عشرين لازم تكون بقبل القسم على تلاتةلازم تقبل
+
+295
+00:23:02,300 --> 00:23:08,140
+القسم ع تلاتة فهي برضه النصرية رقم اربعة او ال
+
+296
+00:23:08,140 --> 00:23:13,820
+fact number four اذا a divides b and b divides c
+
+297
+00:23:13,820 --> 00:23:18,080
+اكيد a divides c
+
+298
+00:23:18,080 --> 00:23:24,600
+طيب هى خلصنا جزئية اللى هي عملية الدرب عملية الدرب
+
+299
+00:23:25,470 --> 00:23:28,590
+Okay نتكلم عن ال primes ال primes عارفين أحنا
+
+300
+00:23:28,590 --> 00:23:32,290
+سابقا ال primes كنا سابقا عارفينها ال prime هو رقم
+
+301
+00:23:32,290 --> 00:23:36,270
+لا يقبل القسم إلا على نفسه أو على الواحد بمعنى
+
+302
+00:23:36,270 --> 00:23:40,270
+مالوش factors مالوش factors مالوش أي رقمين ممكن
+
+303
+00:23:40,270 --> 00:23:43,610
+أضربهم في بعض و أطلعهم مالوش مجموعة factors ال
+
+304
+00:23:43,610 --> 00:23:47,530
+factors الوحيدة تبعته اللي هو نفسه والواحد الصحيح
+
+305
+00:23:47,530 --> 00:23:52,450
+والواحد الصحيح فإذا بنقدر نقول انتجرP أو prime
+
+306
+00:23:52,450 --> 00:23:56,210
+أكبر من واحد هذا ما بنسميه ال P is prime if and
+
+307
+00:23:56,210 --> 00:24:00,210
+only if it's not the product of any two integers
+
+308
+00:24:00,210 --> 00:24:07,070
+هو مش ناتج من ضرب two integers أكبر من واحد الواحد
+
+309
+00:24:07,070 --> 00:24:09,750
+هو الحالة الوحيدة اللي ممكن تنفع ليش لأنه مضروبة
+
+310
+00:24:09,750 --> 00:24:17,360
+في نفسها ال P هيكون عبارة عن ال P في واحد بسأو ما
+
+311
+00:24:17,360 --> 00:24:21,020
+لا يمكن ينتج أو نقدر نلتجه نجيبه من two integers
+
+312
+00:24:21,020 --> 00:24:25,240
+مضرومي في بعض باستثناء الواحد طيب فبنقول P أكبر من
+
+313
+00:24:25,240 --> 00:24:28,900
+واحد فإذا ال .. ال .. ال primes تبعتنا بتبدأ من
+
+314
+00:24:28,900 --> 00:24:35,700
+اتنين اتنين، تلاتة، خمسة، سبعة، احداشر، بتكمل أكبر
+
+315
+00:24:35,700 --> 00:24:40,980
+من واحد and there is no exist لا يوجد a و b لا
+
+316
+00:24:40,980 --> 00:24:46,610
+يوجد أي رقمينbelong to natural number والرقمين
+
+317
+00:24:46,610 --> 00:24:52,670
+لازم يكونوا اكبر من واحد حصل ضربهم يساوي ال B لا
+
+318
+00:24:52,670 --> 00:24:58,390
+يوجد a و b حصل ضربهم يعطي إبراهيم
+
+319
+00:25:02,650 --> 00:25:06,450
+Okay الحالة الوحيدة زى ما قلنا اما اللى هى ال
+
+320
+00:25:06,450 --> 00:25:11,230
+prime نفسه و الواحد الواحد و ال P itself نفسها بس
+
+321
+00:25:11,230 --> 00:25:16,510
+و هدى بتندرجش ضمن التعريف لإن احنا استثنينا هنا A
+
+322
+00:25:16,510 --> 00:25:21,870
+أكبر من واحد و P أكبر من واحد فلا يساوي واحد some
+
+323
+00:25:21,870 --> 00:25:26,390
+primes اتنين تلاتة خمسة سبعة احداشر تلاتاشرالـ 17
+
+324
+00:25:26,390 --> 00:25:31,290
+بتكمله طيب ال non-prime إذا كان رقم non-prime
+
+325
+00:25:31,290 --> 00:25:34,790
+بنسميه composite composite إيش يعني؟ يعني ممكن
+
+326
+00:25:34,790 --> 00:25:38,210
+تأليفه من رقمين أخرين يعني ممكن نقول إن هو
+
+327
+00:25:38,210 --> 00:25:42,250
+composed by multiplying two integers greater than
+
+328
+00:25:42,250 --> 00:25:47,710
+one فإذا بقدر أنتجه من حاصل ضرب رقمين أخرين هذا
+
+329
+00:25:47,710 --> 00:25:51,430
+بنقول إنه non-prime هذا إيش؟ non-prime إذا
+
+330
+00:25:51,430 --> 00:25:55,130
+ماقدرناش بكون اسمه prime على طول بكون اسمه ال
+
+331
+00:25:55,130 --> 00:25:55,330
+prime
+
+332
+00:25:58,850 --> 00:26:04,870
+طيب fundamental theorem of arithmetic every
+
+333
+00:26:04,870 --> 00:26:09,110
+integer greater than one كل رقم integer أكبر من
+
+334
+00:26:09,110 --> 00:26:13,430
+one can be written uniquely as a prime or as the
+
+335
+00:26:13,430 --> 00:26:18,630
+product of two or more primes فإذا كل رقم أكبر من
+
+336
+00:26:19,940 --> 00:26:23,820
+من واحد .. كل رقم .. مافيش إثناء .. كل رقم أكبر من
+
+337
+00:26:23,820 --> 00:26:29,760
+واحد بنقدر نمثله إما ب prime إذا هو نفسه prime أو
+
+338
+00:26:29,760 --> 00:26:34,600
+two primes مضروبين في بعض أو أكثر .. ممكن يكون
+
+339
+00:26:34,600 --> 00:26:36,220
+تلاتة primes مضروبين في بعض .. أربعة primes
+
+340
+00:26:36,220 --> 00:26:39,500
+مضروبين في بعض .. بس جميع الأرقام ممكن تعملوهم
+
+341
+00:26:39,500 --> 00:26:43,520
+مجموعة primes مضروبين في بعضمجموعة الـprimes
+
+342
+00:26:43,520 --> 00:26:46,940
+اتمثلون بمجموعة الـprimes مضرومين في بعض زي ما
+
+343
+00:26:46,940 --> 00:26:50,440
+قلنا product of two or more primes where the prime
+
+344
+00:26:50,440 --> 00:26:54,280
+factors are written in order of non-decreasing
+
+345
+00:26:54,280 --> 00:26:58,000
+size دائما بنبدأ ال analysis تبعتنا بالـprimes
+
+346
+00:26:58,000 --> 00:27:01,600
+الأقل نبدأ بالـprimes الأقل إيش يعني بنبدأ
+
+347
+00:27:01,600 --> 00:27:05,960
+بالـprimes الأقل؟ يعني لو بدنا نجيب ال factors ال
+
+348
+00:27:05,960 --> 00:27:10,180
+prime factors تبعت ناخد رقم كبير الألفين
+
+349
+00:27:12,480 --> 00:27:17,580
+بنبدأ أقل ال prime ايش؟ ال 2 أقل ال prime بنبدأ
+
+350
+00:27:17,580 --> 00:27:20,880
+بال 2 هل بيقبل الجسم على 2؟ أه بيقبل الجسم على 2
+
+351
+00:27:20,880 --> 00:27:25,800
+جدش بيظل؟ ألف طيب الألف بتقبل الجسم على 2؟ أه
+
+352
+00:27:25,800 --> 00:27:35,590
+بتقبل الجسم على 2 طيب بتصير 500 على 2 250 على 2مية
+
+353
+00:27:35,590 --> 00:27:38,410
+خمسة وعشرين، أه مية خمسة وعشرين بتجبلش على اتنين،
+
+354
+00:27:38,410 --> 00:27:41,330
+مية خمسة وعشرين بتجبلش على اتنين، بيضال مية خمسة
+
+355
+00:27:41,330 --> 00:27:44,970
+وعشرين، بدنا برضه نشوف الرقم اللي ورا الاتنين،
+
+356
+00:27:44,970 --> 00:27:48,470
+التلاتة، هل بتجمل اسم على تلاتة؟ لأ، لإنه عندك
+
+357
+00:27:48,470 --> 00:27:50,910
+تلاتة، خمسة، تمانية، تمانية بتجبلش على تلاتة،
+
+358
+00:27:50,910 --> 00:27:53,290
+تمانية بتجبلش على تلاتة، فهذا الرقم كله لا يجبل
+
+359
+00:27:53,290 --> 00:27:56,590
+على تلاتة، طيب، بعد التلاتة، في الخمسة، الخمسة
+
+360
+00:27:56,590 --> 00:28:02,230
+بيجبل على خمسة، أه بيجبل على خمسة، في خمسة، بيضفي
+
+361
+00:28:02,230 --> 00:28:06,310
+كمان خمسة بيظل خمسة الخمسة نفسها prime بتنزل زي ما
+
+362
+00:28:06,310 --> 00:28:10,750
+هي فلاحظوا ان احنا عملناها analysis باستخدام
+
+363
+00:28:10,750 --> 00:28:15,210
+مجموعة of primes نقدر نقول ان هي عبارة عن اتنين
+
+364
+00:28:15,210 --> 00:28:20,770
+اربعة to the power اربعة في خمسة to the power تلتة
+
+365
+00:28:20,770 --> 00:28:24,550
+نقدر
+
+366
+00:28:24,550 --> 00:28:28,350
+نعملها analysis كل رقم موجود بتقدر تعمله بهذا
+
+367
+00:28:28,350 --> 00:28:33,170
+الشكل بتقدر تعمله بهذا الشكل طيب الألفينواحد ..
+
+368
+00:28:33,170 --> 00:28:36,910
+لاحظوا .. اتنين .. واحد تلاتة بتقبل قسم على تلاتة
+
+369
+00:28:36,910 --> 00:28:40,810
+على اتنين لأ .. اتنين لأ لأنه هي أصلا odd .. odd
+
+370
+00:28:40,810 --> 00:28:44,950
+على تلاتة بتقبل .. بتقبل سبعة تلاتة خارج القسمة هل
+
+371
+00:28:44,950 --> 00:28:47,450
+بيقبل القسم على تلاتة؟ هيكون مش هيقبل قسم على
+
+372
+00:28:47,450 --> 00:28:51,830
+تلاتة بتجربوا على خمسة؟ بتجربوا على سبعة؟ على احد
+
+373
+00:28:51,830 --> 00:28:55,790
+.. على احداشر .. لا تسعة لأ تسعة لأ .. تسعة بتقدر
+
+374
+00:28:55,790 --> 00:28:59,690
+تقولي تلاتة في تلاتة احداشر .. تلاتاشر .. سبعتاشر
+
+375
+00:28:59,690 --> 00:29:02,750
+..تلاتة و عشرين عند تلاتة و عشرين او بتقبل على
+
+376
+00:29:02,750 --> 00:29:05,290
+تلاتة و عشرين خارج القسمة بتطلع تسعة و عشرين هي
+
+377
+00:29:05,290 --> 00:29:09,810
+تسعة و عشرين هي itself a prime هي نفسها a prime
+
+378
+00:29:09,810 --> 00:29:13,570
+فهيكون تلاتة بهذا الشكل طيب الألفين و اتنين واضح
+
+379
+00:29:13,570 --> 00:29:16,690
+ان هي اصلا even فبتقبل مباشرة الجسم على اتنين و
+
+380
+00:29:16,690 --> 00:29:18,650
+بتبدأ تعملوا analysis دايما تبتقول analysis من
+
+381
+00:29:18,650 --> 00:29:24,510
+الأقل من الأقل اقل اتنين خلصنا اتنين عند السبعة
+
+382
+00:29:24,510 --> 00:29:29,980
+خلصنا السبعةالناتج مش هيقبل القسم على سبعة بجربش
+
+383
+00:29:29,980 --> 00:29:33,960
+على اتنين لأنه لو أصلا من الأول بيقبل على اتنين
+
+384
+00:29:33,960 --> 00:29:36,860
+كان بتطلعها من الأساس من اتنين فما تغلبوش حركه
+
+385
+00:29:36,860 --> 00:29:39,840
+تبدأ و ترجع و تبدأ من اتنين و تلاتة و خمسة خلاص من
+
+386
+00:29:39,840 --> 00:29:42,360
+بعد السبعة اده ماجسمش على الناتج و ماجسمش على
+
+387
+00:29:42,360 --> 00:29:46,240
+السبعة اده من بعده من احداش طبعا؟ طيب الألفين و
+
+388
+00:29:46,240 --> 00:29:53,100
+تلاتة هي نفسها prime ألفين و تلاتة prime الألفين و
+
+389
+00:29:53,100 --> 00:29:55,780
+تلاتة هي نفسها prime هي نفسها ال prime ال prime
+
+390
+00:29:55,780 --> 00:29:59,550
+مانوش نهايةالـ Primes مالهاش نهاية، هي sequence
+
+391
+00:29:59,550 --> 00:30:02,990
+مستمر، يعني هتطلع .. هذا رقم قوضى لسه كمان بالنسبة
+
+392
+00:30:02,990 --> 00:30:09,870
+لـ Primes تانية، لـ Primes أكبر من هيك بكتير طيب
+
+393
+00:30:09,870 --> 00:30:14,050
+فهذه بنسميها الـ Prime factorization أو ال factors
+
+394
+00:30:14,050 --> 00:30:19,680
+لـالرقم باستخدام ال prime ال prime factors ال
+
+395
+00:30:19,680 --> 00:30:25,880
+division algorithm division algorithm هو مجرد
+
+396
+00:30:25,880 --> 00:30:30,220
+مصطلح هذا كلمة algorithm لأنه algorithm كان موجودة
+
+397
+00:30:30,220 --> 00:30:34,460
+كمصطلح من قبل ال computer أصلا من قبل فكرة ال
+
+398
+00:30:34,460 --> 00:30:38,240
+computer من أصلا هو كلمة algorithm مجرد أنه كان
+
+399
+00:30:38,240 --> 00:30:43,770
+خطوات حلأيام الخوارزمية لما حل مشاكل كتير كان
+
+400
+00:30:43,770 --> 00:30:47,530
+بيعملها في شكل خطوات خطوات الحل بإننا نعمل قسمة
+
+401
+00:30:47,530 --> 00:30:50,910
+القسمة عشان نعمل قسمة واحد بنعمل كذا اتنين بنعمل
+
+402
+00:30:50,910 --> 00:30:54,450
+كذا تلاتة بنعمل كذا اربع بيعمل خطوات فالخطوات هذه
+
+403
+00:30:54,450 --> 00:30:58,530
+صار اسمها خوارزمية خوارزمية الجامعة خوارزمية الطرح
+
+404
+00:30:58,530 --> 00:31:02,470
+خوارزمية المش عارف صار يعملوا خوارزميات كويس بعد
+
+405
+00:31:02,470 --> 00:31:07,230
+هي أخدتها أوروبا صارت algorithmالغوريثم لاحقا لما
+
+406
+00:31:07,230 --> 00:31:10,130
+صاروا يشتغلوا على ال pc وجدوا أنه احنا بدنا نفهم
+
+407
+00:31:10,130 --> 00:31:14,050
+ال pc بطريقة خطوات فضل اتماشي ال algorithm بس احنا
+
+408
+00:31:14,050 --> 00:31:17,730
+هنا بنتكلم عن ال algorithm المصطلح القديم المصطلح
+
+409
+00:31:17,730 --> 00:31:21,050
+او السبب التاريخي السابق ان احنا هنا بنتكلم عن
+
+410
+00:31:21,050 --> 00:31:26,070
+خطوات القسمة خطوات القسمة لو بتشتغلوا على قسمة
+
+411
+00:31:26,070 --> 00:31:31,170
+مطولة قسمة مطولة عشان أضحكوا إياها هيكون في عندكم
+
+412
+00:31:31,170 --> 00:31:42,770
+aعلى D المفروض هيطلع Q و يتبقى R تمام؟ مش هالقسم
+
+413
+00:31:42,770 --> 00:31:46,770
+المطولة بتاعتكم؟ okay هاذي إيش معناها؟ معناها كانت
+
+414
+00:31:46,770 --> 00:31:52,970
+تالي for any integers for any integer dividend ال
+
+415
+00:31:52,970 --> 00:31:53,530
+مقسم
+
+416
+00:31:57,030 --> 00:32:00,610
+هذا بنسميه dividend هي شوية terminology هناخد شوية
+
+417
+00:32:00,610 --> 00:32:07,070
+terminology فهذا dividend A and divisor D القاسم
+
+418
+00:32:07,070 --> 00:32:10,870
+اللي هيعمل عملية القسم اللي هيقسم ف dividend
+
+419
+00:32:10,870 --> 00:32:18,970
+المقسم D القاسم there is a unique integer quotient
+
+420
+00:32:18,970 --> 00:32:29,810
+خارج القسمةخارج القسمة Q and remainder R والمتبقى
+
+421
+00:32:29,810 --> 00:32:39,490
+R وطبعاً A او D divide A هيكونهم unique results Q
+
+422
+00:32:39,490 --> 00:32:44,000
+وRمش معقولة كل مرة تتجسم نفس الرقمين تطلعكوا أرقام
+
+423
+00:32:44,000 --> 00:32:50,200
+مختلفة طبيعي دائما هتطلع نفس Q و نفس R عشان نسميها
+
+424
+00:32:50,200 --> 00:32:55,900
+unique integer quotient and remainder طبعا
+
+425
+00:32:55,900 --> 00:32:59,680
+belonged to a natural number ففي الحالة دي بنقول A
+
+426
+00:32:59,680 --> 00:33:09,500
+تساوي D في Q plus Rplus R خارج القسمة في ال
+
+427
+00:33:09,500 --> 00:33:14,740
+divisor في القاسم plus R كله بطلع ال dividend
+
+428
+00:33:14,740 --> 00:33:19,760
+الأساسيالـ dividend أو المقسم من الأول قيمة الـ
+
+429
+00:33:19,760 --> 00:33:23,720
+variable المقسمة طب ناخد بالنا بس هنا R المتبقي
+
+430
+00:33:23,720 --> 00:33:26,920
+هذا عشان أقول فعلا متبقي لأن مش مضروري دايما تكون
+
+431
+00:33:26,920 --> 00:33:29,780
+متبقي ممكن يطلعلكوا رقم هنا إذا كان بيقبل القسمة
+
+432
+00:33:29,780 --> 00:33:32,900
+على D هذا مش متبقي كملوا قسمتكم القسمة المطولة لسه
+
+433
+00:33:32,900 --> 00:33:39,520
+ماخلصتش طب إنت بيقول خلصت إذا الـ R أقل من D صح؟
+
+434
+00:33:39,520 --> 00:33:42,220
+إذا كان هي أكبر من أو بيسوء صفر لأن إذا كان بيسوء
+
+435
+00:33:42,220 --> 00:33:46,060
+صفر معناته لا يوجد متبقيهدول اتنين بيطلعوا integer
+
+436
+00:33:46,060 --> 00:33:53,120
+مباشرة بيطلعوا integer خلاص فممكن تكون صفر او قيمة
+
+437
+00:33:53,120 --> 00:33:59,060
+اقل من دي تكون اقل من دي طب ممكن تكون دي بال
+
+438
+00:33:59,060 --> 00:34:05,780
+negative فعشانك بنحط absolute بنحطها absolute بنحط
+
+439
+00:34:05,780 --> 00:34:10,260
+قيمتها بالشكل هذا ك absolute كويسة فإذا r لازم
+
+440
+00:34:10,260 --> 00:34:16,230
+تكون من صفر للـ D لأن إذا أكبر من D معناته القسمة
+
+441
+00:34:16,230 --> 00:34:20,310
+ما خلصتش لسه القسمة المطولة لسه ما خلصتها كويس ف
+
+442
+00:34:20,310 --> 00:34:25,490
+formally مكتوبها بالشكل التاني for all A و D D
+
+443
+00:34:25,490 --> 00:34:30,870
+divides A D لازم تكون أكبر من صفر لإن أنا مش هينفع
+
+444
+00:34:30,870 --> 00:34:35,270
+أقسم على صفر أنا مانفعش أقسم على صفر فD أكبر من
+
+445
+00:34:35,270 --> 00:34:44,740
+صفر such thatThere exists only one Q and R that
+
+446
+00:34:44,740 --> 00:34:45,560
+belong to Z
+
+447
+00:35:00,830 --> 00:35:04,470
+أقل من D إذا أكبر من D حصر القسم لسه ما خلصتش
+
+448
+00:35:04,470 --> 00:35:07,730
+القسم المطول لما زالت ما خلصتش فلازم نحدد برضه إنه
+
+449
+00:35:07,730 --> 00:35:11,590
+R عشان أقول إن هذه R القيمة هذه فعلا بقول إنها R
+
+450
+00:35:11,590 --> 00:35:17,990
+إذا كانت أقل من D و A بتساوي QD plus R
+
+451
+00:35:20,760 --> 00:35:27,820
+DQ plus R من الحالة هذه بنقدر برضه نجيب R و Q R و
+
+452
+00:35:27,820 --> 00:35:30,700
+Q بنقدر نجيبهم برضه في الحالة اللي احنا بنشتغل
+
+453
+00:35:30,700 --> 00:35:34,720
+عليها طبعا بالنسبة ل Q لأن هي خارج القسمة اصلا
+
+454
+00:35:34,720 --> 00:35:39,380
+خارج القسمة بس بدنا نستثنى ال R خارج القسمة بدون
+
+455
+00:35:39,380 --> 00:35:45,680
+استثناء ال R ف Q بقدر اقول ان هي تساوي A على D
+
+456
+00:35:45,680 --> 00:35:47,720
+floor
+
+457
+00:35:49,470 --> 00:35:53,530
+على D بيه أصلا مش موجودة بيه عندنا على ال D اللي
+
+458
+00:35:53,530 --> 00:36:00,910
+هي ال divisor floor تمام ف floor على طول جربتلنا
+
+459
+00:36:00,910 --> 00:36:06,170
+ال R قربتها لل صفر جربتها لل صفر فخلاص خارج القسم
+
+460
+00:36:06,170 --> 00:36:11,570
+بقدر أجيبه مرتاح خارج القسم و floor بجيبلنا ال
+
+461
+00:36:11,570 --> 00:36:15,710
+cautionبجبلك .. بجبنا ال .. ال .. ال quotient term
+
+462
+00:36:15,710 --> 00:36:23,650
+أو ال quotient Q طيب ال R عشان نحسب R بتكون تحسبه
+
+463
+00:36:23,650 --> 00:36:32,550
+R R هتكون عبارة عن إيش الفرق بين A و D في Q فإذا A
+
+464
+00:36:32,550 --> 00:36:39,810
+minus D في Qلو مطلوب منكوا تجيبوا ال quotient
+
+465
+00:36:39,810 --> 00:36:45,690
+مباشرة وال R أو ال remainder بشكل مباشر فهي القسمة
+
+466
+00:36:45,690 --> 00:36:49,910
+المطولة فعليا تنعمل بهذا الشكل تنعمل بهذا الشكل
+
+467
+00:36:49,910 --> 00:36:53,750
+لاحقا هناخد algorithm للقسمة المطولة كيف تبدأ ال
+
+468
+00:36:53,750 --> 00:36:57,490
+greatest
+
+469
+00:36:57,490 --> 00:37:02,850
+common divisor أو العامل المشترك الأكبر العامل
+
+470
+00:37:02,850 --> 00:37:07,020
+المشترك الأكبر عنده قيمتينالقيمتين هدولة بتجيبوا
+
+471
+00:37:07,020 --> 00:37:12,120
+العامل المشترك الأكبر بمعنى إيش الرقم اللي كلا
+
+472
+00:37:12,120 --> 00:37:15,680
+الرقمين بيقسم عليه و أكبر رقم ممكن الإتنين يقسموا
+
+473
+00:37:15,680 --> 00:37:19,780
+عليه أكبر رقم ممكن الإتنين يقسموا عليه ببساطة جدا
+
+474
+00:37:19,780 --> 00:37:24,220
+بنسميها greatest common divisor أو GCD greatest
+
+475
+00:37:24,220 --> 00:37:27,060
+common divisor ل A و B فالإتنين هدولة بدنا نجيب
+
+476
+00:37:27,060 --> 00:37:31,370
+العامل المشترك الأكبر لهم لل A و B مع بعضof
+
+477
+00:37:31,370 --> 00:37:35,670
+integers a و b و طبعا مافيش واحد منهم صفر مافيش
+
+478
+00:37:35,670 --> 00:37:40,130
+واحد منهم صفر isish اللي هو ال greatest common
+
+479
+00:37:40,130 --> 00:37:44,270
+divisor هذا is the largest او most positive اكبر
+
+480
+00:37:44,270 --> 00:37:49,630
+رقم موجب اكبر رقم موجب integer d that is divisor
+
+481
+00:37:49,630 --> 00:37:53,810
+both a and b بنقدر نقول ان هو divides a and
+
+482
+00:37:53,810 --> 00:37:58,460
+divides bنقدر نقولهم divides A عن divides B و أكبر
+
+483
+00:37:58,460 --> 00:38:02,060
+رقم ممكن يكون divides ل A و divides ل B مع بعض
+
+484
+00:38:02,060 --> 00:38:06,880
+نكتبها D greatest common divisor A و B عبارة عن
+
+485
+00:38:06,880 --> 00:38:15,640
+maximum D هو أكبر رقم بحيث قابل ان D divides A و D
+
+486
+00:38:15,640 --> 00:38:22,260
+divides B فعلا بيقسم ممكن يقسم A و يمكن يقسم B و
+
+487
+00:38:22,260 --> 00:38:26,650
+الرقم الأكبر منهم for exampleلو قلنا ال greatest
+
+488
+00:38:26,650 --> 00:38:30,410
+common divisor اربع عشرين ستة وتلاتين نمسكهم
+
+489
+00:38:30,410 --> 00:38:35,530
+بالطريقة المملة شوية و بعدين بنشوف ايش الطرق
+
+490
+00:38:35,530 --> 00:38:38,710
+الأفضل خلينا نشوف الاربع عشرين ايش الأرقام اللى
+
+491
+00:38:38,710 --> 00:38:41,690
+ممكن تقسم على اربع عشرين او تقسملنا الاربع عشرين
+
+492
+00:38:41,690 --> 00:38:51,090
+الاتنين تلاتة أربعة خمسة لأ خمسة مفهجة ستة سبعة
+
+493
+00:38:51,090 --> 00:38:59,670
+تمانيةتسعة، عشرة، احداش، اتناش، اه اتناش، تلتاش،
+
+494
+00:38:59,670 --> 00:39:05,270
+اربعتاش، خمستاش، اربع عشرين طيب هذه بتاعة الاربع
+
+495
+00:39:05,270 --> 00:39:10,330
+عشرين، الستة و تلتين، اتنين، تلاتة
+
+496
+00:39:12,270 --> 00:39:30,650
+4,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 قول
+
+497
+00:39:30,650 --> 00:39:35,830
+عند ال 36 كويس هل يمكن أن نشوف من المعاملات هدولة
+
+498
+00:39:35,830 --> 00:39:40,700
+من ال divisor الأكبر مشترك بينهمالأكبر divisor
+
+499
+00:39:40,700 --> 00:39:45,680
+مشترك بينهم اتناش فإذا ال greatest common divisor
+
+500
+00:39:45,680 --> 00:39:50,640
+لاربع عشرين ستة وتلاتين بسوا اتناش ال divider
+
+501
+00:39:50,640 --> 00:39:58,780
+الأكبر لكلاهم لاربع عشرين و لستة تلاتين هذا
+
+502
+00:39:58,780 --> 00:40:01,380
+الطريقة خلاني أقول العقيمة شوية لإن ممكن تدفع في
+
+503
+00:40:01,380 --> 00:40:03,740
+الأرقام الصغيرة اللي جد هيك بس إذا كانت كبرة
+
+504
+00:40:03,740 --> 00:40:07,950
+الأرقام طبعا الموضوع بصير أصعب من هيكمش هنقدر
+
+505
+00:40:07,950 --> 00:40:14,550
+نشتغل بهذا الشكل ف ال greatest is twelve طيب بدنا
+
+506
+00:40:14,550 --> 00:40:20,170
+طريقة رياضية شوية طريقة رياضية شوية نقدر نجيب فيها
+
+507
+00:40:20,170 --> 00:40:23,670
+الحل الطريقة أفضل من هيك الطريقة أحسن من هيك بدنا
+
+508
+00:40:23,670 --> 00:40:28,950
+نرجع لمين ل ال prime factors ال prime factors ممكن
+
+509
+00:40:28,950 --> 00:40:32,640
+يحلولنا الموضوع لو قلنا ال aوالـ B بدينا نجيب ال
+
+510
+00:40:32,640 --> 00:40:35,920
+greatest common divisor للإتنين بين الإتنين فبنجيب
+
+511
+00:40:35,920 --> 00:40:39,180
+ال A و بنجيب ال primes تبعته كل ال prime ممكن
+
+512
+00:40:39,180 --> 00:40:43,500
+تتكرر زي ما توي شفنا في الألفين كان فيان اتنين to
+
+513
+00:40:43,500 --> 00:40:46,640
+the power أربعة فبنحط اتنين to the power أربعة
+
+514
+00:40:46,640 --> 00:40:50,640
+خمسة to the power اتنين و هكذا بنحط جميع ال primes
+
+515
+00:40:50,640 --> 00:40:56,680
+تبعت A و بنحط ال primes تبعت B و بنجي بنشوف ال
+
+516
+00:40:56,680 --> 00:41:02,300
+prime اللي اتكرر من هنا و هنابناخد ال power الأقل
+
+517
+00:41:02,300 --> 00:41:06,540
+له فإذا لما بقول greatest common divisor ل a و b
+
+518
+00:41:06,540 --> 00:41:12,120
+باخد ال prime الأول و
+
+519
+00:41:12,120 --> 00:41:15,940
+بشوف ال power في الحالة الأولى و الحالة التانية
+
+520
+00:41:15,940 --> 00:41:20,480
+الأقل باخدها ال prime التاني
+
+521
+00:41:23,490 --> 00:41:30,810
+الاقل بناخدها سواء a2 او b2 الاقل منهم بنختارها
+
+522
+00:41:30,810 --> 00:41:34,670
+لعند ما نخلص جميع ال factors او ال prime factors
+
+523
+00:41:34,670 --> 00:41:37,970
+بتاعتنا بنضرب في الاخر الرقم اللي ظهر فالرقم هذا
+
+524
+00:41:37,970 --> 00:41:44,670
+هيطلع ال common divisor ناخد مثل محتاجين نعمل ال
+
+525
+00:41:44,670 --> 00:41:54,370
+greatest common divisor ل 84.96 84.96هنبدأ في
+
+526
+00:41:54,370 --> 00:41:56,710
+الاربعة و تمانية، اربعة و تمانية طبعا لحظة اقسموا
+
+527
+00:41:56,710 --> 00:42:00,330
+على اتنين، ما جسمش على اتنين تنقلوا على تلاتة، ما
+
+528
+00:42:00,330 --> 00:42:03,650
+جسمش على تلاتة تنقلوا على خمسة، تنقلوا على سبعة،
+
+529
+00:42:03,650 --> 00:42:06,450
+تاخدوهم تساعدة، خلاص مدام انتم ماشيين تساعدة
+
+530
+00:42:06,450 --> 00:42:11,790
+ترجعوش تنزلوا تاني، ترجعوش تنزلوا تاني، تمامفهنا
+
+531
+00:42:11,790 --> 00:42:15,590
+هيطلع اتنين اتنين تلاتة سبعة اتنين اتنين عندكوا
+
+532
+00:42:15,590 --> 00:42:20,070
+اتنين تتباور اتنين تلاتة تتباور واحد تلاتة تتباور
+
+533
+00:42:20,070 --> 00:42:22,390
+واحد تلاتة تتباور واحد تلاتة تتباور واحد تلاتة
+
+534
+00:42:22,390 --> 00:42:26,830
+تتباور واحد تلاتة
+
+535
+00:42:26,830 --> 00:42:31,910
+تتباور واحد تلاتة تتباور واحد تلاتة تتباور واحد
+
+536
+00:42:31,910 --> 00:42:33,130
+تتباور واحد تلاتة تتباور واحد تتباور واحد تتباور
+
+537
+00:42:33,130 --> 00:42:33,290
+واحد تتباور واحد تتباور واحد تتباور واحد تتباور
+
+538
+00:42:33,290 --> 00:42:36,470
+واحد تتباور واحد تتباور واحد تتباور واحد تتباور
+
+539
+00:42:36,470 --> 00:42:39,990
+واحد
+
+540
+00:42:39,990 --> 00:42:45,900
+تفاتنين الأقل خمسة ولا الاتنين الاتنين to the
+
+541
+00:42:45,900 --> 00:42:52,440
+power اتنين تلاتة متساوين to the power واحد سبعة
+
+542
+00:42:52,440 --> 00:42:58,600
+to the power zero فهذه بواحد وهذه بتلاتة وهذه
+
+543
+00:42:58,600 --> 00:43:01,280
+باربعة اتناشر
+
+544
+00:43:02,330 --> 00:43:06,910
+فهيطلع عندكوا the greatest common divisor ل 84 و
+
+545
+00:43:06,910 --> 00:43:14,090
+96 بساوي 12 مش هتلاقوا أي رقم بعمل divides ل ال 84
+
+546
+00:43:14,090 --> 00:43:17,930
+و 96 أكبر من ال 12
+
+547
+00:43:22,460 --> 00:43:26,960
+طيب ال primes احنا اتفقنا ال primes هو في النهاية
+
+548
+00:43:26,960 --> 00:43:30,960
+مجموعة أرقام كل رقم منهم لا يقبل القسمة إلا على
+
+549
+00:43:30,960 --> 00:43:36,980
+نفسه أو على الواحد أو على الواحد رغم ذلك بنقدر
+
+550
+00:43:36,980 --> 00:43:40,580
+نقول أنه كل رقمين مع بعض ممكن يكونوا relatively
+
+551
+00:43:40,580 --> 00:43:46,200
+primes relatively primes يعني بالنسبة لبعض هم
+
+552
+00:43:46,200 --> 00:43:49,990
+شايفين بعض ال primeشايفين بعض؟ أمتى بقدر أقول
+
+553
+00:43:49,990 --> 00:43:53,890
+الكلام هذا؟ أو بنسميها co-prime كل واحد منهم بصير
+
+554
+00:43:53,890 --> 00:43:57,830
+co-prime للتاني أو relatively relative prime
+
+555
+00:43:57,830 --> 00:44:02,310
+relative prime بالمطلق بقدرش أقول والله الخمسة
+
+556
+00:44:02,310 --> 00:44:06,610
+relative prime واسكت لأ مادام relative بالنسبة
+
+557
+00:44:06,610 --> 00:44:11,630
+لمن؟ لازم أتكلم عن رقمين أما أمتى ببسكت؟ بقول
+
+558
+00:44:11,630 --> 00:44:14,650
+الخمسة prime؟ okay لأن هي أصلا prime لكن أقول
+
+559
+00:44:14,650 --> 00:44:18,310
+والله العشرة relative primeلأ هي لحالها هيك مش
+
+560
+00:44:18,310 --> 00:44:23,770
+relative prime لأنه افرضه انه عشرة مع اتنين لأ في
+
+561
+00:44:23,770 --> 00:44:27,290
+عوامل مشتركة بينهم في عوامل مشتركة بينهم ايه انت
+
+562
+00:44:27,290 --> 00:44:29,350
+مقدر يقول ان هي relative prime لما احط معاها رقم
+
+563
+00:44:29,350 --> 00:44:34,170
+تاني و ال greatest common divisor اللي لهم واحد ال
+
+564
+00:44:34,170 --> 00:44:37,270
+greatest common divisor العامل المشترك الأكبر
+
+565
+00:44:37,270 --> 00:44:41,570
+تبعهم واحد يعني لايوجد اي عوامل مشتركة لايوجد اي
+
+566
+00:44:41,570 --> 00:44:47,420
+عوامل مشتركة بينهم فبقول في الحالة هذهزي مثال هنا
+
+567
+00:44:47,420 --> 00:44:54,420
+ال 21 و العشرة لاوجد اي عامل مشترك بينهم لاوجد اي
+
+568
+00:44:54,420 --> 00:45:00,180
+عامل مشترك بينهم كيف ال 21 عبارة عن تلاتة في سبعة
+
+569
+00:45:00,180 --> 00:45:04,760
+هاي ال two primes بتاعهمحنشوف في الآخر إيش بتسوي
+
+570
+00:45:04,760 --> 00:45:09,960
+هنا طيب العشرة عبارة عن اتنين في خمسة فهذه عبارة
+
+571
+00:45:09,960 --> 00:45:13,180
+عن اتنين to the power صفر مش موجودة الصفر الاتنين
+
+572
+00:45:13,180 --> 00:45:17,540
+تلاتة to the power واحد خمسة to the power zero
+
+573
+00:45:17,540 --> 00:45:20,660
+وسبعة to the power one هنا two to the power one
+
+574
+00:45:20,660 --> 00:45:23,840
+تلاتة to the power zero خمسة to the power one
+
+575
+00:45:23,840 --> 00:45:26,160
+seven to the power zero لما بناخد ال greatest
+
+576
+00:45:26,160 --> 00:45:30,560
+بينهم الأقل دايما بينهمهناخد اتنين zero، تلاتة
+
+577
+00:45:30,560 --> 00:45:35,980
+zero، خمسة zero، سبعة zero، واحد، one فإذا ال
+
+578
+00:45:35,980 --> 00:45:41,980
+greatest common divisor للعشرة و الواحد و عشرين
+
+579
+00:45:41,980 --> 00:45:46,680
+هيساوي واحد بساوي واحد في الحالة هذه بقدر أقول أن
+
+580
+00:45:46,680 --> 00:45:52,840
+الأتنين relative prime مع بعض أو co-prime أو co
+
+581
+00:45:52,840 --> 00:45:57,900
+-prime أو بنسميهم co-prime مع بعضكل واحد لحاله لأ،
+
+582
+00:45:57,900 --> 00:46:02,500
+كل واحد لحاله لأ، هو مش prime لحاله، بس مع بعض co
+
+583
+00:46:02,500 --> 00:46:07,140
+-prime مع بعض الأتنين، فإذا ال .. بنسميها
+
+584
+00:46:07,140 --> 00:46:11,680
+relatively prime أو co-prime if and only if their
+
+585
+00:46:11,680 --> 00:46:16,690
+greatest common divisor equal to oneطيب زى ما قلنا
+
+586
+00:46:16,690 --> 00:46:21,050
+هنا neither لا ال 21 prime ولا العشرة prime بس
+
+587
+00:46:21,050 --> 00:46:24,810
+الأثنين مع بعض كل واحد شايف التاني prime ليه شايف
+
+588
+00:46:24,810 --> 00:46:27,350
+التاني prime؟ لأن مافيش اي عامل مشترك بينهم بين
+
+589
+00:46:27,350 --> 00:46:31,600
+بعض مافيش اي عامل مشترك بينهم وبينبين بعض ف no
+
+590
+00:46:31,600 --> 00:46:35,720
+common factors اكبر من واحد مافيش اي عامل مشترك
+
+591
+00:46:35,720 --> 00:46:41,480
+اكبر من واحد ممكن نحطهم في set A set of integers
+
+592
+00:46:41,480 --> 00:46:48,900
+A1, A2, A3, A4 بحيث ان كل pairwise
+
+593
+00:46:48,900 --> 00:46:55,770
+بينهم كل two elements داخل ال set كوبراهم مع بعضكل
+
+594
+00:46:55,770 --> 00:46:59,830
+two elements داخل ال set prime مع بعض، co-prime مع
+
+595
+00:46:59,830 --> 00:47:05,870
+بعض أو relative prime مع بعض، فهنا بنسميها set of
+
+596
+00:47:05,870 --> 00:47:09,950
+co-prime أو relative prime في الحالة تعتنا، في
+
+597
+00:47:09,950 --> 00:47:13,770
+الحالة تعتنا، إذا كان كل عنصرين مع بعض، بنعمل ال
+
+598
+00:47:13,770 --> 00:47:17,030
+analysis بتاعهم، بيطلعوا co-prime مع بعض، co-prime
+
+599
+00:47:17,030 --> 00:47:19,110
+أو relative prime، relative prime أو co-prime
+
+600
+00:47:20,550 --> 00:47:25,330
+فبنقول إن ال set كلها على بعض relatively prime
+
+601
+00:47:25,330 --> 00:47:31,410
+أخدنا ال greatest common divisor طب في حاجة تانية
+
+602
+00:47:31,410 --> 00:47:37,070
+يقسمها ال least common multiple بمعنى المضاعف
+
+603
+00:47:37,070 --> 00:47:42,930
+المشترك الأصغر اللي بقدر أقول إنه
+
+604
+00:47:46,490 --> 00:47:53,130
+ال A و ال B بيقدروا يقسموا ال A و ال B بيقدروا
+
+605
+00:47:53,130 --> 00:47:57,770
+يقسموا ال A و ال B بيقدروا يقسموا ال A و ال B
+
+606
+00:47:57,770 --> 00:47:58,350
+بيقسموا ال A و ال B بيقسموا ال A و ال B بيقسموا ال
+
+607
+00:47:58,350 --> 00:48:05,730
+A و ال B بيقسموا ال A و ال B بيقسموا ال A و ال B
+
+608
+00:48:05,730 --> 00:48:07,470
+بيقسموا ال A و ال B بيقسموا ال A و ال B بيقسموا ال
+
+609
+00:48:07,470 --> 00:48:09,950
+بيقسموا ال A و ال B بيقسموا ال A و ال B بيقسموا ال
+
+610
+00:48:09,950 --> 00:48:15,870
+A
+
+611
+00:48:15,950 --> 00:48:22,510
+ممكنة اقل قيمة ممكنة عشان تحقق هذا الشرط عشان تحقق
+
+612
+00:48:22,510 --> 00:48:28,350
+ان ال a divide c و ال b divide c و ال b divide c
+
+613
+00:48:28,350 --> 00:48:35,210
+هنا نفس الفكرة بدنا نجيب ال list common multiple
+
+614
+00:48:35,210 --> 00:48:41,170
+للست و عشرة نمسكهم واحدة واحدة ممكن برضه بالطريقة
+
+615
+00:48:41,170 --> 00:48:43,370
+الفدائية نشوف هو ايش يعني عشان نفهم بس ايش يعني
+
+616
+00:48:43,370 --> 00:48:48,900
+multiple هناعشان اقول multiple للستة ممكن تكون
+
+617
+00:48:48,900 --> 00:48:54,440
+الستة ممكن تكون الاتناش تضرب في اتنين في تلاتة
+
+618
+00:48:54,440 --> 00:49:01,680
+تمانتاش في اربعة اربع عشرين في خمسة تلاتين في ستة
+
+619
+00:49:01,680 --> 00:49:07,820
+ستة وتلاتين في سبعة اتنين واربعين كويس العشرة
+
+620
+00:49:07,820 --> 00:49:12,700
+عشرين تلاتين اربعين
+
+621
+00:49:15,430 --> 00:49:21,830
+خمسين ستين و هكذا أقل مرتب المشترك بينهم أقل مرتب
+
+622
+00:49:21,830 --> 00:49:24,610
+المشترك لاحظوا أن الستين ممكن تكون ستين كمان هنا
+
+623
+00:49:24,610 --> 00:49:27,450
+يعني هنا هتلاحظوا أنه هيكون هنا في ستين طب ما
+
+624
+00:49:27,450 --> 00:49:30,490
+الستين ممكن تيجي معاها الستين لأ في لسه أقل منها
+
+625
+00:49:30,490 --> 00:49:33,510
+في أقل منها طيب اتنين و أربعين لأ مش موجودة ستة و
+
+626
+00:49:33,510 --> 00:49:36,970
+تلتين لأ مش موجودة تلتين أه موجودة طب في أقل من
+
+627
+00:49:36,970 --> 00:49:42,270
+تلتين شوف أربع عشرين لأ فإذا هي التلتينفإذا هي
+
+628
+00:49:42,270 --> 00:49:46,450
+التلاتين ال least common multiple هذه الطريقة
+
+629
+00:49:46,450 --> 00:49:52,190
+البدائية بس عشان نعرف مضاعفات الرقم بس إحنا بنقدر
+
+630
+00:49:52,190 --> 00:49:56,670
+نجيبها بطريقة أفضل من هيك برضه باستخدام مين ال
+
+631
+00:49:56,670 --> 00:50:03,170
+prime باستخدام ال prime factors برضه بجيب ال a ال
+
+632
+00:50:03,170 --> 00:50:06,150
+element الأول و بجيب ال primes تبعته و بنجيب ال
+
+633
+00:50:06,150 --> 00:50:08,950
+element التاني ال primes تبعته بس هنا بنختار ال
+
+634
+00:50:08,950 --> 00:50:13,510
+power الأعلىفى ال common .. فى ال greatest common
+
+635
+00:50:13,510 --> 00:50:16,690
+divisor كنا بنختار البوار الأقل الفرق الوحيد هنا
+
+636
+00:50:16,690 --> 00:50:20,010
+بنختار ال common الأعلى common أعلى فلو أخدنا
+
+637
+00:50:20,010 --> 00:50:26,950
+الستة نين فى تلاتة نين فى تلاتة تمام فهذه واحد
+
+638
+00:50:26,950 --> 00:50:30,370
+واحد طيب العشرة نين فى خمسة
+
+639
+00:50:34,510 --> 00:50:39,710
+طيب هذه كأنها خمسة صفر وهذه كأنها تلاتة صفر في
+
+640
+00:50:39,710 --> 00:50:44,550
+خمسة ضبار واحد بنختار زي ما قلنا إيش الأعلى
+
+641
+00:50:46,660 --> 00:50:52,900
+بنختار الأعلى فهنا اتنين واحد هي الأعلى واحد هنا
+
+642
+00:50:52,900 --> 00:50:57,600
+تلاتة الأعلى واحد خمسة الأعلى واحد فصارت ستة في
+
+643
+00:50:57,600 --> 00:51:02,800
+خمسة بتلاتين ستة في خمسة بتلاتين فهذه ال list
+
+644
+00:51:02,800 --> 00:51:07,560
+common multiple of ستة وعشرة طيب ال greatest
+
+645
+00:51:07,560 --> 00:51:14,020
+common divisor لنفسهم الستة والعشرة الأقل هنا صار
+
+646
+00:51:14,020 --> 00:51:14,520
+فيه اتنين
+
+647
+00:51:17,310 --> 00:51:26,570
+تلاتة صفر، خمسة صفر، اتنين، اتنين، اتنين، اتنين،
+
+648
+00:51:26,570 --> 00:51:31,730
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+649
+00:51:31,730 --> 00:51:35,930
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+650
+00:51:35,930 --> 00:51:37,710
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+651
+00:51:37,710 --> 00:51:42,950
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+652
+00:51:42,950 --> 00:51:42,970
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+653
+00:51:42,970 --> 00:51:46,750
+اتنين، اتنين، اتنبالساعة لما أقولكوا الساعة هلوجت
+
+654
+00:51:46,750 --> 00:51:52,990
+أربعة عشر إيش يعني تنتين كيف عرفت أنها تنتين بعد
+
+655
+00:51:52,990 --> 00:51:57,930
+الاطنعش معناته
+
+656
+00:51:57,930 --> 00:52:02,650
+أنا بتكلم عن موديولو اتنعش الموديولو هنا اتنعش او
+
+657
+00:52:02,650 --> 00:52:07,170
+ال modulus تبعنا اتنعش الرقم اللي بعده بصير تكرار
+
+658
+00:52:07,170 --> 00:52:13,130
+طيب لما نقول الزاوية تلتمية وتسعين
+
+659
+00:52:18,500 --> 00:52:24,320
+تلاتين لش عرفته تلاتين لأنه عارفين انه بعد تلاتمية
+
+660
+00:52:24,320 --> 00:52:28,640
+و ستين درجة بترجع نتكرر عند نفس النقطة فالساعة نفس
+
+661
+00:52:28,640 --> 00:52:31,980
+الكلام بتلفه تلاتمية و ستين درجة بترجع على الاتناش
+
+662
+00:52:31,980 --> 00:52:36,700
+فال module تبعكم بتشتغلوا على اتناش لو بتشتغلوا
+
+663
+00:52:36,700 --> 00:52:40,120
+على الساعة الدرجات
+
+664
+00:52:41,280 --> 00:52:44,300
+على ال 360 فانتوا تبدو تجسموا الدرجات تبعاتكم
+
+665
+00:52:44,300 --> 00:52:48,580
+ترجعوا .. بعد ال 360 بترجعوا للزاوية صفر .. ترجعوا
+
+666
+00:52:48,580 --> 00:52:53,600
+للزاوية صفر طيب عند ال 12 بترجعوا للزاوية 12
+
+667
+00:52:53,600 --> 00:52:58,420
+بتاعتكم طيب لما تصلوا لل .. للساعة 24 هتلاقوا
+
+668
+00:52:58,420 --> 00:53:02,560
+الساعة صارت أنكوا صفرصح بتلاجوا ساعاتكوا لو انتوا
+
+669
+00:53:02,560 --> 00:53:06,780
+مظبطين ساعاتكوا الرقمية طبعا الرقمية على ال 24
+
+670
+00:53:06,780 --> 00:53:09,620
+system او ال system 24 لانه هيكون عندكوا فيه
+
+671
+00:53:09,620 --> 00:53:12,680
+إمكانية system 24 او system 12 هتلاجوا انه برجع
+
+672
+00:53:12,680 --> 00:53:17,460
+صفر ترجع ل zero كويس فعندكوا هنا اليوم بيصير هو ال
+
+673
+00:53:17,460 --> 00:53:19,840
+modulus ال modulus تبعكوا ان انتوا بتشتغل عليه هو
+
+674
+00:53:19,840 --> 00:53:24,140
+24 فلما نجيش نتكلم هنا عن ال mod operator هو ده
+
+675
+00:53:24,140 --> 00:53:27,210
+اللي بنشتغل عليه بدنا نشوف ايش .. ايش معناههذا
+
+676
+00:53:27,210 --> 00:53:30,250
+معناه ان انتوا بتعملوا division remainder ايش
+
+677
+00:53:30,250 --> 00:53:36,070
+المتبقى؟ ايش المتبقى؟ يعني لما نقول الساعة اللى
+
+678
+00:53:36,070 --> 00:53:41,810
+بدأنا فيها اربعة عشر ساعة اربعة عشر ايش معناها؟
+
+679
+00:53:41,810 --> 00:53:44,910
+اربعة عشر على المدرس اللى احنا شغالين عليه احنا
+
+680
+00:53:44,910 --> 00:53:48,010
+ايش المدرس اللى بقى؟ اتناشر اتناشر نجسمهم على بعض
+
+681
+00:53:48,010 --> 00:53:55,260
+واحد اتناشر اتنان اتنان اقل من ال Dصح معناته
+
+682
+00:53:55,260 --> 00:53:58,440
+الساعة اتنين، لاحظوا احنا معناته بنشتغل على مين؟
+
+683
+00:53:58,440 --> 00:54:01,540
+على ال remainder، بنشتغل على ال remainder، هذا هو
+
+684
+00:54:01,540 --> 00:54:05,660
+ال equivalent للاربعتاش، هذا ال equivalent لمين؟
+
+685
+00:54:05,660 --> 00:54:09,480
+للاربعتاش، فلو قلنا، فاحنا هنسميها احيانا division
+
+686
+00:54:09,480 --> 00:54:15,450
+remainder operatorمتبقى القسمة او عملية متبقى
+
+687
+00:54:15,450 --> 00:54:20,510
+القسمة طيب لو قلنا a و d عبارة عن z او integers او
+
+688
+00:54:20,510 --> 00:54:25,150
+integers و ال d أكبر من واحد أكبر من واحد عساس ان
+
+689
+00:54:25,150 --> 00:54:28,870
+يكون فيه إمكانية لل modulus ما تكونش انا بتكلم عن
+
+690
+00:54:28,870 --> 00:54:33,250
+واحد واحد معناته تبقى باستمرار اربعتاش على واحد
+
+691
+00:54:33,250 --> 00:54:37,250
+بواحد باربعتاش عفوا خمستاش على واحد خمستاش مش
+
+692
+00:54:37,250 --> 00:54:39,990
+هتفرج كتير يعني انا مش عامل modulus هنا مش عاملين
+
+693
+00:54:39,990 --> 00:54:54,390
+modulus then aمد يولو دي ا مد دي ا مد يولو
+
+694
+00:54:54,390 --> 00:54:58,710
+دي ا مد يولو دي ا مد يولو دي ا مد يولو دي ا مد
+
+695
+00:54:58,710 --> 00:54:59,910
+يولو دي ا مد يولو دي ا مد يولو دي ا مد يولو دي ا
+
+696
+00:54:59,910 --> 00:55:00,110
+مد يولو دي ا مد يولو دي ا مد يولو دي ا مد يولو دي
+
+697
+00:55:00,110 --> 00:55:00,150
+ا مد يولو دي ا مد يولو دي ا مد يولو دي ا مد يولو
+
+698
+00:55:00,150 --> 00:55:00,250
+يولو دي ا مد يولو دي ا مد يولو دي ا مد يولو دي ا
+
+699
+00:55:00,250 --> 00:55:07,740
+مد يولو دي ا مد يولو دي ا مد يولو دي ا مد يفإذا A
+
+700
+00:55:07,740 --> 00:55:12,440
+مد D بساوي R لا أعلم إذا كان مرت عليكوا هذا سابقا
+
+701
+00:55:12,440 --> 00:55:17,560
+المد لازم مر عليكوا مرت طب كويس كتير كويس فال
+
+702
+00:55:17,560 --> 00:55:24,200
+algorithm with dividend A and divisor D بمعنى
+
+703
+00:55:24,200 --> 00:55:30,880
+remainder لما A is divided by Dلما نقول A مقسمة
+
+704
+00:55:30,880 --> 00:55:38,020
+باستخدام D ف D divides A ال R اللي بتطلع هي ناتج
+
+705
+00:55:38,020 --> 00:55:42,580
+ال module تبعنا، ناتج ال module أو ال modular
+
+706
+00:55:42,580 --> 00:55:44,860
+operator
+
+707
+00:55:45,640 --> 00:55:49,120
+هذه طبعا ممكن تستخدم في بعض .. في بعض لغات البرمجة
+
+708
+00:55:49,120 --> 00:55:52,820
+تستخدم أحيانا علامة النسبة المئوية هذه .. هذه
+
+709
+00:55:52,820 --> 00:55:57,160
+بتعطي المعنى للمد .. او للمدولار operator ..
+
+710
+00:55:57,160 --> 00:56:05,380
+للمدولار operator okay المدولار congruence
+
+711
+00:56:05,380 --> 00:56:11,120
+المدولار congruence اللي هي المكافئة المكافئة زي
+
+712
+00:56:11,120 --> 00:56:17,670
+ما هنا اربع عشر مكافئ اتنينبالنسبة للموديلار 16
+
+713
+00:56:17,670 --> 00:56:24,450
+نسبة للموديلار 16 اتنين واربعتاش كل واحدة منهم
+
+714
+00:56:24,450 --> 00:56:28,170
+congrance او congrant للتانية فال congrance او
+
+715
+00:56:28,170 --> 00:56:32,170
+الموديلار congrance هي المشابهة او المناظرة او
+
+716
+00:56:32,170 --> 00:56:38,570
+المكافئةتحت الموديولوس M لو حددنا الموديولوس طبعا
+
+717
+00:56:38,570 --> 00:56:42,730
+الموديولوس هنا اللي هو نشتغل عليه كموديولو ..
+
+718
+00:56:42,730 --> 00:56:48,790
+كالموديولو بتاعتنا اتناش طيب اربعتاش موديولوس او
+
+719
+00:56:48,790 --> 00:56:52,190
+موديولو اتناش بيساوي اتنين فالاتنين هنا مكافئة
+
+720
+00:56:52,190 --> 00:56:58,330
+لمين للاربعتاش اتنين مكافئة او congruent للاربعتاش
+
+721
+00:56:58,330 --> 00:57:04,170
+فهنقول Z positiveهي ال natural او ال n belonging
+
+722
+00:57:04,170 --> 00:57:08,750
+to z شرط ان ال n أكبر من صفر اكبر من صفر فاحنا في
+
+723
+00:57:08,750 --> 00:57:11,230
+النهاية النتائج لعيتنا بتكون كلها بال positive
+
+724
+00:57:11,230 --> 00:57:14,210
+لاحقا هنتكلم عن ال negative ايش ممكن يغير معانا في
+
+725
+00:57:14,210 --> 00:57:16,450
+الشغل لأنه ممكن يغير في الشغل الحقيقه في ال
+
+726
+00:57:16,450 --> 00:57:21,030
+negative في ال modular بيعطينا نتائج حيانا مختلفة
+
+727
+00:57:21,030 --> 00:57:25,490
+شوية هنتكلم عنها لاحقا هنتكلم عنها لاحقا then a is
+
+728
+00:57:25,490 --> 00:57:32,940
+congruent to b modulo m بنكتبها كتالةcongruent
+
+729
+00:57:32,940 --> 00:57:37,220
+مكافئة علمت المكافئة هي مش تساوي لإن فعليا اتنين
+
+730
+00:57:37,220 --> 00:57:42,920
+لا تساوي اربعتاشر ولكن هي مكافئة لهاباستخدام مدلس
+
+731
+00:57:42,920 --> 00:57:46,560
+هذا تحديدا باستخدام مدلس اتناش على مدلس تاني لأ
+
+732
+00:57:46,560 --> 00:57:51,100
+لاتكافئها لو مدلس خمسة لو مدلس تلاتمية و ستين لأ
+
+733
+00:57:51,100 --> 00:57:57,220
+لاتكافئها بس احنا في الحالة هذه مكافئة لل B mod M
+
+734
+00:57:57,220 --> 00:58:01,320
+if and only if هذا الكلام يقوله صحيح انه فعلا A
+
+735
+00:58:01,320 --> 00:58:07,340
+congruent B is if and only if M divides الفرق
+
+736
+00:58:07,340 --> 00:58:11,550
+بينهمطب خلينا نشوف الفرق بينهم فعلا الفرق بينهم
+
+737
+00:58:11,550 --> 00:58:17,670
+اتناش اه صح بيكسم على بعض اتناش بتجسم الفرق بينهم
+
+738
+00:58:17,670 --> 00:58:22,950
+او بتقدر تجسم الفرق بينهم لو قولنا ستة و عشرين
+
+739
+00:58:22,950 --> 00:58:29,230
+congruent
+
+740
+00:58:29,230 --> 00:58:32,990
+to two برضه congruent لأ اتنين ليش لأن الفرق بينهم
+
+741
+00:58:32,990 --> 00:58:37,190
+كده اش اربع عشرين فالاتناش divides اربع عشرين
+
+742
+00:58:38,350 --> 00:58:43,510
+مظبوط، مادام تعطينا تقسيم 24، فإذا الأتنين هدولة
+
+743
+00:58:43,510 --> 00:58:47,450
+فعلا congruence أو لبعض أو كل واحدة منهم congruent
+
+744
+00:58:47,450 --> 00:58:52,570
+للتانية مكافئة، شابعة، مناظرة، whatever،
+
+745
+00:58:52,570 --> 00:58:57,510
+equivalent لبعض في الحالة بتاعتنا طيب، في الآخر A
+
+746
+00:58:57,510 --> 00:59:03,720
+minus Bمد M المفروض يساوي صفر لأنه المفروض هذا
+
+747
+00:59:03,720 --> 00:59:07,680
+يمثل عدد مضاعفات ال modulus تبعكم ال modulus تبعكم
+
+748
+00:59:07,680 --> 00:59:13,200
+اربع واش .. ستة واشرين ناقص اتنين اربع واشرين طيب
+
+749
+00:59:13,200 --> 00:59:19,620
+اربع واشرين مد Zero اتناش احنا بدنا نشتغل هالموجة
+
+750
+00:59:19,620 --> 00:59:22,280
+عالمين على ال remainder اللي بيظل لو قولنا اربع
+
+751
+00:59:22,280 --> 00:59:27,540
+واشرين على اتناش اتنين اربع واشرين صفر اه
+
+752
+00:59:27,540 --> 00:59:35,350
+remainder Zeroremainder 0 ففعلا الفرق لازم يسوي
+
+753
+00:59:35,350 --> 00:59:40,390
+لنا 0 بالنسبة ل ال mood 12 إذا كان الفرق هذا ناتج
+
+754
+00:59:40,390 --> 00:59:45,350
+من two elements ال two elements هدولة أكيد هيكونوا
+
+755
+00:59:45,350 --> 00:59:51,910
+congruent لبعض مكافئين لبعض بحيث أنه أنتجولنا إما
+
+756
+00:59:51,910 --> 00:59:57,910
+ال modulus أو مضاعفاته الفرق بينهم يسوي ال modulus
+
+757
+00:59:57,910 --> 01:00:02,270
+أو مضاعفاتهالاثناش او مضاعفتها فالفرق بينهم اما
+
+758
+01:00:02,270 --> 01:00:06,890
+اتناش او اربع عشرين ستة و تلاتين المهم مضاعفتها
+
+759
+01:00:06,890 --> 01:00:12,190
+مهم مضاعفتها طيب زي ما قلنا بستخدم علامة المكافئة
+
+760
+01:00:12,190 --> 01:00:16,390
+هذه عساس ان هي is defined as ممكن تعريفها كاتنين
+
+761
+01:00:16,390 --> 01:00:22,880
+فالاربعتاش ممكن نعرفها كاتنينبالنسبة للساعة ..
+
+762
+01:00:22,880 --> 01:00:25,540
+بالنسبة للساعة فبدنا نكون ناسبين احنا بالنسبة لمين
+
+763
+01:00:25,540 --> 01:00:29,960
+فهي المد كذا بالنسبة لمين .. بالنسبة لمين
+
+764
+01:00:29,960 --> 01:00:32,880
+الاربعتاش مش بالمطلق دايما بتساوي اتنين او تكافئ
+
+765
+01:00:32,880 --> 01:00:36,460
+اتنين انما بالنسبة للساعة تكافئ اتنين لما انتوا
+
+766
+01:00:36,460 --> 01:00:41,580
+تيجوا تدوروا على البرنامج ال .. القراكل تبعكم و
+
+767
+01:00:41,580 --> 01:00:45,060
+اتلاقوا دخلتوا ع صفحتكم و موعد المحاضرة الساعة
+
+768
+01:00:45,060 --> 01:00:47,820
+اربعتاش فانتوا عارفين ان الساعة اتناش .. الساعة
+
+769
+01:00:47,820 --> 01:00:50,580
+اتنينهتيجوا على الساعة التانية لتكونوا موجودين حتى
+
+770
+01:00:50,580 --> 01:00:55,160
+لو انتوا زبطين ساعتكم عقارب الساعة ومافيش فيها
+
+771
+01:00:55,160 --> 01:00:58,900
+اربع وعشرين فانتوا بتشتغلوا على الاتناش اكيد
+
+772
+01:00:58,900 --> 01:01:01,300
+هتيجوا على التانية لانه صرتوا حافظينها بس مش
+
+773
+01:01:01,300 --> 01:01:04,660
+بالضروري انه كل اربعة عشر هتشوفوها هتكون بالنسبالك
+
+774
+01:01:04,660 --> 01:01:07,280
+equivalent لاتنين لأ لأ
+
+775
+01:01:10,860 --> 01:01:15,140
+خلصنا .. خلصنا .. هاي الكلام الدوائر اللي احنا
+
+776
+01:01:15,140 --> 01:01:18,180
+عملناها اما تلاتمان و سبتين او اتماشى هنا عملناها
+
+777
+01:01:18,180 --> 01:01:23,660
+mod خمسة عملناها هنا mod خمسة ف .. او modulo five
+
+778
+01:01:23,660 --> 01:01:27,760
+ف example modulo five كإنكوا بتبدو مدان modulo
+
+779
+01:01:27,760 --> 01:01:33,220
+five too smallخمس أضلع بهذا الشكل على اساس ان كل
+
+780
+01:01:33,220 --> 01:01:36,500
+واحدة منهم رقم و بعد ما يخلصوا الخمسة تكونوا
+
+781
+01:01:36,500 --> 01:01:40,060
+رجعتوا مرة تانية لنفس ال congruent لنفس ال
+
+782
+01:01:40,060 --> 01:01:43,160
+congruent او لنفس الضلع اول ضلع هيكون اللي هو ال
+
+783
+01:01:43,160 --> 01:01:48,980
+zero one two three four طب equivalent خمسة خمسة
+
+784
+01:01:48,980 --> 01:01:52,140
+equivalent لل zero أصلا خمسة equivalent لل zero زي
+
+785
+01:01:52,140 --> 01:01:54,360
+ما تقولوا اتناش اتناش معايا equivalent لل zero
+
+786
+01:01:55,270 --> 01:01:57,430
+الاثناشنتوا هتكون رفيتوا و رجعتوا تاني عند ال zero
+
+787
+01:01:57,430 --> 01:02:03,310
+عند ال zero كويس ف zero واحد اتنين تلاتة اربعة
+
+788
+01:02:03,310 --> 01:02:09,170
+الخمسة congruent ل zero congruent ل عشرة congruent
+
+789
+01:02:09,170 --> 01:02:15,930
+ل fifteen لشريه لكله طيب التمانية congruent لمن
+
+790
+01:02:15,930 --> 01:02:19,920
+لطلقتعشامتى الكلام هذا بقول انه ده ده ده ده ده ده
+
+791
+01:02:19,920 --> 01:02:20,560
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+792
+01:02:20,560 --> 01:02:21,580
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+793
+01:02:21,580 --> 01:02:25,140
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+794
+01:02:25,140 --> 01:02:25,200
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+795
+01:02:25,200 --> 01:02:25,800
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+796
+01:02:25,800 --> 01:02:34,640
+ده ده ده ده
+
+797
+01:02:34,640 --> 01:02:38,240
+ده ده ده ده ده ده ده ده ده ده ده ده
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a9d6205d1b98631c0b35f1efb63eac369ebb4738
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/SKJuZa9J-ao_raw.json
@@ -0,0 +1 @@
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technically tractable polynomial فأقل attractable فرغم ذلك طريقة حلها هتكون صعبة جدا لأنه", "tokens": [11622, 1829, 11331, 6027, 3660, 39627, 15730, 25124, 28820, 293, 281, 264, 1347, 3714, 20292, 11536, 293, 281, 264, 1347, 3714, 20292, 11536, 29538, 8717, 28543, 2288, 8717, 9381, 1863, 5172, 11296, 20449, 2423, 26110, 6055, 9381, 1863, 5172, 20449, 2423, 26110, 4032, 20449, 29910, 23275, 6156, 3224, 1829, 12120, 24207, 712, 26110, 6156, 10721, 4587, 1211, 5049, 712, 6156, 2288, 17082, 2304, 29910, 23275, 23032, 16572, 28671, 11331, 1211, 11296, 8032, 2655, 30544, 20328, 3615, 49401, 10874, 28259, 5296, 33456, 3224], "avg_logprob": -0.15662650386971164, "compression_ratio": 1.6596858638743455, "no_speech_prob": 1.7285346984863281e-06, "words": [{"start": 78.2, "end": 78.62, "word": "زي", "probability": 0.76708984375}, {"start": 78.62, "end": 79.26, "word": " حالة", "probability": 0.9630533854166666}, {"start": 79.26, "end": 79.5, "word": " بهذا", "probability": 0.920166015625}, 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"word": " معاملات", "probability": 0.98583984375}, {"start": 1106.37, "end": 1106.53, "word": " A", "probability": 0.6787109375}, {"start": 1106.53, "end": 1107.03, "word": " او", "probability": 0.895751953125}, {"start": 1107.03, "end": 1108.55, "word": " divisor", "probability": 0.919677734375}, {"start": 1108.55, "end": 1109.21, "word": " قاسم", "probability": 0.8821614583333334}, {"start": 1109.21, "end": 1110.99, "word": " قاسم", "probability": 0.789306640625}, {"start": 1110.99, "end": 1111.29, "word": " ل", "probability": 0.7216796875}, {"start": 1111.29, "end": 1112.43, "word": " ال", "probability": 0.37646484375}, {"start": 1112.43, "end": 1112.65, "word": " B", "probability": 0.83544921875}, {"start": 1112.65, "end": 1113.25, "word": " قاسم", "probability": 0.8671875}, {"start": 1113.25, "end": 1113.51, "word": " of", "probability": 0.88330078125}, {"start": 1113.51, "end": 1114.01, "word": " B", "probability": 0.9462890625}, {"start": 1114.01, "end": 1114.63, "word": " و", 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بي", "probability": 0.860595703125}, {"start": 1141.52, "end": 1142.16, "word": " إذا", "probability": 0.85546875}, {"start": 1142.16, "end": 1142.46, "word": " فعلا", "probability": 0.9288736979166666}, {"start": 1142.46, "end": 1142.72, "word": " two", "probability": 0.904296875}, {"start": 1142.72, "end": 1143.12, "word": " divides", "probability": 0.95263671875}, {"start": 1143.12, "end": 1143.64, "word": " بي", "probability": 0.94873046875}, {"start": 1143.64, "end": 1143.86, "word": " is", "probability": 0.86328125}, {"start": 1143.86, "end": 1144.24, "word": " true", "probability": 0.97314453125}], "temperature": 1.0}, {"id": 49, "seek": 116968, "start": 1144.98, "end": 1169.68, "text": "معناته ال B دائما even دائما even إذا two divides B is true فإذا دائما even طيب ال zero even بناء على النظرية هذه zero هل هي belong to Z؟ أه خلاص معناته إذا even فإذا even طيب ال minus four", "tokens": [2304, 3615, 8315, 47395, 2423, 363, 11778, 16373, 15042, 754, 11778, 16373, 15042, 754, 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"probability": 0.87890625}, {"start": 1447.89, "end": 1448.11, "word": " ممكن", "probability": 0.984619140625}, {"start": 1448.11, "end": 1448.79, "word": " تنفع", "probability": 0.856689453125}, {"start": 1448.79, "end": 1449.19, "word": " ليش", "probability": 0.734130859375}, {"start": 1449.19, "end": 1449.45, "word": " لأنه", "probability": 0.7473958333333334}, {"start": 1449.45, "end": 1449.75, "word": " مضروبة", "probability": 0.91943359375}, {"start": 1449.75, "end": 1449.87, "word": " في", "probability": 0.97705078125}, {"start": 1449.87, "end": 1450.55, "word": " نفسها", "probability": 0.9972330729166666}, {"start": 1450.55, "end": 1451.65, "word": " ال", "probability": 0.873046875}, {"start": 1451.65, "end": 1451.91, "word": " P", "probability": 0.92578125}, {"start": 1451.91, "end": 1452.41, "word": " هيكون", "probability": 0.88623046875}, {"start": 1452.41, "end": 1452.65, "word": " عبارة", "probability": 0.973876953125}, {"start": 1452.65, "end": 1452.75, "word": " عن", "probability": 0.9921875}, {"start": 1452.75, "end": 1452.89, "word": " ال", "probability": 0.8408203125}, {"start": 1452.89, "end": 1453.07, "word": " P", "probability": 0.95556640625}, {"start": 1453.07, "end": 1453.35, "word": " في", "probability": 0.90380859375}, {"start": 1453.35, "end": 1454.15, "word": " واحد", "probability": 0.97265625}, {"start": 1454.15, "end": 1455.67, "word": " بس", "probability": 0.944580078125}], "temperature": 1.0}, {"id": 61, "seek": 148182, "start": 1457.0, "end": 1481.82, "text": "أو ما لا يمكن ينتج أو نقدر نلتجه نجيبه من two integers مضرومي في بعض باستثناء الواحد طيب فبنقول P أكبر من واحد فإذا ال .. ال .. ال primes تبعتنا بتبدأ من اتنين اتنين، تلاتة، خمسة، سبعة، احداشر، بتكمل أكبر من واحد and there is no exist لا يوجد a و b لا يوجد أي رقمين", "tokens": [10721, 2407, 19446, 20193, 7251, 43020, 7251, 29399, 7435, 34051, 8717, 28543, 2288, 8717, 1211, 2655, 7435, 3224, 8717, 7435, 1829, 3555, 3224, 9154, 732, 41674, 3714, 11242, 2288, 20498, 1829, 8978, 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1457.64, "end": 1457.9, "word": " يمكن", "probability": 0.95654296875}, {"start": 1457.9, "end": 1458.42, "word": " ينتج", "probability": 0.8203938802083334}, {"start": 1458.42, "end": 1458.94, "word": " أو", "probability": 0.54345703125}, {"start": 1458.94, "end": 1459.24, "word": " نقدر", "probability": 0.9685872395833334}, {"start": 1459.24, "end": 1459.7, "word": " نلتجه", "probability": 0.856005859375}, {"start": 1459.7, "end": 1460.18, "word": " نجيبه", "probability": 0.88662109375}, {"start": 1460.18, "end": 1460.32, "word": " من", "probability": 0.9833984375}, {"start": 1460.32, "end": 1460.56, "word": " two", "probability": 0.80029296875}, {"start": 1460.56, "end": 1461.02, "word": " integers", "probability": 0.974609375}, {"start": 1461.02, "end": 1461.42, "word": " مضرومي", "probability": 0.79384765625}, {"start": 1461.42, "end": 1461.52, "word": " في", "probability": 0.9365234375}, {"start": 1461.52, "end": 1461.78, "word": " بعض", "probability": 0.98828125}, {"start": 1461.78, "end": 1462.3, "word": " باستثناء", "probability": 0.95654296875}, {"start": 1462.3, "end": 1462.66, "word": " الواحد", "probability": 0.9695638020833334}, {"start": 1462.66, "end": 1463.24, "word": " طيب", "probability": 0.8489583333333334}, {"start": 1463.24, "end": 1463.72, "word": " فبنقول", "probability": 0.948974609375}, {"start": 1463.72, "end": 1464.3, "word": " P", "probability": 0.78759765625}, {"start": 1464.3, "end": 1465.08, "word": " أكبر", "probability": 0.9609375}, {"start": 1465.08, "end": 1465.24, "word": " من", "probability": 0.99462890625}, {"start": 1465.24, "end": 1465.6, "word": " واحد", "probability": 0.930419921875}, {"start": 1465.6, "end": 1466.92, "word": " فإذا", "probability": 0.8642578125}, {"start": 1466.92, "end": 1467.4, "word": " ال", "probability": 0.9892578125}, {"start": 1467.4, "end": 1467.58, "word": " ..", "probability": 0.251220703125}, {"start": 1467.58, "end": 1467.8, "word": " ال", "probability": 0.9814453125}, {"start": 1467.8, "end": 1467.8, "word": " ..", "probability": 0.50146484375}, {"start": 1467.8, "end": 1467.88, "word": " ال", "probability": 0.98486328125}, {"start": 1467.88, "end": 1468.18, "word": " primes", "probability": 0.55126953125}, {"start": 1468.18, "end": 1468.48, "word": " تبعتنا", "probability": 0.82781982421875}, {"start": 1468.48, "end": 1468.76, "word": " بتبدأ", "probability": 0.93359375}, {"start": 1468.76, "end": 1468.9, "word": " من", "probability": 0.9912109375}, {"start": 1468.9, "end": 1469.32, "word": " اتنين", "probability": 0.9471435546875}, {"start": 1469.32, "end": 1470.66, "word": " اتنين،", "probability": 0.82568359375}, {"start": 1470.66, "end": 1471.4, "word": " تلاتة،", "probability": 0.96298828125}, {"start": 1471.4, "end": 1472.02, "word": " خمسة،", "probability": 0.98701171875}, {"start": 1472.02, "end": 1472.62, "word": " سبعة،", "probability": 0.97607421875}, {"start": 1472.62, "end": 1473.5, "word": " احداشر،", "probability": 0.78466796875}, {"start": 1473.5, "end": 1474.02, "word": " بتكمل", "probability": 0.84033203125}, {"start": 1474.02, "end": 1475.7, "word": " أكبر", "probability": 0.9267578125}, {"start": 1475.7, "end": 1475.88, "word": " من", "probability": 0.998046875}, {"start": 1475.88, "end": 1476.28, "word": " واحد", "probability": 0.99560546875}, {"start": 1476.28, "end": 1476.72, "word": " and", "probability": 0.92578125}, {"start": 1476.72, "end": 1477.8, "word": " there", "probability": 0.84130859375}, {"start": 1477.8, "end": 1477.92, "word": " is", "probability": 0.91650390625}, {"start": 1477.92, "end": 1478.12, "word": " no", "probability": 0.9482421875}, {"start": 1478.12, "end": 1478.68, "word": " exist", "probability": 0.92041015625}, {"start": 1478.68, "end": 1479.32, "word": " لا", "probability": 0.87451171875}, {"start": 1479.32, "end": 1479.98, "word": " يوجد", "probability": 0.9168294270833334}, {"start": 1479.98, "end": 1480.56, "word": " a", "probability": 0.53369140625}, {"start": 1480.56, "end": 1480.68, "word": " و", "probability": 0.91796875}, {"start": 1480.68, "end": 1480.82, "word": " b", "probability": 0.73583984375}, {"start": 1480.82, "end": 1480.98, "word": " لا", "probability": 0.57080078125}, {"start": 1480.98, "end": 1481.2, "word": " يوجد", "probability": 0.9189453125}, {"start": 1481.2, "end": 1481.34, "word": " أي", "probability": 0.39697265625}, {"start": 1481.34, "end": 1481.82, "word": " رقمين", "probability": 0.95458984375}], "temperature": 1.0}, {"id": 62, "seek": 149839, "start": 1484.29, "end": 1498.39, "text": "belong to natural number والرقمين لازم يكونوا اكبر من واحد حصل ضربهم يساوي ال B لا يوجد a و b حصل ضربهم يعطي إبراهيم", "tokens": [5390, 556, 281, 3303, 1230, 16070, 2288, 4587, 2304, 9957, 5296, 31377, 2304, 7251, 30544, 14407, 1975, 4117, 26890, 9154, 36764, 24401, 11331, 36520, 48812, 25513, 16095, 7251, 3794, 995, 45865, 2423, 363, 20193, 7251, 29245, 3215, 257, 4032, 272, 11331, 36520, 48812, 25513, 16095, 37495, 9566, 1829, 11933, 3555, 23557, 3224, 32640], "avg_logprob": -0.21701389440783747, "compression_ratio": 1.3703703703703705, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 1484.29, "end": 1484.67, "word": "belong", "probability": 0.69775390625}, {"start": 1484.67, "end": 1484.81, "word": " to", "probability": 0.939453125}, {"start": 1484.81, "end": 1485.15, "word": " natural", "probability": 0.8642578125}, {"start": 1485.15, "end": 1485.61, "word": " number", "probability": 0.92822265625}, {"start": 1485.61, "end": 1486.61, "word": " والرقمين", "probability": 0.82080078125}, {"start": 1486.61, "end": 1486.87, "word": " لازم", "probability": 0.9640299479166666}, {"start": 1486.87, "end": 1487.11, "word": " يكونوا", "probability": 0.8732096354166666}, {"start": 1487.11, "end": 1487.47, "word": " اكبر", "probability": 0.8328450520833334}, {"start": 1487.47, "end": 1487.65, "word": " من", "probability": 0.98193359375}, {"start": 1487.65, "end": 1488.35, "word": " واحد", "probability": 0.966064453125}, {"start": 1488.35, "end": 1490.95, "word": " حصل", "probability": 0.842041015625}, {"start": 1490.95, "end": 1491.31, "word": " ضربهم", "probability": 0.9801432291666666}, {"start": 1491.31, "end": 1491.79, "word": " يساوي", "probability": 0.9613037109375}, {"start": 1491.79, "end": 1492.13, "word": " ال", "probability": 0.7158203125}, {"start": 1492.13, "end": 1492.31, "word": " B", "probability": 0.3369140625}, {"start": 1492.31, "end": 1492.67, "word": " لا", "probability": 0.68359375}, {"start": 1492.67, "end": 1493.19, "word": " يوجد", "probability": 0.9248046875}, {"start": 1493.19, "end": 1495.19, "word": " a", "probability": 0.15380859375}, {"start": 1495.19, "end": 1495.33, "word": " و", "probability": 0.94970703125}, {"start": 1495.33, "end": 1495.55, "word": " b", "probability": 0.6650390625}, {"start": 1495.55, "end": 1496.21, "word": " حصل", "probability": 0.91357421875}, {"start": 1496.21, "end": 1496.77, "word": " ضربهم", "probability": 0.9928385416666666}, {"start": 1496.77, "end": 1497.67, "word": " يعطي", "probability": 0.9117838541666666}, {"start": 1497.67, "end": 1498.39, "word": " إبراهيم", "probability": 0.74752197265625}], "temperature": 1.0}, {"id": 63, "seek": 152495, "start": 1502.65, "end": 1524.95, "text": "Okay الحالة الوحيدة زى ما قلنا اما اللى هى ال prime نفسه و الواحد الواحد و ال P itself نفسها بس و هدى بتندرجش ضمن التعريف لإن احنا استثنينا هنا A أكبر من واحد و P أكبر من واحد فلا يساوي واحد some primes اتنين تلاتة خمسة سبعة احداشر تلاتاشر", "tokens": [8297, 21542, 6027, 3660, 2423, 2407, 5016, 25708, 3660, 30767, 7578, 19446, 12174, 1211, 8315, 1975, 15042, 13672, 7578, 8032, 7578, 2423, 5835, 8717, 36178, 3224, 4032, 2423, 14407, 24401, 2423, 14407, 24401, 4032, 2423, 430, 2564, 8717, 36178, 11296, 4724, 3794, 4032, 8032, 3215, 7578, 39894, 41260, 47341, 8592, 48812, 27842, 16712, 3615, 16572, 5172, 5296, 28814, 1863, 1975, 5016, 8315, 44713, 12984, 1863, 1829, 8315, 34105, 316, 5551, 4117, 26890, 9154, 36764, 24401, 4032, 430, 5551, 4117, 26890, 9154, 36764, 24401, 6156, 15040, 7251, 3794, 995, 45865, 36764, 24401, 512, 582, 1532, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 8608, 3555, 27884, 1975, 24401, 33599, 2288, 6055, 1211, 9307, 33599, 2288], "avg_logprob": -0.20154936624174358, "compression_ratio": 1.7665198237885462, "no_speech_prob": 0.0, "words": [{"start": 1502.65, "end": 1503.01, "word": "Okay", "probability": 0.59716796875}, {"start": 1503.01, "end": 1503.83, "word": " الحالة", "probability": 0.8868815104166666}, {"start": 1503.83, "end": 1504.17, "word": " الوحيدة", "probability": 0.98115234375}, {"start": 1504.17, "end": 1504.29, "word": " زى", "probability": 0.6500244140625}, {"start": 1504.29, "end": 1504.37, "word": " ما", "probability": 0.98046875}, {"start": 1504.37, "end": 1504.69, "word": " قلنا", "probability": 0.9451497395833334}, {"start": 1504.69, "end": 1505.27, "word": " اما", "probability": 0.6107177734375}, {"start": 1505.27, "end": 1505.65, "word": " اللى", "probability": 0.96240234375}, {"start": 1505.65, "end": 1506.01, "word": " هى", "probability": 0.8369140625}, {"start": 1506.01, "end": 1506.45, "word": " ال", "probability": 0.97802734375}, {"start": 1506.45, "end": 1506.73, "word": " prime", "probability": 0.68408203125}, {"start": 1506.73, "end": 1507.23, "word": " نفسه", "probability": 0.9933268229166666}, {"start": 1507.23, "end": 1507.49, "word": " و", "probability": 0.5615234375}, {"start": 1507.49, "end": 1507.93, "word": " الواحد", "probability": 0.7999674479166666}, {"start": 1507.93, "end": 1508.97, "word": " الواحد", "probability": 0.8395182291666666}, {"start": 1508.97, "end": 1509.19, "word": " و", "probability": 0.97412109375}, {"start": 1509.19, "end": 1509.69, "word": " ال", "probability": 0.97509765625}, {"start": 1509.69, "end": 1509.85, "word": " P", "probability": 0.3251953125}, {"start": 1509.85, "end": 1510.25, "word": " itself", "probability": 0.384765625}, {"start": 1510.25, "end": 1510.89, "word": " نفسها", "probability": 0.98095703125}, {"start": 1510.89, "end": 1511.23, "word": " بس", "probability": 0.89111328125}, {"start": 1511.23, "end": 1511.57, "word": " و", "probability": 0.61279296875}, {"start": 1511.57, "end": 1512.13, "word": " هدى", "probability": 0.70068359375}, {"start": 1512.13, "end": 1513.55, "word": " بتندرجش", "probability": 0.8128662109375}, {"start": 1513.55, "end": 1513.89, "word": " ضمن", "probability": 0.98681640625}, {"start": 1513.89, "end": 1514.85, "word": " التعريف", "probability": 0.992919921875}, {"start": 1514.85, "end": 1515.05, "word": " لإن", "probability": 0.8854166666666666}, {"start": 1515.05, "end": 1515.21, "word": " احنا", "probability": 0.8504231770833334}, {"start": 1515.21, "end": 1515.71, "word": " استثنينا", "probability": 0.6914306640625}, {"start": 1515.71, "end": 1516.09, "word": " هنا", "probability": 0.95703125}, {"start": 1516.09, "end": 1516.51, "word": " A", "probability": 0.724609375}, {"start": 1516.51, "end": 1516.89, 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وهذه كأنها تلاتة صفر في خمسة ضبار واحد بنختار زي ما قلنا إيش الأعلى", "tokens": [9566, 1829, 3555, 29538, 9122, 33456, 11296, 16490, 2304, 3794, 3660, 20328, 5172, 2288, 37037, 24192, 9122, 33456, 11296, 6055, 1211, 9307, 3660, 20328, 5172, 2288, 8978, 16490, 2304, 3794, 3660, 48812, 3555, 9640, 36764, 24401, 44945, 46456, 9640, 30767, 1829, 19446, 12174, 1211, 8315, 11933, 1829, 8592, 16247, 3615, 23942], "avg_logprob": -0.12597656937745902, "compression_ratio": 1.514018691588785, "no_speech_prob": 0.0, "words": [{"start": 3034.51, "end": 3034.87, "word": "طيب", "probability": 0.9816080729166666}, {"start": 3034.87, "end": 3035.09, "word": " هذه", "probability": 0.517578125}, {"start": 3035.09, "end": 3035.59, "word": " كأنها", "probability": 0.97509765625}, {"start": 3035.59, "end": 3036.57, "word": " خمسة", "probability": 0.9471435546875}, {"start": 3036.57, "end": 3037.01, "word": " صفر", "probability": 0.9822591145833334}, {"start": 3037.01, "end": 3037.71, "word": " وهذه", 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مضاعفات ال modulus تبعكم ال modulus تبعكم اربع واش .. ستة واشرين ناقص اتنين اربع واشرين طيب اربع واشرين مد Zero اتناش احنا بدنا نشتغل هالموجة عالمين على ال remainder اللي بيظل لو قولنا اربع واشرين على اتناش اتنين اربع واشرين صفر اه remainder Zero", "tokens": [2304, 3215, 376, 9673, 5172, 32887, 11242, 7251, 3794, 995, 45865, 20328, 5172, 2288, 5296, 33456, 3224, 9673, 5172, 32887, 11242, 23758, 7251, 2304, 12984, 1211, 6225, 3215, 3215, 3714, 11242, 45761, 5172, 9307, 2423, 42287, 6055, 3555, 3615, 24793, 2423, 42287, 6055, 3555, 3615, 24793, 1975, 25513, 3615, 4032, 33599, 4386, 8608, 2655, 3660, 4032, 33599, 2288, 9957, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 1975, 25513, 3615, 4032, 33599, 2288, 9957, 23032, 1829, 3555, 1975, 25513, 3615, 4032, 33599, 2288, 9957, 3714, 3215, 17182, 1975, 2655, 1863, 33599, 1975, 5016, 8315, 47525, 8315, 8717, 8592, 2655, 17082, 1211, 8032, 45340, 29245, 3660, 6225, 45340, 9957, 15844, 2423, 29837, 13672, 1829, 4724, 1829, 19913, 1211, 45164, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dee75bdb7bf701534e92a5caa0d30fc395ce68f3
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs.srt
@@ -0,0 +1,1981 @@
+1
+00:00:20,940 --> 00:00:22,980
+طيب بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,980 --> 00:00:25,620
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,620 --> 00:00:30,660
+أجمعين. نكمل في الـ permutation أو التبديل في الـ
+
+4
+00:00:30,660 --> 00:00:33,920
+permutation. كان آخر شيء أخذناه أننا بدنا نعمل
+
+5
+00:00:33,920 --> 00:00:38,620
+cutting لثلاثة wires من ten wires كانوا موجودين
+
+6
+00:00:38,620 --> 00:00:43,280
+فكانت هنا العملية عملية order، يعني كان لازم العشر
+
+7
+00:00:43,280 --> 00:00:47,660
+أسلاك التي بدنا نقطعها يكونوا مرتبين من العشر
+
+8
+00:00:47,660 --> 00:00:50,200
+أسلاك. الثلاثة التي بدنا نقطعها يكونوا مرتبين، الأول
+
+9
+00:00:50,200 --> 00:00:53,860
+في الـ order تبعه، صح؟ كان فعلاً أول واحد نقطعه، و
+
+10
+00:00:53,860 --> 00:00:58,580
+الثاني في نفس وقته، والثالث أيضاً في نفس اللحظة، و
+
+11
+00:00:58,580 --> 00:01:03,460
+كنا نتكلم فيها عن جدّيش الـ chances أنّه فعلاً ينجح
+
+12
+00:01:03,460 --> 00:01:06,640
+معنا الموضوع ده. فأتكلمنا.. قلنا أننا هنا
+
+13
+00:01:06,640 --> 00:01:09,460
+نتكلم عن permutation.  مدام أنا بتكلم عن إيه؟ عن
+
+14
+00:01:09,460 --> 00:01:15,140
+order، عن order sequence. فكنا بنقول permutation، عشر
+
+15
+00:01:15,140 --> 00:01:19,780
+أسلاك، بدنا نقطع منهم ثلاثة، أو بدنا نختار ثلاثة
+
+16
+00:01:19,780 --> 00:01:23,360
+بمعنى آخر، بدنا نعمل selection لـ three wires from
+
+17
+00:01:23,360 --> 00:01:28,620
+ten wires، okay؟ و حلينا.. اشتغلنا عليها، وطلعنا
+
+18
+00:01:29,570 --> 00:01:34,110
+على أساس أنه يطلع معنا عشرة في تسعة في ثمانية
+
+19
+00:01:34,110 --> 00:01:38,310
+وقلنا فيها أنّه سبعمائة وعشرين. السبعمائة وعشرين
+
+20
+00:01:38,310 --> 00:01:41,290
+هدول عدد الـ chances كلهم على بعض، عدد الـ chances
+
+21
+00:01:41,290 --> 00:01:46,910
+أنّي أختار ثلاث أسلاك من عشرة. طيب، عشان يكون فعلاً
+
+22
+00:01:46,910 --> 00:01:50,810
+ordered، وهو الـ sequence الوحيد اللي لازم، ضروري فهو
+
+23
+00:01:50,810 --> 00:01:56,480
+واحد واحد من سبعمائة وعشرين. فأنا بتكلم عن واحد من
+
+24
+00:01:56,480 --> 00:02:03,520
+سبعمئة وعشرين chances ممكنة. فالـ chance الوحيد of
+
+25
+00:02:03,520 --> 00:02:08,040
+survival هو واحد من السبعمائة وعشرين، هدول واحد من
+
+26
+00:02:08,040 --> 00:02:12,980
+السبعمئة وعشرين. كان هذا آخر شيء أخذناه المرة
+
+27
+00:02:12,980 --> 00:02:18,240
+الماضية. طيب نكمل شوية examples، أيضاً لو أخذنا مثال
+
+28
+00:02:18,950 --> 00:02:21,750
+مثال بسيط، المثال هذا بيقول إنه جدّيش عدد الـ
+
+29
+00:02:21,750 --> 00:02:25,350
+different.. different orders لـ four persons
+
+30
+00:02:25,350 --> 00:02:29,410
+أو أربعة أشخاص يقعدوا على أربع كراسي، في أربعة
+
+31
+00:02:29,410 --> 00:02:33,610
+أشخاص بدهم يقعدوا على أربع كراسي، جدّيش عدد الحالات
+
+32
+00:02:33,610 --> 00:02:38,010
+الممكنة أن يقعدوا أربعة أشخاص على أربع.. على أربع
+
+33
+00:02:38,010 --> 00:02:46,470
+كراسي. فهذه كانت ببساطة الـ permutation لأربعة من
+
+34
+00:02:46,470 --> 00:02:51,810
+أربعة. أربعة من أربعة. من القوانين بتاعتكم بكل بساطة
+
+35
+00:02:51,810 --> 00:02:55,330
+بتقدروا تحسبوها على أساس أنّها الـ N factorial على
+
+36
+00:02:55,330 --> 00:03:01,210
+N minus R، R. جدّيش أن هنا أربعة، فإنّها أربعة، أربعة
+
+37
+00:03:01,210 --> 00:03:06,490
+كله factorial. فكان بيطلع جدّيش؟ أربعة وعشرين. بيطلع
+
+38
+00:03:06,490 --> 00:03:11,500
+هنا عندكم أربعة وعشرون. على أساس أنّ الشخص الأول
+
+39
+00:03:11,500 --> 00:03:13,900
+ممكن يقعد في المكان الأول، أو الثاني، أو الثالث، أو
+
+40
+00:03:13,900 --> 00:03:16,900
+الرابع، ونفس الكلام الشخص الثاني، فممكن يعملوا
+
+41
+00:03:16,900 --> 00:03:20,540
+permutation مع بعض، ممكن يعملوا تبديل مع بعض في
+
+42
+00:03:20,540 --> 00:03:24,780
+عملية الجلوس تبعهم، في عملية الجلوس تبعهم، okay؟
+
+43
+00:03:24,780 --> 00:03:29,160
+طيب، how many different three digit numbers؟ جدّيش
+
+44
+00:03:29,160 --> 00:03:33,560
+ممكن أعمل three digit numbers؟ بمعنى جدّيش عدد
+
+45
+00:03:33,560 --> 00:03:40,460
+الأرقام من الـ three digits، واحد، اثنين، ثلاثة، تحتوي
+
+46
+00:03:40,460 --> 00:03:47,620
+على أرقام خمسة، ستة، سبعة، ثمانية، أو تسعة. واحد من
+
+47
+00:03:47,620 --> 00:03:50,600
+الأرقام هدول، لازم يكون في خانة من الخانات without
+
+48
+00:03:50,600 --> 00:03:54,860
+repetition، بدون تكرار، بدون ما يصير ما يكون عندنا في
+
+49
+00:03:55,980 --> 00:03:58,900
+ما يكون فيه تكرار في الحالة اللي إحنا بنتكلم عنها.
+
+50
+00:03:58,900 --> 00:04:02,060
+ففي الحالة اللي عندنا هنا، هيكون كأنّه عندنا three
+
+51
+00:04:02,060 --> 00:04:06,380
+permutation. فهتكون جدّيش عددهم؟ واحد، اثنين، ثلاثة،
+
+52
+00:04:06,380 --> 00:04:11,140
+أربعة، خمسة. فـ permutation خمسة، بدنا منهم.. بدنا
+
+53
+00:04:11,140 --> 00:04:15,100
+منهم ثلاثة.. بدنا منهم ثلاثة، ومتّفقين إحنا مع
+
+54
+00:04:15,100 --> 00:04:18,980
+حكاية الـ repetition، يعني بالعكس هي تناسب مع الـ
+
+55
+00:04:18,980 --> 00:04:23,540
+permutation، لأنّه قلنا قبل هيك أنّ الـ permutation و
+
+56
+00:04:23,540 --> 00:04:26,640
+الـ combination، الإثنتين يتفقوا أن هما without
+
+57
+00:04:26,640 --> 00:04:32,360
+replacement، بدون تكرار، بدون أن نرجع الـ selected
+
+58
+00:04:32,360 --> 00:04:36,260
+item للـ universe of discourse بتاعتنا عشان نرجع
+
+59
+00:04:36,260 --> 00:04:40,360
+نختارها كمان مرة. فهنا خمسة، بدنا نختار منهم ثلاثة.
+
+60
+00:04:40,360 --> 00:04:43,720
+بدنا نختار منهم ثلاثة، بتقدروا تحسبوها بنفس القانون
+
+61
+00:04:43,720 --> 00:04:47,740
+اللي كنا كاتبينه، بيطلع معاكم ستين. بيطلع معانا ستين.
+
+62
+00:04:47,740 --> 00:04:50,680
+okay؟ طيب الـ permutation إيش كانت تختلف عن الـ
+
+63
+00:04:50,680 --> 00:04:56,100
+combination؟ permutation، اتكلمنا أنّها order، الـ..
+
+64
+00:04:56,100 --> 00:04:59,540
+الـ combination لأ، without order. فلما نيجي نتكلم عن
+
+65
+00:04:59,540 --> 00:05:04,240
+الـ.. الأربعة.. الأربعة persons اللي بيتم يقعدوا
+
+66
+00:05:04,240 --> 00:05:07,670
+على أربع كراسي، ما فيش.. يعني مش هنقعد نقول: آه، والله
+
+67
+00:05:07,670 --> 00:05:09,550
+الشخص الأول قاعد في المكان الأول، أو الثاني، أو
+
+68
+00:05:09,550 --> 00:05:12,210
+الثالث، المهم أنّه قاعد، المهم أنّه خلاص، هو قاعد
+
+69
+00:05:12,210 --> 00:05:15,230
+وخلص، ففي الحالة هذه هيكون لنا احتمال واحد، أنّه
+
+70
+00:05:15,230 --> 00:05:18,530
+الأربعة على الأربعة، خلاص، كيف قاعدوا، وين قاعد
+
+71
+00:05:18,530 --> 00:05:20,510
+الشخص الأول، وين قاعد الشخص الثاني، الثالث، مش
+
+72
+00:05:20,510 --> 00:05:23,370
+إشكال، المهم أنّه في النهاية الأربعة كراسي عليهم
+
+73
+00:05:23,370 --> 00:05:26,490
+أربعة أشخاص وخلصنا، أربعة كراسي عليهم أربعة أشخاص،
+
+74
+00:05:26,490 --> 00:05:30,170
+ففي الحالة هذه الـ order بيفرقش معنا، وين الـ object
+
+75
+00:05:30,170 --> 00:05:34,480
+الأول مكانه، أو في أي اختيار تم اختياره في الاختيار
+
+76
+00:05:34,480 --> 00:05:37,600
+الأول، أو الثاني، أو الثالث، بيفرقش، بيفرقش في الحالة
+
+77
+00:05:37,600 --> 00:05:41,620
+بتاعتنا. فهذه اللي هي الـ combination. هذه جزئية الـ
+
+78
+00:05:41,620 --> 00:05:45,720
+combination. طيب مادام بيفرقش الـ order، بيفرقش في الـ
+
+79
+00:05:45,720 --> 00:05:48,620
+permutation. كنا بنتكلم أنّي بتكلم عن strings
+
+80
+00:05:48,620 --> 00:05:51,180
+وكان دائماً بيقول لكم how many strings، how many
+
+81
+00:05:51,180 --> 00:05:55,840
+strings؟ نتكلم عن order. فالـ order إمّا string، أو
+
+82
+00:05:55,840 --> 00:06:00,720
+sequence. لكن هنا مادام unordered، فأنا بتكلم عن six
+
+83
+00:06:01,800 --> 00:06:06,880
+بنتكلم عن set، أن نختار من الـ.. منكم أربع بنات
+
+84
+00:06:06,880 --> 00:06:10,800
+مثلاً من العدد الإجمالي، بنختار أربع بنات، بيفرقش مين
+
+85
+00:06:10,800 --> 00:06:13,680
+الأول، ومين الثالثة، ومين الرابعة، صحيح؟ مش هتفرق.
+
+86
+00:06:13,680 --> 00:06:16,840
+إحنا ما قلناش أنّ والله اللي هنختاره الأول له ميزة
+
+87
+00:06:16,840 --> 00:06:19,860
+عن الباقيين، خلاص إحنا بنختار ثلاثة، بنختار أربعة..
+
+88
+00:06:19,860 --> 00:06:25,010
+أربعة من اللي موجودين. فالأربعة هدول subset من الـ
+
+89
+00:06:25,010 --> 00:06:29,090
+universe of discourse، صحيح؟ subset من المجموع، لأنّ
+
+90
+00:06:29,090 --> 00:06:32,810
+هم جزء كان من المجموع، ظاهر؟ ففي الحالة هذه الـ
+
+91
+00:06:32,810 --> 00:06:37,930
+permutation، الـ combination بتاعتنا. لما نقول هنا
+
+92
+00:06:37,930 --> 00:06:43,490
+كنا نسمّيها permutation of N، بدنا نختار منهم R، أو
+
+93
+00:06:43,490 --> 00:06:47,010
+permutation لـ R، R permutation، كنا حتّى نسمّيها R
+
+94
+00:06:47,010 --> 00:06:51,030
+permutation from N elements. هنا هنسمّيها C
+
+95
+00:06:51,030 --> 00:06:58,020
+combination، وبدنا نختار منهم R، وبدنا نختار منهم R
+
+96
+00:06:58,020 --> 00:07:07,900
+كويس؟ هدول بكل بساطة بنقدر نقول أنّه T subset of S
+
+97
+00:07:07,900 --> 00:07:14,480
+إيش الـ S، وإيش الـ T؟ الـ S هذه عدد الـ elements اللي
+
+98
+00:07:14,480 --> 00:07:17,340
+عددهم N، هدول اللي هم الـ set للـ elements اللي
+
+99
+00:07:17,340 --> 00:07:22,860
+عددهم N، اللي بدنا نختار منهم. فـ الـ S عندنا اللي هو
+
+100
+00:07:22,860 --> 00:07:27,360
+جدّيش عددكم أنتم الـ.. الـ.. الـ.. الستّ أس، اللي هو
+
+101
+00:07:27,360 --> 00:07:30,320
+أنتم لو بدنا نختار منكم ثلاثة، أو أربعة مثلاً، بدنا
+
+102
+00:07:30,320 --> 00:07:34,620
+نختار ثلاثة، معناه ذلك أنّ أنتم الستّ أس، كويس؟ جدّيش
+
+103
+00:07:34,620 --> 00:07:37,300
+الـ.. الـ.. الـ.. الـ cardinality بتاعتها، عددكم
+
+104
+00:07:37,300 --> 00:07:41,380
+نفس العدد تبعكم اللي هو إيش؟ N، اللي هي قيمتها N.
+
+105
+00:07:41,380 --> 00:07:47,480
+طيب الـ T لأ، الـ T جدّيش عدد هذه الـ subset، subset ستّ
+
+106
+00:07:47,480 --> 00:07:52,000
+جزئية، مجموعة جزئية، اللي بدنا نختارهم، اللي بدنا
+
+107
+00:07:52,000 --> 00:07:55,380
+نختارهم هو جزء منكم، يعني هم الـ subset منكم أصلاً،
+
+108
+00:07:55,380 --> 00:07:57,960
+يعني هم جزء أساساً منكم، فإحنا مش هنروح نختار من
+
+109
+00:07:57,960 --> 00:08:00,400
+الفصل اللي جنبنا، لأ، إحنا هنختار منكم، من عندكم،
+
+110
+00:08:00,400 --> 00:08:04,900
+فإحنا هنختار ثلاثة، الثلاثة هدول هيكونوا العدد R،
+
+111
+00:08:04,900 --> 00:08:07,520
+لما أقول بدنا نختار ثلاثة من خمسة، فأنا بكتبها هي
+
+112
+00:08:07,520 --> 00:08:12,840
+خمسة ثلاثة، ثلاثة من خمسة، فبدنا نختار ثلاثة. هدول
+
+113
+00:08:12,840 --> 00:08:16,200
+الـ cardinality، أو جدّيش عدد الـ elements belonging to
+
+114
+00:08:16,200 --> 00:08:21,310
+the set T، اللي هم الـ set للـ selected items
+
+115
+00:08:21,310 --> 00:08:25,910
+للناس اللي تم اختيارهم في الحالة اللي عندناها، okay؟
+
+116
+00:08:25,910 --> 00:08:30,430
+فهذه هتكون subset. فواضح أنّ هنا combination، أنا
+
+117
+00:08:30,430 --> 00:08:34,770
+بتكلم عن set، النتيجة عندي عبارة عن set، لإنه مش
+
+118
+00:08:34,770 --> 00:08:38,850
+بالضرورة الترتيب، الترتيب مش كتير مهم، والله مين
+
+119
+00:08:38,850 --> 00:08:41,450
+اخترته أول، ومين ثاني، ومين ثالث، مش هتفرق، المهم أنّه
+
+120
+00:08:41,450 --> 00:08:45,690
+في النهاية تم اختياره، خلاص هو داخل الـ set، الترتيب
+
+121
+00:08:45,690 --> 00:08:48,790
+بيفرقش. في الـ permutation لأ، كان الترتيب بيفرق
+
+122
+00:08:48,790 --> 00:08:53,530
+فما كناش نقدر نقول أنّها subset، كنا نقول string، كنا
+
+123
+00:08:53,530 --> 00:08:56,330
+نسمّيه string، هو الناتج، والـ string إحنا عارفين أنّه
+
+124
+00:08:56,330 --> 00:09:00,470
+يعني بيختلف بالترتيب، بالترتيب تبعه بيختلف، ممكن
+
+125
+00:09:00,470 --> 00:09:03,990
+يكون نفس عدد الـ elements، ولكن واحد مكان واحد صار
+
+126
+00:09:03,990 --> 00:09:07,590
+string جديد، string مختلف، لازم يكون له عدد لحاله.
+
+127
+00:09:07,590 --> 00:09:12,770
+فهنا how many strings؟ أنا بتكلم عن.. عن permutation
+
+128
+00:09:12,770 --> 00:09:16,790
+لكن لما بتكلم هنا عن subset.. subset الناتج تبعنا
+
+129
+00:09:16,790 --> 00:09:20,170
+ما بيفرقش، كان الأول، الثاني، الثالث، الرابع، مش هتفرق
+
+130
+00:09:20,170 --> 00:09:25,590
+معنا. ففي الحالة هذه بيكون عندنا combination..
+
+131
+00:09:25,590 --> 00:09:31,510
+combination. طيب الـ combination بتاعتنا هنا هي اللي
+
+132
+00:09:31,510 --> 00:09:37,310
+علاقتها بالـ.. بإيش؟ بالـ permutation مع عدم التكرار
+
+133
+00:09:37,310 --> 00:09:41,940
+كـ حسابات، concept لأ، واضح أنّ هنا بنتكلم عن string
+
+134
+00:09:41,940 --> 00:09:45,820
+هنا بنتكلم عن إيش؟ بنتكلم عن subset.. subset
+
+135
+00:09:45,820 --> 00:09:49,040
+مجموعة جزئية فعلياً.. مجموعة جزئية أنا بدي أختارهم
+
+136
+00:09:49,040 --> 00:09:52,460
+وخلاص، هدول صاروا مجموعة، بس هم فعلياً ينتموا لكم
+
+137
+00:09:52,460 --> 00:09:55,320
+..ينتموا لكم، هم مش.. يعني الثلاثة اللي أختارهم
+
+138
+00:09:55,320 --> 00:09:57,620
+كانوا يدرسون discrete، هم هيدلّوا يدرسوا discrete، و
+
+139
+00:09:57,620 --> 00:09:59,800
+هم ما زالوا يدرسون discrete، ولكن أختارناهم في لجنة
+
+140
+00:09:59,800 --> 00:10:03,100
+أختارناهم في.. في مجموعة، أختارناهم لأي سبب كان
+
+141
+00:10:03,770 --> 00:10:10,410
+فأصبحوا subset. هذه تساوي كقيمة، بدنا نحسبها كمعادلة
+
+142
+00:10:10,410 --> 00:10:18,290
+الـ permutation from n to r، على الـ permutation r r
+
+143
+00:10:18,290 --> 00:10:23,150
+الـ permutation r r، هي أساس أنّها بتختزن لنا عدد
+
+144
+00:10:23,150 --> 00:10:28,350
+التكرارات، عدد مرات التكرار. فهذه بنقدر نقول أنّ هذه
+
+145
+00:10:28,350 --> 00:10:30,690
+بنقدر نختصر منها عدد مرات التكرار.
+
+146
+00:10:33,820 --> 00:10:38,620
+في الحالة اللي عندنا هنا، هيطلع كل الـ term هذا
+
+147
+00:10:38,620 --> 00:10:43,160
+بيساوي، أو الـ permutation هنا هتساوي ماذا؟ ذكرنا
+
+148
+00:10:43,160 --> 00:10:53,020
+القانون، كنا كاتبينها قبل شوية، factorial على R
+
+149
+00:10:57,550 --> 00:11:02,910
+على zero factorial، على zero factorial بواحد. فهنا
+
+150
+00:11:02,910 --> 00:11:06,370
+هتلاقي أنّه هيظهر الـ term كله على بعضه على أساس أنّه
+
+151
+00:11:06,370 --> 00:11:12,710
+N factorial على N minus R factorial، في R factorial.
+
+152
+00:11:12,710 --> 00:11:20,110
+صحيح؟ في R factorial. كويس، المعادلة هذه هنطلع منها
+
+153
+00:11:20,110 --> 00:11:23,950
+بملاحظة مهمة جداً، هنطلع منها بملاحظة مهمة جداً، إيش
+
+154
+00:11:23,950 --> 00:11:27,610
+هي الملاحظة المهمة جداً؟ أنّ الـ combination لـ N و R
+
+155
+00:11:27,610 --> 00:11:36,630
+تساوي تماماً الـ combination لـ N و N minus
+
+156
+00:11:36,630 --> 00:11:42,190
+R. لو
+
+157
+00:11:42,190 --> 00:11:45,850
+بدنا نعود في هذه، هيطلع المعادلة هذه. صحيح؟ طب لو
+
+158
+00:11:45,850 --> 00:11:46,670
+بدنا نعود في هذه
+
+159
+00:11:49,580 --> 00:11:53,500
+هدول اثنين هنعكسهم بس، هدول اثنين هنعكسهم فقط، مش
+
+160
+00:11:53,500 --> 00:11:58,600
+هتغيّر شيء، كل اللي هيصير أنّ المعادلة هذه هتساوي N
+
+161
+00:11:58,600 --> 00:12:06,580
+factorial على R، فعلياً هي الحقيقة أنّها N minus R
+
+162
+00:12:06,580 --> 00:12:11,040
+factorial في R factorial، وهدي المفروض كانت بالعكس
+
+163
+00:12:11,040 --> 00:12:18,360
+وهذي اللي هي R factorial. فهدي خاصة بهدي، وهدي خاصة
+
+164
+00:12:18,360 --> 00:12:24,020
+بهدي. في الآخر مش هتفرق، في الآخر مش هتفرق، والنظرية
+
+165
+00:12:24,020 --> 00:12:27,400
+هذه هنستفيد منها كتير لقدام، هنستفيد منها كويس
+
+166
+00:12:27,400 --> 00:12:31,300
+لقدام، هتلاقي أنّ في بعض الأحيان، بعض terms مش هكون
+
+167
+00:12:31,300 --> 00:12:35,080
+مضطر أحسبهم كلهم، ممكن أضطر أحسب نصّهم، والباقي ما هو
+
+168
+00:12:35,080 --> 00:12:38,740
+مساوي لهم، هي بنفس الفكرة، الباقي هيكون مساوي
+
+169
+00:12:38,740 --> 00:12:43,960
+مساويين لبعض، ليش؟ يعني ليش طلعوا بالشكل هذا فعلاً؟
+
+223
+00:17:03,020 --> 00:17:06,500
+جاعت بقول bit string بس ما تنخدعوش معاه لأنه bit
+
+224
+00:17:06,500 --> 00:17:09,280
+string هو، وجد الأصل أن أنا هفكر بإيش بال
+
+225
+00:17:09,280 --> 00:17:13,400
+permutation خليني أشوف how many bit strings of
+
+226
+00:17:13,400 --> 00:17:16,940
+length four have exactly two ones or exactly two
+
+227
+00:17:16,940 --> 00:17:21,780
+zeros؟ بمعنى ما جدتش عدد الـ bits أو الـ strings اللي
+
+228
+00:17:21,780 --> 00:17:34,600
+ممكن أخدها من four bits عدد الـ
+
+229
+00:17:34,600 --> 00:17:36,100
+strings اللي ممكن أخدها من four
+
+230
+00:17:40,830 --> 00:17:46,690
+هي عندكوا أربعة، الأربعة هدولة بدكوا exactly كده
+
+231
+00:17:46,690 --> 00:17:51,930
+عدد الحالات اللي ممكن يكون فيها two ones exactly
+
+232
+00:17:51,930 --> 00:17:55,970
+two ones بمعنى ما يكونش one واحد وما يكونش three or
+
+233
+00:17:55,970 --> 00:18:01,330
+four، ما يكونش three or four، هذه نفسها مكملة ليش لـ
+
+234
+00:18:01,330 --> 00:18:06,560
+two zeros أو two zeros لأن مادام exactly two ones
+
+235
+00:18:06,560 --> 00:18:12,300
+بالنسبة للأربعة معناته exactly two zeros في الحالة
+
+236
+00:18:12,300 --> 00:18:20,120
+هذه by logic، مادام اللي بنشترط عليها هيكون معاها
+
+237
+00:18:20,120 --> 00:18:27,680
+هيكون معانا الـ one الأولى، الـ one التانية، خلاص أنت
+
+238
+00:18:27,680 --> 00:18:31,860
+حجزت من الأولى فهيكون لها تلاتة
+
+239
+00:18:33,600 --> 00:18:39,400
+Okay، الكلام هذا بيطلع اثنا عشر، exactly هو مش اثنا عشر
+
+240
+00:18:39,400 --> 00:18:46,460
+ليش exactly مش اثنا عشر؟ لأنه ممكن الأولى هنا تكون في
+
+241
+00:18:46,460 --> 00:18:49,200
+الـ location الأول، والتانية في الـ location الأول
+
+242
+00:18:49,200 --> 00:18:55,120
+هذا احتمال مظبوط، طيب ممكن احتمال تاني، الأولى في الـ
+
+243
+00:18:55,120 --> 00:19:01,080
+location التاني، والتانية في الـ location الأول، طب
+
+244
+00:19:01,080 --> 00:19:06,040
+هذا نفسه، واحنا قلنا مش معنيين احنا بالتكرار، خصوصا
+
+245
+00:19:06,040 --> 00:19:10,340
+أن الـ ones بيساووا بعض، فمش هيبين أن هذا غير هذا
+
+246
+00:19:10,340 --> 00:19:13,720
+مادام بتكلم عن أزواج، يعني بمعنى أن الاتنين identical
+
+247
+00:19:13,720 --> 00:19:16,680
+الاتنين متماثلين، فهنا في الحالة هذه مش هينفع الـ
+
+248
+00:19:16,680 --> 00:19:22,960
+order، رغم أن هو كاتب الـ string، بس السؤال مش هتفرق
+
+249
+00:19:22,960 --> 00:19:25,680
+هنا مين الـ one اللي ظهرت هنا، واللي ظهرت هنا؟ لإنه
+
+250
+00:19:25,680 --> 00:19:30,630
+مش هيبين أن في فرق أصلا، فعليا مش هيبين أنه في فرق
+
+251
+00:19:30,630 --> 00:19:39,930
+بمعنى لو بتقولوا مش ones واحدة A، وواحدة B، لاحظوا
+
+252
+00:19:39,930 --> 00:19:44,630
+هنا هيختلف، هتصير هنا الـ A، وهنا الـ B، هنا بتصير B
+
+253
+00:19:44,630 --> 00:19:47,750
+هنا A، طبعا عند الـ A والـ B بيساووا بعض
+
+254
+00:19:50,620 --> 00:19:55,040
+فإذا هنا أصبحت، رغم أن هو طالب bit string، بس أنا
+
+255
+00:19:55,040 --> 00:19:58,540
+بتكلم هنا عن combination، بمعنى جدش الحالات اللي
+
+256
+00:19:58,540 --> 00:20:02,960
+ممكن تصير فيها، في حالة بالشكل هذا، مضاعفة، فالرقم
+
+257
+00:20:02,960 --> 00:20:09,160
+اللي بيطلع هنقسمه على اثنين، على اثنين، لأن الـ
+
+258
+00:20:09,160 --> 00:20:13,640
+two ones دول ممكن يجوا عكس بعض، عكس بعض، فالحالة دي
+
+259
+00:20:13,640 --> 00:20:17,170
+هما الاثنين بيساووا بعض، أساسا هما الاثنين أصلا بيساووا
+
+260
+00:20:17,170 --> 00:20:21,730
+بعض، فلاحظوا أن في هيك حالة هيطلع عندكوا n
+
+261
+00:20:21,730 --> 00:20:29,310
+factorial على r factorial في n minus r factorial
+
+262
+00:20:29,310 --> 00:20:35,450
+فالـ n factorial جدش؟ جدش الـ n؟ أربعة، أربعة، أنا
+
+263
+00:20:35,450 --> 00:20:40,930
+بتكلم عن أربعة، و r اثنين، أنا بتكلم عن two ones
+
+264
+00:20:40,930 --> 00:20:49,050
+فعندنا اثنين factorial، وهنا أربعة ناقص اثنين، اثنين
+
+265
+00:20:49,050 --> 00:20:53,890
+factorial، هتساوي أربعة وعشرين على اثنين في اثنين
+
+266
+00:20:53,890 --> 00:20:58,610
+هتساوي ستة، وهو ده الحل الصحيح، وميعطيكوا هاي
+
+267
+00:20:58,610 --> 00:21:03,410
+الحالات الستة الممكنة، واللي ما فيش غيرهم اللي وجد
+
+268
+00:21:03,410 --> 00:21:07,810
+غيرهم، فعليا اللي وجد، فعليا غيرهم، اللي وجد، غيرهم
+
+269
+00:21:07,810 --> 00:21:11,250
+أنها تكون صفر صفر واحد واحد، لأن هدولة بدلوا بعض
+
+270
+00:21:13,100 --> 00:21:18,600
+مالهاش معنى، one ما كان one، فالاثنين بيساووا بعض، ففي
+
+271
+00:21:18,600 --> 00:21:21,620
+الحالة هذه مش هيفيد التكرار في الحالة اللي .. اللي
+
+272
+00:21:21,620 --> 00:21:25,300
+عندنا هنا، وهي ميعطيكوا، وموضحلكوا أن لو افترضتوا
+
+273
+00:21:25,300 --> 00:21:29,300
+أن واحد من الـ two a's هدولة، واحد منهم a، والتاني b
+
+274
+00:21:29,300 --> 00:21:31,980
+هيبين الاختلاف .. هيبين الاختلاف، احنا عندنا هنا الـ
+
+275
+00:21:31,980 --> 00:21:36,620
+a والـ b بيساووا .. بيساووا بعض، okay، كمان combination
+
+276
+00:21:36,620 --> 00:21:43,610
+example، how many strings of .. of size ten ممكن
+
+277
+00:21:43,610 --> 00:21:47,590
+واضحة ما فيش فيها كتير، الـ size بتاعتنا ten للـ bit
+
+278
+00:21:47,590 --> 00:21:52,910
+string contains four ones، باينة ما فيش فيها كتير
+
+279
+00:21:52,910 --> 00:21:57,310
+يعني الـ combination عشرة أربعة، عندكوا string في
+
+280
+00:21:57,310 --> 00:22:01,590
+عشرة locations، جدش عدد الطرق اللي ممكن يكون فيها
+
+281
+00:22:01,590 --> 00:22:07,930
+أربعة ones، طبعا اتفقنا أن الـ ones واحد مكان واحد
+
+282
+00:22:07,930 --> 00:22:11,820
+مش هيفرق فاحنا نتكلم عن combination هنا، We need to
+
+283
+00:22:11,820 --> 00:22:16,300
+form a committee of seven people، محتاجين نعمل لجنة
+
+284
+00:22:16,300 --> 00:22:18,960
+من سبع أشخاص، السبع أشخاص هدولة لازم يكون منهم
+
+285
+00:22:18,960 --> 00:22:22,660
+تلاتة from math، من الناس اللي بيشتغلوا في
+
+286
+00:22:22,660 --> 00:22:26,860
+الرياضيات، نفترض الـ staff من قسم الرياضيات أربعة، تلت
+
+287
+00:22:26,860 --> 00:22:31,180
+مدرسين من الرياضيات، four from computer science to
+
+288
+00:22:31,180 --> 00:22:36,280
+develop a discrete math course، بدنا نطور المصاد
+
+289
+00:22:36,280 --> 00:22:40,540
+طبعا، فقلنا بدنا نعمل لجنة من سبع أشخاص، السبع
+
+290
+00:22:40,540 --> 00:22:44,800
+أشخاص هدولة تلاتة من الرياضيات، وأربعة من الـ
+
+291
+00:22:44,800 --> 00:22:48,520
+computer science، على أساس إنه يطوروا، طيب روحنا على
+
+292
+00:22:48,520 --> 00:22:53,990
+قسم الرياضيات، وجدنا إنه في عنده تسعة staffs، عنده
+
+293
+00:22:53,990 --> 00:22:56,890
+تسعة مدرسين فعليا في الـ .. في الـ .. فصار بدنا
+
+294
+00:22:56,890 --> 00:23:02,030
+نختار تلاتة من تسعة، okay، روحنا على قسم الـ ..
+
+295
+00:23:02,030 --> 00:23:05,370
+الـ computer science، لجينا أن في عنده 11 staff أو
+
+296
+00:23:05,370 --> 00:23:10,830
+11 مدرس، فصار بدنا نختار أربعة من 11، أربعة من 11
+
+297
+00:23:10,830 --> 00:23:15,370
+أكم طريقة بقدر أشكل فيها اللجنة؟ أكم طريقة في عندنا
+
+298
+00:23:15,370 --> 00:23:20,410
+عشان نشكل فيها اللجنة؟ فهتكون واضحة أن في عندنا
+
+299
+00:23:25,830 --> 00:23:32,090
+combination، لـ .. نقولها كأن فيهم تسعة، تسعة، نبدأ
+
+300
+00:23:32,090 --> 00:23:37,610
+بالرياضيات، تسعة بدنا نختار منهم تلاتة، صحيح؟ وفي
+
+301
+00:23:37,610 --> 00:23:41,790
+عندي combination لـ أحد عشر، بدنا نختار منهم أربعة
+
+302
+00:23:41,790 --> 00:23:46,790
+okay، لحظة، إيش علاقتهم مع بعض؟ يعني كيف بدي أجمعهم؟
+
+303
+00:23:46,790 --> 00:23:49,830
+أضربهم، أقسمهم، إيش أسوي فيهم؟ okay، طلعنا هذا، و
+
+304
+00:23:49,830 --> 00:23:54,320
+طلعنا هذا، طب خلينا نفهم شوي شوي هالوقت، لو في
+
+305
+00:23:54,320 --> 00:24:00,940
+الحالة الأولى، اخترنا من التسعة هدولة A,B,C, D,E
+
+306
+00:24:00,940 --> 00:24:05,880
+و E, F، وده ما اخترناهمش، اخترنا الأشخاص A,B,C، كويس، و
+
+307
+00:24:05,880 --> 00:24:10,220
+من هنا عملنا كل الـ combination بتاعتنا، صار في عندنا
+
+308
+00:24:10,220 --> 00:24:15,080
+هاي تلاتة، ضال الأربعة اللي ضايلين، اللهم جدش عدد
+
+309
+00:24:15,080 --> 00:24:20,400
+ways ممكن اختارهم بهذا الشكل؟ مضروبين
+
+310
+00:24:21,740 --> 00:24:26,880
+بمعنى للـ A والـ B والـ C هم نفس الأشخاص هتتكرر معانا
+
+311
+00:24:26,880 --> 00:24:35,800
+أكم حالة؟ C 11 4، طيب ممكن بعد C 11 4 أختار هنا A B
+
+312
+00:24:35,800 --> 00:24:48,710
+و D برضه كمان C 11 4، ممكن يكون E، معناه تضرب، صحيح؟
+
+313
+00:24:48,710 --> 00:24:50,710
+معناته الـ combination هنا في الحالة التاعتنا
+
+314
+00:24:50,710 --> 00:24:55,770
+هنعمل تربيع، لأن هدولة هيتغيروا لكل شخص أو لكل تلات
+
+315
+00:24:55,770 --> 00:24:58,770
+اختيارات، هنا اختار أول، تاني، تالت، خلاص هدول هيدلوا
+
+316
+00:24:58,770 --> 00:25:07,660
+ثابتين، لـ C 11 4 أو لـ combination اختيار 4 من 11 جدش
+
+317
+00:25:07,660 --> 00:25:09,560
+قيمتهم 1000، 2000، 5000، 5000، 5000، 5000، 5000،
+
+318
+00:25:09,560 --> 00:25:10,780
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+319
+00:25:10,780 --> 00:25:11,340
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+320
+00:25:11,340 --> 00:25:12,600
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+321
+00:25:12,600 --> 00:25:12,720
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+322
+00:25:12,720 --> 00:25:13,280
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+323
+00:25:13,280 --> 00:25:14,140
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+324
+00:25:14,140 --> 00:25:15,920
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+325
+00:25:15,920 --> 00:25:18,900
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+326
+00:25:18,900 --> 00:25:19,780
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+327
+00:25:19,780 --> 00:25:19,860
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+328
+00:25:19,860 --> 00:25:23,880
+5000، 5000، 5000، 5000، 5000،
+
+329
+00:25:25,850 --> 00:25:29,530
+فمعنى ذلك أنه عشان نجيب الـ total كله على بعضه،
+
+330
+00:25:29,530 --> 00:25:33,790
+هيكون ضرب الاثنين، combination تسعة تلاتة في
+
+331
+00:25:33,790 --> 00:25:37,510
+combination أحد عشر أربعة، في أحد عشر أربعة، بيطلع في
+
+332
+00:25:37,510 --> 00:25:41,450
+عندنا سبعة وعشرين ألف وسبع مئة وعشرين طريقة،
+
+333
+00:25:41,450 --> 00:25:44,610
+هذا طبعا في حال افترضنا أنه الكل متساوي في الفرصة
+
+334
+00:25:44,610 --> 00:25:48,370
+أنه يكون في إيش؟ في المجموعة، في مجموعة التطوير
+
+335
+00:25:51,640 --> 00:25:56,740
+suppose you flip a fair coin n times، عندكوا coin
+
+336
+00:25:56,740 --> 00:26:00,480
+اللي هي العملة المعدنية، وبتعملوا flipping
+
+337
+00:26:00,480 --> 00:26:05,240
+بتعملوها، اللي هي الطرة هادي، بترموها، وبتكونوا
+
+338
+00:26:05,240 --> 00:26:07,260
+تشوفوا إيش اللي بيظهر .. اللي حيظهر عندكم، فانتوا
+
+339
+00:26:07,260 --> 00:26:12,480
+في عندكم head or tail، الـ head or tail أو الـ .. إيش
+
+340
+00:26:12,480 --> 00:26:18,440
+بيسموها؟ الصورة والكتابة .. صورة وكتابة، How many
+
+341
+00:26:18,440 --> 00:26:23,900
+different ways can you get no heads؟ with no heads
+
+342
+00:26:23,900 --> 00:26:27,220
+ما فيش heads عندكم، فانتم عندكم من n مرة
+
+343
+00:26:27,220 --> 00:26:34,900
+combination من n مرة، zero من n مرة، في عندكم zero
+
+344
+00:26:34,900 --> 00:26:38,560
+في عندكم zero، طيب هذه كده هتطلع قيمتها؟
+
+345
+00:26:41,870 --> 00:26:45,650
+واحد، هتطلع واحد، لأن فعلا أنتم عندكوا احتمالات كتيرة
+
+346
+00:26:45,650 --> 00:26:50,710
+بس أنه كله ما فيش فيهم أي head، هذا احتمال واحد، حالة
+
+347
+00:26:50,710 --> 00:26:54,050
+واحدة، فهذا واضح أنّه هتطلع واحد، على اعتبار أنها
+
+348
+00:26:54,050 --> 00:27:00,610
+تساوي n factorial على n minus r factorial في r
+
+349
+00:27:00,610 --> 00:27:06,990
+factorial، فهذا zero، هذه هتطلع n، مع n واحد، تتكلموا
+
+350
+00:27:06,990 --> 00:27:14,440
+أنها حالة واحدة، إن كلهم يطلعوا no heads، okay
+
+351
+00:27:14,440 --> 00:27:19,980
+exactly one head، أصبحت سهلة، أصبحت سهلة combination
+
+352
+00:27:19,980 --> 00:27:30,200
+n، طيب two heads، are heads، okay، at least two heads
+
+353
+00:27:30,200 --> 00:27:33,620
+تمام
+
+354
+00:27:33,620 --> 00:27:37,680
+اثنين أو تلاتة أو أربعة أو خمسة، يعني c اثنين، عفوا
+
+355
+00:27:37,680 --> 00:27:38,000
+n
+
+356
+00:27:46,840 --> 00:27:54,140
+n أربعة، طب
+
+357
+00:27:54,140 --> 00:27:55,960
+معقول هيك نكتبها بالشكل هذا بده قيمة؟
+
+358
+00:28:00,410 --> 00:28:02,590
+ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+359
+00:28:02,590 --> 00:28:03,670
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+360
+00:28:03,670 --> 00:28:05,290
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+361
+00:28:05,290 --> 00:28:05,550
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+362
+00:28:05,550 --> 00:28:06,030
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+363
+00:28:06,030 --> 00:28:07,110
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+364
+00:28:07,110 --> 00:28:10,010
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+365
+00:28:10,010 --> 00:28:11,350
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+366
+00:28:11,350 --> 00:28:18,310
+الواحد .. ناخد الواحد .. ناخد الواحد
+
+367
+00:28:18,310 --> 00:28:22,170
+.. ناخد الواحد .. ناخد الواحد ..
+
+368
+00:28:23,530 --> 00:28:29,650
+كل الحالات الممكنة، واطرحوا منها حالة الصفر والواحد
+
+369
+00:28:29,650 --> 00:28:33,610
+طب كل احتمالات الممكنة هي كده؟
+
+370
+00:28:44,470 --> 00:28:49,150
+هذه عشر حالات، أو عشر مرات بتعمل flipping للـ coin
+
+371
+00:28:49,150 --> 00:28:53,030
+عشر مرات بتعمل flipping للـ coin، العشر مرات أول
+
+372
+00:28:53,030 --> 00:28:57,750
+مرة إيش في عنده احتمالات؟ رميتها وأنا .. وهو
+
+373
+00:28:57,750 --> 00:29:02,330
+نازل وأنا مستني إيش؟ head or tail، معنى ذلك عندك ..
+
+374
+00:29:02,330 --> 00:29:06,110
+عندنا احتمالين فقط، فإنا كل احتمالات الاثنين هذه الها
+
+375
+00:29:06,110 --> 00:29:12,250
+احتمالين، طيب التانية احتمالين برضه، فإذا أنا من
+
+376
+00:29:12,250 --> 00:29:16,630
+مرتين، اعمل team of living، أكم combination بقدر
+
+377
+00:29:16,630 --> 00:29:22,340
+اعمل؟ أو أكم حالة بقدر اعمل؟ نقدر نعمل أربعة، إنّ no
+
+378
+00:29:22,340 --> 00:29:27,200
+head, no head، أو head, no head، أو no head, head، أو
+
+379
+00:29:27,200 --> 00:29:31,780
+two heads، أو two heads، فعندنا أربعة حالات، في الحالة
+
+380
+00:29:31,780 --> 00:29:34,500
+هذه، صار عندنا اثنين تربيع، اثنين على اعتبار إني
+
+381
+00:29:34,500 --> 00:29:40,280
+بتكلم عن محاولتين، طب لما يصيروا تلاتة؟ طب لما
+
+382
+00:29:40,280 --> 00:29:48,260
+يصيروا n؟ هذا كل احتمالات الممكنة، هنشيل منها كل
+
+383
+00:29:48,260 --> 00:29:56,500
+احتمالات الممكنة، اثنين تربيع، هنشيل منها الـ C N Zero
+
+384
+00:29:56,500 --> 00:30:
+
+445
+00:34:46,690 --> 00:34:50,710
+zero factorial قيمتها بواحد، فهيظل ايش n minus zero
+
+446
+00:34:50,710 --> 00:34:52,870
+factorial فهي n factorial, n factorial على n
+
+447
+00:34:52,870 --> 00:34:56,390
+factorial هيطلع بواحد، فدائما هتلاقوا واحد، وهذا
+
+448
+00:34:56,390 --> 00:34:58,490
+اللي خلاني دائما وأنا ببدأ بحكي ايش
+
+449
+00:35:01,440 --> 00:35:04,400
+عرفتوا كيف عرفناها؟ ده على طول بيطلع معايا واحد على
+
+450
+00:35:04,400 --> 00:35:08,260
+السري بحط أولها واحد، وآخرها واحد، لأن آخرها ما هو
+
+451
+00:35:08,260 --> 00:35:13,100
+مكمل للأولى، مش هو نفسه مكمل للأولى كمان مرة
+
+452
+00:35:13,100 --> 00:35:16,980
+القانون المهم اللي لازم تكونوا واخدين بالكوا منه n
+
+453
+00:35:16,980 --> 00:35:25,340
+الـ n هنا combination n و r بيساوي
+
+454
+00:35:31,310 --> 00:35:35,190
+فلما ببدأ بصفر هي نفسها في حالة الـ N، وهذه الأخيرة
+
+455
+00:35:35,190 --> 00:35:39,050
+كانت في حالة الـ N، هنا بدأ هنا من صفر to N، فإذا
+
+456
+00:35:39,050 --> 00:35:41,810
+آخر term برضه الـ coefficient تبعه هيكون مشابه لأول
+
+457
+00:35:41,810 --> 00:35:47,630
+term، مشابه لـ لأول .. لأول term، okay X to the
+
+458
+00:35:47,630 --> 00:35:51,790
+power N minus J، ف أنا دايما ببدأ بالصفر، فببدأ بـ X
+
+459
+00:35:51,790 --> 00:35:55,070
+to the power N، فعلا في الـ second هاني بدأت تبقى X
+
+460
+00:35:55,070 --> 00:36:02,070
+تربيع، بعد هيك بتصير واحد، فصارت X<sup>N</sup> minus واحد، وهنا
+
+461
+00:36:02,070 --> 00:36:06,970
+صارت تبدأ Y بواحد، بحيث أن مجموعهم يظل N، اللي هي
+
+462
+00:36:06,970 --> 00:36:09,790
+second order، بده يظل مجموعهم N، third order بده يظل
+
+463
+00:36:09,790 --> 00:36:13,890
+مجموعهم فوق المجموع دايما تلاتة، fourth بده دايما
+
+464
+00:36:13,890 --> 00:36:17,970
+أربعة، five بده يظل دايما خمسة، okay، بتتوسع بالشكل
+
+465
+00:36:17,970 --> 00:36:25,250
+هذا N و Zero للـ X to the power N، N واحد، X<sup>-1</sup>
+
+466
+00:36:25,250 --> 00:36:34,370
+و Y، لعندما نستمر لمين؟ لـ N، و N هذه في حالة مين؟ Y
+
+467
+00:36:34,370 --> 00:36:42,410
+to the power N، Y to the power N، okay، فهدول الـ
+
+468
+00:36:42,410 --> 00:36:45,090
+coefficients للـ binomial
+
+469
+00:36:48,020 --> 00:36:51,400
+خلونا نشوف مثل كيف نستطيع أن نشتغل عليها، what's
+
+470
+00:36:51,400 --> 00:36:54,960
+the coefficient of X to the power 12 أو X to the
+
+471
+00:36:54,960 --> 00:37:02,240
+power 12 في X to the power 13، بدنا الحد X to the
+
+472
+00:37:02,240 --> 00:37:05,240
+power 12 و X to the power 13، جداش الـ coefficient
+
+473
+00:37:05,240 --> 00:37:09,000
+تبعه؟ طيب، واضح أن إحنا الـ order اللي بنشتغل عليها
+
+474
+00:37:09,000 --> 00:37:13,810
+كلها على بعض، جداش مجموعها خمسة وعشرين، وهي لما كنا
+
+475
+00:37:13,810 --> 00:37:17,290
+هنا نقول واحد وواحد، هذا واضح أن هذا أحد حدود
+
+476
+00:37:17,290 --> 00:37:22,690
+second order، طب معناه ذلك أن هذا أحد حدود .. أحد
+
+477
+00:37:22,690 --> 00:37:25,630
+حدود مين؟ الخمسة والعشرين .. الخمسة والعشرين، هذا أحد
+
+478
+00:37:25,630 --> 00:37:28,150
+حدود الخمسة والعشرين، فأنا automatically عارف في
+
+479
+00:37:28,150 --> 00:37:32,210
+الحالة أن الـ N عندي تساوي خمسة وعشرين، يدوم حتى
+
+480
+00:37:32,210 --> 00:37:37,590
+ما يقولك بس بضل أنا محتاج .. محتاج المعادلة ليش؟
+
+481
+00:37:37,590 --> 00:37:40,960
+محتاج المعادلة عشان أتأكد بس أن هل في أي .. أي
+
+482
+00:37:40,960 --> 00:37:44,040
+أجزاء أو أي قيم values مضروبة في الـ X والـ Y، ولا
+
+483
+00:37:44,040 --> 00:37:47,620
+لأ، لأن هذا هيغير النتيجة، هيغير تماما قيمة النتيجة
+
+484
+00:37:47,620 --> 00:37:50,700
+واللازم مش مضروب، خلاص الـ coefficient على طول هو الـ
+
+485
+00:37:50,700 --> 00:37:54,220
+combination، هو الـ combination، ففي الحالة دي هتكون
+
+486
+00:37:54,220 --> 00:37:59,360
+هي الـ combination، بتعتمد
+
+487
+00:37:59,360 --> 00:38:10,220
+25 و 12 أو 25 و 13، لأن الاتنين هيكملوا بعض، واحدة
+
+488
+00:38:10,220 --> 00:38:15,100
+هتكون R، والتانية هتكون N-R، واحدة هيك، وواحدة هيك
+
+489
+00:38:15,100 --> 00:38:19,720
+ف أنتو بتاخدوا الـ power 12 بمشي الحال، وأنتم بتاخدوا
+
+490
+00:38:19,720 --> 00:38:22,800
+الـ power 13 برضه بمشي الحال، برضه هيمشي الحال في
+
+491
+00:38:22,800 --> 00:38:27,400
+الآخر، هيطلعوا بيساووا بعض، عرفتوا إني مش عارفتهم
+
+492
+00:38:27,400 --> 00:38:31,840
+برضه؟ هين شوية شوية عرفتهم، ولو كنت سر الـ .. كيف ..
+
+493
+00:38:31,840 --> 00:38:35,780
+بدكوا بضلني بكمل، بكمل للآخر كمان، بس هين عرفنا ده
+
+494
+00:38:35,780 --> 00:38:40,770
+ما ببدأ بواحد وبنتهي بواحد، عرفنا ليش دايما كل رقم
+
+495
+00:38:40,770 --> 00:38:43,310
+بيكون متكرر، بنعرف أنه لازم يتكرر على ناحية تانية، عرفنا
+
+496
+00:38:43,310 --> 00:38:46,990
+ليش؟ طيب، برضه في أرقام زيادة بتبين مع أن الوجد برضه
+
+497
+00:38:46,990 --> 00:38:53,230
+جاية، هنعرفها كيف كويس، زي ما قلنا، خلاص بنختار 12 و
+
+498
+00:38:53,230 --> 00:38:56,410
+من 25، وبنحسب عليها، بنختار الـ combination بتاعتنا
+
+499
+00:38:56,410 --> 00:38:59,810
+فهيطلع عندنا خمسة مليون ومئتين ألف وثلاثمية، هذا
+
+500
+00:38:59,810 --> 00:39:04,430
+الـ coefficient لمين؟ للحد X to the power إثني عشر في Y
+
+501
+00:39:04,430 --> 00:39:05,690
+to the power ثلاثة عشر
+
+502
+00:39:08,170 --> 00:39:12,890
+طيب، هالوقت مطلوب برضه نفس الكلام، نفس الـ term، بدنا
+
+503
+00:39:12,890 --> 00:39:19,050
+نجيب الـ coefficient بس لمعادلة 2x-3y، كله to
+
+504
+00:39:19,050 --> 00:39:23,130
+the power 25، طيب
+
+505
+00:39:23,130 --> 00:39:29,320
+إحنا الـ combination بتمشي معايا في حالة إن الـ
+
+506
+00:39:29,320 --> 00:39:32,640
+multiplier لكل واحدة منهم، الـ multiplier واحد واحد
+
+507
+00:39:32,640 --> 00:39:36,220
+بيمشي الحالة، بس لما يكون الـ multiplier مختلف، الـ
+
+508
+00:39:36,220 --> 00:39:38,760
+coefficient بيصير من الأساس مختلف، واضح إنه لأ
+
+509
+00:39:38,760 --> 00:39:41,880
+هيختلف الموضوع، ففي الحالة دي بحولها للصورة اللي
+
+510
+00:39:41,880 --> 00:39:46,020
+أنا حافظها، الصورة اللي أنا حافظها x و y، لأ أنا
+
+511
+00:39:46,020 --> 00:39:52,030
+عندي هنا 2x، فبحط 2x عبارة عن a مثلا، طيب minus
+
+512
+00:39:52,030 --> 00:39:56,610
+three y، بحطهم عبارة عن b، وبقول إن هي هي a زائد
+
+513
+00:39:56,610 --> 00:39:59,430
+b to the power خمسة وعشرين، هذه automatically
+
+514
+00:39:59,430 --> 00:40:05,290
+هتساوي بدون أي مشاكل خمسة وعشرين وtwelve، فأنا
+
+515
+00:40:05,290 --> 00:40:08,990
+بجد اختار إثني عشر من خمسة وعشرين، أو الـ
+
+516
+00:40:08,990 --> 00:40:13,410
+combination لخمسة وعشرين وإثني عشر، آه طيب، هذا الكلام
+
+517
+00:40:13,410 --> 00:40:19,490
+لـ a و b، بس هو مش طالب من a و b، هو طالب إنه الحد x to
+
+518
+00:40:19,490 --> 00:40:23,030
+the power 12 و y to the power 13، طيب، ايش الفرق بين
+
+519
+00:40:23,030 --> 00:40:29,310
+الـ x والـ a؟ اتنين، طيب، الاتنين هذه لما نقول خمسة و
+
+520
+00:40:29,310 --> 00:40:34,310
+عشرين أو a to the power خمسة وعشرين، وأنا عارف أن
+
+521
+00:40:34,310 --> 00:40:39,290
+الـ a عبارة عن اتنين x to the power خمسة وعشرين
+
+522
+00:40:39,290 --> 00:40:43,830
+فإذا هذه بتساوي، أنا بدي الـ term، okay، الـ term
+
+523
+00:40:43,830 --> 00:40:48,670
+بنكررها بعدين، بدي الـ term x<sup>25</sup>، معناها
+
+524
+00:40:48,670 --> 00:40:54,830
+ذلك أنه جداش القيمة 2 برضه to the power 25، طيب
+
+525
+00:40:54,830 --> 00:40:59,990
+بنظبط الكلام هذا، وجد على المثال تبعنا 12، لأن هو
+
+526
+00:40:59,990 --> 00:41:05,130
+طالب من ايه؟ 12، أنا بأضربه الـ 12، 12 للـ ايه؟ 12
+
+527
+00:41:05,130 --> 00:41:18,120
+للـ 2x، و12 للـ 2، و12 للـ .. okay، هذا الـ term هو أصلا
+
+528
+00:41:18,120 --> 00:41:23,160
+هي موجود في الـ coefficient بتاعتي، هو اللي أنا طالبه
+
+529
+00:41:23,160 --> 00:41:26,360
+أصلا، لأنه في الآخر بدي أميزه بـ X to the power 12 و
+
+530
+00:41:26,360 --> 00:41:29,700
+Y to the power 13، بدي الـ term اللي جدامه، فالـ term
+
+531
+00:41:29,700 --> 00:41:35,680
+اللي جدامه هيكون فيه 2 to
+
+532
+00:41:35,680 --> 00:41:43,360
+the power 12، هيخلصنا X، ضالة Y، Y بنفس الطريقة، بنفس
+
+533
+00:41:43,360 --> 00:41:49,160
+الفكرة، هتكون minus 3 to the power 13، بنضرب هدول الـ
+
+534
+00:41:49,160 --> 00:41:51,600
+term هذا كله مع بعض، وبنجمعه، بتلا هو الـ
+
+535
+00:41:51,600 --> 00:41:54,740
+coefficient لمين؟ لـ X to the power 12 في Y to the
+
+536
+00:41:54,740 --> 00:42:01,300
+power 13، واضح اللي الجزئية في الآخر هذه؟ الجزئية
+
+537
+00:42:01,300 --> 00:42:05,040
+في الآخر سهلة، مش مشكلة، الـ coefficient بس بتضربوه
+
+538
+00:42:05,040 --> 00:42:09,400
+خارج الـ combination، خارج الـ combination طبعا
+
+539
+00:42:09,400 --> 00:42:15,440
+تحافظوا على الـ power، تحافظوا على الـ power طبعا
+
+540
+00:42:15,440 --> 00:42:22,260
+بتطلع لكم تقريبا 34 في 10 to the power 15، أو
+
+541
+00:42:22,260 --> 00:42:27,080
+minus، الحقيقة فيها minus، تقريبا minus 34 في 10 to
+
+542
+00:42:27,080 --> 00:42:28,540
+the power 15
+
+543
+00:42:30,710 --> 00:42:34,210
+كنتائج أو كنظريات ناتجة من الموضوع هذا، ممكن يطلع
+
+544
+00:42:34,210 --> 00:42:41,690
+كذا نظرية، منهم إن
+
+545
+00:42:41,690 --> 00:42:46,430
+2<sup>N</sup> بتساوي summation from zero
+
+546
+00:42:46,430 --> 00:42:52,290
+to N للـ combination N وJ، من أين جبناها؟ كل اللي
+
+547
+00:42:52,290 --> 00:42:56,090
+عملناه، فرضنا X بتساوي واحد، وY بتساوي واحد، أنا لو
+
+548
+00:42:56,090 --> 00:43:00,850
+عرفت إن X زائد Y to the power n بتساوي الـ summation
+
+549
+00:43:00,850 --> 00:43:04,230
+بتاعتنا، والـ coefficient هادي، أنا مقتنع إن هي فعلا
+
+550
+00:43:04,230 --> 00:43:07,290
+هي الـ coefficient بتاعتنا، بس مضروبة في الـ x والـ y
+
+551
+00:43:07,290 --> 00:43:11,810
+بالـ powers بتاعتهم، طب لما حط هادي بواحد زائد واحد
+
+552
+00:43:11,810 --> 00:43:20,050
+صارت اتنين، أصبح هنا عندي اتنين، وهنا واحد واحد
+
+553
+00:43:20,050 --> 00:43:24,430
+to the power أي شيء، حيطلع واحد، بيظل قيمته بواحد، okay
+
+554
+00:43:24,430 --> 00:43:30,220
+فبيظل عندي مجموع الكوير الـ combination، فبرضه هذه
+
+555
+00:43:30,220 --> 00:43:33,000
+سهلة جدا، كل اللي بتعمله بس هذه المعادلة الرئيسية
+
+556
+00:43:33,000 --> 00:43:38,180
+بتاعتنا، عوض X بواحد، و Y بواحد، طبعا واضح إن تقدروا
+
+557
+00:43:38,180 --> 00:43:41,800
+تعملوا special cases، جد ما بدكم، فيها حطوا X قيمته
+
+558
+00:43:41,800 --> 00:43:45,060
+كذا، و Y قيمته كذا، بتطلعوا كتير نظريات لحالكم
+
+559
+00:43:45,060 --> 00:43:48,960
+هتطلعوها هنا، نفس الكلام، هتلاقوا
+
+560
+00:43:53,710 --> 00:44:01,270
+Summation لـ (-1)<sup>j</sup> في الـ combination n
+
+561
+00:44:01,270 --> 00:44:06,330
+و j، equal to 0، منطقي جدا، ليش؟ j هذه الفردي هتطلع
+
+562
+00:44:06,330 --> 00:44:11,590
+القيمة هذه بالسالب، زوجي موجب، وفي نفس الوقت أنا
+
+563
+00:44:11,590 --> 00:44:14,650
+عارف إن هذه مساوية تماما ل
+
+564
+00:44:18,030 --> 00:44:20,350
+فواحدة term هيطلع موجب، وterm هيطلع سالب، وterm
+
+565
+00:44:20,350 --> 00:44:22,890
+هيطلع موجب، وterm هيطلع سالب، وفي الآخر هيطلع كله
+
+566
+00:44:22,890 --> 00:44:27,470
+بيساوي .. بيساوي zero، من وين اجت؟ برضه بسيطة جدا، كل
+
+567
+00:44:27,470 --> 00:44:32,890
+اللي هتعملوه، في x زائد y to the power أي .. أي n
+
+568
+00:44:32,890 --> 00:44:36,530
+افرضوا هذه بواحد، وهذه بسالب واحد، هي الصفر تبعكم
+
+569
+00:44:36,530 --> 00:44:41,470
+عوضوا هنا واحد، سالب واحد، هيظهر الـ minus one، حيظهر
+
+570
+00:44:41,470 --> 00:44:43,830
+الـ minus one، طبعا الـ one ما حطيناهوش، والأصل فيه كمان
+
+571
+00:44:43,830 --> 00:44:47,210
+one، لأنه بتاعة الـ X، بس one to the power أي شيء مش
+
+572
+00:44:47,210 --> 00:44:52,290
+هيغير، فشالنا هنا، طبعا برضه بتقدروا تحطوا واحد و
+
+573
+00:44:52,290 --> 00:44:57,510
+اتنين، فبتطلع قانون جديد، كل هذه special case من الـ
+
+574
+00:44:57,510 --> 00:45:04,240
+general case اللي أنتم اخذتوها، okay، الأهم واللي
+
+575
+00:45:04,240 --> 00:45:07,960
+هالوقت هيبين كيف أنا اشتغلت الموضوع هذا، كيف عرفتم
+
+576
+00:45:07,960 --> 00:45:12,580
+على طول، وهالوقت هيبين، ها هي واحد، خمسة، عشرة، خمسة،
+
+577
+00:45:12,580 --> 00:45:21,840
+واحد، okay، واضحة صح؟ بيانات حلوة جدا، هالوقت دايما
+
+578
+00:45:21,840 --> 00:45:26,040
+n زائد واحد، j combination لـ n زائد واحد، j، بيساوي
+
+579
+00:45:26,040 --> 00:45:32,360
+n<sub>j-1</sub> زائد n<sub>j</sub>
+
+580
+00:45:34,420 --> 00:45:38,800
+طيب، ايش معنى؟ معنى ذلك إنه هذه احنا قلنا هنا الـ
+
+581
+00:45:38,800 --> 00:45:45,300
+zero order، نمحي هدول عشان نضلنا مع هدول، هذه كانت
+
+582
+00:45:45,300 --> 00:45:49,940
+zero order، هي الـ first order، هذه الـ first هي الـ
+
+583
+00:45:49,940 --> 00:45:58,550
+second، هي الـ third، هي الـ fourth، وهي الـ fifth، okay، لو
+
+584
+00:45:58,550 --> 00:46:02,890
+بدنا الـ term هذا، احنا بتكلم عنه الـ third، فأنا
+
+585
+00:46:02,890 --> 00:46:12,090
+بتكلم عن C<sub>3</sub>، واحد، اتنين، اتنين، تمام
+
+586
+00:46:12,090 --> 00:46:21,130
+واحد، اتنين، حتى هذه، واحد، تلاتة، واحد، تلاتة،
+
+587
+00:46:21,130 --> 00:46:24,930
+واحد، طيب، بيساوي اتنين
+
+588
+00:46:27,660 --> 00:46:34,080
+zero، تمام، اتنين واحد، طب لحظة، بأخذهم من اللي فوق،
+
+589
+00:46:34,080 --> 00:46:38,020
+معناته اتنين من الـ second order، الاتنين اللي
+
+590
+00:46:38,020 --> 00:46:39,320
+حواليه، اللي كانوا فوق، هنا وهنا
+
+591
+00:46:42,440 --> 00:46:45,840
+واحد زائد اتنين، هذه قيمتها كانت واحد، وأنا قيمتها
+
+592
+00:46:45,840 --> 00:46:50,540
+اتنين، تلاتة، نفس الكلام هنا تلاتة، والأرقام اتفجنا
+
+593
+00:46:50,540 --> 00:46:56,180
+إنها دائما once، دائما once، طب واضح إن إحنا قاعدين
+
+594
+00:46:56,180 --> 00:47:02,120
+بنعمل هرم triangle، هذه Pascal's triangle، هذه الـ
+
+595
+00:47:02,120 --> 00:47:05,940
+Pascal اللي عملها، فسموها Pascal's triangle، من
+
+596
+00:47:05,940 --> 00:47:09,540
+القانون، القانون اللي عرفناه، الـ combination لـ N plus
+
+597
+00:47:09,540 --> 00:47:14,740
+واحد J، بيساوي combination لـ N J minus one، plus
+
+598
+00:47:14,740 --> 00:47:23,260
+combination N و J، هذا هيعطينا الـ triangles، عفوا
+
+599
+00:47:23,260 --> 00:47:29,220
+Pascal's triangle، Pascal's triangle، فهنا C<sub>0,0</sub>، C<sub>2,1</sub>
+
+600
+00:47:29,220 --> 00:47:33,720
+بقدر أجيبها من C<sub>1,0</sub> plus C<sub>1,1</sub>، معناه إننا
+
+601
+00:47:36,840 --> 00:47:41,340
+لاحظوا، ففي الآخر واضحة، صارت كيف نقدر نجيب الموضوع
+
+602
+00:47:41,340 --> 00:47:47,440
+هذا، عشان نطلع الـ triangle كلها، الـ triangle كلها، لو
+
+603
+00:47:47,440 --> 00:47:52,100
+عندكم أي .. أي coefficient، بتقدروا تجيبوا الـ
+
+604
+00:47:52,100 --> 00:47:55,180
+coefficient للـ order اللي وراها، بتقدروا تجيبوا
+
+605
+00:47:55,180 --> 00:47:58,920
+الـ coefficient لمين؟ للـ order اللي بعدها، طريقة سهلة
+
+606
+00:47:58,920 --> 00:48:02,600
+وبتقدروا ت .. يعني تعملوا فيها منظر على صفحاتكم
+
+607
+00:48:02,600 --> 00:48:08,220
+على .. تقولوا آه هنا عارفين الـ .. الـ .. الـ .. الـ ..
+
+608
+00:48:08,220 --> 00:48:16,300
+بس كان الـ triangle، okay، لحظة
+
+609
+00:48:16,300 --> 00:48
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b2ff9891cebb411fed796a21599577c7d70033dc
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs_postprocess.srt
@@ -0,0 +1,2464 @@
+1
+00:00:20,940 --> 00:00:22,980
+طيب بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,980 --> 00:00:25,620
+الأنبياء والمرسلين سيدنا محمد وعلى أليه وصحبه
+
+3
+00:00:25,620 --> 00:00:30,660
+أجمعين نكمل في ال permutation أو التبديل في ال
+
+4
+00:00:30,660 --> 00:00:33,920
+permutation كان اخر اشي أخدناه ان احنا بدنا نعمل
+
+5
+00:00:33,920 --> 00:00:38,620
+cutting ل ..three wires من ten wires كانوا موجودين
+
+6
+00:00:38,620 --> 00:00:43,280
+فكانت هنا العملية عملية order يعني كان لازم العشر
+
+7
+00:00:43,280 --> 00:00:47,660
+أسلاك اللي بدنا نقطعهم يكونوا مرتبين من العشر
+
+8
+00:00:47,660 --> 00:00:50,200
+أسلاك التلاتة اللي بدنا نقطعهم يكونوا مرتبين الأول
+
+9
+00:00:50,200 --> 00:00:53,860
+في ال order تبعه صح كان فعلا أول واحد نقطعه و
+
+10
+00:00:53,860 --> 00:00:58,580
+التاني في نفس وقته و التالت برضه في نفس اللحظة و
+
+11
+00:00:58,580 --> 00:01:03,460
+كنا اتكلمنا فيها عنجديش ال chances انه فعلا ينجح
+
+12
+00:01:03,460 --> 00:01:06,640
+معنا الموضوع ده فاتكلمنا .. قولنا ان احنا هنا
+
+13
+00:01:06,640 --> 00:01:09,460
+بنتكلم عن permutation مدام انا بتكلم عن ايه؟ عن
+
+14
+00:01:09,460 --> 00:01:15,140
+order عن order sequence فكنا بنقول permutation عشر
+
+15
+00:01:15,140 --> 00:01:19,780
+اسلاك بدنا نقطع منهم تلاتة او بدنا نختار تلاتة
+
+16
+00:01:19,780 --> 00:01:23,360
+بمعنى اخر بدنا نعمل selection ل three wires from
+
+17
+00:01:23,360 --> 00:01:28,620
+ten wires okay و هد حلنا .. اشتغلنا عليها و طلعنا
+
+18
+00:01:29,570 --> 00:01:34,110
+على أساس أنه يطلع عنا عشرة في تسعة في تمانية
+
+19
+00:01:34,110 --> 00:01:38,310
+وقولنا فيها أننا سبعمية وعشرين السبعمية وعشرين
+
+20
+00:01:38,310 --> 00:01:41,290
+هدولة عدد ال chances كلهم على بعض عدد ال chances
+
+21
+00:01:41,290 --> 00:01:46,910
+أن أنا أختار تلت أسلاك من عشرة طيب عشان يكون فعلا
+
+22
+00:01:46,910 --> 00:01:50,810
+ordered وهو ال sequence وحيد اللي لازم ضروري فهو
+
+23
+00:01:50,810 --> 00:01:56,480
+واحدواحد من سبعمية وعشرين فانا بتكلم عن واحد من
+
+24
+00:01:56,480 --> 00:02:03,520
+سبعمية وعشرين chances ممكنين فال chance الوحيد of
+
+25
+00:02:03,520 --> 00:02:08,040
+survival هو واحد من السبعمية وعشرين هدول واحد من
+
+26
+00:02:08,040 --> 00:02:12,980
+السبعمية وعشرين كان هذا أخر شيء أخدناه المرة
+
+27
+00:02:12,980 --> 00:02:18,240
+الماضية طيب نكمل شوية examples برضه لو أخدنا مثال
+
+28
+00:02:18,950 --> 00:02:21,750
+مثال بسيط، المثال هذا بيقول إنه جديش عدد ال
+
+29
+00:02:21,750 --> 00:02:25,350
+different .. ال different orders كان four persons
+
+30
+00:02:25,350 --> 00:02:29,410
+أو اقتل أربع أشخاص يقعدوا على أربع كراسي، في أربع
+
+31
+00:02:29,410 --> 00:02:33,610
+أشخاص بدهم يقعدوا على أربع كراسي، جديش عدد الحالات
+
+32
+00:02:33,610 --> 00:02:38,010
+الممكنة إن يقعدوا أربع أشخاص على أربع .. على أربع
+
+33
+00:02:38,010 --> 00:02:46,470
+كراسي فهذه كانت ببساطة ال permutation لأربعة من
+
+34
+00:02:46,470 --> 00:02:51,810
+أربعةأربعة من أربعة من القوانين بتاعتكوا بكل بساطة
+
+35
+00:02:51,810 --> 00:02:55,330
+بتقدروا تحسبوها على أساس إن هي ال N factorial على
+
+36
+00:02:55,330 --> 00:03:01,210
+N minus R R جديش أن هنا أربعة فإنها أربعة أربعة
+
+37
+00:03:01,210 --> 00:03:06,490
+كله factorial فكان بيطلع جديش أربعة و عشرين بيطلع
+
+38
+00:03:06,490 --> 00:03:11,500
+هنا عندكوا أربعة و عشرينعلى أساس إن الشخص الأول
+
+39
+00:03:11,500 --> 00:03:13,900
+ممكن يقعد في المكان الأول أو التاني أو التاري او
+
+40
+00:03:13,900 --> 00:03:16,900
+الرابع و نفس الكلام الشخص التاني فممكن يعملوا
+
+41
+00:03:16,900 --> 00:03:20,540
+permutation مع بعض ممكن يعملوا تبديل مع بعض في
+
+42
+00:03:20,540 --> 00:03:24,780
+عملية الجلوس تبعتهم في عملية الجلوس تبعتهم okay
+
+43
+00:03:24,780 --> 00:03:29,160
+طيب how many different three digit numbers جداش
+
+44
+00:03:29,160 --> 00:03:33,560
+ممكن أعمل three digit numbers بمعنى جداش عدد
+
+45
+00:03:33,560 --> 00:03:40,460
+الأرقام من ال three digitsواحد اتنين تلاتة تحتوي
+
+46
+00:03:40,460 --> 00:03:47,620
+على أرقام خمسة ستة سبعة تمانية أو تسعة واحد من
+
+47
+00:03:47,620 --> 00:03:50,600
+الأرقام هدولة لازم يكون في خانة من الخلات without
+
+48
+00:03:50,600 --> 00:03:54,860
+repetition بدون تكرار بدون مايصير مايكون عندنا في
+
+49
+00:03:55,980 --> 00:03:58,900
+ما يكون فيه تكرار في الحالة اللي احنا بتكلم عنها
+
+50
+00:03:58,900 --> 00:04:02,060
+ففي الحالة اللي عندنا هنا هيكون كأنه عندنا three
+
+51
+00:04:02,060 --> 00:04:06,380
+permutation فهتكون جدش عددهم واحد اتنين تلاتة
+
+52
+00:04:06,380 --> 00:04:11,140
+اربعة خمسة ف permutation خمسة بدنا منهم .. بدنا
+
+53
+00:04:11,140 --> 00:04:15,100
+منهم تلاتة .. بدنا منهم تلاتة و متفقين احنا مع
+
+54
+00:04:15,100 --> 00:04:18,980
+حكاية ال repetition يعني بالعكس هي تناسب مع ال
+
+55
+00:04:18,980 --> 00:04:23,540
+permutation لأنه قلنا قبل هيك اللي ال permutationو
+
+56
+00:04:23,540 --> 00:04:26,640
+ال combination التنتين يتفقوا ان هما without
+
+57
+00:04:26,640 --> 00:04:32,360
+replacement بدون تكرار بدون ان نرجع ال selected
+
+58
+00:04:32,360 --> 00:04:36,260
+item ل ال universe of discourse بتاعتنا عشان نرجع
+
+59
+00:04:36,260 --> 00:04:40,360
+نختارها كمان مرة فهنا خمسة بدنا نختار منهم تلتة
+
+60
+00:04:40,360 --> 00:04:43,720
+بدنا نختار منهم تلتة بتقدروا تحسبوها بنفس القانون
+
+61
+00:04:43,720 --> 00:04:47,740
+اللي كنا كتبينه بطلع معاكم ستين بطلع معانا ستين
+
+62
+00:04:47,740 --> 00:04:50,680
+okay طيب ال permutation ايش كانت تختلف عن ال
+
+63
+00:04:50,680 --> 00:04:56,100
+combination؟Permutation اتكلمنا ان هي order، ال ..
+
+64
+00:04:56,100 --> 00:04:59,540
+ال combination لأ without order فلما نيجي نتكلم عن
+
+65
+00:04:59,540 --> 00:05:04,240
+ال .. الاربع .. الاربع persons اللي بيتم يقعدوا
+
+66
+00:05:04,240 --> 00:05:07,670
+على اربع كراسيمافيش .. يعني مش هنقعد نقول أه والله
+
+67
+00:05:07,670 --> 00:05:09,550
+الشخص الأول جاعد في المكان الأول أو التاني أو
+
+68
+00:05:09,550 --> 00:05:12,210
+التاني، المهم إنه جاعد، المهم إنه خلاص، هو جاعد
+
+69
+00:05:12,210 --> 00:05:15,230
+وخلص، ففي الحالة هذه هيكون لنا احتمال واحد، إنه
+
+70
+00:05:15,230 --> 00:05:18,530
+الأربعة على الأربعة، خلاص، كيف جاعدوا، وين جاعد
+
+71
+00:05:18,530 --> 00:05:20,510
+الشخص الأول وين جاعد الشخص التاني، التالت مش
+
+72
+00:05:20,510 --> 00:05:23,370
+إشكال، المهم إنه في النهاية الأربع كراسي عليهم
+
+73
+00:05:23,370 --> 00:05:26,490
+أربعة أشخاص وخلصنا، أربعة كراسي عليهم أربعة أشخاص،
+
+74
+00:05:26,490 --> 00:05:30,170
+ففي الحالة هذه ال order بيفرجش معنا، وين ال object
+
+75
+00:05:30,170 --> 00:05:34,480
+الأول مكانه أو في أياختيار تم اختياره في الاختيار
+
+76
+00:05:34,480 --> 00:05:37,600
+الأول او التاني او التالت بتفرجش بيفرجش في الحالة
+
+77
+00:05:37,600 --> 00:05:41,620
+بتاعتنا فهذه اللي هي ال combination هذه جزئية ال
+
+78
+00:05:41,620 --> 00:05:45,720
+combination طيب مادام بفرجش ال order بفرجش في ال
+
+79
+00:05:45,720 --> 00:05:48,620
+permutation كنا بنتكلم ان انا بتكلم عن strings
+
+80
+00:05:48,620 --> 00:05:51,180
+وكان دايما بيقولكوا how many strings how many
+
+81
+00:05:51,180 --> 00:05:55,840
+strings نتكلم عن order فال order اما string او
+
+82
+00:05:55,840 --> 00:06:00,720
+sequence لكن هنا مادام unordered فانا بتكلم عن six
+
+83
+00:06:01,800 --> 00:06:06,880
+بنتكلم عن set انه نختار من ال .. منكوا أربعة بنات
+
+84
+00:06:06,880 --> 00:06:10,800
+مثلا من العدد الإجمالي بنختار أربعة بنات بفرجش مين
+
+85
+00:06:10,800 --> 00:06:13,680
+الأول و مين التالتة و مين الرابعة صحيح؟ مش هتفرج
+
+86
+00:06:13,680 --> 00:06:16,840
+احنا ماقولناش ان والله اللي هنختاره الأول له ميزة
+
+87
+00:06:16,840 --> 00:06:19,860
+عن الفاجين خلاص احنا بنختار تلاتة بنختار أربعة ..
+
+88
+00:06:19,860 --> 00:06:25,010
+أربعة من اللي موجود فالأربعة هدول sub 6من ال
+
+89
+00:06:25,010 --> 00:06:29,090
+universe of discourse صحيح؟ subset من المجموع لأن
+
+90
+00:06:29,090 --> 00:06:32,810
+هم جزء كان من المجموع مظهر؟ ففي الحالة هذه ال
+
+91
+00:06:32,810 --> 00:06:37,930
+permutation ال combination بتاعتنا لما نقول هنا
+
+92
+00:06:37,930 --> 00:06:43,490
+كنا نسميها permutation of N بدنا نختار منهم R او
+
+93
+00:06:43,490 --> 00:06:47,010
+permutation ل R R permutation كنا حتى نسميها R
+
+94
+00:06:47,010 --> 00:06:51,030
+permutation from N elements هنا هنسميها C
+
+95
+00:06:51,030 --> 00:06:58,020
+combinationن وبدنا نختار منهم R وبدنا نختار منهم R
+
+96
+00:06:58,020 --> 00:07:07,900
+كويس هدولة بكل بساطة بنقدر نقول انه T subset of S
+
+97
+00:07:07,900 --> 00:07:14,480
+ايش ال S و ايش ال T ال S هذه عدد ال elements اللي
+
+98
+00:07:14,480 --> 00:07:17,340
+عددهم N هدولة اللي هم ال set لل elements اللي
+
+99
+00:07:17,340 --> 00:07:22,860
+عددهم N اللي بدنا نختار منهم ف ال S عندنااللي هو
+
+100
+00:07:22,860 --> 00:07:27,360
+جدش عددكوا أنتوا ال .. ال .. ال .. الست أس اللي هو
+
+101
+00:07:27,360 --> 00:07:30,320
+أنتوا لو بدنا نختار منكم تلاتة أو أربع مثلا بدنا
+
+102
+00:07:30,320 --> 00:07:34,620
+نختار تلاتة معناه ذلك أن أنتوا الست أس كويس؟ جدش
+
+103
+00:07:34,620 --> 00:07:37,300
+ال .. ال .. ال .. ال cardinality بتاعتها عددكوا
+
+104
+00:07:37,300 --> 00:07:41,380
+نفس العدد تبعكوا اللي هو إيش؟ n اللي هي قيمتها n
+
+105
+00:07:41,380 --> 00:07:47,480
+طيب ال T لأ ال T جدش عدد هذي subset subset ست
+
+106
+00:07:47,480 --> 00:07:52,000
+جزئية مجموعة جزئية اللي بدنا نختارهماللي بدنا
+
+107
+00:07:52,000 --> 00:07:55,380
+نختاره هو جزء منكوا، يعني هم ال subset منكوا أصلا،
+
+108
+00:07:55,380 --> 00:07:57,960
+يعني هم جزء أساسا منكوا، فاحنا مش هنروح نختار من
+
+109
+00:07:57,960 --> 00:08:00,400
+الفصل اللي جنبنا، لأ احنا هنختار منكوا، من عندكوا،
+
+110
+00:08:00,400 --> 00:08:04,900
+فاحنا هنختار تلاتة، التلاتة هدول هيكونوا العدد R،
+
+111
+00:08:04,900 --> 00:08:07,520
+لما أقول بدنا نختار تلاتة من خمسة، فانا بكتبها هي
+
+112
+00:08:07,520 --> 00:08:12,840
+خمسة تلاتة، تلاتة من خمسة، فبدنا نختار تلاتة هدولة
+
+113
+00:08:12,840 --> 00:08:16,200
+ال cardinality أو جدش عدد ال elements belonging to
+
+114
+00:08:16,200 --> 00:08:21,310
+main to set Tاللي هم ال set ل ال selected items
+
+115
+00:08:21,310 --> 00:08:25,910
+للناس اللي تم اختيارهم في الحالة اللي عندناها okay
+
+116
+00:08:25,910 --> 00:08:30,430
+فهذه هتكون subset فواضح انه هنا combination انا
+
+117
+00:08:30,430 --> 00:08:34,770
+بتكلم عن set النتيجة عندى عبارة عن set لإنه مش
+
+118
+00:08:34,770 --> 00:08:38,850
+بالضرورة الترتيب الترتيب مش كتير مهم والله مين
+
+119
+00:08:38,850 --> 00:08:41,450
+اخترته اول ومين تاني ومين تالت مش هتفرج المهم انه
+
+120
+00:08:41,450 --> 00:08:45,690
+في نهاية تم اختياره خلاصهو داخل ال set الترتيب
+
+121
+00:08:45,690 --> 00:08:48,790
+بيفرجش في ال permutation لأ كان الترتيب بيفرج
+
+122
+00:08:48,790 --> 00:08:53,530
+فماكناش نقدر نقول ان هي subset كنا نقول string كنا
+
+123
+00:08:53,530 --> 00:08:56,330
+نسميه string هو ناتج و ال string احنا عارفين انه
+
+124
+00:08:56,330 --> 00:09:00,470
+يعني بيختلف بالترتيب بالترتيب تبعه بيختلف ممكن
+
+125
+00:09:00,470 --> 00:09:03,990
+يكون نفس عدد ال elements ولكن واحد مكان واحد صار
+
+126
+00:09:03,990 --> 00:09:07,590
+string جديد string مختلف لازم يكون له عدد لحاله
+
+127
+00:09:07,590 --> 00:09:12,770
+فهنا how many strings انا بتكلم عنعن permutation
+
+128
+00:09:12,770 --> 00:09:16,790
+لكن لما بتكلم هنا عن subset .. subset النادج تبعنا
+
+129
+00:09:16,790 --> 00:09:20,170
+ماتفرجش كان الأول التاني التالت الرابع مش هتفرج
+
+130
+00:09:20,170 --> 00:09:25,590
+معانا ففي الحالة هذه بيكون عندنا combination ..
+
+131
+00:09:25,590 --> 00:09:31,510
+combination طيب ال combination بتاعتنا هنا هي اللي
+
+132
+00:09:31,510 --> 00:09:37,310
+علاقة بال .. بإيش؟ بال permutation مع عدم التكرار
+
+133
+00:09:37,310 --> 00:09:41,940
+كحساباتك concept لأ واضح ان هنا بنتكلم عن string
+
+134
+00:09:41,940 --> 00:09:45,820
+هنا بنتكلم عن إيش؟ بنتكلم عن subset .. subset
+
+135
+00:09:45,820 --> 00:09:49,040
+مجموعة جزئية فعليا .. مجموعة جزئية أنا بدي أختارهم
+
+136
+00:09:49,040 --> 00:09:52,460
+و خلاص هدول شاروا مجموعة بس هم فعليا ينتموا إلكوا
+
+137
+00:09:52,460 --> 00:09:55,320
+.. ينتموا إلكوا هم مش .. يعني التلاتة اللي أختارهم
+
+138
+00:09:55,320 --> 00:09:57,620
+كانوا يدرسوا discrete هم هيدلوا يدرسوا discrete و
+
+139
+00:09:57,620 --> 00:09:59,800
+هم مازالوا يدرسوا discrete ولكن أختارناهم في لجنة
+
+140
+00:09:59,800 --> 00:10:03,100
+أختارناهم في .. في مجموعة أختارناهم لأي سبب كان
+
+141
+00:10:03,770 --> 00:10:10,410
+فأصبحوا subset هذه تساوي كقيمة بدنا نحسبها كمعادلة
+
+142
+00:10:10,410 --> 00:10:18,290
+ال permutation from n to r على ال permutation rr
+
+143
+00:10:18,290 --> 00:10:23,150
+ال permutation rr هي عساس انها تختزن لنا عدد
+
+144
+00:10:23,150 --> 00:10:28,350
+تكرارات عدد مرات التكرار فهذه بنقدر نقول ان هذه
+
+145
+00:10:28,350 --> 00:10:30,690
+بنقدر نحتصر منها عدد مرات التكرار
+
+146
+00:10:33,820 --> 00:10:38,620
+فى الحالة اللى عندنا هنا هيطلع كل ال term هذا
+
+147
+00:10:38,620 --> 00:10:43,160
+بيساوي او ال permutation هنا هتساوي ماذا ذكرين
+
+148
+00:10:43,160 --> 00:10:53,020
+القانون كنا كتبناها قبل شوية factorial على R
+
+149
+00:10:57,550 --> 00:11:02,910
+على zero factorial على zero factorial بواحد فهنا
+
+150
+00:11:02,910 --> 00:11:06,370
+هتلاقي انه هيظهر ال term كله على بعضه على اساس انه
+
+151
+00:11:06,370 --> 00:11:12,710
+N factorial على N minus R factorial في R factorial
+
+152
+00:11:12,710 --> 00:11:20,110
+صحيح؟ في R factorialكويس المعادلة هذه هنطلع منها
+
+153
+00:11:20,110 --> 00:11:23,950
+بملاحظة مهمة جدا هنطلع منها بملاحظة مهمة جدا ايش
+
+154
+00:11:23,950 --> 00:11:27,610
+هي الملاحظة المهم جدا ان ال combination ل N و R
+
+155
+00:11:27,610 --> 00:11:36,630
+تساوي تماما ال combination ل N و N minus
+
+156
+00:11:36,630 --> 00:11:42,190
+R لو
+
+157
+00:11:42,190 --> 00:11:45,850
+بدنا نعود في هذه هيطلع المعادلة هذه صحيح طب لو
+
+158
+00:11:45,850 --> 00:11:46,670
+بدنا نعود في هذه
+
+159
+00:11:49,580 --> 00:11:53,500
+هدول اتنين هنعكسوا بس هدول اتنين هنعكسوا فقط مش
+
+160
+00:11:53,500 --> 00:11:58,600
+هتغير اشي كل اللي هيصير انه المعادلة هدا هتساوي n
+
+161
+00:11:58,600 --> 00:12:06,580
+factorial على r فعليا هي الحقيقة ان هي n minus r
+
+162
+00:12:06,580 --> 00:12:11,040
+factorial في r factorial وهدي المفروض كانت بالعكس
+
+163
+00:12:11,040 --> 00:12:18,360
+وهدي اللي هي r factorial فهدي خاصة بهدي وهدي خاصة
+
+164
+00:12:18,360 --> 00:12:24,020
+بهديفي الآخر مش هتفرج في الآخر مش هتفرج والنظرية
+
+165
+00:12:24,020 --> 00:12:27,400
+هذه هنستفيد منها كتير لجدام هنستفيد منها كويس
+
+166
+00:12:27,400 --> 00:12:31,300
+لجدام هلاجي ان في بعض احيانا بعض terms مش هكون
+
+167
+00:12:31,300 --> 00:12:35,080
+مضطر احسبهم كلهم ممكن اضطر احسب نصهم والباجي ما هو
+
+168
+00:12:35,080 --> 00:12:38,740
+مساوي لهم هي بنفس الفكرة الباجي هيكون مساوي
+
+169
+00:12:38,740 --> 00:12:43,960
+مساويين لبعض ليش؟ يعني ليش طلعوا بالشكل هذا فعلا
+
+170
+00:12:43,960 --> 00:12:47,740
+بيكملوا بعض؟ لأن لو فكرنا فيها شوية لو جعدنا نقول
+
+171
+00:12:48,670 --> 00:12:53,690
+جدتش عدد الطرق اللي ممكن اختار منها تلاتة من عشرة
+
+172
+00:12:53,690 --> 00:12:58,390
+تمام؟ مش هيك السؤال؟ هي .. جدتش عدد الطرق اللي
+
+173
+00:12:58,390 --> 00:13:03,890
+ممكن اختار فيها تلت أشخاص من عشرة طب ما هي نفسها
+
+174
+00:13:03,890 --> 00:13:08,170
+عدد الطرق اللي ممكن مااختارش سبع أشخاص من عشرة
+
+175
+00:13:08,170 --> 00:13:10,690
+المكملة
+
+176
+00:13:11,970 --> 00:13:15,090
+ماذا يعني سبع أشخاص؟ لأنه سبع أشخاص مع التلت أشخاص
+
+177
+00:13:15,090 --> 00:13:18,230
+هذا ال total كله العشرة كاملين العشرة كاملين ففي
+
+178
+00:13:18,230 --> 00:13:20,350
+الآخر هنلاقي أنه عدد الطرق اللي بقدر أختار منهم
+
+179
+00:13:20,350 --> 00:13:25,150
+تلاتة من عشرة هم نفسهم عدد الطرق اللي ممكن ماخترش
+
+180
+00:13:25,150 --> 00:13:30,270
+منهم سبعة من عشرة ماخترش منهم سبعة من عشرة فعشان
+
+181
+00:13:30,270 --> 00:13:33,650
+ذلك التنتين فعلا بيكملوا .. بيكملوا بعض تنتين فعلا
+
+182
+00:13:33,650 --> 00:13:36,150
+بيكملوا بعض بيسووا بعض ك .. ك mathematical
+
+183
+00:13:36,150 --> 00:13:46,540
+equation okay for exampleلو how many distinct 7
+
+184
+00:13:46,540 --> 00:13:51,520
+-card hands can drown from standard 22-card desk
+
+185
+00:13:51,520 --> 00:13:56,120
+جداش ممكن اختار سبعة كروت او جداش عدد الطرق اللي
+
+186
+00:13:56,120 --> 00:13:59,400
+ممكن اختار منها سبعة كروت من اتنين و خمسين كرت من
+
+187
+00:13:59,400 --> 00:14:03,240
+اتنين و خمسين كرت في عندنا اتنين و خمسين كرت أكم
+
+188
+00:14:03,240 --> 00:14:07,100
+طريقة بقدر اختار منهم سبعة كروت فرضناهم جدامنا
+
+189
+00:14:07,100 --> 00:14:12,130
+اتنين و خمسين كرتأكتر طريقة بقدر أختار سبعة كروت
+
+190
+00:14:12,130 --> 00:14:14,750
+طبعا في الآخر أنا متفرجش معايا الكروت إذا اتكررت
+
+191
+00:14:14,750 --> 00:14:18,390
+يعني ممكن أختار الكارت الأول والخامس أو أختار
+
+192
+00:14:18,390 --> 00:14:21,530
+الخامس والأول هي هي بتنحسب برا واحدة هذه بتنحسب
+
+193
+00:14:21,530 --> 00:14:27,390
+حاجة واحدة بتنحسب حاجة واحدة ففي الآخر اللي موجود
+
+194
+00:14:27,390 --> 00:14:34,690
+عندنا combination
+
+195
+00:14:34,690 --> 00:14:44,100
+ل 52 وسبعة فانا بتختار سبعة cards من اتنين و خمسين
+
+196
+00:14:44,100 --> 00:14:50,160
+من اتنين و خمسين cards تمام بالقانون تبعنا هتساوي
+
+197
+00:14:50,160 --> 00:14:58,780
+N factorial على R factorial في N minus R factorial
+
+198
+00:14:58,780 --> 00:15:01,720
+هتساوي اتنين و خمسين عفوا
+
+199
+00:15:04,700 --> 00:15:13,520
+تنين و خمسين على سبعة factorial على كده؟ خمسة و
+
+200
+00:15:13,520 --> 00:15:19,920
+أربعين factorial او مباشرة ما انا عارف ان هدا ال
+
+201
+00:15:19,920 --> 00:15:26,580
+permutation بتاعة مين n و r على permutation r و r
+
+202
+00:15:26,580 --> 00:15:31,280
+يعني بقدر اقول ان هي بتساوي اتنين و خمسين في واحد
+
+203
+00:15:31,280 --> 00:15:37,790
+و خمسين في خمسينفي تسعة واربعين في تمانية واربعين
+
+204
+00:15:37,790 --> 00:15:42,550
+صاروا ست سبعة terms على
+
+205
+00:15:42,550 --> 00:15:48,310
+سبعة
+
+206
+00:15:48,310 --> 00:15:57,330
+من سبعة تمام؟
+
+207
+00:15:57,330 --> 00:16:00,410
+خلاص بتقدروا تختصروه إذا كانت طبعا الكلام ممكن
+
+208
+00:16:00,410 --> 00:16:03,700
+تطبخوه مباشرة إذا راجيتوا أن ال R قيمتها صغيرةإذا
+
+209
+00:16:03,700 --> 00:16:06,840
+قيمة ال R صغيرة مناسبة أنكوا تطبقوا بسرعة طبعا
+
+210
+00:16:06,840 --> 00:16:09,240
+ممكن تكون ال R قيمتها كبيرة لو قلنا لكوا لا
+
+211
+00:16:09,240 --> 00:16:13,680
+إختارولنا منهم عشرين كارت طبعا بيصير الأمور كبيرة
+
+212
+00:16:13,680 --> 00:16:17,420
+لأ بيصير هذه أفضلعلى طول على ال calculator و
+
+213
+00:16:17,420 --> 00:16:21,780
+factorial على two factorial و خلاص هذه ممكن
+
+214
+00:16:21,780 --> 00:16:25,820
+تختصروا سبعة مع التسعة و أربعين بتلاجوا سبعة الستة
+
+215
+00:16:25,820 --> 00:16:27,760
+ممكن تختصروها مع التمانية و أربعين هتلاجوا حاجة
+
+216
+00:16:27,760 --> 00:16:32,700
+تقتصر في النهاية هيطلع معاكم تقريبا اه تطلع معاكم
+
+217
+00:16:32,700 --> 00:16:37,500
+مية تلاتة و تلاتين مليون و سبع مية اربعة و تمانين
+
+218
+00:16:37,500 --> 00:16:43,520
+الف و خمس مية و ستينخمسمية أو ستة طبعا عدد كبير
+
+219
+00:16:43,520 --> 00:16:48,420
+جدا لأنه أصلا عدد الكروت نفسها عددهم كبير عددهم
+
+220
+00:16:48,420 --> 00:16:55,500
+كبير عدد الكروت نفسها عددهم عددهم كبير طيب
+
+221
+00:16:55,500 --> 00:16:58,720
+ال
+
+222
+00:16:58,720 --> 00:17:03,020
+.. how many bit string لحظوا هنا bit string أنا
+
+223
+00:17:03,020 --> 00:17:06,500
+جاعت بقول bit string بس ماتنخدعوش معاه لأنه bit
+
+224
+00:17:06,500 --> 00:17:09,280
+string هو وجد الأصل أن أنا هفكر بإيش بال
+
+225
+00:17:09,280 --> 00:17:13,400
+permutation خليني أشوفhow many bits string of
+
+226
+00:17:13,400 --> 00:17:16,940
+length four have exactly two ones or exactly two
+
+227
+00:17:16,940 --> 00:17:21,780
+zeros؟ بمعنى ماجدتش عدد ال bits أو ال strings اللي
+
+228
+00:17:21,780 --> 00:17:34,600
+ممكن أخدها من four bits عدد
+
+229
+00:17:34,600 --> 00:17:36,100
+ال string اللي ممكن أخدها من four
+
+230
+00:17:40,830 --> 00:17:46,690
+هي عندكوا أربعة الأربعة هدولة بدكوا exactly كده
+
+231
+00:17:46,690 --> 00:17:51,930
+عدد الحالات اللي ممكن يكون فيها two ones exactly
+
+232
+00:17:51,930 --> 00:17:55,970
+two ones بمعنى مايكونش one واحد ومايكونش three or
+
+233
+00:17:55,970 --> 00:18:01,330
+four مايكونش three or four هذه نفسها مكملة ليش ل
+
+234
+00:18:01,330 --> 00:18:06,560
+double zero او two zerosلأن مادام exactly two ones
+
+235
+00:18:06,560 --> 00:18:12,300
+بالنسبة للأربعة معناته exactly two zeros في الحالة
+
+236
+00:18:12,300 --> 00:18:20,120
+هذه by logic مادام اللي بنشتر عليها هيكون معاها
+
+237
+00:18:20,120 --> 00:18:27,680
+هيكون معانا ال one الأولى ال one التانية خلاص انت
+
+238
+00:18:27,680 --> 00:18:31,860
+حجزت من الأولى فهيكون لها تلاتة
+
+239
+00:18:33,600 --> 00:18:39,400
+Okay الكلام هذا بحيط طلع اتناش exactly هو مش اتناش
+
+240
+00:18:39,400 --> 00:18:46,460
+ليش exactly مش اتناش لأنه ممكن الأولى هنا تكون في
+
+241
+00:18:46,460 --> 00:18:49,200
+ال location الأول والتانية في ال location الأول
+
+242
+00:18:49,200 --> 00:18:55,120
+هذا احتمال مظبوط طيب ممكن احتمال تانى الأولى في ال
+
+243
+00:18:55,120 --> 00:19:01,080
+location التانى والتانية في ال location الأول طب
+
+244
+00:19:01,080 --> 00:19:06,040
+هذانفسه و احنا قولنا مش معنيين احنا بالتكرار خصوصا
+
+245
+00:19:06,040 --> 00:19:10,340
+ان ال ones بيسووا بعض فمش هيبين ان هذا غير هذا
+
+246
+00:19:10,340 --> 00:19:13,720
+مادام بتكلم عنوز يعني بامتباه ان الاتنين identical
+
+247
+00:19:13,720 --> 00:19:16,680
+الاتنين متماثلين فهنا في الحالة هذا مش هينفع ال
+
+248
+00:19:16,680 --> 00:19:22,960
+order رغم ان هو كاتب ال string بس السؤال مش هتفرج
+
+249
+00:19:22,960 --> 00:19:25,680
+هنا مين ال one اللي زهرت هنا و اللي زهرت هنا لإنه
+
+250
+00:19:25,680 --> 00:19:30,630
+مش هيبين ان في فرج أصلافعليا مش هيبين انه في فرقة
+
+251
+00:19:30,630 --> 00:19:39,930
+بمعنى لو بتقوله مش ones واحدة A واحدة B لاحظوا
+
+252
+00:19:39,930 --> 00:19:44,630
+هنا هيختلف هتصير هنا ال A وهنا ال B هنا بتصير B
+
+253
+00:19:44,630 --> 00:19:47,750
+هنا A طبعا عند ال A و ال B بيسووا بعض
+
+254
+00:19:50,620 --> 00:19:55,040
+فإذا هنا أصبحت رغم أن هو طالب bit strange بس أنا
+
+255
+00:19:55,040 --> 00:19:58,540
+بتكلم هنا عن combination بمعنى جدش الحالات اللي
+
+256
+00:19:58,540 --> 00:20:02,960
+ممكن تصير فيها في حالة بالشكل هذا مضاعفة فالرقم
+
+257
+00:20:02,960 --> 00:20:09,160
+اللي بيطلع هنجسمه على على اتنين على اتنين لأن ال
+
+258
+00:20:09,160 --> 00:20:13,640
+two ones دولة ممكن يجوا عكس بعض عكس بعض فالحالة دي
+
+259
+00:20:13,640 --> 00:20:17,170
+هم الاتنين بيساوي بعض أساسا هم الاتنين أصلابساوة
+
+260
+00:20:17,170 --> 00:20:21,730
+بعض فلاحظوا ان في هيك حالة هيطلع عندكوا n
+
+261
+00:20:21,730 --> 00:20:29,310
+factorial على r factorial في n minus r factorial
+
+262
+00:20:29,310 --> 00:20:35,450
+فال n factorial جديش؟ جديش ال n؟ أربعة أربعة أنا
+
+263
+00:20:35,450 --> 00:20:40,930
+بتكلم عن أربعة و عشرين اتنين انا بتكلم عن two ones
+
+264
+00:20:40,930 --> 00:20:49,050
+فعند اتنينfactorial وهنا اربع ناقص اتنين اتنين
+
+265
+00:20:49,050 --> 00:20:53,890
+factorial هتساوي اربع وعشرين على اتنين في اتنين
+
+266
+00:20:53,890 --> 00:20:58,610
+هتساوي كدهش ستة وهو ده الحل الصحيح وميعطيكوا هاي
+
+267
+00:20:58,610 --> 00:21:03,410
+الحلات الستة الممكنة و اللي مافيش غيرهم اللي ووجد
+
+268
+00:21:03,410 --> 00:21:07,810
+غيرهم فعليا اللي ووجد فعليا غيرهم اللي ووجد غيرهم
+
+269
+00:21:07,810 --> 00:21:11,250
+انها تكون صفر صفر واحد واحد لان هدولة بدلوا بعض
+
+270
+00:21:13,100 --> 00:21:18,600
+مالهاش معنى one ماكان one فالاتنين بيسوا بعض ففي
+
+271
+00:21:18,600 --> 00:21:21,620
+الحالة هذه مش هيفيد التكرار في الحالة اللي .. اللي
+
+272
+00:21:21,620 --> 00:21:25,300
+عندنا هنا و هي ميعطيكوا و موضحلكوا ان لو فترضتوا
+
+273
+00:21:25,300 --> 00:21:29,300
+ان واحد من ال two a's هدولة واحد منهم a والتاني b
+
+274
+00:21:29,300 --> 00:21:31,980
+هيبين الاختلاف .. هيبين الاختلاف احنا عندنا هنا ال
+
+275
+00:21:31,980 --> 00:21:36,620
+a و ال b بيسوا .. بيسوا بعض okay كمان combination
+
+276
+00:21:36,620 --> 00:21:43,610
+example how many strings of .. of size tenممكن
+
+277
+00:21:43,610 --> 00:21:47,590
+واضحة مافيش فيها كتير ال size تبعتنا ten لل bit
+
+278
+00:21:47,590 --> 00:21:52,910
+string contains four ones باينة مافيش فيها كتير
+
+279
+00:21:52,910 --> 00:21:57,310
+يعني ال combination عشرة أربعة عندكوا string في
+
+280
+00:21:57,310 --> 00:22:01,590
+عشرة locations جدش عدد الطرق اللي ممكن يكون فيها
+
+281
+00:22:01,590 --> 00:22:07,930
+أربعة ones طبعا اتفقنا أن ال ones واحد مكان واحد
+
+282
+00:22:07,930 --> 00:22:11,820
+مش هيفرق فاحنا نتكلم عن combination هناWe need to
+
+283
+00:22:11,820 --> 00:22:16,300
+form a community of seven people محتاجين نعمل لجنة
+
+284
+00:22:16,300 --> 00:22:18,960
+من سبع أشخاص السبع أشخاص هدولة لازم يكون منهم
+
+285
+00:22:18,960 --> 00:22:22,660
+تلاتة from math من الناس اللي بيشتغلوا في
+
+286
+00:22:22,660 --> 00:22:26,860
+الرياضيات نفترض ال staff من قسم الرياضيات أربع تلت
+
+287
+00:22:26,860 --> 00:22:31,180
+مدرسين من الرياضياتfour from computer science to
+
+288
+00:22:31,180 --> 00:22:36,280
+develop a discrete math course بدنا نطور المصاد
+
+289
+00:22:36,280 --> 00:22:40,540
+طبعنا فقلنا بدنا نعمل لجنة من سبع أشخاص السبع
+
+290
+00:22:40,540 --> 00:22:44,800
+أشخاص هدولة تلاتة من الرياضيات و أربعة من ال
+
+291
+00:22:44,800 --> 00:22:48,520
+computer science على أساس إنه يطوروا طيب روحنا على
+
+292
+00:22:48,520 --> 00:22:53,990
+قسم الرياضيات وجدنا إنه في عنده تسعة stuffsعنده
+
+293
+00:22:53,990 --> 00:22:56,890
+تسعة مدرسين فعليا في الم .. في ال .. فصار بدنا
+
+294
+00:22:56,890 --> 00:23:02,030
+نختار يدياش تلاتة من تسعة okay روحنا على قسم ال ..
+
+295
+00:23:02,030 --> 00:23:05,370
+ال computer science لجينا أن في عنده 11 staff أو
+
+296
+00:23:05,370 --> 00:23:10,830
+11 مدرس فصار بدنا نختار أربعة من 11 أربعة من 11
+
+297
+00:23:10,830 --> 00:23:15,370
+أكم طريقة بقدر أشكل فيها اللجنة أكم طريقة في عندنا
+
+298
+00:23:15,370 --> 00:23:20,410
+عشان نشكل فيها اللجنة فهتكون واضحة أن في عندنا
+
+299
+00:23:25,830 --> 00:23:32,090
+combination ل .. نقولها كأن فيهم تسعة تسعة نبدأ
+
+300
+00:23:32,090 --> 00:23:37,610
+بالرياضيات تسعة بدنا نختار منهم تلاتة صحيح؟ و في
+
+301
+00:23:37,610 --> 00:23:41,790
+عندي combination ل إحداشر بدنا نختار منهم أربعة
+
+302
+00:23:41,790 --> 00:23:46,790
+okay لحظة إيش علاقتهم مع بعض يعني كيف بدي أجمحهم
+
+303
+00:23:46,790 --> 00:23:49,830
+أضربهم أقسمهم إيش أسوي فيهم؟ okay طلعنا هذا و
+
+304
+00:23:49,830 --> 00:23:54,320
+طلعنا هذا طب خلينا نفسيكم شوي شوي هالوقت لوفي
+
+305
+00:23:54,320 --> 00:24:00,940
+الحالة الأولى اخترنا من التسعة هدولة A,B وC D وE
+
+306
+00:24:00,940 --> 00:24:05,880
+وE وF وده ماخترناهمش اخترنا الأشخاص A,B,C كويس و
+
+307
+00:24:05,880 --> 00:24:10,220
+من هنا اعملنا كل ال combination بتاعتنا صار في عنا
+
+308
+00:24:10,220 --> 00:24:15,080
+هاي تلاتة، ضال الأربع اللي ضايلين اللهم جدش عدد
+
+309
+00:24:15,080 --> 00:24:20,400
+ways ممكن اختارهم بهذا الشكل مضربين
+
+310
+00:24:21,740 --> 00:24:26,880
+بمعنى لل A والB والC هم نفس الأشخاص هتتكرر معانا
+
+311
+00:24:26,880 --> 00:24:35,800
+أكم حالة C 11 4 طيب ممكن بعد C 11 4 أختار هنا A B
+
+312
+00:24:35,800 --> 00:24:48,710
+وD برضه كمان C 11 4 ممكن يكون E معناه تضربصحيح؟
+
+313
+00:24:48,710 --> 00:24:50,710
+معناته ال combination هنا في الحالة التاعتناه
+
+314
+00:24:50,710 --> 00:24:55,770
+هنعمل ترب لإن هدولة هيتغيروا لكل شخص أو لكل تلت
+
+315
+00:24:55,770 --> 00:24:58,770
+اختيارات هنا اختار أول تاني تالت خلاص هدول هيدلوا
+
+316
+00:24:58,770 --> 00:25:07,660
+ثابتينلـ C 11 4 او لcombination اختيار 4 من 11 جدش
+
+317
+00:25:07,660 --> 00:25:09,560
+قيمتهم 1000، 2000، 5000، 5000، 5000، 5000، 5000،
+
+318
+00:25:09,560 --> 00:25:10,780
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+319
+00:25:10,780 --> 00:25:11,340
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+320
+00:25:11,340 --> 00:25:12,600
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+321
+00:25:12,600 --> 00:25:12,720
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+322
+00:25:12,720 --> 00:25:13,280
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+323
+00:25:13,280 --> 00:25:14,140
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+324
+00:25:14,140 --> 00:25:15,920
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+325
+00:25:15,920 --> 00:25:18,900
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+326
+00:25:18,900 --> 00:25:19,780
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+327
+00:25:19,780 --> 00:25:19,860
+5000، 5000، 5000، 5000، 5000، 5000، 5000، 5000،
+
+328
+00:25:19,860 --> 00:25:23,880
+5000، 5000، 5000، 5000، 5000،
+
+329
+00:25:25,850 --> 00:25:29,530
+فمعنى ذلك أنه عشان نجيب ال total كله على بعضه،
+
+330
+00:25:29,530 --> 00:25:33,790
+هيكون ضرب الأتنين combination تسعة تلاتة في
+
+331
+00:25:33,790 --> 00:25:37,510
+combination أحداشر أربعة في أحداشر أربعة، بيطلع في
+
+332
+00:25:37,510 --> 00:25:41,450
+أنديه سبعة و عشرين ألف و سبعة مية و عشرين طريقة،
+
+333
+00:25:41,450 --> 00:25:44,610
+هذا طبعا في حال افترضنا أنه الكل متساوي في الفرصة
+
+334
+00:25:44,610 --> 00:25:48,370
+أنه يكون في إيش؟ في المجموعة، في مجموعة التطوير
+
+335
+00:25:51,640 --> 00:25:56,740
+suppose you flip a fire coin n times عندكوا coin
+
+336
+00:25:56,740 --> 00:26:00,480
+اللي هي العملة المعدنية و بتعملوها flipping
+
+337
+00:26:00,480 --> 00:26:05,240
+بتعملوها اللي هي الطرة ها دي بترموها و بتكونوا
+
+338
+00:26:05,240 --> 00:26:07,260
+تشوفوا إيش اللي بيظهر .. اللي حيظهر عندكم فانتوا
+
+339
+00:26:07,260 --> 00:26:12,480
+في عندكم head or tail ال head or tail أو ال .. إيش
+
+340
+00:26:12,480 --> 00:26:18,440
+بيسموها؟ الصورة و الكتابة .. صورة و كتابةHow many
+
+341
+00:26:18,440 --> 00:26:23,900
+different ways can you get no heads؟ with no heads
+
+342
+00:26:23,900 --> 00:26:27,220
+مافيش heads عندكم فانتم عندكم من عشر من أن مرة
+
+343
+00:26:27,220 --> 00:26:34,900
+combination من أن مرة zero من أن مرة في عندكم zero
+
+344
+00:26:34,900 --> 00:26:38,560
+في عندكم zero طيب هذه كده هتطلع قيمتها؟
+
+345
+00:26:41,870 --> 00:26:45,650
+1 هتطلع واحد لأن فعلا انتوا عندكوا احتمالات كتيرة
+
+346
+00:26:45,650 --> 00:26:50,710
+بس انه كله مافيش فيهم اي head هذا احتمال واحد حالة
+
+347
+00:26:50,710 --> 00:26:54,050
+واحدة فهذا واضح انها هتطلع واحد على اعتبار انها
+
+348
+00:26:54,050 --> 00:27:00,610
+تساوي n factorial على n minus r factorial في r
+
+349
+00:27:00,610 --> 00:27:06,990
+factorial فهذا zero هذه هتطلع n مع n واحد تتكلموا
+
+350
+00:27:06,990 --> 00:27:14,440
+انها حالة واحدةإن كلهم يطلعوا no heads okay
+
+351
+00:27:14,440 --> 00:27:19,980
+exactly one head أصبحت سهلة أصبحت سهلة combination
+
+352
+00:27:19,980 --> 00:27:30,200
+n طيب two heads are heads okay at least two heads
+
+353
+00:27:30,200 --> 00:27:33,620
+تمام
+
+354
+00:27:33,620 --> 00:27:37,680
+اتنين او تلاتة او اربعة او خمسة يعني c اتنين عفوا
+
+355
+00:27:37,680 --> 00:27:38,000
+n
+
+356
+00:27:46,840 --> 00:27:54,140
+ن اربعة طب
+
+357
+00:27:54,140 --> 00:27:55,960
+معقول هيك نكتبها بالشكلها بده قيمة؟
+
+358
+00:28:00,410 --> 00:28:02,590
+ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+359
+00:28:02,590 --> 00:28:03,670
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+360
+00:28:03,670 --> 00:28:05,290
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+361
+00:28:05,290 --> 00:28:05,550
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+362
+00:28:05,550 --> 00:28:06,030
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+363
+00:28:06,030 --> 00:28:07,110
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+364
+00:28:07,110 --> 00:28:10,010
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+365
+00:28:10,010 --> 00:28:11,350
+الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد
+
+366
+00:28:11,350 --> 00:28:18,310
+الواحد .. ناخد الواحد .. ناخد الواحد
+
+367
+00:28:18,310 --> 00:28:22,170
+.. ناخد الواحد .. ناخد الواحد ..
+
+368
+00:28:23,530 --> 00:28:29,650
+كل الحالات الممكنة واطرحوا منها حالة الصفر والواحد
+
+369
+00:28:29,650 --> 00:28:33,610
+طب كل احتمالات الممكنة هي كده؟
+
+370
+00:28:44,470 --> 00:28:49,150
+هذه عشر حالات أو عشر مرات بتعمل flipping ل ال coin
+
+371
+00:28:49,150 --> 00:28:53,030
+عشر مرات بتعمل flipping ل ال coin العشر مرات أول
+
+372
+00:28:53,030 --> 00:28:57,750
+مرة إيش في عنده احتمالات؟ رميتها و أنا .. و هو
+
+373
+00:28:57,750 --> 00:29:02,330
+نازل و أنا مستني إيش؟ hit or tailمعنى ذلك عندك ..
+
+374
+00:29:02,330 --> 00:29:06,110
+عندنا احتمالين فقط فانا كل احتمالات اتنين هذه الها
+
+375
+00:29:06,110 --> 00:29:12,250
+احتمالين طيب التانية احتمالين برضه فإذا انا من
+
+376
+00:29:12,250 --> 00:29:16,630
+مرتين اعمل team of living اكم combination بقدر
+
+377
+00:29:16,630 --> 00:29:22,340
+اعمل او اكم حالة بقدر اعمل نقدر نعمل اربع انهno
+
+378
+00:29:22,340 --> 00:29:27,200
+head, no head او head, no head او no head, head او
+
+379
+00:29:27,200 --> 00:29:31,780
+two heads او two heads فعنا اربع حالات في الحالة
+
+380
+00:29:31,780 --> 00:29:34,500
+هذه صار عندنا اتنين تتبور اتنين على اعتبار اني
+
+381
+00:29:34,500 --> 00:29:40,280
+بتكلم عن محاولتين طب لما يصيروا تلاتة طب لما
+
+382
+00:29:40,280 --> 00:29:48,260
+يصيروا n هذ كل احتمالات الممكنة هنشيل منها كل
+
+383
+00:29:48,260 --> 00:29:56,500
+احتمالات الممكنة اتنين تتبورهنشيل منها ال C N Zero
+
+384
+00:29:56,500 --> 00:30:02,160
+و C N واحد
+
+385
+00:30:02,160 --> 00:30:07,820
+أبسط كتير من الكذا term اللي حلناه قبل شوية
+
+386
+00:30:21,790 --> 00:30:24,470
+Okay في إيش ممكن نستفيد منهم الحقيقة ال
+
+387
+00:30:24,470 --> 00:30:28,450
+combination اللي احنا أخدناها هنستفيد منها في
+
+388
+00:30:28,450 --> 00:30:33,790
+إيجاد ال coefficients لل binomial
+
+389
+00:30:33,790 --> 00:30:36,370
+coefficients لل binomial coefficients ال binomial
+
+390
+00:30:36,370 --> 00:30:39,650
+coefficients هذه اللي هي معادلة متعددة الحدود
+
+391
+00:30:39,650 --> 00:30:44,450
+معادلة متعددة الحدود أو متعددة الحدود نقدر ناخدها
+
+392
+00:30:44,450 --> 00:30:44,650
+من
+
+393
+00:30:50,120 --> 00:30:55,400
+x-y أو زائد y to the power n فهي متعددة الحدود n
+
+394
+00:30:55,400 --> 00:31:00,060
+مرة لأن كدربينها في بعض n مرة هذه لو مضروبة في بعض
+
+395
+00:31:00,060 --> 00:31:05,720
+مرة واحدة بمعنى هي لحالها x زائد واحد زائد y هذه
+
+396
+00:31:05,720 --> 00:31:09,860
+linear first order هذه هيك بيكون اسمها first order
+
+397
+00:31:09,860 --> 00:31:14,140
+طيب لما تكون مضروبة في بعض اتنين مرة كيف هتكون
+
+398
+00:31:14,140 --> 00:31:20,980
+هتكون x تربيع زائد اتنين xyزائد y تربيع هذه second
+
+399
+00:31:20,980 --> 00:31:25,180
+order طب مضروبة في حالة تلت مرات third order
+
+400
+00:31:25,180 --> 00:31:28,880
+fourth
+
+401
+00:31:28,880 --> 00:31:32,600
+order five order جداش عدد مرات ضربها في هذه ال
+
+402
+00:31:32,600 --> 00:31:36,800
+bionomia جداش ال order تبعها جداش ال order تبعها
+
+403
+00:31:36,800 --> 00:31:42,240
+كويس لاحظوا هنا أنا بدي أستفيد من الإمكانيات بتاعة
+
+404
+00:31:42,240 --> 00:31:45,220
+ال combination اللي احنا كنا بنقولها combination n
+
+405
+00:31:45,220 --> 00:31:50,330
+و r بنقدر نكتبها بالشكل هذاأقواز كبيرة و نكتب هنا
+
+406
+00:31:50,330 --> 00:31:54,790
+N و R الشكل هذا هو هو مكافئ ليش لكلمة combination
+
+407
+00:31:54,790 --> 00:31:59,130
+N و R نكتبها بهذا الشكل فهما تنتين مكافئات
+
+408
+00:31:59,130 --> 00:32:03,330
+متكافئات مع بعض تنتين متكافئات مع بعض كويس هذه
+
+409
+00:32:03,330 --> 00:32:08,910
+هنستخدمها ان نجيب ال coefficients اللي هنا هنا ال
+
+410
+00:32:08,910 --> 00:32:12,290
+coefficients ل first order واحد واحد هي واحد واحد
+
+411
+00:32:12,290 --> 00:32:16,390
+ال coefficient لل second عبارة عن واحد اتنين واحد
+
+412
+00:32:16,390 --> 00:32:32,760
+لل thirdواحد تلاتة تلاتة واحد لل fourth طيب
+
+413
+00:32:32,760 --> 00:32:39,180
+ال five تعرفوه؟ طيب عيدكوا هتصيروا تعرفوه كيف؟ ال
+
+414
+00:32:39,180 --> 00:32:42,170
+coefficients هذه احنا بدنا نحسبهاالـ coefficients
+
+415
+00:32:42,170 --> 00:32:45,530
+هذه بدنا نحسبها و بعدين خدوا بالك و أنا عاملهم
+
+416
+00:32:45,530 --> 00:32:49,490
+بالشكل هذا و أنا متأكد منهم لأنه أصلا هذه جدامها
+
+417
+00:32:49,490 --> 00:32:53,190
+واحد و هذه واحد طب ممكن تتغير أصلا يكون هنا 2x
+
+418
+00:32:53,190 --> 00:32:57,130
+زائد 3y تقضيها power onها طبعا هيتغير ال
+
+419
+00:32:57,130 --> 00:32:59,590
+coefficients كلها هيتغير الفكرة هلوة جدا أننا بدنا
+
+420
+00:32:59,590 --> 00:33:02,110
+نجيب عدد ال coefficients أو قد إيجداش قيمة ال
+
+421
+00:33:02,110 --> 00:33:05,910
+coefficients هذه لكل term أو لكل حد من الحدود
+
+422
+00:33:05,910 --> 00:33:11,030
+الموجودة لكل حد من الحدود الموجودة ففي عندنا قانون
+
+423
+00:33:11,750 --> 00:33:14,470
+عساس ان احنا .. بس بدنا ناخد برضه بقالنا من شغلة
+
+424
+00:33:14,470 --> 00:33:20,890
+تانية انا لما بقول second second order لازم دايما
+
+425
+00:33:20,890 --> 00:33:26,610
+ال powers هنا مجموحهم two تتفق مع الاتنين فهنا
+
+426
+00:33:26,610 --> 00:33:29,870
+اتنين اصلا هيها هنا انا واحد و واحد ال two
+
+427
+00:33:29,870 --> 00:33:33,790
+variables مجموحهم اتنين هنا اتنين ال third هتلاقوا
+
+428
+00:33:33,790 --> 00:33:36,150
+نفس الفكرة موجودة في ال fourth من نفس الكلام
+
+429
+00:33:36,150 --> 00:33:40,060
+فهتلاقوا دايماالحدود اللي موجودة هنا ال powers
+
+430
+00:33:40,060 --> 00:33:43,400
+تعادتها مع بعض ال powers تعادتها مع بعض هذا لما
+
+431
+00:33:43,400 --> 00:33:46,060
+تكون ال polynomial ال polynomial بهذا الشكل بهذا
+
+432
+00:33:46,060 --> 00:33:52,200
+الشكل جاية من roots to the power n مجموعة roots to
+
+433
+00:33:52,200 --> 00:33:56,460
+the power n في الحالة هذه بنقدر نميز حتى ان كل
+
+434
+00:33:56,460 --> 00:34:00,660
+الحدود مكتوبة صح لازم كلها دايما مجموحهم n دايما
+
+435
+00:34:00,660 --> 00:34:05,580
+مجموحهم n كويس خلينا نشوفماشي القانون الوطنية x
+
+436
+00:34:05,580 --> 00:34:09,020
+زائد y to the power n هتساوي summation okay طبيعي
+
+437
+00:34:09,020 --> 00:34:12,680
+ال summation هي واضح انها مجموعة حدود مجموعة حدود
+
+438
+00:34:12,680 --> 00:34:16,700
+الحدود هذه وجدنا ان ال coefficients بتاعتهم هي
+
+439
+00:34:16,700 --> 00:34:21,960
+عبارة عن ال combination ل n و j جي هذا بنبدأ من ال
+
+440
+00:34:21,960 --> 00:34:26,920
+.. من الحد صفر لحد n بنبدأ من الصفر
+
+441
+00:34:30,050 --> 00:34:34,190
+للحد الأول طبعا لما تكون هنا جل ساوة زيرو ال
+
+442
+00:34:34,190 --> 00:34:39,230
+coefficient هيطلع بالساوية واحد واحد لإنه هتلاقوا
+
+443
+00:34:39,230 --> 00:34:41,970
+هيطلع في الأخر n factorial على n factorial على
+
+444
+00:34:41,970 --> 00:34:46,690
+اعتبار ان ال R factorial بواحد كقيمة باعتبار ان هي
+
+445
+00:34:46,690 --> 00:34:50,710
+zero factorial قيمتها بواحد فهيظل ايش n minus zero
+
+446
+00:34:50,710 --> 00:34:52,870
+factorial فهي n factorial, n factorial على n
+
+447
+00:34:52,870 --> 00:34:56,390
+factorial هيطلع بواحد فدائما هتلاقوا واحد و هذا
+
+448
+00:34:56,390 --> 00:34:58,490
+اللي خلاني دائما و أنا ببدأ بحكي ايش
+
+449
+00:35:01,440 --> 00:35:04,400
+عرفتوا كيف عرفناها ده على طول بطلع معايا واحد على
+
+450
+00:35:04,400 --> 00:35:08,260
+السري بحط أولها واحد و أخرها واحد لأن أخرها ما هو
+
+451
+00:35:08,260 --> 00:35:13,100
+مكمل للأولى مش هو نفسه مكمل للأولى كمان مرة
+
+452
+00:35:13,100 --> 00:35:16,980
+القانون المهم اللي لازم تكونوا ماخدين بالكوا منه n
+
+453
+00:35:16,980 --> 00:35:25,340
+ال n هنا combination n و r بساوي
+
+454
+00:35:31,310 --> 00:35:35,190
+فلما ببدأ بصفر هي نفسها في حالة ال N وهذه الأخيرة
+
+455
+00:35:35,190 --> 00:35:39,050
+كانت في حالة ال N هانا بدأ هنا من صفر to N فإذا
+
+456
+00:35:39,050 --> 00:35:41,810
+أخر term برضه ال coefficient تبعه هيكون مشابه لأول
+
+457
+00:35:41,810 --> 00:35:47,630
+term مشابه لين لأول .. لأول term okay X to the
+
+458
+00:35:47,630 --> 00:35:51,790
+power N minus J فانا دايما ببدأ بالصفر فببدأ ب X
+
+459
+00:35:51,790 --> 00:35:55,070
+to the power N فعلا في ال second هاني بدأت تبقى X
+
+460
+00:35:55,070 --> 00:36:02,070
+تربية بعد هيك بتصير واحد فصارت XN minus واحد و هنا
+
+461
+00:36:02,070 --> 00:36:06,970
+صارت بدأ Y واحد بحيث أن مجموحهم يظل N اللي هي
+
+462
+00:36:06,970 --> 00:36:09,790
+second order بده يظل مجموحهم N third order بده يظل
+
+463
+00:36:09,790 --> 00:36:13,890
+مجموحهم فوق المجموع دايما تلاتة fourth بده دايما
+
+464
+00:36:13,890 --> 00:36:17,970
+أربعة five بده يظل دايما خمسة okay تتوسع بالشكل
+
+465
+00:36:17,970 --> 00:36:25,250
+هذا N و Zeroلل X to the power N N واحد X minus one
+
+466
+00:36:25,250 --> 00:36:34,370
+و Y لعندما تستمروا لمين ل N و N هذه في حالة مين Y
+
+467
+00:36:34,370 --> 00:36:42,410
+to the power N Y to the power N okay فهدولة ال
+
+468
+00:36:42,410 --> 00:36:45,090
+coefficients ل binomial
+
+469
+00:36:48,020 --> 00:36:51,400
+خلّينا نشوف مثل كيف نستطيع أن نشتغل عليها what's
+
+470
+00:36:51,400 --> 00:36:54,960
+the coefficient of X to the power 12 أو X to the
+
+471
+00:36:54,960 --> 00:37:02,240
+power 12 في X to the power 13 بدنا الحد X to the
+
+472
+00:37:02,240 --> 00:37:05,240
+power 12 و X to the power 13 جداش ال coefficient
+
+473
+00:37:05,240 --> 00:37:09,000
+تبعه طيب واضح أن أحنا ال order اللي بنشتغل عليها
+
+474
+00:37:09,000 --> 00:37:13,810
+كلها على بعض جداش مجموحهخمسة و عشرين وهي لما كنا
+
+475
+00:37:13,810 --> 00:37:17,290
+هنا نقول واحد و واحد هذا واضح أن هذا أحد حدود
+
+476
+00:37:17,290 --> 00:37:22,690
+second order طب معناه ذلك أن هذا أحد حدود .. أحد
+
+477
+00:37:22,690 --> 00:37:25,630
+حدود مين؟ الخمسة و عشرين .. الخمسة و عشرين هذا أحد
+
+478
+00:37:25,630 --> 00:37:28,150
+حدود الخمسة و عشرين فانا automatically عارف في
+
+479
+00:37:28,150 --> 00:37:32,210
+الحالة أن ال N عندني تساوي خمسة و عشرين يدوم حتى
+
+480
+00:37:32,210 --> 00:37:37,590
+ما يقولك بس بضل انا محتاج .. محتاج المعادلة ليش؟
+
+481
+00:37:37,590 --> 00:37:40,960
+محتاج المعادلة عشان أتأكد بس أن هل في أي ..أي
+
+482
+00:37:40,960 --> 00:37:44,040
+أجزاء أو أي قيم values مضروبة في ال X و ال Y و لا
+
+483
+00:37:44,040 --> 00:37:47,620
+لأ لأن هذا هتغير النتيجة هتغير تماما قيمة النتيجة
+
+484
+00:37:47,620 --> 00:37:50,700
+واللازم مش مضروب خلاص ال coefficient على طول هو ال
+
+485
+00:37:50,700 --> 00:37:54,220
+combination هو ال combination ففي الحالة دي هتكون
+
+486
+00:37:54,220 --> 00:37:59,360
+هي ال combination تعتمد
+
+487
+00:37:59,360 --> 00:38:10,220
+25 و 12 أو 25 و 13لأن الاتنين هيكملوا بعض واحدة
+
+488
+00:38:10,220 --> 00:38:15,100
+هتكون R والتانية هتكون N-R واحدة هيك واحدة هيك
+
+489
+00:38:15,100 --> 00:38:19,720
+فانتوا تاخدوا ال power 12 بمشي الحال وانتوا تاخدوا
+
+490
+00:38:19,720 --> 00:38:22,800
+ال power 13 برضه بمشي الحال برضه هيمشي الحال في
+
+491
+00:38:22,800 --> 00:38:27,400
+الآخر هيطلعوا بيساووا بعض عرفتوا اني مش عارفتهم
+
+492
+00:38:27,400 --> 00:38:31,840
+برضه؟ هين شوية شوية عرفتهم ولو كنت سر ال .. كيف ..
+
+493
+00:38:31,840 --> 00:38:35,780
+بدكوا بضلني بكمل بكمل للآخر كمان بس هين عرفنا ده
+
+494
+00:38:35,780 --> 00:38:40,770
+ما ببدأ بواحد و بانتي بواحدعرفنا ليش دايما كل رقم
+
+495
+00:38:40,770 --> 00:38:43,310
+باكود بوناعرف أنه لازم يتكرر على ناحية تانية عرفنا
+
+496
+00:38:43,310 --> 00:38:46,990
+ليش طيب برضه في أرقام زيادة بتبين مع أن الوجد برضه
+
+497
+00:38:46,990 --> 00:38:53,230
+جاينة هنعرفها كيف كويس زي ما قلنا خلاص بنختار 12 و
+
+498
+00:38:53,230 --> 00:38:56,410
+من 25 و بنان عليها بنختار ال combination بتاعتنا
+
+499
+00:38:56,410 --> 00:38:59,810
+فهيطلع عندنا خمسة مليون و متين ألف و تلاتمية هذا
+
+500
+00:38:59,810 --> 00:39:04,430
+ال coefficient لمين للحد X to the power إتناش في Y
+
+501
+00:39:04,430 --> 00:39:05,690
+to the power تلتاش
+
+502
+00:39:08,170 --> 00:39:12,890
+طيب هالوقت مطلوب برضه نفس الكلام نفس ال term بدنا
+
+503
+00:39:12,890 --> 00:39:19,050
+نجيب ال coefficient بس لاقاش المعادلة 2x-3y كله to
+
+504
+00:39:19,050 --> 00:39:23,130
+the power 25 طيب
+
+505
+00:39:23,130 --> 00:39:29,320
+احنا ال combination بتمشي معايا في حالة انهال
+
+506
+00:39:29,320 --> 00:39:32,640
+multiplier لكل واحدة منهم ال multiplier واحد واحد
+
+507
+00:39:32,640 --> 00:39:36,220
+بيمشي الحالة بس لما يكون ال multiplier مختلف ال
+
+508
+00:39:36,220 --> 00:39:38,760
+coefficient حصلة من الأساس مختلف واضح انه لأ
+
+509
+00:39:38,760 --> 00:39:41,880
+هيختلف الموضوع ففي الحالة دي بحولها للصورة اللي
+
+510
+00:39:41,880 --> 00:39:46,020
+انا حافظها الصورة اللي انا حافظها x و y لأ انا
+
+511
+00:39:46,020 --> 00:39:52,030
+عندى هنا 2x فبحط 2x عبارة عن ايهتمام؟ طيب minus
+
+512
+00:39:52,030 --> 00:39:56,610
+three y بحطهم عبارة عن بي و بقول ان هي هي ايه زائد
+
+513
+00:39:56,610 --> 00:39:59,430
+بي to the power خمسة و عشرين هذه automatically
+
+514
+00:39:59,430 --> 00:40:05,290
+هتساوي بدون اي مشاكل خمسة و عشرين و twelve فانا
+
+515
+00:40:05,290 --> 00:40:08,990
+مجدش اختيار اتناش من خمسة و عشرين او ال
+
+516
+00:40:08,990 --> 00:40:13,410
+combination لخمسة و عشرين اتناش اه طيب هذا الكلام
+
+517
+00:40:13,410 --> 00:40:19,490
+ل a و b بس هو مش طالب من a و b هو طالب انه حدثx to
+
+518
+00:40:19,490 --> 00:40:23,030
+the power 12 و y to the power 13 طيب ايش الفرق بين
+
+519
+00:40:23,030 --> 00:40:29,310
+ال x و ال a؟ اتنين طيب الاتنين هذه لما نقول خمسة و
+
+520
+00:40:29,310 --> 00:40:34,310
+عشرين او a to the power خمسة و عشرين و انا عارف ان
+
+521
+00:40:34,310 --> 00:40:39,290
+ال a عبارة عن اتنين x to the power خمسة و عشرين
+
+522
+00:40:39,290 --> 00:40:43,830
+فاذا هذه بتساوي انا بدي ال term okay ال term
+
+523
+00:40:43,830 --> 00:40:48,670
+بنكررها بعدين بدي ال term x خمسة و عشرين مثلامعنى
+
+524
+00:40:48,670 --> 00:40:54,830
+ذلك أنه جديش القيمة 2 برضه to the power 25 طيب
+
+525
+00:40:54,830 --> 00:40:59,990
+نظبط الكلام هذا وجد على المثال تبعنا 12 لان هو
+
+526
+00:40:59,990 --> 00:41:05,130
+طالب من ايه؟ 12 انا بتدصر له ال 12 12 لل إيه؟ 12
+
+527
+00:41:05,130 --> 00:41:18,120
+لل 2x و 12 لل 2 و 12 لل .. okayهذا ال term هو أصلا
+
+528
+00:41:18,120 --> 00:41:23,160
+هي موجود في ال coefficient تبعتي هو اللي أنا طالبه
+
+529
+00:41:23,160 --> 00:41:26,360
+أصلا لأنه في الآخر بدي أميزه ب X to the power 12 و
+
+530
+00:41:26,360 --> 00:41:29,700
+Y to the power 13 بدي ال term اللي جدامه فال term
+
+531
+00:41:29,700 --> 00:41:35,680
+اللي جدامه أشير يظل في 2 to
+
+532
+00:41:35,680 --> 00:41:43,360
+the power 12هيخلصنا X ضالة Y Y بنفس القلية بنفس
+
+533
+00:41:43,360 --> 00:41:49,160
+الفكرة هتكون minus 3 to the power 13 بنضرب هدول ال
+
+534
+00:41:49,160 --> 00:41:51,600
+term هدا كله مع بعض و بنجمعه بتلا هو ال
+
+535
+00:41:51,600 --> 00:41:54,740
+coefficient لمين ل X to the power 12 في Y to the
+
+536
+00:41:54,740 --> 00:42:01,300
+power 13 واضح اللي الجزئية في الآخر هدى؟ الجزئية
+
+537
+00:42:01,300 --> 00:42:05,040
+في الآخر سلسة مش مشكلة ال coefficient بس بتضربوه
+
+538
+00:42:05,040 --> 00:42:09,400
+خارجالـ combination خارج ال combination طبعا
+
+539
+00:42:09,400 --> 00:42:15,440
+تحافظوا على ال power تحافظوا على ال power طبعا
+
+540
+00:42:15,440 --> 00:42:22,260
+بتطلع لكوا تقريبا 34 في 10 to the power 15 او
+
+541
+00:42:22,260 --> 00:42:27,080
+minus الحقيقة فيها minus تقريبا minus 34 في 10 to
+
+542
+00:42:27,080 --> 00:42:28,540
+the power 15
+
+543
+00:42:30,710 --> 00:42:34,210
+كنتائج أو كنظريات ناتجة من الموضوع هذا ممكن يطلع
+
+544
+00:42:34,210 --> 00:42:41,690
+كذا نظرية منهم ان
+
+545
+00:42:41,690 --> 00:42:46,430
+اتنين to the power of N بتساوي summation from zero
+
+546
+00:42:46,430 --> 00:42:52,290
+to N لcombination N وJ من أين جبناها؟ كل اللي
+
+547
+00:42:52,290 --> 00:42:56,090
+عملناه فرضنا X بتساوي واحد وY بتساوي واحد انا لو
+
+548
+00:42:56,090 --> 00:43:00,850
+عرفه ان Xزائد y to the power n بتساوي ال summation
+
+549
+00:43:00,850 --> 00:43:04,230
+تبعنا و ال coefficient ها دي أنا مقتنع ان هي فعلا
+
+550
+00:43:04,230 --> 00:43:07,290
+هي ال coefficient تبعتنا بس مضروبة في ال x و ال y
+
+551
+00:43:07,290 --> 00:43:11,810
+بال powers بتاعتهم طب لما حط ها دي بواحد زائد واحد
+
+552
+00:43:11,810 --> 00:43:20,050
+صارت اتنين اصبح هنا عند اتنين هيها و هنا واحد واحد
+
+553
+00:43:20,050 --> 00:43:24,430
+to the power اي شي حيطل واحد بيظل قيمته بواحد okay
+
+554
+00:43:24,430 --> 00:43:30,220
+فبيظل عندى بسمجموع الكوير ال combination فبرضه هذه
+
+555
+00:43:30,220 --> 00:43:33,000
+سهلة جدا كل اللي بتعمله بس هذه المعادرة الرئاسية
+
+556
+00:43:33,000 --> 00:43:38,180
+بتاعتنا عوضه X بواحد و Y بواحد طبعا واضح ان تقدروا
+
+557
+00:43:38,180 --> 00:43:41,800
+تعملوا special cases جد ما بدكوا فيها حطوا X قيمته
+
+558
+00:43:41,800 --> 00:43:45,060
+كذا و Y قيمته كذا بتطلعوا كتير نظريات لحالكوا
+
+559
+00:43:45,060 --> 00:43:48,960
+هتطلعوها هنا نفس الكلام هتلاقوا
+
+560
+00:43:53,710 --> 00:44:01,270
+Summation ل-1-1 to the power j في ال combination n
+
+561
+00:44:01,270 --> 00:44:06,330
+و j equal to 0 منطقي جدا ليش؟ j هذه الفردي هتطلع
+
+562
+00:44:06,330 --> 00:44:11,590
+القيمة هذه بالسالي زوجي موجب و في نفس الوقت انا
+
+563
+00:44:11,590 --> 00:44:14,650
+عارف ان هذه مساوية تماما ل
+
+564
+00:44:18,030 --> 00:44:20,350
+فواحدة term هيطلع موجة و ترم هيطلع سالب و ترم
+
+565
+00:44:20,350 --> 00:44:22,890
+هيطلع موجة و ترم هيطلع سالب و في الآخر هيطلع كله
+
+566
+00:44:22,890 --> 00:44:27,470
+بساوي .. بساوي zero من وين اجت برضه بسيطة جدا كل
+
+567
+00:44:27,470 --> 00:44:32,890
+اللي هتعودوا في x زائد y to the power أي .. أي n
+
+568
+00:44:32,890 --> 00:44:36,530
+افرضوا هذه بواحد وهذه بسالب واحد هي الصفر تبعكم
+
+569
+00:44:36,530 --> 00:44:41,470
+عوضوا هنا واحد سالب واحد هيظهرالـ minus one حيظهر
+
+570
+00:44:41,470 --> 00:44:43,830
+الـ minus one طبعا ال one ماحطنهش والاصل فيه كمان
+
+571
+00:44:43,830 --> 00:44:47,210
+one لأنه بتاعة ال X بس one to the power اي شيء مش
+
+572
+00:44:47,210 --> 00:44:52,290
+هيغير فشاله فانشال هنا طبعا برضه بتقدر تحطه واحد و
+
+573
+00:44:52,290 --> 00:44:57,510
+اتنين فبتطلع قانون جديد كل هذه special case من ال
+
+574
+00:44:57,510 --> 00:45:04,240
+general case اللي انتوا أخدتوها okay الأهمواللي
+
+575
+00:45:04,240 --> 00:45:07,960
+هلوقت هيبين كيف انا اشتغلت الموضوع هذا كيف عرفتم
+
+576
+00:45:07,960 --> 00:45:12,580
+على طول و هلوقت هيبين ها هي واحد خمسة عشرة عشرة
+
+577
+00:45:12,580 --> 00:45:21,840
+خمسة واحد okay واضحة صح بيانات حلو جدا هلوقت دائما
+
+578
+00:45:21,840 --> 00:45:26,040
+n زائد واحد j combination ل n زائد واحد j بساوي
+
+579
+00:45:26,040 --> 00:45:32,360
+ناجس واحد ناجس واحد زائد nj
+
+580
+00:45:34,420 --> 00:45:38,800
+طيب إيش معنى؟ معنى ذلك إنه هدى احنا قولنا هنا ال
+
+581
+00:45:38,800 --> 00:45:45,300
+zero order نمحى هدول عشان نضلنا مع هدول هدى كانت
+
+582
+00:45:45,300 --> 00:45:49,940
+zero order هى ال first order هدى ال first هى ال
+
+583
+00:45:49,940 --> 00:45:58,550
+second هى ال third هى ال fourth وهى ال fiveOkay لو
+
+584
+00:45:58,550 --> 00:46:02,890
+بدنا ال term هذا احنا بتكلم عنه ال third فانا
+
+585
+00:46:02,890 --> 00:46:12,090
+بتكلم عن C تلاتة واحد اتنين اتنين تمام
+
+586
+00:46:12,090 --> 00:46:21,130
+واحد اتنين حتى هذه واحد تلاتة واحد تلاتة
+
+587
+00:46:21,130 --> 00:46:24,930
+واحد طيب يساوي اتنين
+
+588
+00:46:27,660 --> 00:46:34,080
+zero تمام اتنين واحد طب لحظة باخدهم من اللي فوجه
+
+589
+00:46:34,080 --> 00:46:38,020
+معناته اتنين من ال second order الاتنين اللي
+
+590
+00:46:38,020 --> 00:46:39,320
+حواليه اللي كانوا فوجه هنا و هنا
+
+591
+00:46:42,440 --> 00:46:45,840
+واحد زائد اتنين هذه قيمتها كانت واحد وانا قيمتها
+
+592
+00:46:45,840 --> 00:46:50,540
+اتنين تلاتة نفس الكلام هنا تلاتة و الأقراف اتفجنا
+
+593
+00:46:50,540 --> 00:46:56,180
+انه دائما once دائما once طب واضح ان احنا جاعدين
+
+594
+00:46:56,180 --> 00:47:02,120
+بنعمل هرم triangle هذي Pascal's triangle هذي ال
+
+595
+00:47:02,120 --> 00:47:05,940
+Pascal اللي عملها فسميها Pascal's triangleمن
+
+596
+00:47:05,940 --> 00:47:09,540
+القانون القانون اللى علناه ال combination ل N plus
+
+597
+00:47:09,540 --> 00:47:14,740
+واحد J بساوي combination ل N J minus one plus
+
+598
+00:47:14,740 --> 00:47:23,260
+combination N و J هذا هيعطينا ال triangles عفوا
+
+599
+00:47:23,260 --> 00:47:29,220
+باسكالز triangle باسكالز triangle فهنا C00 C21
+
+600
+00:47:29,220 --> 00:47:33,720
+بقدر اجيبها من C10 plus C11 معناه بنات
+
+601
+00:47:36,840 --> 00:47:41,340
+لحظوا ففي الآخر واضحة صارت كيف نقدر نجيب الموضوع
+
+602
+00:47:41,340 --> 00:47:47,440
+هذا عشان نطلع ال triangle كلها ال triangle كلها لو
+
+603
+00:47:47,440 --> 00:47:52,100
+عندكوا أي .. أي coefficient بتقدروا تجيبوا ال
+
+604
+00:47:52,100 --> 00:47:55,180
+coefficient ل ال order اللي وراها بتقدروا تجيبوا
+
+605
+00:47:55,180 --> 00:47:58,920
+ال coefficient لمن؟ لل order اللي بعدها طريقة سهلة
+
+606
+00:47:58,920 --> 00:48:02,600
+و بتقدروا ت .. يعني تعملوا فيها منظر على صحفاتكوا
+
+607
+00:48:02,600 --> 00:48:08,220
+على ..تقولوا اه هنا عارفين ال .. ال .. ال .. ال ..
+
+608
+00:48:08,220 --> 00:48:16,300
+بس كان ال triangle okay لحظة
+
+609
+00:48:16,300 --> 00:48:26,910
+once لحظة هنا once كله و لحظة هنامتشابهات كله إذا
+
+610
+00:48:26,910 --> 00:48:30,270
+كان كله زوجي هيكون كله identical كله كأنه فيه
+
+611
+00:48:30,270 --> 00:48:33,410
+mirror الفرد لأ هيكون فيه عنصر زيادة في النصر في
+
+612
+00:48:33,410 --> 00:48:37,790
+عنصر زيادة في النصر في الحالة اللي عندنا طبعا ال
+
+613
+00:48:37,790 --> 00:48:40,610
+.. ال .. ال Pascal's triangle فيه كتير علاقات بين
+
+614
+00:48:40,610 --> 00:48:42,830
+الأرقام و بعضها غير الأرقام اللي احنا قلناهم كمان
+
+615
+00:48:42,830 --> 00:48:46,550
+غير اللي احنا قلناهم بس احنا مش بصدر نزود كتير في
+
+616
+00:48:46,550 --> 00:48:49,610
+.. في الشغل okay
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..529c33778b5b01ccab9299ef90fe51f2d900dc1c
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/WgINAVEwlRs_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3470, "start": 20.94, "end": 34.7, "text": "طيب بسم الله الرحمن الرحيم الصلاة والسلام على أشرف الأنبياء والمرسلين سيدنا محمد وعلى أليه وصحبه أجمعين نكمل في ال permutation أو التبديل في ال permutation كان اخر اشي أخدناه ان احنا بدنا نعمل cutting ل ..", "tokens": [9566, 1829, 3555, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 4032, 45340, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 20292, 3224, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 8717, 24793, 1211, 8978, 2423, 4784, 11380, 34051, 16712, 3555, 16254, 1211, 8978, 2423, 4784, 11380, 25961, 1975, 34740, 1975, 8592, 1829, 5551, 9778, 3215, 8315, 3224, 16472, 1975, 5016, 8315, 47525, 8315, 8717, 25957, 1211, 6492, 5296, 4386], "avg_logprob": -0.18899600730931504, "compression_ratio": 1.698019801980198, "no_speech_prob": 2.2649765014648438e-06, "words": [{"start": 20.94, "end": 21.24, "word": "طيب", "probability": 0.7984212239583334}, {"start": 21.24, "end": 21.44, "word": " بسم", "probability": 0.893798828125}, {"start": 21.44, "end": 21.56, "word": " الله", "probability": 0.943359375}, {"start": 21.56, "end": 21.84, "word": " الرحمن", "probability": 0.9441731770833334}, {"start": 21.84, "end": 22.08, "word": " الرحيم", "probability": 0.990234375}, {"start": 22.08, "end": 22.32, "word": " الصلاة", "probability": 0.8694661458333334}, {"start": 22.32, "end": 22.62, "word": " والسلام", "probability": 0.8043619791666666}, {"start": 22.62, "end": 22.76, "word": " على", "probability": 0.53662109375}, {"start": 22.76, "end": 22.98, "word": " أشرف", "probability": 0.97216796875}, {"start": 22.98, "end": 23.22, "word": " الأنبياء", "probability": 0.921630859375}, {"start": 23.22, "end": 23.6, "word": " والمرسلين", "probability": 0.7967936197916666}, {"start": 23.6, "end": 23.9, "word": " سيدنا", "probability": 0.9031575520833334}, {"start": 23.9, "end": 24.4, "word": " محمد", "probability": 0.9918619791666666}, {"start": 24.4, "end": 25.1, "word": " وعلى", "probability": 0.8912760416666666}, {"start": 25.1, "end": 25.3, "word": " أليه", "probability": 0.4734700520833333}, {"start": 25.3, "end": 25.62, "word": " وصحبه", "probability": 0.898828125}, {"start": 25.62, "end": 26.0, "word": " أجمعين", "probability": 0.90087890625}, {"start": 26.0, "end": 27.24, "word": " نكمل", "probability": 0.7862955729166666}, {"start": 27.24, "end": 27.6, "word": " في", "probability": 0.93701171875}, {"start": 27.6, "end": 27.8, "word": " ال", "probability": 0.9736328125}, {"start": 27.8, "end": 28.44, "word": " permutation", "probability": 0.960693359375}, {"start": 28.44, "end": 29.08, "word": " أو", "probability": 0.78955078125}, {"start": 29.08, "end": 29.78, "word": " التبديل", "probability": 0.890380859375}, {"start": 29.78, "end": 30.42, "word": " في", "probability": 0.62548828125}, {"start": 30.42, "end": 30.66, "word": " ال", "probability": 0.857421875}, {"start": 30.66, "end": 31.22, "word": " permutation", "probability": 0.9921875}, {"start": 31.22, "end": 31.5, "word": " كان", "probability": 0.978515625}, {"start": 31.5, "end": 31.92, "word": " اخر", "probability": 0.659423828125}, {"start": 31.92, "end": 32.66, "word": " اشي", "probability": 0.8736979166666666}, {"start": 32.66, "end": 33.2, "word": " أخدناه", "probability": 0.89970703125}, {"start": 33.2, "end": 33.3, "word": " ان", "probability": 0.48193359375}, {"start": 33.3, "end": 33.48, "word": " احنا", "probability": 0.8429361979166666}, {"start": 33.48, "end": 33.68, "word": " بدنا", "probability": 0.87841796875}, {"start": 33.68, "end": 33.92, "word": " نعمل", "probability": 0.9973958333333334}, {"start": 33.92, "end": 34.22, "word": " cutting", "probability": 0.935546875}, {"start": 34.22, "end": 34.46, "word": " ل", "probability": 0.85986328125}, {"start": 34.46, "end": 34.7, "word": " ..", "probability": 0.6259765625}], "temperature": 1.0}, {"id": 2, "seek": 5976, "start": 34.9, "end": 59.76, "text": "three wires من ten wires كانوا موجودين فكانت هنا العملية عملية order يعني كان لازم العشر أسلاك اللي بدنا نقطعهم يكونوا مرتبين من العشر أسلاك التلاتة اللي بدنا نقطعهم يكونوا مرتبين الأول في ال order تبعه صح كان فعلا أول واحد نقطعه و التاني في نفس وقته و التالت برضه في نفس اللحظة و كنا اتكلمنا فيها عن", "tokens": [27583, 15537, 9154, 2064, 15537, 25961, 14407, 3714, 29245, 23328, 9957, 6156, 41361, 2655, 34105, 18863, 42213, 10632, 6225, 42213, 10632, 1668, 37495, 22653, 25961, 5296, 31377, 2304, 18863, 46309, 5551, 3794, 15040, 4117, 13672, 1829, 47525, 8315, 8717, 47432, 3615, 16095, 7251, 30544, 14407, 3714, 43500, 3555, 9957, 9154, 18863, 46309, 5551, 3794, 15040, 4117, 16712, 1211, 9307, 3660, 13672, 1829, 47525, 8315, 8717, 47432, 3615, 16095, 7251, 30544, 14407, 3714, 43500, 3555, 9957, 16247, 12610, 8978, 2423, 1668, 6055, 3555, 3615, 3224, 20328, 5016, 25961, 6156, 3615, 15040, 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permutation", "probability": 0.94140625}], "temperature": 1.0}, {"id": 11, "seek": 29168, "start": 263.28, "end": 291.68, "text": "و ال combination التنتين يتفقوا ان هما without replacement بدون تكرار بدون ان نرجع ال selected item ل ال universe of discourse بتاعتنا عشان نرجع نختارها كمان مرة فهنا خمسة بدنا نختار منهم تلتة بدنا نختار منهم تلتة بتقدروا تحسبوها بنفس القانون اللي كنا كتبينه بطلع معاكم ستين بطلع معانا ستين okay طيب ال permutation ايش كانت تختلف عن ال combination؟", "tokens": [2407, 2423, 6562, 16712, 29399, 9957, 7251, 2655, 5172, 4587, 14407, 16472, 8032, 15042, 1553, 14419, 47525, 11536, 6055, 37983, 9640, 47525, 11536, 16472, 8717, 47341, 3615, 2423, 8209, 3174, 5296, 2423, 6445, 295, 23938, 39894, 995, 34268, 8315, 6225, 8592, 7649, 8717, 47341, 3615, 8717, 46456, 9640, 11296, 9122, 2304, 7649, 3714, 25720, 6156, 3224, 8315, 16490, 2304, 3794, 3660, 47525, 8315, 8717, 46456, 9640, 9154, 16095, 6055, 1211, 2655, 3660, 47525, 8315, 8717, 46456, 9640, 9154, 16095, 6055, 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19, "seek": 49760, "start": 471.62, "end": 497.6, "text": "اللي بدنا نختاره هو جزء منكوا، يعني هم ال subset منكوا أصلا، يعني هم جزء أساسا منكوا، فاحنا مش هنروح نختار من الفصل اللي جنبنا، لأ احنا هنختار منكوا، من عندكوا، فاحنا هنختار تلاتة، التلاتة هدول هيكونوا العدد R، لما أقول بدنا نختار تلاتة من خمسة، فانا بكتبها هي خمسة تلاتة، تلاتة من خمسة، فبدنا نختار تلاتة هدولة ال cardinality أو جدش عدد ال elements belonging to main to set T", "tokens": [6027, 20292, 47525, 8315, 8717, 46456, 9640, 3224, 31439, 10874, 11622, 38207, 9154, 4117, 14407, 12399, 37495, 22653, 8032, 2304, 2423, 25993, 9154, 4117, 14407, 5551, 9381, 15040, 12399, 37495, 22653, 8032, 2304, 10874, 11622, 38207, 5551, 3794, 32277, 995, 9154, 4117, 14407, 12399, 6156, 39319, 8315, 37893, 8032, 1863, 32887, 5016, 8717, 46456, 9640, 9154, 27188, 36520, 13672, 1829, 10874, 1863, 3555, 8315, 12399, 5296, 10721, 1975, 5016, 8315, 8032, 1863, 46456, 9640, 9154, 4117, 14407, 12399, 9154, 43242, 4117, 14407, 12399, 6156, 39319, 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{"start": 478.98, "end": 479.26, "word": " هنختار", "probability": 0.81414794921875}, {"start": 479.26, "end": 479.56, "word": " منكوا،", "probability": 0.889892578125}, {"start": 479.56, "end": 479.64, "word": " من", "probability": 0.96630859375}, {"start": 479.64, "end": 480.4, "word": " عندكوا،", "probability": 0.792724609375}, {"start": 480.4, "end": 480.62, "word": " فاحنا", "probability": 0.9137369791666666}, {"start": 480.62, "end": 480.86, "word": " هنختار", "probability": 0.8221435546875}, {"start": 480.86, "end": 481.56, "word": " تلاتة،", "probability": 0.91962890625}, {"start": 481.56, "end": 481.96, "word": " التلاتة", "probability": 0.96875}, {"start": 481.96, "end": 482.16, "word": " هدول", "probability": 0.9557291666666666}, {"start": 482.16, "end": 482.8, "word": " هيكونوا", "probability": 0.9269205729166666}, {"start": 482.8, "end": 483.8, "word": " العدد", "probability": 0.9527994791666666}, {"start": 483.8, "end": 484.9, "word": " R،", "probability": 0.55419921875}, {"start": 484.9, "end": 485.06, "word": " لما", "probability": 0.9541015625}, {"start": 485.06, "end": 485.2, "word": " أقول", "probability": 0.6400146484375}, {"start": 485.2, "end": 485.36, "word": " بدنا", "probability": 0.905029296875}, {"start": 485.36, "end": 485.66, "word": " نختار", "probability": 0.99462890625}, {"start": 485.66, "end": 486.2, "word": " تلاتة", "probability": 0.982421875}, {"start": 486.2, "end": 486.36, "word": " من", "probability": 0.99560546875}, {"start": 486.36, "end": 486.74, "word": " خمسة،", "probability": 0.92353515625}, {"start": 486.74, "end": 486.88, "word": " فانا", "probability": 0.8665364583333334}, {"start": 486.88, "end": 487.32, "word": " بكتبها", "probability": 0.93544921875}, {"start": 487.32, "end": 487.52, "word": " هي", "probability": 0.6435546875}, {"start": 487.52, "end": 488.12, "word": " خمسة", "probability": 0.9874267578125}, {"start": 488.12, "end": 488.88, "word": " تلاتة،", "probability": 0.89609375}, {"start": 488.88, "end": 489.3, "word": " تلاتة", "probability": 0.9873046875}, {"start": 489.3, "end": 489.4, "word": " من", "probability": 0.99658203125}, {"start": 489.4, "end": 490.18, "word": " خمسة،", "probability": 0.94423828125}, {"start": 490.18, "end": 490.4, "word": " فبدنا", "probability": 0.9466145833333334}, {"start": 490.4, "end": 490.72, "word": " نختار", "probability": 0.9954427083333334}, {"start": 490.72, "end": 491.92, "word": " تلاتة", "probability": 0.992919921875}, {"start": 491.92, "end": 492.84, "word": " هدولة", "probability": 0.861328125}, {"start": 492.84, "end": 493.32, "word": " ال", "probability": 0.85205078125}, {"start": 493.32, "end": 493.92, "word": " cardinality", "probability": 0.8224283854166666}, {"start": 493.92, "end": 494.12, "word": " أو", "probability": 0.87255859375}, {"start": 494.12, "end": 494.42, "word": " جدش", "probability": 0.7252604166666666}, {"start": 494.42, "end": 494.68, "word": " عدد", "probability": 0.9939778645833334}, {"start": 494.68, "end": 494.84, "word": " ال", "probability": 0.98095703125}, {"start": 494.84, "end": 495.34, "word": " elements", "probability": 0.9296875}, {"start": 495.34, "end": 496.0, "word": " belonging", "probability": 0.470703125}, {"start": 496.0, "end": 496.2, "word": " to", "probability": 0.98388671875}, {"start": 496.2, "end": 496.38, "word": " main", "probability": 0.4287109375}, {"start": 496.38, "end": 496.78, "word": " to", "probability": 0.763671875}, {"start": 496.78, "end": 497.08, "word": " set", "probability": 0.9833984375}, {"start": 497.08, "end": 497.6, "word": " T", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 20, "seek": 52249, "start": 498.17, "end": 522.49, "text": "اللي هم ال set ل ال selected items للناس اللي تم اختيارهم في الحالة اللي عندناها okay فهذه هتكون subset فواضح انه هنا combination انا بتكلم عن set النتيجة عندى عبارة عن set لإنه مش بالضرورة الترتيب الترتيب مش كتير مهم والله مين اخترته اول ومين تاني ومين تالت مش هتفرج المهم انه في نهاية تم اختياره خلاص", "tokens": [6027, 20292, 8032, 2304, 2423, 992, 5296, 2423, 8209, 4754, 24976, 8315, 3794, 13672, 1829, 46811, 1975, 9778, 31371, 9640, 16095, 8978, 21542, 6027, 3660, 13672, 1829, 43242, 8315, 11296, 1392, 6156, 3224, 24192, 8032, 2655, 30544, 25993, 6156, 2407, 46958, 5016, 16472, 3224, 34105, 6562, 1975, 8315, 39894, 4117, 19528, 18871, 992, 28239, 31371, 7435, 3660, 43242, 7578, 6225, 3555, 9640, 3660, 18871, 992, 5296, 28814, 1863, 3224, 37893, 20666, 11242, 2288, 13063, 3660, 16712, 2288, 31371, 3555, 16712, 2288, 31371, 3555, 37893, 9122, 2655, 13546, 3714, 16095, 16070, 43761, 3714, 9957, 1975, 46456, 43500, 3224, 1975, 12610, 4032, 2304, 9957, 6055, 7649, 1829, 4032, 2304, 9957, 6055, 6027, 2655, 37893, 8032, 2655, 5172, 47341, 9673, 16095, 16472, 3224, 8978, 8717, 11296, 10632, 46811, 1975, 9778, 31371, 9640, 3224, 16490, 1211, 33546], "avg_logprob": -0.1738572784546596, "compression_ratio": 1.945945945945946, "no_speech_prob": 6.198883056640625e-06, "words": [{"start": 498.17, "end": 498.47, "word": "اللي", "probability": 0.739013671875}, {"start": 498.47, "end": 498.97, "word": " هم", "probability": 0.84375}, {"start": 498.97, "end": 499.21, "word": " ال", "probability": 0.89697265625}, {"start": 499.21, "end": 499.49, "word": " set", "probability": 0.81396484375}, {"start": 499.49, "end": 499.93, "word": " ل", "probability": 0.66357421875}, {"start": 499.93, "end": 500.27, "word": " ال", "probability": 0.434814453125}, {"start": 500.27, "end": 500.69, "word": " selected", "probability": 0.90283203125}, {"start": 500.69, "end": 501.31, "word": " items", "probability": 0.7802734375}, {"start": 501.31, "end": 503.53, "word": " للناس", "probability": 0.7195638020833334}, {"start": 503.53, "end": 503.65, "word": " اللي", "probability": 0.925048828125}, {"start": 503.65, "end": 503.81, "word": " تم", "probability": 0.9931640625}, {"start": 503.81, "end": 504.41, "word": " اختيارهم", "probability": 0.92568359375}, {"start": 504.41, "end": 504.73, "word": " في", "probability": 0.87109375}, {"start": 504.73, "end": 505.03, "word": " الحالة", "probability": 0.9811197916666666}, {"start": 505.03, "end": 505.11, "word": " اللي", "probability": 0.935302734375}, {"start": 505.11, "end": 505.49, "word": " عندناها", "probability": 0.75}, {"start": 505.49, "end": 505.91, "word": " okay", "probability": 0.50390625}, {"start": 505.91, "end": 506.89, "word": " فهذه", "probability": 0.8138020833333334}, {"start": 506.89, "end": 507.29, "word": " هتكون", "probability": 0.8583984375}, {"start": 507.29, "end": 507.59, "word": " subset", "probability": 0.9296875}, {"start": 507.59, "end": 508.69, "word": " فواضح", "probability": 0.9688720703125}, {"start": 508.69, "end": 508.97, "word": " انه", "probability": 0.548583984375}, {"start": 508.97, "end": 509.09, "word": " هنا", "probability": 0.9775390625}, {"start": 509.09, "end": 510.19, "word": " combination", "probability": 0.76806640625}, {"start": 510.19, "end": 510.43, "word": " انا", "probability": 0.803955078125}, {"start": 510.43, "end": 510.79, "word": " بتكلم", "probability": 0.9443359375}, {"start": 510.79, "end": 511.09, "word": " عن", "probability": 0.98974609375}, {"start": 511.09, "end": 511.95, "word": " set", "probability": 0.97314453125}, {"start": 511.95, "end": 512.89, "word": " النتيجة", "probability": 0.947509765625}, {"start": 512.89, "end": 513.37, "word": " عندى", "probability": 0.632080078125}, {"start": 513.37, "end": 513.75, "word": " عبارة", "probability": 0.98876953125}, {"start": 513.75, "end": 513.93, "word": " عن", "probability": 0.9912109375}, {"start": 513.93, "end": 514.21, "word": " set", "probability": 0.96630859375}, {"start": 514.21, "end": 514.51, "word": " لإنه", "probability": 0.74365234375}, {"start": 514.51, "end": 514.77, "word": " مش", "probability": 0.9912109375}, {"start": 514.77, "end": 515.25, "word": " بالضرورة", "probability": 0.8034912109375}, {"start": 515.25, "end": 516.19, "word": " الترتيب", "probability": 0.95068359375}, {"start": 516.19, "end": 516.51, "word": " الترتيب", "probability": 0.95947265625}, {"start": 516.51, "end": 516.65, "word": " مش", "probability": 0.99462890625}, {"start": 516.65, "end": 516.87, "word": " كتير", "probability": 0.96484375}, {"start": 516.87, "end": 517.15, "word": " مهم", "probability": 0.9951171875}, {"start": 517.15, "end": 517.89, "word": " والله", "probability": 0.757080078125}, {"start": 517.89, "end": 518.85, "word": " مين", "probability": 0.9736328125}, {"start": 518.85, "end": 519.25, "word": " اخترته", "probability": 0.92626953125}, {"start": 519.25, "end": 519.43, "word": " اول", "probability": 0.7626953125}, {"start": 519.43, "end": 519.63, "word": " ومين", "probability": 0.7215169270833334}, {"start": 519.63, "end": 519.89, "word": " تاني", "probability": 0.7811686197916666}, {"start": 519.89, "end": 520.05, "word": " ومين", "probability": 0.89208984375}, {"start": 520.05, "end": 520.27, "word": " تالت", "probability": 0.9767252604166666}, {"start": 520.27, "end": 520.39, "word": " مش", "probability": 0.97021484375}, {"start": 520.39, "end": 520.79, "word": " هتفرج", "probability": 0.851806640625}, {"start": 520.79, "end": 521.29, "word": " المهم", "probability": 0.955810546875}, {"start": 521.29, "end": 521.45, "word": " انه", "probability": 0.764404296875}, {"start": 521.45, "end": 521.51, "word": " في", "probability": 0.89599609375}, {"start": 521.51, "end": 521.67, "word": " نهاية", "probability": 0.9060872395833334}, {"start": 521.67, "end": 521.85, "word": " تم", "probability": 0.174560546875}, {"start": 521.85, "end": 522.19, "word": " اختياره", "probability": 0.93994140625}, {"start": 522.19, "end": 522.49, "word": " خلاص", "probability": 0.9690755208333334}], "temperature": 1.0}, {"id": 21, "seek": 55011, "start": 523.21, "end": 550.11, "text": "هو داخل ال set الترتيب بيفرجش في ال permutation لأ كان الترتيب بيفرج فماكناش نقدر نقول ان هي subset كنا نقول string كنا نسميه string هو ناتج و ال string احنا عارفين انه يعني بيختلف بالترتيب بالترتيب تبعه بيختلف ممكن يكون نفس عدد ال elements ولكن واحد مكان واحد صار string جديد string مختلف لازم يكون له عدد لحاله فهنا how many strings انا بتكلم عن", "tokens": [3224, 2407, 11778, 47283, 1211, 2423, 992, 16712, 2288, 31371, 3555, 4724, 33911, 47341, 8592, 8978, 2423, 4784, 11380, 5296, 10721, 25961, 16712, 2288, 31371, 3555, 4724, 33911, 47341, 6156, 15042, 19452, 33599, 8717, 28543, 2288, 8717, 39648, 16472, 39896, 25993, 9122, 8315, 8717, 39648, 6798, 9122, 8315, 8717, 38251, 1829, 3224, 6798, 31439, 8717, 9307, 7435, 4032, 2423, 6798, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 16472, 3224, 37495, 22653, 4724, 1829, 46456, 46538, 20666, 2655, 2288, 31371, 3555, 20666, 2655, 2288, 31371, 3555, 6055, 3555, 3615, 3224, 4724, 1829, 46456, 46538, 3714, 43020, 7251, 30544, 8717, 36178, 6225, 3215, 3215, 2423, 4959, 35525, 19452, 36764, 24401, 3714, 41361, 36764, 24401, 20328, 9640, 6798, 10874, 16254, 3215, 6798, 3714, 46456, 46538, 5296, 31377, 2304, 7251, 30544, 46740, 6225, 3215, 3215, 5296, 5016, 6027, 3224, 6156, 3224, 8315, 577, 867, 13985, 1975, 8315, 39894, 4117, 19528, 18871], "avg_logprob": -0.1321790551615728, "compression_ratio": 2.0035971223021583, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 523.21, "end": 523.53, "word": "هو", "probability": 0.8369140625}, {"start": 523.53, "end": 523.89, "word": " داخل", "probability": 0.9716796875}, {"start": 523.89, "end": 524.05, "word": " ال", "probability": 0.912109375}, {"start": 524.05, "end": 524.35, "word": " set", "probability": 0.90380859375}, {"start": 524.35, "end": 525.69, "word": " الترتيب", "probability": 0.953125}, {"start": 525.69, "end": 526.23, "word": " بيفرجش", "probability": 0.6964111328125}, {"start": 526.23, "end": 526.83, "word": " في", "probability": 0.69580078125}, {"start": 526.83, "end": 527.21, "word": " ال", "probability": 0.97607421875}, {"start": 527.21, "end": 527.67, "word": " permutation", "probability": 0.85888671875}, {"start": 527.67, "end": 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"word": " و", "probability": 0.94873046875}, {"start": 1000.32, "end": 1000.74, "word": " ستين", "probability": 0.8943684895833334}], "temperature": 1.0}, {"id": 39, "seek": 103098, "start": 1001.92, "end": 1030.98, "text": "خمسمية أو ستة طبعا عدد كبير جدا لأنه أصلا عدد الكروت نفسها عددهم كبير عددهم كبير عدد الكروت نفسها عددهم عددهم كبير طيب ال .. how many bit string لحظوا هنا bit string أنا جاعت بقول bit string بس ماتنخدعوش معاه لأنه bit string هو وجد الأصل أن أنا هفكر بإيش بال permutation خليني أشوف", "tokens": [9778, 2304, 38251, 10632, 34051, 8608, 2655, 3660, 23032, 3555, 3615, 995, 6225, 3215, 3215, 9122, 3555, 13546, 10874, 28259, 5296, 33456, 3224, 5551, 9381, 15040, 6225, 3215, 3215, 33251, 32887, 2655, 8717, 36178, 11296, 6225, 3215, 3215, 16095, 9122, 3555, 13546, 6225, 3215, 3215, 16095, 9122, 3555, 13546, 6225, 3215, 3215, 33251, 32887, 2655, 8717, 36178, 11296, 6225, 3215, 3215, 16095, 6225, 3215, 3215, 16095, 9122, 3555, 13546, 23032, 1829, 3555, 2423, 4386, 577, 867, 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"probability": 0.9908854166666666}, {"start": 1009.94, "end": 1010.22, "word": " نفسها", "probability": 0.8216959635416666}, {"start": 1010.22, "end": 1010.62, "word": " عددهم", "probability": 0.9954833984375}, {"start": 1010.62, "end": 1011.76, "word": " عددهم", "probability": 0.92138671875}, {"start": 1011.76, "end": 1012.14, "word": " كبير", "probability": 0.9944661458333334}, {"start": 1012.14, "end": 1015.5, "word": " طيب", "probability": 0.9295247395833334}, {"start": 1015.5, "end": 1018.72, "word": " ال", "probability": 0.8154296875}, {"start": 1018.72, "end": 1019.7, "word": " ..", "probability": 0.58642578125}, {"start": 1019.7, "end": 1020.04, "word": " how", "probability": 0.88232421875}, {"start": 1020.04, "end": 1020.36, "word": " many", "probability": 0.9306640625}, {"start": 1020.36, "end": 1020.94, "word": " bit", "probability": 0.30908203125}, {"start": 1020.94, "end": 1021.4, "word": " string", "probability": 0.3994140625}, {"start": 1021.4, "end": 1021.78, "word": " لحظوا", "probability": 0.782470703125}, {"start": 1021.78, "end": 1022.0, "word": " هنا", "probability": 0.9912109375}, {"start": 1022.0, "end": 1022.44, "word": " bit", "probability": 0.89599609375}, {"start": 1022.44, "end": 1022.8, "word": " string", "probability": 0.888671875}, {"start": 1022.8, "end": 1023.02, "word": " أنا", "probability": 0.70849609375}, {"start": 1023.02, "end": 1023.18, "word": " جاعت", "probability": 0.6149088541666666}, {"start": 1023.18, "end": 1023.36, "word": " بقول", "probability": 0.977294921875}, {"start": 1023.36, "end": 1023.56, "word": " bit", "probability": 0.96142578125}, {"start": 1023.56, "end": 1023.94, "word": " string", "probability": 0.904296875}, {"start": 1023.94, "end": 1025.2, "word": " بس", "probability": 0.95654296875}, {"start": 1025.2, "end": 1025.78, "word": " ماتنخدعوش", "probability": 0.8795166015625}, {"start": 1025.78, "end": 1026.06, "word": " معاه", "probability": 0.81201171875}, {"start": 1026.06, "end": 1026.36, "word": " لأنه", "probability": 0.6722005208333334}, {"start": 1026.36, "end": 1026.5, "word": " bit", "probability": 0.8974609375}, {"start": 1026.5, "end": 1026.82, "word": " string", "probability": 0.94140625}, {"start": 1026.82, "end": 1026.94, "word": " هو", "probability": 0.26611328125}, {"start": 1026.94, "end": 1027.18, "word": " وجد", "probability": 0.697998046875}, {"start": 1027.18, "end": 1027.72, "word": " الأصل", "probability": 0.71044921875}, {"start": 1027.72, "end": 1027.88, "word": " أن", "probability": 0.5478515625}, {"start": 1027.88, "end": 1028.02, "word": " أنا", "probability": 0.642578125}, {"start": 1028.02, "end": 1028.44, "word": " هفكر", "probability": 0.9225260416666666}, {"start": 1028.44, "end": 1028.82, "word": " بإيش", "probability": 0.9390869140625}, {"start": 1028.82, "end": 1029.28, "word": " بال", "probability": 0.73046875}, {"start": 1029.28, "end": 1029.94, "word": " permutation", "probability": 0.904296875}, {"start": 1029.94, "end": 1030.66, "word": " خليني", "probability": 0.9105224609375}, {"start": 1030.66, "end": 1030.98, "word": " أشوف", "probability": 0.815185546875}], "temperature": 1.0}, {"id": 40, "seek": 105609, "start": 1031.74, "end": 1056.1, "text": "how many bits string of length four have exactly two ones or exactly two zeros؟ بمعنى ماجدتش عدد ال bits أو ال strings اللي ممكن أخدها من four bits عدد ال string اللي ممكن أخدها من four", "tokens": [4286, 867, 9239, 6798, 295, 4641, 1451, 362, 2293, 732, 2306, 420, 2293, 732, 35193, 22807, 4724, 2304, 3615, 1863, 7578, 19446, 7435, 3215, 2655, 8592, 6225, 3215, 3215, 2423, 9239, 34051, 2423, 13985, 13672, 1829, 3714, 43020, 5551, 9778, 3215, 11296, 9154, 1451, 9239, 6225, 3215, 3215, 2423, 6798, 13672, 1829, 3714, 43020, 5551, 9778, 3215, 11296, 9154, 1451], "avg_logprob": -0.2292520540659545, "compression_ratio": 1.6066666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1031.74, "end": 1032.2, "word": "how", "probability": 0.400390625}, {"start": 1032.2, "end": 1032.42, "word": " many", "probability": 0.91796875}, {"start": 1032.42, "end": 1032.58, "word": " bits", "probability": 0.59033203125}, {"start": 1032.58, "end": 1032.96, "word": " string", "probability": 0.353271484375}, {"start": 1032.96, "end": 1033.4, "word": " of", "probability": 0.91796875}, {"start": 1033.4, "end": 1033.76, "word": " length", "probability": 0.7490234375}, {"start": 1033.76, "end": 1034.16, "word": " four", "probability": 0.390380859375}, {"start": 1034.16, "end": 1034.48, "word": " have", "probability": 0.86474609375}, {"start": 1034.48, "end": 1035.1, "word": " exactly", "probability": 0.92138671875}, {"start": 1035.1, "end": 1035.36, "word": " two", "probability": 0.9033203125}, {"start": 1035.36, "end": 1035.74, "word": " ones", "probability": 0.81640625}, {"start": 1035.74, "end": 1036.36, "word": " or", "probability": 0.91357421875}, {"start": 1036.36, "end": 1036.7, "word": " exactly", "probability": 0.61083984375}, {"start": 1036.7, "end": 1036.94, "word": " two", "probability": 0.94091796875}, {"start": 1036.94, "end": 1038.44, "word": " zeros؟", "probability": 0.6446533203125}, {"start": 1038.44, "end": 1038.94, "word": " بمعنى", "probability": 0.92216796875}, {"start": 1038.94, "end": 1039.42, "word": " ماجدتش", "probability": 0.66376953125}, {"start": 1039.42, "end": 1039.74, "word": " عدد", "probability": 0.9363606770833334}, {"start": 1039.74, "end": 1040.06, "word": " ال", "probability": 0.8544921875}, {"start": 1040.06, "end": 1040.54, "word": " bits", "probability": 0.78173828125}, {"start": 1040.54, "end": 1041.12, "word": " أو", "probability": 0.61328125}, {"start": 1041.12, "end": 1041.26, "word": " ال", "probability": 0.9091796875}, {"start": 1041.26, "end": 1041.58, "word": " strings", "probability": 0.96337890625}, {"start": 1041.58, "end": 1041.78, "word": " اللي", "probability": 0.872314453125}, {"start": 1041.78, "end": 1042.02, "word": " ممكن", "probability": 0.99072265625}, {"start": 1042.02, "end": 1042.46, "word": " أخدها", "probability": 0.9112548828125}, {"start": 1042.46, "end": 1042.7, "word": " من", "probability": 0.99365234375}, {"start": 1042.7, "end": 1043.64, "word": " four", "probability": 0.86572265625}, {"start": 1043.64, "end": 1044.28, "word": " bits", "probability": 0.90283203125}, {"start": 1044.28, "end": 1054.6, "word": " عدد", "probability": 0.820068359375}, {"start": 1054.6, "end": 1054.74, "word": " ال", "probability": 0.92333984375}, {"start": 1054.74, "end": 1055.06, "word": " string", "probability": 0.50634765625}, {"start": 1055.06, "end": 1055.18, "word": " اللي", "probability": 0.982421875}, {"start": 1055.18, "end": 1055.3, "word": " ممكن", "probability": 0.716064453125}, {"start": 1055.3, "end": 1055.66, "word": " أخدها", "probability": 0.9403076171875}, {"start": 1055.66, "end": 1055.78, "word": " من", "probability": 0.9931640625}, {"start": 1055.78, "end": 1056.1, "word": " four", "probability": 0.82470703125}], "temperature": 1.0}, {"id": 41, "seek": 108345, "start": 1060.83, "end": 1083.45, "text": "هي عندكوا أربعة الأربعة هدولة بدكوا exactly كده عدد الحالات اللي ممكن يكون فيها two ones exactly two ones بمعنى مايكونش one واحد ومايكونش three or four مايكونش three or four هذه نفسها مكملة ليش ل double zero او two zeros", "tokens": [3224, 1829, 43242, 4117, 14407, 5551, 25513, 27884, 16247, 25513, 27884, 8032, 3215, 12610, 3660, 47525, 4117, 14407, 2293, 9122, 3215, 3224, 6225, 3215, 3215, 21542, 6027, 9307, 13672, 1829, 3714, 43020, 7251, 30544, 8978, 11296, 732, 2306, 2293, 732, 2306, 4724, 2304, 3615, 1863, 7578, 19446, 1829, 30544, 8592, 472, 36764, 24401, 4032, 15042, 1829, 30544, 8592, 1045, 420, 1451, 19446, 1829, 30544, 8592, 1045, 420, 1451, 29538, 8717, 36178, 11296, 3714, 24793, 37977, 32239, 8592, 5296, 3834, 4018, 1975, 2407, 732, 35193], "avg_logprob": -0.2384191211532144, "compression_ratio": 1.7407407407407407, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1060.83, "end": 1061.07, "word": "هي", "probability": 0.53564453125}, {"start": 1061.07, "end": 1061.57, "word": " عندكوا", "probability": 0.6922200520833334}, {"start": 1061.57, "end": 1062.55, "word": " أربعة", "probability": 0.8515625}, {"start": 1062.55, "end": 1064.07, "word": " الأربعة", "probability": 0.8291015625}, {"start": 1064.07, "end": 1064.35, "word": " هدولة", "probability": 0.8577880859375}, {"start": 1064.35, "end": 1064.77, "word": " بدكوا", "probability": 0.75732421875}, {"start": 1064.77, "end": 1066.21, "word": " exactly", "probability": 0.77587890625}, {"start": 1066.21, "end": 1066.69, "word": " كده", "probability": 0.5916341145833334}, {"start": 1066.69, "end": 1067.01, "word": " عدد", "probability": 0.9231770833333334}, {"start": 1067.01, "end": 1067.39, "word": " الحالات", "probability": 0.7841796875}, {"start": 1067.39, "end": 1067.51, "word": " اللي", "probability": 0.734619140625}, {"start": 1067.51, "end": 1067.71, "word": " ممكن", "probability": 0.85986328125}, {"start": 1067.71, "end": 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"word": " three", "probability": 0.91357421875}, {"start": 1075.79, "end": 1075.97, "word": " or", "probability": 0.607421875}, {"start": 1075.97, "end": 1076.31, "word": " four", "probability": 0.95263671875}, {"start": 1076.31, "end": 1077.99, "word": " مايكونش", "probability": 0.8150634765625}, {"start": 1077.99, "end": 1078.35, "word": " three", "probability": 0.880859375}, {"start": 1078.35, "end": 1078.61, "word": " or", "probability": 0.8046875}, {"start": 1078.61, "end": 1078.85, "word": " four", "probability": 0.95703125}, {"start": 1078.85, "end": 1079.67, "word": " هذه", "probability": 0.283203125}, {"start": 1079.67, "end": 1080.13, "word": " نفسها", "probability": 0.849609375}, {"start": 1080.13, "end": 1080.59, "word": " مكملة", "probability": 0.96484375}, {"start": 1080.59, "end": 1081.03, "word": " ليش", "probability": 0.781494140625}, {"start": 1081.03, "end": 1081.33, "word": " ل", "probability": 0.83203125}, {"start": 1081.33, "end": 1081.53, "word": " double", "probability": 0.450439453125}, {"start": 1081.53, "end": 1081.89, "word": " zero", "probability": 0.83642578125}, {"start": 1081.89, "end": 1082.25, "word": " او", "probability": 0.844482421875}, {"start": 1082.25, "end": 1083.01, "word": " two", "probability": 0.89453125}, {"start": 1083.01, "end": 1083.45, "word": " zeros", "probability": 0.72900390625}], "temperature": 1.0}, {"id": 42, "seek": 111185, "start": 1084.62, "end": 1111.86, "text": "لأن مادام exactly two ones بالنسبة للأربعة معناته exactly two zeros في الحالة هذه by logic مادام اللي بنشتر عليها هيكون معاها هيكون معانا ال one الأولى ال one التانية خلاص انت حجزت من الأولى فهيكون لها تلاتة", "tokens": [1211, 33456, 3714, 18513, 10943, 2293, 732, 2306, 20666, 1863, 35457, 3660, 24976, 10721, 25513, 27884, 20449, 8315, 47395, 2293, 732, 35193, 8978, 21542, 6027, 3660, 29538, 538, 9952, 3714, 18513, 10943, 13672, 1829, 44945, 8592, 2655, 2288, 25894, 11296, 39896, 30544, 20449, 995, 11296, 39896, 30544, 20449, 7649, 995, 2423, 472, 16247, 12610, 7578, 2423, 472, 16712, 7649, 10632, 16490, 1211, 33546, 16472, 2655, 11331, 7435, 11622, 2655, 9154, 16247, 12610, 7578, 6156, 3224, 1829, 30544, 5296, 11296, 6055, 1211, 9307, 3660], "avg_logprob": -0.25130209433180944, "compression_ratio": 1.7539267015706805, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1084.62, "end": 1084.9, "word": "لأن", "probability": 0.816650390625}, {"start": 1084.9, "end": 1085.24, "word": " مادام", "probability": 0.59521484375}, {"start": 1085.24, "end": 1085.96, "word": " exactly", "probability": 0.7724609375}, {"start": 1085.96, "end": 1086.2, "word": " two", "probability": 0.818359375}, {"start": 1086.2, "end": 1086.56, "word": " ones", "probability": 0.83203125}, {"start": 1086.56, "end": 1087.52, "word": " بالنسبة", "probability": 0.8890380859375}, {"start": 1087.52, "end": 1087.94, "word": " للأربعة", "probability": 0.80810546875}, {"start": 1087.94, "end": 1088.26, "word": " معناته", "probability": 0.79736328125}, {"start": 1088.26, "end": 1088.58, "word": " exactly", "probability": 0.9072265625}, {"start": 1088.58, "end": 1088.78, "word": " two", "probability": 0.892578125}, {"start": 1088.78, "end": 1089.2, "word": " zeros", "probability": 0.82958984375}, {"start": 1089.2, "end": 1090.06, "word": " في", "probability": 0.369384765625}, {"start": 1090.06, "end": 1092.3, "word": " الحالة", "probability": 0.9755859375}, {"start": 1092.3, "end": 1093.4, "word": " هذه", "probability": 0.705078125}, {"start": 1093.4, "end": 1093.86, "word": " by", "probability": 0.464111328125}, {"start": 1093.86, "end": 1094.22, "word": " logic", "probability": 0.97216796875}, {"start": 1094.22, "end": 1095.52, "word": " مادام", "probability": 0.88232421875}, {"start": 1095.52, "end": 1095.6, "word": " اللي", "probability": 0.56146240234375}, {"start": 1095.6, "end": 1095.84, "word": " بنشتر", "probability": 0.71710205078125}, {"start": 1095.84, "end": 1096.12, "word": " عليها", "probability": 0.929931640625}, {"start": 1096.12, "end": 1096.5, "word": " هيكون", "probability": 0.734375}, {"start": 1096.5, "end": 1100.12, "word": " معاها", "probability": 0.6746419270833334}, {"start": 1100.12, "end": 1100.98, "word": " هيكون", "probability": 0.64013671875}, {"start": 1100.98, "end": 1101.42, "word": " معانا", "probability": 0.8766276041666666}, {"start": 1101.42, "end": 1103.14, "word": " ال", "probability": 0.9716796875}, {"start": 1103.14, "end": 1103.34, "word": " one", "probability": 0.91162109375}, {"start": 1103.34, "end": 1104.46, "word": " الأولى", "probability": 0.9765625}, {"start": 1104.46, "end": 1104.74, "word": " ال", "probability": 0.478515625}, {"start": 1104.74, "end": 1106.66, "word": " one", "probability": 0.7685546875}, {"start": 1106.66, "end": 1107.18, "word": " التانية", "probability": 0.943359375}, {"start": 1107.18, "end": 1107.48, "word": " خلاص", "probability": 0.9002278645833334}, {"start": 1107.48, "end": 1107.68, "word": " انت", "probability": 0.446044921875}, 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ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد .. ناخد الواحد ..", "tokens": [1863, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 4386, 8717, 47283, 3215, 2423, 14407, 24401, 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هي واحد خمسة عشرة عشرة خمسة واحد okay واضحة صح بيانات حلو جدا هلوقت دائما n زائد واحد j combination ل n زائد واحد j بساوي ناجس واحد ناجس واحد زائد nj", "tokens": [2407, 6027, 20292, 8032, 1211, 2407, 38149, 39896, 3555, 9957, 9122, 33911, 1975, 8315, 1975, 8592, 2655, 17082, 1211, 2655, 9673, 2407, 11242, 45367, 23758, 9122, 33911, 6225, 28480, 39237, 15844, 23032, 12610, 4032, 8032, 1211, 2407, 38149, 39896, 3555, 9957, 8032, 995, 39896, 36764, 24401, 16490, 2304, 3794, 3660, 6225, 8592, 25720, 6225, 8592, 25720, 16490, 2304, 3794, 3660, 36764, 24401, 1392, 4032, 46958, 5016, 3660, 20328, 5016, 4724, 1829, 7649, 9307, 11331, 1211, 2407, 10874, 28259, 8032, 1211, 2407, 38149, 11778, 16373, 15042, 297, 30767, 16373, 3215, 36764, 24401, 361, 6562, 5296, 297, 30767, 16373, 3215, 36764, 24401, 361, 4724, 3794, 995, 45865, 8717, 26108, 3794, 36764, 24401, 8717, 26108, 3794, 36764, 24401, 30767, 16373, 3215, 297, 73], "avg_logprob": -0.19047004624831776, "compression_ratio": 1.95, 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{"id": 107, "seek": 279932, "start": 2787.66, "end": 2799.32, "text": "zero تمام اتنين واحد طب لحظة باخدهم من اللي فوجه معناته اتنين من ال second order الاتنين اللي حواليه اللي كانوا فوجه هنا و هنا", "tokens": [32226, 46811, 10943, 1975, 2655, 1863, 9957, 36764, 24401, 23032, 3555, 5296, 5016, 19913, 3660, 4724, 47283, 3215, 16095, 9154, 13672, 1829, 6156, 29245, 3224, 20449, 8315, 47395, 1975, 2655, 1863, 9957, 9154, 2423, 1150, 1668, 2423, 9307, 1863, 9957, 13672, 1829, 11331, 2407, 6027, 1829, 3224, 13672, 1829, 25961, 14407, 6156, 29245, 3224, 34105, 4032, 34105], "avg_logprob": -0.14264547182568188, "compression_ratio": 1.6259541984732824, "no_speech_prob": 1.3709068298339844e-06, "words": [{"start": 2787.66, "end": 2788.18, "word": "zero", "probability": 0.339111328125}, {"start": 2788.18, "end": 2788.7, "word": " تمام", "probability": 0.887939453125}, {"start": 2788.7, "end": 2791.22, "word": " اتنين", "probability": 0.8553466796875}, {"start": 2791.22, "end": 2792.26, "word": " 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{"start": 2877.66, "end": 2878.54, "word": " طريقة", "probability": 0.9835611979166666}, {"start": 2878.54, "end": 2878.92, "word": " سهلة", "probability": 0.978515625}, {"start": 2878.92, "end": 2879.28, "word": " و", "probability": 0.7060546875}, {"start": 2879.28, "end": 2879.7, "word": " بتقدروا", "probability": 0.9473876953125}, {"start": 2879.7, "end": 2879.9, "word": " ت", "probability": 0.734375}, {"start": 2879.9, "end": 2880.18, "word": " ..", "probability": 0.87109375}, {"start": 2880.18, "end": 2880.42, "word": " يعني", "probability": 0.957763671875}, {"start": 2880.42, "end": 2880.78, "word": " تعملوا", "probability": 0.9757080078125}, {"start": 2880.78, "end": 2880.94, "word": " فيها", "probability": 0.994384765625}, {"start": 2880.94, "end": 2881.28, "word": " منظر", "probability": 0.8486328125}, {"start": 2881.28, "end": 2881.46, "word": " على", "probability": 0.923828125}, {"start": 2881.46, "end": 2882.6, "word": " صحفاتكوا", "probability": 0.841796875}, {"start": 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{"start": 2884.56, "end": 2884.98, "word": " عارفين", "probability": 0.9857177734375}, {"start": 2884.98, "end": 2885.18, "word": " ال", "probability": 0.63525390625}, {"start": 2885.18, "end": 2887.26, "word": " ..", "probability": 0.7236328125}, {"start": 2887.26, "end": 2887.36, "word": " ال", "probability": 0.6875}, {"start": 2887.36, "end": 2887.62, "word": " ..", "probability": 0.491943359375}, {"start": 2887.62, "end": 2887.9, "word": " ال", "probability": 0.53369140625}, {"start": 2887.9, "end": 2887.92, "word": " ..", "probability": 0.67041015625}, {"start": 2887.92, "end": 2887.92, "word": " ال", "probability": 0.257080078125}, {"start": 2887.92, "end": 2888.22, "word": " ..", "probability": 0.69677734375}, {"start": 2888.22, "end": 2888.7, "word": " بس", "probability": 0.640869140625}, {"start": 2888.7, "end": 2888.86, "word": " كان", "probability": 0.95751953125}, {"start": 2888.86, "end": 2888.94, "word": " ال", "probability": 0.8369140625}, {"start": 2888.94, "end": 2889.34, "word": " triangle", "probability": 0.79052734375}, {"start": 2889.34, "end": 2890.54, "word": " okay", "probability": 0.458251953125}, {"start": 2890.54, "end": 2896.3, "word": " لحظة", "probability": 0.80126953125}, {"start": 2896.3, "end": 2899.08, "word": " once", "probability": 0.42041015625}, {"start": 2899.08, "end": 2900.14, "word": " لحظة", "probability": 0.8883056640625}, {"start": 2900.14, "end": 2900.34, "word": " هنا", "probability": 0.99267578125}, {"start": 2900.34, "end": 2901.72, "word": " once", "probability": 0.8779296875}, {"start": 2901.72, "end": 2902.68, "word": " كله", "probability": 0.934814453125}, {"start": 2902.68, "end": 2903.06, "word": " و", "probability": 0.470703125}, {"start": 2903.06, "end": 2903.34, "word": " لحظة", "probability": 0.990966796875}, {"start": 2903.34, "end": 2903.56, "word": " هنا", "probability": 0.99755859375}], "temperature": 1.0}, {"id": 112, "seek": 292961, "start": 2905.47, "end": 2929.61, "text": "متشابهات كله إذا كان كله زوجي هيكون كله identical كله كأنه فيه mirror الفرد لأ هيكون فيه عنصر زيادة في النصر في عنصر زيادة في النصر في الحالة اللي عندنا طبعا ال .. ال .. ال Pascal's triangle فيه كتير علاقات بين الأرقام و بعضها غير الأرقام اللي احنا قلناهم كمان غير اللي احنا قلناهم بس احنا مش بصدر نزود كتير في .. في الشغل okay", "tokens": [2304, 2655, 8592, 16758, 3224, 9307, 28242, 3224, 11933, 15730, 25961, 28242, 3224, 30767, 29245, 1829, 39896, 30544, 28242, 3224, 14800, 28242, 3224, 9122, 33456, 3224, 8978, 3224, 8013, 27188, 2288, 3215, 5296, 10721, 39896, 30544, 8978, 3224, 18871, 9381, 2288, 30767, 1829, 18513, 3660, 8978, 28239, 9381, 2288, 8978, 18871, 9381, 2288, 30767, 1829, 18513, 3660, 8978, 28239, 9381, 2288, 8978, 21542, 6027, 3660, 13672, 1829, 43242, 8315, 23032, 3555, 3615, 995, 2423, 4386, 2423, 4386, 2423, 41723, 311, 13369, 8978, 3224, 9122, 2655, 13546, 11203, 995, 4587, 9307, 49374, 16247, 2288, 4587, 10943, 4032, 45030, 11242, 11296, 32771, 13546, 16247, 2288, 4587, 10943, 13672, 1829, 1975, 5016, 8315, 12174, 1211, 8315, 16095, 9122, 2304, 7649, 32771, 13546, 13672, 1829, 1975, 5016, 8315, 12174, 1211, 8315, 16095, 4724, 3794, 1975, 5016, 8315, 37893, 4724, 9381, 3215, 2288, 8717, 11622, 23328, 9122, 2655, 13546, 8978, 4386, 8978, 25124, 17082, 1211, 1392], "avg_logprob": -0.14453125058820374, "compression_ratio": 2.037174721189591, "no_speech_prob": 2.9206275939941406e-06, "words": [{"start": 2905.4700000000003, "end": 2906.11, "word": "متشابهات", "probability": 0.9835611979166666}, {"start": 2906.11, "end": 2906.49, "word": " كله", "probability": 0.926025390625}, {"start": 2906.49, "end": 2906.91, "word": " إذا", "probability": 0.61175537109375}, {"start": 2906.91, "end": 2907.11, "word": " كان", "probability": 0.96533203125}, {"start": 2907.11, "end": 2907.41, "word": " كله", "probability": 0.931884765625}, {"start": 2907.41, "end": 2908.07, "word": " زوجي", "probability": 0.9466145833333334}, {"start": 2908.07, "end": 2908.49, "word": " هيكون", "probability": 0.6295166015625}, {"start": 2908.49, "end": 2908.79, "word": " كله", "probability": 0.898193359375}, {"start": 2908.79, "end": 2909.19, "word": " identical", "probability": 0.89208984375}, {"start": 2909.19, "end": 2909.73, "word": " كله", "probability": 0.8125}, {"start": 2909.73, "end": 2910.09, "word": " كأنه", "probability": 0.8570963541666666}, {"start": 2910.09, "end": 2910.27, "word": " فيه", "probability": 0.947265625}, {"start": 2910.27, "end": 2910.51, "word": " mirror", "probability": 0.765625}, {"start": 2910.51, "end": 2911.71, "word": " الفرد", "probability": 0.9523111979166666}, {"start": 2911.71, "end": 2911.87, "word": " لأ", "probability": 0.951171875}, {"start": 2911.87, "end": 2912.13, "word": " هيكون", "probability": 0.923828125}, {"start": 2912.13, "end": 2912.29, "word": " فيه", "probability": 0.684326171875}, {"start": 2912.29, "end": 2912.53, "word": " عنصر", "probability": 0.9777018229166666}, {"start": 2912.53, "end": 2912.79, "word": " زيادة", "probability": 0.9752197265625}, {"start": 2912.79, "end": 2912.89, "word": " في", "probability": 0.970703125}, {"start": 2912.89, "end": 2913.25, "word": " النصر", "probability": 0.7628580729166666}, {"start": 2913.25, "end": 2913.41, "word": " في", "probability": 0.61279296875}, {"start": 2913.41, "end": 2913.99, "word": " عنصر", "probability": 0.947265625}, {"start": 2913.99, "end": 2914.97, "word": " زيادة", "probability": 0.984619140625}, {"start": 2914.97, "end": 2915.09, "word": " في", "probability": 0.98779296875}, {"start": 2915.09, "end": 2915.73, "word": " النصر", "probability": 0.9873046875}, {"start": 2915.73, "end": 2915.89, "word": " في", "probability": 0.89306640625}, {"start": 2915.89, "end": 2916.15, "word": " الحالة", "probability": 0.9871419270833334}, {"start": 2916.15, "end": 2916.27, "word": " اللي", "probability": 0.91357421875}, {"start": 2916.27, "end": 2916.57, "word": " عندنا", "probability": 0.7144775390625}, {"start": 2916.57, "end": 2917.03, "word": " طبعا", "probability": 0.9609375}, {"start": 2917.03, "end": 2917.79, "word": " ال", "probability": 0.958984375}, {"start": 2917.79, "end": 2917.79, "word": " ..", "probability": 0.533203125}, {"start": 2917.79, "end": 2918.21, "word": " ال", "probability": 0.86767578125}, {"start": 2918.21, "end": 2918.21, "word": " ..", "probability": 0.58544921875}, {"start": 2918.21, "end": 2918.31, "word": " ال", "probability": 0.50634765625}, {"start": 2918.31, "end": 2918.73, "word": " Pascal's", "probability": 0.53521728515625}, {"start": 2918.73, "end": 2919.13, "word": " triangle", "probability": 0.71875}, {"start": 2919.13, "end": 2919.41, "word": " فيه", "probability": 0.78759765625}, {"start": 2919.41, "end": 2919.75, "word": " كتير", "probability": 0.96435546875}, {"start": 2919.75, "end": 2920.47, "word": " علاقات", "probability": 0.989013671875}, {"start": 2920.47, "end": 2920.61, "word": " بين", "probability": 0.9443359375}, {"start": 2920.61, "end": 2920.97, "word": " الأرقام", "probability": 0.9744873046875}, {"start": 2920.97, "end": 2921.07, "word": " و", "probability": 0.5078125}, {"start": 2921.07, "end": 2921.31, "word": " بعضها", "probability": 0.9733072916666666}, {"start": 2921.31, "end": 2921.53, "word": " غير", "probability": 0.98779296875}, {"start": 2921.53, "end": 2921.83, "word": " الأرقام", "probability": 0.81378173828125}, {"start": 2921.83, "end": 2921.95, "word": " اللي", "probability": 0.966796875}, {"start": 2921.95, "end": 2922.13, "word": " احنا", "probability": 0.7874348958333334}, {"start": 2922.13, "end": 2922.55, "word": " قلناهم", "probability": 0.801513671875}, {"start": 2922.55, "end": 2922.83, "word": " كمان", "probability": 0.9798177083333334}, {"start": 2922.83, "end": 2923.17, "word": " غير", "probability": 0.858154296875}, {"start": 2923.17, "end": 2923.27, "word": " اللي", "probability": 0.9892578125}, {"start": 2923.27, "end": 2923.39, "word": " احنا", "probability": 0.9493815104166666}, {"start": 2923.39, "end": 2923.83, "word": " قلناهم", "probability": 0.96728515625}, {"start": 2923.83, "end": 2924.23, "word": " بس", "probability": 0.98583984375}, {"start": 2924.23, "end": 2924.37, "word": " احنا", "probability": 0.9013671875}, {"start": 2924.37, "end": 2924.49, "word": " مش", "probability": 0.98193359375}, {"start": 2924.49, "end": 2924.79, "word": " بصدر", "probability": 0.774658203125}, {"start": 2924.79, "end": 2925.43, "word": " نزود", "probability": 0.822265625}, {"start": 2925.43, "end": 2925.83, "word": " كتير", "probability": 0.9930013020833334}, {"start": 2925.83, "end": 2926.55, "word": " في", "probability": 0.96142578125}, {"start": 2926.55, "end": 2926.91, "word": " ..", "probability": 0.84228515625}, {"start": 2926.91, "end": 2927.85, "word": " في", "probability": 0.9677734375}, {"start": 2927.85, "end": 2928.23, "word": " الشغل", "probability": 0.9890950520833334}, {"start": 2928.23, "end": 2929.61, "word": " okay", "probability": 0.8203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2930.869, "duration_after_vad": 2788.9999999999905}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/ZEvX8gfEj2Y_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/ZEvX8gfEj2Y_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fc1a3bb730000726fb617e9ce43730023859e160
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/ZEvX8gfEj2Y_postprocess.srt
@@ -0,0 +1,2732 @@
+1
+00:00:20,960 --> 00:00:22,840
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,840 --> 00:00:25,020
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,020 --> 00:00:28,820
+أجمعين نبدأ اليوم محاضرة جديدة مع درس جديد مع
+
+4
+00:00:28,820 --> 00:00:32,480
+chapter جديد أصلا في المصادق تبعنا هنشتغل على the
+
+5
+00:00:32,480 --> 00:00:36,760
+theory of sets أول section من ال chapter two ان
+
+6
+00:00:36,760 --> 00:00:38,480
+شاء الله تعالى هنتكلم فيه عن حاجة أنتوا أصلا
+
+7
+00:00:38,480 --> 00:00:41,360
+ماخدينها سابقا برضه من الحاجات اللي بس هنعمل كهيك
+
+8
+00:00:41,360 --> 00:00:44,420
+refreshment لها اللي هي ال sets أو المجموعات
+
+9
+00:00:44,420 --> 00:00:47,090
+أخدتوا قبل هيك المجموعاتاتكلمنا في ال predicates
+
+10
+00:00:47,090 --> 00:00:49,990
+لما كنا نحكي عن ال predicates اتكلمنا عن ال
+
+11
+00:00:49,990 --> 00:00:52,910
+universe of discourse و قلنا في عندنا فضاء عينى،
+
+12
+00:00:52,910 --> 00:00:56,230
+فضاء العينى هذا إيش؟ يمثل .. يمثل مجموعة objects،
+
+13
+00:00:56,230 --> 00:00:59,330
+مجموعة objects بصفة عامة، ال objects هذه ممكن تكون
+
+14
+00:00:59,330 --> 00:01:03,510
+أرقام، ممكن تكون numbers تمام؟ بس برضه ممكن تكون
+
+15
+00:01:03,510 --> 00:01:08,870
+أي إشي تاني، أي إشي distinct object في أي شغلة
+
+16
+00:01:08,870 --> 00:01:13,330
+ممكن تكون مجموعة، نحطها ال objects هذه في مجموعة و
+
+17
+00:01:13,330 --> 00:01:18,510
+نتكلم عن ال setsفال city a structure، ال structure
+
+18
+00:01:18,510 --> 00:01:23,710
+هدا بنقدر نمثله ك unordered collection أو group،
+
+19
+00:01:23,710 --> 00:01:27,690
+فunordered مش م .. مش مرتب، مش مضرور يكون مرتب ال
+
+20
+00:01:27,690 --> 00:01:32,350
+elements تبعتنا، ممكن تكون عددهم zero أو أكتر من
+
+21
+00:01:32,350 --> 00:01:36,340
+distinct أو different objectsفممكن تكون zero و
+
+22
+00:01:36,340 --> 00:01:43,360
+zero هذه unique set بنسميها اللي هي ال fi أو ال
+
+23
+00:01:43,360 --> 00:01:47,820
+null أو ال empty set هنتكلم برضه عنها فالقصد أنه
+
+24
+00:01:47,820 --> 00:01:52,720
+ممكن تكون no element ممكن تكون no element أو أكتر
+
+25
+00:01:52,720 --> 00:01:58,500
+و أكتر هذه ممكن تشمل to infinity to infinity أو
+
+26
+00:01:58,500 --> 00:02:04,560
+infinite elements تمام؟زي انتوا برضه بتعرفوا منهم
+
+27
+00:02:04,560 --> 00:02:09,220
+ال real numbers ال natural numbers ال integer
+
+28
+00:02:09,220 --> 00:02:12,360
+numbers هدى مجموعة أرقام هى هدى عبارة عن set أصلا
+
+29
+00:02:12,360 --> 00:02:16,680
+مجموعة أرقام بس لانهائية لانهائية فإذا ال net ده
+
+30
+00:02:16,680 --> 00:02:22,140
+من صفر أو لانهائية أو محددة finite بينهم كويس كل
+
+31
+00:02:22,140 --> 00:02:25,320
+ال mathematics forms اللى ممكن نتكلم عنها بنستخدم
+
+32
+00:02:25,320 --> 00:02:29,820
+فيها ال sets ليش لإن أنا محتاج محتاجال elements
+
+33
+00:02:29,820 --> 00:02:34,440
+اللي انا بقدر اعبر عنها X لما نقول F of X قيم X
+
+34
+00:02:34,440 --> 00:02:38,620
+المحتملة اللي ممكن نستخدمها ل F of X طيب قيم ال F
+
+35
+00:02:38,620 --> 00:02:41,520
+of X اللي ممكن تنتج كلها بدنا نحطهم في النهاية
+
+36
+00:02:41,520 --> 00:02:44,920
+داخل set او مجموعة فإذا انا هيك هيك في جميع
+
+37
+00:02:44,920 --> 00:02:49,880
+الأحوال بتعامل مع مجموعات طيب انتوا كطالبات لما
+
+38
+00:02:49,880 --> 00:02:53,500
+بدي اقول بدي مجموعة الطالبات اللي مسجلين مساق
+
+39
+00:02:53,500 --> 00:02:57,780
+discrete لحظوا مجموعة فانا بتكلم هنا ال objects
+
+40
+00:02:57,780 --> 00:03:03,160
+هنا اسمهمناس ال people ناس ممكن يكون هم ال .. فانا
+
+41
+00:03:03,160 --> 00:03:07,040
+باتكلمش دائما عن أرقام نتعاملش دائما مع أرقام ممكن
+
+42
+00:03:07,040 --> 00:03:12,880
+تكون أي object او element نتعامل معه داخل ال set
+
+43
+00:03:12,880 --> 00:03:17,260
+طيب ال symbols بتاعتنا او ال notation بتاعتنا
+
+44
+00:03:17,260 --> 00:03:21,240
+بنتعامل مع ال capital letter او ال upper case ففي
+
+45
+00:03:21,240 --> 00:03:27,150
+الغرب بنقول S T او U الاكتر استعمال ان هي ال Sset
+
+46
+00:03:27,150 --> 00:03:31,430
+نسميها أسوية أكثر درجة معناها كتير ممكن نستعمل
+
+47
+00:03:31,430 --> 00:03:36,630
+معها T و ال U غالبا نستعملها كتعبير لل universe of
+
+48
+00:03:36,630 --> 00:03:40,130
+discourse فضاء العينة باعتبار أن هي أصلا set هي
+
+49
+00:03:40,130 --> 00:03:45,480
+أساسا set كويسةبنقدر نعرف ال set S على أساس أنها
+
+50
+00:03:45,480 --> 00:03:49,440
+مجموعة elements وعشان نحدد أن أنا بتكلم عن set
+
+51
+00:03:49,440 --> 00:03:55,200
+مجموعة بنحطها داخل curly braces أو الأقواص
+
+52
+00:03:55,200 --> 00:04:00,500
+المجاعدة هذه اللي هي بهذا الشكل هذه تعبر عن مين؟
+
+53
+00:04:00,500 --> 00:04:04,360
+عن ال set بنستعملش الأقواص الصغيرة ولا بنستعمل ال
+
+54
+00:04:04,360 --> 00:04:09,700
+bracketsهذه اللي بنستعملها لمين ل set عشان اعرف ان
+
+55
+00:04:09,700 --> 00:04:14,560
+احنا متكلمين عن set او مجموعة او مجموعة رياضية زى
+
+56
+00:04:14,560 --> 00:04:17,080
+ما قولنا مجموعة رياضية objects مش مضروية أرقام
+
+57
+00:04:17,080 --> 00:04:20,620
+رياضية لا تمثل .. يعني احنا مابنعبّرش عن أرقام بس
+
+58
+00:04:20,620 --> 00:04:27,720
+تمام فلو قولنا مثلا ال set A,B وC بهذا الشكل انا
+
+59
+00:04:27,720 --> 00:04:31,800
+بتعامل مع set تحتوي على three elements ايش هم ال
+
+60
+00:04:31,800 --> 00:04:36,990
+elements دولة؟لحظة letter مجموعة letters alphabet
+
+61
+00:04:36,990 --> 00:04:42,350
+a و b و c مجموعة objects تمام فانا بتعامل مع تلاتة
+
+62
+00:04:42,350 --> 00:04:47,050
+objects اللي هم a و b و c ممكن جدا ان نعبر عن ال
+
+63
+00:04:47,050 --> 00:04:50,910
+set مش بال elements بتاعتها ب expression إلها
+
+64
+00:04:50,910 --> 00:04:55,930
+بمعادلة إلها بنسميها set builder notation أو
+
+65
+00:04:55,930 --> 00:05:00,770
+بنعملها بناء بنبنيها set builder أو باني ال
+
+66
+00:05:00,770 --> 00:05:05,760
+expression هذا فممكن نقولfor any proposition P of
+
+67
+00:05:05,760 --> 00:05:09,420
+X over any universe of discourse بقدر اقول ان ال
+
+68
+00:05:09,420 --> 00:05:17,380
+set بتاعتنا set of X such that X هتحقق لنا P of X
+
+69
+00:05:17,380 --> 00:05:23,720
+فكل element X بيحقق P of X هو belong to this set
+
+70
+00:05:24,500 --> 00:05:28,800
+فهو ينتمي لهذه المجموعة كل element x بيحقق ال
+
+71
+00:05:28,800 --> 00:05:32,840
+function P of X هو ينتمي لهذه المجموعة فبنقدر
+
+72
+00:05:32,840 --> 00:05:37,920
+نعبرها بإيش ب expression رياضي كأني بقول the set
+
+73
+00:05:37,920 --> 00:05:42,140
+of all x such that P of X بتحقق لنا P of X فكل
+
+74
+00:05:42,140 --> 00:05:44,900
+element زي ما قلنا كمان مرة كل element بيحقق لنا
+
+75
+00:05:44,900 --> 00:05:49,190
+ال function P of X يعتبر عنصرفي المجموعة فانا هيك
+
+76
+00:05:49,190 --> 00:05:54,050
+يعني عبرت عن مجموعة ال elements او العناصر X داخل
+
+77
+00:05:54,050 --> 00:05:57,830
+ال set بدون ما اضطر اكتبهم واحد واحد و X هي طبعا
+
+78
+00:05:57,830 --> 00:06:03,210
+زي ما قلنا ممكن تكون عدد كبير من ال sets كويس برضه
+
+79
+00:06:03,210 --> 00:06:05,730
+ما زلنا نتكلم في شوية properties ل ال sets
+
+80
+00:06:05,730 --> 00:06:10,730
+فinherently هي زي ما قلناunordered unordered
+
+81
+00:06:10,730 --> 00:06:16,210
+inherently unordered بمعنى أنه بطريقة أصلية أو
+
+82
+00:06:16,210 --> 00:06:22,050
+بطريقة متأصلة نتعامل مع عناصر غير مرتبة نتعامل مع
+
+83
+00:06:22,050 --> 00:06:26,530
+عناصر غير مرتبة إيش يعني؟ يعني لو قلنا a,b,c هي
+
+84
+00:06:26,530 --> 00:06:32,210
+نفسها المجموعة a,c,b هي نفسها المجموعة b,c,b ترتيب
+
+85
+00:06:32,210 --> 00:06:36,610
+مش ملزمالمهم ان انا في عندى universe of discourse
+
+86
+00:06:36,610 --> 00:06:41,050
+عندى مجموعة تحتوي على مجموعة العناصر هذه كيف
+
+87
+00:06:41,050 --> 00:06:44,490
+ترتبهم العناصر مش هتفرق لو انا قلت والله بدى اسجل
+
+88
+00:06:44,490 --> 00:06:48,190
+أسماء الطالبة اللى بدرسه discrete mathematics خلال
+
+89
+00:06:48,190 --> 00:06:53,070
+الفصل هذا مش هتفرق انا رتبتهم كيف يمكن في قبوله
+
+90
+00:06:53,070 --> 00:06:56,690
+التسجيل يرتبوليهم حسب الرقم الدراسى يمكن انا اقول
+
+91
+00:06:56,690 --> 00:07:01,290
+لأ بترتبهم حسب الأبجديا حسب اسمهم أبجدي واحد تانى
+
+92
+00:07:01,290 --> 00:07:05,580
+يقول لأ بترتبهم طريقة مختلفةصحيح؟ مش هتفرق، في
+
+93
+00:07:05,580 --> 00:07:09,340
+النهاية كلهم مكافئين لبعض، كلهم بيسووا بعض ال 6
+
+94
+00:07:09,340 --> 00:07:11,920
+هذه بهذا الترتيب، هي نفس ال 6 هذه بهذا الترتيب، هي
+
+95
+00:07:11,920 --> 00:07:15,340
+نفسها، ليش؟ لأنه بيحتووا على نفس العناصر، بغض
+
+96
+00:07:15,340 --> 00:07:20,360
+النظر عن الترتيب، كويس الحاجة التانية برضه، all
+
+97
+00:07:20,360 --> 00:07:27,240
+elements are distinct أو unequal unequal لبعض،
+
+98
+00:07:27,240 --> 00:07:30,780
+unequal لبعض، بمعنى مانفعش أكرر العنصر، مانفعش
+
+99
+00:07:30,780 --> 00:07:35,110
+نكرر العنصرال listing المفروض أننا نعمل listing
+
+100
+00:07:35,110 --> 00:07:41,690
+with no أو كلهم يكونوا no difference أو يعني مش
+
+101
+00:07:41,690 --> 00:07:44,810
+غير متشابهات عفوا ف no difference بيه لأ make no
+
+102
+00:07:44,810 --> 00:07:50,470
+difference if a equal to b عشان نوضحها لو قولنا a
+
+103
+00:07:50,470 --> 00:07:57,650
+بتساوي b أساسا then ال set ABC هي نفس ال set AC
+
+104
+00:07:59,240 --> 00:08:02,800
+صحيح؟ على اعتبار ان a و b بيسووا بعض فهم عنصر واحد
+
+105
+00:08:02,800 --> 00:08:07,000
+بيكفي ان ا ابثلهم عنصر واحد منهم او امثلهم ال b ما
+
+106
+00:08:07,000 --> 00:08:11,060
+هي في النهاية a و b نفس العنصر ممكن يكونوا a a, b
+
+107
+00:08:11,060 --> 00:08:17,920
+b, c a a, b a a يعني تتكرروا فيهم زي ما بدكم بس في
+
+108
+00:08:17,920 --> 00:08:24,120
+الآخر لما اجي اتكلم اقول والله ال .. ال .. ال ..
+
+109
+00:08:24,120 --> 00:08:30,960
+الست هذه ايه كم element فيها؟ اتنينإتنين C وA أو B
+
+110
+00:08:30,960 --> 00:08:35,160
+بقولش والله لو عندي واحد اتنين تلاتة أربعة خمسة
+
+111
+00:08:35,160 --> 00:08:37,720
+ستة سبعة تمانية عندي تسعة elements لأ بنجلش تسعة
+
+112
+00:08:37,720 --> 00:08:40,580
+elements لأنه في تكرار هنا فاحنا هنا لازم نشتغل
+
+113
+00:08:40,580 --> 00:08:44,080
+على عدم التكرار بمعنى أنه يكون عندكو distinct
+
+114
+00:08:44,080 --> 00:08:52,160
+elements أو عناصر مميزة متباينة متباينة okay
+
+115
+00:08:53,250 --> 00:08:56,190
+الست ايقاليتي هد بتخلينا ندور على الست ايقاليتي
+
+116
+00:08:56,190 --> 00:08:59,530
+امتى طب بيقولنا ان الست equal لبعض امتى بنقول ان
+
+117
+00:08:59,530 --> 00:09:02,430
+هم equal لبعض واضح جدا اذا كان كلهم بيحتووا على
+
+118
+00:09:02,430 --> 00:09:06,190
+exactly the same elements كلهم بيحتووا على نفس
+
+119
+00:09:06,190 --> 00:09:10,630
+العناصر تمام كلهم اللي لهم نفس العناصر الست الأولى
+
+120
+00:09:10,630 --> 00:09:14,230
+تحتوى على نفس العناصر exactly بالظبط اللي موجودين
+
+121
+00:09:14,230 --> 00:09:16,310
+في الست التانية بقدروا ان الست الأولى والست
+
+122
+00:09:16,310 --> 00:09:20,110
+التانية equal لبعض او equivalent لبعض بسوا بعض
+
+123
+00:09:21,080 --> 00:09:24,160
+كويسة for example لو قلنا مثلا الست عندنا واحد
+
+124
+00:09:24,160 --> 00:09:28,720
+اتنين تلاتة اربعة هى ست تحتوي على اربع عناصر
+
+125
+00:09:28,720 --> 00:09:32,240
+العنصر الاول ال integer واحد العنصر التاني ال
+
+126
+00:09:32,240 --> 00:09:35,020
+integer رقم اتنين العنصر التالت ال integer تلاتة و
+
+127
+00:09:35,020 --> 00:09:38,800
+العنصر الرابع integer يمثل اربعة كويسة ممكن اعبر
+
+128
+00:09:38,800 --> 00:09:42,260
+عنها بطريقة تانية و equivalent لها و انت عبّر احنا
+
+129
+00:09:42,260 --> 00:09:46,890
+نقول والله هي كل هي عبارة عن ستكل العناصر فيها all
+
+130
+00:09:46,890 --> 00:09:51,930
+x such that x is an integer where x أكبر من ..
+
+131
+00:09:51,930 --> 00:09:57,710
+greater than zero and x less than five فعلا هي كل
+
+132
+00:09:57,710 --> 00:10:04,610
+ال integers اللي أقل من خمسة وأكبر من صفر لإيجادهم
+
+133
+00:10:04,610 --> 00:10:09,250
+يتمثل نفس المجموعة هذه نفسها أو حتى اللي يقول لأ
+
+134
+00:10:09,250 --> 00:10:12,110
+أنا بدي أمثلها بطريقة مختلفة بدي أعمل set builder
+
+135
+00:10:12,110 --> 00:10:17,490
+مختلفةهيقول إن هي عبارة عن set of x such that x is
+
+136
+00:10:17,490 --> 00:10:24,090
+a positive integer whose square is أكبر than 0 and
+
+137
+00:10:24,090 --> 00:10:31,700
+less than 25 نفس الفكرة هي كل العناصر الموجبةاللي
+
+138
+00:10:31,700 --> 00:10:35,200
+تربيعها .. تربيعها .. هنا متكلم عن التربيع صار هو
+
+139
+00:10:35,200 --> 00:10:38,240
+ال condition اللي بدنا نحكم فيه تربيعها أقل من صفر
+
+140
+00:10:38,240 --> 00:10:44,100
+.. أكبر من صفر وأقل من خمسة وعشرين وextractly أكبر
+
+141
+00:10:44,100 --> 00:10:47,640
+من صفر .. الزمن أكبر .. بنفعش يساوي صفر والزمن
+
+142
+00:10:47,640 --> 00:10:53,550
+extractly أقل من خمسة وعشرينكويس فالأرقام هذه اللي
+
+143
+00:10:53,550 --> 00:10:56,490
+فعلا تربيحها بين الصفر والخمسة عشرين هي الواحد
+
+144
+00:10:56,490 --> 00:11:00,250
+اتنين تلاتة أربعة بس في غيرهم مش غيرهم واحنا حددنا
+
+145
+00:11:00,250 --> 00:11:02,890
+من الأول positive فال negative تبعهم مستحيل يكون
+
+146
+00:11:02,890 --> 00:11:06,870
+موجود لأنه في التعريف positive صحيح في التعريف
+
+147
+00:11:06,870 --> 00:11:09,990
+positive فأي شكل من التلت أشكال هدول يساوي الآخر
+
+148
+00:11:09,990 --> 00:11:14,910
+كل شكل من التلت أشكال هدول للمجموع بيساوي الآخر
+
+149
+00:11:14,910 --> 00:11:22,190
+infinite sets أو المجموعات اللانهائيةالحقيقة
+
+150
+00:11:22,190 --> 00:11:26,350
+بنتعامل معها، بنتعامل معها باستمرار، اللي هي no
+
+151
+00:11:26,350 --> 00:11:29,650
+finite أو not finite بمعنى أن هي لا نهاية، مالهاش
+
+152
+00:11:29,650 --> 00:11:36,490
+نهاية، without end، بدون نهاية لها أو unending،
+
+153
+00:11:36,490 --> 00:11:40,270
+غير منتهية، غير منتهية، الحاجات المشهورة جدا اللي
+
+154
+00:11:40,270 --> 00:11:43,290
+هي زي ال natural numberاللي هي من صفر to infinity
+
+155
+00:11:43,290 --> 00:11:46,770
+natural numbers الأرقام الطبيعية اللي احنا عادة
+
+156
+00:11:46,770 --> 00:11:50,550
+نستعملها positive طبعا بتكون الجزء ال negative لو
+
+157
+00:11:50,550 --> 00:11:53,950
+أضفناه بيصير أنها ال integer numbers بيصير أننا
+
+158
+00:11:53,950 --> 00:11:56,930
+نتكلم عن ال integer numbers لو زودنا reflections
+
+159
+00:11:56,930 --> 00:12:01,830
+بيصير نتكلم عن ال real numbers طيب هنلاحظ رغم أن
+
+160
+00:12:01,830 --> 00:12:08,820
+هم كلهم infinite sets بس ال size بتاعتهم مختلفةال
+
+161
+00:12:08,820 --> 00:12:11,820
+size مختلفة هذه غير هذه غير هذه مين أكبر واحدة
+
+162
+00:12:11,820 --> 00:12:16,900
+فيهم size كsize أكبر واحدة الريال number أقلهم ال
+
+163
+00:12:16,900 --> 00:12:21,720
+natural number فرغم ذلك رغم أن هم كلهم infinite
+
+164
+00:12:21,720 --> 00:12:25,300
+sets لكن كلهم بيجوا من different sizes كل واحدة
+
+165
+00:12:25,300 --> 00:12:31,780
+إلها size مختلفة عن التانية كويسة ناخد طريقة
+
+166
+00:12:31,780 --> 00:12:35,480
+تمثيلهم بالرسم عن طريق Venn diagram ال Venn
+
+167
+00:12:35,480 --> 00:12:41,210
+diagram طريقة بنستخدمهالتمثيل ال set بنمثل ال set
+
+168
+00:12:41,210 --> 00:12:44,330
+فيها ليش عساس أعرف التقاطعات أعرف ال elements اللي
+
+169
+00:12:44,330 --> 00:12:48,550
+ممكن تكون في أكتر من set التحادات كيف ممكن مجموعة
+
+170
+00:12:48,550 --> 00:12:53,910
+ال sets مع بعض نرسمهم كيف التداخل بينهم هل هم
+
+171
+00:12:53,910 --> 00:12:56,770
+مستقلين عن بعض و لا مش مستقلين عن بعض طبعا هذه
+
+172
+00:12:56,770 --> 00:13:02,150
+مناسبة لما نتكلم عن finiteSets، finite sets، تمام؟
+
+173
+00:13:02,150 --> 00:13:04,770
+أنا بقدر أعبر عنها فلو قلنا عندنا مجموعة الأرقام
+
+174
+00:13:04,770 --> 00:13:08,950
+بهذا الشكل من minus one to nine وموزعة بهذا الشكل
+
+175
+00:13:08,950 --> 00:13:13,270
+وكل مجموعة عاملين لهم set لحالهم كل مجموعة عاملين
+
+176
+00:13:13,270 --> 00:13:17,550
+لهم set لحالهم لو أخدنا المجموعة كلها على بعض ك
+
+177
+00:13:17,550 --> 00:13:21,450
+set as a set بنقدر نسميها إيش ال set هذه ال real
+
+178
+00:13:21,450 --> 00:13:27,380
+number فيها fractionsانتجار انتجار كويس انتجار
+
+179
+00:13:27,380 --> 00:13:29,140
+معناته حفظها من ان هي من minus infinity to
+
+180
+00:13:29,140 --> 00:13:35,840
+infinity معناته بدنا نحدد انتجار من تمام تمام
+
+181
+00:13:35,840 --> 00:13:41,990
+معناته بدنا نحددعشان أكون عرفت ال set بطريقة
+
+182
+00:13:41,990 --> 00:13:44,750
+واضحة، لازم التعريف يكون واضح، بنفعش أقول هي
+
+183
+00:13:44,750 --> 00:13:48,530
+integer وسكوت، integer اللي هيفهمها لو سماعتي
+
+184
+00:13:48,530 --> 00:13:51,710
+هيكمش شايف، لو ع ال radio، قولتولي مجموعة
+
+185
+00:13:51,710 --> 00:13:54,130
+integers، والله المجموعة بتاعتنا integers، خلاص
+
+186
+00:13:54,130 --> 00:13:57,290
+هفهم إن هي من minus infinity to infinity، بس مش
+
+187
+00:13:57,290 --> 00:14:02,460
+هذا الصحيحالفعلية هي مجموعة integers from minus
+
+188
+00:14:02,460 --> 00:14:10,680
+one to nine نسيب المجموعة الكبيرة ناخد المجموعة
+
+189
+00:14:10,680 --> 00:14:15,460
+الأصغر مجموعة
+
+190
+00:14:15,460 --> 00:14:22,530
+integers أقل من عشرة أو من واحد لعشرةأو natural
+
+191
+00:14:22,530 --> 00:14:26,610
+number أقل من عشرة صحيح؟ لأ بس ال natural number
+
+192
+00:14:26,610 --> 00:14:31,270
+برضه فيها الصفر يعني نفس الجثة لازم نحدد من واحد
+
+193
+00:14:31,270 --> 00:14:35,010
+لتسعة أو أكبر من صفر وأقل من عشرة الطريقة اللي
+
+194
+00:14:35,010 --> 00:14:38,650
+بتكونيها بتقدروا تعرفوها فهي positive integers أقل
+
+195
+00:14:38,650 --> 00:14:42,610
+من عشرة برضه هاي التعريف غيرنا هعرفها على أساس ان
+
+196
+00:14:42,610 --> 00:14:46,910
+هي integers أقل من عشرة بس حددها positive ف ال
+
+197
+00:14:46,910 --> 00:14:49,690
+zero و ال negative مش موجودةبرضه هى طريقة غير اللى
+
+198
+00:14:49,690 --> 00:14:52,490
+احنا اتكلمنا فيها بتقدروا تمثلوها بأى طريقة كانت
+
+199
+00:14:52,490 --> 00:14:55,410
+يعني بتقدروا تتكلموا بتمثلوها ب natural ال natural
+
+200
+00:14:55,410 --> 00:15:01,110
+هدى من واحد to nine او integer اكبر من صفر و اقل
+
+201
+00:15:01,110 --> 00:15:04,390
+من عشرة بتقدروا تعملوه بالطريقة اللى بتقوليها طيب
+
+202
+00:15:04,390 --> 00:15:12,270
+ناخد الست اللى هنا ايش هدى؟هذه ال even اللي أكبر
+
+203
+00:15:12,270 --> 00:15:16,490
+من صفر وأقل من عشرة مثلا فهذه ال integers اللي هم
+
+204
+00:15:16,490 --> 00:15:19,710
+من اتنين هاي كلمة حدث من اتنين لتسعة او من صفر
+
+205
+00:15:19,710 --> 00:15:23,510
+أكبر من صفر وأقل من عشرة فبتقدروا تمثلوها بالطريقة
+
+206
+00:15:23,510 --> 00:15:27,350
+اللي بدكم إياها طيب ناخد ال set ال .. هذه ال odd
+
+207
+00:15:27,350 --> 00:15:32,890
+برضه اللي إيه اش from one to nine ممكن from one to
+
+208
+00:15:32,890 --> 00:15:36,210
+nine او أكبر من صفر وأقل من عشرة نفس الكلام
+
+209
+00:15:36,210 --> 00:15:39,510
+بتقدروا تعملوه زي ما بدكم from nine to onefrom one
+
+210
+00:15:39,510 --> 00:15:43,630
+to nine طيب في ست ما زالت موجودة عندنا هنا ال
+
+211
+00:15:43,630 --> 00:15:47,910
+primes تمام مجموعة ال primes اللي اقل من عشرة ف
+
+212
+00:15:47,910 --> 00:15:52,170
+primes اقل من عشرة تمام فهي طريقة التمثيل و بنمثل
+
+213
+00:15:52,170 --> 00:15:54,750
+لازم نحط الدوائر هذه او المكعبات او المربعات بحيث
+
+214
+00:15:54,750 --> 00:15:59,510
+ان انا احدد و انتقطعات المجموعات نحدد و انتقطعات
+
+215
+00:15:59,510 --> 00:16:02,570
+المجموعات تلاحظوا مثلا الرقم اتنين الرقم اتنين
+
+216
+00:16:02,570 --> 00:16:07,830
+اشترك في اربع مجميع في اربع مجميع مجموعة اتن تان
+
+217
+00:16:07,830 --> 00:16:12,610
+تلاتة اربعتمام؟ مجموعة الدوائر اللي مرسومة و ترتيب
+
+218
+00:16:12,610 --> 00:16:16,190
+الأرقام ترتيب ال .. ال numbers هذه أعطتني الإحاء
+
+219
+00:16:16,190 --> 00:16:20,150
+أنه اه والله فعلا هذا موجود في ال set الأولى في ال
+
+220
+00:16:20,150 --> 00:16:23,010
+set التانية و في ال set التالتة هنا في الرابعة ل
+
+221
+00:16:23,010 --> 00:16:26,490
+primes بعرف أن okay الرقم هذا بيحقق الأربع شروط
+
+222
+00:16:26,490 --> 00:16:33,710
+تمام؟ فهذه طريقة لتمثيل ال .. ال set okay
+
+223
+00:16:34,950 --> 00:16:39,350
+الـ basic set relations أو ال number .. ال member
+
+224
+00:16:39,350 --> 00:16:44,410
+of .. member of set بمعنى أنه عنصر داخل ال set إيش
+
+225
+00:16:44,410 --> 00:16:47,770
+علاقته بال set؟ ف ال set relations مع ال elements
+
+226
+00:16:47,770 --> 00:16:50,750
+بتاعتها مع ال number بتاعتها كيف نبتمثلها؟ بنمثلها
+
+227
+00:16:50,750 --> 00:16:56,650
+بالعلامة هذه belong to فبقول x belong to set S
+
+228
+00:16:56,650 --> 00:17:02,680
+فإذا بقول إنه كأنها x is inست اس .. ست اس .. كويس
+
+229
+00:17:02,680 --> 00:17:06,080
+فبرضه في النهاية أنا بتكلم عن X هنا .. X هنا
+
+230
+00:17:06,080 --> 00:17:11,460
+object ال X عبارة عن object object X is an element
+
+231
+00:17:11,460 --> 00:17:14,980
+و هنا منها إجت العلمة من علامة كلمة element ال E
+
+232
+00:17:14,980 --> 00:17:20,820
+فأخدنا ال notation هذه علشان هي belong to set S or
+
+233
+00:17:20,820 --> 00:17:26,060
+member of set S تماممثال لو قلنا three belong to
+
+234
+00:17:26,060 --> 00:17:29,700
+natural number okay صحيح التلاتة هي واحدة من
+
+235
+00:17:29,700 --> 00:17:34,460
+الأرقام الطبيعية كلام صحيح او اقول ان a letter
+
+236
+00:17:34,460 --> 00:17:43,220
+letter a belong to X such that X is a letter of
+
+237
+00:17:43,220 --> 00:17:48,560
+alphabet فعلا واحدة من الحروفالـ A هو حرف من
+
+238
+00:17:48,560 --> 00:17:52,040
+الحروف فبرضه الكلام صحيح عشان امثل ان هو والله
+
+239
+00:17:52,040 --> 00:17:55,120
+فعلا ينتمي لمجموعة حروف بقول ان هو belong to ينتمي
+
+240
+00:17:55,120 --> 00:18:01,500
+ل .. ينتمي لل set اللي اتعرفت okay ال set quality
+
+241
+00:18:01,500 --> 00:18:05,080
+اللي اتكلمنا عنها بقدر امثلها برضه ب .. بال .. بال
+
+242
+00:18:05,080 --> 00:18:11,440
+notation belong to فلو قلنا for all set S set TS
+
+243
+00:18:11,440 --> 00:18:16,900
+equal to T if and only if for all X X belong to S
+
+244
+00:18:16,900 --> 00:18:24,520
+و X belong to T لكل القيم أو ال objects X لكل
+
+245
+00:18:24,520 --> 00:18:32,800
+القيم X ال X تنتمي ل set S و ال X تنتمي ل set T
+
+246
+00:18:32,800 --> 00:18:37,130
+هنا طبعا كتب الكياهة إذا كان X belong to Sif and
+
+247
+00:18:37,130 --> 00:18:40,250
+only if x belongs to T معناته صار محكومة أنه لازم
+
+248
+00:18:40,250 --> 00:18:45,010
+تنتمي لها S إذا كانت فعلا منتمية لمن ل T والزمن
+
+249
+00:18:45,010 --> 00:18:48,430
+لازم تكون منتمية ل T مش منتمية ل T معناته غير
+
+250
+00:18:48,430 --> 00:18:52,410
+منتمية لمن ل S في الحالة دي بنقول أنه منطقي صار
+
+251
+00:18:52,410 --> 00:18:56,930
+إيش كل ال elements اللي موجودة في Tموجودة في S
+
+252
+00:18:56,930 --> 00:19:00,550
+معناته the same elements موجودة في ال two sets
+
+253
+00:19:00,550 --> 00:19:04,490
+معناته في equality الإتنين بيسوا بيسوا بعض فإذا
+
+254
+00:19:04,490 --> 00:19:08,410
+two sets are equal if and only if they have all
+
+255
+00:19:08,410 --> 00:19:15,690
+the same members كويسة لو قلنا not belong to set X
+
+256
+00:19:15,690 --> 00:19:21,550
+not belong to set هدده كافي إيش X belong to set مع
+
+257
+00:19:21,550 --> 00:19:27,110
+ال negation not belong not belong toأو s is not in
+
+258
+00:19:27,110 --> 00:19:35,910
+6s ال empty set أو ال null اللي هو لا يوجد فارغ
+
+259
+00:19:35,910 --> 00:19:43,610
+فاضي أو ال empty set المجموعة الفارغة المجموعة
+
+260
+00:19:43,610 --> 00:19:49,530
+الفاضية كويس هذه بنسميها في فهذه is the unique set
+
+261
+00:19:49,530 --> 00:19:55,010
+that contains no elements whatsoeverلا تحتوي على
+
+262
+00:19:55,010 --> 00:20:00,390
+عناصر بالمطلق مافيش فيها أي عنصر فهي set بدون
+
+263
+00:20:00,390 --> 00:20:05,830
+عناصر مجموعة بدون عناصر مجموعة بدون عناصر في و
+
+264
+00:20:05,830 --> 00:20:11,010
+بنعمل عالم المجموعة كمان فهي كأنها set مافيش فيها
+
+265
+00:20:11,010 --> 00:20:18,110
+عناصر empty او تحتوي على عنصر false فمافيش فيها
+
+266
+00:20:18,110 --> 00:20:23,050
+true مافيش اي عنصر بقدر انه belong to setو بقى و
+
+267
+00:20:23,050 --> 00:20:27,710
+بمثله is it true دائما كل العناصر for all x is
+
+268
+00:20:27,710 --> 00:20:33,570
+false بغض النظر عن ال domain لل discourse او ال
+
+269
+00:20:33,570 --> 00:20:37,130
+universe of discourse بنقدر نقول ال .. ال axiom
+
+270
+00:20:37,130 --> 00:20:43,250
+التالية negation there exist x معناته there is no
+
+271
+00:20:43,250 --> 00:20:49,530
+x such that x belong to phi معناته لا يوجد عنصر x
+
+272
+00:20:49,530 --> 00:20:56,390
+ينتمي لهالـ set في أو ال empty set ليش؟ لأن أصلا
+
+273
+00:20:56,390 --> 00:21:00,210
+لا يوجد فيها عناصر ففعلا لا يوجد أي عنصر ينتمي
+
+274
+00:21:00,210 --> 00:21:08,450
+لset في okay subsetأتوقع كل الموضوع عندكم أخدينه
+
+275
+00:21:08,450 --> 00:21:12,010
+بس كنتوا بتتكلموا عن مجموعات بتتكلموا كنتوا
+
+276
+00:21:12,010 --> 00:21:15,970
+مجموعات فاحنا نفس الكلام بنرجع نهيده هنا ال .. ال
+
+277
+00:21:15,970 --> 00:21:18,990
+subset و ال superset برضه أخدتوها subset و
+
+278
+00:21:18,990 --> 00:21:23,770
+superset relations أخدتوها فكنا نقول ال S subset T
+
+279
+00:21:23,770 --> 00:21:28,690
+معناه ذلك أن ال S is a subset of T معناها عفوا
+
+280
+00:21:30,690 --> 00:21:35,670
+بالظبط هي subset of هي جزء من T تماما وهذه معناه
+
+281
+00:21:35,670 --> 00:21:41,450
+ان every element of S is also an element of T بس
+
+282
+00:21:41,450 --> 00:21:45,850
+العكس غير صحيح تمام معناه ذلك ان اذا ال element
+
+283
+00:21:45,850 --> 00:21:48,570
+بدأت من ال element في T مش بالضروري يكون موجود في
+
+284
+00:21:48,570 --> 00:21:55,810
+S ولكن كل element كل for all X X belong to S
+
+285
+00:21:57,070 --> 00:22:02,010
+بالضروري أن يكون belonging to T فإذا هنا لحظة
+
+286
+00:22:02,010 --> 00:22:06,370
+عملناها implication عملناها as implication for all
+
+287
+00:22:06,370 --> 00:22:13,730
+X X belonging to S بيضمن إذا كانت فعلا X belonging
+
+288
+00:22:13,730 --> 00:22:20,450
+to S then X belonging to T then كويسهذه
+
+289
+00:22:20,450 --> 00:22:23,130
+implication على أساس أنه إذا كان غير موجود هنا
+
+290
+00:22:23,130 --> 00:22:25,830
+الأصل أنه يكون غير موجود هنا فال implication أنسب
+
+291
+00:22:25,830 --> 00:22:29,250
+كانت هنا في التعريف .. أنسب في التعريف تمام
+
+292
+00:22:29,250 --> 00:22:33,430
+فالحالة الوحيدة ال false هنا إيش هي؟ ال
+
+293
+00:22:33,430 --> 00:22:38,270
+implication إيش الحالة الوحيدة false فيها؟ T to
+
+294
+00:22:38,270 --> 00:22:42,050
+false و لا .. و لا .. T to false مش كان ال T تبقى
+
+295
+00:22:42,050 --> 00:22:48,190
+.. معناته ..إذا كانت هنا موجودة و غير موجودة هنا
+
+296
+00:22:48,190 --> 00:22:52,090
+لأ في مشكلة معناته في مشكلة معناته هذا not subset
+
+297
+00:22:52,090 --> 00:22:59,930
+of T كويسة كمان تعريف ال Phi subset من أي set أخرى
+
+298
+00:22:59,930 --> 00:23:03,710
+ال Phi هي مجموعة جزئية من أي مجموعة في العالم في
+
+299
+00:23:03,710 --> 00:23:07,130
+الدنيا في كل الرياضيات هي subset من أي مجموعة طيب
+
+300
+00:23:07,130 --> 00:23:11,690
+أي مجموعة هي subset من نفسها لأن ال subset هي تمثل
+
+301
+00:23:11,690 --> 00:23:15,020
+.. لو بدنا نتكلم عنعال numbers هي كأنها أقل من أو
+
+302
+00:23:15,020 --> 00:23:21,120
+تساوي فأي رقم هو يساوي نفسه فكل رقم بقدر أحط فيه
+
+303
+00:23:21,120 --> 00:23:27,140
+أحطله ال expression هذا كويس فهي subset لنفسها طيب
+
+304
+00:23:27,140 --> 00:23:32,560
+العكس لل subset ال super set هي عكس الاتجاه لما
+
+305
+00:23:32,560 --> 00:23:38,600
+أقول S superset of T كأني بقول T subset ofof S
+
+306
+00:23:38,600 --> 00:23:45,180
+معناته ان S is a superset of T طيب امتى بقدر اقول
+
+307
+00:23:45,180 --> 00:23:48,840
+ان ال S equal to T من خلال معرفتنا هنا بال subset
+
+308
+00:23:48,840 --> 00:23:52,360
+و ال superset اذا كانت ال S subset of T and
+
+309
+00:23:52,360 --> 00:23:58,760
+superset of T بالظبط ليش لان مستحيل رقمين اكبر منه
+
+310
+00:23:58,760 --> 00:24:02,020
+اصغر من بعضبس احنا بدنا ناخد بالة ان في علامة
+
+311
+00:24:02,020 --> 00:24:05,600
+يساوي فال condition الوحيد اللي ممكن فعلا نخليهم
+
+312
+00:24:05,600 --> 00:24:09,300
+اكبر من او يساوي و اصغر من او يساوي هي المساوية هو
+
+313
+00:24:09,300 --> 00:24:14,120
+اليساوي اللي موجودة هنا هي اليساوي فاحنا هنا بيقول
+
+314
+00:24:14,120 --> 00:24:21,040
+ان هذه جزئية من هذه و T جزئية من S تمام فالحالة
+
+315
+00:24:21,040 --> 00:24:23,680
+الوحيدة هنا اللي هو ال condition هذا ان المجموعة
+
+316
+00:24:23,680 --> 00:24:26,560
+ممكن تكون subset من نفسها مساوية لنفسها
+
+317
+00:24:30,650 --> 00:24:34,690
+ما هي نفس المعنى هو نفس المعنى نفس الأشياء هي
+
+318
+00:24:34,690 --> 00:24:39,730
+subset من نفسها لحظة وهذه super set من هذه ما هي
+
+319
+00:24:39,730 --> 00:24:43,010
+نفس الاتجاه بحدين يعني من الاتجاهين اللي اتكلمت
+
+320
+00:24:43,010 --> 00:24:51,410
+تمام okay قعدت كقولناها ال S not subset of T
+
+321
+00:24:51,410 --> 00:24:57,820
+معناته negation S subset of Tnegation as subset of
+
+322
+00:24:57,820 --> 00:25:03,540
+T أو there exist X such that X belong to S and X
+
+323
+00:25:03,540 --> 00:25:07,560
+not belong to T لأن هو العصل إنه إذا كان belong to
+
+324
+00:25:07,560 --> 00:25:13,600
+S يكون belong to T بس لأ هو belong to S و not
+
+325
+00:25:13,600 --> 00:25:21,100
+belong to T الزمنالزامن and هو موجود في S و غير و
+
+326
+00:25:21,100 --> 00:25:27,100
+and و غير موجود في T هذه الحالة خلاص بتنفي لنا ال
+
+327
+00:25:27,100 --> 00:25:32,040
+subset اللي أخدناها بتنفي ال subset الحالة هذه
+
+328
+00:25:32,040 --> 00:25:39,510
+تمامprepare أو extract subsets and supersets هدى
+
+329
+00:25:39,510 --> 00:25:46,010
+بمعنى مجموعة جزئية مقيدة مافيش فيها يساوي او يساوي
+
+330
+00:25:46,010 --> 00:25:49,770
+مافيش فيها او يساوي فهنا ماقدرش اقول ان المجموعة
+
+331
+00:25:49,770 --> 00:25:56,250
+prepare subset من نفسها، مانفعش اما الـ Phi okay
+
+332
+00:25:56,250 --> 00:26:01,450
+ال Phi prepare subset من اي مجموعة تانية غير ال
+
+333
+00:26:01,450 --> 00:26:05,380
+Phi، بمشي الكلامتمام؟ بس مع نفسها مامشيش هنا ليش؟
+
+334
+00:26:05,380 --> 00:26:10,320
+لإن هنا إلزامة أقل من .. هتكون جزئية منها و لا
+
+335
+00:26:10,320 --> 00:26:16,240
+تساوي جزئية منها و لا تساوي طيب فهذه معناها أن S
+
+336
+00:26:16,240 --> 00:26:22,140
+.. لاحظوا هنا subset of T but T not subset of S
+
+337
+00:26:22,140 --> 00:26:27,600
+إيش .. إيش اللي تم استثنائه هنا؟ اللي تم استثنائه
+
+338
+00:26:27,600 --> 00:26:33,630
+إن إحنا استثننا اليساويتم استثناء اليساوي فضلت
+
+339
+00:26:33,630 --> 00:26:38,350
+subset structurally أو prepare subset بدون علامة
+
+340
+00:26:38,350 --> 00:26:42,630
+المساواة فضلت بهذا الشكل زي لما كنتوا بتتكلموا لو
+
+341
+00:26:42,630 --> 00:26:46,230
+نسقط الكلام على الأرقام كنا بنقول أقل من أو يساوي
+
+342
+00:26:46,230 --> 00:26:53,350
+وفي أقل من بس فهذه غير هذه فهنا بنتكلم عن subset
+
+343
+00:26:53,350 --> 00:26:59,350
+وهنا بنتكلم عن prepare subset هذه إشي وهذه .. هذه
+
+344
+00:26:59,350 --> 00:27:05,730
+إشي طيبنفس الكلام هو نقدر نعيده ل مين ل prepare
+
+345
+00:27:05,730 --> 00:27:11,230
+superset prepare superset prepare superset ليش لأن
+
+346
+00:27:11,230 --> 00:27:15,870
+هم عكس بعض اللي احنا عرفنا في prepare subset هو
+
+347
+00:27:15,870 --> 00:27:18,790
+نفسه بقدر اعرفه prepare superset على اعتبار ان هنا
+
+348
+00:27:18,790 --> 00:27:26,790
+T prepare subset of Sprepare super set of T تنتهي
+
+349
+00:27:26,790 --> 00:27:30,290
+منعكس برا طيب example ممكن نكتب هنا مثلا هنمثلها
+
+350
+00:27:30,290 --> 00:27:37,350
+بال Venn diagram و هنا هنمثلها ك example بال sets
+
+351
+00:27:37,350 --> 00:27:41,420
+اللي عندنا فلو قلنا في عندنا set one and twoتحتوي
+
+352
+00:27:41,420 --> 00:27:43,840
+على الـ two elements الـ two elements هدولة واحد و
+
+353
+00:27:43,840 --> 00:27:48,460
+اتنين هذه is prepare subset of واحد اتنين تلاتة
+
+354
+00:27:48,460 --> 00:27:54,920
+prepare subset of set تحتوي على واحد اتنين و تلاتة
+
+355
+00:27:54,920 --> 00:28:02,360
+ليش لأن فعلا واحد و اتنين موجودين و T التانية مش
+
+356
+00:28:02,360 --> 00:28:06,280
+subset من الأولى مش subset من الأولى ليش مش subset
+
+357
+00:28:06,280 --> 00:28:08,760
+من الأولى لأن في element موجود فيها غير موجود في
+
+358
+00:28:08,760 --> 00:28:13,580
+الأولى تمامبال Venn diagram ممكن تمثلوها بهذا
+
+359
+00:28:13,580 --> 00:28:18,360
+الشكل ال S والT لا يمكن يكونوا بيساوي بعض في
+
+360
+00:28:18,360 --> 00:28:25,700
+element هيه موجود في T غير موجود في S توقع واضحة
+
+361
+00:28:25,700 --> 00:28:29,120
+ال relation احنا مجرد بس بنقول كأنه بنتكلم عن
+
+362
+00:28:29,120 --> 00:28:33,540
+الأكبر من أو يساوي وأكبر من أصغر من أو يساوي وأصغر
+
+363
+00:28:33,540 --> 00:28:39,380
+من بس بنسقطها على مين على ال six على المجموعات طيب
+
+364
+00:28:40,690 --> 00:28:43,710
+set are objects too احنا في الأخر الفيديو اللي
+
+365
+00:28:43,710 --> 00:28:48,630
+بنتكلم انه هي مجموعة objects كل set تحتوي على
+
+366
+00:28:48,630 --> 00:28:51,450
+مجموعة elements ال elements هذه objects طيب ال
+
+367
+00:28:51,450 --> 00:28:54,130
+object هذا اللي هو element ممكن هو نفسه يكون
+
+368
+00:28:54,130 --> 00:29:00,290
+مجموعة ممكن هو نفسه يكون عبارة عن إيش set هو نفسه
+
+369
+00:29:00,290 --> 00:29:04,030
+عبارة عن set مش بالضرورة يكون element ك element زي
+
+370
+00:29:04,030 --> 00:29:07,510
+لما تكون بتتكلم عن hard disk و بتبدو تعمله تجسيم
+
+371
+00:29:08,470 --> 00:29:11,270
+المجموع بالنسبة لنا كنت اعمله folder لانه هيحتوي
+
+372
+00:29:11,270 --> 00:29:15,670
+على مجموعة files صحيح؟ فهتعمله folder طب انا مش
+
+373
+00:29:15,670 --> 00:29:19,270
+ملزم اني على طول احط files ممكن داخله احط كمان
+
+374
+00:29:19,270 --> 00:29:23,910
+folders فانا بحط مجموعات بحط كمان مجموعات جوا بجسم
+
+375
+00:29:23,910 --> 00:29:27,550
+ال folder جوا لخمس لخمسة folders مثلا وداخل ال
+
+376
+00:29:27,550 --> 00:29:30,990
+folders ممكن احط كمان تجسمة تانية لعند ما اصل لمين
+
+377
+00:29:30,990 --> 00:29:33,710
+لل file اللي هو ال element اللي انا بتعامل معاه بس
+
+378
+00:29:33,710 --> 00:29:37,650
+في النهاية ال elements بالنسبة لأول folder لل C
+
+379
+00:29:37,650 --> 00:29:45,270
+مثلاكنتوا حاطين مجموعة folders فبالضبط
+
+380
+00:29:45,270 --> 00:29:51,710
+العنصر عندنا ال element هنا عبارة عن set عبارة عن
+
+381
+00:29:51,710 --> 00:29:59,710
+set هو في داخله يحتوي يحتوي على elements او set
+
+382
+00:29:59,710 --> 00:30:03,930
+برضه او مجموعة sets او مجموعة sets تمام فانحن
+
+383
+00:30:03,930 --> 00:30:07,570
+نتكلم عن ال tree هنا كأنها صارت مشابه لفكرة ال
+
+384
+00:30:07,570 --> 00:30:15,440
+treeتمام هذا معناه مدام هي نفسها okay themselves
+
+385
+00:30:15,440 --> 00:30:19,040
+be sets ممكن هي نفسها تكون sets ال elements هذه
+
+386
+00:30:19,040 --> 00:30:22,640
+اللي داخل ال set نفسها تكون sets كأني بقول let s
+
+387
+00:30:22,640 --> 00:30:31,100
+equal to x such that x not belong but subset
+
+388
+00:30:31,100 --> 00:30:34,920
+subset أنا عارف أن ال subset هنا ماتتعاملش مع
+
+389
+00:30:34,920 --> 00:30:40,030
+elements belong أنا بتعامل مع elementsubset بتعامل
+
+390
+00:30:40,030 --> 00:30:44,770
+مع set ماهي اسمها sub set او super set انا بتعامل
+
+391
+00:30:44,770 --> 00:30:48,690
+مع set هنا تمام فإذا ال X هنا واضح انه انا بتعامل
+
+392
+00:30:48,690 --> 00:30:54,050
+مع مين set عبارة عن subset من 123 من ال set 123
+
+393
+00:30:54,050 --> 00:30:59,850
+فإذا المجموعة اللي بنتكلم عنها S هي عبارة عن
+
+394
+00:30:59,850 --> 00:31:04,430
+مجموعة objects ال objects هذه عرفناها ان هي sets
+
+395
+00:31:05,430 --> 00:31:08,830
+ماذا يميز ال sets هذه اللي هي تمثل كأنها element
+
+396
+00:31:08,830 --> 00:31:13,130
+بالنسبة ل S بس element له خصوصية ان هو أصلا set
+
+397
+00:31:13,130 --> 00:31:20,030
+بحياته ال set هذه subset of 1 2 3 فممكن تكون ايش ك
+
+398
+00:31:20,030 --> 00:31:23,530
+subset اول شغلة و احنا بنتكلم عن ال subset و
+
+399
+00:31:23,530 --> 00:31:26,170
+اقولكوا والله هي عندكوا set طلعولي ال subsets
+
+400
+00:31:26,170 --> 00:31:31,810
+ساعتها اول واحدة في على طول و احنا مغمضينأول واحدة
+
+401
+00:31:31,810 --> 00:31:35,810
+بتحط في خلصناها طيب ممكن تكون الواحد واحد لحالها
+
+402
+00:31:35,810 --> 00:31:41,050
+ممكن تكون اتنين لحالها ست تحتوي على العنصر واحد او
+
+403
+00:31:41,050 --> 00:31:44,930
+ست تحتوي على العنصر تلاتة عنصر واحد فقط طيب او
+
+404
+00:31:44,930 --> 00:31:50,710
+واحد و اتنين واحد و تلاتة اتنين و تلاتة اتنين و
+
+405
+00:31:50,710 --> 00:31:55,950
+واحد فكلهم هتكون واحدة احنا قولنا ان هي unordered
+
+406
+00:31:55,950 --> 00:32:02,260
+كويس فبتحطهم كلهم بتكونوا مثلتهالـ expression هذا
+
+407
+00:32:02,260 --> 00:32:06,880
+إن إحنا بنتعامل مع ال element داخل ال set S كإنها
+
+408
+00:32:06,880 --> 00:32:11,440
+مجموعة sets كإنها مجموعة sets طيب هذا يقودنا لإيش
+
+409
+00:32:11,440 --> 00:32:16,020
+إن ال element واحد هو لا يساوي ال set اللي تحتوي
+
+410
+00:32:16,020 --> 00:32:20,520
+على ال element واحد لا تساوي ال set اللي تحتوي على
+
+411
+00:32:20,520 --> 00:32:25,200
+ال set اللي تحتوي على ال element واحد لحظو فكل
+
+412
+00:32:25,200 --> 00:32:30,280
+واحدة غير التانية كل واحدة غير التانية طيب هذه جدا
+
+413
+00:32:30,280 --> 00:32:35,780
+مهمةال cardinality and finiteness ال cardinality
+
+414
+00:32:35,780 --> 00:32:41,100
+اللي هي أو اللي كله محدودية العددية جداش عدد ال
+
+415
+00:32:41,100 --> 00:32:44,600
+elements محدودية ال set بتاعتنا فهنا لما نيجي
+
+416
+00:32:44,600 --> 00:32:50,060
+نتكلم عن ال absolute set S هدى بنسميها cardinality
+
+417
+00:32:50,060 --> 00:32:54,640
+of S cardinality of S هدى بتجسلنا how many
+
+418
+00:32:54,640 --> 00:32:59,730
+different element in set Sأكم element داخل ال 6 او
+
+419
+00:32:59,730 --> 00:33:05,510
+المجموعة S لو قلنا مثلا ال Phi absolute طبعا احنا
+
+420
+00:33:05,510 --> 00:33:07,770
+مش هنقول absolute من يوم طالع احنا هنعمل علامة
+
+421
+00:33:07,770 --> 00:33:11,730
+absolute بس بنقول cardinality of Phi cardinality
+
+422
+00:33:11,730 --> 00:33:16,070
+of Phi الشيه كده؟ صفر لأنه احنا عارفين ان ال 6 Phi
+
+423
+00:33:16,070 --> 00:33:19,810
+تحتوي على كم element؟ zero element لو قلنا
+
+424
+00:33:19,810 --> 00:33:25,140
+cardinality ل 6 1 2 3تلاتة لأنه أكم element فيها
+
+425
+00:33:25,140 --> 00:33:29,920
+تلاتة لو قلنا ال cardinality ل ال set اللي تحتوي
+
+426
+00:33:29,920 --> 00:33:35,740
+على ال letters a و b اتنين لان عندكوا a و b طيب ال
+
+427
+00:33:35,740 --> 00:33:41,520
+cardinality ل أكم واحدة هنا اتنين الشمال اتنين اه
+
+428
+00:33:41,520 --> 00:33:47,440
+لأن هنا لاحظوا في عندنا set ال elements بتاعتها
+
+429
+00:33:47,440 --> 00:33:53,000
+two setsال elements عددهم جوا هما عبارة عن two
+
+430
+00:33:53,000 --> 00:33:55,360
+sets و احنا لسه كنا بنتكلم ان ال element ممكن يكون
+
+431
+00:33:55,360 --> 00:33:59,100
+six ال element ممكن يكون six فواضح ان هنا بنتكلم
+
+432
+00:33:59,100 --> 00:34:04,780
+عن cardinality equal to two إذا
+
+433
+00:34:04,780 --> 00:34:09,160
+كان والله ال cardinality ل to S if cardinality of
+
+434
+00:34:09,160 --> 00:34:12,460
+S belong to natural number فاحنا هنا بنقول ان ال S
+
+435
+00:34:12,460 --> 00:34:17,720
+is finite إذا كانال cardinality بمعنى ما يجدش عدد
+
+436
+00:34:17,720 --> 00:34:23,280
+ال elements داخل الست S ينتمي ل ال natural numbers
+
+437
+00:34:23,280 --> 00:34:27,860
+يعني معناته رقم طبيعي بنقول أن ال S هذه finite
+
+438
+00:34:27,860 --> 00:34:33,640
+محددة بنقدر نقول عنها محددة كويس otherwise لأ هي
+
+439
+00:34:33,640 --> 00:34:38,080
+إيش infinite set
+
+440
+00:34:38,080 --> 00:34:46,130
+ال natural number الشيةخلينا مع بعض طب انا معاك ال
+
+441
+00:34:46,130 --> 00:34:47,930
+natural number ايش هم الأرقام بتاعة ال natural
+
+442
+00:34:47,930 --> 00:34:53,590
+number اللي هم ال integer طب من وين بدنا نجيب واحد
+
+443
+00:34:53,590 --> 00:35:00,630
+و نص ال integer طب otherwise ان هو ما خلص infinite
+
+444
+00:35:00,630 --> 00:35:04,030
+بس دير برك infinite هنا القصد انه ممكن تكون تنتمي
+
+445
+00:35:04,030 --> 00:35:09,060
+لل integerotherwise أنا مش محددة otherwise انت مش
+
+446
+00:35:09,060 --> 00:35:12,520
+محددة مدام مش محددة خلاص التساوت if فيها كسور و لا
+
+447
+00:35:12,520 --> 00:35:14,680
+مش فيها كسور بس احنا نتكلم مش هنا عن كسور نتكلم
+
+448
+00:35:14,680 --> 00:35:17,360
+انه هل هي belong to natural number it's okay
+
+449
+00:35:17,360 --> 00:35:21,280
+otherwise لأ otherwise ممكن تكون تنتمي ل sets أخرى
+
+450
+00:35:21,280 --> 00:35:25,820
+غير ال natural numbers زي ال .. ال integer زي ال
+
+451
+00:35:25,820 --> 00:35:29,180
+.. ال real numbers ال real numbers فيها كسور فهدا
+
+452
+00:35:29,180 --> 00:35:33,720
+أنا بقول infinite و مقدرش أتعامل مع ال .. ال set
+
+453
+00:35:33,720 --> 00:35:38,830
+بتاعناOkay طبعا infinite هتتعاملوا مع كتير أنواع
+
+454
+00:35:38,830 --> 00:35:43,390
+منها بتتعاملوا مع أنواع كتير منها زي ال natural
+
+455
+00:35:43,390 --> 00:35:45,890
+number نفسها طبعا هنا قلنا احنا اتنين ال natural
+
+456
+00:35:45,890 --> 00:35:48,690
+number هي اصلا infinite
+
+457
+00:35:50,310 --> 00:35:52,770
+عددهم جدش عدد ال cardinality جدش قيمتها ال
+
+458
+00:35:52,770 --> 00:35:57,570
+cardinality كبيرة to infinity طيب و ال z اللي هي
+
+459
+00:35:57,570 --> 00:36:01,910
+إيش ال integer و ال real هدولة من الحاجات اللي
+
+460
+00:36:01,910 --> 00:36:05,210
+احنا عارفينهم هدولة من الأمور اللي احنا عارفينها
+
+461
+00:36:05,210 --> 00:36:09,830
+تمام خلصنا ال cardinality بدنا نشوف إيش ال power
+
+462
+00:36:09,830 --> 00:36:14,850
+the power set operation
+
+463
+00:36:18,730 --> 00:36:24,010
+للset هي عبارة عن ال subsets اللي بقدر اطلعها من
+
+464
+00:36:24,010 --> 00:36:27,830
+ال set هذه جداش عدد ال subsets اللي بنقدر نطلعها
+
+465
+00:36:27,830 --> 00:36:32,730
+من ال set S كل set S بقدر اطلع منها مجموعة ايه؟
+
+466
+00:36:32,730 --> 00:36:37,270
+subset جداش عددهم ال subsets هدولة؟قدش ما نقدر
+
+467
+00:36:37,270 --> 00:36:42,530
+نطلع منها بنقول عنها power of set ال power of set
+
+468
+00:36:42,530 --> 00:36:46,950
+فال power of set بنقول عليها power of set S بهذا
+
+469
+00:36:46,950 --> 00:36:53,470
+الشكل P of S of a set S is the set of all subset
+
+470
+00:36:53,470 --> 00:36:58,430
+of S فهي كل ال subset هي عبارة عن set تحتوي على كل
+
+471
+00:36:58,430 --> 00:37:02,770
+ال subset of Sتمام فهي انه لحظه مدام هي بتحتوي على
+
+472
+00:37:02,770 --> 00:37:06,570
+كل ال subset هي هتكون ال elements بتاعتها عبارة عن
+
+473
+00:37:06,570 --> 00:37:12,610
+set لأن هي subset هي فهتكون ال elements بتاعتها
+
+474
+00:37:12,610 --> 00:37:16,930
+عبارة عن set او مجموعة sets ايش اللي يميزهم مجموعة
+
+475
+00:37:16,930 --> 00:37:22,530
+ال sets دول ان هم subset of S زي لو قولنا ال power
+
+476
+00:37:22,530 --> 00:37:28,030
+of6 a و b هذي هتكون عبارة عن ايش اول شغل هقولنا ال
+
+477
+00:37:28,030 --> 00:37:31,050
+five لازم تكون المجموعة الفارغة او المجموعة
+
+478
+00:37:31,050 --> 00:37:34,010
+الخالية واحدة منهم لان هي المجموعة الخالية جزء من
+
+479
+00:37:34,010 --> 00:37:37,710
+اي شي جزء من اي six اخرى او ممكن تكون اخد ال
+
+480
+00:37:37,710 --> 00:37:42,610
+element الاول لحاله هاي six لحالها او بي لحالها او
+
+481
+00:37:42,610 --> 00:37:47,160
+الاتنين مع بعض ليش لان ال subset ممكن equalفممكن
+
+482
+00:37:47,160 --> 00:37:51,140
+تكون هى نفسها فإذا كان subset ال power أول حاجة
+
+483
+00:37:51,140 --> 00:37:57,060
+بتحطوها المعروفين جدا هدولة الفاي و هى نفسها و هى
+
+484
+00:37:57,060 --> 00:37:59,740
+نفسها موجودة خلاص هى نفسها بنحطها بعدين تبدو
+
+485
+00:37:59,740 --> 00:38:02,340
+تاخدوا الأقسام بتاعتها الأجزاء اللى ممكن تكون
+
+486
+00:38:02,340 --> 00:38:06,740
+موجودة فيها طيب هنا بنكتبها ال sometimes أحيانا
+
+487
+00:38:06,740 --> 00:38:10,160
+بكتبوها two to the power s فبعرف أن هى ال power
+
+488
+00:38:11,680 --> 00:38:16,700
+power of S طيب لما نتكلم عن إذا كانت هي finite ال
+
+489
+00:38:16,700 --> 00:38:20,860
+S تبعتنا بقدر أقول ال cardinality لل power عبارة
+
+490
+00:38:20,860 --> 00:38:26,240
+عن two to the power cardinality S two to the power
+
+491
+00:38:26,240 --> 00:38:28,840
+cardinality S يعني هتعملوا أن انتوا عندكوا هنا
+
+492
+00:38:28,840 --> 00:38:31,920
+مجموعة subsets ال subsets هذه كل ال subsets
+
+493
+00:38:31,920 --> 00:38:35,760
+الممكنة من ال set S هتطلعلكوا حاجة هسميها ال power
+
+494
+00:38:35,760 --> 00:38:39,460
+of S صحيح طب قداش عدد ال elements بتاعة ال power
+
+495
+00:38:39,460 --> 00:38:43,860
+of Sبنجيب ال cardinality ل S و بنعمل 2 to the
+
+496
+00:38:43,860 --> 00:38:47,340
+power of cardinality ففي الحالة اللى كانت عندنا
+
+497
+00:38:47,340 --> 00:38:52,780
+جدش ال elements ل S ال cardinality ل S اتنين اتنين
+
+498
+00:38:52,780 --> 00:38:58,700
+فهيكون عندكوا cardinality of S equal to 2 طيب ال
+
+499
+00:38:58,700 --> 00:39:06,320
+cardinality لل power هتكون 2 to the power 2 هتطلع
+
+500
+00:39:06,320 --> 00:39:11,520
+4 طب تعالى نشوف فعلا 1 2 3 4فعلا عدد ال elements
+
+501
+00:39:11,520 --> 00:39:17,180
+بتاعتها أربعة تمام هذه قاعدة باستمرار تستخدمها
+
+502
+00:39:17,180 --> 00:39:22,040
+okay بنقدر
+
+503
+00:39:22,040 --> 00:39:26,860
+برضه نقول ان ال cardinality ل ال P of natural
+
+504
+00:39:26,860 --> 00:39:30,460
+number ل أي finite natural number هيكون أكبر من ال
+
+505
+00:39:30,460 --> 00:39:37,480
+cardinality ل ال set نفسها برضه منطقيمنطق جدا ليش؟
+
+506
+00:39:37,480 --> 00:39:40,860
+لأن كنتوا بتعملوا منها مجموعة subsets بتعملوا منها
+
+507
+00:39:40,860 --> 00:39:47,620
+مجموعة subsets لل .. الفاية زيادة .. الفاية زيادة
+
+508
+00:39:47,620 --> 00:39:51,120
+هو بعدين بتكون بالعكس زيادة بكتير ليش؟ لأنه اتنين
+
+509
+00:39:51,120 --> 00:39:55,680
+to the power ال cardinality تبعتها فبتعطيكوا كمية
+
+510
+00:39:55,680 --> 00:39:58,400
+كبيرة طبعا هتطلع هنا عدد ال card .. او ال
+
+511
+00:39:58,400 --> 00:40:02,120
+cardinality ك value لل power أكيد هتكون أكبر من ال
+
+512
+00:40:02,120 --> 00:40:07,800
+cardinality لل set نفسها لل set نفسهاو هذا برجع
+
+513
+00:40:07,800 --> 00:40:10,800
+بيخلنا نقول أنه فعلا في عندنا different sizes ليش
+
+514
+00:40:10,800 --> 00:40:16,000
+لل infinite sets .. لل infinite sets okay نفس
+
+515
+00:40:16,000 --> 00:40:19,700
+الكلام احنا كله كنا بيقوله جمهيك ليش unordered ..
+
+516
+00:40:19,700 --> 00:40:23,350
+unorderedلأ احنا ممكن هنا لو عملنا ال ordered
+
+517
+00:40:23,350 --> 00:40:27,690
+هنطلع شغلة جديدة هنتكلم عن ال Cartesian لاحقا ال
+
+518
+00:40:27,690 --> 00:40:29,870
+Cartesian اللي هو الترتيب الثنائي أو الترتيب
+
+519
+00:40:29,870 --> 00:40:35,590
+النقاط بشكل Cartesian بإحداثيات هذا بنقدر ناخده من
+
+520
+00:40:35,590 --> 00:40:40,950
+نفس الفكرة set ولكن مرتبة مجموعة عناصر ولكن
+
+521
+00:40:40,950 --> 00:40:47,530
+الترتيب مهم فيها فهذه ال ordered intables او تكرار
+
+522
+00:40:47,530 --> 00:40:53,430
+بعدد n ومرتبةبحيث انه لو قلنا واحد اتنين لا تساوي
+
+523
+00:40:53,430 --> 00:40:57,590
+اتنين واحد لا تساوي اتنين واحد لاحظوا ان احنا ما
+
+524
+00:40:57,590 --> 00:41:05,690
+استعملناش ال curly braces ما استعملناش الاقوات
+
+525
+00:41:05,690 --> 00:41:10,730
+ساعة المجموعة استعملنا اقوات عاديةالاحداثيات اللى
+
+526
+00:41:10,730 --> 00:41:12,890
+هى ال Cartesian اللى هى ال Cartesian احنا قلتلكوا
+
+527
+00:41:12,890 --> 00:41:15,210
+ال Cartesian هنستعمله فى ال Cartesian اللى يمكن ال
+
+528
+00:41:15,210 --> 00:41:18,470
+slide اللى جاول بعدها كويس لها الاحداثيات للنقاط
+
+529
+00:41:18,470 --> 00:41:22,710
+مثلا احداثيات الاتجاهات احداثيات ال .. فهذه لأ
+
+530
+00:41:22,710 --> 00:41:29,690
+بتعبر عن ordered لإنه لما بقولكم بدنا نتحرك x و y
+
+531
+00:41:29,690 --> 00:41:33,010
+بتفرج واحد باتنين عن اتنين و واحد بيفرجوا كتير
+
+532
+00:41:33,830 --> 00:41:39,330
+بفرجوه جدا في الحالة اللي هنا بنتكلم عنها طيب بظل
+
+533
+00:41:39,330 --> 00:41:44,590
+ان ال n هذه اللي هي جدش عدد التكرارات بتاعتنا جدش
+
+534
+00:41:44,590 --> 00:41:49,210
+عدد ال elements داخل ال .. ال .. ال ordered set
+
+535
+00:41:49,210 --> 00:41:53,150
+جدش عددهم عددهم n ال n هذه لازم تكون belong to
+
+536
+00:41:53,150 --> 00:41:56,810
+natural number لازم تكون integer و لازم تكون محددة
+
+537
+00:41:56,810 --> 00:42:00,710
+في نت و لازم تكون positive positive و integer okay
+
+538
+00:42:01,800 --> 00:42:05,340
+ففي الآخر ممكن نعبر عنها عساس ان هي sequence
+
+539
+00:42:05,340 --> 00:42:12,940
+مجموعة من ال elements ال objects المرتبة sequence
+
+540
+00:42:12,940 --> 00:42:16,760
+معناته بتكون مرتبة مرتبة ورا بعض بفرج ان احط
+
+541
+00:42:16,760 --> 00:42:19,480
+الانصر التاني مكان الأول اه بتصير هنا بنتكلم عن
+
+542
+00:42:19,480 --> 00:42:23,060
+sequence مختلف sequence ثاني تماما ال first
+
+543
+00:42:23,060 --> 00:42:26,950
+element تبعه محددفي ال sequence اللي عندنا هنا a1
+
+544
+00:42:26,950 --> 00:42:30,870
+a2 to an محدد ان الاول واحد element لازم اشوفه هو
+
+545
+00:42:30,870 --> 00:42:36,350
+ال a واحد تحديدا كويس في الحالة هذه قلناها اول ما
+
+546
+00:42:36,350 --> 00:42:40,170
+بدنا نتكلم ال 1 و 2 مختلفة و لا تساوي 2 و 1 لا
+
+547
+00:42:40,170 --> 00:42:44,270
+تساوي احداث زيادة هنا صار في عندكم ال n تلاتة كانت
+
+548
+00:42:44,270 --> 00:42:49,680
+ال n ب 2 2 و 1 زودنا عليها كمانكمان element طبعا
+
+549
+00:42:49,680 --> 00:42:55,460
+هذه بتختلف و ممكن تتبين ال n هنا عندنا في بعض
+
+550
+00:42:55,460 --> 00:43:02,740
+مسميات أحيانا درجة لو كان عندنا ال n ب zero لو
+
+551
+00:43:02,740 --> 00:43:07,700
+ال set هذا ال n تبعتها ب zero امتى؟ مافيش .. احنا
+
+552
+00:43:07,700 --> 00:43:09,880
+نتكلم عن sequence مش موجود sequence ال element
+
+553
+00:43:09,880 --> 00:43:18,350
+تبعته ب zero او singlets عنصر واحد ال pairsوضع زوج
+
+554
+00:43:18,350 --> 00:43:21,830
+.. زوج .. زوج من الأرقام أو زوج من الثانوية اللي
+
+555
+00:43:21,830 --> 00:43:24,710
+كنتوا بتستخدمهم في ال X و ال Y في النقاط بتاعتكم
+
+556
+00:43:24,710 --> 00:43:28,850
+كنتوا بتستخدمهم في ال X و ال Y triples ثلاثي رباعي
+
+557
+00:43:28,850 --> 00:43:33,010
+خماسي two n two n tuples في ال quad .. ال quad
+
+558
+00:43:33,010 --> 00:43:37,910
+اللي هي الرباعي و quantable اللي هو الخماس واحدة
+
+559
+00:43:37,910 --> 00:43:41,510
+كده بتكمله لعند ما تشوفوا أنتوا الإحداثيات اللي
+
+560
+00:43:41,510 --> 00:43:43,770
+بتكونوا تستعملوها جدش و ممكن تستعملوها طبعا الكلام
+
+561
+00:43:43,770 --> 00:43:48,840
+هذا ممكن ت ..لا حقا ممكن ماتتتعاملوش كتير فيه،
+
+562
+00:43:48,840 --> 00:43:52,360
+ممكن كتير مابتتعاملوش فيه، ولكن ممكن تتعاملوا فيها
+
+563
+00:43:52,360 --> 00:43:55,200
+في ال problems الكبيرة، إذا كان الإحداثيات أو ال
+
+564
+00:43:55,200 --> 00:43:59,150
+dimensionality للمشكلة عاليةال dimensionality
+
+565
+00:43:59,150 --> 00:44:02,370
+للproblem ممكن تكون عالية احنا عادة اللي انتوا
+
+566
+00:44:02,370 --> 00:44:05,890
+عارفينه ان ال .. بتتعاملوا مع function فيها three
+
+567
+00:44:05,890 --> 00:44:09,570
+dimension هي ملأ ممكن تكون اكتر ممكن تكون اربعة
+
+568
+00:44:09,570 --> 00:44:12,450
+dimension خمسة dimension ستة dimension فانتوا في
+
+569
+00:44:12,450 --> 00:44:15,030
+الحالة هذه إذا ال problem ال dimension بتاعتها ستة
+
+570
+00:44:15,030 --> 00:44:20,630
+النقطة عشان تحطوا إحداثي لنقطة بدوا يكون فيها ستة
+
+571
+00:44:20,630 --> 00:44:24,190
+elements بدوا يكون فيها ستة elements فعليا تمام
+
+572
+00:44:25,730 --> 00:44:28,610
+Okay هنا بتدخلنا هدى على جزئية ال Cartesian
+
+573
+00:44:28,610 --> 00:44:32,850
+product of sets ال Cartesian product of sets لو
+
+574
+00:44:32,850 --> 00:44:38,010
+قلنا for sets A,B فال Cartesian product بتاعتهم A
+
+575
+00:44:38,010 --> 00:44:46,650
+Cartesian product بيه عبارة عن زوج ثنائي هيه A بيه
+
+576
+00:44:46,650 --> 00:44:51,900
+بشرط أن ال element الأول من ال set الأولىال
+
+577
+00:44:51,900 --> 00:44:55,760
+element التاني من ال set التاني فاحنا حطيناه بزوج
+
+578
+00:44:55,760 --> 00:45:03,640
+مرتب ordered order set such that a belong to set a
+
+579
+00:45:03,640 --> 00:45:10,660
+و ال element b belong to set b تمام فلو قلنا عنده
+
+580
+00:45:10,660 --> 00:45:18,300
+two sets set a, b cartesian product by set واحد و
+
+581
+00:45:18,300 --> 00:45:28,570
+اتنينعبارة عن إيش؟ ست لأزواج A واحد, A اتنين, B
+
+582
+00:45:28,570 --> 00:45:35,670
+واحد, B اتنين تمام؟ واضحة يعني مش فيها كتير صعوبة
+
+583
+00:45:35,670 --> 00:45:40,410
+و مش صعبة كتير لسه طيب for finite A, B
+
+584
+00:45:40,410 --> 00:45:48,060
+الcardinality لل product A في Bنفسها تساوي
+
+585
+00:45:48,060 --> 00:45:53,020
+الcardinality ل a في cardinality ل b cardinality ل
+
+586
+00:45:53,020 --> 00:45:59,100
+a هنا جداش cardinality ل a ل ال a كلها على بعض
+
+587
+00:45:59,100 --> 00:46:05,280
+اتنين cardinality ل b اتنين cardinality اتنين اللي
+
+588
+00:46:05,280 --> 00:46:08,200
+هي ال cardinality هنا اتنين و هنا في اتنين اتنين
+
+589
+00:46:08,200 --> 00:46:12,620
+في اتنين اربع طب خلنا نشوف هل فعلاالـ Cartesian
+
+590
+00:46:12,620 --> 00:46:15,600
+product ال cardinality بتاعتهم نفس الشيء لازم تطلع
+
+591
+00:46:15,600 --> 00:46:20,040
+نفس الشيء برضه أربعة اتنين في اتنين بساوي أربعة
+
+592
+00:46:20,040 --> 00:46:24,340
+طيب ال competitive هي not competitive الحقيقة ال
+
+593
+00:46:24,340 --> 00:46:26,900
+operation بتاعتنا ال Cartesian product ليش؟ لإن
+
+594
+00:46:26,900 --> 00:46:33,260
+احنا جولنا واحد A B مختلفة عن B A مختلفة لما أقول
+
+595
+00:46:33,260 --> 00:46:38,320
+A Cartesian B هي مختلفة عن B Cartesian A لإن
+
+596
+00:46:38,320 --> 00:46:42,540
+الأزواج المرتبة هتختلفهتختلف تماما، هتصير هنا
+
+597
+00:46:42,540 --> 00:46:46,280
+الأزواج المرتبة كلها دايما بدية بال letters هتصير
+
+598
+00:46:46,280 --> 00:46:48,980
+بالعكس بدية دايما بال numbers فهتلاجوا ان انتوا
+
+599
+00:46:48,980 --> 00:46:53,700
+طلعتوا set مختلفة تماما عن اللي كنتوا بتتكلموا
+
+600
+00:46:53,700 --> 00:47:00,260
+عنها فمعنى ذلك not for all a b a Cartesian product
+
+601
+00:47:00,260 --> 00:47:05,720
+b equal to b Cartesian product a not for all يعني
+
+602
+00:47:05,720 --> 00:47:09,620
+معنى ذلك انه ممكن تصير ممكن تصير امتى لو اتنين
+
+603
+00:47:09,620 --> 00:47:13,490
+بيسووا بعضلو الاتنين بيصور مش هتفرج كتير يعني في
+
+604
+00:47:13,490 --> 00:47:17,650
+بعض الحالات ممكن تظبط بس مش بالعموم مش بالعموم
+
+605
+00:47:17,650 --> 00:47:23,250
+تمام بنقدر انعمم ان ال Cartesian product بقدر ..
+
+606
+00:47:23,250 --> 00:47:27,090
+ممكن اعملها لأكتر من two sets يعني مش بضروري
+
+607
+00:47:27,090 --> 00:47:31,730
+اعملها ل a في b ممكن تنعمل a1 Cartesian product a2
+
+608
+00:47:31,730 --> 00:47:36,810
+Cartesian product a3 Cartesian product to anto a n
+
+609
+00:47:36,810 --> 00:47:42,450
+فمعنى ذلك ممكن نضرب أكتر من two sets أكتر من two
+
+610
+00:47:42,450 --> 00:47:47,930
+sets طيب الأمور هذه كويسة لعندي الآن تمام بدنا
+
+611
+00:47:47,930 --> 00:47:51,650
+نبدأ نعمل شوية operations على ال sets شوية
+
+612
+00:47:51,650 --> 00:47:55,890
+operations على ال sets ال operation المشهورة جدا
+
+613
+00:47:55,890 --> 00:47:58,990
+كنتوا تعملوا الاتحاد مش كنتوا تعملوا اتحاد
+
+614
+00:47:58,990 --> 00:48:04,730
+للمجموعاتthe union operator اللي هي عملية الاتحاد
+
+615
+00:48:04,730 --> 00:48:07,210
+عملية الاتحاد من الحاجات المشهورة جدا ومعروفة جدا
+
+616
+00:48:07,210 --> 00:48:13,290
+for sets A, B the union A union B is a set
+
+617
+00:48:13,290 --> 00:48:22,410
+containing all elements in A and B or B فهي كل ال
+
+618
+00:48:22,410 --> 00:48:29,310
+elements اللي موجودة في A أو موجودة في Bأو في بي
+
+619
+00:48:29,310 --> 00:48:37,570
+تمام فإذا هذي كأن بعمل or عشان نطلعنا ممكن طبعا in
+
+620
+00:48:37,570 --> 00:48:41,190
+bothممكن تكون هي مشتركة في الاتنين ممكن تكون
+
+621
+00:48:41,190 --> 00:48:43,430
+مشتركة في الاتنين ال elements اللي بدنا نحتويها
+
+622
+00:48:43,430 --> 00:48:50,870
+تمام فلو قلنا هنا for all a و b لو لكل ال sets a و
+
+623
+00:48:50,870 --> 00:48:55,850
+b a union b عبارة عن set جديدة set جديدة طبيعية
+
+624
+00:48:55,850 --> 00:49:00,430
+هتكون عبارة عن set جديدة تحتوي او ل x such that x
+
+625
+00:49:00,430 --> 00:49:05,650
+belong to a or x belong to main to bموجودة هنا أو
+
+626
+00:49:05,650 --> 00:49:08,330
+موجودة هنا معناته موجودة في ال union معناته موجودة
+
+627
+00:49:08,330 --> 00:49:13,770
+في من في ال union بتاعتهم okay فتحتوي على كل ال
+
+628
+00:49:13,770 --> 00:49:17,930
+elements سواء موجودة في a and contain all the
+
+629
+00:49:17,930 --> 00:49:21,570
+element of b ممكن نعبر عنها برضه بطريقة تانية على
+
+630
+00:49:21,570 --> 00:49:28,190
+أساس أن هي for all a, b such that a union b subset
+
+631
+00:49:28,190 --> 00:49:35,600
+of a طبيعيعفوا super set super set لحظة طبيعي لأن
+
+632
+00:49:35,600 --> 00:49:40,660
+انا اساسا ال union ماخدها من ال elements اللي في a
+
+633
+00:49:40,660 --> 00:49:45,800
+زائد element تانية اللي هم تعون بي فطبيعي ان a هي
+
+634
+00:49:45,800 --> 00:49:50,220
+subset من ال union و نفس الكلام لمين لل b نفس
+
+635
+00:49:50,220 --> 00:49:56,060
+الكلام and ال b برضه subset من ال union ل a و b
+
+636
+00:49:56,060 --> 00:50:00,280
+subset من ال union a to b تمام
+
+637
+00:50:05,710 --> 00:50:10,110
+ناخد exam's واضحة طبعا ال exam's هنا لو قلنا a ال
+
+638
+00:50:10,110 --> 00:50:15,210
+6 a b و c union مع two و three واضح أنه بدنا نحطهم
+
+639
+00:50:15,210 --> 00:50:21,670
+كلهم بدنا نحطهم كلهم طب لو قلنا union of two three
+
+640
+00:50:21,670 --> 00:50:26,390
+five union three five seven طبعا انتوا هتحطوا هدول
+
+641
+00:50:26,390 --> 00:50:30,330
+هتحطوا هدول هتلاقوا فيه تكرار شطبوا التكرارات لأن
+
+642
+00:50:30,330 --> 00:50:35,230
+هذه هي المطلوبةبدون تكرارات عادة بدنا ياها بحيث
+
+643
+00:50:35,230 --> 00:50:39,290
+انه العدد اللي انتوا حاطينه يمثل ال cardinality ال
+
+644
+00:50:39,290 --> 00:50:42,070
+cardinality لست خدوا بالكم انه لازم يمثل ال
+
+645
+00:50:42,070 --> 00:50:46,350
+cardinality لست كلام برضه مر علينا سابقا تمام؟
+
+646
+00:50:46,350 --> 00:50:50,990
+كويس فهذا ال required form المطلوب بنسيبهاش بهذا
+
+647
+00:50:50,990 --> 00:50:55,290
+الشكل انا عارف ان انتوا ماخدينها من ال a و من ال b
+
+648
+00:50:55,290 --> 00:50:59,530
+بس بحطهمش ارتبهم جان بعض و خلاص واسيبهم بدنا نشوف
+
+649
+00:50:59,530 --> 00:51:04,410
+الالجزء اللى هنتكلم عليه لاحقا اشي اللى موجود هنا
+
+650
+00:51:04,410 --> 00:51:08,710
+و هنا فلو
+
+651
+00:51:08,710 --> 00:51:12,650
+قلنا هي عندكوا اتنين تلاتة خمسة او تلاتة خمسة سبعة
+
+652
+00:51:12,650 --> 00:51:17,450
+تمثل كلهم مع بعض بروحش بحط بقول اتنين تلاتة خمسة و
+
+653
+00:51:17,450 --> 00:51:21,930
+بحط اضيف لهم تلاتة خمسة سبعة لأ بدنا نشيل منهم
+
+654
+00:51:21,930 --> 00:51:27,530
+الجزء التقاطع جزء التقاطع okay
+
+655
+00:51:29,680 --> 00:51:32,260
+الانترسكشن التقاطع اللي هو إيش ال inter ال
+
+656
+00:51:32,260 --> 00:51:35,800
+intersection ال intersection غير ال union ال
+
+657
+00:51:35,800 --> 00:51:37,880
+intersection اللي بنشوف إيش ال elements اللي
+
+658
+00:51:37,880 --> 00:51:47,640
+موجودة في a هنا كنا نقول or بي and بس فغيرنا
+
+659
+00:51:47,640 --> 00:51:53,380
+or ب and فصار عندنا ال a و b ال intersection
+
+660
+00:51:53,380 --> 00:51:57,540
+بتاعتهم a intersection b is set اللي هي في النهاية
+
+661
+00:51:57,540 --> 00:52:01,410
+setال set هذه تحتوي على كل ال elements that are
+
+662
+00:52:01,410 --> 00:52:06,930
+simultaneously in A and in B في نفس الوقت موجودة
+
+663
+00:52:06,930 --> 00:52:13,750
+في A و موجودة في B فبنقدر نقول أن هي ال set S لكل
+
+664
+00:52:13,750 --> 00:52:18,470
+ال elements S بشرط أن S belong to A and X belong
+
+665
+00:52:18,470 --> 00:52:25,370
+to B فال X هذه لازم تكون belong لل two sets
+
+666
+00:52:26,820 --> 00:52:31,680
+اللي قلناه هناك ان ال union كان super set لكل
+
+667
+00:52:31,680 --> 00:52:34,920
+واحدة من ال two sets هنا بنقول انه لأ ال
+
+668
+00:52:34,920 --> 00:52:40,860
+intersection هو subset من a و subset من b هو
+
+669
+00:52:40,860 --> 00:52:46,340
+subset من a و subset من b ففرق ال a b a
+
+670
+00:52:46,340 --> 00:52:52,640
+intersection b subset من a و subset من b و subset
+
+671
+00:52:52,640 --> 00:53:00,580
+من b اللي عندي الان كله كلام منطقي جداهنا ليش؟
+
+672
+00:53:00,580 --> 00:53:04,560
+مافيش اي تقاطع مافيش اي تقاطع في هذه five التانية
+
+673
+00:53:04,560 --> 00:53:10,340
+الاربعة بس الاربعة بس هنا نفس الكلام زي بالظبط
+
+674
+00:53:10,340 --> 00:53:18,680
+عارفين لما بتتكلموا عن تقاطع تقاطع شوارع الجزء
+
+675
+00:53:18,680 --> 00:53:22,000
+اللي في النص داخل الشارع هذا هذا يبقى محسوب مع اي
+
+676
+00:53:22,000 --> 00:53:27,040
+شارع مع الاتنين عشان هي اسمه تقاطععشان هي اسمه
+
+677
+00:53:27,040 --> 00:53:32,220
+تقاطع لأن هذا بنحسب مع الشارع بهذا الشكل الأفقي ال
+
+678
+00:53:32,220 --> 00:53:34,860
+horizontal و الشارع الأمض و عشان هي اسمه تقاطع
+
+679
+00:53:34,860 --> 00:53:37,700
+فاحنا هنا بنتكلم عن تقاطع فعليا اللي هو الجزء اللي
+
+680
+00:53:37,700 --> 00:53:44,460
+موجود في ال two .. two sets .. موجود في ال two طيب
+
+681
+00:53:44,460 --> 00:53:46,240
+ماشي الله يعطينا العفيا .. اعطوكوا العفيا انتوا
+
+682
+00:53:46,240 --> 00:53:49,500
+كمان للمرة الجاية ان شاء الله بنكمل باقية محاضرتنا
+
+683
+00:53:49,500 --> 00:53:50,820
+باسم الله تعالى سلام عليكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/ZEvX8gfEj2Y_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/ZEvX8gfEj2Y_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fc1a3bb730000726fb617e9ce43730023859e160
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/ZEvX8gfEj2Y_raw.srt
@@ -0,0 +1,2732 @@
+1
+00:00:20,960 --> 00:00:22,840
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,840 --> 00:00:25,020
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:25,020 --> 00:00:28,820
+أجمعين نبدأ اليوم محاضرة جديدة مع درس جديد مع
+
+4
+00:00:28,820 --> 00:00:32,480
+chapter جديد أصلا في المصادق تبعنا هنشتغل على the
+
+5
+00:00:32,480 --> 00:00:36,760
+theory of sets أول section من ال chapter two ان
+
+6
+00:00:36,760 --> 00:00:38,480
+شاء الله تعالى هنتكلم فيه عن حاجة أنتوا أصلا
+
+7
+00:00:38,480 --> 00:00:41,360
+ماخدينها سابقا برضه من الحاجات اللي بس هنعمل كهيك
+
+8
+00:00:41,360 --> 00:00:44,420
+refreshment لها اللي هي ال sets أو المجموعات
+
+9
+00:00:44,420 --> 00:00:47,090
+أخدتوا قبل هيك المجموعاتاتكلمنا في ال predicates
+
+10
+00:00:47,090 --> 00:00:49,990
+لما كنا نحكي عن ال predicates اتكلمنا عن ال
+
+11
+00:00:49,990 --> 00:00:52,910
+universe of discourse و قلنا في عندنا فضاء عينى،
+
+12
+00:00:52,910 --> 00:00:56,230
+فضاء العينى هذا إيش؟ يمثل .. يمثل مجموعة objects،
+
+13
+00:00:56,230 --> 00:00:59,330
+مجموعة objects بصفة عامة، ال objects هذه ممكن تكون
+
+14
+00:00:59,330 --> 00:01:03,510
+أرقام، ممكن تكون numbers تمام؟ بس برضه ممكن تكون
+
+15
+00:01:03,510 --> 00:01:08,870
+أي إشي تاني، أي إشي distinct object في أي شغلة
+
+16
+00:01:08,870 --> 00:01:13,330
+ممكن تكون مجموعة، نحطها ال objects هذه في مجموعة و
+
+17
+00:01:13,330 --> 00:01:18,510
+نتكلم عن ال setsفال city a structure، ال structure
+
+18
+00:01:18,510 --> 00:01:23,710
+هدا بنقدر نمثله ك unordered collection أو group،
+
+19
+00:01:23,710 --> 00:01:27,690
+فunordered مش م .. مش مرتب، مش مضرور يكون مرتب ال
+
+20
+00:01:27,690 --> 00:01:32,350
+elements تبعتنا، ممكن تكون عددهم zero أو أكتر من
+
+21
+00:01:32,350 --> 00:01:36,340
+distinct أو different objectsفممكن تكون zero و
+
+22
+00:01:36,340 --> 00:01:43,360
+zero هذه unique set بنسميها اللي هي ال fi أو ال
+
+23
+00:01:43,360 --> 00:01:47,820
+null أو ال empty set هنتكلم برضه عنها فالقصد أنه
+
+24
+00:01:47,820 --> 00:01:52,720
+ممكن تكون no element ممكن تكون no element أو أكتر
+
+25
+00:01:52,720 --> 00:01:58,500
+و أكتر هذه ممكن تشمل to infinity to infinity أو
+
+26
+00:01:58,500 --> 00:02:04,560
+infinite elements تمام؟زي انتوا برضه بتعرفوا منهم
+
+27
+00:02:04,560 --> 00:02:09,220
+ال real numbers ال natural numbers ال integer
+
+28
+00:02:09,220 --> 00:02:12,360
+numbers هدى مجموعة أرقام هى هدى عبارة عن set أصلا
+
+29
+00:02:12,360 --> 00:02:16,680
+مجموعة أرقام بس لانهائية لانهائية فإذا ال net ده
+
+30
+00:02:16,680 --> 00:02:22,140
+من صفر أو لانهائية أو محددة finite بينهم كويس كل
+
+31
+00:02:22,140 --> 00:02:25,320
+ال mathematics forms اللى ممكن نتكلم عنها بنستخدم
+
+32
+00:02:25,320 --> 00:02:29,820
+فيها ال sets ليش لإن أنا محتاج محتاجال elements
+
+33
+00:02:29,820 --> 00:02:34,440
+اللي انا بقدر اعبر عنها X لما نقول F of X قيم X
+
+34
+00:02:34,440 --> 00:02:38,620
+المحتملة اللي ممكن نستخدمها ل F of X طيب قيم ال F
+
+35
+00:02:38,620 --> 00:02:41,520
+of X اللي ممكن تنتج كلها بدنا نحطهم في النهاية
+
+36
+00:02:41,520 --> 00:02:44,920
+داخل set او مجموعة فإذا انا هيك هيك في جميع
+
+37
+00:02:44,920 --> 00:02:49,880
+الأحوال بتعامل مع مجموعات طيب انتوا كطالبات لما
+
+38
+00:02:49,880 --> 00:02:53,500
+بدي اقول بدي مجموعة الطالبات اللي مسجلين مساق
+
+39
+00:02:53,500 --> 00:02:57,780
+discrete لحظوا مجموعة فانا بتكلم هنا ال objects
+
+40
+00:02:57,780 --> 00:03:03,160
+هنا اسمهمناس ال people ناس ممكن يكون هم ال .. فانا
+
+41
+00:03:03,160 --> 00:03:07,040
+باتكلمش دائما عن أرقام نتعاملش دائما مع أرقام ممكن
+
+42
+00:03:07,040 --> 00:03:12,880
+تكون أي object او element نتعامل معه داخل ال set
+
+43
+00:03:12,880 --> 00:03:17,260
+طيب ال symbols بتاعتنا او ال notation بتاعتنا
+
+44
+00:03:17,260 --> 00:03:21,240
+بنتعامل مع ال capital letter او ال upper case ففي
+
+45
+00:03:21,240 --> 00:03:27,150
+الغرب بنقول S T او U الاكتر استعمال ان هي ال Sset
+
+46
+00:03:27,150 --> 00:03:31,430
+نسميها أسوية أكثر درجة معناها كتير ممكن نستعمل
+
+47
+00:03:31,430 --> 00:03:36,630
+معها T و ال U غالبا نستعملها كتعبير لل universe of
+
+48
+00:03:36,630 --> 00:03:40,130
+discourse فضاء العينة باعتبار أن هي أصلا set هي
+
+49
+00:03:40,130 --> 00:03:45,480
+أساسا set كويسةبنقدر نعرف ال set S على أساس أنها
+
+50
+00:03:45,480 --> 00:03:49,440
+مجموعة elements وعشان نحدد أن أنا بتكلم عن set
+
+51
+00:03:49,440 --> 00:03:55,200
+مجموعة بنحطها داخل curly braces أو الأقواص
+
+52
+00:03:55,200 --> 00:04:00,500
+المجاعدة هذه اللي هي بهذا الشكل هذه تعبر عن مين؟
+
+53
+00:04:00,500 --> 00:04:04,360
+عن ال set بنستعملش الأقواص الصغيرة ولا بنستعمل ال
+
+54
+00:04:04,360 --> 00:04:09,700
+bracketsهذه اللي بنستعملها لمين ل set عشان اعرف ان
+
+55
+00:04:09,700 --> 00:04:14,560
+احنا متكلمين عن set او مجموعة او مجموعة رياضية زى
+
+56
+00:04:14,560 --> 00:04:17,080
+ما قولنا مجموعة رياضية objects مش مضروية أرقام
+
+57
+00:04:17,080 --> 00:04:20,620
+رياضية لا تمثل .. يعني احنا مابنعبّرش عن أرقام بس
+
+58
+00:04:20,620 --> 00:04:27,720
+تمام فلو قولنا مثلا ال set A,B وC بهذا الشكل انا
+
+59
+00:04:27,720 --> 00:04:31,800
+بتعامل مع set تحتوي على three elements ايش هم ال
+
+60
+00:04:31,800 --> 00:04:36,990
+elements دولة؟لحظة letter مجموعة letters alphabet
+
+61
+00:04:36,990 --> 00:04:42,350
+a و b و c مجموعة objects تمام فانا بتعامل مع تلاتة
+
+62
+00:04:42,350 --> 00:04:47,050
+objects اللي هم a و b و c ممكن جدا ان نعبر عن ال
+
+63
+00:04:47,050 --> 00:04:50,910
+set مش بال elements بتاعتها ب expression إلها
+
+64
+00:04:50,910 --> 00:04:55,930
+بمعادلة إلها بنسميها set builder notation أو
+
+65
+00:04:55,930 --> 00:05:00,770
+بنعملها بناء بنبنيها set builder أو باني ال
+
+66
+00:05:00,770 --> 00:05:05,760
+expression هذا فممكن نقولfor any proposition P of
+
+67
+00:05:05,760 --> 00:05:09,420
+X over any universe of discourse بقدر اقول ان ال
+
+68
+00:05:09,420 --> 00:05:17,380
+set بتاعتنا set of X such that X هتحقق لنا P of X
+
+69
+00:05:17,380 --> 00:05:23,720
+فكل element X بيحقق P of X هو belong to this set
+
+70
+00:05:24,500 --> 00:05:28,800
+فهو ينتمي لهذه المجموعة كل element x بيحقق ال
+
+71
+00:05:28,800 --> 00:05:32,840
+function P of X هو ينتمي لهذه المجموعة فبنقدر
+
+72
+00:05:32,840 --> 00:05:37,920
+نعبرها بإيش ب expression رياضي كأني بقول the set
+
+73
+00:05:37,920 --> 00:05:42,140
+of all x such that P of X بتحقق لنا P of X فكل
+
+74
+00:05:42,140 --> 00:05:44,900
+element زي ما قلنا كمان مرة كل element بيحقق لنا
+
+75
+00:05:44,900 --> 00:05:49,190
+ال function P of X يعتبر عنصرفي المجموعة فانا هيك
+
+76
+00:05:49,190 --> 00:05:54,050
+يعني عبرت عن مجموعة ال elements او العناصر X داخل
+
+77
+00:05:54,050 --> 00:05:57,830
+ال set بدون ما اضطر اكتبهم واحد واحد و X هي طبعا
+
+78
+00:05:57,830 --> 00:06:03,210
+زي ما قلنا ممكن تكون عدد كبير من ال sets كويس برضه
+
+79
+00:06:03,210 --> 00:06:05,730
+ما زلنا نتكلم في شوية properties ل ال sets
+
+80
+00:06:05,730 --> 00:06:10,730
+فinherently هي زي ما قلناunordered unordered
+
+81
+00:06:10,730 --> 00:06:16,210
+inherently unordered بمعنى أنه بطريقة أصلية أو
+
+82
+00:06:16,210 --> 00:06:22,050
+بطريقة متأصلة نتعامل مع عناصر غير مرتبة نتعامل مع
+
+83
+00:06:22,050 --> 00:06:26,530
+عناصر غير مرتبة إيش يعني؟ يعني لو قلنا a,b,c هي
+
+84
+00:06:26,530 --> 00:06:32,210
+نفسها المجموعة a,c,b هي نفسها المجموعة b,c,b ترتيب
+
+85
+00:06:32,210 --> 00:06:36,610
+مش ملزمالمهم ان انا في عندى universe of discourse
+
+86
+00:06:36,610 --> 00:06:41,050
+عندى مجموعة تحتوي على مجموعة العناصر هذه كيف
+
+87
+00:06:41,050 --> 00:06:44,490
+ترتبهم العناصر مش هتفرق لو انا قلت والله بدى اسجل
+
+88
+00:06:44,490 --> 00:06:48,190
+أسماء الطالبة اللى بدرسه discrete mathematics خلال
+
+89
+00:06:48,190 --> 00:06:53,070
+الفصل هذا مش هتفرق انا رتبتهم كيف يمكن في قبوله
+
+90
+00:06:53,070 --> 00:06:56,690
+التسجيل يرتبوليهم حسب الرقم الدراسى يمكن انا اقول
+
+91
+00:06:56,690 --> 00:07:01,290
+لأ بترتبهم حسب الأبجديا حسب اسمهم أبجدي واحد تانى
+
+92
+00:07:01,290 --> 00:07:05,580
+يقول لأ بترتبهم طريقة مختلفةصحيح؟ مش هتفرق، في
+
+93
+00:07:05,580 --> 00:07:09,340
+النهاية كلهم مكافئين لبعض، كلهم بيسووا بعض ال 6
+
+94
+00:07:09,340 --> 00:07:11,920
+هذه بهذا الترتيب، هي نفس ال 6 هذه بهذا الترتيب، هي
+
+95
+00:07:11,920 --> 00:07:15,340
+نفسها، ليش؟ لأنه بيحتووا على نفس العناصر، بغض
+
+96
+00:07:15,340 --> 00:07:20,360
+النظر عن الترتيب، كويس الحاجة التانية برضه، all
+
+97
+00:07:20,360 --> 00:07:27,240
+elements are distinct أو unequal unequal لبعض،
+
+98
+00:07:27,240 --> 00:07:30,780
+unequal لبعض، بمعنى مانفعش أكرر العنصر، مانفعش
+
+99
+00:07:30,780 --> 00:07:35,110
+نكرر العنصرال listing المفروض أننا نعمل listing
+
+100
+00:07:35,110 --> 00:07:41,690
+with no أو كلهم يكونوا no difference أو يعني مش
+
+101
+00:07:41,690 --> 00:07:44,810
+غير متشابهات عفوا ف no difference بيه لأ make no
+
+102
+00:07:44,810 --> 00:07:50,470
+difference if a equal to b عشان نوضحها لو قولنا a
+
+103
+00:07:50,470 --> 00:07:57,650
+بتساوي b أساسا then ال set ABC هي نفس ال set AC
+
+104
+00:07:59,240 --> 00:08:02,800
+صحيح؟ على اعتبار ان a و b بيسووا بعض فهم عنصر واحد
+
+105
+00:08:02,800 --> 00:08:07,000
+بيكفي ان ا ابثلهم عنصر واحد منهم او امثلهم ال b ما
+
+106
+00:08:07,000 --> 00:08:11,060
+هي في النهاية a و b نفس العنصر ممكن يكونوا a a, b
+
+107
+00:08:11,060 --> 00:08:17,920
+b, c a a, b a a يعني تتكرروا فيهم زي ما بدكم بس في
+
+108
+00:08:17,920 --> 00:08:24,120
+الآخر لما اجي اتكلم اقول والله ال .. ال .. ال ..
+
+109
+00:08:24,120 --> 00:08:30,960
+الست هذه ايه كم element فيها؟ اتنينإتنين C وA أو B
+
+110
+00:08:30,960 --> 00:08:35,160
+بقولش والله لو عندي واحد اتنين تلاتة أربعة خمسة
+
+111
+00:08:35,160 --> 00:08:37,720
+ستة سبعة تمانية عندي تسعة elements لأ بنجلش تسعة
+
+112
+00:08:37,720 --> 00:08:40,580
+elements لأنه في تكرار هنا فاحنا هنا لازم نشتغل
+
+113
+00:08:40,580 --> 00:08:44,080
+على عدم التكرار بمعنى أنه يكون عندكو distinct
+
+114
+00:08:44,080 --> 00:08:52,160
+elements أو عناصر مميزة متباينة متباينة okay
+
+115
+00:08:53,250 --> 00:08:56,190
+الست ايقاليتي هد بتخلينا ندور على الست ايقاليتي
+
+116
+00:08:56,190 --> 00:08:59,530
+امتى طب بيقولنا ان الست equal لبعض امتى بنقول ان
+
+117
+00:08:59,530 --> 00:09:02,430
+هم equal لبعض واضح جدا اذا كان كلهم بيحتووا على
+
+118
+00:09:02,430 --> 00:09:06,190
+exactly the same elements كلهم بيحتووا على نفس
+
+119
+00:09:06,190 --> 00:09:10,630
+العناصر تمام كلهم اللي لهم نفس العناصر الست الأولى
+
+120
+00:09:10,630 --> 00:09:14,230
+تحتوى على نفس العناصر exactly بالظبط اللي موجودين
+
+121
+00:09:14,230 --> 00:09:16,310
+في الست التانية بقدروا ان الست الأولى والست
+
+122
+00:09:16,310 --> 00:09:20,110
+التانية equal لبعض او equivalent لبعض بسوا بعض
+
+123
+00:09:21,080 --> 00:09:24,160
+كويسة for example لو قلنا مثلا الست عندنا واحد
+
+124
+00:09:24,160 --> 00:09:28,720
+اتنين تلاتة اربعة هى ست تحتوي على اربع عناصر
+
+125
+00:09:28,720 --> 00:09:32,240
+العنصر الاول ال integer واحد العنصر التاني ال
+
+126
+00:09:32,240 --> 00:09:35,020
+integer رقم اتنين العنصر التالت ال integer تلاتة و
+
+127
+00:09:35,020 --> 00:09:38,800
+العنصر الرابع integer يمثل اربعة كويسة ممكن اعبر
+
+128
+00:09:38,800 --> 00:09:42,260
+عنها بطريقة تانية و equivalent لها و انت عبّر احنا
+
+129
+00:09:42,260 --> 00:09:46,890
+نقول والله هي كل هي عبارة عن ستكل العناصر فيها all
+
+130
+00:09:46,890 --> 00:09:51,930
+x such that x is an integer where x أكبر من ..
+
+131
+00:09:51,930 --> 00:09:57,710
+greater than zero and x less than five فعلا هي كل
+
+132
+00:09:57,710 --> 00:10:04,610
+ال integers اللي أقل من خمسة وأكبر من صفر لإيجادهم
+
+133
+00:10:04,610 --> 00:10:09,250
+يتمثل نفس المجموعة هذه نفسها أو حتى اللي يقول لأ
+
+134
+00:10:09,250 --> 00:10:12,110
+أنا بدي أمثلها بطريقة مختلفة بدي أعمل set builder
+
+135
+00:10:12,110 --> 00:10:17,490
+مختلفةهيقول إن هي عبارة عن set of x such that x is
+
+136
+00:10:17,490 --> 00:10:24,090
+a positive integer whose square is أكبر than 0 and
+
+137
+00:10:24,090 --> 00:10:31,700
+less than 25 نفس الفكرة هي كل العناصر الموجبةاللي
+
+138
+00:10:31,700 --> 00:10:35,200
+تربيعها .. تربيعها .. هنا متكلم عن التربيع صار هو
+
+139
+00:10:35,200 --> 00:10:38,240
+ال condition اللي بدنا نحكم فيه تربيعها أقل من صفر
+
+140
+00:10:38,240 --> 00:10:44,100
+.. أكبر من صفر وأقل من خمسة وعشرين وextractly أكبر
+
+141
+00:10:44,100 --> 00:10:47,640
+من صفر .. الزمن أكبر .. بنفعش يساوي صفر والزمن
+
+142
+00:10:47,640 --> 00:10:53,550
+extractly أقل من خمسة وعشرينكويس فالأرقام هذه اللي
+
+143
+00:10:53,550 --> 00:10:56,490
+فعلا تربيحها بين الصفر والخمسة عشرين هي الواحد
+
+144
+00:10:56,490 --> 00:11:00,250
+اتنين تلاتة أربعة بس في غيرهم مش غيرهم واحنا حددنا
+
+145
+00:11:00,250 --> 00:11:02,890
+من الأول positive فال negative تبعهم مستحيل يكون
+
+146
+00:11:02,890 --> 00:11:06,870
+موجود لأنه في التعريف positive صحيح في التعريف
+
+147
+00:11:06,870 --> 00:11:09,990
+positive فأي شكل من التلت أشكال هدول يساوي الآخر
+
+148
+00:11:09,990 --> 00:11:14,910
+كل شكل من التلت أشكال هدول للمجموع بيساوي الآخر
+
+149
+00:11:14,910 --> 00:11:22,190
+infinite sets أو المجموعات اللانهائيةالحقيقة
+
+150
+00:11:22,190 --> 00:11:26,350
+بنتعامل معها، بنتعامل معها باستمرار، اللي هي no
+
+151
+00:11:26,350 --> 00:11:29,650
+finite أو not finite بمعنى أن هي لا نهاية، مالهاش
+
+152
+00:11:29,650 --> 00:11:36,490
+نهاية، without end، بدون نهاية لها أو unending،
+
+153
+00:11:36,490 --> 00:11:40,270
+غير منتهية، غير منتهية، الحاجات المشهورة جدا اللي
+
+154
+00:11:40,270 --> 00:11:43,290
+هي زي ال natural numberاللي هي من صفر to infinity
+
+155
+00:11:43,290 --> 00:11:46,770
+natural numbers الأرقام الطبيعية اللي احنا عادة
+
+156
+00:11:46,770 --> 00:11:50,550
+نستعملها positive طبعا بتكون الجزء ال negative لو
+
+157
+00:11:50,550 --> 00:11:53,950
+أضفناه بيصير أنها ال integer numbers بيصير أننا
+
+158
+00:11:53,950 --> 00:11:56,930
+نتكلم عن ال integer numbers لو زودنا reflections
+
+159
+00:11:56,930 --> 00:12:01,830
+بيصير نتكلم عن ال real numbers طيب هنلاحظ رغم أن
+
+160
+00:12:01,830 --> 00:12:08,820
+هم كلهم infinite sets بس ال size بتاعتهم مختلفةال
+
+161
+00:12:08,820 --> 00:12:11,820
+size مختلفة هذه غير هذه غير هذه مين أكبر واحدة
+
+162
+00:12:11,820 --> 00:12:16,900
+فيهم size كsize أكبر واحدة الريال number أقلهم ال
+
+163
+00:12:16,900 --> 00:12:21,720
+natural number فرغم ذلك رغم أن هم كلهم infinite
+
+164
+00:12:21,720 --> 00:12:25,300
+sets لكن كلهم بيجوا من different sizes كل واحدة
+
+165
+00:12:25,300 --> 00:12:31,780
+إلها size مختلفة عن التانية كويسة ناخد طريقة
+
+166
+00:12:31,780 --> 00:12:35,480
+تمثيلهم بالرسم عن طريق Venn diagram ال Venn
+
+167
+00:12:35,480 --> 00:12:41,210
+diagram طريقة بنستخدمهالتمثيل ال set بنمثل ال set
+
+168
+00:12:41,210 --> 00:12:44,330
+فيها ليش عساس أعرف التقاطعات أعرف ال elements اللي
+
+169
+00:12:44,330 --> 00:12:48,550
+ممكن تكون في أكتر من set التحادات كيف ممكن مجموعة
+
+170
+00:12:48,550 --> 00:12:53,910
+ال sets مع بعض نرسمهم كيف التداخل بينهم هل هم
+
+171
+00:12:53,910 --> 00:12:56,770
+مستقلين عن بعض و لا مش مستقلين عن بعض طبعا هذه
+
+172
+00:12:56,770 --> 00:13:02,150
+مناسبة لما نتكلم عن finiteSets، finite sets، تمام؟
+
+173
+00:13:02,150 --> 00:13:04,770
+أنا بقدر أعبر عنها فلو قلنا عندنا مجموعة الأرقام
+
+174
+00:13:04,770 --> 00:13:08,950
+بهذا الشكل من minus one to nine وموزعة بهذا الشكل
+
+175
+00:13:08,950 --> 00:13:13,270
+وكل مجموعة عاملين لهم set لحالهم كل مجموعة عاملين
+
+176
+00:13:13,270 --> 00:13:17,550
+لهم set لحالهم لو أخدنا المجموعة كلها على بعض ك
+
+177
+00:13:17,550 --> 00:13:21,450
+set as a set بنقدر نسميها إيش ال set هذه ال real
+
+178
+00:13:21,450 --> 00:13:27,380
+number فيها fractionsانتجار انتجار كويس انتجار
+
+179
+00:13:27,380 --> 00:13:29,140
+معناته حفظها من ان هي من minus infinity to
+
+180
+00:13:29,140 --> 00:13:35,840
+infinity معناته بدنا نحدد انتجار من تمام تمام
+
+181
+00:13:35,840 --> 00:13:41,990
+معناته بدنا نحددعشان أكون عرفت ال set بطريقة
+
+182
+00:13:41,990 --> 00:13:44,750
+واضحة، لازم التعريف يكون واضح، بنفعش أقول هي
+
+183
+00:13:44,750 --> 00:13:48,530
+integer وسكوت، integer اللي هيفهمها لو سماعتي
+
+184
+00:13:48,530 --> 00:13:51,710
+هيكمش شايف، لو ع ال radio، قولتولي مجموعة
+
+185
+00:13:51,710 --> 00:13:54,130
+integers، والله المجموعة بتاعتنا integers، خلاص
+
+186
+00:13:54,130 --> 00:13:57,290
+هفهم إن هي من minus infinity to infinity، بس مش
+
+187
+00:13:57,290 --> 00:14:02,460
+هذا الصحيحالفعلية هي مجموعة integers from minus
+
+188
+00:14:02,460 --> 00:14:10,680
+one to nine نسيب المجموعة الكبيرة ناخد المجموعة
+
+189
+00:14:10,680 --> 00:14:15,460
+الأصغر مجموعة
+
+190
+00:14:15,460 --> 00:14:22,530
+integers أقل من عشرة أو من واحد لعشرةأو natural
+
+191
+00:14:22,530 --> 00:14:26,610
+number أقل من عشرة صحيح؟ لأ بس ال natural number
+
+192
+00:14:26,610 --> 00:14:31,270
+برضه فيها الصفر يعني نفس الجثة لازم نحدد من واحد
+
+193
+00:14:31,270 --> 00:14:35,010
+لتسعة أو أكبر من صفر وأقل من عشرة الطريقة اللي
+
+194
+00:14:35,010 --> 00:14:38,650
+بتكونيها بتقدروا تعرفوها فهي positive integers أقل
+
+195
+00:14:38,650 --> 00:14:42,610
+من عشرة برضه هاي التعريف غيرنا هعرفها على أساس ان
+
+196
+00:14:42,610 --> 00:14:46,910
+هي integers أقل من عشرة بس حددها positive ف ال
+
+197
+00:14:46,910 --> 00:14:49,690
+zero و ال negative مش موجودةبرضه هى طريقة غير اللى
+
+198
+00:14:49,690 --> 00:14:52,490
+احنا اتكلمنا فيها بتقدروا تمثلوها بأى طريقة كانت
+
+199
+00:14:52,490 --> 00:14:55,410
+يعني بتقدروا تتكلموا بتمثلوها ب natural ال natural
+
+200
+00:14:55,410 --> 00:15:01,110
+هدى من واحد to nine او integer اكبر من صفر و اقل
+
+201
+00:15:01,110 --> 00:15:04,390
+من عشرة بتقدروا تعملوه بالطريقة اللى بتقوليها طيب
+
+202
+00:15:04,390 --> 00:15:12,270
+ناخد الست اللى هنا ايش هدى؟هذه ال even اللي أكبر
+
+203
+00:15:12,270 --> 00:15:16,490
+من صفر وأقل من عشرة مثلا فهذه ال integers اللي هم
+
+204
+00:15:16,490 --> 00:15:19,710
+من اتنين هاي كلمة حدث من اتنين لتسعة او من صفر
+
+205
+00:15:19,710 --> 00:15:23,510
+أكبر من صفر وأقل من عشرة فبتقدروا تمثلوها بالطريقة
+
+206
+00:15:23,510 --> 00:15:27,350
+اللي بدكم إياها طيب ناخد ال set ال .. هذه ال odd
+
+207
+00:15:27,350 --> 00:15:32,890
+برضه اللي إيه اش from one to nine ممكن from one to
+
+208
+00:15:32,890 --> 00:15:36,210
+nine او أكبر من صفر وأقل من عشرة نفس الكلام
+
+209
+00:15:36,210 --> 00:15:39,510
+بتقدروا تعملوه زي ما بدكم from nine to onefrom one
+
+210
+00:15:39,510 --> 00:15:43,630
+to nine طيب في ست ما زالت موجودة عندنا هنا ال
+
+211
+00:15:43,630 --> 00:15:47,910
+primes تمام مجموعة ال primes اللي اقل من عشرة ف
+
+212
+00:15:47,910 --> 00:15:52,170
+primes اقل من عشرة تمام فهي طريقة التمثيل و بنمثل
+
+213
+00:15:52,170 --> 00:15:54,750
+لازم نحط الدوائر هذه او المكعبات او المربعات بحيث
+
+214
+00:15:54,750 --> 00:15:59,510
+ان انا احدد و انتقطعات المجموعات نحدد و انتقطعات
+
+215
+00:15:59,510 --> 00:16:02,570
+المجموعات تلاحظوا مثلا الرقم اتنين الرقم اتنين
+
+216
+00:16:02,570 --> 00:16:07,830
+اشترك في اربع مجميع في اربع مجميع مجموعة اتن تان
+
+217
+00:16:07,830 --> 00:16:12,610
+تلاتة اربعتمام؟ مجموعة الدوائر اللي مرسومة و ترتيب
+
+218
+00:16:12,610 --> 00:16:16,190
+الأرقام ترتيب ال .. ال numbers هذه أعطتني الإحاء
+
+219
+00:16:16,190 --> 00:16:20,150
+أنه اه والله فعلا هذا موجود في ال set الأولى في ال
+
+220
+00:16:20,150 --> 00:16:23,010
+set التانية و في ال set التالتة هنا في الرابعة ل
+
+221
+00:16:23,010 --> 00:16:26,490
+primes بعرف أن okay الرقم هذا بيحقق الأربع شروط
+
+222
+00:16:26,490 --> 00:16:33,710
+تمام؟ فهذه طريقة لتمثيل ال .. ال set okay
+
+223
+00:16:34,950 --> 00:16:39,350
+الـ basic set relations أو ال number .. ال member
+
+224
+00:16:39,350 --> 00:16:44,410
+of .. member of set بمعنى أنه عنصر داخل ال set إيش
+
+225
+00:16:44,410 --> 00:16:47,770
+علاقته بال set؟ ف ال set relations مع ال elements
+
+226
+00:16:47,770 --> 00:16:50,750
+بتاعتها مع ال number بتاعتها كيف نبتمثلها؟ بنمثلها
+
+227
+00:16:50,750 --> 00:16:56,650
+بالعلامة هذه belong to فبقول x belong to set S
+
+228
+00:16:56,650 --> 00:17:02,680
+فإذا بقول إنه كأنها x is inست اس .. ست اس .. كويس
+
+229
+00:17:02,680 --> 00:17:06,080
+فبرضه في النهاية أنا بتكلم عن X هنا .. X هنا
+
+230
+00:17:06,080 --> 00:17:11,460
+object ال X عبارة عن object object X is an element
+
+231
+00:17:11,460 --> 00:17:14,980
+و هنا منها إجت العلمة من علامة كلمة element ال E
+
+232
+00:17:14,980 --> 00:17:20,820
+فأخدنا ال notation هذه علشان هي belong to set S or
+
+233
+00:17:20,820 --> 00:17:26,060
+member of set S تماممثال لو قلنا three belong to
+
+234
+00:17:26,060 --> 00:17:29,700
+natural number okay صحيح التلاتة هي واحدة من
+
+235
+00:17:29,700 --> 00:17:34,460
+الأرقام الطبيعية كلام صحيح او اقول ان a letter
+
+236
+00:17:34,460 --> 00:17:43,220
+letter a belong to X such that X is a letter of
+
+237
+00:17:43,220 --> 00:17:48,560
+alphabet فعلا واحدة من الحروفالـ A هو حرف من
+
+238
+00:17:48,560 --> 00:17:52,040
+الحروف فبرضه الكلام صحيح عشان امثل ان هو والله
+
+239
+00:17:52,040 --> 00:17:55,120
+فعلا ينتمي لمجموعة حروف بقول ان هو belong to ينتمي
+
+240
+00:17:55,120 --> 00:18:01,500
+ل .. ينتمي لل set اللي اتعرفت okay ال set quality
+
+241
+00:18:01,500 --> 00:18:05,080
+اللي اتكلمنا عنها بقدر امثلها برضه ب .. بال .. بال
+
+242
+00:18:05,080 --> 00:18:11,440
+notation belong to فلو قلنا for all set S set TS
+
+243
+00:18:11,440 --> 00:18:16,900
+equal to T if and only if for all X X belong to S
+
+244
+00:18:16,900 --> 00:18:24,520
+و X belong to T لكل القيم أو ال objects X لكل
+
+245
+00:18:24,520 --> 00:18:32,800
+القيم X ال X تنتمي ل set S و ال X تنتمي ل set T
+
+246
+00:18:32,800 --> 00:18:37,130
+هنا طبعا كتب الكياهة إذا كان X belong to Sif and
+
+247
+00:18:37,130 --> 00:18:40,250
+only if x belongs to T معناته صار محكومة أنه لازم
+
+248
+00:18:40,250 --> 00:18:45,010
+تنتمي لها S إذا كانت فعلا منتمية لمن ل T والزمن
+
+249
+00:18:45,010 --> 00:18:48,430
+لازم تكون منتمية ل T مش منتمية ل T معناته غير
+
+250
+00:18:48,430 --> 00:18:52,410
+منتمية لمن ل S في الحالة دي بنقول أنه منطقي صار
+
+251
+00:18:52,410 --> 00:18:56,930
+إيش كل ال elements اللي موجودة في Tموجودة في S
+
+252
+00:18:56,930 --> 00:19:00,550
+معناته the same elements موجودة في ال two sets
+
+253
+00:19:00,550 --> 00:19:04,490
+معناته في equality الإتنين بيسوا بيسوا بعض فإذا
+
+254
+00:19:04,490 --> 00:19:08,410
+two sets are equal if and only if they have all
+
+255
+00:19:08,410 --> 00:19:15,690
+the same members كويسة لو قلنا not belong to set X
+
+256
+00:19:15,690 --> 00:19:21,550
+not belong to set هدده كافي إيش X belong to set مع
+
+257
+00:19:21,550 --> 00:19:27,110
+ال negation not belong not belong toأو s is not in
+
+258
+00:19:27,110 --> 00:19:35,910
+6s ال empty set أو ال null اللي هو لا يوجد فارغ
+
+259
+00:19:35,910 --> 00:19:43,610
+فاضي أو ال empty set المجموعة الفارغة المجموعة
+
+260
+00:19:43,610 --> 00:19:49,530
+الفاضية كويس هذه بنسميها في فهذه is the unique set
+
+261
+00:19:49,530 --> 00:19:55,010
+that contains no elements whatsoeverلا تحتوي على
+
+262
+00:19:55,010 --> 00:20:00,390
+عناصر بالمطلق مافيش فيها أي عنصر فهي set بدون
+
+263
+00:20:00,390 --> 00:20:05,830
+عناصر مجموعة بدون عناصر مجموعة بدون عناصر في و
+
+264
+00:20:05,830 --> 00:20:11,010
+بنعمل عالم المجموعة كمان فهي كأنها set مافيش فيها
+
+265
+00:20:11,010 --> 00:20:18,110
+عناصر empty او تحتوي على عنصر false فمافيش فيها
+
+266
+00:20:18,110 --> 00:20:23,050
+true مافيش اي عنصر بقدر انه belong to setو بقى و
+
+267
+00:20:23,050 --> 00:20:27,710
+بمثله is it true دائما كل العناصر for all x is
+
+268
+00:20:27,710 --> 00:20:33,570
+false بغض النظر عن ال domain لل discourse او ال
+
+269
+00:20:33,570 --> 00:20:37,130
+universe of discourse بنقدر نقول ال .. ال axiom
+
+270
+00:20:37,130 --> 00:20:43,250
+التالية negation there exist x معناته there is no
+
+271
+00:20:43,250 --> 00:20:49,530
+x such that x belong to phi معناته لا يوجد عنصر x
+
+272
+00:20:49,530 --> 00:20:56,390
+ينتمي لهالـ set في أو ال empty set ليش؟ لأن أصلا
+
+273
+00:20:56,390 --> 00:21:00,210
+لا يوجد فيها عناصر ففعلا لا يوجد أي عنصر ينتمي
+
+274
+00:21:00,210 --> 00:21:08,450
+لset في okay subsetأتوقع كل الموضوع عندكم أخدينه
+
+275
+00:21:08,450 --> 00:21:12,010
+بس كنتوا بتتكلموا عن مجموعات بتتكلموا كنتوا
+
+276
+00:21:12,010 --> 00:21:15,970
+مجموعات فاحنا نفس الكلام بنرجع نهيده هنا ال .. ال
+
+277
+00:21:15,970 --> 00:21:18,990
+subset و ال superset برضه أخدتوها subset و
+
+278
+00:21:18,990 --> 00:21:23,770
+superset relations أخدتوها فكنا نقول ال S subset T
+
+279
+00:21:23,770 --> 00:21:28,690
+معناه ذلك أن ال S is a subset of T معناها عفوا
+
+280
+00:21:30,690 --> 00:21:35,670
+بالظبط هي subset of هي جزء من T تماما وهذه معناه
+
+281
+00:21:35,670 --> 00:21:41,450
+ان every element of S is also an element of T بس
+
+282
+00:21:41,450 --> 00:21:45,850
+العكس غير صحيح تمام معناه ذلك ان اذا ال element
+
+283
+00:21:45,850 --> 00:21:48,570
+بدأت من ال element في T مش بالضروري يكون موجود في
+
+284
+00:21:48,570 --> 00:21:55,810
+S ولكن كل element كل for all X X belong to S
+
+285
+00:21:57,070 --> 00:22:02,010
+بالضروري أن يكون belonging to T فإذا هنا لحظة
+
+286
+00:22:02,010 --> 00:22:06,370
+عملناها implication عملناها as implication for all
+
+287
+00:22:06,370 --> 00:22:13,730
+X X belonging to S بيضمن إذا كانت فعلا X belonging
+
+288
+00:22:13,730 --> 00:22:20,450
+to S then X belonging to T then كويسهذه
+
+289
+00:22:20,450 --> 00:22:23,130
+implication على أساس أنه إذا كان غير موجود هنا
+
+290
+00:22:23,130 --> 00:22:25,830
+الأصل أنه يكون غير موجود هنا فال implication أنسب
+
+291
+00:22:25,830 --> 00:22:29,250
+كانت هنا في التعريف .. أنسب في التعريف تمام
+
+292
+00:22:29,250 --> 00:22:33,430
+فالحالة الوحيدة ال false هنا إيش هي؟ ال
+
+293
+00:22:33,430 --> 00:22:38,270
+implication إيش الحالة الوحيدة false فيها؟ T to
+
+294
+00:22:38,270 --> 00:22:42,050
+false و لا .. و لا .. T to false مش كان ال T تبقى
+
+295
+00:22:42,050 --> 00:22:48,190
+.. معناته ..إذا كانت هنا موجودة و غير موجودة هنا
+
+296
+00:22:48,190 --> 00:22:52,090
+لأ في مشكلة معناته في مشكلة معناته هذا not subset
+
+297
+00:22:52,090 --> 00:22:59,930
+of T كويسة كمان تعريف ال Phi subset من أي set أخرى
+
+298
+00:22:59,930 --> 00:23:03,710
+ال Phi هي مجموعة جزئية من أي مجموعة في العالم في
+
+299
+00:23:03,710 --> 00:23:07,130
+الدنيا في كل الرياضيات هي subset من أي مجموعة طيب
+
+300
+00:23:07,130 --> 00:23:11,690
+أي مجموعة هي subset من نفسها لأن ال subset هي تمثل
+
+301
+00:23:11,690 --> 00:23:15,020
+.. لو بدنا نتكلم عنعال numbers هي كأنها أقل من أو
+
+302
+00:23:15,020 --> 00:23:21,120
+تساوي فأي رقم هو يساوي نفسه فكل رقم بقدر أحط فيه
+
+303
+00:23:21,120 --> 00:23:27,140
+أحطله ال expression هذا كويس فهي subset لنفسها طيب
+
+304
+00:23:27,140 --> 00:23:32,560
+العكس لل subset ال super set هي عكس الاتجاه لما
+
+305
+00:23:32,560 --> 00:23:38,600
+أقول S superset of T كأني بقول T subset ofof S
+
+306
+00:23:38,600 --> 00:23:45,180
+معناته ان S is a superset of T طيب امتى بقدر اقول
+
+307
+00:23:45,180 --> 00:23:48,840
+ان ال S equal to T من خلال معرفتنا هنا بال subset
+
+308
+00:23:48,840 --> 00:23:52,360
+و ال superset اذا كانت ال S subset of T and
+
+309
+00:23:52,360 --> 00:23:58,760
+superset of T بالظبط ليش لان مستحيل رقمين اكبر منه
+
+310
+00:23:58,760 --> 00:24:02,020
+اصغر من بعضبس احنا بدنا ناخد بالة ان في علامة
+
+311
+00:24:02,020 --> 00:24:05,600
+يساوي فال condition الوحيد اللي ممكن فعلا نخليهم
+
+312
+00:24:05,600 --> 00:24:09,300
+اكبر من او يساوي و اصغر من او يساوي هي المساوية هو
+
+313
+00:24:09,300 --> 00:24:14,120
+اليساوي اللي موجودة هنا هي اليساوي فاحنا هنا بيقول
+
+314
+00:24:14,120 --> 00:24:21,040
+ان هذه جزئية من هذه و T جزئية من S تمام فالحالة
+
+315
+00:24:21,040 --> 00:24:23,680
+الوحيدة هنا اللي هو ال condition هذا ان المجموعة
+
+316
+00:24:23,680 --> 00:24:26,560
+ممكن تكون subset من نفسها مساوية لنفسها
+
+317
+00:24:30,650 --> 00:24:34,690
+ما هي نفس المعنى هو نفس المعنى نفس الأشياء هي
+
+318
+00:24:34,690 --> 00:24:39,730
+subset من نفسها لحظة وهذه super set من هذه ما هي
+
+319
+00:24:39,730 --> 00:24:43,010
+نفس الاتجاه بحدين يعني من الاتجاهين اللي اتكلمت
+
+320
+00:24:43,010 --> 00:24:51,410
+تمام okay قعدت كقولناها ال S not subset of T
+
+321
+00:24:51,410 --> 00:24:57,820
+معناته negation S subset of Tnegation as subset of
+
+322
+00:24:57,820 --> 00:25:03,540
+T أو there exist X such that X belong to S and X
+
+323
+00:25:03,540 --> 00:25:07,560
+not belong to T لأن هو العصل إنه إذا كان belong to
+
+324
+00:25:07,560 --> 00:25:13,600
+S يكون belong to T بس لأ هو belong to S و not
+
+325
+00:25:13,600 --> 00:25:21,100
+belong to T الزمنالزامن and هو موجود في S و غير و
+
+326
+00:25:21,100 --> 00:25:27,100
+and و غير موجود في T هذه الحالة خلاص بتنفي لنا ال
+
+327
+00:25:27,100 --> 00:25:32,040
+subset اللي أخدناها بتنفي ال subset الحالة هذه
+
+328
+00:25:32,040 --> 00:25:39,510
+تمامprepare أو extract subsets and supersets هدى
+
+329
+00:25:39,510 --> 00:25:46,010
+بمعنى مجموعة جزئية مقيدة مافيش فيها يساوي او يساوي
+
+330
+00:25:46,010 --> 00:25:49,770
+مافيش فيها او يساوي فهنا ماقدرش اقول ان المجموعة
+
+331
+00:25:49,770 --> 00:25:56,250
+prepare subset من نفسها، مانفعش اما الـ Phi okay
+
+332
+00:25:56,250 --> 00:26:01,450
+ال Phi prepare subset من اي مجموعة تانية غير ال
+
+333
+00:26:01,450 --> 00:26:05,380
+Phi، بمشي الكلامتمام؟ بس مع نفسها مامشيش هنا ليش؟
+
+334
+00:26:05,380 --> 00:26:10,320
+لإن هنا إلزامة أقل من .. هتكون جزئية منها و لا
+
+335
+00:26:10,320 --> 00:26:16,240
+تساوي جزئية منها و لا تساوي طيب فهذه معناها أن S
+
+336
+00:26:16,240 --> 00:26:22,140
+.. لاحظوا هنا subset of T but T not subset of S
+
+337
+00:26:22,140 --> 00:26:27,600
+إيش .. إيش اللي تم استثنائه هنا؟ اللي تم استثنائه
+
+338
+00:26:27,600 --> 00:26:33,630
+إن إحنا استثننا اليساويتم استثناء اليساوي فضلت
+
+339
+00:26:33,630 --> 00:26:38,350
+subset structurally أو prepare subset بدون علامة
+
+340
+00:26:38,350 --> 00:26:42,630
+المساواة فضلت بهذا الشكل زي لما كنتوا بتتكلموا لو
+
+341
+00:26:42,630 --> 00:26:46,230
+نسقط الكلام على الأرقام كنا بنقول أقل من أو يساوي
+
+342
+00:26:46,230 --> 00:26:53,350
+وفي أقل من بس فهذه غير هذه فهنا بنتكلم عن subset
+
+343
+00:26:53,350 --> 00:26:59,350
+وهنا بنتكلم عن prepare subset هذه إشي وهذه .. هذه
+
+344
+00:26:59,350 --> 00:27:05,730
+إشي طيبنفس الكلام هو نقدر نعيده ل مين ل prepare
+
+345
+00:27:05,730 --> 00:27:11,230
+superset prepare superset prepare superset ليش لأن
+
+346
+00:27:11,230 --> 00:27:15,870
+هم عكس بعض اللي احنا عرفنا في prepare subset هو
+
+347
+00:27:15,870 --> 00:27:18,790
+نفسه بقدر اعرفه prepare superset على اعتبار ان هنا
+
+348
+00:27:18,790 --> 00:27:26,790
+T prepare subset of Sprepare super set of T تنتهي
+
+349
+00:27:26,790 --> 00:27:30,290
+منعكس برا طيب example ممكن نكتب هنا مثلا هنمثلها
+
+350
+00:27:30,290 --> 00:27:37,350
+بال Venn diagram و هنا هنمثلها ك example بال sets
+
+351
+00:27:37,350 --> 00:27:41,420
+اللي عندنا فلو قلنا في عندنا set one and twoتحتوي
+
+352
+00:27:41,420 --> 00:27:43,840
+على الـ two elements الـ two elements هدولة واحد و
+
+353
+00:27:43,840 --> 00:27:48,460
+اتنين هذه is prepare subset of واحد اتنين تلاتة
+
+354
+00:27:48,460 --> 00:27:54,920
+prepare subset of set تحتوي على واحد اتنين و تلاتة
+
+355
+00:27:54,920 --> 00:28:02,360
+ليش لأن فعلا واحد و اتنين موجودين و T التانية مش
+
+356
+00:28:02,360 --> 00:28:06,280
+subset من الأولى مش subset من الأولى ليش مش subset
+
+357
+00:28:06,280 --> 00:28:08,760
+من الأولى لأن في element موجود فيها غير موجود في
+
+358
+00:28:08,760 --> 00:28:13,580
+الأولى تمامبال Venn diagram ممكن تمثلوها بهذا
+
+359
+00:28:13,580 --> 00:28:18,360
+الشكل ال S والT لا يمكن يكونوا بيساوي بعض في
+
+360
+00:28:18,360 --> 00:28:25,700
+element هيه موجود في T غير موجود في S توقع واضحة
+
+361
+00:28:25,700 --> 00:28:29,120
+ال relation احنا مجرد بس بنقول كأنه بنتكلم عن
+
+362
+00:28:29,120 --> 00:28:33,540
+الأكبر من أو يساوي وأكبر من أصغر من أو يساوي وأصغر
+
+363
+00:28:33,540 --> 00:28:39,380
+من بس بنسقطها على مين على ال six على المجموعات طيب
+
+364
+00:28:40,690 --> 00:28:43,710
+set are objects too احنا في الأخر الفيديو اللي
+
+365
+00:28:43,710 --> 00:28:48,630
+بنتكلم انه هي مجموعة objects كل set تحتوي على
+
+366
+00:28:48,630 --> 00:28:51,450
+مجموعة elements ال elements هذه objects طيب ال
+
+367
+00:28:51,450 --> 00:28:54,130
+object هذا اللي هو element ممكن هو نفسه يكون
+
+368
+00:28:54,130 --> 00:29:00,290
+مجموعة ممكن هو نفسه يكون عبارة عن إيش set هو نفسه
+
+369
+00:29:00,290 --> 00:29:04,030
+عبارة عن set مش بالضرورة يكون element ك element زي
+
+370
+00:29:04,030 --> 00:29:07,510
+لما تكون بتتكلم عن hard disk و بتبدو تعمله تجسيم
+
+371
+00:29:08,470 --> 00:29:11,270
+المجموع بالنسبة لنا كنت اعمله folder لانه هيحتوي
+
+372
+00:29:11,270 --> 00:29:15,670
+على مجموعة files صحيح؟ فهتعمله folder طب انا مش
+
+373
+00:29:15,670 --> 00:29:19,270
+ملزم اني على طول احط files ممكن داخله احط كمان
+
+374
+00:29:19,270 --> 00:29:23,910
+folders فانا بحط مجموعات بحط كمان مجموعات جوا بجسم
+
+375
+00:29:23,910 --> 00:29:27,550
+ال folder جوا لخمس لخمسة folders مثلا وداخل ال
+
+376
+00:29:27,550 --> 00:29:30,990
+folders ممكن احط كمان تجسمة تانية لعند ما اصل لمين
+
+377
+00:29:30,990 --> 00:29:33,710
+لل file اللي هو ال element اللي انا بتعامل معاه بس
+
+378
+00:29:33,710 --> 00:29:37,650
+في النهاية ال elements بالنسبة لأول folder لل C
+
+379
+00:29:37,650 --> 00:29:45,270
+مثلاكنتوا حاطين مجموعة folders فبالضبط
+
+380
+00:29:45,270 --> 00:29:51,710
+العنصر عندنا ال element هنا عبارة عن set عبارة عن
+
+381
+00:29:51,710 --> 00:29:59,710
+set هو في داخله يحتوي يحتوي على elements او set
+
+382
+00:29:59,710 --> 00:30:03,930
+برضه او مجموعة sets او مجموعة sets تمام فانحن
+
+383
+00:30:03,930 --> 00:30:07,570
+نتكلم عن ال tree هنا كأنها صارت مشابه لفكرة ال
+
+384
+00:30:07,570 --> 00:30:15,440
+treeتمام هذا معناه مدام هي نفسها okay themselves
+
+385
+00:30:15,440 --> 00:30:19,040
+be sets ممكن هي نفسها تكون sets ال elements هذه
+
+386
+00:30:19,040 --> 00:30:22,640
+اللي داخل ال set نفسها تكون sets كأني بقول let s
+
+387
+00:30:22,640 --> 00:30:31,100
+equal to x such that x not belong but subset
+
+388
+00:30:31,100 --> 00:30:34,920
+subset أنا عارف أن ال subset هنا ماتتعاملش مع
+
+389
+00:30:34,920 --> 00:30:40,030
+elements belong أنا بتعامل مع elementsubset بتعامل
+
+390
+00:30:40,030 --> 00:30:44,770
+مع set ماهي اسمها sub set او super set انا بتعامل
+
+391
+00:30:44,770 --> 00:30:48,690
+مع set هنا تمام فإذا ال X هنا واضح انه انا بتعامل
+
+392
+00:30:48,690 --> 00:30:54,050
+مع مين set عبارة عن subset من 123 من ال set 123
+
+393
+00:30:54,050 --> 00:30:59,850
+فإذا المجموعة اللي بنتكلم عنها S هي عبارة عن
+
+394
+00:30:59,850 --> 00:31:04,430
+مجموعة objects ال objects هذه عرفناها ان هي sets
+
+395
+00:31:05,430 --> 00:31:08,830
+ماذا يميز ال sets هذه اللي هي تمثل كأنها element
+
+396
+00:31:08,830 --> 00:31:13,130
+بالنسبة ل S بس element له خصوصية ان هو أصلا set
+
+397
+00:31:13,130 --> 00:31:20,030
+بحياته ال set هذه subset of 1 2 3 فممكن تكون ايش ك
+
+398
+00:31:20,030 --> 00:31:23,530
+subset اول شغلة و احنا بنتكلم عن ال subset و
+
+399
+00:31:23,530 --> 00:31:26,170
+اقولكوا والله هي عندكوا set طلعولي ال subsets
+
+400
+00:31:26,170 --> 00:31:31,810
+ساعتها اول واحدة في على طول و احنا مغمضينأول واحدة
+
+401
+00:31:31,810 --> 00:31:35,810
+بتحط في خلصناها طيب ممكن تكون الواحد واحد لحالها
+
+402
+00:31:35,810 --> 00:31:41,050
+ممكن تكون اتنين لحالها ست تحتوي على العنصر واحد او
+
+403
+00:31:41,050 --> 00:31:44,930
+ست تحتوي على العنصر تلاتة عنصر واحد فقط طيب او
+
+404
+00:31:44,930 --> 00:31:50,710
+واحد و اتنين واحد و تلاتة اتنين و تلاتة اتنين و
+
+405
+00:31:50,710 --> 00:31:55,950
+واحد فكلهم هتكون واحدة احنا قولنا ان هي unordered
+
+406
+00:31:55,950 --> 00:32:02,260
+كويس فبتحطهم كلهم بتكونوا مثلتهالـ expression هذا
+
+407
+00:32:02,260 --> 00:32:06,880
+إن إحنا بنتعامل مع ال element داخل ال set S كإنها
+
+408
+00:32:06,880 --> 00:32:11,440
+مجموعة sets كإنها مجموعة sets طيب هذا يقودنا لإيش
+
+409
+00:32:11,440 --> 00:32:16,020
+إن ال element واحد هو لا يساوي ال set اللي تحتوي
+
+410
+00:32:16,020 --> 00:32:20,520
+على ال element واحد لا تساوي ال set اللي تحتوي على
+
+411
+00:32:20,520 --> 00:32:25,200
+ال set اللي تحتوي على ال element واحد لحظو فكل
+
+412
+00:32:25,200 --> 00:32:30,280
+واحدة غير التانية كل واحدة غير التانية طيب هذه جدا
+
+413
+00:32:30,280 --> 00:32:35,780
+مهمةال cardinality and finiteness ال cardinality
+
+414
+00:32:35,780 --> 00:32:41,100
+اللي هي أو اللي كله محدودية العددية جداش عدد ال
+
+415
+00:32:41,100 --> 00:32:44,600
+elements محدودية ال set بتاعتنا فهنا لما نيجي
+
+416
+00:32:44,600 --> 00:32:50,060
+نتكلم عن ال absolute set S هدى بنسميها cardinality
+
+417
+00:32:50,060 --> 00:32:54,640
+of S cardinality of S هدى بتجسلنا how many
+
+418
+00:32:54,640 --> 00:32:59,730
+different element in set Sأكم element داخل ال 6 او
+
+419
+00:32:59,730 --> 00:33:05,510
+المجموعة S لو قلنا مثلا ال Phi absolute طبعا احنا
+
+420
+00:33:05,510 --> 00:33:07,770
+مش هنقول absolute من يوم طالع احنا هنعمل علامة
+
+421
+00:33:07,770 --> 00:33:11,730
+absolute بس بنقول cardinality of Phi cardinality
+
+422
+00:33:11,730 --> 00:33:16,070
+of Phi الشيه كده؟ صفر لأنه احنا عارفين ان ال 6 Phi
+
+423
+00:33:16,070 --> 00:33:19,810
+تحتوي على كم element؟ zero element لو قلنا
+
+424
+00:33:19,810 --> 00:33:25,140
+cardinality ل 6 1 2 3تلاتة لأنه أكم element فيها
+
+425
+00:33:25,140 --> 00:33:29,920
+تلاتة لو قلنا ال cardinality ل ال set اللي تحتوي
+
+426
+00:33:29,920 --> 00:33:35,740
+على ال letters a و b اتنين لان عندكوا a و b طيب ال
+
+427
+00:33:35,740 --> 00:33:41,520
+cardinality ل أكم واحدة هنا اتنين الشمال اتنين اه
+
+428
+00:33:41,520 --> 00:33:47,440
+لأن هنا لاحظوا في عندنا set ال elements بتاعتها
+
+429
+00:33:47,440 --> 00:33:53,000
+two setsال elements عددهم جوا هما عبارة عن two
+
+430
+00:33:53,000 --> 00:33:55,360
+sets و احنا لسه كنا بنتكلم ان ال element ممكن يكون
+
+431
+00:33:55,360 --> 00:33:59,100
+six ال element ممكن يكون six فواضح ان هنا بنتكلم
+
+432
+00:33:59,100 --> 00:34:04,780
+عن cardinality equal to two إذا
+
+433
+00:34:04,780 --> 00:34:09,160
+كان والله ال cardinality ل to S if cardinality of
+
+434
+00:34:09,160 --> 00:34:12,460
+S belong to natural number فاحنا هنا بنقول ان ال S
+
+435
+00:34:12,460 --> 00:34:17,720
+is finite إذا كانال cardinality بمعنى ما يجدش عدد
+
+436
+00:34:17,720 --> 00:34:23,280
+ال elements داخل الست S ينتمي ل ال natural numbers
+
+437
+00:34:23,280 --> 00:34:27,860
+يعني معناته رقم طبيعي بنقول أن ال S هذه finite
+
+438
+00:34:27,860 --> 00:34:33,640
+محددة بنقدر نقول عنها محددة كويس otherwise لأ هي
+
+439
+00:34:33,640 --> 00:34:38,080
+إيش infinite set
+
+440
+00:34:38,080 --> 00:34:46,130
+ال natural number الشيةخلينا مع بعض طب انا معاك ال
+
+441
+00:34:46,130 --> 00:34:47,930
+natural number ايش هم الأرقام بتاعة ال natural
+
+442
+00:34:47,930 --> 00:34:53,590
+number اللي هم ال integer طب من وين بدنا نجيب واحد
+
+443
+00:34:53,590 --> 00:35:00,630
+و نص ال integer طب otherwise ان هو ما خلص infinite
+
+444
+00:35:00,630 --> 00:35:04,030
+بس دير برك infinite هنا القصد انه ممكن تكون تنتمي
+
+445
+00:35:04,030 --> 00:35:09,060
+لل integerotherwise أنا مش محددة otherwise انت مش
+
+446
+00:35:09,060 --> 00:35:12,520
+محددة مدام مش محددة خلاص التساوت if فيها كسور و لا
+
+447
+00:35:12,520 --> 00:35:14,680
+مش فيها كسور بس احنا نتكلم مش هنا عن كسور نتكلم
+
+448
+00:35:14,680 --> 00:35:17,360
+انه هل هي belong to natural number it's okay
+
+449
+00:35:17,360 --> 00:35:21,280
+otherwise لأ otherwise ممكن تكون تنتمي ل sets أخرى
+
+450
+00:35:21,280 --> 00:35:25,820
+غير ال natural numbers زي ال .. ال integer زي ال
+
+451
+00:35:25,820 --> 00:35:29,180
+.. ال real numbers ال real numbers فيها كسور فهدا
+
+452
+00:35:29,180 --> 00:35:33,720
+أنا بقول infinite و مقدرش أتعامل مع ال .. ال set
+
+453
+00:35:33,720 --> 00:35:38,830
+بتاعناOkay طبعا infinite هتتعاملوا مع كتير أنواع
+
+454
+00:35:38,830 --> 00:35:43,390
+منها بتتعاملوا مع أنواع كتير منها زي ال natural
+
+455
+00:35:43,390 --> 00:35:45,890
+number نفسها طبعا هنا قلنا احنا اتنين ال natural
+
+456
+00:35:45,890 --> 00:35:48,690
+number هي اصلا infinite
+
+457
+00:35:50,310 --> 00:35:52,770
+عددهم جدش عدد ال cardinality جدش قيمتها ال
+
+458
+00:35:52,770 --> 00:35:57,570
+cardinality كبيرة to infinity طيب و ال z اللي هي
+
+459
+00:35:57,570 --> 00:36:01,910
+إيش ال integer و ال real هدولة من الحاجات اللي
+
+460
+00:36:01,910 --> 00:36:05,210
+احنا عارفينهم هدولة من الأمور اللي احنا عارفينها
+
+461
+00:36:05,210 --> 00:36:09,830
+تمام خلصنا ال cardinality بدنا نشوف إيش ال power
+
+462
+00:36:09,830 --> 00:36:14,850
+the power set operation
+
+463
+00:36:18,730 --> 00:36:24,010
+للset هي عبارة عن ال subsets اللي بقدر اطلعها من
+
+464
+00:36:24,010 --> 00:36:27,830
+ال set هذه جداش عدد ال subsets اللي بنقدر نطلعها
+
+465
+00:36:27,830 --> 00:36:32,730
+من ال set S كل set S بقدر اطلع منها مجموعة ايه؟
+
+466
+00:36:32,730 --> 00:36:37,270
+subset جداش عددهم ال subsets هدولة؟قدش ما نقدر
+
+467
+00:36:37,270 --> 00:36:42,530
+نطلع منها بنقول عنها power of set ال power of set
+
+468
+00:36:42,530 --> 00:36:46,950
+فال power of set بنقول عليها power of set S بهذا
+
+469
+00:36:46,950 --> 00:36:53,470
+الشكل P of S of a set S is the set of all subset
+
+470
+00:36:53,470 --> 00:36:58,430
+of S فهي كل ال subset هي عبارة عن set تحتوي على كل
+
+471
+00:36:58,430 --> 00:37:02,770
+ال subset of Sتمام فهي انه لحظه مدام هي بتحتوي على
+
+472
+00:37:02,770 --> 00:37:06,570
+كل ال subset هي هتكون ال elements بتاعتها عبارة عن
+
+473
+00:37:06,570 --> 00:37:12,610
+set لأن هي subset هي فهتكون ال elements بتاعتها
+
+474
+00:37:12,610 --> 00:37:16,930
+عبارة عن set او مجموعة sets ايش اللي يميزهم مجموعة
+
+475
+00:37:16,930 --> 00:37:22,530
+ال sets دول ان هم subset of S زي لو قولنا ال power
+
+476
+00:37:22,530 --> 00:37:28,030
+of6 a و b هذي هتكون عبارة عن ايش اول شغل هقولنا ال
+
+477
+00:37:28,030 --> 00:37:31,050
+five لازم تكون المجموعة الفارغة او المجموعة
+
+478
+00:37:31,050 --> 00:37:34,010
+الخالية واحدة منهم لان هي المجموعة الخالية جزء من
+
+479
+00:37:34,010 --> 00:37:37,710
+اي شي جزء من اي six اخرى او ممكن تكون اخد ال
+
+480
+00:37:37,710 --> 00:37:42,610
+element الاول لحاله هاي six لحالها او بي لحالها او
+
+481
+00:37:42,610 --> 00:37:47,160
+الاتنين مع بعض ليش لان ال subset ممكن equalفممكن
+
+482
+00:37:47,160 --> 00:37:51,140
+تكون هى نفسها فإذا كان subset ال power أول حاجة
+
+483
+00:37:51,140 --> 00:37:57,060
+بتحطوها المعروفين جدا هدولة الفاي و هى نفسها و هى
+
+484
+00:37:57,060 --> 00:37:59,740
+نفسها موجودة خلاص هى نفسها بنحطها بعدين تبدو
+
+485
+00:37:59,740 --> 00:38:02,340
+تاخدوا الأقسام بتاعتها الأجزاء اللى ممكن تكون
+
+486
+00:38:02,340 --> 00:38:06,740
+موجودة فيها طيب هنا بنكتبها ال sometimes أحيانا
+
+487
+00:38:06,740 --> 00:38:10,160
+بكتبوها two to the power s فبعرف أن هى ال power
+
+488
+00:38:11,680 --> 00:38:16,700
+power of S طيب لما نتكلم عن إذا كانت هي finite ال
+
+489
+00:38:16,700 --> 00:38:20,860
+S تبعتنا بقدر أقول ال cardinality لل power عبارة
+
+490
+00:38:20,860 --> 00:38:26,240
+عن two to the power cardinality S two to the power
+
+491
+00:38:26,240 --> 00:38:28,840
+cardinality S يعني هتعملوا أن انتوا عندكوا هنا
+
+492
+00:38:28,840 --> 00:38:31,920
+مجموعة subsets ال subsets هذه كل ال subsets
+
+493
+00:38:31,920 --> 00:38:35,760
+الممكنة من ال set S هتطلعلكوا حاجة هسميها ال power
+
+494
+00:38:35,760 --> 00:38:39,460
+of S صحيح طب قداش عدد ال elements بتاعة ال power
+
+495
+00:38:39,460 --> 00:38:43,860
+of Sبنجيب ال cardinality ل S و بنعمل 2 to the
+
+496
+00:38:43,860 --> 00:38:47,340
+power of cardinality ففي الحالة اللى كانت عندنا
+
+497
+00:38:47,340 --> 00:38:52,780
+جدش ال elements ل S ال cardinality ل S اتنين اتنين
+
+498
+00:38:52,780 --> 00:38:58,700
+فهيكون عندكوا cardinality of S equal to 2 طيب ال
+
+499
+00:38:58,700 --> 00:39:06,320
+cardinality لل power هتكون 2 to the power 2 هتطلع
+
+500
+00:39:06,320 --> 00:39:11,520
+4 طب تعالى نشوف فعلا 1 2 3 4فعلا عدد ال elements
+
+501
+00:39:11,520 --> 00:39:17,180
+بتاعتها أربعة تمام هذه قاعدة باستمرار تستخدمها
+
+502
+00:39:17,180 --> 00:39:22,040
+okay بنقدر
+
+503
+00:39:22,040 --> 00:39:26,860
+برضه نقول ان ال cardinality ل ال P of natural
+
+504
+00:39:26,860 --> 00:39:30,460
+number ل أي finite natural number هيكون أكبر من ال
+
+505
+00:39:30,460 --> 00:39:37,480
+cardinality ل ال set نفسها برضه منطقيمنطق جدا ليش؟
+
+506
+00:39:37,480 --> 00:39:40,860
+لأن كنتوا بتعملوا منها مجموعة subsets بتعملوا منها
+
+507
+00:39:40,860 --> 00:39:47,620
+مجموعة subsets لل .. الفاية زيادة .. الفاية زيادة
+
+508
+00:39:47,620 --> 00:39:51,120
+هو بعدين بتكون بالعكس زيادة بكتير ليش؟ لأنه اتنين
+
+509
+00:39:51,120 --> 00:39:55,680
+to the power ال cardinality تبعتها فبتعطيكوا كمية
+
+510
+00:39:55,680 --> 00:39:58,400
+كبيرة طبعا هتطلع هنا عدد ال card .. او ال
+
+511
+00:39:58,400 --> 00:40:02,120
+cardinality ك value لل power أكيد هتكون أكبر من ال
+
+512
+00:40:02,120 --> 00:40:07,800
+cardinality لل set نفسها لل set نفسهاو هذا برجع
+
+513
+00:40:07,800 --> 00:40:10,800
+بيخلنا نقول أنه فعلا في عندنا different sizes ليش
+
+514
+00:40:10,800 --> 00:40:16,000
+لل infinite sets .. لل infinite sets okay نفس
+
+515
+00:40:16,000 --> 00:40:19,700
+الكلام احنا كله كنا بيقوله جمهيك ليش unordered ..
+
+516
+00:40:19,700 --> 00:40:23,350
+unorderedلأ احنا ممكن هنا لو عملنا ال ordered
+
+517
+00:40:23,350 --> 00:40:27,690
+هنطلع شغلة جديدة هنتكلم عن ال Cartesian لاحقا ال
+
+518
+00:40:27,690 --> 00:40:29,870
+Cartesian اللي هو الترتيب الثنائي أو الترتيب
+
+519
+00:40:29,870 --> 00:40:35,590
+النقاط بشكل Cartesian بإحداثيات هذا بنقدر ناخده من
+
+520
+00:40:35,590 --> 00:40:40,950
+نفس الفكرة set ولكن مرتبة مجموعة عناصر ولكن
+
+521
+00:40:40,950 --> 00:40:47,530
+الترتيب مهم فيها فهذه ال ordered intables او تكرار
+
+522
+00:40:47,530 --> 00:40:53,430
+بعدد n ومرتبةبحيث انه لو قلنا واحد اتنين لا تساوي
+
+523
+00:40:53,430 --> 00:40:57,590
+اتنين واحد لا تساوي اتنين واحد لاحظوا ان احنا ما
+
+524
+00:40:57,590 --> 00:41:05,690
+استعملناش ال curly braces ما استعملناش الاقوات
+
+525
+00:41:05,690 --> 00:41:10,730
+ساعة المجموعة استعملنا اقوات عاديةالاحداثيات اللى
+
+526
+00:41:10,730 --> 00:41:12,890
+هى ال Cartesian اللى هى ال Cartesian احنا قلتلكوا
+
+527
+00:41:12,890 --> 00:41:15,210
+ال Cartesian هنستعمله فى ال Cartesian اللى يمكن ال
+
+528
+00:41:15,210 --> 00:41:18,470
+slide اللى جاول بعدها كويس لها الاحداثيات للنقاط
+
+529
+00:41:18,470 --> 00:41:22,710
+مثلا احداثيات الاتجاهات احداثيات ال .. فهذه لأ
+
+530
+00:41:22,710 --> 00:41:29,690
+بتعبر عن ordered لإنه لما بقولكم بدنا نتحرك x و y
+
+531
+00:41:29,690 --> 00:41:33,010
+بتفرج واحد باتنين عن اتنين و واحد بيفرجوا كتير
+
+532
+00:41:33,830 --> 00:41:39,330
+بفرجوه جدا في الحالة اللي هنا بنتكلم عنها طيب بظل
+
+533
+00:41:39,330 --> 00:41:44,590
+ان ال n هذه اللي هي جدش عدد التكرارات بتاعتنا جدش
+
+534
+00:41:44,590 --> 00:41:49,210
+عدد ال elements داخل ال .. ال .. ال ordered set
+
+535
+00:41:49,210 --> 00:41:53,150
+جدش عددهم عددهم n ال n هذه لازم تكون belong to
+
+536
+00:41:53,150 --> 00:41:56,810
+natural number لازم تكون integer و لازم تكون محددة
+
+537
+00:41:56,810 --> 00:42:00,710
+في نت و لازم تكون positive positive و integer okay
+
+538
+00:42:01,800 --> 00:42:05,340
+ففي الآخر ممكن نعبر عنها عساس ان هي sequence
+
+539
+00:42:05,340 --> 00:42:12,940
+مجموعة من ال elements ال objects المرتبة sequence
+
+540
+00:42:12,940 --> 00:42:16,760
+معناته بتكون مرتبة مرتبة ورا بعض بفرج ان احط
+
+541
+00:42:16,760 --> 00:42:19,480
+الانصر التاني مكان الأول اه بتصير هنا بنتكلم عن
+
+542
+00:42:19,480 --> 00:42:23,060
+sequence مختلف sequence ثاني تماما ال first
+
+543
+00:42:23,060 --> 00:42:26,950
+element تبعه محددفي ال sequence اللي عندنا هنا a1
+
+544
+00:42:26,950 --> 00:42:30,870
+a2 to an محدد ان الاول واحد element لازم اشوفه هو
+
+545
+00:42:30,870 --> 00:42:36,350
+ال a واحد تحديدا كويس في الحالة هذه قلناها اول ما
+
+546
+00:42:36,350 --> 00:42:40,170
+بدنا نتكلم ال 1 و 2 مختلفة و لا تساوي 2 و 1 لا
+
+547
+00:42:40,170 --> 00:42:44,270
+تساوي احداث زيادة هنا صار في عندكم ال n تلاتة كانت
+
+548
+00:42:44,270 --> 00:42:49,680
+ال n ب 2 2 و 1 زودنا عليها كمانكمان element طبعا
+
+549
+00:42:49,680 --> 00:42:55,460
+هذه بتختلف و ممكن تتبين ال n هنا عندنا في بعض
+
+550
+00:42:55,460 --> 00:43:02,740
+مسميات أحيانا درجة لو كان عندنا ال n ب zero لو
+
+551
+00:43:02,740 --> 00:43:07,700
+ال set هذا ال n تبعتها ب zero امتى؟ مافيش .. احنا
+
+552
+00:43:07,700 --> 00:43:09,880
+نتكلم عن sequence مش موجود sequence ال element
+
+553
+00:43:09,880 --> 00:43:18,350
+تبعته ب zero او singlets عنصر واحد ال pairsوضع زوج
+
+554
+00:43:18,350 --> 00:43:21,830
+.. زوج .. زوج من الأرقام أو زوج من الثانوية اللي
+
+555
+00:43:21,830 --> 00:43:24,710
+كنتوا بتستخدمهم في ال X و ال Y في النقاط بتاعتكم
+
+556
+00:43:24,710 --> 00:43:28,850
+كنتوا بتستخدمهم في ال X و ال Y triples ثلاثي رباعي
+
+557
+00:43:28,850 --> 00:43:33,010
+خماسي two n two n tuples في ال quad .. ال quad
+
+558
+00:43:33,010 --> 00:43:37,910
+اللي هي الرباعي و quantable اللي هو الخماس واحدة
+
+559
+00:43:37,910 --> 00:43:41,510
+كده بتكمله لعند ما تشوفوا أنتوا الإحداثيات اللي
+
+560
+00:43:41,510 --> 00:43:43,770
+بتكونوا تستعملوها جدش و ممكن تستعملوها طبعا الكلام
+
+561
+00:43:43,770 --> 00:43:48,840
+هذا ممكن ت ..لا حقا ممكن ماتتتعاملوش كتير فيه،
+
+562
+00:43:48,840 --> 00:43:52,360
+ممكن كتير مابتتعاملوش فيه، ولكن ممكن تتعاملوا فيها
+
+563
+00:43:52,360 --> 00:43:55,200
+في ال problems الكبيرة، إذا كان الإحداثيات أو ال
+
+564
+00:43:55,200 --> 00:43:59,150
+dimensionality للمشكلة عاليةال dimensionality
+
+565
+00:43:59,150 --> 00:44:02,370
+للproblem ممكن تكون عالية احنا عادة اللي انتوا
+
+566
+00:44:02,370 --> 00:44:05,890
+عارفينه ان ال .. بتتعاملوا مع function فيها three
+
+567
+00:44:05,890 --> 00:44:09,570
+dimension هي ملأ ممكن تكون اكتر ممكن تكون اربعة
+
+568
+00:44:09,570 --> 00:44:12,450
+dimension خمسة dimension ستة dimension فانتوا في
+
+569
+00:44:12,450 --> 00:44:15,030
+الحالة هذه إذا ال problem ال dimension بتاعتها ستة
+
+570
+00:44:15,030 --> 00:44:20,630
+النقطة عشان تحطوا إحداثي لنقطة بدوا يكون فيها ستة
+
+571
+00:44:20,630 --> 00:44:24,190
+elements بدوا يكون فيها ستة elements فعليا تمام
+
+572
+00:44:25,730 --> 00:44:28,610
+Okay هنا بتدخلنا هدى على جزئية ال Cartesian
+
+573
+00:44:28,610 --> 00:44:32,850
+product of sets ال Cartesian product of sets لو
+
+574
+00:44:32,850 --> 00:44:38,010
+قلنا for sets A,B فال Cartesian product بتاعتهم A
+
+575
+00:44:38,010 --> 00:44:46,650
+Cartesian product بيه عبارة عن زوج ثنائي هيه A بيه
+
+576
+00:44:46,650 --> 00:44:51,900
+بشرط أن ال element الأول من ال set الأولىال
+
+577
+00:44:51,900 --> 00:44:55,760
+element التاني من ال set التاني فاحنا حطيناه بزوج
+
+578
+00:44:55,760 --> 00:45:03,640
+مرتب ordered order set such that a belong to set a
+
+579
+00:45:03,640 --> 00:45:10,660
+و ال element b belong to set b تمام فلو قلنا عنده
+
+580
+00:45:10,660 --> 00:45:18,300
+two sets set a, b cartesian product by set واحد و
+
+581
+00:45:18,300 --> 00:45:28,570
+اتنينعبارة عن إيش؟ ست لأزواج A واحد, A اتنين, B
+
+582
+00:45:28,570 --> 00:45:35,670
+واحد, B اتنين تمام؟ واضحة يعني مش فيها كتير صعوبة
+
+583
+00:45:35,670 --> 00:45:40,410
+و مش صعبة كتير لسه طيب for finite A, B
+
+584
+00:45:40,410 --> 00:45:48,060
+الcardinality لل product A في Bنفسها تساوي
+
+585
+00:45:48,060 --> 00:45:53,020
+الcardinality ل a في cardinality ل b cardinality ل
+
+586
+00:45:53,020 --> 00:45:59,100
+a هنا جداش cardinality ل a ل ال a كلها على بعض
+
+587
+00:45:59,100 --> 00:46:05,280
+اتنين cardinality ل b اتنين cardinality اتنين اللي
+
+588
+00:46:05,280 --> 00:46:08,200
+هي ال cardinality هنا اتنين و هنا في اتنين اتنين
+
+589
+00:46:08,200 --> 00:46:12,620
+في اتنين اربع طب خلنا نشوف هل فعلاالـ Cartesian
+
+590
+00:46:12,620 --> 00:46:15,600
+product ال cardinality بتاعتهم نفس الشيء لازم تطلع
+
+591
+00:46:15,600 --> 00:46:20,040
+نفس الشيء برضه أربعة اتنين في اتنين بساوي أربعة
+
+592
+00:46:20,040 --> 00:46:24,340
+طيب ال competitive هي not competitive الحقيقة ال
+
+593
+00:46:24,340 --> 00:46:26,900
+operation بتاعتنا ال Cartesian product ليش؟ لإن
+
+594
+00:46:26,900 --> 00:46:33,260
+احنا جولنا واحد A B مختلفة عن B A مختلفة لما أقول
+
+595
+00:46:33,260 --> 00:46:38,320
+A Cartesian B هي مختلفة عن B Cartesian A لإن
+
+596
+00:46:38,320 --> 00:46:42,540
+الأزواج المرتبة هتختلفهتختلف تماما، هتصير هنا
+
+597
+00:46:42,540 --> 00:46:46,280
+الأزواج المرتبة كلها دايما بدية بال letters هتصير
+
+598
+00:46:46,280 --> 00:46:48,980
+بالعكس بدية دايما بال numbers فهتلاجوا ان انتوا
+
+599
+00:46:48,980 --> 00:46:53,700
+طلعتوا set مختلفة تماما عن اللي كنتوا بتتكلموا
+
+600
+00:46:53,700 --> 00:47:00,260
+عنها فمعنى ذلك not for all a b a Cartesian product
+
+601
+00:47:00,260 --> 00:47:05,720
+b equal to b Cartesian product a not for all يعني
+
+602
+00:47:05,720 --> 00:47:09,620
+معنى ذلك انه ممكن تصير ممكن تصير امتى لو اتنين
+
+603
+00:47:09,620 --> 00:47:13,490
+بيسووا بعضلو الاتنين بيصور مش هتفرج كتير يعني في
+
+604
+00:47:13,490 --> 00:47:17,650
+بعض الحالات ممكن تظبط بس مش بالعموم مش بالعموم
+
+605
+00:47:17,650 --> 00:47:23,250
+تمام بنقدر انعمم ان ال Cartesian product بقدر ..
+
+606
+00:47:23,250 --> 00:47:27,090
+ممكن اعملها لأكتر من two sets يعني مش بضروري
+
+607
+00:47:27,090 --> 00:47:31,730
+اعملها ل a في b ممكن تنعمل a1 Cartesian product a2
+
+608
+00:47:31,730 --> 00:47:36,810
+Cartesian product a3 Cartesian product to anto a n
+
+609
+00:47:36,810 --> 00:47:42,450
+فمعنى ذلك ممكن نضرب أكتر من two sets أكتر من two
+
+610
+00:47:42,450 --> 00:47:47,930
+sets طيب الأمور هذه كويسة لعندي الآن تمام بدنا
+
+611
+00:47:47,930 --> 00:47:51,650
+نبدأ نعمل شوية operations على ال sets شوية
+
+612
+00:47:51,650 --> 00:47:55,890
+operations على ال sets ال operation المشهورة جدا
+
+613
+00:47:55,890 --> 00:47:58,990
+كنتوا تعملوا الاتحاد مش كنتوا تعملوا اتحاد
+
+614
+00:47:58,990 --> 00:48:04,730
+للمجموعاتthe union operator اللي هي عملية الاتحاد
+
+615
+00:48:04,730 --> 00:48:07,210
+عملية الاتحاد من الحاجات المشهورة جدا ومعروفة جدا
+
+616
+00:48:07,210 --> 00:48:13,290
+for sets A, B the union A union B is a set
+
+617
+00:48:13,290 --> 00:48:22,410
+containing all elements in A and B or B فهي كل ال
+
+618
+00:48:22,410 --> 00:48:29,310
+elements اللي موجودة في A أو موجودة في Bأو في بي
+
+619
+00:48:29,310 --> 00:48:37,570
+تمام فإذا هذي كأن بعمل or عشان نطلعنا ممكن طبعا in
+
+620
+00:48:37,570 --> 00:48:41,190
+bothممكن تكون هي مشتركة في الاتنين ممكن تكون
+
+621
+00:48:41,190 --> 00:48:43,430
+مشتركة في الاتنين ال elements اللي بدنا نحتويها
+
+622
+00:48:43,430 --> 00:48:50,870
+تمام فلو قلنا هنا for all a و b لو لكل ال sets a و
+
+623
+00:48:50,870 --> 00:48:55,850
+b a union b عبارة عن set جديدة set جديدة طبيعية
+
+624
+00:48:55,850 --> 00:49:00,430
+هتكون عبارة عن set جديدة تحتوي او ل x such that x
+
+625
+00:49:00,430 --> 00:49:05,650
+belong to a or x belong to main to bموجودة هنا أو
+
+626
+00:49:05,650 --> 00:49:08,330
+موجودة هنا معناته موجودة في ال union معناته موجودة
+
+627
+00:49:08,330 --> 00:49:13,770
+في من في ال union بتاعتهم okay فتحتوي على كل ال
+
+628
+00:49:13,770 --> 00:49:17,930
+elements سواء موجودة في a and contain all the
+
+629
+00:49:17,930 --> 00:49:21,570
+element of b ممكن نعبر عنها برضه بطريقة تانية على
+
+630
+00:49:21,570 --> 00:49:28,190
+أساس أن هي for all a, b such that a union b subset
+
+631
+00:49:28,190 --> 00:49:35,600
+of a طبيعيعفوا super set super set لحظة طبيعي لأن
+
+632
+00:49:35,600 --> 00:49:40,660
+انا اساسا ال union ماخدها من ال elements اللي في a
+
+633
+00:49:40,660 --> 00:49:45,800
+زائد element تانية اللي هم تعون بي فطبيعي ان a هي
+
+634
+00:49:45,800 --> 00:49:50,220
+subset من ال union و نفس الكلام لمين لل b نفس
+
+635
+00:49:50,220 --> 00:49:56,060
+الكلام and ال b برضه subset من ال union ل a و b
+
+636
+00:49:56,060 --> 00:50:00,280
+subset من ال union a to b تمام
+
+637
+00:50:05,710 --> 00:50:10,110
+ناخد exam's واضحة طبعا ال exam's هنا لو قلنا a ال
+
+638
+00:50:10,110 --> 00:50:15,210
+6 a b و c union مع two و three واضح أنه بدنا نحطهم
+
+639
+00:50:15,210 --> 00:50:21,670
+كلهم بدنا نحطهم كلهم طب لو قلنا union of two three
+
+640
+00:50:21,670 --> 00:50:26,390
+five union three five seven طبعا انتوا هتحطوا هدول
+
+641
+00:50:26,390 --> 00:50:30,330
+هتحطوا هدول هتلاقوا فيه تكرار شطبوا التكرارات لأن
+
+642
+00:50:30,330 --> 00:50:35,230
+هذه هي المطلوبةبدون تكرارات عادة بدنا ياها بحيث
+
+643
+00:50:35,230 --> 00:50:39,290
+انه العدد اللي انتوا حاطينه يمثل ال cardinality ال
+
+644
+00:50:39,290 --> 00:50:42,070
+cardinality لست خدوا بالكم انه لازم يمثل ال
+
+645
+00:50:42,070 --> 00:50:46,350
+cardinality لست كلام برضه مر علينا سابقا تمام؟
+
+646
+00:50:46,350 --> 00:50:50,990
+كويس فهذا ال required form المطلوب بنسيبهاش بهذا
+
+647
+00:50:50,990 --> 00:50:55,290
+الشكل انا عارف ان انتوا ماخدينها من ال a و من ال b
+
+648
+00:50:55,290 --> 00:50:59,530
+بس بحطهمش ارتبهم جان بعض و خلاص واسيبهم بدنا نشوف
+
+649
+00:50:59,530 --> 00:51:04,410
+الالجزء اللى هنتكلم عليه لاحقا اشي اللى موجود هنا
+
+650
+00:51:04,410 --> 00:51:08,710
+و هنا فلو
+
+651
+00:51:08,710 --> 00:51:12,650
+قلنا هي عندكوا اتنين تلاتة خمسة او تلاتة خمسة سبعة
+
+652
+00:51:12,650 --> 00:51:17,450
+تمثل كلهم مع بعض بروحش بحط بقول اتنين تلاتة خمسة و
+
+653
+00:51:17,450 --> 00:51:21,930
+بحط اضيف لهم تلاتة خمسة سبعة لأ بدنا نشيل منهم
+
+654
+00:51:21,930 --> 00:51:27,530
+الجزء التقاطع جزء التقاطع okay
+
+655
+00:51:29,680 --> 00:51:32,260
+الانترسكشن التقاطع اللي هو إيش ال inter ال
+
+656
+00:51:32,260 --> 00:51:35,800
+intersection ال intersection غير ال union ال
+
+657
+00:51:35,800 --> 00:51:37,880
+intersection اللي بنشوف إيش ال elements اللي
+
+658
+00:51:37,880 --> 00:51:47,640
+موجودة في a هنا كنا نقول or بي and بس فغيرنا
+
+659
+00:51:47,640 --> 00:51:53,380
+or ب and فصار عندنا ال a و b ال intersection
+
+660
+00:51:53,380 --> 00:51:57,540
+بتاعتهم a intersection b is set اللي هي في النهاية
+
+661
+00:51:57,540 --> 00:52:01,410
+setال set هذه تحتوي على كل ال elements that are
+
+662
+00:52:01,410 --> 00:52:06,930
+simultaneously in A and in B في نفس الوقت موجودة
+
+663
+00:52:06,930 --> 00:52:13,750
+في A و موجودة في B فبنقدر نقول أن هي ال set S لكل
+
+664
+00:52:13,750 --> 00:52:18,470
+ال elements S بشرط أن S belong to A and X belong
+
+665
+00:52:18,470 --> 00:52:25,370
+to B فال X هذه لازم تكون belong لل two sets
+
+666
+00:52:26,820 --> 00:52:31,680
+اللي قلناه هناك ان ال union كان super set لكل
+
+667
+00:52:31,680 --> 00:52:34,920
+واحدة من ال two sets هنا بنقول انه لأ ال
+
+668
+00:52:34,920 --> 00:52:40,860
+intersection هو subset من a و subset من b هو
+
+669
+00:52:40,860 --> 00:52:46,340
+subset من a و subset من b ففرق ال a b a
+
+670
+00:52:46,340 --> 00:52:52,640
+intersection b subset من a و subset من b و subset
+
+671
+00:52:52,640 --> 00:53:00,580
+من b اللي عندي الان كله كلام منطقي جداهنا ليش؟
+
+672
+00:53:00,580 --> 00:53:04,560
+مافيش اي تقاطع مافيش اي تقاطع في هذه five التانية
+
+673
+00:53:04,560 --> 00:53:10,340
+الاربعة بس الاربعة بس هنا نفس الكلام زي بالظبط
+
+674
+00:53:10,340 --> 00:53:18,680
+عارفين لما بتتكلموا عن تقاطع تقاطع شوارع الجزء
+
+675
+00:53:18,680 --> 00:53:22,000
+اللي في النص داخل الشارع هذا هذا يبقى محسوب مع اي
+
+676
+00:53:22,000 --> 00:53:27,040
+شارع مع الاتنين عشان هي اسمه تقاطععشان هي اسمه
+
+677
+00:53:27,040 --> 00:53:32,220
+تقاطع لأن هذا بنحسب مع الشارع بهذا الشكل الأفقي ال
+
+678
+00:53:32,220 --> 00:53:34,860
+horizontal و الشارع الأمض و عشان هي اسمه تقاطع
+
+679
+00:53:34,860 --> 00:53:37,700
+فاحنا هنا بنتكلم عن تقاطع فعليا اللي هو الجزء اللي
+
+680
+00:53:37,700 --> 00:53:44,460
+موجود في ال two .. two sets .. موجود في ال two طيب
+
+681
+00:53:44,460 --> 00:53:46,240
+ماشي الله يعطينا العفيا .. اعطوكوا العفيا انتوا
+
+682
+00:53:46,240 --> 00:53:49,500
+كمان للمرة الجاية ان شاء الله بنكمل باقية محاضرتنا
+
+683
+00:53:49,500 --> 00:53:50,820
+باسم الله تعالى سلام عليكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f024b87b602abd69d5ea28b0b7fa71d86ba1c0a8
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o.srt
@@ -0,0 +1,3176 @@
+
+1
+00:00:20,960 --> 00:00:23,120
+بسم الله الرحمن الرحيم الصلاة والسلام عليكم ورحمة
+
+2
+00:00:23,120 --> 00:00:25,500
+الله وبركاته يا سيدنا محمد وعلي أهله وصحابه أجمعين
+
+3
+00:00:25,500 --> 00:00:28,380
+اليوم هنبدأ في موضوع جديد إن شاء الله recurrence
+
+4
+00:00:28,380 --> 00:00:31,400
+relations  هنشوف الـ recurrence relations أو إيش هي
+
+5
+00:00:31,400 --> 00:00:35,720
+علاقة انتقارية نتكلم عليها، نشوف تعريفها أولا، نعمل
+
+6
+00:00:35,720 --> 00:00:39,880
+definition لها، وبعد الـ definition تبعنا هناخد كيف
+
+7
+00:00:39,880 --> 00:00:44,520
+احنا نجيب الـ general equation للـ recurrence
+
+8
+00:00:44,520 --> 00:00:45,080
+relation
+
+9
+00:00:50,400 --> 00:00:53,020
+مجموعة الـ elements  السابقين له أو مجموعة الـ
+
+10
+00:00:53,020 --> 00:00:56,100
+elements قبله، فمجموعة الـ elements اللي قبلها، دولة
+
+11
+00:00:56,100 --> 00:01:01,080
+مجموعة الـ elements اللي قبله نقدر نستعين عنهم، إن
+
+12
+00:01:01,080 --> 00:01:04,780
+احنا نجيب relation خاصة أو كـ function في الـ
+
+13
+00:01:04,780 --> 00:01:10,020
+location، في الـ location بحيث إن an بدل ما هي
+
+14
+00:01:10,020 --> 00:01:16,540
+function في a n-1 و n-2 وممكن يكون n-3
+
+15
+00:01:40,520 --> 00:01:43,880
+مش مشكلة، بس هانجي نجيب من الاتنين، دولة العنصر
+
+16
+00:01:43,880 --> 00:01:46,160
+التالي، بعدين الرابع، بعدين الخامس، أقدر أمشي
+
+17
+00:01:46,160 --> 00:01:50,680
+للالف؟ طبعا الطريقة not efficient، مش هتكون
+
+18
+00:01:50,680 --> 00:01:55,060
+efficient نهائيا، فهتصير مناسب أفضل إن أنا أحولها
+
+19
+00:01:55,060 --> 00:01:58,780
+لمعادلة from function في مين في أن نفسها، فبعوض
+
+20
+00:01:58,780 --> 00:02:01,540
+الـ n دي بالألف أو بالمية أو بالرقم اللي أنا بديه
+
+21
+00:02:01,540 --> 00:02:04,920
+عشان نحصل على قيمة العنصر في الـ location
+
+22
+00:02:08,050 --> 00:02:10,610
+عشان نشوف إن فعلا الموضوع فيه إمكانية لتحميلها،
+
+23
+00:02:10,610 --> 00:02:13,810
+العملية فيه إمكانية، خلينا نشوف الـ relation اللي
+
+24
+00:02:13,810 --> 00:02:19,730
+موجودة علينا هنا An بتساوي 2 An-1 minus An-1، طبعا
+
+25
+00:02:19,730 --> 00:02:23,750
+لازم يكون هنا N أكبر من أو يساوي 2، على اعتبار إن
+
+26
+00:02:23,750 --> 00:02:23,990
+فيها
+
+27
+00:03:23,360 --> 00:03:30,280
+بمعنى هل الستة هذي تساوي تلاتة ناقص صفر، تلاتة، اتنين
+
+28
+00:03:30,280 --> 00:03:39,360
+طبعا ناقص صفر، أوكي، هاي صفر، طيب، أيه تلاتة ده
+
+29
+00:03:39,360 --> 00:03:48,860
+مفروض تسعة من المعادلة، تسعة، فهل فعلا تسعة تساوي
+
+30
+00:03:48,860 --> 00:03:49,480
+اتنين؟
+
+31
+00:04:00,530 --> 00:04:05,430
+هو أكبر من المعادلة، لأن المعادلة تتناسب تماما مع
+
+32
+00:04:05,430 --> 00:04:09,150
+الـ Recurrence relation، المعطاة تتناسب تماما
+
+33
+00:04:09,150 --> 00:04:13,550
+فمعنى ذلك، ممكن يكون هذا تمثيل للـ Recurrence
+
+34
+00:04:13,550 --> 00:04:14,730
+relation
+
+35
+00:04:23,450 --> 00:04:27,090
+لو عوضنا فيها في تانية، إيش بدي يطلع؟  حكمها أن E
+
+36
+00:04:27,090 --> 00:04:31,710
+نون تساوي واحد، E واحد تساوي أربعة، E واحد تساوي
+
+37
+00:04:31,710 --> 00:04:35,830
+اتنين، E اتنين تساوي أربعة، E اتنين تساوي أربعة، E
+
+38
+00:04:35,830 --> 00:04:36,130
+اتنين تساوي أربعة، E اتنين تساوي أربعة، E اتنين
+
+39
+00:04:36,130 --> 00:04:37,490
+تساوي أربعة، E اتنين تساوي أربعة، E اتنين تساوي
+
+40
+00:04:37,490 --> 00:04:37,510
+أربعة، E اتنين تساوي أربعة، E اتنين تساوي أربعة، E
+
+41
+00:04:37,510 --> 00:04:39,150
+اتنين تساوي أربعة، E اتنين تساوي أربعة، E اتنين
+
+42
+00:04:39,150 --> 00:04:40,690
+تساوي أربعة، E اتنين تسا
+
+43
+00:04:54,470 --> 00:04:57,150
+الـ relation هذه هي أول.. أول عنصر، بالسبب اللي
+
+44
+00:04:57,150 --> 00:04:57,970
+نحس أنه بيعمل check
+
+45
+00:05:49,680 --> 00:05:53,680
+يكونوا كافيين لتعريف sequence معين أو string معين
+
+46
+00:05:53,680 --> 00:05:59,200
+الـ sequence المعين هذا، قلنا قبل هيك أنه قد يتفق
+
+47
+00:05:59,200 --> 00:06:03,560
+أكثر من sequence في الـ initial values ده، وقلنا
+
+48
+00:06:03,560 --> 00:06:12,320
+قبلها، مثلا أول عنصرين لـ.. لنختار مثلا اثنين
+
+49
+00:06:12,320 --> 00:06:17,300
+احنا أخدنا مثال قبل هيك على الأرقام الفردية، أعتقد
+
+50
+00:06:17,300 --> 00:06:17,780
+والـ prime
+
+51
+00:06:25,460 --> 00:06:34,500
+لو قلنا الأرقام من n أكبر من واحد، وقالت
+
+52
+00:06:34,500 --> 00:06:37,920
+لك
+
+53
+00:06:37,920 --> 00:06:44,720
+أكبر
+
+54
+00:06:44,720 --> 00:06:47,560
+من n، أكبر من واحد، أكبر من n، أكبر من واحد
+
+55
+00:06:57,000 --> 00:06:59,720
+ممكن تكون أربعة، خلاص الوصفة ستبقى في العالم الـ
+
+56
+00:06:59,720 --> 00:07:03,880
+positive numbers، فهنا واقع إن احنا التعريف مش دقيق
+
+57
+00:07:03,880 --> 00:07:06,860
+تعريفنا هنا ممكن مش دقيق، محتاجين يقولوا لنا كمان
+
+58
+00:07:06,860 --> 00:07:10,220
+element، كمان element، فهذه واحدة من الحالات اللي
+
+59
+00:07:10,220 --> 00:07:18,960
+نبتعد عنها أو مش معرفة بصورة جيدة، okay، ناخد example
+
+60
+00:07:39,660 --> 00:07:44,480
+ممكن تكون معطاة، أو عبارة عن اللي هي نمو حسابي
+
+61
+00:07:44,480 --> 00:07:52,220
+للبنك، أو الـ bank account with P كنسبة، بنسبة P، هل
+
+62
+00:07:52,220 --> 00:07:55,080
+اللي اللي أنتم بتفكروا فيه، على أكمل وجه في القرن لما
+
+63
+00:07:55,080 --> 00:07:59,880
+الواحد يروح ياخد من البنك مبلغ، وبعدين يرجعوا
+
+64
+00:07:59,880 --> 00:08:08,800
+المبلغ زائد قيمة P، زائد قيمة P، الفائدة
+
+65
+00:08:08,800 --> 00:08:14,880
+الفائدة طبعا بتكون على فترة معينة، ممكن تكون شهرية
+
+66
+00:08:14,880 --> 00:08:19,020
+ممكن تكون سنوية، بيصيروا اتفاق عليها، في الحالة هذه
+
+67
+00:08:19,020 --> 00:08:23,820
+في زيادة، الزيادة معتمدة على قيمة الشهر الجاي
+
+68
+00:08:23,820 --> 00:08:25,220
+المفروض أدفع بناء على
+
+69
+00:08:32,190 --> 00:08:37,490
+ويأخذ عليه الفائدة، طيب مرت سنة واستحق الفائدة، هل
+
+70
+00:08:37,490 --> 00:08:41,430
+الفائدة هذه لو أخدها، ممكن ياخد قيمة الفائدة ويظل
+
+71
+00:08:41,430 --> 00:08:43,670
+المبلغ زي ما هو، يشتغل السنة اللي جاية ياخد نفس
+
+72
+00:08:43,670 --> 00:08:49,170
+الفائدة أو يسيبها، فهيك رأس المال نفسه يتغير، بيزيد
+
+73
+00:08:49,170 --> 00:08:52,610
+فمعنى ذلك، إنه بنفس قيمة الفائدة المرة اللي جاية
+
+74
+00:08:52,610 --> 00:08:56,150
+قيمة الفائدة بتزيد، ولكن نسبة الفائدة هي نسبة
+
+75
+00:08:56,150 --> 00:08:57,690
+الفائدة هتكون هي هي
+
+76
+00:09:01,820 --> 00:09:05,460
+المشاكل اللي عاملة أساسا هي.. يعني خليني أقول..
+
+77
+00:09:05,460 --> 00:09:09,580
+طلعنا شوية عن الـ.. مش عارف بسجل ولا بسجل مش
+
+78
+00:09:09,580 --> 00:09:13,920
+فمبدئيا
+
+79
+00:09:13,920 --> 00:09:21,520
+هذه واحدة من الإشكاليات اللي عاملة أساسا فروق فكرة
+
+80
+00:09:21,520 --> 00:09:25,240
+أنه في فجر وفي غنى، هذه واحدة من مصايبها، واحدة من
+
+81
+00:09:25,240 --> 00:09:28,280
+مصايب تاعة الحاجات هذه، خليني احنا.. احنا قلنا في
+
+82
+00:09:28,280 --> 00:09:33,140
+التطبيق كتطبيق رياضي، فردنا يبعدنا عن التطبيق الفعلي
+
+83
+00:09:33,140 --> 00:09:40,160
+كويس، فلو قلنا الـ month أو الشهر n هيساوي، قديش
+
+84
+00:09:40,160 --> 00:09:44,180
+المبلغ اللي أنا معايا في شهر n هيكون عبارة عن
+
+85
+00:09:44,180 --> 00:09:51,000
+الشهر n ناقص واحد، الشهر السابق، زائد الفائدة
+
+86
+00:09:51,000 --> 00:09:55,140
+الفائدة في الحالة محسوبة على إيش؟ محسوبة على بداية
+
+87
+00:09:55,140 --> 00:10:00,140
+الشهر اللي فات، يعني على الشهر الماضي، زائد الـ b، الـ
+
+88
+00:10:00,140 --> 00:10:07,320
+P هذه هي نسبة الزيادة، في مدة percent، بحطها عالمية في
+
+89
+00:10:07,320 --> 00:10:13,290
+الشهر السابق، السابق، بقدر أقول إنه كلها على بعض
+
+90
+00:10:13,290 --> 00:10:18,150
+بنسميها واحد زائد قيمة النسبة، أو النسبة في الشهر
+
+91
+00:10:18,150 --> 00:10:22,670
+السابق، طيب، ماهي نفس الفكرة هي هي، أو خلينا كلها
+
+92
+00:10:22,670 --> 00:10:27,750
+نسميها R، يعني تسهيلا للموضوع، نفس الشغلة، طب المبلغ
+
+93
+00:10:27,750 --> 00:10:31,210
+اللي كان الشهر الفات موجود، هو أساسا جاي من الشهر
+
+94
+00:10:31,210 --> 00:10:36,390
+اللي قبله، فنفس الكلام Mn ماينص وان أو في الـ month
+
+95
+00:10:36,390 --> 00:10:42,090
+n ناقص واحد كانت عبارة عن نفس الـ R، هي المبلغ زائد
+
+96
+00:10:42,090 --> 00:10:46,250
+زيادة، والزيادة سنسميها قيمة R، كانت إيش متساوية
+
+97
+00:10:46,250 --> 00:10:51,410
+برضه R في الـ month اللي قبله، اللي قبله، مع اللي
+
+98
+00:10:51,410 --> 00:10:56,480
+قبله، لعند ما نصل لبداية ما أخدت المبلغ، أو بداية ما
+
+99
+00:10:56,480 --> 00:10:57,540
+أخذت المبلغ، أو بداية ما أخدت المبلغ، أو بداية ما
+
+100
+00:10:57,540 --> 00:10:57,960
+أخذت المبلغ، أو بداية ما أخدت المبلغ، أو بداية ما
+
+101
+00:10:57,960 --> 00:10:59,480
+أخذت المبلغ، أو بداية ما أخدت المبلغ، أو بداية ما
+
+102
+00:10:59,480 --> 00:11:01,680
+أخذت المبلغ، أو بداية ما أخدت المبلغ، أو بداية ما
+
+103
+00:11:01,680 --> 00:11:01,740
+أخذت المبلغ، أو بداية ما أخدت المبلغ، أو بداية ما
+
+104
+00:11:01,740 --> 00:11:03,260
+أخذت المبلغ، أو بداية ما أخدت المبلغ، أو بداية ما
+
+105
+00:11:03,260 --> 00:11:08,590
+أخذت المبلغ، أو بداية ما أخدت المبلغ، أو بداية، جاعدة
+
+106
+00:11:08,590 --> 00:11:13,690
+busy، كويس، في الحالة هذه لو أنا فرضا واحد حط فلوسه
+
+107
+00:11:13,690 --> 00:11:17,870
+وبده يحسب بعد عشر سنين، بده يحط المبلغ، وبده ينسل
+
+108
+00:11:17,870 --> 00:11:21,510
+عشر سنين، طبعا يقعد يحسبها، الشهر هذا، طب الشهر اللي
+
+109
+00:11:21,510 --> 00:11:23,530
+قبله قديش، طب الشهر اللي بعده قديش، طب الشهر اللي
+
+110
+00:11:23,530 --> 00:11:27,210
+بعده قديش، مش هتنفع، لأن كان من الأسهل، عشرة في إثنا عشر
+
+111
+00:11:27,210 --> 00:11:31,370
+عدد الشهور، هاي مئة وعشرون شهر، يضربهم في الـ.. بتصير
+
+112
+00:11:31,370 --> 00:11:33,990
+R، قديش النسبة المطلوبة، أو النسبة اللي هو هياخدها
+
+113
+00:11:34,960 --> 00:11:37,960
+يضربها في 120، وخلاص، في المبلغ اللي حطه أول مرة
+
+114
+00:11:37,960 --> 00:11:43,180
+بيحسبها مرة واحدة، مش مضطر يعمل يحسب كل الـ terms
+
+115
+00:11:43,180 --> 00:11:45,700
+لعند ما يصل للشهر اللي بده يحسب قديش قيمة الفائدة
+
+116
+00:11:45,700 --> 00:11:50,360
+فيه، سواء إله أو عليه، سواء إله أو عليه، أو عليه طبعا
+
+117
+00:11:50,360 --> 00:11:53,080
+لإن الناس كتير بتنخلوط بيته من ورا الكلام هذا لما
+
+118
+00:11:53,080 --> 00:11:56,940
+تكون عليه، يروح ياخد قرض، وبعدين مايعرفش يخلص حاجة
+
+119
+00:11:56,940 --> 00:12:01,930
+كويسة، واضح إن احنا هنا حولناها من إيش؟ من
+
+120
+00:12:01,930 --> 00:12:05,450
+recurrence relation لـ general relation، لاحظوا هنا
+
+121
+00:12:05,450 --> 00:12:09,630
+معتمدة على الـ n بس، معتمدة على قيمة الـ n، المبلغ
+
+122
+00:12:09,630 --> 00:12:12,450
+اللي هنحطه في الأول، ما احنا عارفينه قديش، نحط مبلغ
+
+123
+00:12:12,450 --> 00:12:16,330
+في الأول، وقدرنا نحسب المبلغ كقيمة في الأول، معروف قديش
+
+124
+00:12:16,330 --> 00:12:20,030
+فترة الاستحقاق معروفة، اللي هيصير بناء عليها تكرار
+
+125
+00:12:20,030 --> 00:12:26,620
+n، إن هي تمثل إيش؟ شهري؟ نص سنوي؟ سنوي؟ قديش؟ والـ R
+
+126
+00:12:26,620 --> 00:12:30,340
+لها قديش؟ نسبة زيادة؟ قديش؟ نسبة زيادة؟ فهي واحدة من
+
+127
+00:12:30,340 --> 00:12:33,580
+الأمثلة اللي قدرنا نحولها من recurrence relation لـ
+
+128
+00:12:33,580 --> 00:12:37,220
+general equation، function في مين؟ في n، نقدر نسبها
+
+129
+00:12:37,220 --> 00:12:42,180
+وجد ما بدنا، نقدر نسبها، وجد ما بدنا، كمان مثال تاني
+
+130
+00:12:42,180 --> 00:12:46,500
+مثال تاني، وبعرفش إذا كان موجود حتى كـ game موجود
+
+131
+00:12:46,500 --> 00:12:53,550
+يعني اللي هو الـ Tower of Hanoi example، برج Hanoi
+
+132
+00:12:53,550 --> 00:12:58,310
+برج Hanoi، مجموعة disks فوق بعض، مجموعة disks فوق
+
+133
+00:12:58,310 --> 00:13:02,970
+بعض، مطلوب منكم كلهم تنقلوهم على وتة تانية، أو على
+
+134
+00:13:02,970 --> 00:13:08,490
+وتة تانية، على وتة تانية، بدون.. بدون ما تيجي  كرتونة
+
+135
+00:13:08,490 --> 00:13:11,750
+كبيرة، أو بدون ما ييجي disk كبير على disk صغير أثناء
+
+136
+00:13:11,750 --> 00:13:15,830
+النقل، أثناء النقل مايكونش فيه disk صغير تحت disk
+
+137
+00:13:15,830 --> 00:13:22,030
+كبير، ومسموح لكم بـ one move each time، يعني كل مرة
+
+138
+00:13:22,030 --> 00:13:24,550
+بتكون تنقلوا، بنقولش اتنين اتنين، بنقول واحد واحد
+
+139
+00:13:24,550 --> 00:13:29,090
+وهي كل اللي عندكم طبعا الـ big two اللي بتكون تنقلوا
+
+140
+00:13:29,090 --> 00:13:35,790
+عليها، وعندكم spare واحد، واحد spare بس، كم move
+
+141
+00:13:35,790 --> 00:13:39,910
+محتاجين عشان ننقل كل الـ tower من big number one to
+
+142
+00:13:39,910 --> 00:13:44,990
+big number two أو big three، مش هتفرق، مش هتفرق كم
+
+143
+00:13:44,990 --> 00:13:52,390
+move محتاجين، كم move محتاجين، مبدأيا كيف أنتم
+
+144
+00:13:52,390 --> 00:13:55,510
+طبعا هتقعدوا تشتغلوا فيها، بدها عدد كبير، يعني هذه
+
+145
+00:13:55,510 --> 00:13:58,990
+على الأقل بدها واحد وثلاثين move، كويسة، بس كيف
+
+146
+00:13:58,990 --> 00:14:06,190
+نحسبهم، عدد الـ moves هذه، بنقول Hn، بمعنى الـ N
+
+147
+00:14:06,190 --> 00:14:11,190
+هنا، هي المقصود فيها عدد الـ disks، عدد الـ
+
+148
+00:14:11,190 --> 00:14:18,730
+disks اللي نريد أن ننقلها، لو قلنا الـ Hn هذول عدد
+
+149
+00:14:18,730 --> 00:14:23,870
+الـ moves اللي أنا محتاجهم عشان أنقل N disks هذول
+
+150
+00:14:23,870 --> 00:14:30,070
+إيش بيساووا فعليا؟ بيساووا اثنين في H n ناقص واحد
+
+151
+00:14:30,070 --> 00:14:39,250
+زائد واحد، بمعنى محتاجين ضعف نقل أربعة disks زائد
+
+152
+00:14:39,250 --> 00:14:44,350
+واحد، ليش؟ لحظة، لو فعلا بدنا ننقل أربعة disks
+
+153
+00:14:44,350 --> 00:14:49,410
+اللي هي بتصير H n ناقص واحد، مظبوط؟ لو فرضنا أنه
+
+154
+00:14:49,410 --> 00:14:51,990
+بدهم عشرة moves، بدهم عشرين moves، قديش ما يطلع، يطلع
+
+155
+00:14:52,720 --> 00:14:56,120
+عدد الـ moves المهم إن استخدمتهم، ونقلتهم هنا فعلا
+
+156
+00:14:56,120 --> 00:15:01,800
+نقلناهم هنا، صارت اسمها Hn-1 moves، بعدين أخدنا move
+
+157
+00:15:01,800 --> 00:15:08,200
+واحدة للأخيرة، ده نقلناها هنا، هاي الواحد، بعدين
+
+158
+00:15:08,200 --> 00:15:13,640
+رجعنا نفسهم من هنا نقلناهم هنا، طيب طب أنتم
+
+159
+00:15:13,640 --> 00:15:18,180
+ماحلناش إشي، احنا كنا بنقول Hn محتاجينها، وجدناها
+
+160
+00:15:18,180 --> 00:15:25,150
+صارت دلالة Hn-1-1، برضه بقدر أجيبها من إيش؟ ناقص
+
+161
+00:15:25,150 --> 00:15:30,750
+اثنين، لأن هي بنفس الشكل هتكون اثنين زائد واحد، لعند
+
+162
+00:15:30,750 --> 00:15:35,710
+ما نصل لإيش؟ صفر، أو طبعا هنا هيكون الـ zero تبعا
+
+163
+00:15:35,710 --> 00:15:39,910
+اللي هي disk واحد، كم move محتاج عشان أنقل disk
+
+164
+00:15:39,910 --> 00:15:45,660
+واحد؟ حركة واحدة، H واحد في النهاية بتساوي واحد، H1 في
+
+165
+00:15:45,660 --> 00:15:50,840
+النهاية هتساوي 1، فبنشتغلها وبنرجع رجوع فيها، و
+
+166
+00:15:50,840 --> 00:15:54,080
+بنقدر نحسبها، في الحالة دي، طيب، عشان نعمل الـ general
+
+167
+00:15:54,080 --> 00:15:58,440
+form أو الـ general equation بتاعتنا، هنشتغل بهذا الـ
+
+168
+00:15:58,440 --> 00:16:08,340
+sequence بالشكل هذا، فهنقول إن Hn هتساوي 2Hn-1 plus
+
+169
+00:16:08,340 --> 00:16:15,070
+1، وعرفنا ليش، عرفناها ليش؟ بنقول أربعة، قديش ما يطلع
+
+170
+00:16:15,070 --> 00:16:17,830
+عدد الـ moves، ساعتهم يطلع، أنا مش معنى، هلوجد، أحسبهم
+
+171
+
+223
+00:19:53,420 --> 00:19:56,260
+اشرح العنصر اللي ممكن يطلبه باعتبار أنه ممكن جدا
+
+224
+00:19:56,260 --> 00:20:01,440
+يعمل لنا example للبكتيريا وهذا example موجود في
+
+225
+00:20:01,440 --> 00:20:05,380
+الكتاب في أحد حلول الـ ... في الـ ... في الـ problem
+
+226
+00:20:05,380 --> 00:20:11,270
+sets في الآخر موجود إن والله عندكوا مش عارف بكتيريا
+
+227
+00:20:11,270 --> 00:20:15,530
+واحدة، خلية بكتيريا واحدة، بعد مش عارف سنة كم
+
+228
+00:20:15,530 --> 00:20:19,650
+خلية هتكون هو يعطيكوا معلومات إنك تعمل انقسام كل
+
+229
+00:20:19,650 --> 00:20:24,250
+جديش طيب هل بعد سنة طبعا جالكوا إنه بعد كل تلت
+
+230
+00:20:24,250 --> 00:20:29,270
+ساعات هتتكاثر يعني بتنقسم طب هل أبدأ أقعد أحسبها
+
+231
+00:20:29,270 --> 00:20:34,690
+لِعند ما أصل لسنة عشان أشوف الرقم  نوية طبعا مستحيل
+
+232
+00:20:34,690 --> 00:20:38,850
+حد يقعد يشتغل سنة يحسبها كل تلت ساعات تلت ساعات كم
+
+233
+00:20:38,850 --> 00:20:42,010
+مرة بتكون تعملوا recurrence relation للموضوع مش
+
+234
+00:20:42,010 --> 00:20:45,470
+بتصير بالشكل هذا فمحتاجين احنا نعمله معادلة
+
+235
+00:20:45,470 --> 00:20:48,510
+محتاجين نعمله معادلة كيف المعادلة هذه الـ logic هي
+
+236
+00:20:48,510 --> 00:20:52,530
+نتكلم عنها في الـ section الثاني من chapter 6 اللي
+
+237
+00:20:52,530 --> 00:20:56,210
+هو solving recurrences هذه هنشتغل على linear
+
+238
+00:20:56,210 --> 00:20:59,470
+homogeneous recurrence of degree k with constant
+
+239
+00:20:59,470 --> 00:21:02,310
+coefficients هنسميها k linear homogeneous
+
+240
+00:21:02,310 --> 00:21:07,480
+recurrence with constant coefficients على اعتبار أن
+
+241
+00:21:07,480 --> 00:21:10,640
+الـ K هذه الـ degree هذه هي عدد الـ elements اللي
+
+242
+00:21:10,640 --> 00:21:14,920
+أنا محتاجها عشان أجيب أي element زيادة بمعنى الـ
+
+243
+00:21:14,920 --> 00:21:22,020
+element N محتاج مدام K محتاج أجيبه K elements عشان
+
+244
+00:21:22,020 --> 00:21:28,620
+نحسبه فهو function في K elements جابله فهتلاقوا
+
+245
+00:21:28,620 --> 00:21:36,990
+coefficient معين في مين؟ في AN-1, N-2, N-3 to n-k
+
+246
+00:21:36,990 --> 00:21:41,830
+فأنا فعليا AN معتمد على k elements جابله فبنسميها
+
+247
+00:21:41,830 --> 00:21:48,410
+k degree الـ C ده طبعا هي الـ coefficients ثابتة هي
+
+248
+00:21:48,410 --> 00:21:51,590
+كده تكرارات كل عنصر لحاله كل عنصر من العناصر
+
+249
+00:21:51,590 --> 00:21:55,650
+السابقة لحاله كويسة وكلها لا تساوي صفر على أساس
+
+250
+00:21:55,650 --> 00:22:00,150
+أننا نتكلم عن k elements جابلة الحل هنا لازم
+
+251
+00:22:00,150 --> 00:22:04,570
+يكون uniquely determined if k initial conditions
+
+252
+00:22:04,570 --> 00:22:11,810
+are found بمعنى أو are provided أي node موجودة أي
+
+253
+00:22:11,810 --> 00:22:16,030
+واحد موجودة to أي k minus one يكون معطيني إياهم
+
+254
+00:22:16,030 --> 00:22:22,220
+كقيم فالـ sequence اللي احنا توه كتبناها مبدأيا عشان
+
+255
+00:22:22,220 --> 00:22:24,780
+أنا أحدد الـ sequence وأعرف كل الـ elements  ثابتة
+
+256
+00:22:24,780 --> 00:22:28,680
+لازم نحدد على الأقل أول three elements منهم أول
+
+257
+00:22:28,680 --> 00:22:31,280
+three elements أو two elements k elements in
+
+258
+00:22:31,280 --> 00:22:36,260
+general هنقول k elements أعطاني إياهم واحد تلاتة خمسة
+
+259
+00:22:36,260 --> 00:22:42,160
+نفترض سبعة وبعدين بيعمل هيك خلاص بس هنا حدد ليها
+
+260
+00:22:42,160 --> 00:22:48,200
+إن هي الـ k بأربعة k بأربعة في عندي A node A واحد
+
+261
+00:22:48,200 --> 00:22:52,200
+اتنين تلاتة في عندي أربعة elements منهم المفروض
+
+262
+00:22:52,200 --> 00:22:55,040
+يطلب مني يقول لي والله هات لي الـ element في الـ
+
+263
+00:22:55,040 --> 00:23:01,140
+location مية مثلا بدنا نعرفه بالظبط بدنا نعرفه
+
+264
+00:23:01,140 --> 00:23:03,800
+طبعا احنا ممكن نشتغل بهذا الشكل نقعد نقول اه والله
+
+265
+00:23:03,800 --> 00:23:06,740
+هذا شكله واضح إنه الأرقام الفردية لأ واضح شكل
+
+266
+00:23:06,740 --> 00:23:09,460
+الأرقام مش عارف إيش شكل الأرقام وبنبدأ نكمل عليها
+
+267
+00:23:09,460 --> 00:23:16,030
+طب هاي عنصر رقم هنا a node هنا E3 أو E4 أو E9 أو E5
+
+268
+00:23:16,030 --> 00:23:19,950
+أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو
+
+269
+00:23:19,950 --> 00:23:22,730
+E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9
+
+270
+00:23:22,730 --> 00:23:23,910
+أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو
+
+271
+00:23:23,910 --> 00:23:35,770
+E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9 أو E9
+
+272
+00:23:35,770 --> 00:23:41,550
+أو E9
+
+273
+00:23:42,290 --> 00:23:46,130
+هدول بيحلهم كالتالي إن أنا بدي أحولها الـ a إن هي دي
+
+274
+00:23:46,130 --> 00:23:51,280
+كـ function في مين في n لحالها عن طريق الـ roots الـ
+
+275
+00:23:51,280 --> 00:23:54,500
+roots هذه بدنا نحسبها طبعا هنضطر بدنا نحسبها بدنا
+
+276
+00:23:54,500 --> 00:23:59,920
+نشتغل عليها فـ relation فعليا للـ k degree هتكون R
+
+277
+00:23:59,920 --> 00:24:03,000
+to the power N هذه اللي أنا بدي أحصل عليها لازم
+
+278
+00:24:03,000 --> 00:24:06,040
+تكون function في مين في الـ coefficient الأول هو هو
+
+279
+00:24:06,040 --> 00:24:10,120
+بس هتصير في R to the power N minus one هذه كانت A
+
+280
+00:24:10,120 --> 00:24:15,700
+N minus one هتصير R to the power N minus one هنا
+
+281
+00:24:15,700 --> 00:24:24,550
+كانت AN-K هتصير Rⁿ-K هذه بنسميها الـ form هذا الجديد
+
+282
+00:24:24,550 --> 00:24:27,330
+بنسميه characteristic equation characteristic
+
+283
+00:24:27,330 --> 00:24:31,950
+equation للـ recurrence للـ recurrence relation كويس
+
+284
+00:24:31,950 --> 00:24:36,210
+من الـ function هذه لو كل الـ terms هدول أخدتهم عن
+
+285
+00:24:36,210 --> 00:24:40,280
+ناحية ثانية و equal to zero صارت المعادلة هتصير
+
+286
+00:24:40,280 --> 00:24:44,800
+equal to zero طيب، لاحظوا أن كلهم مشتركين في R R R
+
+287
+00:24:44,800 --> 00:24:45,340
+R
+
+288
+00:24:45,340 --> 00:25:03,060
+ررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررر
+
+289
+00:25:06,010 --> 00:25:09,750
+هي نزلت الـ coefficient بس نزلت طبعا راحت على ناحية
+
+290
+00:25:09,750 --> 00:25:12,510
+ثانية بالسالب وهذه كلها terms هتروح بالسالب
+
+291
+00:25:12,510 --> 00:25:18,330
+فهتنتج معاكوا r to the power k على اعتبار أنتم
+
+292
+00:25:18,330 --> 00:25:23,350
+قسمتوها على r n minus k فكل اللي بعمله بِطرح الـ
+
+293
+00:25:23,350 --> 00:25:32,070
+powers فصارت n minus n minus k صارت مين؟ الـ K فـ R
+
+294
+00:25:32,070 --> 00:25:36,830
+to the power of K minus C1 to the power of K minus
+
+295
+00:25:36,830 --> 00:25:42,890
+1 C2 to the power of K minus 2 لما نصل لـ CK to the
+
+296
+00:25:42,890 --> 00:25:47,690
+power .. فـ R to the power of 0 اللي هي واحد equal
+
+297
+00:25:47,690 --> 00:25:50,290
+to zero صارت هذي كل الطريقة في الشغل اللي
+
+298
+00:25:50,290 --> 00:25:53,210
+محتاجينها إن احنا نحل الـ characteristic equation
+
+299
+00:25:53,210 --> 00:25:57,050
+إننا نجيب الـ roots بتاعتنا أو الـ characteristic
+
+300
+00:25:57,050 --> 00:25:59,330
+roots بدنا نجيب الـ characteristic
+
+301
+00:26:02,280 --> 00:26:08,540
+على حسب الـ degree بتاعتكم بيبين الـ order للـ
+
+302
+00:26:08,540 --> 00:26:15,320
+equation فواضح إن الـ order هنا k إذا والله بنقدر
+
+303
+00:26:15,320 --> 00:26:19,060
+نحل order k خلاص انحلت للتبسيط هنشتغل في المصادق
+
+304
+00:26:19,060 --> 00:26:24,160
+تبعنا على جد بس اتنين على جد degree اتنين أساس إنه
+
+305
+00:26:24,160 --> 00:26:27,120
+هي بتصير quadratic هو عشان نقدر نجيب لها الـ roots
+
+306
+00:26:27,120 --> 00:26:31,220
+متذكرين لسه قانون تبع الـ roots للـ quadratic form
+
+307
+00:26:31,220 --> 00:26:37,020
+أو للـ quadratic equation؟ كويس فهنشتغل في المصادق
+
+308
+00:26:37,020 --> 00:26:40,360
+تبعنا كبداية إن والله خلاص عرفنا الفكرة بعدين
+
+309
+00:26:40,360 --> 00:26:43,740
+بيصير والله لو في techniques تحللنا أكثر degree
+
+310
+00:26:43,740 --> 00:26:47,920
+أكبر من الاثنين okay لاحقا ممكن تشتغلوا عليها في
+
+311
+00:26:47,920 --> 00:26:51,360
+مصادقنا هنشتغل على solving two degree للـ linear
+
+312
+00:26:51,360 --> 00:26:55,640
+homogeneous recurrence of constant coefficients أو
+
+313
+00:26:55,640 --> 00:27:00,180
+with constant coefficients تمام فهتصير a n عبارة
+
+314
+00:27:00,180 --> 00:27:04,850
+عن two terms فقط عشان تكون two degree معتمدة على الـ
+
+315
+00:27:04,850 --> 00:27:08,530
+two terms قبلها فقط، مش تلاتة، تلاتة هتتحول لـ
+
+316
+00:27:08,530 --> 00:27:13,570
+three degree فنتكلم عن two terms سابقين فالـ two
+
+317
+00:27:13,570 --> 00:27:16,930
+terms automatically، مدام أنا بتكلم عن اثنين، الـ A
+
+318
+00:27:16,930 --> 00:27:20,750
+هذي بتتحول لـ R to the power اثنين، مدام هي degree
+
+319
+00:27:20,750 --> 00:27:23,830
+اثنين اصلا، أنا بتكلم عن degree اثنين، كيف أعرف أن
+
+320
+00:27:23,830 --> 00:27:27,690
+هي degree اثنين؟ إن هو معتمد على two elements
+
+321
+00:27:27,690 --> 00:27:30,750
+سابقين على two elements سابقين فبعرف إيه R to the
+
+322
+00:27:30,750 --> 00:27:33,690
+power 2 كويس الـ C هذه هتروح الناحية الثانية
+
+323
+00:27:33,690 --> 00:27:40,610
+بالسالب فصارت الـ C سالب C 1 في R طيب هذه برضه
+
+324
+00:27:40,610 --> 00:27:46,190
+هتروح الناحية الثانية تصير سالب C 2 في R to the
+
+325
+00:27:46,190 --> 00:27:46,630
+power 0
+
+326
+00:27:50,290 --> 00:27:54,190
+هذا كله equal to zero فصارت معادلة quadratic
+
+327
+00:27:54,190 --> 00:27:56,770
+equation أو الـ characteristic equation بتاعتنا
+
+328
+00:27:56,770 --> 00:28:01,290
+صارت من الدرجة الثانية نقدر نشتغلها لو متذكرين
+
+329
+00:28:01,290 --> 00:28:02,090
+قانونكوا
+
+330
+00:28:11,720 --> 00:28:15,700
+R تربيع R تربيع اه من الفهمة يعني عشان أنا معتمد
+
+331
+00:28:15,700 --> 00:28:18,140
+على عنصرين تربيعين بالظبط على عنصرين معناه إن أنا
+
+332
+00:28:18,140 --> 00:28:21,500
+بتكلم عن two degree two degree خلاص automatically
+
+333
+00:28:21,500 --> 00:28:29,500
+بتصير R to the power اثنين كويس هذه بدنا نجيب الـ
+
+334
+00:28:29,500 --> 00:28:33,480
+roots بتاعتنا فمن القانون جبناهم الـ roots طيب برضه
+
+335
+00:28:33,480 --> 00:28:35,900
+احنا كل اللي عملناه إننا جبنا roots أنا بدي
+
+336
+00:28:35,900 --> 00:28:40,080
+معادلة بدي معادلة في النهاية القصر تكون عبارة عن a
+
+337
+00:28:40,080 --> 00:28:46,620
+n تساوي function في n أنا هي اللي بدي إياها طب أنت
+
+338
+00:28:46,620 --> 00:28:51,400
+جيبت لي r الشيء r هذه معناته محتاجين theorem محتاجين
+
+339
+00:28:51,400 --> 00:28:55,440
+theorem  تربط لنا كيف أقدر أجيب الـ an من الـ roots
+
+340
+00:28:55,440 --> 00:28:57,280
+اللي أنا جبتها للمعادلة من الـ roots اللي احنا
+
+341
+00:28:57,280 --> 00:29:00,320
+جبناها ففي theorem أولى وفي theorem ثانية الـ
+
+342
+00:29:00,320 --> 00:29:03,440
+theorem الأولى الفرق بينهم بس إنه لو الـ roots
+
+343
+00:29:03,440 --> 00:29:07,200
+متشابهة أو لو الـ roots مختلفة لا أكثر ولا أقل أنت
+
+344
+00:29:07,200 --> 00:29:11,020
+بتكون متشابهة الـ roots إذا كان الحد المميز هذا
+
+345
+00:29:11,020 --> 00:29:15,540
+equal to zero إذا كان والله equal to zero معناته
+
+346
+00:29:15,540 --> 00:29:18,460
+مش هتفرج موجبة بسالب في الآخر هيطلع نفس الـ root
+
+347
+00:29:18,460 --> 00:29:23,100
+هيطلع نفس الـ root okay إِلّا قيمة واضحة إنها هيطلع في
+
+348
+00:29:23,100 --> 00:29:26,220
+إنكوا two roots different two roots different two
+
+349
+00:29:26,220 --> 00:29:30,620
+roots okay هنبدأ بالـ theorem الأولى والله إذا كان
+
+350
+00:29:30,620 --> 00:29:33,580
+الـ characteristic equation has two roots وبيساويوش
+
+351
+00:29:33,580 --> 00:29:36,500
+بعض بنِشتغل على القانون التالي إن الـ a n
+
+352
+00:29:36,500 --> 00:29:40,200
+هيربط لنا إياها يربط لنا الـ roots اللي احنا هنجيبها كيف
+
+353
+00:29:40,200 --> 00:29:46,420
+نحطها في form للـ an الآن هتساوي الـ root الأولى to
+
+354
+00:29:46,420 --> 00:29:50,380
+the power n والـ root الثانية to the power n برضه n
+
+355
+00:29:50,380 --> 00:29:54,180
+في n هي كلها n بس الأولى محتاجين نضربها في
+
+356
+00:29:54,180 --> 00:29:57,160
+constant معين والثانية في constant معين ألف واحد
+
+357
+00:29:57,160 --> 00:30:01,940
+ألف اثنين تمام طب ما أنت دخلتني في ألف واحد و
+
+358
+00:30:01,940 --> 00:30:07,540
+ألف اثنين بدنا إياهم Constants هدول Constants بدنا
+
+359
+00:30:07,540 --> 00:30:14,270
+نجيب قيمهم لأ هم هدول أنت جيبت الـ root الأولى في
+
+360
+00:30:14,270 --> 00:30:17,550
+n أنا مش ضامن قد ايش المفروض يتكرر الـ root الأولى
+
+361
+00:30:17,550 --> 00:30:20,950
+ثلاث مرات مرتين خمس مرات عشر مرات عشان نجيب الـ an
+
+362
+00:30:20,950 --> 00:30:25,270
+ولا قد ايش فحاطط ضرب في constant هنا اللي هو المفروض
+
+363
+00:30:25,270 --> 00:30:29,090
+عدد تكرارات الـ root عدد تكرارات الـ root كويسة
+
+364
+00:30:29,090 --> 00:30:32,750
+الاثنين هدول القيمتين هدول ما فيش أسهل من إيجابتهم
+
+365
+00:30:32,750 --> 00:30:37,950
+ليش؟ كيف نجيبهم؟ نجيبهم من الـ initial values اللي
+
+366
+00:30:37,950 --> 00:30:42,310
+معطيني إياهم تأكدوا .. sequence بدون initial values
+
+367
+00:30:42,310 --> 00:30:44,390
+ما فيش حاجة اسمها sequence بدون initial values
+
+368
+00:30:44,390 --> 00:30:48,590
+فطبيعي .. منطقي جدا إنه لازم يكون فيه على الأقل في
+
+369
+00:30:48,590 --> 00:30:52,170
+.. مدام بتكلم عن second يعني في two degree لازم
+
+370
+00:30:52,170 --> 00:30:54,430
+يكون في عندكوا على الأقل في two elements موجودين
+
+371
+00:30:54,430 --> 00:30:59,110
+اللي هم a node و a واحد لازم يكونوا موجودين هدول
+
+372
+00:30:59,110 --> 00:31:05,070
+.. ضروري كويس .. مدام موجودين عوضوا مرة بـ a node و
+
+373
+00:31:05,070 --> 00:31:08,150
+مرة بـ a واحد فصار إنكم معادلتين وهم two variables
+
+374
+00:31:08,150 --> 00:31:12,470
+بنجيبهم فبتصير الأمور سهلة بيصير بالعكس سهلة جدا
+
+375
+00:31:12,470 --> 00:31:21,040
+كمان سهلة جدا تمام مثال بيربط إن كل الـ .. المعلومات
+
+376
+00:31:21,040 --> 00:31:24,720
+وبنشوف بالظبط الـ sequence للحل كيف بتتم طبعا الـ
+
+377
+00:31:24,720 --> 00:31:27,480
+sequence بسيط جدا ما فيش مشكلة لو افترضنا sort the
+
+378
+00:31:27,480 --> 00:31:33,620
+recurrence a n تساوي a n minus one plus two a n
+
+379
+00:31:33,620 --> 00:31:37,180
+minus two فهي عندنا الـ coefficients بتاعتنا c1
+
+380
+00:31:37,180 --> 00:31:43,000
+بتساوي واحد و c2 بتساوي اثنين c1 واحد و c2 اثنين و
+
+381
+00:31:43,000 --> 00:31:47,500
+اثنين okay وبيعطينا هو two initial values اثنين و
+
+382
+00:31:47,500 --> 00:31:50,940
+سبعة اثنين وسبعة وهذول برضه هنحتاجهم في الآخر
+
+383
+00:31:50,940 --> 00:31:52,920
+نعوض عشان نجيب alpha واحد و alpha اثنين بس
+
+384
+00:31:52,920 --> 00:31:56,320
+هنحتاجهم في alpha واحد okay مدام عندي c واحد و c
+
+385
+00:31:56,320 --> 00:32:00,060
+اثنين أعطاني إياهم automatically وأنا عارف إن هي
+
+386
+00:32:00,060 --> 00:32:04,380
+اثنين معتمدة على two terms فـ automatically R تربيع
+
+387
+00:32:04,380 --> 00:32:11,180
+ناقص c واحد خلاص هي c واحد في R ناقص اثنين
+
+388
+00:32:40,360 --> 00:32:41,760
+C2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2
+
+389
+00:32:42,810 --> 00:32:51,550
+alpha اثنين في الـ root الثانية to the power المعادلة
+
+390
+00:32:51,550 --> 00:32:55,730
+هذه بدنا نج
+
+445
+00:37:30,590 --> 00:37:34,230
+ناقص 36، وواضح أن هذه صفر، يعني كل الحل هيكون
+
+446
+00:37:34,230 --> 00:37:41,200
+عندكوا minus b over 2a - b over 2a فهيطلع تلاتة
+
+447
+00:37:41,200 --> 00:37:44,220
+هيطلع عندكوا تلاتة automatically، مدام تلاتة صارت
+
+448
+00:37:44,220 --> 00:37:51,560
+الـ A<sub>n</sub> إيش بتساوي؟ Alpha واحد في تلاتة to the power
+
+449
+00:37:51,560 --> 00:38:02,260
+N زائد Alpha تنين في N تلاتة to the power N، عوضه
+
+450
+00:38:02,260 --> 00:38:07,040
+في Alpha في A صفر و A واحد، عوضه مرة هنا و مرة هنا
+
+451
+00:38:07,400 --> 00:38:16,540
+فـ A صفر تساوي A واحد بجداش تلاتة  ضرب صفر
+
+452
+00:38:16,540 --> 00:38:24,020
+واحد خلاص زائد A زيرو، كلها راحت، كله راحت، فإذا
+
+453
+00:38:24,020 --> 00:38:27,880
+هذا الماتريكس اللي هي طلعت لحالة بتساوي جداش كانت الـ
+
+454
+00:38:27,880 --> 00:38:32,260
+A واحد هنا واحد واحد، فعندكوا الـ A واحد بتساوي واحد
+
+455
+00:38:32,260 --> 00:38:36,890
+هي أول معادلة طلعتوها، بتعودوا في الثانية عشان تجيبوا
+
+456
+00:38:36,890 --> 00:38:44,010
+alpha 2، فـ A<sub>1</sub> تساوي alpha 1 بـ 1، وهنا to the power 1
+
+457
+00:38:44,010 --> 00:38:51,790
+بتساوي 3 زائد alpha 2 في 1 لأن بـ 1، تلاتة في تلاتة
+
+458
+00:38:51,790 --> 00:38:58,330
+هذا بيساوي 6، هذا في الحلقة بيساوي 6 automatically
+
+459
+00:38:58,330 --> 00:39:01,400
+ليه؟ هذه هتروح الناحية الثانية اللي هي الستة يعني
+
+460
+00:39:01,400 --> 00:39:05,500
+قيمة ستة، هيطلع تلاتة، بتساوي alpha اتنين في تلاتة
+
+461
+00:39:05,500 --> 00:39:08,580
+واحد
+
+462
+00:39:08,580 --> 00:39:12,680
+خلاص، وين المعادلة؟ هي المعادلة الأصلية، كنا نعوض
+
+463
+00:39:12,680 --> 00:39:21,740
+فيها، نشتغل عليها، أصبحت واحد واحد، خلاص هي المعادلة
+
+464
+00:39:21,740 --> 00:39:28,670
+بس اللي هي آخر معادلة، نقرّر آخر معادلة موجودة لدينا
+
+465
+00:39:28,670 --> 00:39:35,630
+Okay، هذا كان الجزء اللي ضايل، وخليني أقول أن هذا
+
+466
+00:39:35,630 --> 00:39:39,550
+جزء مهم، يعني عادة الجزئية الأخيرة هي جزئية مهمة
+
+467
+00:39:39,550 --> 00:39:44,250
+جزئية مهمة
+
+468
+00:39:44,250 --> 00:39:49,310
+طيب، مدام إحنا بنتكلم في الـ recurrence relation
+
+469
+00:39:49,310 --> 00:39:53,780
+خليني أكمل في جزئية كلمة relation بتاعتنا، في كلمة
+
+470
+00:39:53,780 --> 00:39:57,140
+relation، ونشوف إيش يعني relation أصلاً، نعمّم هذه الـ
+
+471
+00:39:57,140 --> 00:39:59,840
+logic، قاعدين نتكلم من بدلي على recurrence relation
+
+472
+00:39:59,840 --> 00:40:04,240
+relation، relation، إيش يعني relation؟ فهندخل هذه الـ
+
+473
+00:40:04,240 --> 00:40:07,380
+logic، فيه شوية في جزئية إيش يعني relation أو إيش
+
+474
+00:40:07,380 --> 00:40:10,980
+شوية الـ relations فعلياً، شوية الـ relations فعلياً
+
+475
+00:40:10,980 --> 00:40:15,160
+فعلياً الـ relations هي فعلياً علاقة بين مجموعة
+
+476
+00:40:15,160 --> 00:40:20,020
+elements موجودين لست A مع مجموعة elements موجودين
+
+477
+00:40:20,020 --> 00:40:26,810
+لست B، بحيث أن العلاقة دي هتكون ثنائية، وهنحدد
+
+478
+00:40:26,810 --> 00:40:30,250
+تلوجية كل شغلنا هيكون عبارة عن binary relation
+
+479
+00:40:30,250 --> 00:40:34,870
+بمعنى عندنا two sets، الـ two sets هدول في relation
+
+480
+00:40:34,870 --> 00:40:38,190
+بين element في الـ set الأولى مع element في الـ set
+
+481
+00:40:38,190 --> 00:40:42,330
+الثانية، فهذا ثنائي، ثنائي على اعتبار أنه هيكون كأنه
+
+482
+00:40:42,330 --> 00:40:47,390
+عندكوا زوج مرتب، الأول جزء الأول منه من set A، وجزء
+
+483
+00:40:47,390 --> 00:40:52,690
+ثاني من set B، فهذا بنسميه binary، عشان هيك بنسميه
+
+484
+00:40:52,690 --> 00:40:57,090
+binary، okay
+
+485
+00:40:59,190 --> 00:41:03,890
+الـ relation from A to B، وهنا فوق إحنا محددين أن
+
+486
+00:41:03,890 --> 00:41:07,130
+الـ A والـ B دول مجموعة، two sets، عبارة عن set، set
+
+487
+00:41:07,130 --> 00:41:10,490
+يعني فيها إيش؟ مجموعة elements، فيها عناصر، العناصر
+
+488
+00:41:10,490 --> 00:41:13,490
+هذه ممكن تكون objects، ممكن تكون numbers، ممكن
+
+489
+00:41:13,490 --> 00:41:15,930
+تكون يا هيك يا هيك، ما تفرقش، معناه المهم إنه في
+
+490
+00:41:15,930 --> 00:41:19,890
+relation from A to B، هذه هتكون عبارة الـ relation
+
+491
+00:41:19,890 --> 00:41:22,610
+نفسها أو الـ elements اللي هتحقق الـ relation اللي
+
+492
+00:41:22,610 --> 00:41:27,470
+هنعرفها، هتكون عبارة عن subset، subset من، من كل
+
+493
+00:41:27,470 --> 00:41:32,460
+العناصر الممكنة بين A و B، طب إيش كل العناصر الممكنة
+
+494
+00:41:32,460 --> 00:41:40,620
+من A لـ B؟ هي الـ Cartesian product، بمعنى لو عندكوا A
+
+495
+00:41:40,620 --> 00:41:51,020
+فرضاً واحد، اتنين، وثلاثة، وعندكوا B بتساوي A و B، الـ
+
+496
+00:41:51,020 --> 00:41:54,360
+relations الممكنة، كل الـ relations الممكنة فعلياً
+
+497
+00:41:54,360 --> 00:42:01,380
+بين elements من A مع element من B، هيبقى بغض النظر إيش
+
+498
+00:42:01,380 --> 00:42:03,360
+الـ relation، طبعاً هي logic، لما نعرف الـ relation
+
+499
+00:42:03,360 --> 00:42:07,000
+ممكن يا بتقبل بعضهم يا بترفض بعضهم، يعني مش
+
+500
+00:42:07,000 --> 00:42:09,980
+بالضرورة كلهم، بس الـ relation هذه حسب تعريفنا للـ
+
+501
+00:42:09,980 --> 00:42:16,460
+relation لاحقاً، هذه ممكن تكون واحد و A، تمام، وواحد
+
+502
+00:42:16,460 --> 00:42:23,880
+و B، ممكن تكون اتنين و A، ممكن تكون اتنين و B، تلاتة
+
+503
+00:42:23,880 --> 00:42:32,270
+A، تلاتة B، فيش إمكانية غير هدول، فهدول بالنسبة لنا هم
+
+504
+00:42:32,270 --> 00:42:35,730
+الـ universe of discourse، هدول كل الاحتمالات
+
+505
+00:42:35,730 --> 00:42:40,850
+الممكنة، هدول كل الـ relations اللي ممكن تكون موجودة
+
+506
+00:42:40,850 --> 00:42:45,560
+بين element في A مع element في B، هذا الكل، طب هذا
+
+507
+00:42:45,560 --> 00:42:50,600
+إيش يمثل فعلاً؟ يمثل Cartesian product between A و B
+
+508
+00:42:50,600 --> 00:42:56,120
+فهي فعلاً A Cartesian product B، فإذا أي relation
+
+509
+00:42:56,120 --> 00:43:03,120
+لاحقاً هنتكلم عنها، هي هتكون عبارة عن subset من الـ
+
+510
+00:43:03,120 --> 00:43:06,060
+Cartesian product، من الـ Cartesian product، لأنه لا
+
+511
+00:43:06,060 --> 00:43:08,560
+يمكن أن تكون أكبر منها، لا يمكن أن تكون أكبر منها
+
+512
+00:43:08,560 --> 00:43:12,500
+ليه؟ ما فيش أي عنصر غير هدول أساساً، لا يمكن يكون أي
+
+513
+00:43:12,500 --> 00:43:17,060
+عنصر من هدول يعمل relation element من A مع element
+
+514
+00:43:17,060 --> 00:43:20,880
+من B، ما فيش .. هاي كل الاحتمالات الممكنة، هاي كل الـ
+
+515
+00:43:20,880 --> 00:43:24,840
+relations الممكنة، ففي الحالة هذه أي relation from
+
+516
+00:43:24,840 --> 00:43:28,920
+A to B هتكون subset من الـ Cartesian product
+
+517
+00:43:28,920 --> 00:43:33,320
+between A و B، for example، ناخد example، الـ relation
+
+518
+00:43:33,320 --> 00:43:38,520
+أصغر منه، less than، أصغر من، هذه from natural number
+
+519
+00:43:38,520 --> 00:43:41,700
+to natural number، هيحدد لي الـ a natural number
+
+520
+00:43:41,700 --> 00:43:45,140
+وحدد لي الـ b natural number، طيب الـ relation هذه
+
+521
+00:43:45,140 --> 00:43:49,320
+إيش؟ عبارة عن إيش؟ عبارة عن زوج مرتب، هاي الـ n والـ
+
+522
+00:43:49,320 --> 00:43:54,160
+m، بشرط إن الـ n لازم تكون أصغر من إيش؟ من m، الـ n
+
+523
+00:43:54,160 --> 00:43:58,500
+أصغر من الـ m، فكأنه الأصغر من هذا هي الـ relation
+
+524
+00:43:58,500 --> 00:44:02,720
+أصغر من، هاي الـ relation هذه هي الـ relation بتاعتنا
+
+525
+00:44:02,720 --> 00:44:07,850
+كويس، بدايةً طبعاً ناخد بالنا أن مدام relation يعني
+
+526
+00:44:07,850 --> 00:44:12,770
+هي related to شغلة، related to شغلة ثانية يعني
+
+527
+00:44:12,770 --> 00:44:19,050
+دايماً في reference، لما نقول مثلاً خمسة أكبر من
+
+528
+00:44:19,050 --> 00:44:22,950
+اتنين، فبالنسبة للخمسة الـ reference هي الاتنين، هي
+
+529
+00:44:22,950 --> 00:44:26,730
+الاتنين، لأن related للاتنين، الخمسة أكبر، فصار الـ
+
+530
+00:44:26,730 --> 00:44:31,410
+relation بتاعتنا أكبر منه، هنا نتكلم عن أصغر من، الـ
+
+531
+00:44:31,410 --> 00:44:38,220
+N هذه أصغر من الـ M، الـ N أصغر من الـ M، على اعتبار أن
+
+532
+00:44:38,220 --> 00:44:41,300
+الـ relation هنا أصغر من، الـ relation هنا عندنا أصغر
+
+533
+00:44:41,300 --> 00:44:48,880
+من، فهذه معناها أن A و B كزوج مرتب belong to set
+
+534
+00:44:48,880 --> 00:44:53,700
+جديدة، اللي هي الـ subset من كلهم، الـ set هذه عبارة
+
+535
+00:44:53,700 --> 00:44:59,800
+عن أصغر من، عبارة عن أصغر من، لو غيرنا هنا وحطيناها
+
+536
+00:44:59,800 --> 00:45:09,780
+أرقام برضه، نشوف الأصغر من إيش بتطلع معنا، قلنا
+
+537
+00:45:09,780 --> 00:45:16,880
+واحد واثنين مثلاً، طيب
+
+538
+00:45:16,880 --> 00:45:19,640
+هذه مش الـ relation، هذه هيك صارت، هذه كل الـ universe
+
+539
+00:45:19,640 --> 00:45:22,080
+of discourse، هذه الـ Cartesian product، هذه الـ
+
+540
+00:45:22,080 --> 00:45:26,500
+Cartesian product بتاعتنا كلها، طيب أصغر من هتكون
+
+541
+00:45:26,500 --> 00:45:27,500
+إيش بتساوي منهم؟
+
+542
+00:45:37,320 --> 00:45:42,100
+خلاص هو عنصر واحد، عنصر واحد فيه، مش غيره، ليه؟ وجد
+
+543
+00:45:42,100 --> 00:45:47,720
+غيره، فإذا لحظة الواحد واثنين هي subset من، من الـ
+
+544
+00:45:47,720 --> 00:45:50,440
+Cartesian product، هي فعلاً subset من الـ Cartesian
+
+545
+00:45:50,440 --> 00:45:55,280
+product، في الحالة اللي عندنا، طيب فإذا عنصر واحد
+
+546
+00:45:55,280 --> 00:45:59,320
+واثنين belong to relation أصغر من، هي الـ relation
+
+547
+00:45:59,320 --> 00:46:03,100
+أصغر من، العنصر الوحيد اللي belong إلها هو الواحد
+
+548
+00:46:03,100 --> 00:46:06,480
+واثنين، ففي الحالة هذه الزوج واحد واثنين ينتمي
+
+549
+00:46:06,480 --> 00:46:10,700
+لأصغر من، relation، okay، يبدو،  كتابة a
+
+550
+00:46:10,700 --> 00:46:17,480
+relation b، أو a is related to b، أو a، أو by related
+
+551
+00:46:17,480 --> 00:46:23,360
+to r، أو under relation r، التسمية مش هتفرق كتير،
+
+552
+00:46:23,360 --> 00:46:26,700
+بتقدر تسموها هيك أو هيك، related to relation r، أو
+
+553
+00:46:26,700 --> 00:46:31,480
+under relation r، كلها في النهاية إن الـ A بالنسبة
+
+554
+00:46:31,480 --> 00:46:35,440
+لـ B، هل حقق الـ relation أو لأ، حقق الـ relation أو
+
+555
+00:46:35,440 --> 00:46:36,420
+محققش
+
+556
+00:46:39,120 --> 00:46:44,360
+الـ R مش .. الـ Cartesian product مش علاقة، معناه هي
+
+557
+00:46:44,360 --> 00:46:47,060
+subset، يعني فيه .. لأ، أنا ما قلتش مش علاقة، أنا
+
+558
+00:46:47,060 --> 00:46:50,520
+بقول الأصغر من مش .. مش هتمثل العلاقة، أنا هنا
+
+559
+00:46:50,520 --> 00:46:53,600
+لأني بدأت أتكلم عن أصغر من، فقلت لكوا لأ هذه مش هي
+
+560
+00:46:53,600 --> 00:46:56,780
+الـ relation بتاعتنا، قلت لكوا لأ مش هذه العلاقة
+
+561
+00:46:56,780 --> 00:46:59,560
+اللي إحنا بنشتغل عليها، صرنا بنشتغل على أصغر من،
+
+562
+00:46:59,560 --> 00:47:03,920
+فصارت subset من الـ Cartesian product، ممكن يكون في
+
+563
+00:47:03,920 --> 00:47:09,100
+relation، نعمل relation تشمل الكل، ممكن نعمل relation
+
+564
+00:47:09,100 --> 00:47:15,120
+تشمل الكل، لو قلنا مثلاً الـ relation بتاعتنا أنه الـ
+
+565
+00:47:15,120 --> 00:47:21,360
+.. كل الأرقام اللي مجموعها خمسة أو أقل، كله .. هي
+
+566
+00:47:21,360 --> 00:47:24,460
+دخلت كلها الـ Cartesian product، صح؟ خمسة أو أقل
+
+567
+00:47:24,460 --> 00:47:30,740
+مجموع A زائد B أكبر .. أصغر من أو أقل من خمسة، أصغر
+
+568
+00:47:30,740 --> 00:47:33,520
+من أو يساوي خمسة، فمعنى ذلك أخدناها كلها الـ
+
+569
+00:47:33,520 --> 00:47:36,780
+relation، بس لأن أنا بدأت حددت الأصغر من .. قلت لكوا
+
+570
+00:47:36,780 --> 00:47:39,760
+لأ ديروا بالكوا، بطلنا نحكي عن الـ relation أصغر من
+
+571
+00:47:39,760 --> 00:47:43,660
+هنا، أو بطلنا نتكلم in general، لأ هي صارت relation
+
+572
+00:47:43,660 --> 00:47:46,840
+ثانية، كتبناها، وقلت لكوا ده هي subset من كله، بس لأ
+
+573
+00:47:46,840 --> 00:47:49,780
+ممكن تكون هي كلها على بعض relation حسب التعريف للـ
+
+574
+00:47:49,780 --> 00:47:55,270
+relation، okay، let relation from A to B، R binary
+
+575
+00:47:55,270 --> 00:47:58,590
+relation، معناته إن إحنا بنتكلم عن two sets، الأول
+
+576
+00:47:58,590 --> 00:48:03,310
+relation مع الثاني، الـ complementary relations أو
+
+577
+00:48:03,310 --> 00:48:08,990
+الـ complement of R، هنسميه R slash، اللي هي الـ R مع
+
+578
+00:48:08,990 --> 00:48:12,910
+الـ slash هذه ليست relation، بمعنى إنه ليست الـ
+
+579
+00:48:12,910 --> 00:48:18,350
+relation، relation، أو الـ inverse، الـ complement لأن
+
+580
+00:48:18,350 --> 00:48:23,940
+الـ inverse مختلفة، الـ complement R from A to B عبارة
+
+581
+00:48:23,940 --> 00:48:29,060
+عن إيش؟ the complement of R هي المكملة لـ R، على
+
+582
+00:48:29,060 --> 00:48:32,060
+اعتبار مدام مكملة، يعني معناته في عندي universe of
+
+583
+00:48:32,060 --> 00:48:35,040
+discourse، طب أنا فعلاً عندي universe of discourse
+
+584
+00:48:35,040 --> 00:48:37,980
+إيش هو الـ universe of discourse طبعاً؟ الـ Cartesian
+
+585
+00:48:37,980 --> 00:48:45,540
+الـ Cartesian، فهي دي مثلاً، هيها الأصغر من واحد و
+
+586
+00:48:45,540 --> 00:48:49,660
+اتنين، طب المكمل بتاعتها، بشطب واحد واثنين، والباقي
+
+587
+00:48:49,660 --> 00:48:55,160
+الباقي كله، هل يوجد؟ هيكون المكمل، لأ أصغر من، بمعنى أصغر
+
+588
+00:48:55,160 --> 00:49:00,600
+slash، ليست أصغر من، فهنا الـ relation صارت إيش؟ ليست
+
+589
+00:49:00,600 --> 00:49:05,060
+أصغر من، بحط لها الـ slash، بس هيك صارت ليست أصغر من
+
+590
+00:49:05,060 --> 00:49:08,420
+طب مدام ليست أصغر من، معناته ممكن تكون أكبر أو
+
+591
+00:49:08,420 --> 00:49:12,380
+يساوي، طب فعلاً لو شطبنا هذه، الباقين أكبر أو يساوي
+
+592
+00:49:12,380 --> 00:49:15,560
+الباقين هتلاقيهم يا أكبر يا بيساوي، فعلاً فهي
+
+593
+00:49:15,560 --> 00:49:20,560
+compliment لـ R، compliment of R، تمام، هاي
+
+594
+00:49:20,560 --> 00:49:26,320
+compliment of R، الـ complement of R عبارة عن A و B
+
+595
+00:49:26,320 --> 00:49:32,080
+بشرط أن A و B لا تنتمي للـ relation نفسها، فما دام
+
+596
+00:49:32,080 --> 00:49:35,060
+لا تنتمي للـ relation، هتكون الـ complement تبعها
+
+597
+00:49:35,060 --> 00:49:40,560
+بالنسبة لمين؟ هيها الـ universal discourse، لما
+
+598
+00:49:40,560 --> 00:49:46,300
+عرفناها أيام الـ sets، كنا بنقول U minus A، U minus A
+
+599
+00:49:46,300 --> 00:49:49,840
+طيب الـ A عندنا اللي هي relation، هيها، والـ U خلاص
+
+600
+00:49:49,840 --> 00:49:52,380
+اتفقنا إن هي الـ Cartesian product، الـ Cartesian
+
+601
+00:49:52,380 --> 00:49:56,620
+product، okay، لاحقاً إحنا كنا بنكتبها برضه الـ
+
+602
+00:49:56,620 --> 00:50:00,880
+complement أيام الـ sets كنا بنكتبها bar، متذكرين؟ R
+
+603
+00:50:00,880 --> 00:50:04,320
+complement، أو R bar، فهي الـ universe of discourse
+
+604
+00:50:04,320 --> 00:50:08,240
+بتاعتنا في الحالة هذه اللي هي الـ Cartesian، أو
+
+605
+00:50:08,240 --> 00:50:13,300
+بنسميها complement، لو قلنا the complement of R
+
+606
+00:50:13,300 --> 00:50:17,900
+slash، هي الـ R، الـ compliment of compliment هترجع للـ
+
+607
+00:50:17,900 --> 00:50:23,800
+relation نفسها، okay، هي أصغر من slash، معناته ليست
+
+608
+00:50:23,800 --> 00:50:29,520
+أصغر من، مدام ليست أصغر من، معناته كل زوج مرتب A و B
+
+609
+00:50:29,520 --> 00:50:33,200
+بشرط أن A و B not belong to أصغر من، في الحالة هذه
+
+610
+00:50:33,200 --> 00:50:39,420
+معناته A و B ليست A أصغر من B، أو A ليست أصغر من B
+
+611
+00:50:39,420 --> 00:50:43,560
+طب ليست أصغر من B، يعني ممكن تكون تساوي أو أكبر، فإذا
+
+612
+00:50:43,560 --> 00:50:50,660
+هذه حددت تساوي، أكبر من أو يساوي، صارت not أصغر
+
+613
+00:50:50,660 --> 00:50:55,020
+من، أو ليست أصغر من،
+
+667
+00:54:42,350 --> 00:54:46,470
+ستة عشر، ممكن يكون كبير، ففي لاحقًا نحن هناخذ كيف
+
+668
+00:54:46,470 --> 00:54:53,120
+نقدر نمثل الـ relations، بدنا نسبق شوية، خلينا نمثلها
+
+669
+00:54:53,120 --> 00:54:56,020
+من الآن، كيف نستطيع أن نكتبها relation عشان لا
+
+670
+00:54:56,020 --> 00:54:58,940
+نستطيع أن نطول كثير، فأبسط طريقة أن أنا أعمل على الـ
+
+671
+00:54:58,940 --> 00:55:04,220
+matrix، أحطها كـ matrix، فـ relation، وبنحط الـ matrix
+
+672
+00:55:04,220 --> 00:55:17,780
+1 2 3 4 فهي from a to a to a برضه اللي هي 1 2 3 4
+
+673
+00:55:17,780 --> 00:55:23,800
+بصير إذا والله الـ relation موجودة بنحط true، غير
+
+674
+00:55:23,800 --> 00:55:29,260
+موجودة false، فهي صارت one zero أو zero one matrix
+
+675
+00:55:29,260 --> 00:55:36,620
+طيب، نبدأ a أصغر من b، فهي from هنا لهنا، فهل الـ a
+
+676
+00:55:36,620 --> 00:55:40,340
+الواحد أصغر من الواحد؟ لأ، هذا مش موجود، واحد أصغر من
+
+677
+00:55:40,340 --> 00:55:45,060
+اتنين yes، واحد أصغر من تلاتة yes، واحد أصغر من
+
+678
+00:55:45,060 --> 00:55:49,890
+أربعة yes، فهدول belong to relation، هدول في الحالات
+
+679
+00:55:49,890 --> 00:55:53,550
+that belong to relation، طيب اتنين مع واحد؟ لأ، اتنين
+
+680
+00:55:53,550 --> 00:56:00,830
+مع اتنين، اتنين مع تلاتة، تلاتة مع أربعة، أربعة، تمام
+
+681
+00:56:00,830 --> 00:56:05,650
+تمام، فبنقدر هين نتمثلها بسهولة، صار عندي واحد لما
+
+682
+00:56:05,650 --> 00:56:16,190
+بقول الـ R بتساوي واحد اتنين، واحد تلاتة، واحد أربعة،
+
+683
+00:56:17,200 --> 00:56:25,160
+اتنين تلاتة، اتنين أربعة، وتلاتة أربعة، فصار الرؤية
+
+684
+00:56:25,160 --> 00:56:28,340
+أوضح، هنا عندنا كيف نقدر نمثلهم بدل من أن نكتبهم
+
+685
+00:56:28,340 --> 00:56:31,080
+على الأسطر ورا بعض ورا بعض، ويمكن نتلخبط، ويمكن
+
+686
+00:56:31,080 --> 00:56:33,920
+واحدة تجعل معنا واحدة مانجيبهاش، واحدة مانعرفهاش،
+
+687
+00:56:33,920 --> 00:56:39,120
+أسهل، صارت الأمور في تمثيل الـ relation بتصير أسهل
+
+688
+00:56:39,120 --> 00:56:42,360
+في تمثيل الـ relation، طبعًا هذا نوع أول، لاحقًا برضه
+
+689
+00:56:42,360 --> 00:56:47,140
+هنتكلم عن الـ graph، كيف ممكن أستخدم الـ graph لتمثيل
+
+690
+00:56:47,140 --> 00:56:50,780
+الـ relation، وهذه ستكون المدخل بعد أن نخلص الـ
+
+691
+00:56:50,780 --> 00:56:54,180
+relation، للـ graphs نفسها، إيش يعني graph؟ كيف
+
+692
+00:56:54,180 --> 00:56:56,320
+نمثل الـ graph؟ لأن الـ graph في النهاية هي relation
+
+693
+00:56:56,320 --> 00:57:00,620
+هي فعلا relation، لما بتحددوا نقطة هي relation بين
+
+694
+00:57:00,620 --> 00:57:04,060
+x و y، بعدين لما تحددوا من نقطة لنقطة بتعملوا graph
+
+695
+00:57:04,060 --> 00:57:07,820
+بينهم، أو line بينهم، أو خط بينهم، هي علاقة ثنائية
+
+696
+00:57:07,820 --> 00:57:12,700
+فعليًا، فهذه ستكون مدخلنا لاحقًا لما نبدأ نشتغل عليها
+
+697
+00:57:15,120 --> 00:57:21,000
+A to A، فواحد اتنين، ولازم السهم عشان أعرف مين
+
+698
+00:57:21,000 --> 00:57:26,340
+الأولى ومين التانية، فبعرف واحد أصغر من اتنين
+
+699
+00:57:26,340 --> 00:57:30,980
+ماحدش يجرأها بالعكس، عكس السهم، فعشان كذا السهم ضروري،
+
+700
+00:57:30,980 --> 00:57:35,140
+directed أو direct graph، direct graph ضروري ترسم
+
+701
+00:57:35,140 --> 00:57:41,060
+as a direct graph، واحد لتلاتة، اتنين لتلاتة، تلاتة
+
+702
+00:57:41,060 --> 00:57:46,560
+لأربعة، وهكذا وهكذا، Okay، طب how many different
+
+703
+00:57:46,560 --> 00:57:51,320
+relations can we define on a set A with n
+
+704
+00:57:51,320 --> 00:57:55,880
+elements؟ لو عندنا set فيها n elements زي الحالة
+
+705
+00:57:55,880 --> 00:57:59,680
+اللي عندنا هنا فيها أربع elements، فيها الحالة اللي
+
+706
+00:57:59,680 --> 00:58:04,700
+عندنا هنا أربع elements، كم relation ممكن يكون للـ
+
+707
+00:58:04,700 --> 00:58:09,060
+set هذه؟ ستة عشر، الستة عشر هدول عدد الـ Cartesian
+
+708
+00:58:09,060 --> 00:58:17,120
+product، بمعنى هدول العدد الأقصى، أو العدد خلينا
+
+709
+00:58:17,120 --> 00:58:24,500
+نقول اللي ممكن إما آه أو لأ، بمعنى كل زوج من هدول
+
+710
+00:58:24,500 --> 00:58:29,440
+يعتبر واحد من الستة عشر، إله احتمالين، إما belong للـ
+
+711
+00:58:29,440 --> 00:58:35,900
+relation أو not belong للـ relation، معنى ذلك أنه
+
+712
+00:58:35,900 --> 00:58:41,510
+ممكن العنصر الأول هنا ممكن يكون true أو false أو
+
+713
+00:58:41,510 --> 00:58:47,610
+one أو zero، طيب خلينا شوية شوية، هدول مبدئيًا قداش
+
+714
+00:58:47,610 --> 00:58:51,390
+عددهم 16
+
+715
+00:58:51,390 --> 00:58:55,270
+هدول قداش عددهم؟ 16، طب لما نعمل generalization
+
+716
+00:58:55,270 --> 00:59:03,730
+للموضوع، n الـ elements، عددهم n، يعني a عبارة عن n
+
+717
+00:59:03,730 --> 00:59:04,310
+elements
+
+718
+00:59:08,910 --> 00:59:13,650
+تربيع، هدول عددهم تربيع؟ هدول كلهم هيك عددهم
+
+719
+00:59:13,650 --> 00:59:19,670
+إيش؟ تربيع، مظبوط؟ طيب كم احتمالات combination
+
+720
+00:59:22,020 --> 00:59:27,780
+ممكن نعمل لعدد relations ممكنة من الـ universe of
+
+721
+00:59:27,780 --> 00:59:31,660
+discourse هذه، هذه صارت هيك بالنسبة لنا universe of
+
+722
+00:59:31,660 --> 00:59:35,520
+discourse بتاعتنا، عدد الـ elements بتاعتها تربيع،
+
+723
+00:59:35,520 --> 00:59:38,220
+هذه صارت خلاص، هدول عدد الـ elements للـ universe of
+
+724
+00:59:38,220 --> 00:59:42,420
+discourse، طيب combination، كم relation ممكن أطلع
+
+725
+00:59:42,420 --> 00:59:45,740
+منهم؟ كم relation؟ إيش معناها؟ متذكرين أول ما بدأنا
+
+726
+00:59:45,740 --> 00:59:49,000
+في الـ relations قلنا إن الـ relation is a subset
+
+727
+00:59:51,000 --> 00:59:55,760
+معناته كم subset بقدر أطلع من الـ.. من الـ sequence
+
+728
+00:59:55,760 --> 00:59:58,580
+هذا، أو من.. من عدد الـ.. من الـ set كلها على بعضها،
+
+729
+00:59:58,580 --> 01:00:04,780
+كم subset بقدر أطلع منها؟ هنا الـ relation الأولى أو
+
+730
+01:00:04,780 --> 01:00:08,760
+عفوًا الـ.. الزوج الأول، إما أنه يكون صفر أو واحد، طب
+
+731
+01:00:08,760 --> 01:00:13,720
+الزوج الثاني برضه يا صفر يا واحد، طب لحالهم هدول
+
+732
+01:00:13,720 --> 01:00:17,930
+اتنين مع بعض بيعطوني أربعة، بيعطوني أربعة احتمالات
+
+733
+01:00:17,930 --> 01:00:21,150
+ممكنة، أربعة combination، إما أن الاثنين مش موجودين
+
+734
+01:00:21,150 --> 01:00:26,990
+في الـ relation، هذه حالة، أو أن الأولى موجودة
+
+735
+01:00:26,990 --> 01:00:30,050
+في الـ relation والثانية لأ، فهذه relation لحالها
+
+736
+01:00:30,050 --> 01:00:33,250
+أصبحت relation، ممكن تكون تعريف لحالها، أو الثانية
+
+737
+01:00:33,250 --> 01:00:36,610
+موجودة والأولى لأ، برضه relation، هي تعريف مختلف، أو
+
+738
+01:00:36,610 --> 01:00:40,350
+الاثنين موجودين في الـ relation بناءً على تعريف الـ
+
+739
+01:00:40,350 --> 01:00:47,160
+relation، طيب لما نصير ثلاثة، صار ثمانية، صار
+
+740
+01:00:47,160 --> 01:00:50,040
+ثمانية، معناته هنا في عندي احتمالين، عندي اثنين،
+
+741
+01:00:50,040 --> 01:00:55,780
+اثنين، اثنين، two ways بقدر أمثل فيهم الـ element
+
+742
+01:00:55,780 --> 01:00:59,300
+الأول للـ relation، الـ element الثاني برضه فيه two
+
+743
+01:00:59,300 --> 01:01:09,780
+ways، أن مرة، فصرت إيش؟ اثنين to the power أن تربيع،
+
+744
+01:01:11,170 --> 01:01:14,650
+على اعتبار أن عددهم أصلًا تربيع، عددهم أساسًا
+
+745
+01:01:14,650 --> 01:01:21,770
+تربيع، فكل element منهم من إيش؟ من الـ Cartesian
+
+746
+01:01:21,770 --> 01:01:27,930
+elements، الـ A Cartesian product of A، كل element
+
+747
+01:01:27,930 --> 01:01:32,950
+داخل الـ set هذه ممكن يكون يا belong to relation أو
+
+748
+01:01:32,950 --> 01:01:35,690
+not belong to relation، فمعنى ذلك أنه ماوجدش عدد
+
+749
+01:01:35,690 --> 01:01:38,870
+الـ ways اللي بقدر أمثل فيها اثنين، طيب اللي جنبه
+
+750
+01:01:38,870 --> 01:01:43,260
+نفس الموضوع، بس الاثنين هدول لازم يكون مع بعض ضمن الـ
+
+751
+01:01:43,260 --> 01:01:46,740
+relation أو واحد منهم بس، في نهاية بمثلهم مع بعض للـ
+
+752
+01:01:46,740 --> 01:01:51,580
+relation، فمعنى ذلك هتكون ضرب اثنين في اثنين في
+
+753
+01:01:51,580 --> 01:01:54,460
+اثنين في اثنين في اثنين في اثنين، ستة عشر
+
+754
+01:01:54,460 --> 01:01:58,300
+مرة، طبعًا ستة عشر مرة لأن أنا مخصص الموضوع لأربعة في
+
+755
+01:01:58,300 --> 01:02:02,500
+أربعة، لأربعة تربيع، لما بتكون n في n معناته to n
+
+756
+01:02:02,500 --> 01:02:06,920
+مرة، to n مرة، فصار عندي كلها to n مرة، اثنين to the
+
+757
+01:02:06,920 --> 01:02:12,900
+power n تربيع، اثنين to the power n تربيع، واضحة ليش
+
+758
+01:02:12,900 --> 01:02:17,920
+عملناها اثنين to the power of n تربيع، okay، شوية
+
+759
+01:02:17,920 --> 01:02:20,440
+properties، هالوقت ناخدها على الـ relations هذه، إيش
+
+760
+01:02:20,440 --> 01:02:24,200
+ممكن تكون الـ relations؟ كيف نمثلها أو كيف نعبر
+
+761
+01:02:24,200 --> 01:02:28,500
+عنها؟ أول حاجة الـ reflexive أو reflexivity
+
+762
+01:02:28,500 --> 01:02:31,520
+reflexivity
+
+763
+01:02:31,520 --> 01:02:36,200
+بمعنى الإنعكسية، الإنقلابية، الإنعكسية أو الإنقلابية
+
+764
+01:02:36,200 --> 01:02:40,250
+بمعنى لو انعكست الـ relation، أو لو عكسنا الـ two
+
+765
+01:02:40,250 --> 01:02:44,690
+elements، الـ relation هتظل ثابتة، هتظل ثابتة بينهم،
+
+766
+01:02:44,690 --> 01:02:47,850
+طبعًا الكلام ده لن يحصل إلا إذا كانوا الـ two
+
+767
+01:02:47,850 --> 01:02:50,890
+elements بيساووا بعض، إذا كانوا الـ two elements فعليًا
+
+768
+01:02:50,890 --> 01:02:54,650
+بيساووا بعض، في الحالة هذه بنقول أن الـ relation R
+
+769
+01:02:54,650 --> 01:03:01,750
+relation R on a set A is reflexive، متى؟ if for all
+
+770
+01:03:01,750 --> 01:03:08,370
+A belong to set A، A relation A هي مع نفسها، العنصر
+
+771
+01:03:08,370 --> 01:03:12,350
+مع نفسه موجودين، بمعنى لو انعكسوا هتظل الـ relation
+
+772
+01:03:12,350 --> 01:03:17,450
+ثابتة، هتظل الـ relation بينهم ثابتة، زي لما بتتكلموا
+
+773
+01:03:17,450 --> 01:03:21,870
+مثلًا عن.. هناخد إحنا logic مثال، وهناخد مثال عنها،
+
+774
+01:03:21,870 --> 01:03:25,510
+بدون ما نقول أمثلة.. الـ slides الجاية كلها أمثلة عن
+
+775
+01:03:25,510 --> 01:03:28,610
+الموضوع، خلينا بس نشوف الـ.. الـ irreflexive الـ
+
+776
+01:03:28,610 --> 01:03:34,830
+irreflexive، المفروض أن هي ليست reflexive، بس مش
+
+777
+01:03:34,830 --> 01:03:37,810
+بالسهولة هذه، ليش؟ لأن أحيانًا ممكن تكون في relation
+
+778
+01:03:37,810 --> 01:03:44,430
+لا هي reflexive ولا هي irreflexive، كيف؟ بمعنى لو
+
+779
+01:03:44,430 --> 01:03:53,990
+عندكوا relation فيها واحد واحد وهي
+
+780
+01:03:53,990 --> 01:03:58,750
+أساسًا كانت الـ a عبارة عن واحد واثنين مثلًا، واحد
+
+781
+01:03:58,750 --> 01:04:04,610
+واحد، في الحالة هذه بقدرش أقول إن هي reflexive، ليش؟
+
+782
+01:04:04,610 --> 01:04:09,710
+لأن واحد وواحد، okay، a relation a هي واضحة، إيه إيه
+
+783
+01:04:09,710 --> 01:04:14,370
+بس مش كل، مش
+
+784
+01:04:14,370 --> 01:04:17,330
+كل الـ elements موجودة، فعليًا الاثنين واثنين مش
+
+785
+01:04:17,330 --> 01:04:24,190
+موجودة، معناته بقدرش أقول إن هي reflexive، الشرط for
+
+786
+01:04:24,190 --> 01:04:30,250
+all a belong to capital A، يعني كل عنصر ينتمي لـ set
+
+787
+01:04:30,250 --> 01:04:34,890
+A يجب أن يكون مع نفسه، عشان أقول إن والله فعلا الـ
+
+788
+01:04:34,890 --> 01:04:37,250
+relation كلها على بعض reflexive، ممكن يكون في other
+
+789
+01:04:37,250 --> 01:04:40,390
+terms، هم أحرار، يعني ممكن يكون في واحد واثنين،
+
+790
+01:04:40,390 --> 01:04:45,270
+مالناش مشكلة، خليهم بس، أنا اللي بهمني الواحد وواحد،
+
+791
+01:04:45,270 --> 01:04:48,330
+والاثنين واثنين، ولو في تلاتة وتلاتة.. و
+
+792
+01:04:48,330 --> 01:04:50,990
+التلاتة وتلاتة تكون كمان موجودة، ولو في أربعة..
+
+793
+01:04:50,990 --> 01:04:55,890
+الأربعة وأربعة تكون موجودة، طيب واحد وواحد موجودة،
+
+794
+01:04:55,890 --> 01:05:00,390
+اثنين واثنين مش موجودة، معناته هي دي not reflexive
+
+795
+01:05:01,570 --> 01:05:04,510
+طيب، كويس، not reflexive، طب هل ممكن نكون
+
+796
+01:05:04,510 --> 01:05:09,510
+irreflexive؟ الـ irreflexive ببساطة جدًا، إذا كانت الـ
+
+797
+01:05:09,510 --> 01:05:12,030
+relation بنقول عليها irreflexive، إذا كان الـ
+
+798
+01:05:12,030 --> 01:05:17,810
+complementary أو الـ complement تبعها reflexive، إذا
+
+799
+01:05:17,810 --> 01:05:20,650
+كان الـ complement تبعها reflexive، طيب بنشوف الـ
+
+800
+01:05:20,650 --> 01:05:25,310
+complement لها دي، معناته أي otherwise، كل العناصر
+
+801
+01:05:25,310 --> 01:05:28,610
+أو كل العناصر الممكنة للـ Cartesian باستثناء الواحد
+
+802
+01:05:28,610 --> 01:05:32,410
+وواحد، يعني أنا متوقع هيطلع معانا اثنين واثنين، و
+
+803
+01:05:32,410 --> 01:05:36,330
+هيطلع معانا تلاتة وتلاتة، بس هدول غير كافيين إن هي
+
+804
+01:05:36,330 --> 01:05:39,910
+تكون reflexive، لأن واحد واحد مش موجودة، معناته الـ
+
+805
+01:05:39,910 --> 01:05:44,750
+relation هنا برضه not reflexive، فهي لا هي
+
+806
+01:05:44,750 --> 01:05:49,050
+reflexive ولا هي reflexive ولا هي reflexive، خدوا
+
+807
+01:05:49,050 --> 01:05:53,070
+بالكم، الـ reflexive مش معناها إن هي not reflexive،
+
+808
+01:05:53,070 --> 01:05:58,430
+reflexive لازم يكون جميع الـ elements داخل الـ set
+
+809
+01:05:59,750 --> 01:06:03,710
+موجودين مع نفسهم، يعني واحد وواحد، اثنين واثنين،
+
+810
+01:06:03,710 --> 01:06:05,910
+تلاتة وتلاتة، إذا كانوا هم موجودين لحالهم هيك، بقول
+
+811
+01:06:05,910 --> 01:06:09,810
+إن هي reflexive، إن هي reflexive، إن هي reflexive
+
+812
+01:06:09,810 --> 01:06:15,650
+طيب لو عندنا هنا واحد واثنين بس، الـ relation هذه،
+
+813
+01:06:15,650 --> 01:06:19,730
+الـ reflexive بتصير، هتصير irreflexive، هتصير
+
+814
+01:06:19,730 --> 01:06:23,810
+irreflexive، ليش؟ لأن الـ complement تبعها هيكون
+
+815
+01:06:23,810 --> 01:06:26,610
+reflexive، هيكون موجود في الواحد وواحد، هيكون موجود
+
+816
+01:06:26,610 --> 01:06:31,160
+في الواحد واثنين، واثنين، تلاتة وتلاتة، فبتصير
+
+817
+01:06:31,160 --> 01:06:35,580
+reflexive، طيب الحالة اللي بتكون فيها نصهم موجود ونصهم
+
+818
+01:06:35,580 --> 01:06:38,940
+مش موجود، أو على الأقل واحد موجود والباقي لأ،
+
+819
+01:06:38,940 --> 01:06:43,260
+هذه لها، هتطلع لا reflexive ولا irreflexive، مثال، و
+
+820
+01:06:43,260 --> 01:06:45,440
+زي ما قلنا إحنا في النهاية الأمثلة بتاعتنا مش
+
+821
+01:06:45,440 --> 01:06:49,820
+مضروة فقط على أرقام، ممكن هي على objects، على أشياء،
+
+822
+01:06:49,820 --> 01:06:54,220
+اللي هي الـ function أو الـ relation likes between
+
+823
+01:06:54,220 --> 01:07:00,290
+people، between people، الـ likes relation هذه لا هي
+
+824
+01:07:00,290 --> 01:07:04,350
+reflexive ولا هي irreflexive، ليش؟ لأنه عشان أقول إن
+
+825
+01:07:04,350 --> 01:07:07,790
+هي reflexive، معناته كل واحد المفروض أنه likes
+
+826
+01:07:07,790 --> 01:07:14,060
+himself، صحيح؟ لازم.. يعني هو بحب حاله، أو يعني
+
+827
+01:07:14,060 --> 01:07:16,420
+خليني أقول بفضل حاله، يعني هو معتز بنفسه، خليني
+
+828
+01:07:16,420 --> 01:07:21,300
+أقول، أو مغرور شوية، فهو حابب.. شايف أنه هو أفضل
+
+829
+01:07:21,300 --> 01:07:25,640
+واحد، فممكن هنا مش كل الناس هيك، صحيح؟ فبقدرش أعمل
+
+830
+01:07:25,640 --> 01:07:30,080
+أن كل الناس هيك، وفي نفس الوقت هي not reflexive،
+
+831
+01:07:30,080 --> 01:07:35,300
+ليش؟ لأن فعلا في ناس هيك، يعني معناته نص الـ
+
+832
+01:07:35,300 --> 01:07:39,880
+universe discourse متحققة ونصهم لأ، ما أقدر أقول
+
+833
+01:07:39,880 --> 01:07:42,820
+عليها reflexive ولا بقدر أقول عليها irreflexive،
+
+834
+01:07:42,820 --> 01:07:49,960
+فهذه not reflexive وnot irreflexive، فلا هيك ولا
+
+835
+01:07:49,960 --> 01:07:53,200
+هيك، ليش؟ لأن زي ما قلنا likes هذه يمكن.. قلت لكم
+
+836
+01:07:53,200 --> 01:07:57,980
+يمكن في أول الفصل، الـ relation likes هذه من أعقد الـ
+
+8
+
+889
+01:12:28,440 --> 01:12:32,220
+to a تكون belong لمن؟ لل inverse بتاعة ال relation
+
+890
+01:12:32,220 --> 01:12:37,240
+ال inverse بتاعة ال relation فهتكون b و a و نعكس
+
+891
+01:12:37,240 --> 01:12:42,290
+هدول أكبر منه فصارت تساوي أكبر منه وليست أكبر من
+
+892
+01:12:42,290 --> 01:12:46,910
+أو يساوي هناك ال complement كانت أو يساوي لأنه لو
+
+893
+01:12:46,910 --> 01:12:52,750
+حطينا هنا يساوي من الأساس a و b مش أصغر من بعض فهي
+
+894
+01:12:52,750 --> 01:12:55,250
+أصلا مش موجودة في ال relation عشان أجيب ال inverse
+
+895
+01:12:55,250 --> 01:12:59,290
+بتبقى بالشكل هذا فواضح هنا مش موجود يساوي رغم أنه
+
+896
+01:12:59,290 --> 01:13:02,610
+كان في ال complement موجود، ال complement مكمل هذا
+
+897
+01:13:02,610 --> 01:13:09,610
+عكس هذا، عكس مكمل غير العكس، طيب مجرد بس إعادة ترتيب
+
+898
+01:13:09,610 --> 01:13:14,610
+يعني إعادة ترتيبهم، اللي بيجي قبل ال a فقط، طيب
+
+899
+01:13:14,610 --> 01:13:18,410
+وبناء عليها بنجيب ال inverse لـ ال relation اللي
+
+900
+01:13:18,410 --> 01:13:22,850
+هتكون بينهم، for example لو أخدنا relation from
+
+901
+01:13:22,850 --> 01:13:24,290
+people to foods
+
+902
+01:13:27,140 --> 01:13:31,780
+ناس بتاكل الناس والأكل، فممكن الناس هدول نحط والله
+
+903
+01:13:31,780 --> 01:13:36,780
+تلاتة أربعة أشخاص نقول والله محمد علي عمر مش عارف مين
+
+904
+01:13:36,780 --> 01:13:42,760
+ما يكون يكون مجموعة هنا، نفترض أنه الشخص A الشخص B
+
+905
+01:13:42,760 --> 01:13:47,780
+الشخص C وهدول بدهم ياكلوا، بدهم ياكلوا واحد بدهم
+
+906
+01:13:47,780 --> 01:13:54,460
+ياكله مش عارف الـ الـ الأكلة الأولى
+
+907
+01:13:59,090 --> 01:14:05,250
+Apple خلّينا نشوف Banana بيكفي
+
+908
+01:14:05,250 --> 01:14:11,030
+هاي اللي بدنا إياه نشوفه أكتر من هيك، طيب فلحظة في
+
+909
+01:14:11,030 --> 01:14:17,810
+الحالة هذه بقدر أقول له a eats apple، a eats banana
+
+910
+01:14:17,810 --> 01:14:22,090
+b eats banana، إذا كان ال relation موجودة بيصير
+
+911
+01:14:22,090 --> 01:14:27,690
+والله هنا بس بنعمل x معناته a بيأكل تفاح، بيأكل
+
+912
+01:14:27,690 --> 01:14:37,330
+تفاح وموز، C بياكل مثلا موز، كويس؟ هذه إيش؟ هذه الـ R
+
+913
+01:14:37,330 --> 01:14:41,330
+صارت اللي هو بياكل، هذه ال relation، بياكل الـ
+
+914
+01:14:41,330 --> 01:14:49,270
+relation، طب لو عكسناهم صارت apple is eaten، مأكل،
+
+915
+01:14:49,270 --> 01:14:54,220
+فصارت الأكل عكسها مأكول، فهي ال inverse تبعها، هتبقى
+
+916
+01:14:54,220 --> 01:14:57,860
+هتبقى إيش قلت ال inverse تبعها اللي هو ال inverse
+
+917
+01:14:57,860 --> 01:15:03,000
+فصارت كل اللي هنعمله relation بالعكس،  بي R to the
+
+918
+01:15:03,000 --> 01:15:08,100
+power أو inverse R، بي inverse R، بس بحكي أنه b is
+
+919
+01:15:08,100 --> 01:15:16,140
+eaten by A، فصارت banana is eaten by b، هذه موجودة
+
+920
+01:15:16,140 --> 01:15:19,640
+أصلا يعني مش كل الناس بيحبوا كل الطبخات، يعني صحيح؟
+
+921
+01:15:19,640 --> 01:15:22,620
+فممكن يكون بيفضل طبخات و بيعمل طبخات، فممكن جدا
+
+922
+01:15:22,620 --> 01:15:26,520
+تعملوا table بهذا الشكل، تحطوا كل الطبخات الممكنة
+
+923
+01:15:26,520 --> 01:15:31,000
+خلال الأسبوع، و تحطوا على فرض العائلة عندكم و
+
+924
+01:15:31,000 --> 01:15:33,380
+تحددوا فلان آه بيحب الأكل الفلانية و بيحبش الأكل
+
+925
+01:15:33,380 --> 01:15:38,080
+الفلانية، صحيح؟ فبتعملوها برضه، فهن ال relation
+
+926
+01:15:38,080 --> 01:15:43,750
+ممكنة معقولة، ممكنة مش بالضرورة أنه a eats any b، مش
+
+927
+01:15:43,750 --> 01:15:47,790
+بالضرورة أن الـ a بياكل أي شغلة في الـ b، فهذا كل
+
+928
+01:15:47,790 --> 01:15:51,350
+اللي بنعمله بس إن احنا بنحولها لـ passive voice لـ
+
+929
+01:15:51,350 --> 01:15:55,390
+passive voice، المفعول به بيجي في الأول، مفعول به
+
+930
+01:15:55,390 --> 01:16:00,630
+بيجي في الأول، فهياخد التصريف الثالث لل verb، الثالث
+
+931
+01:16:00,630 --> 01:16:03,570
+لل verb، فواضح أن التصريف الثالث لل verb هذا اللي
+
+932
+01:16:03,570 --> 01:16:07,330
+هو ال inverse تبع ال verb نفسه، هيكون ال inverse تعـ
+
+933
+01:16:07,330 --> 01:16:12,480
+ال verb هو نفسه ال inverse، في إيش بنستغلها يعني
+
+934
+01:16:12,480 --> 01:16:15,400
+احنا okay، تعرفنا إن في حاجة اسمها inverse، في إيش
+
+935
+01:16:15,400 --> 01:16:19,820
+ممكن نستعملها، أو في إيش ممكن تفيدنا، هتفيدنا إن
+
+936
+01:16:19,820 --> 01:16:25,960
+أعرف هل ال relation symmetric أو antisymmetric، هل
+
+937
+01:16:25,960 --> 01:16:30,500
+بقدر أقول إن ال relation عندنا symmetric أو
+
+938
+01:16:30,500 --> 01:16:36,500
+symmetric أو antisymmetric، لحظة، antisymmetric برضه
+
+939
+01:16:36,500 --> 01:16:39,320
+مش معناها إن هي asymmetric
+
+940
+01:16:42,330 --> 01:16:47,430
+Symmetric عكسها Asymmetric، صحيح؟ طيب Anti-
+
+941
+01:16:47,430 --> 01:16:50,570
+symmetric إيش تاني؟ هذه حاجة مختلفة تماما، مالهاش
+
+942
+01:16:50,570 --> 01:16:54,070
+علاقة بالـ Asymmetric اللي أنتو عارفينها، اللي هي
+
+943
+01:16:54,070 --> 01:16:57,830
+العكس تبعها، خلّيني أخدهم واحدة واحدة، ال relation R
+
+944
+01:16:57,830 --> 01:17:01,650
+on a set A is symmetric، إيه أنت بتكون symmetric؟
+
+945
+01:17:01,650 --> 01:17:06,710
+فعلا بقدر أسميها symmetric if and only if R equal
+
+946
+01:17:06,710 --> 01:17:10,990
+to inverse R، إذا والله الـ R بتساوي الـ inverse R
+
+947
+01:17:10,990 --> 01:17:14,450
+باسمّيها symmetric خلاص، إذا الـ R بتساوي الـ inverse R
+
+948
+01:17:14,450 --> 01:17:20,110
+بنقول والله خلاص symmetric، بمعنى لو عندكوا الـ ..
+
+949
+01:17:20,110 --> 01:17:25,250
+كل ال relations اللي موجودة عندكوا هنا، هذه احنا
+
+950
+01:17:25,250 --> 01:17:31,590
+سميناها إيه؟ 1 1، 2 2، 3 3، لو جيبنا ال inverse تبعها
+
+951
+01:17:33,970 --> 01:17:38,250
+بنسخ بعض، بسنخ بعض، صحيح؟ معناته أصلا الـ R دي
+
+952
+01:17:38,250 --> 01:17:41,910
+symmetric، لو جبت ال inverse تبعها، هيظل نفسها،
+
+953
+01:17:41,910 --> 01:17:51,450
+هيظل نفسها، طيب ممكن جدا يكون معاها تلاتة و اتنين،
+
+954
+01:17:51,450 --> 01:17:55,750
+لاحظوا، ونسكر القوس هنا، طيب في الحالة دي بيصير الـ
+
+955
+01:17:55,750 --> 01:18:01,970
+inverse R، واحد واحد، اتنين اتنين، تلاتة تلاتة، اتنين
+
+956
+01:18:01,970 --> 01:18:07,810
+تلاتة، هاذي بطلت symmetric، بقدر أقولكوا احنا خلّينا
+
+957
+01:18:07,810 --> 01:18:10,670
+واحدة واحدة، ما بديش اللي خبطهم الدنيا في بعض، علاجات
+
+958
+01:18:10,670 --> 01:18:13,590
+symmetric، هل هي symmetric؟ لأ، مش symmetric، بس الـ
+
+959
+01:18:13,590 --> 01:18:16,290
+asymmetric و ال antisymmetric، خلينا شوية شوية
+
+960
+01:18:16,290 --> 01:18:18,770
+ما بدناش اللي خبطهم في بعض، لأن التلاتة ممكن اللي
+
+961
+01:18:18,770 --> 01:18:25,070
+خبطهم، فخلينا حاجة حاجة، طيب لو اتنين و تلاتة
+
+962
+01:18:30,060 --> 01:18:34,440
+صارت symmetric، صارت هيك symmetric، بمعنى أنا ما بديش
+
+963
+01:18:34,440 --> 01:18:37,780
+أحط في بالك إن ال symmetric هي بس المتشابهات، لأ
+
+964
+01:18:37,780 --> 01:18:49,620
+ممكن هي term زي هذا يكون فيه symmetric، okay، فإذا
+
+965
+01:18:49,620 --> 01:18:56,700
+مثال على ال symmetric، إذا كانت a, b belong to
+
+966
+01:18:56,700 --> 01:19:03,340
+relation R if and only if b, a برضه belong لـ
+
+967
+01:19:03,340 --> 01:19:08,040
+relation R، فإذا كان كل عنصر عكسه موجود فهي
+
+968
+01:19:08,040 --> 01:19:11,480
+symmetric، فهي symmetric، طيب example، ال equality
+
+969
+01:19:11,480 --> 01:19:19,310
+السيمتريك، الأقل من لأ، بالظبط، لأن لما أقول واحد أقل
+
+970
+01:19:19,310 --> 01:19:23,210
+من اتنين، بقدرش أقول اتنين أقل من واحد، لما عكسهم
+
+971
+01:19:23,210 --> 01:19:26,570
+بتضبطش، لكن لما أقول واحد بيساوي واحد، آه واحد بيساوي
+
+972
+01:19:26,570 --> 01:19:31,430
+واحد، بتمشي الحال، وأنتم بتحلوا alpha واحد
+
+973
+01:19:31,430 --> 01:19:36,070
+تساوي واحد، أو اجت معاكم واحد تساوي alpha، واحد، بتمشي
+
+974
+01:19:36,070 --> 01:19:40,710
+الحال، لكن لو قلنا أثناء الشغل وأنتم
+
+975
+01:19:40,710 --> 01:19:43,650
+بتعملوا مجموعة relations، قلتم alpha واحد أكبر ..
+
+976
+01:19:43,650 --> 01:19:46,690
+أصغر من واحد، وبعدين تيجي تقولوا لو واحد أصغر
+
+977
+01:19:46,690 --> 01:19:50,330
+من alpha واحد، ما نفعش، بتضبطش هذه .. طبعا هدول غلط
+
+978
+01:19:50,330 --> 01:19:54,290
+لكن تساوي آه بتمشي الحال، يعني وأنتم بتحلوا الطرف
+
+979
+01:19:54,290 --> 01:19:55,890
+الشمال، حطيتوا يمين، وليه يمين وليه يمين وليه يمين
+
+980
+01:19:55,890 --> 01:19:56,070
+وليه يمين وليه يمين وليه يمين وليه يمين وليه يمين
+
+981
+01:19:56,070 --> 01:19:56,810
+وليه يمين وليه يمين وليه يمين وليه يمين وليه يمين
+
+982
+01:19:56,810 --> 01:20:05,790
+وليه يمين وليه يمين وليه يمين و
+
+983
+01:20:06,170 --> 01:20:11,390
+A is married to B، نفس هي B is married to A، نفس
+
+984
+01:20:11,390 --> 01:20:17,070
+الشغل، نفس الشيء، طيب likes، لأ مش بالضرورة A likes B
+
+985
+01:20:17,070 --> 01:20:20,850
+معناته B likes A، واحد بيحب مثلا يدرس مع التاني،
+
+986
+01:20:20,850 --> 01:20:29,130
+التاني بيحبش يدرس معاه، بيحبش يقول this likes A، طيب
+
+987
+01:20:29,130 --> 01:20:36,210
+a binary relation R is antisymmetric if A و B
+
+988
+01:20:36,210 --> 01:20:41,110
+belong to R implies
+
+989
+01:20:41,110 --> 01:20:45,950
+أو implication، بدنا ناخد بالنا منها، B و A not
+
+990
+01:20:45,950 --> 01:20:52,210
+belong to R، not belong to R، فإذا الأقل من is
+
+991
+01:20:52,210 --> 01:20:58,370
+antisymmetric، أقل من is antisymmetric، بس likes is
+
+992
+01:20:58,370 --> 01:21:02,070
+not، قولتلكوا ال likes هذه ولا relation مظبوطة معها،
+
+993
+01:21:02,070 --> 01:21:07,210
+ال likes ولا إشي بظبط معها، ليش؟ لأنه ما .. ما ..
+
+994
+01:21:07,210 --> 01:21:10,650
+ما بنعرفش، يعني مالهاش أي قواعد، مالهاش أي relations
+
+995
+01:21:10,650 --> 01:21:13,950
+الحقيقة، فدائما هتلاقوا لما بدنا نقول is not
+
+996
+01:21:13,950 --> 01:21:18,050
+هتكونوا likes، هتلاقوا likes، طيب أصغر من asymmetric
+
+997
+01:21:18,050 --> 01:21:24,050
+برضه، هتبين أكتر يمكن مع الـ التلات تعريفات هدول
+
+998
+01:21:24,050 --> 01:21:26,430
+ناخدهم، والمرة الجاية ناخد عليهم applications
+
+999
+01:21:26,430 --> 01:21:30,030
+بتكون أنتو حتى يمكن قرأتوهم كويس، ناخدهم، ناخد عليهم
+
+1000
+01:21:30,030 --> 01:21:30,370
+applications
+
+1001
+01:21:34,680 --> 01:21:39,060
+خلاص، المرة اللي جاية احنا .. احنا اليوم مشينا منيح
+
+1002
+01:21:39,060 --> 01:21:41,440
+يعني كويس، يلا أعطيكوا العافية، المرة اللي جاية بنـ
+
+1003
+01:21:41,440 --> 01:21:44,340
+.. بنبدأ من هنا وبنكمل examples عليها إن شاء الله
+
+1004
+01:21:44,340 --> 01:21:45,120
+يعطيكم العافية
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eb8d8be825d62ca0f56301edab6a11e5ac1be7ca
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_postprocess.srt
@@ -0,0 +1,4016 @@
+1
+00:00:20,960 --> 00:00:23,120
+بسم الله الرحمن الرحيم الصلاة والسلام عليكم ورحمة
+
+2
+00:00:23,120 --> 00:00:25,500
+الله وبركاته يا سيدنا محمد وعلي أهلي وصحابي أجمعين
+
+3
+00:00:25,500 --> 00:00:28,380
+اليوم هنبدأ في موضوع جديد ان شاء الله recurrence
+
+4
+00:00:28,380 --> 00:00:31,400
+relations هنشوف ال recurrence relations او ايش هي
+
+5
+00:00:31,400 --> 00:00:35,720
+علاقة انتقارية نتكلم عليها نشوف تعريفها أولا نعمل
+
+6
+00:00:35,720 --> 00:00:39,880
+definition لها و بعد ال definition تبعنا هناخد كيف
+
+7
+00:00:39,880 --> 00:00:44,520
+احنا نجيب ال general equation ل recurrence
+
+8
+00:00:44,520 --> 00:00:45,080
+relation
+
+9
+00:00:50,400 --> 00:00:53,020
+مجموعة الـ elements سابقين له أو مجموعة الـ
+
+10
+00:00:53,020 --> 00:00:56,100
+elements قبله فمجموعة الـ elements اللي قبلها دولة
+
+11
+00:00:56,100 --> 00:01:01,080
+مجموعة الـ elements اللي قبله نقدر نستعين عنهم ان
+
+12
+00:01:01,080 --> 00:01:04,780
+احنا نجيب relation خاصة او ك function في ال
+
+13
+00:01:04,780 --> 00:01:10,020
+location في ال location بحيث ان an بدل ما هي
+
+14
+00:01:10,020 --> 00:01:16,540
+function في a n-1 و n-2 و ممكن يكون n-3
+
+15
+00:01:40,520 --> 00:01:43,880
+مش مشكلة، بس هاندي أجيب من الاتنين دولة العنصر
+
+16
+00:01:43,880 --> 00:01:46,160
+التالي، بعدين الرابع، بعدين الخامس، مقدرني ماشي
+
+17
+00:01:46,160 --> 00:01:50,680
+للألف؟ طبعا الطريقة not efficient مش هتكون
+
+18
+00:01:50,680 --> 00:01:55,060
+efficient نهائيا، فهتصير مناسب أفضل إن أنا أحولها
+
+19
+00:01:55,060 --> 00:01:58,780
+لمعادلة from function في مين في أن نفسها، فبعوض
+
+20
+00:01:58,780 --> 00:02:01,540
+الانها دي بالألف أو بالمية أو بالرقم اللي أنا بديه
+
+21
+00:02:01,540 --> 00:02:04,920
+عشان نحسي قيمة العنصر في ال location
+
+22
+00:02:08,050 --> 00:02:10,610
+عشان نشوف إن فعلا الموضوع فيه الكانية لتحميلها،
+
+23
+00:02:10,610 --> 00:02:13,810
+العملية فيه الكانية، خلّينا نشوف ال relation اللي
+
+24
+00:02:13,810 --> 00:02:19,730
+موجودة علينا هنا An بتساوى 2 An-1 minus An-1، طبعا
+
+25
+00:02:19,730 --> 00:02:23,750
+لازم يكون هنا N أكبر من أو يساوي 2، على أقرار إن
+
+26
+00:02:23,750 --> 00:02:23,990
+فيها
+
+27
+00:03:23,360 --> 00:03:30,280
+بمعنى هل الستة هذي تساوي تلاتة نقص صفر تلاتة اتنين
+
+28
+00:03:30,280 --> 00:03:39,360
+طبعا نقص صفر اوكي هاي صفر طيب قلم ايه تلاتة ده
+
+29
+00:03:39,360 --> 00:03:48,860
+مفروض تسعة من المعادلة تسعة فهل فعلا تسعة تساوي
+
+30
+00:03:48,860 --> 00:03:49,480
+اتنين
+
+31
+00:04:00,530 --> 00:04:05,430
+هو أكبر من المعادلة لأن المعادلة تتناسب تماماً مع
+
+32
+00:04:05,430 --> 00:04:09,150
+الـ Recurrence relation المعطاقة تتناسب تماماً
+
+33
+00:04:09,150 --> 00:04:13,550
+فمعناه ذلك ممكن يكون هذا تمثيل لـ Recurrence
+
+34
+00:04:13,550 --> 00:04:14,730
+relation
+
+35
+00:04:23,450 --> 00:04:27,090
+لو عوضنا فيها في تانية، إيش بدي يطلع؟ حكمها أن E
+
+36
+00:04:27,090 --> 00:04:31,710
+نون تساوي واحد، E واحد تساوي اربعة، E واحد تساوي
+
+37
+00:04:31,710 --> 00:04:35,830
+اتنين، E اتنين تساوي اربعة، E اتنين تساوي اربعة، E
+
+38
+00:04:35,830 --> 00:04:36,130
+اتنين تساوي اربعة، E اتنين تساوي اربعة، E اتنين
+
+39
+00:04:36,130 --> 00:04:37,490
+تساوي اربعة، E اتنين تساوي اربعة، E اتنين تساوي
+
+40
+00:04:37,490 --> 00:04:37,510
+اربعة، E اتنين تساوي اربعة، E اتنين تساوي اربعة، E
+
+41
+00:04:37,510 --> 00:04:39,150
+اتنين تساوي اربعة، E اتنين تساوي اربعة، E اتنين
+
+42
+00:04:39,150 --> 00:04:40,690
+تساوي اربعة، E اتنين تسا
+
+43
+00:04:54,470 --> 00:04:57,150
+ال relation هذه هي أول .. أول أنصر بالسبب اللي
+
+44
+00:04:57,150 --> 00:04:57,970
+نحسه أنه يعمل check
+
+45
+00:05:49,680 --> 00:05:53,680
+يكونوا كافيين لتعريف sequence معين او string معين
+
+46
+00:05:53,680 --> 00:05:59,200
+ال sequence المعين هذا قولنا قبل هيك انه قد يتفق
+
+47
+00:05:59,200 --> 00:06:03,560
+اكثر من sequence في ال initial values ده و قولنا
+
+48
+00:06:03,560 --> 00:06:12,320
+قبلهم مثلا اول امصرين ل .. لنختار مثلا نين
+
+49
+00:06:12,320 --> 00:06:17,300
+احنا اخدنا مثال قبل هيك على الأرقام الفردية اعتقد
+
+50
+00:06:17,300 --> 00:06:17,780
+و ال prime
+
+51
+00:06:25,460 --> 00:06:34,500
+لو قلنا الأرقام من انس أكبر من واحد وقالت
+
+52
+00:06:34,500 --> 00:06:37,920
+لك
+
+53
+00:06:37,920 --> 00:06:44,720
+اكبر
+
+54
+00:06:44,720 --> 00:06:47,560
+من انا اكبر من واحد اكبر من انا اكبر من واحد
+
+55
+00:06:57,000 --> 00:06:59,720
+ممكن تكون اربع خلاص الوصيفة ستبقى في العالم ال
+
+56
+00:06:59,720 --> 00:07:03,880
+positive numbers فهنا واقع ان احنا التعريف مش دقيق
+
+57
+00:07:03,880 --> 00:07:06,860
+تعريفنا هنا ممكن مش دقيق محتاجين يقولنا كمان
+
+58
+00:07:06,860 --> 00:07:10,220
+element كمان element فهذه واحدة من الحالات اللي
+
+59
+00:07:10,220 --> 00:07:18,960
+نبتق عن او مش معرفة بصورة جيدة okay ناخد example
+
+60
+00:07:39,660 --> 00:07:44,480
+ممكن تكون معطاة او عبارة عن اللي هي نمو الحساب
+
+61
+00:07:44,480 --> 00:07:52,220
+البنك او ال bank account with P كنسبة بنسبة P هل
+
+62
+00:07:52,220 --> 00:07:55,080
+اللي اللي انتوا بتفكيره على اكمل في القرن لما
+
+63
+00:07:55,080 --> 00:07:59,880
+الواحد يروح بياخد من البنك مبلغ و بعدينبيرجعوا
+
+64
+00:07:59,880 --> 00:08:08,800
+المبلغ زائد قيمة P زائد قيمة P الفائدة
+
+65
+00:08:08,800 --> 00:08:14,880
+الفائدة طبعا بتكون على فترة معينة ممكن تكون شهرية
+
+66
+00:08:14,880 --> 00:08:19,020
+ممكن تكون سنوية بيصيروا اتفاق عليها في الحالة هذه
+
+67
+00:08:19,020 --> 00:08:23,820
+في زيادة الزيادة معتمدة على جدش الشهر الجاى
+
+68
+00:08:23,820 --> 00:08:25,220
+المفروض ادفع بناء على
+
+69
+00:08:32,190 --> 00:08:37,490
+و ياخد عليه الفائدة طيب مرت سنة و استحق الفائدة هل
+
+70
+00:08:37,490 --> 00:08:41,430
+الفائدة هذه لو أخدها ممكن ياخد قيمة الفائدة و يظل
+
+71
+00:08:41,430 --> 00:08:43,670
+المبلغ زي ما هو اشتغل السنة اللي جاية ياخد نفس
+
+72
+00:08:43,670 --> 00:08:49,170
+الفائدة او يسيبها فهيك رأس المال نفسه يتغير بزيب
+
+73
+00:08:49,170 --> 00:08:52,610
+فمعنى ذلك انه بنفس قيمة الفائدة المرة اللي جاية
+
+74
+00:08:52,610 --> 00:08:56,150
+قيمة الفائدة بيزيب ولكن نسبة الفائدة هي نسبة
+
+75
+00:08:56,150 --> 00:08:57,690
+الفائدة هتكون هي هي
+
+76
+00:09:01,820 --> 00:09:05,460
+المشاكل اللي عاملة أساسا هي .. يعني خليني أقول ..
+
+77
+00:09:05,460 --> 00:09:09,580
+طلعنا شوية عن ال .. مش عارف بسجل ولا بسجل مش
+
+78
+00:09:09,580 --> 00:09:13,920
+فمبدئيا
+
+79
+00:09:13,920 --> 00:09:21,520
+هذه واحدة من الإشكاليات اللي عاملة أساسا فروق فكرة
+
+80
+00:09:21,520 --> 00:09:25,240
+أنه في فجر وفي غنى هذه واحدة من مصايبها واحدة من
+
+81
+00:09:25,240 --> 00:09:28,280
+مصايب تاعة الحاجات هذه خليني احنا .. احنا قيلنا في
+
+82
+00:09:28,280 --> 00:09:33,140
+التطبيق كتطبيق رياضيفردنا يبعدنا عن التطبيق الفعلي
+
+83
+00:09:33,140 --> 00:09:40,160
+كويس فلو قولنا ال month أو الشهر n هيساوي جدش
+
+84
+00:09:40,160 --> 00:09:44,180
+المبلغ اللي أنا معايا في شهر n هيكون عبارة عن
+
+85
+00:09:44,180 --> 00:09:51,000
+الشهر n minus one الشهر السابق زائد الفائدة
+
+86
+00:09:51,000 --> 00:09:55,140
+الفائدة في الحالة محسوبة على ايش محسوبة على بداية
+
+87
+00:09:55,140 --> 00:10:00,140
+الشهر اللي فات يعني على الشهر الماضي زائد ال bالـ
+
+88
+00:10:00,140 --> 00:10:07,320
+P هذه هي نسبة زيادة فمدان percent بحط عالمية في
+
+89
+00:10:07,320 --> 00:10:13,290
+الشهر السابقالسابق بقدر اقول انه كلها على بعض
+
+90
+00:10:13,290 --> 00:10:18,150
+بنتسميها واحد زائد قيمة النسبة او النسبة في الشهر
+
+91
+00:10:18,150 --> 00:10:22,670
+السابق طيب ماهي نفس الفكرة هي هي او خلينا كلها
+
+92
+00:10:22,670 --> 00:10:27,750
+نسميها R يعني تسهيرا للموضوع نفس الشغلاء طب المبلغ
+
+93
+00:10:27,750 --> 00:10:31,210
+اللي كان الشهر الفات موجود هو أساسا جاي من الشهر
+
+94
+00:10:31,210 --> 00:10:36,390
+اللي جابله فنفس الكلام Mن ماينوس وان او في الmonth
+
+95
+00:10:36,390 --> 00:10:42,090
+n minus one كانت عبارة عن نفس ال R هي المبلغ زائد
+
+96
+00:10:42,090 --> 00:10:46,250
+زيادة مع الزيادة سنسميها قيمة R كانت ايش متساوي
+
+97
+00:10:46,250 --> 00:10:51,410
+برضه R في ال month اللي جابله اللي جابله مع اللي
+
+98
+00:10:51,410 --> 00:10:56,480
+جابله لعند ما نصلىبداية ما أخدت المبلغ او بداية ما
+
+99
+00:10:56,480 --> 00:10:57,540
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+100
+00:10:57,540 --> 00:10:57,960
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+101
+00:10:57,960 --> 00:10:59,480
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+102
+00:10:59,480 --> 00:11:01,680
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+103
+00:11:01,680 --> 00:11:01,740
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+104
+00:11:01,740 --> 00:11:03,260
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+105
+00:11:03,260 --> 00:11:08,590
+أخدت المبلغ او بداية ما أخدت المبلغ او بدايةجاعدة
+
+106
+00:11:08,590 --> 00:11:13,690
+busy كويس في الحالة هذه لو انا فرضا واحد حط فلوسه
+
+107
+00:11:13,690 --> 00:11:17,870
+و بده يحسب بعد عشر سنين بده يحط المبلغ و بده ينسل
+
+108
+00:11:17,870 --> 00:11:21,510
+عشر سنين طبعا يقعد يحسبها الشهر هذا طب الشهر اللي
+
+109
+00:11:21,510 --> 00:11:23,530
+برا جديش طب الشهر اللي بعده جديش طب الشهر اللي
+
+110
+00:11:23,530 --> 00:11:27,210
+بعده جديش مش هتنفع لأ كان من الأسهل عشرة في اتناش
+
+111
+00:11:27,210 --> 00:11:31,370
+عدد الشهور هاي مية عشرين شهر يضربهم في ال .. بتصير
+
+112
+00:11:31,370 --> 00:11:33,990
+R جديش النسبة المطلوبة او النسبة اللي هو هياخدها
+
+113
+00:11:34,960 --> 00:11:37,960
+تتبور 120 و خلاص في المبلغ اللي حطه أول مرة
+
+114
+00:11:37,960 --> 00:11:43,180
+بيحسبها مرة واحدة مش مضطر يعمل يحسب كل ال terms
+
+115
+00:11:43,180 --> 00:11:45,700
+لعند ما يصل للشهر اللي بده يحسب جدش قيمة الفائدة
+
+116
+00:11:45,700 --> 00:11:50,360
+فيه سواء إله أو عليه سواء إله أو عليه أو عليه طبعا
+
+117
+00:11:50,360 --> 00:11:53,080
+لإن الناس كتير انخلوط بيتها من ورا الكلام هذا لما
+
+118
+00:11:53,080 --> 00:11:56,940
+تكون عليه يروح ياخد قرض و بعدين مايعرفش يخلص حاجة
+
+119
+00:11:56,940 --> 00:12:01,930
+كويسةفواضح ان احنا هنا حولناها من ايش؟ من
+
+120
+00:12:01,930 --> 00:12:05,450
+recurrence relation ل general relation لاحظوا هنا
+
+121
+00:12:05,450 --> 00:12:09,630
+معتمدة على ال n بس معتمدين على قيمة ال n المبلغ
+
+122
+00:12:09,630 --> 00:12:12,450
+اللي هنحطه في الأول ما احنا عارفينه جدش نحط مبلغ
+
+123
+00:12:12,450 --> 00:12:16,330
+في الأول و جدش أخدنا مبلغ كقارن في الأول معروف جدش
+
+124
+00:12:16,330 --> 00:12:20,030
+فترة الاستحقاق معروفة اللي هيصير بناء عليها تكرار
+
+125
+00:12:20,030 --> 00:12:26,620
+n انها دي تمثل ايش؟ شهري؟نص سنوي سنوي جداش وال R
+
+126
+00:12:26,620 --> 00:12:30,340
+ليها جداش نسبة زيادة جداش نسبة زيادة فهي واحدة من
+
+127
+00:12:30,340 --> 00:12:33,580
+الأمثلة اللي قدرنا نحولها من recurrence relation ل
+
+128
+00:12:33,580 --> 00:12:37,220
+general equation function في مين في أن نقدر نسبها
+
+129
+00:12:37,220 --> 00:12:42,180
+وجد ما بدنا نقدر نسبها وجد ما بدنا كمان مثال تاني
+
+130
+00:12:42,180 --> 00:12:46,500
+مثال تاني و بعرفش إذا كان موجود حتى ك game موجود
+
+131
+00:12:46,500 --> 00:12:53,550
+يعني اللي هو ال towerof Hanoi example برج Hanoi
+
+132
+00:12:53,550 --> 00:12:58,310
+برج Hanoi مجموعة disks فوق بعض مجموعة disks فوق
+
+133
+00:12:58,310 --> 00:13:02,970
+بعض مطلوب منكوا كلهم تنقلوهم على big تاني او على
+
+134
+00:13:02,970 --> 00:13:08,490
+وتة تاني على وتة تاني بدون بدون ماتيجي كرتونة
+
+135
+00:13:08,490 --> 00:13:11,750
+كبيرة او بدون ماييجي disk كبير على disk صغير اثناء
+
+136
+00:13:11,750 --> 00:13:15,830
+النقلأثناء النقل مايكونش فيه disk صغير تحت disk
+
+137
+00:13:15,830 --> 00:13:22,030
+كبير ومسموح لكوا ب one move each time يعني كل مرة
+
+138
+00:13:22,030 --> 00:13:24,550
+بتكون تنقلوا بنقولش اتنين اتنين بنقول واحد واحد
+
+139
+00:13:24,550 --> 00:13:29,090
+وهي كل عندكوا طبعا ال big two اللي بتكون تنقلوا
+
+140
+00:13:29,090 --> 00:13:35,790
+عليه وعندكوا spare واحد واحد spare بسأكم move
+
+141
+00:13:35,790 --> 00:13:39,910
+محتاجين عشان ننقل كل ال tower من big number one to
+
+142
+00:13:39,910 --> 00:13:44,990
+big number two او big three مش هتفرق مش هتفرق أكم
+
+143
+00:13:44,990 --> 00:13:52,390
+move محتاجين أكم move محتاجين مبدأيا كيف انتوا
+
+144
+00:13:52,390 --> 00:13:55,510
+طبعا هتقعدوا تشتغلوا فيها بدها عدد كبير يعني هذه
+
+145
+00:13:55,510 --> 00:13:58,990
+على الأقل بدها واحد تلاتين move كويسة بس كيف
+
+146
+00:13:58,990 --> 00:14:06,190
+نحسبهم عدد ال moves هذه بنقولHanoi N بمعنى الـ N
+
+147
+00:14:06,190 --> 00:14:11,190
+هنا لم أجد ما هي المقصود فيها عدد ال disks عدد ال
+
+148
+00:14:11,190 --> 00:14:18,730
+disks اللي نريد ان ننجلهم لو قلنا ال H N هذول عدد
+
+149
+00:14:18,730 --> 00:14:23,870
+ال moves اللي انا محتاجهم عشان انجل N disk هذول
+
+150
+00:14:23,870 --> 00:14:30,070
+ايش بيساووا فعليا بيساووا اتنين في H N minus one
+
+151
+00:14:30,070 --> 00:14:39,250
+زائد واحدبمعنى محتاجين ضعف نقل أربعة disks زائد
+
+152
+00:14:39,250 --> 00:14:44,350
+واحد، ليش؟ لحظة، لو فعلا بدنا ننقل أربعة disks
+
+153
+00:14:44,350 --> 00:14:49,410
+اللي هي بتصير H and minus one، مظبوط؟ لو فرضنا أنه
+
+154
+00:14:49,410 --> 00:14:51,990
+بدهم عشر moves، بدهم عشرين moves، جد ما يطلع، يطلع
+
+155
+00:14:52,720 --> 00:14:56,120
+عدد ال moves المهم ان استخدمتهم و نجلتهم هنا فعلا
+
+156
+00:14:56,120 --> 00:15:01,800
+انتجلوا هنا صار اسمها hn-1 moves بعدين أخدنا move
+
+157
+00:15:01,800 --> 00:15:08,200
+واحدة للأخيرة ده نجلناها هنا هاي الواحد بعدين
+
+158
+00:15:08,200 --> 00:15:13,640
+رجعنا نفسهم من هنا نجلناهم هنا طيب طب انتوا
+
+159
+00:15:13,640 --> 00:15:18,180
+ماحلناش اشي احنا كنا بنقول hn محتاجينها وجدناها
+
+160
+00:15:18,180 --> 00:15:25,150
+صارت دلالة hn-1-1 برده بقدر اجيبها من ايش minus
+
+161
+00:15:25,150 --> 00:15:30,750
+two لان هي بنفس الشكل هتكون اتنين زائد واحد لعند
+
+162
+00:15:30,750 --> 00:15:35,710
+ما نصل ايش zero او طبعا هنا هيكون ال zero تبعا
+
+163
+00:15:35,710 --> 00:15:39,910
+اللي هي disk واحد ان اكم move محتاج عشان انقل disk
+
+164
+00:15:39,910 --> 00:15:45,660
+واحد حركة واحدة H واحد في النهاية بتساوي واحدH1 في
+
+165
+00:15:45,660 --> 00:15:50,840
+النهاية هتساوي 1 فبنشغلها و بنرجع رجوع فيها و
+
+166
+00:15:50,840 --> 00:15:54,080
+بنقدر نحسبها في الحالة دي طيب عشان نعمل ال general
+
+167
+00:15:54,080 --> 00:15:58,440
+form أو ال general equation بتاعتنا هنشغل بهذا ال
+
+168
+00:15:58,440 --> 00:16:08,340
+sequence بالشكل هذا فهنقول ان HN هتساوي 2HN-1 plus
+
+169
+00:16:08,340 --> 00:16:15,070
+1 و عرفنا ليش عرفناها ليش بنقول أربعةجد ما يطلع
+
+170
+00:16:15,070 --> 00:16:17,830
+عدد ال moves ساعتهم يطلع انا مش معنى هلوجد احسبهم
+
+171
+00:16:17,830 --> 00:16:23,950
+كحساب بس هو عددهم نجلهم على big number two بعدين
+
+172
+00:16:23,950 --> 00:16:27,930
+اخر disk هاي ال move الواحدة بعدين هم نفسهم بنفس
+
+173
+00:16:27,930 --> 00:16:33,890
+العدد هرجحهم فوق ال disk الأخير اللي تم نقله okay
+
+174
+00:16:33,890 --> 00:16:42,250
+في الحالة هذه هاي القانون تبعناتأتنين هنضع hn-1
+
+175
+00:16:42,250 --> 00:16:46,850
+ودلالة hn-2 نفس الفكرة و نضرب ندخل الأتنين جوا
+
+176
+00:16:46,850 --> 00:16:49,450
+هتصير هنا اتنين توته باور اتنين و هنا في عندنا
+
+177
+00:16:49,450 --> 00:16:54,050
+اتنين زائد واحد اتنين توته باور اتنين وهذه الـ-3
+
+178
+00:16:54,050 --> 00:16:58,430
+صار عندنا اتنين توته باور تلاتة زائد اتنين توته
+
+179
+00:16:58,430 --> 00:17:01,750
+باور اتنين زائد اتنين توته باور واحد زائد اتنين
+
+180
+00:17:01,750 --> 00:17:06,810
+توته باور Zero لاحظوا إيش أنا بدي أوصل هي اتنين
+
+181
+00:17:06,810 --> 00:17:11,910
+توته باورعدد التكرارات طيب لعند ما نصل في الآخر
+
+182
+00:17:11,910 --> 00:17:19,190
+فعلا أن هي هتطلع 2ⁿ-1 plus 2ⁿ⁻¹
+
+183
+00:17:19,190 --> 00:17:20,230
+في H1
+
+184
+00:17:22,500 --> 00:17:26,780
+الواحد هذي هي قيمة واحدة بمعتبر أنه أكمل نجلة
+
+185
+00:17:26,780 --> 00:17:27,760
+واحدة بقيمة واحدة بمعتبر أنه أكمل نجلة واحدة بقيمة
+
+186
+00:17:27,760 --> 00:17:30,240
+واحدة بمعتبر أنه أكمل نجلة واحدة بقيمة واحدة بقيمة
+
+187
+00:17:30,240 --> 00:17:31,600
+واحدة بقيمة واحدة بقيمة واحدة واحدة واحدة واحدة
+
+188
+00:17:31,600 --> 00:17:32,700
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+189
+00:17:32,700 --> 00:17:34,480
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+190
+00:17:34,480 --> 00:17:36,860
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+191
+00:17:36,860 --> 00:17:41,080
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+192
+00:17:41,080 --> 00:17:47,260
+واحدة واحدة واحدة واحدة واحدة واحدة وا
+
+193
+00:17:51,750 --> 00:17:55,930
+I و ال I زي ما قلنا من صفر ل N-1 طب هى دى
+
+194
+00:17:55,930 --> 00:18:00,310
+Geometric هال Geometric بتذاكرينها؟ Geometric
+
+195
+00:18:00,310 --> 00:18:03,230
+بنحلها بنعود في القانون هتطلع بتساوي 2 to the
+
+196
+00:18:03,230 --> 00:18:08,850
+power N-1 ف2 to the power N عندكوا هنا مثلا كان
+
+197
+00:18:08,850 --> 00:18:13,570
+خمسة حركة محتاجين أو move محتاجين عشان تنقلوا
+
+198
+00:18:13,570 --> 00:18:17,350
+tower فيه خمسة discs من big number one to big to
+
+199
+00:18:17,350 --> 00:18:21,500
+other big two أو threeمحتاجين two to the power of
+
+200
+00:18:21,500 --> 00:18:26,900
+five minus واحد فكداش بتطلع واحد تلاتين موف
+
+201
+00:18:26,900 --> 00:18:33,340
+محتاجين واحد تلاتين موف عملية الحل فعليا احنا
+
+202
+00:18:33,340 --> 00:18:37,910
+اخدنا مثلينفي طبعا أمثلة كتير هتلاقيوا في الكتاب
+
+203
+00:18:37,910 --> 00:18:41,890
+كمان في المثال تبع fabonacci fabonacci هذا اللي هو
+
+204
+00:18:41,890 --> 00:18:46,610
+خاص بال .. بال generations للأرانب كل شهرين بيصير
+
+205
+00:18:46,610 --> 00:18:49,590
+فيه جيل جديد او بيكون الجيل الجديد قادر ان هو كمان
+
+206
+00:18:49,590 --> 00:18:53,270
+يعمل generation فبتطلع ال series او ال sequence
+
+207
+00:18:53,270 --> 00:18:56,370
+اللي أخدناها مرة تبع fabonacci لو منذكرينه اللي هو
+
+208
+00:18:56,370 --> 00:19:03,050
+واحد واحد اتنين تلاتة خمسة تمانية تلات عشر واحد
+
+209
+00:19:03,050 --> 00:19:08,080
+وعشريناللي هو كل رقم مجموع الرقمين اللي جابله و
+
+210
+00:19:08,080 --> 00:19:13,200
+initially B node بتساوي واحد و B واحد بتساوي واحد
+
+211
+00:19:13,200 --> 00:19:16,660
+و بعدين بيصيروا كلهم .. كل عنصر مجموع الاتنين اللي
+
+212
+00:19:16,660 --> 00:19:19,140
+جابله .. مجموع الاتنين اللي جابله .. مجموع الاتنين
+
+213
+00:19:19,140 --> 00:19:23,460
+اللي جابله .. تقرؤوهاموجودة في الكتاب، في أي مشكلة
+
+214
+00:19:23,460 --> 00:19:26,720
+في الأرقام، في جدول في الكتاب موجود إليها، في أي
+
+215
+00:19:26,720 --> 00:19:29,740
+مشاكل بتسألوني فيها، بتقولولي إيش ال .. كيف معروف،
+
+216
+00:19:29,740 --> 00:19:32,100
+هي سهل يعني أنه كيف .. من وين عامل generation
+
+217
+00:19:32,100 --> 00:19:35,660
+للأرقام هذه، من وين عامل generation للأرقام هذه،
+
+218
+00:19:35,660 --> 00:19:39,680
+okayماشي هدولة كانت مواضيع المثالين تلاتة اللي
+
+219
+00:19:39,680 --> 00:19:42,440
+خدناهم المثالين زاد المثال اللي موجود في الكتاب
+
+220
+00:19:42,440 --> 00:19:45,820
+موضوعهم سهل ليش لأنه مفهوم طب ممكن يجيبلي أي
+
+221
+00:19:45,820 --> 00:19:50,260
+relation ويقولي حوليها ل general equation احسبلي
+
+222
+00:19:50,260 --> 00:19:53,420
+العنصر رقم الف مثلا او رقم الفين او رقم .. ماعرفش
+
+223
+00:19:53,420 --> 00:19:56,260
+اشرح العنصر اللي ممكن يطلبه باعتبار انه ممكن جدا
+
+224
+00:19:56,260 --> 00:20:01,440
+يعملنا example للبكتيريا وهذا example موجود في
+
+225
+00:20:01,440 --> 00:20:05,380
+الكتاب في أحد حلول ال .. في ال .. في ال problem
+
+226
+00:20:05,380 --> 00:20:11,270
+sets في الآخرموجود ان والله عندكوا مش عارف بكتيريا
+
+227
+00:20:11,270 --> 00:20:15,530
+واحدة، خلية بكتيريا واحدة، بعد مش عارف سنة أكم
+
+228
+00:20:15,530 --> 00:20:19,650
+خلية هتكونهو يعطيكوا معلومات انك تعمل انقسام كل
+
+229
+00:20:19,650 --> 00:20:24,250
+جديش طيب هل بعد سنة طبعا جالكوا انه بعد كل تلت
+
+230
+00:20:24,250 --> 00:20:29,270
+ساعات هتبتتكاتر يعني بتنقسم طب هل بدأ اقعد أحسبها
+
+231
+00:20:29,270 --> 00:20:34,690
+لعند ما أصل لسنة عشان أشوف الرقم نوية طبعا مستحيل
+
+232
+00:20:34,690 --> 00:20:38,850
+حد يقعد يشتغل سنة يجسمها كل تلت ساعات تلت ساعات كم
+
+233
+00:20:38,850 --> 00:20:42,010
+مرة بتكون تعملوا recurrence relationلأ الموضوع مش
+
+234
+00:20:42,010 --> 00:20:45,470
+بتصيرش بالشكل هذا فمحتاجين احنا نعمله معادلة
+
+235
+00:20:45,470 --> 00:20:48,510
+محتاجين نعمله معادلة كيف المعادلة هذه ال logic هي
+
+236
+00:20:48,510 --> 00:20:52,530
+نتكلم عنها في ال section التاني من chapter 6 اللي
+
+237
+00:20:52,530 --> 00:20:56,210
+هو solving recurrences هذه هنشغل على linear
+
+238
+00:20:56,210 --> 00:20:59,470
+homogeneous recurrence of degree k with constant
+
+239
+00:20:59,470 --> 00:21:02,310
+coefficients هنسميها k linear homogeneous
+
+240
+00:21:02,310 --> 00:21:07,480
+recurrence with constant coefficientsعلى اعتبار ان
+
+241
+00:21:07,480 --> 00:21:10,640
+الـ K هذه ال degree هذه هي عدد ال elements اللي
+
+242
+00:21:10,640 --> 00:21:14,920
+انا محتاجه عشان اجيب اي element زيادة بمعنى ال
+
+243
+00:21:14,920 --> 00:21:22,020
+element N محتاج مدام K محتاج جابله K elements عشان
+
+244
+00:21:22,020 --> 00:21:28,620
+نحسبه فهو function في K elements جابله فهتلاقوا
+
+245
+00:21:28,620 --> 00:21:36,990
+coefficient معين في مين؟ في AN-1 N-2 N-3to n-k
+
+246
+00:21:36,990 --> 00:21:41,830
+فانا فعليا en معتمد على k elements جابله فبنسميها
+
+247
+00:21:41,830 --> 00:21:48,410
+k degree ال C ده طبعا هي ال coefficients سبعتنا هي
+
+248
+00:21:48,410 --> 00:21:51,590
+كده تكرارات كل عنصر لحاله كل عنصر من العناصر
+
+249
+00:21:51,590 --> 00:21:55,650
+السابقة لحاله كويسة وكلها لاتساوي صفر على أساس
+
+250
+00:21:55,650 --> 00:22:00,150
+أننا نتكلم عن k elements جابلهالسلوشن هنا لازم
+
+251
+00:22:00,150 --> 00:22:04,570
+يكون uniquely determined if k initial conditions
+
+252
+00:22:04,570 --> 00:22:11,810
+is found بمعنى او are provided اي node موجودة اي
+
+253
+00:22:11,810 --> 00:22:16,030
+واحد موجودة to اي k minus one يكون معطين اياهم
+
+254
+00:22:16,030 --> 00:22:22,220
+كقيم فال sequence اللي احنا توه كتبناهامبدأيا عشان
+
+255
+00:22:22,220 --> 00:22:24,780
+انا احدد ال sequence و اعرف كل ال elements سبعته
+
+256
+00:22:24,780 --> 00:22:28,680
+لازم نحدد على الأقل اول three elements منهم اول
+
+257
+00:22:28,680 --> 00:22:31,280
+three elements او two elements K elements in
+
+258
+00:22:31,280 --> 00:22:36,260
+general هنقول K elements اعطانيهم واحد تلاتة خمسة
+
+259
+00:22:36,260 --> 00:22:42,160
+نفترض سبعة و بعدين بيعملي هيك خلاص بس هنا حدد ليها
+
+260
+00:22:42,160 --> 00:22:48,200
+ان هي ال K باربعة K باربعة في عند A node A واحد
+
+261
+00:22:48,200 --> 00:22:52,200
+اتنين اتلاتةفي عندي أربع elements منهم المفروض
+
+262
+00:22:52,200 --> 00:22:55,040
+يطلب مني يقولي والله هاتلي ال element في ال
+
+263
+00:22:55,040 --> 00:23:01,140
+location مية مثلا بدنا نعرفه بالظبط بدنا نعرفه
+
+264
+00:23:01,140 --> 00:23:03,800
+طبعا احنا ممكن نشتل بهذا الشكل نقعد نقول اه والله
+
+265
+00:23:03,800 --> 00:23:06,740
+هذا شكله واضح انه الأرقام الفردية لأ واضح شكل
+
+266
+00:23:06,740 --> 00:23:09,460
+الأرقام مش عارف ايش شكل الأرقام و بنبدأ نكمل عليها
+
+267
+00:23:09,460 --> 00:23:16,030
+طب هاي عنصر رقم هنا a nodeهنا E3 او E4 او E9 او E5
+
+268
+00:23:16,030 --> 00:23:19,950
+او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او
+
+269
+00:23:19,950 --> 00:23:22,730
+E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9
+
+270
+00:23:22,730 --> 00:23:23,910
+او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او
+
+271
+00:23:23,910 --> 00:23:35,770
+E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9
+
+272
+00:23:35,770 --> 00:23:41,550
+او E9
+
+273
+00:23:42,290 --> 00:23:46,130
+هدول بيحلهم كالتالي ان انا بدي احولها ال a انها دي
+
+274
+00:23:46,130 --> 00:23:51,280
+ك function في مين في n لحالهاعن طريق الـ roots الـ
+
+275
+00:23:51,280 --> 00:23:54,500
+roots هذه بدنا نحسبها طبعا هنضطر بدنا نحسبها بدنا
+
+276
+00:23:54,500 --> 00:23:59,920
+نشتغل عليها ف relation فعليا لل K degree هتكون R
+
+277
+00:23:59,920 --> 00:24:03,000
+to the power N هذي اللي أنا بده أحصل عليها لازم
+
+278
+00:24:03,000 --> 00:24:06,040
+تكون function في مين في ال coefficient الأول هو هو
+
+279
+00:24:06,040 --> 00:24:10,120
+بس هتصير في R to the power N minus one هذي كانت A
+
+280
+00:24:10,120 --> 00:24:15,700
+N minus one هتصير R to the power N minus one هنا
+
+281
+00:24:15,700 --> 00:24:24,550
+كانت Aن-K هصير Rⁿ-K هذه بنسميها ال form هذا لجديد
+
+282
+00:24:24,550 --> 00:24:27,330
+بنسميه characteristic equation characteristic
+
+283
+00:24:27,330 --> 00:24:31,950
+equation لل recurrence لل recurrence relation كويس
+
+284
+00:24:31,950 --> 00:24:36,210
+من ال function هذه لو كل ال terms هدولة أخدتهم عن
+
+285
+00:24:36,210 --> 00:24:40,280
+ناحية تانية و equal to zero صارت المعادلةهتصير
+
+286
+00:24:40,280 --> 00:24:44,800
+equal to zero طيب، لاحظوا أن كلهم مشتركين في R R R
+
+287
+00:24:44,800 --> 00:24:45,340
+R
+
+288
+00:24:45,340 --> 00:25:03,060
+ررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررر
+
+289
+00:25:06,010 --> 00:25:09,750
+هي نزلت ال coefficient بس نزلت طبعا راح على ناحية
+
+290
+00:25:09,750 --> 00:25:12,510
+تانى بالسالب و هدول كلهم التانس هيروحوا بالسالب
+
+291
+00:25:12,510 --> 00:25:18,330
+فهتنتج معاكوا r to the power k على اعتبار انتم
+
+292
+00:25:18,330 --> 00:25:23,350
+قسمتوها على r n minus k فكل اللي بتعمله بتطرحه ال
+
+293
+00:25:23,350 --> 00:25:32,070
+powers فصارت n minus n minus kصارت مين؟ الـ K فR
+
+294
+00:25:32,070 --> 00:25:36,830
+to the power of K minus C1 to the power of K minus
+
+295
+00:25:36,830 --> 00:25:42,890
+1 C2 to the power of K minus 2 لما نصلّى CK to the
+
+296
+00:25:42,890 --> 00:25:47,690
+power .. فR to the power of 0 اللي هي واحد equal
+
+297
+00:25:47,690 --> 00:25:50,290
+to zero صار هالوجهة كل الطريقة في الشغل اللي
+
+298
+00:25:50,290 --> 00:25:53,210
+محتاجينها ان احنا نحل ال characteristic equation
+
+299
+00:25:53,210 --> 00:25:57,050
+اننا نجيب ال roots تبعتنا او ال characteristic
+
+300
+00:25:57,050 --> 00:25:59,330
+roots بدنا نجيب ال characteristic
+
+301
+00:26:02,280 --> 00:26:08,540
+على حسب ال degree بتاعتكم بيبين ال order لل
+
+302
+00:26:08,540 --> 00:26:15,320
+equation فواضح ان ال order هنا kإذا و الله بنقدر
+
+303
+00:26:15,320 --> 00:26:19,060
+نحل order k خلاص انحلت للتبسيط هنشتغل في المصاد
+
+304
+00:26:19,060 --> 00:26:24,160
+تبعنا على جد بس اتنين على جد degree اتنين عساس انه
+
+305
+00:26:24,160 --> 00:26:27,120
+هي بتصير quadratic هو عشان نقدر نجيب لها ال roots
+
+306
+00:26:27,120 --> 00:26:31,220
+متذكرين لسه قانون تبع ال roots لل quadratic form
+
+307
+00:26:31,220 --> 00:26:37,020
+او لل quadratic equation؟كويس فحنشتغل في المصادق
+
+308
+00:26:37,020 --> 00:26:40,360
+تبعنا كبداية ان و الله خلاص عرفنا الفكرة بعدين
+
+309
+00:26:40,360 --> 00:26:43,740
+بيصير و الله لو في techniques تحللنا اكتر degree
+
+310
+00:26:43,740 --> 00:26:47,920
+اكبر من الاتنين okay لاحقا ممكن تشتغلوا عليها في
+
+311
+00:26:47,920 --> 00:26:51,360
+مصادقنا هنشتغل على solving two degree لlinear
+
+312
+00:26:51,360 --> 00:26:55,640
+homogeneous recurrence of constant coefficients او
+
+313
+00:26:55,640 --> 00:27:00,180
+with constant coefficients تمام فهتصير a n عبارة
+
+314
+00:27:00,180 --> 00:27:04,850
+عن two terms فقط عشان تكون two degreeمعتمد على ال
+
+315
+00:27:04,850 --> 00:27:08,530
+two terms قبلها فقط، مش تلاتة، تلاتة هتتحول ل
+
+316
+00:27:08,530 --> 00:27:13,570
+three degree فنتكلم عن two terms سابقين فال two
+
+317
+00:27:13,570 --> 00:27:16,930
+terms automatically، مدام أنا بتكلم عن اتنين، ال A
+
+318
+00:27:16,930 --> 00:27:20,750
+هد بتتحول ل R to the power اتنين، مدام هي degree
+
+319
+00:27:20,750 --> 00:27:23,830
+اتنين اصلا، انا بتكلم عن degree اتنين، كيف بعرف ان
+
+320
+00:27:23,830 --> 00:27:27,690
+هي degree اتنين؟ ان هو معتمد على twoElements
+
+321
+00:27:27,690 --> 00:27:30,750
+سابقين على two elements سابقين فبعرف ايه R to the
+
+322
+00:27:30,750 --> 00:27:33,690
+power 2 كويس ال C هذه هتروح الناحية التانية
+
+323
+00:27:33,690 --> 00:27:40,610
+بالسالب فصارت ال C سالب C 1 في R طيب هذه برضه
+
+324
+00:27:40,610 --> 00:27:46,190
+هتروح الناحية التانية تصير سالب C 2 في R to the
+
+325
+00:27:46,190 --> 00:27:46,630
+power 0
+
+326
+00:27:50,290 --> 00:27:54,190
+هذا كله equal to zero فصارت معادلة quadratic
+
+327
+00:27:54,190 --> 00:27:56,770
+equation او ال characteristic equation بتاعتنا
+
+328
+00:27:56,770 --> 00:28:01,290
+صارت من الدرجة التانية نقدر نشتغلها لو متذكرين
+
+329
+00:28:01,290 --> 00:28:02,090
+قانونكوا
+
+330
+00:28:11,720 --> 00:28:15,700
+R تربيع R تربيع اه من الفهمة يعني عشان انا مقتمد
+
+331
+00:28:15,700 --> 00:28:18,140
+على عنصرين تربيعين بالظبط على عنصرين معناه ان انا
+
+332
+00:28:18,140 --> 00:28:21,500
+بتكلم عن two degree two degree خلاص automatically
+
+333
+00:28:21,500 --> 00:28:29,500
+بتصير R to the power اتنينكويس هذه بدنا نجيب ال
+
+334
+00:28:29,500 --> 00:28:33,480
+roots بتاعتنا فمن القنوة جيبناهم ال roots طيب برضه
+
+335
+00:28:33,480 --> 00:28:35,900
+احنا كل اللي عملناه اننا جيبنا roots انا بدى
+
+336
+00:28:35,900 --> 00:28:40,080
+معادلة بدى معادلة في النهاية القصر تكون عبارة عن a
+
+337
+00:28:40,080 --> 00:28:46,620
+n تساوي function في n انا هي اللي بديهاها طب انت
+
+338
+00:28:46,620 --> 00:28:51,400
+جيبتلي r الشي ر هذي معناته محتاجين theorem محتاجين
+
+339
+00:28:51,400 --> 00:28:55,440
+theorem اترتبلناكيف بقدر أجيب الان من ال roots
+
+340
+00:28:55,440 --> 00:28:57,280
+اللي انا جبتها للمعادلة من ال roots اللي احنا
+
+341
+00:28:57,280 --> 00:29:00,320
+جبناها ففي theorem أولى وفي theorem تانية ال
+
+342
+00:29:00,320 --> 00:29:03,440
+theorem الأولى الفرق بينهم بس أنه لو ال roots
+
+343
+00:29:03,440 --> 00:29:07,200
+متشابهة أو لو ال roots مختلفة لا أكثر ولا أقل أنت
+
+344
+00:29:07,200 --> 00:29:11,020
+بتكون متشابه ال roots إذا كان الحد المميز هذا
+
+345
+00:29:11,020 --> 00:29:15,540
+equal to zeroإذا كان و الله equal to zero معناته
+
+346
+00:29:15,540 --> 00:29:18,460
+مش هتفرج موجة بسالب في الآخر هيطلع نفس ال root
+
+347
+00:29:18,460 --> 00:29:23,100
+هيطلع نفس ال root okay إله قيمة واضح أنها هيطلع في
+
+348
+00:29:23,100 --> 00:29:26,220
+أنكوا two roots different two roots different two
+
+349
+00:29:26,220 --> 00:29:30,620
+roots okay هنبدأ بال theorem الأولى و الله إذا كان
+
+350
+00:29:30,620 --> 00:29:33,580
+ال characteristic equation has two roots و بيساووش
+
+351
+00:29:33,580 --> 00:29:36,500
+بعض بنسلع على القانون التالف أن ال a n
+
+352
+00:29:36,500 --> 00:29:40,200
+هيرتبلناياها ربطلنا ال roots اللي إحنا هنجيبها كيف
+
+353
+00:29:40,200 --> 00:29:46,420
+نحطها في form لل a mالان هتساوي ال route الأولى to
+
+354
+00:29:46,420 --> 00:29:50,380
+the power n وال route التانى to the power n برضه n
+
+355
+00:29:50,380 --> 00:29:54,180
+في n هي كلهم n بس الأولى محتاجين نضربها في
+
+356
+00:29:54,180 --> 00:29:57,160
+constant معين و التانى في constant معين ألف واحد
+
+357
+00:29:57,160 --> 00:30:01,940
+ألف اتنين تمام طب ما أنت هيدخلتوني في ألف واحد و
+
+358
+00:30:01,940 --> 00:30:07,540
+ألف اتنين بدنا ياهم Constants هدول Constants بدنا
+
+359
+00:30:07,540 --> 00:30:14,270
+نجيب قيمهملأ هم هدولة انت جيبت ال route الأولى في
+
+360
+00:30:14,270 --> 00:30:17,550
+n أنا مش ضامن جديش المفروض يتكرر ال route الأولى
+
+361
+00:30:17,550 --> 00:30:20,950
+تلت مرات مرتين خمس مرات عشر مرات عشان نجيب ال a n
+
+362
+00:30:20,950 --> 00:30:25,270
+ولا جديش فحاطن درب في constant هنا اللي هو المفروض
+
+363
+00:30:25,270 --> 00:30:29,090
+عدد تكرارات ال route عدد تكرارات ال route كويسة
+
+364
+00:30:29,090 --> 00:30:32,750
+التنتين هدولة القمتين هدول مافيش أبساط من جيبتهم
+
+365
+00:30:32,750 --> 00:30:37,950
+ليش؟ كيف نجيبهم؟ نجيبهم من ال initial values اللي
+
+366
+00:30:37,950 --> 00:30:42,310
+ميعطينياهمتأكدوا .. sequence بدون initial values
+
+367
+00:30:42,310 --> 00:30:44,390
+مافيش حاجة اسمها sequence بدون initial values
+
+368
+00:30:44,390 --> 00:30:48,590
+فطبيعي .. منطقي جدا أنه لازم يكون فيه على الأقل في
+
+369
+00:30:48,590 --> 00:30:52,170
+.. مادام بتكلم عن second يعني في two degree لازم
+
+370
+00:30:52,170 --> 00:30:54,430
+يكون في عندكوا على الأقل في two elements موجودين
+
+371
+00:30:54,430 --> 00:30:59,110
+اللي هم a node و a واحد لازم يكونوا موجودين هدول
+
+372
+00:30:59,110 --> 00:31:05,070
+.. ضروري كويس .. مادام موجودين عوضوا مرة ب a nodeو
+
+373
+00:31:05,070 --> 00:31:08,150
+مرة بقى واحد فصار انكم معادلتين و هم two variables
+
+374
+00:31:08,150 --> 00:31:12,470
+بنجابه فبتصير الأمور سهلة بيصير بالعكس سهلة جدا
+
+375
+00:31:12,470 --> 00:31:21,040
+كمان سهلة جدا تمام مثال بيربط أن كل ال ..المعلومات
+
+376
+00:31:21,040 --> 00:31:24,720
+و بنشوف بالظبط ال sequence للحل كيف بتتم طبعا ال
+
+377
+00:31:24,720 --> 00:31:27,480
+sequence بسيط جدا مافيش مشكلة لو افترضنا sort the
+
+378
+00:31:27,480 --> 00:31:33,620
+recurrence a n تساوي a n minus one plus two a n
+
+379
+00:31:33,620 --> 00:31:37,180
+minus two فهي عندنا ال coefficients بتاعتنا c1
+
+380
+00:31:37,180 --> 00:31:43,000
+بتساوي واحد و c2 بتساوي اتنين c1 واحد و c2 اتنين و
+
+381
+00:31:43,000 --> 00:31:47,500
+اتنين okay و ميعطينا هى two initial values اتنين و
+
+382
+00:31:47,500 --> 00:31:50,940
+سبعة اتنينو سبعة و هدول برضه هنحتاجهم في الآخر
+
+383
+00:31:50,940 --> 00:31:52,920
+نعوض عشان نجيب alpha واحد و alpha اتنين بس
+
+384
+00:31:52,920 --> 00:31:56,320
+هنحتاجهم في alpha واحد okay مدام يعندي c واحد و c
+
+385
+00:31:56,320 --> 00:32:00,060
+اتنين اعطاني يهم automatically و انا عارف ان هي
+
+386
+00:32:00,060 --> 00:32:04,380
+اتنين معتمد على two terms ف automatically R تربيع
+
+387
+00:32:04,380 --> 00:32:11,180
+ناقص c واحد خلاص هي c واحد في R ناقص اتنين
+
+388
+00:32:40,360 --> 00:32:41,760
+C2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2
+
+389
+00:32:42,810 --> 00:32:51,550
+الفا اتنين في ال route التانية to the bar المعادلة
+
+390
+00:32:51,550 --> 00:32:55,730
+هذه بدنا نجيب الفا واحد و الفا اتنين في عندنا a
+
+391
+00:32:55,730 --> 00:33:01,350
+node و a واحد خلاص هي a node تساوي a node معناته
+
+392
+00:33:01,350 --> 00:33:06,830
+كل n بتساوي zero فتصير الفا واحد هذه واحد زائد
+
+393
+00:33:06,830 --> 00:33:08,630
+واحد
+
+394
+00:33:14,750 --> 00:33:21,550
+المعادلة التانية اي واحد تساوي جداش بواحد فهنا
+
+395
+00:33:21,550 --> 00:33:30,410
+هتساوي alpha واحد في اتنين زائد بتصير ناقص هنا
+
+396
+00:33:30,410 --> 00:33:34,470
+بتصير two minus one فminus alpha اتنين
+
+397
+00:33:39,500 --> 00:33:45,420
+هذه اتنين اشمعوا الاتنين مع بعض تلاتة الفا واحد
+
+398
+00:33:45,420 --> 00:33:53,280
+تساوي تسعة الفا واحد تلاتة الفا
+
+399
+00:33:53,280 --> 00:33:57,760
+واحد تساوي تسعة الفا واحد تسعة الفا واحد تسعة الفا
+
+400
+00:33:57,760 --> 00:34:03,180
+تسعة الفا واحد تسعة الفا واحد تسعة الفا واحد تسعة
+
+401
+00:34:03,180 --> 00:34:05,640
+الفا واحد تسعة الفا واحد تسعة الفا واحد تسعة الفا
+
+402
+00:34:05,640 --> 00:34:05,660
+واحد تسعة الفا واحد تسعة الفا واحد تسعة الفا واحد
+
+403
+00:34:05,660 --> 00:34:05,680
+تسعة الفا واحد تسعة الفا واحد تسعة الفا واحد تسعة
+
+404
+00:34:05,680 --> 00:34:11,430
+واحد تسعة الفا واحد تسعة الفا واحدن بتساوي الف و
+
+405
+00:34:11,430 --> 00:34:18,130
+واحد بتلاتة تلاتة في اتنين to the power ن ناقص
+
+406
+00:34:18,130 --> 00:34:23,090
+سالب واحد to the power ن خلاص هاي المعادلة
+
+407
+00:34:23,090 --> 00:34:27,370
+بتاعتكوا بدنا ال element رقم الف فليكن عوضه هنا ب
+
+408
+00:34:27,370 --> 00:34:31,510
+الف وعوضه هنا ب الف خلصناه رقم مية هاي بيجي برقم
+
+409
+00:34:31,510 --> 00:34:35,130
+مية العنصر في ال location رقم إيش ما يكون يكون بس
+
+410
+00:34:35,130 --> 00:34:41,100
+بتعوضه في مين فيفي قيمته بتطلع قيمة الانصر نفسه طب
+
+411
+00:34:41,100 --> 00:34:44,780
+اعمل check بتقدر تعمل check اتجربه عند الصفر و عند
+
+412
+00:34:44,780 --> 00:34:47,600
+الواحد و ممكن تجربه عند الاتنين و التلاتة يعني من
+
+413
+00:34:47,600 --> 00:34:50,940
+هنا بتقدر تجيبهك as a recurrence relation اتنين و
+
+414
+00:34:50,940 --> 00:34:53,940
+تلاتة و اربعة و تجربه هنا شوف اتأكد و اعمل check
+
+415
+00:34:53,940 --> 00:34:59,480
+اعمله check فواضح ان فعلا تطلع معنى ال end تسوي
+
+416
+00:34:59,480 --> 00:35:03,820
+تلاتة في اتنين to the power n minus one to the
+
+417
+00:35:03,820 --> 00:35:09,260
+power to the power nو هاي ميعطيكوا مجموعة elements
+
+418
+00:35:09,260 --> 00:35:12,580
+other elements عشان تعملوا ال check لو حبيتوا
+
+419
+00:35:12,580 --> 00:35:15,700
+تجربوا طيب هذه الحالة الأولى ال theorem الأولى
+
+420
+00:35:15,700 --> 00:35:20,160
+قولنا في حالة انه ال two roots بيسووش بعض طب في
+
+421
+00:35:20,160 --> 00:35:24,500
+حال بيسووا بعض في حال طلعوا بيسووا بعض ال roots
+
+422
+00:35:24,500 --> 00:35:30,020
+ايش الحل؟ الحل انه هنشتغل على theorem تانية واحدة
+
+423
+00:35:30,020 --> 00:35:35,460
+من ال two terms هنضربها في endكل اللي حزيروا ان
+
+424
+00:35:35,460 --> 00:35:38,440
+واحدة من ال two terms احنا متفقين كانت alpha واحد
+
+425
+00:35:38,440 --> 00:35:42,880
+في R واحد to the power N Alpha اتنين في R اتنين to
+
+426
+00:35:42,880 --> 00:35:46,980
+the power N طيب احنا لوجة ال root مشترك لانه نفس
+
+427
+00:35:46,980 --> 00:35:52,240
+ال root نفس ال root فحنسميه root 00 لانه مشترك هذا
+
+428
+00:35:52,240 --> 00:35:57,000
+ال root هو نفس ال root هدا هنضرب واحد منهم في N مش
+
+429
+00:35:57,000 --> 00:36:02,010
+هتفرق الأولى او التانية مفرجشهتحطه الأولى كل اللى
+
+430
+00:36:02,010 --> 00:36:05,810
+هسير بس ان قيمة الف واحد هتعادل مع الف اتنين ده
+
+431
+00:36:05,810 --> 00:36:08,470
+فارقش معانا اشي مش هفارقش اشي المهم ان واحدة من ال
+
+432
+00:36:08,470 --> 00:36:11,390
+two terms هضبها في مين فئة و بتكمل نفس الحل عادى
+
+433
+00:36:11,390 --> 00:36:13,870
+بتجيبه الف واحد بتجيبه الف اتنين ال sequence هو هو
+
+434
+00:36:15,720 --> 00:36:24,560
+هيعطينا مثلًا، لو الان بتساوي 6an-1-9an-2 ويمعطينا
+
+435
+00:36:24,560 --> 00:36:35,760
+a node او a0 و a1 من شكل المعادلة المعادلة
+
+436
+00:36:35,760 --> 00:36:41,320
+فيها two terms يعني انا عارف مسبقًا انه هتكون R
+
+437
+00:36:41,320 --> 00:36:49,670
+تربيععارفين مسبقا انه حيكون في عندنا R تربيع وفي
+
+438
+00:36:49,670 --> 00:36:52,410
+عندى R وفي بعدين عندى constant و بعدين كله equal
+
+439
+00:36:52,410 --> 00:36:58,450
+to zero طيب هاي ال R طيب ال R .. هاد ال R تربيع
+
+440
+00:36:58,450 --> 00:37:02,670
+مافيش فيها مشكلة ال R في 6 هتيجي عن ناحية التانية
+
+441
+00:37:02,670 --> 00:37:08,670
+minus 6 طيب في عندى minus 9 هتيجي عن ناحية التانية
+
+442
+00:37:08,670 --> 00:37:16,390
+موجة ب 9خلاص بدي ال route لهذه طبعا واضح أنه الجزء
+
+443
+00:37:16,390 --> 00:37:24,050
+المميز اللي هو جذر b تربيع ناقص 4ac هتساوي صفر
+
+444
+00:37:24,050 --> 00:37:30,590
+لإيش لأن هنا عندكوا 4 في 9 و هنا في 6 تربيع ف36
+
+445
+00:37:30,590 --> 00:37:34,230
+ناقص 36 و واضح أن هذه صفر يعني كل الحل هيكون
+
+446
+00:37:34,230 --> 00:37:41,200
+عندكوا minus b over 2a-B over 2A فهيطلع تلاتة
+
+447
+00:37:41,200 --> 00:37:44,220
+هيطلع عندكوا تلاتة automatically مدام تلاتة صارت
+
+448
+00:37:44,220 --> 00:37:51,560
+ال A N إيش بتساوي Alpha واحد في تلاتة to the power
+
+449
+00:37:51,560 --> 00:38:02,260
+N زائد Alpha تنين في N تلاتة to the power N عوضه
+
+450
+00:38:02,260 --> 00:38:07,040
+في Alpha في A Zero و A واحد عوضه مرة هنا و مرة هنا
+
+451
+00:38:07,400 --> 00:38:16,540
+ف ايه؟ zero تساوي الف واحد بجداش تلاتة ضبار zero
+
+452
+00:38:16,540 --> 00:38:24,020
+واحد خلاص زائد الف زيرو كلها راحت كله راحت فإذا
+
+453
+00:38:24,020 --> 00:38:27,880
+هاد اتماتك اللي هي طلعت لحالة بتساوي جداش كانت ال
+
+454
+00:38:27,880 --> 00:38:32,260
+a واحد هنا واحد واحد فعنكوا الف واحد بتساوي واحد
+
+455
+00:38:32,260 --> 00:38:36,890
+هيأول معادرة طلعتوها بتعودوا في التاني عشان تجيبوا
+
+456
+00:38:36,890 --> 00:38:44,010
+alpha 2 ف a1 تساوي alpha 1 ب1 و هنا to the power 1
+
+457
+00:38:44,010 --> 00:38:51,790
+بتساوي 3 زائد alpha 2 في 1 لأن ب1 تلاتة في تلاتة
+
+458
+00:38:51,790 --> 00:38:58,330
+هذا بيساوي 6 هذا في الحلقة بيساوي 6 automatically
+
+459
+00:38:58,330 --> 00:39:01,400
+ليه؟هذه هتروح الناحية التانية اللى هى الستة يعنى
+
+460
+00:39:01,400 --> 00:39:05,500
+قيمة ستة هيطلع تلاتة بساوية الف اتنين في تلاتة
+
+461
+00:39:05,500 --> 00:39:08,580
+واحد
+
+462
+00:39:08,580 --> 00:39:12,680
+خلاص وين المعادلة هى المعادلة الأصلية كنا نعوض
+
+463
+00:39:12,680 --> 00:39:21,740
+فيها نشتغل عليها أصبحت واحد واحد خلاص هى المعادلة
+
+464
+00:39:21,740 --> 00:39:28,670
+بس اللى هى أخر معادلةنقر أخر معادلة موجودة لدينا
+
+465
+00:39:28,670 --> 00:39:35,630
+okay هذا كان الجزء اللي ضايل و خلّيني أقول إن هذا
+
+466
+00:39:35,630 --> 00:39:39,550
+جزء مهم يعني عادة الجزئية الأخيرة هي جزئية مهمة
+
+467
+00:39:39,550 --> 00:39:44,250
+جزئية مهمة
+
+468
+00:39:44,250 --> 00:39:49,310
+طيب مدام إحنا بنتكلم في ال recurrence relation
+
+469
+00:39:49,310 --> 00:39:53,780
+خلّيني أكملي في جزئية كلمة relation بتاعتنافي كلمة
+
+470
+00:39:53,780 --> 00:39:57,140
+relation ونشوف ايش يعني relation اصلا نعمم هذه ال
+
+471
+00:39:57,140 --> 00:39:59,840
+logic جاعدين نتكلم من بدلي على recurrence relation
+
+472
+00:39:59,840 --> 00:40:04,240
+relation relation ايش يعني relation فهندخل هذه ال
+
+473
+00:40:04,240 --> 00:40:07,380
+logic فيه شوية في جزئيه ايش يعني relation او ايش
+
+474
+00:40:07,380 --> 00:40:10,980
+شيه ال relations فعليا شيه ال relations فعليا
+
+475
+00:40:10,980 --> 00:40:15,160
+فعليا ال relations هي فعليا علاقة بين مجموعة
+
+476
+00:40:15,160 --> 00:40:20,020
+elements موجودين لست a مع مجموعة elements موجودين
+
+477
+00:40:20,020 --> 00:40:26,810
+لست b بحيث انهالعلاقة دي هتكون ثنائية و هنحدد
+
+478
+00:40:26,810 --> 00:40:30,250
+تلوجة كل شغلنا هيكون عبارة عن binary relation
+
+479
+00:40:30,250 --> 00:40:34,870
+بمعنى عندنا two sets ال two sets هدولة في relation
+
+480
+00:40:34,870 --> 00:40:38,190
+بين element في ال set الأولى مع element في ال set
+
+481
+00:40:38,190 --> 00:40:42,330
+التاني فهذا ثنائي ثنائي على اعتبار أنه هيكون كأنه
+
+482
+00:40:42,330 --> 00:40:47,390
+عندكوا زوج مرتب الأول جزء الأول منهمن set A و جزء
+
+483
+00:40:47,390 --> 00:40:52,690
+ثاني من set B فهذا بنسميه binary عشان هيك بنسميه
+
+484
+00:40:52,690 --> 00:40:57,090
+binary okay
+
+485
+00:40:59,190 --> 00:41:03,890
+الـ relation from A to B وهنا فوق احنا محددين ان
+
+486
+00:41:03,890 --> 00:41:07,130
+الـA و الـB دولة مجموعة two sets عبارة عن set set
+
+487
+00:41:07,130 --> 00:41:10,490
+يعني فيها إيش؟ مجموعة elements، فيها عناصر العناصر
+
+488
+00:41:10,490 --> 00:41:13,490
+هذه ممكن تكون objects، ممكن تكون numbers، ممكن
+
+489
+00:41:13,490 --> 00:41:15,930
+تكون يا هيك يا هيك، ماتفرجش معناه المهم إنه في
+
+490
+00:41:15,930 --> 00:41:19,890
+relation from A to B هذه هتكون عبارة ال relation
+
+491
+00:41:19,890 --> 00:41:22,610
+نفسها أو ال elements اللي هتحقق ال relation اللي
+
+492
+00:41:22,610 --> 00:41:27,470
+هنعرفها هتكون عبارة عن subset subset من من كل
+
+493
+00:41:27,470 --> 00:41:32,460
+العناصر الممكنةبين a و b طب إيش كل العداصر الممكنة
+
+494
+00:41:32,460 --> 00:41:40,620
+من a ل b هي ال Cartesian product بمعنى لو عندكوا a
+
+495
+00:41:40,620 --> 00:41:51,020
+فرضا واحد اتنين و ثلاثة و عندكوا b بتساوي a و b ال
+
+496
+00:41:51,020 --> 00:41:54,360
+relations الممكنة كل ال relations الممكنة فعليا
+
+497
+00:41:54,360 --> 00:42:01,380
+بين elements من a مع element من b هيبغض النظر إيش
+
+498
+00:42:01,380 --> 00:42:03,360
+ال relation طبعا هي logic لما نعرف ال relation
+
+499
+00:42:03,360 --> 00:42:07,000
+ممكن يا بتقبل بعضهم يا بترفض بعضهم يعني مش
+
+500
+00:42:07,000 --> 00:42:09,980
+بالضرورة كلهم بس ال relation هذه حسب تعريفنا لل
+
+501
+00:42:09,980 --> 00:42:16,460
+relation لاحقا هذه ممكن تكون واحد و a تمام و واحد
+
+502
+00:42:16,460 --> 00:42:23,880
+و بي ممكن تكون اتنين و a ممكن تكون اتنين و b تلاتة
+
+503
+00:42:23,880 --> 00:42:32,270
+a تلاتة bفيش إمكانية غير هدول فهدول بالنسبالنا هم
+
+504
+00:42:32,270 --> 00:42:35,730
+ال universe of discourse هدول كل الاحتمالات
+
+505
+00:42:35,730 --> 00:42:40,850
+الممكنة هدول كل ال relations اللي ممكن تكون موجودة
+
+506
+00:42:40,850 --> 00:42:45,560
+بين element في a مع element في bهذا الكل طب هذا
+
+507
+00:42:45,560 --> 00:42:50,600
+ايش يمثل فعلا يمثل Cartesian product between A وB
+
+508
+00:42:50,600 --> 00:42:56,120
+فهي فعلا A Cartesian product B فإذا أي relation
+
+509
+00:42:56,120 --> 00:43:03,120
+لاحقا هنتكلم عنها هي هتكون عبارة عن subset من ال
+
+510
+00:43:03,120 --> 00:43:06,060
+Cartesian productمن الـ Cartesian product لأنه لا
+
+511
+00:43:06,060 --> 00:43:08,560
+يمكن أن تكون أكبر منها لا يمكن أن تكون أكبر منها
+
+512
+00:43:08,560 --> 00:43:12,500
+ليش؟ مافيش أي عنصر غير هدول أساساً لا يمكن يكون أي
+
+513
+00:43:12,500 --> 00:43:17,060
+عنصر من هدول يعمل relation element من A مع element
+
+514
+00:43:17,060 --> 00:43:20,880
+من B مافيش .. هاي كل الاحتمالات الممكنة هاي كل ال
+
+515
+00:43:20,880 --> 00:43:24,840
+relations الممكنة ففي الحالة هذه أي relation from
+
+516
+00:43:24,840 --> 00:43:28,920
+A to B هتكون subset من ال Cartesian product
+
+517
+00:43:28,920 --> 00:43:33,320
+between A وB for example ناخد example ال relation
+
+518
+00:43:33,320 --> 00:43:38,520
+أصغر منهless than أصغر من هذه from natural number
+
+519
+00:43:38,520 --> 00:43:41,700
+to natural number هيحدد لي ال a natural number
+
+520
+00:43:41,700 --> 00:43:45,140
+وحدد لنا ال b natural number طيب ال relation هذه
+
+521
+00:43:45,140 --> 00:43:49,320
+إيش؟ عبارة عن إيش؟ عبارة عن زوج مرتب هاي ال n و ال
+
+522
+00:43:49,320 --> 00:43:54,160
+m بشرط إن ال n لازم تكون أصغر من إيش؟ من m ال n
+
+523
+00:43:54,160 --> 00:43:58,500
+أصغر من ال m فكأنه الأصغر من هذا هي ال relation
+
+524
+00:43:58,500 --> 00:44:02,720
+أصغر من هاي ال relation هذه هي ال relation بتاعتنا
+
+525
+00:44:02,720 --> 00:44:07,850
+كويسمبدأيا طبعا ناخد بالنا أن مادام relation يعني
+
+526
+00:44:07,850 --> 00:44:12,770
+هي related to شغلة related to شغلة تانية يعني
+
+527
+00:44:12,770 --> 00:44:19,050
+دايما في reference لما نقول مثلا خمسة أكبر من
+
+528
+00:44:19,050 --> 00:44:22,950
+اتنين فبالنسبة للخمسة ال reference هي الاتنين هي
+
+529
+00:44:22,950 --> 00:44:26,730
+الاتنين لأن related للاتنين الخمسة أكبر فصار ال
+
+530
+00:44:26,730 --> 00:44:31,410
+relation بتاعتنا أكبر منه هنا نتكلم عن أصغر من ال
+
+531
+00:44:31,410 --> 00:44:38,220
+N هذه أصغر منال M ال N أصغر من ال M على اعتبار أن
+
+532
+00:44:38,220 --> 00:44:41,300
+ال relation هنا أصغر من ال relation هنا عندنا أصغر
+
+533
+00:44:41,300 --> 00:44:48,880
+من فهذه معناها أن A و B كزوج مرتب belong to set
+
+534
+00:44:48,880 --> 00:44:53,700
+جديدة اللي هي ال subset من كلهم ال set هذه عبارة
+
+535
+00:44:53,700 --> 00:44:59,800
+عن أصغر من عبارة عن أصغر من لو غيرنا هنا و حطناها
+
+536
+00:44:59,800 --> 00:45:09,780
+أرقام برضهنشوف الأصغر من إيش بتطلع معنا جولنا
+
+537
+00:45:09,780 --> 00:45:16,880
+واحد واثنين مثلا طيب
+
+538
+00:45:16,880 --> 00:45:19,640
+هذه مش ال relation هذه هيك صارت هذه كل ال universe
+
+539
+00:45:19,640 --> 00:45:22,080
+of discourse هذه ال Cartesian product هذه ال
+
+540
+00:45:22,080 --> 00:45:26,500
+Cartesian product بتاعتنا كلها طيب أصغر من هتكون
+
+541
+00:45:26,500 --> 00:45:27,500
+إيش بتساوي منهم؟
+
+542
+00:45:37,320 --> 00:45:42,100
+خلاص هو عنصر واحد عنصر واحد فيه مش غيره ليه وجد
+
+543
+00:45:42,100 --> 00:45:47,720
+غيره فإذا لحظة الواحد واثنين هي subset من من ال
+
+544
+00:45:47,720 --> 00:45:50,440
+Cartesian product هي فعلا subset من ال Cartesian
+
+545
+00:45:50,440 --> 00:45:55,280
+product في الحالة اللي عندنا طيب فإذا عنصر واحد
+
+546
+00:45:55,280 --> 00:45:59,320
+واثنين belong torelation أصغر من هي ال relation
+
+547
+00:45:59,320 --> 00:46:03,100
+أصغر من العنصر الوحيد اللي belong إلها هو الواحد
+
+548
+00:46:03,100 --> 00:46:06,480
+واثنين ففي الحالة هذه الزوجة واحد واثنين ينتمي
+
+549
+00:46:06,480 --> 00:46:10,700
+لأصغر من relation okay يبدو كتوبها كتالة a
+
+550
+00:46:10,700 --> 00:46:17,480
+relation b أو a is related to b أو a أو by related
+
+551
+00:46:17,480 --> 00:46:23,360
+to r أو under relation rالتسمية مش هتفرق كتير،
+
+552
+00:46:23,360 --> 00:46:26,700
+بتقدر تسموها هيك أو هيك related to relation are أو
+
+553
+00:46:26,700 --> 00:46:31,480
+under relation are كلها في النهاية إن ال A بالنسبة
+
+554
+00:46:31,480 --> 00:46:35,440
+ل B هل حقق ال relation أو لأ، حقق ال relation أو
+
+555
+00:46:35,440 --> 00:46:36,420
+محققش
+
+556
+00:46:39,120 --> 00:46:44,360
+ال R مش .. ال Cartesian product مش علاقة، معناه هي
+
+557
+00:46:44,360 --> 00:46:47,060
+subset، يعني فيه .. لأ، أنا مابقولتش مش علاقة، أنا
+
+558
+00:46:47,060 --> 00:46:50,520
+بقول الأصغر من مش .. مش هتمثل العلاقة، أنا هنا
+
+559
+00:46:50,520 --> 00:46:53,600
+لإني بدأت أتكلم عن أصغر من، فقلتلكوا لأ هذه مش هي
+
+560
+00:46:53,600 --> 00:46:56,780
+ال relation بتاعتنا، قلتلكوا لأ مش هذه العلاقة
+
+561
+00:46:56,780 --> 00:46:59,560
+اللي احنا بنشتغل عليها، صرنا بنشتغل على أصغر من،
+
+562
+00:46:59,560 --> 00:47:03,920
+فصارت subset من ال Cartesian product، ممكن يكون في
+
+563
+00:47:03,920 --> 00:47:09,100
+relation، نعمل relation تشمل كلهممكن نعمل relation
+
+564
+00:47:09,100 --> 00:47:15,120
+تشمل الكل لو قلنا مثلا ال relation بتاعتنا انه ال
+
+565
+00:47:15,120 --> 00:47:21,360
+.. كل الأرقام اللي مجموحها خمسة او اقل كله .. هي
+
+566
+00:47:21,360 --> 00:47:24,460
+دخلت كلها ال Cartesian product صح؟ خمسة او اقل
+
+567
+00:47:24,460 --> 00:47:30,740
+مجموح A زائد B اكبر .. اصغر من او اقل من خمسة اصغر
+
+568
+00:47:30,740 --> 00:47:33,520
+من او يساوي خمسة فمعنى ذلك أخدناها كلها ال
+
+569
+00:47:33,520 --> 00:47:36,780
+relationبس لإن أنا بدأت حددت الأصغر من .. قولتلكوا
+
+570
+00:47:36,780 --> 00:47:39,760
+لأ ديروا بالكوا بطلنا نحكي عن ال relation أصغر من
+
+571
+00:47:39,760 --> 00:47:43,660
+هنا أو بطلنا نتكلم in general لأ هي صارت relation
+
+572
+00:47:43,660 --> 00:47:46,840
+تانية كتبناها و قولتلكوا ده هي subset من كله بس لأ
+
+573
+00:47:46,840 --> 00:47:49,780
+ممكن تكون هي كلها على بعض relation حسب التعريف لل
+
+574
+00:47:49,780 --> 00:47:55,270
+relation okay let relation from A to BR binary
+
+575
+00:47:55,270 --> 00:47:58,590
+relation معناته ان احنا بتكلم عن two sets الأول
+
+576
+00:47:58,590 --> 00:48:03,310
+relation مع التاني ال complementary relations او
+
+577
+00:48:03,310 --> 00:48:08,990
+ال complement of R هنسميه R slash اللي هي ال R مع
+
+578
+00:48:08,990 --> 00:48:12,910
+ال slash هذه ليست relation بمعنى انه ليست ال
+
+579
+00:48:12,910 --> 00:48:18,350
+relation relation او ال inverse ال complement لان
+
+580
+00:48:18,350 --> 00:48:23,940
+ال inverse مختلفة ال complement R from A to Bعبارة
+
+581
+00:48:23,940 --> 00:48:29,060
+عن ايش؟ the complement of R هي المكملة ل R على
+
+582
+00:48:29,060 --> 00:48:32,060
+اعتبار مدام مكملة يعني معناته في عندي universe of
+
+583
+00:48:32,060 --> 00:48:35,040
+discourse طب انا فعلا عندي universe of discourse
+
+584
+00:48:35,040 --> 00:48:37,980
+ايش هو ال universe of discourse طبعا؟ ال Cartesian
+
+585
+00:48:37,980 --> 00:48:45,540
+ال Cartesian فهي دي مثلا هيها الأصغر من واحد و
+
+586
+00:48:45,540 --> 00:48:49,660
+اتنين طب المكمل اتعتها بشطب واحد و اتنين و الباقي
+
+587
+00:48:49,660 --> 00:48:55,160
+الباقي كله هلوجد هيكون المكمللأ أصغر من بمعنى أصغر
+
+588
+00:48:55,160 --> 00:49:00,600
+slash ليست أصغر من فهنا ال relation صارت إيش ليست
+
+589
+00:49:00,600 --> 00:49:05,060
+أصغر من بحط لها ال slash بس هيك صارت ليست أصغر من
+
+590
+00:49:05,060 --> 00:49:08,420
+طب مدام ليست أصغر من معناته ممكن تكون أكبر أو
+
+591
+00:49:08,420 --> 00:49:12,380
+يساوي طب فعلا لو شطبته هذه الباقين أكبر أو يساوي
+
+592
+00:49:12,380 --> 00:49:15,560
+الباقين هتلاقيهم يا أكبر يا بيساوي فعلا فهي
+
+593
+00:49:15,560 --> 00:49:20,560
+compliment لمن لR compliment of of R تمام هاي
+
+594
+00:49:20,560 --> 00:49:26,320
+compliment of Rال complement of R عبارة عن a و b
+
+595
+00:49:26,320 --> 00:49:32,080
+بشرط أن a و b لا تنتمي لل relation نفسها فما دام
+
+596
+00:49:32,080 --> 00:49:35,060
+لا تنتمي لل relation هتكون ال complement تبعها
+
+597
+00:49:35,060 --> 00:49:40,560
+بالنسبة لمين هيها ال universal discourse لما
+
+598
+00:49:40,560 --> 00:49:46,300
+عرفناها أيام ال sets كنا بنقول u minus aU minus A
+
+599
+00:49:46,300 --> 00:49:49,840
+طيب ال A عندنا اللي هي relation هيها و ال U خلاص
+
+600
+00:49:49,840 --> 00:49:52,380
+اتفجنا ان هي ال Cartesian product ال Cartesian
+
+601
+00:49:52,380 --> 00:49:56,620
+product okay لاحقا احنا كنا بنكتبها برضه ال
+
+602
+00:49:56,620 --> 00:50:00,880
+complement أيام ال six كنا بنكتبها bar متذكرين؟ R
+
+603
+00:50:00,880 --> 00:50:04,320
+complement او R bar فهي ال universe of discourse
+
+604
+00:50:04,320 --> 00:50:08,240
+بتاعتنا في الحالة هذه اللي هي ال Cartesian أو
+
+605
+00:50:08,240 --> 00:50:13,300
+بنسميها complement لو قلنا the complement of R
+
+606
+00:50:13,300 --> 00:50:17,900
+slashهي ال R ال compliment of compliment هترجع لل
+
+607
+00:50:17,900 --> 00:50:23,800
+relation نفسها okay هي أصغر من slash معناته ليست
+
+608
+00:50:23,800 --> 00:50:29,520
+أصغر من مدام ليست أصغر من معناته كل زوج مرتب a و b
+
+609
+00:50:29,520 --> 00:50:33,200
+بشرط أن a و b not belong to أصغر من في الحالة هذه
+
+610
+00:50:33,200 --> 00:50:39,420
+معناته a و b ليست a أصغر من b أو a ليست أصغر من b
+
+611
+00:50:39,420 --> 00:50:43,560
+طب ليست أصغر من b يعني ممكن تكون تساويأو أكبر فإذا
+
+612
+00:50:43,560 --> 00:50:50,660
+هذه حد تساوي أكبر من أو يساوي صارت not أصغر
+
+613
+00:50:50,660 --> 00:50:55,020
+من أو ليست أصغر من تكافي أكبر من أو يساوي أكبر من
+
+614
+00:50:55,020 --> 00:51:01,140
+أو يساوي ك relation .. ك relation okay ال relation
+
+615
+00:51:01,140 --> 00:51:05,840
+on a set Aفهنا بنعمل relation على set واحدة، قبل
+
+616
+00:51:05,840 --> 00:51:09,460
+هيك كنا هيدا بناخد two sets و بنشتغل عليهم، لأ
+
+617
+00:51:09,460 --> 00:51:12,560
+احنا أصغر منه، أكبر منه، كل الكلام هذا بنشتغله على
+
+618
+00:51:12,560 --> 00:51:15,820
+مين؟ على ال natural number، يعني أنا بتكلم عن set
+
+619
+00:51:15,820 --> 00:51:21,440
+واحدة، هي ال set واحدة، كتبنا are from natural
+
+620
+00:51:21,440 --> 00:51:26,540
+number to natural number، يعني من a to aactually
+
+621
+00:51:26,540 --> 00:51:29,920
+هي من a to a فمعظم ال relations الحقيقة هتصير ..
+
+622
+00:51:29,920 --> 00:51:35,760
+هنعممها لوجة انه احنا بنتكلم the same set او لنفس
+
+623
+00:51:35,760 --> 00:51:40,140
+ال set فهنقول ان انا بتكلم عن ال .. ال .. a binary
+
+624
+00:51:40,140 --> 00:51:44,620
+relation from a set A to itself لنفسها مع نفسها زي
+
+625
+00:51:44,620 --> 00:51:47,040
+الحكاية التو اللي كنا بنتكلم عن natural number to
+
+626
+00:51:47,040 --> 00:51:51,810
+natural numberالأصغر من اللي احنا اشتغلناها طوي
+
+627
+00:51:51,810 --> 00:51:54,710
+كنا بنتكلم عن ال natural number فكانت فعلا من ال
+
+628
+00:51:54,710 --> 00:51:57,590
+natural number لل .. لنفس ال natural number وهذه
+
+629
+00:51:57,590 --> 00:52:02,210
+عادة بنسميها ال identity relation لل .. لل ست إيش؟
+
+630
+00:52:02,210 --> 00:52:08,130
+لل ست A identity relation لل ست A من A لنفسها من A
+
+631
+00:52:08,130 --> 00:52:14,290
+لنفسها فالست A is a set لاحظوا A و A هو الزوج
+
+632
+00:52:14,290 --> 00:52:20,410
+الثنائي تبعنا بس مش معناه هيك أن A تسوي Aالـ a لما
+
+633
+00:52:20,410 --> 00:52:26,790
+بقول a small هذا القصد فيها أنه هذا element belong
+
+634
+00:52:26,790 --> 00:52:35,190
+to a capital set فإذا أي عنصر داخل ال set capital
+
+635
+00:52:35,190 --> 00:52:39,890
+A بسميه a هنا ما تتخدوش في بالك أنه هذا لازم
+
+636
+00:52:39,890 --> 00:52:43,450
+exactly بيسوا بعض، لأ مش بالضروري كل الهدف منها أن
+
+637
+00:52:43,450 --> 00:52:48,320
+ال a هذه belong to set Aالـ a ال small belonged to
+
+638
+00:52:48,320 --> 00:52:51,240
+set A تاول لو كنا بنتكلم عن ال capital P كنا
+
+639
+00:52:51,240 --> 00:52:55,200
+بنسيبها بي small عساس ان هي تتفق معاها بس small و
+
+640
+00:52:55,200 --> 00:52:58,900
+capital لمجرد انه هل ده element او set لا اكتر ولا
+
+641
+00:52:58,900 --> 00:53:03,040
+اقل ماتخلوش ان المتشابهات اللي اخبطكم معناته ان
+
+642
+00:53:03,040 --> 00:53:05,500
+انا بتكلم عن واحد واحد اتنين و اتنين لأ ممكن تكون
+
+643
+00:53:05,500 --> 00:53:08,720
+واحد و اتنين اتنين و واحد عادي كل ال relations
+
+644
+00:53:08,720 --> 00:53:11,820
+هدولة كل الأزواج اللي تكون ايه الموجودة عندها ممكن
+
+645
+00:53:11,820 --> 00:53:18,860
+تكون هنا ممكن تكون نفسها okayطيب definition برضه
+
+646
+00:53:18,860 --> 00:53:21,880
+احنا نتكلم هنا عن ال relation ال relations on a
+
+647
+00:53:21,880 --> 00:53:25,940
+set طبعا نتكلم عن set واحدة one set فال relation
+
+648
+00:53:25,940 --> 00:53:31,680
+on the set A is a relation from A to A او from A
+
+649
+00:53:31,680 --> 00:53:35,180
+to itself in other word هي برضه في جميع الأحوال
+
+650
+00:53:35,180 --> 00:53:39,640
+هتكون subset من مين؟ من A Cartesian product A A
+
+651
+00:53:39,640 --> 00:53:43,420
+Cartesian product A هتكون ال relation اللي هو ال
+
+652
+00:53:43,420 --> 00:53:46,720
+universe of discourse كلها على بعض okay ناخد مثال
+
+653
+00:53:47,710 --> 00:53:51,070
+لت A، واحد، اتنين، تلاتة، أربعة، فهي يعطيني مجموعة
+
+654
+00:53:51,070 --> 00:53:55,030
+elements، هم هدول فقط ال elements اللي نقدر نقول
+
+655
+00:53:55,030 --> 00:53:58,490
+belong to capital A، اللي belong to capital A،
+
+656
+00:53:58,490 --> 00:54:03,970
+okay which ordered pairs are in the relation R؟ وR
+
+657
+00:54:03,970 --> 00:54:08,130
+عبارة عن A وB بشرط إنه A أصغر من B، فاحنا مازلنا
+
+658
+00:54:08,130 --> 00:54:10,750
+هنا في نفس ال relation اللي هي أصغرأصغر من .. أصغر
+
+659
+00:54:10,750 --> 00:54:14,650
+من .. بدنا نحدد مين ال elements أو مين ال elements
+
+660
+00:54:14,650 --> 00:54:17,250
+داخل ال universe of discourse اللي تحقق ال
+
+661
+00:54:17,250 --> 00:54:20,330
+relation يا هادي وهي عرفلي ال relation ال relation
+
+662
+00:54:20,330 --> 00:54:25,090
+اللي عرفليها اللي هي أصغر .. أصغر من .. okay أصغر
+
+663
+00:54:25,090 --> 00:54:30,210
+من طبعا بتقدر تقعدوا تحلوهم واحدة واحدة زي ما احنا
+
+664
+00:54:30,210 --> 00:54:34,830
+اشتغلنا هنا تعملوهمواحد واحد، واحد اتنين، واحد
+
+665
+00:54:34,830 --> 00:54:39,250
+تلاتة، واحد اربع، واحد خمسة، واحد ستة، اتنين واحد،
+
+666
+00:54:39,250 --> 00:54:42,350
+اتنين اتنين، اتنين تلاتة، بس طبعا عددهم هتطلع
+
+667
+00:54:42,350 --> 00:54:46,470
+ستاشر، ممكن يكون كبير، ففي لاحقا احنا هناخد كيف
+
+668
+00:54:46,470 --> 00:54:53,120
+نقدر نمثل ال relationsبدنا نسبق شوية خلينا نمثلها
+
+669
+00:54:53,120 --> 00:54:56,020
+من الآن كيف نستطيع أن نكتبها relation عشان لا
+
+670
+00:54:56,020 --> 00:54:58,940
+نستطيع أن نطول كثير فأبسط طريقة أن أنا أعمل على ال
+
+671
+00:54:58,940 --> 00:55:04,220
+matrix أحطها ك matrix ف relation و بنحط ال matrix
+
+672
+00:55:04,220 --> 00:55:17,780
+1 2 3 4 فهي from a to a to a برضه اللي هي 1 2 3 4
+
+673
+00:55:17,780 --> 00:55:23,800
+بصير إذا والله ال relation موجودةبنحط true غير
+
+674
+00:55:23,800 --> 00:55:29,260
+موجودة false فهي صارت one zero او zero one matrix
+
+675
+00:55:29,260 --> 00:55:36,620
+طيب نبدأ a أصغر من b فهي from هنا ل هنا فهل ال a
+
+676
+00:55:36,620 --> 00:55:40,340
+الواحد أصغر من الواحد لأ هذا مش موجود واحد أصغر من
+
+677
+00:55:40,340 --> 00:55:45,060
+اتنين yes واحد أصغر من تلاتة yes واحد أصغر من
+
+678
+00:55:45,060 --> 00:55:49,890
+أربعة yes فهدولة belong to relationهدول في الحالات
+
+679
+00:55:49,890 --> 00:55:53,550
+that belong to religion طيب اتنين مع واحد لأ اتنين
+
+680
+00:55:53,550 --> 00:56:00,830
+مع اتنين اتنين مع تلاتة تلاتة مع اربعة اربعة فلس
+
+681
+00:56:00,830 --> 00:56:05,650
+تمام فبنقدر هين اتمثلها بسهولة صار عندي واحد لما
+
+682
+00:56:05,650 --> 00:56:16,190
+بقول ال R بتساوي واحد اتنين واحد تلاتة واحد اربعة
+
+683
+00:56:17,200 --> 00:56:25,160
+اتنين تلاتة اتنين اربعة و تلاتة اربعة فصار الرؤية
+
+684
+00:56:25,160 --> 00:56:28,340
+أوضح هنا عندنا كيف نقدر نمثلهم بدل من أن نكتبهم
+
+685
+00:56:28,340 --> 00:56:31,080
+على الأسطور ورا بعض ورا بعض و يمكن نتلخبط و يمكن
+
+686
+00:56:31,080 --> 00:56:33,920
+واحدة تجعل معانا واحدة مانجيبهاش واحدة مانعرفهاش
+
+687
+00:56:33,920 --> 00:56:39,120
+أسهل صارت الأمور في تمثيل ال relation بتصير أسهل
+
+688
+00:56:39,120 --> 00:56:42,360
+في تمثيل ال relation طبعا هذا نوع أول لاحقا برضه
+
+689
+00:56:42,360 --> 00:56:47,140
+هنتكلم عن ال graphكيف ممكن أستخدم ال graph لتمثيل
+
+690
+00:56:47,140 --> 00:56:50,780
+ال relation وهذه ستكون المدخل بعد أن نخلص ال
+
+691
+00:56:50,780 --> 00:56:54,180
+relation ل ال graphs نفسها إيش يعني graph؟ كيف
+
+692
+00:56:54,180 --> 00:56:56,320
+نمثل ال graph؟ لأن ال graph في النهاية هي relation
+
+693
+00:56:56,320 --> 00:57:00,620
+هي فعلا relation لما بتحددوا نقطة هي relation بين
+
+694
+00:57:00,620 --> 00:57:04,060
+x و y بعدين لما تحددوا من نقطة لنقطة بتعملوا graph
+
+695
+00:57:04,060 --> 00:57:07,820
+بينهم أو line بينهم أو خط بينهم هي علاقة ثنائية
+
+696
+00:57:07,820 --> 00:57:12,700
+فعليا فهذه ستكون مدخلنا لاحقا لما نبدأ نشتغل عليها
+
+697
+00:57:15,120 --> 00:57:21,000
+A to A فواحد اتنين و لازم السهم عشان اعرف مين
+
+698
+00:57:21,000 --> 00:57:26,340
+الاولى و مين التانية فبعرف واحد اصغر من اتنين
+
+699
+00:57:26,340 --> 00:57:30,980
+ماحدش يجرأها بالعكس عكس السهم فعشانك السهم ضرورى
+
+700
+00:57:30,980 --> 00:57:35,140
+directed او direct graph direct graph ضرورى ترسم
+
+701
+00:57:35,140 --> 00:57:41,060
+as a direct graph واحد لتلاتة اتنين لتلاتة تلاتة
+
+702
+00:57:41,060 --> 00:57:46,560
+لاربعة و هكذا و هكذاOkay طب how many different
+
+703
+00:57:46,560 --> 00:57:51,320
+relations can we define on a set A with n
+
+704
+00:57:51,320 --> 00:57:55,880
+elements؟ لو عندنا set فيها n elements زي الحالة
+
+705
+00:57:55,880 --> 00:57:59,680
+اللي عندنا هنا فيها أربع elements فيها الحالة اللي
+
+706
+00:57:59,680 --> 00:58:04,700
+عندنا هنا أربع elements أكم relation ممكن يكون لل
+
+707
+00:58:04,700 --> 00:58:09,060
+set هذه؟ ستة عشرالستاش هدولة عدد ال Cartesian
+
+708
+00:58:09,060 --> 00:58:17,120
+product بمعنى هدولة العدد الأقصى أو العدد خلينا
+
+709
+00:58:17,120 --> 00:58:24,500
+نقول اللي ممكن إما أه أو لأ بمعنى كل زوج من هدول
+
+710
+00:58:24,500 --> 00:58:29,440
+يعتبر واحد من الستاش إله احتمالين إما belong لل
+
+711
+00:58:29,440 --> 00:58:35,900
+relation أو not belong لل relation معنى ذلك أنه
+
+712
+00:58:35,900 --> 00:58:41,510
+ممكنالعنصر الأول هنا ممكن يكون true او false او
+
+713
+00:58:41,510 --> 00:58:47,610
+one او zero طيب خلينا شوية شوية هدول مبدئيا قداش
+
+714
+00:58:47,610 --> 00:58:51,390
+عددهم 16
+
+715
+00:58:51,390 --> 00:58:55,270
+هدول قداش عددهم 16 طب لما نعمل generalization
+
+716
+00:58:55,270 --> 00:59:03,730
+للموضوع n ال elements عددهم n يعني a عبارة عن n
+
+717
+00:59:03,730 --> 00:59:04,310
+elements
+
+718
+00:59:08,910 --> 00:59:13,650
+انتربيع هدول عددهم انتربيع؟ هدول كلهم هيك عددهم
+
+719
+00:59:13,650 --> 00:59:19,670
+إيش؟ انتربيع، مظبوط؟ طيب جداش احتمالات combination
+
+720
+00:59:22,020 --> 00:59:27,780
+ممكن نعمل لعدد relations ممكنة من ال universe of
+
+721
+00:59:27,780 --> 00:59:31,660
+discourse هذه هذه صارت هيك بالنسبالنا universe of
+
+722
+00:59:31,660 --> 00:59:35,520
+discourse بتاعتنا عدد ال elements بتاعتها انتربيع
+
+723
+00:59:35,520 --> 00:59:38,220
+هذه صارت خلاص هدول عدد ال elements لل universe of
+
+724
+00:59:38,220 --> 00:59:42,420
+discourse طيب combination أكم relation ممكن أطلع
+
+725
+00:59:42,420 --> 00:59:45,740
+منهم أكم relation إيش معناها متذكرين أول ما بدأنا
+
+726
+00:59:45,740 --> 00:59:49,000
+في ال relations قلنا إن ال relation is a subset
+
+727
+00:59:51,000 --> 00:59:55,760
+معناته اكم سب ست بقدر اطلع من ال .. من ال sequence
+
+728
+00:59:55,760 --> 00:59:58,580
+هدا او من .. من عدد ال .. من ال set كلها علي بعضها
+
+729
+00:59:58,580 --> 01:00:04,780
+اكم سب ست بقدر اطلع منها هنا ال relation الاولى او
+
+730
+01:00:04,780 --> 01:00:08,760
+عفوا ال .. الزوج الاول اما انه يكون صفر او واحد طب
+
+731
+01:00:08,760 --> 01:00:13,720
+الزوج التانى برضه يا صفر يا واحد طب لحالهم هدول
+
+732
+01:00:13,720 --> 01:00:17,930
+اتنين مع بعضبيعطوني أربعة بيعطوني أربعة احتمالات
+
+733
+01:00:17,930 --> 01:00:21,150
+ممكنة أربعة combination إما أن الأتنين مش موجودين
+
+734
+01:00:21,150 --> 01:00:26,990
+في ال relation هذه حالة ف في أو أن الأولى موجودة
+
+735
+01:00:26,990 --> 01:00:30,050
+في ال relation والتانية لأ فهذه relation لحالها
+
+736
+01:00:30,050 --> 01:00:33,250
+أصبحت relation ممكن تكون تعريف لحالها أو التانية
+
+737
+01:00:33,250 --> 01:00:36,610
+موجودة والأولى لأ برضه relation هي تعريف مختلف أو
+
+738
+01:00:36,610 --> 01:00:40,350
+الأتنين موجودين في ال relation بناء على تعريف ال
+
+739
+01:00:40,350 --> 01:00:47,160
+relation طيب لما نصيروا تلاتةصار تمانية، صار
+
+740
+01:00:47,160 --> 01:00:50,040
+تمانية، معناته هنا في عندي احتمالين، عندي اتنين،
+
+741
+01:00:50,040 --> 01:00:55,780
+اتنين، اتنين، two ways بقدر امثل فيهم ال element
+
+742
+01:00:55,780 --> 01:00:59,300
+الأول لل relation ال element التاني برضه فيله two
+
+743
+01:00:59,300 --> 01:01:09,780
+ways أن مرة، فصرت ايش؟ اتنين to the power أن تربيع
+
+744
+01:01:11,170 --> 01:01:14,650
+على اعتبار ان عددهم اصلا انتر بيئة عددهم أساسا
+
+745
+01:01:14,650 --> 01:01:21,770
+انتر بيئة فكل element منهم من ايش؟ من ال Cartesian
+
+746
+01:01:21,770 --> 01:01:27,930
+elements ال A Cartesian product of Aكل element
+
+747
+01:01:27,930 --> 01:01:32,950
+داخل ال set هذه ممكن يكون يا belong to relation او
+
+748
+01:01:32,950 --> 01:01:35,690
+not belong to relation فمعنى ذلك انه ماوجددش عدد
+
+749
+01:01:35,690 --> 01:01:38,870
+ال ways اللي بقدر امثل فيها اتنين طيب اللي جنبه
+
+750
+01:01:38,870 --> 01:01:43,260
+نفس الموضوع بس الاتنين هدول لازم يكون مع بعضضمن ال
+
+751
+01:01:43,260 --> 01:01:46,740
+relation أو واحد منهم بس في نهاية بمثلهم مع بعض لل
+
+752
+01:01:46,740 --> 01:01:51,580
+relation فمعنى ذلك هتكون ضرب اتنين في اتنين في
+
+753
+01:01:51,580 --> 01:01:54,460
+اتنين في اتنين في اتنين في اتنين في اتنين ستاشر
+
+754
+01:01:54,460 --> 01:01:58,300
+مرة طبعا ستاشر مرة لإن انا مخصص الموضوع لاربعة في
+
+755
+01:01:58,300 --> 01:02:02,500
+اربعة لاربعة تربيع لما بتكون n في n معناته to n
+
+756
+01:02:02,500 --> 01:02:06,920
+مرة to n مرة فصار عندى كلها to n مرة اتنين to the
+
+757
+01:02:06,920 --> 01:02:12,900
+power n تربيع اتنين to the powerإن تربيع واضحة ليش
+
+758
+01:02:12,900 --> 01:02:17,920
+عملناها اتنين to the power of n تربيع okay شوية
+
+759
+01:02:17,920 --> 01:02:20,440
+properties هالوقت ناخدها على ال relations هذه إيش
+
+760
+01:02:20,440 --> 01:02:24,200
+ممكن تكون ال relations كيف نمثلها أو كيف نعبّر
+
+761
+01:02:24,200 --> 01:02:28,500
+عنها أول حاجة ال reflexive أو reflexivity
+
+762
+01:02:28,500 --> 01:02:31,520
+reflexivity
+
+763
+01:02:31,520 --> 01:02:36,200
+بمعنى الإنعكسية الإنقلابية الإنعكسية أو الإنقلابية
+
+764
+01:02:36,200 --> 01:02:40,250
+بمعنى لو انعكست ال relationأو لو عكسنا ال two
+
+765
+01:02:40,250 --> 01:02:44,690
+elements ال relation هتظل ثابتة هتظل ثابتة بينهم
+
+766
+01:02:44,690 --> 01:02:47,850
+طبعا الكلام ده لن يحصل إم إلا إذا كانوا ال two
+
+767
+01:02:47,850 --> 01:02:50,890
+elements بيسوا بعض إذا كانوا ال two elements فعليا
+
+768
+01:02:50,890 --> 01:02:54,650
+بيسوا بعض في الحالة هذه بنقول أن ال relation R
+
+769
+01:02:54,650 --> 01:03:01,750
+relation R on a set A is reflexive إمتى if for all
+
+770
+01:03:01,750 --> 01:03:08,370
+A belong to set AA relation A هي مع نفسها العنصر
+
+771
+01:03:08,370 --> 01:03:12,350
+مع نفسه موجودين بمعنى لو انعكسوا هتظل ال relation
+
+772
+01:03:12,350 --> 01:03:17,450
+ثابتة هتظل ال relation بينهم ثابتة زي لما بتتكلموا
+
+773
+01:03:17,450 --> 01:03:21,870
+مثلا عن .. هناخد احنا logic مثال و هناخد مثال عنها
+
+774
+01:03:21,870 --> 01:03:25,510
+بدونش نقول أمثلة .. ال slides الجاية كلها أمثلة عن
+
+775
+01:03:25,510 --> 01:03:28,610
+الموضوع خلنا بس نشوف ال .. ال irreflexive ال
+
+776
+01:03:28,610 --> 01:03:34,830
+irreflexive المفروض أن هي ليستreflexive بس مش
+
+777
+01:03:34,830 --> 01:03:37,810
+بالسهولة هذه ليش؟ لأن أحيانا ممكن تكون في relation
+
+778
+01:03:37,810 --> 01:03:44,430
+لا هي reflexive ولا هي irreflexive كيف؟ بمعنى لو
+
+779
+01:03:44,430 --> 01:03:53,990
+عندكوا relation فيها واحد واحد وهي
+
+780
+01:03:53,990 --> 01:03:58,750
+أساسا كانت ال a عبارة عن واحد واثنين مثلا واحد
+
+781
+01:03:58,750 --> 01:04:04,610
+واحدفي الحالة هذه بقدرش أقول إن هي reflexive ليش؟
+
+782
+01:04:04,610 --> 01:04:09,710
+لأن واحد وواحد okay a relation a هي واضحة ايه ايه
+
+783
+01:04:09,710 --> 01:04:14,370
+بس مش كل مش
+
+784
+01:04:14,370 --> 01:04:17,330
+كل ال elements موجودة فعليا الإتنين و إتنين مش
+
+785
+01:04:17,330 --> 01:04:24,190
+موجودة معناته بقدرش أقول إن هي reflexiveالشرط for
+
+786
+01:04:24,190 --> 01:04:30,250
+all a belong to capital A، يعني كل عنصر ينتمي لset
+
+787
+01:04:30,250 --> 01:04:34,890
+A يجب أن يكون مع نفسهعشان أقول إن والله فعلا ال
+
+788
+01:04:34,890 --> 01:04:37,250
+relation كلها على بعض reflexive ممكن يكون في other
+
+789
+01:04:37,250 --> 01:04:40,390
+terms هم أحرار يعني ممكن يكون في واحد و اتنين
+
+790
+01:04:40,390 --> 01:04:45,270
+مالناش مشكلة خليهم بس أنا اللي بهمني الواحد و واحد
+
+791
+01:04:45,270 --> 01:04:48,330
+و الاتنين و اتنين و لو في تلاتة و تلاتة .. و
+
+792
+01:04:48,330 --> 01:04:50,990
+التلاتة و تلاتة تكون كمان موجودة لو في أربعة ..
+
+793
+01:04:50,990 --> 01:04:55,890
+الأربعة و أربعة تكون موجودة طيب واحد و واحد موجودة
+
+794
+01:04:55,890 --> 01:05:00,390
+اتنين و اتنين مش موجودة معناته هي دي not reflexive
+
+795
+01:05:01,570 --> 01:05:04,510
+طيب كويس not reflexive طب هل ممكن نكون
+
+796
+01:05:04,510 --> 01:05:09,510
+irreflexive؟ ال irreflexive ببساطة جدا إذا كانت ال
+
+797
+01:05:09,510 --> 01:05:12,030
+relation بنقول عليها irreflexive إذا كان ال
+
+798
+01:05:12,030 --> 01:05:17,810
+complementary أو ال compliment تبعها reflexive إذا
+
+799
+01:05:17,810 --> 01:05:20,650
+كان ال compliment تبعها reflexive طيب بنشوف ال
+
+800
+01:05:20,650 --> 01:05:25,310
+compliment لها دي معناته أي otherwise كل العناصر
+
+801
+01:05:25,310 --> 01:05:28,610
+أو كل العناصر الممكن لل Cartesian باستثناء الواحد
+
+802
+01:05:28,610 --> 01:05:32,410
+وواحديعني أنا متوقع هيطلع معانا اتنين و اتنين و
+
+803
+01:05:32,410 --> 01:05:36,330
+هيطلع معانا تلاتة و تلاتة بس هدول غير كافين ان هي
+
+804
+01:05:36,330 --> 01:05:39,910
+تكون reflexive لأن واحد واحد مش موجودة معناته ال
+
+805
+01:05:39,910 --> 01:05:44,750
+relation هنا برضه not reflexive فهي لا هي
+
+806
+01:05:44,750 --> 01:05:49,050
+reflexive ولا هي reflexive ولا هي reflexive خدوا
+
+807
+01:05:49,050 --> 01:05:53,070
+بالكم ال reflexive مش معناها ان هي not reflexive
+
+808
+01:05:53,070 --> 01:05:58,430
+reflexive لازم يكون جميع ال elements داخل ال set
+
+809
+01:05:59,750 --> 01:06:03,710
+موجودين مع نفسهم يعني واحد و واحد اتنين و اتنين
+
+810
+01:06:03,710 --> 01:06:05,910
+تلاتة و تلاتة اذا كانوا هم موجودين لحالهم هيك بقول
+
+811
+01:06:05,910 --> 01:06:09,810
+ان هي reflexive ان هي reflexive ان هي reflexive
+
+812
+01:06:09,810 --> 01:06:15,650
+طيب لو عندنا هنا واحد و اتنين بس ال relation هذي
+
+813
+01:06:15,650 --> 01:06:19,730
+ال reflexive بتصير هتصير irreflexive هتصير
+
+814
+01:06:19,730 --> 01:06:23,810
+irreflexive ليش لأن ال complement تبعها هيكون
+
+815
+01:06:23,810 --> 01:06:26,610
+reflexive هيكون موجود في الواحد و واحد هيكون موجود
+
+816
+01:06:26,610 --> 01:06:31,160
+في الواحد و اتنين و اتنين تلاتة و تلاتةفبتصير
+
+817
+01:06:31,160 --> 01:06:35,580
+reflexive طيب الحالة اللي بتكون فيها نصهم موجود و
+
+818
+01:06:35,580 --> 01:06:38,940
+نصهم مش موجود أو على الأقل واحد موجود و الباقي لأ
+
+819
+01:06:38,940 --> 01:06:43,260
+هذه لها هتطلع لا reflexive ولا irreflexive مثال و
+
+820
+01:06:43,260 --> 01:06:45,440
+زي ما قلنا احنا في النهاية الأمثلة بتاعتنا مش
+
+821
+01:06:45,440 --> 01:06:49,820
+مضرورة فقط على أرقام ممكن هي على objects على أشياء
+
+822
+01:06:49,820 --> 01:06:54,220
+اللي هي ال function أو ال relation likes between
+
+823
+01:06:54,220 --> 01:07:00,290
+peoplebetween people ال likes relation هذه لا هي
+
+824
+01:07:00,290 --> 01:07:04,350
+reflexive ولا هي reflexive، ليش؟ لأنه عشان أقول إن
+
+825
+01:07:04,350 --> 01:07:07,790
+هي reflexive معناته كل واحد المفروض أنه likes
+
+826
+01:07:07,790 --> 01:07:14,060
+himself، صحيح؟لازم .. يعني هو بحب حاله أو يعني
+
+827
+01:07:14,060 --> 01:07:16,420
+خليني أقول بفضل حاله، يعني هو معتز بنفسه خليني
+
+828
+01:07:16,420 --> 01:07:21,300
+أقول أو مغرور شوية، فهو حابب .. شايف أن هو أفضل
+
+829
+01:07:21,300 --> 01:07:25,640
+واحد، فممكن هنا مش كل الناس هيك، صحيح؟ فبقدرش أعمل
+
+830
+01:07:25,640 --> 01:07:30,080
+أن كل الناس هيك، و في نفس الوقت هي not reflexive،
+
+831
+01:07:30,080 --> 01:07:35,300
+ليش؟ لأن فعلا في ناس هيكيعني معناته نص ال
+
+832
+01:07:35,300 --> 01:07:39,880
+universive discourse متحققة و نصهم لأ لابقدر أقول
+
+833
+01:07:39,880 --> 01:07:42,820
+عليها reflexive ولا بقدر أقول عليها irreflexive
+
+834
+01:07:42,820 --> 01:07:49,960
+فهذه not reflexive و not irreflexive فلا هيك ولا
+
+835
+01:07:49,960 --> 01:07:53,200
+هيك ليش لأن زي ما قلنا likes هذه يمكن .. قلتلكوا
+
+836
+01:07:53,200 --> 01:07:57,980
+يمكن في أول الفصل ال relation likes هذه من أعقد ال
+
+837
+01:07:57,980 --> 01:08:01,850
+relations اللي مالهاش قواعدلأنه ممكن واحد likes
+
+838
+01:08:01,850 --> 01:08:07,510
+التاني، التاني بيبدلوش ال relation بيبدلوش ال
+
+839
+01:08:07,510 --> 01:08:11,850
+relation يعني كويسة فهي واحدة من الأمثلة اللي هي
+
+840
+01:08:11,850 --> 01:08:14,790
+لم نقدر نقول عليها reflexive ولم نقدر نقول عليها
+
+841
+01:08:14,790 --> 01:08:18,770
+irreflexive طيب نرجع شوية للأرقام اللي احنا مهتمين
+
+842
+01:08:18,770 --> 01:08:24,010
+فيها في شغلنا ونشوف في عندنا تلاتة relationsبدنا
+
+843
+01:08:24,010 --> 01:08:27,430
+نحدد .. احددوا معايا كل واحدة من ال relations
+
+844
+01:08:27,430 --> 01:08:34,270
+هدولة هل هي reflexive او reflexive او not لا هي
+
+845
+01:08:34,270 --> 01:08:38,310
+هيك ولا هي هيك لو قلنا .. طبعا بدنا نعرف أساسا ال
+
+846
+01:08:38,310 --> 01:08:40,790
+.. ال .. الست ال .. ال .. ايه تعتنا من الأول واحد
+
+847
+01:08:40,790 --> 01:08:44,810
+اتنين تلاتة أربعة يعني معنى ذلك انه الفيصل في
+
+848
+01:08:44,810 --> 01:08:47,410
+موضوع ان انا احكم reflexive ولا لأ الواحد واحد
+
+849
+01:08:47,410 --> 01:08:50,870
+اتنين اتنين تلاتة تلاتة اربعة واربعة طيب نمسك
+
+850
+01:08:50,870 --> 01:08:57,480
+الأولةليش not reflexive؟ الاتنين و التانين موجودة
+
+851
+01:08:57,480 --> 01:09:02,100
+طب هل ممكن تكون reflexive؟ برضه لأ فإذا الأولى no
+
+852
+01:09:02,100 --> 01:09:07,160
+طيب التانية reflexive reflexive على اعتبار أن في
+
+853
+01:09:07,160 --> 01:09:09,040
+عندنا الواحد و واحد موجودة اتنين و اتنين موجودة
+
+854
+01:09:09,040 --> 01:09:12,960
+تلاتة و تلاتة موجودة أربعة و أربعة موجودة okay طيب
+
+855
+01:09:12,960 --> 01:09:18,240
+الأخيرة not reflexive ليش؟ في عندنا الأربعة و
+
+856
+01:09:18,240 --> 01:09:24,640
+أربعة غير موجودة غير موجودة طيبلو أخدنا relation
+
+857
+01:09:24,640 --> 01:09:28,780
+لو
+
+858
+01:09:28,780 --> 01:09:34,180
+قولنا في relation عندنا عبارة عن واحد واتنين واحد
+
+859
+01:09:34,180 --> 01:09:46,160
+وتلاتة اتنين واربعة اتنين وتلاتة واحد واربعة اربعة
+
+860
+01:09:46,160 --> 01:09:52,940
+وتلاتةأربعة و .. أكمل ولا خلاص .. خلاص ما هي كاملة
+
+861
+01:09:52,940 --> 01:09:59,000
+ال compliment بتاعتها اللي عكسوها لو عكستوا .. لو
+
+862
+01:09:59,000 --> 01:10:04,500
+قولنا ان هدولة بدنا نستثنيهم من ال .. ال a كارتيزن
+
+863
+01:10:04,500 --> 01:10:11,040
+product a نفسها هتظهر ال compliment هي اللي
+
+864
+01:10:11,040 --> 01:10:14,480
+reflexive فهذه بنسميها هنا irreflexive هتكون
+
+865
+01:10:14,480 --> 01:10:15,140
+irreflexive
+
+866
+01:10:18,560 --> 01:10:26,440
+Okay ال inverse .. ال .. ال inverse و
+
+867
+01:10:26,440 --> 01:10:30,310
+بدنا ناخد بالنا ال inverse مش هي ال complementال
+
+868
+01:10:30,310 --> 01:10:34,130
+inverse حاجة و ال complement حاجة تانية تماماً
+
+869
+01:10:34,130 --> 01:10:41,290
+حاجة تانية تماماً كويس فإني binary relation R from
+
+870
+01:10:41,290 --> 01:10:46,830
+A to B has an inverse okay تمام هنسميها R to the
+
+871
+01:10:46,830 --> 01:10:50,290
+power minus one أو ال inverse of R relation هنقول
+
+872
+01:10:50,290 --> 01:10:55,250
+إن ال inverse of R صارت من مين؟ مش من A to B من B
+
+873
+01:10:55,250 --> 01:11:01,450
+to A من B to A فإذا والله فعلامن B to A بنعرفها
+
+874
+01:11:01,450 --> 01:11:08,850
+كتالة ال inverse of relation هتساوي كل زوج B و A
+
+875
+01:11:08,850 --> 01:11:15,170
+بشرط ان A و B can't belong لل relation can't
+
+876
+01:11:15,170 --> 01:11:20,930
+belong لل relation بمعنى ان ال relation ال
+
+877
+01:11:20,930 --> 01:11:24,250
+relation هذه فرضا ال inverse تبعها
+
+878
+01:11:27,060 --> 01:11:32,140
+هيكون واحد و واحد اتنين و واحد تلاتة و اتنين تلاتة
+
+879
+01:11:32,140 --> 01:11:38,600
+و تلاتة اربع و اربع عكسهم بس فقط هذه هتكون ايش ال
+
+880
+01:11:38,600 --> 01:11:49,100
+inverse ل ال relation تمام
+
+881
+01:11:49,100 --> 01:11:52,700
+فلو قلنا مثلا الأصغر من لان احنا مسكنها هنا في كذا
+
+882
+01:11:52,700 --> 01:11:55,760
+example ناخد برضه اصغر من ال relation اصغر منه
+
+883
+01:11:56,820 --> 01:11:59,560
+وأخدنا ال complement لل relation أصغر من لو
+
+884
+01:11:59,560 --> 01:12:03,040
+متذكرينه وكانت أكبر من أو ساوي، كويس، طيب ال
+
+885
+01:12:03,040 --> 01:12:10,960
+inverse للأصغر من هي عبارة عن B و A بشرط أن A أصغر
+
+886
+01:12:10,960 --> 01:12:17,200
+من B فلحظة صارت كأن A و B belong لل relation
+
+887
+01:12:20,600 --> 01:12:23,300
+اللي هي أصغر من .. احنا نتكلم أصلا عن الأصغر من
+
+888
+01:12:23,300 --> 01:12:28,440
+فهي a أصغر من b فهي belong لل relation فالأصل أن b
+
+889
+01:12:28,440 --> 01:12:32,220
+to a تكون belong لمن؟ لل inverse بتاعة ال relation
+
+890
+01:12:32,220 --> 01:12:37,240
+ال inverse بتاعة ال relation فهتكون b و a و نعكس
+
+891
+01:12:37,240 --> 01:12:42,290
+هدولب أكبر منه فصارت تساوي أكبر منه وليست أكبر من
+
+892
+01:12:42,290 --> 01:12:46,910
+أو يساوي هناك ال complement كانت أو يساوي لأنه لو
+
+893
+01:12:46,910 --> 01:12:52,750
+حطينا هنا يساوي من الأساس a و b مش أصغر من بعض فهي
+
+894
+01:12:52,750 --> 01:12:55,250
+أصلا مش موجودة في ال relation عشان أجيب ال inverse
+
+895
+01:12:55,250 --> 01:12:59,290
+بتبحر الشكل هذا فواضح هنا مش موجود يساوي رغم أنه
+
+896
+01:12:59,290 --> 01:13:02,610
+كان في ال complement موجود ال complement مكمل هذا
+
+897
+01:13:02,610 --> 01:13:09,610
+عكس هذا عكس مكمل غير العكس طيبمجرد بس إعادة ترتيب
+
+898
+01:13:09,610 --> 01:13:14,610
+يعني إعادة ترتيبهم اللي بيبتيجي قبل ال a فقط طيب
+
+899
+01:13:14,610 --> 01:13:18,410
+وبنان عليها بنجيب ال inverse ل ال relation اللي
+
+900
+01:13:18,410 --> 01:13:22,850
+هتكون بينهم for example لو أخدنا relation from
+
+901
+01:13:22,850 --> 01:13:24,290
+people to foods
+
+902
+01:13:27,140 --> 01:13:31,780
+ناس بتاكل الناس و الأكل فممكن الناس هدول نحط والله
+
+903
+01:13:31,780 --> 01:13:36,780
+تلت أربع أشخاص نقول والله محمد علي عمر مش عارف مين
+
+904
+01:13:36,780 --> 01:13:42,760
+ما يكون يكون مجموعة هنا نفترض أنه الشخص A الشخص B
+
+905
+01:13:42,760 --> 01:13:47,780
+الشخص C وهدول بدهم ياكلوا بدهم ياكلوا واحد بدهم
+
+906
+01:13:47,780 --> 01:13:54,460
+ياكله مش عارف ال .. ال .. الأكلة الأولى
+
+907
+01:13:59,090 --> 01:14:05,250
+Apple خلّينا نشوف Banana بيكفي
+
+908
+01:14:05,250 --> 01:14:11,030
+هاي اللي بدناش نشوفه أكتر من هيك طيب فلحظة في
+
+909
+01:14:11,030 --> 01:14:17,810
+الحالة هذه بقدر أقول له a eats apple a eats banana
+
+910
+01:14:17,810 --> 01:14:22,090
+بي eats banana إذا كان ال relation موجودة بيصير
+
+911
+01:14:22,090 --> 01:14:27,690
+والله هنا بس بنعمل x معناته a بيأكل تفاح بيأكل
+
+912
+01:14:27,690 --> 01:14:37,330
+تفاح وموزC بياكل مثلا موز، كويس؟ هذه إيش؟ هذه ال R
+
+913
+01:14:37,330 --> 01:14:41,330
+صارت اللي هو بياكل هذه ال relation، بياكل ال
+
+914
+01:14:41,330 --> 01:14:49,270
+religion طب لو عكسناهم صارت apple is eaten، مأكل،
+
+915
+01:14:49,270 --> 01:14:54,220
+فصارت الأكل عكسها مأكلفهي ال inverse تبعها هتبصي
+
+916
+01:14:54,220 --> 01:14:57,860
+ريكي إيش قلت ال inverse تبعها اللي هو ال inverse
+
+917
+01:14:57,860 --> 01:15:03,000
+فصارت كل اللي هنعمله relation بالعكس بي R to the
+
+918
+01:15:03,000 --> 01:15:08,100
+power أو inverse R بي inverse RA بس بحكي أنه بي is
+
+919
+01:15:08,100 --> 01:15:16,140
+eaten by A فصارت banana is eaten by بيو هذه موجودة
+
+920
+01:15:16,140 --> 01:15:19,640
+أصلا يعني مش كل الناس بيحبوا كل الطبخات يعني صحيح؟
+
+921
+01:15:19,640 --> 01:15:22,620
+فممكن يكون بيفضل طبخات و بيعمل طبخات فممكن جدا
+
+922
+01:15:22,620 --> 01:15:26,520
+تعمله table بهذا الشكل تحطوا كل الطبخات الممكنة
+
+923
+01:15:26,520 --> 01:15:31,000
+خلال الأسبوع و تحطوا على فرض العائلة عندكم و
+
+924
+01:15:31,000 --> 01:15:33,380
+تحددوا فلان أه بيحب الأكل الفلانية و بيحبش الأكل
+
+925
+01:15:33,380 --> 01:15:38,080
+الفلانية صحيح؟ فبتعملوها برضه فهن ال relation
+
+926
+01:15:38,080 --> 01:15:43,750
+ممكنة معقولة ممكنة مش بالضرورة أنه a eats any bمش
+
+927
+01:15:43,750 --> 01:15:47,790
+بالضرورة ان ال a بياكل اي شغلة في ال b فهذا كل
+
+928
+01:15:47,790 --> 01:15:51,350
+اللي بنعمل بس ان احنا بنحولها ل passive voice ل
+
+929
+01:15:51,350 --> 01:15:55,390
+passive voice المفعول بيه بيجي في الأول مفعول بيه
+
+930
+01:15:55,390 --> 01:16:00,630
+بدخل في الأول فهياخد التصريف التالت لل verb التالت
+
+931
+01:16:00,630 --> 01:16:03,570
+لل verb فواضح ان التصريف التالت لل verb هذا اللي
+
+932
+01:16:03,570 --> 01:16:07,330
+هو ال inverse تبع ال verb نفسه هكون ال inverse تع
+
+933
+01:16:07,330 --> 01:16:12,480
+ال verb هو نفسه ال inverseفي ايش بنستغلها يعني
+
+934
+01:16:12,480 --> 01:16:15,400
+احنا okay تعرفنا ان في حاجة اسمها inverse في ايش
+
+935
+01:16:15,400 --> 01:16:19,820
+ممكن نستعملها او في ايش ممكن تفيدنا هتفيدنا ان
+
+936
+01:16:19,820 --> 01:16:25,960
+اعرف هل ال relation symmetry او antisymmetric هل
+
+937
+01:16:25,960 --> 01:16:30,500
+بقدر اقول ان ال relation عندنا symmetry او
+
+938
+01:16:30,500 --> 01:16:36,500
+symmetric او antisymmetric لحظة antisymmetric برضه
+
+939
+01:16:36,500 --> 01:16:39,320
+مش معناها ان هي asymmetric
+
+940
+01:16:42,330 --> 01:16:47,430
+Symmetric عكسها Asymmetric صحيح؟ طيب Anti
+
+941
+01:16:47,430 --> 01:16:50,570
+-symmetric إيش تاني؟ هذه حاجة مختلفة تمام، مالهاش
+
+942
+01:16:50,570 --> 01:16:54,070
+علاقة بالـ Asymmetric اللي أنتوا عارفينها، اللي هي
+
+943
+01:16:54,070 --> 01:16:57,830
+العكس تبعها خلّيني أخدهم واحدة واحدة ال relation R
+
+944
+01:16:57,830 --> 01:17:01,650
+on a set A is symmetric إيه أنت بتكون symmetric؟
+
+945
+01:17:01,650 --> 01:17:06,710
+فعلا بقدر بسميها symmetric if and only if R equal
+
+946
+01:17:06,710 --> 01:17:10,990
+to inverse Rإذا والله ال R بتسوي ال inverse R
+
+947
+01:17:10,990 --> 01:17:14,450
+بسميها symmetric خلاص إذا ال R بتسوي ال inverse R
+
+948
+01:17:14,450 --> 01:17:20,110
+بنقول والله خلاص symmetric بمعنى لو عندكوا ال ..
+
+949
+01:17:20,110 --> 01:17:25,250
+كل ال relations اللي موجودة عندكوا هنا هذه احنا
+
+950
+01:17:25,250 --> 01:17:31,590
+سميناها إيه؟ 1 1 2 2 3 3 لو جيبنا ال inverse تبعها
+
+951
+01:17:33,970 --> 01:17:38,250
+بسوء بعض، بسوء بعض، صحيح؟ معناته أصلا ال R دي
+
+952
+01:17:38,250 --> 01:17:41,910
+symmetric لو جبت ال inverse تبعها، هيظل نفسها،
+
+953
+01:17:41,910 --> 01:17:51,450
+هيظل نفسها، طيب ممكن جدا يكون معاها تلاتة و اتنين،
+
+954
+01:17:51,450 --> 01:17:55,750
+لحظوا، و نسكر القص هنا، طيب في الحالة دي بيصير ال
+
+955
+01:17:55,750 --> 01:18:01,970
+inverse Rواحد واحد اتنين اتنين تلاتة تلاتة اتنين
+
+956
+01:18:01,970 --> 01:18:07,810
+تلاتة هاذي بطلت symmetric بقدر اقولكوا احنا خلنا
+
+957
+01:18:07,810 --> 01:18:10,670
+واحدة واحدة بديش اللي خبطهم الدنيا في بعض علاجات
+
+958
+01:18:10,670 --> 01:18:13,590
+symmetric هل هي symmetric لأ مش symmetric بس ال
+
+959
+01:18:13,590 --> 01:18:16,290
+asymmetric و ال antisymmetric خلينا شوية شوية
+
+960
+01:18:16,290 --> 01:18:18,770
+بدناش اللي خبطهم في بعض لأن التلاتة ممكن اللي
+
+961
+01:18:18,770 --> 01:18:25,070
+خبطهم فخلينا حاجة حاجة طيب لو اتنين و تلاتة
+
+962
+01:18:30,060 --> 01:18:34,440
+صارت symmetric صارت هيك symmetric بمعنى أنا مابديش
+
+963
+01:18:34,440 --> 01:18:37,780
+احط في بالك ان ال symmetric هي بس المتشابهات لأ
+
+964
+01:18:37,780 --> 01:18:49,620
+ممكن هي term زي هذا يكون فيه symmetric okay فإذا
+
+965
+01:18:49,620 --> 01:18:56,700
+مثال على ال symmetric إذا كانت aB belong to
+
+966
+01:18:56,700 --> 01:19:03,340
+relation R if and only if B و A برضه belong ل
+
+967
+01:19:03,340 --> 01:19:08,040
+relation R فإذا كان كل عنصر عكسه موجود فهي
+
+968
+01:19:08,040 --> 01:19:11,480
+symmetric فهي symmetric طيب example ال equality
+
+969
+01:19:11,480 --> 01:19:19,310
+السيمتريك الأقل من لأبالظبط لأن لما أقول واحد أقل
+
+970
+01:19:19,310 --> 01:19:23,210
+من اتنين بقدرش أقول اتنين أقل من واحد لما عكسهم
+
+971
+01:19:23,210 --> 01:19:26,570
+تصبتش لكن لما أقول واحد بيساوي واحد اه واحد أولى
+
+972
+01:19:26,570 --> 01:19:31,430
+بيساوي واحد بمش الحل وانتوا بتحلوا alpha واحد
+
+973
+01:19:31,430 --> 01:19:36,070
+تساوي واحد او اجت معاكم واحد تساوي alpha واحد بمش
+
+974
+01:19:36,070 --> 01:19:40,710
+الحلبمش الحال لكن لو قلنا أثناء الشغل و انتوا
+
+975
+01:19:40,710 --> 01:19:43,650
+بتعملوا مجموعة relations قلتوا alpha واحد أكبر ..
+
+976
+01:19:43,650 --> 01:19:46,690
+أصغر من واحد و بعدين تيجي تقولوا لو الله واحد أصغر
+
+977
+01:19:46,690 --> 01:19:50,330
+من alpha واحد مانفعش تظبطش هذه .. طبعا هدولة غلط
+
+978
+01:19:50,330 --> 01:19:54,290
+لكن تساوي أه بمش الحال يعني و انتوا بتحلوا الطرف
+
+979
+01:19:54,290 --> 01:19:55,890
+الشمال حطته يمين وليه يمين وليه يمين وليه يمين
+
+980
+01:19:55,890 --> 01:19:56,070
+وليه يمين وليه يمين وليه يمين وليه يمين وليه يمين
+
+981
+01:19:56,070 --> 01:19:56,810
+وليه يمين وليه يمين وليه يمين وليه يمين وليه يمين
+
+982
+01:19:56,810 --> 01:20:05,790
+وليه يمين وليه يمين وليه يمين و
+
+983
+01:20:06,170 --> 01:20:11,390
+A is married to B نفس هي B is married to A نفس
+
+984
+01:20:11,390 --> 01:20:17,070
+الشغل نفس الشي طيب likes لأ مش بالضروري A likes B
+
+985
+01:20:17,070 --> 01:20:20,850
+معناته بيه likes A واحد بيحب مثلا يدرس مع التاني
+
+986
+01:20:20,850 --> 01:20:29,130
+التاني بيحبش يدرس معاه بيحبش يقول this likes A طيب
+
+987
+01:20:29,130 --> 01:20:36,210
+a binary relation R is antisymmetric ifA و B
+
+988
+01:20:36,210 --> 01:20:41,110
+belong to R employes
+
+989
+01:20:41,110 --> 01:20:45,950
+او implication بدنا ناخد بالنا منها B و A not
+
+990
+01:20:45,950 --> 01:20:52,210
+belong to R not belong to R فإذا الأقل من is
+
+991
+01:20:52,210 --> 01:20:58,370
+antisymmetric أقل من is antisymmetric بس likes is
+
+992
+01:20:58,370 --> 01:21:02,070
+not قولتلكوا ال likes هذه ولا relation مظبطة معها
+
+993
+01:21:02,070 --> 01:21:07,210
+ال likes ولا إشي بظبط معهاليش؟ لأنه ما .. ما ..
+
+994
+01:21:07,210 --> 01:21:10,650
+مابنعرفش يعني مالهاش أي قواعد مالهاش أي relations
+
+995
+01:21:10,650 --> 01:21:13,950
+الحقيقة فدائما هتلاقوا لما بدنا نقول is not
+
+996
+01:21:13,950 --> 01:21:18,050
+هتكونوا likes هتلاقوا likes طيب أصغر من asymmetric
+
+997
+01:21:18,050 --> 01:21:24,050
+برضه هتبين أكتر يمكن مع ال .. التلات تعريفات هدول
+
+998
+01:21:24,050 --> 01:21:26,430
+ناخدهم و المرة الجاية ناخد عليهم applications
+
+999
+01:21:26,430 --> 01:21:30,030
+بتكون انت حتى يمكن قرأتهم كويس ناخدهم ناخد عليهم
+
+1000
+01:21:30,030 --> 01:21:30,370
+applications
+
+1001
+01:21:34,680 --> 01:21:39,060
+خلاص المرة اللي جاية احنا .. احنا اليوم مشينا منيح
+
+1002
+01:21:39,060 --> 01:21:41,440
+يعني كويس يلا اعطيكوا العافية المرة اللي جاية بن
+
+1003
+01:21:41,440 --> 01:21:44,340
+.. بنبدأ من هنا و بنكمل examples عليها ان شاء الله
+
+1004
+01:21:44,340 --> 01:21:45,120
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..798097d838d3cac1bdf34bc79a1b4c9f4c808d7b
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4508, "start": 20.96, "end": 45.08, "text": "بسم الله الرحمن الرحيم الصلاة والسلام عليكم ورحمة الله وبركاته يا سيدنا محمد وعلي أهلي وصحابي أجمعين اليوم هنبدأ في موضوع جديد ان شاء الله recurrence relations هنشوف ال recurrence relations او ايش هي علاقة انتقارية نتكلم عليها نشوف تعريفها أولا نعمل definition لها و بعد ال definition تبعنا هناخد كيف احنا نجيب ال general equation ل recurrence relation", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 35186, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 20292, 5551, 3224, 20292, 4032, 9381, 5016, 16758, 1829, 5551, 7435, 2304, 3615, 9957, 45595, 20498, 8032, 1863, 44510, 10721, 8978, 3714, 2407, 11242, 45367, 10874, 16254, 3215, 16472, 13412, 16606, 21984, 18680, 10760, 2299, 8032, 1863, 8592, 38688, 2423, 18680, 10760, 2299, 1975, 2407, 1975, 1829, 8592, 39896, 11203, 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" أصغر", "probability": 0.972900390625}, {"start": 2639.74, "end": 2639.9, "word": " من", "probability": 0.99658203125}, {"start": 2639.9, "end": 2640.36, "word": " هاي", "probability": 0.611328125}, {"start": 2640.36, "end": 2640.44, "word": " ال", "probability": 0.81787109375}, {"start": 2640.44, "end": 2640.86, "word": " relation", "probability": 0.99462890625}, {"start": 2640.86, "end": 2641.38, "word": " هذه", "probability": 0.282958984375}, {"start": 2641.38, "end": 2641.7, "word": " هي", "probability": 0.7763671875}, {"start": 2641.7, "end": 2642.04, "word": " ال", "probability": 0.96142578125}, {"start": 2642.04, "end": 2642.3, "word": " relation", "probability": 0.99462890625}, {"start": 2642.3, "end": 2642.72, "word": " بتاعتنا", "probability": 0.9305419921875}, {"start": 2642.72, "end": 2643.26, "word": " كويس", "probability": 0.8522135416666666}], "temperature": 1.0}, {"id": 101, "seek": 267299, "start": 2644.29, "end": 2672.99, "text": "مبدأيا طبعا ناخد بالنا أن مادام relation يعني هي related to شغلة related to شغلة تانية يعني دايما في reference لما نقول مثلا خمسة أكبر من اتنين فبالنسبة للخمسة ال reference هي الاتنين هي الاتنين لأن related للاتنين الخمسة أكبر فصار ال relation بتاعتنا أكبر منه هنا نتكلم عن أصغر من ال N هذه أصغر من", "tokens": [2304, 44510, 10721, 25528, 23032, 3555, 3615, 995, 8717, 47283, 3215, 20666, 8315, 14739, 3714, 18513, 10943, 9721, 37495, 22653, 39896, 4077, 281, 13412, 17082, 37977, 4077, 281, 13412, 17082, 37977, 6055, 7649, 10632, 37495, 22653, 11778, 47302, 15042, 8978, 6408, 5296, 15042, 8717, 39648, 50113, 15040, 16490, 2304, 3794, 3660, 5551, 4117, 26890, 9154, 1975, 2655, 1863, 9957, 6156, 3555, 6027, 1863, 35457, 3660, 24976, 9778, 2304, 3794, 3660, 2423, 6408, 39896, 2423, 9307, 1863, 9957, 39896, 2423, 9307, 1863, 9957, 5296, 33456, 4077, 24976, 9307, 1863, 9957, 33962, 2304, 3794, 3660, 5551, 4117, 26890, 6156, 9381, 9640, 2423, 9721, 39894, 995, 34268, 8315, 5551, 4117, 26890, 9154, 3224, 34105, 8717, 2655, 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"text": "ال M ال N أصغر من ال M على اعتبار أن ال relation هنا أصغر من ال relation هنا عندنا أصغر من فهذه معناها أن A و B كزوج مرتب belong to set جديدة اللي هي ال subset من كلهم ال set هذه عبارة عن أصغر من عبارة عن أصغر من لو غيرنا هنا و حطناها أرقام برضه", "tokens": [6027, 376, 2423, 426, 5551, 9381, 17082, 2288, 9154, 2423, 376, 15844, 1975, 34268, 3555, 9640, 14739, 2423, 9721, 34105, 5551, 9381, 17082, 2288, 9154, 2423, 9721, 34105, 43242, 8315, 5551, 9381, 17082, 2288, 9154, 6156, 3224, 24192, 20449, 8315, 11296, 14739, 316, 4032, 363, 9122, 11622, 29245, 3714, 43500, 3555, 5784, 281, 992, 10874, 16254, 41891, 13672, 1829, 39896, 2423, 25993, 9154, 28242, 16095, 2423, 992, 29538, 6225, 3555, 9640, 3660, 18871, 5551, 9381, 17082, 2288, 9154, 6225, 3555, 9640, 3660, 18871, 5551, 9381, 17082, 2288, 9154, 45164, 32771, 13546, 8315, 34105, 4032, 11331, 9566, 8315, 11296, 5551, 2288, 4587, 10943, 4724, 43042, 3224], "avg_logprob": -0.1454156812913013, "compression_ratio": 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351622, "start": 3486.88, "end": 3516.22, "text": "الستاش هدولة عدد ال Cartesian product بمعنى هدولة العدد الأقصى أو العدد خلينا نقول اللي ممكن إما أه أو لأ بمعنى كل زوج من هدول يعتبر واحد من الستاش إله احتمالين إما belong لل relation أو not belong لل relation معنى ذلك أنه ممكن", "tokens": [6027, 14851, 33599, 8032, 3215, 12610, 3660, 6225, 3215, 3215, 2423, 22478, 42434, 1674, 4724, 2304, 3615, 1863, 7578, 8032, 3215, 12610, 3660, 18863, 3215, 3215, 16247, 4587, 9381, 7578, 34051, 18863, 3215, 3215, 16490, 20292, 8315, 8717, 39648, 13672, 1829, 3714, 43020, 11933, 15042, 5551, 3224, 34051, 5296, 10721, 4724, 2304, 3615, 1863, 7578, 28242, 30767, 29245, 9154, 8032, 3215, 12610, 7251, 34268, 26890, 36764, 24401, 9154, 2423, 14851, 33599, 11933, 43761, 1975, 33753, 2304, 6027, 9957, 11933, 15042, 5784, 24976, 9721, 34051, 406, 5784, 24976, 9721, 20449, 1863, 7578, 29910, 23275, 14739, 3224, 3714, 43020], "avg_logprob": -0.17187500471363262, "compression_ratio": 1.82, "no_speech_prob": 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موجودة تلاتة و تلاتة موجودة أربعة و أربعة موجودة okay طيب الأخيرة not reflexive ليش؟ في عندنا الأربعة و أربعة غير موجودة غير موجودة طيب", "tokens": [20292, 8592, 406, 23802, 488, 22807, 2423, 9307, 1863, 9957, 4032, 16712, 7649, 9957, 3714, 29245, 23328, 3660, 23032, 3555, 8032, 1211, 3714, 43020, 6055, 30544, 23802, 488, 22807, 4724, 43042, 3224, 5296, 10721, 6156, 28814, 15730, 16247, 12610, 7578, 572, 23032, 1829, 3555, 16712, 7649, 10632, 23802, 488, 23802, 488, 15844, 1975, 34268, 3555, 9640, 14739, 8978, 43242, 8315, 2423, 14407, 24401, 4032, 36764, 24401, 3714, 29245, 23328, 3660, 1975, 2655, 1863, 9957, 4032, 1975, 2655, 1863, 9957, 3714, 29245, 23328, 3660, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 3660, 3714, 29245, 23328, 3660, 5551, 25513, 27884, 4032, 5551, 25513, 27884, 3714, 29245, 23328, 3660, 1392, 23032, 1829, 3555, 16247, 9778, 48923, 406, 23802, 488, 32239, 8592, 22807, 8978, 43242, 8315, 16247, 25513, 27884, 4032, 5551, 25513, 27884, 32771, 13546, 3714, 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"end": 4138.02, "word": " ممكن", "probability": 0.992431640625}, {"start": 4138.02, "end": 4138.2, "word": " تكون", "probability": 0.976806640625}, {"start": 4138.2, "end": 4138.86, "word": " reflexive؟", "probability": 0.7864583333333334}, {"start": 4138.86, "end": 4139.84, "word": " برضه", "probability": 0.726806640625}, {"start": 4139.84, "end": 4140.02, "word": " لأ", "probability": 0.929931640625}, {"start": 4140.02, "end": 4140.48, "word": " فإذا", "probability": 0.6905924479166666}, {"start": 4140.48, "end": 4141.52, "word": " الأولى", "probability": 0.8689778645833334}, {"start": 4141.52, "end": 4142.1, "word": " no", "probability": 0.450927734375}, {"start": 4142.1, "end": 4142.88, "word": " طيب", "probability": 0.9547526041666666}, {"start": 4142.88, "end": 4143.38, "word": " التانية", "probability": 0.9440104166666666}, {"start": 4143.38, "end": 4145.52, "word": " reflexive", "probability": 0.915283203125}, {"start": 4145.52, "end": 4146.3, "word": " reflexive", "probability": 0.613525390625}, {"start": 4146.3, "end": 4146.62, "word": " على", "probability": 0.7763671875}, {"start": 4146.62, "end": 4146.94, "word": " اعتبار", "probability": 0.96533203125}, {"start": 4146.94, "end": 4147.04, "word": " أن", "probability": 0.560546875}, {"start": 4147.04, "end": 4147.16, "word": " في", "probability": 0.71923828125}, {"start": 4147.16, "end": 4147.38, "word": " عندنا", "probability": 0.85205078125}, {"start": 4147.38, "end": 4147.62, "word": " الواحد", "probability": 0.95654296875}, {"start": 4147.62, "end": 4147.7, "word": " و", "probability": 0.556640625}, {"start": 4147.7, "end": 4147.92, "word": " واحد", "probability": 0.930419921875}, {"start": 4147.92, "end": 4148.36, "word": " موجودة", "probability": 0.96435546875}, {"start": 4148.36, "end": 4148.54, "word": " اتنين", "probability": 0.86029052734375}, {"start": 4148.54, "end": 4148.64, "word": " و", "probability": 0.966796875}, {"start": 4148.64, "end": 4148.76, "word": " اتنين", "probability": 0.9310302734375}, {"start": 4148.76, "end": 4149.04, "word": " موجودة", "probability": 0.988037109375}, {"start": 4149.04, "end": 4149.3, "word": " تلاتة", "probability": 0.7957763671875}, {"start": 4149.3, "end": 4149.4, "word": " و", "probability": 0.96240234375}, {"start": 4149.4, "end": 4149.58, "word": " تلاتة", "probability": 0.981689453125}, {"start": 4149.58, "end": 4149.88, "word": " موجودة", "probability": 0.980224609375}, {"start": 4149.88, "end": 4150.1, "word": " أربعة", "probability": 0.7298990885416666}, {"start": 4150.1, "end": 4150.18, "word": " و", "probability": 0.8671875}, {"start": 4150.18, "end": 4150.3, "word": " أربعة", "probability": 0.9451497395833334}, {"start": 4150.3, "end": 4150.8, "word": " موجودة", "probability": 0.9918212890625}, {"start": 4150.8, "end": 4151.24, "word": " okay", "probability": 0.325439453125}, {"start": 4151.24, "end": 4152.96, "word": " طيب", "probability": 0.9558919270833334}, {"start": 4152.96, "end": 4153.54, "word": " الأخيرة", "probability": 0.9698893229166666}, {"start": 4153.54, "end": 4154.58, "word": " not", "probability": 0.75146484375}, {"start": 4154.58, "end": 4156.12, "word": " reflexive", "probability": 0.968994140625}, {"start": 4156.12, "end": 4157.56, "word": " ليش؟", "probability": 0.89306640625}, {"start": 4157.56, "end": 4157.66, "word": " في", "probability": 0.50390625}, {"start": 4157.66, "end": 4157.88, "word": " عندنا", "probability": 0.986083984375}, {"start": 4157.88, "end": 4158.18, "word": " الأربعة", "probability": 0.9290364583333334}, {"start": 4158.18, "end": 4158.24, "word": " و", "probability": 0.97607421875}, {"start": 4158.24, "end": 4158.54, "word": " أربعة", "probability": 0.9112955729166666}, {"start": 4158.54, "end": 4158.92, "word": " غير", "probability": 0.9970703125}, {"start": 4158.92, "end": 4159.46, "word": " موجودة", "probability": 0.9876708984375}, {"start": 4159.46, "end": 4160.0, "word": " غير", "probability": 0.87255859375}, {"start": 4160.0, "end": 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"word": " أخدنا", "probability": 0.971923828125}, {"start": 4163.48, "end": 4164.64, "word": " relation", "probability": 0.99658203125}, {"start": 4164.64, "end": 4168.78, "word": " لو", "probability": 0.497314453125}, {"start": 4168.78, "end": 4169.02, "word": " قولنا", "probability": 0.8151041666666666}, {"start": 4169.02, "end": 4169.14, "word": " في", "probability": 0.912109375}, {"start": 4169.14, "end": 4169.5, "word": " relation", "probability": 0.62158203125}, {"start": 4169.5, "end": 4170.42, "word": " عندنا", "probability": 0.9482421875}, {"start": 4170.42, "end": 4170.86, "word": " عبارة", "probability": 0.9833984375}, {"start": 4170.86, "end": 4171.02, "word": " عن", "probability": 0.9873046875}, {"start": 4171.02, "end": 4171.54, "word": " واحد", "probability": 0.980712890625}, {"start": 4171.54, "end": 4172.42, "word": " واتنين", "probability": 0.8114013671875}, {"start": 4172.42, "end": 4174.18, "word": " واحد", "probability": 0.808837890625}, {"start": 4174.18, "end": 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compliment هي اللي reflexive فهذه بنسميها هنا irreflexive هتكون irreflexive", "tokens": [10721, 25513, 27884, 4032, 4386, 5551, 24793, 1211, 49429, 16490, 1211, 33546, 4386, 16490, 1211, 33546, 19446, 39896, 9122, 10943, 37977, 2423, 16250, 39894, 995, 34268, 11296, 13672, 1829, 6225, 4117, 3794, 2407, 11296, 45164, 6225, 4117, 14851, 14407, 4386, 45164, 12174, 12610, 8315, 16472, 8032, 3215, 12610, 3660, 47525, 8315, 8717, 14851, 12984, 22653, 16095, 9154, 2423, 4386, 2423, 257, 9122, 9640, 31371, 11622, 1863, 1674, 257, 8717, 36178, 11296, 8032, 2655, 19913, 3224, 2288, 2423, 16250, 39896, 13672, 1829, 23802, 488, 6156, 3224, 24192, 44945, 38251, 1829, 11296, 34105, 16014, 69, 2021, 488, 8032, 2655, 30544, 16014, 69, 2021, 488], "avg_logprob": -0.25804003639128603, "compression_ratio": 1.7072072072072073, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4188.44, "end": 4189.14, "word": "أربعة", "probability": 0.8505859375}, {"start": 4189.14, "end": 4189.42, "word": " و", 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بتاعتها", "probability": 0.908203125}, {"start": 4196.24, "end": 4197.96, "word": " اللي", "probability": 0.712646484375}, {"start": 4197.96, "end": 4198.38, "word": " عكسوها", "probability": 0.96416015625}, {"start": 4198.38, "end": 4198.52, "word": " لو", "probability": 0.85107421875}, {"start": 4198.52, "end": 4198.86, "word": " عكستوا", "probability": 0.864501953125}, {"start": 4198.86, "end": 4198.9, "word": " ..", "probability": 0.356689453125}, {"start": 4198.9, "end": 4199.0, "word": " لو", "probability": 0.96728515625}, {"start": 4199.0, "end": 4199.3, "word": " قولنا", "probability": 0.8175455729166666}, {"start": 4199.3, "end": 4199.46, "word": " ان", "probability": 0.33203125}, {"start": 4199.46, "end": 4199.82, "word": " هدولة", "probability": 0.853515625}, {"start": 4199.82, "end": 4200.02, "word": " بدنا", "probability": 0.96875}, {"start": 4200.02, "end": 4201.02, "word": " نستثنيهم", "probability": 0.9181640625}, {"start": 4201.02, "end": 4202.1, "word": " من", "probability": 0.98828125}, {"start": 4202.1, "end": 4203.06, "word": " ال", "probability": 0.7607421875}, {"start": 4203.06, "end": 4203.08, "word": " ..", "probability": 0.488037109375}, {"start": 4203.08, "end": 4203.24, "word": " ال", "probability": 0.84130859375}, {"start": 4203.24, "end": 4203.5, "word": " a", "probability": 0.489990234375}, {"start": 4203.5, "end": 4204.5, "word": " كارتيزن", "probability": 0.681298828125}, {"start": 4204.5, "end": 4204.78, "word": " product", "probability": 0.79150390625}, {"start": 4204.78, "end": 4205.44, "word": " a", "probability": 0.3564453125}, {"start": 4205.44, "end": 4207.32, "word": " نفسها", "probability": 0.93359375}, {"start": 4207.32, "end": 4209.54, "word": " هتظهر", "probability": 0.93828125}, {"start": 4209.54, "end": 4209.7, "word": " ال", "probability": 0.9638671875}, {"start": 4209.7, "end": 4210.14, "word": " compliment", "probability": 0.93994140625}, {"start": 4210.14, "end": 4210.8, "word": " هي", "probability": 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"word": " ناخد", "probability": 0.9905598958333334}, {"start": 4226.86, "end": 4227.14, "word": " بالنا", "probability": 0.672119140625}, {"start": 4227.14, "end": 4227.28, "word": " ال", "probability": 0.90234375}, {"start": 4227.28, "end": 4227.7, "word": " inverse", "probability": 0.9658203125}, {"start": 4227.7, "end": 4228.02, "word": " مش", "probability": 0.97705078125}, {"start": 4228.02, "end": 4228.22, "word": " هي", "probability": 0.65380859375}, {"start": 4228.22, "end": 4228.32, "word": " ال", "probability": 0.9326171875}, {"start": 4228.32, "end": 4228.68, "word": " complement", "probability": 0.56689453125}], "temperature": 1.0}, {"id": 163, "seek": 425839, "start": 4230.05, "end": 4258.39, "text": "ال inverse حاجة و ال complement حاجة تانية تماماً حاجة تانية تماماً كويس فإني binary relation R from A to B has an inverse okay تمام هنسميها R to the power minus one أو ال inverse of R relation هنقول إن ال inverse of R صارت من مين؟ مش من A to B من B to A من B to A فإذا والله 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"probability": 0.9072265625}, {"start": 4249.71, "end": 4250.29, "word": " هنقول", "probability": 0.9586588541666666}, {"start": 4250.29, "end": 4250.43, "word": " إن", "probability": 0.446044921875}, {"start": 4250.43, "end": 4250.75, "word": " ال", "probability": 0.95068359375}, {"start": 4250.75, "end": 4251.03, "word": " inverse", "probability": 0.93017578125}, {"start": 4251.03, "end": 4251.21, "word": " of", "probability": 0.9609375}, {"start": 4251.21, "end": 4251.59, "word": " R", "probability": 0.98828125}, {"start": 4251.59, "end": 4252.33, "word": " صارت", "probability": 0.9140625}, {"start": 4252.33, "end": 4252.47, "word": " من", "probability": 0.9873046875}, {"start": 4252.47, "end": 4252.81, "word": " مين؟", "probability": 0.784423828125}, {"start": 4252.81, "end": 4252.95, "word": " مش", "probability": 0.9208984375}, {"start": 4252.95, "end": 4253.15, "word": " من", "probability": 0.974609375}, {"start": 4253.15, "end": 4253.33, "word": " A", "probability": 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4258.39, "word": " فعلا", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 164, "seek": 428425, "start": 4259.25, "end": 4284.25, "text": "من B to A بنعرفها كتالة ال inverse of relation هتساوي كل زوج B و A بشرط ان A و B can't belong لل relation can't belong لل relation بمعنى ان ال relation ال relation هذه فرضا ال inverse تبعها", "tokens": [27842, 363, 281, 316, 44945, 3615, 28480, 11296, 9122, 2655, 6027, 3660, 2423, 17340, 295, 9721, 8032, 2655, 3794, 995, 45865, 28242, 30767, 29245, 363, 4032, 316, 4724, 8592, 2288, 9566, 16472, 316, 4032, 363, 393, 380, 5784, 24976, 9721, 393, 380, 5784, 24976, 9721, 4724, 2304, 3615, 1863, 7578, 16472, 2423, 9721, 2423, 9721, 29538, 6156, 43042, 995, 2423, 17340, 6055, 3555, 3615, 11296], "avg_logprob": -0.24763258117617984, "compression_ratio": 1.5521472392638036, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4259.25, "end": 4259.53, "word": "من", "probability": 0.6962890625}, {"start": 4259.53, "end": 4260.23, "word": " 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"probability": 0.60400390625}, {"start": 4268.09, "end": 4268.59, "word": " و", "probability": 0.8896484375}, {"start": 4268.59, "end": 4268.85, "word": " A", "probability": 0.63330078125}, {"start": 4268.85, "end": 4269.57, "word": " بشرط", "probability": 0.7286376953125}, {"start": 4269.57, "end": 4270.21, "word": " ان", "probability": 0.60498046875}, {"start": 4270.21, "end": 4270.51, "word": " A", "probability": 0.5068359375}, {"start": 4270.51, "end": 4270.63, "word": " و", "probability": 0.9736328125}, {"start": 4270.63, "end": 4270.77, "word": " B", "probability": 0.6337890625}, {"start": 4270.77, "end": 4271.05, "word": " can't", "probability": 0.6048583984375}, {"start": 4271.05, "end": 4271.39, "word": " belong", "probability": 0.9248046875}, {"start": 4271.39, "end": 4271.75, "word": " لل", "probability": 0.58349609375}, {"start": 4271.75, "end": 4272.21, "word": " relation", "probability": 0.97119140625}, {"start": 4272.21, "end": 4275.17, "word": " can't", "probability": 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0.91845703125}, {"start": 4283.31, "end": 4283.71, "word": " inverse", "probability": 0.9443359375}, {"start": 4283.71, "end": 4284.25, "word": " تبعها", "probability": 0.68927001953125}], "temperature": 1.0}, {"id": 165, "seek": 431576, "start": 4287.06, "end": 4315.76, "text": "هيكون واحد و واحد اتنين و واحد تلاتة و اتنين تلاتة و تلاتة اربع و اربع عكسهم بس فقط هذه هتكون ايش ال inverse ل ال relation تمام فلو قلنا مثلا الأصغر من لان احنا مسكنها هنا في كذا example ناخد برضه اصغر من ال relation اصغر منه", "tokens": [3224, 1829, 30544, 36764, 24401, 4032, 36764, 24401, 1975, 2655, 1863, 9957, 4032, 36764, 24401, 6055, 1211, 9307, 3660, 4032, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 3660, 1975, 25513, 3615, 4032, 1975, 25513, 3615, 6225, 4117, 3794, 16095, 4724, 3794, 6156, 47432, 29538, 8032, 2655, 30544, 1975, 1829, 8592, 2423, 17340, 5296, 2423, 9721, 46811, 10943, 6156, 1211, 2407, 12174, 1211, 8315, 50113, 15040, 16247, 9381, 17082, 2288, 9154, 5296, 7649, 1975, 5016, 8315, 47524, 19452, 11296, 34105, 8978, 9122, 15730, 1365, 8717, 47283, 3215, 4724, 43042, 3224, 1975, 9381, 17082, 2288, 9154, 2423, 9721, 1975, 9381, 17082, 2288, 9154, 3224], "avg_logprob": -0.17476851782864994, "compression_ratio": 1.8838383838383839, "no_speech_prob": 0.0, "words": [{"start": 4287.06, "end": 4287.52, "word": "هيكون", "probability": 0.749755859375}, {"start": 4287.52, "end": 4287.9, "word": " واحد", "probability": 0.7403564453125}, {"start": 4287.9, "end": 4288.02, "word": " و", "probability": 0.89306640625}, {"start": 4288.02, "end": 4288.42, "word": " واحد", "probability": 0.943115234375}, {"start": 4288.42, "end": 4289.3, "word": " اتنين", "probability": 0.8681640625}, {"start": 4289.3, "end": 4289.42, "word": " و", "probability": 0.923828125}, {"start": 4289.42, "end": 4289.82, "word": " واحد", "probability": 0.937255859375}, {"start": 4289.82, "end": 4290.78, "word": " تلاتة", "probability": 0.88671875}, {"start": 4290.78, "end": 4290.88, 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4489.27, "end": 4489.85, "word": " فصارت", "probability": 0.9742431640625}, {"start": 4489.85, "end": 4490.31, "word": " الأكل", "probability": 0.967529296875}, {"start": 4490.31, "end": 4490.95, "word": " عكسها", "probability": 0.99560546875}, {"start": 4490.95, "end": 4491.59, "word": " مأكل", "probability": 0.9493815104166666}], "temperature": 1.0}, {"id": 173, "seek": 451404, "start": 4492.22, "end": 4514.04, "text": "فهي ال inverse تبعها هتبصي ريكي إيش قلت ال inverse تبعها اللي هو ال inverse فصارت كل اللي هنعمله relation بالعكس بي R to the power أو inverse R بي inverse RA بس بحكي أنه بي is eaten by A فصارت banana is eaten by بي", "tokens": [5172, 3224, 1829, 2423, 17340, 6055, 3555, 3615, 11296, 8032, 2655, 3555, 9381, 1829, 12602, 1829, 4117, 1829, 11933, 1829, 8592, 12174, 1211, 2655, 2423, 17340, 6055, 3555, 3615, 11296, 13672, 1829, 31439, 2423, 17340, 6156, 9381, 9640, 2655, 28242, 13672, 1829, 8032, 1863, 25957, 43761, 9721, 20666, 3615, 4117, 3794, 4724, 1829, 497, 281, 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7251, 43020, 20449, 2423, 4386, 16712, 1211, 9307, 37279, 16572, 5172, 9307, 8032, 3215, 12610, 8717, 47283, 3215, 16095, 4032, 9673, 25720, 25724, 995, 10632, 8717, 47283, 3215, 25894, 16095, 5821, 39894, 30544, 16472, 2655, 11331, 49975, 7251, 43020, 12174, 2288, 10721, 2655, 16095, 9122, 45865, 3794, 8717, 47283, 3215, 16095, 8717, 47283, 3215, 25894, 16095, 5821], "avg_logprob": -0.141065137592, "compression_ratio": 1.8857142857142857, "no_speech_prob": 0.0, "words": [{"start": 4865.99, "end": 4866.41, "word": "ليش؟", "probability": 0.8600260416666666}, {"start": 4866.41, "end": 4866.65, "word": " لأنه", "probability": 0.8899739583333334}, {"start": 4866.65, "end": 4866.75, "word": " ما", "probability": 0.7421875}, {"start": 4866.75, "end": 4866.77, "word": " ..", "probability": 0.70947265625}, {"start": 4866.77, "end": 4867.11, "word": " ما", "probability": 0.7705078125}, {"start": 4867.11, "end": 4867.21, "word": " ..", "probability": 0.87890625}, {"start": 4867.21, "end": 4867.71, "word": " مابنعرفش", "probability": 0.8062744140625}, {"start": 4867.71, "end": 4868.15, "word": " يعني", "probability": 0.747314453125}, {"start": 4868.15, "end": 4868.79, "word": " مالهاش", "probability": 0.8509521484375}, {"start": 4868.79, "end": 4869.07, "word": " أي", "probability": 0.80126953125}, {"start": 4869.07, "end": 4869.75, "word": " قواعد", "probability": 0.9864908854166666}, {"start": 4869.75, "end": 4870.05, "word": " مالهاش", "probability": 0.84124755859375}, {"start": 4870.05, "end": 4870.21, "word": " أي", "probability": 0.90966796875}, {"start": 4870.21, "end": 4870.65, "word": " relations", "probability": 0.87890625}, {"start": 4870.65, "end": 4871.21, "word": " الحقيقة", "probability": 0.9638671875}, {"start": 4871.21, "end": 4872.23, "word": " فدائما", "probability": 0.8377685546875}, {"start": 4872.23, "end": 4872.75, "word": " هتلاقوا", "probability": 0.89853515625}, {"start": 4872.75, "end": 4873.07, "word": " لما", "probability": 0.709228515625}, {"start": 4873.07, "end": 4873.37, "word": " بدنا", "probability": 0.92724609375}, {"start": 4873.37, "end": 4873.53, "word": " نقول", "probability": 0.99609375}, {"start": 4873.53, "end": 4873.73, "word": " is", "probability": 0.94677734375}, {"start": 4873.73, "end": 4873.95, "word": " not", "probability": 0.9697265625}, {"start": 4873.95, "end": 4874.39, "word": " هتكونوا", "probability": 0.84576416015625}, {"start": 4874.39, "end": 4874.69, "word": " likes", "probability": 0.64501953125}, {"start": 4874.69, "end": 4875.31, "word": " هتلاقوا", "probability": 0.91923828125}, {"start": 4875.31, "end": 4875.67, "word": " likes", "probability": 0.94384765625}, {"start": 4875.67, "end": 4876.87, "word": " طيب", "probability": 0.95849609375}, {"start": 4876.87, "end": 4877.33, "word": " أصغر", "probability": 0.9609375}, {"start": 4877.33, "end": 4877.47, "word": " من", "probability": 0.99365234375}, {"start": 4877.47, "end": 4878.05, "word": " asymmetric", "probability": 0.61029052734375}, {"start": 4878.05, "end": 4878.39, "word": " برضه", "probability": 0.9811197916666666}, {"start": 4878.39, "end": 4878.91, "word": " هتبين", "probability": 0.969970703125}, {"start": 4878.91, "end": 4879.29, "word": " أكتر", "probability": 0.9100341796875}, {"start": 4879.29, "end": 4879.71, "word": " يمكن", "probability": 0.98388671875}, {"start": 4879.71, "end": 4881.51, "word": " مع", "probability": 0.982421875}, {"start": 4881.51, "end": 4882.23, "word": " ال", "probability": 0.95263671875}, {"start": 4882.23, "end": 4882.51, "word": " ..", "probability": 0.8447265625}, {"start": 4882.51, "end": 4883.47, "word": " التلات", "probability": 0.8177083333333334}, {"start": 4883.47, "end": 4883.87, "word": " تعريفات", "probability": 0.991943359375}, {"start": 4883.87, "end": 4884.05, "word": " هدول", "probability": 0.9013671875}, {"start": 4884.05, "end": 4884.63, "word": " ناخدهم", "probability": 0.854248046875}, {"start": 4884.63, "end": 4885.01, "word": " و", "probability": 0.87939453125}, {"start": 4885.01, "end": 4885.25, "word": " المرة", "probability": 0.912841796875}, {"start": 4885.25, "end": 4885.45, "word": " الجاية", "probability": 0.8748372395833334}, {"start": 4885.45, "end": 4885.71, "word": " ناخد", "probability": 0.99462890625}, {"start": 4885.71, "end": 4885.95, "word": " عليهم", "probability": 0.992431640625}, {"start": 4885.95, "end": 4886.43, "word": " applications", "probability": 0.96630859375}, {"start": 4886.43, "end": 4887.15, "word": " بتكون", "probability": 0.95703125}, {"start": 4887.15, "end": 4887.27, "word": " انت", "probability": 0.775390625}, {"start": 4887.27, "end": 4887.51, "word": " حتى", "probability": 0.8662109375}, {"start": 4887.51, "end": 4887.65, "word": " يمكن", "probability": 0.80908203125}, {"start": 4887.65, "end": 4888.09, "word": " قرأتهم", "probability": 0.815185546875}, {"start": 4888.09, "end": 4888.65, "word": " كويس", "probability": 0.9903971354166666}, {"start": 4888.65, "end": 4889.49, "word": " ناخدهم", "probability": 0.981201171875}, {"start": 4889.49, "end": 4889.79, "word": " ناخد", "probability": 0.8717447916666666}, {"start": 4889.79, "end": 4890.03, "word": " عليهم", "probability": 0.98779296875}, {"start": 4890.03, "end": 4890.37, "word": " applications", "probability": 0.91552734375}], "temperature": 1.0}, {"id": 188, "seek": 490512, "start": 4894.68, "end": 4905.12, "text": "خلاص المرة اللي جاية احنا .. احنا اليوم مشينا منيح يعني كويس يلا اعطيكوا العافية المرة اللي جاية بن .. بنبدأ من هنا و بنكمل examples عليها ان شاء الله يعطيكوا العافية", "tokens": [9778, 1211, 33546, 9673, 25720, 13672, 1829, 10874, 995, 10632, 1975, 5016, 8315, 4386, 1975, 5016, 8315, 45595, 20498, 3714, 8592, 1829, 8315, 9154, 1829, 5016, 37495, 22653, 9122, 45865, 3794, 7251, 15040, 1975, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 9673, 25720, 13672, 1829, 10874, 995, 10632, 44945, 4386, 44945, 44510, 10721, 9154, 34105, 4032, 44945, 24793, 1211, 5110, 25894, 11296, 16472, 13412, 16606, 21984, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.17115543351361626, "compression_ratio": 1.80625, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4894.68, "end": 4895.04, "word": "خلاص", "probability": 0.9480794270833334}, {"start": 4895.04, "end": 4895.32, "word": " المرة", "probability": 0.904296875}, {"start": 4895.32, "end": 4895.48, "word": " اللي", "probability": 0.589111328125}, {"start": 4895.48, "end": 4895.74, "word": " جاية", "probability": 0.9547526041666666}, {"start": 4895.74, "end": 4896.72, "word": " احنا", "probability": 0.8527018229166666}, {"start": 4896.72, "end": 4896.92, "word": " ..", "probability": 0.712890625}, {"start": 4896.92, "end": 4898.22, "word": " احنا", "probability": 0.9822591145833334}, {"start": 4898.22, "end": 4898.44, "word": " اليوم", "probability": 0.97314453125}, {"start": 4898.44, "end": 4898.76, "word": " مشينا", "probability": 0.82098388671875}, {"start": 4898.76, "end": 4899.06, "word": " منيح", "probability": 0.9205729166666666}, {"start": 4899.06, "end": 4899.28, "word": " يعني", "probability": 0.870361328125}, {"start": 4899.28, "end": 4899.82, "word": " كويس", "probability": 0.8587239583333334}, {"start": 4899.82, "end": 4900.3, "word": " يلا", "probability": 0.7021484375}, {"start": 4900.3, "end": 4900.58, "word": " اعطيكوا", "probability": 0.8310546875}, {"start": 4900.58, "end": 4900.82, "word": " العافية", "probability": 0.8668619791666666}, {"start": 4900.82, "end": 4901.04, "word": " المرة", "probability": 0.84326171875}, {"start": 4901.04, "end": 4901.14, "word": " اللي", "probability": 0.9814453125}, {"start": 4901.14, "end": 4901.28, "word": " جاية", "probability": 0.9842122395833334}, {"start": 4901.28, "end": 4901.44, "word": " بن", "probability": 0.8076171875}, {"start": 4901.44, "end": 4901.5, "word": " ..", "probability": 0.67138671875}, {"start": 4901.5, "end": 4901.92, "word": " بنبدأ", "probability": 0.7724609375}, {"start": 4901.92, "end": 4902.04, "word": " من", "probability": 0.98828125}, {"start": 4902.04, "end": 4902.28, "word": " هنا", "probability": 0.9970703125}, {"start": 4902.28, "end": 4902.58, "word": " و", "probability": 0.8193359375}, {"start": 4902.58, "end": 4903.28, "word": " بنكمل", "probability": 0.84912109375}, {"start": 4903.28, "end": 4903.62, "word": " examples", "probability": 0.7734375}, {"start": 4903.62, "end": 4903.96, "word": " عليها", "probability": 0.987060546875}, {"start": 4903.96, "end": 4904.04, "word": " ان", "probability": 0.8115234375}, {"start": 4904.04, "end": 4904.24, "word": " شاء", "probability": 0.979736328125}, {"start": 4904.24, "end": 4904.34, "word": " الله", "probability": 0.9609375}, {"start": 4904.34, "end": 4904.8, "word": " يعطيكوا", "probability": 0.8025146484375}, {"start": 4904.8, "end": 4905.12, "word": " العافية", "probability": 0.9708658854166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4907.1425, "duration_after_vad": 4544.440624999997}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d531503a892c88b3d8e76d234f68bce7e8c77f17
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/Zq9WqKI9N8o_raw.srt
@@ -0,0 +1,4036 @@
+1
+00:00:20,960 --> 00:00:23,120
+بسم الله الرحمن الرحيم الصلاة والسلام عليكم ورحمة
+
+2
+00:00:23,120 --> 00:00:25,500
+الله وبركاته يا سيدنا محمد وعلي أهلي وصحابي أجمعين
+
+3
+00:00:25,500 --> 00:00:28,380
+اليوم هنبدأ في موضوع جديد ان شاء الله recurrence
+
+4
+00:00:28,380 --> 00:00:31,400
+relations هنشوف ال recurrence relations او ايش هي
+
+5
+00:00:31,400 --> 00:00:35,720
+علاقة انتقارية نتكلم عليها نشوف تعريفها أولا نعمل
+
+6
+00:00:35,720 --> 00:00:39,880
+definition لها و بعد ال definition تبعنا هناخد كيف
+
+7
+00:00:39,880 --> 00:00:44,520
+احنا نجيب ال general equation ل recurrence
+
+8
+00:00:44,520 --> 00:00:45,080
+relation
+
+9
+00:00:50,400 --> 00:00:53,020
+مجموعة الـ elements سابقين له أو مجموعة الـ
+
+10
+00:00:53,020 --> 00:00:56,100
+elements قبله فمجموعة الـ elements اللي قبلها دولة
+
+11
+00:00:56,100 --> 00:01:01,080
+مجموعة الـ elements اللي قبله نقدر نستعين عنهم ان
+
+12
+00:01:01,080 --> 00:01:04,780
+احنا نجيب relation خاصة او ك function في ال
+
+13
+00:01:04,780 --> 00:01:10,020
+location في ال location بحيث ان an بدل ما هي
+
+14
+00:01:10,020 --> 00:01:16,540
+function في a n-1 و n-2 و ممكن يكون n-3
+
+15
+00:01:40,520 --> 00:01:43,880
+مش مشكلة، بس هاندي أجيب من الاتنين دولة العنصر
+
+16
+00:01:43,880 --> 00:01:46,160
+التالي، بعدين الرابع، بعدين الخامس، مقدرني ماشي
+
+17
+00:01:46,160 --> 00:01:50,680
+للألف؟ طبعا الطريقة not efficient مش هتكون
+
+18
+00:01:50,680 --> 00:01:55,060
+efficient نهائيا، فهتصير مناسب أفضل إن أنا أحولها
+
+19
+00:01:55,060 --> 00:01:58,780
+لمعادلة from function في مين في أن نفسها، فبعوض
+
+20
+00:01:58,780 --> 00:02:01,540
+الانها دي بالألف أو بالمية أو بالرقم اللي أنا بديه
+
+21
+00:02:01,540 --> 00:02:04,920
+عشان نحسي قيمة العنصر في ال location
+
+22
+00:02:08,050 --> 00:02:10,610
+عشان نشوف إن فعلا الموضوع فيه الكانية لتحميلها،
+
+23
+00:02:10,610 --> 00:02:13,810
+العملية فيه الكانية، خلّينا نشوف ال relation اللي
+
+24
+00:02:13,810 --> 00:02:19,730
+موجودة علينا هنا An بتساوى 2 An-1 minus An-1، طبعا
+
+25
+00:02:19,730 --> 00:02:23,750
+لازم يكون هنا N أكبر من أو يساوي 2، على أقرار إن
+
+26
+00:02:23,750 --> 00:02:23,990
+فيها
+
+27
+00:03:23,360 --> 00:03:30,280
+بمعنى هل الستة هذي تساوي تلاتة نقص صفر تلاتة اتنين
+
+28
+00:03:30,280 --> 00:03:39,360
+طبعا نقص صفر اوكي هاي صفر طيب قلم ايه تلاتة ده
+
+29
+00:03:39,360 --> 00:03:48,860
+مفروض تسعة من المعادلة تسعة فهل فعلا تسعة تساوي
+
+30
+00:03:48,860 --> 00:03:49,480
+اتنين
+
+31
+00:04:00,530 --> 00:04:05,430
+هو أكبر من المعادلة لأن المعادلة تتناسب تماماً مع
+
+32
+00:04:05,430 --> 00:04:09,150
+الـ Recurrence relation المعطاقة تتناسب تماماً
+
+33
+00:04:09,150 --> 00:04:13,550
+فمعناه ذلك ممكن يكون هذا تمثيل لـ Recurrence
+
+34
+00:04:13,550 --> 00:04:14,730
+relation
+
+35
+00:04:23,450 --> 00:04:27,090
+لو عوضنا فيها في تانية، إيش بدي يطلع؟ حكمها أن E
+
+36
+00:04:27,090 --> 00:04:31,710
+نون تساوي واحد، E واحد تساوي اربعة، E واحد تساوي
+
+37
+00:04:31,710 --> 00:04:35,830
+اتنين، E اتنين تساوي اربعة، E اتنين تساوي اربعة، E
+
+38
+00:04:35,830 --> 00:04:36,130
+اتنين تساوي اربعة، E اتنين تساوي اربعة، E اتنين
+
+39
+00:04:36,130 --> 00:04:37,490
+تساوي اربعة، E اتنين تساوي اربعة، E اتنين تساوي
+
+40
+00:04:37,490 --> 00:04:37,510
+اربعة، E اتنين تساوي اربعة، E اتنين تساوي اربعة، E
+
+41
+00:04:37,510 --> 00:04:39,150
+اتنين تساوي اربعة، E اتنين تساوي اربعة، E اتنين
+
+42
+00:04:39,150 --> 00:04:40,690
+تساوي اربعة، E اتنين تسا
+
+43
+00:04:54,470 --> 00:04:57,150
+ال relation هذه هي أول .. أول أنصر بالسبب اللي
+
+44
+00:04:57,150 --> 00:04:57,970
+نحسه أنه يعمل check
+
+45
+00:05:49,680 --> 00:05:53,680
+يكونوا كافيين لتعريف sequence معين او string معين
+
+46
+00:05:53,680 --> 00:05:59,200
+ال sequence المعين هذا قولنا قبل هيك انه قد يتفق
+
+47
+00:05:59,200 --> 00:06:03,560
+اكثر من sequence في ال initial values ده و قولنا
+
+48
+00:06:03,560 --> 00:06:12,320
+قبلهم مثلا اول امصرين ل .. لنختار مثلا نين
+
+49
+00:06:12,320 --> 00:06:17,300
+احنا اخدنا مثال قبل هيك على الأرقام الفردية اعتقد
+
+50
+00:06:17,300 --> 00:06:17,780
+و ال prime
+
+51
+00:06:25,460 --> 00:06:34,500
+لو قلنا الأرقام من انس أكبر من واحد وقالت
+
+52
+00:06:34,500 --> 00:06:37,920
+لك
+
+53
+00:06:37,920 --> 00:06:44,720
+اكبر
+
+54
+00:06:44,720 --> 00:06:47,560
+من انا اكبر من واحد اكبر من انا اكبر من واحد
+
+55
+00:06:57,000 --> 00:06:59,720
+ممكن تكون اربع خلاص الوصيفة ستبقى في العالم ال
+
+56
+00:06:59,720 --> 00:07:03,880
+positive numbers فهنا واقع ان احنا التعريف مش دقيق
+
+57
+00:07:03,880 --> 00:07:06,860
+تعريفنا هنا ممكن مش دقيق محتاجين يقولنا كمان
+
+58
+00:07:06,860 --> 00:07:10,220
+element كمان element فهذه واحدة من الحالات اللي
+
+59
+00:07:10,220 --> 00:07:18,960
+نبتق عن او مش معرفة بصورة جيدة okay ناخد example
+
+60
+00:07:39,660 --> 00:07:44,480
+ممكن تكون معطاة او عبارة عن اللي هي نمو الحساب
+
+61
+00:07:44,480 --> 00:07:52,220
+البنك او ال bank account with P كنسبة بنسبة P هل
+
+62
+00:07:52,220 --> 00:07:55,080
+اللي اللي انتوا بتفكيره على اكمل في القرن لما
+
+63
+00:07:55,080 --> 00:07:59,880
+الواحد يروح بياخد من البنك مبلغ و بعدينبيرجعوا
+
+64
+00:07:59,880 --> 00:08:08,800
+المبلغ زائد قيمة P زائد قيمة P الفائدة
+
+65
+00:08:08,800 --> 00:08:14,880
+الفائدة طبعا بتكون على فترة معينة ممكن تكون شهرية
+
+66
+00:08:14,880 --> 00:08:19,020
+ممكن تكون سنوية بيصيروا اتفاق عليها في الحالة هذه
+
+67
+00:08:19,020 --> 00:08:23,820
+في زيادة الزيادة معتمدة على جدش الشهر الجاى
+
+68
+00:08:23,820 --> 00:08:25,220
+المفروض ادفع بناء على
+
+69
+00:08:32,190 --> 00:08:37,490
+و ياخد عليه الفائدة طيب مرت سنة و استحق الفائدة هل
+
+70
+00:08:37,490 --> 00:08:41,430
+الفائدة هذه لو أخدها ممكن ياخد قيمة الفائدة و يظل
+
+71
+00:08:41,430 --> 00:08:43,670
+المبلغ زي ما هو اشتغل السنة اللي جاية ياخد نفس
+
+72
+00:08:43,670 --> 00:08:49,170
+الفائدة او يسيبها فهيك رأس المال نفسه يتغير بزيب
+
+73
+00:08:49,170 --> 00:08:52,610
+فمعنى ذلك انه بنفس قيمة الفائدة المرة اللي جاية
+
+74
+00:08:52,610 --> 00:08:56,150
+قيمة الفائدة بيزيب ولكن نسبة الفائدة هي نسبة
+
+75
+00:08:56,150 --> 00:08:57,690
+الفائدة هتكون هي هي
+
+76
+00:09:01,820 --> 00:09:05,460
+المشاكل اللي عاملة أساسا هي .. يعني خليني أقول ..
+
+77
+00:09:05,460 --> 00:09:09,580
+طلعنا شوية عن ال .. مش عارف بسجل ولا بسجل مش
+
+78
+00:09:09,580 --> 00:09:13,920
+فمبدئيا
+
+79
+00:09:13,920 --> 00:09:21,520
+هذه واحدة من الإشكاليات اللي عاملة أساسا فروق فكرة
+
+80
+00:09:21,520 --> 00:09:25,240
+أنه في فجر وفي غنى هذه واحدة من مصايبها واحدة من
+
+81
+00:09:25,240 --> 00:09:28,280
+مصايب تاعة الحاجات هذه خليني احنا .. احنا قيلنا في
+
+82
+00:09:28,280 --> 00:09:33,140
+التطبيق كتطبيق رياضيفردنا يبعدنا عن التطبيق الفعلي
+
+83
+00:09:33,140 --> 00:09:40,160
+كويس فلو قولنا ال month أو الشهر n هيساوي جدش
+
+84
+00:09:40,160 --> 00:09:44,180
+المبلغ اللي أنا معايا في شهر n هيكون عبارة عن
+
+85
+00:09:44,180 --> 00:09:51,000
+الشهر n minus one الشهر السابق زائد الفائدة
+
+86
+00:09:51,000 --> 00:09:55,140
+الفائدة في الحالة محسوبة على ايش محسوبة على بداية
+
+87
+00:09:55,140 --> 00:10:00,140
+الشهر اللي فات يعني على الشهر الماضي زائد ال bالـ
+
+88
+00:10:00,140 --> 00:10:07,320
+P هذه هي نسبة زيادة فمدان percent بحط عالمية في
+
+89
+00:10:07,320 --> 00:10:13,290
+الشهر السابقالسابق بقدر اقول انه كلها على بعض
+
+90
+00:10:13,290 --> 00:10:18,150
+بنتسميها واحد زائد قيمة النسبة او النسبة في الشهر
+
+91
+00:10:18,150 --> 00:10:22,670
+السابق طيب ماهي نفس الفكرة هي هي او خلينا كلها
+
+92
+00:10:22,670 --> 00:10:27,750
+نسميها R يعني تسهيرا للموضوع نفس الشغلاء طب المبلغ
+
+93
+00:10:27,750 --> 00:10:31,210
+اللي كان الشهر الفات موجود هو أساسا جاي من الشهر
+
+94
+00:10:31,210 --> 00:10:36,390
+اللي جابله فنفس الكلام Mن ماينوس وان او في الmonth
+
+95
+00:10:36,390 --> 00:10:42,090
+n minus one كانت عبارة عن نفس ال R هي المبلغ زائد
+
+96
+00:10:42,090 --> 00:10:46,250
+زيادة مع الزيادة سنسميها قيمة R كانت ايش متساوي
+
+97
+00:10:46,250 --> 00:10:51,410
+برضه R في ال month اللي جابله اللي جابله مع اللي
+
+98
+00:10:51,410 --> 00:10:56,480
+جابله لعند ما نصلىبداية ما أخدت المبلغ او بداية ما
+
+99
+00:10:56,480 --> 00:10:57,540
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+100
+00:10:57,540 --> 00:10:57,960
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+101
+00:10:57,960 --> 00:10:59,480
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+102
+00:10:59,480 --> 00:11:01,680
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+103
+00:11:01,680 --> 00:11:01,680
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+104
+00:11:01,680 --> 00:11:01,740
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+105
+00:11:01,740 --> 00:11:03,260
+أخدت المبلغ او بداية ما أخدت المبلغ او بداية ما
+
+106
+00:11:03,260 --> 00:11:08,590
+أخدت المبلغ او بداية ما أخدت المبلغ او بدايةجاعدة
+
+107
+00:11:08,590 --> 00:11:13,690
+busy كويس في الحالة هذه لو انا فرضا واحد حط فلوسه
+
+108
+00:11:13,690 --> 00:11:17,870
+و بده يحسب بعد عشر سنين بده يحط المبلغ و بده ينسل
+
+109
+00:11:17,870 --> 00:11:21,510
+عشر سنين طبعا يقعد يحسبها الشهر هذا طب الشهر اللي
+
+110
+00:11:21,510 --> 00:11:23,530
+برا جديش طب الشهر اللي بعده جديش طب الشهر اللي
+
+111
+00:11:23,530 --> 00:11:27,210
+بعده جديش مش هتنفع لأ كان من الأسهل عشرة في اتناش
+
+112
+00:11:27,210 --> 00:11:31,370
+عدد الشهور هاي مية عشرين شهر يضربهم في ال .. بتصير
+
+113
+00:11:31,370 --> 00:11:33,990
+R جديش النسبة المطلوبة او النسبة اللي هو هياخدها
+
+114
+00:11:34,960 --> 00:11:37,960
+تتبور 120 و خلاص في المبلغ اللي حطه أول مرة
+
+115
+00:11:37,960 --> 00:11:43,180
+بيحسبها مرة واحدة مش مضطر يعمل يحسب كل ال terms
+
+116
+00:11:43,180 --> 00:11:45,700
+لعند ما يصل للشهر اللي بده يحسب جدش قيمة الفائدة
+
+117
+00:11:45,700 --> 00:11:50,360
+فيه سواء إله أو عليه سواء إله أو عليه أو عليه طبعا
+
+118
+00:11:50,360 --> 00:11:53,080
+لإن الناس كتير انخلوط بيتها من ورا الكلام هذا لما
+
+119
+00:11:53,080 --> 00:11:56,940
+تكون عليه يروح ياخد قرض و بعدين مايعرفش يخلص حاجة
+
+120
+00:11:56,940 --> 00:12:01,930
+كويسةفواضح ان احنا هنا حولناها من ايش؟ من
+
+121
+00:12:01,930 --> 00:12:05,450
+recurrence relation ل general relation لاحظوا هنا
+
+122
+00:12:05,450 --> 00:12:09,630
+معتمدة على ال n بس معتمدين على قيمة ال n المبلغ
+
+123
+00:12:09,630 --> 00:12:12,450
+اللي هنحطه في الأول ما احنا عارفينه جدش نحط مبلغ
+
+124
+00:12:12,450 --> 00:12:16,330
+في الأول و جدش أخدنا مبلغ كقارن في الأول معروف جدش
+
+125
+00:12:16,330 --> 00:12:20,030
+فترة الاستحقاق معروفة اللي هيصير بناء عليها تكرار
+
+126
+00:12:20,030 --> 00:12:26,620
+n انها دي تمثل ايش؟ شهري؟نص سنوي سنوي جداش وال R
+
+127
+00:12:26,620 --> 00:12:30,340
+ليها جداش نسبة زيادة جداش نسبة زيادة فهي واحدة من
+
+128
+00:12:30,340 --> 00:12:33,580
+الأمثلة اللي قدرنا نحولها من recurrence relation ل
+
+129
+00:12:33,580 --> 00:12:37,220
+general equation function في مين في أن نقدر نسبها
+
+130
+00:12:37,220 --> 00:12:42,180
+وجد ما بدنا نقدر نسبها وجد ما بدنا كمان مثال تاني
+
+131
+00:12:42,180 --> 00:12:46,500
+مثال تاني و بعرفش إذا كان موجود حتى ك game موجود
+
+132
+00:12:46,500 --> 00:12:53,550
+يعني اللي هو ال towerof Hanoi example برج Hanoi
+
+133
+00:12:53,550 --> 00:12:58,310
+برج Hanoi مجموعة disks فوق بعض مجموعة disks فوق
+
+134
+00:12:58,310 --> 00:13:02,970
+بعض مطلوب منكوا كلهم تنقلوهم على big تاني او على
+
+135
+00:13:02,970 --> 00:13:08,490
+وتة تاني على وتة تاني بدون بدون ماتيجي كرتونة
+
+136
+00:13:08,490 --> 00:13:11,750
+كبيرة او بدون ماييجي disk كبير على disk صغير اثناء
+
+137
+00:13:11,750 --> 00:13:15,830
+النقلأثناء النقل مايكونش فيه disk صغير تحت disk
+
+138
+00:13:15,830 --> 00:13:22,030
+كبير ومسموح لكوا ب one move each time يعني كل مرة
+
+139
+00:13:22,030 --> 00:13:24,550
+بتكون تنقلوا بنقولش اتنين اتنين بنقول واحد واحد
+
+140
+00:13:24,550 --> 00:13:29,090
+وهي كل عندكوا طبعا ال big two اللي بتكون تنقلوا
+
+141
+00:13:29,090 --> 00:13:35,790
+عليه وعندكوا spare واحد واحد spare بسأكم move
+
+142
+00:13:35,790 --> 00:13:39,910
+محتاجين عشان ننقل كل ال tower من big number one to
+
+143
+00:13:39,910 --> 00:13:44,990
+big number two او big three مش هتفرق مش هتفرق أكم
+
+144
+00:13:44,990 --> 00:13:52,390
+move محتاجين أكم move محتاجين مبدأيا كيف انتوا
+
+145
+00:13:52,390 --> 00:13:55,510
+طبعا هتقعدوا تشتغلوا فيها بدها عدد كبير يعني هذه
+
+146
+00:13:55,510 --> 00:13:58,990
+على الأقل بدها واحد تلاتين move كويسة بس كيف
+
+147
+00:13:58,990 --> 00:14:06,190
+نحسبهم عدد ال moves هذه بنقولHanoi N بمعنى الـ N
+
+148
+00:14:06,190 --> 00:14:11,190
+هنا لم أجد ما هي المقصود فيها عدد ال disks عدد ال
+
+149
+00:14:11,190 --> 00:14:18,730
+disks اللي نريد ان ننجلهم لو قلنا ال H N هذول عدد
+
+150
+00:14:18,730 --> 00:14:23,870
+ال moves اللي انا محتاجهم عشان انجل N disk هذول
+
+151
+00:14:23,870 --> 00:14:30,070
+ايش بيساووا فعليا بيساووا اتنين في H N minus one
+
+152
+00:14:30,070 --> 00:14:39,250
+زائد واحدبمعنى محتاجين ضعف نقل أربعة disks زائد
+
+153
+00:14:39,250 --> 00:14:44,350
+واحد، ليش؟ لحظة، لو فعلا بدنا ننقل أربعة disks
+
+154
+00:14:44,350 --> 00:14:49,410
+اللي هي بتصير H and minus one، مظبوط؟ لو فرضنا أنه
+
+155
+00:14:49,410 --> 00:14:51,990
+بدهم عشر moves، بدهم عشرين moves، جد ما يطلع، يطلع
+
+156
+00:14:52,720 --> 00:14:56,120
+عدد ال moves المهم ان استخدمتهم و نجلتهم هنا فعلا
+
+157
+00:14:56,120 --> 00:15:01,800
+انتجلوا هنا صار اسمها hn-1 moves بعدين أخدنا move
+
+158
+00:15:01,800 --> 00:15:08,200
+واحدة للأخيرة ده نجلناها هنا هاي الواحد بعدين
+
+159
+00:15:08,200 --> 00:15:13,640
+رجعنا نفسهم من هنا نجلناهم هنا طيب طب انتوا
+
+160
+00:15:13,640 --> 00:15:18,180
+ماحلناش اشي احنا كنا بنقول hn محتاجينها وجدناها
+
+161
+00:15:18,180 --> 00:15:25,150
+صارت دلالة hn-1-1 برده بقدر اجيبها من ايش minus
+
+162
+00:15:25,150 --> 00:15:30,750
+two لان هي بنفس الشكل هتكون اتنين زائد واحد لعند
+
+163
+00:15:30,750 --> 00:15:35,710
+ما نصل ايش zero او طبعا هنا هيكون ال zero تبعا
+
+164
+00:15:35,710 --> 00:15:39,910
+اللي هي disk واحد ان اكم move محتاج عشان انقل disk
+
+165
+00:15:39,910 --> 00:15:45,660
+واحد حركة واحدة H واحد في النهاية بتساوي واحدH1 في
+
+166
+00:15:45,660 --> 00:15:50,840
+النهاية هتساوي 1 فبنشغلها و بنرجع رجوع فيها و
+
+167
+00:15:50,840 --> 00:15:54,080
+بنقدر نحسبها في الحالة دي طيب عشان نعمل ال general
+
+168
+00:15:54,080 --> 00:15:58,440
+form أو ال general equation بتاعتنا هنشغل بهذا ال
+
+169
+00:15:58,440 --> 00:16:08,340
+sequence بالشكل هذا فهنقول ان HN هتساوي 2HN-1 plus
+
+170
+00:16:08,340 --> 00:16:15,070
+1 و عرفنا ليش عرفناها ليش بنقول أربعةجد ما يطلع
+
+171
+00:16:15,070 --> 00:16:17,830
+عدد ال moves ساعتهم يطلع انا مش معنى هلوجد احسبهم
+
+172
+00:16:17,830 --> 00:16:23,950
+كحساب بس هو عددهم نجلهم على big number two بعدين
+
+173
+00:16:23,950 --> 00:16:27,930
+اخر disk هاي ال move الواحدة بعدين هم نفسهم بنفس
+
+174
+00:16:27,930 --> 00:16:33,890
+العدد هرجحهم فوق ال disk الأخير اللي تم نقله okay
+
+175
+00:16:33,890 --> 00:16:42,250
+في الحالة هذه هاي القانون تبعناتأتنين هنضع hn-1
+
+176
+00:16:42,250 --> 00:16:46,850
+ودلالة hn-2 نفس الفكرة و نضرب ندخل الأتنين جوا
+
+177
+00:16:46,850 --> 00:16:49,450
+هتصير هنا اتنين توته باور اتنين و هنا في عندنا
+
+178
+00:16:49,450 --> 00:16:54,050
+اتنين زائد واحد اتنين توته باور اتنين وهذه الـ-3
+
+179
+00:16:54,050 --> 00:16:58,430
+صار عندنا اتنين توته باور تلاتة زائد اتنين توته
+
+180
+00:16:58,430 --> 00:17:01,750
+باور اتنين زائد اتنين توته باور واحد زائد اتنين
+
+181
+00:17:01,750 --> 00:17:06,810
+توته باور Zero لاحظوا إيش أنا بدي أوصل هي اتنين
+
+182
+00:17:06,810 --> 00:17:11,910
+توته باورعدد التكرارات طيب لعند ما نصل في الآخر
+
+183
+00:17:11,910 --> 00:17:19,190
+فعلا أن هي هتطلع 2ⁿ-1 plus 2ⁿ⁻¹
+
+184
+00:17:19,190 --> 00:17:20,230
+في H1
+
+185
+00:17:22,500 --> 00:17:26,780
+الواحد هذي هي قيمة واحدة بمعتبر أنه أكمل نجلة
+
+186
+00:17:26,780 --> 00:17:27,760
+واحدة بقيمة واحدة بمعتبر أنه أكمل نجلة واحدة بقيمة
+
+187
+00:17:27,760 --> 00:17:30,240
+واحدة بمعتبر أنه أكمل نجلة واحدة بقيمة واحدة بقيمة
+
+188
+00:17:30,240 --> 00:17:31,600
+واحدة بقيمة واحدة بقيمة واحدة واحدة واحدة واحدة
+
+189
+00:17:31,600 --> 00:17:32,700
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+190
+00:17:32,700 --> 00:17:34,480
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+191
+00:17:34,480 --> 00:17:36,860
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+192
+00:17:36,860 --> 00:17:41,080
+واحدة واحدة واحدة واحدة واحدة واحدة واحدة واحدة
+
+193
+00:17:41,080 --> 00:17:47,260
+واحدة واحدة واحدة واحدة واحدة واحدة وا
+
+194
+00:17:51,750 --> 00:17:55,930
+I و ال I زي ما قلنا من صفر ل N-1 طب هى دى
+
+195
+00:17:55,930 --> 00:18:00,310
+Geometric هال Geometric بتذاكرينها؟ Geometric
+
+196
+00:18:00,310 --> 00:18:03,230
+بنحلها بنعود في القانون هتطلع بتساوي 2 to the
+
+197
+00:18:03,230 --> 00:18:08,850
+power N-1 ف2 to the power N عندكوا هنا مثلا كان
+
+198
+00:18:08,850 --> 00:18:13,570
+خمسة حركة محتاجين أو move محتاجين عشان تنقلوا
+
+199
+00:18:13,570 --> 00:18:17,350
+tower فيه خمسة discs من big number one to big to
+
+200
+00:18:17,350 --> 00:18:21,500
+other big two أو threeمحتاجين two to the power of
+
+201
+00:18:21,500 --> 00:18:26,900
+five minus واحد فكداش بتطلع واحد تلاتين موف
+
+202
+00:18:26,900 --> 00:18:33,340
+محتاجين واحد تلاتين موف عملية الحل فعليا احنا
+
+203
+00:18:33,340 --> 00:18:37,910
+اخدنا مثلينفي طبعا أمثلة كتير هتلاقيوا في الكتاب
+
+204
+00:18:37,910 --> 00:18:41,890
+كمان في المثال تبع fabonacci fabonacci هذا اللي هو
+
+205
+00:18:41,890 --> 00:18:46,610
+خاص بال .. بال generations للأرانب كل شهرين بيصير
+
+206
+00:18:46,610 --> 00:18:49,590
+فيه جيل جديد او بيكون الجيل الجديد قادر ان هو كمان
+
+207
+00:18:49,590 --> 00:18:53,270
+يعمل generation فبتطلع ال series او ال sequence
+
+208
+00:18:53,270 --> 00:18:56,370
+اللي أخدناها مرة تبع fabonacci لو منذكرينه اللي هو
+
+209
+00:18:56,370 --> 00:19:03,050
+واحد واحد اتنين تلاتة خمسة تمانية تلات عشر واحد
+
+210
+00:19:03,050 --> 00:19:08,080
+وعشريناللي هو كل رقم مجموع الرقمين اللي جابله و
+
+211
+00:19:08,080 --> 00:19:13,200
+initially B node بتساوي واحد و B واحد بتساوي واحد
+
+212
+00:19:13,200 --> 00:19:16,660
+و بعدين بيصيروا كلهم .. كل عنصر مجموع الاتنين اللي
+
+213
+00:19:16,660 --> 00:19:19,140
+جابله .. مجموع الاتنين اللي جابله .. مجموع الاتنين
+
+214
+00:19:19,140 --> 00:19:23,460
+اللي جابله .. تقرؤوهاموجودة في الكتاب، في أي مشكلة
+
+215
+00:19:23,460 --> 00:19:26,720
+في الأرقام، في جدول في الكتاب موجود إليها، في أي
+
+216
+00:19:26,720 --> 00:19:29,740
+مشاكل بتسألوني فيها، بتقولولي إيش ال .. كيف معروف،
+
+217
+00:19:29,740 --> 00:19:32,100
+هي سهل يعني أنه كيف .. من وين عامل generation
+
+218
+00:19:32,100 --> 00:19:35,660
+للأرقام هذه، من وين عامل generation للأرقام هذه،
+
+219
+00:19:35,660 --> 00:19:39,680
+okayماشي هدولة كانت مواضيع المثالين تلاتة اللي
+
+220
+00:19:39,680 --> 00:19:42,440
+خدناهم المثالين زاد المثال اللي موجود في الكتاب
+
+221
+00:19:42,440 --> 00:19:45,820
+موضوعهم سهل ليش لأنه مفهوم طب ممكن يجيبلي أي
+
+222
+00:19:45,820 --> 00:19:50,260
+relation ويقولي حوليها ل general equation احسبلي
+
+223
+00:19:50,260 --> 00:19:53,420
+العنصر رقم الف مثلا او رقم الفين او رقم .. ماعرفش
+
+224
+00:19:53,420 --> 00:19:56,260
+اشرح العنصر اللي ممكن يطلبه باعتبار انه ممكن جدا
+
+225
+00:19:56,260 --> 00:20:01,440
+يعملنا example للبكتيريا وهذا example موجود في
+
+226
+00:20:01,440 --> 00:20:05,380
+الكتاب في أحد حلول ال .. في ال .. في ال problem
+
+227
+00:20:05,380 --> 00:20:11,270
+sets في الآخرموجود ان والله عندكوا مش عارف بكتيريا
+
+228
+00:20:11,270 --> 00:20:15,530
+واحدة، خلية بكتيريا واحدة، بعد مش عارف سنة أكم
+
+229
+00:20:15,530 --> 00:20:19,650
+خلية هتكونهو يعطيكوا معلومات انك تعمل انقسام كل
+
+230
+00:20:19,650 --> 00:20:24,250
+جديش طيب هل بعد سنة طبعا جالكوا انه بعد كل تلت
+
+231
+00:20:24,250 --> 00:20:29,270
+ساعات هتبتتكاتر يعني بتنقسم طب هل بدأ اقعد أحسبها
+
+232
+00:20:29,270 --> 00:20:34,690
+لعند ما أصل لسنة عشان أشوف الرقم نوية طبعا مستحيل
+
+233
+00:20:34,690 --> 00:20:38,850
+حد يقعد يشتغل سنة يجسمها كل تلت ساعات تلت ساعات كم
+
+234
+00:20:38,850 --> 00:20:42,010
+مرة بتكون تعملوا recurrence relationلأ الموضوع مش
+
+235
+00:20:42,010 --> 00:20:45,470
+بتصيرش بالشكل هذا فمحتاجين احنا نعمله معادلة
+
+236
+00:20:45,470 --> 00:20:48,510
+محتاجين نعمله معادلة كيف المعادلة هذه ال logic هي
+
+237
+00:20:48,510 --> 00:20:52,530
+نتكلم عنها في ال section التاني من chapter 6 اللي
+
+238
+00:20:52,530 --> 00:20:56,210
+هو solving recurrences هذه هنشغل على linear
+
+239
+00:20:56,210 --> 00:20:59,470
+homogeneous recurrence of degree k with constant
+
+240
+00:20:59,470 --> 00:21:02,310
+coefficients هنسميها k linear homogeneous
+
+241
+00:21:02,310 --> 00:21:07,480
+recurrence with constant coefficientsعلى اعتبار ان
+
+242
+00:21:07,480 --> 00:21:10,640
+الـ K هذه ال degree هذه هي عدد ال elements اللي
+
+243
+00:21:10,640 --> 00:21:14,920
+انا محتاجه عشان اجيب اي element زيادة بمعنى ال
+
+244
+00:21:14,920 --> 00:21:22,020
+element N محتاج مدام K محتاج جابله K elements عشان
+
+245
+00:21:22,020 --> 00:21:28,620
+نحسبه فهو function في K elements جابله فهتلاقوا
+
+246
+00:21:28,620 --> 00:21:36,990
+coefficient معين في مين؟ في AN-1 N-2 N-3to n-k
+
+247
+00:21:36,990 --> 00:21:41,830
+فانا فعليا en معتمد على k elements جابله فبنسميها
+
+248
+00:21:41,830 --> 00:21:48,410
+k degree ال C ده طبعا هي ال coefficients سبعتنا هي
+
+249
+00:21:48,410 --> 00:21:51,590
+كده تكرارات كل عنصر لحاله كل عنصر من العناصر
+
+250
+00:21:51,590 --> 00:21:55,650
+السابقة لحاله كويسة وكلها لاتساوي صفر على أساس
+
+251
+00:21:55,650 --> 00:22:00,150
+أننا نتكلم عن k elements جابلهالسلوشن هنا لازم
+
+252
+00:22:00,150 --> 00:22:04,570
+يكون uniquely determined if k initial conditions
+
+253
+00:22:04,570 --> 00:22:11,810
+is found بمعنى او are provided اي node موجودة اي
+
+254
+00:22:11,810 --> 00:22:16,030
+واحد موجودة to اي k minus one يكون معطين اياهم
+
+255
+00:22:16,030 --> 00:22:22,220
+كقيم فال sequence اللي احنا توه كتبناهامبدأيا عشان
+
+256
+00:22:22,220 --> 00:22:24,780
+انا احدد ال sequence و اعرف كل ال elements سبعته
+
+257
+00:22:24,780 --> 00:22:28,680
+لازم نحدد على الأقل اول three elements منهم اول
+
+258
+00:22:28,680 --> 00:22:31,280
+three elements او two elements K elements in
+
+259
+00:22:31,280 --> 00:22:36,260
+general هنقول K elements اعطانيهم واحد تلاتة خمسة
+
+260
+00:22:36,260 --> 00:22:42,160
+نفترض سبعة و بعدين بيعملي هيك خلاص بس هنا حدد ليها
+
+261
+00:22:42,160 --> 00:22:48,200
+ان هي ال K باربعة K باربعة في عند A node A واحد
+
+262
+00:22:48,200 --> 00:22:52,200
+اتنين اتلاتةفي عندي أربع elements منهم المفروض
+
+263
+00:22:52,200 --> 00:22:55,040
+يطلب مني يقولي والله هاتلي ال element في ال
+
+264
+00:22:55,040 --> 00:23:01,140
+location مية مثلا بدنا نعرفه بالظبط بدنا نعرفه
+
+265
+00:23:01,140 --> 00:23:03,800
+طبعا احنا ممكن نشتل بهذا الشكل نقعد نقول اه والله
+
+266
+00:23:03,800 --> 00:23:06,740
+هذا شكله واضح انه الأرقام الفردية لأ واضح شكل
+
+267
+00:23:06,740 --> 00:23:09,460
+الأرقام مش عارف ايش شكل الأرقام و بنبدأ نكمل عليها
+
+268
+00:23:09,460 --> 00:23:16,030
+طب هاي عنصر رقم هنا a nodeهنا E3 او E4 او E9 او E5
+
+269
+00:23:16,030 --> 00:23:19,950
+او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او
+
+270
+00:23:19,950 --> 00:23:22,730
+E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9
+
+271
+00:23:22,730 --> 00:23:23,910
+او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او
+
+272
+00:23:23,910 --> 00:23:23,910
+E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9
+
+273
+00:23:23,910 --> 00:23:23,910
+او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او
+
+274
+00:23:23,910 --> 00:23:35,770
+E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9 او E9
+
+275
+00:23:35,770 --> 00:23:41,550
+او E9
+
+276
+00:23:42,290 --> 00:23:46,130
+هدول بيحلهم كالتالي ان انا بدي احولها ال a انها دي
+
+277
+00:23:46,130 --> 00:23:51,280
+ك function في مين في n لحالهاعن طريق الـ roots الـ
+
+278
+00:23:51,280 --> 00:23:54,500
+roots هذه بدنا نحسبها طبعا هنضطر بدنا نحسبها بدنا
+
+279
+00:23:54,500 --> 00:23:59,920
+نشتغل عليها ف relation فعليا لل K degree هتكون R
+
+280
+00:23:59,920 --> 00:24:03,000
+to the power N هذي اللي أنا بده أحصل عليها لازم
+
+281
+00:24:03,000 --> 00:24:06,040
+تكون function في مين في ال coefficient الأول هو هو
+
+282
+00:24:06,040 --> 00:24:10,120
+بس هتصير في R to the power N minus one هذي كانت A
+
+283
+00:24:10,120 --> 00:24:15,700
+N minus one هتصير R to the power N minus one هنا
+
+284
+00:24:15,700 --> 00:24:24,550
+كانت Aن-K هصير Rⁿ-K هذه بنسميها ال form هذا لجديد
+
+285
+00:24:24,550 --> 00:24:27,330
+بنسميه characteristic equation characteristic
+
+286
+00:24:27,330 --> 00:24:31,950
+equation لل recurrence لل recurrence relation كويس
+
+287
+00:24:31,950 --> 00:24:36,210
+من ال function هذه لو كل ال terms هدولة أخدتهم عن
+
+288
+00:24:36,210 --> 00:24:40,280
+ناحية تانية و equal to zero صارت المعادلةهتصير
+
+289
+00:24:40,280 --> 00:24:44,800
+equal to zero طيب، لاحظوا أن كلهم مشتركين في R R R
+
+290
+00:24:44,800 --> 00:24:45,340
+R
+
+291
+00:24:45,340 --> 00:25:03,060
+ررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررررر
+
+292
+00:25:06,010 --> 00:25:09,750
+هي نزلت ال coefficient بس نزلت طبعا راح على ناحية
+
+293
+00:25:09,750 --> 00:25:12,510
+تانى بالسالب و هدول كلهم التانس هيروحوا بالسالب
+
+294
+00:25:12,510 --> 00:25:18,330
+فهتنتج معاكوا r to the power k على اعتبار انتم
+
+295
+00:25:18,330 --> 00:25:23,350
+قسمتوها على r n minus k فكل اللي بتعمله بتطرحه ال
+
+296
+00:25:23,350 --> 00:25:32,070
+powers فصارت n minus n minus kصارت مين؟ الـ K فR
+
+297
+00:25:32,070 --> 00:25:36,830
+to the power of K minus C1 to the power of K minus
+
+298
+00:25:36,830 --> 00:25:42,890
+1 C2 to the power of K minus 2 لما نصلّى CK to the
+
+299
+00:25:42,890 --> 00:25:47,690
+power .. فR to the power of 0 اللي هي واحد equal
+
+300
+00:25:47,690 --> 00:25:50,290
+to zero صار هالوجهة كل الطريقة في الشغل اللي
+
+301
+00:25:50,290 --> 00:25:53,210
+محتاجينها ان احنا نحل ال characteristic equation
+
+302
+00:25:53,210 --> 00:25:57,050
+اننا نجيب ال roots تبعتنا او ال characteristic
+
+303
+00:25:57,050 --> 00:25:59,330
+roots بدنا نجيب ال characteristic
+
+304
+00:26:02,280 --> 00:26:08,540
+على حسب ال degree بتاعتكم بيبين ال order لل
+
+305
+00:26:08,540 --> 00:26:15,320
+equation فواضح ان ال order هنا kإذا و الله بنقدر
+
+306
+00:26:15,320 --> 00:26:19,060
+نحل order k خلاص انحلت للتبسيط هنشتغل في المصاد
+
+307
+00:26:19,060 --> 00:26:24,160
+تبعنا على جد بس اتنين على جد degree اتنين عساس انه
+
+308
+00:26:24,160 --> 00:26:27,120
+هي بتصير quadratic هو عشان نقدر نجيب لها ال roots
+
+309
+00:26:27,120 --> 00:26:31,220
+متذكرين لسه قانون تبع ال roots لل quadratic form
+
+310
+00:26:31,220 --> 00:26:37,020
+او لل quadratic equation؟كويس فحنشتغل في المصادق
+
+311
+00:26:37,020 --> 00:26:40,360
+تبعنا كبداية ان و الله خلاص عرفنا الفكرة بعدين
+
+312
+00:26:40,360 --> 00:26:43,740
+بيصير و الله لو في techniques تحللنا اكتر degree
+
+313
+00:26:43,740 --> 00:26:47,920
+اكبر من الاتنين okay لاحقا ممكن تشتغلوا عليها في
+
+314
+00:26:47,920 --> 00:26:51,360
+مصادقنا هنشتغل على solving two degree لlinear
+
+315
+00:26:51,360 --> 00:26:55,640
+homogeneous recurrence of constant coefficients او
+
+316
+00:26:55,640 --> 00:27:00,180
+with constant coefficients تمام فهتصير a n عبارة
+
+317
+00:27:00,180 --> 00:27:04,850
+عن two terms فقط عشان تكون two degreeمعتمد على ال
+
+318
+00:27:04,850 --> 00:27:08,530
+two terms قبلها فقط، مش تلاتة، تلاتة هتتحول ل
+
+319
+00:27:08,530 --> 00:27:13,570
+three degree فنتكلم عن two terms سابقين فال two
+
+320
+00:27:13,570 --> 00:27:16,930
+terms automatically، مدام أنا بتكلم عن اتنين، ال A
+
+321
+00:27:16,930 --> 00:27:20,750
+هد بتتحول ل R to the power اتنين، مدام هي degree
+
+322
+00:27:20,750 --> 00:27:23,830
+اتنين اصلا، انا بتكلم عن degree اتنين، كيف بعرف ان
+
+323
+00:27:23,830 --> 00:27:27,690
+هي degree اتنين؟ ان هو معتمد على twoElements
+
+324
+00:27:27,690 --> 00:27:30,750
+سابقين على two elements سابقين فبعرف ايه R to the
+
+325
+00:27:30,750 --> 00:27:33,690
+power 2 كويس ال C هذه هتروح الناحية التانية
+
+326
+00:27:33,690 --> 00:27:40,610
+بالسالب فصارت ال C سالب C 1 في R طيب هذه برضه
+
+327
+00:27:40,610 --> 00:27:46,190
+هتروح الناحية التانية تصير سالب C 2 في R to the
+
+328
+00:27:46,190 --> 00:27:46,630
+power 0
+
+329
+00:27:50,290 --> 00:27:54,190
+هذا كله equal to zero فصارت معادلة quadratic
+
+330
+00:27:54,190 --> 00:27:56,770
+equation او ال characteristic equation بتاعتنا
+
+331
+00:27:56,770 --> 00:28:01,290
+صارت من الدرجة التانية نقدر نشتغلها لو متذكرين
+
+332
+00:28:01,290 --> 00:28:02,090
+قانونكوا
+
+333
+00:28:11,720 --> 00:28:15,700
+R تربيع R تربيع اه من الفهمة يعني عشان انا مقتمد
+
+334
+00:28:15,700 --> 00:28:18,140
+على عنصرين تربيعين بالظبط على عنصرين معناه ان انا
+
+335
+00:28:18,140 --> 00:28:21,500
+بتكلم عن two degree two degree خلاص automatically
+
+336
+00:28:21,500 --> 00:28:29,500
+بتصير R to the power اتنينكويس هذه بدنا نجيب ال
+
+337
+00:28:29,500 --> 00:28:33,480
+roots بتاعتنا فمن القنوة جيبناهم ال roots طيب برضه
+
+338
+00:28:33,480 --> 00:28:35,900
+احنا كل اللي عملناه اننا جيبنا roots انا بدى
+
+339
+00:28:35,900 --> 00:28:40,080
+معادلة بدى معادلة في النهاية القصر تكون عبارة عن a
+
+340
+00:28:40,080 --> 00:28:46,620
+n تساوي function في n انا هي اللي بديهاها طب انت
+
+341
+00:28:46,620 --> 00:28:51,400
+جيبتلي r الشي ر هذي معناته محتاجين theorem محتاجين
+
+342
+00:28:51,400 --> 00:28:55,440
+theorem اترتبلناكيف بقدر أجيب الان من ال roots
+
+343
+00:28:55,440 --> 00:28:57,280
+اللي انا جبتها للمعادلة من ال roots اللي احنا
+
+344
+00:28:57,280 --> 00:29:00,320
+جبناها ففي theorem أولى وفي theorem تانية ال
+
+345
+00:29:00,320 --> 00:29:03,440
+theorem الأولى الفرق بينهم بس أنه لو ال roots
+
+346
+00:29:03,440 --> 00:29:07,200
+متشابهة أو لو ال roots مختلفة لا أكثر ولا أقل أنت
+
+347
+00:29:07,200 --> 00:29:11,020
+بتكون متشابه ال roots إذا كان الحد المميز هذا
+
+348
+00:29:11,020 --> 00:29:15,540
+equal to zeroإذا كان و الله equal to zero معناته
+
+349
+00:29:15,540 --> 00:29:18,460
+مش هتفرج موجة بسالب في الآخر هيطلع نفس ال root
+
+350
+00:29:18,460 --> 00:29:23,100
+هيطلع نفس ال root okay إله قيمة واضح أنها هيطلع في
+
+351
+00:29:23,100 --> 00:29:26,220
+أنكوا two roots different two roots different two
+
+352
+00:29:26,220 --> 00:29:30,620
+roots okay هنبدأ بال theorem الأولى و الله إذا كان
+
+353
+00:29:30,620 --> 00:29:33,580
+ال characteristic equation has two roots و بيساووش
+
+354
+00:29:33,580 --> 00:29:36,500
+بعض بنسلع على القانون التالف أن ال a n
+
+355
+00:29:36,500 --> 00:29:40,200
+هيرتبلناياها ربطلنا ال roots اللي إحنا هنجيبها كيف
+
+356
+00:29:40,200 --> 00:29:46,420
+نحطها في form لل a mالان هتساوي ال route الأولى to
+
+357
+00:29:46,420 --> 00:29:50,380
+the power n وال route التانى to the power n برضه n
+
+358
+00:29:50,380 --> 00:29:54,180
+في n هي كلهم n بس الأولى محتاجين نضربها في
+
+359
+00:29:54,180 --> 00:29:57,160
+constant معين و التانى في constant معين ألف واحد
+
+360
+00:29:57,160 --> 00:30:01,940
+ألف اتنين تمام طب ما أنت هيدخلتوني في ألف واحد و
+
+361
+00:30:01,940 --> 00:30:07,540
+ألف اتنين بدنا ياهم Constants هدول Constants بدنا
+
+362
+00:30:07,540 --> 00:30:14,270
+نجيب قيمهملأ هم هدولة انت جيبت ال route الأولى في
+
+363
+00:30:14,270 --> 00:30:17,550
+n أنا مش ضامن جديش المفروض يتكرر ال route الأولى
+
+364
+00:30:17,550 --> 00:30:20,950
+تلت مرات مرتين خمس مرات عشر مرات عشان نجيب ال a n
+
+365
+00:30:20,950 --> 00:30:25,270
+ولا جديش فحاطن درب في constant هنا اللي هو المفروض
+
+366
+00:30:25,270 --> 00:30:29,090
+عدد تكرارات ال route عدد تكرارات ال route كويسة
+
+367
+00:30:29,090 --> 00:30:32,750
+التنتين هدولة القمتين هدول مافيش أبساط من جيبتهم
+
+368
+00:30:32,750 --> 00:30:37,950
+ليش؟ كيف نجيبهم؟ نجيبهم من ال initial values اللي
+
+369
+00:30:37,950 --> 00:30:42,310
+ميعطينياهمتأكدوا .. sequence بدون initial values
+
+370
+00:30:42,310 --> 00:30:44,390
+مافيش حاجة اسمها sequence بدون initial values
+
+371
+00:30:44,390 --> 00:30:48,590
+فطبيعي .. منطقي جدا أنه لازم يكون فيه على الأقل في
+
+372
+00:30:48,590 --> 00:30:52,170
+.. مادام بتكلم عن second يعني في two degree لازم
+
+373
+00:30:52,170 --> 00:30:54,430
+يكون في عندكوا على الأقل في two elements موجودين
+
+374
+00:30:54,430 --> 00:30:59,110
+اللي هم a node و a واحد لازم يكونوا موجودين هدول
+
+375
+00:30:59,110 --> 00:31:05,070
+.. ضروري كويس .. مادام موجودين عوضوا مرة ب a nodeو
+
+376
+00:31:05,070 --> 00:31:08,150
+مرة بقى واحد فصار انكم معادلتين و هم two variables
+
+377
+00:31:08,150 --> 00:31:12,470
+بنجابه فبتصير الأمور سهلة بيصير بالعكس سهلة جدا
+
+378
+00:31:12,470 --> 00:31:21,040
+كمان سهلة جدا تمام مثال بيربط أن كل ال ..المعلومات
+
+379
+00:31:21,040 --> 00:31:24,720
+و بنشوف بالظبط ال sequence للحل كيف بتتم طبعا ال
+
+380
+00:31:24,720 --> 00:31:27,480
+sequence بسيط جدا مافيش مشكلة لو افترضنا sort the
+
+381
+00:31:27,480 --> 00:31:33,620
+recurrence a n تساوي a n minus one plus two a n
+
+382
+00:31:33,620 --> 00:31:37,180
+minus two فهي عندنا ال coefficients بتاعتنا c1
+
+383
+00:31:37,180 --> 00:31:43,000
+بتساوي واحد و c2 بتساوي اتنين c1 واحد و c2 اتنين و
+
+384
+00:31:43,000 --> 00:31:47,500
+اتنين okay و ميعطينا هى two initial values اتنين و
+
+385
+00:31:47,500 --> 00:31:50,940
+سبعة اتنينو سبعة و هدول برضه هنحتاجهم في الآخر
+
+386
+00:31:50,940 --> 00:31:52,920
+نعوض عشان نجيب alpha واحد و alpha اتنين بس
+
+387
+00:31:52,920 --> 00:31:56,320
+هنحتاجهم في alpha واحد okay مدام يعندي c واحد و c
+
+388
+00:31:56,320 --> 00:32:00,060
+اتنين اعطاني يهم automatically و انا عارف ان هي
+
+389
+00:32:00,060 --> 00:32:04,380
+اتنين معتمد على two terms ف automatically R تربيع
+
+390
+00:32:04,380 --> 00:32:11,180
+ناقص c واحد خلاص هي c واحد في R ناقص اتنين
+
+391
+00:32:40,360 --> 00:32:41,760
+C2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2R2
+
+392
+00:32:42,810 --> 00:32:51,550
+الفا اتنين في ال route التانية to the bar المعادلة
+
+393
+00:32:51,550 --> 00:32:55,730
+هذه بدنا نجيب الفا واحد و الفا اتنين في عندنا a
+
+394
+00:32:55,730 --> 00:33:01,350
+node و a واحد خلاص هي a node تساوي a node معناته
+
+395
+00:33:01,350 --> 00:33:06,830
+كل n بتساوي zero فتصير الفا واحد هذه واحد زائد
+
+396
+00:33:06,830 --> 00:33:08,630
+واحد
+
+397
+00:33:14,750 --> 00:33:21,550
+المعادلة التانية اي واحد تساوي جداش بواحد فهنا
+
+398
+00:33:21,550 --> 00:33:30,410
+هتساوي alpha واحد في اتنين زائد بتصير ناقص هنا
+
+399
+00:33:30,410 --> 00:33:34,470
+بتصير two minus one فminus alpha اتنين
+
+400
+00:33:39,500 --> 00:33:45,420
+هذه اتنين اشمعوا الاتنين مع بعض تلاتة الفا واحد
+
+401
+00:33:45,420 --> 00:33:53,280
+تساوي تسعة الفا واحد تلاتة الفا
+
+402
+00:33:53,280 --> 00:33:57,760
+واحد تساوي تسعة الفا واحد تسعة الفا واحد تسعة الفا
+
+403
+00:33:57,760 --> 00:33:57,760
+واحد تسعة الفا واحد تسعة الفا واحد تسعة الفا واحد
+
+404
+00:33:57,760 --> 00:34:03,180
+تسعة الفا واحد تسعة الفا واحد تسعة الفا واحد تسعة
+
+405
+00:34:03,180 --> 00:34:05,640
+الفا واحد تسعة الفا واحد تسعة الفا واحد تسعة الفا
+
+406
+00:34:05,640 --> 00:34:05,660
+واحد تسعة الفا واحد تسعة الفا واحد تسعة الفا واحد
+
+407
+00:34:05,660 --> 00:34:05,680
+تسعة الفا واحد تسعة الفا واحد تسعة الفا واحد تسعة
+
+408
+00:34:05,680 --> 00:34:05,680
+الفا واحد تسعة الفا واحد تسعة الفا واحد تسعة الفا
+
+409
+00:34:05,680 --> 00:34:11,430
+واحد تسعة الفا واحد تسعة الفا واحدن بتساوي الف و
+
+410
+00:34:11,430 --> 00:34:18,130
+واحد بتلاتة تلاتة في اتنين to the power ن ناقص
+
+411
+00:34:18,130 --> 00:34:23,090
+سالب واحد to the power ن خلاص هاي المعادلة
+
+412
+00:34:23,090 --> 00:34:27,370
+بتاعتكوا بدنا ال element رقم الف فليكن عوضه هنا ب
+
+413
+00:34:27,370 --> 00:34:31,510
+الف وعوضه هنا ب الف خلصناه رقم مية هاي بيجي برقم
+
+414
+00:34:31,510 --> 00:34:35,130
+مية العنصر في ال location رقم إيش ما يكون يكون بس
+
+415
+00:34:35,130 --> 00:34:41,100
+بتعوضه في مين فيفي قيمته بتطلع قيمة الانصر نفسه طب
+
+416
+00:34:41,100 --> 00:34:44,780
+اعمل check بتقدر تعمل check اتجربه عند الصفر و عند
+
+417
+00:34:44,780 --> 00:34:47,600
+الواحد و ممكن تجربه عند الاتنين و التلاتة يعني من
+
+418
+00:34:47,600 --> 00:34:50,940
+هنا بتقدر تجيبهك as a recurrence relation اتنين و
+
+419
+00:34:50,940 --> 00:34:53,940
+تلاتة و اربعة و تجربه هنا شوف اتأكد و اعمل check
+
+420
+00:34:53,940 --> 00:34:59,480
+اعمله check فواضح ان فعلا تطلع معنى ال end تسوي
+
+421
+00:34:59,480 --> 00:35:03,820
+تلاتة في اتنين to the power n minus one to the
+
+422
+00:35:03,820 --> 00:35:09,260
+power to the power nو هاي ميعطيكوا مجموعة elements
+
+423
+00:35:09,260 --> 00:35:12,580
+other elements عشان تعملوا ال check لو حبيتوا
+
+424
+00:35:12,580 --> 00:35:15,700
+تجربوا طيب هذه الحالة الأولى ال theorem الأولى
+
+425
+00:35:15,700 --> 00:35:20,160
+قولنا في حالة انه ال two roots بيسووش بعض طب في
+
+426
+00:35:20,160 --> 00:35:24,500
+حال بيسووا بعض في حال طلعوا بيسووا بعض ال roots
+
+427
+00:35:24,500 --> 00:35:30,020
+ايش الحل؟ الحل انه هنشتغل على theorem تانية واحدة
+
+428
+00:35:30,020 --> 00:35:35,460
+من ال two terms هنضربها في endكل اللي حزيروا ان
+
+429
+00:35:35,460 --> 00:35:38,440
+واحدة من ال two terms احنا متفقين كانت alpha واحد
+
+430
+00:35:38,440 --> 00:35:42,880
+في R واحد to the power N Alpha اتنين في R اتنين to
+
+431
+00:35:42,880 --> 00:35:46,980
+the power N طيب احنا لوجة ال root مشترك لانه نفس
+
+432
+00:35:46,980 --> 00:35:52,240
+ال root نفس ال root فحنسميه root 00 لانه مشترك هذا
+
+433
+00:35:52,240 --> 00:35:57,000
+ال root هو نفس ال root هدا هنضرب واحد منهم في N مش
+
+434
+00:35:57,000 --> 00:36:02,010
+هتفرق الأولى او التانية مفرجشهتحطه الأولى كل اللى
+
+435
+00:36:02,010 --> 00:36:05,810
+هسير بس ان قيمة الف واحد هتعادل مع الف اتنين ده
+
+436
+00:36:05,810 --> 00:36:08,470
+فارقش معانا اشي مش هفارقش اشي المهم ان واحدة من ال
+
+437
+00:36:08,470 --> 00:36:11,390
+two terms هضبها في مين فئة و بتكمل نفس الحل عادى
+
+438
+00:36:11,390 --> 00:36:13,870
+بتجيبه الف واحد بتجيبه الف اتنين ال sequence هو هو
+
+439
+00:36:15,720 --> 00:36:24,560
+هيعطينا مثلًا، لو الان بتساوي 6an-1-9an-2 ويمعطينا
+
+440
+00:36:24,560 --> 00:36:35,760
+a node او a0 و a1 من شكل المعادلة المعادلة
+
+441
+00:36:35,760 --> 00:36:41,320
+فيها two terms يعني انا عارف مسبقًا انه هتكون R
+
+442
+00:36:41,320 --> 00:36:49,670
+تربيععارفين مسبقا انه حيكون في عندنا R تربيع وفي
+
+443
+00:36:49,670 --> 00:36:52,410
+عندى R وفي بعدين عندى constant و بعدين كله equal
+
+444
+00:36:52,410 --> 00:36:58,450
+to zero طيب هاي ال R طيب ال R .. هاد ال R تربيع
+
+445
+00:36:58,450 --> 00:37:02,670
+مافيش فيها مشكلة ال R في 6 هتيجي عن ناحية التانية
+
+446
+00:37:02,670 --> 00:37:08,670
+minus 6 طيب في عندى minus 9 هتيجي عن ناحية التانية
+
+447
+00:37:08,670 --> 00:37:16,390
+موجة ب 9خلاص بدي ال route لهذه طبعا واضح أنه الجزء
+
+448
+00:37:16,390 --> 00:37:24,050
+المميز اللي هو جذر b تربيع ناقص 4ac هتساوي صفر
+
+449
+00:37:24,050 --> 00:37:30,590
+لإيش لأن هنا عندكوا 4 في 9 و هنا في 6 تربيع ف36
+
+450
+00:37:30,590 --> 00:37:34,230
+ناقص 36 و واضح أن هذه صفر يعني كل الحل هيكون
+
+451
+00:37:34,230 --> 00:37:41,200
+عندكوا minus b over 2a-B over 2A فهيطلع تلاتة
+
+452
+00:37:41,200 --> 00:37:44,220
+هيطلع عندكوا تلاتة automatically مدام تلاتة صارت
+
+453
+00:37:44,220 --> 00:37:51,560
+ال A N إيش بتساوي Alpha واحد في تلاتة to the power
+
+454
+00:37:51,560 --> 00:38:02,260
+N زائد Alpha تنين في N تلاتة to the power N عوضه
+
+455
+00:38:02,260 --> 00:38:07,040
+في Alpha في A Zero و A واحد عوضه مرة هنا و مرة هنا
+
+456
+00:38:07,400 --> 00:38:16,540
+ف ايه؟ zero تساوي الف واحد بجداش تلاتة ضبار zero
+
+457
+00:38:16,540 --> 00:38:24,020
+واحد خلاص زائد الف زيرو كلها راحت كله راحت فإذا
+
+458
+00:38:24,020 --> 00:38:27,880
+هاد اتماتك اللي هي طلعت لحالة بتساوي جداش كانت ال
+
+459
+00:38:27,880 --> 00:38:32,260
+a واحد هنا واحد واحد فعنكوا الف واحد بتساوي واحد
+
+460
+00:38:32,260 --> 00:38:36,890
+هيأول معادرة طلعتوها بتعودوا في التاني عشان تجيبوا
+
+461
+00:38:36,890 --> 00:38:44,010
+alpha 2 ف a1 تساوي alpha 1 ب1 و هنا to the power 1
+
+462
+00:38:44,010 --> 00:38:51,790
+بتساوي 3 زائد alpha 2 في 1 لأن ب1 تلاتة في تلاتة
+
+463
+00:38:51,790 --> 00:38:58,330
+هذا بيساوي 6 هذا في الحلقة بيساوي 6 automatically
+
+464
+00:38:58,330 --> 00:39:01,400
+ليه؟هذه هتروح الناحية التانية اللى هى الستة يعنى
+
+465
+00:39:01,400 --> 00:39:05,500
+قيمة ستة هيطلع تلاتة بساوية الف اتنين في تلاتة
+
+466
+00:39:05,500 --> 00:39:08,580
+واحد
+
+467
+00:39:08,580 --> 00:39:12,680
+خلاص وين المعادلة هى المعادلة الأصلية كنا نعوض
+
+468
+00:39:12,680 --> 00:39:21,740
+فيها نشتغل عليها أصبحت واحد واحد خلاص هى المعادلة
+
+469
+00:39:21,740 --> 00:39:28,670
+بس اللى هى أخر معادلةنقر أخر معادلة موجودة لدينا
+
+470
+00:39:28,670 --> 00:39:35,630
+okay هذا كان الجزء اللي ضايل و خلّيني أقول إن هذا
+
+471
+00:39:35,630 --> 00:39:39,550
+جزء مهم يعني عادة الجزئية الأخيرة هي جزئية مهمة
+
+472
+00:39:39,550 --> 00:39:44,250
+جزئية مهمة
+
+473
+00:39:44,250 --> 00:39:49,310
+طيب مدام إحنا بنتكلم في ال recurrence relation
+
+474
+00:39:49,310 --> 00:39:53,780
+خلّيني أكملي في جزئية كلمة relation بتاعتنافي كلمة
+
+475
+00:39:53,780 --> 00:39:57,140
+relation ونشوف ايش يعني relation اصلا نعمم هذه ال
+
+476
+00:39:57,140 --> 00:39:59,840
+logic جاعدين نتكلم من بدلي على recurrence relation
+
+477
+00:39:59,840 --> 00:40:04,240
+relation relation ايش يعني relation فهندخل هذه ال
+
+478
+00:40:04,240 --> 00:40:07,380
+logic فيه شوية في جزئيه ايش يعني relation او ايش
+
+479
+00:40:07,380 --> 00:40:10,980
+شيه ال relations فعليا شيه ال relations فعليا
+
+480
+00:40:10,980 --> 00:40:15,160
+فعليا ال relations هي فعليا علاقة بين مجموعة
+
+481
+00:40:15,160 --> 00:40:20,020
+elements موجودين لست a مع مجموعة elements موجودين
+
+482
+00:40:20,020 --> 00:40:26,810
+لست b بحيث انهالعلاقة دي هتكون ثنائية و هنحدد
+
+483
+00:40:26,810 --> 00:40:30,250
+تلوجة كل شغلنا هيكون عبارة عن binary relation
+
+484
+00:40:30,250 --> 00:40:34,870
+بمعنى عندنا two sets ال two sets هدولة في relation
+
+485
+00:40:34,870 --> 00:40:38,190
+بين element في ال set الأولى مع element في ال set
+
+486
+00:40:38,190 --> 00:40:42,330
+التاني فهذا ثنائي ثنائي على اعتبار أنه هيكون كأنه
+
+487
+00:40:42,330 --> 00:40:47,390
+عندكوا زوج مرتب الأول جزء الأول منهمن set A و جزء
+
+488
+00:40:47,390 --> 00:40:52,690
+ثاني من set B فهذا بنسميه binary عشان هيك بنسميه
+
+489
+00:40:52,690 --> 00:40:57,090
+binary okay
+
+490
+00:40:59,190 --> 00:41:03,890
+الـ relation from A to B وهنا فوق احنا محددين ان
+
+491
+00:41:03,890 --> 00:41:07,130
+الـA و الـB دولة مجموعة two sets عبارة عن set set
+
+492
+00:41:07,130 --> 00:41:10,490
+يعني فيها إيش؟ مجموعة elements، فيها عناصر العناصر
+
+493
+00:41:10,490 --> 00:41:13,490
+هذه ممكن تكون objects، ممكن تكون numbers، ممكن
+
+494
+00:41:13,490 --> 00:41:15,930
+تكون يا هيك يا هيك، ماتفرجش معناه المهم إنه في
+
+495
+00:41:15,930 --> 00:41:19,890
+relation from A to B هذه هتكون عبارة ال relation
+
+496
+00:41:19,890 --> 00:41:22,610
+نفسها أو ال elements اللي هتحقق ال relation اللي
+
+497
+00:41:22,610 --> 00:41:27,470
+هنعرفها هتكون عبارة عن subset subset من من كل
+
+498
+00:41:27,470 --> 00:41:32,460
+العناصر الممكنةبين a و b طب إيش كل العداصر الممكنة
+
+499
+00:41:32,460 --> 00:41:40,620
+من a ل b هي ال Cartesian product بمعنى لو عندكوا a
+
+500
+00:41:40,620 --> 00:41:51,020
+فرضا واحد اتنين و ثلاثة و عندكوا b بتساوي a و b ال
+
+501
+00:41:51,020 --> 00:41:54,360
+relations الممكنة كل ال relations الممكنة فعليا
+
+502
+00:41:54,360 --> 00:42:01,380
+بين elements من a مع element من b هيبغض النظر إيش
+
+503
+00:42:01,380 --> 00:42:03,360
+ال relation طبعا هي logic لما نعرف ال relation
+
+504
+00:42:03,360 --> 00:42:07,000
+ممكن يا بتقبل بعضهم يا بترفض بعضهم يعني مش
+
+505
+00:42:07,000 --> 00:42:09,980
+بالضرورة كلهم بس ال relation هذه حسب تعريفنا لل
+
+506
+00:42:09,980 --> 00:42:16,460
+relation لاحقا هذه ممكن تكون واحد و a تمام و واحد
+
+507
+00:42:16,460 --> 00:42:23,880
+و بي ممكن تكون اتنين و a ممكن تكون اتنين و b تلاتة
+
+508
+00:42:23,880 --> 00:42:32,270
+a تلاتة bفيش إمكانية غير هدول فهدول بالنسبالنا هم
+
+509
+00:42:32,270 --> 00:42:35,730
+ال universe of discourse هدول كل الاحتمالات
+
+510
+00:42:35,730 --> 00:42:40,850
+الممكنة هدول كل ال relations اللي ممكن تكون موجودة
+
+511
+00:42:40,850 --> 00:42:45,560
+بين element في a مع element في bهذا الكل طب هذا
+
+512
+00:42:45,560 --> 00:42:50,600
+ايش يمثل فعلا يمثل Cartesian product between A وB
+
+513
+00:42:50,600 --> 00:42:56,120
+فهي فعلا A Cartesian product B فإذا أي relation
+
+514
+00:42:56,120 --> 00:43:03,120
+لاحقا هنتكلم عنها هي هتكون عبارة عن subset من ال
+
+515
+00:43:03,120 --> 00:43:06,060
+Cartesian productمن الـ Cartesian product لأنه لا
+
+516
+00:43:06,060 --> 00:43:08,560
+يمكن أن تكون أكبر منها لا يمكن أن تكون أكبر منها
+
+517
+00:43:08,560 --> 00:43:12,500
+ليش؟ مافيش أي عنصر غير هدول أساساً لا يمكن يكون أي
+
+518
+00:43:12,500 --> 00:43:17,060
+عنصر من هدول يعمل relation element من A مع element
+
+519
+00:43:17,060 --> 00:43:20,880
+من B مافيش .. هاي كل الاحتمالات الممكنة هاي كل ال
+
+520
+00:43:20,880 --> 00:43:24,840
+relations الممكنة ففي الحالة هذه أي relation from
+
+521
+00:43:24,840 --> 00:43:28,920
+A to B هتكون subset من ال Cartesian product
+
+522
+00:43:28,920 --> 00:43:33,320
+between A وB for example ناخد example ال relation
+
+523
+00:43:33,320 --> 00:43:38,520
+أصغر منهless than أصغر من هذه from natural number
+
+524
+00:43:38,520 --> 00:43:41,700
+to natural number هيحدد لي ال a natural number
+
+525
+00:43:41,700 --> 00:43:45,140
+وحدد لنا ال b natural number طيب ال relation هذه
+
+526
+00:43:45,140 --> 00:43:49,320
+إيش؟ عبارة عن إيش؟ عبارة عن زوج مرتب هاي ال n و ال
+
+527
+00:43:49,320 --> 00:43:54,160
+m بشرط إن ال n لازم تكون أصغر من إيش؟ من m ال n
+
+528
+00:43:54,160 --> 00:43:58,500
+أصغر من ال m فكأنه الأصغر من هذا هي ال relation
+
+529
+00:43:58,500 --> 00:44:02,720
+أصغر من هاي ال relation هذه هي ال relation بتاعتنا
+
+530
+00:44:02,720 --> 00:44:07,850
+كويسمبدأيا طبعا ناخد بالنا أن مادام relation يعني
+
+531
+00:44:07,850 --> 00:44:12,770
+هي related to شغلة related to شغلة تانية يعني
+
+532
+00:44:12,770 --> 00:44:19,050
+دايما في reference لما نقول مثلا خمسة أكبر من
+
+533
+00:44:19,050 --> 00:44:22,950
+اتنين فبالنسبة للخمسة ال reference هي الاتنين هي
+
+534
+00:44:22,950 --> 00:44:26,730
+الاتنين لأن related للاتنين الخمسة أكبر فصار ال
+
+535
+00:44:26,730 --> 00:44:31,410
+relation بتاعتنا أكبر منه هنا نتكلم عن أصغر من ال
+
+536
+00:44:31,410 --> 00:44:38,220
+N هذه أصغر منال M ال N أصغر من ال M على اعتبار أن
+
+537
+00:44:38,220 --> 00:44:41,300
+ال relation هنا أصغر من ال relation هنا عندنا أصغر
+
+538
+00:44:41,300 --> 00:44:48,880
+من فهذه معناها أن A و B كزوج مرتب belong to set
+
+539
+00:44:48,880 --> 00:44:53,700
+جديدة اللي هي ال subset من كلهم ال set هذه عبارة
+
+540
+00:44:53,700 --> 00:44:59,800
+عن أصغر من عبارة عن أصغر من لو غيرنا هنا و حطناها
+
+541
+00:44:59,800 --> 00:45:09,780
+أرقام برضهنشوف الأصغر من إيش بتطلع معنا جولنا
+
+542
+00:45:09,780 --> 00:45:16,880
+واحد واثنين مثلا طيب
+
+543
+00:45:16,880 --> 00:45:19,640
+هذه مش ال relation هذه هيك صارت هذه كل ال universe
+
+544
+00:45:19,640 --> 00:45:22,080
+of discourse هذه ال Cartesian product هذه ال
+
+545
+00:45:22,080 --> 00:45:26,500
+Cartesian product بتاعتنا كلها طيب أصغر من هتكون
+
+546
+00:45:26,500 --> 00:45:27,500
+إيش بتساوي منهم؟
+
+547
+00:45:37,320 --> 00:45:42,100
+خلاص هو عنصر واحد عنصر واحد فيه مش غيره ليه وجد
+
+548
+00:45:42,100 --> 00:45:47,720
+غيره فإذا لحظة الواحد واثنين هي subset من من ال
+
+549
+00:45:47,720 --> 00:45:50,440
+Cartesian product هي فعلا subset من ال Cartesian
+
+550
+00:45:50,440 --> 00:45:55,280
+product في الحالة اللي عندنا طيب فإذا عنصر واحد
+
+551
+00:45:55,280 --> 00:45:59,320
+واثنين belong torelation أصغر من هي ال relation
+
+552
+00:45:59,320 --> 00:46:03,100
+أصغر من العنصر الوحيد اللي belong إلها هو الواحد
+
+553
+00:46:03,100 --> 00:46:06,480
+واثنين ففي الحالة هذه الزوجة واحد واثنين ينتمي
+
+554
+00:46:06,480 --> 00:46:10,700
+لأصغر من relation okay يبدو كتوبها كتالة a
+
+555
+00:46:10,700 --> 00:46:17,480
+relation b أو a is related to b أو a أو by related
+
+556
+00:46:17,480 --> 00:46:23,360
+to r أو under relation rالتسمية مش هتفرق كتير،
+
+557
+00:46:23,360 --> 00:46:26,700
+بتقدر تسموها هيك أو هيك related to relation are أو
+
+558
+00:46:26,700 --> 00:46:31,480
+under relation are كلها في النهاية إن ال A بالنسبة
+
+559
+00:46:31,480 --> 00:46:35,440
+ل B هل حقق ال relation أو لأ، حقق ال relation أو
+
+560
+00:46:35,440 --> 00:46:36,420
+محققش
+
+561
+00:46:39,120 --> 00:46:44,360
+ال R مش .. ال Cartesian product مش علاقة، معناه هي
+
+562
+00:46:44,360 --> 00:46:47,060
+subset، يعني فيه .. لأ، أنا مابقولتش مش علاقة، أنا
+
+563
+00:46:47,060 --> 00:46:50,520
+بقول الأصغر من مش .. مش هتمثل العلاقة، أنا هنا
+
+564
+00:46:50,520 --> 00:46:53,600
+لإني بدأت أتكلم عن أصغر من، فقلتلكوا لأ هذه مش هي
+
+565
+00:46:53,600 --> 00:46:56,780
+ال relation بتاعتنا، قلتلكوا لأ مش هذه العلاقة
+
+566
+00:46:56,780 --> 00:46:59,560
+اللي احنا بنشتغل عليها، صرنا بنشتغل على أصغر من،
+
+567
+00:46:59,560 --> 00:47:03,920
+فصارت subset من ال Cartesian product، ممكن يكون في
+
+568
+00:47:03,920 --> 00:47:09,100
+relation، نعمل relation تشمل كلهممكن نعمل relation
+
+569
+00:47:09,100 --> 00:47:15,120
+تشمل الكل لو قلنا مثلا ال relation بتاعتنا انه ال
+
+570
+00:47:15,120 --> 00:47:21,360
+.. كل الأرقام اللي مجموحها خمسة او اقل كله .. هي
+
+571
+00:47:21,360 --> 00:47:24,460
+دخلت كلها ال Cartesian product صح؟ خمسة او اقل
+
+572
+00:47:24,460 --> 00:47:30,740
+مجموح A زائد B اكبر .. اصغر من او اقل من خمسة اصغر
+
+573
+00:47:30,740 --> 00:47:33,520
+من او يساوي خمسة فمعنى ذلك أخدناها كلها ال
+
+574
+00:47:33,520 --> 00:47:36,780
+relationبس لإن أنا بدأت حددت الأصغر من .. قولتلكوا
+
+575
+00:47:36,780 --> 00:47:39,760
+لأ ديروا بالكوا بطلنا نحكي عن ال relation أصغر من
+
+576
+00:47:39,760 --> 00:47:43,660
+هنا أو بطلنا نتكلم in general لأ هي صارت relation
+
+577
+00:47:43,660 --> 00:47:46,840
+تانية كتبناها و قولتلكوا ده هي subset من كله بس لأ
+
+578
+00:47:46,840 --> 00:47:49,780
+ممكن تكون هي كلها على بعض relation حسب التعريف لل
+
+579
+00:47:49,780 --> 00:47:55,270
+relation okay let relation from A to BR binary
+
+580
+00:47:55,270 --> 00:47:58,590
+relation معناته ان احنا بتكلم عن two sets الأول
+
+581
+00:47:58,590 --> 00:48:03,310
+relation مع التاني ال complementary relations او
+
+582
+00:48:03,310 --> 00:48:08,990
+ال complement of R هنسميه R slash اللي هي ال R مع
+
+583
+00:48:08,990 --> 00:48:12,910
+ال slash هذه ليست relation بمعنى انه ليست ال
+
+584
+00:48:12,910 --> 00:48:18,350
+relation relation او ال inverse ال complement لان
+
+585
+00:48:18,350 --> 00:48:23,940
+ال inverse مختلفة ال complement R from A to Bعبارة
+
+586
+00:48:23,940 --> 00:48:29,060
+عن ايش؟ the complement of R هي المكملة ل R على
+
+587
+00:48:29,060 --> 00:48:32,060
+اعتبار مدام مكملة يعني معناته في عندي universe of
+
+588
+00:48:32,060 --> 00:48:35,040
+discourse طب انا فعلا عندي universe of discourse
+
+589
+00:48:35,040 --> 00:48:37,980
+ايش هو ال universe of discourse طبعا؟ ال Cartesian
+
+590
+00:48:37,980 --> 00:48:45,540
+ال Cartesian فهي دي مثلا هيها الأصغر من واحد و
+
+591
+00:48:45,540 --> 00:48:49,660
+اتنين طب المكمل اتعتها بشطب واحد و اتنين و الباقي
+
+592
+00:48:49,660 --> 00:48:55,160
+الباقي كله هلوجد هيكون المكمللأ أصغر من بمعنى أصغر
+
+593
+00:48:55,160 --> 00:49:00,600
+slash ليست أصغر من فهنا ال relation صارت إيش ليست
+
+594
+00:49:00,600 --> 00:49:05,060
+أصغر من بحط لها ال slash بس هيك صارت ليست أصغر من
+
+595
+00:49:05,060 --> 00:49:08,420
+طب مدام ليست أصغر من معناته ممكن تكون أكبر أو
+
+596
+00:49:08,420 --> 00:49:12,380
+يساوي طب فعلا لو شطبته هذه الباقين أكبر أو يساوي
+
+597
+00:49:12,380 --> 00:49:15,560
+الباقين هتلاقيهم يا أكبر يا بيساوي فعلا فهي
+
+598
+00:49:15,560 --> 00:49:20,560
+compliment لمن لR compliment of of R تمام هاي
+
+599
+00:49:20,560 --> 00:49:26,320
+compliment of Rال complement of R عبارة عن a و b
+
+600
+00:49:26,320 --> 00:49:32,080
+بشرط أن a و b لا تنتمي لل relation نفسها فما دام
+
+601
+00:49:32,080 --> 00:49:35,060
+لا تنتمي لل relation هتكون ال complement تبعها
+
+602
+00:49:35,060 --> 00:49:40,560
+بالنسبة لمين هيها ال universal discourse لما
+
+603
+00:49:40,560 --> 00:49:46,300
+عرفناها أيام ال sets كنا بنقول u minus aU minus A
+
+604
+00:49:46,300 --> 00:49:49,840
+طيب ال A عندنا اللي هي relation هيها و ال U خلاص
+
+605
+00:49:49,840 --> 00:49:52,380
+اتفجنا ان هي ال Cartesian product ال Cartesian
+
+606
+00:49:52,380 --> 00:49:56,620
+product okay لاحقا احنا كنا بنكتبها برضه ال
+
+607
+00:49:56,620 --> 00:50:00,880
+complement أيام ال six كنا بنكتبها bar متذكرين؟ R
+
+608
+00:50:00,880 --> 00:50:04,320
+complement او R bar فهي ال universe of discourse
+
+609
+00:50:04,320 --> 00:50:08,240
+بتاعتنا في الحالة هذه اللي هي ال Cartesian أو
+
+610
+00:50:08,240 --> 00:50:13,300
+بنسميها complement لو قلنا the complement of R
+
+611
+00:50:13,300 --> 00:50:17,900
+slashهي ال R ال compliment of compliment هترجع لل
+
+612
+00:50:17,900 --> 00:50:23,800
+relation نفسها okay هي أصغر من slash معناته ليست
+
+613
+00:50:23,800 --> 00:50:29,520
+أصغر من مدام ليست أصغر من معناته كل زوج مرتب a و b
+
+614
+00:50:29,520 --> 00:50:33,200
+بشرط أن a و b not belong to أصغر من في الحالة هذه
+
+615
+00:50:33,200 --> 00:50:39,420
+معناته a و b ليست a أصغر من b أو a ليست أصغر من b
+
+616
+00:50:39,420 --> 00:50:43,560
+طب ليست أصغر من b يعني ممكن تكون تساويأو أكبر فإذا
+
+617
+00:50:43,560 --> 00:50:50,660
+هذه حد تساوي أكبر من أو يساوي صارت not أصغر
+
+618
+00:50:50,660 --> 00:50:55,020
+من أو ليست أصغر من تكافي أكبر من أو يساوي أكبر من
+
+619
+00:50:55,020 --> 00:51:01,140
+أو يساوي ك relation .. ك relation okay ال relation
+
+620
+00:51:01,140 --> 00:51:05,840
+on a set Aفهنا بنعمل relation على set واحدة، قبل
+
+621
+00:51:05,840 --> 00:51:09,460
+هيك كنا هيدا بناخد two sets و بنشتغل عليهم، لأ
+
+622
+00:51:09,460 --> 00:51:12,560
+احنا أصغر منه، أكبر منه، كل الكلام هذا بنشتغله على
+
+623
+00:51:12,560 --> 00:51:15,820
+مين؟ على ال natural number، يعني أنا بتكلم عن set
+
+624
+00:51:15,820 --> 00:51:21,440
+واحدة، هي ال set واحدة، كتبنا are from natural
+
+625
+00:51:21,440 --> 00:51:26,540
+number to natural number، يعني من a to aactually
+
+626
+00:51:26,540 --> 00:51:29,920
+هي من a to a فمعظم ال relations الحقيقة هتصير ..
+
+627
+00:51:29,920 --> 00:51:35,760
+هنعممها لوجة انه احنا بنتكلم the same set او لنفس
+
+628
+00:51:35,760 --> 00:51:40,140
+ال set فهنقول ان انا بتكلم عن ال .. ال .. a binary
+
+629
+00:51:40,140 --> 00:51:44,620
+relation from a set A to itself لنفسها مع نفسها زي
+
+630
+00:51:44,620 --> 00:51:47,040
+الحكاية التو اللي كنا بنتكلم عن natural number to
+
+631
+00:51:47,040 --> 00:51:51,810
+natural numberالأصغر من اللي احنا اشتغلناها طوي
+
+632
+00:51:51,810 --> 00:51:54,710
+كنا بنتكلم عن ال natural number فكانت فعلا من ال
+
+633
+00:51:54,710 --> 00:51:57,590
+natural number لل .. لنفس ال natural number وهذه
+
+634
+00:51:57,590 --> 00:52:02,210
+عادة بنسميها ال identity relation لل .. لل ست إيش؟
+
+635
+00:52:02,210 --> 00:52:08,130
+لل ست A identity relation لل ست A من A لنفسها من A
+
+636
+00:52:08,130 --> 00:52:14,290
+لنفسها فالست A is a set لاحظوا A و A هو الزوج
+
+637
+00:52:14,290 --> 00:52:20,410
+الثنائي تبعنا بس مش معناه هيك أن A تسوي Aالـ a لما
+
+638
+00:52:20,410 --> 00:52:26,790
+بقول a small هذا القصد فيها أنه هذا element belong
+
+639
+00:52:26,790 --> 00:52:35,190
+to a capital set فإذا أي عنصر داخل ال set capital
+
+640
+00:52:35,190 --> 00:52:39,890
+A بسميه a هنا ما تتخدوش في بالك أنه هذا لازم
+
+641
+00:52:39,890 --> 00:52:43,450
+exactly بيسوا بعض، لأ مش بالضروري كل الهدف منها أن
+
+642
+00:52:43,450 --> 00:52:48,320
+ال a هذه belong to set Aالـ a ال small belonged to
+
+643
+00:52:48,320 --> 00:52:51,240
+set A تاول لو كنا بنتكلم عن ال capital P كنا
+
+644
+00:52:51,240 --> 00:52:55,200
+بنسيبها بي small عساس ان هي تتفق معاها بس small و
+
+645
+00:52:55,200 --> 00:52:58,900
+capital لمجرد انه هل ده element او set لا اكتر ولا
+
+646
+00:52:58,900 --> 00:53:03,040
+اقل ماتخلوش ان المتشابهات اللي اخبطكم معناته ان
+
+647
+00:53:03,040 --> 00:53:05,500
+انا بتكلم عن واحد واحد اتنين و اتنين لأ ممكن تكون
+
+648
+00:53:05,500 --> 00:53:08,720
+واحد و اتنين اتنين و واحد عادي كل ال relations
+
+649
+00:53:08,720 --> 00:53:11,820
+هدولة كل الأزواج اللي تكون ايه الموجودة عندها ممكن
+
+650
+00:53:11,820 --> 00:53:18,860
+تكون هنا ممكن تكون نفسها okayطيب definition برضه
+
+651
+00:53:18,860 --> 00:53:21,880
+احنا نتكلم هنا عن ال relation ال relations on a
+
+652
+00:53:21,880 --> 00:53:25,940
+set طبعا نتكلم عن set واحدة one set فال relation
+
+653
+00:53:25,940 --> 00:53:31,680
+on the set A is a relation from A to A او from A
+
+654
+00:53:31,680 --> 00:53:35,180
+to itself in other word هي برضه في جميع الأحوال
+
+655
+00:53:35,180 --> 00:53:39,640
+هتكون subset من مين؟ من A Cartesian product A A
+
+656
+00:53:39,640 --> 00:53:43,420
+Cartesian product A هتكون ال relation اللي هو ال
+
+657
+00:53:43,420 --> 00:53:46,720
+universe of discourse كلها على بعض okay ناخد مثال
+
+658
+00:53:47,710 --> 00:53:51,070
+لت A، واحد، اتنين، تلاتة، أربعة، فهي يعطيني مجموعة
+
+659
+00:53:51,070 --> 00:53:55,030
+elements، هم هدول فقط ال elements اللي نقدر نقول
+
+660
+00:53:55,030 --> 00:53:58,490
+belong to capital A، اللي belong to capital A،
+
+661
+00:53:58,490 --> 00:54:03,970
+okay which ordered pairs are in the relation R؟ وR
+
+662
+00:54:03,970 --> 00:54:08,130
+عبارة عن A وB بشرط إنه A أصغر من B، فاحنا مازلنا
+
+663
+00:54:08,130 --> 00:54:10,750
+هنا في نفس ال relation اللي هي أصغرأصغر من .. أصغر
+
+664
+00:54:10,750 --> 00:54:14,650
+من .. بدنا نحدد مين ال elements أو مين ال elements
+
+665
+00:54:14,650 --> 00:54:17,250
+داخل ال universe of discourse اللي تحقق ال
+
+666
+00:54:17,250 --> 00:54:20,330
+relation يا هادي وهي عرفلي ال relation ال relation
+
+667
+00:54:20,330 --> 00:54:25,090
+اللي عرفليها اللي هي أصغر .. أصغر من .. okay أصغر
+
+668
+00:54:25,090 --> 00:54:30,210
+من طبعا بتقدر تقعدوا تحلوهم واحدة واحدة زي ما احنا
+
+669
+00:54:30,210 --> 00:54:34,830
+اشتغلنا هنا تعملوهمواحد واحد، واحد اتنين، واحد
+
+670
+00:54:34,830 --> 00:54:39,250
+تلاتة، واحد اربع، واحد خمسة، واحد ستة، اتنين واحد،
+
+671
+00:54:39,250 --> 00:54:42,350
+اتنين اتنين، اتنين تلاتة، بس طبعا عددهم هتطلع
+
+672
+00:54:42,350 --> 00:54:46,470
+ستاشر، ممكن يكون كبير، ففي لاحقا احنا هناخد كيف
+
+673
+00:54:46,470 --> 00:54:53,120
+نقدر نمثل ال relationsبدنا نسبق شوية خلينا نمثلها
+
+674
+00:54:53,120 --> 00:54:56,020
+من الآن كيف نستطيع أن نكتبها relation عشان لا
+
+675
+00:54:56,020 --> 00:54:58,940
+نستطيع أن نطول كثير فأبسط طريقة أن أنا أعمل على ال
+
+676
+00:54:58,940 --> 00:55:04,220
+matrix أحطها ك matrix ف relation و بنحط ال matrix
+
+677
+00:55:04,220 --> 00:55:17,780
+1 2 3 4 فهي from a to a to a برضه اللي هي 1 2 3 4
+
+678
+00:55:17,780 --> 00:55:23,800
+بصير إذا والله ال relation موجودةبنحط true غير
+
+679
+00:55:23,800 --> 00:55:29,260
+موجودة false فهي صارت one zero او zero one matrix
+
+680
+00:55:29,260 --> 00:55:36,620
+طيب نبدأ a أصغر من b فهي from هنا ل هنا فهل ال a
+
+681
+00:55:36,620 --> 00:55:40,340
+الواحد أصغر من الواحد لأ هذا مش موجود واحد أصغر من
+
+682
+00:55:40,340 --> 00:55:45,060
+اتنين yes واحد أصغر من تلاتة yes واحد أصغر من
+
+683
+00:55:45,060 --> 00:55:49,890
+أربعة yes فهدولة belong to relationهدول في الحالات
+
+684
+00:55:49,890 --> 00:55:53,550
+that belong to religion طيب اتنين مع واحد لأ اتنين
+
+685
+00:55:53,550 --> 00:56:00,830
+مع اتنين اتنين مع تلاتة تلاتة مع اربعة اربعة فلس
+
+686
+00:56:00,830 --> 00:56:05,650
+تمام فبنقدر هين اتمثلها بسهولة صار عندي واحد لما
+
+687
+00:56:05,650 --> 00:56:16,190
+بقول ال R بتساوي واحد اتنين واحد تلاتة واحد اربعة
+
+688
+00:56:17,200 --> 00:56:25,160
+اتنين تلاتة اتنين اربعة و تلاتة اربعة فصار الرؤية
+
+689
+00:56:25,160 --> 00:56:28,340
+أوضح هنا عندنا كيف نقدر نمثلهم بدل من أن نكتبهم
+
+690
+00:56:28,340 --> 00:56:31,080
+على الأسطور ورا بعض ورا بعض و يمكن نتلخبط و يمكن
+
+691
+00:56:31,080 --> 00:56:33,920
+واحدة تجعل معانا واحدة مانجيبهاش واحدة مانعرفهاش
+
+692
+00:56:33,920 --> 00:56:39,120
+أسهل صارت الأمور في تمثيل ال relation بتصير أسهل
+
+693
+00:56:39,120 --> 00:56:42,360
+في تمثيل ال relation طبعا هذا نوع أول لاحقا برضه
+
+694
+00:56:42,360 --> 00:56:47,140
+هنتكلم عن ال graphكيف ممكن أستخدم ال graph لتمثيل
+
+695
+00:56:47,140 --> 00:56:50,780
+ال relation وهذه ستكون المدخل بعد أن نخلص ال
+
+696
+00:56:50,780 --> 00:56:54,180
+relation ل ال graphs نفسها إيش يعني graph؟ كيف
+
+697
+00:56:54,180 --> 00:56:56,320
+نمثل ال graph؟ لأن ال graph في النهاية هي relation
+
+698
+00:56:56,320 --> 00:57:00,620
+هي فعلا relation لما بتحددوا نقطة هي relation بين
+
+699
+00:57:00,620 --> 00:57:04,060
+x و y بعدين لما تحددوا من نقطة لنقطة بتعملوا graph
+
+700
+00:57:04,060 --> 00:57:07,820
+بينهم أو line بينهم أو خط بينهم هي علاقة ثنائية
+
+701
+00:57:07,820 --> 00:57:12,700
+فعليا فهذه ستكون مدخلنا لاحقا لما نبدأ نشتغل عليها
+
+702
+00:57:15,120 --> 00:57:21,000
+A to A فواحد اتنين و لازم السهم عشان اعرف مين
+
+703
+00:57:21,000 --> 00:57:26,340
+الاولى و مين التانية فبعرف واحد اصغر من اتنين
+
+704
+00:57:26,340 --> 00:57:30,980
+ماحدش يجرأها بالعكس عكس السهم فعشانك السهم ضرورى
+
+705
+00:57:30,980 --> 00:57:35,140
+directed او direct graph direct graph ضرورى ترسم
+
+706
+00:57:35,140 --> 00:57:41,060
+as a direct graph واحد لتلاتة اتنين لتلاتة تلاتة
+
+707
+00:57:41,060 --> 00:57:46,560
+لاربعة و هكذا و هكذاOkay طب how many different
+
+708
+00:57:46,560 --> 00:57:51,320
+relations can we define on a set A with n
+
+709
+00:57:51,320 --> 00:57:55,880
+elements؟ لو عندنا set فيها n elements زي الحالة
+
+710
+00:57:55,880 --> 00:57:59,680
+اللي عندنا هنا فيها أربع elements فيها الحالة اللي
+
+711
+00:57:59,680 --> 00:58:04,700
+عندنا هنا أربع elements أكم relation ممكن يكون لل
+
+712
+00:58:04,700 --> 00:58:09,060
+set هذه؟ ستة عشرالستاش هدولة عدد ال Cartesian
+
+713
+00:58:09,060 --> 00:58:17,120
+product بمعنى هدولة العدد الأقصى أو العدد خلينا
+
+714
+00:58:17,120 --> 00:58:24,500
+نقول اللي ممكن إما أه أو لأ بمعنى كل زوج من هدول
+
+715
+00:58:24,500 --> 00:58:29,440
+يعتبر واحد من الستاش إله احتمالين إما belong لل
+
+716
+00:58:29,440 --> 00:58:35,900
+relation أو not belong لل relation معنى ذلك أنه
+
+717
+00:58:35,900 --> 00:58:41,510
+ممكنالعنصر الأول هنا ممكن يكون true او false او
+
+718
+00:58:41,510 --> 00:58:47,610
+one او zero طيب خلينا شوية شوية هدول مبدئيا قداش
+
+719
+00:58:47,610 --> 00:58:51,390
+عددهم 16
+
+720
+00:58:51,390 --> 00:58:55,270
+هدول قداش عددهم 16 طب لما نعمل generalization
+
+721
+00:58:55,270 --> 00:59:03,730
+للموضوع n ال elements عددهم n يعني a عبارة عن n
+
+722
+00:59:03,730 --> 00:59:04,310
+elements
+
+723
+00:59:08,910 --> 00:59:13,650
+انتربيع هدول عددهم انتربيع؟ هدول كلهم هيك عددهم
+
+724
+00:59:13,650 --> 00:59:19,670
+إيش؟ انتربيع، مظبوط؟ طيب جداش احتمالات combination
+
+725
+00:59:22,020 --> 00:59:27,780
+ممكن نعمل لعدد relations ممكنة من ال universe of
+
+726
+00:59:27,780 --> 00:59:31,660
+discourse هذه هذه صارت هيك بالنسبالنا universe of
+
+727
+00:59:31,660 --> 00:59:35,520
+discourse بتاعتنا عدد ال elements بتاعتها انتربيع
+
+728
+00:59:35,520 --> 00:59:38,220
+هذه صارت خلاص هدول عدد ال elements لل universe of
+
+729
+00:59:38,220 --> 00:59:42,420
+discourse طيب combination أكم relation ممكن أطلع
+
+730
+00:59:42,420 --> 00:59:45,740
+منهم أكم relation إيش معناها متذكرين أول ما بدأنا
+
+731
+00:59:45,740 --> 00:59:49,000
+في ال relations قلنا إن ال relation is a subset
+
+732
+00:59:51,000 --> 00:59:55,760
+معناته اكم سب ست بقدر اطلع من ال .. من ال sequence
+
+733
+00:59:55,760 --> 00:59:58,580
+هدا او من .. من عدد ال .. من ال set كلها علي بعضها
+
+734
+00:59:58,580 --> 01:00:04,780
+اكم سب ست بقدر اطلع منها هنا ال relation الاولى او
+
+735
+01:00:04,780 --> 01:00:08,760
+عفوا ال .. الزوج الاول اما انه يكون صفر او واحد طب
+
+736
+01:00:08,760 --> 01:00:13,720
+الزوج التانى برضه يا صفر يا واحد طب لحالهم هدول
+
+737
+01:00:13,720 --> 01:00:17,930
+اتنين مع بعضبيعطوني أربعة بيعطوني أربعة احتمالات
+
+738
+01:00:17,930 --> 01:00:21,150
+ممكنة أربعة combination إما أن الأتنين مش موجودين
+
+739
+01:00:21,150 --> 01:00:26,990
+في ال relation هذه حالة ف في أو أن الأولى موجودة
+
+740
+01:00:26,990 --> 01:00:30,050
+في ال relation والتانية لأ فهذه relation لحالها
+
+741
+01:00:30,050 --> 01:00:33,250
+أصبحت relation ممكن تكون تعريف لحالها أو التانية
+
+742
+01:00:33,250 --> 01:00:36,610
+موجودة والأولى لأ برضه relation هي تعريف مختلف أو
+
+743
+01:00:36,610 --> 01:00:40,350
+الأتنين موجودين في ال relation بناء على تعريف ال
+
+744
+01:00:40,350 --> 01:00:47,160
+relation طيب لما نصيروا تلاتةصار تمانية، صار
+
+745
+01:00:47,160 --> 01:00:50,040
+تمانية، معناته هنا في عندي احتمالين، عندي اتنين،
+
+746
+01:00:50,040 --> 01:00:55,780
+اتنين، اتنين، two ways بقدر امثل فيهم ال element
+
+747
+01:00:55,780 --> 01:00:59,300
+الأول لل relation ال element التاني برضه فيله two
+
+748
+01:00:59,300 --> 01:01:09,780
+ways أن مرة، فصرت ايش؟ اتنين to the power أن تربيع
+
+749
+01:01:11,170 --> 01:01:14,650
+على اعتبار ان عددهم اصلا انتر بيئة عددهم أساسا
+
+750
+01:01:14,650 --> 01:01:21,770
+انتر بيئة فكل element منهم من ايش؟ من ال Cartesian
+
+751
+01:01:21,770 --> 01:01:27,930
+elements ال A Cartesian product of Aكل element
+
+752
+01:01:27,930 --> 01:01:32,950
+داخل ال set هذه ممكن يكون يا belong to relation او
+
+753
+01:01:32,950 --> 01:01:35,690
+not belong to relation فمعنى ذلك انه ماوجددش عدد
+
+754
+01:01:35,690 --> 01:01:38,870
+ال ways اللي بقدر امثل فيها اتنين طيب اللي جنبه
+
+755
+01:01:38,870 --> 01:01:43,260
+نفس الموضوع بس الاتنين هدول لازم يكون مع بعضضمن ال
+
+756
+01:01:43,260 --> 01:01:46,740
+relation أو واحد منهم بس في نهاية بمثلهم مع بعض لل
+
+757
+01:01:46,740 --> 01:01:51,580
+relation فمعنى ذلك هتكون ضرب اتنين في اتنين في
+
+758
+01:01:51,580 --> 01:01:54,460
+اتنين في اتنين في اتنين في اتنين في اتنين ستاشر
+
+759
+01:01:54,460 --> 01:01:58,300
+مرة طبعا ستاشر مرة لإن انا مخصص الموضوع لاربعة في
+
+760
+01:01:58,300 --> 01:02:02,500
+اربعة لاربعة تربيع لما بتكون n في n معناته to n
+
+761
+01:02:02,500 --> 01:02:06,920
+مرة to n مرة فصار عندى كلها to n مرة اتنين to the
+
+762
+01:02:06,920 --> 01:02:12,900
+power n تربيع اتنين to the powerإن تربيع واضحة ليش
+
+763
+01:02:12,900 --> 01:02:17,920
+عملناها اتنين to the power of n تربيع okay شوية
+
+764
+01:02:17,920 --> 01:02:20,440
+properties هالوقت ناخدها على ال relations هذه إيش
+
+765
+01:02:20,440 --> 01:02:24,200
+ممكن تكون ال relations كيف نمثلها أو كيف نعبّر
+
+766
+01:02:24,200 --> 01:02:28,500
+عنها أول حاجة ال reflexive أو reflexivity
+
+767
+01:02:28,500 --> 01:02:31,520
+reflexivity
+
+768
+01:02:31,520 --> 01:02:36,200
+بمعنى الإنعكسية الإنقلابية الإنعكسية أو الإنقلابية
+
+769
+01:02:36,200 --> 01:02:40,250
+بمعنى لو انعكست ال relationأو لو عكسنا ال two
+
+770
+01:02:40,250 --> 01:02:44,690
+elements ال relation هتظل ثابتة هتظل ثابتة بينهم
+
+771
+01:02:44,690 --> 01:02:47,850
+طبعا الكلام ده لن يحصل إم إلا إذا كانوا ال two
+
+772
+01:02:47,850 --> 01:02:50,890
+elements بيسوا بعض إذا كانوا ال two elements فعليا
+
+773
+01:02:50,890 --> 01:02:54,650
+بيسوا بعض في الحالة هذه بنقول أن ال relation R
+
+774
+01:02:54,650 --> 01:03:01,750
+relation R on a set A is reflexive إمتى if for all
+
+775
+01:03:01,750 --> 01:03:08,370
+A belong to set AA relation A هي مع نفسها العنصر
+
+776
+01:03:08,370 --> 01:03:12,350
+مع نفسه موجودين بمعنى لو انعكسوا هتظل ال relation
+
+777
+01:03:12,350 --> 01:03:17,450
+ثابتة هتظل ال relation بينهم ثابتة زي لما بتتكلموا
+
+778
+01:03:17,450 --> 01:03:21,870
+مثلا عن .. هناخد احنا logic مثال و هناخد مثال عنها
+
+779
+01:03:21,870 --> 01:03:25,510
+بدونش نقول أمثلة .. ال slides الجاية كلها أمثلة عن
+
+780
+01:03:25,510 --> 01:03:28,610
+الموضوع خلنا بس نشوف ال .. ال irreflexive ال
+
+781
+01:03:28,610 --> 01:03:34,830
+irreflexive المفروض أن هي ليستreflexive بس مش
+
+782
+01:03:34,830 --> 01:03:37,810
+بالسهولة هذه ليش؟ لأن أحيانا ممكن تكون في relation
+
+783
+01:03:37,810 --> 01:03:44,430
+لا هي reflexive ولا هي irreflexive كيف؟ بمعنى لو
+
+784
+01:03:44,430 --> 01:03:53,990
+عندكوا relation فيها واحد واحد وهي
+
+785
+01:03:53,990 --> 01:03:58,750
+أساسا كانت ال a عبارة عن واحد واثنين مثلا واحد
+
+786
+01:03:58,750 --> 01:04:04,610
+واحدفي الحالة هذه بقدرش أقول إن هي reflexive ليش؟
+
+787
+01:04:04,610 --> 01:04:09,710
+لأن واحد وواحد okay a relation a هي واضحة ايه ايه
+
+788
+01:04:09,710 --> 01:04:14,370
+بس مش كل مش
+
+789
+01:04:14,370 --> 01:04:17,330
+كل ال elements موجودة فعليا الإتنين و إتنين مش
+
+790
+01:04:17,330 --> 01:04:24,190
+موجودة معناته بقدرش أقول إن هي reflexiveالشرط for
+
+791
+01:04:24,190 --> 01:04:30,250
+all a belong to capital A، يعني كل عنصر ينتمي لset
+
+792
+01:04:30,250 --> 01:04:34,890
+A يجب أن يكون مع نفسهعشان أقول إن والله فعلا ال
+
+793
+01:04:34,890 --> 01:04:37,250
+relation كلها على بعض reflexive ممكن يكون في other
+
+794
+01:04:37,250 --> 01:04:40,390
+terms هم أحرار يعني ممكن يكون في واحد و اتنين
+
+795
+01:04:40,390 --> 01:04:45,270
+مالناش مشكلة خليهم بس أنا اللي بهمني الواحد و واحد
+
+796
+01:04:45,270 --> 01:04:48,330
+و الاتنين و اتنين و لو في تلاتة و تلاتة .. و
+
+797
+01:04:48,330 --> 01:04:50,990
+التلاتة و تلاتة تكون كمان موجودة لو في أربعة ..
+
+798
+01:04:50,990 --> 01:04:55,890
+الأربعة و أربعة تكون موجودة طيب واحد و واحد موجودة
+
+799
+01:04:55,890 --> 01:05:00,390
+اتنين و اتنين مش موجودة معناته هي دي not reflexive
+
+800
+01:05:01,570 --> 01:05:04,510
+طيب كويس not reflexive طب هل ممكن نكون
+
+801
+01:05:04,510 --> 01:05:09,510
+irreflexive؟ ال irreflexive ببساطة جدا إذا كانت ال
+
+802
+01:05:09,510 --> 01:05:12,030
+relation بنقول عليها irreflexive إذا كان ال
+
+803
+01:05:12,030 --> 01:05:17,810
+complementary أو ال compliment تبعها reflexive إذا
+
+804
+01:05:17,810 --> 01:05:20,650
+كان ال compliment تبعها reflexive طيب بنشوف ال
+
+805
+01:05:20,650 --> 01:05:25,310
+compliment لها دي معناته أي otherwise كل العناصر
+
+806
+01:05:25,310 --> 01:05:28,610
+أو كل العناصر الممكن لل Cartesian باستثناء الواحد
+
+807
+01:05:28,610 --> 01:05:32,410
+وواحديعني أنا متوقع هيطلع معانا اتنين و اتنين و
+
+808
+01:05:32,410 --> 01:05:36,330
+هيطلع معانا تلاتة و تلاتة بس هدول غير كافين ان هي
+
+809
+01:05:36,330 --> 01:05:39,910
+تكون reflexive لأن واحد واحد مش موجودة معناته ال
+
+810
+01:05:39,910 --> 01:05:44,750
+relation هنا برضه not reflexive فهي لا هي
+
+811
+01:05:44,750 --> 01:05:49,050
+reflexive ولا هي reflexive ولا هي reflexive خدوا
+
+812
+01:05:49,050 --> 01:05:53,070
+بالكم ال reflexive مش معناها ان هي not reflexive
+
+813
+01:05:53,070 --> 01:05:58,430
+reflexive لازم يكون جميع ال elements داخل ال set
+
+814
+01:05:59,750 --> 01:06:03,710
+موجودين مع نفسهم يعني واحد و واحد اتنين و اتنين
+
+815
+01:06:03,710 --> 01:06:05,910
+تلاتة و تلاتة اذا كانوا هم موجودين لحالهم هيك بقول
+
+816
+01:06:05,910 --> 01:06:09,810
+ان هي reflexive ان هي reflexive ان هي reflexive
+
+817
+01:06:09,810 --> 01:06:15,650
+طيب لو عندنا هنا واحد و اتنين بس ال relation هذي
+
+818
+01:06:15,650 --> 01:06:19,730
+ال reflexive بتصير هتصير irreflexive هتصير
+
+819
+01:06:19,730 --> 01:06:23,810
+irreflexive ليش لأن ال complement تبعها هيكون
+
+820
+01:06:23,810 --> 01:06:26,610
+reflexive هيكون موجود في الواحد و واحد هيكون موجود
+
+821
+01:06:26,610 --> 01:06:31,160
+في الواحد و اتنين و اتنين تلاتة و تلاتةفبتصير
+
+822
+01:06:31,160 --> 01:06:35,580
+reflexive طيب الحالة اللي بتكون فيها نصهم موجود و
+
+823
+01:06:35,580 --> 01:06:38,940
+نصهم مش موجود أو على الأقل واحد موجود و الباقي لأ
+
+824
+01:06:38,940 --> 01:06:43,260
+هذه لها هتطلع لا reflexive ولا irreflexive مثال و
+
+825
+01:06:43,260 --> 01:06:45,440
+زي ما قلنا احنا في النهاية الأمثلة بتاعتنا مش
+
+826
+01:06:45,440 --> 01:06:49,820
+مضرورة فقط على أرقام ممكن هي على objects على أشياء
+
+827
+01:06:49,820 --> 01:06:54,220
+اللي هي ال function أو ال relation likes between
+
+828
+01:06:54,220 --> 01:07:00,290
+peoplebetween people ال likes relation هذه لا هي
+
+829
+01:07:00,290 --> 01:07:04,350
+reflexive ولا هي reflexive، ليش؟ لأنه عشان أقول إن
+
+830
+01:07:04,350 --> 01:07:07,790
+هي reflexive معناته كل واحد المفروض أنه likes
+
+831
+01:07:07,790 --> 01:07:14,060
+himself، صحيح؟لازم .. يعني هو بحب حاله أو يعني
+
+832
+01:07:14,060 --> 01:07:16,420
+خليني أقول بفضل حاله، يعني هو معتز بنفسه خليني
+
+833
+01:07:16,420 --> 01:07:21,300
+أقول أو مغرور شوية، فهو حابب .. شايف أن هو أفضل
+
+834
+01:07:21,300 --> 01:07:25,640
+واحد، فممكن هنا مش كل الناس هيك، صحيح؟ فبقدرش أعمل
+
+835
+01:07:25,640 --> 01:07:30,080
+أن كل الناس هيك، و في نفس الوقت هي not reflexive،
+
+836
+01:07:30,080 --> 01:07:35,300
+ليش؟ لأن فعلا في ناس هيكيعني معناته نص ال
+
+837
+01:07:35,300 --> 01:07:39,880
+universive discourse متحققة و نصهم لأ لابقدر أقول
+
+838
+01:07:39,880 --> 01:07:42,820
+عليها reflexive ولا بقدر أقول عليها irreflexive
+
+839
+01:07:42,820 --> 01:07:49,960
+فهذه not reflexive و not irreflexive فلا هيك ولا
+
+840
+01:07:49,960 --> 01:07:53,200
+هيك ليش لأن زي ما قلنا likes هذه يمكن .. قلتلكوا
+
+841
+01:07:53,200 --> 01:07:57,980
+يمكن في أول الفصل ال relation likes هذه من أعقد ال
+
+842
+01:07:57,980 --> 01:08:01,850
+relations اللي مالهاش قواعدلأنه ممكن واحد likes
+
+843
+01:08:01,850 --> 01:08:07,510
+التاني، التاني بيبدلوش ال relation بيبدلوش ال
+
+844
+01:08:07,510 --> 01:08:11,850
+relation يعني كويسة فهي واحدة من الأمثلة اللي هي
+
+845
+01:08:11,850 --> 01:08:14,790
+لم نقدر نقول عليها reflexive ولم نقدر نقول عليها
+
+846
+01:08:14,790 --> 01:08:18,770
+irreflexive طيب نرجع شوية للأرقام اللي احنا مهتمين
+
+847
+01:08:18,770 --> 01:08:24,010
+فيها في شغلنا ونشوف في عندنا تلاتة relationsبدنا
+
+848
+01:08:24,010 --> 01:08:27,430
+نحدد .. احددوا معايا كل واحدة من ال relations
+
+849
+01:08:27,430 --> 01:08:34,270
+هدولة هل هي reflexive او reflexive او not لا هي
+
+850
+01:08:34,270 --> 01:08:38,310
+هيك ولا هي هيك لو قلنا .. طبعا بدنا نعرف أساسا ال
+
+851
+01:08:38,310 --> 01:08:40,790
+.. ال .. الست ال .. ال .. ايه تعتنا من الأول واحد
+
+852
+01:08:40,790 --> 01:08:44,810
+اتنين تلاتة أربعة يعني معنى ذلك انه الفيصل في
+
+853
+01:08:44,810 --> 01:08:47,410
+موضوع ان انا احكم reflexive ولا لأ الواحد واحد
+
+854
+01:08:47,410 --> 01:08:50,870
+اتنين اتنين تلاتة تلاتة اربعة واربعة طيب نمسك
+
+855
+01:08:50,870 --> 01:08:57,480
+الأولةليش not reflexive؟ الاتنين و التانين موجودة
+
+856
+01:08:57,480 --> 01:09:02,100
+طب هل ممكن تكون reflexive؟ برضه لأ فإذا الأولى no
+
+857
+01:09:02,100 --> 01:09:07,160
+طيب التانية reflexive reflexive على اعتبار أن في
+
+858
+01:09:07,160 --> 01:09:09,040
+عندنا الواحد و واحد موجودة اتنين و اتنين موجودة
+
+859
+01:09:09,040 --> 01:09:12,960
+تلاتة و تلاتة موجودة أربعة و أربعة موجودة okay طيب
+
+860
+01:09:12,960 --> 01:09:18,240
+الأخيرة not reflexive ليش؟ في عندنا الأربعة و
+
+861
+01:09:18,240 --> 01:09:24,640
+أربعة غير موجودة غير موجودة طيبلو أخدنا relation
+
+862
+01:09:24,640 --> 01:09:28,780
+لو
+
+863
+01:09:28,780 --> 01:09:34,180
+قولنا في relation عندنا عبارة عن واحد واتنين واحد
+
+864
+01:09:34,180 --> 01:09:46,160
+وتلاتة اتنين واربعة اتنين وتلاتة واحد واربعة اربعة
+
+865
+01:09:46,160 --> 01:09:52,940
+وتلاتةأربعة و .. أكمل ولا خلاص .. خلاص ما هي كاملة
+
+866
+01:09:52,940 --> 01:09:59,000
+ال compliment بتاعتها اللي عكسوها لو عكستوا .. لو
+
+867
+01:09:59,000 --> 01:10:04,500
+قولنا ان هدولة بدنا نستثنيهم من ال .. ال a كارتيزن
+
+868
+01:10:04,500 --> 01:10:11,040
+product a نفسها هتظهر ال compliment هي اللي
+
+869
+01:10:11,040 --> 01:10:14,480
+reflexive فهذه بنسميها هنا irreflexive هتكون
+
+870
+01:10:14,480 --> 01:10:15,140
+irreflexive
+
+871
+01:10:18,560 --> 01:10:26,440
+Okay ال inverse .. ال .. ال inverse و
+
+872
+01:10:26,440 --> 01:10:30,310
+بدنا ناخد بالنا ال inverse مش هي ال complementال
+
+873
+01:10:30,310 --> 01:10:34,130
+inverse حاجة و ال complement حاجة تانية تماماً
+
+874
+01:10:34,130 --> 01:10:41,290
+حاجة تانية تماماً كويس فإني binary relation R from
+
+875
+01:10:41,290 --> 01:10:46,830
+A to B has an inverse okay تمام هنسميها R to the
+
+876
+01:10:46,830 --> 01:10:50,290
+power minus one أو ال inverse of R relation هنقول
+
+877
+01:10:50,290 --> 01:10:55,250
+إن ال inverse of R صارت من مين؟ مش من A to B من B
+
+878
+01:10:55,250 --> 01:11:01,450
+to A من B to A فإذا والله فعلامن B to A بنعرفها
+
+879
+01:11:01,450 --> 01:11:08,850
+كتالة ال inverse of relation هتساوي كل زوج B و A
+
+880
+01:11:08,850 --> 01:11:15,170
+بشرط ان A و B can't belong لل relation can't
+
+881
+01:11:15,170 --> 01:11:20,930
+belong لل relation بمعنى ان ال relation ال
+
+882
+01:11:20,930 --> 01:11:24,250
+relation هذه فرضا ال inverse تبعها
+
+883
+01:11:27,060 --> 01:11:32,140
+هيكون واحد و واحد اتنين و واحد تلاتة و اتنين تلاتة
+
+884
+01:11:32,140 --> 01:11:38,600
+و تلاتة اربع و اربع عكسهم بس فقط هذه هتكون ايش ال
+
+885
+01:11:38,600 --> 01:11:49,100
+inverse ل ال relation تمام
+
+886
+01:11:49,100 --> 01:11:52,700
+فلو قلنا مثلا الأصغر من لان احنا مسكنها هنا في كذا
+
+887
+01:11:52,700 --> 01:11:55,760
+example ناخد برضه اصغر من ال relation اصغر منه
+
+888
+01:11:56,820 --> 01:11:59,560
+وأخدنا ال complement لل relation أصغر من لو
+
+889
+01:11:59,560 --> 01:12:03,040
+متذكرينه وكانت أكبر من أو ساوي، كويس، طيب ال
+
+890
+01:12:03,040 --> 01:12:10,960
+inverse للأصغر من هي عبارة عن B و A بشرط أن A أصغر
+
+891
+01:12:10,960 --> 01:12:17,200
+من B فلحظة صارت كأن A و B belong لل relation
+
+892
+01:12:20,600 --> 01:12:23,300
+اللي هي أصغر من .. احنا نتكلم أصلا عن الأصغر من
+
+893
+01:12:23,300 --> 01:12:28,440
+فهي a أصغر من b فهي belong لل relation فالأصل أن b
+
+894
+01:12:28,440 --> 01:12:32,220
+to a تكون belong لمن؟ لل inverse بتاعة ال relation
+
+895
+01:12:32,220 --> 01:12:37,240
+ال inverse بتاعة ال relation فهتكون b و a و نعكس
+
+896
+01:12:37,240 --> 01:12:42,290
+هدولب أكبر منه فصارت تساوي أكبر منه وليست أكبر من
+
+897
+01:12:42,290 --> 01:12:46,910
+أو يساوي هناك ال complement كانت أو يساوي لأنه لو
+
+898
+01:12:46,910 --> 01:12:52,750
+حطينا هنا يساوي من الأساس a و b مش أصغر من بعض فهي
+
+899
+01:12:52,750 --> 01:12:55,250
+أصلا مش موجودة في ال relation عشان أجيب ال inverse
+
+900
+01:12:55,250 --> 01:12:59,290
+بتبحر الشكل هذا فواضح هنا مش موجود يساوي رغم أنه
+
+901
+01:12:59,290 --> 01:13:02,610
+كان في ال complement موجود ال complement مكمل هذا
+
+902
+01:13:02,610 --> 01:13:09,610
+عكس هذا عكس مكمل غير العكس طيبمجرد بس إعادة ترتيب
+
+903
+01:13:09,610 --> 01:13:14,610
+يعني إعادة ترتيبهم اللي بيبتيجي قبل ال a فقط طيب
+
+904
+01:13:14,610 --> 01:13:18,410
+وبنان عليها بنجيب ال inverse ل ال relation اللي
+
+905
+01:13:18,410 --> 01:13:22,850
+هتكون بينهم for example لو أخدنا relation from
+
+906
+01:13:22,850 --> 01:13:24,290
+people to foods
+
+907
+01:13:27,140 --> 01:13:31,780
+ناس بتاكل الناس و الأكل فممكن الناس هدول نحط والله
+
+908
+01:13:31,780 --> 01:13:36,780
+تلت أربع أشخاص نقول والله محمد علي عمر مش عارف مين
+
+909
+01:13:36,780 --> 01:13:42,760
+ما يكون يكون مجموعة هنا نفترض أنه الشخص A الشخص B
+
+910
+01:13:42,760 --> 01:13:47,780
+الشخص C وهدول بدهم ياكلوا بدهم ياكلوا واحد بدهم
+
+911
+01:13:47,780 --> 01:13:54,460
+ياكله مش عارف ال .. ال .. الأكلة الأولى
+
+912
+01:13:59,090 --> 01:14:05,250
+Apple خلّينا نشوف Banana بيكفي
+
+913
+01:14:05,250 --> 01:14:11,030
+هاي اللي بدناش نشوفه أكتر من هيك طيب فلحظة في
+
+914
+01:14:11,030 --> 01:14:17,810
+الحالة هذه بقدر أقول له a eats apple a eats banana
+
+915
+01:14:17,810 --> 01:14:22,090
+بي eats banana إذا كان ال relation موجودة بيصير
+
+916
+01:14:22,090 --> 01:14:27,690
+والله هنا بس بنعمل x معناته a بيأكل تفاح بيأكل
+
+917
+01:14:27,690 --> 01:14:37,330
+تفاح وموزC بياكل مثلا موز، كويس؟ هذه إيش؟ هذه ال R
+
+918
+01:14:37,330 --> 01:14:41,330
+صارت اللي هو بياكل هذه ال relation، بياكل ال
+
+919
+01:14:41,330 --> 01:14:49,270
+religion طب لو عكسناهم صارت apple is eaten، مأكل،
+
+920
+01:14:49,270 --> 01:14:54,220
+فصارت الأكل عكسها مأكلفهي ال inverse تبعها هتبصي
+
+921
+01:14:54,220 --> 01:14:57,860
+ريكي إيش قلت ال inverse تبعها اللي هو ال inverse
+
+922
+01:14:57,860 --> 01:15:03,000
+فصارت كل اللي هنعمله relation بالعكس بي R to the
+
+923
+01:15:03,000 --> 01:15:08,100
+power أو inverse R بي inverse RA بس بحكي أنه بي is
+
+924
+01:15:08,100 --> 01:15:16,140
+eaten by A فصارت banana is eaten by بيو هذه موجودة
+
+925
+01:15:16,140 --> 01:15:19,640
+أصلا يعني مش كل الناس بيحبوا كل الطبخات يعني صحيح؟
+
+926
+01:15:19,640 --> 01:15:22,620
+فممكن يكون بيفضل طبخات و بيعمل طبخات فممكن جدا
+
+927
+01:15:22,620 --> 01:15:26,520
+تعمله table بهذا الشكل تحطوا كل الطبخات الممكنة
+
+928
+01:15:26,520 --> 01:15:31,000
+خلال الأسبوع و تحطوا على فرض العائلة عندكم و
+
+929
+01:15:31,000 --> 01:15:33,380
+تحددوا فلان أه بيحب الأكل الفلانية و بيحبش الأكل
+
+930
+01:15:33,380 --> 01:15:38,080
+الفلانية صحيح؟ فبتعملوها برضه فهن ال relation
+
+931
+01:15:38,080 --> 01:15:43,750
+ممكنة معقولة ممكنة مش بالضرورة أنه a eats any bمش
+
+932
+01:15:43,750 --> 01:15:47,790
+بالضرورة ان ال a بياكل اي شغلة في ال b فهذا كل
+
+933
+01:15:47,790 --> 01:15:51,350
+اللي بنعمل بس ان احنا بنحولها ل passive voice ل
+
+934
+01:15:51,350 --> 01:15:55,390
+passive voice المفعول بيه بيجي في الأول مفعول بيه
+
+935
+01:15:55,390 --> 01:16:00,630
+بدخل في الأول فهياخد التصريف التالت لل verb التالت
+
+936
+01:16:00,630 --> 01:16:03,570
+لل verb فواضح ان التصريف التالت لل verb هذا اللي
+
+937
+01:16:03,570 --> 01:16:07,330
+هو ال inverse تبع ال verb نفسه هكون ال inverse تع
+
+938
+01:16:07,330 --> 01:16:12,480
+ال verb هو نفسه ال inverseفي ايش بنستغلها يعني
+
+939
+01:16:12,480 --> 01:16:15,400
+احنا okay تعرفنا ان في حاجة اسمها inverse في ايش
+
+940
+01:16:15,400 --> 01:16:19,820
+ممكن نستعملها او في ايش ممكن تفيدنا هتفيدنا ان
+
+941
+01:16:19,820 --> 01:16:25,960
+اعرف هل ال relation symmetry او antisymmetric هل
+
+942
+01:16:25,960 --> 01:16:30,500
+بقدر اقول ان ال relation عندنا symmetry او
+
+943
+01:16:30,500 --> 01:16:36,500
+symmetric او antisymmetric لحظة antisymmetric برضه
+
+944
+01:16:36,500 --> 01:16:39,320
+مش معناها ان هي asymmetric
+
+945
+01:16:42,330 --> 01:16:47,430
+Symmetric عكسها Asymmetric صحيح؟ طيب Anti
+
+946
+01:16:47,430 --> 01:16:50,570
+-symmetric إيش تاني؟ هذه حاجة مختلفة تمام، مالهاش
+
+947
+01:16:50,570 --> 01:16:54,070
+علاقة بالـ Asymmetric اللي أنتوا عارفينها، اللي هي
+
+948
+01:16:54,070 --> 01:16:57,830
+العكس تبعها خلّيني أخدهم واحدة واحدة ال relation R
+
+949
+01:16:57,830 --> 01:17:01,650
+on a set A is symmetric إيه أنت بتكون symmetric؟
+
+950
+01:17:01,650 --> 01:17:06,710
+فعلا بقدر بسميها symmetric if and only if R equal
+
+951
+01:17:06,710 --> 01:17:10,990
+to inverse Rإذا والله ال R بتسوي ال inverse R
+
+952
+01:17:10,990 --> 01:17:14,450
+بسميها symmetric خلاص إذا ال R بتسوي ال inverse R
+
+953
+01:17:14,450 --> 01:17:20,110
+بنقول والله خلاص symmetric بمعنى لو عندكوا ال ..
+
+954
+01:17:20,110 --> 01:17:25,250
+كل ال relations اللي موجودة عندكوا هنا هذه احنا
+
+955
+01:17:25,250 --> 01:17:31,590
+سميناها إيه؟ 1 1 2 2 3 3 لو جيبنا ال inverse تبعها
+
+956
+01:17:33,970 --> 01:17:38,250
+بسوء بعض، بسوء بعض، صحيح؟ معناته أصلا ال R دي
+
+957
+01:17:38,250 --> 01:17:41,910
+symmetric لو جبت ال inverse تبعها، هيظل نفسها،
+
+958
+01:17:41,910 --> 01:17:51,450
+هيظل نفسها، طيب ممكن جدا يكون معاها تلاتة و اتنين،
+
+959
+01:17:51,450 --> 01:17:55,750
+لحظوا، و نسكر القص هنا، طيب في الحالة دي بيصير ال
+
+960
+01:17:55,750 --> 01:18:01,970
+inverse Rواحد واحد اتنين اتنين تلاتة تلاتة اتنين
+
+961
+01:18:01,970 --> 01:18:07,810
+تلاتة هاذي بطلت symmetric بقدر اقولكوا احنا خلنا
+
+962
+01:18:07,810 --> 01:18:10,670
+واحدة واحدة بديش اللي خبطهم الدنيا في بعض علاجات
+
+963
+01:18:10,670 --> 01:18:13,590
+symmetric هل هي symmetric لأ مش symmetric بس ال
+
+964
+01:18:13,590 --> 01:18:16,290
+asymmetric و ال antisymmetric خلينا شوية شوية
+
+965
+01:18:16,290 --> 01:18:18,770
+بدناش اللي خبطهم في بعض لأن التلاتة ممكن اللي
+
+966
+01:18:18,770 --> 01:18:25,070
+خبطهم فخلينا حاجة حاجة طيب لو اتنين و تلاتة
+
+967
+01:18:30,060 --> 01:18:34,440
+صارت symmetric صارت هيك symmetric بمعنى أنا مابديش
+
+968
+01:18:34,440 --> 01:18:37,780
+احط في بالك ان ال symmetric هي بس المتشابهات لأ
+
+969
+01:18:37,780 --> 01:18:49,620
+ممكن هي term زي هذا يكون فيه symmetric okay فإذا
+
+970
+01:18:49,620 --> 01:18:56,700
+مثال على ال symmetric إذا كانت aB belong to
+
+971
+01:18:56,700 --> 01:19:03,340
+relation R if and only if B و A برضه belong ل
+
+972
+01:19:03,340 --> 01:19:08,040
+relation R فإذا كان كل عنصر عكسه موجود فهي
+
+973
+01:19:08,040 --> 01:19:11,480
+symmetric فهي symmetric طيب example ال equality
+
+974
+01:19:11,480 --> 01:19:19,310
+السيمتريك الأقل من لأبالظبط لأن لما أقول واحد أقل
+
+975
+01:19:19,310 --> 01:19:23,210
+من اتنين بقدرش أقول اتنين أقل من واحد لما عكسهم
+
+976
+01:19:23,210 --> 01:19:26,570
+تصبتش لكن لما أقول واحد بيساوي واحد اه واحد أولى
+
+977
+01:19:26,570 --> 01:19:31,430
+بيساوي واحد بمش الحل وانتوا بتحلوا alpha واحد
+
+978
+01:19:31,430 --> 01:19:36,070
+تساوي واحد او اجت معاكم واحد تساوي alpha واحد بمش
+
+979
+01:19:36,070 --> 01:19:40,710
+الحلبمش الحال لكن لو قلنا أثناء الشغل و انتوا
+
+980
+01:19:40,710 --> 01:19:43,650
+بتعملوا مجموعة relations قلتوا alpha واحد أكبر ..
+
+981
+01:19:43,650 --> 01:19:46,690
+أصغر من واحد و بعدين تيجي تقولوا لو الله واحد أصغر
+
+982
+01:19:46,690 --> 01:19:50,330
+من alpha واحد مانفعش تظبطش هذه .. طبعا هدولة غلط
+
+983
+01:19:50,330 --> 01:19:54,290
+لكن تساوي أه بمش الحال يعني و انتوا بتحلوا الطرف
+
+984
+01:19:54,290 --> 01:19:55,890
+الشمال حطته يمين وليه يمين وليه يمين وليه يمين
+
+985
+01:19:55,890 --> 01:19:56,070
+وليه يمين وليه يمين وليه يمين وليه يمين وليه يمين
+
+986
+01:19:56,070 --> 01:19:56,810
+وليه يمين وليه يمين وليه يمين وليه يمين وليه يمين
+
+987
+01:19:56,810 --> 01:20:05,790
+وليه يمين وليه يمين وليه يمين و
+
+988
+01:20:06,170 --> 01:20:11,390
+A is married to B نفس هي B is married to A نفس
+
+989
+01:20:11,390 --> 01:20:17,070
+الشغل نفس الشي طيب likes لأ مش بالضروري A likes B
+
+990
+01:20:17,070 --> 01:20:20,850
+معناته بيه likes A واحد بيحب مثلا يدرس مع التاني
+
+991
+01:20:20,850 --> 01:20:29,130
+التاني بيحبش يدرس معاه بيحبش يقول this likes A طيب
+
+992
+01:20:29,130 --> 01:20:36,210
+a binary relation R is antisymmetric ifA و B
+
+993
+01:20:36,210 --> 01:20:41,110
+belong to R employes
+
+994
+01:20:41,110 --> 01:20:45,950
+او implication بدنا ناخد بالنا منها B و A not
+
+995
+01:20:45,950 --> 01:20:52,210
+belong to R not belong to R فإذا الأقل من is
+
+996
+01:20:52,210 --> 01:20:58,370
+antisymmetric أقل من is antisymmetric بس likes is
+
+997
+01:20:58,370 --> 01:21:02,070
+not قولتلكوا ال likes هذه ولا relation مظبطة معها
+
+998
+01:21:02,070 --> 01:21:07,210
+ال likes ولا إشي بظبط معهاليش؟ لأنه ما .. ما ..
+
+999
+01:21:07,210 --> 01:21:10,650
+مابنعرفش يعني مالهاش أي قواعد مالهاش أي relations
+
+1000
+01:21:10,650 --> 01:21:13,950
+الحقيقة فدائما هتلاقوا لما بدنا نقول is not
+
+1001
+01:21:13,950 --> 01:21:18,050
+هتكونوا likes هتلاقوا likes طيب أصغر من asymmetric
+
+1002
+01:21:18,050 --> 01:21:24,050
+برضه هتبين أكتر يمكن مع ال .. التلات تعريفات هدول
+
+1003
+01:21:24,050 --> 01:21:26,430
+ناخدهم و المرة الجاية ناخد عليهم applications
+
+1004
+01:21:26,430 --> 01:21:30,030
+بتكون انت حتى يمكن قرأتهم كويس ناخدهم ناخد عليهم
+
+1005
+01:21:30,030 --> 01:21:30,370
+applications
+
+1006
+01:21:34,680 --> 01:21:39,060
+خلاص المرة اللي جاية احنا .. احنا اليوم مشينا منيح
+
+1007
+01:21:39,060 --> 01:21:41,440
+يعني كويس يلا اعطيكوا العافية المرة اللي جاية بن
+
+1008
+01:21:41,440 --> 01:21:44,340
+.. بنبدأ من هنا و بنكمل examples عليها ان شاء الله
+
+1009
+01:21:44,340 --> 01:21:45,120
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iJnQv9sY0uk_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iJnQv9sY0uk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..88a4076f37f2d8da01e70d15590c8b80a38411ff
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iJnQv9sY0uk_raw.json
@@ -0,0 +1 @@
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كتير يمكن في التلفزيون او في برامج او حاجة بتلاقوا اللي هي احجار ال domino بيرتبوهم ممكن يعملوها على جد الأوضة هذه يرتبوها نفترض مليون جطعة", "tokens": [3224, 29399, 4117, 19528, 18871, 2423, 33371, 4032, 2423, 20560, 313, 2423, 33371, 13672, 1829, 39896, 21542, 12984, 6225, 42213, 10632, 21542, 12984, 29538, 39894, 8592, 38688, 2407, 11296, 9122, 2655, 13546, 7251, 43020, 8978, 16712, 46538, 11622, 1829, 11536, 1975, 2407, 8978, 4724, 2288, 10943, 7435, 1975, 2407, 11331, 26108, 3660, 39894, 15040, 4587, 14407, 13672, 1829, 39896, 1975, 5016, 7435, 9640, 2423, 3285, 2982, 4724, 13546, 2655, 3555, 2407, 16095, 3714, 43020, 7251, 25957, 1211, 2407, 11296, 15844, 10874, 3215, 16247, 2407, 11242, 3660, 29538, 7251, 43500, 3555, 2407, 11296, 8717, 5172, 2655, 43042, 3714, 20292, 11536, 10874, 9566, 27884], "avg_logprob": -0.12226941848842843, "compression_ratio": 1.7592592592592593, "no_speech_prob": 0.0, "words": [{"start": 1084.59, "end": 1085.11, "word": "هنتكلم", "probability": 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الأوضة", "probability": 0.8387451171875}, {"start": 1106.93, "end": 1107.27, "word": " هذه", "probability": 0.8779296875}, {"start": 1107.27, "end": 1108.55, "word": " يرتبوها", "probability": 0.95283203125}, {"start": 1108.55, "end": 1109.61, "word": " نفترض", "probability": 0.96923828125}, {"start": 1109.61, "end": 1109.95, "word": " مليون", "probability": 0.9915364583333334}, {"start": 1109.95, "end": 1110.29, "word": " جطعة", "probability": 0.9474283854166666}], "temperature": 1.0}, {"id": 45, "seek": 113765, "start": 1111.23, "end": 1137.65, "text": "الجطع رقم مليون أنا عارف إنه هتجع إذا وجعت رقم واحد، مظبوط؟ فإذا هذا الحث، هذا induction، في حاجة هتصير لو أنا عملت حاجة تانية، ففي دايما initial condition لو انعمل أكيد باقي المعادلة هتتحقق، لو هيك ناخدها للمعادلات، معناته باقي المعادلة هتتحقق، في trigger", "tokens": [6027, 7435, 9566, 3615, 12602, 4587, 2304, 3714, 20292, 11536, 41850, 6225, 9640, 5172, 36145, 3224, 8032, 2655, 7435, 3615, 11933, 15730, 49610, 34268, 12602, 4587, 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0.9774169921875}, {"start": 1134.55, "end": 1135.45, "word": " للمعادلات،", "probability": 0.9271065848214286}, {"start": 1135.45, "end": 1135.71, "word": " معناته", "probability": 0.8883463541666666}, {"start": 1135.71, "end": 1135.89, "word": " باقي", "probability": 0.9710286458333334}, {"start": 1135.89, "end": 1136.27, "word": " المعادلة", "probability": 0.9935302734375}, {"start": 1136.27, "end": 1136.99, "word": " هتتحقق،", "probability": 0.9563337053571429}, {"start": 1136.99, "end": 1137.11, "word": " في", "probability": 0.95166015625}, {"start": 1137.11, "end": 1137.65, "word": " trigger", "probability": 0.845703125}], "temperature": 1.0}, {"id": 46, "seek": 115254, "start": 1138.34, "end": 1152.54, "text": "في initial value لازقة في initial condition بده ينعمل إذا أعطيتوا one معناته ال one هذه هتصل أكيد لل domino الحجر ال domino رقم مليون لو أكتر أكتر تمام هذا by logic", "tokens": [41185, 5883, 2158, 5296, 31377, 28671, 8978, 5883, 4188, 47525, 3224, 7251, 1863, 25957, 1211, 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\ No newline at end of file
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new file mode 100644
index 0000000000000000000000000000000000000000..a9d7e910b128581da3b6cd399f84e1cb2d619890
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iJnQv9sY0uk_raw.srt
@@ -0,0 +1,3456 @@
+1
+00:00:21,260 --> 00:00:23,260
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:23,260 --> 00:00:26,060
+الأنبياء والمشترين سيدنا محمد وعلى أهله وصحبه
+
+3
+00:00:26,060 --> 00:00:30,480
+أجمعين بداية بنرحب فيكوا في بداية الفصل الأول
+
+4
+00:00:30,480 --> 00:00:35,940
+للعام 2014-2015 ونأمل إن شاء الله أنه يكون عام خير
+
+5
+00:00:35,940 --> 00:00:42,600
+عام تجدد الحقيقة تجدد الأمل في مستقبلنا وفي حياتنا
+
+6
+00:00:42,600 --> 00:00:46,680
+بعد هذه الأزمات وهذه الأمور نرجو ذلك نلتقي اليوم
+
+7
+00:00:46,680 --> 00:00:51,690
+الحقيقة مع بعض لتدريس مساقdiscrete mathematics
+
+8
+00:00:51,690 --> 00:00:56,430
+وكلكم سجلتهوا عندكم هنبدأ اليوم ان شاء الله
+
+9
+00:00:56,430 --> 00:01:00,810
+محاضرتنا مجرد introduction مقدمات هناخد بالظبط عن
+
+10
+00:01:00,810 --> 00:01:04,530
+إيش هنتكلم المحاضرة تاعتنا أو ال course تبعنا كله
+
+11
+00:01:04,530 --> 00:01:09,890
+عن إيش هنتكلم، إيش ال .. ال chapters اللي
+
+12
+00:01:09,890 --> 00:01:13,690
+هنشتغلها، إيش ال text book تبعنا أمور كتيرة
+
+13
+00:01:13,690 --> 00:01:17,860
+الحقيقة هنتكلم بس كلها في النهاية معلوماتعامة
+
+14
+00:01:17,860 --> 00:01:22,360
+اليوم اليوم هتكون كلها معلومات عامة طيب بداية زي
+
+15
+00:01:22,360 --> 00:01:28,240
+ما قلنا هنشتغل مع بعض المثاق المعنوان ب Ecom 2311
+
+16
+00:01:28,240 --> 00:01:31,240
+اللي هو discrete mathematics زي ما انتوا سجلته
+
+17
+00:01:31,240 --> 00:01:37,000
+هيكون معاكم الدكتور محمد الحنجوري بداية ال course
+
+18
+00:01:37,000 --> 00:01:40,840
+عشان بس نوضح ال course هو هيكون فيه مجموعة items
+
+19
+00:01:40,840 --> 00:01:46,240
+مجموعة concepts بدنا نتعلمهم اونشوف ال description
+
+20
+00:01:46,240 --> 00:01:48,880
+تبع ال course تبعنا فحنلاقي ال description تبعنا
+
+21
+00:01:48,880 --> 00:01:52,840
+فيه مجموعة عناصر بدنا نتعلمها خلال الفصل اللي هو
+
+22
+00:01:52,840 --> 00:01:56,980
+الاربعتاش خمستاشر أسبوع ان شاء الله تعالى طيب
+
+23
+00:01:56,980 --> 00:02:00,900
+بداية هناخد شوية basic عن ال logic هتلاحظوا
+
+24
+00:02:00,900 --> 00:02:04,820
+المفارضات على فكرة يمكن لو انتوا معظم المفارضات دي
+
+25
+00:02:04,820 --> 00:02:07,860
+كنتوا تاخدوها زمانجنب هالمصطلح ال English تبحث
+
+26
+00:02:07,860 --> 00:02:10,380
+هتلاقي ان معظمها انتوا مار عليكوا قبل هيك انتوا
+
+27
+00:02:10,380 --> 00:02:12,960
+بالعربي انا متأكد كله ماخدينه معظمه ماخدينه معظم
+
+28
+00:02:12,960 --> 00:02:16,060
+ال course كنتوا مدرجين فيه وعارفين بعض أمور عنه
+
+29
+00:02:16,060 --> 00:02:21,180
+ولكن هناخده بوجهة نظر مختلفة وجهة نظر أول شي ان
+
+30
+00:02:21,180 --> 00:02:24,500
+انتوا بتتعاملوا مع ال PC فانتوا بتكونوا مبرمجين لل
+
+31
+00:02:24,500 --> 00:02:28,560
+computer مبرمج computer بتتعامل مع discrete مع
+
+32
+00:02:28,560 --> 00:02:31,310
+discrete signaldiscrete signal اذا أنا مش عارف
+
+33
+00:02:31,310 --> 00:02:33,790
+المعلومة اللى بتفهم فيها الكمبيوتر كيف انا بده
+
+34
+00:02:33,790 --> 00:02:36,270
+اعطيها كيف انا بده اعمله ال code كيف بده اعمله ال
+
+35
+00:02:36,270 --> 00:02:39,550
+algorithm فعشان هيك طبيعى جدا بدنابنعمل
+
+36
+00:02:39,550 --> 00:02:42,990
+refreshment للمعلومات تبعتنا بطريقة مختلفة، بصورة
+
+37
+00:02:42,990 --> 00:02:47,610
+مختلفة شوية بصورة أول شي بنتكلم English language
+
+38
+00:02:47,610 --> 00:02:51,290
+فاحنا بدنا ناخد المصطلحات ال English اللي .. اللي
+
+39
+00:02:51,290 --> 00:02:54,230
+.. اللي بتاعتنا اللي هي العالمية لو قرأته كتاب،
+
+40
+00:02:54,230 --> 00:02:58,090
+قرأته إشي، شفته أي يوتيوب .. محاضر على يوتيوب إشي
+
+41
+00:02:58,090 --> 00:03:00,370
+فانتوا فاهمين المصطلحات، تكونوا عارفين إيش
+
+42
+00:03:00,370 --> 00:03:03,990
+المصطلحات اللي بتتكلموا .. اللي بتكلم عنهاكويس،
+
+43
+00:03:03,990 --> 00:03:07,150
+هتلاقوا أنك تتكلم عن ال basic logic ال and، ال or،
+
+44
+00:03:07,150 --> 00:03:10,070
+ال nor، ال and، مرت عليكوا، ال gates هذه ال logic
+
+45
+00:03:10,070 --> 00:03:13,090
+gates كلها مرت عليكوا، هناخدها .. بنتناولها بطريقة
+
+46
+00:03:13,090 --> 00:03:15,610
+مختلفة شوية، بصورة مختلفة شوية، ولكن في النهاية
+
+47
+00:03:15,610 --> 00:03:19,510
+المفهوم واحد، هو نفس المفهوم، كويس ال sets،
+
+48
+00:03:19,510 --> 00:03:22,330
+المجموعات، مرت عليكوا المجموعات، بكل كم مرت عليكوا
+
+49
+00:03:22,330 --> 00:03:26,360
+المجموعات، بكل تفاصيلها، بكل ..اشكالياتها بكل طرق
+
+50
+00:03:26,360 --> 00:03:29,440
+التعامل أو ال operation استعدتها فهناخدها هنرجع
+
+51
+00:03:29,440 --> 00:03:33,980
+نعيد عليها برضه نتكلم عن ال sets بتناول أنه أنا
+
+52
+00:03:33,980 --> 00:03:37,820
+بده أفهمها لل PC عن طريق code معين فانا كيف بده
+
+53
+00:03:37,820 --> 00:03:42,820
+أفهمها بطريقة discrete عساس ان اتفاعل بعدين مع ال
+
+54
+00:03:42,820 --> 00:03:47,940
+PC اللي احنا أساسا مهندسين حسوب احنا أساسا مسمانة
+
+55
+00:03:47,940 --> 00:03:52,300
+مرتبط صار بالحسوب فبدنا نكون فاهمينكيف نتفاهم
+
+56
+00:03:52,300 --> 00:03:55,620
+معاه، كيف نعمله ال formula بتاعة أي problem بده
+
+57
+00:03:55,620 --> 00:03:58,000
+يشتغل عليها لأنه في النهاية انتوا ال problem
+
+58
+00:03:58,000 --> 00:04:01,660
+بتاعتكوا عبارة عن إيش؟ عبارة عن language، هيجيكوا
+
+59
+00:04:01,660 --> 00:04:04,220
+ال .. ال .. ال customer تبعكم، هيقولكوا والله أنا
+
+60
+00:04:04,220 --> 00:04:07,000
+عندي المشكلة الفلانية، حلوليها، اعملولي code،
+
+61
+00:04:07,000 --> 00:04:11,160
+اعملولي برنامج، اعملولي الاصيل، اعملولي مش عارف ال
+
+62
+00:04:11,160 --> 00:04:14,960
+.. اعملولي MATLAB، اعملولي أي code معين، اعملولي
+
+63
+00:04:14,960 --> 00:04:18,870
+compilerفي الآخر ال compiler ده او ال .. ال .. ال
+
+64
+00:04:18,870 --> 00:04:22,250
+code بأبسط صوره بده ينحط على ال pc او على ال
+
+65
+00:04:22,250 --> 00:04:24,170
+laptop يعني في النهاية انتوا بتتكلموا عن نفس الشغل
+
+66
+00:04:24,170 --> 00:04:28,090
+كويس بدي اكون فاهم هذا كيف بتتعامل و بناء عليه بدي
+
+67
+00:04:28,090 --> 00:04:33,410
+اكون انا اصلا كاتبله البرنامج و انا فاهم ال .. كيف
+
+68
+00:04:33,410 --> 00:04:36,610
+هتعامل معاه تمام فهناخد ال sets هناخد ال
+
+69
+00:04:36,610 --> 00:04:39,850
+combinational theory هناخد شوية حاجات عن ال .. ال
+
+70
+00:04:39,850 --> 00:04:44,680
+.. ال poly algebraال set theory برضه امتدد ل ..
+
+71
+00:04:44,680 --> 00:04:48,380
+للمجموعات .. لشغل المجموعات ال symbolic logic ال
+
+72
+00:04:48,380 --> 00:04:51,540
+predicate logic ال .. ال .. ال functions كلنا
+
+73
+00:04:51,540 --> 00:04:54,850
+عارفين ال functions okayكلنا فاهمين إنه function
+
+74
+00:04:54,850 --> 00:04:58,090
+لما بتكلم عن ال function أبسط صورها أنت بتتكلموا
+
+75
+00:04:58,090 --> 00:05:03,730
+عن نفترض y equal to f of x function function فيها
+
+76
+00:05:03,730 --> 00:05:07,450
+variable و فيها objective ال variable و ال
+
+77
+00:05:07,450 --> 00:05:10,270
+objective واحد معتمد على التاني واحد بيعتمد على
+
+78
+00:05:10,270 --> 00:05:13,790
+التاني هنتكلم عن الكلام هذا و هناخده و هناخد ايش
+
+79
+00:05:13,790 --> 00:05:18,240
+الالـ Range اللي هيطلع فيه الـ Y يعني إيش قيم Y
+
+80
+00:05:18,240 --> 00:05:22,400
+المحتملة بناء على إيش؟ بناء على ال domain اللي
+
+81
+00:05:22,400 --> 00:05:26,600
+ممكن X ياخد قيمه منه فلاحظوا إحنا دخلنا هنا شوية
+
+82
+00:05:26,600 --> 00:05:29,400
+مفاهيم شوية أزود شوية عن اللي أنتوا فاهمينه لأ
+
+83
+00:05:29,400 --> 00:05:33,680
+إنها لواجهة مرتبط إن X إيش القيم اللي بتاخدها؟بنان
+
+84
+00:05:33,680 --> 00:05:36,880
+عليها why إيش ممكن يطلع فبصير عندكوا ال logic إنه
+
+85
+00:05:36,880 --> 00:05:40,280
+النواتج اللي بتطلع دي صح مش صح، كويسة مش كويسة،
+
+86
+00:05:40,280 --> 00:05:43,960
+معقولة مش معقولة، فهذه بدايات الخطوات للتعامل مع
+
+87
+00:05:43,960 --> 00:05:48,880
+ال functions، كويسة هنتعامل مع ال equivalence
+
+88
+00:05:48,880 --> 00:05:52,300
+relations التكافؤ، الأوقات التكافؤ، كيف ممكن أقول
+
+89
+00:05:52,300 --> 00:05:55,420
+إن هذه بتكافئ هذه، الجانب هذا بتكافئ الجانب هذا، و
+
+90
+00:05:55,420 --> 00:06:01,360
+هنتكلم برضه عن ال graphs الرسومات، الرسم، ال
+
+91
+00:06:01,360 --> 00:06:04,720
+graphs لما بتتعامل معاه graphsبداية ال graph نفسه،
+
+92
+00:06:04,720 --> 00:06:08,400
+كيف بعبر عنه رياضيا؟ هنتعلم، هنشوف والله إن أنا
+
+93
+00:06:08,400 --> 00:06:14,080
+بدي أصنف أو أوصف graph معين، إيش ال elements اللي
+
+94
+00:06:14,080 --> 00:06:16,920
+أنا محتاج أعرفها إليه؟ هنتكلم عنها و هنتكلم عن
+
+95
+00:06:16,920 --> 00:06:19,880
+مجموعة graphs معينة و كيف ممكن نتعامل معها و
+
+96
+00:06:19,880 --> 00:06:23,020
+مجموعة equations لكل graph من ال graphs اللي
+
+97
+00:06:23,020 --> 00:06:27,640
+هنتعامل معها ال counting، basic counting العد،
+
+98
+00:06:27,640 --> 00:06:30,780
+انتوا هتيجي تقولوا العد إيش العد؟ احنا زمان
+
+99
+00:06:30,780 --> 00:06:34,270
+متعلمين العد، صح؟متعلمين العدد هناخد شوية theory
+
+100
+00:06:34,270 --> 00:06:38,210
+أو counting theory هناخد شوية معلومات إضافية زي ما
+
+101
+00:06:38,210 --> 00:06:42,150
+قلتلكوا وجهة نظر مختلفة شوية بس المعلومة هي هي
+
+102
+00:06:42,150 --> 00:06:45,250
+هتلاقوا أن معظمكم عندكم معلومة ولكن هنتناولها
+
+103
+00:06:45,250 --> 00:06:48,650
+بطريقة مختلفة ليش؟ اللي هي علاقة بال discrete؟
+
+104
+00:06:48,650 --> 00:06:52,850
+اللي هي علاقة بما يخدم ال field تبعكم بما يخدم ال
+
+105
+00:06:52,850 --> 00:06:55,350
+field تبعكم اللي جدام ان شاء الله هتاخدوا شغل
+
+106
+00:06:55,350 --> 00:06:58,250
+برمجة كتير وشغل في ال data structures وفي الأمور
+
+107
+00:06:58,250 --> 00:07:02,300
+كتير حاجاتفي ال database فاحنا هنحاول نطوع ال
+
+108
+00:07:02,300 --> 00:07:06,240
+knowledge اللي احنا عارفين عن ال counting بطريقة
+
+109
+00:07:06,240 --> 00:07:10,400
+تخدمكم في المثلقات الأخرى وتخدمكم كمهندسين في
+
+110
+00:07:10,400 --> 00:07:14,640
+النهاية كمهندسين computer كويس الحاجة المهمة برضه
+
+111
+00:07:14,640 --> 00:07:19,200
+ل proof strategies كيف تثبته او ايش ال strategias
+
+112
+00:07:19,200 --> 00:07:24,530
+للإثباتات عندكم إثبات معين بتكون تثبته طيب كويسإيش
+
+113
+00:07:24,530 --> 00:07:27,130
+ال strategy عشان أثبته؟ يعني إيش ال strategy
+
+114
+00:07:27,130 --> 00:07:31,070
+المنطقية اللي فعلا لو أثبت باستخدامها فانا فعلا
+
+115
+00:07:31,070 --> 00:07:37,190
+بكون عملت أثبات مش strategy هستعملها زيها زي جلتها
+
+116
+00:07:37,190 --> 00:07:41,050
+طب ماشي يعني كأنه زي ما بيقولوا فسر الماء بعد جهد
+
+117
+00:07:41,050 --> 00:07:45,230
+بالماء ماعملناش أشي فلأ هنتعلم شوية strategies
+
+118
+00:07:45,230 --> 00:07:51,620
+تستخدم للبرو بحيث تم استخدامهاال set برضه هيرنجعنا
+
+119
+00:07:51,620 --> 00:07:55,840
+ل set partitions ال combinations ال tree نوع من
+
+120
+00:07:55,840 --> 00:07:59,740
+أنواع ال graph اللي هي ال trees أو مش شجيرات
+
+121
+00:07:59,740 --> 00:08:02,940
+الشجرة .. الشجرة هنشوف برضه فيش ممكن نستخدمها
+
+122
+00:08:02,940 --> 00:08:06,520
+انتوا بتستخدموها ب .. بصورة كبيرة جدا حقيقة و
+
+123
+00:08:06,520 --> 00:08:10,700
+انتوا مش .. مش حاسين أولها شجرة العيلةأبسط شغلة
+
+124
+00:08:10,700 --> 00:08:14,420
+شجرة العيلة فعلا شجرة العيلة و بتطلع بفروع و كل
+
+125
+00:08:14,420 --> 00:08:17,580
+فرع بنحط عليه اسم و كل اسم بيطلع مجموعة فروع تانية
+
+126
+00:08:17,580 --> 00:08:20,720
+شجرة العيلة فعلا هذه واحدة من الحاجات اللي هنتكلم
+
+127
+00:08:20,720 --> 00:08:24,500
+عنها حقيقة و أقولكوا مصطلحات ال tree هتكون متاخدة
+
+128
+00:08:24,500 --> 00:08:28,000
+من شجرة العيلة أساسا فلاحظوا هي في حاجات برضه طيب
+
+129
+00:08:28,000 --> 00:08:30,840
+هتقولوا لو احنا مش دخل العيلة في ال .. في ال
+
+130
+00:08:30,840 --> 00:08:34,940
+discrete لأ فيها دخل ليش لأن انتوا في عندكوا حاجات
+
+131
+00:08:34,940 --> 00:08:37,260
+كتير الحقيقة بتستعملوها هي اللي علاقة بال tree
+
+132
+00:08:37,260 --> 00:08:41,460
+أولها ال partitions اللي بتعملوها لل hard diskانتو
+
+133
+00:08:41,460 --> 00:08:44,440
+كيف بتجسموا ال hard disk؟ عندكوا hard disk؟ ال
+
+134
+00:08:44,440 --> 00:08:50,720
+hard disk هذا بتجسمه بداية لل C D E صحيح؟ طيب جوا
+
+135
+00:08:50,720 --> 00:08:55,380
+بتجسمه folders ال folders هذه بتجسم جواها طيب
+
+136
+00:08:55,380 --> 00:08:58,120
+هتقولوا والله بدي أحط ال C هذا يمكن دايما بنستعمله
+
+137
+00:08:58,120 --> 00:09:01,400
+لل .. لل windows للاشي خليني أقول دي والله أجيت
+
+138
+00:09:01,400 --> 00:09:06,180
+وحطيته عليهاال courses بتاعتكم أول شي حاببتكوا
+
+139
+00:09:06,180 --> 00:09:12,400
+تجسموها حسب السنة هتقول والله 2014 2015 هنا
+
+140
+00:09:12,400 --> 00:09:17,520
+هتجسموا جواها الفصل الأول الفصل الثاني والصيفي
+
+141
+00:09:17,520 --> 00:09:22,720
+هتجسموا جواها لحظة تريها هتجسموا جواها هنا ايش
+
+142
+00:09:22,720 --> 00:09:26,650
+المثاقات folder لكل مثاقطب كل مصاق هتحطه فيه
+
+143
+00:09:26,650 --> 00:09:29,850
+مجموعة ال items تبعته او مجموعة ال elements تبعته
+
+144
+00:09:29,850 --> 00:09:33,430
+اللي هي عبارة عن ال textbook تبعكم عبارة عن ال
+
+145
+00:09:33,430 --> 00:09:35,930
+power point files عبارة عن ال exercises اللي
+
+146
+00:09:35,930 --> 00:09:40,930
+هتاخدوها و ال assignments اي معلومات اضافية عن
+
+147
+00:09:40,930 --> 00:09:45,790
+الموضوع عن ال course هذا فهتلاحظوا جيتوا طلعتوا
+
+148
+00:09:45,790 --> 00:09:49,570
+tree انتوا عملتوها و انتوا مش عارفين ان انتوا
+
+149
+00:09:49,570 --> 00:09:52,790
+عاملين tree هي tree فلو جيتوا طلعتوا كل واحدة
+
+150
+00:09:52,790 --> 00:09:55,860
+منكوا على جهازهاجهاز الحاسوب تبعها أو لابتوب في
+
+151
+00:09:55,860 --> 00:09:58,960
+البيت هتلاقيه ان هو أصلا نتري هو أساسا فعلا مجسم
+
+152
+00:09:58,960 --> 00:10:01,180
+partitions a tree فهنتعلم شوية عن ال tree
+
+153
+00:10:01,180 --> 00:10:04,800
+summations هناخد برضه شوية concepts عن ال
+
+154
+00:10:04,800 --> 00:10:08,740
+summations ال recurrences أو ال recursion أحيانا
+
+155
+00:10:08,740 --> 00:10:14,100
+بيسموها ال summation معروفة عملية جمع مش ماجولة
+
+156
+00:10:14,100 --> 00:10:16,720
+لما بدنا نجمع نفترض أرقام من واحد لعشرة أو من واحد
+
+157
+00:10:16,720 --> 00:10:19,940
+لمية أجوب ده أكتب للكمبيوتر one plus two plus
+
+158
+00:10:19,940 --> 00:10:24,740
+three plus مش منطق فبدنا ناخد شوية نظرياتأعتقد أنه
+
+159
+00:10:24,740 --> 00:10:29,080
+يمكن معظمها أو خلّيني أقول جزء منها مر عليكوا مر
+
+160
+00:10:29,080 --> 00:10:32,300
+عليكوا قبل هيكة في عملية ال summation لما بدنا
+
+161
+00:10:32,300 --> 00:10:34,720
+نجمع أرقام من واحد لعشرة بدنا نجمع أرقام من واحد
+
+162
+00:10:34,720 --> 00:10:37,700
+لمية بدنا نجمع نفترض لأ بديش من واحد لمية بديش
+
+163
+00:10:37,700 --> 00:10:40,970
+أبدأ من واحد بدنا نجمع أرقام نفترض من خمسين لميةطب
+
+164
+00:10:40,970 --> 00:10:44,290
+إيش ال .. كيف الحل؟ إيش نعمل فيها؟ بحيث إن ماقعدش
+
+165
+00:10:44,290 --> 00:10:46,850
+أكتب خمسين زياد و أحد و خمسين زياد اتنين و خمسين
+
+166
+00:10:46,850 --> 00:10:51,770
+زياد .. الموضوع مش صح و ولا هو شغلت مهندس حسوب
+
+167
+00:10:51,770 --> 00:10:54,710
+يقعد يشتغلها بالشكل هذا يعني إحنا ماتعلمش عشان في
+
+168
+00:10:54,710 --> 00:10:57,510
+الآخر نقعد نعمل زي الابتدائي واحد زي اتنين زي
+
+169
+00:10:57,510 --> 00:11:01,030
+التلاتة نقعد نجمع فبدنا ناخد شوية theory اتساعدنا
+
+170
+00:11:01,030 --> 00:11:05,460
+في الأمور هذه و هناخد مجموعاتsummations مختلفة ل
+
+171
+00:11:05,460 --> 00:11:09,040
+series مختلفة لأن هنا نتكلم عن series نتكلم عن
+
+172
+00:11:09,040 --> 00:11:12,160
+سلسلة و بدنا نجمحها او بدنا نجمحها في ال
+
+173
+00:11:12,160 --> 00:11:15,020
+recurrence او ال recursion احيانا التكرار وهذا
+
+174
+00:11:15,020 --> 00:11:18,220
+انتوا عادة بتستعمله برضه بدون ما تشعروا في الأكوات
+
+175
+00:11:18,220 --> 00:11:21,280
+بتاعتكوا في ال code اللي بتعمله مش بتعمله for loop
+
+176
+00:11:21,280 --> 00:11:24,680
+ال for loop ما هم انتوا حاجة و قاعدين بتكرروا فيها
+
+177
+00:11:24,680 --> 00:11:29,810
+طب ليش ما كتبتوهاش ورا بعض؟نفترض ال for loop اللي
+
+178
+00:11:29,810 --> 00:11:31,690
+كنتي تعملوه من واحد لعشرة ليش ما كتبتوش ال
+
+179
+00:11:31,690 --> 00:11:35,930
+statements سبعتكم عشر ورا بعض لأ بدنا نوفر وجهة و
+
+180
+00:11:35,930 --> 00:11:38,430
+بدنا نوفر جهد و بدنا نوفر كتابة و بدنا نوفر ..
+
+181
+00:11:38,430 --> 00:11:42,970
+فبرضه هناخدلنا شوية هيك introduction شوية معلومات
+
+182
+00:11:42,970 --> 00:11:47,330
+عن ال recursion زى ما قلتلكوا هكون معاكم دكتور
+
+183
+00:11:47,330 --> 00:11:51,870
+محمد الحنجوري يمكن بس هنا القاعة .. القاعة
+
+184
+00:11:51,870 --> 00:11:56,270
+هتلاقوني دائما في ال IT 414
+
+185
+00:11:57,810 --> 00:12:03,210
+فقه اربعمية اربعتاشر تمام انا برضه حتى ال
+
+186
+00:12:03,210 --> 00:12:07,450
+extension تبعي مش صحيح عشرة هذا الجديد هو لاني
+
+187
+00:12:07,450 --> 00:12:11,990
+تمام فيما يخص المادة العلمية بتاعتنا المادة
+
+188
+00:12:11,990 --> 00:12:14,890
+العلمية كلها ال materials بتاعتنا will be
+
+189
+00:12:14,890 --> 00:12:18,850
+available at model اعتقد معظمكم برضه اتعامل مع ال
+
+190
+00:12:18,850 --> 00:12:21,910
+model اللي ما اتعاملش مع ال model بده يفعل بس
+
+191
+00:12:21,910 --> 00:12:25,550
+صفحته مجرد انكم اتعاملتم مع ال model و لو في مساق
+
+192
+00:12:25,550 --> 00:12:30,480
+واحدفانتوا activated يعني الحساب تبعكم activated
+
+193
+00:12:30,480 --> 00:12:36,060
+نشط ادخلوا عليه automatic مدام انتوا مسجلين المصاق
+
+194
+00:12:36,060 --> 00:12:39,880
+هتلاقوا المصاق موجود عندكم ادخلوا عليه هتلاقوا
+
+195
+00:12:39,880 --> 00:12:43,060
+برضه كل ال materials أول بأول أسبوع بأسبوع weekly
+
+196
+00:12:43,060 --> 00:12:47,440
+بنزللكم powerpoint files المحاضرات هذه اللي
+
+197
+00:12:47,440 --> 00:12:50,780
+بنشرحها هذه واحدة من ال items اللي هتلاقوها موجودة
+
+198
+00:12:50,780 --> 00:12:55,590
+الكتابsoft copy و نسخة كويسة ملونة جيدة يعني
+
+199
+00:12:55,590 --> 00:13:03,410
+هتلاقوها موجودة قلكوا على جد بس طبعا مصاق في ممكن
+
+200
+00:13:03,410 --> 00:13:06,310
+ال exercise او ال assignments automatically برضه
+
+201
+00:13:06,310 --> 00:13:09,770
+أسبوعيا لإن كل أسبوع غالبا كل أسبوع هيكون فيه هنا
+
+202
+00:13:09,770 --> 00:13:14,770
+homework أو assignment كويس فأسبوعيا ليش أسبوعيا
+
+203
+00:13:14,770 --> 00:13:18,810
+لإن احنا مضطرين نعمل هيك احنا متكلم عن mathematics
+
+204
+00:13:18,810 --> 00:13:22,330
+okay هي فرع من أفرع ال mathematics اسمها discrete
+
+205
+00:13:22,620 --> 00:13:27,760
+مااختلفناش بس في النهاية مادربناش إيدنا ال brain
+
+206
+00:13:27,760 --> 00:13:31,420
+مش هيوصل للإيد يوم الابتحان هتقعد تقوله أنا عارف
+
+207
+00:13:31,420 --> 00:13:34,180
+متأكد من المعلومة أنا بعرف أحلها بس مش عارف من وين
+
+208
+00:13:34,180 --> 00:13:37,700
+أبدأ طب من وين أبدأ هو السؤال اللى بيكون بالشكل
+
+209
+00:13:37,700 --> 00:13:40,460
+هذا الدكتور كيف بدأ .. كيف بدأ حله أنا عارف الحل
+
+210
+00:13:40,460 --> 00:13:44,500
+يعني هو الطريقة ما زالت موجودة عندى بس مش عارف
+
+211
+00:13:44,500 --> 00:13:47,160
+أكتبها من اللي هيحلنا الموضوع هذا ال exercises
+
+212
+00:13:47,160 --> 00:13:50,400
+فعشان هيك هنزودلكم شوية في ال exercises هنشوفها لو
+
+213
+00:13:50,400 --> 00:13:54,810
+جت جدول برضهلل activities بتاعت المصابة كويسة
+
+214
+00:13:54,810 --> 00:13:59,090
+هيكون فينا تلت ساعات weekly زي ما قلنا التلت ساعات
+
+215
+00:13:59,090 --> 00:14:04,770
+هدولة الأحد والتلات من تسعة و نص لحداشر الحقيقة
+
+216
+00:14:04,770 --> 00:14:07,630
+هنا مكتوبة غلط برضه من تسعة و نص لحداشر بنصلحها و
+
+217
+00:14:07,630 --> 00:14:12,110
+بنزلكيها على ال model من تسعة و نص لحداشر يمكن
+
+218
+00:14:12,110 --> 00:14:14,390
+الشيء المميز انه هتكون recorded زي ما قلنا
+
+219
+00:14:14,390 --> 00:14:16,970
+المحاضرات يعني احنا حاليا هنا قاعدين بنسجل ف
+
+220
+00:14:16,970 --> 00:14:21,480
+automaticallyهتلاقوها نازل عندكم على ال .. موقع
+
+221
+00:14:21,480 --> 00:14:23,760
+المحاضرات المصورة اللي خاص بالجامعة الإسلامية
+
+222
+00:14:23,760 --> 00:14:28,120
+تمام؟ فهذا هيفيدكم .. هيفيدكم بعد المحاضرة هيفيدكم
+
+223
+00:14:28,120 --> 00:14:31,040
+اللي ممكن تكون اتأخرت العشر دجاج في .. في .. او
+
+224
+00:14:31,040 --> 00:14:34,980
+إشي حاجة إشي فماضعش عليها حاجة لو اضطرنا إن
+
+225
+00:14:34,980 --> 00:14:38,260
+المعلومات بتكون أحيانا متراكبة على بعض معتمدة على
+
+226
+00:14:38,260 --> 00:14:41,400
+حاجة قلناها قبل هيك فبتكون في إمكانية إن هي
+
+227
+00:14:41,400 --> 00:14:44,420
+اتراجحة لحالها في أيام الامتحانات أيام إشي يعني ..
+
+228
+00:14:44,420 --> 00:14:47,230
+يعني إيه؟ وجد ما بتتراجح على آخر الأسبوعبعرفش إذا
+
+229
+00:14:47,230 --> 00:14:50,290
+كان انتوا من اللي بيحب مثلا كل أسبوع يكون لمادة
+
+230
+00:14:50,290 --> 00:14:54,050
+تراجعوها بدون امتحانات يعني فبرضه هتلاقي انه هذه
+
+231
+00:14:54,050 --> 00:14:59,470
+مادة إثرائية كويسة لكم تتراجعوا منها طيب ال
+
+232
+00:14:59,470 --> 00:15:01,990
+objectives او ال course objectives ال outcomes
+
+233
+00:15:01,990 --> 00:15:05,530
+تبعتنا من ال course يعني في أخر ال course إيش
+
+234
+00:15:05,530 --> 00:15:07,290
+المفروض تكونوا طلعتوا انتوا؟ يعني إيش اللي
+
+235
+00:15:07,290 --> 00:15:09,870
+هتستفيدوا من نهايتك في نهاية ال course؟ هتستفيدوا
+
+236
+00:15:09,870 --> 00:15:12,010
+لحفظها knowledge كويسة ال knowledge هذه اللي احنا
+
+237
+00:15:12,010 --> 00:15:17,840
+هنهتم فيها ان تكونوا انتوا تعلمتوها اللي هيكيف أول
+
+238
+00:15:17,840 --> 00:15:21,700
+شغلة نعمل conversion أو كيف نحوّل ال language
+
+239
+00:15:21,700 --> 00:15:28,280
+بتاعتنا ال real life concepts بتاعتنا لمثماتيكس زى
+
+240
+00:15:28,280 --> 00:15:32,040
+ما قلتلكم ال customer تبعكم كمبرمجين بكرا هيجى
+
+241
+00:15:32,040 --> 00:15:35,880
+يقولكوا مشكلة الراجل مابعرفش رياضيات مش هيقولكوا
+
+242
+00:15:35,880 --> 00:15:39,540
+والله أنا الحالت تبعى هي معدلته هيقولكوا أنا عند
+
+243
+00:15:39,540 --> 00:15:43,280
+المشكلة الفلانية عند المشكلة العلانية تعالوا شوفوا
+
+244
+00:15:43,280 --> 00:15:46,730
+ال computer مش راضى يشتغلكلام بيحكي .. بيحكي كلام
+
+245
+00:15:46,730 --> 00:15:50,330
+.. انتوا بتكونوا تحولوه ل formula .. بتحولوها
+
+246
+00:15:50,330 --> 00:15:55,030
+لمجموعة formula يفهمها ال .. ال BC تبعكم .. يفهمها
+
+247
+00:15:55,030 --> 00:15:59,510
+ال BC فدي أول هدف .. هناخد شوية applications عن
+
+248
+00:15:59,510 --> 00:16:02,590
+الموضوع هذا language و نحولها مجموعة رياضية ..
+
+249
+00:16:02,590 --> 00:16:05,350
+لمجموعة symbols .. لمجموعة notations و نتعامل
+
+250
+00:16:05,350 --> 00:16:10,900
+معاها رياضيا بهذا الشكلOkay أو العكس زي ما قلنا مع
+
+251
+00:16:10,900 --> 00:16:13,860
+ال logic gates و الأمور هذه برضه ممكن ندخلها معانا
+
+252
+00:16:13,860 --> 00:16:17,000
+كيف نستفيد منها كيف نربط الجمل ببعض كيف الأمور هذه
+
+253
+00:16:17,000 --> 00:16:20,860
+كلها هنستفيد منها هنتكلم عن ال propositional logic
+
+254
+00:16:20,860 --> 00:16:24,600
+و ال predicate logic الحقيقة ال proposition logic
+
+255
+00:16:24,600 --> 00:16:28,200
+أو اللي هي العبارة عبارة بس العبارة بدو يكون لها
+
+256
+00:16:28,200 --> 00:16:32,040
+truth value عشان أقول عنها a proposition ال
+
+257
+00:16:32,040 --> 00:16:35,240
+proposition غير ال sentence ال sentence ممكن تكون
+
+258
+00:16:35,240 --> 00:16:35,960
+question
+
+259
+00:16:38,570 --> 00:16:42,430
+زي نقولكوا إيش اليوم من الأيام؟ okay إيش اليوم من
+
+260
+00:16:42,430 --> 00:16:45,870
+الأيام؟ هذا سؤال بس هل بقدر أقول إنه .. إنه الكلام
+
+261
+00:16:45,870 --> 00:16:50,730
+صح ولا غلط؟ مالوش قيمة لكن لما أقول فلسطين ال
+
+262
+00:16:50,730 --> 00:16:55,790
+goods عصمة فلسطين أه إلها truth value قيمة حقيقة
+
+263
+00:16:55,790 --> 00:17:00,010
+إلها قيمة حقيقة إيش بتساوي قيمة الحقيقة هذه true؟
+
+264
+00:17:00,010 --> 00:17:07,300
+لحظة طيب لو قلنا اليوم الدنيا مطراليوم الدنيا مطر
+
+265
+00:17:07,300 --> 00:17:10,760
+مع ال situation تبعنا ان احنا عارفين .. شايفين هنا
+
+266
+00:17:10,760 --> 00:17:13,120
+عندنا شباك و شايفين كيف الوضع برا، إلها truth
+
+267
+00:17:13,120 --> 00:17:16,160
+value مش ملهاشة .. إلها truth value .. truth value
+
+268
+00:17:16,160 --> 00:17:22,060
+بتاعتها falseلحظة فإذا في truth value في قيمة
+
+269
+00:17:22,060 --> 00:17:26,020
+حقيقة بمعنى إن أنا عندي حقيقة بقدر أحكم فيها عن
+
+270
+00:17:26,020 --> 00:17:29,880
+الجملة هذه حقيقة صح ولا غلط هي معناها مش لما أقول
+
+271
+00:17:29,880 --> 00:17:33,060
+truth value معناه إن هي دايما true لأ إنه إلها
+
+272
+00:17:33,060 --> 00:17:37,140
+قيمة فهذه بتسميها proposition proposition تمام
+
+273
+00:17:37,140 --> 00:17:41,660
+عبارةالها حقيقة، الحقيقة هذه مش بدرور تكون true،
+
+274
+00:17:41,660 --> 00:17:46,620
+هي إما true or false، كويس، هنتعلم الكلام هذا و
+
+275
+00:17:46,620 --> 00:17:49,340
+هناخده بالتفصيل و بال examples و بأمثلة كتير
+
+276
+00:17:49,340 --> 00:17:53,360
+الحاجة المهمة جدا اللي هتتعرفوا عليها ال proofs،
+
+277
+00:17:53,360 --> 00:17:56,280
+الإثباتات، كيف نثبتها، بال strategies بتاعتها،
+
+278
+00:17:56,280 --> 00:18:00,860
+هناخد شوية strategies to produce proofs هناخدها مع
+
+279
+00:18:00,860 --> 00:18:03,660
+examples كتير، الحقيقة و مع شغل كتير، هناخده في
+
+280
+00:18:03,660 --> 00:18:09,470
+الموضوع هذاهنتكلم عن ال induction و ال recursion
+
+281
+00:18:09,470 --> 00:18:16,710
+ال induction اللي هي الحث عملية الحث هذه بتشوفوها
+
+282
+00:18:16,710 --> 00:18:22,250
+كتير يمكن في التلفزيون او في برامج او حاجة بتلاقوا
+
+283
+00:18:22,250 --> 00:18:26,430
+اللي هي احجار ال domino بيرتبوهم ممكن يعملوها على
+
+284
+00:18:26,430 --> 00:18:32,230
+جد الأوضة هذه يرتبوها نفترض مليون جطعةالجطع رقم
+
+285
+00:18:32,230 --> 00:18:37,310
+مليون أنا عارف إنه هتجع إذا وجعت رقم واحد، مظبوط؟
+
+286
+00:18:37,310 --> 00:18:43,550
+فإذا هذا الحث، هذا induction، في حاجة هتصير لو أنا
+
+287
+00:18:43,550 --> 00:18:48,770
+عملت حاجة تانية، ففي دايما initial condition لو
+
+288
+00:18:48,770 --> 00:18:54,550
+انعمل أكيد باقي المعادلة هتتحقق، لو هيك ناخدها
+
+289
+00:18:54,550 --> 00:18:57,650
+للمعادلات، معناته باقي المعادلة هتتحقق، في trigger
+
+290
+00:18:58,340 --> 00:19:02,160
+في initial value لازقة في initial condition بده
+
+291
+00:19:02,160 --> 00:19:05,800
+ينعمل إذا أعطيتوا one معناته ال one هذه هتصل أكيد
+
+292
+00:19:05,800 --> 00:19:10,300
+لل domino الحجر ال domino رقم مليون لو أكتر أكتر
+
+293
+00:19:10,300 --> 00:19:14,380
+تمام هذا by logicإلا إذا كان واحد إجا في النص جطع
+
+294
+00:19:14,380 --> 00:19:19,240
+مننا لجطعنا الحجار بس by logic إذا الصورة مظبوطة و
+
+295
+00:19:19,240 --> 00:19:23,080
+الحجار مسفطة صح المفروض أنه أوجه أول واحد ال
+
+296
+00:19:23,080 --> 00:19:27,160
+initial تبعنا يجي أخر واحد فهد برضه موضوع هنتكلم
+
+297
+00:19:27,160 --> 00:19:29,740
+بتفاصيله بمواضيع و أنا حاولت بس يعني أعطيكوا هيك
+
+298
+00:19:29,740 --> 00:19:31,500
+الفكرة اللي توضح عن إيش بدنا نتكلم
+
+299
+00:19:34,810 --> 00:19:37,170
+recursion زى ما قلنا اللى هى من ال recurrence
+
+300
+00:19:37,170 --> 00:19:42,310
+التكرار عملية التكرار اللى ممكن نستفيد منها بدل
+
+301
+00:19:42,310 --> 00:19:45,330
+مجهود اكتب ال statement كذا مرة لأ بعملها for loop
+
+302
+00:19:45,330 --> 00:19:50,070
+او بعملها طريقة معينة بحيث ان هى اتحللنا الموضوع
+
+303
+00:19:50,070 --> 00:19:53,430
+بدون مجهود اكتب شغل كتير طيب الكلام ده دايما
+
+304
+00:19:53,430 --> 00:19:56,430
+بنستعمله نستعمله لما نتكلم عن algorithms فاحنا
+
+305
+00:19:56,430 --> 00:19:59,750
+هنتكلم عن ال algorithms ال algorithms هى هنتعامل
+
+306
+00:19:59,750 --> 00:20:06,920
+مع لغة وصفيةلغة برمجة لا هي C++ ولا هي Java بس في
+
+307
+00:20:06,920 --> 00:20:10,200
+النهاية هذه ال M بتاعت كلهم .. بتاعتهم كلهم ليش؟
+
+308
+00:20:10,200 --> 00:20:14,460
+لأنه هذه وصفية الكل متفق عليها اللي بيبرمج بال C++
+
+309
+00:20:14,460 --> 00:20:18,160
+و اللي بيبرمج بال Java و اللي بيبرمج بال Pascal
+
+310
+00:20:18,160 --> 00:20:21,680
+إيش ما تبرمجوا في النهاية الكل متعارف على اللغة
+
+311
+00:20:21,680 --> 00:20:25,550
+هذه بحيث إنه حتى في الأبحاث لما بدهم يوصفواال
+
+312
+00:20:25,550 --> 00:20:28,970
+actions اللى هو عملها عشان يحل task معين و بكتبها
+
+313
+00:20:28,970 --> 00:20:32,170
+باللغة اللى هنتعلمها اللى هي ال pseudo code ال
+
+314
+00:20:32,170 --> 00:20:36,570
+pseudo code بمعنى ال code شبيه ال code او ال code
+
+315
+00:20:36,570 --> 00:20:40,490
+الزائف انا بعمل عملية وصف له بعمل عملية وصف لل
+
+316
+00:20:40,490 --> 00:20:43,730
+actions اللى بدنا نعملها ايش بدنا نعمل عشان نحل
+
+317
+00:20:43,730 --> 00:20:48,360
+problem معينةال actions هذه بنرتبها بطريقة معينة
+
+318
+00:20:48,360 --> 00:20:50,820
+وممكن يكون فيها .. حيكون فيها for loop وحيكون فيها
+
+319
+00:20:50,820 --> 00:20:54,060
+كل ال conditions اللي احنا بنتعامل معها بس زي ما
+
+320
+00:20:54,060 --> 00:20:57,740
+اتقول .. زي ما قلتلكوا هتكون عبارة عن وصف لل code
+
+321
+00:20:57,740 --> 00:21:03,460
+مش له موجه لل C++ ولا Java ولا لأي language محددة
+
+322
+00:21:03,460 --> 00:21:07,180
+هو عملية وصف وشائعة و الكل بيستخدمها حتى لعندي
+
+323
+00:21:07,180 --> 00:21:11,140
+الآن في الأبحاث .. في الأبحاث العلمية بتستخدم ل ..
+
+324
+00:21:12,260 --> 00:21:15,040
+واصف ال problem بغض النظر عن إيش ال language اللي
+
+325
+00:21:15,040 --> 00:21:21,160
+استخدمته كويس هنكمل مع ال algorithms و نتكلم عن
+
+326
+00:21:21,160 --> 00:21:25,060
+حاجة مهمة جدا ال complexity ال complexity هيهمنا
+
+327
+00:21:25,060 --> 00:21:27,800
+من جميع .. في أنواع كتيرة من ال complexity اللي
+
+328
+00:21:27,800 --> 00:21:31,720
+هيهمنا منها إيش ال time complexity لإن احنا بيهمنا
+
+329
+00:21:31,720 --> 00:21:34,760
+ال time انتوا بتتعاملوا مع كمبيوتر مع بي سي ال بي
+
+330
+00:21:34,760 --> 00:21:39,400
+سي هذا لو واحدة منكوا عملت code والتانية عملت code
+
+331
+00:21:39,400 --> 00:21:44,390
+يحل نفس ال task و أناخيرتوني كشركة ك manager لشركة
+
+332
+00:21:44,390 --> 00:21:47,170
+و بدي أختار واحدة منكم طب بنها أنا هلاقيش بدي
+
+333
+00:21:47,170 --> 00:21:50,470
+أختارها هنفذ okay بتطلع نتيجة و هده بتطلع نتيجة
+
+334
+00:21:50,470 --> 00:21:53,950
+التنتين الكويسين بتطلعوا نتيجة بتصير الصراع أو
+
+335
+00:21:53,950 --> 00:21:58,090
+المفادلة في ال complexity بتاعة البرنامج في ال
+
+336
+00:21:58,090 --> 00:22:01,210
+complexity بتاعة البرنامج ال time complexity بدنا
+
+337
+00:22:01,210 --> 00:22:04,470
+نشوف إيش ال time complexity لهدا و إيش ال time
+
+338
+00:22:04,470 --> 00:22:07,210
+complexity لهدا كل ما زادت ال time complexity لأ
+
+339
+00:22:07,210 --> 00:22:11,140
+هذا مينفعنيش لأن هذا معناته بيكلفنا وقت زيادةزي
+
+340
+00:22:11,140 --> 00:22:15,800
+لما تجربوا مثلا antivirus معين اتلاقوه بسرعة بيخلص
+
+341
+00:22:15,800 --> 00:22:19,800
+طب antivirus تاني بتلاقوه موة الجهاز لأ كلنا هنسيب
+
+342
+00:22:19,800 --> 00:22:22,160
+أبو الموة الجهاز هذا لإنه صار بده جهاز مواصفات
+
+343
+00:22:22,160 --> 00:22:25,780
+معينة و صار بده .. بده gest لحاله لأ أنا جهاز
+
+344
+00:22:25,780 --> 00:22:28,700
+متواضع بدور على إيش؟ على ال time complexity بدور
+
+345
+00:22:28,700 --> 00:22:31,280
+على ال complexity الأقل عشان أشغل عليه أحط عليه
+
+346
+00:22:31,280 --> 00:22:35,260
+على جهازي فنفس الفكرة هننتب ال algorithm تبعنا ال
+
+347
+00:22:35,260 --> 00:22:37,540
+code تبعنا ال pseudocode اللي احنا بتكلم عنه و
+
+348
+00:22:37,540 --> 00:22:43,520
+هنحسبله ال time complexityOkay هنتكلم برضه هيك
+
+349
+00:22:43,520 --> 00:22:48,460
+شوية knowledge هناخدها بكمية محددة يعني مش هناخد
+
+350
+00:22:48,460 --> 00:22:52,400
+كتير فيها بس بكمية معقولة عن ال functions كنت
+
+351
+00:22:52,400 --> 00:22:55,360
+نتعامل مع ال functions عن ال number theory number
+
+352
+00:22:55,360 --> 00:22:58,200
+theory الارقام فعلا هنتكلم عن نظرية الأرقام و
+
+353
+00:22:58,200 --> 00:23:01,950
+الأعداد ال counting و الأرقام و الأعداد فعلاهنتكلم
+
+354
+00:23:01,950 --> 00:23:04,870
+عنا أرقام و حاجات انتوا هتحسوا انها بدائية ولكن
+
+355
+00:23:04,870 --> 00:23:08,110
+طريقة تناولنا هتختلف لو ان طريقة التناول مختلفة
+
+356
+00:23:08,110 --> 00:23:11,730
+شوية اللي هي تخدم المجال تبعنا تخدم انتوا كيف بكرا
+
+357
+00:23:11,730 --> 00:23:14,670
+هتكتبوا الأقوال بتاعتكم كويس هنتكلم عن ال counting
+
+358
+00:23:14,670 --> 00:23:20,710
+هنتكلم عن ال equivalence relations text book اللي
+
+359
+00:23:20,710 --> 00:23:23,750
+هنشتغل عليه الحقيقة ال text book اللي هنشتغل عليه
+
+360
+00:23:23,750 --> 00:23:32,650
+هو ال text book هذااللي هو خاص بمين؟ ب Kenneth
+
+361
+00:23:32,650 --> 00:23:35,890
+Rosen اللي هو discrete mathematics and its
+
+362
+00:23:35,890 --> 00:23:40,290
+applications ال version أو ال edition .. seventh
+
+363
+00:23:40,290 --> 00:23:44,990
+edition ال edition السابعة على الصينوهات الأحدث
+
+364
+00:23:44,990 --> 00:23:53,570
+أخر ال updated edition بتاعته أخر edition في 2012
+
+365
+00:23:53,570 --> 00:23:57,010
+في
+
+366
+00:23:57,010 --> 00:24:01,490
+2012 أتوقع هتكون مناسبة يعنيمواكب لل .. للتطور مش
+
+367
+00:24:01,490 --> 00:24:04,230
+مالهاش كتير يعني احنا بنتكلم عن سنتين زمان، يدوب
+
+368
+00:24:04,230 --> 00:24:07,610
+إليها سنتين زمان، ماعملش أي edition بعدها، لو عمل
+
+369
+00:24:07,610 --> 00:24:10,770
+edition بعدها كان لجو تونة جيبناها على طول اشتغلنا
+
+370
+00:24:10,770 --> 00:24:13,410
+عليها، لاحظوا الكتاب ملون و كويس يعني ال soft copy
+
+371
+00:24:13,410 --> 00:24:16,370
+اللي هتلاقوها عندكو هو هتكون حلو يعني ملونة و كتاب
+
+372
+00:24:16,370 --> 00:24:21,970
+كويس، كويس، بقدرش أقولكوا أنه الباجين مش
+
+373
+00:24:21,970 --> 00:24:24,930
+هيفيدوكوا، الباجين هيفيدوكوالو واحد بده يستزيد
+
+374
+00:24:24,930 --> 00:24:28,230
+ولكن بدنا مش كتير نشوشكه لإن ممكن مصطلحات تختلف
+
+375
+00:24:28,230 --> 00:24:31,370
+معانيها أو ال symbols أحيانا فخليني أقول إن هذا
+
+376
+00:24:31,370 --> 00:24:34,650
+الأساس و كل ال homework سبعتكوا هتكون من هنا أساسا
+
+377
+00:24:34,650 --> 00:24:38,730
+لإن في كمية exercises كويسة في شغل كويس يعني حتى
+
+378
+00:24:38,730 --> 00:24:42,570
+مراجعات تراجعوا أنتوا تحلوا لحالكوا homework
+
+379
+00:24:42,570 --> 00:24:48,210
+exercises تشتغلوا أكترموجودة، كل section هتلاقيه
+
+380
+00:24:48,210 --> 00:24:51,890
+في آخره في ال end of chapter أو ال end of section
+
+381
+00:24:51,890 --> 00:24:55,610
+كمية كبيرة جدا جدا جدا من ال exercises و كل
+
+382
+00:24:55,610 --> 00:24:59,910
+edition بيزود عليهم، كل edition بيزود عليهم، كويس
+
+383
+00:25:01,500 --> 00:25:04,460
+الباقي ان في حاجات كويسة الحقيقة لو واحد حابب
+
+384
+00:25:04,460 --> 00:25:07,220
+يستزيد في الموضوع discrete mathematics with
+
+385
+00:25:07,220 --> 00:25:09,800
+applications discrete mathematics and introduction
+
+386
+00:25:09,800 --> 00:25:13,260
+for software engineers ال .. ال essential discrete
+
+387
+00:25:13,260 --> 00:25:16,240
+mathematics الحقيقة في حاجات كويسة بس ان احنا
+
+388
+00:25:16,240 --> 00:25:19,680
+خلينا كويس في هذا اذا انتوا هتحسوا و اتلخبطوا و
+
+389
+00:25:19,680 --> 00:25:26,360
+هتحسوا حاجة ال .. ال textbook طبعنا كويس ال course
+
+390
+00:25:26,360 --> 00:25:31,170
+work او ال grades بتاعتنايمكن هذه الحاجة اللى
+
+391
+00:25:31,170 --> 00:25:34,990
+انتوا اهمش عندكم كنتوا تعرفوا طب احنا كويس هنفهم
+
+392
+00:25:34,990 --> 00:25:37,750
+المادة العلمية و هن .. طب كيف بدنا نتعامل معاها
+
+393
+00:25:37,750 --> 00:25:40,630
+درجات بدنا نشوف احنا جسمنا درجاتنا خلانا نعرف في
+
+394
+00:25:40,630 --> 00:25:44,910
+ايش .. و اين نركز و اين نسيب و اين .. اه طيب هنركز
+
+395
+00:25:44,910 --> 00:25:48,650
+كويس على ال assignments زى ما قلنا في حلول في
+
+396
+00:25:48,650 --> 00:25:52,570
+exercises بدنا نركز عليها هيكون عليها عشرة فلمية
+
+397
+00:25:52,570 --> 00:25:57,030
+في ال quizzes ال quizzes كان بيها اذا كان والله
+
+398
+00:25:57,030 --> 00:26:00,630
+لجنانا هيك مرة وجدنا فاضي حاجة قدرنا نخلصبس يمكن
+
+399
+00:26:00,630 --> 00:26:05,850
+مايتحلناش الوقت لإن المصاق شوية مليان رغم بساطته
+
+400
+00:26:05,850 --> 00:26:10,990
+بس طويل لإن في مفردات لازم نخلصها بس احنا في الآخر
+
+401
+00:26:10,990 --> 00:26:14,730
+بنتكلم عن numbers و counting و summation بس بدنا
+
+402
+00:26:14,730 --> 00:26:18,430
+نخلصهم فإذا قدرنا نعملنا نا quiz اتنين الباجي
+
+403
+00:26:18,430 --> 00:26:21,430
+هيكون عند المهندس ان شاء الله في ال discussion ..
+
+404
+00:26:21,430 --> 00:26:24,910
+في ال discussionفده عليها عشرة في المية برضه هتكون
+
+405
+00:26:24,910 --> 00:26:28,370
+في عندكم ال midterm تلاتين درجة و ال final exam
+
+406
+00:26:28,370 --> 00:26:34,830
+خمسين درجة okay بالنسبالنا ال impression الأول ال
+
+407
+00:26:34,830 --> 00:26:39,780
+first impressionabout you هو ال academic integrity
+
+408
+00:26:39,780 --> 00:26:43,840
+انه ال honest انه احنا الحمد لله ال integrity
+
+409
+00:26:43,840 --> 00:26:46,960
+عندنا عالية الاستقام عندنا عالية مش هيكون في غش مش
+
+410
+00:26:46,960 --> 00:26:49,940
+هيكون في .. و هذا ال .. زي ما قلنا ال first
+
+411
+00:26:49,940 --> 00:26:53,260
+impression عندنا ان شاء الله مايتغيرش و نرجو و انا
+
+412
+00:26:53,260 --> 00:26:58,860
+متأكد انه ان شاء الله مش هيتغير تمام؟ okay
+
+413
+00:27:00,130 --> 00:27:03,210
+نشوف ال schedule تبعنا ال schedule تبعنا إيش بدنا
+
+414
+00:27:03,210 --> 00:27:07,290
+نشتغل بالظبط و في أي sections هنلاقي المعلومة
+
+415
+00:27:07,290 --> 00:27:10,150
+بتاعتنا ال readings تبعتنا وين ممكن نقرأ عشان نقرأ
+
+416
+00:27:10,150 --> 00:27:13,210
+عن الموضوع هذا فالأسبوع الأول ده هيكون
+
+417
+00:27:13,210 --> 00:27:16,370
+introduction هنكون introduction على ال logic ال
+
+418
+00:27:16,370 --> 00:27:18,730
+logic الحاجات البسيطة إيش يعني logic إيش يعني and
+
+419
+00:27:18,730 --> 00:27:22,280
+or مش عارف إيش الأمور هذهحنتكلمها خلال أول أسبوع
+
+420
+00:27:22,280 --> 00:27:25,220
+وإن كان يمكن الأسبوع .. المحاضرة اليوم مش هيكون
+
+421
+00:27:25,220 --> 00:27:30,100
+فيه كتير إشي كبير في المادة أكتر من إنه هين مجرد
+
+422
+00:27:30,100 --> 00:27:33,080
+تعرف على المادة، احنا بنحاول نتعرف على المادة لسه
+
+423
+00:27:35,440 --> 00:27:39,860
+فهذه ممكن تكون في الأسبوع الأول ال first week
+
+424
+00:27:39,860 --> 00:27:46,180
+section number one point one أو point two بعد هيك
+
+425
+00:27:46,180 --> 00:27:50,460
+logic هنكمل فيها الأسبوع التاني ال proof الأسبوع
+
+426
+00:27:50,460 --> 00:27:52,960
+التالت الأسبوع الرابع ال sets و ال functions
+
+427
+00:27:52,960 --> 00:27:56,840
+الأسبوع الخامس summation and matrices الأسبوع
+
+428
+00:27:56,840 --> 00:27:59,760
+السادس ال algorithms هنتكلم عن ال algorithms و زي
+
+429
+00:27:59,760 --> 00:28:04,460
+ما قلنا ال complexity تبعتهthe order of growth كيف
+
+430
+00:28:04,460 --> 00:28:09,420
+ممكن يتطور بتطور بناء على ال input سبعته هندرس
+
+431
+00:28:09,420 --> 00:28:13,200
+فيها حاجات كويسة طيب في الأسبوع السابع هنتكلم عن
+
+432
+00:28:13,200 --> 00:28:17,560
+ال integers و ال number theory هنتكلم برضه الأعداد
+
+433
+00:28:17,560 --> 00:28:21,280
+الصحيحة و نظرية الأرقام أو نظرية الأعداد نظرية
+
+434
+00:28:21,280 --> 00:28:24,600
+الأرقام كويسة ال induction و ال recursion في
+
+435
+00:28:24,600 --> 00:28:27,440
+الأسبوع التامن الأسبوع التاسع هيكون عادة برضه
+
+436
+00:28:27,440 --> 00:28:32,390
+هنبدأ في ال countingو هيكون ال mid-term هيكون ال
+
+437
+00:28:32,390 --> 00:28:36,850
+mid-term في الأسبوع التاسع ان شاء الله تعالى كويسة
+
+438
+00:28:36,850 --> 00:28:39,890
+الأسبوع العاشر و الاحداشر هتلاقي انه استمرارا لميل
+
+439
+00:28:39,890 --> 00:28:42,770
+ال counting برضه يعني برضه في نظرية العد هنظرنا ..
+
+440
+00:28:42,770 --> 00:28:46,230
+هنضلنا شغالين في ال counting او في عملية العد
+
+441
+00:28:46,230 --> 00:28:51,190
+بتاعتنا طيب هنتكلم عن ال advanced counting على
+
+442
+00:28:51,190 --> 00:28:53,730
+أسبوعين يعني عندنا تلت أسابيع هنشتغل counting
+
+443
+00:28:53,730 --> 00:28:57,830
+هنشتغل counting بعدك في ال relationsإيش ال
+
+444
+00:28:57,830 --> 00:29:00,670
+relation بين function و التانية؟ كيف ممكن أعبر؟
+
+445
+00:29:00,670 --> 00:29:04,050
+إيش العلاقة بين هذه و هذه؟ إيش ال .. ال .. هنتكلم
+
+446
+00:29:04,050 --> 00:29:08,610
+عنه كتير فيها تفاصيل برضه بعدك ال graphs كيف أعبر
+
+447
+00:29:08,610 --> 00:29:11,570
+عن ال graph؟ إيش ال elements اللي ممكن أوصف فيها
+
+448
+00:29:11,570 --> 00:29:17,050
+graph معين؟ graph و كيف نوصفه؟ و من وصف كيف أرسم
+
+449
+00:29:17,050 --> 00:29:20,050
+ال graph؟ يعني هنتعلم شوية حاجات طبعا احنا مش
+
+450
+00:29:20,050 --> 00:29:23,810
+بدرور نكون أخد .. ناخد كل التفاصيل بس على الأقل ال
+
+451
+00:29:23,810 --> 00:29:27,680
+concept يكون صار موجود عندنانوع من أنواع ال graphs
+
+452
+00:29:27,680 --> 00:29:31,060
+زي ما قلنا ليه trees، برضه هنتكلم في عجلة يمكن
+
+453
+00:29:31,060 --> 00:29:34,100
+عليها، هناخد شوية حاجات خفيفة عليها، بعد هيكون
+
+454
+00:29:34,100 --> 00:29:37,390
+فينا أسبوع ان شاء الله يعني ما ي ..ما .. ما نتأخرش
+
+455
+00:29:37,390 --> 00:29:40,350
+هنا و يدخل على الأسبوع الخمسة عشر نضطر ناخد في
+
+456
+00:29:40,350 --> 00:29:43,030
+الأسبوع الخمسة عشر بيكون فينا revision ال revision
+
+457
+00:29:43,030 --> 00:29:48,610
+هذا أنا مش هحسه من الآن في تلاتة powerpoint files
+
+458
+00:29:48,610 --> 00:29:51,430
+جاهزين هتكون revision على كل المصاق بحيث أن
+
+459
+00:29:51,430 --> 00:29:54,170
+الأسبوع هذا إذا كان أمكن يعني و ان شاء الله تعالى
+
+460
+00:29:54,170 --> 00:30:00,110
+ما يكونش أتأخرنا دخلت عليه ال .. باقى المفردات
+
+461
+00:30:00,110 --> 00:30:04,510
+بناخده و بنعمل مراجعة على كل السابق يكون قبل
+
+462
+00:30:04,510 --> 00:30:07,690
+الامتحان ان شاء الله تعالىالاسبوع السبتاشر طبعا
+
+463
+00:30:07,690 --> 00:30:11,890
+خلصوه ال final .. ال final exam في المقابل هتلاقوا
+
+464
+00:30:11,890 --> 00:30:18,290
+أنه أسبوعيا في عندكم assignment assignments .. في
+
+465
+00:30:18,290 --> 00:30:22,890
+أسبوعيا عندنا assignments أسبوع هسلمكم، أسبوع اللي
+
+466
+00:30:22,890 --> 00:30:26,290
+ورا هسلم و هسلم اللي ورا هسلم ال assignment التاني
+
+467
+00:30:26,290 --> 00:30:28,350
+هنسلم و هسلم ال assignment التاني هنسلم و هنسلم
+
+468
+00:30:28,350 --> 00:30:35,410
+ليش؟ عشان نضمن إيدكوا نحركهاإيدكوا ال brain و ال
+
+469
+00:30:35,410 --> 00:30:38,610
+arm تبعتكوا موصولين البعض لما تشوف السؤال على طول
+
+470
+00:30:38,610 --> 00:30:41,950
+أه إيش اللي بيطلع من هنا الإيد الطاوعي بدناش إيها
+
+471
+00:30:41,950 --> 00:30:48,490
+تجف بدنا إيها دائما مطوع .. مطوع ال brain تمام ما
+
+472
+00:30:48,490 --> 00:30:50,910
+زلنا فيه؟ لاحظوا zero يعني ما زلنا في introduction
+
+473
+00:30:50,910 --> 00:30:54,570
+ما زلنا نتكلم عن overview للمصاب مجرد إنه بدنا
+
+474
+00:30:54,570 --> 00:30:58,570
+نتكلم ملوجة عن إيش يعني إيش mathematics؟خلّينا قبل
+
+475
+00:30:58,570 --> 00:31:02,470
+ما نبدأ مدام احنا اصلا الموضوع هنا فيه شوية فلسفة
+
+476
+00:31:02,470 --> 00:31:06,130
+انه بدنا نفهم كل المعلومات السابقة اللي احنا
+
+477
+00:31:06,130 --> 00:31:12,350
+عارفينها بس بطريقة تتماشى مع الأكواد ومع خدمة ال
+
+478
+00:31:12,350 --> 00:31:14,830
+courses اللي جاية طب خلّينا احنا من الأساس نبدأ من
+
+479
+00:31:14,830 --> 00:31:18,450
+الأول ايش يعني mathematics اصلا؟ لما بقول
+
+480
+00:31:18,450 --> 00:31:23,960
+mathematics ايش يعني؟ لأ هي مش numbersالكل بيجي
+
+481
+00:31:23,960 --> 00:31:26,660
+على باله ان هي الأرقام ان انا بتتعامل مع أرقام اه
+
+482
+00:31:26,660 --> 00:31:29,480
+هذه العلم الجاف هذا تبع الأرقام لأ هو مش الأرقام
+
+483
+00:31:29,480 --> 00:31:33,240
+حقيقتا هي أكثر من مجرد ان انا بتعامل مع numbers
+
+484
+00:31:33,240 --> 00:31:37,260
+ببساطة ال mathematics in general the study of any
+
+485
+00:31:37,260 --> 00:31:42,600
+and all absolutely certain truths about any and
+
+486
+00:31:42,600 --> 00:31:47,180
+all perfectly well defined concepts ايش يعني؟
+
+487
+00:31:47,180 --> 00:31:54,750
+بمعنى انهأي شئ له قيمة مطلقة ومعرف بصورة جيدة يدخل
+
+488
+00:31:54,750 --> 00:31:59,870
+مع الرياضيات كل شئ له قيمة حقيقية له قيمة حقيقة
+
+489
+00:31:59,870 --> 00:32:05,350
+false مش مشكلة المهم انه له قيمة حقيقة trueفليكن
+
+490
+00:32:05,350 --> 00:32:08,010
+true or false المهم أنه إله قيمة بقدر أحكم عليه
+
+491
+00:32:08,010 --> 00:32:13,310
+حقيقي و غير حقيقي فإذا إله قيمة لأي شيء معرف بصورة
+
+492
+00:32:13,310 --> 00:32:18,770
+جيدة well-defined concepts concept معرف بصورة جيدة
+
+493
+00:32:18,770 --> 00:32:21,670
+أنا ضمن أن تعريفه أصلا صح عشان أقدر أحكم عليه صح
+
+494
+00:32:21,670 --> 00:32:25,270
+هو معرف بصورة جيدة فبقدر أحكم عليه بصورة جيدة أي
+
+495
+00:32:25,270 --> 00:32:29,130
+شيء ضمن هذا التعريف فهو mathematics هو mathematics
+
+496
+00:32:29,130 --> 00:32:32,470
+mathematics الحقيقة هذا الكلام ينطبق على الأعداد
+
+497
+00:32:32,470 --> 00:32:36,560
+باعتبار أن واحد okay هو واحدبس خدوا بالكم هو واحد
+
+498
+00:32:36,560 --> 00:32:43,460
+.. إيش يعني واحد؟ واحد نسبيا بالنسبة لصفر أنا حاطه
+
+499
+00:32:43,460 --> 00:32:46,260
+في ال brain تبعي .. في المخ احنا كلنا اتفقنا أنه
+
+500
+00:32:46,260 --> 00:32:49,320
+صفر يعني ولا إشي معناته لما بقول واحد هو بالنسبة
+
+501
+00:32:49,320 --> 00:32:54,100
+للصفر لما بقول مية .. مية بالنسبة للصفر فهي كل شيء
+
+502
+00:32:54,100 --> 00:32:59,890
+نسبي .. كل شيء نسبيتمام؟ كويس فإذا ال numbers okay
+
+503
+00:32:59,890 --> 00:33:02,870
+بقدر أقول إن هي بالنسبالي لواحد أه يعني مسافة
+
+504
+00:33:02,870 --> 00:33:06,390
+بعيدة متر مثلا عن النقطة الفلانية فإذا لازم أكون
+
+505
+00:33:06,390 --> 00:33:10,150
+عنده نقطة فلانية ال reference تبعي لحظو أرقام أه
+
+506
+00:33:10,150 --> 00:33:13,250
+بس أنا لازم أكون عارف إن هي reference لشيء أو يعني
+
+507
+00:33:13,250 --> 00:33:17,590
+هي نسبة لشيء لما بقول عندي تلاتة متر تلاتة متر
+
+508
+00:33:17,590 --> 00:33:20,850
+بدنا ن bullet هم طب وين بالظبط؟ اعطيني ال
+
+509
+00:33:20,850 --> 00:33:22,870
+reference تبعي عشان أعرف أمشي تلاتة متر هنا ولا
+
+510
+00:33:22,870 --> 00:33:25,760
+أمشي خمسة متر ولا ..فدائما في عندنا reference رقم
+
+511
+00:33:25,760 --> 00:33:31,080
+لحاله بكفيش، كويس، فإذا ال numbers هي جزء من ال
+
+512
+00:33:31,080 --> 00:33:35,400
+mathematics، ال symbols، ال objects، objects مجرد
+
+513
+00:33:35,400 --> 00:33:38,760
+إن في عندي objects، ال object هذا ممكن أي حاجة
+
+514
+00:33:38,760 --> 00:33:43,370
+بقدر أقول إنه إيه قيمةالو truth value حقيقي او غير
+
+515
+00:33:43,370 --> 00:33:47,590
+حقيقي بمعنى true or false اي شغلة طول ما احنا
+
+516
+00:33:47,590 --> 00:33:50,570
+ماشيين بدا انا بقدر اقولها true or false و هناخدها
+
+517
+00:33:50,570 --> 00:33:54,050
+في أول محاضرة تعناها كل شيء بقدر اعطيه قيمة زي ما
+
+518
+00:33:54,050 --> 00:34:01,550
+قلنا اليوم الصبح جيت على الجامعة okay true لاحظوا
+
+519
+00:34:01,550 --> 00:34:05,010
+مع ان انا ماقلتش أي رقم انا قاعد بقول proposition
+
+520
+00:34:05,010 --> 00:34:06,570
+.. proposition
+
+521
+00:34:08,650 --> 00:34:11,810
+فمدام إله قيمة حقيقة فهو خلاص بدخل معاه في
+
+522
+00:34:11,810 --> 00:34:17,950
+الرياضيات بدخل في الرياضيات okay ال objects زي ما
+
+523
+00:34:17,950 --> 00:34:21,890
+قلنا ال images الصور تدخل مع الرياضيات ال sounds
+
+524
+00:34:21,890 --> 00:34:26,390
+anything كالحقيقة أي شيء إله قيمة حقيقة إله حقيقة
+
+525
+00:34:26,390 --> 00:34:30,970
+و واقعية و معرّف بصورة جيدة و إله قيمة حقيقة يعني
+
+526
+00:34:30,970 --> 00:34:34,390
+أنا بقدر أحكم عليه إنه هذا true or false فإذن هو
+
+527
+00:34:34,390 --> 00:34:36,270
+قابل إنه يدخل في الرياضيات
+
+528
+00:34:43,570 --> 00:34:46,810
+شوف ال sound في الآخر انت بتقدر تحكم عليه ليش؟ لأن
+
+529
+00:34:46,810 --> 00:34:51,710
+هو عبارة عن object محدد فانت بتقدر تقول ال sound
+
+530
+00:34:51,710 --> 00:34:56,270
+هي ده ال sound تبع فلان أو تبع اللان يعني إيه قيمة
+
+531
+00:34:56,270 --> 00:35:00,450
+محددة؟ انت مجرد ما صرت بما بتسمع مثلا صوت التليفون
+
+532
+00:35:00,450 --> 00:35:06,830
+اه كيف حالك يا فلانة؟ صح؟ طب كيف عرفتي؟ صار في
+
+533
+00:35:06,830 --> 00:35:11,130
+عندك truth value اعطت القيمة او حد مثلا يتصل فيك
+
+534
+00:35:11,130 --> 00:35:16,600
+انا صاحبتك فلانةبس لأ مش صوتك اه انت عندك ال .. ال
+
+535
+00:35:16,600 --> 00:35:19,700
+.. ال indication اللي صار عندك انه لأ فيه false
+
+536
+00:35:19,700 --> 00:35:25,760
+فأي قيمة بما فيها ال sounds حتى الأصوات الصور اما
+
+537
+00:35:25,760 --> 00:35:30,100
+انك تقول true or false فبنان عليها بتتحدد هذي
+
+538
+00:35:30,100 --> 00:35:32,460
+صحيحة ولا مش صحيحة في ال images لو اتكلمنا في ال
+
+539
+00:35:32,460 --> 00:35:38,180
+images هذي جزئية true or false في ال image فتحتلنا
+
+540
+00:35:38,180 --> 00:35:43,250
+مجال كبير جدا في حاجة اسمها ال image retrievalفي
+
+541
+00:35:43,250 --> 00:35:45,610
+حاجة اسمها ال image retrieval لما بتدخلوا على ال
+
+542
+00:35:45,610 --> 00:35:50,570
+google و بتدخلوا على image و بتكتبوا أي حاجة و
+
+543
+00:35:50,570 --> 00:35:53,490
+بروح بجيبلكوا كل الصور اللي لها علاقة بالموضوع هذا
+
+544
+00:35:53,490 --> 00:35:57,050
+طب ما هو قاعد بقارن images يعني أنا بشتغل على
+
+545
+00:35:57,050 --> 00:36:00,270
+images الكلام هذا اتطور اكتر ان انا لأ انا بعطيه
+
+546
+00:36:00,270 --> 00:36:03,670
+صورة و بخليه يدورلي على الصور اللي زيها طب ما هي
+
+547
+00:36:03,670 --> 00:36:05,430
+نفس الفكرة يعني انتوا صارتوا بتتكلموا عن ال
+
+548
+00:36:05,430 --> 00:36:08,610
+mathematicsنجلنا الموضوع لمثاماتكس رغم ان انتوا
+
+549
+00:36:08,610 --> 00:36:12,350
+شايفينها images و sounds لأ إلهم علاقة مدام أنا
+
+550
+00:36:12,350 --> 00:36:15,090
+بدرس في علم زى هذا كله إله علاقة مدام بدنا نبرمج
+
+551
+00:36:15,090 --> 00:36:17,430
+computer و بدنا نشتغل فيه بده يكون له formula
+
+552
+00:36:17,430 --> 00:36:21,330
+واضحة okay
+
+553
+00:36:21,330 --> 00:36:24,730
+هذه المثاماتكس طب احنا لأ احنا جزء من المثاماتكس
+
+554
+00:36:24,730 --> 00:36:28,790
+هندرسه اسمه discretediscrete بالصورة هذه مش
+
+555
+00:36:28,790 --> 00:36:33,630
+بالصيغة هذه هذه يمكن رغم ان هي بتنطق نفس الشيء
+
+556
+00:36:33,630 --> 00:36:39,710
+معناها شوية جاي على حذر او يعني حذر بحكمة يعني انه
+
+557
+00:36:39,710 --> 00:36:42,870
+حذر او اشي لأ احنا مش .. مش .. نكتوبهاش بالشكل هذا
+
+558
+00:36:42,870 --> 00:36:45,150
+بنكتوبها بالشكل هذا ال discrete معناها منفصلة
+
+559
+00:36:45,150 --> 00:36:50,170
+منفصل او متقطع منفصل او متقطع فهي مش الحالة okay
+
+560
+00:36:50,170 --> 00:36:56,380
+هي عبارة عنأو مؤلفة من مجموعة distinct حاجات
+
+561
+00:36:56,380 --> 00:37:01,440
+منفصلة حاجات مميزة منفصلة فهي عبارة عن parts أو
+
+562
+00:37:01,440 --> 00:37:04,820
+separable parts زي ما قلنا أي إشي عبارة عن parts
+
+563
+00:37:04,820 --> 00:37:08,640
+بقدر أعبّر عنه parts بقدر أقول إن هو discrete طيب
+
+564
+00:37:08,640 --> 00:37:14,200
+خلينا ناخد مثال كويس واضح لما نقول بدنا مصورة بدنا
+
+565
+00:37:14,200 --> 00:37:17,400
+نشتري مصورة مصورة ميه بدنا نركبها هنا أو باربيش
+
+566
+00:37:18,160 --> 00:37:21,380
+هلوجت للبربيش لما بدي أروح للسباق، إيش بدي أقوله؟
+
+567
+00:37:21,380 --> 00:37:26,440
+بدي أقوله بدي بربيش، هقولي قداش؟ هقوله يا نص انش،
+
+568
+00:37:26,440 --> 00:37:30,340
+يا تلت اربعة، يا انش، بنفعش أقوله والله اعطيني
+
+569
+00:37:30,340 --> 00:37:35,120
+فاصلة تمانية انش، هقولي مش موجود، فإذا احنا بنتكلم
+
+570
+00:37:35,120 --> 00:37:39,020
+عن discrete، ال parts اللي موجودة فعلا منه يا كذا
+
+571
+00:37:39,020 --> 00:37:42,960
+يا كذا يا كذابنفعش تقولي و الله أي شي بعطيك ..
+
+572
+00:37:42,960 --> 00:37:45,740
+تروح و تشتري و لمبة هيقولك و الله فيه اتنين و
+
+573
+00:37:45,740 --> 00:37:47,300
+تلاتين .. فيه سبتة عشرين فيه اتنين و تلاتين وات
+
+574
+00:37:47,300 --> 00:37:49,840
+وفيه مش عارف كده بتقولي لأ و الله انا بدي تلاتين و
+
+575
+00:37:49,840 --> 00:37:55,700
+نص مافيش تلاتين و نص فإذا ال product نفسه discrete
+
+576
+00:37:55,700 --> 00:37:59,760
+المجموعة ال items تبعته اللي متوفرة هي discrete يا
+
+577
+00:37:59,760 --> 00:38:03,920
+كذا يا كذا هي parts اختاروا ال parts اللي بتكوينها
+
+578
+00:38:03,920 --> 00:38:10,730
+منها فهذه فكرة عن إيش يعني discrete تماماللي هي ال
+
+579
+00:38:10,730 --> 00:38:15,330
+separable parts فإذا انت بتتعامل معها discrete هي
+
+580
+00:38:15,330 --> 00:38:19,010
+العبارة عن a discrete opposite لمين continuous
+
+581
+00:38:19,010 --> 00:38:24,110
+كويسة continuous احنا عارفين انه تتعاملوا مع حاجة
+
+582
+00:38:24,110 --> 00:38:28,930
+مستمرة و خلينا نجربكوا شوية انتوا متعودين على ال
+
+583
+00:38:28,930 --> 00:38:36,410
+signal ال signal عادة مفترض حاجة بهذا الشكل هذه
+
+584
+00:38:36,410 --> 00:38:40,650
+continuous مستمرة لاحظوامن الالف لأ من .. يعني
+
+585
+00:38:40,650 --> 00:38:44,250
+خلينا نقول من الصفر هنا لأ T جد ما تكون T هي
+
+586
+00:38:44,250 --> 00:38:48,790
+مستمرة بمعنى أي time between zero و T عند أي time
+
+587
+00:38:48,790 --> 00:38:52,450
+بقدر أعرف قيمة ال .. ال function بالضبط عند أي
+
+588
+00:38:52,450 --> 00:38:59,530
+time anytime أنا بختاره تمام؟ و ممكن أدل اللي
+
+589
+00:38:59,530 --> 00:39:03,510
+براحتي أقول والله عند واحد فاصلة صفر صفر اتنين
+
+590
+00:39:03,510 --> 00:39:07,750
+تلاتة خمسة second okay؟هذه continuous انطق حرار
+
+591
+00:39:07,750 --> 00:39:10,590
+اعمل اللي بتجيبه اللي .. فعلا بتجيبه القيمة بالظبط
+
+592
+00:39:10,590 --> 00:39:14,210
+اللي بتجيبها كويس هذه العكس تبعها ان انا اقول
+
+593
+00:39:14,210 --> 00:39:20,410
+discrete discrete بمعنى انه لأ انا عند قيم parts
+
+594
+00:39:20,410 --> 00:39:26,430
+بس كل فترة و فترة كل زمن باخد sample بنسميها
+
+595
+00:39:26,430 --> 00:39:31,990
+فبتصير هنا discrete لاحظوا كل فترة بناخدلنا قيمة
+
+596
+00:39:31,990 --> 00:39:35,190
+صار عندي discrete فصارت المنظر بهذا الشكل
+
+597
+00:39:43,830 --> 00:39:50,310
+لحظة .. خلاص هذه discrete .. samples .. parts ..
+
+598
+00:39:50,310 --> 00:39:53,030
+مجموعة parts positive negative مش ليست .. بس في
+
+599
+00:39:53,030 --> 00:39:57,950
+النهاية مجموعة parts .. كويس .. هذه discrete ..
+
+600
+00:39:57,950 --> 00:40:01,350
+طيب تماما في عندكوا حاجة اسمها digital مقابل ال
+
+601
+00:40:01,350 --> 00:40:06,270
+analog طيب .. هل في فرق بين ال discrete و ال
+
+602
+00:40:06,270 --> 00:40:12,290
+digital؟ اه في فرق .. ال discrete ممكن يتكون
+
+603
+00:40:12,290 --> 00:40:17,600
+analogوممكن تكون digital طيب كيف؟ هالواجهة اللي
+
+604
+00:40:17,600 --> 00:40:22,540
+قدامي هنا لعند اللحظة هذه هي analog هي discrete أه
+
+605
+00:40:22,540 --> 00:40:26,840
+بس في النهاية analog ليش analog؟ هي عبارة عن parts
+
+606
+00:40:26,840 --> 00:40:31,220
+في ال time بس في ال amplitude ما زالت continuous
+
+607
+00:40:31,220 --> 00:40:34,820
+ما زالت continuous بمعنى أنه جداش ال amplitude
+
+608
+00:40:34,820 --> 00:40:39,040
+جداش قيمة كل level من هدوله أنا ماحددتش ماعملتش
+
+609
+00:40:39,040 --> 00:40:45,030
+parts إله بياخد أي قيمة analogهذا هيك analog كويس
+
+610
+00:40:45,030 --> 00:40:49,870
+لكن لو حددنا وقلنا والله بديها تلاتة levels او
+
+611
+00:40:49,870 --> 00:40:58,390
+اربعة levels فرضا بالشكل هذا هذا حتى هيك صارت خمسة
+
+612
+00:40:58,390 --> 00:41:01,490
+احنا بقى صفر واحد اتنين تلاتة اخليها على جد تلاتة
+
+613
+00:41:01,490 --> 00:41:06,440
+عساس انه اقرب لحاجة موجودة فعلالو أخدنا بالشكل هذا
+
+614
+00:41:06,440 --> 00:41:10,160
+ال levels هذه كل قيمة من هدولا بتجربها لل level
+
+615
+00:41:10,160 --> 00:41:14,260
+تبعها فبتصير القيمة أول قيمة هنا صفر واحد اتنين
+
+616
+00:41:14,260 --> 00:41:21,300
+تلاتة كأن هنا بقول ايش واحد اتنين تلاتة تلاتة
+
+617
+00:41:21,300 --> 00:41:26,140
+تلاتة تلاتة خليني أقول هذه أقل من النص شويه اتنين
+
+618
+00:41:26,140 --> 00:41:35,010
+واحد لحظه هذه هيك digitalبس لاحظوا digital quad
+
+619
+00:41:35,010 --> 00:41:41,410
+رباعي ال binary أنا بتكلم عن ثنائي بس two levels
+
+620
+00:41:41,410 --> 00:41:45,590
+عندي هنا لأ quad أنا عندي أربعة levels فانا بجرب
+
+621
+00:41:45,590 --> 00:41:49,990
+القيم تبعتي ال amplitude بجربه لأربع قيم خلاص quad
+
+622
+00:41:49,990 --> 00:41:53,750
+هذا ال quad system أما لما أقول binary لأ أنا
+
+623
+00:41:53,750 --> 00:41:57,930
+بجربه لأ يا صفر يا واحد هقول يا صفر يا واحد اسمها
+
+624
+00:41:57,930 --> 00:42:03,070
+binaryby اللي هو الثنائي فهي نفس القصة اسمها صارت
+
+625
+00:42:03,070 --> 00:42:07,930
+إيش؟ digital فلاحظوا هذه إشي وهذه إشي واضحة هنا
+
+626
+00:42:07,930 --> 00:42:11,250
+واضحة صار في عندي ال discrete هي مقابل ال
+
+627
+00:42:11,250 --> 00:42:13,410
+continuous okay ليش؟ لأننا بتكلم عن time
+
+628
+00:42:13,410 --> 00:42:16,550
+continuous في ال time لأ بديش يا continuous في ال
+
+629
+00:42:16,550 --> 00:42:21,530
+time صارت discreteanalog في ال amplitude بتاخد أي
+
+630
+00:42:21,530 --> 00:42:26,190
+قيم بتهييها analog okay digital لأ بحدد لها levels
+
+631
+00:42:26,190 --> 00:42:29,910
+ال levels دي بناء على جداش عدد ال levels بتغير إيش
+
+632
+00:42:29,910 --> 00:42:32,610
+المصطلح اللي بدي أستعمله لو هي عبارة عن two levels
+
+633
+00:42:32,610 --> 00:42:38,790
+فقط اسمها binary ثنائي باي باي كويس quad بنجسم زي
+
+634
+00:42:38,790 --> 00:42:41,770
+هيك مثلا أربعة هذا طبعا لو افترض أنه مافيش
+
+635
+00:42:41,770 --> 00:42:44,150
+negative عساس أنه ال negative أحيانا بياخدله بال
+
+636
+00:42:44,150 --> 00:42:48,100
+digit هو التاني لحاله تمام؟هذه مفهوم بسيط هنا هذا
+
+637
+00:42:48,100 --> 00:42:50,380
+على الهامش يعني زي ما بقوله بس عشان تكونوا انتوا
+
+638
+00:42:50,380 --> 00:42:56,640
+عارفين ايش المصطلحات اللي احنا بنحكيها هذه ممكن مش
+
+639
+00:42:56,640 --> 00:42:59,240
+داخلة كتير في المصادق عنا بس مدام ان ذكرت تكونوا
+
+640
+00:42:59,240 --> 00:43:03,500
+عارفين تميزوهم يعني هتمر عليكم كتير لجدام هتمر
+
+641
+00:43:03,500 --> 00:43:05,840
+عليكم يمكن في ال signal يمكن في ال .. يعني هتمر
+
+642
+00:43:05,840 --> 00:43:11,660
+عليكم في ال DSP يمكن .. كويس خلاص
+
+643
+00:43:11,660 --> 00:43:14,240
+اتفقنا انه discrete معناته ان انا بتعامل مع parts
+
+644
+00:43:14,600 --> 00:43:17,380
+صار في عندكوا هلوقت بعدين structures ال structures
+
+645
+00:43:17,380 --> 00:43:22,100
+هي عبارة عن objects built up from similar objects
+
+646
+00:43:22,100 --> 00:43:26,760
+according to some definite pattern definite
+
+647
+00:43:26,760 --> 00:43:29,180
+pattern اللي هو عبارة عن قالب محدد يعني بيرونه
+
+648
+00:43:29,180 --> 00:43:36,120
+بناء على operation محددة بقى بنى مجموعةال parts
+
+649
+00:43:36,120 --> 00:43:39,840
+الصغيرة هذه مجموعة ال parts الصغيرة هذه اللي كل
+
+650
+00:43:39,840 --> 00:43:44,520
+واحدة لحالها إلها truth value ببنيهم بطريقة معينة
+
+651
+00:43:44,520 --> 00:43:49,280
+مع بعض بطلعولي structure ببنيهم كيف؟ عن طريق ال
+
+652
+00:43:49,280 --> 00:43:54,260
+logic gates اللي انتخبتوهم الروابط and أو or أو
+
+653
+00:43:54,260 --> 00:43:56,500
+whatever يعني زي لما أقول والله أنا جيت اليوم
+
+654
+00:43:56,500 --> 00:43:59,040
+الصبح على الجامعة okay الناس كلها شفتني جيت على
+
+655
+00:43:59,040 --> 00:44:05,610
+الجامعة فإذا true true الدنيا بتشتيfalse ممكن
+
+656
+00:44:05,610 --> 00:44:08,750
+اقوله انا عشت اليوم على الجامعة و الدنيا بتشتي هذا
+
+657
+00:44:08,750 --> 00:44:11,770
+ال structure صار له قيمة truth value مختلفة شوية
+
+658
+00:44:11,770 --> 00:44:20,110
+او or مثلا الدنيا بتشتي لحظه او ان الدنيا بتشتي
+
+659
+00:44:20,110 --> 00:44:23,910
+هيك صارت ال true فهنتكلم شوي شوي عن ال operations
+
+660
+00:44:23,910 --> 00:44:29,770
+هذه كيف ممكن تحكم اللي على ال structure ككل ال
+
+661
+00:44:29,770 --> 00:44:32,610
+truth value تبعته هتظل true ولا هتروح ل false او
+
+662
+00:44:32,610 --> 00:44:37,620
+العكس هنشوففإذا في حاجة اسمها structure بتبنى من
+
+663
+00:44:37,620 --> 00:44:42,680
+مجموعة parts صغيرة okay discrete mathematics
+
+664
+00:44:42,680 --> 00:44:48,380
+الحقيقة يعني هو بيدرس discrete the study of
+
+665
+00:44:48,380 --> 00:44:51,780
+discrete mathematical objects and structures فإذا
+
+666
+00:44:51,780 --> 00:44:55,660
+إحنا بندرس فيه ال parts ال objects الصغيرة و ال
+
+667
+00:44:55,660 --> 00:44:58,870
+structuresالحاجات اللى هنبنيها منها من ال objects
+
+668
+00:44:58,870 --> 00:45:02,150
+هذه فإذا ال object الجزء الصغير ال part الواحد
+
+669
+00:45:02,150 --> 00:45:05,450
+اللى بقدر اعبر عنه انه ال truth value تبعته ايش
+
+670
+00:45:05,450 --> 00:45:08,870
+بالظبط و هنجمحهم مع بعض عشان يعطينا structure
+
+671
+00:45:08,870 --> 00:45:13,510
+التنتين الحقيقة بنشتغل فيهم مع ال discrete تبعنا
+
+672
+00:45:13,510 --> 00:45:19,290
+في ال course تبعنا في discrete structures تلاحظوا
+
+673
+00:45:19,290 --> 00:45:24,030
+structures وين ممكن نشوفها في خلال ال course تبعنا
+
+674
+00:45:24,030 --> 00:45:27,530
+هنشوفها في ال propositionsهنشوفها في ال predicates
+
+675
+00:45:27,530 --> 00:45:30,050
+ال predicates دي على فكرة هي برضه proposition ولكن
+
+676
+00:45:30,050 --> 00:45:34,030
+بتكون معتمدة شوية على ال situation على ال
+
+677
+00:45:34,030 --> 00:45:36,950
+situation اللي احنا بنشتغل فيه لإن ممكن ال truth
+
+678
+00:45:36,950 --> 00:45:40,670
+value تعتمد على situation معين تعتمد على variable
+
+679
+00:45:40,670 --> 00:45:45,630
+معين تعتمد على شغلة معينة إذا اتحققت true ماتحققتش
+
+680
+00:45:45,630 --> 00:45:49,990
+false أو العكس أو العكس فهذه بتدخل شوية في
+
+681
+00:45:49,990 --> 00:45:55,690
+predicatesممكن تاخد طبعا زي ال function تكون إليها
+
+682
+00:45:55,690 --> 00:45:59,530
+أكثر من .. تكون عبارة عن variable انعرفها، كويس ال
+
+683
+00:45:59,530 --> 00:46:02,630
+proofs هنتكلم برضه فيها بتدخل فيها ال structures
+
+684
+00:46:02,630 --> 00:46:07,130
+ال sets ال functions ال orders of growth هذه إليها
+
+685
+00:46:07,130 --> 00:46:11,410
+علاقة بال algorithm عساس انه منها بنحسب ال
+
+686
+00:46:11,410 --> 00:46:14,410
+complexity ال complexity أو ال time complexity
+
+687
+00:46:14,410 --> 00:46:19,480
+تحديداال integers, summations, sequences, strings
+
+688
+00:46:19,480 --> 00:46:22,640
+ال permutations و ال combinations هدول انتوا
+
+689
+00:46:22,640 --> 00:46:26,820
+ماخدينها من قبل هيك تحت مسمة تبديل و توافق مرت
+
+690
+00:46:26,820 --> 00:46:30,620
+عليكوا لاحظوا احنا هناخدها برضه بس المصطلح صار
+
+691
+00:46:30,620 --> 00:46:34,440
+جديد عليكوا شوية أخدناها بلغة مختلفة هناخدها برضه
+
+692
+00:46:34,440 --> 00:46:37,980
+نفس المعادلة اللي مرت عليكوا هنرجع ناخدها بس طبعا
+
+693
+00:46:37,980 --> 00:46:42,240
+هناخدها بال notations العالمية بال notations
+
+694
+00:46:42,240 --> 00:46:45,920
+العالمية اللي تستخدم في كل العالمrelations,
+
+695
+00:46:46,400 --> 00:46:50,340
+graphs, trees برضه في ال circuits عادة انتوا في ال
+
+696
+00:46:50,340 --> 00:46:52,840
+logic circuits و في ال .. في الدوائر يعني في
+
+697
+00:46:52,840 --> 00:46:59,100
+الدوائر و في الأتمة في ال tomato بتستخدم برضه ال
+
+698
+00:46:59,100 --> 00:47:02,100
+structures هذه أو اللي هي الأتمة أتمة الأشياء في
+
+699
+00:47:02,100 --> 00:47:05,500
+ال control بيعملوا حاجة automatic بيسموها أتمة
+
+700
+00:47:05,500 --> 00:47:10,100
+أتمتوها يعني خلوها تصير automatic okay بعض ال
+
+701
+00:47:10,100 --> 00:47:13,920
+notations اللي على أخر الفصل هتكون كل هدولة بتعرف
+
+702
+00:47:13,920 --> 00:47:17,390
+تقرؤهمكل واحدة من هدولة هي عبارة عن .. عن جملة
+
+703
+00:47:17,390 --> 00:47:20,090
+يعني، بتعطيكوا معنى، كل واحدة من هدولة بتعطيكوا
+
+704
+00:47:20,090 --> 00:47:24,570
+معنى المفروض، فاحنا أسبوع أسبوع، شوية شوية، هناخد
+
+705
+00:47:24,570 --> 00:47:27,290
+.. كل مرة هناخد واحدة منهم و هنتكفي، هنتعامل
+
+706
+00:47:27,290 --> 00:47:28,690
+معاها، دي إيش معناها، دي إيش معناها، دي إيش
+
+707
+00:47:28,690 --> 00:47:30,430
+معناها، دي إيش معناها، دي إيش معناها، دي إيش
+
+708
+00:47:30,430 --> 00:47:36,370
+معناها، دي إيش معناها، دي إيش معناها، دي إيش
+
+709
+00:47:36,370 --> 00:47:38,390
+معناها، دي إيش معناها، دي إيش معناها، دي إيش
+
+710
+00:47:38,390 --> 00:47:44,130
+معناها، دي إيش معناها، ديOkay طيب من كل اللي قلنا
+
+711
+00:47:44,130 --> 00:47:47,110
+ليش انا بتدرس discrete mathematics؟ ال course
+
+712
+00:47:47,110 --> 00:47:49,730
+تبعنا احنا ليش بدنا ندرسه؟ الحقيقة اللي هندرسه لأن
+
+713
+00:47:49,730 --> 00:47:52,550
+هو ال structure الأساسية او discrete structures هي
+
+714
+00:47:52,550 --> 00:47:55,670
+ال .. ال .. ال .. الأساس في representation لل
+
+715
+00:47:55,670 --> 00:47:59,590
+memory ال memory بتاعتكم هي عبارة عن discrete
+
+716
+00:47:59,590 --> 00:48:03,290
+أساسا ال memory discrete عارفين اللي هو
+
+717
+00:48:03,290 --> 00:48:07,170
+continuous؟يعني الاصل ان هي بتقدر تخزن لنا
+
+718
+00:48:07,170 --> 00:48:12,050
+infinity information او infinity data وهي طبعا
+
+719
+00:48:12,050 --> 00:48:15,470
+مستحيل عشان هي كل اللي بيقدر يطوره انه بيزوده في
+
+720
+00:48:15,470 --> 00:48:19,190
+السرعات زود السرعة زود الساعات زود مش عارف ايش كل
+
+721
+00:48:19,190 --> 00:48:22,250
+ما بيزوده في السرعة ايش معناها؟ معناته اه ال
+
+722
+00:48:22,250 --> 00:48:26,190
+samples بتاعتنا هذه بيجللوا المسافة بين كل sample
+
+723
+00:48:26,190 --> 00:48:31,180
+و التانيةبيجلوا المسافة بيزيد ال rate زادت السرعة
+
+724
+00:48:31,180 --> 00:48:34,820
+فجاعدين بيزودوا في السرعات من هذا المنطلق بس اما
+
+725
+00:48:34,820 --> 00:48:38,020
+انك تقولولي تصل لمرحلة انه infinity معناته انه
+
+726
+00:48:38,020 --> 00:48:42,480
+المسافة بين هنا لهنا zero وهذه صعبة جدا لان بيصير
+
+727
+00:48:42,480 --> 00:48:46,200
+بدنا infinity ال size بتاعتنا بيقدروا يطوروا اه
+
+728
+00:48:46,200 --> 00:48:49,760
+لعن سرعات محددة نتكلم عن ال جيجا سرنا نسمع عن ال
+
+729
+00:48:49,760 --> 00:48:52,620
+وجيت يمكن صارت تيرة بالنسبة لل hard disks زارت
+
+730
+00:48:52,620 --> 00:48:56,300
+شوية شوية بس في النهاية احنا محكمين مازلنا مازلنا
+
+731
+00:48:56,300 --> 00:49:04,050
+محكمينOkay الحقيقة بندرسها لأنها ال basic language
+
+732
+00:49:04,050 --> 00:49:07,370
+لكل ال computer science لكل علوم ال computer
+
+733
+00:49:07,370 --> 00:49:13,150
+science بندرسها لأن ال concept ساعتها widely used
+
+734
+00:49:13,150 --> 00:49:16,270
+في ال mathematics في ال science في ال engineering
+
+735
+00:49:16,270 --> 00:49:19,950
+في ال economics في ال biology كل العلوم في معظم
+
+736
+00:49:19,950 --> 00:49:22,730
+العلوماللي صارت بتدخل في ال computer .. في ال
+
+737
+00:49:22,730 --> 00:49:26,210
+computerization صار كلها معتمدة على جزئية ال
+
+738
+00:49:26,210 --> 00:49:30,090
+discrete مش ان انا مابينها طيب حقيقة هي ال tool
+
+739
+00:49:30,090 --> 00:49:34,650
+الأهم لل rational .. لل rational thought، للتفكير
+
+740
+00:49:34,650 --> 00:49:39,470
+العقليلما نيجي نتكلم عن المنطق و عن objects و كيف
+
+741
+00:49:39,470 --> 00:49:42,510
+علاقتهم البعض فهذا بيقودنا للتفكير العقلي ايش ال
+
+742
+00:49:42,510 --> 00:49:45,810
+.. ال .. ان اعمل prove لحاجة مع حاجة اعمل relation
+
+743
+00:49:45,810 --> 00:49:48,390
+بين حاجة و تانية اعمل equivalence ان والله
+
+744
+00:49:48,390 --> 00:49:50,970
+بيكافؤوا بعض ولا بيكافؤوش بعض و اعتقد انه يمكن
+
+745
+00:49:50,970 --> 00:49:54,050
+برضه انتوا كنتوا تاخدوها يمكن في الرياضيات لما
+
+746
+00:49:54,050 --> 00:49:57,630
+تيجي تعملوا الجزء اليمين هل يساوي اليسار او لأ
+
+747
+00:49:57,630 --> 00:50:00,210
+يعني ال .. ال .. ال right side و ال left side
+
+748
+00:50:00,210 --> 00:50:03,290
+equal ولا لأ و إثبتواكنتوا بتعملوا تجدوا بتعملوا
+
+749
+00:50:03,290 --> 00:50:05,950
+into proofs و بتجدوا تثبته أكيد مرت عليكوا في
+
+750
+00:50:05,950 --> 00:50:08,650
+examples كتيرة أوي يعني في عينات ..امتحانات كتيرة
+
+751
+00:50:08,650 --> 00:50:13,870
+بالشكل هذا تمام فبتقودنا لل rational thought أو
+
+752
+00:50:13,870 --> 00:50:18,010
+التفكير العقلاني okay discrete mathematics في ال
+
+753
+00:50:18,010 --> 00:50:21,890
+computer science وين ممكن تفيدنا؟ لأ هي بتفيد كتير
+
+754
+00:50:21,890 --> 00:50:26,240
+لأنه مبني عليها كل العلوم التانية اللي قادمةفي ال
+
+755
+00:50:26,240 --> 00:50:31,060
+.. ال computer science ال algorithms ال data
+
+756
+00:50:31,060 --> 00:50:34,180
+structures أتوقع ال data structure يمكن يكون الفصل
+
+757
+00:50:34,180 --> 00:50:37,720
+الجاي أو السنة اللي بعده هتاخدوا data structures
+
+758
+00:50:37,720 --> 00:50:44,160
+ال .. ال برمجة ال compilers ال computer networks
+
+759
+00:50:44,160 --> 00:50:48,590
+هتاخدوها لاحقا برضه معتمدة على فكرة discreteال
+
+760
+00:50:48,590 --> 00:50:51,870
+operating systems ال computer architecture ال
+
+761
+00:50:51,870 --> 00:50:55,790
+database ال cryptography هناخد على فكرة ال
+
+762
+00:50:55,790 --> 00:50:59,090
+cryptography هناخد برضه طريقة طريقتين هيك عملية
+
+763
+00:50:59,090 --> 00:51:03,190
+التشفير هنتعلم برضه و احنا بنتكلم عن ال counting و
+
+764
+00:51:03,190 --> 00:51:06,110
+الأرقام ال numbers كيف ممكن انا اعمل تشفير لها
+
+765
+00:51:06,110 --> 00:51:11,270
+فهذه الطرق البدائية هنتكلم عنها التشفير هنفهم بس
+
+766
+00:51:11,270 --> 00:51:13,370
+ان هو ال concept تكون عارفين انه إيش يعني تشفير
+
+767
+00:51:13,370 --> 00:51:16,610
+لأن انتوا لاحقا هتاخدوها في مصادقات كتيرالمفروض
+
+768
+00:51:16,610 --> 00:51:21,530
+تمر عليكم زائد error correction codes كيف عملية
+
+769
+00:51:21,530 --> 00:51:24,750
+إصلاح ال code تبعتنا بطريقة automatic يعني بتصير
+
+770
+00:51:24,750 --> 00:51:29,630
+برمجية graphics و ال graphics بتشمل معاكمان ال
+
+771
+00:51:29,630 --> 00:51:32,570
+animation algorithms هذا كله هيقودنا لمين إذا كنت
+
+772
+00:51:32,570 --> 00:51:35,650
+بتتكلم عن graphics و عن animation على ال games و
+
+773
+00:51:35,650 --> 00:51:39,810
+صناعة ال gamesوشغل ال .. ال .. ال .. ال computer
+
+774
+00:51:39,810 --> 00:51:42,870
+engineers في جزئيتي ال games و الحاجات هذه برضه
+
+775
+00:51:42,870 --> 00:51:45,930
+بنبدأ مدام أنا بدي من الأساس أعرف إيش يعني graphs
+
+776
+00:51:45,930 --> 00:51:49,470
+و بدنا نشتغل عليها فإذا هتخدمنا في المجال الحقيقة
+
+777
+00:51:49,470 --> 00:51:52,650
+لو اطلعتوا هتلاقيوا أنها هتخدمكم في كل ال .. ال
+
+778
+00:51:52,650 --> 00:51:58,770
+field تبع ال computer science طيب بناخد جزئية
+
+779
+00:51:58,770 --> 00:52:03,300
+أخيرة هيك مجرد يعني زي ما بقوله exampleأو هيك
+
+780
+00:52:03,300 --> 00:52:06,740
+refreshment نغير شوية ناخد حاجة من الحاجات اللي
+
+781
+00:52:06,740 --> 00:52:10,520
+لها علاقة بال rational thought ل Pythagorean
+
+782
+00:52:10,520 --> 00:52:18,080
+theorem او Pythagoras اللي هو سميه احنا ايه في ..
+
+783
+00:52:18,080 --> 00:52:21,140
+في ثغورث في ثغورث كيف فكر في نظرية تبعته؟ عارفين
+
+784
+00:52:21,140 --> 00:52:28,670
+نظريته؟ اللي هي تحت المثلث قائم الزاويةاحنا بدنا
+
+785
+00:52:28,670 --> 00:52:33,850
+نشوف طريقة كيف الراجل فكر مع أنه إله آلاف سنين بس
+
+786
+00:52:33,850 --> 00:52:37,610
+فكر فيها بطريقة معينة proved معينة ده مجرد example
+
+787
+00:52:37,610 --> 00:52:39,770
+يعني لاها داخل معانا في امتحان ولا إشي مجرد أنه بس
+
+788
+00:52:39,770 --> 00:52:42,910
+بدنا نعطيكوا هيكي نغيرلكوا شوية حاجة أنتوا
+
+789
+00:52:42,910 --> 00:52:47,050
+عارفينها فنشوف هو كيف أثبتها نشوف كيف أثبتها تغيير
+
+790
+00:52:47,050 --> 00:52:53,450
+للجو الراجل كله اللي جاله أنه لو في عندنا مثلث
+
+791
+00:52:53,450 --> 00:53:00,870
+قائم الزاويةاللي هو right triangle عندنا وين اللي
+
+792
+00:53:00,870 --> 00:53:06,870
+سماها a و b تحت سماها a و b القاعدة عنده a ال
+
+793
+00:53:06,870 --> 00:53:11,270
+height أو الارتفاع تبعه b فمعنى ذلك ال water تبعه
+
+794
+00:53:11,270 --> 00:53:16,170
+بيقدر يحسبه c عن طريق equation سماها c squared
+
+795
+00:53:16,170 --> 00:53:21,370
+بتساوي a squared plus b squared من وين؟ من وين
+
+796
+00:53:21,370 --> 00:53:25,700
+جابها؟ هو ماعندهش إلا معلومة واحدةبس إن المربع
+
+797
+00:53:25,700 --> 00:53:31,240
+مساحته الطول في العرض من معلومة واحدة إن المربع
+
+798
+00:53:31,240 --> 00:53:34,780
+مساحته طول في العرض جابلنا النظرية طلّحها كيف
+
+799
+00:53:34,780 --> 00:53:41,940
+طلّحها طلّحها بطريقة كتير بسيطة الطريقة تبعته إن
+
+800
+00:53:41,940 --> 00:53:47,000
+هو من المثلث هذا ركّبهم في بعض أربع أربع مثلث أربع
+
+801
+00:53:47,000 --> 00:53:50,960
+مثلثات في بعض ركّبهم بطريقة معينة بحيث أنه طلعوا
+
+802
+00:53:50,960 --> 00:53:52,560
+الشكل الشكل هذا
+
+803
+00:53:56,220 --> 00:53:59,080
+هو جاعد بلعب عملها على ورجة و اللي عملها زمان على
+
+804
+00:53:59,080 --> 00:54:02,600
+صخرة يمكن جاعد ينحد في الصخرة و جاعد يظبط فيهم و
+
+805
+00:54:02,600 --> 00:54:05,320
+يرسمها على الأرض جاعد رسمهم و يظبطوا مع بعض طلع
+
+806
+00:54:05,320 --> 00:54:08,180
+الشكل هذا طيب لاحظوا زي ما قلنا هو ماعندهش معلومة
+
+807
+00:54:08,180 --> 00:54:12,680
+إلا مين مساحة مربع إذا لاحظ هيك أنه طب الدليل هذا
+
+808
+00:54:12,680 --> 00:54:15,320
+هو نفسه الدليل هذا هو نفس هذا نفس هذا فإذا أنا
+
+809
+00:54:15,320 --> 00:54:22,940
+عندي مربع مربع مساحته C تربيع طول في العرض طب
+
+810
+00:54:22,940 --> 00:54:27,160
+الطول في العرض بيساوي بعضفإذن بيسوّبوا طيب لو
+
+811
+00:54:27,160 --> 00:54:31,840
+مسكنا المثلث هذا وكملناه
+
+812
+00:54:31,840 --> 00:54:41,260
+برضه هيه شكل رباعي عبارة عن إيش A هيها A في B فإذن
+
+813
+00:54:41,260 --> 00:54:48,520
+مساحته المربع A B طيب نصه لحظة أن انت جسمته بالنص
+
+814
+00:54:48,520 --> 00:54:50,480
+نص
+
+815
+00:54:52,760 --> 00:54:55,140
+صحيح؟ فإذا أنتوا بتتكلموا عن المساحة الخضراء اللي
+
+816
+00:54:55,140 --> 00:55:01,140
+تحت هنا تمام
+
+817
+00:55:01,140 --> 00:55:08,880
+طيب الأربع مساحات في أربعة مظبوط طيب كويس إيش
+
+818
+00:55:08,880 --> 00:55:13,420
+العلاقة بين هذا وهذا لأ لسه بيساويش بعض في المساحة
+
+819
+00:55:13,420 --> 00:55:16,360
+اللي في النص اللي أنا سايبها هذه طيب خلينا نشوف
+
+820
+00:55:16,360 --> 00:55:23,300
+المساحة اللي في النص الدليع هذا كلهB طيب اتضلع هذا
+
+821
+00:55:23,300 --> 00:55:31,320
+لحاله A فإذا إيش اللي ضال منه؟ و نفس الكلام هنا
+
+822
+00:55:31,320 --> 00:55:37,400
+فإذا برضه A minus B واحد طول واحد عرض و ضربهم في
+
+823
+00:55:37,400 --> 00:55:43,140
+بعض صارت تربيع هذا الجزء المفروض ينطرح من هذا أو
+
+824
+00:55:43,140 --> 00:55:47,760
+ينجمع على هذا عشان يطلعلنا هذا صحيح فمجرد يجمعهم
+
+825
+00:55:47,760 --> 00:55:53,690
+مع بعضالرجل جمحهم مع بعض لحظة كل اللي عمله كله انه
+
+826
+00:55:53,690 --> 00:55:57,710
+بس عارف ان المربع طول في عرض طول في عرض طول في عرض
+
+827
+00:55:57,710 --> 00:56:03,050
+بس ماعندهش معلومة لا هيك طلع منها نظرية فإذا هذه
+
+828
+00:56:03,050 --> 00:56:08,230
+زائد الطول في العرض D minus A تربيع اللي هي مساحة
+
+829
+00:56:08,230 --> 00:56:14,210
+الجزء الجزء الأخر هذا المفروض هذا يساوي C هذه
+
+830
+00:56:14,210 --> 00:56:19,650
+هفكها عملية فك بتفكوها نغسط 2A
+
+831
+00:56:23,480 --> 00:56:29,760
+B-A تربيع وهذه الطبعا اتنين بتصير فانتوا عندكوا
+
+832
+00:56:29,760 --> 00:56:33,220
+الجزر هذا مع الجزر هذا فلاحظوا C تربيع ايش صارت
+
+833
+00:56:33,220 --> 00:56:37,060
+بتساوي من
+
+834
+00:56:37,060 --> 00:56:38,800
+ايش؟ من معلومة بسيطة انا عارف ان هال logic انتوا
+
+835
+00:56:38,800 --> 00:56:41,760
+بتقدروا تثبتوها بنظريات اعقد من هيك بس هو على وقت
+
+836
+00:56:41,760 --> 00:56:44,100
+ماكانش النظريات هذه موجودة ماكانش عنده معلومة
+
+837
+00:56:44,100 --> 00:56:49,050
+واحدةماكنش عنده إلا معلومة واحدة بس اللي هو طول في
+
+838
+00:56:49,050 --> 00:56:52,030
+العرض بيعطينا مساحة الشكل الرباعي وهذه كانت بسيطة
+
+839
+00:56:52,030 --> 00:56:55,830
+جدا برضه من discrete كانت وصلهم ببساطة جدا ليش؟
+
+840
+00:56:55,830 --> 00:57:01,410
+لأن لو كرتونة البيض جداش
+
+841
+00:57:01,410 --> 00:57:05,090
+طولها في عرضها أكان بيضة بالطول و أكان بيضة في
+
+842
+00:57:05,090 --> 00:57:09,430
+العرض اه معناته اضرب هدي في هدي بتعطينا كل عدد
+
+843
+00:57:09,430 --> 00:57:13,780
+البيض المساحةنظرية كانت بسيطة ومعروفة من زمان منها
+
+844
+00:57:13,780 --> 00:57:17,840
+طلّع نظرية لعند الآن مازالوا بيشتغلوا عليها و
+
+845
+00:57:17,840 --> 00:57:20,580
+بيدرسوا عليها و بقايمة عليها نظريات الإنشاءات و
+
+846
+00:57:20,580 --> 00:57:26,440
+الأعمدة و الشغل كله في العلم الهندسي يعني أو في ال
+
+847
+00:57:26,440 --> 00:57:30,660
+geometry ال science تبعتنا تمام كل اللي مكتوب هنا
+
+848
+00:57:30,660 --> 00:57:34,200
+الشرح اللي احنا بس قلناه مجرد انه طول في عرض في
+
+849
+00:57:34,200 --> 00:57:39,840
+إشة هذه مجرد هيك زي ما بقول تمهيدلحاجات من اللي
+
+850
+00:57:39,840 --> 00:57:41,960
+هناخدها انه نظريات معروفة احنا عارفين انها
+
+851
+00:57:41,960 --> 00:57:47,160
+النظريات دي بدنا نثبتها بطريقة مبسطة بطريقة مبسطة
+
+852
+00:57:47,160 --> 00:57:49,720
+عشان لما نوصلها لنا نعمل برنامج نعمل إيش تكون
+
+853
+00:57:49,720 --> 00:57:52,820
+لأمور واضحة المرة الجاية ان شاء الله بندخل ..
+
+854
+00:57:52,820 --> 00:57:56,660
+بنبدأ في مين؟ في ال foundations of logic من المرة
+
+855
+00:57:56,660 --> 00:58:00,240
+الجاية بنبدأ في المسار طبعا فالمرة الجاية هنبدأ
+
+856
+00:58:00,240 --> 00:58:04,600
+لحظه لسه من أول section من أول section اليوم كانت
+
+857
+00:58:04,600 --> 00:58:09,630
+مجرد مقدمة لل .. لل ..لل course، عن إيش بدنا
+
+858
+00:58:09,630 --> 00:58:13,010
+نتكلم، عن إيش بيحتوي ال course، إيش أهمية ال
+
+859
+00:58:13,010 --> 00:58:15,810
+course، مش أكتر و إيه هيك زي ما بيقولوا في الآخر
+
+860
+00:58:15,810 --> 00:58:18,530
+example تغيير جوة و هيك في الآخر حاجة أنتوا
+
+861
+00:58:18,530 --> 00:58:23,530
+عارفينها نعملها إثبات و خلصنا شغلنا بالشكل هذا
+
+862
+00:58:23,530 --> 00:58:25,690
+لهذه المحاضرة فبنشوفكوا ان شاء الله المحاضرة
+
+863
+00:58:25,690 --> 00:58:30,750
+الجاية في نفس المعهد في نفس الأسبوع ليوم التلاتة
+
+864
+00:58:30,750 --> 00:58:31,770
+ان شاء الله تعالى أعطيكوا الله عفيا
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2b9d98581e9b8f4b953f3f86897e4920be9280fb
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_postprocess.srt
@@ -0,0 +1,2356 @@
+1
+00:00:18,880 --> 00:00:20,860
+بسم الله الرحمن الرحيم والصلاة والسلام علي أشرف
+
+2
+00:00:20,860 --> 00:00:23,240
+الأنبياء والمرسلين سيدنا محمد وعلى أليه وصحبه ليه
+
+3
+00:00:23,240 --> 00:00:27,900
+أجمعين بعد العيد كل عام تبخير ان شاء الله بنبدأ
+
+4
+00:00:27,900 --> 00:00:31,660
+اليوم في موضوع جديد ان شاء الله تعالى بعد ما خلصنا
+
+5
+00:00:31,660 --> 00:00:34,320
+ال propositions وخلصنا ال quantifications وخلصنا
+
+6
+00:00:34,320 --> 00:00:37,760
+ال quantifiers أخدناها و أخدنا ال predicate و ال
+
+7
+00:00:37,760 --> 00:00:42,940
+propositional function و خلصنا كل الشغل تبعنا وهنا
+
+8
+00:00:42,940 --> 00:00:48,000
+حددنالكم ال homework الجايان شاء الله تعالى اللي
+
+9
+00:00:48,000 --> 00:00:53,080
+هتسلموا يوم الأحد القادم، اليوم بنبدأ مع ال proofs
+
+10
+00:00:53,080 --> 00:00:58,840
+أو ال proof methods، ال proof methods فبنبدأ مع ال
+
+11
+00:00:58,840 --> 00:01:03,990
+.. ال proof method كطريقة رياضيةأو methods of
+
+12
+00:01:03,990 --> 00:01:08,870
+mathematical argument نقاش جدال ل .. بنسميها
+
+13
+00:01:08,870 --> 00:01:12,870
+approved methods can be formalized in terms of
+
+14
+00:01:12,870 --> 00:01:18,270
+rules of logical inference هذه عبارة عن .. عن
+
+15
+00:01:18,270 --> 00:01:22,790
+مجموعة statements بتبتها عن طريق logical inference
+
+16
+00:01:22,790 --> 00:01:26,850
+أو استدلالات منطقية الاستدلالات المنطقية هنعرفها
+
+17
+00:01:26,850 --> 00:01:30,050
+لقدام هنقول ان هي مجموعة patterns قوالب ثابتة
+
+18
+00:01:30,050 --> 00:01:34,590
+قوانينقوانين إنتوا لما كنتوا تثبتوا شغلة بتدوروا
+
+19
+00:01:34,590 --> 00:01:37,670
+إذا في قوانين تثبتها بتدوروا على القوانين و
+
+20
+00:01:37,670 --> 00:01:40,470
+بتحاولوا تطبقوا القانون اللي بتبدأوا تشتغلوا هنقول
+
+21
+00:01:40,470 --> 00:01:44,610
+الله let مثلا R اللي هي المقاومة بيثوي كذا بيثوي
+
+22
+00:01:44,610 --> 00:01:51,110
+كذا let ال volt بيثوي كذا then .. لحظة .. then I
+
+23
+00:01:51,110 --> 00:01:54,250
+ال current equal to كذا من وين جبته equal to كذا
+
+24
+00:01:54,250 --> 00:01:59,730
+هذه؟ من قانون Ohm فإذا في .. في ruleفي انكو rule
+
+25
+00:01:59,730 --> 00:02:05,350
+أثبتتوا منها جداش قيمة المقاومة أو ال current من
+
+26
+00:02:05,350 --> 00:02:12,350
+معلومتين سابقات جداش قيمة ال R and جداش قيمة ال
+
+27
+00:02:12,350 --> 00:02:17,550
+volt صح؟ تمام احنا مش هنشتغل اكتر من هيك اكتر من
+
+28
+00:02:17,550 --> 00:02:20,030
+هيك مش هنشتغل هاي اللي بدنا نشتغله وهي اللي بدنا
+
+29
+00:02:20,030 --> 00:02:25,560
+نعمله طرق أثباتنا هنشتغل بطريقتينطريقتين مرادفات
+
+30
+00:02:25,560 --> 00:02:28,600
+لبعض ولكن التنتين بيشتغلوا .. التنتين بنفعوا، كل
+
+31
+00:02:28,600 --> 00:02:31,860
+واحدة إلها حالات اللي ماشتغل فيها، إما إن أنا
+
+32
+00:02:31,860 --> 00:02:37,320
+أحاول أثبت ال .. ال correct لل conclusion صحة
+
+33
+00:02:37,320 --> 00:02:43,260
+الاستنتاج اللي بدي أثبته هذه الطريقة أو العكسأو
+
+34
+00:02:43,260 --> 00:02:49,140
+خطأ عكسها او خطأ عكسها و هنشوف لأن في حالات كتير
+
+35
+00:02:49,140 --> 00:02:53,560
+ممكن ماجدرش انا اثبت الشغل مباشرة فبضطر اشوف ايش
+
+36
+00:02:53,560 --> 00:02:57,500
+عكسها يمكن عكسها يكون اسهل اثباته فلو اثبتت ان
+
+37
+00:02:57,500 --> 00:03:04,400
+عكسها false فإذا هي true فهذه ال methods هنتكلم
+
+38
+00:03:04,400 --> 00:03:08,370
+عنها او ال technology هنتكلم عنها فيال .. ال
+
+39
+00:03:08,370 --> 00:03:12,650
+proves تمام شوية terminology بس قبل ما نبدأ نشتغل
+
+40
+00:03:12,650 --> 00:03:16,770
+شوية مصطلحات .. شوية مصطلحات بدنا نشتغل عليها ال
+
+41
+00:03:16,770 --> 00:03:19,410
+theorem ال theorem هي statement .. a statement
+
+42
+00:03:19,410 --> 00:03:23,810
+that has been proven to be true هي فعليا statement
+
+43
+00:03:23,810 --> 00:03:30,390
+عبارة تم إثبات صحتها هي في البلد تم إثبات صحتها
+
+44
+00:03:30,600 --> 00:03:34,360
+فإذا إذا كان فعلا ال statement اللي موجودة عندي أو
+
+45
+00:03:34,360 --> 00:03:38,900
+relation معينة علاقة معينة proposition معين اقدرت
+
+46
+00:03:38,900 --> 00:03:43,100
+أثبت إن هو true دائما أنا عملت نظرية أو أثبت نظرية
+
+47
+00:03:43,100 --> 00:03:48,140
+أثبت theorem أثبتنا ال theorem بتاعتنا حاجة تانية
+
+48
+00:03:48,140 --> 00:03:53,520
+برضه ال axioms بديهيات في حاجات أحيانا عشان نثبت
+
+49
+00:03:53,520 --> 00:03:57,450
+شغلة أنا محتاج معلومة مسبقةالمعلومة المسبقة قد
+
+50
+00:03:57,450 --> 00:04:01,490
+تكون أحد الأربعة اللي هنتكلم عنها اليوم، قد تكون
+
+51
+00:04:01,490 --> 00:04:08,890
+axioms أو بديهيات، قد تكون postulates أو
+
+52
+00:04:08,890 --> 00:04:16,090
+مسلمات، شيء مسلم فيه، ممكن تكون hypothesis، فرضيات
+
+53
+00:04:16,090 --> 00:04:20,170
+أو premises، معطيات
+
+54
+00:04:22,810 --> 00:04:26,270
+طيب ال axioms خلاص احنا عارفين ان هي ال .. او
+
+55
+00:04:26,270 --> 00:04:29,990
+البديهيات شئ معروف و بديهي ممكن يكون مثبت و ممكن
+
+56
+00:04:29,990 --> 00:04:33,230
+مايكونش مثبت و هنتكلم عن تعريف شغل مش مثبتة إيش
+
+57
+00:04:33,230 --> 00:04:36,970
+ممكن نعرفها يعني ف .. بس هي بديهيات دائما صحيحة
+
+58
+00:04:36,970 --> 00:04:40,910
+مسلمات شئ مسلم فيه معلومة مسلم فيها بقدر مباشرة
+
+59
+00:04:40,910 --> 00:04:44,190
+أبدأ منها و أشتغل نبدأ منها .. ال .. ال hypothesis
+
+60
+00:04:44,190 --> 00:04:49,270
+أو ال .. الفرضيات بنفرض شغل و انتوا دايما في
+
+61
+00:04:49,270 --> 00:04:53,880
+أثبتاتكوا كنتوا تستعملوهادائما بتبدأ let كذا
+
+62
+00:04:53,880 --> 00:04:58,260
+assume كذا فرضية بتفرضوا شغلها مش بضروري ان هي
+
+63
+00:04:58,260 --> 00:05:02,720
+دائما صح بس بتفرضوها بتفرضوا الاثبات تبعكوا لحالة
+
+64
+00:05:02,720 --> 00:05:06,680
+خاصة و بعدين بتعمموها مظبوط فانتوا دائما بتبدأ let
+
+65
+00:05:06,680 --> 00:05:11,120
+assume that و بتحطوا الفرضية بتاعتكم بتحطوا
+
+66
+00:05:11,120 --> 00:05:14,180
+الفرضية فانتوا بتبدأوا بمعلومة فعليا فيها فرضية ال
+
+67
+00:05:14,180 --> 00:05:20,440
+premises لأ ال premises معطية زي لما أقولكوا إذاال
+
+68
+00:05:20,440 --> 00:05:22,800
+form الفلاني او ال statement الفلانية is true
+
+69
+00:05:22,800 --> 00:05:26,820
+اثبتلي ان ال form الفلانية is true فإذا انا
+
+70
+00:05:26,820 --> 00:05:30,480
+اعطيتكوا حاجة انتوا مش مجبرين تثبتوها حاجة انا
+
+71
+00:05:30,480 --> 00:05:33,360
+بقولكوا والله given انا معطية هاي بدي اعطيكوا معطة
+
+72
+00:05:33,360 --> 00:05:37,540
+اذا كان ال .. ال .. ال proposition الفلاني true
+
+73
+00:05:37,540 --> 00:05:42,040
+اثبتولي كذا انه ال true هل هو دائما هذا مش اشي
+
+74
+00:05:42,040 --> 00:05:47,500
+مسلم فيه لأ مش مسلم فيه ولا هي فرضية ولا هي شئ
+
+75
+00:05:47,500 --> 00:05:51,600
+بديهي هي حاجة givenفهذه بيسميها premises بقولكوا
+
+76
+00:05:51,600 --> 00:05:57,040
+إذا كان صار كذا فإذا كذا وهذه عادة الجزئية اللي
+
+77
+00:05:57,040 --> 00:06:01,080
+دايما بتشتغل فيها في F then في جزئية F then كويسة
+
+78
+00:06:01,080 --> 00:06:05,220
+فإذا في عندى theorem وفي عندى مجموعة المقدمات لل
+
+79
+00:06:05,220 --> 00:06:08,120
+theorem عشان F بال theorem معينة و بعدين في عندنا
+
+80
+00:06:08,120 --> 00:06:12,070
+بين الاتنينال techniques اللى بدى استخدمها ال
+
+81
+00:06:12,070 --> 00:06:14,390
+rules اللى بدى استخدمها القوانين اللى لازم
+
+82
+00:06:14,390 --> 00:06:18,050
+أستعملها القوانين هذه بنسميها rules of inference
+
+83
+00:06:18,050 --> 00:06:24,490
+أو قواعد الاستدلال قواعد الاستدلال inference او
+
+84
+00:06:24,490 --> 00:06:31,450
+استدلال فبدى أستدل على معلومة من وجود مقطة معينة
+
+85
+00:06:31,450 --> 00:06:34,190
+مش بالضرورة ان ال theorem اللى بدى اشتغل عليها
+
+86
+00:06:34,190 --> 00:06:38,110
+مباشرة هكون بدى استدلال واحد وخلص إذا كان صار كذا
+
+87
+00:06:38,110 --> 00:06:41,690
+معناته اه هي النتيجة كذالأ انتوا هتحتاجوا اكتر من
+
+88
+00:06:41,690 --> 00:06:44,870
+rule فهذه اللي اسمها rules هي عبارة عن patterns
+
+89
+00:06:44,870 --> 00:06:50,150
+عبارة عن قالب ثابت قانون بتكون تستخدموه قانون
+
+90
+00:06:50,150 --> 00:06:54,570
+بتكون تستخدموه مش مضطرين تثبتوه انتوا فعليا مش
+
+91
+00:06:54,570 --> 00:06:57,770
+مضطرين تثبتوه معظم الحاجات اللي احنا هناخدها هي
+
+92
+00:06:57,770 --> 00:07:01,190
+أصلا مثبتة معناها مسبقا احنا ماخدينها مسبقا أساسا
+
+93
+00:07:01,190 --> 00:07:04,430
+أخدناها من كل ال truth tables اللي احنا درسناها
+
+94
+00:07:04,430 --> 00:07:09,350
+حتى الآن كويس فهذه مجموعة patterns بتقودني من
+
+95
+00:07:09,700 --> 00:07:14,080
+المسلمات خلّينا نسميها أو البديهيات أو الفرضيات أو
+
+96
+00:07:14,080 --> 00:07:20,280
+المعطيات عشان أثبت ال conclusions الاستنتاجات
+
+97
+00:07:20,280 --> 00:07:24,340
+المطلوبة منها عشان نثبت الاستنتاج المطلوب منها
+
+98
+00:07:24,340 --> 00:07:29,640
+فهذه مجموعة قوانين قواعد التلتة دول هم العناصر
+
+99
+00:07:29,640 --> 00:07:33,900
+المهمة عشان أقدر أثبت شغلها طيب بنعيدها كمان مرة
+
+100
+00:07:33,900 --> 00:07:38,600
+ال theorem زي ما قلنا هي شئ مثبت قدرنا نثبتهأو can
+
+101
+00:07:38,600 --> 00:07:43,860
+be shown to be true بقدر أورّي إنه والله صحيح أو
+
+102
+00:07:43,860 --> 00:07:47,540
+بيعطيين قيمة true إذا كدرنا نحصل على mathematical
+
+103
+00:07:47,540 --> 00:07:50,680
+statement بقدر أحصل عليها أو أثبت إن هي دايما true
+
+104
+00:07:50,680 --> 00:07:54,440
+فإذا theorem خلاص، دائما ال condition هذا is true
+
+105
+00:07:54,440 --> 00:08:00,790
+طيب ال hypothesisال form طبعا في الأيام بقول H1
+
+106
+00:08:00,790 --> 00:08:09,250
+and H2 and H3 and H4 and H5 and H6 and H7 and H8
+
+107
+00:08:09,250 --> 00:08:14,010
+and H9 and H10 and H11 and H12 and H13 and H14 and
+
+108
+00:08:14,010 --> 00:08:15,450
+H15 and H16 and H17 and H18 and H19 and H20 and
+
+109
+00:08:15,450 --> 00:08:20,110
+H21 and H22 and H21 and H22 and H21 and H21 and
+
+110
+00:08:20,110 --> 00:08:24,050
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+111
+00:08:24,050 --> 00:08:24,310
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+112
+00:08:24,310 --> 00:08:24,790
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+113
+00:08:24,790 --> 00:08:24,850
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+114
+00:08:24,850 --> 00:08:24,930
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+115
+00:08:24,930 --> 00:08:25,210
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+116
+00:08:25,210 --> 00:08:28,990
+H21 and H21 and H21فكل الفكرة بس أنه بدنا نحقق أن
+
+117
+00:08:28,990 --> 00:08:33,310
+هدول كلهم يكونوا true عشان أحصل على ال true لمين،
+
+118
+00:08:33,310 --> 00:08:36,830
+لل conclusion اللي مطلوب اثباته، اللي مطلوب
+
+119
+00:08:36,830 --> 00:08:40,630
+اثباته، اللي عندنا احنا بتتكلم كلام عام، كلام بس
+
+120
+00:08:40,630 --> 00:08:44,430
+لمجرد الفهم، مادخلناش لسه في أي قوانين، لم ندخل في
+
+121
+00:08:44,430 --> 00:08:48,970
+أي قوانين، فعرفنا ال H اللي هي ال hypothesis و ال
+
+122
+00:08:48,970 --> 00:08:55,700
+C ال conclusionOkay ال theorem can be proven using
+
+123
+00:08:55,700 --> 00:09:00,640
+أما other theorems عن طريق نظريات أخرى بستخدم
+
+124
+00:09:00,640 --> 00:09:04,640
+نظرية أخرى و بحاول أثبت منها النظرية تبعتي أو
+
+125
+00:09:04,640 --> 00:09:09,000
+axioms مجموعة statements مسلم فيها ممكن ما تكونش
+
+126
+00:09:09,000 --> 00:09:12,330
+..مثبتة، ممكن ما تكونش مثبتة وحنا نتكلم عن جزيه
+
+127
+00:09:12,330 --> 00:09:16,570
+هيك طيب او انا بدي أثبتها عن طريق rules of
+
+128
+00:09:16,570 --> 00:09:21,730
+inference عن طريق شوية قواعد استدلال قواعد انا بدي
+
+129
+00:09:21,730 --> 00:09:26,430
+استدل منها بشوية خطوات أطلع شوية conclusions عشان
+
+130
+00:09:26,430 --> 00:09:28,970
+أصل ال conclusion الأساسية اللى بدي أصلها اللى
+
+131
+00:09:28,970 --> 00:09:35,370
+بدنا نصلهاأحيانا نظر ال .. ممكن أثناء شغل أطلع
+
+132
+00:09:35,370 --> 00:09:38,430
+نظرية في النص مثلا لسه ماوصلتش للي بديها و
+
+133
+00:09:38,430 --> 00:09:43,730
+ماوصلناش للي بدناها فهذه بسميها ال pre theorem لسه
+
+134
+00:09:43,730 --> 00:09:48,530
+ماوصلناش يعني مقدمة ل theorem تبعتي نظرية سابقة ل
+
+135
+00:09:48,530 --> 00:09:51,230
+theorem تبعتي عشان تتحقق ال theorem تبعتي لازم
+
+136
+00:09:51,230 --> 00:09:55,700
+تتحقق النظرية هذه الأولفأثناء شغله هتلاقوا أنه
+
+137
+00:09:55,700 --> 00:10:00,200
+حققنا نظرية قبل ما نصل للي بدناها فهذه بنسميها pre
+
+138
+00:10:00,200 --> 00:10:06,460
+-theorem أو لما .. لما .. كويس فهذه بنكون أحيانا
+
+139
+00:10:06,460 --> 00:10:10,580
+محتاجينها لتكميل ال proof تبعنا عشان نكمل ال
+
+140
+00:10:10,580 --> 00:10:13,440
+theorem تبعنا و نثبت ال theorem تبعنا بالعكس في
+
+141
+00:10:13,440 --> 00:10:16,600
+حاجة اسمها ال past theorem ال past اللي هي اللاحق
+
+142
+00:10:16,600 --> 00:10:20,460
+النظرية تعاليتنا أثبتناها بس ممكن ب process بسيط
+
+143
+00:10:20,460 --> 00:10:26,780
+أطلع نظرية تانيةفهي نظرية بقدر أثبتها من إثبات
+
+144
+00:10:26,780 --> 00:10:29,120
+نظريتنا اللي إحنا بنشتغل فيها نظرية اللي إحنا
+
+145
+00:10:29,120 --> 00:10:34,500
+بنشتغل فيها اللي هي Corollary كويس فهذه أو ال post
+
+146
+00:10:34,500 --> 00:10:39,920
+theorem تمام يعني بقدر ناخدها directly من ال
+
+147
+00:10:39,920 --> 00:10:44,060
+theorem اللي إحنا بنشتغل فيها كويس ال conjectures
+
+148
+00:10:44,060 --> 00:10:50,200
+أو ال conjecture هذه statement whose truth value
+
+149
+00:10:50,200 --> 00:10:56,930
+is a nounحاجة انا مسلم فيها ولكن ماقدرش اثبتها شيء
+
+150
+00:10:56,930 --> 00:10:59,610
+مسلم فيه ولكن مش قادرين نثبته وفي حاجات كتير مسلم
+
+151
+00:10:59,610 --> 00:11:04,070
+فيها بدهيات بس احنا نقولكوا و الله اثبتها مافيش
+
+152
+00:11:04,070 --> 00:11:10,930
+ممكنية نقعد نثبتها زي لو قلتلكوا كل رقم فيه لأكبر
+
+153
+00:11:10,930 --> 00:11:16,870
+منه طب اثبتوها كويس
+
+154
+00:11:16,870 --> 00:11:24,720
+اثبتوها انه لايوجد رقم أكبرلا يوجد رقم أكبر طب
+
+155
+00:11:24,720 --> 00:11:29,440
+ماوفيش، بس تقدر تثبتها؟ ليش؟ لأنه هضل واصل to
+
+156
+00:11:29,440 --> 00:11:35,560
+infinity كل رقم هلاجي فيه رقم أكبر منه هقولكوا لأ
+
+157
+00:11:35,560 --> 00:11:37,840
+ماهي الرقم الأكبر، و واحد تاني يقولوا لأ ما مش هذا
+
+158
+00:11:37,840 --> 00:11:40,740
+أكبر، فيه رقم أكبر منه طب لأمتى؟ فإذا في حاجات
+
+159
+00:11:40,740 --> 00:11:44,340
+مسلمة فيها بناخدها زي ما هي، بس إثبات مش مثبتة
+
+160
+00:11:44,340 --> 00:11:52,840
+فهذه برضه مجموعة نظريات فيconjecture أو مسلمات مش
+
+161
+00:11:52,840 --> 00:11:59,400
+مثبتة كويس ال inference rules الجزء الأهم خلصناها
+
+162
+00:11:59,400 --> 00:12:02,740
+لو اتكلمنا عن inference اتكلمنا عن المقدمات اللي
+
+163
+00:12:02,740 --> 00:12:08,240
+هنحتاجها اما مسلمات او بدهيات او فرضيات او معطيات
+
+164
+00:12:08,240 --> 00:12:11,100
+whatever يعني كلهم هنحتاجهم اي واحدة منهم ممكن
+
+165
+00:12:11,100 --> 00:12:14,140
+نحتاجها بس كل نظرية محتاجين واحدة منهم محتاجين
+
+166
+00:12:14,140 --> 00:12:18,040
+واحدة منهم نبدأ منها الشغل طيب ال inference rule
+
+167
+00:12:18,680 --> 00:12:22,740
+فعليا القواعدة اللى بنستخدمها للاستدلال بتتم عن
+
+168
+00:12:22,740 --> 00:12:26,220
+طريق patterns زى ما قولنا قوالة ثابتة، قوانين ..
+
+169
+00:12:26,220 --> 00:12:31,320
+قوانين ثابتة بنشتغل عليها بحيث انه بصير أعمل عملية
+
+170
+00:12:31,320 --> 00:12:38,640
+محاكا، إيش اللى موجود عندى؟ عندى antecedent واحدة
+
+171
+00:12:38,640 --> 00:12:44,340
+.. two antecedents أكم .. أكم معطى عنها، أكم سابق
+
+172
+00:12:44,340 --> 00:12:47,910
+عنها، أكم معلومة سابقة، خدنا نسميهاأكن معلومة
+
+173
+00:12:47,910 --> 00:12:52,210
+سابقة موجودة لدينا عشان أقدر أستنتج منها ال
+
+174
+00:12:52,210 --> 00:12:57,170
+consequence العاقبة للمعلومات السابقة هدول اللي هي
+
+175
+00:12:57,170 --> 00:13:02,330
+النتيجة بمعنى .. بمعنى النتيجةبقدر أعمل محاكاة،
+
+176
+00:13:02,330 --> 00:13:04,530
+إيش اللي موجود عندى، ومجموعة القوانين اللي الواحد
+
+177
+00:13:04,530 --> 00:13:08,010
+حافظها، اللي الواحد عارفها، إيش اللي تمشي بحيث أني
+
+178
+00:13:08,010 --> 00:13:11,690
+أطبقها، أطلع نتيجة، النتيجة دي اللي بدي إياها، مش
+
+179
+00:13:11,690 --> 00:13:13,830
+بالضرورة تكون مباشرة هي اللي بدي إياها، ممكن
+
+180
+00:13:13,830 --> 00:13:16,710
+النتيجة اللي أستخدمها عشان أجيب نتيجة تانية، لعند
+
+181
+00:13:16,710 --> 00:13:21,910
+ما نصل إياش لل conclusion المطلوب، المطلوب، تمام
+
+182
+00:13:24,730 --> 00:13:28,850
+ال implication ال implication احنا هيك هيك محتاجين
+
+183
+00:13:28,850 --> 00:13:33,510
+نحن نصله ليش لأن ال .. ال antecedent if antecedent
+
+184
+00:13:33,510 --> 00:13:37,270
+number one is true and antecedent number two is
+
+185
+00:13:37,270 --> 00:13:42,250
+true then the consequent is true فإذا أنا محتاج
+
+186
+00:13:42,250 --> 00:13:47,750
+then هذه if then فإذا أنا مقدرش أتحرك بدون ال
+
+187
+00:13:47,750 --> 00:13:52,070
+implication في ال proofs ال proofs محتاجة .. if
+
+188
+00:13:52,070 --> 00:13:58,510
+thenif then و هذه مدخل ال conditions عندكم في
+
+189
+00:13:58,510 --> 00:14:01,490
+البرمجة انت بتشتغل و مش بتشتغل على if then else
+
+190
+00:14:01,490 --> 00:14:06,110
+هذه مدخلها مدخلها ال implication شغلنا كله كنا
+
+191
+00:14:06,110 --> 00:14:08,050
+نكون شغالين على ال implication فانتوا لازم تكونوا
+
+192
+00:14:08,050 --> 00:14:10,030
+فاهمين ال implication صح عشان لما تحطوا ال
+
+193
+00:14:10,030 --> 00:14:13,010
+condition تكونوا فاهمين ال condition امتى هيكون
+
+194
+00:14:13,010 --> 00:14:16,770
+true و امتى هيكون false امتى هيكون true امتى هيكون
+
+195
+00:14:16,770 --> 00:14:21,610
+false فهذه تمثل فعليا ال antecedent one antecedent
+
+196
+00:14:21,610 --> 00:14:21,970
+two
+
+197
+00:14:24,980 --> 00:14:30,300
+الاتنين are given then consequent is true هذا
+
+198
+00:14:30,300 --> 00:14:34,020
+يمثلكوا antecedent number one and antecedent
+
+199
+00:14:34,020 --> 00:14:37,060
+number two فإذا هذه لازم تكون true و هذه لازم تكون
+
+200
+00:14:37,060 --> 00:14:40,360
+true جدش في عندكوا antecedents لازم كله يكون true
+
+201
+00:14:40,360 --> 00:14:44,440
+لإن هي المعطيات هو مدام معطيتلكوا فلازم تكون true
+
+202
+00:14:44,440 --> 00:14:51,550
+أو axiomsممكن تكون فرضيات، مديهيات، مسلمات، بس هي
+
+203
+00:14:51,550 --> 00:14:56,690
+لازم تكون true، كويس، then .. then معناته implies
+
+204
+00:14:56,690 --> 00:15:01,590
+implication .. بيستعمل implication consequent،
+
+205
+00:15:01,590 --> 00:15:06,690
+معناته بتمنلى حدوث النتيجة، بتمنلى حدوث النتيجة،
+
+206
+00:15:06,690 --> 00:15:12,610
+لعندي الآن كلام بيسميه عام نبدأ شوية في .. شوية
+
+207
+00:15:12,610 --> 00:15:19,430
+inference .. some inference rulesrule of addition
+
+208
+00:15:19,430 --> 00:15:25,530
+هالوقت لما نيجي نتكلم عن مشكلة هذا لو قولنا P is
+
+209
+00:15:25,530 --> 00:15:34,830
+true طيب P or أي شيء is true أكيد is true فإذا لو
+
+210
+00:15:34,830 --> 00:15:41,590
+كان عندكوا P is true then P or Q أكيد is true P or
+
+211
+00:15:41,590 --> 00:15:48,150
+K أكيد is true P or Z أكيد is true أكيدis it true؟
+
+212
+00:15:48,150 --> 00:15:51,610
+شيء بديهي جدا وهنا معلومة ماخدينها من مين من ال
+
+213
+00:15:51,610 --> 00:15:54,090
+disjunction أو ال or فهي الترث تابع اللي احنا
+
+214
+00:15:54,090 --> 00:15:59,470
+ماخدينه سابق نوعاك خلاص مضمونة طيب لو بالشكل هذا
+
+215
+00:15:59,470 --> 00:16:09,570
+عندكم P and Q is true فإذا إيش P is true و Q is
+
+216
+00:16:09,570 --> 00:16:13,390
+true صح برضه بديهية بديهية جدا من الترث تابع اللي
+
+217
+00:16:13,390 --> 00:16:19,300
+احنا أخدناهفهذه الـ simplification طيب لو قلنا P
+
+218
+00:16:19,300 --> 00:16:26,760
+is true and Q is true معناته هي and برضه is true
+
+219
+00:16:26,760 --> 00:16:32,960
+لأن هم أصلا هدولة الرابط بينهم and البديهية ان هو
+
+220
+00:16:32,960 --> 00:16:35,320
+الرابط بينهم and لأن احنا لسه قبل شويه قاعدين
+
+221
+00:16:35,320 --> 00:16:39,460
+بنحكي ايش antecedent one and antecedent two فهنا
+
+222
+00:16:39,460 --> 00:16:40,180
+هنا نسميهم
+
+223
+00:16:42,680 --> 00:16:46,140
+antecedent number one and antecedent number two
+
+224
+00:16:46,140 --> 00:16:55,820
+هدى true وهدى true فالان is true okay طيب ال .. ال
+
+225
+00:16:55,820 --> 00:16:59,160
+.. ال affirming أو التأكيد فيلمونيشيا نتكلم هنا عن
+
+226
+00:16:59,160 --> 00:17:02,880
+التأكيد و هنا بدنا هنا ناخد mean ال implication
+
+227
+00:17:02,880 --> 00:17:07,460
+فعشان ناخد ال implication خلينا نحط ال truth table
+
+228
+00:17:07,460 --> 00:17:09,980
+ل ال implication متذكرينه؟
+
+229
+00:17:16,410 --> 00:17:22,430
+ماذا يوجد هنا تمام
+
+230
+00:17:22,430 --> 00:17:32,950
+تمام دعوني أخد هنا ال P is true لاحظوا P is true
+
+231
+00:17:32,950 --> 00:17:40,290
+فإذا أنا بتكلم عن النجوطين هدول صح؟ هاي ال P is
+
+232
+00:17:40,290 --> 00:17:46,900
+true بتكلم عن الحالتين هدول طيب andP implies Q is
+
+233
+00:17:46,900 --> 00:17:56,920
+true صح وينها من هنا التانية فإذا Q is true ثم Q
+
+234
+00:17:56,920 --> 00:18:03,920
+is true تحظوا عملت تأكيد للنتيجة عملنا هنا تأكيد
+
+235
+00:18:03,920 --> 00:18:11,480
+لمين للنتيجة ان فعلا هاد trueو ال implication true
+
+236
+00:18:11,480 --> 00:18:16,920
+فإذا أكيد q لازم تكون true لازم تكون true هذه
+
+237
+00:18:16,920 --> 00:18:22,640
+الحالة طيب denying أو الإنكار نظرية الإنكار تحت
+
+238
+00:18:22,640 --> 00:18:29,760
+هنشوف إيش الفرضيات بتاعتها الفرضيات
+
+239
+00:18:29,760 --> 00:18:41,640
+كتالة الفرضيات بتاعتها هتكون كتالة negation qهي q،
+
+240
+00:18:41,640 --> 00:18:45,460
+negation يعني أنا بتكلم عن مين؟ false، false، فإذا
+
+241
+00:18:45,460 --> 00:18:51,560
+هاي حالة وهي حالة، ليش؟ لأن هذه false وهذه false،
+
+242
+00:18:51,560 --> 00:19:00,940
+تمام؟ كويسة P implies q, is it true؟ هال negation
+
+243
+00:19:00,940 --> 00:19:07,860
+true، معناته q is false، هنا P implies q
+
+244
+00:19:09,610 --> 00:19:14,770
+true طب وين ال true من الحالتين هدول؟ هيها فإذا في
+
+245
+00:19:14,770 --> 00:19:18,090
+نيجيشن
+
+246
+00:19:18,090 --> 00:19:25,910
+P فإذا نيجيشن P must be true تمام فإذا نيجيشن P
+
+247
+00:19:25,910 --> 00:19:32,290
+وعشان هي دي denying الإنقار أنقرنا بمجرد ما زهرش
+
+248
+00:19:32,290 --> 00:19:36,230
+معانا النتيجة فإذا أكيد المعطى ماكنش موجود المعطى
+
+249
+00:19:36,230 --> 00:19:38,910
+false فأكيد المعطى false
+
+250
+00:19:41,500 --> 00:19:48,940
+Okay طيب الsyllogism أو الاستدلال المنطقي خلينا
+
+251
+00:19:48,940 --> 00:19:54,640
+نسميه الاستدلال المنطقي لو قولنا P
+
+252
+00:19:54,640 --> 00:20:02,000
+employees Q is true and Q employees R is Q then P
+
+253
+00:20:02,000 --> 00:20:10,730
+employees R is Q صح صحيح إذا درست هتنجحإذا نجحت
+
+254
+00:20:10,730 --> 00:20:15,870
+هجيبلك هدية فإذا إذا درست هجيبلك هدية إذا طبعا
+
+255
+00:20:15,870 --> 00:20:20,370
+مشيت كلها تحققت صح إذا الفرضية كانت مشهورة طيب
+
+256
+00:20:20,370 --> 00:20:28,110
+برضه في الاستدلال لل or لل disjunctive ل ال
+
+257
+00:20:28,110 --> 00:20:37,970
+disjunctive إذا P or Q is true is true لحظة طيب
+
+258
+00:20:37,970 --> 00:20:44,130
+negationP is true معناته P false طبعا أنا جاعت
+
+259
+00:20:44,130 --> 00:20:49,410
+بقول هذه كلها true وهذا طلعت false هذه must be
+
+260
+00:20:49,410 --> 00:20:55,870
+true ليش؟ عشان كلها تطلع true لأنه خلاص هذه حكمنا
+
+261
+00:20:55,870 --> 00:21:00,810
+عليها false or محتاجة واحد true فإذا لازم تكون هذه
+
+262
+00:21:00,810 --> 00:21:06,830
+لازم تكون هذه فإذا Q is true
+
+263
+00:21:12,850 --> 00:21:20,570
+Okay فإذا أخدنا مجموعة من ال
+
+264
+00:21:20,570 --> 00:21:27,370
+rules of inference إذا كان .. طبعا لحظة ال .. ال
+
+265
+00:21:27,370 --> 00:21:32,710
+.. ال .. ال .. ال antecedent مع ال consequence لما
+
+266
+00:21:32,710 --> 00:21:37,990
+نيجي تنتين نعملهمimplication المفروض أن احصل على
+
+267
+00:21:37,990 --> 00:21:41,990
+tautology لإن إذا هذه true فهذه true لما باجب
+
+268
+00:21:41,990 --> 00:21:44,370
+أعملهم implication لازم يكونوا true true فإذن
+
+269
+00:21:44,370 --> 00:21:47,530
+طبيعي أنه لازم يعطيني tautology دائما ال relation
+
+270
+00:21:47,530 --> 00:21:51,650
+بينهم true لإنه دائما بيسووا بعض مدام أنا بتكلم عن
+
+271
+00:21:51,650 --> 00:21:57,970
+rule قاعدة إذا اتحقق الشرط بده يتحقق النهيجة فإذا
+
+272
+00:21:57,970 --> 00:22:00,570
+الأثنين لازم يكونوا true إذا أنا ماشي فعلا على ال
+
+273
+00:22:00,570 --> 00:22:06,190
+rules تبعتنا على ال rules كويسة فإذا فيis true
+
+274
+00:22:06,190 --> 00:22:13,630
+اكيد بيه مع or اي proposition اخر اكيد هتكون true
+
+275
+00:22:13,630 --> 00:22:17,210
+نفس الكلافة اذا لما بجرى بعمل implication لازم هذه
+
+276
+00:22:17,210 --> 00:22:21,910
+تطلع دايما true دايما تطلع true ليش دايما تطلع
+
+277
+00:22:21,910 --> 00:22:25,430
+true لأن احنا هنا دايما نتكلم عن اما false false
+
+278
+00:22:25,430 --> 00:22:29,990
+ماتحققوش او true true اتحققت فهذه دايما تطلع true
+
+279
+00:22:29,990 --> 00:22:35,270
+في ال implication مع ال implication تمام
+
+280
+00:22:37,580 --> 00:22:45,300
+P and Q معناته كل واحدة منهم true أكيد إذا كان ال
+
+281
+00:22:45,300 --> 00:22:49,340
+and للتنتين مع بعض true فإذا كل واحدة منهم لحالها
+
+282
+00:22:49,340 --> 00:22:54,460
+true، منطقي، كويسة هنا التنتين كل واحدة منهم true
+
+283
+00:22:54,460 --> 00:22:58,800
+فأكيد ال or تبع الأتنين ال and تبع الأتنين true
+
+284
+00:22:58,800 --> 00:23:05,720
+منطقي، برضه منطقي من معرفتنا بال and connectionطيب
+
+285
+00:23:05,720 --> 00:23:12,360
+أخدنا برضه ال negation q و p وهذا سمنها denying أو
+
+286
+00:23:12,360 --> 00:23:16,800
+الإنكار، مدام أنكرنا النتيجة فإذا أكيد ال .. ال ..
+
+287
+00:23:16,800 --> 00:23:21,830
+ال antecedent كانت false، أكيد كانت falseكويسة، و
+
+288
+00:23:21,830 --> 00:23:27,990
+بعدين أخدتنا السيولوجيزم الأخيرة جزئية .. فضلي ..
+
+289
+00:23:27,990 --> 00:23:33,270
+هده .. هده .. تمام، نرجع معناته نرسم، نكتب ال
+
+290
+00:23:33,270 --> 00:23:35,010
+table تبعنا
+
+291
+00:23:46,000 --> 00:23:50,900
+تمام هنا ايش .. ايش الفرضية؟ لحظة هذه الفرضية
+
+292
+00:23:50,900 --> 00:23:55,660
+المفروضة ان هي true وهذه فرضية ان هي تكون true هذه
+
+293
+00:23:55,660 --> 00:24:00,040
+ايش لازم تطلع؟ خليني اجربها و نشوف negation Q is
+
+294
+00:24:00,040 --> 00:24:06,640
+true معناته Q ايش؟ false ل Q هذه حالة وهذه حالة
+
+295
+00:24:06,640 --> 00:24:10,280
+فاذا انا بتكلم عن مين؟ عن هذا .. الحالة هذه
+
+296
+00:24:10,280 --> 00:24:16,750
+والحالة هناتمام من الشرط الأول عرفنا ان انا بتكلم
+
+297
+00:24:16,750 --> 00:24:22,750
+عن واحد من ال true rows هدول طيب كويس P employs Q
+
+298
+00:24:22,750 --> 00:24:27,030
+true طيب هي ال implication هنا true وهنا false لأ
+
+299
+00:24:27,030 --> 00:24:31,590
+انا بتكلم عن هنا معناته انا موجود في ال row الأول
+
+300
+00:24:31,590 --> 00:24:39,810
+هذه false وهذه true اكيد معناته بيش negation
+
+301
+00:24:41,840 --> 00:24:49,640
+فإذا negation بي ال false ل بي فإذا negation بي is
+
+302
+00:24:49,640 --> 00:24:57,060
+true لأن بي false negation بي is true okay زي ما
+
+303
+00:24:57,060 --> 00:25:02,660
+قلنا بي implies q and q implies r فإذا قلنا بي
+
+304
+00:25:02,660 --> 00:25:10,640
+بتضمنلي q و q بتضمنلي r بديهي بي بتضمنلي r okay
+
+305
+00:25:12,070 --> 00:25:15,370
+فلما نجي نتكلم هنا عن ال proves فعليا بنبدأ عشان
+
+306
+00:25:15,370 --> 00:25:21,550
+نثبت نعمل ال former row of a conclusion C بدنا
+
+307
+00:25:21,550 --> 00:25:25,250
+يكون عندنا مجموعة givens المجموعة ال givens هذه
+
+308
+00:25:25,250 --> 00:25:29,630
+اللي هي ال premises أو المعطيات ال premises P1 P2
+
+309
+00:25:29,630 --> 00:25:32,410
+P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P12 P13 P12 P12
+
+310
+00:25:32,410 --> 00:25:32,530
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+311
+00:25:32,530 --> 00:25:32,810
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+312
+00:25:32,810 --> 00:25:32,910
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+313
+00:25:32,910 --> 00:25:33,170
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+314
+00:25:36,670 --> 00:25:41,590
+بدنا منهم نثبت C فهدولة كلهم ال premises نتعامل
+
+315
+00:25:41,590 --> 00:25:45,890
+معهم عساس ان هم ال antecedents تعودنا المعطيات
+
+316
+00:25:45,890 --> 00:25:49,990
+تعودنا المقدمات للإثبات مقدمات الإثبات تبعنا و ال
+
+317
+00:25:49,990 --> 00:25:54,850
+conclusion هو ال consequent عندنا مجموعة قواعة و
+
+318
+00:25:54,850 --> 00:25:58,910
+قراءة شفناهاو أثبتناها و أتأكدنا منها بنشتغل و
+
+319
+00:25:58,910 --> 00:26:02,970
+بنشتغل عليها بنحاول نشوف مين اللي بتتناسب معانا
+
+320
+00:26:02,970 --> 00:26:10,130
+بحيث أنه والله إذا ال premises are true then the
+
+321
+00:26:10,130 --> 00:26:13,870
+conclusion is true هذا اللي بدنا نصلّم هذا اللي
+
+322
+00:26:13,870 --> 00:26:21,070
+بدنا نصلّم ناخد example لو قلنا suppose we have
+
+323
+00:26:21,070 --> 00:26:25,420
+the following premisesلأ معطيات مش بالضروري أن هي
+
+324
+00:26:25,420 --> 00:26:29,700
+مسلمات بالنسبالنا بس هي معطيات بقدر أقولكنه معطيات
+
+325
+00:26:29,700 --> 00:26:35,380
+حسب حالة معينة كلهم are true حسب حالة معينة طيب
+
+326
+00:26:35,380 --> 00:26:40,060
+it's not sunny and it's cold هي مش مشمسة الدنيا مش
+
+327
+00:26:40,060 --> 00:26:48,170
+مشمسة و بريد تمامwe will swim only if it's sunny
+
+328
+00:26:48,170 --> 00:26:54,450
+احنا هنسبح إذا كان الدنيا شمس أو مش شمسة طيب if we
+
+329
+00:26:54,450 --> 00:26:59,710
+don't swim then we will play volley إذا ما لجناها
+
+330
+00:26:59,710 --> 00:27:04,710
+مش مش شمسة أو يعني إذا ماسبحناش هنلعب كرة طائرة،
+
+331
+00:27:04,710 --> 00:27:07,650
+بنضل ع الشط و مش هنسبح، هنلعب طائرة و خلاص، كويسة
+
+332
+00:27:08,060 --> 00:27:14,560
+if we play volley then we will be home early هنرجع
+
+333
+00:27:14,560 --> 00:27:20,040
+للبيت مبكر طيب بدنا نثبت ان we will be home early
+
+334
+00:27:20,040 --> 00:27:26,060
+بدنا .. لحظة كلنا قولنا اه اه ماهي منطقى منطق ليش
+
+335
+00:27:26,060 --> 00:27:31,900
+لأن احنا بدين .. not sent لحظة
+
+336
+00:27:31,900 --> 00:27:35,740
+احنا بدين اصلا ان هي فعلا مش مو شمسةفمدام مش مش بس
+
+337
+00:27:35,740 --> 00:27:40,000
+طبيعي و برد كمان أكيد مش هنسبح و مدام مش هسبح
+
+338
+00:27:40,000 --> 00:27:43,340
+معناته هنلعب طائرة و اكيد مدام اللعبنا طائرة هنروح
+
+339
+00:27:43,340 --> 00:27:48,400
+بدري فهي biologic منطقية بس بدنا اثبات بدنا نثبتها
+
+340
+00:27:48,400 --> 00:27:52,960
+رياضيا عشان نثبتها رياضيا بنختصر بنعمل مختصرات
+
+341
+00:27:52,960 --> 00:27:58,600
+فهنقول it's sunny هنعطيها ال function sunny بس
+
+342
+00:27:58,600 --> 00:28:04,210
+cold عساس ان معناها it's coldبنحاول نختصر الجمال
+
+343
+00:28:04,210 --> 00:28:06,990
+بتاعتنا عشان تمشي مع الرياضية أو ال mathematical
+
+344
+00:28:06,990 --> 00:28:11,910
+form اللي هنشتغل عليه swim volley خلاص معناته we
+
+345
+00:28:11,910 --> 00:28:16,330
+will play volley early خلاص معناته ان انا هروح او
+
+346
+00:28:16,330 --> 00:28:21,390
+هنروح بدر فإذا بنترجم ال premises اللي كانت هنا ال
+
+347
+00:28:21,390 --> 00:28:25,330
+premises اللي كانت هنا it's not sunny and cold
+
+348
+00:28:25,330 --> 00:28:34,220
+okay if we swimwe swim then sunny فإذا كانت sunny
+
+349
+00:28:34,220 --> 00:28:41,280
+هنسبح أو هنسبح إذا كانت sunny إذا كانت sunny وهذه
+
+350
+00:28:41,280 --> 00:28:48,820
+بدي إياكم ترجعوا لل implication و الترجمه هذه بناء
+
+351
+00:28:48,820 --> 00:28:52,260
+على مجموعة الجمل اللي أعطيناكوا إياها تعبر عن ال
+
+352
+00:28:52,260 --> 00:28:56,480
+implication تذكرينها؟ تذكرتواها كويس؟ فشوفوا ليه
+
+353
+00:28:56,480 --> 00:29:09,470
+only ifمين ال B ومين ال Q ال B ثانو ثانو انا
+
+354
+00:29:09,470 --> 00:29:13,310
+بالعمد بقولتلكوا عليها عشان ما تخلطوش فبترجعوا للي
+
+355
+00:29:13,310 --> 00:29:20,150
+أخدناها سابقا لإنه only if وليس if only if if only
+
+356
+00:29:20,150 --> 00:29:24,430
+if هدي إشي تاني if only أو زي ما هي مكتوبة عندكم
+
+357
+00:29:24,430 --> 00:29:32,250
+هناonly if هذه P only if Q فترجع لمجموعة ال forms
+
+358
+00:29:32,250 --> 00:29:33,970
+اللي أخدناها أو المجموعة ال words اللي أخدناها
+
+359
+00:29:33,970 --> 00:29:37,770
+تعبر عن ال implication هتلاقوا أن ال P في الأول و
+
+360
+00:29:37,770 --> 00:29:41,250
+ال Q في التاني P أول و Q تاني ليش لأنه بناء عليها
+
+361
+00:29:41,250 --> 00:29:46,370
+لازم أحطهم هنا فعليا P في الأول و Q في التاني إذا
+
+362
+00:29:46,370 --> 00:29:48,890
+انتوا بتقولوا هيكوا كانت ال Q P المفروض كان قلتله
+
+363
+00:29:48,890 --> 00:29:53,280
+غلط هذه كان المفروض ان هي بالعكسبس لأ هي هذه صح
+
+364
+00:29:53,280 --> 00:29:58,220
+لأنه فعلا ال expression السابق يعبر عن بي Q
+
+365
+00:29:58,220 --> 00:30:03,200
+بترجعولهم عشان تتأكدوا يعني انا بقولكوا note عشان
+
+366
+00:30:03,200 --> 00:30:07,180
+برضه و انتوا لو بتذاكروا المحاضرة تتأكدوا منها طيب
+
+367
+00:30:07,180 --> 00:30:15,080
+وصلنا إذا .. إذا كان مسبحناش if مسبحناش then هنلعب
+
+368
+00:30:15,080 --> 00:30:20,970
+volley okay طيب إذا لعبنا volleyهذه ال expressions
+
+369
+00:30:20,970 --> 00:30:24,910
+لم تكن فيها مشكلة لأنها كانت مباشرة if ثم if ثم
+
+370
+00:30:24,910 --> 00:30:27,990
+هذا اللي كان يمكن تترجعها شوية لأنها كانت only if
+
+371
+00:30:27,990 --> 00:30:32,150
+تترجعها شوية تشوف وين ال P وين ال Q وين ال P وين
+
+372
+00:30:32,150 --> 00:30:36,230
+ال Q كويس
+
+373
+00:30:36,230 --> 00:30:38,870
+هذه مجموعة ال premises بتاعتنا هذه مجموعة ال
+
+374
+00:30:38,870 --> 00:30:42,390
+premises بنبدأ من ال premises الأولى هذه ال steps
+
+375
+00:30:42,390 --> 00:30:49,760
+للإثبات negation sunny and coldpremise number one
+
+376
+00:30:49,760 --> 00:30:56,540
+طيب madam and معناته الأولى true والتانية true
+
+377
+00:30:56,540 --> 00:31:00,480
+فإذا ال negation sunny is true negation sunny is
+
+378
+00:31:00,480 --> 00:31:05,320
+true طيب احنا عارفين انه swim implies sunny طب انا
+
+379
+00:31:05,320 --> 00:31:11,300
+عندي negation denying negation sunny فإذا ال
+
+380
+00:31:11,300 --> 00:31:17,620
+negation ال حالة اللي لسه كنا نتكلم فيهاالحالة
+
+381
+00:31:17,620 --> 00:31:21,380
+اللي كنا نحكي فيها فإذا مدام هذه negation أكيد
+
+382
+00:31:21,380 --> 00:31:26,080
+التانية ال P بتاعة ال negation فهي negation P طيب
+
+383
+00:31:26,080 --> 00:31:29,100
+لحظة هنا negation P و أنا عندي ال premise أساسا
+
+384
+00:31:29,100 --> 00:31:32,920
+موجودة اللي هي negation swim then volley تحققت
+
+385
+00:31:32,920 --> 00:31:40,600
+affirming تأكيد هذه true و هنا ما تحقق عنك وهيها
+
+386
+00:31:40,600 --> 00:31:46,690
+فإذا volley is true volley is trueقاعدين نشتغل على
+
+387
+00:31:46,690 --> 00:31:51,910
+نفس ال rules اللي اتكلمنا عنهم تمام volley is true
+
+388
+00:31:51,910 --> 00:31:56,190
+فإذن volley employs early برضه هذي ال premise هذي
+
+389
+00:31:56,190 --> 00:32:03,210
+given مقتنية given is true برضه early is true لإنه
+
+390
+00:32:03,210 --> 00:32:06,470
+برضه بتكلم عن ال affirment بتكلم على التأكيد هنا
+
+391
+00:32:06,470 --> 00:32:12,030
+بتكلم على التأكيد فإذن early مدى محققنا في الآخر
+
+392
+00:32:12,030 --> 00:32:17,610
+early is true فإذن أنا أكيد هروح بدريأثبتت رغم أنه
+
+393
+00:32:17,610 --> 00:32:21,670
+احنا من الأول بقيلة أنه okay as expressions منطقية
+
+394
+00:32:21,670 --> 00:32:24,690
+لأنه احنا من الأول قلنا إنه هي .. هي not sunny
+
+395
+00:32:24,690 --> 00:32:31,330
+الدنيا it's not sunny تمام
+
+396
+00:32:31,330 --> 00:32:38,910
+ناخد مجموعة rules مهمة عن اللي فاتوا لأن هنا ال
+
+397
+00:32:38,910 --> 00:32:43,710
+rules هذه مرتبطة بمين بال quantifiers مرتبطة بال
+
+398
+00:32:43,710 --> 00:32:45,370
+quantifiers نبدأ
+
+399
+00:32:49,410 --> 00:32:54,950
+بال universal instantiation أو التعويض بأي object
+
+400
+00:32:54,950 --> 00:33:03,170
+لو قلنا for all x b of x معنى ذلك أن أي element
+
+401
+00:33:03,170 --> 00:33:07,830
+داخل universe of discourse is true يعني بقدر أقول
+
+402
+00:33:07,830 --> 00:33:12,350
+b of o و o هذا أي element من داخله أي element
+
+403
+00:33:12,350 --> 00:33:19,700
+عشوائياعشوائيا لو قلت في الجرة هذه في مجموعة كور
+
+404
+00:33:19,700 --> 00:33:23,420
+ومثبت ان فعلا كل اللي موجود في الجرة كور فإذا
+
+405
+00:33:23,420 --> 00:33:26,780
+عشوائيا لو مديت إيدي و طلعت اي شغل اكيد هتطلع كورة
+
+406
+00:33:26,780 --> 00:33:32,440
+مظبوط؟ اكيد بيولوجيك منطق جدا اي object جوا حامد
+
+407
+00:33:32,440 --> 00:33:35,840
+إيدي وانا مش شايف بطلعه هقولك ان انا هطلعلك كورة
+
+408
+00:33:35,840 --> 00:33:38,360
+طب ما احنا عارفين ان انا هطلعك كورة ليش؟ لأن for
+
+409
+00:33:38,360 --> 00:33:46,080
+all x كل ال object داخل الجرةالأرم هي core منطقي
+
+410
+00:33:46,080 --> 00:33:52,340
+جدا فإذا أي شغل حد هدخل أطلع أكيد هتطلع core كويسة
+
+411
+00:33:52,340 --> 00:34:01,460
+أه العكس العكس P of Z هذا universal generalization
+
+412
+00:34:01,460 --> 00:34:08,180
+هنا ب arbitrary element إيش يعني يعني بشكل عشوائي
+
+413
+00:34:08,180 --> 00:34:13,320
+بشكل اعتباطي بشكلإنه لو قدرنا نقول إن ال G هذه
+
+414
+00:34:13,320 --> 00:34:17,620
+حاجة عشوائية ممكن تظهر معاك بمعنى كل مرة بدخل إيدي
+
+415
+00:34:17,620 --> 00:34:21,520
+في ال .. في ال .. في ال iron كل مرة بدخل إيدي في
+
+416
+00:34:21,520 --> 00:34:25,020
+الجرة بطلع كورة المرة التانية كل مرة بدخل إيدي في
+
+417
+00:34:25,020 --> 00:34:28,220
+الجرة بطلع كورة كل مرة بطلع .. بحط إيدي في الجرة
+
+418
+00:34:28,220 --> 00:34:32,320
+بطلع كورة بشكل عشوائي .. بشكل عشوائي ال G هنا
+
+419
+00:34:32,320 --> 00:34:37,380
+تختار بشكل عشوائي غير منظر بشكل مافيش control عليه
+
+420
+00:34:38,420 --> 00:34:40,800
+كل واحدة .. أي واحدة منكم هتدخل إيه؟ ده هتطلع
+
+421
+00:34:40,800 --> 00:34:44,240
+كورة، هترجحها، اللي وراها هتيجي تدخل إيه؟ إذا فعلا
+
+422
+00:34:44,240 --> 00:34:48,740
+الـG دي بشكل عشوائي بتم إختيارها بهذا الشكل،
+
+423
+00:34:48,740 --> 00:34:53,780
+معناته بقدر أقول أو بقدر أستنتج for all x P of X،
+
+424
+00:34:53,780 --> 00:34:59,020
+بدنا ناخد بالنا إن الـG دي مش زي الـO هنا، الـO أي
+
+425
+00:34:59,020 --> 00:35:04,440
+واحدة ممكن تكون selected، مجرد إنها selected،
+
+426
+00:35:04,440 --> 00:35:09,430
+باختارها إختيار، بس التانية لأ،عشوائيا، بشكل
+
+427
+00:35:09,430 --> 00:35:13,110
+عشوائي، وعملناها كذا مرة في مرة في مرة، اللي جرّا،
+
+428
+00:35:13,110 --> 00:35:17,310
+كل واحدة منكوا إجت، طلعت، لجت كورة، بشكل عشوائي،
+
+429
+00:35:17,310 --> 00:35:22,190
+في هذه الحالة بقدر أقول إنه for all x u of x،
+
+430
+00:35:22,190 --> 00:35:26,530
+واضحة الـG هذه، لأنه دايما الـG هذه، لعند الآن، في
+
+431
+00:35:26,530 --> 00:35:30,740
+كل سنة بتلخبطوا فيهاوهو بيظلوا يسألوا فيها طب كيف
+
+432
+00:35:30,740 --> 00:35:34,580
+جي يعني معناته يمكن جيها دي واحدة منهم بس كيف انت
+
+433
+00:35:34,580 --> 00:35:38,240
+عمّمت اه بعمم اذا كانت جي بتم اختيارها بشكل عشوائي
+
+434
+00:35:38,240 --> 00:35:42,280
+في كل مرة في كل مرة بيختارها عشوائيا و كل مرة
+
+435
+00:35:42,280 --> 00:35:46,600
+بتطلع true كل مرة بتحقق ليه ال function P معناته
+
+436
+00:35:46,600 --> 00:35:50,280
+for all x of x P of X تمام
+
+437
+00:35:53,720 --> 00:35:58,440
+There exists x P of x قريبة من نفس الفكرة على فكرة
+
+438
+00:35:58,440 --> 00:36:07,060
+لسه لأن there exists x P of x employs P of C كل
+
+439
+00:36:07,060 --> 00:36:11,900
+اللي بنعمله هنا كأنه C just a new constant ممكن
+
+440
+00:36:11,900 --> 00:36:20,440
+يكون أي واحد من ال elements محددناش
+
+441
+00:36:20,440 --> 00:36:26,770
+إذا حددنا بتخربإذا حددنا C هتخرب كل ال .. ال .. ال
+
+442
+00:36:26,770 --> 00:36:31,030
+.. ال inference هذه واضحة؟ ال rule كلها هتخرب ليش؟
+
+443
+00:36:31,030 --> 00:36:34,810
+لأن إذا بدي أحدد يمكن ماتطلعش هي ال true فيهم لأن
+
+444
+00:36:34,810 --> 00:36:37,910
+احنا قلنا there exist معناته ممكن تكون واحدة من
+
+445
+00:36:37,910 --> 00:36:44,270
+مجموعة عشرة من عشرة elements واحدة منهم بتحققنا ال
+
+446
+00:36:44,270 --> 00:36:49,150
+P of X كويس؟ فإذا بدي أحددها any منهم بقدرش
+
+447
+00:36:49,150 --> 00:36:53,580
+بقولكوا هقولكوا لأ مش بالضرورةولكن إذا كانت ال new
+
+448
+00:36:53,580 --> 00:36:56,780
+constant C مجرد أن أنا بدل ما حط X حطيتها C و C
+
+449
+00:36:56,780 --> 00:37:03,120
+هذه لحظة ممكن تكون أي element داخل ال universal
+
+450
+00:37:03,120 --> 00:37:08,480
+discourse إذا حددناها بشكل ضبابي خلينا هيك بشكل
+
+451
+00:37:08,480 --> 00:37:14,180
+ضبابي إنه ممكن تكون أي واحدة ماحددناش فإذا is true
+
+452
+00:37:14,180 --> 00:37:21,910
+واضحة فالتلتين هدولة يمكن فيهم شوية lapsed pHفي
+
+453
+00:37:21,910 --> 00:37:25,650
+التعريف هنا بتكون تعرفوا أن هذا البرتري بشكل
+
+454
+00:37:25,650 --> 00:37:31,610
+عشوائي وهذا أي واحدة ماحددناش برضه برضه مش هنحدد
+
+455
+00:37:31,610 --> 00:37:39,130
+طيب الأخيرة P of O لاحظوا is a P of O وهذا محدد
+
+456
+00:37:39,130 --> 00:37:44,370
+واحدة منهم بكفي واحدة منهم من ال elements is true
+
+457
+00:37:44,370 --> 00:37:50,510
+عشان أقوليوجد في فضاء العينة element واحد على
+
+458
+00:37:50,510 --> 00:38:05,170
+الأقل بحققنا ال function P of X طيب،
+
+459
+00:38:05,170 --> 00:38:11,950
+كويس ال fallacy is an inference rule or other
+
+460
+00:38:11,950 --> 00:38:17,440
+proof method is not logically validزي ان انتوا
+
+461
+00:38:17,440 --> 00:38:26,480
+تثبته عكس ال true تثبته ان ال function false اذا
+
+462
+00:38:26,480 --> 00:38:31,760
+كانت false معناته عكسها true هنا انكوا تثبته العكس
+
+463
+00:38:33,980 --> 00:38:37,760
+بتصير الحقيقة مغلطات أحيانا في هذا الموضوع فال ..
+
+464
+00:38:37,760 --> 00:38:42,180
+ال fallacy لما نيجي نتكلم عن المغلطة اللي ممكن
+
+465
+00:38:42,180 --> 00:38:46,120
+تتصير من هيك إشي إن أنا أثبت العكس و تفاجأوا أنه
+
+466
+00:38:46,120 --> 00:38:52,740
+طب ماشي ما هي مش بضروري أن العكس يثبت الصحة
+
+467
+00:38:52,740 --> 00:38:58,860
+هذا ممكن يعمللنا حاجة بتسميها fallacy أو مغلطةهي
+
+468
+00:38:58,860 --> 00:39:02,160
+عملنا مغلطة، إيش المغلطة هذه؟ من وين بتتم المغلطة
+
+469
+00:39:02,160 --> 00:39:06,820
+هذه؟ بتتم من .. برضه هي نفس ال implication لأن ال
+
+470
+00:39:06,820 --> 00:39:09,680
+implication قلنا إن فيها false ال false هذه هي
+
+471
+00:39:09,680 --> 00:39:13,240
+اللي بتعملنا المشكلة عشان تبين معانا أكتر، خلينا
+
+472
+00:39:13,240 --> 00:39:17,120
+نرسم، نرجع نكتم، اللحظوا إن ال implication هو اللي
+
+473
+00:39:17,120 --> 00:39:20,420
+مدوخنا وراها، احنا قاعدين نجري كلنا ورا جزئية ال
+
+474
+00:39:20,420 --> 00:39:22,580
+implication، فهذه عشان يكي اللحظوا إنه أهمية ال
+
+475
+00:39:22,580 --> 00:39:28,350
+implicationال implication من أهم ال .. ال
+
+476
+00:39:28,350 --> 00:39:29,290
+operators اللي قعدنا
+
+477
+00:39:41,280 --> 00:39:46,240
+تمام طيب عشان نوضحها ال policy اللي بتصير في عملية
+
+478
+00:39:46,240 --> 00:39:50,460
+ال affirming في عملية التأكيد إن أنا أروح أأكد
+
+479
+00:39:50,460 --> 00:39:56,040
+معلومة بينما في احتمال انه لأ ماتكونش مؤكدة زي لو
+
+480
+00:39:56,040 --> 00:40:02,500
+قلنا P employs Q is it true؟ okay and Q is true؟
+
+481
+00:40:02,500 --> 00:40:06,840
+طب ناخدها شوي شوي هنا إيش بيقولكوا؟ so P must be
+
+482
+00:40:06,840 --> 00:40:11,960
+true هذه المقولة هل المقولة دايما صح؟ هنشوفحنشوف
+
+483
+00:40:11,960 --> 00:40:18,600
+خلينا نمسك is it true هيه لأ التلاتة حتى في عندنا
+
+484
+00:40:18,600 --> 00:40:23,220
+تلاتة is it true يعني بمعنى أن أنا ممكن هي
+
+485
+00:40:23,220 --> 00:40:28,460
+التانتين وهي التالتة صحيح؟ هدول ممكن يتنطبق عليهم
+
+486
+00:40:28,460 --> 00:40:32,480
+ال condition الأول طيب Q is it true؟ وين ال Q؟ هي
+
+487
+00:40:32,480 --> 00:40:37,120
+Q هي في عندكوا true وهي عندكوا true صرت أنا بتكلم
+
+488
+00:40:37,120 --> 00:40:37,940
+عن الحالتين هدول
+
+489
+00:40:41,120 --> 00:40:43,760
+الحالتين هدولة بقدرش أقول منهم so أطلع ال
+
+490
+00:40:43,760 --> 00:40:47,680
+conclusion بقدرش أقول أن A and B is true ليش؟ لأنه
+
+491
+00:40:47,680 --> 00:40:52,480
+أه ممكن تكون true بس برضه ممكن تكون false لاحظته؟
+
+492
+00:40:52,480 --> 00:40:57,320
+فإذا لأ في لسه احتمال أنا نسيته فعملت مغلطة في
+
+493
+00:40:57,320 --> 00:41:01,300
+الاستنتاج، عملنا مغلطة في الاستنتاج فإذا المقولة
+
+494
+00:41:01,300 --> 00:41:09,700
+هذه غلط، هذه خطأ أو بديش أقول خطأ غير مضمونةبتكون
+
+495
+00:41:09,700 --> 00:41:12,820
+اوقع شوية غير مضمونة لان ممكن تصدق في بعض الحالات
+
+496
+00:41:12,820 --> 00:41:16,160
+اه بس في بعض مش في كل الحالات مش في كل الحالات فهد
+
+497
+00:41:16,160 --> 00:41:20,500
+فيه مغلطة طيب في ال denying برضه نفس الفكرة لو
+
+498
+00:41:20,500 --> 00:41:28,560
+قلنا بي employees q is true and he is false ممكن
+
+499
+00:41:28,560 --> 00:41:32,700
+يكون واحد يقولكوا على طول then q must be false طيب
+
+500
+00:41:32,700 --> 00:41:36,760
+لأ هد برضه بتصبتش لان لو مسكنهم هلاقي ان انا بتكلم
+
+501
+00:41:36,760 --> 00:41:42,760
+عن تالت حالات صحيحالثلاث حالات مظبوط اللي احنا
+
+502
+00:41:42,760 --> 00:41:47,340
+حكيناهم هيهم ولكن ال condition هنا لمين معاها ل ال
+
+503
+00:41:47,340 --> 00:41:52,080
+P ال P is false فالثلاث حالات هدول هعندي false هنا
+
+504
+00:41:52,080 --> 00:41:54,080
+وعندي false هنا هدي true لأ معناته ان انا بتكلم عن
+
+505
+00:41:54,080 --> 00:41:59,520
+الحالتين الحالتين هدول بقدرش اثبت منهم Q اقول
+
+506
+00:41:59,520 --> 00:42:02,160
+معناته اذا هدي false و هدي true معناته فاتفوت طب
+
+507
+00:42:02,160 --> 00:42:06,760
+مافي حالة تانية في حالة true في حالة هيها موجودة
+
+508
+00:42:08,390 --> 00:42:18,810
+فإذن هبنقدرش نشتغل عليها لأنه في fallacy كويس من
+
+509
+00:42:18,810 --> 00:42:21,050
+بين الحاجات ال fallacy خليني أشوف مثلا ال proof زي
+
+510
+00:42:21,050 --> 00:42:25,070
+هذا لو ال proof بالشكل هذا واحد كتب ال proof
+
+511
+00:42:25,070 --> 00:42:29,690
+بالشكل هذا و بعدين أثبت الكو أن اتنين بتساوي واحد
+
+512
+00:42:29,690 --> 00:42:33,470
+أكيد في fallacy في المصطلح فيه مغلطة في اشي عمله
+
+513
+00:42:33,470 --> 00:42:38,600
+غلطمنطق جدا يعني كيف انت تبدأ بيقولوا a and b
+
+514
+00:42:38,600 --> 00:42:42,800
+positive integers و a بتساوي b احب دمع ايه بتساوي؟
+
+515
+00:42:42,800 --> 00:42:45,860
+كويس فليا كده و بعدين عمل اثبات اثبات ان في الآخر
+
+516
+00:42:45,860 --> 00:42:50,280
+الاثنين بتساوي واحد طلعوا
+
+517
+00:42:50,280 --> 00:42:55,580
+عليها كل شيء فيها منطقي صح وين في عندنا مشكلة
+
+518
+00:42:55,580 --> 00:43:02,610
+هابدأقولك اه هاي واحد اتنين تلاتةأربعة خمسة ستة
+
+519
+00:43:02,610 --> 00:43:05,950
+سبعة في سبعة lines عندنا في المثال في ال proof
+
+520
+00:43:05,950 --> 00:43:10,150
+اللي عندنا واضح انه هيكون فيمشكلة في step رقم
+
+521
+00:43:10,150 --> 00:43:14,290
+أربعة لخمسة لإيش لأن في أربعة احنا اضطرينا نقسم
+
+522
+00:43:14,290 --> 00:43:17,990
+على صفر باعتبار ان احنا قسمنا على a minus b و a
+
+523
+00:43:17,990 --> 00:43:25,430
+minus b بيساوي صفر فصرت a plus b على zero و b على
+
+524
+00:43:25,430 --> 00:43:29,430
+zero طبعا أي term على zero بيعطينا قيمة غير محددة
+
+525
+00:43:29,430 --> 00:43:33,490
+غير معرفة فمعنى ذلك انهال step رقم خامسة لأصل إنه
+
+526
+00:43:33,490 --> 00:43:37,270
+هي غير معرفة فهنا بيجي في ال proof كله بيصير في
+
+527
+00:43:37,270 --> 00:43:39,950
+خطأ أصلا في ال process اللي انعمل أو في المعالجة
+
+528
+00:43:39,950 --> 00:43:44,610
+اللي تمت بالقسم على صفر و هيك بتكون واضح ليش
+
+529
+00:43:44,610 --> 00:43:49,870
+المثال هذا فيه إشكالي أو فيه مشكلةتما هلوجد خلصنا
+
+530
+00:43:49,870 --> 00:43:55,350
+مقدمات نعتبرها، خلصنا جزية مقدمات، الجزء الأهم من
+
+531
+00:43:55,350 --> 00:43:58,310
+المقدمات، كل اللي أخدناها مقدمات مجرد أخدنا ال
+
+532
+00:43:58,310 --> 00:44:02,630
+inferences، مجموعة rules و اتعاملنا معها و أخدنا
+
+533
+00:44:02,630 --> 00:44:05,790
+مثال عليها، الأهم إيش ال methodology اللي بدنا
+
+534
+00:44:05,790 --> 00:44:09,450
+نشتغل فيها، إيش ال methods اللي بدنا نستعملها،
+
+535
+00:44:09,450 --> 00:44:14,180
+يعني إيه؟هل اللي بيجيني هشتغل يلا أي إشي بيطلع
+
+536
+00:44:14,180 --> 00:44:17,600
+معايا و بس نحفظ شوية ال rules هذه و نشتغل و خلاص؟
+
+537
+00:44:17,600 --> 00:44:22,240
+في categories ال categories هذه بتحددلنا أنواع ال
+
+538
+00:44:22,240 --> 00:44:24,920
+methods اللي بدنا نشتغل عليها في عندنا فعليا
+
+539
+00:44:24,920 --> 00:44:31,920
+مجموعة methods في method مباشرة طريقة مباشرة طريقة
+
+540
+00:44:31,920 --> 00:44:38,340
+direct مباشرة خلاص بنفرض P و منها نثمة Q مباشرة
+
+541
+00:44:38,340 --> 00:44:39,900
+لإن احنا كل شغلنا علاقاش
+
+542
+00:44:43,900 --> 00:44:48,240
+هذه مجموعة ال premises ممكن تكون premises واحدة او
+
+543
+00:44:48,240 --> 00:44:55,520
+مجموعة تمام؟ بدنا نثبت منها ال conclusion اما ان
+
+544
+00:44:55,520 --> 00:45:00,660
+بفرض هذه وبشوية rules بحاول أثبت منها هذه مباشرة
+
+545
+00:45:00,660 --> 00:45:05,840
+بشكل مباشر نبدأ مباشرة بشكل طبيعي حسب اتجاه تبعنا
+
+546
+00:45:05,840 --> 00:45:13,270
+لحظه او indirect ال indirect بدي أثبتnegation Q
+
+547
+00:45:13,270 --> 00:45:19,390
+إذا قدرنا من negation Q نفرضها هي الفرضية هو هيطلب
+
+548
+00:45:19,390 --> 00:45:22,270
+منكوا اثبتولي كذا طب الكذا هذا ناخد ال negation
+
+549
+00:45:22,270 --> 00:45:27,270
+تبعه implication
+
+550
+00:45:27,270 --> 00:45:30,770
+negation
+
+551
+00:45:30,770 --> 00:45:36,670
+P إذا قدرنا نثبت الجزء هذا فإذا هذا صح متذكرين ال
+
+552
+00:45:36,670 --> 00:45:41,400
+counter positive؟ مش هي ال counter positive؟مش هذا
+
+553
+00:45:41,400 --> 00:45:43,960
+ال contrapositive اللي كنا نشتغل عليها قلنا فيه ال
+
+554
+00:45:43,960 --> 00:45:48,120
+inverse و ال converse و ال contrapositive كنا
+
+555
+00:45:48,120 --> 00:45:53,080
+بنجيب negation للطرفين و بنبدلهم و قلنا هي الحالة
+
+556
+00:45:53,080 --> 00:45:57,380
+الوحيدة المكافئة لل implication الأصلي فإذا كانت
+
+557
+00:45:57,380 --> 00:46:00,740
+مكافئة لل implication الأصلي لو تحققت أكيد هيتحقق
+
+558
+00:46:00,740 --> 00:46:05,160
+الأصلي بدا مكافئة فعلا فإذا لو أنا مش قادر أثبت
+
+559
+00:46:05,160 --> 00:46:09,990
+الجزء هذامش قادرين نثبت الجزء هذا التعريف هنا صعب
+
+560
+00:46:09,990 --> 00:46:15,030
+شوية مش عارفين نفككه مش عارفين نحلله تعريف المقلوب
+
+561
+00:46:15,030 --> 00:46:22,970
+أسهل فلس بفترض أن هذا inverse او بعمله negation و
+
+562
+00:46:22,970 --> 00:46:29,330
+بنفترض العكس و بأنه بنحاول نثبت عكس المعطى لو
+
+563
+00:46:29,330 --> 00:46:32,690
+قدرنا نثبت الجزء هذا automatically بقول أن هذا
+
+564
+00:46:32,690 --> 00:46:38,460
+true لأن هما equivalent لبعضهذه الcontra positive
+
+565
+00:46:38,460 --> 00:46:49,520
+نستطيع أن نشتغل عليها و نكمل شغلنا طيب في
+
+566
+00:46:49,520 --> 00:46:57,320
+ال vacuous approve او اثبت انه من نفس ال P اللي
+
+567
+00:46:57,320 --> 00:47:02,900
+ماعطينا إياها اثبت negation P فهو بيعطيني ان P is
+
+568
+00:47:02,900 --> 00:47:08,170
+true اروح اثبتله انnegation بيه هي ال true فهذه
+
+569
+00:47:08,170 --> 00:47:13,850
+صارت عديمة الفائدة فك يصف او عديمة الفائدة مالهاش
+
+570
+00:47:13,850 --> 00:47:20,110
+فائدة فهنا أثبتنا اثبات انه مش حاج درجي بالناتج
+
+571
+00:47:20,110 --> 00:47:23,470
+هذه عديمة الفائدة و هناخد حالات هنا طبعا حالتها
+
+572
+00:47:23,470 --> 00:47:26,170
+نادرة خفيفة مافيش حالات كتيرة احنا معظم شغلنا
+
+573
+00:47:26,170 --> 00:47:32,350
+هيكون هنا طيب trivial proof هذه بنثبت منها ال Q من
+
+574
+00:47:32,350 --> 00:47:38,040
+نفسهاأنا مش محتاج ال premises، احنا مش محتاجين ال
+
+575
+00:47:38,040 --> 00:47:42,700
+premises، من ال Q نفسها بفقدها، فهدئ trivial أو
+
+576
+00:47:42,700 --> 00:47:47,660
+تافت، يعني بمعنى ال premises تبعتي مش محتاجها، مش
+
+577
+00:47:47,660 --> 00:47:51,240
+محتاجينها، طبعا حالات نادرة هذه ولا مش كتير، الشغل
+
+578
+00:47:51,240 --> 00:47:58,360
+المعظم هو هيكون في الجزئيتين اللي في الأولالمرة
+
+579
+00:47:58,360 --> 00:48:01,380
+الجاي نبدأ في ال strategies هذه نبدأ في أول طريقة
+
+580
+00:48:01,380 --> 00:48:04,660
+ناخد ال direct و بعدين نعرج ناخد examples عليها و
+
+581
+00:48:04,660 --> 00:48:09,200
+بعدين نشتغل على ال indirect لأن
+
+582
+00:48:09,200 --> 00:48:12,700
+في عندنا ال contradiction برضه هنتكلم عنها كطريقة
+
+583
+00:48:12,700 --> 00:48:16,640
+خامسة و هم الأهم هيكون في شغلنا ال direct و ال
+
+584
+00:48:16,640 --> 00:48:19,360
+indirect و ال indirect زي ما قلنا دايما خلوا في
+
+585
+00:48:19,360 --> 00:48:22,720
+بالكوا ال contrapositive و في حاجة تانية ال
+
+586
+00:48:22,720 --> 00:48:26,870
+contradictionال .. ال contradiction هم التلاتة
+
+587
+00:48:26,870 --> 00:48:29,290
+اللي خلينا .. اللي هنقول هم فعليا بنستخدم ..
+
+588
+00:48:29,290 --> 00:48:32,410
+بنستخدمهم و هنستعملهم، يعطيكوا العافية، السلام
+
+589
+00:48:32,410 --> 00:48:32,710
+عليكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f27ebe59cdc2e76ba3e10db42880f222fec8e597
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_raw.json
@@ -0,0 +1 @@
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"start": 262.81, "end": 290.61, "text": "طيب ال axioms خلاص احنا عارفين ان هي ال .. او البديهيات شئ معروف و بديهي ممكن يكون مثبت و ممكن مايكونش مثبت و هنتكلم عن تعريف شغل مش مثبتة إيش ممكن نعرفها يعني ف .. بس هي بديهيات دائما صحيحة مسلمات شئ مسلم فيه معلومة مسلم فيها بقدر مباشرة أبدأ منها و أشتغل نبدأ منها .. ال .. ال hypothesis أو ال .. الفرضيات بنفرض شغل و انتوا دايما في أثبتاتكوا كنتوا تستعملوها", "tokens": [9566, 1829, 3555, 2423, 6360, 72, 4785, 16490, 1211, 33546, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 16472, 39896, 2423, 4386, 1975, 2407, 29739, 16254, 3224, 1829, 9307, 13412, 19986, 20449, 32887, 5172, 4032, 4724, 16254, 3224, 1829, 3714, 43020, 7251, 30544, 3714, 12984, 3555, 2655, 4032, 3714, 43020, 19446, 1829, 30544, 8592, 3714, 12984, 3555, 2655, 4032, 8032, 29399, 4117, 19528, 18871, 37279, 16572, 5172, 13412, 17082, 1211, 37893, 3714, 12984, 3555, 2655, 3660, 11933, 1829, 8592, 3714, 43020, 8717, 3615, 28480, 11296, 37495, 22653, 6156, 4386, 4724, 3794, 39896, 4724, 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بعدين بتعمموها مظبوط فانتوا دائما بتبدأ let assume that و بتحطوا الفرضية بتاعتكم بتحطوا الفرضية فانتوا بتبدأوا بمعلومة فعليا فيها فرضية ال premises لأ ال premises معطية زي لما أقولكوا إذا", "tokens": [3215, 16373, 15042, 39894, 44510, 10721, 718, 9122, 15730, 6552, 9122, 15730, 6156, 43042, 10632, 39894, 5172, 43042, 14407, 13412, 17082, 1211, 11296, 37893, 4724, 11242, 2288, 13063, 1829, 16472, 39896, 11778, 16373, 15042, 20328, 5016, 4724, 3794, 39894, 5172, 43042, 2407, 11296, 39894, 5172, 43042, 14407, 2423, 5718, 104, 3555, 9307, 6055, 3555, 3615, 4117, 14407, 5296, 5016, 6027, 3660, 16490, 33546, 3660, 4032, 39182, 9957, 39894, 25957, 2304, 2407, 11296, 3714, 19913, 3555, 2407, 9566, 6156, 7649, 2655, 14407, 11778, 16373, 15042, 39894, 44510, 10721, 718, 6552, 300, 4032, 39894, 5016, 9566, 14407, 27188, 43042, 10632, 39894, 995, 34268, 24793, 39894, 5016, 9566, 14407, 27188, 43042, 10632, 6156, 7649, 2655, 14407, 39894, 44510, 10721, 14407, 4724, 2304, 30241, 20498, 3660, 6156, 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0.78759765625}, {"start": 308.5, "end": 309.04, "word": " بتحطوا", "probability": 0.9569091796875}, {"start": 309.04, "end": 310.06, "word": " الفرضية", "probability": 0.96240234375}, {"start": 310.06, "end": 310.5, "word": " بتاعتكم", "probability": 0.8541259765625}, {"start": 310.5, "end": 311.12, "word": " بتحطوا", "probability": 0.89404296875}, {"start": 311.12, "end": 311.44, "word": " الفرضية", "probability": 0.9820963541666666}, {"start": 311.44, "end": 311.7, "word": " فانتوا", "probability": 0.9658203125}, {"start": 311.7, "end": 312.06, "word": " بتبدأوا", "probability": 0.81500244140625}, {"start": 312.06, "end": 312.4, "word": " بمعلومة", "probability": 0.87099609375}, {"start": 312.4, "end": 312.76, "word": " فعليا", "probability": 0.925048828125}, {"start": 312.76, "end": 313.08, "word": " فيها", "probability": 0.772216796875}, {"start": 313.08, "end": 313.48, "word": " فرضية", "probability": 0.9835611979166666}, {"start": 313.48, "end": 314.18, "word": " ال", "probability": 0.9384765625}, {"start": 314.18, "end": 314.46, "word": " premises", "probability": 0.96435546875}, {"start": 314.46, "end": 314.9, "word": " لأ", "probability": 0.813720703125}, {"start": 314.9, "end": 315.64, "word": " ال", "probability": 0.88330078125}, {"start": 315.64, "end": 315.88, "word": " premises", "probability": 0.8974609375}, {"start": 315.88, "end": 316.8, "word": " معطية", "probability": 0.7272135416666666}, {"start": 316.8, "end": 317.12, "word": " زي", "probability": 0.913818359375}, {"start": 317.12, "end": 317.28, "word": " لما", "probability": 0.90869140625}, {"start": 317.28, "end": 318.1, "word": " أقولكوا", "probability": 0.8197021484375}, {"start": 318.1, "end": 318.52, "word": " إذا", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 13, "seek": 34870, "start": 320.18, "end": 348.7, "text": "ال form الفلاني او ال statement الفلانية is true اثبتلي ان ال form الفلانية is true فإذا انا اعطيتكوا حاجة انتوا مش مجبرين تثبتوها حاجة انا بقولكوا 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طريق rules of inference عن طريق شوية قواعد استدلال قواعد انا بدي استدل منها بشوية خطوات أطلع شوية conclusions عشان أصل ال conclusion الأساسية اللى بدي أصلها اللى بدنا نصلها", "tokens": [2304, 12984, 3555, 2655, 3660, 12399, 3714, 43020, 19446, 6055, 30544, 8592, 50113, 3555, 2655, 3660, 4032, 5016, 8315, 8717, 2655, 4117, 19528, 18871, 10874, 11622, 1829, 3224, 39896, 4117, 23032, 1829, 3555, 1975, 2407, 1975, 8315, 4724, 16254, 5551, 12984, 3555, 2655, 11296, 18871, 23032, 16572, 4587, 4474, 295, 38253, 18871, 23032, 16572, 4587, 13412, 2407, 10632, 12174, 14407, 22488, 44713, 3215, 1211, 6027, 12174, 14407, 22488, 1975, 8315, 4724, 16254, 44713, 3215, 1211, 9154, 11296, 4724, 8592, 2407, 10632, 16490, 9566, 2407, 9307, 5551, 9566, 1211, 3615, 13412, 2407, 10632, 22865, 6225, 8592, 7649, 5551, 36520, 2423, 10063, 16247, 3794, 32277, 10632, 13672, 7578, 4724, 16254, 5551, 36520, 11296, 13672, 7578, 47525, 8315, 8717, 36520, 11296], "avg_logprob": -0.19209558598133697, 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0.9761962890625}, {"start": 1189.18, "end": 1189.68, "word": " الاستدلال", "probability": 0.98486328125}, {"start": 1189.68, "end": 1190.24, "word": " المنطقي", "probability": 0.96923828125}, {"start": 1190.24, "end": 1190.68, "word": " لو", "probability": 0.95654296875}, {"start": 1190.68, "end": 1191.16, "word": " قولنا", "probability": 0.9296875}, {"start": 1191.16, "end": 1194.64, "word": " P", "probability": 0.37109375}, {"start": 1194.64, "end": 1195.22, "word": " employees", "probability": 0.37841796875}, {"start": 1195.22, "end": 1195.6, "word": " Q", "probability": 0.71533203125}, {"start": 1195.6, "end": 1195.96, "word": " is", "probability": 0.896484375}, {"start": 1195.96, "end": 1196.3, "word": " true", "probability": 0.88623046875}, {"start": 1196.3, "end": 1197.74, "word": " and", "probability": 0.77880859375}, {"start": 1197.74, "end": 1198.94, "word": " Q", "probability": 0.85400390625}, {"start": 1198.94, "end": 1199.4, "word": " employees", "probability": 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"end": 1208.18, "word": " درست", "probability": 0.90478515625}, {"start": 1208.18, "end": 1208.9, "word": " هتنجح", "probability": 0.93115234375}], "temperature": 1.0}, {"id": 46, "seek": 123936, "start": 1209.97, "end": 1239.37, "text": "إذا نجحت هجيبلك هدية فإذا إذا درست هجيبلك هدية إذا طبعا مشيت كلها تحققت صح إذا الفرضية كانت مشهورة طيب برضه في الاستدلال لل or لل disjunctive ل ال disjunctive إذا P or Q is true is true لحظة طيب negation", "tokens": [28814, 15730, 8717, 7435, 33753, 8032, 7435, 1829, 3555, 23275, 8032, 3215, 10632, 6156, 28814, 15730, 11933, 15730, 11778, 2288, 14851, 8032, 7435, 1829, 3555, 23275, 8032, 3215, 10632, 11933, 15730, 23032, 3555, 3615, 995, 37893, 36081, 28242, 11296, 6055, 5016, 4587, 38149, 20328, 5016, 11933, 15730, 27188, 43042, 10632, 25961, 2655, 37893, 3224, 13063, 3660, 23032, 1829, 3555, 4724, 43042, 3224, 8978, 42963, 14851, 3215, 1211, 6027, 24976, 420, 24976, 717, 10010, 20221, 5296, 2423, 717, 10010, 20221, 11933, 15730, 430, 420, 1249, 307, 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"word": " في", "probability": 0.939453125}, {"start": 1222.67, "end": 1223.47, "word": " الاستدلال", "probability": 0.9474609375}, {"start": 1223.47, "end": 1223.83, "word": " لل", "probability": 0.900390625}, {"start": 1223.83, "end": 1224.35, "word": " or", "probability": 0.7041015625}, {"start": 1224.35, "end": 1224.67, "word": " لل", "probability": 0.69384765625}, {"start": 1224.67, "end": 1227.11, "word": " disjunctive", "probability": 0.7647298177083334}, {"start": 1227.11, "end": 1227.83, "word": " ل", "probability": 0.3447265625}, {"start": 1227.83, "end": 1228.11, "word": " ال", "probability": 0.21826171875}, {"start": 1228.11, "end": 1229.01, "word": " disjunctive", "probability": 0.8173828125}, {"start": 1229.01, "end": 1230.25, "word": " إذا", "probability": 0.86181640625}, {"start": 1230.25, "end": 1230.91, "word": " P", "probability": 0.4345703125}, {"start": 1230.91, "end": 1231.67, "word": " or", "probability": 0.90185546875}, {"start": 1231.67, "end": 1232.63, "word": " Q", "probability": 0.97314453125}, {"start": 1232.63, "end": 1233.09, "word": " is", "probability": 0.91796875}, {"start": 1233.09, "end": 1233.47, "word": " true", "probability": 0.927734375}, {"start": 1233.47, "end": 1234.77, "word": " is", "probability": 0.59326171875}, {"start": 1234.77, "end": 1235.25, "word": " true", "probability": 0.9853515625}, {"start": 1235.25, "end": 1236.35, "word": " لحظة", "probability": 0.8076171875}, {"start": 1236.35, "end": 1237.97, "word": " طيب", "probability": 0.8660481770833334}, {"start": 1237.97, "end": 1239.37, "word": " negation", "probability": 0.7391357421875}], "temperature": 1.0}, {"id": 47, "seek": 126683, "start": 1239.99, "end": 1266.83, "text": "P is true معناته P false طبعا أنا جاعت بقول هذه كلها true وهذا طلعت false هذه must be true ليش؟ عشان كلها تطلع true لأنه خلاص هذه حكمنا عليها false or محتاجة واحد true فإذا لازم تكون هذه لازم تكون هذه فإذا Q is true", "tokens": [47, 307, 2074, 20449, 8315, 47395, 430, 7908, 23032, 3555, 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"probability": 0.873046875}, {"start": 1255.87, "end": 1256.05, "word": " عليها", "probability": 0.98681640625}, {"start": 1256.05, "end": 1256.33, "word": " false", "probability": 0.88916015625}, {"start": 1256.33, "end": 1256.99, "word": " or", "probability": 0.7529296875}, {"start": 1256.99, "end": 1257.65, "word": " محتاجة", "probability": 0.983642578125}, {"start": 1257.65, "end": 1257.95, "word": " واحد", "probability": 0.997314453125}, {"start": 1257.95, "end": 1258.37, "word": " true", "probability": 0.9755859375}, {"start": 1258.37, "end": 1259.83, "word": " فإذا", "probability": 0.75439453125}, {"start": 1259.83, "end": 1260.27, "word": " لازم", "probability": 0.9796549479166666}, {"start": 1260.27, "end": 1260.57, "word": " تكون", "probability": 0.993896484375}, {"start": 1260.57, "end": 1260.81, "word": " هذه", "probability": 0.75146484375}, {"start": 1260.81, "end": 1262.49, "word": " لازم", "probability": 0.9388020833333334}, {"start": 1262.49, "end": 1262.79, "word": " تكون", "probability": 0.99169921875}, {"start": 1262.79, "end": 1263.07, "word": " هذه", "probability": 0.95068359375}, {"start": 1263.07, "end": 1263.73, "word": " فإذا", "probability": 0.9404296875}, {"start": 1263.73, "end": 1264.65, "word": " Q", "probability": 0.7431640625}, {"start": 1264.65, "end": 1265.25, "word": " is", "probability": 0.8515625}, {"start": 1265.25, "end": 1266.83, "word": " true", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 48, "seek": 129397, "start": 1272.85, "end": 1293.97, "text": "Okay فإذا أخدنا مجموعة من ال rules of inference إذا كان .. طبعا لحظة ال .. ال .. ال .. ال .. ال antecedent مع ال consequence لما نيجي تنتين نعملهم", "tokens": [8297, 6156, 28814, 15730, 5551, 9778, 3215, 8315, 3714, 7435, 2304, 2407, 27884, 9154, 2423, 4474, 295, 38253, 11933, 15730, 25961, 4386, 23032, 3555, 3615, 995, 5296, 5016, 19913, 3660, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 23411, 1232, 317, 20449, 2423, 18326, 5296, 15042, 8717, 1829, 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P12", "probability": 0.992431640625}, {"start": 1532.91, "end": 1532.91, "word": " P12", "probability": 0.992431640625}, {"start": 1532.91, "end": 1533.11, "word": " P12", "probability": 0.99267578125}, {"start": 1533.11, "end": 1533.11, "word": " P12", "probability": 0.99267578125}, {"start": 1533.11, "end": 1533.11, "word": " P12", "probability": 0.99267578125}, {"start": 1533.11, "end": 1533.11, "word": " P12", "probability": 0.99267578125}, {"start": 1533.11, "end": 1533.17, "word": " P12", "probability": 0.99267578125}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.99267578125}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.99267578125}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.99267578125}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.992431640625}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.992431640625}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.99267578125}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.992431640625}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.992431640625}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.99267578125}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.99267578125}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.9921875}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.99169921875}, {"start": 1533.17, "end": 1533.17, "word": " P12", "probability": 0.991943359375}], "temperature": 1.0}, {"id": 58, "seek": 155565, "start": 1536.67, "end": 1555.65, "text": "بدنا منهم نثبت C فهدولة كلهم ال premises نتعامل معهم عساس ان هم ال antecedents تعودنا المعطيات تعودنا المقدمات للإثبات مقدمات الإثبات تبعنا و ال conclusion هو ال consequent عندنا مجموعة قواعة و قراءة شفناها", "tokens": [44510, 8315, 9154, 16095, 8717, 12984, 3555, 2655, 383, 6156, 3224, 3215, 12610, 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1539.67, "word": " فهدولة", "probability": 0.86533203125}, {"start": 1539.67, "end": 1540.21, "word": " كلهم", "probability": 0.957275390625}, {"start": 1540.21, "end": 1540.41, "word": " ال", "probability": 0.92822265625}, {"start": 1540.41, "end": 1540.75, "word": " premises", "probability": 0.931640625}, {"start": 1540.75, "end": 1541.59, "word": " نتعامل", "probability": 0.8455078125}, {"start": 1541.59, "end": 1541.83, "word": " معهم", "probability": 0.79541015625}, {"start": 1541.83, "end": 1542.11, "word": " عساس", "probability": 0.6234537760416666}, {"start": 1542.11, "end": 1542.21, "word": " ان", "probability": 0.51025390625}, {"start": 1542.21, "end": 1542.51, "word": " هم", "probability": 0.81005859375}, {"start": 1542.51, "end": 1543.19, "word": " ال", "probability": 0.94580078125}, {"start": 1543.19, "end": 1543.93, "word": " antecedents", "probability": 0.8562825520833334}, {"start": 1543.93, "end": 1544.57, "word": " تعودنا", "probability": 0.73486328125}, {"start": 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{"start": 1551.19, "end": 1553.17, "word": " consequent", "probability": 0.763916015625}, {"start": 1553.17, "end": 1553.97, "word": " عندنا", "probability": 0.6446533203125}, {"start": 1553.97, "end": 1554.25, "word": " مجموعة", "probability": 0.926171875}, {"start": 1554.25, "end": 1554.65, "word": " قواعة", "probability": 0.7400716145833334}, {"start": 1554.65, "end": 1554.85, "word": " و", "probability": 0.74853515625}, {"start": 1554.85, "end": 1555.19, "word": " قراءة", "probability": 0.7823486328125}, {"start": 1555.19, "end": 1555.65, "word": " شفناها", "probability": 0.8841552734375}], "temperature": 1.0}, {"id": 59, "seek": 158211, "start": 1556.21, "end": 1582.11, "text": "و أثبتناها و أتأكدنا منها بنشتغل و بنشتغل عليها بنحاول نشوف مين اللي بتتناسب معانا بحيث أنه والله إذا ال premises are true then the conclusion is true هذا اللي بدنا نصلّم هذا اللي بدنا نصلّم ناخد example لو قلنا suppose we have the following premises", "tokens": [2407, 5551, 12984, 3555, 2655, 8315, 11296, 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"word": " بحيث", "probability": 0.85723876953125}, {"start": 1564.93, "end": 1565.13, "word": " أنه", "probability": 0.4810791015625}, {"start": 1565.13, "end": 1565.45, "word": " والله", "probability": 0.8271484375}, {"start": 1565.45, "end": 1566.31, "word": " إذا", "probability": 0.9404296875}, {"start": 1566.31, "end": 1567.33, "word": " ال", "probability": 0.9130859375}, {"start": 1567.33, "end": 1567.67, "word": " premises", "probability": 0.94580078125}, {"start": 1567.67, "end": 1568.19, "word": " are", "probability": 0.9482421875}, {"start": 1568.19, "end": 1568.63, "word": " true", "probability": 0.98779296875}, {"start": 1568.63, "end": 1569.29, "word": " then", "probability": 0.74365234375}, {"start": 1569.29, "end": 1570.13, "word": " the", "probability": 0.8623046875}, {"start": 1570.13, "end": 1570.53, "word": " conclusion", "probability": 0.919921875}, {"start": 1570.53, "end": 1570.83, "word": " is", "probability": 0.96875}, {"start": 1570.83, "end": 1571.17, "word": " true", "probability": 0.974609375}, {"start": 1571.17, "end": 1572.47, "word": " هذا", "probability": 0.66845703125}, {"start": 1572.47, "end": 1572.57, "word": " اللي", "probability": 0.9853515625}, {"start": 1572.57, "end": 1572.75, "word": " بدنا", "probability": 0.948486328125}, {"start": 1572.75, "end": 1573.21, "word": " نصلّم", "probability": 0.6851806640625}, {"start": 1573.21, "end": 1573.53, "word": " هذا", "probability": 0.260986328125}, {"start": 1573.53, "end": 1573.87, "word": " اللي", "probability": 0.98974609375}, {"start": 1573.87, "end": 1574.23, "word": " بدنا", "probability": 0.969970703125}, {"start": 1574.23, "end": 1575.13, "word": " نصلّم", "probability": 0.9464111328125}, {"start": 1575.13, "end": 1575.95, "word": " ناخد", "probability": 0.9464518229166666}, {"start": 1575.95, "end": 1577.61, "word": " example", "probability": 0.81591796875}, {"start": 1577.61, "end": 1579.13, "word": " لو", "probability": 0.966796875}, {"start": 1579.13, "end": 1579.49, "word": " قلنا", "probability": 0.9386393229166666}, {"start": 1579.49, "end": 1580.09, "word": " suppose", "probability": 0.541015625}, {"start": 1580.09, "end": 1580.81, "word": " we", "probability": 0.9482421875}, {"start": 1580.81, "end": 1581.07, "word": " have", "probability": 0.94677734375}, {"start": 1581.07, "end": 1581.21, "word": " the", "probability": 0.90576171875}, {"start": 1581.21, "end": 1581.59, "word": " following", "probability": 0.8720703125}, {"start": 1581.59, "end": 1582.11, "word": " premises", "probability": 0.974609375}], "temperature": 1.0}, {"id": 60, "seek": 160260, "start": 1583.18, "end": 1602.6, "text": "لأ معطيات مش بالضروري أن هي مسلمات بالنسبالنا بس هي معطيات بقدر أقولكنه معطيات حسب حالة معينة كلهم are true حسب حالة معينة طيب it's not sunny and it's cold هي مش مشمسة الدنيا مش مشمسة و بريد تمام", "tokens": [1211, 10721, 20449, 9566, 1829, 9307, 37893, 20666, 11242, 2288, 13063, 1829, 14739, 39896, 47524, 19528, 9307, 20666, 1863, 35457, 6027, 8315, 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"end": 1585.42, "word": " هي", "probability": 0.82470703125}, {"start": 1585.42, "end": 1586.74, "word": " مسلمات", "probability": 0.9401041666666666}, {"start": 1586.74, "end": 1587.14, "word": " بالنسبالنا", "probability": 0.97431640625}, {"start": 1587.14, "end": 1587.3, "word": " بس", "probability": 0.76220703125}, {"start": 1587.3, "end": 1587.38, "word": " هي", "probability": 0.83251953125}, {"start": 1587.38, "end": 1587.82, "word": " معطيات", "probability": 0.992431640625}, {"start": 1587.82, "end": 1588.56, "word": " بقدر", "probability": 0.806640625}, {"start": 1588.56, "end": 1589.06, "word": " أقولكنه", "probability": 0.8233642578125}, {"start": 1589.06, "end": 1589.7, "word": " معطيات", "probability": 0.947021484375}, {"start": 1589.7, "end": 1589.96, "word": " حسب", "probability": 0.987548828125}, {"start": 1589.96, "end": 1590.24, "word": " حالة", "probability": 0.9943033854166666}, {"start": 1590.24, "end": 1590.9, "word": " معينة", "probability": 0.9864908854166666}, 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0.7989908854166666}], "temperature": 1.0}, {"id": 82, "seek": 221057, "start": 2182.73, "end": 2210.57, "text": "إذا حددنا C هتخرب كل ال .. ال .. ال .. ال inference هذه واضحة؟ ال rule كلها هتخرب ليش؟ لأن إذا بدي أحدد يمكن ماتطلعش هي ال true فيهم لأن احنا قلنا there exist معناته ممكن تكون واحدة من مجموعة عشرة من عشرة elements واحدة منهم بتحققنا ال P of X كويس؟ فإذا بدي أحددها any منهم بقدرش بقولكوا هقولكوا لأ مش بالضرورة", "tokens": [28814, 15730, 11331, 3215, 3215, 8315, 383, 8032, 2655, 9778, 25513, 28242, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 38253, 29538, 4032, 46958, 5016, 3660, 22807, 2423, 4978, 28242, 11296, 8032, 2655, 9778, 25513, 32239, 8592, 22807, 5296, 33456, 11933, 15730, 4724, 16254, 5551, 24401, 3215, 7251, 43020, 3714, 9307, 9566, 1211, 3615, 8592, 39896, 2423, 2074, 8978, 16095, 5296, 33456, 1975, 5016, 8315, 12174, 1211, 8315, 456, 2514, 20449, 8315, 47395, 3714, 43020, 6055, 30544, 36764, 24401, 3660, 9154, 3714, 7435, 2304, 2407, 27884, 6225, 8592, 25720, 9154, 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عشان", "probability": 0.9547526041666666}, {"start": 2265.13, "end": 2265.29, "word": " أقول", "probability": 0.697265625}], "temperature": 1.0}, {"id": 85, "seek": 229448, "start": 2267.33, "end": 2294.49, "text": "يوجد في فضاء العينة element واحد على الأقل بحققنا ال function P of X طيب، كويس ال fallacy is an inference rule or other proof method is not logically valid", "tokens": [1829, 29245, 3215, 8978, 6156, 11242, 16606, 18863, 9957, 3660, 4478, 36764, 24401, 15844, 16247, 4587, 1211, 4724, 5016, 4587, 4587, 8315, 2423, 2445, 430, 295, 1783, 23032, 1829, 3555, 12399, 9122, 45865, 3794, 2423, 2100, 2551, 307, 364, 38253, 4978, 420, 661, 8177, 3170, 307, 406, 38887, 7363], "avg_logprob": -0.3274999898672104, "compression_ratio": 1.2181818181818183, "no_speech_prob": 0.0, "words": [{"start": 2267.33, "end": 2268.27, "word": "يوجد", "probability": 0.7020670572916666}, {"start": 2268.27, "end": 2268.35, "word": " في", "probability": 0.8916015625}, {"start": 2268.35, "end": 2268.65, 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"end": 2293.25, "word": " is", "probability": 0.91064453125}, {"start": 2293.25, "end": 2293.45, "word": " not", "probability": 0.953125}, {"start": 2293.45, "end": 2293.93, "word": " logically", "probability": 0.87646484375}, {"start": 2293.93, "end": 2294.49, "word": " valid", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 86, "seek": 231176, "start": 2295.94, "end": 2311.76, "text": "زي ان انتوا تثبته عكس ال true تثبته ان ال function false اذا كانت false معناته عكسها true هنا انكوا تثبته العكس", "tokens": [11622, 1829, 16472, 16472, 2655, 14407, 6055, 12984, 3555, 47395, 6225, 4117, 3794, 2423, 2074, 6055, 12984, 3555, 47395, 16472, 2423, 2445, 7908, 1975, 15730, 25961, 2655, 7908, 20449, 8315, 47395, 6225, 4117, 3794, 11296, 2074, 34105, 16472, 4117, 14407, 6055, 12984, 3555, 47395, 18863, 4117, 3794], "avg_logprob": -0.1949869723369678, "compression_ratio": 1.5350877192982457, "no_speech_prob": 0.0, "words": [{"start": 2295.94, "end": 2296.34, "word": "زي", 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إن أنا أثبت العكس و تفاجأوا أنه طب ماشي ما هي مش بضروري أن العكس يثبت الصحة هذا ممكن يعمللنا حاجة بتسميها fallacy أو مغلطة", "tokens": [3555, 2655, 9381, 13546, 21542, 38436, 28671, 3714, 17082, 1211, 9566, 9307, 5551, 5016, 1829, 7649, 995, 8978, 23758, 9673, 2407, 11242, 45367, 6156, 6027, 4386, 2423, 2100, 2551, 5296, 15042, 8717, 1829, 7435, 1829, 8717, 2655, 4117, 19528, 18871, 9673, 17082, 1211, 9566, 3660, 13672, 1829, 3714, 43020, 6055, 2655, 9381, 13546, 9154, 39896, 4117, 11933, 8592, 1829, 36145, 41850, 5551, 12984, 3555, 2655, 18863, 4117, 3794, 4032, 6055, 5172, 26108, 10721, 14407, 14739, 3224, 23032, 3555, 3714, 33599, 1829, 19446, 39896, 37893, 4724, 11242, 2288, 13063, 1829, 14739, 18863, 4117, 3794, 7251, 12984, 3555, 2655, 31767, 5016, 3660, 23758, 3714, 43020, 7251, 25957, 1211, 1211, 8315, 11331, 26108, 3660, 39894, 38251, 1829, 11296, 2100, 2551, 34051, 3714, 17082, 1211, 9566, 3660], "avg_logprob": -0.1441532213601374, "compression_ratio": 1.7672413793103448, 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"word": " proof", "probability": 0.65380859375}, {"start": 2848.11, "end": 2848.77, "word": " هذه", "probability": 0.58447265625}, {"start": 2848.77, "end": 2849.71, "word": " بنثبت", "probability": 0.9444580078125}, {"start": 2849.71, "end": 2850.19, "word": " منها", "probability": 0.989990234375}, {"start": 2850.19, "end": 2851.47, "word": " ال", "probability": 0.252197265625}, {"start": 2851.47, "end": 2851.77, "word": " Q", "probability": 0.35107421875}, {"start": 2851.77, "end": 2852.35, "word": " من", "probability": 0.98681640625}, {"start": 2852.35, "end": 2852.91, "word": " نفسها", "probability": 0.9952799479166666}], "temperature": 1.0}, {"id": 108, "seek": 287552, "start": 2854.42, "end": 2875.52, "text": "أنا مش محتاج ال premises، احنا مش محتاجين ال premises، من ال Q نفسها بفقدها، فهدئ trivial أو تافت، يعني بمعنى ال premises تبعتي مش محتاجها، مش محتاجينها، طبعا حالات نادرة هذه ولا مش كتير، الشغل المعظم هو هيكون في الجزئيتين اللي في الأول", "tokens": [10721, 8315, 37893, 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"word": " مش", "probability": 0.97900390625}, {"start": 2867.66, "end": 2868.52, "word": " محتاجينها،", "probability": 0.929443359375}, {"start": 2868.52, "end": 2868.7, "word": " طبعا", "probability": 0.992919921875}, {"start": 2868.7, "end": 2869.04, "word": " حالات", "probability": 0.8987630208333334}, {"start": 2869.04, "end": 2869.3, "word": " نادرة", "probability": 0.9376627604166666}, {"start": 2869.3, "end": 2869.48, "word": " هذه", "probability": 0.20556640625}, {"start": 2869.48, "end": 2869.6, "word": " ولا", "probability": 0.58544921875}, {"start": 2869.6, "end": 2869.74, "word": " مش", "probability": 0.9951171875}, {"start": 2869.74, "end": 2870.58, "word": " كتير،", "probability": 0.9554443359375}, {"start": 2870.58, "end": 2871.24, "word": " الشغل", "probability": 0.9090169270833334}, {"start": 2871.24, "end": 2871.6, "word": " المعظم", "probability": 0.936767578125}, {"start": 2871.6, "end": 2871.68, "word": " هو", "probability": 0.8701171875}, {"start": 2871.68, "end": 2872.06, "word": " هيكون", "probability": 0.833251953125}, {"start": 2872.06, "end": 2873.08, "word": " في", "probability": 0.90234375}, {"start": 2873.08, "end": 2873.76, "word": " الجزئيتين", "probability": 0.82578125}, {"start": 2873.76, "end": 2874.82, "word": " اللي", "probability": 0.938232421875}, {"start": 2874.82, "end": 2875.2, "word": " في", "probability": 0.611328125}, {"start": 2875.2, "end": 2875.52, "word": " الأول", "probability": 0.957763671875}], "temperature": 1.0}, {"id": 109, "seek": 290316, "start": 2877.68, "end": 2903.16, "text": "المرة الجاي نبدأ في ال strategies هذه نبدأ في أول طريقة ناخد ال direct و بعدين نعرج ناخد examples عليها و بعدين نشتغل على ال indirect لأن في عندنا ال contradiction برضه هنتكلم عنها كطريقة خامسة و هم الأهم هيكون في شغلنا ال direct و ال indirect و ال indirect زي ما قلنا دايما خلوا في بالكوا ال contrapositive و في حاجة تانية ال contradiction", "tokens": [45340, 25720, 25724, 47302, 8717, 44510, 10721, 8978, 2423, 9029, 29538, 8717, 44510, 10721, 8978, 5551, 12610, 23032, 16572, 28671, 8717, 47283, 3215, 2423, 2047, 4032, 39182, 9957, 8717, 3615, 47341, 8717, 47283, 3215, 5110, 25894, 11296, 4032, 39182, 9957, 8717, 8592, 2655, 17082, 1211, 15844, 2423, 19523, 5296, 33456, 8978, 43242, 8315, 2423, 34937, 4724, 43042, 3224, 8032, 29399, 4117, 19528, 18871, 11296, 9122, 9566, 16572, 28671, 16490, 10943, 3794, 3660, 4032, 8032, 2304, 16247, 16095, 39896, 30544, 8978, 13412, 17082, 1211, 8315, 2423, 2047, 4032, 2423, 19523, 4032, 2423, 19523, 30767, 1829, 19446, 12174, 1211, 8315, 11778, 47302, 15042, 16490, 1211, 14407, 8978, 20666, 4117, 14407, 2423, 660, 4007, 329, 2187, 4032, 8978, 11331, 26108, 3660, 6055, 7649, 10632, 2423, 34937], "avg_logprob": -0.10987903093618731, "compression_ratio": 1.9550561797752808, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2877.6800000000003, "end": 2878.36, "word": "المرة", "probability": 0.900634765625}, {"start": 2878.36, "end": 2878.56, "word": " الجاي", "probability": 0.6148681640625}, {"start": 2878.56, "end": 2879.14, "word": " نبدأ", "probability": 0.9816080729166666}, {"start": 2879.14, "end": 2879.44, "word": " في", "probability": 0.87158203125}, {"start": 2879.44, "end": 2879.6, "word": " ال", "probability": 0.9541015625}, {"start": 2879.6, "end": 2879.98, "word": " strategies", "probability": 0.900390625}, {"start": 2879.98, "end": 2880.28, "word": " هذه", "probability": 0.80859375}, {"start": 2880.28, "end": 2880.62, "word": " نبدأ", "probability": 0.8826497395833334}, {"start": 2880.62, "end": 2880.74, "word": " في", "probability": 0.888671875}, {"start": 2880.74, "end": 2881.04, "word": " أول", "probability": 0.96044921875}, {"start": 2881.04, "end": 2881.38, "word": " طريقة", "probability": 0.96142578125}, {"start": 2881.38, "end": 2881.72, "word": " ناخد", "probability": 0.9059244791666666}, {"start": 2881.72, "end": 2881.82, "word": " ال", "probability": 0.96728515625}, {"start": 2881.82, "end": 2882.1, "word": " direct", "probability": 0.953125}, {"start": 2882.1, "end": 2882.32, "word": " و", "probability": 0.849609375}, {"start": 2882.32, "end": 2882.66, "word": " بعدين", "probability": 0.92822265625}, {"start": 2882.66, "end": 2883.4, "word": " نعرج", "probability": 0.90673828125}, {"start": 2883.4, "end": 2883.78, "word": " ناخد", "probability": 0.8986002604166666}, {"start": 2883.78, "end": 2884.18, "word": " examples", "probability": 0.78759765625}, {"start": 2884.18, "end": 2884.54, "word": " عليها", "probability": 0.990234375}, {"start": 2884.54, "end": 2884.66, "word": " و", "probability": 0.94921875}, {"start": 2884.66, "end": 2884.88, "word": " بعدين", "probability": 0.97705078125}, {"start": 2884.88, "end": 2885.24, "word": " نشتغل", "probability": 0.99521484375}, {"start": 2885.24, "end": 2885.36, "word": " على", "probability": 0.8642578125}, {"start": 2885.36, "end": 2885.48, "word": " ال", "probability": 0.9853515625}, {"start": 2885.48, "end": 2885.84, "word": " indirect", "probability": 0.982421875}, {"start": 2885.84, "end": 2889.2, "word": " لأن", "probability": 0.750732421875}, {"start": 2889.2, "end": 2889.4, "word": " في", "probability": 0.64404296875}, {"start": 2889.4, "end": 2889.78, "word": " عندنا", "probability": 0.8681640625}, {"start": 2889.78, "end": 2889.96, "word": " ال", "probability": 0.9873046875}, {"start": 2889.96, "end": 2890.52, "word": " contradiction", "probability": 0.80615234375}, {"start": 2890.52, "end": 2891.32, "word": " برضه", "probability": 0.95263671875}, {"start": 2891.32, "end": 2891.84, "word": " هنتكلم", "probability": 0.955810546875}, {"start": 2891.84, "end": 2892.18, "word": " عنها", "probability": 0.99755859375}, {"start": 2892.18, "end": 2892.7, "word": " كطريقة", "probability": 0.9853515625}, {"start": 2892.7, "end": 2893.44, "word": " خامسة", "probability": 0.9737548828125}, {"start": 2893.44, "end": 2893.86, "word": " و", "probability": 0.92578125}, {"start": 2893.86, "end": 2894.04, "word": " هم", "probability": 0.9404296875}, {"start": 2894.04, "end": 2894.42, "word": " الأهم", "probability": 0.984619140625}, {"start": 2894.42, "end": 2894.8, "word": " هيكون", "probability": 0.782958984375}, {"start": 2894.8, "end": 2894.92, "word": " في", "probability": 0.93896484375}, {"start": 2894.92, "end": 2895.36, "word": " شغلنا", "probability": 0.9918212890625}, {"start": 2895.36, "end": 2895.66, "word": " ال", "probability": 0.356689453125}, {"start": 2895.66, "end": 2896.02, "word": " direct", "probability": 0.96044921875}, {"start": 2896.02, "end": 2896.56, "word": " و", "probability": 0.97021484375}, {"start": 2896.56, "end": 2896.64, "word": " ال", "probability": 0.98388671875}, {"start": 2896.64, "end": 2897.04, "word": " indirect", "probability": 0.98095703125}, {"start": 2897.04, "end": 2897.22, "word": " و", "probability": 0.87255859375}, {"start": 2897.22, "end": 2897.26, "word": " ال", "probability": 0.98486328125}, {"start": 2897.26, "end": 2897.56, "word": " indirect", "probability": 0.974609375}, {"start": 2897.56, "end": 2897.76, "word": " زي", "probability": 0.929931640625}, {"start": 2897.76, "end": 2897.82, "word": " ما", "probability": 0.97900390625}, {"start": 2897.82, "end": 2898.14, "word": " قلنا", "probability": 0.87646484375}, {"start": 2898.14, "end": 2898.96, "word": " دايما", "probability": 0.9296875}, {"start": 2898.96, "end": 2899.26, "word": " خلوا", "probability": 0.8733723958333334}, {"start": 2899.26, "end": 2899.36, "word": " في", "probability": 0.923828125}, {"start": 2899.36, "end": 2899.78, "word": " بالكوا", "probability": 0.8089192708333334}, {"start": 2899.78, "end": 2900.02, "word": " ال", "probability": 0.93603515625}, {"start": 2900.02, "end": 2900.86, "word": " contrapositive", "probability": 0.754150390625}, {"start": 2900.86, "end": 2901.94, "word": " و", "probability": 0.94091796875}, {"start": 2901.94, "end": 2902.08, "word": " في", "probability": 0.76318359375}, {"start": 2902.08, "end": 2902.38, "word": " حاجة", "probability": 0.9954427083333334}, {"start": 2902.38, "end": 2902.6, "word": " تانية", "probability": 0.9921875}, {"start": 2902.6, "end": 2902.72, "word": " ال", "probability": 0.52587890625}, {"start": 2902.72, "end": 2903.16, "word": " contradiction", "probability": 0.80029296875}], "temperature": 1.0}, {"id": 110, "seek": 291271, "start": 2904.19, "end": 2912.71, "text": "ال .. ال contradiction هم التلاتة اللي خلينا .. اللي هنقول هم فعليا بنستخدم .. بنستخدمهم و هنستعملهم، يعطيكوا العافية، السلام عليكم", "tokens": [6027, 4386, 2423, 34937, 8032, 2304, 16712, 1211, 9307, 3660, 13672, 1829, 16490, 1211, 9957, 995, 4386, 13672, 1829, 8032, 1863, 39648, 8032, 2304, 6156, 3615, 20292, 995, 44945, 14851, 9778, 40448, 4386, 44945, 14851, 9778, 40448, 16095, 4032, 8032, 1863, 14851, 25957, 1211, 16095, 12399, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 12399, 21136, 37440, 25894, 24793], "avg_logprob": -0.22526042386889458, "compression_ratio": 1.5416666666666667, "no_speech_prob": 1.3709068298339844e-06, "words": [{"start": 2904.19, "end": 2904.51, "word": "ال", "probability": 0.93896484375}, {"start": 2904.51, "end": 2904.79, "word": " ..", "probability": 0.3466796875}, {"start": 2904.79, "end": 2904.95, "word": " ال", "probability": 0.9111328125}, {"start": 2904.95, "end": 2905.43, "word": " contradiction", "probability": 0.64404296875}, {"start": 2905.43, "end": 2906.43, "word": " هم", "probability": 0.8671875}, {"start": 2906.43, "end": 2906.87, "word": " التلاتة", "probability": 0.9644775390625}, {"start": 2906.87, "end": 2906.95, "word": " اللي", "probability": 0.908203125}, {"start": 2906.95, "end": 2907.31, "word": " خلينا", "probability": 0.7808837890625}, {"start": 2907.31, "end": 2907.43, "word": " ..", "probability": 0.5107421875}, {"start": 2907.43, "end": 2907.65, "word": " اللي", "probability": 0.99609375}, {"start": 2907.65, "end": 2907.93, "word": " هنقول", "probability": 0.7903645833333334}, {"start": 2907.93, "end": 2908.13, "word": " هم", "probability": 0.962890625}, {"start": 2908.13, "end": 2908.69, "word": " فعليا", "probability": 0.88671875}, {"start": 2908.69, "end": 2909.21, "word": " بنستخدم", "probability": 0.7674560546875}, {"start": 2909.21, "end": 2909.29, "word": " ..", "probability": 0.407958984375}, {"start": 2909.29, "end": 2909.87, "word": " بنستخدمهم", "probability": 0.92177734375}, {"start": 2909.87, "end": 2909.97, "word": " و", "probability": 0.49169921875}, {"start": 2909.97, "end": 2910.95, "word": " هنستعملهم،", "probability": 0.7623465401785714}, {"start": 2910.95, "end": 2911.29, "word": " يعطيكوا", "probability": 0.84033203125}, {"start": 2911.29, "end": 2912.17, "word": " العافية،", "probability": 0.8116455078125}, {"start": 2912.17, "end": 2912.41, "word": " السلام", "probability": 0.9345703125}, {"start": 2912.41, "end": 2912.71, "word": " عليكم", "probability": 0.883544921875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2913.547, "duration_after_vad": 2793.866249999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1b0836083ec605f6cca679006fec4fab388e73f8
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iWBsfo1xuN4_raw.srt
@@ -0,0 +1,2364 @@
+1
+00:00:18,880 --> 00:00:20,860
+بسم الله الرحمن الرحيم والصلاة والسلام علي أشرف
+
+2
+00:00:20,860 --> 00:00:23,240
+الأنبياء والمرسلين سيدنا محمد وعلى أليه وصحبه ليه
+
+3
+00:00:23,240 --> 00:00:27,900
+أجمعين بعد العيد كل عام تبخير ان شاء الله بنبدأ
+
+4
+00:00:27,900 --> 00:00:31,660
+اليوم في موضوع جديد ان شاء الله تعالى بعد ما خلصنا
+
+5
+00:00:31,660 --> 00:00:34,320
+ال propositions وخلصنا ال quantifications وخلصنا
+
+6
+00:00:34,320 --> 00:00:37,760
+ال quantifiers أخدناها و أخدنا ال predicate و ال
+
+7
+00:00:37,760 --> 00:00:42,940
+propositional function و خلصنا كل الشغل تبعنا وهنا
+
+8
+00:00:42,940 --> 00:00:48,000
+حددنالكم ال homework الجايان شاء الله تعالى اللي
+
+9
+00:00:48,000 --> 00:00:53,080
+هتسلموا يوم الأحد القادم، اليوم بنبدأ مع ال proofs
+
+10
+00:00:53,080 --> 00:00:58,840
+أو ال proof methods، ال proof methods فبنبدأ مع ال
+
+11
+00:00:58,840 --> 00:01:03,990
+.. ال proof method كطريقة رياضيةأو methods of
+
+12
+00:01:03,990 --> 00:01:08,870
+mathematical argument نقاش جدال ل .. بنسميها
+
+13
+00:01:08,870 --> 00:01:12,870
+approved methods can be formalized in terms of
+
+14
+00:01:12,870 --> 00:01:18,270
+rules of logical inference هذه عبارة عن .. عن
+
+15
+00:01:18,270 --> 00:01:22,790
+مجموعة statements بتبتها عن طريق logical inference
+
+16
+00:01:22,790 --> 00:01:26,850
+أو استدلالات منطقية الاستدلالات المنطقية هنعرفها
+
+17
+00:01:26,850 --> 00:01:30,050
+لقدام هنقول ان هي مجموعة patterns قوالب ثابتة
+
+18
+00:01:30,050 --> 00:01:34,590
+قوانينقوانين إنتوا لما كنتوا تثبتوا شغلة بتدوروا
+
+19
+00:01:34,590 --> 00:01:37,670
+إذا في قوانين تثبتها بتدوروا على القوانين و
+
+20
+00:01:37,670 --> 00:01:40,470
+بتحاولوا تطبقوا القانون اللي بتبدأوا تشتغلوا هنقول
+
+21
+00:01:40,470 --> 00:01:44,610
+الله let مثلا R اللي هي المقاومة بيثوي كذا بيثوي
+
+22
+00:01:44,610 --> 00:01:51,110
+كذا let ال volt بيثوي كذا then .. لحظة .. then I
+
+23
+00:01:51,110 --> 00:01:54,250
+ال current equal to كذا من وين جبته equal to كذا
+
+24
+00:01:54,250 --> 00:01:59,730
+هذه؟ من قانون Ohm فإذا في .. في ruleفي انكو rule
+
+25
+00:01:59,730 --> 00:02:05,350
+أثبتتوا منها جداش قيمة المقاومة أو ال current من
+
+26
+00:02:05,350 --> 00:02:12,350
+معلومتين سابقات جداش قيمة ال R and جداش قيمة ال
+
+27
+00:02:12,350 --> 00:02:17,550
+volt صح؟ تمام احنا مش هنشتغل اكتر من هيك اكتر من
+
+28
+00:02:17,550 --> 00:02:20,030
+هيك مش هنشتغل هاي اللي بدنا نشتغله وهي اللي بدنا
+
+29
+00:02:20,030 --> 00:02:25,560
+نعمله طرق أثباتنا هنشتغل بطريقتينطريقتين مرادفات
+
+30
+00:02:25,560 --> 00:02:28,600
+لبعض ولكن التنتين بيشتغلوا .. التنتين بنفعوا، كل
+
+31
+00:02:28,600 --> 00:02:31,860
+واحدة إلها حالات اللي ماشتغل فيها، إما إن أنا
+
+32
+00:02:31,860 --> 00:02:37,320
+أحاول أثبت ال .. ال correct لل conclusion صحة
+
+33
+00:02:37,320 --> 00:02:43,260
+الاستنتاج اللي بدي أثبته هذه الطريقة أو العكسأو
+
+34
+00:02:43,260 --> 00:02:49,140
+خطأ عكسها او خطأ عكسها و هنشوف لأن في حالات كتير
+
+35
+00:02:49,140 --> 00:02:53,560
+ممكن ماجدرش انا اثبت الشغل مباشرة فبضطر اشوف ايش
+
+36
+00:02:53,560 --> 00:02:57,500
+عكسها يمكن عكسها يكون اسهل اثباته فلو اثبتت ان
+
+37
+00:02:57,500 --> 00:03:04,400
+عكسها false فإذا هي true فهذه ال methods هنتكلم
+
+38
+00:03:04,400 --> 00:03:08,370
+عنها او ال technology هنتكلم عنها فيال .. ال
+
+39
+00:03:08,370 --> 00:03:12,650
+proves تمام شوية terminology بس قبل ما نبدأ نشتغل
+
+40
+00:03:12,650 --> 00:03:16,770
+شوية مصطلحات .. شوية مصطلحات بدنا نشتغل عليها ال
+
+41
+00:03:16,770 --> 00:03:19,410
+theorem ال theorem هي statement .. a statement
+
+42
+00:03:19,410 --> 00:03:23,810
+that has been proven to be true هي فعليا statement
+
+43
+00:03:23,810 --> 00:03:30,390
+عبارة تم إثبات صحتها هي في البلد تم إثبات صحتها
+
+44
+00:03:30,600 --> 00:03:34,360
+فإذا إذا كان فعلا ال statement اللي موجودة عندي أو
+
+45
+00:03:34,360 --> 00:03:38,900
+relation معينة علاقة معينة proposition معين اقدرت
+
+46
+00:03:38,900 --> 00:03:43,100
+أثبت إن هو true دائما أنا عملت نظرية أو أثبت نظرية
+
+47
+00:03:43,100 --> 00:03:48,140
+أثبت theorem أثبتنا ال theorem بتاعتنا حاجة تانية
+
+48
+00:03:48,140 --> 00:03:53,520
+برضه ال axioms بديهيات في حاجات أحيانا عشان نثبت
+
+49
+00:03:53,520 --> 00:03:57,450
+شغلة أنا محتاج معلومة مسبقةالمعلومة المسبقة قد
+
+50
+00:03:57,450 --> 00:04:01,490
+تكون أحد الأربعة اللي هنتكلم عنها اليوم، قد تكون
+
+51
+00:04:01,490 --> 00:04:08,890
+axioms أو بديهيات، قد تكون postulates أو
+
+52
+00:04:08,890 --> 00:04:16,090
+مسلمات، شيء مسلم فيه، ممكن تكون hypothesis، فرضيات
+
+53
+00:04:16,090 --> 00:04:20,170
+أو premises، معطيات
+
+54
+00:04:22,810 --> 00:04:26,270
+طيب ال axioms خلاص احنا عارفين ان هي ال .. او
+
+55
+00:04:26,270 --> 00:04:29,990
+البديهيات شئ معروف و بديهي ممكن يكون مثبت و ممكن
+
+56
+00:04:29,990 --> 00:04:33,230
+مايكونش مثبت و هنتكلم عن تعريف شغل مش مثبتة إيش
+
+57
+00:04:33,230 --> 00:04:36,970
+ممكن نعرفها يعني ف .. بس هي بديهيات دائما صحيحة
+
+58
+00:04:36,970 --> 00:04:40,910
+مسلمات شئ مسلم فيه معلومة مسلم فيها بقدر مباشرة
+
+59
+00:04:40,910 --> 00:04:44,190
+أبدأ منها و أشتغل نبدأ منها .. ال .. ال hypothesis
+
+60
+00:04:44,190 --> 00:04:49,270
+أو ال .. الفرضيات بنفرض شغل و انتوا دايما في
+
+61
+00:04:49,270 --> 00:04:53,880
+أثبتاتكوا كنتوا تستعملوهادائما بتبدأ let كذا
+
+62
+00:04:53,880 --> 00:04:58,260
+assume كذا فرضية بتفرضوا شغلها مش بضروري ان هي
+
+63
+00:04:58,260 --> 00:05:02,720
+دائما صح بس بتفرضوها بتفرضوا الاثبات تبعكوا لحالة
+
+64
+00:05:02,720 --> 00:05:06,680
+خاصة و بعدين بتعمموها مظبوط فانتوا دائما بتبدأ let
+
+65
+00:05:06,680 --> 00:05:11,120
+assume that و بتحطوا الفرضية بتاعتكم بتحطوا
+
+66
+00:05:11,120 --> 00:05:14,180
+الفرضية فانتوا بتبدأوا بمعلومة فعليا فيها فرضية ال
+
+67
+00:05:14,180 --> 00:05:20,440
+premises لأ ال premises معطية زي لما أقولكوا إذاال
+
+68
+00:05:20,440 --> 00:05:22,800
+form الفلاني او ال statement الفلانية is true
+
+69
+00:05:22,800 --> 00:05:26,820
+اثبتلي ان ال form الفلانية is true فإذا انا
+
+70
+00:05:26,820 --> 00:05:30,480
+اعطيتكوا حاجة انتوا مش مجبرين تثبتوها حاجة انا
+
+71
+00:05:30,480 --> 00:05:33,360
+بقولكوا والله given انا معطية هاي بدي اعطيكوا معطة
+
+72
+00:05:33,360 --> 00:05:37,540
+اذا كان ال .. ال .. ال proposition الفلاني true
+
+73
+00:05:37,540 --> 00:05:42,040
+اثبتولي كذا انه ال true هل هو دائما هذا مش اشي
+
+74
+00:05:42,040 --> 00:05:47,500
+مسلم فيه لأ مش مسلم فيه ولا هي فرضية ولا هي شئ
+
+75
+00:05:47,500 --> 00:05:51,600
+بديهي هي حاجة givenفهذه بيسميها premises بقولكوا
+
+76
+00:05:51,600 --> 00:05:57,040
+إذا كان صار كذا فإذا كذا وهذه عادة الجزئية اللي
+
+77
+00:05:57,040 --> 00:06:01,080
+دايما بتشتغل فيها في F then في جزئية F then كويسة
+
+78
+00:06:01,080 --> 00:06:05,220
+فإذا في عندى theorem وفي عندى مجموعة المقدمات لل
+
+79
+00:06:05,220 --> 00:06:08,120
+theorem عشان F بال theorem معينة و بعدين في عندنا
+
+80
+00:06:08,120 --> 00:06:12,070
+بين الاتنينال techniques اللى بدى استخدمها ال
+
+81
+00:06:12,070 --> 00:06:14,390
+rules اللى بدى استخدمها القوانين اللى لازم
+
+82
+00:06:14,390 --> 00:06:18,050
+أستعملها القوانين هذه بنسميها rules of inference
+
+83
+00:06:18,050 --> 00:06:24,490
+أو قواعد الاستدلال قواعد الاستدلال inference او
+
+84
+00:06:24,490 --> 00:06:31,450
+استدلال فبدى أستدل على معلومة من وجود مقطة معينة
+
+85
+00:06:31,450 --> 00:06:34,190
+مش بالضرورة ان ال theorem اللى بدى اشتغل عليها
+
+86
+00:06:34,190 --> 00:06:38,110
+مباشرة هكون بدى استدلال واحد وخلص إذا كان صار كذا
+
+87
+00:06:38,110 --> 00:06:41,690
+معناته اه هي النتيجة كذالأ انتوا هتحتاجوا اكتر من
+
+88
+00:06:41,690 --> 00:06:44,870
+rule فهذه اللي اسمها rules هي عبارة عن patterns
+
+89
+00:06:44,870 --> 00:06:50,150
+عبارة عن قالب ثابت قانون بتكون تستخدموه قانون
+
+90
+00:06:50,150 --> 00:06:54,570
+بتكون تستخدموه مش مضطرين تثبتوه انتوا فعليا مش
+
+91
+00:06:54,570 --> 00:06:57,770
+مضطرين تثبتوه معظم الحاجات اللي احنا هناخدها هي
+
+92
+00:06:57,770 --> 00:07:01,190
+أصلا مثبتة معناها مسبقا احنا ماخدينها مسبقا أساسا
+
+93
+00:07:01,190 --> 00:07:04,430
+أخدناها من كل ال truth tables اللي احنا درسناها
+
+94
+00:07:04,430 --> 00:07:09,350
+حتى الآن كويس فهذه مجموعة patterns بتقودني من
+
+95
+00:07:09,700 --> 00:07:14,080
+المسلمات خلّينا نسميها أو البديهيات أو الفرضيات أو
+
+96
+00:07:14,080 --> 00:07:20,280
+المعطيات عشان أثبت ال conclusions الاستنتاجات
+
+97
+00:07:20,280 --> 00:07:24,340
+المطلوبة منها عشان نثبت الاستنتاج المطلوب منها
+
+98
+00:07:24,340 --> 00:07:29,640
+فهذه مجموعة قوانين قواعد التلتة دول هم العناصر
+
+99
+00:07:29,640 --> 00:07:33,900
+المهمة عشان أقدر أثبت شغلها طيب بنعيدها كمان مرة
+
+100
+00:07:33,900 --> 00:07:38,600
+ال theorem زي ما قلنا هي شئ مثبت قدرنا نثبتهأو can
+
+101
+00:07:38,600 --> 00:07:43,860
+be shown to be true بقدر أورّي إنه والله صحيح أو
+
+102
+00:07:43,860 --> 00:07:47,540
+بيعطيين قيمة true إذا كدرنا نحصل على mathematical
+
+103
+00:07:47,540 --> 00:07:50,680
+statement بقدر أحصل عليها أو أثبت إن هي دايما true
+
+104
+00:07:50,680 --> 00:07:54,440
+فإذا theorem خلاص، دائما ال condition هذا is true
+
+105
+00:07:54,440 --> 00:08:00,790
+طيب ال hypothesisال form طبعا في الأيام بقول H1
+
+106
+00:08:00,790 --> 00:08:09,250
+and H2 and H3 and H4 and H5 and H6 and H7 and H8
+
+107
+00:08:09,250 --> 00:08:14,010
+and H9 and H10 and H11 and H12 and H13 and H14 and
+
+108
+00:08:14,010 --> 00:08:15,450
+H15 and H16 and H17 and H18 and H19 and H20 and
+
+109
+00:08:15,450 --> 00:08:20,110
+H21 and H22 and H21 and H22 and H21 and H21 and
+
+110
+00:08:20,110 --> 00:08:24,050
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+111
+00:08:24,050 --> 00:08:24,310
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+112
+00:08:24,310 --> 00:08:24,790
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+113
+00:08:24,790 --> 00:08:24,850
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+114
+00:08:24,850 --> 00:08:24,850
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+115
+00:08:24,850 --> 00:08:24,930
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+116
+00:08:24,930 --> 00:08:25,210
+H21 and H21 and H21 and H21 and H21 and H21 and
+
+117
+00:08:25,210 --> 00:08:28,990
+H21 and H21 and H21فكل الفكرة بس أنه بدنا نحقق أن
+
+118
+00:08:28,990 --> 00:08:33,310
+هدول كلهم يكونوا true عشان أحصل على ال true لمين،
+
+119
+00:08:33,310 --> 00:08:36,830
+لل conclusion اللي مطلوب اثباته، اللي مطلوب
+
+120
+00:08:36,830 --> 00:08:40,630
+اثباته، اللي عندنا احنا بتتكلم كلام عام، كلام بس
+
+121
+00:08:40,630 --> 00:08:44,430
+لمجرد الفهم، مادخلناش لسه في أي قوانين، لم ندخل في
+
+122
+00:08:44,430 --> 00:08:48,970
+أي قوانين، فعرفنا ال H اللي هي ال hypothesis و ال
+
+123
+00:08:48,970 --> 00:08:55,700
+C ال conclusionOkay ال theorem can be proven using
+
+124
+00:08:55,700 --> 00:09:00,640
+أما other theorems عن طريق نظريات أخرى بستخدم
+
+125
+00:09:00,640 --> 00:09:04,640
+نظرية أخرى و بحاول أثبت منها النظرية تبعتي أو
+
+126
+00:09:04,640 --> 00:09:09,000
+axioms مجموعة statements مسلم فيها ممكن ما تكونش
+
+127
+00:09:09,000 --> 00:09:12,330
+..مثبتة، ممكن ما تكونش مثبتة وحنا نتكلم عن جزيه
+
+128
+00:09:12,330 --> 00:09:16,570
+هيك طيب او انا بدي أثبتها عن طريق rules of
+
+129
+00:09:16,570 --> 00:09:21,730
+inference عن طريق شوية قواعد استدلال قواعد انا بدي
+
+130
+00:09:21,730 --> 00:09:26,430
+استدل منها بشوية خطوات أطلع شوية conclusions عشان
+
+131
+00:09:26,430 --> 00:09:28,970
+أصل ال conclusion الأساسية اللى بدي أصلها اللى
+
+132
+00:09:28,970 --> 00:09:35,370
+بدنا نصلهاأحيانا نظر ال .. ممكن أثناء شغل أطلع
+
+133
+00:09:35,370 --> 00:09:38,430
+نظرية في النص مثلا لسه ماوصلتش للي بديها و
+
+134
+00:09:38,430 --> 00:09:43,730
+ماوصلناش للي بدناها فهذه بسميها ال pre theorem لسه
+
+135
+00:09:43,730 --> 00:09:48,530
+ماوصلناش يعني مقدمة ل theorem تبعتي نظرية سابقة ل
+
+136
+00:09:48,530 --> 00:09:51,230
+theorem تبعتي عشان تتحقق ال theorem تبعتي لازم
+
+137
+00:09:51,230 --> 00:09:55,700
+تتحقق النظرية هذه الأولفأثناء شغله هتلاقوا أنه
+
+138
+00:09:55,700 --> 00:10:00,200
+حققنا نظرية قبل ما نصل للي بدناها فهذه بنسميها pre
+
+139
+00:10:00,200 --> 00:10:06,460
+-theorem أو لما .. لما .. كويس فهذه بنكون أحيانا
+
+140
+00:10:06,460 --> 00:10:10,580
+محتاجينها لتكميل ال proof تبعنا عشان نكمل ال
+
+141
+00:10:10,580 --> 00:10:13,440
+theorem تبعنا و نثبت ال theorem تبعنا بالعكس في
+
+142
+00:10:13,440 --> 00:10:16,600
+حاجة اسمها ال past theorem ال past اللي هي اللاحق
+
+143
+00:10:16,600 --> 00:10:20,460
+النظرية تعاليتنا أثبتناها بس ممكن ب process بسيط
+
+144
+00:10:20,460 --> 00:10:26,780
+أطلع نظرية تانيةفهي نظرية بقدر أثبتها من إثبات
+
+145
+00:10:26,780 --> 00:10:29,120
+نظريتنا اللي إحنا بنشتغل فيها نظرية اللي إحنا
+
+146
+00:10:29,120 --> 00:10:34,500
+بنشتغل فيها اللي هي Corollary كويس فهذه أو ال post
+
+147
+00:10:34,500 --> 00:10:39,920
+theorem تمام يعني بقدر ناخدها directly من ال
+
+148
+00:10:39,920 --> 00:10:44,060
+theorem اللي إحنا بنشتغل فيها كويس ال conjectures
+
+149
+00:10:44,060 --> 00:10:50,200
+أو ال conjecture هذه statement whose truth value
+
+150
+00:10:50,200 --> 00:10:56,930
+is a nounحاجة انا مسلم فيها ولكن ماقدرش اثبتها شيء
+
+151
+00:10:56,930 --> 00:10:59,610
+مسلم فيه ولكن مش قادرين نثبته وفي حاجات كتير مسلم
+
+152
+00:10:59,610 --> 00:11:04,070
+فيها بدهيات بس احنا نقولكوا و الله اثبتها مافيش
+
+153
+00:11:04,070 --> 00:11:10,930
+ممكنية نقعد نثبتها زي لو قلتلكوا كل رقم فيه لأكبر
+
+154
+00:11:10,930 --> 00:11:16,870
+منه طب اثبتوها كويس
+
+155
+00:11:16,870 --> 00:11:24,720
+اثبتوها انه لايوجد رقم أكبرلا يوجد رقم أكبر طب
+
+156
+00:11:24,720 --> 00:11:29,440
+ماوفيش، بس تقدر تثبتها؟ ليش؟ لأنه هضل واصل to
+
+157
+00:11:29,440 --> 00:11:35,560
+infinity كل رقم هلاجي فيه رقم أكبر منه هقولكوا لأ
+
+158
+00:11:35,560 --> 00:11:37,840
+ماهي الرقم الأكبر، و واحد تاني يقولوا لأ ما مش هذا
+
+159
+00:11:37,840 --> 00:11:40,740
+أكبر، فيه رقم أكبر منه طب لأمتى؟ فإذا في حاجات
+
+160
+00:11:40,740 --> 00:11:44,340
+مسلمة فيها بناخدها زي ما هي، بس إثبات مش مثبتة
+
+161
+00:11:44,340 --> 00:11:52,840
+فهذه برضه مجموعة نظريات فيconjecture أو مسلمات مش
+
+162
+00:11:52,840 --> 00:11:59,400
+مثبتة كويس ال inference rules الجزء الأهم خلصناها
+
+163
+00:11:59,400 --> 00:12:02,740
+لو اتكلمنا عن inference اتكلمنا عن المقدمات اللي
+
+164
+00:12:02,740 --> 00:12:08,240
+هنحتاجها اما مسلمات او بدهيات او فرضيات او معطيات
+
+165
+00:12:08,240 --> 00:12:11,100
+whatever يعني كلهم هنحتاجهم اي واحدة منهم ممكن
+
+166
+00:12:11,100 --> 00:12:14,140
+نحتاجها بس كل نظرية محتاجين واحدة منهم محتاجين
+
+167
+00:12:14,140 --> 00:12:18,040
+واحدة منهم نبدأ منها الشغل طيب ال inference rule
+
+168
+00:12:18,680 --> 00:12:22,740
+فعليا القواعدة اللى بنستخدمها للاستدلال بتتم عن
+
+169
+00:12:22,740 --> 00:12:26,220
+طريق patterns زى ما قولنا قوالة ثابتة، قوانين ..
+
+170
+00:12:26,220 --> 00:12:31,320
+قوانين ثابتة بنشتغل عليها بحيث انه بصير أعمل عملية
+
+171
+00:12:31,320 --> 00:12:38,640
+محاكا، إيش اللى موجود عندى؟ عندى antecedent واحدة
+
+172
+00:12:38,640 --> 00:12:44,340
+.. two antecedents أكم .. أكم معطى عنها، أكم سابق
+
+173
+00:12:44,340 --> 00:12:47,910
+عنها، أكم معلومة سابقة، خدنا نسميهاأكن معلومة
+
+174
+00:12:47,910 --> 00:12:52,210
+سابقة موجودة لدينا عشان أقدر أستنتج منها ال
+
+175
+00:12:52,210 --> 00:12:57,170
+consequence العاقبة للمعلومات السابقة هدول اللي هي
+
+176
+00:12:57,170 --> 00:13:02,330
+النتيجة بمعنى .. بمعنى النتيجةبقدر أعمل محاكاة،
+
+177
+00:13:02,330 --> 00:13:04,530
+إيش اللي موجود عندى، ومجموعة القوانين اللي الواحد
+
+178
+00:13:04,530 --> 00:13:08,010
+حافظها، اللي الواحد عارفها، إيش اللي تمشي بحيث أني
+
+179
+00:13:08,010 --> 00:13:11,690
+أطبقها، أطلع نتيجة، النتيجة دي اللي بدي إياها، مش
+
+180
+00:13:11,690 --> 00:13:13,830
+بالضرورة تكون مباشرة هي اللي بدي إياها، ممكن
+
+181
+00:13:13,830 --> 00:13:16,710
+النتيجة اللي أستخدمها عشان أجيب نتيجة تانية، لعند
+
+182
+00:13:16,710 --> 00:13:21,910
+ما نصل إياش لل conclusion المطلوب، المطلوب، تمام
+
+183
+00:13:24,730 --> 00:13:28,850
+ال implication ال implication احنا هيك هيك محتاجين
+
+184
+00:13:28,850 --> 00:13:33,510
+نحن نصله ليش لأن ال .. ال antecedent if antecedent
+
+185
+00:13:33,510 --> 00:13:37,270
+number one is true and antecedent number two is
+
+186
+00:13:37,270 --> 00:13:42,250
+true then the consequent is true فإذا أنا محتاج
+
+187
+00:13:42,250 --> 00:13:47,750
+then هذه if then فإذا أنا مقدرش أتحرك بدون ال
+
+188
+00:13:47,750 --> 00:13:52,070
+implication في ال proofs ال proofs محتاجة .. if
+
+189
+00:13:52,070 --> 00:13:58,510
+thenif then و هذه مدخل ال conditions عندكم في
+
+190
+00:13:58,510 --> 00:14:01,490
+البرمجة انت بتشتغل و مش بتشتغل على if then else
+
+191
+00:14:01,490 --> 00:14:06,110
+هذه مدخلها مدخلها ال implication شغلنا كله كنا
+
+192
+00:14:06,110 --> 00:14:08,050
+نكون شغالين على ال implication فانتوا لازم تكونوا
+
+193
+00:14:08,050 --> 00:14:10,030
+فاهمين ال implication صح عشان لما تحطوا ال
+
+194
+00:14:10,030 --> 00:14:13,010
+condition تكونوا فاهمين ال condition امتى هيكون
+
+195
+00:14:13,010 --> 00:14:16,770
+true و امتى هيكون false امتى هيكون true امتى هيكون
+
+196
+00:14:16,770 --> 00:14:21,610
+false فهذه تمثل فعليا ال antecedent one antecedent
+
+197
+00:14:21,610 --> 00:14:21,970
+two
+
+198
+00:14:24,980 --> 00:14:30,300
+الاتنين are given then consequent is true هذا
+
+199
+00:14:30,300 --> 00:14:34,020
+يمثلكوا antecedent number one and antecedent
+
+200
+00:14:34,020 --> 00:14:37,060
+number two فإذا هذه لازم تكون true و هذه لازم تكون
+
+201
+00:14:37,060 --> 00:14:40,360
+true جدش في عندكوا antecedents لازم كله يكون true
+
+202
+00:14:40,360 --> 00:14:44,440
+لإن هي المعطيات هو مدام معطيتلكوا فلازم تكون true
+
+203
+00:14:44,440 --> 00:14:51,550
+أو axiomsممكن تكون فرضيات، مديهيات، مسلمات، بس هي
+
+204
+00:14:51,550 --> 00:14:56,690
+لازم تكون true، كويس، then .. then معناته implies
+
+205
+00:14:56,690 --> 00:15:01,590
+implication .. بيستعمل implication consequent،
+
+206
+00:15:01,590 --> 00:15:06,690
+معناته بتمنلى حدوث النتيجة، بتمنلى حدوث النتيجة،
+
+207
+00:15:06,690 --> 00:15:12,610
+لعندي الآن كلام بيسميه عام نبدأ شوية في .. شوية
+
+208
+00:15:12,610 --> 00:15:19,430
+inference .. some inference rulesrule of addition
+
+209
+00:15:19,430 --> 00:15:25,530
+هالوقت لما نيجي نتكلم عن مشكلة هذا لو قولنا P is
+
+210
+00:15:25,530 --> 00:15:34,830
+true طيب P or أي شيء is true أكيد is true فإذا لو
+
+211
+00:15:34,830 --> 00:15:41,590
+كان عندكوا P is true then P or Q أكيد is true P or
+
+212
+00:15:41,590 --> 00:15:48,150
+K أكيد is true P or Z أكيد is true أكيدis it true؟
+
+213
+00:15:48,150 --> 00:15:51,610
+شيء بديهي جدا وهنا معلومة ماخدينها من مين من ال
+
+214
+00:15:51,610 --> 00:15:54,090
+disjunction أو ال or فهي الترث تابع اللي احنا
+
+215
+00:15:54,090 --> 00:15:59,470
+ماخدينه سابق نوعاك خلاص مضمونة طيب لو بالشكل هذا
+
+216
+00:15:59,470 --> 00:16:09,570
+عندكم P and Q is true فإذا إيش P is true و Q is
+
+217
+00:16:09,570 --> 00:16:13,390
+true صح برضه بديهية بديهية جدا من الترث تابع اللي
+
+218
+00:16:13,390 --> 00:16:19,300
+احنا أخدناهفهذه الـ simplification طيب لو قلنا P
+
+219
+00:16:19,300 --> 00:16:26,760
+is true and Q is true معناته هي and برضه is true
+
+220
+00:16:26,760 --> 00:16:32,960
+لأن هم أصلا هدولة الرابط بينهم and البديهية ان هو
+
+221
+00:16:32,960 --> 00:16:35,320
+الرابط بينهم and لأن احنا لسه قبل شويه قاعدين
+
+222
+00:16:35,320 --> 00:16:39,460
+بنحكي ايش antecedent one and antecedent two فهنا
+
+223
+00:16:39,460 --> 00:16:40,180
+هنا نسميهم
+
+224
+00:16:42,680 --> 00:16:46,140
+antecedent number one and antecedent number two
+
+225
+00:16:46,140 --> 00:16:55,820
+هدى true وهدى true فالان is true okay طيب ال .. ال
+
+226
+00:16:55,820 --> 00:16:59,160
+.. ال affirming أو التأكيد فيلمونيشيا نتكلم هنا عن
+
+227
+00:16:59,160 --> 00:17:02,880
+التأكيد و هنا بدنا هنا ناخد mean ال implication
+
+228
+00:17:02,880 --> 00:17:07,460
+فعشان ناخد ال implication خلينا نحط ال truth table
+
+229
+00:17:07,460 --> 00:17:09,980
+ل ال implication متذكرينه؟
+
+230
+00:17:16,410 --> 00:17:22,430
+ماذا يوجد هنا تمام
+
+231
+00:17:22,430 --> 00:17:32,950
+تمام دعوني أخد هنا ال P is true لاحظوا P is true
+
+232
+00:17:32,950 --> 00:17:40,290
+فإذا أنا بتكلم عن النجوطين هدول صح؟ هاي ال P is
+
+233
+00:17:40,290 --> 00:17:46,900
+true بتكلم عن الحالتين هدول طيب andP implies Q is
+
+234
+00:17:46,900 --> 00:17:56,920
+true صح وينها من هنا التانية فإذا Q is true ثم Q
+
+235
+00:17:56,920 --> 00:18:03,920
+is true تحظوا عملت تأكيد للنتيجة عملنا هنا تأكيد
+
+236
+00:18:03,920 --> 00:18:11,480
+لمين للنتيجة ان فعلا هاد trueو ال implication true
+
+237
+00:18:11,480 --> 00:18:16,920
+فإذا أكيد q لازم تكون true لازم تكون true هذه
+
+238
+00:18:16,920 --> 00:18:22,640
+الحالة طيب denying أو الإنكار نظرية الإنكار تحت
+
+239
+00:18:22,640 --> 00:18:29,760
+هنشوف إيش الفرضيات بتاعتها الفرضيات
+
+240
+00:18:29,760 --> 00:18:41,640
+كتالة الفرضيات بتاعتها هتكون كتالة negation qهي q،
+
+241
+00:18:41,640 --> 00:18:45,460
+negation يعني أنا بتكلم عن مين؟ false، false، فإذا
+
+242
+00:18:45,460 --> 00:18:51,560
+هاي حالة وهي حالة، ليش؟ لأن هذه false وهذه false،
+
+243
+00:18:51,560 --> 00:19:00,940
+تمام؟ كويسة P implies q, is it true؟ هال negation
+
+244
+00:19:00,940 --> 00:19:07,860
+true، معناته q is false، هنا P implies q
+
+245
+00:19:09,610 --> 00:19:14,770
+true طب وين ال true من الحالتين هدول؟ هيها فإذا في
+
+246
+00:19:14,770 --> 00:19:18,090
+نيجيشن
+
+247
+00:19:18,090 --> 00:19:25,910
+P فإذا نيجيشن P must be true تمام فإذا نيجيشن P
+
+248
+00:19:25,910 --> 00:19:32,290
+وعشان هي دي denying الإنقار أنقرنا بمجرد ما زهرش
+
+249
+00:19:32,290 --> 00:19:36,230
+معانا النتيجة فإذا أكيد المعطى ماكنش موجود المعطى
+
+250
+00:19:36,230 --> 00:19:38,910
+false فأكيد المعطى false
+
+251
+00:19:41,500 --> 00:19:48,940
+Okay طيب الsyllogism أو الاستدلال المنطقي خلينا
+
+252
+00:19:48,940 --> 00:19:54,640
+نسميه الاستدلال المنطقي لو قولنا P
+
+253
+00:19:54,640 --> 00:20:02,000
+employees Q is true and Q employees R is Q then P
+
+254
+00:20:02,000 --> 00:20:10,730
+employees R is Q صح صحيح إذا درست هتنجحإذا نجحت
+
+255
+00:20:10,730 --> 00:20:15,870
+هجيبلك هدية فإذا إذا درست هجيبلك هدية إذا طبعا
+
+256
+00:20:15,870 --> 00:20:20,370
+مشيت كلها تحققت صح إذا الفرضية كانت مشهورة طيب
+
+257
+00:20:20,370 --> 00:20:28,110
+برضه في الاستدلال لل or لل disjunctive ل ال
+
+258
+00:20:28,110 --> 00:20:37,970
+disjunctive إذا P or Q is true is true لحظة طيب
+
+259
+00:20:37,970 --> 00:20:44,130
+negationP is true معناته P false طبعا أنا جاعت
+
+260
+00:20:44,130 --> 00:20:49,410
+بقول هذه كلها true وهذا طلعت false هذه must be
+
+261
+00:20:49,410 --> 00:20:55,870
+true ليش؟ عشان كلها تطلع true لأنه خلاص هذه حكمنا
+
+262
+00:20:55,870 --> 00:21:00,810
+عليها false or محتاجة واحد true فإذا لازم تكون هذه
+
+263
+00:21:00,810 --> 00:21:06,830
+لازم تكون هذه فإذا Q is true
+
+264
+00:21:12,850 --> 00:21:20,570
+Okay فإذا أخدنا مجموعة من ال
+
+265
+00:21:20,570 --> 00:21:27,370
+rules of inference إذا كان .. طبعا لحظة ال .. ال
+
+266
+00:21:27,370 --> 00:21:32,710
+.. ال .. ال .. ال antecedent مع ال consequence لما
+
+267
+00:21:32,710 --> 00:21:37,990
+نيجي تنتين نعملهمimplication المفروض أن احصل على
+
+268
+00:21:37,990 --> 00:21:41,990
+tautology لإن إذا هذه true فهذه true لما باجب
+
+269
+00:21:41,990 --> 00:21:44,370
+أعملهم implication لازم يكونوا true true فإذن
+
+270
+00:21:44,370 --> 00:21:47,530
+طبيعي أنه لازم يعطيني tautology دائما ال relation
+
+271
+00:21:47,530 --> 00:21:51,650
+بينهم true لإنه دائما بيسووا بعض مدام أنا بتكلم عن
+
+272
+00:21:51,650 --> 00:21:57,970
+rule قاعدة إذا اتحقق الشرط بده يتحقق النهيجة فإذا
+
+273
+00:21:57,970 --> 00:22:00,570
+الأثنين لازم يكونوا true إذا أنا ماشي فعلا على ال
+
+274
+00:22:00,570 --> 00:22:06,190
+rules تبعتنا على ال rules كويسة فإذا فيis true
+
+275
+00:22:06,190 --> 00:22:13,630
+اكيد بيه مع or اي proposition اخر اكيد هتكون true
+
+276
+00:22:13,630 --> 00:22:17,210
+نفس الكلافة اذا لما بجرى بعمل implication لازم هذه
+
+277
+00:22:17,210 --> 00:22:21,910
+تطلع دايما true دايما تطلع true ليش دايما تطلع
+
+278
+00:22:21,910 --> 00:22:25,430
+true لأن احنا هنا دايما نتكلم عن اما false false
+
+279
+00:22:25,430 --> 00:22:29,990
+ماتحققوش او true true اتحققت فهذه دايما تطلع true
+
+280
+00:22:29,990 --> 00:22:35,270
+في ال implication مع ال implication تمام
+
+281
+00:22:37,580 --> 00:22:45,300
+P and Q معناته كل واحدة منهم true أكيد إذا كان ال
+
+282
+00:22:45,300 --> 00:22:49,340
+and للتنتين مع بعض true فإذا كل واحدة منهم لحالها
+
+283
+00:22:49,340 --> 00:22:54,460
+true، منطقي، كويسة هنا التنتين كل واحدة منهم true
+
+284
+00:22:54,460 --> 00:22:58,800
+فأكيد ال or تبع الأتنين ال and تبع الأتنين true
+
+285
+00:22:58,800 --> 00:23:05,720
+منطقي، برضه منطقي من معرفتنا بال and connectionطيب
+
+286
+00:23:05,720 --> 00:23:12,360
+أخدنا برضه ال negation q و p وهذا سمنها denying أو
+
+287
+00:23:12,360 --> 00:23:16,800
+الإنكار، مدام أنكرنا النتيجة فإذا أكيد ال .. ال ..
+
+288
+00:23:16,800 --> 00:23:21,830
+ال antecedent كانت false، أكيد كانت falseكويسة، و
+
+289
+00:23:21,830 --> 00:23:27,990
+بعدين أخدتنا السيولوجيزم الأخيرة جزئية .. فضلي ..
+
+290
+00:23:27,990 --> 00:23:33,270
+هده .. هده .. تمام، نرجع معناته نرسم، نكتب ال
+
+291
+00:23:33,270 --> 00:23:35,010
+table تبعنا
+
+292
+00:23:46,000 --> 00:23:50,900
+تمام هنا ايش .. ايش الفرضية؟ لحظة هذه الفرضية
+
+293
+00:23:50,900 --> 00:23:55,660
+المفروضة ان هي true وهذه فرضية ان هي تكون true هذه
+
+294
+00:23:55,660 --> 00:24:00,040
+ايش لازم تطلع؟ خليني اجربها و نشوف negation Q is
+
+295
+00:24:00,040 --> 00:24:06,640
+true معناته Q ايش؟ false ل Q هذه حالة وهذه حالة
+
+296
+00:24:06,640 --> 00:24:10,280
+فاذا انا بتكلم عن مين؟ عن هذا .. الحالة هذه
+
+297
+00:24:10,280 --> 00:24:16,750
+والحالة هناتمام من الشرط الأول عرفنا ان انا بتكلم
+
+298
+00:24:16,750 --> 00:24:22,750
+عن واحد من ال true rows هدول طيب كويس P employs Q
+
+299
+00:24:22,750 --> 00:24:27,030
+true طيب هي ال implication هنا true وهنا false لأ
+
+300
+00:24:27,030 --> 00:24:31,590
+انا بتكلم عن هنا معناته انا موجود في ال row الأول
+
+301
+00:24:31,590 --> 00:24:39,810
+هذه false وهذه true اكيد معناته بيش negation
+
+302
+00:24:41,840 --> 00:24:49,640
+فإذا negation بي ال false ل بي فإذا negation بي is
+
+303
+00:24:49,640 --> 00:24:57,060
+true لأن بي false negation بي is true okay زي ما
+
+304
+00:24:57,060 --> 00:25:02,660
+قلنا بي implies q and q implies r فإذا قلنا بي
+
+305
+00:25:02,660 --> 00:25:10,640
+بتضمنلي q و q بتضمنلي r بديهي بي بتضمنلي r okay
+
+306
+00:25:12,070 --> 00:25:15,370
+فلما نجي نتكلم هنا عن ال proves فعليا بنبدأ عشان
+
+307
+00:25:15,370 --> 00:25:21,550
+نثبت نعمل ال former row of a conclusion C بدنا
+
+308
+00:25:21,550 --> 00:25:25,250
+يكون عندنا مجموعة givens المجموعة ال givens هذه
+
+309
+00:25:25,250 --> 00:25:29,630
+اللي هي ال premises أو المعطيات ال premises P1 P2
+
+310
+00:25:29,630 --> 00:25:32,410
+P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P12 P13 P12 P12
+
+311
+00:25:32,410 --> 00:25:32,530
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+312
+00:25:32,530 --> 00:25:32,810
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+313
+00:25:32,810 --> 00:25:32,910
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+314
+00:25:32,910 --> 00:25:33,170
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+315
+00:25:33,170 --> 00:25:33,170
+P12 P12 P12 P12 P12 P12 P12 P12 P12 P12 P12
+
+316
+00:25:36,670 --> 00:25:41,590
+بدنا منهم نثبت C فهدولة كلهم ال premises نتعامل
+
+317
+00:25:41,590 --> 00:25:45,890
+معهم عساس ان هم ال antecedents تعودنا المعطيات
+
+318
+00:25:45,890 --> 00:25:49,990
+تعودنا المقدمات للإثبات مقدمات الإثبات تبعنا و ال
+
+319
+00:25:49,990 --> 00:25:54,850
+conclusion هو ال consequent عندنا مجموعة قواعة و
+
+320
+00:25:54,850 --> 00:25:58,910
+قراءة شفناهاو أثبتناها و أتأكدنا منها بنشتغل و
+
+321
+00:25:58,910 --> 00:26:02,970
+بنشتغل عليها بنحاول نشوف مين اللي بتتناسب معانا
+
+322
+00:26:02,970 --> 00:26:10,130
+بحيث أنه والله إذا ال premises are true then the
+
+323
+00:26:10,130 --> 00:26:13,870
+conclusion is true هذا اللي بدنا نصلّم هذا اللي
+
+324
+00:26:13,870 --> 00:26:21,070
+بدنا نصلّم ناخد example لو قلنا suppose we have
+
+325
+00:26:21,070 --> 00:26:25,420
+the following premisesلأ معطيات مش بالضروري أن هي
+
+326
+00:26:25,420 --> 00:26:29,700
+مسلمات بالنسبالنا بس هي معطيات بقدر أقولكنه معطيات
+
+327
+00:26:29,700 --> 00:26:35,380
+حسب حالة معينة كلهم are true حسب حالة معينة طيب
+
+328
+00:26:35,380 --> 00:26:40,060
+it's not sunny and it's cold هي مش مشمسة الدنيا مش
+
+329
+00:26:40,060 --> 00:26:48,170
+مشمسة و بريد تمامwe will swim only if it's sunny
+
+330
+00:26:48,170 --> 00:26:54,450
+احنا هنسبح إذا كان الدنيا شمس أو مش شمسة طيب if we
+
+331
+00:26:54,450 --> 00:26:59,710
+don't swim then we will play volley إذا ما لجناها
+
+332
+00:26:59,710 --> 00:27:04,710
+مش مش شمسة أو يعني إذا ماسبحناش هنلعب كرة طائرة،
+
+333
+00:27:04,710 --> 00:27:07,650
+بنضل ع الشط و مش هنسبح، هنلعب طائرة و خلاص، كويسة
+
+334
+00:27:08,060 --> 00:27:14,560
+if we play volley then we will be home early هنرجع
+
+335
+00:27:14,560 --> 00:27:20,040
+للبيت مبكر طيب بدنا نثبت ان we will be home early
+
+336
+00:27:20,040 --> 00:27:26,060
+بدنا .. لحظة كلنا قولنا اه اه ماهي منطقى منطق ليش
+
+337
+00:27:26,060 --> 00:27:31,900
+لأن احنا بدين .. not sent لحظة
+
+338
+00:27:31,900 --> 00:27:35,740
+احنا بدين اصلا ان هي فعلا مش مو شمسةفمدام مش مش بس
+
+339
+00:27:35,740 --> 00:27:40,000
+طبيعي و برد كمان أكيد مش هنسبح و مدام مش هسبح
+
+340
+00:27:40,000 --> 00:27:43,340
+معناته هنلعب طائرة و اكيد مدام اللعبنا طائرة هنروح
+
+341
+00:27:43,340 --> 00:27:48,400
+بدري فهي biologic منطقية بس بدنا اثبات بدنا نثبتها
+
+342
+00:27:48,400 --> 00:27:52,960
+رياضيا عشان نثبتها رياضيا بنختصر بنعمل مختصرات
+
+343
+00:27:52,960 --> 00:27:58,600
+فهنقول it's sunny هنعطيها ال function sunny بس
+
+344
+00:27:58,600 --> 00:28:04,210
+cold عساس ان معناها it's coldبنحاول نختصر الجمال
+
+345
+00:28:04,210 --> 00:28:06,990
+بتاعتنا عشان تمشي مع الرياضية أو ال mathematical
+
+346
+00:28:06,990 --> 00:28:11,910
+form اللي هنشتغل عليه swim volley خلاص معناته we
+
+347
+00:28:11,910 --> 00:28:16,330
+will play volley early خلاص معناته ان انا هروح او
+
+348
+00:28:16,330 --> 00:28:21,390
+هنروح بدر فإذا بنترجم ال premises اللي كانت هنا ال
+
+349
+00:28:21,390 --> 00:28:25,330
+premises اللي كانت هنا it's not sunny and cold
+
+350
+00:28:25,330 --> 00:28:34,220
+okay if we swimwe swim then sunny فإذا كانت sunny
+
+351
+00:28:34,220 --> 00:28:41,280
+هنسبح أو هنسبح إذا كانت sunny إذا كانت sunny وهذه
+
+352
+00:28:41,280 --> 00:28:48,820
+بدي إياكم ترجعوا لل implication و الترجمه هذه بناء
+
+353
+00:28:48,820 --> 00:28:52,260
+على مجموعة الجمل اللي أعطيناكوا إياها تعبر عن ال
+
+354
+00:28:52,260 --> 00:28:56,480
+implication تذكرينها؟ تذكرتواها كويس؟ فشوفوا ليه
+
+355
+00:28:56,480 --> 00:29:09,470
+only ifمين ال B ومين ال Q ال B ثانو ثانو انا
+
+356
+00:29:09,470 --> 00:29:13,310
+بالعمد بقولتلكوا عليها عشان ما تخلطوش فبترجعوا للي
+
+357
+00:29:13,310 --> 00:29:20,150
+أخدناها سابقا لإنه only if وليس if only if if only
+
+358
+00:29:20,150 --> 00:29:24,430
+if هدي إشي تاني if only أو زي ما هي مكتوبة عندكم
+
+359
+00:29:24,430 --> 00:29:32,250
+هناonly if هذه P only if Q فترجع لمجموعة ال forms
+
+360
+00:29:32,250 --> 00:29:33,970
+اللي أخدناها أو المجموعة ال words اللي أخدناها
+
+361
+00:29:33,970 --> 00:29:37,770
+تعبر عن ال implication هتلاقوا أن ال P في الأول و
+
+362
+00:29:37,770 --> 00:29:41,250
+ال Q في التاني P أول و Q تاني ليش لأنه بناء عليها
+
+363
+00:29:41,250 --> 00:29:46,370
+لازم أحطهم هنا فعليا P في الأول و Q في التاني إذا
+
+364
+00:29:46,370 --> 00:29:48,890
+انتوا بتقولوا هيكوا كانت ال Q P المفروض كان قلتله
+
+365
+00:29:48,890 --> 00:29:53,280
+غلط هذه كان المفروض ان هي بالعكسبس لأ هي هذه صح
+
+366
+00:29:53,280 --> 00:29:58,220
+لأنه فعلا ال expression السابق يعبر عن بي Q
+
+367
+00:29:58,220 --> 00:30:03,200
+بترجعولهم عشان تتأكدوا يعني انا بقولكوا note عشان
+
+368
+00:30:03,200 --> 00:30:07,180
+برضه و انتوا لو بتذاكروا المحاضرة تتأكدوا منها طيب
+
+369
+00:30:07,180 --> 00:30:15,080
+وصلنا إذا .. إذا كان مسبحناش if مسبحناش then هنلعب
+
+370
+00:30:15,080 --> 00:30:20,970
+volley okay طيب إذا لعبنا volleyهذه ال expressions
+
+371
+00:30:20,970 --> 00:30:24,910
+لم تكن فيها مشكلة لأنها كانت مباشرة if ثم if ثم
+
+372
+00:30:24,910 --> 00:30:27,990
+هذا اللي كان يمكن تترجعها شوية لأنها كانت only if
+
+373
+00:30:27,990 --> 00:30:32,150
+تترجعها شوية تشوف وين ال P وين ال Q وين ال P وين
+
+374
+00:30:32,150 --> 00:30:36,230
+ال Q كويس
+
+375
+00:30:36,230 --> 00:30:38,870
+هذه مجموعة ال premises بتاعتنا هذه مجموعة ال
+
+376
+00:30:38,870 --> 00:30:42,390
+premises بنبدأ من ال premises الأولى هذه ال steps
+
+377
+00:30:42,390 --> 00:30:49,760
+للإثبات negation sunny and coldpremise number one
+
+378
+00:30:49,760 --> 00:30:56,540
+طيب madam and معناته الأولى true والتانية true
+
+379
+00:30:56,540 --> 00:31:00,480
+فإذا ال negation sunny is true negation sunny is
+
+380
+00:31:00,480 --> 00:31:05,320
+true طيب احنا عارفين انه swim implies sunny طب انا
+
+381
+00:31:05,320 --> 00:31:11,300
+عندي negation denying negation sunny فإذا ال
+
+382
+00:31:11,300 --> 00:31:17,620
+negation ال حالة اللي لسه كنا نتكلم فيهاالحالة
+
+383
+00:31:17,620 --> 00:31:21,380
+اللي كنا نحكي فيها فإذا مدام هذه negation أكيد
+
+384
+00:31:21,380 --> 00:31:26,080
+التانية ال P بتاعة ال negation فهي negation P طيب
+
+385
+00:31:26,080 --> 00:31:29,100
+لحظة هنا negation P و أنا عندي ال premise أساسا
+
+386
+00:31:29,100 --> 00:31:32,920
+موجودة اللي هي negation swim then volley تحققت
+
+387
+00:31:32,920 --> 00:31:40,600
+affirming تأكيد هذه true و هنا ما تحقق عنك وهيها
+
+388
+00:31:40,600 --> 00:31:46,690
+فإذا volley is true volley is trueقاعدين نشتغل على
+
+389
+00:31:46,690 --> 00:31:51,910
+نفس ال rules اللي اتكلمنا عنهم تمام volley is true
+
+390
+00:31:51,910 --> 00:31:56,190
+فإذن volley employs early برضه هذي ال premise هذي
+
+391
+00:31:56,190 --> 00:32:03,210
+given مقتنية given is true برضه early is true لإنه
+
+392
+00:32:03,210 --> 00:32:06,470
+برضه بتكلم عن ال affirment بتكلم على التأكيد هنا
+
+393
+00:32:06,470 --> 00:32:12,030
+بتكلم على التأكيد فإذن early مدى محققنا في الآخر
+
+394
+00:32:12,030 --> 00:32:17,610
+early is true فإذن أنا أكيد هروح بدريأثبتت رغم أنه
+
+395
+00:32:17,610 --> 00:32:21,670
+احنا من الأول بقيلة أنه okay as expressions منطقية
+
+396
+00:32:21,670 --> 00:32:24,690
+لأنه احنا من الأول قلنا إنه هي .. هي not sunny
+
+397
+00:32:24,690 --> 00:32:31,330
+الدنيا it's not sunny تمام
+
+398
+00:32:31,330 --> 00:32:38,910
+ناخد مجموعة rules مهمة عن اللي فاتوا لأن هنا ال
+
+399
+00:32:38,910 --> 00:32:43,710
+rules هذه مرتبطة بمين بال quantifiers مرتبطة بال
+
+400
+00:32:43,710 --> 00:32:45,370
+quantifiers نبدأ
+
+401
+00:32:49,410 --> 00:32:54,950
+بال universal instantiation أو التعويض بأي object
+
+402
+00:32:54,950 --> 00:33:03,170
+لو قلنا for all x b of x معنى ذلك أن أي element
+
+403
+00:33:03,170 --> 00:33:07,830
+داخل universe of discourse is true يعني بقدر أقول
+
+404
+00:33:07,830 --> 00:33:12,350
+b of o و o هذا أي element من داخله أي element
+
+405
+00:33:12,350 --> 00:33:19,700
+عشوائياعشوائيا لو قلت في الجرة هذه في مجموعة كور
+
+406
+00:33:19,700 --> 00:33:23,420
+ومثبت ان فعلا كل اللي موجود في الجرة كور فإذا
+
+407
+00:33:23,420 --> 00:33:26,780
+عشوائيا لو مديت إيدي و طلعت اي شغل اكيد هتطلع كورة
+
+408
+00:33:26,780 --> 00:33:32,440
+مظبوط؟ اكيد بيولوجيك منطق جدا اي object جوا حامد
+
+409
+00:33:32,440 --> 00:33:35,840
+إيدي وانا مش شايف بطلعه هقولك ان انا هطلعلك كورة
+
+410
+00:33:35,840 --> 00:33:38,360
+طب ما احنا عارفين ان انا هطلعك كورة ليش؟ لأن for
+
+411
+00:33:38,360 --> 00:33:46,080
+all x كل ال object داخل الجرةالأرم هي core منطقي
+
+412
+00:33:46,080 --> 00:33:52,340
+جدا فإذا أي شغل حد هدخل أطلع أكيد هتطلع core كويسة
+
+413
+00:33:52,340 --> 00:34:01,460
+أه العكس العكس P of Z هذا universal generalization
+
+414
+00:34:01,460 --> 00:34:08,180
+هنا ب arbitrary element إيش يعني يعني بشكل عشوائي
+
+415
+00:34:08,180 --> 00:34:13,320
+بشكل اعتباطي بشكلإنه لو قدرنا نقول إن ال G هذه
+
+416
+00:34:13,320 --> 00:34:17,620
+حاجة عشوائية ممكن تظهر معاك بمعنى كل مرة بدخل إيدي
+
+417
+00:34:17,620 --> 00:34:21,520
+في ال .. في ال .. في ال iron كل مرة بدخل إيدي في
+
+418
+00:34:21,520 --> 00:34:25,020
+الجرة بطلع كورة المرة التانية كل مرة بدخل إيدي في
+
+419
+00:34:25,020 --> 00:34:28,220
+الجرة بطلع كورة كل مرة بطلع .. بحط إيدي في الجرة
+
+420
+00:34:28,220 --> 00:34:32,320
+بطلع كورة بشكل عشوائي .. بشكل عشوائي ال G هنا
+
+421
+00:34:32,320 --> 00:34:37,380
+تختار بشكل عشوائي غير منظر بشكل مافيش control عليه
+
+422
+00:34:38,420 --> 00:34:40,800
+كل واحدة .. أي واحدة منكم هتدخل إيه؟ ده هتطلع
+
+423
+00:34:40,800 --> 00:34:44,240
+كورة، هترجحها، اللي وراها هتيجي تدخل إيه؟ إذا فعلا
+
+424
+00:34:44,240 --> 00:34:48,740
+الـG دي بشكل عشوائي بتم إختيارها بهذا الشكل،
+
+425
+00:34:48,740 --> 00:34:53,780
+معناته بقدر أقول أو بقدر أستنتج for all x P of X،
+
+426
+00:34:53,780 --> 00:34:59,020
+بدنا ناخد بالنا إن الـG دي مش زي الـO هنا، الـO أي
+
+427
+00:34:59,020 --> 00:35:04,440
+واحدة ممكن تكون selected، مجرد إنها selected،
+
+428
+00:35:04,440 --> 00:35:09,430
+باختارها إختيار، بس التانية لأ،عشوائيا، بشكل
+
+429
+00:35:09,430 --> 00:35:13,110
+عشوائي، وعملناها كذا مرة في مرة في مرة، اللي جرّا،
+
+430
+00:35:13,110 --> 00:35:17,310
+كل واحدة منكوا إجت، طلعت، لجت كورة، بشكل عشوائي،
+
+431
+00:35:17,310 --> 00:35:22,190
+في هذه الحالة بقدر أقول إنه for all x u of x،
+
+432
+00:35:22,190 --> 00:35:26,530
+واضحة الـG هذه، لأنه دايما الـG هذه، لعند الآن، في
+
+433
+00:35:26,530 --> 00:35:30,740
+كل سنة بتلخبطوا فيهاوهو بيظلوا يسألوا فيها طب كيف
+
+434
+00:35:30,740 --> 00:35:34,580
+جي يعني معناته يمكن جيها دي واحدة منهم بس كيف انت
+
+435
+00:35:34,580 --> 00:35:38,240
+عمّمت اه بعمم اذا كانت جي بتم اختيارها بشكل عشوائي
+
+436
+00:35:38,240 --> 00:35:42,280
+في كل مرة في كل مرة بيختارها عشوائيا و كل مرة
+
+437
+00:35:42,280 --> 00:35:46,600
+بتطلع true كل مرة بتحقق ليه ال function P معناته
+
+438
+00:35:46,600 --> 00:35:50,280
+for all x of x P of X تمام
+
+439
+00:35:53,720 --> 00:35:58,440
+There exists x P of x قريبة من نفس الفكرة على فكرة
+
+440
+00:35:58,440 --> 00:36:07,060
+لسه لأن there exists x P of x employs P of C كل
+
+441
+00:36:07,060 --> 00:36:11,900
+اللي بنعمله هنا كأنه C just a new constant ممكن
+
+442
+00:36:11,900 --> 00:36:20,440
+يكون أي واحد من ال elements محددناش
+
+443
+00:36:20,440 --> 00:36:26,770
+إذا حددنا بتخربإذا حددنا C هتخرب كل ال .. ال .. ال
+
+444
+00:36:26,770 --> 00:36:31,030
+.. ال inference هذه واضحة؟ ال rule كلها هتخرب ليش؟
+
+445
+00:36:31,030 --> 00:36:34,810
+لأن إذا بدي أحدد يمكن ماتطلعش هي ال true فيهم لأن
+
+446
+00:36:34,810 --> 00:36:37,910
+احنا قلنا there exist معناته ممكن تكون واحدة من
+
+447
+00:36:37,910 --> 00:36:44,270
+مجموعة عشرة من عشرة elements واحدة منهم بتحققنا ال
+
+448
+00:36:44,270 --> 00:36:49,150
+P of X كويس؟ فإذا بدي أحددها any منهم بقدرش
+
+449
+00:36:49,150 --> 00:36:53,580
+بقولكوا هقولكوا لأ مش بالضرورةولكن إذا كانت ال new
+
+450
+00:36:53,580 --> 00:36:56,780
+constant C مجرد أن أنا بدل ما حط X حطيتها C و C
+
+451
+00:36:56,780 --> 00:37:03,120
+هذه لحظة ممكن تكون أي element داخل ال universal
+
+452
+00:37:03,120 --> 00:37:08,480
+discourse إذا حددناها بشكل ضبابي خلينا هيك بشكل
+
+453
+00:37:08,480 --> 00:37:14,180
+ضبابي إنه ممكن تكون أي واحدة ماحددناش فإذا is true
+
+454
+00:37:14,180 --> 00:37:21,910
+واضحة فالتلتين هدولة يمكن فيهم شوية lapsed pHفي
+
+455
+00:37:21,910 --> 00:37:25,650
+التعريف هنا بتكون تعرفوا أن هذا البرتري بشكل
+
+456
+00:37:25,650 --> 00:37:31,610
+عشوائي وهذا أي واحدة ماحددناش برضه برضه مش هنحدد
+
+457
+00:37:31,610 --> 00:37:39,130
+طيب الأخيرة P of O لاحظوا is a P of O وهذا محدد
+
+458
+00:37:39,130 --> 00:37:44,370
+واحدة منهم بكفي واحدة منهم من ال elements is true
+
+459
+00:37:44,370 --> 00:37:50,510
+عشان أقوليوجد في فضاء العينة element واحد على
+
+460
+00:37:50,510 --> 00:38:05,170
+الأقل بحققنا ال function P of X طيب،
+
+461
+00:38:05,170 --> 00:38:11,950
+كويس ال fallacy is an inference rule or other
+
+462
+00:38:11,950 --> 00:38:17,440
+proof method is not logically validزي ان انتوا
+
+463
+00:38:17,440 --> 00:38:26,480
+تثبته عكس ال true تثبته ان ال function false اذا
+
+464
+00:38:26,480 --> 00:38:31,760
+كانت false معناته عكسها true هنا انكوا تثبته العكس
+
+465
+00:38:33,980 --> 00:38:37,760
+بتصير الحقيقة مغلطات أحيانا في هذا الموضوع فال ..
+
+466
+00:38:37,760 --> 00:38:42,180
+ال fallacy لما نيجي نتكلم عن المغلطة اللي ممكن
+
+467
+00:38:42,180 --> 00:38:46,120
+تتصير من هيك إشي إن أنا أثبت العكس و تفاجأوا أنه
+
+468
+00:38:46,120 --> 00:38:52,740
+طب ماشي ما هي مش بضروري أن العكس يثبت الصحة
+
+469
+00:38:52,740 --> 00:38:58,860
+هذا ممكن يعمللنا حاجة بتسميها fallacy أو مغلطةهي
+
+470
+00:38:58,860 --> 00:39:02,160
+عملنا مغلطة، إيش المغلطة هذه؟ من وين بتتم المغلطة
+
+471
+00:39:02,160 --> 00:39:06,820
+هذه؟ بتتم من .. برضه هي نفس ال implication لأن ال
+
+472
+00:39:06,820 --> 00:39:09,680
+implication قلنا إن فيها false ال false هذه هي
+
+473
+00:39:09,680 --> 00:39:13,240
+اللي بتعملنا المشكلة عشان تبين معانا أكتر، خلينا
+
+474
+00:39:13,240 --> 00:39:17,120
+نرسم، نرجع نكتم، اللحظوا إن ال implication هو اللي
+
+475
+00:39:17,120 --> 00:39:20,420
+مدوخنا وراها، احنا قاعدين نجري كلنا ورا جزئية ال
+
+476
+00:39:20,420 --> 00:39:22,580
+implication، فهذه عشان يكي اللحظوا إنه أهمية ال
+
+477
+00:39:22,580 --> 00:39:28,350
+implicationال implication من أهم ال .. ال
+
+478
+00:39:28,350 --> 00:39:29,290
+operators اللي قعدنا
+
+479
+00:39:41,280 --> 00:39:46,240
+تمام طيب عشان نوضحها ال policy اللي بتصير في عملية
+
+480
+00:39:46,240 --> 00:39:50,460
+ال affirming في عملية التأكيد إن أنا أروح أأكد
+
+481
+00:39:50,460 --> 00:39:56,040
+معلومة بينما في احتمال انه لأ ماتكونش مؤكدة زي لو
+
+482
+00:39:56,040 --> 00:40:02,500
+قلنا P employs Q is it true؟ okay and Q is true؟
+
+483
+00:40:02,500 --> 00:40:06,840
+طب ناخدها شوي شوي هنا إيش بيقولكوا؟ so P must be
+
+484
+00:40:06,840 --> 00:40:11,960
+true هذه المقولة هل المقولة دايما صح؟ هنشوفحنشوف
+
+485
+00:40:11,960 --> 00:40:18,600
+خلينا نمسك is it true هيه لأ التلاتة حتى في عندنا
+
+486
+00:40:18,600 --> 00:40:23,220
+تلاتة is it true يعني بمعنى أن أنا ممكن هي
+
+487
+00:40:23,220 --> 00:40:28,460
+التانتين وهي التالتة صحيح؟ هدول ممكن يتنطبق عليهم
+
+488
+00:40:28,460 --> 00:40:32,480
+ال condition الأول طيب Q is it true؟ وين ال Q؟ هي
+
+489
+00:40:32,480 --> 00:40:37,120
+Q هي في عندكوا true وهي عندكوا true صرت أنا بتكلم
+
+490
+00:40:37,120 --> 00:40:37,940
+عن الحالتين هدول
+
+491
+00:40:41,120 --> 00:40:43,760
+الحالتين هدولة بقدرش أقول منهم so أطلع ال
+
+492
+00:40:43,760 --> 00:40:47,680
+conclusion بقدرش أقول أن A and B is true ليش؟ لأنه
+
+493
+00:40:47,680 --> 00:40:52,480
+أه ممكن تكون true بس برضه ممكن تكون false لاحظته؟
+
+494
+00:40:52,480 --> 00:40:57,320
+فإذا لأ في لسه احتمال أنا نسيته فعملت مغلطة في
+
+495
+00:40:57,320 --> 00:41:01,300
+الاستنتاج، عملنا مغلطة في الاستنتاج فإذا المقولة
+
+496
+00:41:01,300 --> 00:41:09,700
+هذه غلط، هذه خطأ أو بديش أقول خطأ غير مضمونةبتكون
+
+497
+00:41:09,700 --> 00:41:12,820
+اوقع شوية غير مضمونة لان ممكن تصدق في بعض الحالات
+
+498
+00:41:12,820 --> 00:41:16,160
+اه بس في بعض مش في كل الحالات مش في كل الحالات فهد
+
+499
+00:41:16,160 --> 00:41:20,500
+فيه مغلطة طيب في ال denying برضه نفس الفكرة لو
+
+500
+00:41:20,500 --> 00:41:28,560
+قلنا بي employees q is true and he is false ممكن
+
+501
+00:41:28,560 --> 00:41:32,700
+يكون واحد يقولكوا على طول then q must be false طيب
+
+502
+00:41:32,700 --> 00:41:36,760
+لأ هد برضه بتصبتش لان لو مسكنهم هلاقي ان انا بتكلم
+
+503
+00:41:36,760 --> 00:41:42,760
+عن تالت حالات صحيحالثلاث حالات مظبوط اللي احنا
+
+504
+00:41:42,760 --> 00:41:47,340
+حكيناهم هيهم ولكن ال condition هنا لمين معاها ل ال
+
+505
+00:41:47,340 --> 00:41:52,080
+P ال P is false فالثلاث حالات هدول هعندي false هنا
+
+506
+00:41:52,080 --> 00:41:54,080
+وعندي false هنا هدي true لأ معناته ان انا بتكلم عن
+
+507
+00:41:54,080 --> 00:41:59,520
+الحالتين الحالتين هدول بقدرش اثبت منهم Q اقول
+
+508
+00:41:59,520 --> 00:42:02,160
+معناته اذا هدي false و هدي true معناته فاتفوت طب
+
+509
+00:42:02,160 --> 00:42:06,760
+مافي حالة تانية في حالة true في حالة هيها موجودة
+
+510
+00:42:08,390 --> 00:42:18,810
+فإذن هبنقدرش نشتغل عليها لأنه في fallacy كويس من
+
+511
+00:42:18,810 --> 00:42:21,050
+بين الحاجات ال fallacy خليني أشوف مثلا ال proof زي
+
+512
+00:42:21,050 --> 00:42:25,070
+هذا لو ال proof بالشكل هذا واحد كتب ال proof
+
+513
+00:42:25,070 --> 00:42:29,690
+بالشكل هذا و بعدين أثبت الكو أن اتنين بتساوي واحد
+
+514
+00:42:29,690 --> 00:42:33,470
+أكيد في fallacy في المصطلح فيه مغلطة في اشي عمله
+
+515
+00:42:33,470 --> 00:42:38,600
+غلطمنطق جدا يعني كيف انت تبدأ بيقولوا a and b
+
+516
+00:42:38,600 --> 00:42:42,800
+positive integers و a بتساوي b احب دمع ايه بتساوي؟
+
+517
+00:42:42,800 --> 00:42:45,860
+كويس فليا كده و بعدين عمل اثبات اثبات ان في الآخر
+
+518
+00:42:45,860 --> 00:42:50,280
+الاثنين بتساوي واحد طلعوا
+
+519
+00:42:50,280 --> 00:42:55,580
+عليها كل شيء فيها منطقي صح وين في عندنا مشكلة
+
+520
+00:42:55,580 --> 00:43:02,610
+هابدأقولك اه هاي واحد اتنين تلاتةأربعة خمسة ستة
+
+521
+00:43:02,610 --> 00:43:05,950
+سبعة في سبعة lines عندنا في المثال في ال proof
+
+522
+00:43:05,950 --> 00:43:10,150
+اللي عندنا واضح انه هيكون فيمشكلة في step رقم
+
+523
+00:43:10,150 --> 00:43:14,290
+أربعة لخمسة لإيش لأن في أربعة احنا اضطرينا نقسم
+
+524
+00:43:14,290 --> 00:43:17,990
+على صفر باعتبار ان احنا قسمنا على a minus b و a
+
+525
+00:43:17,990 --> 00:43:25,430
+minus b بيساوي صفر فصرت a plus b على zero و b على
+
+526
+00:43:25,430 --> 00:43:29,430
+zero طبعا أي term على zero بيعطينا قيمة غير محددة
+
+527
+00:43:29,430 --> 00:43:33,490
+غير معرفة فمعنى ذلك انهال step رقم خامسة لأصل إنه
+
+528
+00:43:33,490 --> 00:43:37,270
+هي غير معرفة فهنا بيجي في ال proof كله بيصير في
+
+529
+00:43:37,270 --> 00:43:39,950
+خطأ أصلا في ال process اللي انعمل أو في المعالجة
+
+530
+00:43:39,950 --> 00:43:44,610
+اللي تمت بالقسم على صفر و هيك بتكون واضح ليش
+
+531
+00:43:44,610 --> 00:43:49,870
+المثال هذا فيه إشكالي أو فيه مشكلةتما هلوجد خلصنا
+
+532
+00:43:49,870 --> 00:43:55,350
+مقدمات نعتبرها، خلصنا جزية مقدمات، الجزء الأهم من
+
+533
+00:43:55,350 --> 00:43:58,310
+المقدمات، كل اللي أخدناها مقدمات مجرد أخدنا ال
+
+534
+00:43:58,310 --> 00:44:02,630
+inferences، مجموعة rules و اتعاملنا معها و أخدنا
+
+535
+00:44:02,630 --> 00:44:05,790
+مثال عليها، الأهم إيش ال methodology اللي بدنا
+
+536
+00:44:05,790 --> 00:44:09,450
+نشتغل فيها، إيش ال methods اللي بدنا نستعملها،
+
+537
+00:44:09,450 --> 00:44:14,180
+يعني إيه؟هل اللي بيجيني هشتغل يلا أي إشي بيطلع
+
+538
+00:44:14,180 --> 00:44:17,600
+معايا و بس نحفظ شوية ال rules هذه و نشتغل و خلاص؟
+
+539
+00:44:17,600 --> 00:44:22,240
+في categories ال categories هذه بتحددلنا أنواع ال
+
+540
+00:44:22,240 --> 00:44:24,920
+methods اللي بدنا نشتغل عليها في عندنا فعليا
+
+541
+00:44:24,920 --> 00:44:31,920
+مجموعة methods في method مباشرة طريقة مباشرة طريقة
+
+542
+00:44:31,920 --> 00:44:38,340
+direct مباشرة خلاص بنفرض P و منها نثمة Q مباشرة
+
+543
+00:44:38,340 --> 00:44:39,900
+لإن احنا كل شغلنا علاقاش
+
+544
+00:44:43,900 --> 00:44:48,240
+هذه مجموعة ال premises ممكن تكون premises واحدة او
+
+545
+00:44:48,240 --> 00:44:55,520
+مجموعة تمام؟ بدنا نثبت منها ال conclusion اما ان
+
+546
+00:44:55,520 --> 00:45:00,660
+بفرض هذه وبشوية rules بحاول أثبت منها هذه مباشرة
+
+547
+00:45:00,660 --> 00:45:05,840
+بشكل مباشر نبدأ مباشرة بشكل طبيعي حسب اتجاه تبعنا
+
+548
+00:45:05,840 --> 00:45:13,270
+لحظه او indirect ال indirect بدي أثبتnegation Q
+
+549
+00:45:13,270 --> 00:45:19,390
+إذا قدرنا من negation Q نفرضها هي الفرضية هو هيطلب
+
+550
+00:45:19,390 --> 00:45:22,270
+منكوا اثبتولي كذا طب الكذا هذا ناخد ال negation
+
+551
+00:45:22,270 --> 00:45:27,270
+تبعه implication
+
+552
+00:45:27,270 --> 00:45:30,770
+negation
+
+553
+00:45:30,770 --> 00:45:36,670
+P إذا قدرنا نثبت الجزء هذا فإذا هذا صح متذكرين ال
+
+554
+00:45:36,670 --> 00:45:41,400
+counter positive؟ مش هي ال counter positive؟مش هذا
+
+555
+00:45:41,400 --> 00:45:43,960
+ال contrapositive اللي كنا نشتغل عليها قلنا فيه ال
+
+556
+00:45:43,960 --> 00:45:48,120
+inverse و ال converse و ال contrapositive كنا
+
+557
+00:45:48,120 --> 00:45:53,080
+بنجيب negation للطرفين و بنبدلهم و قلنا هي الحالة
+
+558
+00:45:53,080 --> 00:45:57,380
+الوحيدة المكافئة لل implication الأصلي فإذا كانت
+
+559
+00:45:57,380 --> 00:46:00,740
+مكافئة لل implication الأصلي لو تحققت أكيد هيتحقق
+
+560
+00:46:00,740 --> 00:46:05,160
+الأصلي بدا مكافئة فعلا فإذا لو أنا مش قادر أثبت
+
+561
+00:46:05,160 --> 00:46:09,990
+الجزء هذامش قادرين نثبت الجزء هذا التعريف هنا صعب
+
+562
+00:46:09,990 --> 00:46:15,030
+شوية مش عارفين نفككه مش عارفين نحلله تعريف المقلوب
+
+563
+00:46:15,030 --> 00:46:22,970
+أسهل فلس بفترض أن هذا inverse او بعمله negation و
+
+564
+00:46:22,970 --> 00:46:29,330
+بنفترض العكس و بأنه بنحاول نثبت عكس المعطى لو
+
+565
+00:46:29,330 --> 00:46:32,690
+قدرنا نثبت الجزء هذا automatically بقول أن هذا
+
+566
+00:46:32,690 --> 00:46:38,460
+true لأن هما equivalent لبعضهذه الcontra positive
+
+567
+00:46:38,460 --> 00:46:49,520
+نستطيع أن نشتغل عليها و نكمل شغلنا طيب في
+
+568
+00:46:49,520 --> 00:46:57,320
+ال vacuous approve او اثبت انه من نفس ال P اللي
+
+569
+00:46:57,320 --> 00:47:02,900
+ماعطينا إياها اثبت negation P فهو بيعطيني ان P is
+
+570
+00:47:02,900 --> 00:47:08,170
+true اروح اثبتله انnegation بيه هي ال true فهذه
+
+571
+00:47:08,170 --> 00:47:13,850
+صارت عديمة الفائدة فك يصف او عديمة الفائدة مالهاش
+
+572
+00:47:13,850 --> 00:47:20,110
+فائدة فهنا أثبتنا اثبات انه مش حاج درجي بالناتج
+
+573
+00:47:20,110 --> 00:47:23,470
+هذه عديمة الفائدة و هناخد حالات هنا طبعا حالتها
+
+574
+00:47:23,470 --> 00:47:26,170
+نادرة خفيفة مافيش حالات كتيرة احنا معظم شغلنا
+
+575
+00:47:26,170 --> 00:47:32,350
+هيكون هنا طيب trivial proof هذه بنثبت منها ال Q من
+
+576
+00:47:32,350 --> 00:47:38,040
+نفسهاأنا مش محتاج ال premises، احنا مش محتاجين ال
+
+577
+00:47:38,040 --> 00:47:42,700
+premises، من ال Q نفسها بفقدها، فهدئ trivial أو
+
+578
+00:47:42,700 --> 00:47:47,660
+تافت، يعني بمعنى ال premises تبعتي مش محتاجها، مش
+
+579
+00:47:47,660 --> 00:47:51,240
+محتاجينها، طبعا حالات نادرة هذه ولا مش كتير، الشغل
+
+580
+00:47:51,240 --> 00:47:58,360
+المعظم هو هيكون في الجزئيتين اللي في الأولالمرة
+
+581
+00:47:58,360 --> 00:48:01,380
+الجاي نبدأ في ال strategies هذه نبدأ في أول طريقة
+
+582
+00:48:01,380 --> 00:48:04,660
+ناخد ال direct و بعدين نعرج ناخد examples عليها و
+
+583
+00:48:04,660 --> 00:48:09,200
+بعدين نشتغل على ال indirect لأن
+
+584
+00:48:09,200 --> 00:48:12,700
+في عندنا ال contradiction برضه هنتكلم عنها كطريقة
+
+585
+00:48:12,700 --> 00:48:16,640
+خامسة و هم الأهم هيكون في شغلنا ال direct و ال
+
+586
+00:48:16,640 --> 00:48:19,360
+indirect و ال indirect زي ما قلنا دايما خلوا في
+
+587
+00:48:19,360 --> 00:48:22,720
+بالكوا ال contrapositive و في حاجة تانية ال
+
+588
+00:48:22,720 --> 00:48:26,870
+contradictionال .. ال contradiction هم التلاتة
+
+589
+00:48:26,870 --> 00:48:29,290
+اللي خلينا .. اللي هنقول هم فعليا بنستخدم ..
+
+590
+00:48:29,290 --> 00:48:32,410
+بنستخدمهم و هنستعملهم، يعطيكوا العافية، السلام
+
+591
+00:48:32,410 --> 00:48:32,710
+عليكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f3fbf84fab744d34467be046b9e8a380e22d649c
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo.srt
@@ -0,0 +1,2755 @@
+1
+00:00:21,430 --> 00:00:23,510
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:23,510 --> 00:00:26,750
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه أجمعين
+
+3
+00:00:27,490 --> 00:00:30,790
+خلصنا المرة اللي فاتت موضوع الـ sets والمجموعات و
+
+4
+00:00:30,790 --> 00:00:33,730
+الـ .. أخدنا الـ theories بتاعتها واتكلمنا عن
+
+5
+00:00:33,730 --> 00:00:38,090
+مجموعة operators ممكن نطبقها عليها. اليوم نبدأ في
+
+6
+00:00:38,090 --> 00:00:40,630
+موضوع جديد اللي هو الـ functions ودي مرة عليكم
+
+7
+00:00:40,630 --> 00:00:43,030
+تجيبوا هيك بس زي ما قلنا هنتناول .. هنتناول ..
+
+8
+00:00:43,030 --> 00:00:48,530
+نتناولها بطريقة تتناسب مع الـ discrete تتناسب مع
+
+9
+00:00:48,530 --> 00:00:53,140
+المادة اللي عندي، لقيّتها خلصناها وبدنا نوضح كيف أن كل
+
+10
+00:00:53,140 --> 00:00:57,040
+المواضيع اللي أخدناها سابقا إحنا ممكن نعبر عنها as
+
+11
+00:00:57,040 --> 00:01:01,740
+a function .. as a function. فنبدأ مع الـ function
+
+12
+00:01:01,740 --> 00:01:03,740
+اللي إنتوا عارفينها .. إنتوا أخدتوا الـ function
+
+13
+00:01:03,740 --> 00:01:07,300
+على أساس أن هي .. يعني أخدتوه على أساس أن هي
+
+14
+00:01:07,300 --> 00:01:14,290
+function أو بمعنى variable متغير independent مستقل
+
+15
+00:01:14,290 --> 00:01:17,890
+إنتوا بتدخلوه منين؟ من مجموعة إيش؟ مجموعة
+
+16
+00:01:17,890 --> 00:01:21,390
+universal discourse أو مجموعة .. مجموعة حاطينها في
+
+17
+00:01:21,390 --> 00:01:26,870
+set .. هنسميها set A. القيم اللي موجودة داخل set A
+
+18
+00:01:26,870 --> 00:01:32,230
+نستخدمها علشان نطبق عليها function معينة.
+
+19
+00:01:32,230 --> 00:01:35,410
+الـ function المعينة دي هتطلع outputs. الـ outputs دي
+
+20
+00:01:35,410 --> 00:01:39,850
+هنحطها في set اسمها B. فإنتوا كنتوا في الآخر
+
+21
+00:01:39,850 --> 00:01:42,950
+بترسموها أو بتتكلموا عنها على أساس أن هي f of x
+
+22
+00:01:42,950 --> 00:01:49,110
+فلنقل y = f(x). فـ x كان بالنسبالكم independent
+
+23
+00:01:49,110 --> 00:01:53,160
+variable مستقل، ده اللي بدكم تدخلوه هو الـ input
+
+24
+00:01:53,160 --> 00:01:59,140
+للـ function. وبعدين بناء على الـ function أو x under
+
+25
+00:01:59,140 --> 00:02:03,120
+the function f كان بيطلع لكم قيمة اسمها y. الـ y هذه
+
+26
+00:02:03,120 --> 00:02:08,680
+عبارة عن إيش؟ عبارة عن x under the function f بعد ما
+
+27
+00:02:08,680 --> 00:02:12,760
+طبّقنا عليها الـ function f بالظبط تماما زي لما
+
+28
+00:02:12,760 --> 00:02:16,600
+تتكلموا عن المراية. المراية لما تكون normal إنتوا
+
+29
+00:02:16,600 --> 00:02:19,460
+بتشوفوا صورتكم زي ما إنتوا بالظبط، يعني كأنها f(x)
+
+30
+00:02:19,460 --> 00:02:22,960
+y = x. إنتوا بتشوفوا صورتكم زي ما إنتوا
+
+31
+00:02:22,960 --> 00:02:26,350
+شايفينها. ولكن افرض أن هي مقعّرة أو محدّبة، إنتوا
+
+32
+00:02:26,350 --> 00:02:29,130
+هتشوفوا صورة تانية، إيش الصورة اللي إنتوا شايفينها
+
+33
+00:02:29,130 --> 00:02:32,750
+في المرايا؟ هي صورتكم بعد تطبيق الـ function
+
+34
+00:02:32,750 --> 00:02:35,250
+عليها، إيش هي الـ function؟ الـ .. سطح الـ ..
+
+35
+00:02:35,250 --> 00:02:39,490
+المرايا، سطح المرايا، تمام؟ فهتلاقوا .. طب أنا
+
+36
+00:02:39,490 --> 00:02:42,990
+جايبه المثال هذا بالعمد، لأنه هنتكلم عن كلمة
+
+37
+00:02:42,990 --> 00:02:45,730
+image، أن في واحدة منهم image للتانية وفي واحدة
+
+38
+00:02:45,730 --> 00:02:49,030
+pre-image للتانية، هنتكلم عليهم، عشان ممكن كان
+
+39
+00:02:49,030 --> 00:02:53,550
+موضوع المرايا هذا كان في السياق على أساس أنه يجرب
+
+40
+00:02:53,550 --> 00:02:58,010
+المفهوم عندنا. تمام. ففي الآخر أنا بتعامل مع function
+
+41
+00:02:58,010 --> 00:03:05,290
+بقول أن هي y = f(x) و y ∈ ℝ و x
+
+42
+00:03:05,290 --> 00:03:08,270
+طبعا أساسا كانت برضه ∈ ℝ. ف أنا عندي الـ
+
+43
+00:03:08,270 --> 00:03:12,170
+universe of discourse لـ x هي الـ real numbers و
+
+44
+00:03:12,170 --> 00:03:17,650
+المتوقع أن الـ y هيكون برضه الـ real numbers كـ
+
+45
+00:03:17,650 --> 00:03:22,790
+universe of discourse لها. الـ function نقدر نطبقها
+
+46
+00:03:22,790 --> 00:03:27,390
+على أي shape بحيث أنّه ممكن تطبّق على أي element لأي
+
+47
+00:03:27,390 --> 00:03:34,430
+set بحيث أنّه يطلعنا element في أي set أخرى. كيف؟
+
+48
+00:03:34,430 --> 00:03:37,490
+إنتوا هالوقت اللي هتتكلموا على الـ X، الـ X دي زي ما
+
+49
+00:03:37,490 --> 00:03:40,110
+قلنا إحنا ∈ إيه؟ to R حسب الـ example اللي
+
+50
+00:03:40,110 --> 00:03:44,070
+قعدنا عليه، يعني معناته الـ R بتاعتنا دي صارت هي إيه؟ الـ
+
+51
+00:03:44,070 --> 00:03:52,340
+set بتاعة x، هي set x، element منها، okay؟ عشان يطلعنا
+
+52
+00:03:52,340 --> 00:03:58,600
+set أخرى تمثل إيش؟ تمثل جميع الـ elements لـ y اللي
+
+53
+00:03:58,600 --> 00:04:04,000
+استخرجناهم من كل الـ elements بتاعة x. تمام. فحسب
+
+54
+00:04:04,000 --> 00:04:06,660
+اللي موجود عندنا طلعت برضه ∈ إيش؟ to R.
+
+55
+00:04:06,660 --> 00:04:11,740
+فبرضه إحنا استنتجنا set from other set from other
+
+56
+00:04:11,740 --> 00:04:15,270
+set. طبعا other set معناته بدي أعمل applying لمين؟
+
+57
+00:04:15,270 --> 00:04:18,790
+لكل الـ elements داخل الـ set عشان أطلع منهم مين؟
+
+58
+00:04:18,790 --> 00:04:23,770
+مجموعة elements يمثلوا لـ set جديدة، يمثلها set جديدة.
+
+59
+00:04:23,770 --> 00:04:27,730
+تمام. formally كيف ممكن نكتب الكلام ده؟ هنقول
+
+60
+00:04:27,730 --> 00:04:33,590
+أنّه لأي two sets، هنتعامل مع two sets A و B، بنقدر
+
+61
+00:04:33,590 --> 00:04:37,630
+نقول أن هو يمثل أو نقدر نمثل الـ function a
+
+62
+00:04:37,630 --> 00:04:44,040
+function F from A to B أو الـ function f mapping a
+
+63
+00:04:44,040 --> 00:04:50,780
+to b تعمل mapping من a to b، relation علاقة بين a و
+
+64
+00:04:50,780 --> 00:04:56,480
+b بين a و b أو هي عبارة عن function دالة من set a
+
+65
+00:04:56,480 --> 00:05:03,540
+to set b. فبقول الـ function f from set a to set b.
+
+66
+00:05:03,540 --> 00:05:08,160
+هنا إيه هذه؟ هذه الـ universe of discourse لمين؟ للـ
+
+67
+00:05:08,160 --> 00:05:14,220
+x. أولا الـ a، أنا باخد منها قيم small a اللي هي
+
+68
+00:05:14,220 --> 00:05:16,480
+القيمة اللي هتطبق عليها الـ function عشان تطلع لي
+
+69
+00:05:16,480 --> 00:05:20,680
+مين؟ تطلع لي b، و b، الـ small b هذه هتكون ∈
+
+70
+00:05:20,680 --> 00:05:29,100
+set B، okay؟ فهي في الآخر مدام هتطلعنا ناتج ∈
+
+71
+00:05:29,100 --> 00:05:34,520
+to B، معناته الـ f(x) هي ∈ B لأن الـ f(x)
+
+72
+00:05:34,520 --> 00:05:42,770
+هذه هي تمثل لنا الـ b small تمثل b small. كويسة من
+
+73
+00:05:42,770 --> 00:05:48,390
+وين جبناها؟ من تطبيق x على الـ function أو الـ
+
+74
+00:05:48,390 --> 00:05:52,690
+function applied على الـ value x. و x هذه لازم تكون
+
+75
+00:05:52,690 --> 00:05:57,630
+belonging to، يعني to a. فإذا أنا محكوم هنا بالـ two
+
+76
+00:05:57,630 --> 00:06:02,940
+sets. صرت محكوم أن الـ input لازم يكون ∈ set
+
+77
+00:06:02,940 --> 00:06:06,740
+A، و الـ output لازم يكون ∈ set B. فهذا
+
+78
+00:06:06,740 --> 00:06:09,080
+تعريفنا لمين؟ للـ function حتى اللحظة.
+
+79
+00:06:12,350 --> 00:06:15,770
+الـ total ممكن في الآخر الـ function if assigns 0
+
+80
+00:06:15,770 --> 00:06:19,890
+or 1 elements of B، ممكن ما يكون لوش نتيجة في B ويكون
+
+81
+00:06:19,890 --> 00:06:24,290
+يكون خارج الـ .. الـ .. الـ .. الـ domain بتاعنا أو
+
+82
+00:06:24,290 --> 00:06:28,290
+يكون خارج الـ set B، أو ممكن يكون عبارة عن element
+
+83
+00:06:28,290 --> 00:06:34,790
+واحد بس، أكتر لأ. بمعنى لكل input المفروض ما يكونش
+
+84
+00:06:34,790 --> 00:06:38,590
+فيه two outputs، إن الـ output يكون له two inputs
+
+85
+00:06:38,590 --> 00:06:43,570
+ماشي، زي التربيع. زي التربيع فهمناها، ماشي. تربيع
+
+86
+00:06:43,570 --> 00:06:47,510
+مقبولة أن يكون في عندكم function تربيع، two inputs
+
+87
+00:06:47,510 --> 00:06:51,530
+بيعطينا نفس الـ output. فليكن ماشي، نفترض أنّه minus
+
+88
+00:06:51,530 --> 00:06:55,270
+two، two، بيعطينا أربعة، الاتنين هيعطينا نفس الـ
+
+89
+00:06:55,270 --> 00:07:01,660
+output، مقبولة. ولكن input واحد يعطينا two outputs، لأ.
+
+90
+00:07:01,660 --> 00:07:04,640
+يمكن، لأن حتى الـ system اللي بنتكلم عنه هنا بيصير
+
+91
+00:07:04,640 --> 00:07:08,380
+unstable و بيصير فيه مشكلة في الـ system بتاعنا، هذه
+
+92
+00:07:08,380 --> 00:07:11,380
+بنقدر نقول عنها أنها مش function من أصله، إذا مرّت
+
+93
+00:07:11,380 --> 00:07:14,300
+عليكم، تعاملوا معاها أن هذه مش function، مش هينفع
+
+94
+00:07:14,300 --> 00:07:18,920
+نتعامل معاها، مش هينفع نتعامل معاها، في الحالة
+
+95
+00:07:18,920 --> 00:07:23,960
+بتاعتنا. تخيلوا تماما بالظبط زي لو أنّه الزمن هو الـ X
+
+96
+00:07:23,960 --> 00:07:27,900
+و الـ location اللي إحنا واقفين فيه هذا الـ Y، أنا
+
+97
+00:07:27,900 --> 00:07:33,300
+عند كل time أنا وين موجود؟ طب هل بقدر .. هل بنقدر في
+
+98
+00:07:33,300 --> 00:07:36,540
+نفس اللحظة، في نفس الـ input، في نفس الـ time أكون
+
+99
+00:07:36,540 --> 00:07:40,060
+موجود في مكانين، في two locations؟ لأ يمكن .. لأ
+
+100
+00:07:40,060 --> 00:07:42,700
+يمكن. بقدر أقول إن والله أنا سريع لدرجة إن ممكن في
+
+101
+00:07:42,700 --> 00:07:45,280
+.. في أقل وقت ممكن أكون انتقلت من واحد لواحد
+
+102
+00:07:45,280 --> 00:07:49,260
+ماشي، فالـ slope بتاعي يكون كتير عالي كقيمة كـ
+
+103
+00:07:49,260 --> 00:07:52,320
+absolute، قيمته عالية، المعدل التغير عالي، بس إنّه
+
+104
+00:07:52,320 --> 00:07:55,460
+أكون في نفس اللحظة لأ يمكن. فعشان هيك الـ output
+
+105
+00:07:55,460 --> 00:08:00,320
+لازم يكون جاي من input، من input واحدة، و الـ input
+
+106
+00:08:00,320 --> 00:08:03,440
+الواحدة لأ يمكن يطلع لنا two outputs. لأ يمكن من
+
+107
+00:08:03,440 --> 00:08:08,340
+input واحدة يكون two outputs. okay. graphical
+
+108
+00:08:08,340 --> 00:08:13,640
+representations لمن؟ للـ .. للـ set .. للـ
+
+109
+00:08:13,640 --> 00:08:16,020
+functions. عفوا للـ functions. فهنبدأ بإيش؟ بالـ Venn
+
+110
+00:08:16,020 --> 00:08:20,220
+diagram. Venn diagram. هنقول أننا set A، مجموعة الـ
+
+111
+00:08:20,220 --> 00:08:26,270
+elements اللي مسموح ليه أطبّقها كـ X في f(x)، في f
+
+112
+00:08:26,270 --> 00:08:31,210
+of x بحيث أن هي تعطيني outputs. كل الـ outputs هذه
+
+113
+00:08:31,210 --> 00:08:35,050
+موجودة في set تانية بنسميها B. فهيكون في عندنا from
+
+114
+00:08:35,050 --> 00:08:40,990
+A to B في function f. الـ function f هذه عبارة عن
+
+115
+00:08:40,990 --> 00:08:47,720
+إيش هي؟ عبارة عن function from A1 مثلا to B1. فإذا
+
+116
+00:08:47,720 --> 00:08:53,540
+طبّقنا الـ function على الـ element A1 هيعطينا ناتج
+
+117
+00:08:53,540 --> 00:08:59,240
+B1 small طبعا. مجموعة elements. فكل element موجود
+
+118
+00:08:59,240 --> 00:09:05,440
+هنا لازم يكون الناتج بتاعه موجود في الـ set B. Okay.
+
+119
+00:09:05,440 --> 00:09:11,060
+هذا عن طريق Venn diagram. طيب bipartite graph، الـ
+
+120
+00:09:11,060 --> 00:09:15,060
+bipartite graph هيكون عندنا two parts أو two
+
+121
+00:09:15,060 --> 00:09:18,300
+columns. الـ column الأول عبارة عن dots، الـ dots هذه
+
+122
+00:09:18,300 --> 00:09:21,100
+تمثل الـ elements بتاعة الـ input.
+
+123
+00:09:25,910 --> 00:09:31,250
+الـ column التاني يمثل برضه مجموعة dots، عبارة عن الـ
+
+124
+00:09:31,250 --> 00:09:37,750
+elements داخل set B. فبنعمل relation إذا كان الـ
+
+125
+00:09:37,750 --> 00:09:43,070
+element الأول في set A under the function f
+
+126
+00:09:43,070 --> 00:09:48,650
+بيعطينا العنصر التاني فبنعمل بينهم خط. فهنا الـ
+
+127
+00:09:48,650 --> 00:09:54,960
+function from first element A to second element
+
+128
+00:09:54,960 --> 00:09:59,740
+from B. تمام؟ بنرسمها سهل على أساس أنّه under the
+
+129
+00:09:59,740 --> 00:10:02,800
+function في relation between الـ element هذا و الـ
+
+130
+00:10:02,800 --> 00:10:05,340
+element هذا. طيب بين الـ element التاني و الـ element
+
+131
+00:10:05,340 --> 00:10:09,920
+الأول، ممكن في الآخر بنرسم طبيعة أو الـ function
+
+132
+00:10:09,920 --> 00:10:15,740
+from A to B، from element موجود في set A to element
+
+133
+00:10:15,740 --> 00:10:20,420
+موجود في set B. هذه طريقة تانية برضه في الـ
+
+134
+00:10:20,420 --> 00:10:23,340
+representation للـ function. طريقة التالتة اللي
+
+135
+00:10:23,340 --> 00:10:28,240
+إنتوا عارفينها، الـ plot. الـ dots هذه بتحطوها عند كل
+
+136
+00:10:28,240 --> 00:10:31,280
+X، بتجيبوا قيمة Y بتاعتها، فبتحطوا مجموعة نقاط وبعدين
+
+137
+00:10:31,280 --> 00:10:35,290
+بترسموها، الـ plot بتاعكم، فبترسموا شكل الـ function
+
+138
+00:10:35,290 --> 00:10:37,610
+بهذا الشكل، ويمكن إنتوا متعودين على النوع هذا.
+
+139
+00:10:37,610 --> 00:10:42,450
+بيعطيكم التصور إنّ كيف relation between الـ X و الـ
+
+140
+00:10:42,450 --> 00:10:46,730
+Y. الـ X و الـ Y طبعا إحنا بنتكلم أن الـ X هتكون
+
+141
+00:10:46,730 --> 00:10:51,890
+∈ إيه؟ to set A، و الـ y ∈ set B اللي
+
+142
+00:10:51,890 --> 00:10:55,970
+هي عبارة عن f(x)، دي، يبقى عارف عن f(x)، okay؟
+
+143
+00:10:55,970 --> 00:10:59,630
+functions إحنا اتعاملنا معاها حتى اللحظة في
+
+144
+00:10:59,630 --> 00:11:01,990
+functions كتير، إحنا اتعاملنا معاها حتى اللحظة و
+
+145
+00:11:01,990 --> 00:11:04,950
+اتكلمنا يمكن عنها. من أهمها اللي هي الـ proposition.
+
+146
+00:11:04,950 --> 00:11:08,690
+الـ proposition، لما كنا بنتكلم عن الـ proposition
+
+147
+00:11:08,690 --> 00:11:12,490
+يعتمد على situation معينة، زي الـ example اللي بيبقى
+
+148
+00:11:12,490 --> 00:11:16,550
+عليه، "it's raining"، بتشتي. لو قلنا الكلام هذا اليوم
+
+149
+00:11:16,550 --> 00:11:21,090
+هتقولوا false. طب لو قلناها قبل العيد أسبوع، زمان
+
+150
+00:11:21,090 --> 00:11:23,550
+كانت بتشتي، لو قلناها في وقتها، في الـ situation
+
+151
+00:11:23,550 --> 00:11:26,470
+هداك، كنا هنقول true، فإذا معتمدين على الـ
+
+152
+00:11:26,470 --> 00:11:29,350
+situation، فهنا بعتبر .. بتعمل مع الـ proposition
+
+153
+00:11:29,350 --> 00:11:34,320
+كأنها function of situation، حسب الـ situation، حسب
+
+154
+00:11:34,320 --> 00:11:38,200
+الحالة، حسب الـ state، الوضع اللي إحنا فيه، حسب الحالة
+
+155
+00:11:38,200 --> 00:11:41,340
+بتاعتنا، بقدر أقول أن هو true or false، يعني بتتغير
+
+156
+00:11:41,340 --> 00:11:46,440
+بناء على الحالة، بناء على الحالة، أما true or false.
+
+157
+00:11:46,440 --> 00:11:50,100
+فهذه logical system بنسميها situation theory.
+
+158
+00:11:50,100 --> 00:11:55,840
+situation theory، okay؟ زي ما قلنا، "it's raining"، الـ S
+
+159
+00:11:55,840 --> 00:12:00,550
+هنا our situation here حاليا، our situation، بناة
+
+160
+00:12:00,550 --> 00:12:04,410
+عادية، بقدر أقرر. أما تقولوا لي والله كمان شهر هتكون
+
+161
+00:12:04,410 --> 00:12:10,290
+بتشتي، هقول لكم معرفش. يعني حتى التنبؤات أو التوقعات
+
+162
+00:12:10,290 --> 00:12:14,510
+الجوية قبل بيوم يومين ممكن يتوقعوا لنا، بس تقولوا لي
+
+163
+00:12:14,510 --> 00:12:18,530
+بعد شهر إيش، بدوس معرفش. توقعات معرفش، حسب الـ
+
+164
+00:12:18,530 --> 00:12:22,230
+situation في وقتها، حسب الـ situation في وقتها. طيب
+
+165
+00:12:22,230 --> 00:12:25,690
+فبنقدر نقول P(S)، و الـ S دي اللي هي situation
+
+166
+00:12:26,890 --> 00:12:31,810
+هتكون ∈ {true, false}. function. لحظة، هي
+
+167
+00:12:31,810 --> 00:12:33,410
+function، هي نوع من أنواع الـ functions إحنا
+
+168
+00:12:33,410 --> 00:12:36,890
+اتعاملنا مع حاجة بالهيك، هي نوضح أنّه كانت عبارة عن
+
+169
+00:12:36,890 --> 00:12:41,410
+function. quick propositional operator. الـ operators
+
+170
+00:12:41,410 --> 00:12:43,910
+اللي أخدناها، أخدنا إيش؟ أخدنا الـ and، أخدنا الـ or،
+
+171
+00:12:43,910 --> 00:12:46,730
+أخدنا الـ negation، أخدنا الـ xor، أخدنا الـ .. كل
+
+172
+00:12:46,730 --> 00:12:5
+
+223
+00:16:42,560 --> 00:16:45,700
+هالكلام هذا سابقا الـ predicate كـ predicate بحد
+
+224
+00:16:45,700 --> 00:16:49,200
+ذاتها هي مش proposition، بقدرش أقول هي true or false
+
+225
+00:16:49,200 --> 00:16:54,140
+ولكن لما هحطلها الـ variable تبعها أصبحت بقدر أحكم
+
+226
+00:16:54,140 --> 00:16:56,740
+عليه هي true or false بناء على مين اللي حطّها
+
+227
+00:16:56,740 --> 00:17:00,480
+variable، بناء على اللي حطينا variable، تمام فأصبحت
+
+228
+00:17:00,480 --> 00:17:06,620
+هي واضحة f of x، بي of my، حطينا variable في الـ bit
+
+229
+00:17:06,620 --> 00:17:11,200
+string، نفس الكلام، بي of length n can be viewed as
+
+230
+00:17:11,200 --> 00:17:16,600
+a function from the numbers one to n، هذا بناء على
+
+231
+00:17:16,600 --> 00:17:20,560
+الـ index للـ location، أو الـ location نفسه، الـ index للـ
+
+232
+00:17:20,560 --> 00:17:27,360
+elements، إحنا لما نقول مثلاً الـ bit string بي one
+
+233
+00:17:27,360 --> 00:17:33,500
+zero one، إحنا عارفين إن الـ bit string مرتب، صحيح
+
+234
+00:17:33,500 --> 00:17:37,020
+مهم الترتيب، يعني بقدر أتعامل مع الـ location
+
+235
+00:17:37,020 --> 00:17:43,450
+بتاعتهم، على أساس إن هي variable، وأنا عارف إنه دائماً في
+
+236
+00:17:43,450 --> 00:17:47,530
+الـ bit string، هذا أول element دائماً هيكون واحد، هذا
+
+237
+00:17:47,530 --> 00:17:51,750
+مش زي الـ set، unordered، لأ، الـ set okay، أي واحدة
+
+238
+00:17:51,750 --> 00:17:54,070
+جابتها، مش هتفرق كتير، بس في الـ bit string لأ
+
+239
+00:17:54,070 --> 00:17:57,250
+مهم الترتيب، لما اتكلمنا المرة اللي فاتت في الـ ...
+
+240
+00:17:57,250 --> 00:18:01,510
+في الـ set، قولنا إنه لما بيصير ordered بيصير عندنا
+
+241
+00:18:01,510 --> 00:18:04,710
+بنتكلم عن string، فعملنا الـ bit string
+
+242
+00:18:04,710 --> 00:18:08,800
+representation، لما اتكلمنا عن الـ bit ... الـ bit
+
+243
+00:18:08,800 --> 00:18:11,760
+string representation، قولنا إن دائماً الـ element
+
+244
+00:18:11,760 --> 00:18:17,080
+الشمال هو الـ element الأول، هو الـ element الأول
+
+245
+00:18:17,080 --> 00:18:20,500
+قولناها فين؟ في آخر محاضرة من المحاضرات أعتقد، في
+
+246
+00:18:20,500 --> 00:18:24,920
+آخر واحدة من المحاضرات، تمام، طيب لما نيجي نتكلم عن
+
+247
+00:18:24,920 --> 00:18:28,860
+الـ set، قولنا قبل هيك الـ set هي unordered، يعني أنا
+
+248
+00:18:28,860 --> 00:18:32,440
+مقدرش أ ... يعني مقدرش نستفيد من فكرة إيش؟ من فكرة
+
+249
+00:18:32,440 --> 00:18:37,270
+الـ location، الترتيب، طب ها إيش ... إيش الحاجة اللي
+
+250
+00:18:37,270 --> 00:18:40,030
+... اللي بتضمن دائماً إن هي موجودة؟ إنه العنصر موجود
+
+251
+00:18:40,030 --> 00:18:44,890
+أو لأ؟ هذه بالنسبة لنا واضحة، لأن هو إحنا بنعتمد
+
+252
+00:18:44,890 --> 00:18:47,310
+أساساً في الـ set إن هل العنصر موجود أو غير موجود
+
+253
+00:18:47,310 --> 00:18:51,150
+أما وين الـ location تبعه؟ ما عندناش معلومة الـ
+
+254
+00:18:51,150 --> 00:18:53,490
+location تبعه، إجا رقم 1، إجا رقم 2، إجا رقم 5، إجا
+
+255
+00:18:53,490 --> 00:18:57,270
+رقم 10، إجا آخر element، مش هتفرق، بمعنى إن لو عندنا
+
+256
+00:18:57,270 --> 00:19:05,830
+الـ set S عبارة عن one, two, three، إجى واحد كتب لها
+
+257
+00:19:05,830 --> 00:19:09,110
+طبعاً كويس إن تكون مرتبة، مش غلط، ولكن إجى واحد كتب
+
+258
+00:19:09,110 --> 00:19:15,830
+لها اتنين، واحد، تلاتة، المهم إن الـ elements موجودة
+
+259
+00:19:15,830 --> 00:19:20,030
+الـ elements كاملة موجودة، مش متكررة، ولا يعني بمعنى
+
+260
+00:19:20,030 --> 00:19:22,550
+لو بدي أعملها cardinality بقدر أجيبهم وخلاص يعني
+
+261
+00:19:22,550 --> 00:19:24,770
+كل الـ operations اللي أنا محتاجها بقدر أطلّعها
+
+262
+00:19:24,770 --> 00:19:27,690
+بنقدر نشتغل عليها، بما فيها الـ function، فهنا الـ
+
+263
+00:19:27,690 --> 00:19:30,450
+function بتصير function في مين؟ في الـ element نفسه
+
+264
+00:19:31,850 --> 00:19:35,490
+كـ function بتصير في الـ element نفسه، وبتصير الناتج تبعي
+
+265
+00:19:35,490 --> 00:19:41,370
+true or false، belong to or not belong to، هل هو الـ
+
+266
+00:19:41,370 --> 00:19:45,510
+element اللي أعطاني إياه كـ variable، belong to بحط له
+
+267
+00:19:45,510 --> 00:19:53,110
+true، not belong to بحط له F، زي لو قلنا الـ set S
+
+268
+00:19:53,110 --> 00:19:58,370
+equal to element 3، بس هي عبارة عن set تحتوي على
+
+269
+00:19:58,370 --> 00:20:02,430
+element واحد، فلو قلنا S of 0، فالـ false، لأن الـ
+
+270
+00:20:02,430 --> 00:20:06,590
+zero غير موجود، الـ element zero مش موجود هنا، ولكن S
+
+271
+00:20:06,590 --> 00:20:12,170
+of 3 موجود، بقول true، فهي برضه تعاملنا مع الـ set as
+
+272
+00:20:12,170 --> 00:20:17,570
+a function، معها as a function، الكلام اللي قلناه في
+
+273
+00:20:17,570 --> 00:20:20,610
+الـ or قبل شوية، في الـ operator اللي خاصة بالـ
+
+274
+00:20:20,610 --> 00:20:23,010
+proposition، بنقدر نقوله برضه في الـ operator اللي
+
+275
+00:20:23,010 --> 00:20:26,650
+خاصة بيه، بالـ sets، بالـ sets اللي هي مين؟ الـ
+
+276
+00:20:26,650 --> 00:20:32,410
+intersection، union، complement، تمام، ما بقولش هنا
+
+277
+00:20:32,410 --> 00:20:36,270
+negation كانت في الـ proposition، زي لما قلت هنا
+
+278
+00:20:36,270 --> 00:20:39,730
+intersection، ما قلتش and هنا، intersection، فهنا
+
+279
+00:20:39,730 --> 00:20:44,100
+complement، تمام، اللي هي الـ operators واحدة وبتحسّ
+
+280
+00:20:44,100 --> 00:20:47,420
+إن تأثيرها واحد، بس طبعاً بناء على أنا applied على
+
+281
+00:20:47,420 --> 00:20:50,780
+إيش، بتتغير المصطلح تبعها، بتتغير المصطلح، فهذه
+
+282
+00:20:50,780 --> 00:20:55,580
+compliment okay، نقدر نقولها function على أساس إن
+
+283
+00:20:55,580 --> 00:20:58,920
+أنا بعمل نفس الفكرة زي ما كنا نتكلم عن or، لأ، هي الـ
+
+284
+00:20:58,920 --> 00:21:02,840
+function تبعت هنا، intersection، وهي فتحنا الأقواس
+
+285
+00:21:02,840 --> 00:21:06,560
+بتاعة الـ function، طيب نحدد الـ inputs، الـ inputs
+
+286
+00:21:06,560 --> 00:21:10,540
+طبعاً مش بده تكون sets، لأن أنا بتعامل مع operator لـ
+
+287
+00:21:10,540 --> 00:21:15,560
+sets، فأتوقع إن الـ input لازم تكون sets عشان من الـ
+
+288
+00:21:15,560 --> 00:21:17,980
+sets هدولة من الـ two sets هدولة، ومن الـ function
+
+289
+00:21:17,980 --> 00:21:22,800
+أطلّع الناتج اللي هو عبارة عن، جدّيش، تلاتة، الناتج
+
+290
+00:21:22,800 --> 00:21:25,060
+هيكون تلاتة، اللي هو الـ intersection between الـ two
+
+291
+00:21:25,060 --> 00:21:31,440
+sets اللي قدامنا هدول، تمام، فلاحظوا برضه بنتعامل
+
+292
+00:21:31,440 --> 00:21:39,060
+معها as sets a function، okay، خلصنا من توضيح إن إحنا
+
+293
+00:21:39,060 --> 00:21:42,480
+فعلاً تعاملنا مع functions كتيرة، كنا فعلاً نتعامل
+
+294
+00:21:42,480 --> 00:21:46,640
+معها، وبتقدر هنا نكتبها بشكل function، مع كل
+
+295
+00:21:46,640 --> 00:21:52,100
+المواضيع أو الـ subjects اللي إحنا شرحناها، نيجي شوية
+
+296
+00:21:52,100 --> 00:21:54,880
+terminology، نركز شوية في مين؟ في الـ function
+
+297
+00:21:54,880 --> 00:21:58,320
+نفسها، خلينا نركز في الـ function، نركز في الـ
+
+298
+00:21:58,320 --> 00:22:00,340
+function، إحنا عرفنا الـ function إن هي الـ function
+
+299
+00:22:00,340 --> 00:22:07,500
+f from a to b، set A to set B، معناته الـ input إجباري
+
+300
+00:22:07,500 --> 00:22:11,140
+لازم يكون belong to set A، والـ output لازم
+
+301
+00:22:11,140 --> 00:22:17,200
+يكون belong to set B، okay، and F of A، و A هذه لازم
+
+302
+00:22:17,200 --> 00:22:23,680
+تكون belong to capital A، to set A، equal to B، بحيث
+
+303
+00:22:23,680 --> 00:22:27,960
+أنه زي ما قلنا A belong to set A، و B belong to set
+
+304
+00:22:28,870 --> 00:22:32,390
+Okay، إذا فعلاً عندنا الـ function هذه بنقدر نعمل
+
+305
+00:22:32,390 --> 00:22:35,130
+شوية التسميات هدول، إيش هما التسميات هدول، أو
+
+306
+00:22:35,130 --> 00:22:40,770
+المسميات، A اللي هي set A، بنسميها domain، set A
+
+307
+00:22:40,770 --> 00:22:45,250
+بنسميها domain، طيب الـ B أو الـ set B بنسميها الـ
+
+308
+00:22:45,250 --> 00:22:48,710
+codomain، codomain، تابع للـ domain، يتبع للـ domain
+
+309
+00:22:51,670 --> 00:22:56,730
+مناظر للـ domain، أو مقابل للـ domain، الـ small b
+
+310
+00:22:56,730 --> 00:23:03,270
+يُلاحظ إنه element أو الناتج، الـ element، ويل هي الـ
+
+311
+00:23:03,270 --> 00:23:08,810
+ناتج هذا بنسميها الـ image of a under function f
+
+312
+00:23:08,810 --> 00:23:12,950
+بمعنى هو a بس بعد ما طبّقنا على الـ a من الـ function
+
+313
+00:23:12,950 --> 00:23:17,850
+f، تمام؟ فهي الـ image، وقلت الكتابة الصورة، وقلنا
+
+314
+00:23:17,850 --> 00:23:21,210
+الكتابة حكاية المراية، المراية إذا كان normal ...
+
+315
+00:23:21,210 --> 00:23:24,810
+normal، معناته x بتساوي y، أو y بتساوي x، أو a بتساوي b
+
+316
+00:23:24,810 --> 00:23:29,470
+... a بتساوي b، فـ a هتساوي b، خلاص، أنا في الآخر بتعامل
+
+317
+00:23:29,470 --> 00:23:32,880
+مع إن الـ b هي الـ image بتاعة a، لما أشوف صورتي،
+
+318
+00:23:32,880 --> 00:23:37,340
+صورتي هي الـ image بتعتي، هي الـ image بتعتي، لو سطح
+
+319
+00:23:37,340 --> 00:23:42,260
+المرايا مقعّر، محدّد فيه أي functionality معيّنة
+
+320
+00:23:42,260 --> 00:23:45,280
+معمولة فيه، هالّاجنة الصورة مختلفة، ولكن هي في
+
+321
+00:23:45,280 --> 00:23:49,080
+النهاية تمثّل صورتي برضه، بس under the function
+
+322
+00:23:49,730 --> 00:23:53,510
+under the function، بعد ما طبّقنا عليها الـ function
+
+323
+00:23:53,510 --> 00:23:56,270
+اللي هو سطح المرايا، أو المقعّرة، أو المحدّد، أو اللي
+
+324
+00:23:56,270 --> 00:24:01,150
+يمثّل بـ function معيّنة، الـ A بالمقابل هي الـ pre
+
+325
+00:24:01,150 --> 00:24:06,610
+image، هي الصورة المسبقة، الصورة المسبقة لـ B under
+
+326
+00:24:06,610 --> 00:24:13,430
+the function F، under function F، okay، in general B
+
+327
+00:24:13,430 --> 00:24:17,910
+may have more than one pre-image، ممكن زي التربيع
+
+328
+00:24:18,830 --> 00:24:23,690
+التربيع، ممكن يكون له أكتر من pre-image، على
+
+329
+00:24:23,690 --> 00:24:26,670
+اعتبار إن هي عندكم مثلاً، قولناها اتنين و minus
+
+330
+00:24:26,670 --> 00:24:30,210
+اتنين، هيكون لهم اتنين، القيمتين مثلاً اللي هم نفس
+
+331
+00:24:30,210 --> 00:24:36,770
+الـ أربعة، هذه الـ image أو الـ B لها اتنين pre-image، هي
+
+332
+00:24:36,770 --> 00:24:41,290
+pre-image أولى، وهي pre-image تانية، لاحظوا two
+
+333
+00:24:41,290 --> 00:24:45,810
+pre-images، زي ما قلنا العكس لأ، العكس لأ، يعني لا
+
+334
+00:24:45,810 --> 00:24:53,280
+يمكن لـ a يكون فيه two images، لأ يمكن، تمام، then نتكلم
+
+335
+00:24:53,280 --> 00:24:56,520
+عن الـ range، هالواجهة، الـ range هي subset بنسميها R
+
+336
+00:24:56,520 --> 00:25:00,980
+طبعاً هي subset من الـ codomain، جزء من الـ code
+
+337
+00:25:00,980 --> 00:25:06,460
+domain of F is set، إحنا بنتكلم عن subset، هيها
+
+338
+00:25:06,460 --> 00:25:11,440
+معناته بتعرفها as a set، فبنحط لها علامات الـ set
+
+339
+00:25:11,440 --> 00:25:17,650
+الـ curly process تبعتنا، of B هي set of B such that
+
+340
+00:25:17,650 --> 00:25:24,010
+there exists a which is a pre-image a، تنتج لنا b
+
+341
+00:25:24,010 --> 00:25:29,090
+معناته هي في النهاية set لمجموعة outputs، outputs
+
+342
+00:25:29,090 --> 00:25:32,830
+مش الـ b، عرفناها أساساً هي الـ output، الـ outputs إنه
+
+343
+00:25:32,830 --> 00:25:36,230
+يوجد قيم للـ outputs، أو كل قيم الـ outputs اللي
+
+344
+00:25:36,230 --> 00:25:45,150
+ناتجة من applied أو تطبيق الـ f على كل قيم a، بمعنى
+
+345
+00:25:45,150 --> 00:25:49,390
+هي الـ actual output، هي الـ actual، الـ experimental
+
+346
+00:25:49,390 --> 00:25:54,490
+output، هو التجريب فعلاً إن أنا جربت كل قيم a، مسكت
+
+347
+00:25:54,490 --> 00:25:58,530
+الـ set a، كل القيم اللي فيها، جربتهم under the
+
+348
+00:25:58,530 --> 00:26:01,930
+function، طلعنا ناتج، الناتج هذا حطّيناه في set
+
+349
+00:26:01,930 --> 00:26:06,970
+سمّيناها R، actual هذا، هذا الحقيقي، هذا الناتج الفعلي
+
+350
+00:26:06,970 --> 00:26:09,610
+النتيجة الفعلية للـ function
+
+351
+00:26:12,640 --> 00:26:17,600
+Range vs Codomain، هدى شيء وهدى شيء، الـ Codomain زي ما
+
+352
+00:26:17,600 --> 00:26:21,560
+قلنا إحنا هي الـ domain المقابل أو المظير للـ
+
+353
+00:26:21,560 --> 00:26:26,040
+domain للـ input، وهدى بتكون عبارة عن الـ P، قبل ما
+
+354
+00:26:26,040 --> 00:26:28,820
+نطبّق لسه الـ function، اللي هو متوقع أنه هتكون ...
+
+355
+00:26:28,820 --> 00:26:31,440
+لما نتكلم عن الـ real number بالنسبة للـ domain
+
+356
+00:26:31,440 --> 00:26:35,360
+متوقع إنه برضه إنه هتكون كلها real number، فبقول إن
+
+357
+00:26:35,360 --> 00:26:39,860
+هي belong to R، to real number، طب actually خلينا
+
+358
+00:26:39,860 --> 00:26:44,280
+ندخل القيم exactly بالضبط اللي داخل الـ set A،
+
+359
+00:26:44,280 --> 00:26:49,500
+نطبّقهم under the function، ونشوف actual outputs،
+
+360
+00:26:49,500 --> 00:26:53,040
+نطلع النتائج الحقيقية، النتائج الحقيقية بنحصرها،
+
+361
+00:26:53,040 --> 00:26:58,060
+بنقول هذه إيش؟ R، هذه الـ range، هذه R أو الـ range،
+
+362
+00:26:58,060 --> 00:27:02,510
+تمام، فبتعمل mapping زي ما قلنا في الآخر الـ code
+
+363
+00:27:02,510 --> 00:27:06,970
+domain، هذا بيعمل map لكل الـ domain values، أو هم
+
+364
+00:27:06,970 --> 00:27:11,210
+التصريح للـ domain، هو التصريح للـ domain، مادام الـ
+
+365
+00:27:11,210 --> 00:27:13,830
+domain real numbers، معناته الـ codomain بيكون
+
+366
+00:27:13,830 --> 00:27:18,910
+real numbers، بالعموم actual لأ، بتصير اسمها range
+
+367
+00:27:18,910 --> 00:27:21,970
+actual، لما نيجي نطبّقها واحدة واحدة، بتصير اللي هي
+
+368
+00:27:21,970 --> 00:27:25,070
+الـ range، أو اللي هي الـ actually maps elements of
+
+369
+00:27:25,070 --> 00:27:30,110
+the domain، example، ناخد example على الموضوع، خلينا
+
+370
+00:27:30,110 --> 00:27:34,550
+نقول إنه إنه عندنا function، if is a function
+
+371
+00:27:34,550 --> 00:27:38,470
+mapping students in the class، في الـ class تبعنا، to
+
+372
+00:27:38,470 --> 00:27:42,210
+a set of grades، لمجموعة الـ grades ساعتنا، أو
+
+373
+00:27:42,210 --> 00:27:47,490
+التقديرات بتاعتنا، التقديرات اللي هي a, b, c, d, e
+
+374
+00:27:47,490 --> 00:27:50,950
+بدل الـ ... بدل الثاني يعني لأنه ما ... ما أعتقدش إنه
+
+375
+00:27:50,950 --> 00:27:54,190
+فيه grade a ... e، بس إحنا زي ما بقول الـ ... بدنا
+
+376
+00:27:54,190 --> 00:27:59,520
+عشان هشيل الـ ... عندنا خمسة grades، وبدنا نوزّع الطلاب
+
+377
+00:27:59,520 --> 00:28:02,960
+عليهم، طبيعي إحنا لسه ما عملناش امتحانات، أنا مش عارف
+
+378
+00:28:02,960 --> 00:28:05,980
+فإذا كان at this point إن إحنا لسه ما عملناش أي
+
+379
+00:28:05,980 --> 00:28:09,960
+امتحان عشان أعرف كيف أوزّع، ففي الحالة هذه الـ code
+
+380
+00:28:09,960 --> 00:28:14,220
+domain إيش هيكون؟ كلهم، الـ codomain كلهم، هذا مش
+
+381
+00:28:14,220 --> 00:28:18,320
+هيتغيّر، الـ codomain كلهم، طيب الـ range لسه
+
+382
+00:28:18,320 --> 00:28:23,620
+ما عملناش شيء، and none، أنا مش عارف، أنا مش عارف، لأ
+
+383
+00:28:23,620 --> 00:28:26,720
+إحنا مش عارفين، إحنا لسه ... ما قيّمناش لسه، فإحنا مش
+
+384
+00:28:26,720 --> 00:28:29,620
+عارفين، لإنه ما عنديش أي معلومة، ما عنديش function،
+
+385
+00:28:29,620 --> 00:28:31,480
+ما عندي ... الـ function في النهاية اللي هي إيش كانت
+
+386
+00:28:31,480 --> 00:28:34,800
+المفروض ... الامتحان، الامتحان هيكون هو الـ function
+
+387
+00:28:35,650 --> 00:28:40,050
+بناءً على نتائج الامتحان، بنحط الـ outputs، بنحط
+
+388
+00:28:40,050 --> 00:28:43,910
+الـ outputs، فهنا unknown، طيب لو بعد الامتحان عملنا
+
+389
+00:28:43,910 --> 00:28:48,530
+
+445
+00:32:55,040 --> 00:33:04,690
+R to Rf plus g of x عبارة عن f of x plus g of x
+
+446
+00:33:04,690 --> 00:33:10,030
+نفس الكلام multiplication برضه هتكون f multiplied
+
+447
+00:33:10,030 --> 00:33:16,630
+by g of x عبارة عن f of x multiplied by g of x
+
+448
+00:33:16,630 --> 00:33:22,870
+ننقل
+
+449
+00:33:22,870 --> 00:33:27,140
+لعندي كل الأمور سهلة و بسيطة، ننتقل ل operator تانية
+
+450
+00:33:27,140 --> 00:33:33,940
+اللي هي ال composition، فضّل ال dot
+
+451
+00:33:33,940 --> 00:33:37,960
+بتكون ترتيبية، ال dot عادة بتكون ترتيبية كتير
+
+452
+00:33:37,960 --> 00:33:40,260
+بتستخدم في ال ... ال ... ال ... اللي هي ال Cartesian
+
+453
+00:33:40,260 --> 00:33:43,600
+product، بتكون اللي هي علاقة بال Cartesian product
+
+454
+00:33:43,600 --> 00:33:47,580
+إحنا لما بنعمل dot عادية، dot العادية خلاص ضرب عادي
+
+455
+00:33:47,580 --> 00:33:50,680
+اللي هي multiplication عادية، ضرب عادي، بس لما نيجي
+
+456
+00:33:50,680 --> 00:33:53,820
+نعمل Cartesian product، لأ، ال Cartesian product
+
+457
+00:33:53,820 --> 00:33:58,450
+ترتيبي، لازم نحافظ على الترتيب فيه، بمعنى أنه عادة
+
+458
+00:33:58,450 --> 00:34:02,770
+بتكون لمصفوفات، لمجموعات، بنعملها dots، بنعملها
+
+459
+00:34:02,770 --> 00:34:07,370
+dots في الحالة هذه، مازلنا في ال composition،
+
+460
+00:34:07,370 --> 00:34:14,710
+composition operator هي ببساطة، بأخذ، عندنا two
+
+461
+00:34:14,710 --> 00:34:18,990
+functions، واحدة compose التانية، الأولى compose
+
+462
+00:34:18,990 --> 00:34:22,810
+التانية، خليني أكتبها عشان أشرحها، الأولى compose
+
+463
+00:34:22,810 --> 00:34:28,350
+التانية، لو افترضنا بالشكل هذا، ناتج التانية input
+
+464
+00:34:28,350 --> 00:34:32,710
+للأولى، بسيطة
+
+465
+00:34:32,710 --> 00:34:37,050
+جدا، مر عليكم أكيد، أنا متأكد أنه لازم يمر
+
+466
+00:34:37,050 --> 00:34:42,240
+عليكم، ناتج التانية input للأولى، بنسميها
+
+467
+00:34:42,240 --> 00:34:44,840
+composition، composition، ما أعرفش إيش كنتوا
+
+468
+00:34:44,840 --> 00:34:47,420
+تسموها سابقا، إحنا عندنا إيه اسم ال composition ...
+
+469
+00:34:47,420 --> 00:34:51,620
+فإحنا هنا بنقولها compose أو big O، زي عاملة زي ال
+
+470
+00:34:51,620 --> 00:34:54,820
+big O هيك، طيب عشان تكون صحيحة و تطلع نتائج
+
+471
+00:34:54,820 --> 00:35:00,780
+صحيحة، هنقول أن ال G from A to B، هذه اللي هي
+
+472
+00:35:00,780 --> 00:35:05,220
+التانية، التانية، هتبدأ من ال domain تبعها لل
+
+473
+00:35:05,220 --> 00:35:07,480
+codomain تبعها، ال codomain تبعها لازم
+
+474
+00:35:07,480 --> 00:35:12,190
+يكون هو ال domain للتانية، لل ... لل ... لل F، صحيح؟
+
+475
+00:35:12,190 --> 00:35:18,990
+لأن الناتج تبعها هو input لمن؟ لل F، ف from B to C
+
+476
+00:35:18,990 --> 00:35:25,990
+في الحالة، الناتج ككل هيكون من A to C، كل الناتج
+
+477
+00:35:25,990 --> 00:35:28,530
+اللي هو ال composition كله على بعضه هيكون من A to
+
+478
+00:35:28,530 --> 00:35:33,450
+C، from A to C، و زي ما قلنا بنعطيه ال cycle الكبيرة
+
+479
+00:35:33,450 --> 00:35:38,140
+هذه، تمام، هي بنعمل فيها composition أو
+
+480
+00:35:38,140 --> 00:35:42,480
+creation أو generation ل new function، ل new
+
+481
+00:35:42,480 --> 00:35:45,080
+function، لأن function تعويض في function، function
+
+482
+00:35:45,080 --> 00:35:49,000
+معوضة في جُلّ function، بدل ال x بتاعة ال function
+
+483
+00:35:49,000 --> 00:35:53,380
+بنعوض بقيمة ال function السابقة، قيمتها كلها على
+
+484
+00:35:53,380 --> 00:36:01,340
+بعض، قيمتها كلها على بعض، زي نقربها أكتر برضه لو
+
+485
+00:36:01,340 --> 00:36:11,570
+قلنا ال ... ال g عبارة عن X تربيع plus two فرضا، و ال F
+
+486
+00:36:11,570 --> 00:36:21,530
+ما عشان عارف، خلينا ناخد ... اتنين X تربيع ناقص X
+
+487
+00:36:21,530 --> 00:36:30,330
+بيكفي تمام؟ هذا اللي ما بنيجي نكتبه، F compose G، لحظة
+
+488
+00:36:30,330 --> 00:36:36,750
+ناتج ال G يكون input لمن؟ لل F، طيب هاي ال input
+
+489
+00:36:36,750 --> 00:36:44,890
+تبع ال F، معناته كل X بنحط مكانها، نضربها على F، لحظة
+
+490
+00:36:44,890 --> 00:36:47,890
+هتطلع 2 X تربيع
+
+491
+00:36:55,740 --> 00:37:00,540
+ناتج التانية نعوضه ك input لمن؟ للأولى، ك input
+
+492
+00:37:00,540 --> 00:37:04,140
+للأولى، طيب كويسة، هذا المفهوم، خلينا نشوف كيف
+
+493
+00:37:04,140 --> 00:37:06,840
+أسقطناه في شوية المعادلات و شوية ال expressions
+
+494
+00:37:06,840 --> 00:37:13,020
+اللي عندنا، فحنقول if compose G from A to C، نكتبها
+
+495
+00:37:13,020 --> 00:37:19,000
+f compose G of A عبارة عن إيش؟ f ال function
+
+496
+00:37:19,000 --> 00:37:24,300
+الأولى ك function في ناتج ال function التانية، لحظة
+
+497
+00:37:24,300 --> 00:37:29,060
+ال input تبعها هو ناتج ال function التانية، هي g of
+
+498
+00:37:29,060 --> 00:37:32,800
+a، خلاص، لو حسبناها، ال term هذا كله هيعتبر ناتج
+
+499
+00:37:32,800 --> 00:37:37,540
+ال function g، طيب الناتج لل function g هو input لل
+
+500
+00:37:37,540 --> 00:37:42,420
+function f، طبعا
+
+501
+00:37:42,420 --> 00:37:46,280
+في الآخر، g of a هذا مين؟ هذا ال output لمين؟ لل
+
+502
+00:37:46,280 --> 00:37:50,280
+function g، المفروض belonging to مين؟ to B، هي ال
+
+503
+00:37:50,280 --> 00:37:54,420
+function g، ال output تبعها belong to، يعني to set B
+
+504
+00:37:54,420 --> 00:38:00,400
+okay، so f of g of a بنعرفها على أساس أنها لازم
+
+505
+00:38:00,400 --> 00:38:05,240
+تكون belong to، يعني to C، f of anything هي ال
+
+506
+00:38:05,240 --> 00:38:08,480
+output لل function f، فال output لل function f
+
+507
+00:38:08,480 --> 00:38:15,140
+belong to، يعني to C، Okay، ال ... ال big O هذه أو ال
+
+508
+00:38:15,140 --> 00:38:18,040
+... ال cycle الكبيرة، طبعا big O، بدنا نحاول أن
+
+509
+00:38:18,040 --> 00:38:21,700
+ما نستخدمهاش كتير، لأنه لها استخدامات جاية، ال cycle
+
+510
+00:38:21,700 --> 00:38:26,420
+الكبيرة، أو ال compose هذه زي ال Cartesian product
+
+511
+00:38:26,420 --> 00:38:32,280
+زي ال Cartesian product، مش تبديلية، بمعنى لما نقول F
+
+512
+00:38:32,280 --> 00:38:37,400
+compose G لا تساوي G compose F، لا تساويها، هتلاقوا
+
+513
+00:38:37,400 --> 00:38:40,750
+هذه function وهذه function، هنا لو بدنا نعكس، نقص
+
+514
+00:38:40,750 --> 00:38:43,710
+الكلام ده، هتطلع function مختلفة تماما، هتطلع عبارة
+
+515
+00:38:43,710 --> 00:38:49,450
+عن اتنين X تربيع ناقص X كله تربيع زائد اتنين، هذه
+
+516
+00:38:49,450 --> 00:38:53,230
+غير هذه تماما، يعني حتى لو فكيتوهم و حولتُوهم، لا
+
+517
+00:38:53,230 --> 00:38:55,770
+يمكن يساوي، مش هيساوي بعض، هذه function وهذه
+
+518
+00:38:55,770 --> 00:38:58,490
+function تماما مختلفة، طبعا هذه عشان برضه هذه
+
+519
+00:38:58,490 --> 00:38:59,570
+compose F
+
+520
+00:39:04,580 --> 00:39:10,140
+بعكس ... بعكس مين؟ ال ... ال plus، ال or، ال and، ال
+
+521
+00:39:10,140 --> 00:39:14,360
+... ال union، ال ... ال intersection، كلهم هدول
+
+522
+00:39:14,360 --> 00:39:17,880
+نقدر نقول أن هما تبديلية، عملية تبديلية، الأولى
+
+523
+00:39:17,880 --> 00:39:20,100
+قابلة للتانية أو التانية قابلة للأولى، بتفرقش معانا
+
+524
+00:39:20,100 --> 00:39:22,460
+فيها، في ال operator، ولكن في ال ... في ال
+
+525
+00:39:22,460 --> 00:39:27,560
+composition لأ، في ال composition لأ، طيب نخلص هنا
+
+526
+00:39:27,560 --> 00:39:30,200
+ال two operators، تعاونّا ال multiplication اللي
+
+527
+00:39:30,200 --> 00:39:32,980
+أخدناها و اتكلمنا عن ال composition، المهم جدا ال
+
+528
+00:39:32,980 --> 00:39:36,280
+composition اللي إحنا أخدناها، نيجي نتكلم عن أنواع
+
+529
+00:39:36,280 --> 00:39:39,860
+ال functions، عن أنواع ال functions بتاعتي، أنواع ال
+
+530
+00:39:39,860 --> 00:39:43,260
+functions، حقيقة في عندنا نوعين، و هنستخرج منهم نوع
+
+531
+00:39:43,260 --> 00:39:47,680
+تالت، أول نوع one to one functions، برضه أتوقع أنه
+
+532
+00:39:47,680 --> 00:39:52,040
+مر عليكم، أتوقع أنه مر عليكم، تمام، one to one، فإذا
+
+533
+00:39:52,040 --> 00:39:54,720
+نقدر نقول أن ال function is one to one، أو واحد تو
+
+534
+00:39:54,720 --> 00:40:00,930
+واحد، أو injective، أو injection، أو injection، if and
+
+535
+00:40:00,930 --> 00:40:05,770
+only if every element of its range has only one
+
+536
+00:40:05,770 --> 00:40:09,230
+preimage، has only one preimage، إحنا عارفين أنه في
+
+537
+00:40:09,230 --> 00:40:13,870
+ال ... ال range ممكن يكون له one preimage أو أكتر،
+
+538
+00:40:13,870 --> 00:40:17,720
+ممكن يكون له two، ممكن يكون له two preimage، زي في ال
+
+539
+00:40:17,720 --> 00:40:21,660
+function x تربيع، زي في ال function x تربيع، لأ هنا
+
+540
+00:40:21,660 --> 00:40:28,400
+في ال one to one فقط one preimage، فمعنى ذلك أن كل
+
+541
+00:40:28,400 --> 00:40:33,320
+ناتج هو جاي من input واحد، كل input هذا هيعكس لنا
+
+542
+00:40:33,320 --> 00:40:37,500
+الموضوع، أن معناته كل input هينتج لنا ناتج واحد فقط
+
+543
+00:40:39,160 --> 00:40:43,780
+الناتج، دائما ناتج واحد فقط لكل ال inputs، وكل ناتج
+
+544
+00:40:43,780 --> 00:40:48,680
+جاي من input واحد بس، من input واحد فقط، طيب هذه
+
+545
+00:40:48,680 --> 00:40:52,340
+بقدر نقول أن ال X is injective، أو ال X is one to
+
+546
+00:40:52,340 --> 00:40:56,200
+one، معناه
+
+547
+00:40:56,200 --> 00:41:04,740
+أن there is no exist X and Y، لحظة، و X لا تساوي Y
+
+548
+00:41:04,740 --> 00:41:09,840
+and F of X تساوي F of Y، لأ، بدنا نفهمها دي، بدنا
+
+549
+00:41:09,840 --> 00:41:12,620
+نفهمها، كيف هذه عرفناها على أساس أنها one to one
+
+550
+00:41:12,620 --> 00:41:19,720
+خليني أشوف، عشان أقول أن فعلا كل output، كل element
+
+551
+00:41:19,720 --> 00:41:24,420
+في ال range، له preimage واحدة، له preimage واحدة
+
+552
+00:41:24,420 --> 00:41:29,560
+فقط، معنى ذلك أن ال f of x لا يمكن تنتج إلا من
+
+553
+00:41:29,560 --> 00:41:34,160
+element واحد، مظبوط، هذه ال output هي هذه هيك output
+
+554
+00:41:34,160 --> 00:41:36,960
+يعني المفروض أنها رايحة لل range، ال value بتاعتها
+
+555
+00:41:37,800 --> 00:41:42,620
+كلها رايحة على أساس أنها element في ال range، الأصل أن
+
+556
+00:41:42,620 --> 00:41:47,940
+x وحيدة فقط اللي تنتج لنا ال term هذا، القيمة هذه
+
+557
+00:41:47,940 --> 00:41:54,140
+لما أقول equal، تساوي f of y، معناه يوجد element
+
+558
+00:41:54,140 --> 00:42:01,220
+تاني، بتنتج لنا نفس ال output، ناخد بالنا، ماشي، لعند
+
+559
+00:42:01,220 --> 00:42:06,840
+الآن، ماشي، ممكن نتسائل نقول: طب ممكن x بتساوي y، يعني
+
+560
+00:42:06,840 --> 00:42:09,420
+برضه، حضرتك اللي إحنا مازلنا في نفس الكلام، أن لو
+
+561
+00:42:09,420 --> 00:42:12,820
+أثبتنا أن x بتساوي y، إحنا مازلنا تحت نفس التعريف
+
+562
+00:42:12,820 --> 00:42:16,580
+أنها مازالت one to one، مازالت one to one، إذا كانت
+
+563
+00:42:16,580 --> 00:42:21,000
+بيساوي بعض، لأ، راح يقول لي لا يساوي بعض، لا يساوي بعض،
+
+564
+00:42:21,000 --> 00:42:26,600
+x لا تساوي y، معناته واضح أنه صار في عندي two pre
+
+565
+00:42:26,600 --> 00:42:32,420
+image لنفس ال output، معناته نفيت ال one to one، تم
+
+566
+00:42:32,420 --> 00:42:35,040
+نفي ال one to one، و هو فعلا بيقول لي there is no
+
+567
+00:42:35,040 --> 00:42:43,100
+exist، لا يوجد قيمتين في ال domain، يعني في ال input
+
+568
+00:42:43,100 --> 00:42:46,480
+لا يوجد قيمتين في ال input بيساووا بعض و بيعطونا
+
+569
+00:42:46,480 --> 00:42:50,260
+نفس ال output، صحيح؟
+
+570
+00:42:50,260 --> 00:42:54,740
+صارت هيك منطقية، أصبحت هيك منطقية، فعلا لا يوجد في
+
+571
+00:42:54,740 --> 00:42:57,740
+negation في الأول، معناته هو نفي وجود أنه يحصل
+
+572
+00:42:57,740 --> 00:43:02,380
+هذا الكلام، أن يكون فينا two preimage لنفس ال
+
+573
+00:43:02,380 --> 00:43:04,640
+output، لنفس ال output، تمام
+
+574
+00:43:10,990 --> 00:43:15,810
+Okay، ف only one element of the domain is mapped to
+
+575
+00:43:15,810 --> 00:43:19,870
+any given one element of the range، كل element في
+
+576
+00:43:19,870 --> 00:43:22,870
+ال range هو جاي من one element في ال domain، ال
+
+577
+00:43:22,870 --> 00:43:25,150
+one element اللي في ال domain، هذا سمّيناه بالنسبة لل
+
+578
+00:43:25,150 --> 00:43:31,090
+element في ال range، pre image، okay، معنى ذلك أن كل
+
+579
+00:43:31,090 --> 00:43:34,110
+element في ال domain is injected into the
+
+580
+00:43:34,110 --> 00:43:37,690
+different element of the range، كل element في ال
+
+581
+00:43:37,690 --> 00:43:42,670
+domain، طلع لنا ناتج element مختلف في ال range، مافيش
+
+582
+00:43:42,670 --> 00:43:46,810
+اتنين بيشابهوا بعض في نفس ال ... الناتج، لا يوجد
+
+583
+00:43:46,810 --> 00:43:50,310
+قيمتين في ال domain بيساووا بعض أو بيطلعوا لنا نفس
+
+584
+00:43:50,310 --> 00:43:54,230
+الناتج في ال range، لا يوجد قيمتين، معنى ذلك أنه لا
+
+585
+00:43:54,230 --> 00:43:59,750
+يوجد two pre-images اللي هم نفس ال element في، من
+
+586
+00:43:59,750 --> 00:44:03,410
+في ال range، بنكرر و بنزل عشان نظل ثابت عن كل واحد
+
+587
+00:44:03,410 --> 00:44:07,130
+طيب ال
+
+588
+00:44:07,130 --> 00:44:09,250
+domain و ال range، cardinality اللي إحنا اتكلمنا عنها
+
+589
+00:44:09,250 --> 00:44:14,910
+قبل، هيك، أنه ممكن يكون ال domain أكبر من ال range
+
+590
+00:44:14,910 --> 00:44:17,810
+في النهاية، و ال codomain، ال codomain ممكن
+
+591
+00:44:17,810 --> 00:44:20,250
+يكون أكبر منهم، يعني هنا في الحالة هذه لازم ال
+
+592
+00:44:20,250 --> 00:44:26,510
+domain و ال range يساوي بعض، ليش؟ عشان يكون كل
+
+593
+00:44:26,510 --> 00:44:30,870
+input ... كل ... بالضبط كل input يلاقي output واحد، كل
+
+594
+00:44:30,870 --> 00:44:36,290
+input يلاقي output واحد، لأ، يمكن أوضح لو حسبنا بال
+
+595
+00:44:36,290 --> 00:44:41,890
+bipartite، لو هدول عندنا خمسة في ال input
+
+596
+00:44:45,880 --> 00:44:49,760
+لازم كل واحدة يكون لها output واحد بس، كل واحدة
+
+597
+00:44:49,760 --> 00:44:54,280
+لازم يكون لها output واحد، مثلا، خلاص، ما دام كل واحدة
+
+598
+00:44:54,280 --> 00:44:57,580
+لها output واحد، معناته عدد ال output مش مساوية عدد
+
+599
+00:44:57,580 --> 00:45:03,020
+ال input، معنى ذلك أن ال range مساوية ال domain
+
+600
+00:45:06,880 --> 00:45:10,180
+ال issue المساواة، إحنا بنتكلم هنا عن إيش؟ بنتكلم عن
+
+601
+00:45:10,180 --> 00:45:13,400
+set، معناته عشان ال C أقول إن هي بتساووا بعض، معناته
+
+602
+00:45:13,400 --> 00:45:16,640
+ال cardinality بتاعتهم بيساووا بعض، cardinality
+
+603
+00:45:16,640 --> 00:45:20,160
+بيساوا بعض، طيب ال codomain إيش وضعه في النص، هي
+
+604
+00:45:20,160 --> 00:45:23,420
+كده؟ نفس ال ... نفس ال ... نفس ال ... مش بالضروري
+
+605
+00:45:23,420 --> 00:45:28,240
+ممكن يكون في عندنا element زيادة هنا، بتفرقش، ال
+
+606
+00:45:28,240 --> 00:45:31,920
+codomain لأ، ممكن يكون أكبر، ممكن، و ممكن يكون بيساويه
+
+607
+00:45:35,910 --> 00:45:40,890
+طيب، for examples، هالوقت هي هذه one to one ولا ...
+
+608
+00:45:40,890 --> 00:45:47,870
+one to one، تمام، التانية لأ، لإيش؟ two pre images
+
+609
+00:45:47,870 --> 00:45:52,930
+هاي two pre images أعطوا لنفس ال ... لنفس ال
+
+610
+00:45:52,930 --> 00:45:54,670
+element في ال range، لنفس ال element في ال range
+
+611
+00:45:54,670 --> 00:46:00,690
+فهذه not one to one، التالتة not function من أصله، ليش؟ لأن
+
+612
+00:46:00,690 --> 00:46:04,550
+في one input، في عندنا one input أعطانا two outputs
+
+613
+00:46:04,550 --> 00:46:06,910
+فهذه قلنا نتعامل معها أنها مش function، لأنها
+
+614
+00:46:06,910 --> 00:46:11,090
+unstable، أساسا يمكن أكون في نفس اللحظة في
+
+615
+00:46:11,090 --> 00:46:16,690
+مكانين، تمام؟ فإذا not even a function، okay
+
+616
+00:46:16,690 --> 00:46:21,250
+sufficient conditions for one-to-one function، إيه
+
+617
+00:46:21,250 --> 00:46:23,630
+بقدر أقول إنه أو لا ال function ده كافي جدا عشان
+
+618
+00:4
+
+667
+00:50:23,370 --> 00:50:34,530
+necessarily true زي one over x ليش؟ نرسمها ونشوف
+
+668
+00:50:34,530 --> 00:50:35,490
+ليش
+
+669
+00:50:43,000 --> 00:50:49,420
+مش هي شكلها؟ وهي بتساوي واحد على إكس، طب وين المشكلة
+
+670
+00:50:49,420 --> 00:50:52,920
+فيها هذه؟
+
+671
+00:50:52,920 --> 00:50:58,220
+لأ، عند ال zero إلها قيمتين infinity و minus infinity
+
+672
+00:50:58,220 --> 00:51:01,460
+عند ال zero إلها قيمتين، بس طبعا وين؟ مش
+
+673
+00:51:01,460 --> 00:51:05,080
+هنشوفه في ال infinity، فواضح إنه عند ال zero في
+
+674
+00:51:05,080 --> 00:51:09,500
+مشكلة عند ال zero، هي في مشكلة رغم إن احنا ممكن
+
+675
+00:51:09,500 --> 00:51:15,680
+نتعامل معها، نهايتها decreasing، صحيح؟ وهنا برضه نفس
+
+676
+00:51:15,680 --> 00:51:19,460
+الكلام، بس واضح أنه لأ، في نقطة انقلاب بتصير عند ال
+
+677
+00:51:19,460 --> 00:51:22,980
+zero، هتعملنا مشكلة لأنه صار عند ال zero في عندنا
+
+678
+00:51:22,980 --> 00:51:27,200
+two outputs، two outputs لنفس ال input، لنفس ال
+
+679
+00:51:27,200 --> 00:51:32,720
+input، طيب ال onto، ال onto function أو ال
+
+680
+00:51:32,720 --> 00:51:37,920
+surjective onto،  هدى ببساطة جداً إذا كان ال
+
+681
+00:51:37,920 --> 00:51:43,370
+code domain، يساوي ال range، فهي onto، بنسميها onto بمعنى
+
+682
+00:51:43,370 --> 00:51:47,670
+أن كل القيم بتاعة ال code domain مستخدمة في ال
+
+683
+00:51:47,670 --> 00:51:53,610
+range، كلها واقعة في ال range، في ال range كويسة، ففي
+
+684
+00:51:53,610 --> 00:51:56,030
+الحالة هي دي، زي ما قولنا، ال if from أو ال function
+
+685
+00:51:56,030 --> 00:52:01,290
+if from A to B is onto or surjective or surjection
+
+686
+00:52:01,290 --> 00:52:05,410
+if and only if its range is equal to its codomain
+
+687
+00:52:05,410 --> 00:52:09,750
+في الحالة هي دي، for all B belong to, there
+
+688
+00:52:09,750 --> 00:52:13,370
+exists a belonging to A، بحقق لنا ال function f of x
+
+689
+00:52:13,370 --> 00:52:17,490
+equal to b، بمعنى
+
+690
+00:52:17,490 --> 00:52:24,970
+لكل قيم ال code domain يوجد
+
+691
+00:52:24,970 --> 00:52:29,110
+element في ال domain بنتجها، بطلقنا إياها، طب مادام
+
+692
+00:52:29,110 --> 00:52:33,120
+أنتجت، معناته راحت لل range على طول، صحيح؟ actually
+
+693
+00:52:33,120 --> 00:52:37,140
+مادام نقدر ننتجها، معناته بتروح لمين؟ لل range
+
+694
+00:52:37,140 --> 00:52:42,100
+أوتوماتيكلي، أنا قاعد بقول for all B، لكل قيم B اللي
+
+695
+00:52:42,100 --> 00:52:47,780
+تنتمي لل set B، لل code domain، يوجد قيمة في ال
+
+696
+00:52:47,780 --> 00:52:51,520
+domain تنتجها، طب ما خلاص أنا أصلاً كيف بحسبه ال
+
+697
+00:52:51,520 --> 00:52:56,960
+range؟ ال range بنحسبه إنه فيه فعلاً قيم أو توجد
+
+698
+00:52:56,960 --> 00:53:01,250
+قيمة في ال domain تنتجها، وهو فعلاً احنا قاعدين نقول
+
+699
+00:53:01,250 --> 00:53:04,950
+فلكل قيم ال code domain أوتوماتيكلي هيك صارت ال
+
+700
+00:53:04,950 --> 00:53:09,610
+code domain كله نفسه ال range، نفسه ال range، كويس
+
+701
+00:53:09,610 --> 00:53:16,630
+فإذا ال onto function maps the set A onto or the
+
+702
+00:53:16,630 --> 00:53:21,110
+entirety of the set B، معناه ذلك أن ال function A
+
+703
+00:53:21,110 --> 00:53:30,580
+هتنتج لنا outputs داخل، أو كامل
+
+704
+00:53:30,580 --> 00:53:35,840
+ال set B، بمعنى كامل ال set أو كامل ال elements في
+
+705
+00:53:35,840 --> 00:53:40,600
+ال code domain يمكن انتاجها من ال domain، كامل ال
+
+706
+00:53:40,600 --> 00:53:44,880
+elements في ال code domain يمكن انتاجها من ال
+
+707
+00:53:44,880 --> 00:53:47,880
+domain، طب احنا عارفين أن كل element ينتج من ال
+
+708
+00:53:47,880 --> 00:53:51,540
+domain هو range، automatically صارت هيك ال range
+
+709
+00:53:51,540 --> 00:53:52,900
+يساوي لل code domain
+
+710
+00:53:57,990 --> 00:54:02,410
+Okay، خلّينا نشوف ال function اللي لسه كنا راسمينها
+
+711
+00:54:02,410 --> 00:54:11,290
+تكعيب، اللي هي cubic، هذي
+
+712
+00:54:11,290 --> 00:54:14,830
+اتفقنا أن هي one to one المرة اللي فاتت قبل شوية
+
+713
+00:54:14,830 --> 00:54:19,090
+لسه في الساعة اللي فاتت اتفقنا، طيب بالنسبة ل onto
+
+714
+00:54:19,090 --> 00:54:24,890
+كيف تحسبوها onto؟ نشوف ال domain، ال code domain
+
+715
+00:54:24,890 --> 00:54:28,310
+طيب ال code domain وين ال code domain؟ I طلعه على
+
+716
+00:54:28,310 --> 00:54:33,970
+الـ x axis من minus infinity to infinity، طيب actually
+
+717
+00:54:33,970 --> 00:54:37,230
+هل ال function فعلاً تصل ل minus infinity و بتطلع ل
+
+718
+00:54:37,230 --> 00:54:44,430
+positive infinity، فإذن بيساووا بعض، فإذن onto، طيب
+
+719
+00:54:44,430 --> 00:54:52,010
+هذه ال onto أو هذه ال X تربيع، نشوف ال X تربيع
+
+720
+00:54:57,020 --> 00:55:01,920
+الـ codomain جداش؟ R من minus infinitive إلى
+
+721
+00:55:01,920 --> 00:55:05,220
+infinitive، خلاص احنا محددينه من الأول R، طيب ال
+
+722
+00:55:05,220 --> 00:55:09,580
+range من zero to positive infinity، بمعنى أن احنا
+
+723
+00:55:09,580 --> 00:55:17,080
+بنتكلم عن ال none negative real numbers، none
+
+724
+00:55:17,080 --> 00:55:19,660
+negative real numbers، بمعنى أن هي من zero to
+
+725
+00:55:19,660 --> 00:55:23,120
+positive infinity، لكل ال positive to infinity، none negative
+
+726
+00:55:23,120 --> 00:55:27,840
+elements، Okay، why عرفنا، why، نرسمها ونشوف ليش
+
+727
+00:55:27,840 --> 00:55:34,040
+واحدة منهم onto، وواحدة منهم not، طيب نشوف هنا مين
+
+728
+00:55:34,040 --> 00:55:36,780
+منهم onto ومين one to one من الحالات اللي موجودة
+
+729
+00:55:36,780 --> 00:55:41,480
+عندنا، نمسكهم واحدة واحدة، الأولى هذي مش one to one
+
+730
+00:55:41,480 --> 00:55:44,460
+one to one، لأ، مش one to one، ليش؟ لأ، أنهم three
+
+731
+00:55:44,460 --> 00:55:50,990
+طيب onto، onto، فإذا الأولى هنا one to one ولكن مش
+
+732
+00:55:50,990 --> 00:55:55,170
+one to one، طيب التانية one to one ولا one to one ولا
+
+733
+00:55:55,170 --> 00:55:58,270
+one to one ولا one to one ولا one to one ولا one
+
+734
+00:55:58,270 --> 00:55:58,430
+one ولا one to one ولا one to one ولا one to one
+
+735
+00:55:58,430 --> 00:55:58,590
+ولا one to one ولا one to one ولا one to one ولا
+
+736
+00:55:58,590 --> 00:55:59,990
+one to one ولا one to one ولا one to one ولا one
+
+737
+00:55:59,990 --> 00:56:02,570
+to one ولا one to one ولا one to one ولا one to
+
+738
+00:56:02,570 --> 00:56:02,590
+one ولا one to one ولا one to one ولا one to one
+
+739
+00:56:02,590 --> 00:56:02,630
+ولا one to one ولا one to one ولا one to one ولا
+
+740
+00:56:02,630 --> 00:56:02,870
+to one ولا one to one ولا one to one ولا one to
+
+741
+00:56:02,870 --> 00:56:05,370
+one ولا one to one ولا one to one ولا one to one
+
+742
+00:56:05,370 --> 00:56:07,430
+ولا one to one ولا one to one ولا one to one ولا
+
+743
+00:56:07,430 --> 00:56:07,770
+to one ولا one to one ولا one to one ولا one to
+
+744
+00:56:07,770 --> 00:56:12,120
+one ولا one to one ولا one to one ولا one to هي one
+
+745
+00:56:12,120 --> 00:56:16,160
+to one، اه، ولكن ليست onto، ليش مش onto؟ لأن في عندها
+
+746
+00:56:16,160 --> 00:56:19,260
+element فيه موجود، موجود في ال code domain و غير
+
+747
+00:56:19,260 --> 00:56:23,780
+موجود في ال range، و غير موجود في ال range، تمام، طيب
+
+748
+00:56:23,780 --> 00:56:29,620
+ال bijections أو ال one to one correspondence أو
+
+749
+00:56:29,620 --> 00:56:33,580
+ال reversible أو ال invertible، أي تسمية من التسميات
+
+750
+00:56:33,580 --> 00:56:37,040
+هذه، بس الغالب يمكن أكثر اللي هي ال bijection أو
+
+751
+00:56:39,230 --> 00:56:42,790
+one to one correspondence، كويس، هذي إمتى نقدر نقول
+
+752
+00:56:42,790 --> 00:56:46,790
+أن ال function bijection function إذا كانت one to
+
+753
+00:56:46,790 --> 00:56:51,090
+one و onto في نفس الوقت، خلاص بنسميها إيش؟ bijection
+
+754
+00:56:51,090 --> 00:56:56,170
+if and only if it's both one to one and onto، فال
+
+755
+00:56:56,170 --> 00:57:00,810
+bijection اللى ال function if from a to b there
+
+756
+00:57:00,810 --> 00:57:06,620
+exists an inverse of f، عشان هيك اسمها reversible أو
+
+757
+00:57:06,620 --> 00:57:09,360
+invertible، على أساس أنه إذا كان فعلاً بتحقق لنا
+
+758
+00:57:09,360 --> 00:57:13,620
+الكلام هذا، إيش بتحقق؟ أن هي one to one، فكل element
+
+759
+00:57:13,620 --> 00:57:21,000
+في ال domain يوجد له قيمة واحدة في ال range، لحظة
+
+760
+00:57:21,000 --> 00:57:24,220
+في ال range، لسه احنا بنتكلم عن ال one to one، لسه
+
+761
+00:57:24,220 --> 00:57:28,080
+وكل element في ال range جاي من element واحد في ال
+
+762
+00:57:28,080 --> 00:57:33,390
+domain، وال range يساوي ال code domain، معناه ذلك
+
+763
+00:57:33,390 --> 00:57:36,370
+اللي قلناه على ال range بقدر أطبقه على ال code
+
+764
+00:57:36,370 --> 00:57:39,810
+domain، كل element في ال code domain جاي من element
+
+765
+00:57:39,810 --> 00:57:44,530
+واحد في ال domain، معناته لو انعكست، العلاقة
+
+766
+00:57:44,530 --> 00:57:47,930
+موجودة، ليش علاقة موجودة؟ لأن ال code domain بده
+
+767
+00:57:47,930 --> 00:57:50,790
+يصير domain، ال domain بده يصير code domain، ال
+
+768
+00:57:50,790 --> 00:57:54,370
+relation  واحدة، فعلاً كل element موجود في ال domain
+
+769
+00:57:54,370 --> 00:57:58,960
+كان له element واحد في ال code domain، معنى ذلك أن
+
+770
+00:57:58,960 --> 00:58:02,280
+الـ function في الحالة دي لها inverse، بنقدر نجيب
+
+771
+00:58:02,280 --> 00:58:07,300
+لها ال inverse تبعها، المعكوس تبعها، جبنا مجموعة ال
+
+772
+00:58:07,300 --> 00:58:09,940
+outputs، ال outputs هذه لو طبقنا عليها function
+
+773
+00:58:09,940 --> 00:58:13,620
+معينة، كل ال output هيرجع لل input تبعه، كل output
+
+774
+00:58:13,620 --> 00:58:16,500
+هيرجعنا لل input تبعه، فبنقدر نقول إنه، بنكتبها
+
+775
+00:58:16,500 --> 00:58:21,400
+إزايش؟ Inverse of F أو F to the power minus one، اللي
+
+776
+00:58:21,400 --> 00:58:27,180
+هي Inverse of F from ال domain لل codomain، لحظة، طيب
+
+777
+00:58:27,180 --> 00:58:30,060
+احنا ضمنين إنه أكيد ال elements هذه متوافقة مع بعض
+
+778
+00:58:30,060 --> 00:58:35,580
+لأنه أساساً هنا كان كل element في ال A له output في
+
+779
+00:58:35,580 --> 00:58:40,360
+ال B، و ال B مساوية لل range، هي نفس ال range، معناه
+
+780
+00:58:40,360 --> 00:58:43,280
+ذلك أنه بقدر أطبقه وأقول أن ال B برضه كل element
+
+781
+00:58:43,280 --> 00:58:47,100
+موجود في ال code domain بقدر أنتج منه element
+
+782
+00:58:47,100 --> 00:58:54,640
+موجود في ال domain بالعكس نفسه، طيب لحظة لو تغاضينا
+
+783
+00:58:54,640 --> 00:58:59,800
+عن الشرط هذا اللي هي one to one، معناه ذلك أنه لما
+
+784
+00:58:59,800 --> 00:59:05,720
+كنا بنتكلم، أو اللي هي ال range، لو قلنا التربيع
+
+785
+00:59:07,600 --> 00:59:13,260
+التربيع، كل لحظة كل output فيه له two pre-image، طب
+
+786
+00:59:13,260 --> 00:59:18,280
+لو عكسناهم بيصير not a function، هصير not a function
+
+787
+00:59:18,280 --> 00:59:22,460
+ففي الحالة دي مقدرش أقول أن فيها inverse، عشان يكون
+
+788
+00:59:22,460 --> 00:59:26,260
+أنها inverse لازم تكون one to one وتكون onto، و
+
+789
+00:59:26,260 --> 00:59:30,080
+تكون onto، اتفقنا أن هي one to one، ليش؟ لأن ال pre-
+
+790
+00:59:30,080 --> 00:59:33,260
+image هتصير image، فإذا كان في عنده two pre-image
+
+791
+00:59:33,260 --> 00:59:36,640
+ما يتحولش ل two image، فتطلع من ال functionality
+
+792
+00:59:36,640 --> 00:59:41,120
+طيب الحالة التانية ال onto، أنا محتاج إنها تكون onto
+
+793
+00:59:41,120 --> 00:59:44,840
+onto، ليش؟ لأن في ال onto في ال function لازم كل عنصر في
+
+794
+00:59:44,840 --> 00:59:49,200
+ال domain أقدر أطبق عليه ال function، طيب إذا كانت
+
+795
+00:59:49,200 --> 00:59:52,100
+مش onto، معناته في عناصر في ال domain غير موجودة
+
+796
+00:59:52,100 --> 00:59:55,620
+في ال range، مش هألاقي لها قيمة، كانت في ال domain
+
+797
+00:59:55,620 --> 01:00:00,660
+السابق، غير موجود لها قيمة مقابلة إلها، مع أن ذلك
+
+798
+01:00:00,660 --> 01:00:03,640
+أن أنا برضه مش ... ماقدرش أجيب لها ال inverse أو ال
+
+799
+01:00:03,640 --> 01:00:06,860
+inverse، طبعاً مجهول، مش ... مش عارف إنه هال حيناضر
+
+800
+01:00:06,860 --> 01:00:13,620
+تماماً أو هيعطيني identity function لو عكسناها لل F
+
+801
+01:00:13,620 --> 01:00:17,360
+لأن كيف أنا أعرف أن هذه inverse حقيقي؟ أن لو ضربنا
+
+802
+01:00:17,360 --> 01:00:20,300
+ال inverse function في ال function الأصلية، المفروض
+
+803
+01:00:20,300 --> 01:00:25,680
+يطلع ليه identity، و identity حسب أنا بتعامل مع set
+
+804
+01:00:25,680 --> 01:00:29,020
+بتعامل مع numbers
+
+805
+01:00:32,190 --> 01:00:35,330
+matrix، بنتعامل مع إيش بالظبط؟ لو بنتعامل مع مجرد
+
+806
+01:00:35,330 --> 01:00:40,030
+number، ال identity هي الرقم واحد، لو بنتعامل مثلاً
+
+807
+01:00:40,030 --> 01:00:45,050
+مع matrix هي ال identity matrix اللي مش بضرورة
+
+808
+01:00:45,050 --> 01:00:49,010
+تكون كلها ones، ال diagonal بس تبعها one، صحيح؟ ال
+
+809
+01:00:49,010 --> 01:00:52,410
+diagonal فقط اللي بيكون ones، كويس، فهنا بتقدر نقول
+
+810
+01:00:52,410 --> 01:00:59,940
+أن ال F أو ال inverse، ال function composition لأ
+
+811
+01:00:59,940 --> 01:01:04,360
+هذي إيش اسمه؟ dot dot F equal to إيش؟ to identity
+
+812
+01:01:04,360 --> 01:01:08,420
+value equal to identity function to identity
+
+813
+01:01:08,420 --> 01:01:14,720
+function، لأ، هذي dot عادي، هذي ضرب، ضرب
+
+814
+01:01:14,720 --> 01:01:15,160
+multiplication
+
+815
+01:01:19,320 --> 01:01:22,860
+كيف؟ لأ، ال composition أكبر من هيك، هذه مجرد
+
+816
+01:01:22,860 --> 01:01:26,100
+ضرب، بس ال function في ال function، ال function
+
+817
+01:01:26,100 --> 01:01:35,160
+لأ، لحظة، ال F ... ال F المفروض عكسها ضربها ... احنا
+
+818
+01:01:35,160 --> 01:01:39,720
+كنا كاتبين توينا أمثلة، صح؟ لو ال inverse تبعها
+
+819
+01:01:39,720 --> 01:01:42,900
+الأصل، composition، صح كلامك، صحيح composition، لأنه
+
+820
+01:01:42,900 --> 01:01:45,920
+فعلاً في الآخر المفروض كله هيتشطب مع بعضه، لو عملت
+
+821
+01:01:45,920 --> 01:01:49,640
+ال composition مع ال inverse تبعها، هتلاقي أن كل
+
+822
+01:01:49,640 --> 01:01:54,080
+ال X هتتشطب مع بعض، كل X هتتشطب مع بعض، كلامك صحيح
+
+823
+01:01:54,080 --> 01:01:58,120
+عشان تطلع identity function، المفروض هتكون مع ال
+
+824
+01:01:58,120 --> 01:02:01,980
+composition، composition، طيب ال ... هنتكلم عن
+
+825
+01:02:01,980 --> 01:02:07,710
+identity function، ال identity function from A to A
+
+826
+01:02:07,710 --> 01:02:16,450
+بنكتبها as identity A أو one A،  one for A is the
+
+827
+01:02:16,450 --> 01:02:20,570
+unique function such that for all A belong to A
+
+828
+01:02:20,570 --> 01:02:25,650
+identity function of A بتساوي A، ال identity
+
+829
+01:02:25,650 --> 01:02:30,030
+function of A بتساوي A، تمام؟ إذا تحقق الكلام، هدف
+
+830
+01:02:30,030 --> 01:02:33,450
+إذا هدف نقدر نقول أنها identity function في الحالة
+
+831
+01:02:33,450 --> 01:02:36,230
+التاعة، طبعاً احنا اتعاملنا معها كتير، اتعاملتوا
+
+832
+01:02:36,230 --> 01:02:42,730
+معها كتير في ال ... ال summation، كان zero، ال
+
+833
+01:02:42,730 --> 01:02:45,990
+summation zero، لما بتشمعوا مع zero ال element
+
+834
+01:02:45,990 --> 01:02:48,530
+بتظهر زي ما هو ال element، بتظهر زي ما هو، أو لما
+
+835
+01:02:48,530 --> 01:02:52,770
+كنتوا بتعملوا multiplication by one، by one، أو
+
+836
+01:02:52,770 --> 01:02:58,610
+بتعملوا and مع ال true، صحيح؟ إذا كان false بتظهر
+
+837
+01:02:58,610 --> 01:03:03,030
+false، إذا كان true بتظهر true، طيب أو o-ring مع ال
+
+838
+01:03:03,030 --> 01:03:09,390
+false، مع false، ال union، ال union مع ال في أي set
+
+839
+01:03:09,390 --> 01:03:13,510
+union مع ال universe هتظهر نفس ال set، طيب ال intersection
+
+840
+01:03:13,510 --> 01:03:18,390
+مع ال universe of discourse هتظهر نفس ال set، هي هي
+
+841
+01:03:18,390 --> 01:03:23,530
+طيب، note that identity function is both one to one
+
+842
+01:03:23,530 --> 01:03:28,010
+و onto، one to one، وأنتوا ما هي فعلياً جاية من
+
+843
+01
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5ba1f965790e081542a5fc75f602369e3f4aad72
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo_postprocess.srt
@@ -0,0 +1,3384 @@
+1
+00:00:21,430 --> 00:00:23,510
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:23,510 --> 00:00:26,750
+الأنبياء والرسلين سيدنا محمد وعلى أله وصحبه أجمعين
+
+3
+00:00:27,490 --> 00:00:30,790
+خلصنا المرة اللى فاتت موضوع ال sets و المجموعات و
+
+4
+00:00:30,790 --> 00:00:33,730
+ال .. أخدنا ال theories بتاعتها و اتكلمنا عن
+
+5
+00:00:33,730 --> 00:00:38,090
+مجموعة operators ممكن نطبقها عليها اليوم نبدأ في
+
+6
+00:00:38,090 --> 00:00:40,630
+موضوع جديد اللى هو ال functions وهدي مرة عليكوا
+
+7
+00:00:40,630 --> 00:00:43,030
+جابل هيك بس زى ما قلنا هتتناول .. هتناول ..
+
+8
+00:00:43,030 --> 00:00:48,530
+نتناولها بطريقة تتناسب مع ال discrete تتناسب مع
+
+9
+00:00:48,530 --> 00:00:53,140
+المادة اللى عندى لقى خلصناهاو بدنا نوضح كيف ان كل
+
+10
+00:00:53,140 --> 00:00:57,040
+المواضيع اللي أخدناها سابقا احنا ممكن نعبر عنها as
+
+11
+00:00:57,040 --> 00:01:01,740
+a function .. as a function فنبدأ مع ال function
+
+12
+00:01:01,740 --> 00:01:03,740
+اللي انتوا عارفينها .. انتوا أخدتوا ال function
+
+13
+00:01:03,740 --> 00:01:07,300
+على أساس ان هي .. يعني أخدتوه على أساس ان هي
+
+14
+00:01:07,300 --> 00:01:14,290
+function أو بمعنى variable متغيرindependent مستقل
+
+15
+00:01:14,290 --> 00:01:17,890
+انتوا بتدخله من وين؟ من مجموعة ايش؟ مجموعة
+
+16
+00:01:17,890 --> 00:01:21,390
+universal discourse او مجموعة .. مجموعة حاطينها في
+
+17
+00:01:21,390 --> 00:01:26,870
+set .. هنسميها set Aالقيم اللى موجودة داخل set A
+
+18
+00:01:26,870 --> 00:01:32,230
+نستخدمها علشان نطبق عليها function فنشن معينة
+
+19
+00:01:32,230 --> 00:01:35,410
+الفنشن المعينة دي هتطلع outputs ال outputs هدى
+
+20
+00:01:35,410 --> 00:01:39,850
+هنحطها في set اسمها B فانتوا كنتوا في الآخر
+
+21
+00:01:39,850 --> 00:01:42,950
+بترسموها او بتتكلموا عنها على اساس ان هي f of x
+
+22
+00:01:42,950 --> 00:01:49,110
+فلنقول y of f of x فx كان بالنسبالكوا independent
+
+23
+00:01:49,110 --> 00:01:53,160
+variableمستقلها ده اللي بدكوا تدخلوه هو ال input
+
+24
+00:01:53,160 --> 00:01:59,140
+لل function وبعدين بناء على ال function او x under
+
+25
+00:01:59,140 --> 00:02:03,120
+the function f كان بيطلعكوا قيمة اسمها y ال y هذه
+
+26
+00:02:03,120 --> 00:02:08,680
+عبارة عن ايش عبارة عن xunder the function f بعد ما
+
+27
+00:02:08,680 --> 00:02:12,760
+طبقنا عليها ال function f بالظبط تماما زي لما
+
+28
+00:02:12,760 --> 00:02:16,600
+تتكلموا عن المراية المراية لما تكون normal انتوا
+
+29
+00:02:16,600 --> 00:02:19,460
+بتشوفوا صورتكوا زي ما انتوا بالظبط يعني كأنها f of
+
+30
+00:02:19,460 --> 00:02:22,960
+x y بتسوي x انتوا بتشوفوا صورتكوا زي ما انتوا
+
+31
+00:02:22,960 --> 00:02:26,350
+شايفينها ولكن افرض ان هي مقعرة او محددةانتوا
+
+32
+00:02:26,350 --> 00:02:29,130
+هتشوفوا صورة تانية، ايش الصورة اللي انتوا شايفينها
+
+33
+00:02:29,130 --> 00:02:32,750
+في المرايا؟ هي صورتكوا بعد تطبيق ال function
+
+34
+00:02:32,750 --> 00:02:35,250
+عليها، ايش هي ال function؟ ال .. سطح ال ..
+
+35
+00:02:35,250 --> 00:02:39,490
+المرايا، سطح المرايا، تمام؟ فهتلاقوا .. طب انا
+
+36
+00:02:39,490 --> 00:02:42,990
+راقول المثال هذا بالعمدان، لإنه هنتكلم عن كلمة
+
+37
+00:02:42,990 --> 00:02:45,730
+image، انه في واحدة منهم image للتانية وفي واحدة
+
+38
+00:02:45,730 --> 00:02:49,030
+pre image للتانية، هنتكلم عليهم عشانك ممكن كان
+
+39
+00:02:49,030 --> 00:02:53,550
+موضوع المرايا هذا كان في الصياق على أساس انه يجرب
+
+40
+00:02:53,550 --> 00:02:58,010
+المفهوم عندناتمام ففي الآخر أنا بتعامل مع function
+
+41
+00:02:58,010 --> 00:03:05,290
+بقول أن هي y equal to f of x و y belong to R و x
+
+42
+00:03:05,290 --> 00:03:08,270
+طبعا أساسا كانت برضه belong to R فانا عندي ال
+
+43
+00:03:08,270 --> 00:03:12,170
+universe of discourse ل x هي ال real numbers و
+
+44
+00:03:12,170 --> 00:03:17,650
+المتوقع أن ال y هيكون برضه ال real numbers ك
+
+45
+00:03:17,650 --> 00:03:22,790
+universe of discourse لهاالـ function نقدر نطبقها
+
+46
+00:03:22,790 --> 00:03:27,390
+على أي shape بحيث انه ممكن تطبق على أي element لأي
+
+47
+00:03:27,390 --> 00:03:34,430
+set بحيث انه يطلعنا element في أي set أخرى كيف؟
+
+48
+00:03:34,430 --> 00:03:37,490
+انتوا هالوقت اللي هتتكلموا على ال X ال X هذي زي ما
+
+49
+00:03:37,490 --> 00:03:40,110
+قلنا احنا belong to ايه؟ to R حسب ال example اللي
+
+50
+00:03:40,110 --> 00:03:44,070
+قعدتنا يعني معناته ال R تبعتنا هذي صارت هي ايه؟ ال
+
+51
+00:03:44,070 --> 00:03:52,340
+setبتاعة x هي set x element منها okay عشان يطلعنا
+
+52
+00:03:52,340 --> 00:03:58,600
+set أخرى تمثل ايش تمثل جميع ال elements ل y اللي
+
+53
+00:03:58,600 --> 00:04:04,000
+استخرجناهم من كل ال elements بتاعة x تمام فحسب
+
+54
+00:04:04,000 --> 00:04:06,660
+اللي موجود عندنا طلعت برضه belong to ايش to R
+
+55
+00:04:06,660 --> 00:04:11,740
+فبرضه احنا استنتجنا set from other set from other
+
+56
+00:04:11,740 --> 00:04:15,270
+setطبعا other set معناته بدي أعمل applying لمين
+
+57
+00:04:15,270 --> 00:04:18,790
+لكل ال elements داخل ال set عشان أطلع منهم مين
+
+58
+00:04:18,790 --> 00:04:23,770
+مجموعة elements يمثلوا ل set جديدة يمثله set جديدة
+
+59
+00:04:23,770 --> 00:04:27,730
+تمام formally كيف ممكن نكتب هذا الكلام ده هنقول
+
+60
+00:04:27,730 --> 00:04:33,590
+انه لأي two sets هنتعامل مع two sets A وB بنقدر
+
+61
+00:04:33,590 --> 00:04:37,630
+نقول ان هو يمثل او نقدر نمثل ال function a
+
+62
+00:04:37,630 --> 00:04:44,040
+function F from A to Bأو ال function f mapping a
+
+63
+00:04:44,040 --> 00:04:50,780
+to b تعمل mapping من a to b relation علاقة بين a و
+
+64
+00:04:50,780 --> 00:04:56,480
+b بين a و b أو هي عبارة عن function ديالة من set a
+
+65
+00:04:56,480 --> 00:05:03,540
+to set b فبقول ال function f from set a to set b
+
+66
+00:05:03,540 --> 00:05:08,160
+هنا ايه هذه؟ هذه ال universe of discourse لمين؟ لل
+
+67
+00:05:08,160 --> 00:05:14,220
+exceptأولا ال a أنا باخد منها قيم small a اللي هي
+
+68
+00:05:14,220 --> 00:05:16,480
+القيمة اللي هتطبق عليها ال function عشان تطلعلي
+
+69
+00:05:16,480 --> 00:05:20,680
+مين تطلعلي b و b ال small b هذه هتكون belong to
+
+70
+00:05:20,680 --> 00:05:29,100
+set B okay فهي في الآخر مدام هتطلعنا ناتج belong
+
+71
+00:05:29,100 --> 00:05:34,520
+to B معناته ال F of X هي belong to B لأن ال F of X
+
+72
+00:05:34,520 --> 00:05:42,770
+هذه هي تمثل لنا ال D smallتمثل بي small كويسة من
+
+73
+00:05:42,770 --> 00:05:48,390
+وين جيبناها من تطبيق x على ال function أو ال
+
+74
+00:05:48,390 --> 00:05:52,690
+function applied على ال value x و x هذه لازم تكون
+
+75
+00:05:52,690 --> 00:05:57,630
+belonging to mean to a فإذا أنا محكوم هنا بال two
+
+76
+00:05:57,630 --> 00:06:02,940
+setsصرت محكوم أن ال input لازم يكون belong to set
+
+77
+00:06:02,940 --> 00:06:06,740
+A و ال output لازم يكون belong to set B فهذا
+
+78
+00:06:06,740 --> 00:06:09,080
+تعريفنا لمين لل function حتى اللحظة
+
+79
+00:06:12,350 --> 00:06:15,770
+الـ total ممكن في الأخر الـ function if assigns 0
+
+80
+00:06:15,770 --> 00:06:19,890
+or 1 elements of B ممكن مايكونولوش نتيجة في B و
+
+81
+00:06:19,890 --> 00:06:24,290
+يكون خارج ال .. ال .. ال .. ال domain تبعنا أو
+
+82
+00:06:24,290 --> 00:06:28,290
+يكون خارج ال set B أو ممكن يكون عبارة عن element
+
+83
+00:06:28,290 --> 00:06:34,790
+واحد بس أكتر لأ بمعنى لكل input المفروض مايكونش
+
+84
+00:06:34,790 --> 00:06:38,590
+فيه two outputs ان ال output يكون له two inputs
+
+85
+00:06:38,590 --> 00:06:43,570
+ماشيزي التربيع زي التربيع فهمناها ماشي تربيع
+
+86
+00:06:43,570 --> 00:06:47,510
+مقبولة ان يكون في عندكم function تربيع two inputs
+
+87
+00:06:47,510 --> 00:06:51,530
+بيعطينا نفس ال output فليكن ماشي نفترض انه minus
+
+88
+00:06:51,530 --> 00:06:55,270
+two two بيعطينا أربعة التنتين هيعطينا نفس ال
+
+89
+00:06:55,270 --> 00:07:01,660
+output مقبولة ولكن input واحد يعطينا twooutputs لا
+
+90
+00:07:01,660 --> 00:07:04,640
+يمكن لأن حتى ال system اللي بنتكلم عنه هنا بصير
+
+91
+00:07:04,640 --> 00:07:08,380
+unstable و بصير فيه مشكلة في ال system تبعنا، هذه
+
+92
+00:07:08,380 --> 00:07:11,380
+بنقدر نقول عنها أنها مش function من أصله، إذا مرت
+
+93
+00:07:11,380 --> 00:07:14,300
+عليكم، اتعاملوا معاها أن هذه مش function، مش هينفع
+
+94
+00:07:14,300 --> 00:07:18,920
+نتعامل معاها، مش هينفع نتعامل معاها، في الحالة
+
+95
+00:07:18,920 --> 00:07:23,960
+تاعتنا تخيلوا تماما بالظبط زي لو أنه الزمن هو ال X
+
+96
+00:07:23,960 --> 00:07:27,900
+وال location اللي احنا واقفين فيه هذا ال Y، أنا
+
+97
+00:07:27,900 --> 00:07:33,300
+عند كل time أنا وين موجودطب هل بقدر .. هل بنقدر في
+
+98
+00:07:33,300 --> 00:07:36,540
+نفس اللحظة في نفس ال input في نفس ال time أكون
+
+99
+00:07:36,540 --> 00:07:40,060
+موجود في مكانين في two locations؟ لا يمكن .. لا
+
+100
+00:07:40,060 --> 00:07:42,700
+يمكن بقدر أقول إن والله أنا سريع لدرجة إن ممكن في
+
+101
+00:07:42,700 --> 00:07:45,280
+.. في أقل وقت ممكن أكون انتقلت من واحد لو واحد
+
+102
+00:07:45,280 --> 00:07:49,260
+ماشي فال slope تبعي يكون كتير عالي كقيمة ك
+
+103
+00:07:49,260 --> 00:07:52,320
+absolute قيمته عالية المعدل التغير عالي بس إنه
+
+104
+00:07:52,320 --> 00:07:55,460
+أكون في نفس اللحظة لا يمكن فعشان هيك ال output
+
+105
+00:07:55,460 --> 00:08:00,320
+لازم يكون جاي من inputمن input واحدة و ال input
+
+106
+00:08:00,320 --> 00:08:03,440
+الواحدة لايمكن نطلع لنا two outputs لايمكن من
+
+107
+00:08:03,440 --> 00:08:08,340
+input واحدة يكون two outputs okay graphical
+
+108
+00:08:08,340 --> 00:08:13,640
+representations لمن ل ال .. ل ال set .. لل
+
+109
+00:08:13,640 --> 00:08:16,020
+functions عفوا ل ال functions فحنبدأ بإيش بال Venn
+
+110
+00:08:16,020 --> 00:08:20,220
+diagram Venn diagram هنقول أننا set A مجموعة ال
+
+111
+00:08:20,220 --> 00:08:26,270
+elements اللي مسموح ليه أطبقها ك Xفى f of x فى f
+
+112
+00:08:26,270 --> 00:08:31,210
+of x بحيث ان هي تعطينى outputs كل ال outputs هذه
+
+113
+00:08:31,210 --> 00:08:35,050
+موجودة فى set تانية بتسميها b فهيكون في عندنا from
+
+114
+00:08:35,050 --> 00:08:40,990
+a to b فى function f ال function f هذه عبارة عن
+
+115
+00:08:40,990 --> 00:08:47,720
+ايش هي عبارة عن function fromA1 مثلا to B1 فإذا
+
+116
+00:08:47,720 --> 00:08:53,540
+طبقنا ال function على ال element A1 هيعطينا ناتج
+
+117
+00:08:53,540 --> 00:08:59,240
+B1 بي سمول طبعا مجموعة elements فكل element موجود
+
+118
+00:08:59,240 --> 00:09:05,440
+هنا لازم يكون الناتج تبعه موجود في ال set BOkay
+
+119
+00:09:05,440 --> 00:09:11,060
+هذا عن طريق Venn diagram طيب bipartate graph ال
+
+120
+00:09:11,060 --> 00:09:15,060
+bipartate graph هيكون عندنا two parts أو two
+
+121
+00:09:15,060 --> 00:09:18,300
+columns ال column الأول عبارة عن dots ال dots هذه
+
+122
+00:09:18,300 --> 00:09:21,100
+تمثل ال elements بتاعة ال input
+
+123
+00:09:25,910 --> 00:09:31,250
+القلم التاني يمثل برضه مجموعة dots عبارة عن ال
+
+124
+00:09:31,250 --> 00:09:37,750
+elements داخل set B فبنعمل relation إذا كان ال
+
+125
+00:09:37,750 --> 00:09:43,070
+element الأول في set A under the function f
+
+126
+00:09:43,070 --> 00:09:48,650
+بيعطينا العنصر التاني فبنعمل بينهم خط فهنا ال
+
+127
+00:09:48,650 --> 00:09:54,960
+function from first elementA to second element
+
+128
+00:09:54,960 --> 00:09:59,740
+from B تمام؟ بنرسمها سهل على أساس أنه under the
+
+129
+00:09:59,740 --> 00:10:02,800
+function في relation between ال element هذا و ال
+
+130
+00:10:02,800 --> 00:10:05,340
+element هذا طيب بين ال element التاني و ال element
+
+131
+00:10:05,340 --> 00:10:09,920
+الأول ممكن في الآخر بنرسم طبيعة أو ال function
+
+132
+00:10:09,920 --> 00:10:15,740
+from A to Bfrom element موجود في set A to element
+
+133
+00:10:15,740 --> 00:10:20,420
+موجود في set B هذه طريقة تانية برضه في ال
+
+134
+00:10:20,420 --> 00:10:23,340
+representation لل function طريقة التالتة اللي
+
+135
+00:10:23,340 --> 00:10:28,240
+انتوا عارفينها ال blood ال dots هذه بتحطوا عند كل
+
+136
+00:10:28,240 --> 00:10:31,280
+X مجدش قيمة Y بتاعتها فبتحطوا مجموعة نقاط و بعدين
+
+137
+00:10:31,280 --> 00:10:35,290
+بترسموهاالـ plot تبعكم فبترسموه الشكل ال function
+
+138
+00:10:35,290 --> 00:10:37,610
+بهذا الشكل و يمكن انتوا متعودين على النوع هذا
+
+139
+00:10:37,610 --> 00:10:42,450
+بيعطيكوا التصور ان كيف relation between ال X و ال
+
+140
+00:10:42,450 --> 00:10:46,730
+Y ال X و ال Y طبعا احنا بنتكلم ان ال X هتكون
+
+141
+00:10:46,730 --> 00:10:51,890
+belong to ايهto set a و ال y belong to set b اللي
+
+142
+00:10:51,890 --> 00:10:55,970
+هي عبارة عن f of x دي يبقى عارف عن f of x okay
+
+143
+00:10:55,970 --> 00:10:59,630
+functions احنا اتعاملنا معاها حتى اللحظة في
+
+144
+00:10:59,630 --> 00:11:01,990
+functions كتير احنا اتعاملنا معاها حتى اللحظة و
+
+145
+00:11:01,990 --> 00:11:04,950
+اتكلمنا يمكن عنها من أهمها اللي هي ال proposition
+
+146
+00:11:04,950 --> 00:11:08,690
+ال proposition لما كنا بنتكلم عن ال proposition
+
+147
+00:11:08,690 --> 00:11:12,490
+يعتمد على situation معين زي ال example اللي بيبقى
+
+148
+00:11:12,490 --> 00:11:16,550
+عني it's raining تشتي لو قولنا الكلام هذا اليوم
+
+149
+00:11:16,550 --> 00:11:21,090
+هتقولوا falseطب لو قلناها قبل العيد أسبوع زمان
+
+150
+00:11:21,090 --> 00:11:23,550
+كانت بتشتي، لو قلناها في وجتها، في ال situation
+
+151
+00:11:23,550 --> 00:11:26,470
+هداك، كان قولنا true، فإذا معتمدين على ال
+
+152
+00:11:26,470 --> 00:11:29,350
+situation، فهنا بعتبر .. بتعمل مع ال proposition
+
+153
+00:11:29,350 --> 00:11:34,320
+كأنها function of situationحسب ال situation حسب
+
+154
+00:11:34,320 --> 00:11:38,200
+الحالة حسب ال state الوضع اللي احنا فيه حسب الحالة
+
+155
+00:11:38,200 --> 00:11:41,340
+بتاعتنا بقدر اقول ان هو true or false يعني بتتغير
+
+156
+00:11:41,340 --> 00:11:46,440
+بناء على الحالة بناء على الحالة اما true or false
+
+157
+00:11:46,440 --> 00:11:50,100
+فهذه logical system بنسميها situation theory
+
+158
+00:11:50,100 --> 00:11:55,840
+situation theory okay زي ما قلنا it's raining ال S
+
+159
+00:11:55,840 --> 00:12:00,550
+هنا our situation here حالياour situation بناة
+
+160
+00:12:00,550 --> 00:12:04,410
+عادية بقدر أقرر أما تقولولي والله كمان شهر هتكون
+
+161
+00:12:04,410 --> 00:12:10,290
+بتشتي هقولكوا بعرفش يعني حتى التنبؤات أو التوقعات
+
+162
+00:12:10,290 --> 00:12:14,510
+الجوية قبل بيوم يومين ممكن يتوقعوا لنا بس تقولولي
+
+163
+00:12:14,510 --> 00:12:18,530
+بعد شهر إيش بدوس بعرفش توقعات بعرفش حسب ال
+
+164
+00:12:18,530 --> 00:12:22,230
+situation في وقتها حسب ال situation في وقتها طيب
+
+165
+00:12:22,230 --> 00:12:25,690
+فبنقدر نقول P of S و ال S دي اللي هي situation
+
+166
+00:12:26,890 --> 00:12:31,810
+هتكون belong to true or false function لحظة هى
+
+167
+00:12:31,810 --> 00:12:33,410
+function هى نوع من أنواع ال functions احنا
+
+168
+00:12:33,410 --> 00:12:36,890
+اتعاملنا مع حاجة بالهك هى نوضح انه كانت عبارة عن
+
+169
+00:12:36,890 --> 00:12:41,410
+function quick propositional operator ال operators
+
+170
+00:12:41,410 --> 00:12:43,910
+اللي أخدناها أخدنا ايش أخدنا ال and أخدنا ال or
+
+171
+00:12:43,910 --> 00:12:46,730
+أخدنا ال negation أخدنا ال x or أخدنا ال .. كل
+
+172
+00:12:46,730 --> 00:12:50,610
+هدولة بنقدر نمثلهم ك function ك function كيف لحظة
+
+173
+00:12:50,610 --> 00:12:55,530
+بقدر أقول ان هو or of x
+
+174
+00:12:57,830 --> 00:13:05,290
+هذه الوقت لما أقول لكم f of x مش هاد هيك function
+
+175
+00:13:05,290 --> 00:13:10,990
+محتاجة input عشان اطلع output هي ايش ال function
+
+176
+00:13:10,990 --> 00:13:17,150
+اكتر من هيك output بطلع بناء على input under the
+
+177
+00:13:17,150 --> 00:13:20,350
+function f طب ناخدها شوي شوي ال function هاد بتقول
+
+178
+00:13:20,350 --> 00:13:26,160
+ان هي ال orالـ function ال operator هي ال or بدخل
+
+179
+00:13:26,160 --> 00:13:29,180
+إلى مجموعة inputs بتطلعلي output مش بدرور يكون
+
+180
+00:13:29,180 --> 00:13:33,300
+زيهم حسب ال condition بالظبط إيش طبيعتي ال input
+
+181
+00:13:33,300 --> 00:13:38,040
+بتطلعلي output بس فيه حالة طريقة بتطلعنا عليها ال
+
+182
+00:13:38,040 --> 00:13:42,240
+output هنا بدنا نفتح الأقواص و بدنا ندخل ال inputs
+
+183
+00:13:42,240 --> 00:13:47,200
+طب هد احنا عارفين إن هي binary operatorيعني محتاجة
+
+184
+00:13:47,200 --> 00:13:51,600
+two inputs فال two inputs ساعتنا بدنا ندخلهم على
+
+185
+00:13:51,600 --> 00:13:59,360
+أساس إن هم زوج if true هاي ال inputs تبعوننا فهذه
+
+186
+00:13:59,360 --> 00:14:05,440
+أصبحت بالنسبالنا كإنها if or ت
+
+187
+00:14:05,440 --> 00:14:10,020
+تمام أتوقع هيك صارت function هيك أصبحت function
+
+188
+00:14:10,020 --> 00:14:15,590
+بقدر أطلّق النتج تبعهاtrue فإذا بقدر أقول إنه هذا
+
+189
+00:14:15,590 --> 00:14:20,410
+true ال y true إنها تجي true فلاحظوا function هي
+
+190
+00:14:20,410 --> 00:14:25,630
+في النهاية عبارة عن function القيمة بتاعتها true
+
+191
+00:14:25,630 --> 00:14:29,970
+طبعا مهم جدا الترتيب في بعضهم ممكن مايكونش مهم في
+
+192
+00:14:29,970 --> 00:14:33,250
+بعضهم مهم بس الأحواط أنكم تاخدوا بالكم من الترتيب
+
+193
+00:14:33,250 --> 00:14:36,670
+ليش لأنه ممكن تجيكوا ال implication ال implication
+
+194
+00:14:36,670 --> 00:14:40,980
+هذا طبعا هتخرب ال ..ال .. الترتيب إذا انتوا خرّبته
+
+195
+00:14:40,980 --> 00:14:42,960
+يعني إذا انتوا حطيتوا التانية أولى و الأولى تانية
+
+196
+00:14:42,960 --> 00:14:48,280
+هتفرق معناه لو قولنا ال implication of true و
+
+197
+00:14:48,280 --> 00:14:49,680
+false
+
+198
+00:14:55,710 --> 00:14:59,950
+ماحدش يتعامل معاها عشان ان هي false employs true
+
+199
+00:14:59,950 --> 00:15:05,790
+لحظة غيرته هي كلمته للنتج لأ ان اتعامل معاها
+
+200
+00:15:05,790 --> 00:15:10,890
+بترتيبها حسب ترتيبها ف true employs false طبعا
+
+201
+00:15:10,890 --> 00:15:15,250
+واضح هتطلع ال output تبعها او ال y بتاعتها false
+
+202
+00:15:15,250 --> 00:15:19,930
+تمام واضحة هي هذا برضه انه احنا خدناه اتكلمنا عنه
+
+203
+00:15:19,930 --> 00:15:25,160
+هنا بنقدر نمثله as a function كويسةاشي تاني ال
+
+204
+00:15:25,160 --> 00:15:28,240
+predicate لما اتكلمنا في ال predicate هي اصلا كانت
+
+205
+00:15:28,240 --> 00:15:30,860
+عبارة عن a propositional function اصلا هي اصلا
+
+206
+00:15:30,860 --> 00:15:33,480
+كانت عبارة عن a propositional function و لو
+
+207
+00:15:33,480 --> 00:15:38,120
+متذكرين اتكلمنا عن مش عارف احنا ميسمينا كان Mike
+
+208
+00:15:38,120 --> 00:15:42,520
+gave Mary a grade A متذكرينه؟ طب ما هي برضه هي
+
+209
+00:15:42,520 --> 00:15:44,820
+عبارة عن variables لما ده ما حطيت variables أصبحت
+
+210
+00:15:44,820 --> 00:15:49,320
+function لما نقول مثلا be a predicate is seven
+
+211
+00:15:49,320 --> 00:15:54,600
+feet tallلما اقول والله ال .. ال predicate تبعتنا
+
+212
+00:15:54,600 --> 00:15:56,860
+ال predicate تبعتنا او ال propositional function
+
+213
+00:15:56,860 --> 00:16:03,820
+بتاعتنا هي انه كذا يكون سبع أقدام طولا سبع أقدام
+
+214
+00:16:03,820 --> 00:16:08,360
+طولا يعني في حدود يمكن متين و عشرة سانتي متين و
+
+215
+00:16:08,360 --> 00:16:11,200
+عشرة سانتي طبعا واضح انه هنا بقدرش اقول ان هي
+
+216
+00:16:11,200 --> 00:16:13,800
+biologic دايما true لأ هذا بده اشوف في ال
+
+217
+00:16:13,800 --> 00:16:18,700
+situation تبعنا مين اللي بده يجي قدام x هذا مكان x
+
+218
+00:16:18,700 --> 00:16:23,980
+is seven feet طولفلو قلنا mike و قلنا انه هتصبح P
+
+219
+00:16:23,980 --> 00:16:29,700
+of mike function أصبحت function ال X بتاعتها هي
+
+220
+00:16:29,700 --> 00:16:35,420
+الاسم اللي انا هحطه هنا P of علي P of محمد تمام؟
+
+221
+00:16:35,420 --> 00:16:39,520
+بنجيسه و بنشوف is it true or false؟ false جابل هيك
+
+222
+00:16:39,520 --> 00:16:42,560
+بالشكل هذا مقدرش اقول ان هي true or false قولنا
+
+223
+00:16:42,560 --> 00:16:45,700
+هالكلام هذا السابقا ال predicate ك predicate بحد
+
+224
+00:16:45,700 --> 00:16:49,200
+ذاتها هي مش propositionبقدرش أقول هى true or false
+
+225
+00:16:49,200 --> 00:16:54,140
+ولكن لما هحطلها ال variable تبعها أصبحت بقدر أحكم
+
+226
+00:16:54,140 --> 00:16:56,740
+عليه هى true or false بناء على مين اللى حطته
+
+227
+00:16:56,740 --> 00:17:00,480
+variable بناء على اللى حطنا variable تمام فأصبحت
+
+228
+00:17:00,480 --> 00:17:06,620
+هى واضحة f of x بي of my حطنا variable في ال bit
+
+229
+00:17:06,620 --> 00:17:11,200
+string نفس الكلام بي of length n can be viewed as
+
+230
+00:17:11,200 --> 00:17:16,600
+a function from the numbersone to n هذا بناء على
+
+231
+00:17:16,600 --> 00:17:20,560
+ال index للوكيشن أو ال location نفسه ال index لل
+
+232
+00:17:20,560 --> 00:17:27,360
+elements احنا لما نقول مثلا ال bit string بي one
+
+233
+00:17:27,360 --> 00:17:33,500
+zero one احنا عارفين ان ال bit string مرتب صحيح
+
+234
+00:17:33,500 --> 00:17:37,020
+مهم الترتيب يعني بقدر اتعامل مع ال location
+
+235
+00:17:37,020 --> 00:17:43,450
+بتاعتهم عساس ان هي variableو انا عارف انه دائما في
+
+236
+00:17:43,450 --> 00:17:47,530
+ال bit string هذا اول element دائما هيكون واحد هذا
+
+237
+00:17:47,530 --> 00:17:51,750
+مش زي ال set unordered لأ ال set okay اي واحدة
+
+238
+00:17:51,750 --> 00:17:54,070
+جابت بتانه مش هتفرج كتير بس في ال bit string لأ
+
+239
+00:17:54,070 --> 00:17:57,250
+مهم الترتيب لما اتكلمنا المرة اللي فاتت في ال ..
+
+240
+00:17:57,250 --> 00:18:01,510
+في ال set قولنا انه لما بيصير ordered بصير عندنا
+
+241
+00:18:01,510 --> 00:18:04,710
+بنتكلم عن string فعملنا ال bit string
+
+242
+00:18:04,710 --> 00:18:08,800
+representationلما اتكلمنا عن ال bit .. ال bit
+
+243
+00:18:08,800 --> 00:18:11,760
+string representation قولنا إن دايما ال element
+
+244
+00:18:11,760 --> 00:18:17,080
+الشمال هو ال element الأول هو ال element الأول
+
+245
+00:18:17,080 --> 00:18:20,500
+قولناها فين؟ في آخر محاضرة من المحاضرات أعتقد، في
+
+246
+00:18:20,500 --> 00:18:24,920
+آخر واحدة من المحاضرات، تمام طيب لما نيجي نتكلم عن
+
+247
+00:18:24,920 --> 00:18:28,860
+ال set قولنا قبل هيك ال set هي unordered يعني أنا
+
+248
+00:18:28,860 --> 00:18:32,440
+مقدرش ا .. يعني مقدرش نستفيد من فكرة إيش؟ من فكرة
+
+249
+00:18:32,440 --> 00:18:37,270
+ال location، الترتيبطب ها إيش .. إيش الحاجة اللي
+
+250
+00:18:37,270 --> 00:18:40,030
+.. اللي بتمن دايما إن هي موجودة؟ إنه العنصر موجود
+
+251
+00:18:40,030 --> 00:18:44,890
+أو لأ؟ هذه بالنسبالنا واضحة لإن هو إحنا بنعتمد
+
+252
+00:18:44,890 --> 00:18:47,310
+أساسا في ال set إن هل العنصر موجود أو غير موجود
+
+253
+00:18:47,310 --> 00:18:51,150
+أما وين ال location تبعه؟ ماعناش معلومة ال
+
+254
+00:18:51,150 --> 00:18:53,490
+location تبعه إجا رقم 1، إجا رقم 2، إجا رقم 5، إجا
+
+255
+00:18:53,490 --> 00:18:57,270
+رقم 10، إجا أخر element مش هتفرق بمعنى إن لو عندنا
+
+256
+00:18:57,270 --> 00:19:05,830
+ال set S عبارة عن one, two, threeأجى واحد كتب ليها
+
+257
+00:19:05,830 --> 00:19:09,110
+طبعا كويس أن تكون مرتبة مش غلط ولكن اجى واحد كتب
+
+258
+00:19:09,110 --> 00:19:15,830
+ليها اتنين واحد تلاتة المهم ان ال elements موجودة
+
+259
+00:19:15,830 --> 00:19:20,030
+ال elements كاملة موجودة مش متكررة و لا يعني بمعنى
+
+260
+00:19:20,030 --> 00:19:22,550
+لو بدي اعملها cardinality بقدر اجيبهم و خلاص يعني
+
+261
+00:19:22,550 --> 00:19:24,770
+كل ال operations اللي انا محتاجها بقدر اطلحها
+
+262
+00:19:24,770 --> 00:19:27,690
+بنقدر نشتغل عليها بما فيها ال function فهنا ال
+
+263
+00:19:27,690 --> 00:19:30,450
+function بتصير function في مين في ال element نفسه
+
+264
+00:19:31,850 --> 00:19:35,490
+كفنكشن بتصير في ال element نفسه وبتصير الناتج تبعي
+
+265
+00:19:35,490 --> 00:19:41,370
+true or false belong to or not belong to هل هو ال
+
+266
+00:19:41,370 --> 00:19:45,510
+element اللي أعطانيها ك variable belong to بحطله
+
+267
+00:19:45,510 --> 00:19:53,110
+true not belong to بحطله F زي لو قلنا ال set S
+
+268
+00:19:53,110 --> 00:19:58,370
+equal toElement 3 بس هي عبارة عن set تحتوي على
+
+269
+00:19:58,370 --> 00:20:02,430
+element واحد فلو قلنا S of 0 فالـ false لأن ال
+
+270
+00:20:02,430 --> 00:20:06,590
+zero غير موجود ال element zero مش موجود هنا ولكن S
+
+271
+00:20:06,590 --> 00:20:12,170
+of 3 موجود بقول true فهي برضه تعاملنا مع ال set as
+
+272
+00:20:12,170 --> 00:20:17,570
+a function معها as a function الكلام اللي قلناه في
+
+273
+00:20:17,570 --> 00:20:20,610
+ال or قبل شويةفي ال operator اللي خاصة بال
+
+274
+00:20:20,610 --> 00:20:23,010
+proposition بنقدر نقوله برضه في ال operator اللي
+
+275
+00:20:23,010 --> 00:20:26,650
+خاصة بيه بال sets بال sets اللي هي مين ال
+
+276
+00:20:26,650 --> 00:20:32,410
+intersection union way complement تمام بقولش هنا
+
+277
+00:20:32,410 --> 00:20:36,270
+negation كانت في ال proposition زي لما قلت هنا
+
+278
+00:20:36,270 --> 00:20:39,730
+intersection ماقلتش and هنا intersection فهنا
+
+279
+00:20:39,730 --> 00:20:44,100
+complement تماماللي هي ال operators واحدة و بتحس
+
+280
+00:20:44,100 --> 00:20:47,420
+أن تأثيرها واحد بس طبعا بناء على انا applied على
+
+281
+00:20:47,420 --> 00:20:50,780
+إيش بتتغير المصطلح تبعها بتتغير المصطلح فهذه
+
+282
+00:20:50,780 --> 00:20:55,580
+compliment okay نقدر نقولها function على أساس إن
+
+283
+00:20:55,580 --> 00:20:58,920
+أنا بعمل نفس الفكرة زي ما كنا نتوي or لأ هي ال
+
+284
+00:20:58,920 --> 00:21:02,840
+function تبعت هنا intersection وهي فتحنا الأقوات
+
+285
+00:21:02,840 --> 00:21:06,560
+بتاعة ال functionطيب انحدد ال inputs ال inputs
+
+286
+00:21:06,560 --> 00:21:10,540
+طبعا مش بده تكون sets لان انا بتعامل مع operator ل
+
+287
+00:21:10,540 --> 00:21:15,560
+sets فاتوقع ان ال input لازم تكون sets عشان من ال
+
+288
+00:21:15,560 --> 00:21:17,980
+sets هدولة من ال two sets هدولة و من ال function
+
+289
+00:21:17,980 --> 00:21:22,800
+اطلق الناتج اللي هو عبارة عن جديش تلاتة الناتج
+
+290
+00:21:22,800 --> 00:21:25,060
+هيكون تلاتة اللي هو ال intersection between ال two
+
+291
+00:21:25,060 --> 00:21:31,440
+sets اللي قدامنا هدولة تمام فلاحظوا برضه بنتعامل
+
+292
+00:21:31,440 --> 00:21:39,060
+معها setas a function okay خلصنا من توضيح ان احنا
+
+293
+00:21:39,060 --> 00:21:42,480
+فعلا اتعاملنا مع functions كتيرة كنا فعلا نتعامل
+
+294
+00:21:42,480 --> 00:21:46,640
+معها و بتقدر هنا نكتبها بشكل function مع كل
+
+295
+00:21:46,640 --> 00:21:52,100
+المواضيع او ال subjects اللي احنا شرحناها نجي شوية
+
+296
+00:21:52,100 --> 00:21:54,880
+terminology انركز شوية في مين؟ في ال function
+
+297
+00:21:54,880 --> 00:21:58,320
+نفسها خلينا نركز في ال function انركز في ال
+
+298
+00:21:58,320 --> 00:22:00,340
+function احنا عرفنا ال function ان هي ال function
+
+299
+00:22:00,340 --> 00:22:07,500
+f from a to bset A to set B معناته ال input إجباري
+
+300
+00:22:07,500 --> 00:22:11,140
+لازم يكون belong to mean to set A و ال output لازم
+
+301
+00:22:11,140 --> 00:22:17,200
+يكون belong to set B okay and F of A و A هذه لازم
+
+302
+00:22:17,200 --> 00:22:23,680
+تكون belong to capital A to set A equal to B بحيث
+
+303
+00:22:23,680 --> 00:22:27,960
+أنه زي ما قلنا A belong to set A و B belong to set
+
+304
+00:22:28,870 --> 00:22:32,390
+Okay إذا فعلا عندنا ال function هذه بنقدر نعمل
+
+305
+00:22:32,390 --> 00:22:35,130
+شوية التسميات هدولة إيش هما التسميات هدولة أو
+
+306
+00:22:35,130 --> 00:22:40,770
+المسميات A اللي هي set A بنسميها domain set A
+
+307
+00:22:40,770 --> 00:22:45,250
+بنسميها domain طيب ال B أو ال set B بنسميها ال
+
+308
+00:22:45,250 --> 00:22:48,710
+codomain codomain تابع لل domain يتبع لل domain
+
+309
+00:22:51,670 --> 00:22:56,730
+مناظر لل domain او مقابل لل domain ال small b
+
+310
+00:22:56,730 --> 00:23:03,270
+يلاحظ انه element او الناتج ال element ويل هي ال
+
+311
+00:23:03,270 --> 00:23:08,810
+ناتج هذا بنسميها ال image of a under function f
+
+312
+00:23:08,810 --> 00:23:12,950
+بمعنى هو a بس بعد ما طبقنا على ال a من ال function
+
+313
+00:23:12,950 --> 00:23:17,850
+fتمام؟ فهي ال image و قلت الكتو الصورة و قلنا
+
+314
+00:23:17,850 --> 00:23:21,210
+الكتو حكاية المراية المراية إذا كان normal ..
+
+315
+00:23:21,210 --> 00:23:24,810
+normal معناته x بتسوي y أو y بتسوي x أو a بتسوي b
+
+316
+00:23:24,810 --> 00:23:29,470
+.. a بتسوي b ف a هتسوي b خلاص أنا في الآخر بتعامل
+
+317
+00:23:29,470 --> 00:23:32,880
+مع أن ال b هي ال image بتاعة aلما أشوف صورتي،
+
+318
+00:23:32,880 --> 00:23:37,340
+صورتي هي ال image تبعتي، هي ال image تبعتي، لو سطح
+
+319
+00:23:37,340 --> 00:23:42,260
+المرايا مقعر محدد فيه أي functionality معينة
+
+320
+00:23:42,260 --> 00:23:45,280
+معمولة فيه، هلاجنه الصورة مختلفة، ولكن هي في
+
+321
+00:23:45,280 --> 00:23:49,080
+النهاية تمثل صورتي برضه، بس under the function
+
+322
+00:23:49,730 --> 00:23:53,510
+under the function بعد ما طبقنا عليها ال function
+
+323
+00:23:53,510 --> 00:23:56,270
+اللي هو سطح المرايا أو المقعرة أو المحدد أو اللي
+
+324
+00:23:56,270 --> 00:24:01,150
+يمثل ب function معينة ال A بالمقابل هي ال pre
+
+325
+00:24:01,150 --> 00:24:06,610
+image هي الصورة المسبقة الصورة المسبقة ل B under
+
+326
+00:24:06,610 --> 00:24:13,430
+the function F under function F okay in general B
+
+327
+00:24:13,430 --> 00:24:17,910
+may have more than one pre image ممكن زي التربيع
+
+328
+00:24:18,830 --> 00:24:23,690
+التربية ممكن يكون لها اكتر من preimage على
+
+329
+00:24:23,690 --> 00:24:26,670
+اعتبار ان هي عندكم مثلا قولناها اتنين و minus
+
+330
+00:24:26,670 --> 00:24:30,210
+اتنين هيكون لهم اتنين القيمتين مثلا اللي هم نفس
+
+331
+00:24:30,210 --> 00:24:36,770
+الاربعة هذه ال image او ال B لها اتنين preimage هي
+
+332
+00:24:36,770 --> 00:24:41,290
+preimage أولى وهي preimage تانية لاحظوا two
+
+333
+00:24:41,290 --> 00:24:45,810
+preimages زي ما قلنا العكس لأ العكس لأ يعني لا
+
+334
+00:24:45,810 --> 00:24:53,280
+يمكن ل a يكون في two imagesلأ يمكن تمام then نتكلم
+
+335
+00:24:53,280 --> 00:24:56,520
+عن ال range هالواجهة ال range هي subset بنسميها R
+
+336
+00:24:56,520 --> 00:25:00,980
+طبعا هي subset من ال code domain جزء من ال code
+
+337
+00:25:00,980 --> 00:25:06,460
+domain of F is set احنا بنتكلم عن subset هيها
+
+338
+00:25:06,460 --> 00:25:11,440
+معناته بتدعرفها as a set فبنحط لها علامات ال set
+
+339
+00:25:11,440 --> 00:25:17,650
+ال curly process تبعتنا of B هي set of Bsuch that
+
+340
+00:25:17,650 --> 00:25:24,010
+there exists a which is a pre-image a تنتج لنا b
+
+341
+00:25:24,010 --> 00:25:29,090
+معناته هي في النهاية set لمجموعة outputs outputs
+
+342
+00:25:29,090 --> 00:25:32,830
+مش ال b عرفناها أساسا هي ال output ال outputs انه
+
+343
+00:25:32,830 --> 00:25:36,230
+يوجد قيم لل outputs او كل قيم ال outputs اللي
+
+344
+00:25:36,230 --> 00:25:45,150
+ناتجة من applied او تطبيق ال f على كل قيم aبمعنى
+
+345
+00:25:45,150 --> 00:25:49,390
+هي ال actual output هي ال actual ال experimental
+
+346
+00:25:49,390 --> 00:25:54,490
+output هو التجريب فعلا ان انا جربت كل قيم a امسكت
+
+347
+00:25:54,490 --> 00:25:58,530
+ال set a كل القيم اللي فيها جربتهم under the
+
+348
+00:25:58,530 --> 00:26:01,930
+function طلعنا ناتج الناتج هذا حطناه في set
+
+349
+00:26:01,930 --> 00:26:06,970
+سميناها R actual هذا هذا الحقيقي هذا الناتج الفعلي
+
+350
+00:26:06,970 --> 00:26:09,610
+الناتج الفعلي لل function
+
+351
+00:26:12,640 --> 00:26:17,600
+Range vs Codomain هدى إشي و هدى إشي ال Codomain زى
+
+352
+00:26:17,600 --> 00:26:21,560
+ما قلنا احنا هي ال domain المقابل أو المظير لل
+
+353
+00:26:21,560 --> 00:26:26,040
+domain لل input و هدى بتكون عبارة عن ال P جبل ما
+
+354
+00:26:26,040 --> 00:26:28,820
+نطبق لسه ال function اللى هو متوقع أنه هتكون ..
+
+355
+00:26:28,820 --> 00:26:31,440
+لما نتكلم عن ال real number بالنسبة لل domain
+
+356
+00:26:31,440 --> 00:26:35,360
+متوقع أنه برضه انه هتكون كلها real number فبقول ان
+
+357
+00:26:35,360 --> 00:26:39,860
+هي belong to R to real number طب actuallyخلّينا
+
+358
+00:26:39,860 --> 00:26:44,280
+ندخل القيم exactly بالظبط اللي داخل ال set A،
+
+359
+00:26:44,280 --> 00:26:49,500
+نطبقهم under the function و نشوف actual outputs،
+
+360
+00:26:49,500 --> 00:26:53,040
+نطلع النتائج الحقيقية، النتائج الحقيقية بنحصرها،
+
+361
+00:26:53,040 --> 00:26:58,060
+بنقول هذه ايش؟ R، هذه ال range، هذه R أو ال range،
+
+362
+00:26:58,060 --> 00:27:02,510
+تمامفبتعمل mapping زى ما قلنا فى الآخر ال code
+
+363
+00:27:02,510 --> 00:27:06,970
+domain هذا بيعمل map لكل ال domain values او هم
+
+364
+00:27:06,970 --> 00:27:11,210
+التصريح لل domain هو التصريح لل domain مادام ال
+
+365
+00:27:11,210 --> 00:27:13,830
+domain real numbers معناته ال code domain بيكون
+
+366
+00:27:13,830 --> 00:27:18,910
+real numbers بالعموم actual لأ بتصير اسمها range
+
+367
+00:27:18,910 --> 00:27:21,970
+actual لما نيجى نطبقها واحدة واحدة بتصير اللى هى
+
+368
+00:27:21,970 --> 00:27:25,070
+ال range او اللى هى ال actually maps elements of
+
+369
+00:27:25,070 --> 00:27:30,110
+the domainexample ناخد example على الموضوع خلينا
+
+370
+00:27:30,110 --> 00:27:34,550
+نقول انه انه عندنا function if is a function
+
+371
+00:27:34,550 --> 00:27:38,470
+mapping students in the class في ال class تبعنا to
+
+372
+00:27:38,470 --> 00:27:42,210
+ish to set of grades لمجموعة ال grades ساعتنا او
+
+373
+00:27:42,210 --> 00:27:47,490
+التقديرات بتاعتنا التقديرات اللي هي ish a b c d e
+
+374
+00:27:47,490 --> 00:27:50,950
+بدل ال .. بدل التاني يعني لأنه ما .. ماعتقدش انه
+
+375
+00:27:50,950 --> 00:27:54,190
+في grade a .. e بس احنا زى ما بقول ال .. بدناه
+
+376
+00:27:54,190 --> 00:27:59,520
+عشان هشيل ال ..عنا خمسة grades و بدنا نوزع الطلاب
+
+377
+00:27:59,520 --> 00:28:02,960
+عليهم طبيعي احنا لسه ماعملناش امتحانات انا مش عارف
+
+378
+00:28:02,960 --> 00:28:05,980
+فإذا كان at this point ان احنا لسه ماعملناش اي
+
+379
+00:28:05,980 --> 00:28:09,960
+امتحان عشان اعرف كيف اوزع ففي الحالة هذه ال code
+
+380
+00:28:09,960 --> 00:28:14,220
+domain ايش هيكون كلهم ال code domain كلهم هذا مش
+
+381
+00:28:14,220 --> 00:28:18,320
+هيتغير ال code domain كلهم طيب ال range لسه
+
+382
+00:28:18,320 --> 00:28:23,620
+ماعملناش اشي and none انا مش عارفأنا مش عارف، لأ
+
+383
+00:28:23,620 --> 00:28:26,720
+احنا مش عارفين، احنا لسه .. ماقيمناش لسه، فاحنا مش
+
+384
+00:28:26,720 --> 00:28:29,620
+عارفين، لإنه ماعنديش أي معلومة، ماعنديش function،
+
+385
+00:28:29,620 --> 00:28:31,480
+ماعندي .. ال function في النهاية اللي هي إيش كانت
+
+386
+00:28:31,480 --> 00:28:34,800
+المفروض .. الامتحان، الامتحان هيكون هو ال function
+
+387
+00:28:35,650 --> 00:28:40,050
+بنان على نواة نتائج الامتحان بنحط ال outputs بنحط
+
+388
+00:28:40,050 --> 00:28:43,910
+ال outputs فهنا unknown طيب لو بعد الامتحان عملنا
+
+389
+00:28:43,910 --> 00:28:48,530
+مثلا امتحان exam quiz أي شيء و ال grade بتاعتنا
+
+390
+00:28:48,530 --> 00:28:55,590
+turns out all ones and zero and a's and b's فإذا
+
+391
+00:28:55,590 --> 00:28:59,910
+كلهم يا a يا b أي طالبة بلا استثناء لو طلعت اسمها
+
+392
+00:28:59,910 --> 00:29:03,960
+من الكشف هتكون يا a يا bمخدة معدل يا A يا B ففي
+
+393
+00:29:03,960 --> 00:29:07,940
+الحالة هذه بنقول ان ال range ايش A وB فقط ال range
+
+394
+00:29:07,940 --> 00:29:11,660
+تبعنا اللي هو ال actual output ال actual output في
+
+395
+00:29:11,660 --> 00:29:13,920
+ال function تبعنا في الحالة تبعنا ال function
+
+396
+00:29:13,920 --> 00:29:16,140
+تبعنا اللي هو ال test اللي احنا عملنا هاي ال
+
+397
+00:29:16,140 --> 00:29:19,620
+function يمكن نعمل بعد هيك function تانية اختبار
+
+398
+00:29:19,620 --> 00:29:23,180
+تاني test تاني تطلعله output تانية بس حتى اللحظة
+
+399
+00:29:23,180 --> 00:29:25,700
+ال function تبعنا اللي هي الامتحان اللي احنا عملنا
+
+400
+00:29:25,700 --> 00:29:28,940
+عملنا امتحان واحد okay هذا بالنسبالي functionفنكشن
+
+401
+00:29:28,940 --> 00:29:33,800
+بتطلع منه نتائج بتطلع منه نتائج okay الكودومين كله
+
+402
+00:29:33,800 --> 00:29:36,920
+مش هيتغير الكودومين still ABCDE
+
+403
+00:29:39,120 --> 00:29:43,820
+Okay ال operator هي هي اللي نقدر نتعامل زي ما قلنا
+
+404
+00:29:43,820 --> 00:29:49,200
+معاها .. معاهم as a function في الحالة طلعتنا ال
+
+405
+00:29:49,200 --> 00:29:53,720
+set اللي هي ال true and false و ال negation نقدر
+
+406
+00:29:53,720 --> 00:29:59,820
+نتعامل معاه عساس انه NRA operator .. NRA operator
+
+407
+00:29:59,820 --> 00:30:04,620
+و ال and و ال or و ال by و ال union و ال .. كله
+
+408
+00:30:04,620 --> 00:30:09,200
+كله binary كل هدولة binary تمامو احنا شوفناهم اصلا
+
+409
+00:30:09,200 --> 00:30:12,600
+و اتعاملنا معاهم Constructing Function Operators
+
+410
+00:30:12,600 --> 00:30:16,780
+هنا بدنا نبدأ نعمل operators جديدة او نعمل
+
+411
+00:30:16,780 --> 00:30:21,020
+generation ل functions جديدة ل function جديدة منها
+
+412
+00:30:21,020 --> 00:30:23,520
+اول operator بنشتغل عليها نشتغل عليها اللي هي ال
+
+413
+00:30:23,520 --> 00:30:27,300
+dot ال dot الدرب عملية الدرب ال dot اللي انتوا
+
+414
+00:30:27,300 --> 00:30:31,360
+خدتوها سابقا و عارفين عملية ايش الدرب فلو قلنا ان
+
+415
+00:30:31,360 --> 00:30:35,480
+ال dot احنا عارفينها هي عملية operation على set B
+
+416
+00:30:35,480 --> 00:30:40,760
+فانا بعمل درب لل set Bمثلا، معنا ذلك إن أنا بعمل
+
+417
+00:30:40,760 --> 00:30:45,060
+ضرب لل elements اللي داخلها، في الحالة هذه،
+
+418
+00:30:45,060 --> 00:30:48,840
+بنعرفها على أساس إن هي cycle بالشكل هذا solid،
+
+419
+00:30:48,840 --> 00:30:54,420
+solid cycle، نقطة سودة، bold شوية و نقطة سودة،
+
+420
+00:30:54,420 --> 00:30:57,580
+فهذه بعرف إن هي إيش، ال dot، هنطبقها على مين؟ على
+
+421
+00:30:57,580 --> 00:31:02,580
+ال function f from a to bحتى اللحظة تمام هنعوضها
+
+422
+00:31:02,580 --> 00:31:06,500
+من A to B طيب ال binary operator طبعتنا طبعا احنا
+
+423
+00:31:06,500 --> 00:31:10,700
+عارفين لو بنطبخها بس على ال B هي هتكون B في B
+
+424
+00:31:10,700 --> 00:31:15,580
+وبيعطينا ال domain ال codomain B هيكون برضه نواتج
+
+425
+00:31:15,580 --> 00:31:19,160
+من نفس ال function طيب خلينا نطبخها لأ احنا على ال
+
+426
+00:31:19,160 --> 00:31:21,640
+functions ال actual functions طبعتنا اللي بنسرع لو
+
+427
+00:31:21,640 --> 00:31:26,930
+افترضنا ان فينا function Fفنشن g فسيصبح لدينا ايش؟
+
+428
+00:31:26,930 --> 00:31:32,870
+two functions ال two functions from a to b تنتين
+
+429
+00:31:32,870 --> 00:31:35,910
+يتفقوا ان هم هياخدوا ال elements ال inputs بتاعتهم
+
+430
+00:31:35,910 --> 00:31:39,690
+من ال set a و ال outputs بتاعتهم من ال set b
+
+431
+00:31:39,690 --> 00:31:47,070
+فبنعرفهم كتالة if dot g from a to b بنعرفها عساسيا
+
+432
+00:31:47,070 --> 00:31:55,310
+for all a لكل ال inputsبتاعتنا اللي هي belong to
+
+433
+00:31:55,310 --> 00:32:01,590
+set A F dot G of A زي ما قلنا A هذه belong to
+
+434
+00:32:01,590 --> 00:32:06,030
+capital A ممكن تكون أي element داخل ال set A إيش
+
+435
+00:32:06,030 --> 00:32:09,650
+بيساوي ال term هذا بيساوي ال F of A dot G of A
+
+436
+00:32:09,650 --> 00:32:15,680
+بيساوي ناتج الأولى في ناتج التانيةبساوي ناتج
+
+437
+00:32:15,680 --> 00:32:22,080
+الأولى فى ناتج التانية بنكتبها f dot g of a هي
+
+438
+00:32:22,080 --> 00:32:29,720
+عبارة عن f of a dot g of a سهلة مافيش فيها مشكلة
+
+439
+00:32:29,720 --> 00:32:34,800
+ومش معقدة ومافيش فيها إشكالالكلام نفسه بنقدر نصغته
+
+440
+00:32:34,800 --> 00:32:38,500
+على مين؟ على ال plus و ال times او ال
+
+441
+00:32:38,500 --> 00:32:43,280
+multiplication بمعنى ان انا بقدر اقول طبعا ان لو
+
+442
+00:32:43,280 --> 00:32:47,140
+في عندنا function f و g from real number to real
+
+443
+00:32:47,140 --> 00:32:50,920
+number الامة بتساعدها real number و ال output real
+
+444
+00:32:50,920 --> 00:32:55,040
+number في الحالة هذه بقدر اقول ان ال f plus g from
+
+445
+00:32:55,040 --> 00:33:04,690
+R to Rf plus g of x عبارة عن f of x plus g of x
+
+446
+00:33:04,690 --> 00:33:10,030
+نفس الكلام multiplication برضه هتكون f multiplied
+
+447
+00:33:10,030 --> 00:33:16,630
+by g of x عبارة عن f of x multiplied by g of x
+
+448
+00:33:16,630 --> 00:33:22,870
+ننقل
+
+449
+00:33:22,870 --> 00:33:27,140
+لعندي كل الأمور سهلة وسيطة ننتقلoperator تانية
+
+450
+00:33:27,140 --> 00:33:33,940
+اللى هى ال composition فضلى ال dot
+
+451
+00:33:33,940 --> 00:33:37,960
+بتكون ترتيبية ال dot عادة بتكون ترتيبية كتير
+
+452
+00:33:37,960 --> 00:33:40,260
+بتستخدم في ال .. ال .. ال .. اللى هى ال Cartesian
+
+453
+00:33:40,260 --> 00:33:43,600
+product بتكون اللى هى علاقة بال Cartesian product
+
+454
+00:33:43,600 --> 00:33:47,580
+احنا لما بنعمل dot عادية dot العادية خلاص ضرب عادي
+
+455
+00:33:47,580 --> 00:33:50,680
+اللى هى multiplication عادية ضرب عادي بس لما نيجى
+
+456
+00:33:50,680 --> 00:33:53,820
+نعمل Cartesian product لأ ال Cartesian product
+
+457
+00:33:53,820 --> 00:33:58,450
+ترتيبيلازم نحافظ على الترتيب فيه، بمعنى أنه عادة
+
+458
+00:33:58,450 --> 00:34:02,770
+بتكون لمصففات، لمجموعات، بنعملها dots، بنعملها
+
+459
+00:34:02,770 --> 00:34:07,370
+dots في الحالة هذه مازلنا في ال composition،
+
+460
+00:34:07,370 --> 00:34:14,710
+composition operator هي ببساطة، باخد، عندنا two
+
+461
+00:34:14,710 --> 00:34:18,990
+functions، واحدة compose التانيةالأولى compose
+
+462
+00:34:18,990 --> 00:34:22,810
+التانية، خلّيني أكتبها عشان أشرحها، الأولى compose
+
+463
+00:34:22,810 --> 00:34:28,350
+التانية، لو افترضنا بالشكل هذا، ناتج التانية input
+
+464
+00:34:28,350 --> 00:34:32,710
+للأولى، بسيطة
+
+465
+00:34:32,710 --> 00:34:37,050
+جدا، مرّ عليكم أكيد، أنا متأكد إنه لازم يمرّ
+
+466
+00:34:37,050 --> 00:34:42,240
+عليكم، ناتج التانية input للأولىفبنسميها
+
+467
+00:34:42,240 --> 00:34:44,840
+composition .. composition .. ماعرفش إيش كنتوا
+
+468
+00:34:44,840 --> 00:34:47,420
+تسموها سابقا .. إحنا عنا إيه اسم ال composition ..
+
+469
+00:34:47,420 --> 00:34:51,620
+فإحنا هنا بنقولها compose أو big O زي عاملة زي ال
+
+470
+00:34:51,620 --> 00:34:54,820
+big O هيك .. طيب عشان تكون صحيحة و تطلع نتائج
+
+471
+00:34:54,820 --> 00:35:00,780
+صحيحة .. هنقول إن ال G from A to B .. هذه اللي هي
+
+472
+00:35:00,780 --> 00:35:05,220
+التانية .. تانية .. هتبدأ من ال domain تبعها لل
+
+473
+00:35:05,220 --> 00:35:07,480
+code domain تبعها .. ال code domain تبعها لازم
+
+474
+00:35:07,480 --> 00:35:12,190
+يكون هو ال domain للتانية .. لل .. لل .. لل Fصحيح؟
+
+475
+00:35:12,190 --> 00:35:18,990
+لأن الناتج تبحى هو input لمن؟ لل F ف from B to C
+
+476
+00:35:18,990 --> 00:35:25,990
+في الحالة الناتج ككل هيكون من A to C كل الناتج
+
+477
+00:35:25,990 --> 00:35:28,530
+اللي هو ال composition كله على بعضه هيكون من A to
+
+478
+00:35:28,530 --> 00:35:33,450
+C from A to C و زي ما قلنا بنعطيه ال cycle الكبيرة
+
+479
+00:35:33,450 --> 00:35:38,140
+هذه تمامcomposes هي بنعمل فيها composition أو
+
+480
+00:35:38,140 --> 00:35:42,480
+creation أو generation ل new function ل new
+
+481
+00:35:42,480 --> 00:35:45,080
+function لأن function تعويضا في function function
+
+482
+00:35:45,080 --> 00:35:49,000
+معوضة في جلب function بدل ال x بتاعة ال function
+
+483
+00:35:49,000 --> 00:35:53,380
+بنعوض بقيمة ال function السابقة قيمتها كلها على
+
+484
+00:35:53,380 --> 00:36:01,340
+بعض قيمتها كلها على بعض زي نقربها أكتر برضه لو
+
+485
+00:36:01,340 --> 00:36:11,570
+قلنا ال ال g عبارة عنX تربيع plus two فرضا و ال F
+
+486
+00:36:11,570 --> 00:36:21,530
+ماعشان عارف خلينا ناخد .. اتنين X تربيع ناقص X
+
+487
+00:36:21,530 --> 00:36:30,330
+بيكفي تمام؟ هاد اللي مابنيجي نكتبهF compose G لحظة
+
+488
+00:36:30,330 --> 00:36:36,750
+ناتج ال G يكون input لمن؟ لل F طيب هاي ال input
+
+489
+00:36:36,750 --> 00:36:44,890
+تبع ال F معناته كل X بنحط مكان اضطره على F لحظة
+
+490
+00:36:44,890 --> 00:36:47,890
+هتطلع 2 X ربيع
+
+491
+00:36:55,740 --> 00:37:00,540
+ناتج التانية نعوضه ك input لمن؟ للأولى ك input
+
+492
+00:37:00,540 --> 00:37:04,140
+للأولى طيب كويسة هذا المفهوم خلينا نشوف كيف
+
+493
+00:37:04,140 --> 00:37:06,840
+أسقطناه في شوية المعادلات و شوية ال expressions
+
+494
+00:37:06,840 --> 00:37:13,020
+اللي عندنا فحنقول if compose G from A to C نكتبها
+
+495
+00:37:13,020 --> 00:37:19,000
+if compose G of A عبارة عن إيش؟ if ال function
+
+496
+00:37:19,000 --> 00:37:24,300
+الأولى ك function في ناتج ال function التانيةلحظة
+
+497
+00:37:24,300 --> 00:37:29,060
+ال input تبعها هو ناتج ال function التانية هي g of
+
+498
+00:37:29,060 --> 00:37:32,800
+a .. خلاص لو حسبناها ال term هذا كله هيعتبر ناتج
+
+499
+00:37:32,800 --> 00:37:37,540
+ال function g طيب الناتج لل function g هو input لل
+
+500
+00:37:37,540 --> 00:37:42,420
+function f طبعا
+
+501
+00:37:42,420 --> 00:37:46,280
+في الآخر g of a هذا مين؟ هذا ال output لمين؟ لل
+
+502
+00:37:46,280 --> 00:37:50,280
+function g المفروض belonging to مين؟to b هي ال
+
+503
+00:37:50,280 --> 00:37:54,420
+function g ال output تبعها belong to mean to set b
+
+504
+00:37:54,420 --> 00:38:00,400
+okay so f of g of a بنعرفها على أساس أنها لازم
+
+505
+00:38:00,400 --> 00:38:05,240
+تكون belong to mean to c f of anything هي ال
+
+506
+00:38:05,240 --> 00:38:08,480
+output لل function f فال output لل function f
+
+507
+00:38:08,480 --> 00:38:15,140
+belong to mean to cOkay ال .. ال big O هذه او ال
+
+508
+00:38:15,140 --> 00:38:18,040
+.. ال cycle الكبيرة طبعا big O بدنا نحاول ان
+
+509
+00:38:18,040 --> 00:38:21,700
+مانستخدمهاش كتير لأنه لها استخدامات جاية ال cycle
+
+510
+00:38:21,700 --> 00:38:26,420
+الكبيرة او ال compose هذه زي ال Cartesian product
+
+511
+00:38:26,420 --> 00:38:32,280
+زي ال Cartesian product مش تبدلية بمعنى لما نقول F
+
+512
+00:38:32,280 --> 00:38:37,400
+compose G لا تساوي G compose F لا تساويها هتلاقيوا
+
+513
+00:38:37,400 --> 00:38:40,750
+هذه function وهذه function هنا لو بدنا نعكسنقص
+
+514
+00:38:40,750 --> 00:38:43,710
+الكلام ده هتطلع function مختلفة تماما، هتطلع عبارة
+
+515
+00:38:43,710 --> 00:38:49,450
+عن اتنين X تربيع ناقص X كله تربيع زائد اتنين، هذه
+
+516
+00:38:49,450 --> 00:38:53,230
+غير هذه تماما، يعني حتى لو فكتوهم و حولعتوهم، لا
+
+517
+00:38:53,230 --> 00:38:55,770
+يمكن يساوي، مش هيساوي بعض، هذه function وهذه
+
+518
+00:38:55,770 --> 00:38:58,490
+function تماما مختلفة، طبعا هذه عشان برضه هذه
+
+519
+00:38:58,490 --> 00:38:59,570
+compose F
+
+520
+00:39:04,580 --> 00:39:10,140
+بعكس .. بعكس مين ال .. ال plus، ال or، ال and، ال
+
+521
+00:39:10,140 --> 00:39:14,360
+.. ال union، ال .. ال intersection، كلهم هدولة
+
+522
+00:39:14,360 --> 00:39:17,880
+نقدر نقول أن هما تبدلية، عملية تبدلية، الأولة
+
+523
+00:39:17,880 --> 00:39:20,100
+جابلة التانية أو التانية جابلة الأولة بتفرجش معانا
+
+524
+00:39:20,100 --> 00:39:22,460
+فيش، في ال operator، ولكن في ال .. في ال
+
+525
+00:39:22,460 --> 00:39:27,560
+composition لأ، في ال composition لأ، طيبخلصنا هنا
+
+526
+00:39:27,560 --> 00:39:30,200
+ال two operators تعاوننا ال multiplication اللي
+
+527
+00:39:30,200 --> 00:39:32,980
+أخدناها و اتكلمنا عن ال composition المهم جدا ال
+
+528
+00:39:32,980 --> 00:39:36,280
+composition اللي احنا أخدناها نجي نتكلم عن أنواع
+
+529
+00:39:36,280 --> 00:39:39,860
+ال functions عن أنواع ال functions بتاعتي أنواع ال
+
+530
+00:39:39,860 --> 00:39:43,260
+functions حقيقة في عندنا نوعين و هنستخرج منهم نوع
+
+531
+00:39:43,260 --> 00:39:47,680
+تالت أول نوع one to one functions برضه اتوقع انه
+
+532
+00:39:47,680 --> 00:39:52,040
+مر عليكم توقع انه مر عليكم تمام one to one فإذا
+
+533
+00:39:52,040 --> 00:39:54,720
+نقدر نقول ان ال function is one to one او واحد تو
+
+534
+00:39:54,720 --> 00:40:00,930
+واحداو injective او injection او injection if and
+
+535
+00:40:00,930 --> 00:40:05,770
+only if every element of its range has only one
+
+536
+00:40:05,770 --> 00:40:09,230
+preimage has only one preimage احنا عارفين انه في
+
+537
+00:40:09,230 --> 00:40:13,870
+ال .. ال range ممكن يكون له one preimage او اكتر
+
+538
+00:40:13,870 --> 00:40:17,720
+ممكن يكون له twoممكن يكون له two preimage زي في ال
+
+539
+00:40:17,720 --> 00:40:21,660
+function x تربيع زي في ال function x تربيع لأ هنا
+
+540
+00:40:21,660 --> 00:40:28,400
+في ال one to one فقط one preimage فمعنى ذلك ان كل
+
+541
+00:40:28,400 --> 00:40:33,320
+ناتج هو جاي من input واحد كل input هذا هيعكسنا
+
+542
+00:40:33,320 --> 00:40:37,500
+الموضوع ان معناته كل input هينتجنا ناتج واحد فقط
+
+543
+00:40:39,160 --> 00:40:43,780
+الناتج دائما ناتج واحد فقط لكل ال inputs وكل ناتج
+
+544
+00:40:43,780 --> 00:40:48,680
+جاي من input واحد بس من input واحد فقط طيب هذه
+
+545
+00:40:48,680 --> 00:40:52,340
+بقدر نقول ان ال X is injective او ال X is one to
+
+546
+00:40:52,340 --> 00:40:56,200
+one معناه
+
+547
+00:40:56,200 --> 00:41:04,740
+ان there is no exist X and Y لحظة و X لا تساوي Y
+
+548
+00:41:04,740 --> 00:41:09,840
+and F of X تساوي F of Yلأ بدنا نفهمها دي بدنا
+
+549
+00:41:09,840 --> 00:41:12,620
+نفهمها كيف هدى عرفناها على أساس ان هى one to one
+
+550
+00:41:12,620 --> 00:41:19,720
+خلينى نشوف عشان اقول ان فعلا كل output كل element
+
+551
+00:41:19,720 --> 00:41:24,420
+فى ال range الو بري إمج واحدة الو بري إمج واحدة
+
+552
+00:41:24,420 --> 00:41:29,560
+فقط معنى ذلك ان ال f of x لا يمكن تنتج الا من
+
+553
+00:41:29,560 --> 00:41:34,160
+element واحد مظبوط هدى ال output هي هدى هيك output
+
+554
+00:41:34,160 --> 00:41:36,960
+يعني المفروض ان هي رايحة لل range ال value بتاعتها
+
+555
+00:41:37,800 --> 00:41:42,620
+كلها رايحة عساس ان هي element في ال range الاصل ان
+
+556
+00:41:42,620 --> 00:41:47,940
+x وحيدة فقط اللى تنتجلنا ال term هذا القيمة هذه
+
+557
+00:41:47,940 --> 00:41:54,140
+لما اقول equal تساوي f of y معناه يوجد element
+
+558
+00:41:54,140 --> 00:42:01,220
+تاني بنتجلنا نفس ال output ناخد بالنا ماشي لعند
+
+559
+00:42:01,220 --> 00:42:06,840
+الان ماشي ممكن نتسهر نقول طب ممكن x بتساوي yيعني
+
+560
+00:42:06,840 --> 00:42:09,420
+برضه حضر اللي احنا مزلنا في نفس الكلام ان لو
+
+561
+00:42:09,420 --> 00:42:12,820
+اثبتنا ان x بتساوي y احنا مازلنا تحت نفس التعريف
+
+562
+00:42:12,820 --> 00:42:16,580
+ان هي مازلة one to one مازلة one to one اذا كانت
+
+563
+00:42:16,580 --> 00:42:21,000
+بيساوي بعض لأ راح يقوللي لا يساوي بعض لا يساوي بعض
+
+564
+00:42:21,000 --> 00:42:26,600
+x لا تساوي y معناته واضح انه صار في عندي two pre
+
+565
+00:42:26,600 --> 00:42:32,420
+image لنفس ال output معناته نفيت ال one to one تم
+
+566
+00:42:32,420 --> 00:42:35,040
+نفي ال one to one و هو فعلا بيقوللي there is no
+
+567
+00:42:35,040 --> 00:42:43,100
+existلا يوجد قيمتين في ال domain يعني في ال input
+
+568
+00:42:43,100 --> 00:42:46,480
+لا يوجد قيمتين في ال input بيساويش بعض و بيعطونا
+
+569
+00:42:46,480 --> 00:42:50,260
+نفس ال output صحيح؟
+
+570
+00:42:50,260 --> 00:42:54,740
+صارت هيك منطقية أصبحت هيك منطقية فعلا لا يوجد في
+
+571
+00:42:54,740 --> 00:42:57,740
+negotiation في الأول معناته هو نفه الوجد أنه تحصل
+
+572
+00:42:57,740 --> 00:43:02,380
+هذا الكلام أن يكون فينا two preimage لنفس ال
+
+573
+00:43:02,380 --> 00:43:04,640
+output لنفس ال output تمام
+
+574
+00:43:10,990 --> 00:43:15,810
+Okay ف only one element of the domain is mapped to
+
+575
+00:43:15,810 --> 00:43:19,870
+any given one element of the range كل element في
+
+576
+00:43:19,870 --> 00:43:22,870
+ال range هو جاينة من one element في ال domain ال
+
+577
+00:43:22,870 --> 00:43:25,150
+one element اللي في ال domain هذا سمنا بالنسبة لل
+
+578
+00:43:25,150 --> 00:43:31,090
+element في ال range pre image okay معنى ذلك ان كل
+
+579
+00:43:31,090 --> 00:43:34,110
+element في ال domain is injected into the
+
+580
+00:43:34,110 --> 00:43:37,690
+different element of the rangeكل element في ال
+
+581
+00:43:37,690 --> 00:43:42,670
+domain طلعلنا ناتج element مختلف في ال range مافيش
+
+582
+00:43:42,670 --> 00:43:46,810
+اتنين بيشابهوا بعض في نفس ال .. الناتج لا يوجد
+
+583
+00:43:46,810 --> 00:43:50,310
+قيمتين في ال domain بيساووا بعض او بيطلعونا نفس
+
+584
+00:43:50,310 --> 00:43:54,230
+الناتج في ال rangeلا يوجد قيمتين، معناه ذلك أنه لا
+
+585
+00:43:54,230 --> 00:43:59,750
+يوجد two pre-images اللي هم نفس ال element في من
+
+586
+00:43:59,750 --> 00:44:03,410
+في ال range بنكرر و بنزل عشان نظل ثابت عن كل واحد
+
+587
+00:44:03,410 --> 00:44:07,130
+طيب ال
+
+588
+00:44:07,130 --> 00:44:09,250
+domain و ال range cardinal اللي احنا اتكلمنا عنها
+
+589
+00:44:09,250 --> 00:44:14,910
+قبل هيكة انه ممكن يكون ال domain أكبر من ال range
+
+590
+00:44:14,910 --> 00:44:17,810
+في النهايةو ال code domain ال code domain ممكن
+
+591
+00:44:17,810 --> 00:44:20,250
+يكون اكبر منهم يعني هنا في الحالة هذه لازم ال
+
+592
+00:44:20,250 --> 00:44:26,510
+domain و ال range يساوي بعض ليش؟ بشان يكون كل
+
+593
+00:44:26,510 --> 00:44:30,870
+input .. كل .. بالظبط كل input يلو output واحد كل
+
+594
+00:44:30,870 --> 00:44:36,290
+input يلو output واحد لأ يمكن اوضح لو حسبنا بال
+
+595
+00:44:36,290 --> 00:44:41,890
+bipartate لو هدلوا عندنا خمسة في ال input
+
+596
+00:44:45,880 --> 00:44:49,760
+لازم كل واحدة يكون لها output واحد بس كل واحدة
+
+597
+00:44:49,760 --> 00:44:54,280
+لازم يكون لها output واحد مثلا خلاص مادام كل واحدة
+
+598
+00:44:54,280 --> 00:44:57,580
+لها output واحد معناته عدد ال output مش مساوية عدد
+
+599
+00:44:57,580 --> 00:45:03,020
+ال input معناه ذلك انه ال range مساوية ال domain
+
+600
+00:45:06,880 --> 00:45:10,180
+ال issue المساوي احنا بنتكلم هنا عن إيش؟ بنتكلم عن
+
+601
+00:45:10,180 --> 00:45:13,400
+set معناته عشان ال C أقول إن هى بتسووا بعض معناته
+
+602
+00:45:13,400 --> 00:45:16,640
+ال cardinality بتاعتهم بيسووا بعض cardinality
+
+603
+00:45:16,640 --> 00:45:20,160
+بيسووا بعض طيب ال codomain إيش وضعه في النص هي
+
+604
+00:45:20,160 --> 00:45:23,420
+كده؟ نفس ال .. نفس ال .. نفس ال .. مش بالضروري
+
+605
+00:45:23,420 --> 00:45:28,240
+ممكن يكون في عندنا element زيادة هنا تفرجش ال
+
+606
+00:45:28,240 --> 00:45:31,920
+codomain لأ ممكن يكون أكبر ممكن و ممكن يكون بيسويه
+
+607
+00:45:35,910 --> 00:45:40,890
+طيب for examples هالوقت هي ديهذه one to one ولا ..
+
+608
+00:45:40,890 --> 00:45:47,870
+one to one تمام تانية لأ لإيش .. two pre images
+
+609
+00:45:47,870 --> 00:45:52,930
+هاي two pre images اعطوا لنفس ال .. لنفس ال
+
+610
+00:45:52,930 --> 00:45:54,670
+element في ال range لنفس ال element في ال range
+
+611
+00:45:54,670 --> 00:46:00,690
+فهذه not one التالتة not function من أصله ليش لإن
+
+612
+00:46:00,690 --> 00:46:04,550
+في one input في عندنا one input اعطانا two outputs
+
+613
+00:46:04,550 --> 00:46:06,910
+فهذه قلنا نتعامل معها انها مش function لإنها
+
+614
+00:46:06,910 --> 00:46:11,090
+unstable أساسالا يمكن أكون في نفس اللحظة في
+
+615
+00:46:11,090 --> 00:46:16,690
+مكانين، تمام؟ فإذا not even a function okay
+
+616
+00:46:16,690 --> 00:46:21,250
+sufficient conditions for one-to-one function إيه
+
+617
+00:46:21,250 --> 00:46:23,630
+بقدر أقول إنه او لا ال function ده كافي جدا عشان
+
+618
+00:46:23,630 --> 00:46:27,670
+أقول إن ال function تبعتنا one-to-one if is
+
+619
+00:46:27,670 --> 00:46:33,310
+strictly or monotonically، monotonic جاية من mono
+
+620
+00:46:33,310 --> 00:46:38,780
+كلمة mono أحاديمونو أحادي monotonically increasing
+
+621
+00:46:38,780 --> 00:46:44,280
+بمعنى ال function أحادية الاتجاه وتزايدية أحضر
+
+622
+00:46:44,280 --> 00:46:49,520
+خلاص طول عمرها أحادية الاتجاه فإذا كان فعلا تزايد
+
+623
+00:46:49,520 --> 00:46:53,680
+تزايدية باستمرار طبعا الكلام نفسه ينطبق على
+
+624
+00:46:53,680 --> 00:46:57,000
+monotonically decreasing أنها تكون تناقصية
+
+625
+00:46:57,000 --> 00:47:03,980
+باستمرار هذا معناته إيش لما أقول تزايدية تزايدية
+
+626
+00:47:06,770 --> 00:47:12,030
+باستمرار، معناه ذلك لو أخدنا x و y و قولنا أن x
+
+627
+00:47:12,030 --> 00:47:21,670
+أكبر من y كقيمة الأصل أن f of x برضه تكون أكبر من
+
+628
+00:47:21,670 --> 00:47:26,430
+f of y في الحالة هذه بقول أن الدالة أو ال function
+
+629
+00:47:26,430 --> 00:47:31,870
+تزايدية، monotonicمعناته أحادية الاتجاه و احنا
+
+630
+00:47:31,870 --> 00:47:35,090
+حددناها وراها monotonically increasing أحادية
+
+631
+00:47:35,090 --> 00:47:39,490
+الاتجاه وهي تزايدية باستمرار هتظهر معناته مش هتكسر
+
+632
+00:47:39,490 --> 00:47:44,870
+مش هتعكس هتظل mono و هتظل mono أحادية وتزايدية
+
+633
+00:47:44,870 --> 00:47:48,750
+مدام احنا حددناها هتظل باستمرار متزايدة مش هأفاجأ
+
+634
+00:47:48,750 --> 00:47:50,950
+أنه فجأة ألاجيها نزلت
+
+635
+00:47:53,590 --> 00:47:57,310
+لأن إذا نزلت هنا هضطر أقول إنها مش one to one
+
+636
+00:47:57,310 --> 00:48:00,610
+لإيش؟ لأن عند القيمة، القيمة اللي هنا و القيمة
+
+637
+00:48:00,610 --> 00:48:04,770
+اللي هنا، لاحظوا، هيكون نفس ال output لأ، بس إذا
+
+638
+00:48:04,770 --> 00:48:09,530
+دلنا متزايدية باستمرار، لا يمكن تصير الحالة هذه
+
+639
+00:48:09,530 --> 00:48:13,450
+إذا دلت باستمرار متزايدة، ال function تزايدية،
+
+640
+00:48:13,450 --> 00:48:16,880
+طبعا تزايدية ممكن تدل مكملة برضه هكذامن minus
+
+641
+00:48:16,880 --> 00:48:20,220
+infinity to infinity بشكل تزايدى الكلب نفسه ينطبق
+
+642
+00:48:20,220 --> 00:48:25,260
+علي مين decreasing لو بنتعامل مع decreasing بهذا
+
+643
+00:48:25,260 --> 00:48:32,580
+الشكل بس كل اللى هنعمله هنا ال inequality هنعكسها
+
+644
+00:48:32,580 --> 00:48:40,960
+ال inequality هنعكسها لو x أكبر من y فإذا ال f of
+
+645
+00:48:40,960 --> 00:48:47,340
+x أقلمن f of y بس ال inequality عكسناها بدل كأكبر
+
+646
+00:48:47,340 --> 00:48:51,220
+من صارت أصغر من بس باستمرار عمرو ماحنلاجي هنا
+
+647
+00:48:51,220 --> 00:48:56,180
+output ناتج من two pre image عمرو ده ماحنلاجي
+
+648
+00:48:56,180 --> 00:49:00,000
+element في ال output ناتج من two pre image تمام
+
+649
+00:49:00,000 --> 00:49:03,400
+فإذا اتحققوا الشرطين هدو .. أحد الشرطين .. أحد
+
+650
+00:49:03,400 --> 00:49:08,260
+الشرطين يعني يكفي أنها تكونيكفي انها تكون
+
+651
+00:49:08,260 --> 00:49:11,200
+monotonically increasing او monotonically
+
+652
+00:49:11,200 --> 00:49:16,560
+decreasing strictly الزمن انها تكون او زي متزايدة
+
+653
+00:49:16,560 --> 00:49:22,220
+او متنقصة تمام فبنقول
+
+654
+00:49:22,220 --> 00:49:26,380
+automatically ان هي increasing زي ال X تكعيب
+
+655
+00:49:27,900 --> 00:49:34,920
+تزايدية او تنقصية تزايدية تزايدية
+
+656
+00:49:34,920 --> 00:49:40,660
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+657
+00:49:40,660 --> 00:49:43,120
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+658
+00:49:43,120 --> 00:49:46,360
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+659
+00:49:46,360 --> 00:49:46,460
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+660
+00:49:46,460 --> 00:49:47,320
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+661
+00:49:47,320 --> 00:49:54,360
+تزايدية تزايدية تزايدية تزايدية
+
+662
+00:49:54,360 --> 00:49:54,380
+تز
+
+663
+00:49:58,640 --> 00:50:05,620
+بتزيد معاكم هتلاقوه
+
+664
+00:50:05,620 --> 00:50:11,360
+بهذا الشكل x تكريب y تساوي x تكريب فواضح ان هي
+
+665
+00:50:11,970 --> 00:50:17,890
+monotonically increasing تساعدية في هذه one to one
+
+666
+00:50:17,890 --> 00:50:23,370
+طيب في المقابل في برضه ال converse is not
+
+667
+00:50:23,370 --> 00:50:34,530
+necessarily true زي one over x ليش؟ نرسمها و
+
+668
+00:50:34,530 --> 00:50:35,490
+نشوف ليش
+
+669
+00:50:43,000 --> 00:50:49,420
+مش هي شكلها؟ وي بتساوي واحد على إكس طب وين المشكلة
+
+670
+00:50:49,420 --> 00:50:52,920
+فيها هذه؟
+
+671
+00:50:52,920 --> 00:50:58,220
+لأ عند ال zero إلها قيمتين infinity و minus
+
+672
+00:50:58,220 --> 00:51:01,460
+infinity عند ال zero إلها قيمتين بس طبعا وين؟ مش
+
+673
+00:51:01,460 --> 00:51:05,080
+هنشوفه في ال infinity فواضح إنه عند ال zero في
+
+674
+00:51:05,080 --> 00:51:09,500
+مشكلة عند ال zero هي في مشكلة رغم إن احنا ممكن
+
+675
+00:51:09,500 --> 00:51:15,680
+نتعامل معها نهيها decreasingصحيح؟ و هنا برضه نفس
+
+676
+00:51:15,680 --> 00:51:19,460
+الكلام بس واضح أنه لأ في نقطة انقلاب بتصير عند ال
+
+677
+00:51:19,460 --> 00:51:22,980
+zero هتعملنا مشكلة لأنه صار عند ال zero في عندنا
+
+678
+00:51:22,980 --> 00:51:27,200
+two outputs two outputs لنفس ال input لنفس ال
+
+679
+00:51:27,200 --> 00:51:32,720
+input طيب ال onto ال onto function أو ال
+
+680
+00:51:32,720 --> 00:51:37,920
+surjective onto هدى ببساطة جدا إذا كان ال code
+
+681
+00:51:37,920 --> 00:51:43,370
+main بسوء ال range فهي ontoفهي بنسميها onto بمعنى
+
+682
+00:51:43,370 --> 00:51:47,670
+ان كل القيم بتاعة ال code domain مستخدمة في ال
+
+683
+00:51:47,670 --> 00:51:53,610
+range كلها واقعة في ال range في ال range كويسة ففي
+
+684
+00:51:53,610 --> 00:51:56,030
+الحالة هي دي زي ما قولنا ال if from او ال function
+
+685
+00:51:56,030 --> 00:52:01,290
+if from A to B is onto or surjective or surjection
+
+686
+00:52:01,290 --> 00:52:05,410
+if and only if its range is equal to its code
+
+687
+00:52:05,410 --> 00:52:09,750
+domain في الحالة هي دي for all B belong toThere
+
+688
+00:52:09,750 --> 00:52:13,370
+exists a belonging to A بحققنا ال function f of x
+
+689
+00:52:13,370 --> 00:52:17,490
+equal to b بمعنى
+
+690
+00:52:17,490 --> 00:52:24,970
+لكل قيم ال code domain يوجد
+
+691
+00:52:24,970 --> 00:52:29,110
+element في ال domain بنتجها بطلّقنا إياها طب مادام
+
+692
+00:52:29,110 --> 00:52:33,120
+أنتجت معناته راحت لل range على طولصحيح؟ actually
+
+693
+00:52:33,120 --> 00:52:37,140
+مادام نقدر ننتجها معناته بتروح لمين؟ لل range
+
+694
+00:52:37,140 --> 00:52:42,100
+اوتوماتيكل انا قاعد بقول for all B لكل قيم B اللي
+
+695
+00:52:42,100 --> 00:52:47,780
+تنتمي لل set B ل ال code domain يوجد قيمة في ال
+
+696
+00:52:47,780 --> 00:52:51,520
+domain تنتجها طب ما خلاص انا اصلا كيف بحسبه ال
+
+697
+00:52:51,520 --> 00:52:56,960
+range؟ ال range بنحسب انه فيه فعلا قيم أو توجد
+
+698
+00:52:56,960 --> 00:53:01,250
+قيمة في ال domain تنتجهاو هو فعلا احنا قاعدين نقول
+
+699
+00:53:01,250 --> 00:53:04,950
+فلكل قيم ال code domain اوتوماتيكلي هيك صارت ال
+
+700
+00:53:04,950 --> 00:53:09,610
+code domain كله نفسه ال range نفسه ال range كويس
+
+701
+00:53:09,610 --> 00:53:16,630
+فإذا ال onto function maps the set A onto او the
+
+702
+00:53:16,630 --> 00:53:21,110
+entirety the set B معناه ذلك انه ال function A
+
+703
+00:53:21,110 --> 00:53:30,580
+هتنتجلنا outputs داخلأو كامل
+
+704
+00:53:30,580 --> 00:53:35,840
+ال set P بمعنى كامل ال set أو كامل ال elements في
+
+705
+00:53:35,840 --> 00:53:40,600
+ال code domain يمكن انتاجها من ال domain كامل ال
+
+706
+00:53:40,600 --> 00:53:44,880
+elements في ال code domain يمكن انتاجها من ال
+
+707
+00:53:44,880 --> 00:53:47,880
+domain طب احنا عارفين ان كل element ينتج من ال
+
+708
+00:53:47,880 --> 00:53:51,540
+domain هو range automatically صارت هيك ال range
+
+709
+00:53:51,540 --> 00:53:52,900
+يساوي لل code domain
+
+710
+00:53:57,990 --> 00:54:02,410
+Okay خلّينا نشوف ال function اللي لسه كنا رسمينها
+
+711
+00:54:02,410 --> 00:54:11,290
+تكعيب اللي هي تكعيب cubic هذي
+
+712
+00:54:11,290 --> 00:54:14,830
+اتفقنا ان هي one to one المرة اللي فاتت قبل شوية
+
+713
+00:54:14,830 --> 00:54:19,090
+لسه فالساعة اللي فاتت اتفقنا طيب بالنسبة ل onto
+
+714
+00:54:19,090 --> 00:54:24,890
+كيف تحسبوها onto؟نشوف ال domain .. ال code domain
+
+715
+00:54:24,890 --> 00:54:28,310
+طيب ال code domain وين ال code domain؟ I طلعه على
+
+716
+00:54:28,310 --> 00:54:33,970
+I أكسس من minus infinity to infinity طيب actually
+
+717
+00:54:33,970 --> 00:54:37,230
+هل ال function فعلا تصل ل minus infinity و بتطلع ل
+
+718
+00:54:37,230 --> 00:54:44,430
+positive infinity فإذن بيسووا بعض فإذن on two طيب
+
+719
+00:54:44,430 --> 00:54:52,010
+هذه ال on two او هذه ال X تربيه نشوف ال X تربيه
+
+720
+00:54:57,020 --> 00:55:01,920
+الـ codomain جديش؟ R من minus infinitive إلى
+
+721
+00:55:01,920 --> 00:55:05,220
+infinitive خلاص احنا محددنا من الأول R طيب ال
+
+722
+00:55:05,220 --> 00:55:09,580
+range من zero to positive infinity بمعنى ان احنا
+
+723
+00:55:09,580 --> 00:55:17,080
+بنتكلم عن ال none negative real numbers none
+
+724
+00:55:17,080 --> 00:55:19,660
+negative real numbers بمعنى ان هي من zero to
+
+725
+00:55:19,660 --> 00:55:23,120
+positive لكل ال positive to infinity none negative
+
+726
+00:55:23,120 --> 00:55:27,840
+elementsOkay why عرفنا why نرسمناه و نشوفنا ليش
+
+727
+00:55:27,840 --> 00:55:34,040
+واحدة منهم on to واحدة منهم none طيب نشوف هنا مين
+
+728
+00:55:34,040 --> 00:55:36,780
+منهم on to و مين one to one من الحالات اللي موجودة
+
+729
+00:55:36,780 --> 00:55:41,480
+عندنا نمسكهم واحدة واحدة الأولى هذى مش one to one
+
+730
+00:55:41,480 --> 00:55:44,460
+one to one لأ مش one to one ليش لأ لأ انهم three
+
+731
+00:55:44,460 --> 00:55:50,990
+طيب on to on toفإذا الأولى هنا one to one ولكن مش
+
+732
+00:55:50,990 --> 00:55:55,170
+one to one طيب تانية one to one ولا one to one ولا
+
+733
+00:55:55,170 --> 00:55:58,270
+one to one ولا one to one ولا one to one ولا one
+
+734
+00:55:58,270 --> 00:55:58,430
+one ولا one to one ولا one to one ولا one to one
+
+735
+00:55:58,430 --> 00:55:58,590
+ولا one to one ولا one to one ولا one to one ولا
+
+736
+00:55:58,590 --> 00:55:59,990
+one to one ولا one to one ولا one to one ولا one
+
+737
+00:55:59,990 --> 00:56:02,570
+to one ولا one to one ولا one to one ولا one to
+
+738
+00:56:02,570 --> 00:56:02,590
+one ولا one to one ولا one to one ولا one to one
+
+739
+00:56:02,590 --> 00:56:02,630
+ولا one to one ولا one to one ولا one to one ولا
+
+740
+00:56:02,630 --> 00:56:02,870
+to one ولا one to one ولا one to one ولا one to
+
+741
+00:56:02,870 --> 00:56:05,370
+one ولا one to one ولا one to one ولا one to one
+
+742
+00:56:05,370 --> 00:56:07,430
+ولا one to one ولا one to one ولا one to one ولا
+
+743
+00:56:07,430 --> 00:56:07,770
+to one ولا one to one ولا one to one ولا one to
+
+744
+00:56:07,770 --> 00:56:12,120
+one ولا one to one ولا one to one ولا one toهي one
+
+745
+00:56:12,120 --> 00:56:16,160
+to one اه ولكن ليست on to ليش مش on to لأن في عنده
+
+746
+00:56:16,160 --> 00:56:19,260
+element فيه موجود موجود في ال code domain و غير
+
+747
+00:56:19,260 --> 00:56:23,780
+موجود في ال range و غير موجود في ال range تمام طيب
+
+748
+00:56:23,780 --> 00:56:29,620
+ال bijections او ال one to one correspondence او
+
+749
+00:56:29,620 --> 00:56:33,580
+ال reversible او ال invertible اي تسمية من التسمية
+
+750
+00:56:33,580 --> 00:56:37,040
+هذه بس الغالب يمكن اكتر اللي هي ال bijection او
+
+751
+00:56:39,230 --> 00:56:42,790
+one to one correspondence كويس هدى امتى نقدر نقول
+
+752
+00:56:42,790 --> 00:56:46,790
+ان ال function bijection function اذا كانت one to
+
+753
+00:56:46,790 --> 00:56:51,090
+one و unto في نفس الوقت خلاص بنسميها ايش bijection
+
+754
+00:56:51,090 --> 00:56:56,170
+if and only if it's both one to one and unto فال
+
+755
+00:56:56,170 --> 00:57:00,810
+bijection اللى ال function if from a to b there
+
+756
+00:57:00,810 --> 00:57:06,620
+exists an inverse of f عشان هيك اسمهاreversible او
+
+757
+00:57:06,620 --> 00:57:09,360
+invertible على اساس انه اذا كان فعلا تتحققنا
+
+758
+00:57:09,360 --> 00:57:13,620
+الكلام هذا ايش بتحقق ان هي one to one فكل element
+
+759
+00:57:13,620 --> 00:57:21,000
+في ال domain يوجد له قيمة واحدة في ال range لحظة
+
+760
+00:57:21,000 --> 00:57:24,220
+في ال range لسه احنا بنتكلم عن ال one to one لسه
+
+761
+00:57:24,220 --> 00:57:28,080
+وكل element في ال range جاي من element واحد في ال
+
+762
+00:57:28,080 --> 00:57:33,390
+domainوال range يساوي ال code domain معناه ذلك
+
+763
+00:57:33,390 --> 00:57:36,370
+اللي قلناه على ال range بقدر اطبقه على ال code
+
+764
+00:57:36,370 --> 00:57:39,810
+domain كل element في ال code domain جاي من element
+
+765
+00:57:39,810 --> 00:57:44,530
+واحد في ال domain معناته لو انعكسه بقدر العلاقة
+
+766
+00:57:44,530 --> 00:57:47,930
+موجودة ليش علاقة موجودة لأن ال code domain بده
+
+767
+00:57:47,930 --> 00:57:50,790
+يصير domain الدمين بده يصير code domain ال
+
+768
+00:57:50,790 --> 00:57:54,370
+relation واحدة فعلا كل element موجود في ال domain
+
+769
+00:57:54,370 --> 00:57:58,960
+كان له element واحد في ال code domainمعنى ذلك أن
+
+770
+00:57:58,960 --> 00:58:02,280
+الـ function في الحالة دي لها inverse، بنقدر نجيب
+
+771
+00:58:02,280 --> 00:58:07,300
+لها ال inverse تبعها، المعكوز تبعها جبنا مجموعة ال
+
+772
+00:58:07,300 --> 00:58:09,940
+outputs، ال outputs هذه لو طبقنا عليها function
+
+773
+00:58:09,940 --> 00:58:13,620
+معينة، كل ال output هيرجع لل input تبعه، كل output
+
+774
+00:58:13,620 --> 00:58:16,500
+هيرجعنا لل input تبعه، فبنقدر نقول إنه، بنكتبها
+
+775
+00:58:16,500 --> 00:58:21,400
+أزايشInverse of F أو F to the power minus one اللي
+
+776
+00:58:21,400 --> 00:58:27,180
+هي Inverse of F from ال domain لل domain لحظة طيب
+
+777
+00:58:27,180 --> 00:58:30,060
+احنا ضمنين انه اكيد ال elements هذه متوافقة مع بعض
+
+778
+00:58:30,060 --> 00:58:35,580
+لأنه اساسا هنا كان كل element في ال A له output في
+
+779
+00:58:35,580 --> 00:58:40,360
+ال B و ال B مساوية لل rangeهي نفس ال range معناه
+
+780
+00:58:40,360 --> 00:58:43,280
+ذلك أنه بقدر أطبقها و أقول أن ال B برضه كل element
+
+781
+00:58:43,280 --> 00:58:47,100
+موجود في ال code domain بقدر أنتج منه element
+
+782
+00:58:47,100 --> 00:58:54,640
+موجود في ال domain بالعكس نفسي طيب لحظة لو تغاضينا
+
+783
+00:58:54,640 --> 00:58:59,800
+عن الشرط هذا اللي هي one to one معناه ذلك أنه لما
+
+784
+00:58:59,800 --> 00:59:05,720
+كنا بنتكلم أو اللي هي ال range لو قولنا التربيع
+
+785
+00:59:07,600 --> 00:59:13,260
+التربيع كل لحظة كل output فيه له two preimage طب
+
+786
+00:59:13,260 --> 00:59:18,280
+لو عكسناهم بيصير not function هصير not function
+
+787
+00:59:18,280 --> 00:59:22,460
+ففي الحالة ده مقدرش اقول ان فيها inverse عشان يكون
+
+788
+00:59:22,460 --> 00:59:26,260
+انها inverse لازم تكون one to oneو تكون on to و
+
+789
+00:59:26,260 --> 00:59:30,080
+تكون on to اتفجنا ان هي one to one ليش لأن ال pre
+
+790
+00:59:30,080 --> 00:59:33,260
+image هتصير image فإذا كان في عنده two pre image
+
+791
+00:59:33,260 --> 00:59:36,640
+مايتحول مش ل two image فتطلع من ال functionality
+
+792
+00:59:36,640 --> 00:59:41,120
+طيب الحالة التانية ال on to انا محتاج انها تكون on
+
+793
+00:59:41,120 --> 00:59:44,840
+to ليش لأن في ال on في ال function لازم كل عنصر في
+
+794
+00:59:44,840 --> 00:59:49,200
+ال domain اقدر اطبق عليه ال function طيب إذا كانت
+
+795
+00:59:49,200 --> 00:59:52,100
+مش on to معناته في عناصر في ال domain غير موجودة
+
+796
+00:59:52,100 --> 00:59:55,620
+في ال rangeمش هلاجيه لها قيمة كانت في ال domain
+
+797
+00:59:55,620 --> 01:00:00,660
+السابق، غير موجود لها قيمة مقابلة إلها، مع أن ذلك
+
+798
+01:00:00,660 --> 01:00:03,640
+أن أنا برضه مش .. ماقدرش أجيب لها ال inverse أو ال
+
+799
+01:00:03,640 --> 01:00:06,860
+inverse طبعا مجهول، مش .. مش عارف إنه هال حيناضر
+
+800
+01:00:06,860 --> 01:00:13,620
+تماما أو هيعطيني identity، functionلو عكسناها لل F
+
+801
+01:00:13,620 --> 01:00:17,360
+لأن كيف انا اعرف ان هذه inverse حقيقي ان لو ضربنا
+
+802
+01:00:17,360 --> 01:00:20,300
+ال inverse function في ال function الأصلية المفروض
+
+803
+01:00:20,300 --> 01:00:25,680
+يطلع ليه identity و identity حسب انا بتعامل مع set
+
+804
+01:00:25,680 --> 01:00:29,020
+بتعامل مع numbers
+
+805
+01:00:32,190 --> 01:00:35,330
+ماتريكس بنتعامل مع ايش بالظبط؟ لو بنتعامل مع مجرد
+
+806
+01:00:35,330 --> 01:00:40,030
+number ال identity هي الرقم واحد لو بنتعامل مثلا
+
+807
+01:00:40,030 --> 01:00:45,050
+مع matrix هي ال identity matrix اللي مش بضرورة
+
+808
+01:00:45,050 --> 01:00:49,010
+تكون كلها ones ال diagonal بس تبعها one صحيح؟ ال
+
+809
+01:00:49,010 --> 01:00:52,410
+diagonal فقط اللي بيكون ones، كويس فهنا بتقدر نقول
+
+810
+01:00:52,410 --> 01:00:59,940
+ان ال Fأو ال inverse ال function composition لأ
+
+811
+01:00:59,940 --> 01:01:04,360
+هذي اش اسمه dot dot F equal to ايش to identity
+
+812
+01:01:04,360 --> 01:01:08,420
+value equal to identity function to identity
+
+813
+01:01:08,420 --> 01:01:14,720
+function لأ هذي dot عادي هذي ضرب ضرب
+
+814
+01:01:14,720 --> 01:01:15,160
+multiplication
+
+815
+01:01:19,320 --> 01:01:22,860
+كيف؟ لأ ال composition أكبر من هيك، هذه مجرد
+
+816
+01:01:22,860 --> 01:01:26,100
+تضربة، بس ال function في ال function، ال function
+
+817
+01:01:26,100 --> 01:01:35,160
+لأ لحظة ال F .. ال F المفروض عكسها ضربها .. احنا
+
+818
+01:01:35,160 --> 01:01:39,720
+كنا كاتبين توينا مثلين صح؟لو ال inverse تبعها
+
+819
+01:01:39,720 --> 01:01:42,900
+الاصل composition صح كلامك صحيح composition لأنه
+
+820
+01:01:42,900 --> 01:01:45,920
+فعلا في الآخر المفروض كله هيتشطب مع بعضه لو عملت
+
+821
+01:01:45,920 --> 01:01:49,640
+ال composition مع ال inverse تبعتها هتلاقي ان كل
+
+822
+01:01:49,640 --> 01:01:54,080
+ال X هتتشطب مع بعض كل X هتتشطب مع بعض كلامك صحيح
+
+823
+01:01:54,080 --> 01:01:58,120
+عشان تطلع identity function المفروض هتكون مع ال
+
+824
+01:01:58,120 --> 01:02:01,980
+composition composition طيب ال ه هنتكلم عن
+
+825
+01:02:01,980 --> 01:02:07,710
+identity function ال identity function fromA to A
+
+826
+01:02:07,710 --> 01:02:16,450
+بنكتبها as identity A أو one أو one for A is the
+
+827
+01:02:16,450 --> 01:02:20,570
+unique function such that for all A belong to A
+
+828
+01:02:20,570 --> 01:02:25,650
+identity function of A بساوي A ال identity
+
+829
+01:02:25,650 --> 01:02:30,030
+function of A بتساوي A تمام؟إذا تحقق الكلام هدف
+
+830
+01:02:30,030 --> 01:02:33,450
+إذا هدف نقدر نقول أنها identity function في الحالة
+
+831
+01:02:33,450 --> 01:02:36,230
+التاعتناه طبعا احنا اتعاملنا معها كتير اتعاملتوا
+
+832
+01:02:36,230 --> 01:02:42,730
+معها كتير في ال .. ال summation كان zero ال
+
+833
+01:02:42,730 --> 01:02:45,990
+summation zero لما بتشمعوا مع zero ال element
+
+834
+01:02:45,990 --> 01:02:48,530
+بتظهر زي ما هو ال element بتظهر زي ما هو او لما
+
+835
+01:02:48,530 --> 01:02:52,770
+كنتوا بتعملوا multiplication by one by one او
+
+836
+01:02:52,770 --> 01:02:58,610
+بتعملوا and مع ال trueصحيح؟ إذا كان false بتظهر
+
+837
+01:02:58,610 --> 01:03:03,030
+false إذا كان true بتظهر true طيب أو o-ring مع ال
+
+838
+01:03:03,030 --> 01:03:09,390
+false مع false ال union ال union مع ال في أي set
+
+839
+01:03:09,390 --> 01:03:13,510
+union مع في هتظهر نفس ال set طيب ال intersection
+
+840
+01:03:13,510 --> 01:03:18,390
+مع ال universe of discourse هتظهر نفس ال set هي هي
+
+841
+01:03:18,390 --> 01:03:23,530
+طيب note that identity function is both one to one
+
+842
+01:03:23,530 --> 01:03:28,010
+و one to oneone to one و أنتوا ما هي فعليا جاية من
+
+843
+01:03:28,010 --> 01:03:31,870
+ال function، ال function في انفرس ف one to one و
+
+844
+01:03:31,870 --> 01:03:34,630
+أنتوا ما انزلك ان هي bijective او bijection
+
+845
+01:03:34,630 --> 01:03:41,010
+function okay بكفي بكفي هنا المرة الجاية يعطيكوا
+
+846
+01:03:41,010 --> 01:03:41,270
+العافية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cd1852e9df65d0ff8868acc89a1a949fd9183286
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/iyuDUY3pzPo_raw.srt
@@ -0,0 +1,3400 @@
+1
+00:00:21,430 --> 00:00:23,510
+بسم الله الرحمن الرحيم والصلاة والسلام على أشرف
+
+2
+00:00:23,510 --> 00:00:26,750
+الأنبياء والرسلين سيدنا محمد وعلى أله وصحبه أجمعين
+
+3
+00:00:27,490 --> 00:00:30,790
+خلصنا المرة اللى فاتت موضوع ال sets و المجموعات و
+
+4
+00:00:30,790 --> 00:00:33,730
+ال .. أخدنا ال theories بتاعتها و اتكلمنا عن
+
+5
+00:00:33,730 --> 00:00:38,090
+مجموعة operators ممكن نطبقها عليها اليوم نبدأ في
+
+6
+00:00:38,090 --> 00:00:40,630
+موضوع جديد اللى هو ال functions وهدي مرة عليكوا
+
+7
+00:00:40,630 --> 00:00:43,030
+جابل هيك بس زى ما قلنا هتتناول .. هتناول ..
+
+8
+00:00:43,030 --> 00:00:48,530
+نتناولها بطريقة تتناسب مع ال discrete تتناسب مع
+
+9
+00:00:48,530 --> 00:00:53,140
+المادة اللى عندى لقى خلصناهاو بدنا نوضح كيف ان كل
+
+10
+00:00:53,140 --> 00:00:57,040
+المواضيع اللي أخدناها سابقا احنا ممكن نعبر عنها as
+
+11
+00:00:57,040 --> 00:01:01,740
+a function .. as a function فنبدأ مع ال function
+
+12
+00:01:01,740 --> 00:01:03,740
+اللي انتوا عارفينها .. انتوا أخدتوا ال function
+
+13
+00:01:03,740 --> 00:01:07,300
+على أساس ان هي .. يعني أخدتوه على أساس ان هي
+
+14
+00:01:07,300 --> 00:01:14,290
+function أو بمعنى variable متغيرindependent مستقل
+
+15
+00:01:14,290 --> 00:01:17,890
+انتوا بتدخله من وين؟ من مجموعة ايش؟ مجموعة
+
+16
+00:01:17,890 --> 00:01:21,390
+universal discourse او مجموعة .. مجموعة حاطينها في
+
+17
+00:01:21,390 --> 00:01:26,870
+set .. هنسميها set Aالقيم اللى موجودة داخل set A
+
+18
+00:01:26,870 --> 00:01:32,230
+نستخدمها علشان نطبق عليها function فنشن معينة
+
+19
+00:01:32,230 --> 00:01:35,410
+الفنشن المعينة دي هتطلع outputs ال outputs هدى
+
+20
+00:01:35,410 --> 00:01:39,850
+هنحطها في set اسمها B فانتوا كنتوا في الآخر
+
+21
+00:01:39,850 --> 00:01:42,950
+بترسموها او بتتكلموا عنها على اساس ان هي f of x
+
+22
+00:01:42,950 --> 00:01:49,110
+فلنقول y of f of x فx كان بالنسبالكوا independent
+
+23
+00:01:49,110 --> 00:01:53,160
+variableمستقلها ده اللي بدكوا تدخلوه هو ال input
+
+24
+00:01:53,160 --> 00:01:59,140
+لل function وبعدين بناء على ال function او x under
+
+25
+00:01:59,140 --> 00:02:03,120
+the function f كان بيطلعكوا قيمة اسمها y ال y هذه
+
+26
+00:02:03,120 --> 00:02:08,680
+عبارة عن ايش عبارة عن xunder the function f بعد ما
+
+27
+00:02:08,680 --> 00:02:12,760
+طبقنا عليها ال function f بالظبط تماما زي لما
+
+28
+00:02:12,760 --> 00:02:16,600
+تتكلموا عن المراية المراية لما تكون normal انتوا
+
+29
+00:02:16,600 --> 00:02:19,460
+بتشوفوا صورتكوا زي ما انتوا بالظبط يعني كأنها f of
+
+30
+00:02:19,460 --> 00:02:22,960
+x y بتسوي x انتوا بتشوفوا صورتكوا زي ما انتوا
+
+31
+00:02:22,960 --> 00:02:26,350
+شايفينها ولكن افرض ان هي مقعرة او محددةانتوا
+
+32
+00:02:26,350 --> 00:02:29,130
+هتشوفوا صورة تانية، ايش الصورة اللي انتوا شايفينها
+
+33
+00:02:29,130 --> 00:02:32,750
+في المرايا؟ هي صورتكوا بعد تطبيق ال function
+
+34
+00:02:32,750 --> 00:02:35,250
+عليها، ايش هي ال function؟ ال .. سطح ال ..
+
+35
+00:02:35,250 --> 00:02:39,490
+المرايا، سطح المرايا، تمام؟ فهتلاقوا .. طب انا
+
+36
+00:02:39,490 --> 00:02:42,990
+راقول المثال هذا بالعمدان، لإنه هنتكلم عن كلمة
+
+37
+00:02:42,990 --> 00:02:45,730
+image، انه في واحدة منهم image للتانية وفي واحدة
+
+38
+00:02:45,730 --> 00:02:49,030
+pre image للتانية، هنتكلم عليهم عشانك ممكن كان
+
+39
+00:02:49,030 --> 00:02:53,550
+موضوع المرايا هذا كان في الصياق على أساس انه يجرب
+
+40
+00:02:53,550 --> 00:02:58,010
+المفهوم عندناتمام ففي الآخر أنا بتعامل مع function
+
+41
+00:02:58,010 --> 00:03:05,290
+بقول أن هي y equal to f of x و y belong to R و x
+
+42
+00:03:05,290 --> 00:03:08,270
+طبعا أساسا كانت برضه belong to R فانا عندي ال
+
+43
+00:03:08,270 --> 00:03:12,170
+universe of discourse ل x هي ال real numbers و
+
+44
+00:03:12,170 --> 00:03:17,650
+المتوقع أن ال y هيكون برضه ال real numbers ك
+
+45
+00:03:17,650 --> 00:03:22,790
+universe of discourse لهاالـ function نقدر نطبقها
+
+46
+00:03:22,790 --> 00:03:27,390
+على أي shape بحيث انه ممكن تطبق على أي element لأي
+
+47
+00:03:27,390 --> 00:03:34,430
+set بحيث انه يطلعنا element في أي set أخرى كيف؟
+
+48
+00:03:34,430 --> 00:03:37,490
+انتوا هالوقت اللي هتتكلموا على ال X ال X هذي زي ما
+
+49
+00:03:37,490 --> 00:03:40,110
+قلنا احنا belong to ايه؟ to R حسب ال example اللي
+
+50
+00:03:40,110 --> 00:03:44,070
+قعدتنا يعني معناته ال R تبعتنا هذي صارت هي ايه؟ ال
+
+51
+00:03:44,070 --> 00:03:52,340
+setبتاعة x هي set x element منها okay عشان يطلعنا
+
+52
+00:03:52,340 --> 00:03:58,600
+set أخرى تمثل ايش تمثل جميع ال elements ل y اللي
+
+53
+00:03:58,600 --> 00:04:04,000
+استخرجناهم من كل ال elements بتاعة x تمام فحسب
+
+54
+00:04:04,000 --> 00:04:06,660
+اللي موجود عندنا طلعت برضه belong to ايش to R
+
+55
+00:04:06,660 --> 00:04:11,740
+فبرضه احنا استنتجنا set from other set from other
+
+56
+00:04:11,740 --> 00:04:15,270
+setطبعا other set معناته بدي أعمل applying لمين
+
+57
+00:04:15,270 --> 00:04:18,790
+لكل ال elements داخل ال set عشان أطلع منهم مين
+
+58
+00:04:18,790 --> 00:04:23,770
+مجموعة elements يمثلوا ل set جديدة يمثله set جديدة
+
+59
+00:04:23,770 --> 00:04:27,730
+تمام formally كيف ممكن نكتب هذا الكلام ده هنقول
+
+60
+00:04:27,730 --> 00:04:33,590
+انه لأي two sets هنتعامل مع two sets A وB بنقدر
+
+61
+00:04:33,590 --> 00:04:37,630
+نقول ان هو يمثل او نقدر نمثل ال function a
+
+62
+00:04:37,630 --> 00:04:44,040
+function F from A to Bأو ال function f mapping a
+
+63
+00:04:44,040 --> 00:04:50,780
+to b تعمل mapping من a to b relation علاقة بين a و
+
+64
+00:04:50,780 --> 00:04:56,480
+b بين a و b أو هي عبارة عن function ديالة من set a
+
+65
+00:04:56,480 --> 00:05:03,540
+to set b فبقول ال function f from set a to set b
+
+66
+00:05:03,540 --> 00:05:08,160
+هنا ايه هذه؟ هذه ال universe of discourse لمين؟ لل
+
+67
+00:05:08,160 --> 00:05:14,220
+exceptأولا ال a أنا باخد منها قيم small a اللي هي
+
+68
+00:05:14,220 --> 00:05:16,480
+القيمة اللي هتطبق عليها ال function عشان تطلعلي
+
+69
+00:05:16,480 --> 00:05:20,680
+مين تطلعلي b و b ال small b هذه هتكون belong to
+
+70
+00:05:20,680 --> 00:05:29,100
+set B okay فهي في الآخر مدام هتطلعنا ناتج belong
+
+71
+00:05:29,100 --> 00:05:34,520
+to B معناته ال F of X هي belong to B لأن ال F of X
+
+72
+00:05:34,520 --> 00:05:42,770
+هذه هي تمثل لنا ال D smallتمثل بي small كويسة من
+
+73
+00:05:42,770 --> 00:05:48,390
+وين جيبناها من تطبيق x على ال function أو ال
+
+74
+00:05:48,390 --> 00:05:52,690
+function applied على ال value x و x هذه لازم تكون
+
+75
+00:05:52,690 --> 00:05:57,630
+belonging to mean to a فإذا أنا محكوم هنا بال two
+
+76
+00:05:57,630 --> 00:06:02,940
+setsصرت محكوم أن ال input لازم يكون belong to set
+
+77
+00:06:02,940 --> 00:06:06,740
+A و ال output لازم يكون belong to set B فهذا
+
+78
+00:06:06,740 --> 00:06:09,080
+تعريفنا لمين لل function حتى اللحظة
+
+79
+00:06:12,350 --> 00:06:15,770
+الـ total ممكن في الأخر الـ function if assigns 0
+
+80
+00:06:15,770 --> 00:06:19,890
+or 1 elements of B ممكن مايكونولوش نتيجة في B و
+
+81
+00:06:19,890 --> 00:06:24,290
+يكون خارج ال .. ال .. ال .. ال domain تبعنا أو
+
+82
+00:06:24,290 --> 00:06:28,290
+يكون خارج ال set B أو ممكن يكون عبارة عن element
+
+83
+00:06:28,290 --> 00:06:34,790
+واحد بس أكتر لأ بمعنى لكل input المفروض مايكونش
+
+84
+00:06:34,790 --> 00:06:38,590
+فيه two outputs ان ال output يكون له two inputs
+
+85
+00:06:38,590 --> 00:06:43,570
+ماشيزي التربيع زي التربيع فهمناها ماشي تربيع
+
+86
+00:06:43,570 --> 00:06:47,510
+مقبولة ان يكون في عندكم function تربيع two inputs
+
+87
+00:06:47,510 --> 00:06:51,530
+بيعطينا نفس ال output فليكن ماشي نفترض انه minus
+
+88
+00:06:51,530 --> 00:06:55,270
+two two بيعطينا أربعة التنتين هيعطينا نفس ال
+
+89
+00:06:55,270 --> 00:07:01,660
+output مقبولة ولكن input واحد يعطينا twooutputs لا
+
+90
+00:07:01,660 --> 00:07:04,640
+يمكن لأن حتى ال system اللي بنتكلم عنه هنا بصير
+
+91
+00:07:04,640 --> 00:07:08,380
+unstable و بصير فيه مشكلة في ال system تبعنا، هذه
+
+92
+00:07:08,380 --> 00:07:11,380
+بنقدر نقول عنها أنها مش function من أصله، إذا مرت
+
+93
+00:07:11,380 --> 00:07:14,300
+عليكم، اتعاملوا معاها أن هذه مش function، مش هينفع
+
+94
+00:07:14,300 --> 00:07:18,920
+نتعامل معاها، مش هينفع نتعامل معاها، في الحالة
+
+95
+00:07:18,920 --> 00:07:23,960
+تاعتنا تخيلوا تماما بالظبط زي لو أنه الزمن هو ال X
+
+96
+00:07:23,960 --> 00:07:27,900
+وال location اللي احنا واقفين فيه هذا ال Y، أنا
+
+97
+00:07:27,900 --> 00:07:33,300
+عند كل time أنا وين موجودطب هل بقدر .. هل بنقدر في
+
+98
+00:07:33,300 --> 00:07:36,540
+نفس اللحظة في نفس ال input في نفس ال time أكون
+
+99
+00:07:36,540 --> 00:07:40,060
+موجود في مكانين في two locations؟ لا يمكن .. لا
+
+100
+00:07:40,060 --> 00:07:42,700
+يمكن بقدر أقول إن والله أنا سريع لدرجة إن ممكن في
+
+101
+00:07:42,700 --> 00:07:45,280
+.. في أقل وقت ممكن أكون انتقلت من واحد لو واحد
+
+102
+00:07:45,280 --> 00:07:49,260
+ماشي فال slope تبعي يكون كتير عالي كقيمة ك
+
+103
+00:07:49,260 --> 00:07:52,320
+absolute قيمته عالية المعدل التغير عالي بس إنه
+
+104
+00:07:52,320 --> 00:07:55,460
+أكون في نفس اللحظة لا يمكن فعشان هيك ال output
+
+105
+00:07:55,460 --> 00:08:00,320
+لازم يكون جاي من inputمن input واحدة و ال input
+
+106
+00:08:00,320 --> 00:08:03,440
+الواحدة لايمكن نطلع لنا two outputs لايمكن من
+
+107
+00:08:03,440 --> 00:08:08,340
+input واحدة يكون two outputs okay graphical
+
+108
+00:08:08,340 --> 00:08:13,640
+representations لمن ل ال .. ل ال set .. لل
+
+109
+00:08:13,640 --> 00:08:16,020
+functions عفوا ل ال functions فحنبدأ بإيش بال Venn
+
+110
+00:08:16,020 --> 00:08:20,220
+diagram Venn diagram هنقول أننا set A مجموعة ال
+
+111
+00:08:20,220 --> 00:08:26,270
+elements اللي مسموح ليه أطبقها ك Xفى f of x فى f
+
+112
+00:08:26,270 --> 00:08:31,210
+of x بحيث ان هي تعطينى outputs كل ال outputs هذه
+
+113
+00:08:31,210 --> 00:08:35,050
+موجودة فى set تانية بتسميها b فهيكون في عندنا from
+
+114
+00:08:35,050 --> 00:08:40,990
+a to b فى function f ال function f هذه عبارة عن
+
+115
+00:08:40,990 --> 00:08:47,720
+ايش هي عبارة عن function fromA1 مثلا to B1 فإذا
+
+116
+00:08:47,720 --> 00:08:53,540
+طبقنا ال function على ال element A1 هيعطينا ناتج
+
+117
+00:08:53,540 --> 00:08:59,240
+B1 بي سمول طبعا مجموعة elements فكل element موجود
+
+118
+00:08:59,240 --> 00:09:05,440
+هنا لازم يكون الناتج تبعه موجود في ال set BOkay
+
+119
+00:09:05,440 --> 00:09:11,060
+هذا عن طريق Venn diagram طيب bipartate graph ال
+
+120
+00:09:11,060 --> 00:09:15,060
+bipartate graph هيكون عندنا two parts أو two
+
+121
+00:09:15,060 --> 00:09:18,300
+columns ال column الأول عبارة عن dots ال dots هذه
+
+122
+00:09:18,300 --> 00:09:21,100
+تمثل ال elements بتاعة ال input
+
+123
+00:09:25,910 --> 00:09:31,250
+القلم التاني يمثل برضه مجموعة dots عبارة عن ال
+
+124
+00:09:31,250 --> 00:09:37,750
+elements داخل set B فبنعمل relation إذا كان ال
+
+125
+00:09:37,750 --> 00:09:43,070
+element الأول في set A under the function f
+
+126
+00:09:43,070 --> 00:09:48,650
+بيعطينا العنصر التاني فبنعمل بينهم خط فهنا ال
+
+127
+00:09:48,650 --> 00:09:54,960
+function from first elementA to second element
+
+128
+00:09:54,960 --> 00:09:59,740
+from B تمام؟ بنرسمها سهل على أساس أنه under the
+
+129
+00:09:59,740 --> 00:10:02,800
+function في relation between ال element هذا و ال
+
+130
+00:10:02,800 --> 00:10:05,340
+element هذا طيب بين ال element التاني و ال element
+
+131
+00:10:05,340 --> 00:10:09,920
+الأول ممكن في الآخر بنرسم طبيعة أو ال function
+
+132
+00:10:09,920 --> 00:10:15,740
+from A to Bfrom element موجود في set A to element
+
+133
+00:10:15,740 --> 00:10:20,420
+موجود في set B هذه طريقة تانية برضه في ال
+
+134
+00:10:20,420 --> 00:10:23,340
+representation لل function طريقة التالتة اللي
+
+135
+00:10:23,340 --> 00:10:28,240
+انتوا عارفينها ال blood ال dots هذه بتحطوا عند كل
+
+136
+00:10:28,240 --> 00:10:31,280
+X مجدش قيمة Y بتاعتها فبتحطوا مجموعة نقاط و بعدين
+
+137
+00:10:31,280 --> 00:10:35,290
+بترسموهاالـ plot تبعكم فبترسموه الشكل ال function
+
+138
+00:10:35,290 --> 00:10:37,610
+بهذا الشكل و يمكن انتوا متعودين على النوع هذا
+
+139
+00:10:37,610 --> 00:10:42,450
+بيعطيكوا التصور ان كيف relation between ال X و ال
+
+140
+00:10:42,450 --> 00:10:46,730
+Y ال X و ال Y طبعا احنا بنتكلم ان ال X هتكون
+
+141
+00:10:46,730 --> 00:10:51,890
+belong to ايهto set a و ال y belong to set b اللي
+
+142
+00:10:51,890 --> 00:10:55,970
+هي عبارة عن f of x دي يبقى عارف عن f of x okay
+
+143
+00:10:55,970 --> 00:10:59,630
+functions احنا اتعاملنا معاها حتى اللحظة في
+
+144
+00:10:59,630 --> 00:11:01,990
+functions كتير احنا اتعاملنا معاها حتى اللحظة و
+
+145
+00:11:01,990 --> 00:11:04,950
+اتكلمنا يمكن عنها من أهمها اللي هي ال proposition
+
+146
+00:11:04,950 --> 00:11:08,690
+ال proposition لما كنا بنتكلم عن ال proposition
+
+147
+00:11:08,690 --> 00:11:12,490
+يعتمد على situation معين زي ال example اللي بيبقى
+
+148
+00:11:12,490 --> 00:11:16,550
+عني it's raining تشتي لو قولنا الكلام هذا اليوم
+
+149
+00:11:16,550 --> 00:11:21,090
+هتقولوا falseطب لو قلناها قبل العيد أسبوع زمان
+
+150
+00:11:21,090 --> 00:11:23,550
+كانت بتشتي، لو قلناها في وجتها، في ال situation
+
+151
+00:11:23,550 --> 00:11:26,470
+هداك، كان قولنا true، فإذا معتمدين على ال
+
+152
+00:11:26,470 --> 00:11:29,350
+situation، فهنا بعتبر .. بتعمل مع ال proposition
+
+153
+00:11:29,350 --> 00:11:34,320
+كأنها function of situationحسب ال situation حسب
+
+154
+00:11:34,320 --> 00:11:38,200
+الحالة حسب ال state الوضع اللي احنا فيه حسب الحالة
+
+155
+00:11:38,200 --> 00:11:41,340
+بتاعتنا بقدر اقول ان هو true or false يعني بتتغير
+
+156
+00:11:41,340 --> 00:11:46,440
+بناء على الحالة بناء على الحالة اما true or false
+
+157
+00:11:46,440 --> 00:11:50,100
+فهذه logical system بنسميها situation theory
+
+158
+00:11:50,100 --> 00:11:55,840
+situation theory okay زي ما قلنا it's raining ال S
+
+159
+00:11:55,840 --> 00:12:00,550
+هنا our situation here حالياour situation بناة
+
+160
+00:12:00,550 --> 00:12:04,410
+عادية بقدر أقرر أما تقولولي والله كمان شهر هتكون
+
+161
+00:12:04,410 --> 00:12:10,290
+بتشتي هقولكوا بعرفش يعني حتى التنبؤات أو التوقعات
+
+162
+00:12:10,290 --> 00:12:14,510
+الجوية قبل بيوم يومين ممكن يتوقعوا لنا بس تقولولي
+
+163
+00:12:14,510 --> 00:12:18,530
+بعد شهر إيش بدوس بعرفش توقعات بعرفش حسب ال
+
+164
+00:12:18,530 --> 00:12:22,230
+situation في وقتها حسب ال situation في وقتها طيب
+
+165
+00:12:22,230 --> 00:12:25,690
+فبنقدر نقول P of S و ال S دي اللي هي situation
+
+166
+00:12:26,890 --> 00:12:31,810
+هتكون belong to true or false function لحظة هى
+
+167
+00:12:31,810 --> 00:12:33,410
+function هى نوع من أنواع ال functions احنا
+
+168
+00:12:33,410 --> 00:12:36,890
+اتعاملنا مع حاجة بالهك هى نوضح انه كانت عبارة عن
+
+169
+00:12:36,890 --> 00:12:41,410
+function quick propositional operator ال operators
+
+170
+00:12:41,410 --> 00:12:43,910
+اللي أخدناها أخدنا ايش أخدنا ال and أخدنا ال or
+
+171
+00:12:43,910 --> 00:12:46,730
+أخدنا ال negation أخدنا ال x or أخدنا ال .. كل
+
+172
+00:12:46,730 --> 00:12:50,610
+هدولة بنقدر نمثلهم ك function ك function كيف لحظة
+
+173
+00:12:50,610 --> 00:12:55,530
+بقدر أقول ان هو or of x
+
+174
+00:12:57,830 --> 00:13:05,290
+هذه الوقت لما أقول لكم f of x مش هاد هيك function
+
+175
+00:13:05,290 --> 00:13:10,990
+محتاجة input عشان اطلع output هي ايش ال function
+
+176
+00:13:10,990 --> 00:13:17,150
+اكتر من هيك output بطلع بناء على input under the
+
+177
+00:13:17,150 --> 00:13:20,350
+function f طب ناخدها شوي شوي ال function هاد بتقول
+
+178
+00:13:20,350 --> 00:13:26,160
+ان هي ال orالـ function ال operator هي ال or بدخل
+
+179
+00:13:26,160 --> 00:13:29,180
+إلى مجموعة inputs بتطلعلي output مش بدرور يكون
+
+180
+00:13:29,180 --> 00:13:33,300
+زيهم حسب ال condition بالظبط إيش طبيعتي ال input
+
+181
+00:13:33,300 --> 00:13:38,040
+بتطلعلي output بس فيه حالة طريقة بتطلعنا عليها ال
+
+182
+00:13:38,040 --> 00:13:42,240
+output هنا بدنا نفتح الأقواص و بدنا ندخل ال inputs
+
+183
+00:13:42,240 --> 00:13:47,200
+طب هد احنا عارفين إن هي binary operatorيعني محتاجة
+
+184
+00:13:47,200 --> 00:13:51,600
+two inputs فال two inputs ساعتنا بدنا ندخلهم على
+
+185
+00:13:51,600 --> 00:13:59,360
+أساس إن هم زوج if true هاي ال inputs تبعوننا فهذه
+
+186
+00:13:59,360 --> 00:14:05,440
+أصبحت بالنسبالنا كإنها if or ت
+
+187
+00:14:05,440 --> 00:14:10,020
+تمام أتوقع هيك صارت function هيك أصبحت function
+
+188
+00:14:10,020 --> 00:14:15,590
+بقدر أطلّق النتج تبعهاtrue فإذا بقدر أقول إنه هذا
+
+189
+00:14:15,590 --> 00:14:20,410
+true ال y true إنها تجي true فلاحظوا function هي
+
+190
+00:14:20,410 --> 00:14:25,630
+في النهاية عبارة عن function القيمة بتاعتها true
+
+191
+00:14:25,630 --> 00:14:29,970
+طبعا مهم جدا الترتيب في بعضهم ممكن مايكونش مهم في
+
+192
+00:14:29,970 --> 00:14:33,250
+بعضهم مهم بس الأحواط أنكم تاخدوا بالكم من الترتيب
+
+193
+00:14:33,250 --> 00:14:36,670
+ليش لأنه ممكن تجيكوا ال implication ال implication
+
+194
+00:14:36,670 --> 00:14:40,980
+هذا طبعا هتخرب ال ..ال .. الترتيب إذا انتوا خرّبته
+
+195
+00:14:40,980 --> 00:14:42,960
+يعني إذا انتوا حطيتوا التانية أولى و الأولى تانية
+
+196
+00:14:42,960 --> 00:14:48,280
+هتفرق معناه لو قولنا ال implication of true و
+
+197
+00:14:48,280 --> 00:14:49,680
+false
+
+198
+00:14:55,710 --> 00:14:59,950
+ماحدش يتعامل معاها عشان ان هي false employs true
+
+199
+00:14:59,950 --> 00:15:05,790
+لحظة غيرته هي كلمته للنتج لأ ان اتعامل معاها
+
+200
+00:15:05,790 --> 00:15:10,890
+بترتيبها حسب ترتيبها ف true employs false طبعا
+
+201
+00:15:10,890 --> 00:15:15,250
+واضح هتطلع ال output تبعها او ال y بتاعتها false
+
+202
+00:15:15,250 --> 00:15:19,930
+تمام واضحة هي هذا برضه انه احنا خدناه اتكلمنا عنه
+
+203
+00:15:19,930 --> 00:15:25,160
+هنا بنقدر نمثله as a function كويسةاشي تاني ال
+
+204
+00:15:25,160 --> 00:15:28,240
+predicate لما اتكلمنا في ال predicate هي اصلا كانت
+
+205
+00:15:28,240 --> 00:15:30,860
+عبارة عن a propositional function اصلا هي اصلا
+
+206
+00:15:30,860 --> 00:15:33,480
+كانت عبارة عن a propositional function و لو
+
+207
+00:15:33,480 --> 00:15:38,120
+متذكرين اتكلمنا عن مش عارف احنا ميسمينا كان Mike
+
+208
+00:15:38,120 --> 00:15:42,520
+gave Mary a grade A متذكرينه؟ طب ما هي برضه هي
+
+209
+00:15:42,520 --> 00:15:44,820
+عبارة عن variables لما ده ما حطيت variables أصبحت
+
+210
+00:15:44,820 --> 00:15:49,320
+function لما نقول مثلا be a predicate is seven
+
+211
+00:15:49,320 --> 00:15:54,600
+feet tallلما اقول والله ال .. ال predicate تبعتنا
+
+212
+00:15:54,600 --> 00:15:56,860
+ال predicate تبعتنا او ال propositional function
+
+213
+00:15:56,860 --> 00:16:03,820
+بتاعتنا هي انه كذا يكون سبع أقدام طولا سبع أقدام
+
+214
+00:16:03,820 --> 00:16:08,360
+طولا يعني في حدود يمكن متين و عشرة سانتي متين و
+
+215
+00:16:08,360 --> 00:16:11,200
+عشرة سانتي طبعا واضح انه هنا بقدرش اقول ان هي
+
+216
+00:16:11,200 --> 00:16:13,800
+biologic دايما true لأ هذا بده اشوف في ال
+
+217
+00:16:13,800 --> 00:16:18,700
+situation تبعنا مين اللي بده يجي قدام x هذا مكان x
+
+218
+00:16:18,700 --> 00:16:23,980
+is seven feet طولفلو قلنا mike و قلنا انه هتصبح P
+
+219
+00:16:23,980 --> 00:16:29,700
+of mike function أصبحت function ال X بتاعتها هي
+
+220
+00:16:29,700 --> 00:16:35,420
+الاسم اللي انا هحطه هنا P of علي P of محمد تمام؟
+
+221
+00:16:35,420 --> 00:16:39,520
+بنجيسه و بنشوف is it true or false؟ false جابل هيك
+
+222
+00:16:39,520 --> 00:16:42,560
+بالشكل هذا مقدرش اقول ان هي true or false قولنا
+
+223
+00:16:42,560 --> 00:16:45,700
+هالكلام هذا السابقا ال predicate ك predicate بحد
+
+224
+00:16:45,700 --> 00:16:49,200
+ذاتها هي مش propositionبقدرش أقول هى true or false
+
+225
+00:16:49,200 --> 00:16:54,140
+ولكن لما هحطلها ال variable تبعها أصبحت بقدر أحكم
+
+226
+00:16:54,140 --> 00:16:56,740
+عليه هى true or false بناء على مين اللى حطته
+
+227
+00:16:56,740 --> 00:17:00,480
+variable بناء على اللى حطنا variable تمام فأصبحت
+
+228
+00:17:00,480 --> 00:17:06,620
+هى واضحة f of x بي of my حطنا variable في ال bit
+
+229
+00:17:06,620 --> 00:17:11,200
+string نفس الكلام بي of length n can be viewed as
+
+230
+00:17:11,200 --> 00:17:16,600
+a function from the numbersone to n هذا بناء على
+
+231
+00:17:16,600 --> 00:17:20,560
+ال index للوكيشن أو ال location نفسه ال index لل
+
+232
+00:17:20,560 --> 00:17:27,360
+elements احنا لما نقول مثلا ال bit string بي one
+
+233
+00:17:27,360 --> 00:17:33,500
+zero one احنا عارفين ان ال bit string مرتب صحيح
+
+234
+00:17:33,500 --> 00:17:37,020
+مهم الترتيب يعني بقدر اتعامل مع ال location
+
+235
+00:17:37,020 --> 00:17:43,450
+بتاعتهم عساس ان هي variableو انا عارف انه دائما في
+
+236
+00:17:43,450 --> 00:17:47,530
+ال bit string هذا اول element دائما هيكون واحد هذا
+
+237
+00:17:47,530 --> 00:17:51,750
+مش زي ال set unordered لأ ال set okay اي واحدة
+
+238
+00:17:51,750 --> 00:17:54,070
+جابت بتانه مش هتفرج كتير بس في ال bit string لأ
+
+239
+00:17:54,070 --> 00:17:57,250
+مهم الترتيب لما اتكلمنا المرة اللي فاتت في ال ..
+
+240
+00:17:57,250 --> 00:18:01,510
+في ال set قولنا انه لما بيصير ordered بصير عندنا
+
+241
+00:18:01,510 --> 00:18:04,710
+بنتكلم عن string فعملنا ال bit string
+
+242
+00:18:04,710 --> 00:18:08,800
+representationلما اتكلمنا عن ال bit .. ال bit
+
+243
+00:18:08,800 --> 00:18:11,760
+string representation قولنا إن دايما ال element
+
+244
+00:18:11,760 --> 00:18:17,080
+الشمال هو ال element الأول هو ال element الأول
+
+245
+00:18:17,080 --> 00:18:20,500
+قولناها فين؟ في آخر محاضرة من المحاضرات أعتقد، في
+
+246
+00:18:20,500 --> 00:18:24,920
+آخر واحدة من المحاضرات، تمام طيب لما نيجي نتكلم عن
+
+247
+00:18:24,920 --> 00:18:28,860
+ال set قولنا قبل هيك ال set هي unordered يعني أنا
+
+248
+00:18:28,860 --> 00:18:32,440
+مقدرش ا .. يعني مقدرش نستفيد من فكرة إيش؟ من فكرة
+
+249
+00:18:32,440 --> 00:18:37,270
+ال location، الترتيبطب ها إيش .. إيش الحاجة اللي
+
+250
+00:18:37,270 --> 00:18:40,030
+.. اللي بتمن دايما إن هي موجودة؟ إنه العنصر موجود
+
+251
+00:18:40,030 --> 00:18:44,890
+أو لأ؟ هذه بالنسبالنا واضحة لإن هو إحنا بنعتمد
+
+252
+00:18:44,890 --> 00:18:47,310
+أساسا في ال set إن هل العنصر موجود أو غير موجود
+
+253
+00:18:47,310 --> 00:18:51,150
+أما وين ال location تبعه؟ ماعناش معلومة ال
+
+254
+00:18:51,150 --> 00:18:53,490
+location تبعه إجا رقم 1، إجا رقم 2، إجا رقم 5، إجا
+
+255
+00:18:53,490 --> 00:18:57,270
+رقم 10، إجا أخر element مش هتفرق بمعنى إن لو عندنا
+
+256
+00:18:57,270 --> 00:19:05,830
+ال set S عبارة عن one, two, threeأجى واحد كتب ليها
+
+257
+00:19:05,830 --> 00:19:09,110
+طبعا كويس أن تكون مرتبة مش غلط ولكن اجى واحد كتب
+
+258
+00:19:09,110 --> 00:19:15,830
+ليها اتنين واحد تلاتة المهم ان ال elements موجودة
+
+259
+00:19:15,830 --> 00:19:20,030
+ال elements كاملة موجودة مش متكررة و لا يعني بمعنى
+
+260
+00:19:20,030 --> 00:19:22,550
+لو بدي اعملها cardinality بقدر اجيبهم و خلاص يعني
+
+261
+00:19:22,550 --> 00:19:24,770
+كل ال operations اللي انا محتاجها بقدر اطلحها
+
+262
+00:19:24,770 --> 00:19:27,690
+بنقدر نشتغل عليها بما فيها ال function فهنا ال
+
+263
+00:19:27,690 --> 00:19:30,450
+function بتصير function في مين في ال element نفسه
+
+264
+00:19:31,850 --> 00:19:35,490
+كفنكشن بتصير في ال element نفسه وبتصير الناتج تبعي
+
+265
+00:19:35,490 --> 00:19:41,370
+true or false belong to or not belong to هل هو ال
+
+266
+00:19:41,370 --> 00:19:45,510
+element اللي أعطانيها ك variable belong to بحطله
+
+267
+00:19:45,510 --> 00:19:53,110
+true not belong to بحطله F زي لو قلنا ال set S
+
+268
+00:19:53,110 --> 00:19:58,370
+equal toElement 3 بس هي عبارة عن set تحتوي على
+
+269
+00:19:58,370 --> 00:20:02,430
+element واحد فلو قلنا S of 0 فالـ false لأن ال
+
+270
+00:20:02,430 --> 00:20:06,590
+zero غير موجود ال element zero مش موجود هنا ولكن S
+
+271
+00:20:06,590 --> 00:20:12,170
+of 3 موجود بقول true فهي برضه تعاملنا مع ال set as
+
+272
+00:20:12,170 --> 00:20:17,570
+a function معها as a function الكلام اللي قلناه في
+
+273
+00:20:17,570 --> 00:20:20,610
+ال or قبل شويةفي ال operator اللي خاصة بال
+
+274
+00:20:20,610 --> 00:20:23,010
+proposition بنقدر نقوله برضه في ال operator اللي
+
+275
+00:20:23,010 --> 00:20:26,650
+خاصة بيه بال sets بال sets اللي هي مين ال
+
+276
+00:20:26,650 --> 00:20:32,410
+intersection union way complement تمام بقولش هنا
+
+277
+00:20:32,410 --> 00:20:36,270
+negation كانت في ال proposition زي لما قلت هنا
+
+278
+00:20:36,270 --> 00:20:39,730
+intersection ماقلتش and هنا intersection فهنا
+
+279
+00:20:39,730 --> 00:20:44,100
+complement تماماللي هي ال operators واحدة و بتحس
+
+280
+00:20:44,100 --> 00:20:47,420
+أن تأثيرها واحد بس طبعا بناء على انا applied على
+
+281
+00:20:47,420 --> 00:20:50,780
+إيش بتتغير المصطلح تبعها بتتغير المصطلح فهذه
+
+282
+00:20:50,780 --> 00:20:55,580
+compliment okay نقدر نقولها function على أساس إن
+
+283
+00:20:55,580 --> 00:20:58,920
+أنا بعمل نفس الفكرة زي ما كنا نتوي or لأ هي ال
+
+284
+00:20:58,920 --> 00:21:02,840
+function تبعت هنا intersection وهي فتحنا الأقوات
+
+285
+00:21:02,840 --> 00:21:06,560
+بتاعة ال functionطيب انحدد ال inputs ال inputs
+
+286
+00:21:06,560 --> 00:21:10,540
+طبعا مش بده تكون sets لان انا بتعامل مع operator ل
+
+287
+00:21:10,540 --> 00:21:15,560
+sets فاتوقع ان ال input لازم تكون sets عشان من ال
+
+288
+00:21:15,560 --> 00:21:17,980
+sets هدولة من ال two sets هدولة و من ال function
+
+289
+00:21:17,980 --> 00:21:22,800
+اطلق الناتج اللي هو عبارة عن جديش تلاتة الناتج
+
+290
+00:21:22,800 --> 00:21:25,060
+هيكون تلاتة اللي هو ال intersection between ال two
+
+291
+00:21:25,060 --> 00:21:31,440
+sets اللي قدامنا هدولة تمام فلاحظوا برضه بنتعامل
+
+292
+00:21:31,440 --> 00:21:39,060
+معها setas a function okay خلصنا من توضيح ان احنا
+
+293
+00:21:39,060 --> 00:21:42,480
+فعلا اتعاملنا مع functions كتيرة كنا فعلا نتعامل
+
+294
+00:21:42,480 --> 00:21:46,640
+معها و بتقدر هنا نكتبها بشكل function مع كل
+
+295
+00:21:46,640 --> 00:21:52,100
+المواضيع او ال subjects اللي احنا شرحناها نجي شوية
+
+296
+00:21:52,100 --> 00:21:54,880
+terminology انركز شوية في مين؟ في ال function
+
+297
+00:21:54,880 --> 00:21:58,320
+نفسها خلينا نركز في ال function انركز في ال
+
+298
+00:21:58,320 --> 00:22:00,340
+function احنا عرفنا ال function ان هي ال function
+
+299
+00:22:00,340 --> 00:22:07,500
+f from a to bset A to set B معناته ال input إجباري
+
+300
+00:22:07,500 --> 00:22:11,140
+لازم يكون belong to mean to set A و ال output لازم
+
+301
+00:22:11,140 --> 00:22:17,200
+يكون belong to set B okay and F of A و A هذه لازم
+
+302
+00:22:17,200 --> 00:22:23,680
+تكون belong to capital A to set A equal to B بحيث
+
+303
+00:22:23,680 --> 00:22:27,960
+أنه زي ما قلنا A belong to set A و B belong to set
+
+304
+00:22:28,870 --> 00:22:32,390
+Okay إذا فعلا عندنا ال function هذه بنقدر نعمل
+
+305
+00:22:32,390 --> 00:22:35,130
+شوية التسميات هدولة إيش هما التسميات هدولة أو
+
+306
+00:22:35,130 --> 00:22:40,770
+المسميات A اللي هي set A بنسميها domain set A
+
+307
+00:22:40,770 --> 00:22:45,250
+بنسميها domain طيب ال B أو ال set B بنسميها ال
+
+308
+00:22:45,250 --> 00:22:48,710
+codomain codomain تابع لل domain يتبع لل domain
+
+309
+00:22:51,670 --> 00:22:56,730
+مناظر لل domain او مقابل لل domain ال small b
+
+310
+00:22:56,730 --> 00:23:03,270
+يلاحظ انه element او الناتج ال element ويل هي ال
+
+311
+00:23:03,270 --> 00:23:08,810
+ناتج هذا بنسميها ال image of a under function f
+
+312
+00:23:08,810 --> 00:23:12,950
+بمعنى هو a بس بعد ما طبقنا على ال a من ال function
+
+313
+00:23:12,950 --> 00:23:17,850
+fتمام؟ فهي ال image و قلت الكتو الصورة و قلنا
+
+314
+00:23:17,850 --> 00:23:21,210
+الكتو حكاية المراية المراية إذا كان normal ..
+
+315
+00:23:21,210 --> 00:23:24,810
+normal معناته x بتسوي y أو y بتسوي x أو a بتسوي b
+
+316
+00:23:24,810 --> 00:23:29,470
+.. a بتسوي b ف a هتسوي b خلاص أنا في الآخر بتعامل
+
+317
+00:23:29,470 --> 00:23:32,880
+مع أن ال b هي ال image بتاعة aلما أشوف صورتي،
+
+318
+00:23:32,880 --> 00:23:37,340
+صورتي هي ال image تبعتي، هي ال image تبعتي، لو سطح
+
+319
+00:23:37,340 --> 00:23:42,260
+المرايا مقعر محدد فيه أي functionality معينة
+
+320
+00:23:42,260 --> 00:23:45,280
+معمولة فيه، هلاجنه الصورة مختلفة، ولكن هي في
+
+321
+00:23:45,280 --> 00:23:49,080
+النهاية تمثل صورتي برضه، بس under the function
+
+322
+00:23:49,730 --> 00:23:53,510
+under the function بعد ما طبقنا عليها ال function
+
+323
+00:23:53,510 --> 00:23:56,270
+اللي هو سطح المرايا أو المقعرة أو المحدد أو اللي
+
+324
+00:23:56,270 --> 00:24:01,150
+يمثل ب function معينة ال A بالمقابل هي ال pre
+
+325
+00:24:01,150 --> 00:24:06,610
+image هي الصورة المسبقة الصورة المسبقة ل B under
+
+326
+00:24:06,610 --> 00:24:13,430
+the function F under function F okay in general B
+
+327
+00:24:13,430 --> 00:24:17,910
+may have more than one pre image ممكن زي التربيع
+
+328
+00:24:18,830 --> 00:24:23,690
+التربية ممكن يكون لها اكتر من preimage على
+
+329
+00:24:23,690 --> 00:24:26,670
+اعتبار ان هي عندكم مثلا قولناها اتنين و minus
+
+330
+00:24:26,670 --> 00:24:30,210
+اتنين هيكون لهم اتنين القيمتين مثلا اللي هم نفس
+
+331
+00:24:30,210 --> 00:24:36,770
+الاربعة هذه ال image او ال B لها اتنين preimage هي
+
+332
+00:24:36,770 --> 00:24:41,290
+preimage أولى وهي preimage تانية لاحظوا two
+
+333
+00:24:41,290 --> 00:24:45,810
+preimages زي ما قلنا العكس لأ العكس لأ يعني لا
+
+334
+00:24:45,810 --> 00:24:53,280
+يمكن ل a يكون في two imagesلأ يمكن تمام then نتكلم
+
+335
+00:24:53,280 --> 00:24:56,520
+عن ال range هالواجهة ال range هي subset بنسميها R
+
+336
+00:24:56,520 --> 00:25:00,980
+طبعا هي subset من ال code domain جزء من ال code
+
+337
+00:25:00,980 --> 00:25:06,460
+domain of F is set احنا بنتكلم عن subset هيها
+
+338
+00:25:06,460 --> 00:25:11,440
+معناته بتدعرفها as a set فبنحط لها علامات ال set
+
+339
+00:25:11,440 --> 00:25:17,650
+ال curly process تبعتنا of B هي set of Bsuch that
+
+340
+00:25:17,650 --> 00:25:24,010
+there exists a which is a pre-image a تنتج لنا b
+
+341
+00:25:24,010 --> 00:25:29,090
+معناته هي في النهاية set لمجموعة outputs outputs
+
+342
+00:25:29,090 --> 00:25:32,830
+مش ال b عرفناها أساسا هي ال output ال outputs انه
+
+343
+00:25:32,830 --> 00:25:36,230
+يوجد قيم لل outputs او كل قيم ال outputs اللي
+
+344
+00:25:36,230 --> 00:25:45,150
+ناتجة من applied او تطبيق ال f على كل قيم aبمعنى
+
+345
+00:25:45,150 --> 00:25:49,390
+هي ال actual output هي ال actual ال experimental
+
+346
+00:25:49,390 --> 00:25:54,490
+output هو التجريب فعلا ان انا جربت كل قيم a امسكت
+
+347
+00:25:54,490 --> 00:25:58,530
+ال set a كل القيم اللي فيها جربتهم under the
+
+348
+00:25:58,530 --> 00:26:01,930
+function طلعنا ناتج الناتج هذا حطناه في set
+
+349
+00:26:01,930 --> 00:26:06,970
+سميناها R actual هذا هذا الحقيقي هذا الناتج الفعلي
+
+350
+00:26:06,970 --> 00:26:09,610
+الناتج الفعلي لل function
+
+351
+00:26:12,640 --> 00:26:17,600
+Range vs Codomain هدى إشي و هدى إشي ال Codomain زى
+
+352
+00:26:17,600 --> 00:26:21,560
+ما قلنا احنا هي ال domain المقابل أو المظير لل
+
+353
+00:26:21,560 --> 00:26:26,040
+domain لل input و هدى بتكون عبارة عن ال P جبل ما
+
+354
+00:26:26,040 --> 00:26:28,820
+نطبق لسه ال function اللى هو متوقع أنه هتكون ..
+
+355
+00:26:28,820 --> 00:26:31,440
+لما نتكلم عن ال real number بالنسبة لل domain
+
+356
+00:26:31,440 --> 00:26:35,360
+متوقع أنه برضه انه هتكون كلها real number فبقول ان
+
+357
+00:26:35,360 --> 00:26:39,860
+هي belong to R to real number طب actuallyخلّينا
+
+358
+00:26:39,860 --> 00:26:44,280
+ندخل القيم exactly بالظبط اللي داخل ال set A،
+
+359
+00:26:44,280 --> 00:26:49,500
+نطبقهم under the function و نشوف actual outputs،
+
+360
+00:26:49,500 --> 00:26:53,040
+نطلع النتائج الحقيقية، النتائج الحقيقية بنحصرها،
+
+361
+00:26:53,040 --> 00:26:58,060
+بنقول هذه ايش؟ R، هذه ال range، هذه R أو ال range،
+
+362
+00:26:58,060 --> 00:27:02,510
+تمامفبتعمل mapping زى ما قلنا فى الآخر ال code
+
+363
+00:27:02,510 --> 00:27:06,970
+domain هذا بيعمل map لكل ال domain values او هم
+
+364
+00:27:06,970 --> 00:27:11,210
+التصريح لل domain هو التصريح لل domain مادام ال
+
+365
+00:27:11,210 --> 00:27:13,830
+domain real numbers معناته ال code domain بيكون
+
+366
+00:27:13,830 --> 00:27:18,910
+real numbers بالعموم actual لأ بتصير اسمها range
+
+367
+00:27:18,910 --> 00:27:21,970
+actual لما نيجى نطبقها واحدة واحدة بتصير اللى هى
+
+368
+00:27:21,970 --> 00:27:25,070
+ال range او اللى هى ال actually maps elements of
+
+369
+00:27:25,070 --> 00:27:30,110
+the domainexample ناخد example على الموضوع خلينا
+
+370
+00:27:30,110 --> 00:27:34,550
+نقول انه انه عندنا function if is a function
+
+371
+00:27:34,550 --> 00:27:38,470
+mapping students in the class في ال class تبعنا to
+
+372
+00:27:38,470 --> 00:27:42,210
+ish to set of grades لمجموعة ال grades ساعتنا او
+
+373
+00:27:42,210 --> 00:27:47,490
+التقديرات بتاعتنا التقديرات اللي هي ish a b c d e
+
+374
+00:27:47,490 --> 00:27:50,950
+بدل ال .. بدل التاني يعني لأنه ما .. ماعتقدش انه
+
+375
+00:27:50,950 --> 00:27:54,190
+في grade a .. e بس احنا زى ما بقول ال .. بدناه
+
+376
+00:27:54,190 --> 00:27:59,520
+عشان هشيل ال ..عنا خمسة grades و بدنا نوزع الطلاب
+
+377
+00:27:59,520 --> 00:28:02,960
+عليهم طبيعي احنا لسه ماعملناش امتحانات انا مش عارف
+
+378
+00:28:02,960 --> 00:28:05,980
+فإذا كان at this point ان احنا لسه ماعملناش اي
+
+379
+00:28:05,980 --> 00:28:09,960
+امتحان عشان اعرف كيف اوزع ففي الحالة هذه ال code
+
+380
+00:28:09,960 --> 00:28:14,220
+domain ايش هيكون كلهم ال code domain كلهم هذا مش
+
+381
+00:28:14,220 --> 00:28:18,320
+هيتغير ال code domain كلهم طيب ال range لسه
+
+382
+00:28:18,320 --> 00:28:23,620
+ماعملناش اشي and none انا مش عارفأنا مش عارف، لأ
+
+383
+00:28:23,620 --> 00:28:26,720
+احنا مش عارفين، احنا لسه .. ماقيمناش لسه، فاحنا مش
+
+384
+00:28:26,720 --> 00:28:29,620
+عارفين، لإنه ماعنديش أي معلومة، ماعنديش function،
+
+385
+00:28:29,620 --> 00:28:31,480
+ماعندي .. ال function في النهاية اللي هي إيش كانت
+
+386
+00:28:31,480 --> 00:28:34,800
+المفروض .. الامتحان، الامتحان هيكون هو ال function
+
+387
+00:28:35,650 --> 00:28:40,050
+بنان على نواة نتائج الامتحان بنحط ال outputs بنحط
+
+388
+00:28:40,050 --> 00:28:43,910
+ال outputs فهنا unknown طيب لو بعد الامتحان عملنا
+
+389
+00:28:43,910 --> 00:28:48,530
+مثلا امتحان exam quiz أي شيء و ال grade بتاعتنا
+
+390
+00:28:48,530 --> 00:28:55,590
+turns out all ones and zero and a's and b's فإذا
+
+391
+00:28:55,590 --> 00:28:59,910
+كلهم يا a يا b أي طالبة بلا استثناء لو طلعت اسمها
+
+392
+00:28:59,910 --> 00:29:03,960
+من الكشف هتكون يا a يا bمخدة معدل يا A يا B ففي
+
+393
+00:29:03,960 --> 00:29:07,940
+الحالة هذه بنقول ان ال range ايش A وB فقط ال range
+
+394
+00:29:07,940 --> 00:29:11,660
+تبعنا اللي هو ال actual output ال actual output في
+
+395
+00:29:11,660 --> 00:29:13,920
+ال function تبعنا في الحالة تبعنا ال function
+
+396
+00:29:13,920 --> 00:29:16,140
+تبعنا اللي هو ال test اللي احنا عملنا هاي ال
+
+397
+00:29:16,140 --> 00:29:19,620
+function يمكن نعمل بعد هيك function تانية اختبار
+
+398
+00:29:19,620 --> 00:29:23,180
+تاني test تاني تطلعله output تانية بس حتى اللحظة
+
+399
+00:29:23,180 --> 00:29:25,700
+ال function تبعنا اللي هي الامتحان اللي احنا عملنا
+
+400
+00:29:25,700 --> 00:29:28,940
+عملنا امتحان واحد okay هذا بالنسبالي functionفنكشن
+
+401
+00:29:28,940 --> 00:29:33,800
+بتطلع منه نتائج بتطلع منه نتائج okay الكودومين كله
+
+402
+00:29:33,800 --> 00:29:36,920
+مش هيتغير الكودومين still ABCDE
+
+403
+00:29:39,120 --> 00:29:43,820
+Okay ال operator هي هي اللي نقدر نتعامل زي ما قلنا
+
+404
+00:29:43,820 --> 00:29:49,200
+معاها .. معاهم as a function في الحالة طلعتنا ال
+
+405
+00:29:49,200 --> 00:29:53,720
+set اللي هي ال true and false و ال negation نقدر
+
+406
+00:29:53,720 --> 00:29:59,820
+نتعامل معاه عساس انه NRA operator .. NRA operator
+
+407
+00:29:59,820 --> 00:30:04,620
+و ال and و ال or و ال by و ال union و ال .. كله
+
+408
+00:30:04,620 --> 00:30:09,200
+كله binary كل هدولة binary تمامو احنا شوفناهم اصلا
+
+409
+00:30:09,200 --> 00:30:12,600
+و اتعاملنا معاهم Constructing Function Operators
+
+410
+00:30:12,600 --> 00:30:16,780
+هنا بدنا نبدأ نعمل operators جديدة او نعمل
+
+411
+00:30:16,780 --> 00:30:21,020
+generation ل functions جديدة ل function جديدة منها
+
+412
+00:30:21,020 --> 00:30:23,520
+اول operator بنشتغل عليها نشتغل عليها اللي هي ال
+
+413
+00:30:23,520 --> 00:30:27,300
+dot ال dot الدرب عملية الدرب ال dot اللي انتوا
+
+414
+00:30:27,300 --> 00:30:31,360
+خدتوها سابقا و عارفين عملية ايش الدرب فلو قلنا ان
+
+415
+00:30:31,360 --> 00:30:35,480
+ال dot احنا عارفينها هي عملية operation على set B
+
+416
+00:30:35,480 --> 00:30:40,760
+فانا بعمل درب لل set Bمثلا، معنا ذلك إن أنا بعمل
+
+417
+00:30:40,760 --> 00:30:45,060
+ضرب لل elements اللي داخلها، في الحالة هذه،
+
+418
+00:30:45,060 --> 00:30:48,840
+بنعرفها على أساس إن هي cycle بالشكل هذا solid،
+
+419
+00:30:48,840 --> 00:30:54,420
+solid cycle، نقطة سودة، bold شوية و نقطة سودة،
+
+420
+00:30:54,420 --> 00:30:57,580
+فهذه بعرف إن هي إيش، ال dot، هنطبقها على مين؟ على
+
+421
+00:30:57,580 --> 00:31:02,580
+ال function f from a to bحتى اللحظة تمام هنعوضها
+
+422
+00:31:02,580 --> 00:31:06,500
+من A to B طيب ال binary operator طبعتنا طبعا احنا
+
+423
+00:31:06,500 --> 00:31:10,700
+عارفين لو بنطبخها بس على ال B هي هتكون B في B
+
+424
+00:31:10,700 --> 00:31:15,580
+وبيعطينا ال domain ال codomain B هيكون برضه نواتج
+
+425
+00:31:15,580 --> 00:31:19,160
+من نفس ال function طيب خلينا نطبخها لأ احنا على ال
+
+426
+00:31:19,160 --> 00:31:21,640
+functions ال actual functions طبعتنا اللي بنسرع لو
+
+427
+00:31:21,640 --> 00:31:26,930
+افترضنا ان فينا function Fفنشن g فسيصبح لدينا ايش؟
+
+428
+00:31:26,930 --> 00:31:32,870
+two functions ال two functions from a to b تنتين
+
+429
+00:31:32,870 --> 00:31:35,910
+يتفقوا ان هم هياخدوا ال elements ال inputs بتاعتهم
+
+430
+00:31:35,910 --> 00:31:39,690
+من ال set a و ال outputs بتاعتهم من ال set b
+
+431
+00:31:39,690 --> 00:31:47,070
+فبنعرفهم كتالة if dot g from a to b بنعرفها عساسيا
+
+432
+00:31:47,070 --> 00:31:55,310
+for all a لكل ال inputsبتاعتنا اللي هي belong to
+
+433
+00:31:55,310 --> 00:32:01,590
+set A F dot G of A زي ما قلنا A هذه belong to
+
+434
+00:32:01,590 --> 00:32:06,030
+capital A ممكن تكون أي element داخل ال set A إيش
+
+435
+00:32:06,030 --> 00:32:09,650
+بيساوي ال term هذا بيساوي ال F of A dot G of A
+
+436
+00:32:09,650 --> 00:32:15,680
+بيساوي ناتج الأولى في ناتج التانيةبساوي ناتج
+
+437
+00:32:15,680 --> 00:32:22,080
+الأولى فى ناتج التانية بنكتبها f dot g of a هي
+
+438
+00:32:22,080 --> 00:32:29,720
+عبارة عن f of a dot g of a سهلة مافيش فيها مشكلة
+
+439
+00:32:29,720 --> 00:32:34,800
+ومش معقدة ومافيش فيها إشكالالكلام نفسه بنقدر نصغته
+
+440
+00:32:34,800 --> 00:32:38,500
+على مين؟ على ال plus و ال times او ال
+
+441
+00:32:38,500 --> 00:32:43,280
+multiplication بمعنى ان انا بقدر اقول طبعا ان لو
+
+442
+00:32:43,280 --> 00:32:47,140
+في عندنا function f و g from real number to real
+
+443
+00:32:47,140 --> 00:32:50,920
+number الامة بتساعدها real number و ال output real
+
+444
+00:32:50,920 --> 00:32:55,040
+number في الحالة هذه بقدر اقول ان ال f plus g from
+
+445
+00:32:55,040 --> 00:33:04,690
+R to Rf plus g of x عبارة عن f of x plus g of x
+
+446
+00:33:04,690 --> 00:33:10,030
+نفس الكلام multiplication برضه هتكون f multiplied
+
+447
+00:33:10,030 --> 00:33:16,630
+by g of x عبارة عن f of x multiplied by g of x
+
+448
+00:33:16,630 --> 00:33:22,870
+ننقل
+
+449
+00:33:22,870 --> 00:33:27,140
+لعندي كل الأمور سهلة وسيطة ننتقلoperator تانية
+
+450
+00:33:27,140 --> 00:33:33,940
+اللى هى ال composition فضلى ال dot
+
+451
+00:33:33,940 --> 00:33:37,960
+بتكون ترتيبية ال dot عادة بتكون ترتيبية كتير
+
+452
+00:33:37,960 --> 00:33:40,260
+بتستخدم في ال .. ال .. ال .. اللى هى ال Cartesian
+
+453
+00:33:40,260 --> 00:33:43,600
+product بتكون اللى هى علاقة بال Cartesian product
+
+454
+00:33:43,600 --> 00:33:47,580
+احنا لما بنعمل dot عادية dot العادية خلاص ضرب عادي
+
+455
+00:33:47,580 --> 00:33:50,680
+اللى هى multiplication عادية ضرب عادي بس لما نيجى
+
+456
+00:33:50,680 --> 00:33:53,820
+نعمل Cartesian product لأ ال Cartesian product
+
+457
+00:33:53,820 --> 00:33:58,450
+ترتيبيلازم نحافظ على الترتيب فيه، بمعنى أنه عادة
+
+458
+00:33:58,450 --> 00:34:02,770
+بتكون لمصففات، لمجموعات، بنعملها dots، بنعملها
+
+459
+00:34:02,770 --> 00:34:07,370
+dots في الحالة هذه مازلنا في ال composition،
+
+460
+00:34:07,370 --> 00:34:14,710
+composition operator هي ببساطة، باخد، عندنا two
+
+461
+00:34:14,710 --> 00:34:18,990
+functions، واحدة compose التانيةالأولى compose
+
+462
+00:34:18,990 --> 00:34:22,810
+التانية، خلّيني أكتبها عشان أشرحها، الأولى compose
+
+463
+00:34:22,810 --> 00:34:28,350
+التانية، لو افترضنا بالشكل هذا، ناتج التانية input
+
+464
+00:34:28,350 --> 00:34:32,710
+للأولى، بسيطة
+
+465
+00:34:32,710 --> 00:34:37,050
+جدا، مرّ عليكم أكيد، أنا متأكد إنه لازم يمرّ
+
+466
+00:34:37,050 --> 00:34:42,240
+عليكم، ناتج التانية input للأولىفبنسميها
+
+467
+00:34:42,240 --> 00:34:44,840
+composition .. composition .. ماعرفش إيش كنتوا
+
+468
+00:34:44,840 --> 00:34:47,420
+تسموها سابقا .. إحنا عنا إيه اسم ال composition ..
+
+469
+00:34:47,420 --> 00:34:51,620
+فإحنا هنا بنقولها compose أو big O زي عاملة زي ال
+
+470
+00:34:51,620 --> 00:34:54,820
+big O هيك .. طيب عشان تكون صحيحة و تطلع نتائج
+
+471
+00:34:54,820 --> 00:35:00,780
+صحيحة .. هنقول إن ال G from A to B .. هذه اللي هي
+
+472
+00:35:00,780 --> 00:35:05,220
+التانية .. تانية .. هتبدأ من ال domain تبعها لل
+
+473
+00:35:05,220 --> 00:35:07,480
+code domain تبعها .. ال code domain تبعها لازم
+
+474
+00:35:07,480 --> 00:35:12,190
+يكون هو ال domain للتانية .. لل .. لل .. لل Fصحيح؟
+
+475
+00:35:12,190 --> 00:35:18,990
+لأن الناتج تبحى هو input لمن؟ لل F ف from B to C
+
+476
+00:35:18,990 --> 00:35:25,990
+في الحالة الناتج ككل هيكون من A to C كل الناتج
+
+477
+00:35:25,990 --> 00:35:28,530
+اللي هو ال composition كله على بعضه هيكون من A to
+
+478
+00:35:28,530 --> 00:35:33,450
+C from A to C و زي ما قلنا بنعطيه ال cycle الكبيرة
+
+479
+00:35:33,450 --> 00:35:38,140
+هذه تمامcomposes هي بنعمل فيها composition أو
+
+480
+00:35:38,140 --> 00:35:42,480
+creation أو generation ل new function ل new
+
+481
+00:35:42,480 --> 00:35:45,080
+function لأن function تعويضا في function function
+
+482
+00:35:45,080 --> 00:35:49,000
+معوضة في جلب function بدل ال x بتاعة ال function
+
+483
+00:35:49,000 --> 00:35:53,380
+بنعوض بقيمة ال function السابقة قيمتها كلها على
+
+484
+00:35:53,380 --> 00:36:01,340
+بعض قيمتها كلها على بعض زي نقربها أكتر برضه لو
+
+485
+00:36:01,340 --> 00:36:11,570
+قلنا ال ال g عبارة عنX تربيع plus two فرضا و ال F
+
+486
+00:36:11,570 --> 00:36:21,530
+ماعشان عارف خلينا ناخد .. اتنين X تربيع ناقص X
+
+487
+00:36:21,530 --> 00:36:30,330
+بيكفي تمام؟ هاد اللي مابنيجي نكتبهF compose G لحظة
+
+488
+00:36:30,330 --> 00:36:36,750
+ناتج ال G يكون input لمن؟ لل F طيب هاي ال input
+
+489
+00:36:36,750 --> 00:36:44,890
+تبع ال F معناته كل X بنحط مكان اضطره على F لحظة
+
+490
+00:36:44,890 --> 00:36:47,890
+هتطلع 2 X ربيع
+
+491
+00:36:55,740 --> 00:37:00,540
+ناتج التانية نعوضه ك input لمن؟ للأولى ك input
+
+492
+00:37:00,540 --> 00:37:04,140
+للأولى طيب كويسة هذا المفهوم خلينا نشوف كيف
+
+493
+00:37:04,140 --> 00:37:06,840
+أسقطناه في شوية المعادلات و شوية ال expressions
+
+494
+00:37:06,840 --> 00:37:13,020
+اللي عندنا فحنقول if compose G from A to C نكتبها
+
+495
+00:37:13,020 --> 00:37:19,000
+if compose G of A عبارة عن إيش؟ if ال function
+
+496
+00:37:19,000 --> 00:37:24,300
+الأولى ك function في ناتج ال function التانيةلحظة
+
+497
+00:37:24,300 --> 00:37:29,060
+ال input تبعها هو ناتج ال function التانية هي g of
+
+498
+00:37:29,060 --> 00:37:32,800
+a .. خلاص لو حسبناها ال term هذا كله هيعتبر ناتج
+
+499
+00:37:32,800 --> 00:37:37,540
+ال function g طيب الناتج لل function g هو input لل
+
+500
+00:37:37,540 --> 00:37:42,420
+function f طبعا
+
+501
+00:37:42,420 --> 00:37:46,280
+في الآخر g of a هذا مين؟ هذا ال output لمين؟ لل
+
+502
+00:37:46,280 --> 00:37:50,280
+function g المفروض belonging to مين؟to b هي ال
+
+503
+00:37:50,280 --> 00:37:54,420
+function g ال output تبعها belong to mean to set b
+
+504
+00:37:54,420 --> 00:38:00,400
+okay so f of g of a بنعرفها على أساس أنها لازم
+
+505
+00:38:00,400 --> 00:38:05,240
+تكون belong to mean to c f of anything هي ال
+
+506
+00:38:05,240 --> 00:38:08,480
+output لل function f فال output لل function f
+
+507
+00:38:08,480 --> 00:38:15,140
+belong to mean to cOkay ال .. ال big O هذه او ال
+
+508
+00:38:15,140 --> 00:38:18,040
+.. ال cycle الكبيرة طبعا big O بدنا نحاول ان
+
+509
+00:38:18,040 --> 00:38:21,700
+مانستخدمهاش كتير لأنه لها استخدامات جاية ال cycle
+
+510
+00:38:21,700 --> 00:38:26,420
+الكبيرة او ال compose هذه زي ال Cartesian product
+
+511
+00:38:26,420 --> 00:38:32,280
+زي ال Cartesian product مش تبدلية بمعنى لما نقول F
+
+512
+00:38:32,280 --> 00:38:37,400
+compose G لا تساوي G compose F لا تساويها هتلاقيوا
+
+513
+00:38:37,400 --> 00:38:40,750
+هذه function وهذه function هنا لو بدنا نعكسنقص
+
+514
+00:38:40,750 --> 00:38:43,710
+الكلام ده هتطلع function مختلفة تماما، هتطلع عبارة
+
+515
+00:38:43,710 --> 00:38:49,450
+عن اتنين X تربيع ناقص X كله تربيع زائد اتنين، هذه
+
+516
+00:38:49,450 --> 00:38:53,230
+غير هذه تماما، يعني حتى لو فكتوهم و حولعتوهم، لا
+
+517
+00:38:53,230 --> 00:38:55,770
+يمكن يساوي، مش هيساوي بعض، هذه function وهذه
+
+518
+00:38:55,770 --> 00:38:58,490
+function تماما مختلفة، طبعا هذه عشان برضه هذه
+
+519
+00:38:58,490 --> 00:38:59,570
+compose F
+
+520
+00:39:04,580 --> 00:39:10,140
+بعكس .. بعكس مين ال .. ال plus، ال or، ال and، ال
+
+521
+00:39:10,140 --> 00:39:14,360
+.. ال union، ال .. ال intersection، كلهم هدولة
+
+522
+00:39:14,360 --> 00:39:17,880
+نقدر نقول أن هما تبدلية، عملية تبدلية، الأولة
+
+523
+00:39:17,880 --> 00:39:20,100
+جابلة التانية أو التانية جابلة الأولة بتفرجش معانا
+
+524
+00:39:20,100 --> 00:39:22,460
+فيش، في ال operator، ولكن في ال .. في ال
+
+525
+00:39:22,460 --> 00:39:27,560
+composition لأ، في ال composition لأ، طيبخلصنا هنا
+
+526
+00:39:27,560 --> 00:39:30,200
+ال two operators تعاوننا ال multiplication اللي
+
+527
+00:39:30,200 --> 00:39:32,980
+أخدناها و اتكلمنا عن ال composition المهم جدا ال
+
+528
+00:39:32,980 --> 00:39:36,280
+composition اللي احنا أخدناها نجي نتكلم عن أنواع
+
+529
+00:39:36,280 --> 00:39:39,860
+ال functions عن أنواع ال functions بتاعتي أنواع ال
+
+530
+00:39:39,860 --> 00:39:43,260
+functions حقيقة في عندنا نوعين و هنستخرج منهم نوع
+
+531
+00:39:43,260 --> 00:39:47,680
+تالت أول نوع one to one functions برضه اتوقع انه
+
+532
+00:39:47,680 --> 00:39:52,040
+مر عليكم توقع انه مر عليكم تمام one to one فإذا
+
+533
+00:39:52,040 --> 00:39:54,720
+نقدر نقول ان ال function is one to one او واحد تو
+
+534
+00:39:54,720 --> 00:40:00,930
+واحداو injective او injection او injection if and
+
+535
+00:40:00,930 --> 00:40:05,770
+only if every element of its range has only one
+
+536
+00:40:05,770 --> 00:40:09,230
+preimage has only one preimage احنا عارفين انه في
+
+537
+00:40:09,230 --> 00:40:13,870
+ال .. ال range ممكن يكون له one preimage او اكتر
+
+538
+00:40:13,870 --> 00:40:17,720
+ممكن يكون له twoممكن يكون له two preimage زي في ال
+
+539
+00:40:17,720 --> 00:40:21,660
+function x تربيع زي في ال function x تربيع لأ هنا
+
+540
+00:40:21,660 --> 00:40:28,400
+في ال one to one فقط one preimage فمعنى ذلك ان كل
+
+541
+00:40:28,400 --> 00:40:33,320
+ناتج هو جاي من input واحد كل input هذا هيعكسنا
+
+542
+00:40:33,320 --> 00:40:37,500
+الموضوع ان معناته كل input هينتجنا ناتج واحد فقط
+
+543
+00:40:39,160 --> 00:40:43,780
+الناتج دائما ناتج واحد فقط لكل ال inputs وكل ناتج
+
+544
+00:40:43,780 --> 00:40:48,680
+جاي من input واحد بس من input واحد فقط طيب هذه
+
+545
+00:40:48,680 --> 00:40:52,340
+بقدر نقول ان ال X is injective او ال X is one to
+
+546
+00:40:52,340 --> 00:40:56,200
+one معناه
+
+547
+00:40:56,200 --> 00:41:04,740
+ان there is no exist X and Y لحظة و X لا تساوي Y
+
+548
+00:41:04,740 --> 00:41:09,840
+and F of X تساوي F of Yلأ بدنا نفهمها دي بدنا
+
+549
+00:41:09,840 --> 00:41:12,620
+نفهمها كيف هدى عرفناها على أساس ان هى one to one
+
+550
+00:41:12,620 --> 00:41:19,720
+خلينى نشوف عشان اقول ان فعلا كل output كل element
+
+551
+00:41:19,720 --> 00:41:24,420
+فى ال range الو بري إمج واحدة الو بري إمج واحدة
+
+552
+00:41:24,420 --> 00:41:29,560
+فقط معنى ذلك ان ال f of x لا يمكن تنتج الا من
+
+553
+00:41:29,560 --> 00:41:34,160
+element واحد مظبوط هدى ال output هي هدى هيك output
+
+554
+00:41:34,160 --> 00:41:36,960
+يعني المفروض ان هي رايحة لل range ال value بتاعتها
+
+555
+00:41:37,800 --> 00:41:42,620
+كلها رايحة عساس ان هي element في ال range الاصل ان
+
+556
+00:41:42,620 --> 00:41:47,940
+x وحيدة فقط اللى تنتجلنا ال term هذا القيمة هذه
+
+557
+00:41:47,940 --> 00:41:54,140
+لما اقول equal تساوي f of y معناه يوجد element
+
+558
+00:41:54,140 --> 00:42:01,220
+تاني بنتجلنا نفس ال output ناخد بالنا ماشي لعند
+
+559
+00:42:01,220 --> 00:42:06,840
+الان ماشي ممكن نتسهر نقول طب ممكن x بتساوي yيعني
+
+560
+00:42:06,840 --> 00:42:09,420
+برضه حضر اللي احنا مزلنا في نفس الكلام ان لو
+
+561
+00:42:09,420 --> 00:42:12,820
+اثبتنا ان x بتساوي y احنا مازلنا تحت نفس التعريف
+
+562
+00:42:12,820 --> 00:42:16,580
+ان هي مازلة one to one مازلة one to one اذا كانت
+
+563
+00:42:16,580 --> 00:42:21,000
+بيساوي بعض لأ راح يقوللي لا يساوي بعض لا يساوي بعض
+
+564
+00:42:21,000 --> 00:42:26,600
+x لا تساوي y معناته واضح انه صار في عندي two pre
+
+565
+00:42:26,600 --> 00:42:32,420
+image لنفس ال output معناته نفيت ال one to one تم
+
+566
+00:42:32,420 --> 00:42:35,040
+نفي ال one to one و هو فعلا بيقوللي there is no
+
+567
+00:42:35,040 --> 00:42:43,100
+existلا يوجد قيمتين في ال domain يعني في ال input
+
+568
+00:42:43,100 --> 00:42:46,480
+لا يوجد قيمتين في ال input بيساويش بعض و بيعطونا
+
+569
+00:42:46,480 --> 00:42:50,260
+نفس ال output صحيح؟
+
+570
+00:42:50,260 --> 00:42:54,740
+صارت هيك منطقية أصبحت هيك منطقية فعلا لا يوجد في
+
+571
+00:42:54,740 --> 00:42:57,740
+negotiation في الأول معناته هو نفه الوجد أنه تحصل
+
+572
+00:42:57,740 --> 00:43:02,380
+هذا الكلام أن يكون فينا two preimage لنفس ال
+
+573
+00:43:02,380 --> 00:43:04,640
+output لنفس ال output تمام
+
+574
+00:43:10,990 --> 00:43:15,810
+Okay ف only one element of the domain is mapped to
+
+575
+00:43:15,810 --> 00:43:19,870
+any given one element of the range كل element في
+
+576
+00:43:19,870 --> 00:43:22,870
+ال range هو جاينة من one element في ال domain ال
+
+577
+00:43:22,870 --> 00:43:25,150
+one element اللي في ال domain هذا سمنا بالنسبة لل
+
+578
+00:43:25,150 --> 00:43:31,090
+element في ال range pre image okay معنى ذلك ان كل
+
+579
+00:43:31,090 --> 00:43:34,110
+element في ال domain is injected into the
+
+580
+00:43:34,110 --> 00:43:37,690
+different element of the rangeكل element في ال
+
+581
+00:43:37,690 --> 00:43:42,670
+domain طلعلنا ناتج element مختلف في ال range مافيش
+
+582
+00:43:42,670 --> 00:43:46,810
+اتنين بيشابهوا بعض في نفس ال .. الناتج لا يوجد
+
+583
+00:43:46,810 --> 00:43:50,310
+قيمتين في ال domain بيساووا بعض او بيطلعونا نفس
+
+584
+00:43:50,310 --> 00:43:54,230
+الناتج في ال rangeلا يوجد قيمتين، معناه ذلك أنه لا
+
+585
+00:43:54,230 --> 00:43:59,750
+يوجد two pre-images اللي هم نفس ال element في من
+
+586
+00:43:59,750 --> 00:44:03,410
+في ال range بنكرر و بنزل عشان نظل ثابت عن كل واحد
+
+587
+00:44:03,410 --> 00:44:07,130
+طيب ال
+
+588
+00:44:07,130 --> 00:44:09,250
+domain و ال range cardinal اللي احنا اتكلمنا عنها
+
+589
+00:44:09,250 --> 00:44:14,910
+قبل هيكة انه ممكن يكون ال domain أكبر من ال range
+
+590
+00:44:14,910 --> 00:44:17,810
+في النهايةو ال code domain ال code domain ممكن
+
+591
+00:44:17,810 --> 00:44:20,250
+يكون اكبر منهم يعني هنا في الحالة هذه لازم ال
+
+592
+00:44:20,250 --> 00:44:26,510
+domain و ال range يساوي بعض ليش؟ بشان يكون كل
+
+593
+00:44:26,510 --> 00:44:30,870
+input .. كل .. بالظبط كل input يلو output واحد كل
+
+594
+00:44:30,870 --> 00:44:36,290
+input يلو output واحد لأ يمكن اوضح لو حسبنا بال
+
+595
+00:44:36,290 --> 00:44:41,890
+bipartate لو هدلوا عندنا خمسة في ال input
+
+596
+00:44:45,880 --> 00:44:49,760
+لازم كل واحدة يكون لها output واحد بس كل واحدة
+
+597
+00:44:49,760 --> 00:44:54,280
+لازم يكون لها output واحد مثلا خلاص مادام كل واحدة
+
+598
+00:44:54,280 --> 00:44:57,580
+لها output واحد معناته عدد ال output مش مساوية عدد
+
+599
+00:44:57,580 --> 00:45:03,020
+ال input معناه ذلك انه ال range مساوية ال domain
+
+600
+00:45:06,880 --> 00:45:10,180
+ال issue المساوي احنا بنتكلم هنا عن إيش؟ بنتكلم عن
+
+601
+00:45:10,180 --> 00:45:13,400
+set معناته عشان ال C أقول إن هى بتسووا بعض معناته
+
+602
+00:45:13,400 --> 00:45:16,640
+ال cardinality بتاعتهم بيسووا بعض cardinality
+
+603
+00:45:16,640 --> 00:45:20,160
+بيسووا بعض طيب ال codomain إيش وضعه في النص هي
+
+604
+00:45:20,160 --> 00:45:23,420
+كده؟ نفس ال .. نفس ال .. نفس ال .. مش بالضروري
+
+605
+00:45:23,420 --> 00:45:28,240
+ممكن يكون في عندنا element زيادة هنا تفرجش ال
+
+606
+00:45:28,240 --> 00:45:31,920
+codomain لأ ممكن يكون أكبر ممكن و ممكن يكون بيسويه
+
+607
+00:45:35,910 --> 00:45:40,890
+طيب for examples هالوقت هي ديهذه one to one ولا ..
+
+608
+00:45:40,890 --> 00:45:47,870
+one to one تمام تانية لأ لإيش .. two pre images
+
+609
+00:45:47,870 --> 00:45:52,930
+هاي two pre images اعطوا لنفس ال .. لنفس ال
+
+610
+00:45:52,930 --> 00:45:54,670
+element في ال range لنفس ال element في ال range
+
+611
+00:45:54,670 --> 00:46:00,690
+فهذه not one التالتة not function من أصله ليش لإن
+
+612
+00:46:00,690 --> 00:46:04,550
+في one input في عندنا one input اعطانا two outputs
+
+613
+00:46:04,550 --> 00:46:06,910
+فهذه قلنا نتعامل معها انها مش function لإنها
+
+614
+00:46:06,910 --> 00:46:11,090
+unstable أساسالا يمكن أكون في نفس اللحظة في
+
+615
+00:46:11,090 --> 00:46:16,690
+مكانين، تمام؟ فإذا not even a function okay
+
+616
+00:46:16,690 --> 00:46:21,250
+sufficient conditions for one-to-one function إيه
+
+617
+00:46:21,250 --> 00:46:23,630
+بقدر أقول إنه او لا ال function ده كافي جدا عشان
+
+618
+00:46:23,630 --> 00:46:27,670
+أقول إن ال function تبعتنا one-to-one if is
+
+619
+00:46:27,670 --> 00:46:33,310
+strictly or monotonically، monotonic جاية من mono
+
+620
+00:46:33,310 --> 00:46:38,780
+كلمة mono أحاديمونو أحادي monotonically increasing
+
+621
+00:46:38,780 --> 00:46:44,280
+بمعنى ال function أحادية الاتجاه وتزايدية أحضر
+
+622
+00:46:44,280 --> 00:46:49,520
+خلاص طول عمرها أحادية الاتجاه فإذا كان فعلا تزايد
+
+623
+00:46:49,520 --> 00:46:53,680
+تزايدية باستمرار طبعا الكلام نفسه ينطبق على
+
+624
+00:46:53,680 --> 00:46:57,000
+monotonically decreasing أنها تكون تناقصية
+
+625
+00:46:57,000 --> 00:47:03,980
+باستمرار هذا معناته إيش لما أقول تزايدية تزايدية
+
+626
+00:47:06,770 --> 00:47:12,030
+باستمرار، معناه ذلك لو أخدنا x و y و قولنا أن x
+
+627
+00:47:12,030 --> 00:47:21,670
+أكبر من y كقيمة الأصل أن f of x برضه تكون أكبر من
+
+628
+00:47:21,670 --> 00:47:26,430
+f of y في الحالة هذه بقول أن الدالة أو ال function
+
+629
+00:47:26,430 --> 00:47:31,870
+تزايدية، monotonicمعناته أحادية الاتجاه و احنا
+
+630
+00:47:31,870 --> 00:47:35,090
+حددناها وراها monotonically increasing أحادية
+
+631
+00:47:35,090 --> 00:47:39,490
+الاتجاه وهي تزايدية باستمرار هتظهر معناته مش هتكسر
+
+632
+00:47:39,490 --> 00:47:44,870
+مش هتعكس هتظل mono و هتظل mono أحادية وتزايدية
+
+633
+00:47:44,870 --> 00:47:48,750
+مدام احنا حددناها هتظل باستمرار متزايدة مش هأفاجأ
+
+634
+00:47:48,750 --> 00:47:50,950
+أنه فجأة ألاجيها نزلت
+
+635
+00:47:53,590 --> 00:47:57,310
+لأن إذا نزلت هنا هضطر أقول إنها مش one to one
+
+636
+00:47:57,310 --> 00:48:00,610
+لإيش؟ لأن عند القيمة، القيمة اللي هنا و القيمة
+
+637
+00:48:00,610 --> 00:48:04,770
+اللي هنا، لاحظوا، هيكون نفس ال output لأ، بس إذا
+
+638
+00:48:04,770 --> 00:48:09,530
+دلنا متزايدية باستمرار، لا يمكن تصير الحالة هذه
+
+639
+00:48:09,530 --> 00:48:13,450
+إذا دلت باستمرار متزايدة، ال function تزايدية،
+
+640
+00:48:13,450 --> 00:48:16,880
+طبعا تزايدية ممكن تدل مكملة برضه هكذامن minus
+
+641
+00:48:16,880 --> 00:48:20,220
+infinity to infinity بشكل تزايدى الكلب نفسه ينطبق
+
+642
+00:48:20,220 --> 00:48:25,260
+علي مين decreasing لو بنتعامل مع decreasing بهذا
+
+643
+00:48:25,260 --> 00:48:32,580
+الشكل بس كل اللى هنعمله هنا ال inequality هنعكسها
+
+644
+00:48:32,580 --> 00:48:40,960
+ال inequality هنعكسها لو x أكبر من y فإذا ال f of
+
+645
+00:48:40,960 --> 00:48:47,340
+x أقلمن f of y بس ال inequality عكسناها بدل كأكبر
+
+646
+00:48:47,340 --> 00:48:51,220
+من صارت أصغر من بس باستمرار عمرو ماحنلاجي هنا
+
+647
+00:48:51,220 --> 00:48:56,180
+output ناتج من two pre image عمرو ده ماحنلاجي
+
+648
+00:48:56,180 --> 00:49:00,000
+element في ال output ناتج من two pre image تمام
+
+649
+00:49:00,000 --> 00:49:03,400
+فإذا اتحققوا الشرطين هدو .. أحد الشرطين .. أحد
+
+650
+00:49:03,400 --> 00:49:08,260
+الشرطين يعني يكفي أنها تكونيكفي انها تكون
+
+651
+00:49:08,260 --> 00:49:11,200
+monotonically increasing او monotonically
+
+652
+00:49:11,200 --> 00:49:16,560
+decreasing strictly الزمن انها تكون او زي متزايدة
+
+653
+00:49:16,560 --> 00:49:22,220
+او متنقصة تمام فبنقول
+
+654
+00:49:22,220 --> 00:49:26,380
+automatically ان هي increasing زي ال X تكعيب
+
+655
+00:49:27,900 --> 00:49:34,920
+تزايدية او تنقصية تزايدية تزايدية
+
+656
+00:49:34,920 --> 00:49:40,660
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+657
+00:49:40,660 --> 00:49:43,120
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+658
+00:49:43,120 --> 00:49:46,360
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+659
+00:49:46,360 --> 00:49:46,460
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+660
+00:49:46,460 --> 00:49:46,460
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+661
+00:49:46,460 --> 00:49:47,320
+تزايدية تزايدية تزايدية تزايدية تزايدية تزايدية
+
+662
+00:49:47,320 --> 00:49:54,360
+تزايدية تزايدية تزايدية تزايدية
+
+663
+00:49:54,360 --> 00:49:54,380
+تز
+
+664
+00:49:58,640 --> 00:50:05,620
+بتزيد معاكم هتلاقوه
+
+665
+00:50:05,620 --> 00:50:11,360
+بهذا الشكل x تكريب y تساوي x تكريب فواضح ان هي
+
+666
+00:50:11,970 --> 00:50:17,890
+monotonically increasing تساعدية في هذه one to one
+
+667
+00:50:17,890 --> 00:50:23,370
+طيب في المقابل في برضه ال converse is not
+
+668
+00:50:23,370 --> 00:50:34,530
+necessarily true زي one over x ليش؟ نرسمها و
+
+669
+00:50:34,530 --> 00:50:35,490
+نشوف ليش
+
+670
+00:50:43,000 --> 00:50:49,420
+مش هي شكلها؟ وي بتساوي واحد على إكس طب وين المشكلة
+
+671
+00:50:49,420 --> 00:50:52,920
+فيها هذه؟
+
+672
+00:50:52,920 --> 00:50:58,220
+لأ عند ال zero إلها قيمتين infinity و minus
+
+673
+00:50:58,220 --> 00:51:01,460
+infinity عند ال zero إلها قيمتين بس طبعا وين؟ مش
+
+674
+00:51:01,460 --> 00:51:05,080
+هنشوفه في ال infinity فواضح إنه عند ال zero في
+
+675
+00:51:05,080 --> 00:51:09,500
+مشكلة عند ال zero هي في مشكلة رغم إن احنا ممكن
+
+676
+00:51:09,500 --> 00:51:15,680
+نتعامل معها نهيها decreasingصحيح؟ و هنا برضه نفس
+
+677
+00:51:15,680 --> 00:51:19,460
+الكلام بس واضح أنه لأ في نقطة انقلاب بتصير عند ال
+
+678
+00:51:19,460 --> 00:51:22,980
+zero هتعملنا مشكلة لأنه صار عند ال zero في عندنا
+
+679
+00:51:22,980 --> 00:51:27,200
+two outputs two outputs لنفس ال input لنفس ال
+
+680
+00:51:27,200 --> 00:51:32,720
+input طيب ال onto ال onto function أو ال
+
+681
+00:51:32,720 --> 00:51:37,920
+surjective onto هدى ببساطة جدا إذا كان ال code
+
+682
+00:51:37,920 --> 00:51:43,370
+main بسوء ال range فهي ontoفهي بنسميها onto بمعنى
+
+683
+00:51:43,370 --> 00:51:47,670
+ان كل القيم بتاعة ال code domain مستخدمة في ال
+
+684
+00:51:47,670 --> 00:51:53,610
+range كلها واقعة في ال range في ال range كويسة ففي
+
+685
+00:51:53,610 --> 00:51:56,030
+الحالة هي دي زي ما قولنا ال if from او ال function
+
+686
+00:51:56,030 --> 00:52:01,290
+if from A to B is onto or surjective or surjection
+
+687
+00:52:01,290 --> 00:52:05,410
+if and only if its range is equal to its code
+
+688
+00:52:05,410 --> 00:52:09,750
+domain في الحالة هي دي for all B belong toThere
+
+689
+00:52:09,750 --> 00:52:13,370
+exists a belonging to A بحققنا ال function f of x
+
+690
+00:52:13,370 --> 00:52:17,490
+equal to b بمعنى
+
+691
+00:52:17,490 --> 00:52:24,970
+لكل قيم ال code domain يوجد
+
+692
+00:52:24,970 --> 00:52:29,110
+element في ال domain بنتجها بطلّقنا إياها طب مادام
+
+693
+00:52:29,110 --> 00:52:33,120
+أنتجت معناته راحت لل range على طولصحيح؟ actually
+
+694
+00:52:33,120 --> 00:52:37,140
+مادام نقدر ننتجها معناته بتروح لمين؟ لل range
+
+695
+00:52:37,140 --> 00:52:42,100
+اوتوماتيكل انا قاعد بقول for all B لكل قيم B اللي
+
+696
+00:52:42,100 --> 00:52:47,780
+تنتمي لل set B ل ال code domain يوجد قيمة في ال
+
+697
+00:52:47,780 --> 00:52:51,520
+domain تنتجها طب ما خلاص انا اصلا كيف بحسبه ال
+
+698
+00:52:51,520 --> 00:52:56,960
+range؟ ال range بنحسب انه فيه فعلا قيم أو توجد
+
+699
+00:52:56,960 --> 00:53:01,250
+قيمة في ال domain تنتجهاو هو فعلا احنا قاعدين نقول
+
+700
+00:53:01,250 --> 00:53:04,950
+فلكل قيم ال code domain اوتوماتيكلي هيك صارت ال
+
+701
+00:53:04,950 --> 00:53:09,610
+code domain كله نفسه ال range نفسه ال range كويس
+
+702
+00:53:09,610 --> 00:53:16,630
+فإذا ال onto function maps the set A onto او the
+
+703
+00:53:16,630 --> 00:53:21,110
+entirety the set B معناه ذلك انه ال function A
+
+704
+00:53:21,110 --> 00:53:30,580
+هتنتجلنا outputs داخلأو كامل
+
+705
+00:53:30,580 --> 00:53:35,840
+ال set P بمعنى كامل ال set أو كامل ال elements في
+
+706
+00:53:35,840 --> 00:53:40,600
+ال code domain يمكن انتاجها من ال domain كامل ال
+
+707
+00:53:40,600 --> 00:53:44,880
+elements في ال code domain يمكن انتاجها من ال
+
+708
+00:53:44,880 --> 00:53:47,880
+domain طب احنا عارفين ان كل element ينتج من ال
+
+709
+00:53:47,880 --> 00:53:51,540
+domain هو range automatically صارت هيك ال range
+
+710
+00:53:51,540 --> 00:53:52,900
+يساوي لل code domain
+
+711
+00:53:57,990 --> 00:54:02,410
+Okay خلّينا نشوف ال function اللي لسه كنا رسمينها
+
+712
+00:54:02,410 --> 00:54:11,290
+تكعيب اللي هي تكعيب cubic هذي
+
+713
+00:54:11,290 --> 00:54:14,830
+اتفقنا ان هي one to one المرة اللي فاتت قبل شوية
+
+714
+00:54:14,830 --> 00:54:19,090
+لسه فالساعة اللي فاتت اتفقنا طيب بالنسبة ل onto
+
+715
+00:54:19,090 --> 00:54:24,890
+كيف تحسبوها onto؟نشوف ال domain .. ال code domain
+
+716
+00:54:24,890 --> 00:54:28,310
+طيب ال code domain وين ال code domain؟ I طلعه على
+
+717
+00:54:28,310 --> 00:54:33,970
+I أكسس من minus infinity to infinity طيب actually
+
+718
+00:54:33,970 --> 00:54:37,230
+هل ال function فعلا تصل ل minus infinity و بتطلع ل
+
+719
+00:54:37,230 --> 00:54:44,430
+positive infinity فإذن بيسووا بعض فإذن on two طيب
+
+720
+00:54:44,430 --> 00:54:52,010
+هذه ال on two او هذه ال X تربيه نشوف ال X تربيه
+
+721
+00:54:57,020 --> 00:55:01,920
+الـ codomain جديش؟ R من minus infinitive إلى
+
+722
+00:55:01,920 --> 00:55:05,220
+infinitive خلاص احنا محددنا من الأول R طيب ال
+
+723
+00:55:05,220 --> 00:55:09,580
+range من zero to positive infinity بمعنى ان احنا
+
+724
+00:55:09,580 --> 00:55:17,080
+بنتكلم عن ال none negative real numbers none
+
+725
+00:55:17,080 --> 00:55:19,660
+negative real numbers بمعنى ان هي من zero to
+
+726
+00:55:19,660 --> 00:55:23,120
+positive لكل ال positive to infinity none negative
+
+727
+00:55:23,120 --> 00:55:27,840
+elementsOkay why عرفنا why نرسمناه و نشوفنا ليش
+
+728
+00:55:27,840 --> 00:55:34,040
+واحدة منهم on to واحدة منهم none طيب نشوف هنا مين
+
+729
+00:55:34,040 --> 00:55:36,780
+منهم on to و مين one to one من الحالات اللي موجودة
+
+730
+00:55:36,780 --> 00:55:41,480
+عندنا نمسكهم واحدة واحدة الأولى هذى مش one to one
+
+731
+00:55:41,480 --> 00:55:44,460
+one to one لأ مش one to one ليش لأ لأ انهم three
+
+732
+00:55:44,460 --> 00:55:50,990
+طيب on to on toفإذا الأولى هنا one to one ولكن مش
+
+733
+00:55:50,990 --> 00:55:55,170
+one to one طيب تانية one to one ولا one to one ولا
+
+734
+00:55:55,170 --> 00:55:58,270
+one to one ولا one to one ولا one to one ولا one
+
+735
+00:55:58,270 --> 00:55:58,270
+to one ولا one to one ولا one to one ولا one to
+
+736
+00:55:58,270 --> 00:55:58,430
+one ولا one to one ولا one to one ولا one to one
+
+737
+00:55:58,430 --> 00:55:58,590
+ولا one to one ولا one to one ولا one to one ولا
+
+738
+00:55:58,590 --> 00:55:59,990
+one to one ولا one to one ولا one to one ولا one
+
+739
+00:55:59,990 --> 00:56:02,570
+to one ولا one to one ولا one to one ولا one to
+
+740
+00:56:02,570 --> 00:56:02,590
+one ولا one to one ولا one to one ولا one to one
+
+741
+00:56:02,590 --> 00:56:02,630
+ولا one to one ولا one to one ولا one to one ولا
+
+742
+00:56:02,630 --> 00:56:02,630
+one to one ولا one to one ولا one to one ولا one
+
+743
+00:56:02,630 --> 00:56:02,870
+to one ولا one to one ولا one to one ولا one to
+
+744
+00:56:02,870 --> 00:56:05,370
+one ولا one to one ولا one to one ولا one to one
+
+745
+00:56:05,370 --> 00:56:07,430
+ولا one to one ولا one to one ولا one to one ولا
+
+746
+00:56:07,430 --> 00:56:07,430
+one to one ولا one to one ولا one to one ولا one
+
+747
+00:56:07,430 --> 00:56:07,770
+to one ولا one to one ولا one to one ولا one to
+
+748
+00:56:07,770 --> 00:56:12,120
+one ولا one to one ولا one to one ولا one toهي one
+
+749
+00:56:12,120 --> 00:56:16,160
+to one اه ولكن ليست on to ليش مش on to لأن في عنده
+
+750
+00:56:16,160 --> 00:56:19,260
+element فيه موجود موجود في ال code domain و غير
+
+751
+00:56:19,260 --> 00:56:23,780
+موجود في ال range و غير موجود في ال range تمام طيب
+
+752
+00:56:23,780 --> 00:56:29,620
+ال bijections او ال one to one correspondence او
+
+753
+00:56:29,620 --> 00:56:33,580
+ال reversible او ال invertible اي تسمية من التسمية
+
+754
+00:56:33,580 --> 00:56:37,040
+هذه بس الغالب يمكن اكتر اللي هي ال bijection او
+
+755
+00:56:39,230 --> 00:56:42,790
+one to one correspondence كويس هدى امتى نقدر نقول
+
+756
+00:56:42,790 --> 00:56:46,790
+ان ال function bijection function اذا كانت one to
+
+757
+00:56:46,790 --> 00:56:51,090
+one و unto في نفس الوقت خلاص بنسميها ايش bijection
+
+758
+00:56:51,090 --> 00:56:56,170
+if and only if it's both one to one and unto فال
+
+759
+00:56:56,170 --> 00:57:00,810
+bijection اللى ال function if from a to b there
+
+760
+00:57:00,810 --> 00:57:06,620
+exists an inverse of f عشان هيك اسمهاreversible او
+
+761
+00:57:06,620 --> 00:57:09,360
+invertible على اساس انه اذا كان فعلا تتحققنا
+
+762
+00:57:09,360 --> 00:57:13,620
+الكلام هذا ايش بتحقق ان هي one to one فكل element
+
+763
+00:57:13,620 --> 00:57:21,000
+في ال domain يوجد له قيمة واحدة في ال range لحظة
+
+764
+00:57:21,000 --> 00:57:24,220
+في ال range لسه احنا بنتكلم عن ال one to one لسه
+
+765
+00:57:24,220 --> 00:57:28,080
+وكل element في ال range جاي من element واحد في ال
+
+766
+00:57:28,080 --> 00:57:33,390
+domainوال range يساوي ال code domain معناه ذلك
+
+767
+00:57:33,390 --> 00:57:36,370
+اللي قلناه على ال range بقدر اطبقه على ال code
+
+768
+00:57:36,370 --> 00:57:39,810
+domain كل element في ال code domain جاي من element
+
+769
+00:57:39,810 --> 00:57:44,530
+واحد في ال domain معناته لو انعكسه بقدر العلاقة
+
+770
+00:57:44,530 --> 00:57:47,930
+موجودة ليش علاقة موجودة لأن ال code domain بده
+
+771
+00:57:47,930 --> 00:57:50,790
+يصير domain الدمين بده يصير code domain ال
+
+772
+00:57:50,790 --> 00:57:54,370
+relation واحدة فعلا كل element موجود في ال domain
+
+773
+00:57:54,370 --> 00:57:58,960
+كان له element واحد في ال code domainمعنى ذلك أن
+
+774
+00:57:58,960 --> 00:58:02,280
+الـ function في الحالة دي لها inverse، بنقدر نجيب
+
+775
+00:58:02,280 --> 00:58:07,300
+لها ال inverse تبعها، المعكوز تبعها جبنا مجموعة ال
+
+776
+00:58:07,300 --> 00:58:09,940
+outputs، ال outputs هذه لو طبقنا عليها function
+
+777
+00:58:09,940 --> 00:58:13,620
+معينة، كل ال output هيرجع لل input تبعه، كل output
+
+778
+00:58:13,620 --> 00:58:16,500
+هيرجعنا لل input تبعه، فبنقدر نقول إنه، بنكتبها
+
+779
+00:58:16,500 --> 00:58:21,400
+أزايشInverse of F أو F to the power minus one اللي
+
+780
+00:58:21,400 --> 00:58:27,180
+هي Inverse of F from ال domain لل domain لحظة طيب
+
+781
+00:58:27,180 --> 00:58:30,060
+احنا ضمنين انه اكيد ال elements هذه متوافقة مع بعض
+
+782
+00:58:30,060 --> 00:58:35,580
+لأنه اساسا هنا كان كل element في ال A له output في
+
+783
+00:58:35,580 --> 00:58:40,360
+ال B و ال B مساوية لل rangeهي نفس ال range معناه
+
+784
+00:58:40,360 --> 00:58:43,280
+ذلك أنه بقدر أطبقها و أقول أن ال B برضه كل element
+
+785
+00:58:43,280 --> 00:58:47,100
+موجود في ال code domain بقدر أنتج منه element
+
+786
+00:58:47,100 --> 00:58:54,640
+موجود في ال domain بالعكس نفسي طيب لحظة لو تغاضينا
+
+787
+00:58:54,640 --> 00:58:59,800
+عن الشرط هذا اللي هي one to one معناه ذلك أنه لما
+
+788
+00:58:59,800 --> 00:59:05,720
+كنا بنتكلم أو اللي هي ال range لو قولنا التربيع
+
+789
+00:59:07,600 --> 00:59:13,260
+التربيع كل لحظة كل output فيه له two preimage طب
+
+790
+00:59:13,260 --> 00:59:18,280
+لو عكسناهم بيصير not function هصير not function
+
+791
+00:59:18,280 --> 00:59:22,460
+ففي الحالة ده مقدرش اقول ان فيها inverse عشان يكون
+
+792
+00:59:22,460 --> 00:59:26,260
+انها inverse لازم تكون one to oneو تكون on to و
+
+793
+00:59:26,260 --> 00:59:30,080
+تكون on to اتفجنا ان هي one to one ليش لأن ال pre
+
+794
+00:59:30,080 --> 00:59:33,260
+image هتصير image فإذا كان في عنده two pre image
+
+795
+00:59:33,260 --> 00:59:36,640
+مايتحول مش ل two image فتطلع من ال functionality
+
+796
+00:59:36,640 --> 00:59:41,120
+طيب الحالة التانية ال on to انا محتاج انها تكون on
+
+797
+00:59:41,120 --> 00:59:44,840
+to ليش لأن في ال on في ال function لازم كل عنصر في
+
+798
+00:59:44,840 --> 00:59:49,200
+ال domain اقدر اطبق عليه ال function طيب إذا كانت
+
+799
+00:59:49,200 --> 00:59:52,100
+مش on to معناته في عناصر في ال domain غير موجودة
+
+800
+00:59:52,100 --> 00:59:55,620
+في ال rangeمش هلاجيه لها قيمة كانت في ال domain
+
+801
+00:59:55,620 --> 01:00:00,660
+السابق، غير موجود لها قيمة مقابلة إلها، مع أن ذلك
+
+802
+01:00:00,660 --> 01:00:03,640
+أن أنا برضه مش .. ماقدرش أجيب لها ال inverse أو ال
+
+803
+01:00:03,640 --> 01:00:06,860
+inverse طبعا مجهول، مش .. مش عارف إنه هال حيناضر
+
+804
+01:00:06,860 --> 01:00:13,620
+تماما أو هيعطيني identity، functionلو عكسناها لل F
+
+805
+01:00:13,620 --> 01:00:17,360
+لأن كيف انا اعرف ان هذه inverse حقيقي ان لو ضربنا
+
+806
+01:00:17,360 --> 01:00:20,300
+ال inverse function في ال function الأصلية المفروض
+
+807
+01:00:20,300 --> 01:00:25,680
+يطلع ليه identity و identity حسب انا بتعامل مع set
+
+808
+01:00:25,680 --> 01:00:29,020
+بتعامل مع numbers
+
+809
+01:00:32,190 --> 01:00:35,330
+ماتريكس بنتعامل مع ايش بالظبط؟ لو بنتعامل مع مجرد
+
+810
+01:00:35,330 --> 01:00:40,030
+number ال identity هي الرقم واحد لو بنتعامل مثلا
+
+811
+01:00:40,030 --> 01:00:45,050
+مع matrix هي ال identity matrix اللي مش بضرورة
+
+812
+01:00:45,050 --> 01:00:49,010
+تكون كلها ones ال diagonal بس تبعها one صحيح؟ ال
+
+813
+01:00:49,010 --> 01:00:52,410
+diagonal فقط اللي بيكون ones، كويس فهنا بتقدر نقول
+
+814
+01:00:52,410 --> 01:00:59,940
+ان ال Fأو ال inverse ال function composition لأ
+
+815
+01:00:59,940 --> 01:01:04,360
+هذي اش اسمه dot dot F equal to ايش to identity
+
+816
+01:01:04,360 --> 01:01:08,420
+value equal to identity function to identity
+
+817
+01:01:08,420 --> 01:01:14,720
+function لأ هذي dot عادي هذي ضرب ضرب
+
+818
+01:01:14,720 --> 01:01:15,160
+multiplication
+
+819
+01:01:19,320 --> 01:01:22,860
+كيف؟ لأ ال composition أكبر من هيك، هذه مجرد
+
+820
+01:01:22,860 --> 01:01:26,100
+تضربة، بس ال function في ال function، ال function
+
+821
+01:01:26,100 --> 01:01:35,160
+لأ لحظة ال F .. ال F المفروض عكسها ضربها .. احنا
+
+822
+01:01:35,160 --> 01:01:39,720
+كنا كاتبين توينا مثلين صح؟لو ال inverse تبعها
+
+823
+01:01:39,720 --> 01:01:42,900
+الاصل composition صح كلامك صحيح composition لأنه
+
+824
+01:01:42,900 --> 01:01:45,920
+فعلا في الآخر المفروض كله هيتشطب مع بعضه لو عملت
+
+825
+01:01:45,920 --> 01:01:49,640
+ال composition مع ال inverse تبعتها هتلاقي ان كل
+
+826
+01:01:49,640 --> 01:01:54,080
+ال X هتتشطب مع بعض كل X هتتشطب مع بعض كلامك صحيح
+
+827
+01:01:54,080 --> 01:01:58,120
+عشان تطلع identity function المفروض هتكون مع ال
+
+828
+01:01:58,120 --> 01:02:01,980
+composition composition طيب ال ه هنتكلم عن
+
+829
+01:02:01,980 --> 01:02:07,710
+identity function ال identity function fromA to A
+
+830
+01:02:07,710 --> 01:02:16,450
+بنكتبها as identity A أو one أو one for A is the
+
+831
+01:02:16,450 --> 01:02:20,570
+unique function such that for all A belong to A
+
+832
+01:02:20,570 --> 01:02:25,650
+identity function of A بساوي A ال identity
+
+833
+01:02:25,650 --> 01:02:30,030
+function of A بتساوي A تمام؟إذا تحقق الكلام هدف
+
+834
+01:02:30,030 --> 01:02:33,450
+إذا هدف نقدر نقول أنها identity function في الحالة
+
+835
+01:02:33,450 --> 01:02:36,230
+التاعتناه طبعا احنا اتعاملنا معها كتير اتعاملتوا
+
+836
+01:02:36,230 --> 01:02:42,730
+معها كتير في ال .. ال summation كان zero ال
+
+837
+01:02:42,730 --> 01:02:45,990
+summation zero لما بتشمعوا مع zero ال element
+
+838
+01:02:45,990 --> 01:02:48,530
+بتظهر زي ما هو ال element بتظهر زي ما هو او لما
+
+839
+01:02:48,530 --> 01:02:52,770
+كنتوا بتعملوا multiplication by one by one او
+
+840
+01:02:52,770 --> 01:02:58,610
+بتعملوا and مع ال trueصحيح؟ إذا كان false بتظهر
+
+841
+01:02:58,610 --> 01:03:03,030
+false إذا كان true بتظهر true طيب أو o-ring مع ال
+
+842
+01:03:03,030 --> 01:03:09,390
+false مع false ال union ال union مع ال في أي set
+
+843
+01:03:09,390 --> 01:03:13,510
+union مع في هتظهر نفس ال set طيب ال intersection
+
+844
+01:03:13,510 --> 01:03:18,390
+مع ال universe of discourse هتظهر نفس ال set هي هي
+
+845
+01:03:18,390 --> 01:03:23,530
+طيب note that identity function is both one to one
+
+846
+01:03:23,530 --> 01:03:28,010
+و one to oneone to one و أنتوا ما هي فعليا جاية من
+
+847
+01:03:28,010 --> 01:03:31,870
+ال function، ال function في انفرس ف one to one و
+
+848
+01:03:31,870 --> 01:03:34,630
+أنتوا ما انزلك ان هي bijective او bijection
+
+849
+01:03:34,630 --> 01:03:41,010
+function okay بكفي بكفي هنا المرة الجاية يعطيكوا
+
+850
+01:03:41,010 --> 01:03:41,270
+العافية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d8d83fa18422739adcc0edcaac6f2f196265f60d
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0.srt
@@ -0,0 +1,2143 @@
+1
+00:00:20,770 --> 00:00:23,230
+طيب بسم الله الرحمن الرحيم والصلاة والسلام علي
+
+2
+00:00:23,230 --> 00:00:28,110
+أشرف الأنبياء سيدنا محمد وعليه وصحبه أجمعين، وجزاكم
+
+3
+00:00:28,110 --> 00:00:30,110
+المرة اللي فاتت كنا عند موضوع predicate logic
+
+4
+00:00:30,110 --> 00:00:35,170
+وقلنا هنكمله اليوم، ممكن اتكلمنا هيك بصورة مستعجلة
+
+5
+00:00:35,170 --> 00:00:38,290
+شوية عن إيش يعني الـ predicate logic أو سميناها
+
+6
+00:00:38,290 --> 00:00:41,110
+propositional function، سميناها propositional
+
+7
+00:00:41,110 --> 00:00:44,070
+function، فهي فعلاً a propositional function، والهدف
+
+8
+00:00:44,070 --> 00:00:48,010
+من الـ ... من الـ function أساساً أن أنا أقدر أو
+
+9
+00:00:48,010 --> 00:00:52,900
+يعطيني سماحية أني أعبر عن عدة objects بجملة واحدة ...
+
+10
+00:00:52,900 --> 00:00:57,820
+بجملة واحدة، فبنسميها function في variable معين، الـ
+
+11
+00:00:57,820 --> 00:01:01,320
+variable هذا ممكن ياخد أكثر من قيمة ... أكثر من
+
+12
+00:01:01,320 --> 00:01:04,360
+قيمة، ففي الحالة هذه إن بكون أنا أقدرت أسمح لنفسي
+
+13
+00:01:04,360 --> 00:01:08,420
+أن أعمل مجموعة of propositions في جملة واحدة، في
+
+14
+00:01:08,420 --> 00:01:11,220
+إيش؟ في جملة واحدة، وهو هذا الموضوع اللي احنا بدأنا
+
+15
+00:01:11,220 --> 00:01:13,820
+نتكلم عنه وناخذه بالتفاصيل إن شاء الله تعالى
+
+16
+00:01:13,820 --> 00:01:19,000
+فإحنا اتكلمنا عن الـ proposition أو propositional
+
+17
+00:01:19,000 --> 00:01:24,080
+function، فيه إمكانية إن أنا أعبر عن مجموعة، thanks
+
+18
+00:01:24,080 --> 00:01:28,920
+أو مجموعة classes بجملة واحدة، ففي الآخر عشان أعبر
+
+19
+00:01:28,920 --> 00:01:34,180
+عنهم بجملة واحدة، بقول إن f of x، والـ x هذه قد تأخذ
+
+20
+00:01:34,180 --> 00:01:42,180
+مجموعة قيم، فببدأ أكون محدد إيش العينة بتاعتنا اللي
+
+21
+00:01:42,180 --> 00:01:45,180
+ممكن نأخذ منها قيم، main قيم x، فأصبحت هذه بالنسبة لي
+
+22
+00:01:45,180 --> 00:01:50,200
+لو قلنا مثلاً واحد، اثنين، ثلاثة، أربعة، هي كأنها أصبحت
+
+23
+00:01:50,200 --> 00:01:59,640
+f of واحد and f of اثنين and f of three and f
+
+24
+00:01:59,640 --> 00:02:04,840
+of four، طب بدل ما أكتب كلها، الكمية من الـ expressions
+
+25
+00:02:05,750 --> 00:02:08,530
+أو من الـ propositions، طب أنا بكتبها بحاجة ... بحالة
+
+26
+00:02:08,530 --> 00:02:12,830
+واحدة، وبتظل عندي معروفة، معرفة الـ variable محددة بس
+
+27
+00:02:12,830 --> 00:02:16,070
+بيظل اسمها predicate، إذا أنا ما عرفتش الـ variable
+
+28
+00:02:16,070 --> 00:02:20,270
+هذه، هي بالنسبة لي not a proposition لأن ما أقدرش أعطيها
+
+29
+00:02:20,970 --> 00:02:24,710
+true value، ما أقدرش أعطيها قيمة، أقول إن هي true or
+
+30
+00:02:24,710 --> 00:02:28,310
+false، ففي الآخر الـ propositional logic إحنا
+
+31
+00:02:28,310 --> 00:02:31,890
+بنتعامل فيه، الـ propositional logic بنتعامل فيه مع
+
+32
+00:02:31,890 --> 00:02:36,190
+مين؟ مع propositions أو sentence، الـ sentence هذه
+
+33
+00:02:36,190 --> 00:02:39,530
+الجملة هذه لازم تكون لها معنى، عشان تكون لها معنى،
+
+34
+00:02:39,530 --> 00:02:41,930
+بقدر أقول، أنتم قلتولي sentence معينة، فأنا
+
+35
+00:02:41,930 --> 00:02:44,710
+بقدر أقول لكم، اه صح أو خطأ، بقول لكم اه والله
+
+36
+00:02:44,710 --> 00:02:48,840
+المعلومة صحيحة أو خاطئة، بس مش تكون ناقصة، تكون
+
+37
+00:02:48,840 --> 00:02:52,780
+incomplete sentence، كويس، هذه زي ما قلنا، اتكلمنا
+
+38
+00:02:52,780 --> 00:02:57,360
+عنها، وسميناها الـ atomic proposition أو atomic
+
+39
+00:02:57,360 --> 00:03:00,880
+entities، في المقابل في حاجة اسمها الـ predicate
+
+40
+00:03:00,880 --> 00:03:05,580
+logic، وهذه distinguish the subject of a sentence
+
+41
+00:03:05,580 --> 00:03:09,860
+from its predicate، هذه بتميز لي مجموعة الـ subjects
+
+42
+00:03:09,860 --> 00:03:13,540
+بتاعتنا، مجموعة الفاعل أو ممكن تكون object بصورة
+
+43
+00:03:13,540 --> 00:03:20,230
+عامة، object، مجموعة أشياء بقدر يعني نعبر عنهم كـ
+
+44
+00:03:20,230 --> 00:03:26,050
+variable، وبعدين بنشوف كيف ممكن أحددها، الـ
+
+45
+00:03:26,050 --> 00:03:30,730
+variables هذه، عشان أحددها محتاج أحط الـ ... الـ ... الـ
+
+46
+00:03:30,730 --> 00:03:33,950
+... الـ predicate أو الـ propositional function، و
+
+47
+00:03:33,950 --> 00:03:38,310
+بعدين أحط where x equal to كذا مثلاً، حولتها لاقش هنا
+
+48
+00:03:38,310 --> 00:03:43,090
+لـ proposition، لأن عرفنا الـ variable، عرفنا الـ
+
+49
+00:03:43,090 --> 00:03:46,290
+variable، هذا طريقة من طرق تحويل الـ predicate الـ
+
+50
+00:03:46,290 --> 00:03:49,630
+predicate بتاعتنا لمين؟ لـ proposition، لـ proposition
+
+51
+00:03:49,630 --> 00:03:57,000
+نأخذ مثال عشان نتكلم فيه ونوضح منها هالوقت، لو
+
+52
+00:03:57,000 --> 00:04:01,020
+قلنا الـ sentence بتاعتنا the dog is an animal، روحنا
+
+53
+00:04:01,020 --> 00:04:05,140
+على حديقة الحيوان، وقلنا the dog is an animal، طبعاً
+
+54
+00:04:05,140 --> 00:04:07,780
+هتلاقي في حديقة الحيوان أو في الزاوية اللي موجودة في
+
+55
+00:04:07,780 --> 00:04:11,600
+أكثر من one animal، صحيح؟ في مجموعة animals كتيرة
+
+56
+00:04:11,600 --> 00:04:17,460
+مجموعة، وكل واحد في قفصه، فـ the dog is نفسها هذه
+
+57
+00:04:17,460 --> 00:04:19,600
+اللي هي الـ subject أو الـ object اللي بتتعامل معاه
+
+58
+00:04:19,600 --> 00:04:24,000
+هذه الشيء، فممكن أعبر عنه بـ X، لإنه ممكن يكون في هنا
+
+59
+00:04:25,640 --> 00:04:32,480
+جنبه كلب، جنبه قطة، جنبه أسد، فيه مجموعة، لو
+
+60
+00:04:32,480 --> 00:04:35,780
+بدي أعمل generalization للـ expression تبعي، للـ
+
+61
+00:04:35,780 --> 00:04:40,060
+proposition بتاعتي، بنحطها x، و x بعدين تاخد أي قيمة
+
+62
+00:04:40,060 --> 00:04:44,780
+بس نحدد لها أنا عن إيش بتكلم، فعشان نحدد لها، هنأخذ
+
+63
+00:04:44,780 --> 00:04:48,450
+لاحقاً حاجة هنسميها فضاء العينة، في الإحصاء بتاخدوا
+
+64
+00:04:48,450 --> 00:04:50,630
+حاجة اسمه فضاء العينة، أنا من وين أختار القيم
+
+65
+00:04:50,630 --> 00:04:53,890
+بتاعتي؟ هنتكلم عنها لاحقاً إن شاء الله، طيب is animal
+
+66
+00:04:53,890 --> 00:04:57,790
+هذه الـ predicate بتاعتنا، هذه الـ predicate بتاعتنا
+
+67
+00:04:57,790 --> 00:05:02,550
+اللي هي الصفة المشتركة لكل الـ X الممكنة، الصفة
+
+68
+00:05:02,550 --> 00:05:08,190
+المشتركة، هذا هو الفرضية، predicate، أو بمعنى الفرضية
+
+69
+00:05:08,190 --> 00:05:13,150
+لكل الـ X الممكنة، الـ X زي ما قلنا الـ object أو اللي
+
+70
+00:05:13,150 --> 00:05:16,170
+هو ممكن يكون subject للجملة بتاعتنا، فإحنا هنا نتكلم
+
+71
+00:05:16,170 --> 00:05:20,520
+عن Predicate logic، طبعاً إذا أنا ما قلت لحالها
+
+72
+00:05:20,520 --> 00:05:24,500
+predicate، وهذه لا تعبر عن الـ proposition لحالها
+
+73
+00:05:24,500 --> 00:05:29,380
+بهذا الشكل، لا تعبر عن الـ proposition، كجملة
+
+74
+00:05:29,380 --> 00:05:34,060
+predicate لحالها، طيب لازم تتعرف الـ x عشان أقول هذا
+
+75
+00:05:34,060 --> 00:05:38,320
+فعلاً proposition كاملة، تمام، في الآخر أنا بأعبر، إحنا
+
+76
+00:05:38,320 --> 00:05:42,910
+كـ function P of variables، بحط مجموعة الـ variables
+
+77
+00:05:42,910 --> 00:05:45,310
+اللي بدي إياها، ممكن تكون one variable، ممكن تكون أكثر
+
+78
+00:05:45,310 --> 00:05:51,250
+من one variable، from objects to propositions، for
+
+79
+00:05:51,250 --> 00:05:55,330
+example، P، للمثال اللي إحنا اتكلمنا عنه هنا، قلنا P of
+
+80
+00:05:55,330 --> 00:06:04,410
+X equal to X is an animal، والـ X هنا is an object من
+
+81
+00:06:04,410 --> 00:06:08,190
+وين؟ أي object، من مين؟ من فضاء العينة اللي هنتكلم
+
+82
+00:06:08,190 --> 00:06:12,400
+عنه، الـ universe of discourse، أنا بتكلم عن إيش
+
+83
+00:06:12,400 --> 00:06:14,540
+الاحتمالات أو إيش الـ possibilities اللي ممكن آخذ
+
+84
+00:06:14,540 --> 00:06:18,460
+منها قيمة X، بنسميها فضاء العينة ... بنسميها فضاء
+
+85
+00:06:18,460 --> 00:06:21,420
+العينة، وبدنا نكون محددينها، إذا بدي برضه أحولها لـ
+
+86
+00:06:21,420 --> 00:06:24,840
+proposition، فهنتكلم عن الأجزاء دي بس اللي بدنا
+
+87
+00:06:24,840 --> 00:06:29,080
+نكون عارفينه، أن الـ predicate ... الـ predicate نفسها
+
+88
+00:06:29,080 --> 00:06:33,280
+بحد ذاتها ... بحد ذاتها هي ... هي not a proposition، هي
+
+89
+00:06:33,280 --> 00:06:35,960
+not a proposition، ليش؟ لأنها تحتوي على variable free
+
+90
+00:06:35,960 --> 00:06:42,950
+variable، variable، لسه مش محدد، فهذه بتكون in itself not
+
+91
+00:06:42,950 --> 00:06:48,790
+a proposition، طيب قبل هيك إحنا أخذنا ... أخذتوها
+
+92
+00:06:48,790 --> 00:06:53,030
+سابقاً الـ variables بتاعتنا بنستعملها small letters
+
+93
+00:06:53,030 --> 00:06:59,610
+أو lower case variables، x, y, z، بهذا الشكل بتكون
+
+94
+00:06:59,610 --> 00:07:03,390
+حروف صغيرة، طيب في المقابل الـ uppercase variables
+
+95
+00:07:03,390 --> 00:07:07,750
+P, Q, R، هذه اللي هي الـ predicate نفسها اللي بسميها
+
+96
+00:07:07,750 --> 00:07:13,390
+لها، الـ predicate، P of X، الـ P capital، الـ X small
+
+97
+00:07:13,390 --> 00:07:19,630
+تمام، فهذه بتكون بتعبر لنا عن مين؟ propositional
+
+98
+00:07:19,630 --> 00:07:25,830
+functions أو predicate أو الـ predicate، طيب الـ P هي
+
+99
+00:07:25,830 --> 00:07:30,610
+بحد ذاتها زي ما قلنا not a proposition لأن ما أقدرش
+
+100
+00:07:30,610 --> 00:07:37,730
+أحكم عليها true or false، طيب لكن إذا استعملت P of
+
+101
+00:07:37,730 --> 00:07:44,350
+X، وعرفنا الـ X، تعرفت الـ X فعلاً هي معرفة بشكل دقيق
+
+102
+00:07:44,350 --> 00:07:50,000
+هتصبح الـ predicate مباشرة proposition، هتصبح
+
+103
+00:07:50,000 --> 00:07:54,720
+proposition، زي لو قلنا عندنا الـ predicate P of X
+
+104
+00:07:54,720 --> 00:08:00,040
+equal to X is a prime number، X is a prime number
+
+105
+00:08:00,040 --> 00:08:04,120
+بهذا الشكل هي not a proposition لأن أنا مش محدد X
+
+106
+00:08:04,120 --> 00:08:09,120
+فممكن أختار واحد يحط من باله قيمة لـ X تطلع true
+
+107
+00:08:09,120 --> 00:08:13,440
+واحد ثاني يحط false، بس أنا ما عنديش شيء موحد، ولكن
+
+108
+00:08:13,440 --> 00:08:17,900
+إذا قلت P of 3، اه صارت proposition لأن
+
+109
+00:08:18,250 --> 00:08:22,410
+automatically الـ X هنا هأحولها لإيش؟ لـ 3، فصارت 3
+
+110
+00:08:22,410 --> 00:08:26,630
+is a prime number، proposition ... proposition، واضح
+
+111
+00:08:26,630 --> 00:08:29,450
+أنه proposition، هيك صارت تمام، فإمتى بتكون الـ
+
+112
+00:08:29,450 --> 00:08:33,610
+proposition؟ إذا كان عندكم في الجملة zero free
+
+113
+00:08:33,610 --> 00:08:37,670
+variable، ما فيش أي variables موجودين هنا ... هنا كان
+
+114
+00:08:37,670 --> 00:08:41,070
+في variable، هيكون موجود variable، هي predicate
+
+115
+00:08:41,070 --> 00:08:45,970
+وليس proposition، هنا ما فيش أي x أو أي y، كلهم
+
+116
+00:08:45,970 --> 00:08:49,610
+الجملة ما فيش فيها أي variable، معناته proposition،
+
+117
+00:08:49,610 --> 00:08:55,510
+zero free variable، propositional function، يعبر
+
+118
+00:08:55,510 --> 00:09:00,350
+عنها P of X equal، وبنحط هنا إيش قيمة الـ predicate
+
+119
+00:09:00,350 --> 00:09:03,810
+بتاعتنا أو إيش الـ function نفسها، فهنقول x greater
+
+120
+00:09:03,810 --> 00:09:10,770
+than 7، في الحالة بتاعتنا الـ x variable، اتفقنا الـ x
+
+121
+00:09:10,770 --> 00:09:17,530
+هذه هي الـ variable بتاعتنا، الـ x greater than 7، هذه
+
+122
+00:09:17,530 --> 00:09:25,790
+الـ predicate، هذا الفرضية بتاعتنا، بيظل P of x has
+
+123
+00:09:25,790 --> 00:09:30,230
+no value، صحيح؟ ما أقدرش أقول true، ما أقدرش أقول false،
+
+124
+00:09:30,230 --> 00:09:33,390
+فإذا هذه ما أقدرش أقول إنها proposition، طيب P of
+
+125
+00:09:33,390 --> 00:09:39,310
+three، اه proposition، بس إيش قيمته؟ false، P of ...
+
+126
+00:09:39,310 --> 00:09:43,290
+إيه ... إيه ... true، بقدر أقول إنه اه والله هذه
+
+127
+00:09:43,290 --> 00:09:49,120
+proposition وقيمته ... قيمته تبعته true، كمان
+
+128
+00:09:49,120 --> 00:09:53,080
+proposition أو propositional function ثانية بأكثر
+
+129
+00:09:53,080 --> 00:09:56,520
+من one variable، هنا هنتكلم عن الـ three variables
+
+130
+00:09:56,520 --> 00:10:02,280
+زي لما نقول P of X Y Z equal to X plus Y greater
+
+131
+00:10:02,280 --> 00:10:10,440
+than Z، لما أقول P of X three five has no value، هذه
+
+132
+00:10:10,440 --> 00:10:14,500
+has no value، ليش؟ لأن في ما زال عندي one free
+
+133
+00:10:14,500 --> 00:10:18,620
+variable، لو عندكم عشرة variables، تسعة منهم معرفين
+
+134
+00:10:18,620 --> 00:10:23,640
+وواحد مش معرف، predicate، لأنه بيظل عندكم واحد
+
+135
+00:10:23,640 --> 00:10:29,400
+free variable، ممكن يغير في قيمة الـ truth value
+
+136
+00:10:29,400 --> 00:10:32,560
+بتاعتكم، ممكن يغير في قيمة الـ truth value، طيب P of
+
+137
+00:10:32,560 --> 00:10:37,630
+three, two, four، بتصير proposition، عفواً،
+
+138
+00:10:37,630 --> 00:10:41,550
+proposition، إيش قيمته؟ true، بس بتعوضه، بتشوف هو هل
+
+139
+00:10:41,550 --> 00:10:48,350
+هي true or false، P 2 4 8 is false، برضه بتعوضه، بتشوفه
+
+140
+00:10:48,350 --> 00:10:52,050
+ينطبق مع الـ ... الـ predicate function بتاعتك أو لا
+
+141
+00:10:52,050 --> 00:11:02,030
+طيب كمان example، let P X Y Z، الـ ... الـ predicate
+
+142
+00:11:02,030 --> 00:11:09,010
+نفسها، X gave Y the grade Z، هنا ممكن نحدد، لو قلنا
+
+143
+00:11:09,010 --> 00:11:14,090
+عرفناها، أن الـ X هذه هي المدرسين اللي بيدرسوا في
+
+144
+00:11:14,090 --> 00:11:19,530
+مستوى ثالث مثلاً أو ثاني، الـ Y هم طلاب مستوى ثاني أو
+
+145
+00:11:19,530 --> 00:11:25,510
+ثالث، و Z لـ grade أو الـ grades الممكنة حسب نظام
+
+146
+00:11:25,510 --> 00:11:30,690
+الجامعة، a، يمكن يكون في a minus أو بي، مباشرة بي سي
+
+147
+00:11:30,690 --> 00:11:36,790
+دي لحد الـ F، فبنحصرهم، مدام حصرناهم، حددنا فضاء
+
+148
+00:11:36,790 --> 00:11:39,810
+العينة لكل واحدة منهم، ممكن نأخذ من فضاء العينة أي
+
+149
+00:11:39,810 --> 00:11:43,530
+قيمة، لو عرفناهم كلهم وقلنا x مثلاً تساوي Mike، و y تساوي
+
+150
+00:11:43,530 --> 00:11:48,700
+Mary، و z تساوي a، أصبحت proposition، لأن لو جينا
+
+151
+00:11:48,700 --> 00:11:55,060
+ترجمناها، كتبناها، هنجد أن هي proposition بدون أي
+
+152
+00:11:55,060 --> 00:12:00,100
+free variable، لاحظوا Mike gave Mary the grade A،
+
+153
+00:12:00,100 --> 00:12:04,800
+جملة منطقية، جملة صحيحة، بنيجي نشوف Mary في
+
+154
+00:12:04,800 --> 00:12:09,720
+المساق اللي بيدرسه Mike، أخذت A، isn't true، ما أخذتش A،
+
+155
+00:12:09,720 --> 00:12:13,220
+false، خلاص إلها قيمة، يعني إن صار في عندنا
+
+156
+00:12:13,220 --> 00:12:18,300
+proposition، تصريح، أصبح في عندكم تصريح واضح، بقدر
+
+157
+00:12:18,300 --> 00:12:24,220
+أحكم عليه، أما فرضية predicate، لا، لأن هي ما زالت
+
+158
+00:12:24,220 --> 00:12:28,520
+قيمتها تفترض معرفتي بالـ variables اللي موجودة فيها
+
+159
+00:12:28,520 --> 00:12:32,780
+بالـ variables اللي موجودة فيها، okay، زي ما قلنا
+
+160
+00:12:32,780 --> 00:12:36,460
+هنتكلم عن الـ universe of discourse، universal
+
+161
+00:12:36,460 --> 00:12:38,820
+discourse، فضاء العينة، أنتم كنتوا بتاخدوا في
+
+162
+00:12:38,820 --> 00:12:42,100
+الإحصاء حاجة اسمها فضاء العينة، إيش هي فضاء العينة؟
+
+163
+00:12:42,100 --> 00:12:46,780
+هي set، مجموعة ... مجموعة من الـ objects اللي بقدر
+
+164
+00:12:46,780 --> 00:12:50,720
+أختار منها قيمة الـ variables بتاعتنا، اللي بنقدر
+
+165
+00:12:50,720 --> 00:12:54,600
+نختار منها قيمة الـ variables بتاعتنا، طبعاً الكلام
+
+166
+00:12:54,600 --> 00:12:58,000
+هذا لقدام، هنفصله بمعاني أخرى، بس إحنا  الواجهة تخلينا
+
+167
+00:12:58,000 --> 00:13:01,070
+... على universal discourse أو universal discourse
+
+168
+00:13:01,070 --> 00:13:06,590
+لو قلنا، وإيش الهدف منه؟ الحقيقة هي الهدف الأساسي
+
+169
+00:13:06,590 --> 00:13:09,310
+منه إنه يخدم لي الـ predicate function أو الـ
+
+170
+00:13:09,310 --> 00:13:12,190
+propositional function، بحيث إنه say، في عندكم
+
+171
+00:13:12,190 --> 00:13:16,950
+distinguishing objects from predicates is that it
+
+172
+00:13:16,950 --> 00:13:21,350
+lets you state things about many objects at once،
+
+173
+
+223
+00:17:19,020 --> 00:17:24,740
+الوجودية محدد الوجودية there exists x such that p
+
+224
+00:17:24,740 --> 00:17:29,680
+of x معناها there exists an x in the universe of
+
+225
+00:17:29,680 --> 00:17:36,140
+the squares such that p of x is true وفي الحالة
+
+226
+00:17:36,140 --> 00:17:42,050
+هنا هنتكلم عن x إما قيمة واحدة أو أكثر، يعني يكفي
+
+227
+00:17:42,050 --> 00:17:45,410
+قيمة واحدة من الـ ... من الـ ... من الكل تحققت عشان أقول
+
+228
+00:17:45,410 --> 00:17:49,450
+أن الـ there exists هنا أو الجملة كلها is
+
+229
+00:17:49,450 --> 00:17:54,690
+true يكفيني واحد بس يكفي طالب واحد يعني ممكن نقول
+
+230
+00:17:54,690 --> 00:17:58,670
+من الطالبات اللي موجودين في واحدة هتجيب امتياز
+
+231
+00:17:58,670 --> 00:18:05,910
+ممكن تكون أكثر من واحدة ممكن تكون كلهن صح؟ تمام؟
+
+232
+00:18:05,910 --> 00:18:07,670
+الحالة الوحيدة اللي ممكن تكون فيها ده ماحدش يجيب
+
+233
+00:18:07,670 --> 00:18:12,210
+امتياز بس إذا قلت يوجد طالبة هتجيب امتياز، ما هنا
+
+234
+00:18:12,210 --> 00:18:14,830
+there exists معناته أنا بتكلم عن there exists ممكن
+
+235
+00:18:14,830 --> 00:18:18,570
+تكون واحدة وممكن تكون اثنتان وممكن تكونوا خمسة عشر
+
+236
+00:18:18,570 --> 00:18:22,930
+فإذا في هنا برغم أن أنا عملت تحديد، بس التحديد هذا
+
+237
+00:18:22,930 --> 00:18:26,750
+لواحد أو أكثر، وأكثر هذه ممكن تصل لمرحلة الشمولية
+
+238
+00:18:28,030 --> 00:18:32,630
+أن ممكن تصل تضم معاها for all ممكن تضم معاها for
+
+239
+00:18:32,630 --> 00:18:38,090
+all تمام فهي هذه الشمولية والوجودية تمام تعبيرين
+
+240
+00:18:38,090 --> 00:18:41,670
+هذان هنقدر من خلالهم أو الـ two quantifiers هذان
+
+241
+00:18:41,670 --> 00:18:45,930
+نقدر من خلالهم نحول الـ predicate أو نحدد الـ
+
+242
+00:18:45,930 --> 00:18:49,350
+predicate بحيث أنها تصبح proposition تعطيني
+
+243
+00:18:49,350 --> 00:18:54,030
+معنى واضح أقدر أترجمها بلغة حقيقية، بلغة حقيقية
+
+244
+00:18:54,030 --> 00:18:58,420
+مظبوطة، ناخذ examples و نبدأ بمين؟ بالـ ... الـ
+
+245
+00:18:58,420 --> 00:19:01,640
+quantifier أو الـ universal quantifier let the
+
+246
+00:19:01,640 --> 00:19:05,720
+universal discourse of X be parking spaces at
+
+247
+00:19:05,720 --> 00:19:08,620
+Islamic university of Gaza لو قلنا أن الـ parking
+
+248
+00:19:08,620 --> 00:19:14,900
+spaces أو الأماكن، مواقف السيارات هذه اللي موجودة في
+
+249
+00:19:14,900 --> 00:19:19,920
+الساحات في الجامعة، موجود مجموعة spaces as a
+
+250
+00:19:19,920 --> 00:19:23,440
+parking يعني هي هذه الفضاء العيني تاعتنا هي هذه
+
+251
+00:19:23,440 --> 00:19:27,560
+الـ universe of these cars okay let's say P of X أو
+
+252
+00:19:27,560 --> 00:19:34,360
+للبريدكيت تاعتنا X is full جيت الصبح لعبت لف لف مش
+
+253
+00:19:34,360 --> 00:19:38,620
+لاقي أي parking space مش لاقي أي parking space
+
+254
+00:19:38,620 --> 00:19:41,460
+فإذا كله هيكون full لو بتتكلم عن universal
+
+255
+00:19:41,460 --> 00:19:45,940
+quantifier كأني بقول كلهم مليانين لكن in general
+
+256
+00:19:45,940 --> 00:19:49,620
+بقول x is full ممكن تكون واحدة منهم أو تكون مجموعة
+
+257
+00:19:49,620 --> 00:19:52,460
+أو نصفهم أو ثلثهم أو خمسهم أو كلهم فهذه هي الـ
+
+258
+00:19:52,460 --> 00:19:56,600
+predicate أن x is full x احنا عارفين أن الـ mean الـ
+
+259
+00:19:56,600 --> 00:20:00,660
+parking spaces وين اللي عندنا في الجامعة تمام فهنا
+
+260
+00:20:00,660 --> 00:20:05,880
+لما آجي أتكلم for all x P of x P of x is true هذه
+
+261
+00:20:05,880 --> 00:20:10,240
+الـ sentence is the proposition هنا هذه أصبحت
+
+262
+00:20:10,240 --> 00:20:12,320
+proposition هيك ... ليش؟ لأن أنا عملت
+
+263
+00:20:12,320 --> 00:20:17,340
+quantification على الـ variable الوحيد اللي فيها الـ
+
+264
+00:20:17,340 --> 00:20:22,880
+variable كان free لأ خلته bound ... ربطناه ...
+
+265
+00:20:22,880 --> 00:20:26,340
+ربطناه بشيء محدد ... ربطناه بشيء محدد ... فهنا
+
+266
+00:20:26,340 --> 00:20:35,220
+هأقول أن all parking spaces at I.G are ... أو
+
+267
+00:20:35,220 --> 00:20:43,140
+every parking spaces at I.G are full كلهم all أو
+
+268
+00:20:43,140 --> 00:20:47,960
+every parking space is full هذه ممكن تكون بالشكل
+
+269
+00:20:47,960 --> 00:20:53,560
+هذا أو every is full أو for each part of space at I
+
+270
+00:20:53,560 --> 00:20:58,280
+and G that space is full بالطريقة اللي بتبقوا
+
+271
+00:20:58,280 --> 00:21:01,520
+إياها كاتبينها المهم في الآخر أعرف أنه كل الـ spaces
+
+272
+00:21:01,520 --> 00:21:06,180
+full فلاحظوا
+
+273
+00:21:06,180 --> 00:21:11,460
+إحنا كتبنا هاي واحدة اثنين ثلاث three sentences
+
+274
+00:21:11,460 --> 00:21:16,100
+بتعبر عن المعنى تبعنا هذا، كلهم كتبناهم بدون ما
+
+275
+00:21:16,100 --> 00:21:22,050
+نضطر نكتب variables صحيح؟ في أي x موجودة هنا أو هنا
+
+276
+00:21:22,050 --> 00:21:26,010
+أو هنا فإذا أصبحت proposition حولناها لـ
+
+277
+00:21:26,010 --> 00:21:29,160
+proposition طبعاً كل واحدة الترجمة هي الطريقة اللي
+
+278
+00:21:29,160 --> 00:21:31,140
+بدها إياها، هتترجم واحدة ... هتأخذ الشكل هذا وواحدة
+
+279
+00:21:31,140 --> 00:21:33,820
+هذا وواحدة ... مش أشكال ... في جميع الأحوال أصبحنا
+
+280
+00:21:33,820 --> 00:21:38,600
+بنتعامل مع proposition ... مع proposition بطلت ...
+
+281
+00:21:38,600 --> 00:21:42,780
+predicate ... ليش؟ لأن عملت quantification ...
+
+282
+00:21:42,780 --> 00:21:47,920
+استعملت الـ universal quantifier فحدد لي الـ X أو الـ
+
+283
+00:21:47,920 --> 00:21:52,460
+free variable اللي كان موجود في الجملة طيب الـ
+
+284
+00:21:52,460 --> 00:21:57,180
+existential quantifier أو محدد الوجودية زي ما قلنا
+
+285
+00:21:57,180 --> 00:22:02,420
+أنه على الأقل يوجد ... يوجد object واحد يحقق الـ
+
+286
+00:22:02,420 --> 00:22:06,340
+predicate برضه نفس الـ example هو ... هو لو افترضنا
+
+287
+00:22:06,340 --> 00:22:09,440
+نقول أن الـ universe of discourse of X هو الـ
+
+288
+00:22:09,440 --> 00:22:13,860
+parking spaces at I.G فقلنا الـ P of X أو الـ
+
+289
+00:22:13,860 --> 00:22:17,880
+predicate بتاعتنا ما زالت هي الـ X is full هنا لما
+
+290
+00:22:17,880 --> 00:22:25,120
+نتكلم عن there exists x such that p of x هتصبح أنه
+
+291
+00:22:25,120 --> 00:22:30,600
+at least في one parking space is full صحيح؟ at
+
+292
+00:22:30,600 --> 00:22:38,520
+least في one أو there is one parking space is full
+
+293
+00:22:38,520 --> 00:22:42,280
+فهنا ممكن نقول some parking space برضه some واحد
+
+294
+00:22:42,280 --> 00:22:46,980
+أو أكثر واحد أو أكثر أو there is a parking space
+
+295
+00:22:46,980 --> 00:22:51,570
+at I.G that is full أو زي ما قلنا at least one
+
+296
+00:22:51,570 --> 00:22:56,630
+parking space on I.G is full كلهم في الآخر
+
+297
+00:22:56,630 --> 00:23:01,730
+عرفت منهم إيش إنه يوجد على الأقل واحد أو أكثر أو
+
+298
+00:23:01,730 --> 00:23:06,110
+أكثر أو أكثر كلهم هنا إحنا بنتعامل مع مين؟ مع أن
+
+299
+00:23:06,110 --> 00:23:09,630
+the exists الـ quantifiers تبعنا there exists فإذا
+
+300
+00:23:09,630 --> 00:23:13,670
+two quantifiers for all there exists عرفنا الفرق
+
+301
+00:23:13,670 --> 00:23:18,370
+بينهم بدنا نميزهم كويس عن بعض هذا quantifier أول و
+
+302
+00:23:18,370 --> 00:23:21,010
+quantifier ثاني، الاثنين أهميتهم أنهم بيعملوا لي
+
+303
+00:23:21,010 --> 00:23:26,670
+quantification لـ variable معين فبحاولوا من free لـ
+
+304
+00:23:26,670 --> 00:23:32,930
+bound عشان الـ predicate نفسه يحاولوا لـ proposition
+
+305
+00:23:32,930 --> 00:23:38,010
+لـ proposition طيب فهنا بنتكلم عن free bound
+
+306
+00:23:38,010 --> 00:23:41,590
+variables متى بيكون free ومتى بيكون bound لو
+
+307
+00:23:41,590 --> 00:23:46,450
+قلنا الـ expression تبعنا P of X P of X، X ما فيش أي
+
+308
+00:23:46,450 --> 00:23:49,410
+quantification عليها، في أي quantifier قبلها ما فيش،
+
+309
+00:23:49,410 --> 00:23:53,190
+فإذا هذه معناته أن X undefined، X undefined،
+
+310
+00:23:53,190 --> 00:23:58,030
+معناته أنا بتكلم عن predicate، مش proposition، هنا
+
+311
+00:23:58,030 --> 00:24:02,330
+مش proposition، ليش؟ لأن الـ X undefined، معناته الـ
+
+312
+00:24:02,330 --> 00:24:07,190
+X هذه متغير حر، متغير حر،
+
+313
+00:24:07,190 --> 00:24:12,070
+ما عملنا لها أي تقييد، ما عرفناهاش، ما حددناهاش كويسة a
+
+314
+00:24:12,070 --> 00:24:17,910
+quantifier either for all or exists operates on an
+
+315
+00:24:17,910 --> 00:24:20,950
+expression having one or more free variables and
+
+316
+00:24:20,950 --> 00:24:26,510
+binds one or more of these variables ليش؟ to
+
+317
+00:24:26,510 --> 00:24:30,370
+produce an expression having one or more bound
+
+318
+00:24:30,370 --> 00:24:34,030
+variables إيش يعني؟ بمعنى أن الـ quantifier تبعنا
+
+319
+00:24:34,030 --> 00:24:41,610
+الهدف منه أنه يعمل لنا ... طبعاً إحنا بنطبق أولاً على
+
+320
+00:24:41,610 --> 00:24:47,910
+إيش؟ على expression موجود فيه free variables طب لو
+
+321
+00:24:47,910 --> 00:24:51,690
+ما فيش free variables ما لوش أي معنى أطبقه أولاً فإذا
+
+322
+00:24:51,690 --> 00:24:56,090
+لغاية الآن لغاية هنا هيك أنا بأطبقه على إيش؟ على
+
+323
+00:24:56,090 --> 00:25:00,790
+expression فيها one أو أكثر يعني فيها free
+
+324
+00:25:00,790 --> 00:25:04,000
+variable أو أكثر طب لو ما فيش فيها free variable
+
+325
+00:25:04,000 --> 00:25:08,920
+ما لوش معنى أطبقه هذا بداية طيب خلصنا and binds
+
+326
+00:25:08,920 --> 00:25:14,560
+وبيعمل تقييد، تقييد لـ one or more of these
+
+327
+00:25:14,560 --> 00:25:18,480
+variables بيقيد لي واحد أو أكثر من مجموعة الـ
+
+328
+00:25:18,480 --> 00:25:22,920
+variables هذه ليش؟ برضه بنقيدهم ليش؟ to produce an
+
+329
+00:25:22,920 --> 00:25:27,220
+expression having one or more bound variables مدام
+
+330
+00:25:27,220 --> 00:25:32,560
+ربطته معناته صار في عندي expression مقيدة أو أصبح
+
+331
+00:25:32,560 --> 00:25:36,940
+الـ variable مقيدة بقيم محددة، القيم المحددة دي
+
+332
+00:25:36,940 --> 00:25:45,580
+بقدر أكتبها إما all أو there exists ففي الآخر أنا
+
+333
+00:25:45,580 --> 00:25:50,300
+لغيت الـ free variable من الجملة، لغينا الـ free
+
+334
+00:25:50,300 --> 00:25:56,090
+variable بتاعتنا من الجملة، كويس for example ناخذ
+
+335
+00:25:56,090 --> 00:26:00,830
+مجموعة examples لو قلنا P of X, Y has two free
+
+336
+00:26:00,830 --> 00:26:03,730
+variables طبيعي اللي هم ماشي هم two variables
+
+337
+00:26:03,730 --> 00:26:06,690
+دعونا الـ X و الـ Y الاثنين ما فيش علم أي
+
+338
+00:26:06,690 --> 00:26:11,610
+quantification  free و free فما زالوا الاثنين
+
+339
+00:26:11,610 --> 00:26:15,670
+free هذه predicate صريحة هذه predicate صريحة أو
+
+340
+00:26:15,670 --> 00:26:20,750
+propositional function صريحة واضحة طيب for all X P
+
+341
+00:26:20,750 --> 00:26:29,290
+of X and Y is true لحظة for all x فإذا x هنا bound
+
+342
+00:26:29,290 --> 00:26:35,090
+و y free و
+
+343
+00:26:35,090 --> 00:26:41,890
+x bound variable طيب P of x where x equal to three
+
+344
+00:26:41,890 --> 00:26:45,210
+إحنا قلنا فيه طريقتين أن أنا أعمل quantification
+
+345
+00:26:45,210 --> 00:26:49,750
+أو أن أنا أعمل definition، أن أعرف الـ variable هنا
+
+346
+00:26:49,750 --> 00:26:52,270
+إحنا عرفنا الـ variable فبرضه proposition صارت
+
+347
+00:26:52,270 --> 00:26:56,130
+ليش؟ لأن هو أصلاً فعلاً أصبح bound variable هو بالعكس
+
+348
+00:26:56,130 --> 00:26:59,770
+هو محدد جداً حتى إحنا قيدناه بثلاثة بس لأن قيمته
+
+349
+00:26:59,770 --> 00:27:03,210
+الوحيدة هي ثلاثة فهنا أصبح أنكم zero free
+
+350
+00:27:03,210 --> 00:27:07,790
+variables هذه واضح جداً أنها bona fide أو actual
+
+351
+00:27:07,790 --> 00:27:13,970
+proposition proposition صريحة حقيقية واضحة
+
+352
+00:27:13,970 --> 00:27:19,930
+proposition أصيلة تمام an expression with one or
+
+353
+00:27:19,930 --> 00:27:24,400
+more free variables is still in the game يعني لو
+
+354
+00:27:24,400 --> 00:27:27,240
+عندكم عشرة variables تسعة منهم معمولة بالـ
+
+355
+00:27:27,240 --> 00:27:33,060
+qualifications الـ quantifications واحدة ضالة free
+
+356
+00:27:33,060 --> 00:27:35,540
+ما زلت أنا بتكلم عن الـ predicate ما أقدرش أقول إنها
+
+357
+00:27:35,540 --> 00:27:43,380
+proposition still one free variable معناته أنا
+
+358
+00:27:43,380 --> 00:27:46,220
+ما زلت بتحدث عن إيش؟ predicate ما أقدرش أقول إنها
+
+359
+00:27:46,220 --> 00:27:49,300
+proposition ما أقدرش أقول إنها proposition زي المثال
+
+360
+00:27:49,300 --> 00:27:55,860
+اللي عندكم for all x P of X is true حددنا الـ X بس
+
+361
+00:27:55,860 --> 00:28:01,520
+الـ Y ظلت free الـ
+
+362
+00:28:01,520 --> 00:28:04,680
+listing
+
+363
+00:28:04,680 --> 00:28:08,400
+of qualifiers ممكن تكون أكثر من الـ quantifier
+
+364
+00:28:08,400 --> 00:28:11,280
+عندكم، بدأنا نتكلم إنه ممكن يكون يدي أكثر من
+
+365
+00:28:11,280 --> 00:28:14,560
+variables معنى ذلك أنه برضه بالضرورة ممكن أكون
+
+366
+00:28:14,560 --> 00:28:19,770
+حاطط أكثر من الـ quantifier لكل واحد لـ variable لو
+
+367
+00:28:19,770 --> 00:28:23,470
+أخذنا example let the universal discourse of x and
+
+368
+00:28:23,470 --> 00:28:28,010
+y be people لو أخذنا الناس هم الـ universal
+
+369
+00:28:28,010 --> 00:28:33,550
+discourse بتاعتنا، الناس العادية let L أو الـ
+
+370
+00:28:33,550 --> 00:28:41,990
+predicate L of x and y عبارة عن x likes y بالشكل
+
+371
+00:28:41,990 --> 00:28:46,490
+اللي إحنا شايفينه هنا، اثنين free صحيح؟ فإذن هي
+
+372
+00:28:46,490 --> 00:28:52,710
+عبارة عن predicate with two free variables
+
+373
+00:28:52,710 --> 00:28:56,530
+الاثنين مش محددين لا حددنا هذا ولا حددنا هذا طيب
+
+374
+00:28:56,530 --> 00:29:03,470
+لما أقول there exists y such that L of X and Y هذه
+
+375
+00:29:03,470 --> 00:29:10,690
+معناها أنا حددت الـ Y طيب بس الـ Y محددينهم
+
+376
+00:29:10,690 --> 00:29:14,710
+ومحددينهم إيش؟ there exists وأنا بتكلم عن people
+
+377
+00:29:14,710 --> 00:29:20,190
+معناته someone معناته أنا بتكلم هنا عن someone بعض
+
+378
+00:29:20,190 --> 00:29:25,090
+... بعض الناس بتكلم عن بعض الناس كويس بس بدنا ناخذ
+
+379
+00:29:25,090 --> 00:29:27,570
+بالنا قبل ما أبدأ أترجم، قبل ما أبدأ أعمل وقبل ما
+
+380
+00:29:27,570 --> 00:29:33,310
+أحط الـ expression بتاعتنا هذه اللي اتحددت إيش موقع
+
+381
+00:29:33,310 --> 00:29:40,330
+أصلاً كانت في الـ predicate؟ لاحظوا x likes y من الـ
+
+382
+00:29:40,330 --> 00:29:47,360
+subject؟ مين الـ object؟ why؟ بدنا نحافظ على أن الـ
+
+383
+00:29:47,360 --> 00:29:51,380
+y هنا اللي أنا عرفتها ما زالت هي المفعول به في
+
+384
+00:29:51,380 --> 00:29:55,940
+الجملة، هي ليست الفاعل، فخذوا بالكم من ترتيب الـ
+
+385
+00:29:55,940 --> 00:29:58,780
+predicate من أصله، عشان لما تيجي ترجمتها،
+
+386
+00:29:58,780 --> 00:30:02,940
+تُكتب صح، فهنا لاحظوا there exists someone، آه
+
+387
+00:30:02,940 --> 00:30:07,100
+خذوا بالكم، بدنا نكمل هذه بحيث أنه فعلاً، نعبر
+
+388
+00:30:07,100 --> 00:30:13,240
+أن الـ someone هذول مفعول به مش فاعل، whom x likes
+
+389
+00:30:13,240 --> 00:30:17,060
+فإذا x ما زالت هي إيش؟ الفاعل subject تبع الجملة
+
+390
+00:30:17,060 --> 00:30:22,660
+اللي بيعرفوا أن الـ quantifier بتترجم أول شغلة و
+
+391
+00:30:22,660 --> 00:30:30,400
+بعدين بتحوله ب who أو whom هل هو مفعول به أو فاعل
+
+392
+00:30:30,400 --> 00:30:34,440
+فـ there exists على طول بكتب مباشرة there exists أو
+
+393
+00:30:34,440 --> 00:30:37,500
+there is someone بدون ما أتكلم عن people بتصير
+
+394
+00:30:37,500 --> 00:30:42,580
+someone كويس؟ طيب someone هذول فاعل ... فاعل ولا
+
+395
+00:30:42,580 --> 00:30:48,180
+مفعول به؟ مفعول به هم ... وبحط الفاعل اللي x
+
+396
+00:30:48,180 --> 00:30:52,240
+بيعتمدوا عليه ... بيفضلوهم فـ هذول someone اللي x
+
+397
+00:30:52,240 --> 00:30:59,080
+بيفضلوهم، بس لاحظوا أنا عندي هنا الـ ... الـ x free
+
+398
+00:30:59,080 --> 00:31:04,600
+صحيح؟ x free ما قدرت أعمل لها quantification مدام
+
+399
+00:31:04,600 --> 00:31:06,640
+ما قدرت أعمل لها quantification لاحظوا إنها ظلت
+
+400
+0
+
+445
+00:34:43,340 --> 00:34:44,760
+هو اللي جاي في الأول .. الفعل عفوا اللي جاي في
+
+446
+00:34:44,760 --> 00:34:50,200
+الأول .. rely .. to rely on. Okay, everyone has
+
+447
+00:34:50,200 --> 00:34:53,800
+someone. تمام منطقية جدا حتى مع الترتيب، هاي الـ
+
+448
+00:34:53,800 --> 00:34:56,820
+everyone جاي في الأول، و ال someone جاي في الثاني
+
+449
+00:34:56,820 --> 00:34:59,680
+بعدين أنتو كملوها زي ما بدكم، أعطوا المعنى اللي
+
+450
+00:34:59,680 --> 00:35:02,460
+بدكم يوضحوه، بس تكون واضحة ال everyone و الـ
+
+451
+00:35:02,460 --> 00:35:05,800
+someone، ترتيبهم يكون ماشي مع مين؟ مع الـ
+
+452
+00:35:05,800 --> 00:35:09,260
+mathematical expression تبعنا. طيب، هنا لأن someone
+
+453
+00:35:09,260 --> 00:35:14,580
+someone whom everyone relies on
+
+454
+00:35:17,370 --> 00:35:21,890
+تمام، فإذا there is someone who every... فهي واضحة أن
+
+455
+00:35:21,890 --> 00:35:25,490
+فعلا أنا حطيت there exists في الأول، وبعدين
+
+456
+00:35:25,490 --> 00:35:33,230
+everyone. تمام؟ جويس الـ .. okay، الباقية أتصور صارت
+
+457
+00:35:33,230 --> 00:35:38,290
+واضحة برضه. هتبدو هنا بإيش؟ someone someone has
+
+458
+00:35:39,590 --> 00:35:44,650
+everyone. بس لما .. okay، someone هنا ممكن أنتو
+
+459
+00:35:44,650 --> 00:35:48,150
+أحيانا أعتقد الجملة هنا بس مزود فيها. ممكن أنتو
+
+460
+00:35:48,150 --> 00:35:51,710
+تكتبوا someone مباشرة بدون الكلمة هذه. someone و
+
+461
+00:35:51,710 --> 00:35:56,990
+تكملوا جملتكم عادي. كويس، هنا احنا إيش .. ليش
+
+462
+00:35:56,990 --> 00:35:59,330
+كتبناها بهذا الشكل؟ كتبناها بهذا الشكل على أساس
+
+463
+00:35:59,330 --> 00:36:06,560
+أنه إذا كان all و هنا .. أو someone relies على
+
+464
+00:36:06,560 --> 00:36:11,760
+الكل، معناته هو بطبعه محتاج يعني، هو شخص محتاج،
+
+465
+00:36:11,760 --> 00:36:14,780
+needy person. هذه مجرد بلاغة بتكون .. بتساودوها.
+
+466
+00:36:14,780 --> 00:36:18,160
+أنتو أحرار، بتكونش تساودوها بلاش، هذه يعني جملة
+
+467
+00:36:18,160 --> 00:36:21,680
+هيك استقراضية زيادة على أساس أنه مادام هو معتمد
+
+468
+00:36:21,680 --> 00:36:27,610
+على كل الناس، معناته هو محتاج، فقط أنه بدل ما سميناه
+
+469
+00:36:27,610 --> 00:36:31,550
+one، لأ احنا سمينا ال one هذا، أعطينا صفة اللي هو
+
+470
+00:36:31,550 --> 00:36:36,830
+needy person، شخص محتاج، some needy person، مجرد أنه
+
+471
+00:36:36,830 --> 00:36:39,970
+بس تعريف. ممكن أنتو كلها تجيلوها، و تخلوها some one
+
+472
+00:36:39,970 --> 00:36:43,670
+عادية، و تكملوا جملتكم بدون .. بدون إشكال. بس بدنا
+
+473
+00:36:43,670 --> 00:36:46,830
+نضل محافظين زي ما قلنا، الأهم شغل على ترتيب الـ
+
+474
+00:36:46,830 --> 00:36:50,350
+quantifiers، ال quantifiers بتاعتنا تكون مرتبة حسب
+
+475
+00:36:50,350 --> 00:36:54,370
+ظهورها فعلا في ال expression تبعنا. الثالثة، الرابعة،
+
+476
+00:36:54,370 --> 00:37:00,610
+الرابعة نفس اللي صح. everyone هتبدو everyone whom
+
+477
+00:37:00,610 --> 00:37:06,290
+someone relies on. كويس
+
+478
+00:37:06,290 --> 00:37:11,150
+بالأخيرة، every كلها every، و every كلها everyone،
+
+479
+00:37:11,150 --> 00:37:16,030
+everyone بالظبط. ف everyone relies upon everyone.
+
+480
+00:37:17,620 --> 00:37:22,680
+كله بيعتمد على كله .. كله معتمد على كله .. تمام ..
+
+481
+00:37:22,680 --> 00:37:26,400
+واضحة الجملة هذه .. لما تيجي تترجمه .. ما .. سيبونا
+
+482
+00:37:26,400 --> 00:37:29,340
+من المهارات بتاعتكم .. بتاعت الإنجليزي .. خلونا
+
+483
+00:37:29,340 --> 00:37:33,680
+على جد .. اللي موجود .. حطوه لي بنفس الترتيب ..
+
+484
+00:37:33,680 --> 00:37:37,400
+ليش؟ مش لأنه أنا هيك بدي .. ولكن عشان نكون حافظنا
+
+485
+00:37:37,400 --> 00:37:41,060
+على ال mathematical expression .. بحيث أن الجملة
+
+486
+00:37:41,060 --> 00:37:46,200
+هذه لو بدي أرجحها للرياضيات، ترجع نفسها، مش أفاجأ أن
+
+487
+00:37:46,200 --> 00:37:52,300
+أنتو عملتوها بطريقتكم، فترجع لي هذه. لأن فعلا ممكن
+
+488
+00:37:52,300 --> 00:37:56,040
+هذه واحد يروح يترجمها بالشكل هذا، صح؟ حسب فهمه أنه
+
+489
+00:37:56,040 --> 00:37:58,920
+ما هو المهم أنه المعنى، لأ هو مش المهم المعنى جدّا،
+
+490
+00:37:58,920 --> 00:38:01,800
+بهمنا في ال mathematics هنا ترتيبها، كمان كيف تكون
+
+491
+00:38:01,800 --> 00:38:05,440
+عشان لما نيجي نرجحها من ال language للـ
+
+492
+00:38:05,440 --> 00:38:08,820
+mathematical expression، ترجع نفس ما هي، ترجع كما هي.
+
+493
+00:38:08,820 --> 00:38:10,760
+okay
+
+494
+00:38:15,860 --> 00:38:18,080
+Okay, sometimes the universe of discourse is
+
+495
+00:38:18,080 --> 00:38:22,000
+restricted within the quantification. أنا ممكن أعمل
+
+496
+00:38:22,000 --> 00:38:27,140
+restriction كمان عليه. ممكن نعمل restriction أو
+
+497
+00:38:27,140 --> 00:38:31,120
+restrictions على ال quantifier نفسه، على الـ
+
+498
+00:38:31,120 --> 00:38:34,940
+quantifier نفسه. زي أن أقول for all x، لأ وأحط كمان
+
+499
+00:38:34,940 --> 00:38:39,800
+condition من عندي. for all x أكبر من zero. طب ممكن x
+
+500
+00:38:39,800 --> 00:38:43,670
+تكون هذه، أنا بيعطيها من minus five to five مثلا، صح؟
+
+501
+00:38:43,670 --> 00:38:46,490
+ممكن تكون من minus five to five، لكن لما أقول for
+
+502
+00:38:46,490 --> 00:38:50,870
+all x greater than zero، لأ أنا كمان عملت تحديد
+
+503
+00:38:50,870 --> 00:38:54,390
+داخل التحديد اللي أنا عامله، داخل ال quantifier
+
+504
+00:38:54,390 --> 00:38:57,670
+اللي احنا عاملينه، عاملين restrictions زيادة، قيود
+
+505
+00:38:57,670 --> 00:39:03,030
+زيادة. for all p of x is true، هذه معناها for all x
+
+506
+00:39:03,030 --> 00:39:09,110
+that are greater than zero, p of x is true. يعني
+
+507
+00:39:09,110 --> 00:39:13,440
+كأنه هذه الجملة جايانة من ال condition اللي أنا
+
+508
+00:39:13,440 --> 00:39:17,580
+أضفته، جايانة من ال condition اللي احنا أضفناها، هذه
+
+509
+00:39:17,580 --> 00:39:20,900
+إيش معناها؟ معناها تكون أنا بقول for all x، وبدنا
+
+510
+00:39:20,900 --> 00:39:27,300
+نفتح قوس، if x greater than zero, then p of x is
+
+511
+00:39:27,300 --> 00:39:31,860
+true. فإذا رابطناها هنا ب condition ثاني، رابطناها بـ
+
+512
+00:39:31,860 --> 00:39:38,240
+f جديدة، اللي هي إذا كان x أكبر من zero، it's okay، أو
+
+513
+00:39:38,240 --> 00:39:45,580
+p of x is true. طيب، نفس الكلام، مادام استعملناه لـ for
+
+514
+00:39:45,580 --> 00:39:49,940
+all، ممكن نستعمل there exists، فهنقول there exists x
+
+515
+00:39:49,940 --> 00:39:55,340
+greater than zero such that p of x is true. هذه
+
+516
+00:39:55,340 --> 00:40:00,920
+ممكن نكتبها there is an x greater than zero such
+
+517
+00:40:00,920 --> 00:40:09,710
+that p of x is true. تمام، معناها there exists x
+
+518
+00:40:09,710 --> 00:40:13,870
+هنفتح الأقواس ساعتنا عشان نحط ال condition تبعنا. x
+
+519
+00:40:13,870 --> 00:40:19,730
+greater than zero and p of x is true. and p of x is
+
+520
+00:40:19,730 --> 00:40:26,050
+true. على الأقل واحد يحقق الشرط هذا، بس لازم يتحقق
+
+521
+00:40:26,050 --> 00:40:30,880
+الشرط كامل. لو واحد بس بيكفي، يعني واحد يكون أكبر من
+
+522
+00:40:30,880 --> 00:40:36,360
+صفر، ويكون حققنا ال P of X. فبكون there exists أنه
+
+523
+00:40:36,360 --> 00:40:40,820
+يكفي واحد بس. عشان ذلك يجب يحقق الشرطين مع بعض، يكفي
+
+524
+00:40:40,820 --> 00:40:45,660
+واحد يحقق الشرطين مع بعض، اللي هي أكبر من صفر و P
+
+525
+00:40:45,660 --> 00:40:49,760
+of X is true. ف P of X is true، عشان ذلك حطينا لها
+
+526
+00:40:49,760 --> 00:40:50,600
+and
+
+527
+00:41:02,210 --> 00:41:05,470
+Okay، لو اتكلم .. هنتكلم أكتر على حكاية ال bending
+
+528
+00:41:05,470 --> 00:41:09,270
+و الـ .. و ال bound variables بصورة أكبر، وكيف ممكن
+
+529
+00:41:09,270 --> 00:41:14,050
+أقول أن هذه free or bound variables. لو قولنا for
+
+530
+00:41:14,050 --> 00:41:20,270
+all x there exists x p of x، بستغرب، احنا كل اللي
+
+531
+00:41:20,270 --> 00:41:24,310
+عندنا variable واحد. ليش عملنا اتنين quantifier؟ مش
+
+532
+00:41:24,310 --> 00:41:27,030
+في عندنا اتنين quantifier زي هال logic؟ طبعا، عنده
+
+533
+00:41:27,030 --> 00:41:30,310
+كله variable واحد. ما بنفعش نستعمل two quantifiers
+
+534
+00:41:30,310 --> 00:41:34,470
+لنفس ال variable. بناخد
+
+535
+00:41:34,470 --> 00:41:42,250
+مين منهم الأعامل الأكثر عمومية اللي بيشمل الثاني؟
+
+536
+00:41:42,250 --> 00:41:47,070
+يعني لما أقول كل القيم داخل universe of discourse
+
+537
+00:41:47,070 --> 00:41:52,030
+بيحققوا الشرط، وبعدين أقول لكم لأ، وواحد على الأقل
+
+538
+00:41:52,030 --> 00:41:56,710
+يحقق الشرط، معناته الأوضح واللي هتكون أشمل، إنه على
+
+539
+00:41:56,710 --> 00:42:00,310
+الأقل واحد يحقق الشرط، لإنه هي نفسها بتشمل معها إنه
+
+540
+00:42:00,310 --> 00:42:03,590
+الكل يحقق نفس الشرط. لإنه زي ما قلنا there exists
+
+541
+00:42:03,590 --> 00:42:09,050
+ممكن تكون واحد أو اتنين أو تلاتة أو all. فإذن هي
+
+542
+00:42:09,050 --> 00:42:14,030
+شاملة معها ال all. ها دي مالهاش معنى، لأن هي فعليا
+
+543
+00:42:14,030 --> 00:42:18,830
+مشمولة مع there exists. ففعليا
+
+544
+00:42:18,830 --> 00:42:24,510
+نكتبها إيش؟ there exists such that U of X. دائما خدوا
+
+545
+00:42:24,510 --> 00:42:27,970
+بالكم، ما بحطش أننا تعرفين لنفس ال variable، معناته
+
+546
+00:42:27,970 --> 00:42:31,510
+واحد بيتقاطع مع الثاني، أكيد واحد بيتقاطع مع الثاني،
+
+547
+00:42:31,510 --> 00:42:35,030
+بتكونوا تشوفوا مين الأشمل منهم، اللي بيشمل الـ
+
+548
+00:42:35,030 --> 00:42:37,570
+condition الثاني، عشان يظل condition واحد، أو
+
+549
+00:42:37,570 --> 00:42:41,350
+quantifier واحد بس. بالنسبة لل all و ال there exists،
+
+550
+00:42:41,350 --> 00:42:45,710
+ال there exists هو الأقوى، هو اللي بيشمل مع all.
+
+551
+00:42:45,710 --> 00:42:49,950
+فأنتو هنا فعليا كأنكم شملتو اتنين مع بعض، there
+
+552
+00:42:49,950 --> 00:42:52,830
+exists، كأنكم شملتو اتنين مع بعض، تمام.
+
+553
+00:42:56,880 --> 00:43:03,120
+هنا لو أخدنا الطريقة الثانية، for all x p of x and
+
+554
+00:43:03,120 --> 00:43:11,060
+q of x، آه هذا في واحد free، ضائع، ليش؟ لأن الـ
+
+555
+00:43:11,060 --> 00:43:15,740
+quantifier هنا أنا محدده لمين؟ لل function p، أما الـ
+
+556
+00:43:15,740 --> 00:43:20,420
+function x، لأ، ال function x لأ، ما حددناش إيش للـ
+
+557
+00:43:20,420 --> 00:43:28,360
+function x. ليش؟ هالوقت ممكن أقول هنا الطلاب
+
+558
+00:43:28,360 --> 00:43:31,740
+مثلا، هنا الطلاب الـ .. أو كل الطلاب، الطلبة اللي
+
+559
+00:43:31,740 --> 00:43:36,940
+موجودين، اللي عندنا مسجلين مساق ال discrete و مساق
+
+560
+00:43:36,940 --> 00:43:42,010
+ال logic. لأ، ال logic أنا مش معرف عنه شيء، أما اللي
+
+561
+00:43:42,010 --> 00:43:44,690
+بقدر أعرف، أن كل اللي موجودين هنا آه مسجلينه، ليش؟ لإنه
+
+562
+00:43:44,690 --> 00:43:47,930
+بدليل أنه حاضر المحاضرة، بدليل أنه حاضر المحاضرة.
+
+563
+00:43:47,930 --> 00:43:51,910
+فهو فعلا مسجل مساق ال discrete. فهدول هم ال universe
+
+564
+00:43:51,910 --> 00:43:55,810
+of discourse بتاع مين؟ بتاع ال P of X، بس مش هم
+
+565
+00:43:55,810 --> 00:44:00,730
+بتاعون ال Q. ممكن تكون فيه تفاوت، يعني مش كلكم
+
+566
+00:44:00,730 --> 00:44:04,030
+مسجلين ال logic، صح؟ مش كلكم، في بعض منكم مسجلها، و
+
+567
+00:44:04,030 --> 00:44:07,400
+في بعض منكم لأ، مش مسجلها. فبقدرش أحكم فيها، هذه ما فيش
+
+568
+00:44:07,400 --> 00:44:10,460
+عليها quantifier، هذه ما فيش عليها quantifier، تمام.
+
+569
+00:44:10,460 --> 00:44:14,060
+فهذه هتبقى free، رغم أن هي x، رغم أن هي x وأنا
+
+570
+00:44:14,060 --> 00:44:16,600
+بتكلم عن نفسي، اللي موجودة قدامنا، الطالبات اللي
+
+571
+00:44:16,600 --> 00:44:19,980
+موجودين قدامنا. بس هنا أنا معرفهم بطريقة، وهنا اللي
+
+572
+00:44:19,980 --> 00:44:25,330
+هم معرفين بطريقة ثانية. طيب، فإذا الـ .. ال outside of
+
+573
+00:44:25,330 --> 00:44:29,530
+the scope of the universe of this .. for all
+
+574
+00:44:29,530 --> 00:44:35,110
+quantifier، هو بيضل free، هيضل عندكم free. فهدا
+
+575
+00:44:35,110 --> 00:44:38,850
+ما بقدرش أقول أن هي proposition، ما بقدرش أقول أن هي
+
+576
+00:44:38,850 --> 00:44:42,530
+proposition، بعكس اللي فوق، بعكس اللي فوق اللي
+
+577
+00:44:42,530 --> 00:44:48,970
+كانت فعلا proposition. فإذا هذا bound variable، هذا
+
+578
+00:44:48,970 --> 00:44:54,300
+لأ، هذا free. ما يغركمش أن أنا بتكلم عن نفس ال X، تمام؟
+
+579
+00:44:54,300 --> 00:44:57,360
+دائما بهمني أن ال predicate نفسه فيه ال quantifier
+
+580
+00:44:57,360 --> 00:45:04,780
+أو لأ. واضح أن ال Q .. ال Q غير ال P. ال P هذا
+
+581
+00:45:04,780 --> 00:45:09,260
+quantifier إله تعريفه، و ال Q إلها تعريف ثاني، هتكون
+
+582
+00:45:09,260 --> 00:45:12,560
+التعريف مختلف تماما. ال predicate function مختلفة.
+
+583
+00:45:12,560 --> 00:45:15,780
+بغض النظر أن ال variable طلع واحد، بغض النظر أن الـ
+
+584
+00:45:15,780 --> 00:45:22,060
+variable نفسه. طيب .. طيب .. أصح أنها تكون بالشكل
+
+585
+00:45:22,060 --> 00:45:26,160
+التالي، كل واحدة إلها التعريف، أو إلها ال quantifier
+
+586
+00:45:26,160 --> 00:45:30,900
+تبعها. فأقول for all x p of x and there exists x
+
+587
+00:45:30,900 --> 00:45:35,680
+such that q of x. okay, it's okay. الحالة هذه ما فيش
+
+588
+00:45:35,680 --> 00:45:39,680
+فيها مشكلة، وجيدة، وتمام، تمام، و this is legal.
+
+589
+00:45:39,680 --> 00:45:44,620
+كويسة على أساس أن الإثنين عندكم مختلفين عن بعض.
+
+590
+00:45:44,620 --> 00:45:49,060
+الإثنين بيكونوا مختلفين عن بعض.
+
+591
+00:45:55,400 --> 00:46:02,260
+فبتلاحظوا أن هنا ال X هذه مقيدة، بس هذه لأ، هذه خارج
+
+592
+00:46:02,260 --> 00:46:09,800
+ال quantifier. الـ
+
+593
+00:46:09,800 --> 00:46:14,480
+quantifier equivalence laws. ال quantifiers هذه زي
+
+594
+00:46:14,480 --> 00:46:16,900
+ما كنا بنتكلم في ال propositional equivalence
+
+595
+00:46:16,900 --> 00:46:20,280
+المرة اللي فاتت. برضه في ال quantifiers، فيه إلها
+
+596
+00:46:20,280 --> 00:46:26,310
+equivalence أو equivalent expressions. for all هي
+
+597
+00:46:26,310 --> 00:46:30,550
+فعليا تعبر عن for all x P of x. هي فعليا كأن أنا
+
+598
+00:46:30,550 --> 00:46:38,030
+بقول P، عارف، تبعنا. a number x is even. number x is
+
+599
+00:46:38,030 --> 00:46:44,370
+even. هقول E of x. E اختصار لإنها جاية من even، للتسهيل. طيب
+
+600
+00:46:44,370 --> 00:46:49,710
+إمتى الكلمة بتحقق؟ if and only if it's equal to two
+
+601
+00:46:49,710 --> 00:46:53,220
+times some other number. احنا عارفين عشان تكون even
+
+602
+00:46:53,220 --> 00:46:57,400
+المفروض أن هي تساوي 2 في رقم ثاني، مظبوط؟ يعني أو
+
+603
+00:46:57,400 --> 00:47:02,720
+بمعنى آخر بتقسم على 2. بمعنى آخر أن هي رقم بيقسم
+
+604
+00:47:02,720 --> 00:47:06,820
+على 2. طيب، هنتأكد من الكلمة ده، هل هو فعلا في عندي
+
+605
+00:47:06,820 --> 00:47:10,280
+رقم بيقسم على 2 بيمشي الكلمة ده؟ كيف ممكن أن أعبر
+
+606
+00:47:10,280 --> 00:47:18,610
+عنها رياضيا؟ فهقول، مادام even، كل القيم، كل x اللي ممكن
+
+607
+00:47:18,610 --> 00:47:21,710
+نعبر عنها أن هي even، المفروض تحقيق لنا الشغل
+
+608
+00:47:21,710 --> 00:47:28,830
+التالي، أن هي even، by conditional. there exists y
+
+609
+00:47:28,830 --> 00:47:36,470
+such that x equal to 2y. معناته هي even إذا كان
+
+610
+00:47:36,470 --> 00:47:44,830
+موجود لكل قيمة ل x، هتكون even إمتى؟ إذا كانت يوجد y
+
+611
+00:47:44,830 --> 00:47:52,020
+نص x. هي معناها، فمعناها ضامن أن X يُعتبر ضعف أي رقم
+
+612
+00:47:52,020 --> 00:47:56,560
+ثاني، ضعف some number، ضعف أي رقم ثاني، مادام ضعف
+
+613
+00:47:56,560 --> 00:48:00,100
+أي رقم ثاني، بتجبل قسمته مع
+
+614
+00:48:00,100 --> 00:48:05,100
+اتنين، أكيد even، أكيد even، أكيد even، زوجي، رقم
+
+615
+00:48:05,100 --> 00:48:09,840
+زوجي، أكيد هتكون رقم زوجي. كمان مرة، for all X،
+
+616
+00:48:09,840 --> 00:48:
+
+667
+00:51:48,520 --> 00:51:53,500
+سبعة في واحد عشان ما يروح الـ computer و أنت بتعمل له
+
+668
+00:51:53,500 --> 00:51:57,380
+code بالـ expression هذا ما يروحش يعتبر أن هي هذه
+
+669
+00:51:57,380 --> 00:52:01,600
+واحدة، وهي حصل ضرب رقمين في الحال لأ، بدنا نقول له أن
+
+670
+00:52:01,600 --> 00:52:07,640
+لأ، دير بالك الـ y لازم لا تساوي واحد، and زي لا
+
+671
+00:52:07,640 --> 00:52:14,920
+تساوي واحد، تمام؟ في اللحظة صار بنقدر من الجملة إذا عندنا
+
+672
+00:52:14,920 --> 00:52:20,460
+تعريف لمجموعة معينة من الـ numbers، بنقدر نعرف منها
+
+673
+00:52:20,460 --> 00:52:24,760
+إيش الـ expression تبعنا أو بنقدر نكتب الـ
+
+674
+00:52:24,760 --> 00:52:28,940
+expression الرياضي تبعنا.  رجعوا في البيت هتلاقوا
+
+675
+00:52:28,940 --> 00:52:32,930
+أنه فعلاً، أمسكوا كلمة كلمة، واحدة واحدة، هتركبوا وراء
+
+676
+00:52:32,930 --> 00:52:37,930
+بعض، هتركبوا وراء بعض، تمام؟ هيك احنا نخلص...
+
+677
+00:52:37,930 --> 00:52:43,610
+خلصنا، كل عام بخير، الـ... طبعاً الـ... الـ homework
+
+678
+00:52:43,610 --> 00:52:48,530
+مش هتسلمونا إياه للأحد الجاي، هيكون عيد، فبيضل للي
+
+679
+00:52:48,530 --> 00:52:51,530
+بعده إن شاء الله تعالى، للي بعده بإذن الله تعالى،
+
+680
+00:52:51,530 --> 00:52:52,090
+يطبخوا، وعافية.
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0b3328c9f52523042fe425745767ffff635b343a
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 5019, "start": 20.77, "end": 50.19, "text": "طيب بسم الله الرحمن الرحيم و الصلاة و السلام علي أشرف الأنبياء سيدنا محمد وعليه وصحبه أجمعين وجفنا المرة اللي فاتت عند موضوع ال predicate logic وقولنا هنكمله اليوم ممكن اتكلمنا هيك بصورة مستعجلة شوية عن إيش يعني ال predicate logic أو سميناها propositional function سميناها propositional function فهي فعلا a propositional function و الهدف من ال .. من ال function أساسا أن أنا أقدر أو يعطيني سماحية أني أعبر عن كذا", "tokens": [9566, 1829, 3555, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 4032, 31767, 15040, 3660, 4032, 21136, 37440, 25894, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 20292, 3224, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 49610, 5172, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 43242, 3714, 2407, 11242, 45367, 2423, 3852, 8700, 9952, 4032, 39648, 8315, 8032, 1863, 24793, 1211, 3224, 45595, 20498, 3714, 43020, 1975, 2655, 4117, 19528, 8315, 39896, 4117, 4724, 9381, 13063, 3660, 3714, 14851, 3615, 7435, 37977, 13412, 2407, 10632, 18871, 11933, 1829, 8592, 37495, 22653, 2423, 3852, 8700, 9952, 34051, 8608, 2304, 1829, 8315, 11296, 7532, 2628, 2445, 8608, 2304, 1829, 8315, 11296, 7532, 2628, 2445, 6156, 3224, 1829, 6156, 3615, 15040, 257, 7532, 2628, 2445, 4032, 2423, 3224, 3215, 5172, 9154, 2423, 4386, 9154, 2423, 2445, 5551, 3794, 32277, 995, 14739, 41850, 5551, 28543, 2288, 34051, 37495, 9566, 9957, 1829, 8608, 15042, 5016, 10632, 14739, 1829, 5551, 3615, 3555, 2288, 18871, 9122, 15730], "avg_logprob": -0.17431358174781578, "compression_ratio": 1.9847560975609757, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 20.77, "end": 21.09, "word": "طيب", "probability": 0.8474934895833334}, {"start": 21.09, "end": 21.73, "word": " بسم", "probability": 0.684326171875}, {"start": 21.73, "end": 21.85, "word": " الله", "probability": 0.9501953125}, {"start": 21.85, "end": 22.09, "word": " 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three", "probability": 0.5771484375}], "temperature": 1.0}, {"id": 25, "seek": 63562, "start": 607.68, "end": 635.62, "text": "five has no value هذه has no value ليش؟ لأن في مزال عندي one free variable لو عندكوا عشرة variables تسعة منهم معرفين و واحد مش معرف predicate لأنه هيضل عندكوا واحد free variable ممكن يغير في قيمة ال truth value بتاعتكم ممكن يغير في قيمة ال truth value طيب P of three, two, four predicate", "tokens": [18621, 575, 572, 2158, 29538, 575, 572, 2158, 32239, 8592, 22807, 5296, 33456, 8978, 3714, 11622, 6027, 18871, 16254, 472, 1737, 7006, 45164, 43242, 4117, 14407, 6225, 8592, 25720, 9102, 6055, 3794, 27884, 9154, 16095, 20449, 28480, 9957, 4032, 36764, 24401, 37893, 20449, 28480, 3852, 8700, 5296, 33456, 3224, 39896, 11242, 1211, 43242, 4117, 14407, 36764, 24401, 1737, 7006, 3714, 43020, 7251, 17082, 13546, 8978, 12174, 32640, 3660, 2423, 3494, 2158, 39894, 995, 34268, 24793, 3714, 43020, 7251, 17082, 13546, 8978, 12174, 32640, 3660, 2423, 3494, 2158, 23032, 1829, 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"probability": 0.924072265625}, {"start": 860.81, "end": 862.05, "word": " universe", "probability": 0.8623046875}, {"start": 862.05, "end": 862.29, "word": " of", "probability": 0.9736328125}, {"start": 862.29, "end": 862.75, "word": " discourse", "probability": 0.478515625}, {"start": 862.75, "end": 863.51, "word": " بسميها", "probability": 0.787567138671875}, {"start": 863.51, "end": 863.77, "word": " فضاء", "probability": 0.9752604166666666}, {"start": 863.77, "end": 864.21, "word": " العينة", "probability": 0.8509114583333334}, {"start": 864.21, "end": 865.01, "word": " تبعتنا", "probability": 0.84271240234375}, {"start": 865.01, "end": 865.83, "word": " فضاء", "probability": 0.92578125}, {"start": 865.83, "end": 866.75, "word": " العينة", "probability": 0.8932291666666666}, {"start": 866.75, "end": 867.21, "word": " فهذه", "probability": 0.9298502604166666}, {"start": 867.21, "end": 867.61, "word": " هي", "probability": 0.9638671875}, {"start": 867.61, "end": 869.15, "word": " القيم", "probability": 0.922607421875}, {"start": 869.15, "end": 869.33, "word": " اللي", "probability": 0.838623046875}, {"start": 869.33, "end": 869.89, "word": " ممكن", "probability": 0.993408203125}, {"start": 869.89, "end": 871.03, "word": " تُعطى", "probability": 0.84208984375}, {"start": 871.03, "end": 871.35, "word": " ل", "probability": 0.80224609375}, {"start": 871.35, "end": 871.93, "word": " X", "probability": 0.452880859375}], "temperature": 1.0}, {"id": 36, "seek": 90034, "start": 873.26, "end": 900.34, "text": "هذه كلها بتجمع في set مجموعة بنسميها universe of discourse كويس قلنا إن أنا عشان أحول ل predicate لأ proposition محتاج أعرف ال variables صحيح؟ طيب هذه طريقة الطريقة التانية أحدد ال variable داخل universe of discourse", "tokens": [3224, 24192, 28242, 11296, 39894, 7435, 2304, 3615, 8978, 992, 3714, 7435, 2304, 2407, 27884, 44945, 38251, 1829, 11296, 6445, 295, 23938, 9122, 45865, 3794, 12174, 1211, 8315, 36145, 41850, 6225, 8592, 7649, 5551, 5016, 12610, 5296, 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"word": " universe", "probability": 0.86474609375}, {"start": 877.64, "end": 878.1, "word": " of", "probability": 0.97314453125}, {"start": 878.1, "end": 878.72, "word": " discourse", "probability": 0.9453125}, {"start": 878.72, "end": 879.64, "word": " كويس", "probability": 0.8006184895833334}, {"start": 879.64, "end": 880.56, "word": " قلنا", "probability": 0.604248046875}, {"start": 880.56, "end": 880.7, "word": " إن", "probability": 0.52490234375}, {"start": 880.7, "end": 880.84, "word": " أنا", "probability": 0.79248046875}, {"start": 880.84, "end": 881.06, "word": " عشان", "probability": 0.9627278645833334}, {"start": 881.06, "end": 881.5, "word": " أحول", "probability": 0.86181640625}, {"start": 881.5, "end": 882.02, "word": " ل", "probability": 0.462646484375}, {"start": 882.02, "end": 882.54, "word": " predicate", "probability": 0.79443359375}, {"start": 882.54, "end": 882.98, "word": " لأ", "probability": 0.629638671875}, {"start": 882.98, "end": 885.04, "word": " proposition", "probability": 0.65966796875}, {"start": 885.04, "end": 888.22, "word": " محتاج", "probability": 0.7867024739583334}, {"start": 888.22, "end": 889.38, "word": " أعرف", "probability": 0.9152018229166666}, {"start": 889.38, "end": 890.46, "word": " ال", "probability": 0.91357421875}, {"start": 890.46, "end": 890.8, "word": " variables", "probability": 0.966796875}, {"start": 890.8, "end": 892.52, "word": " صحيح؟", "probability": 0.88779296875}, {"start": 892.52, "end": 892.84, "word": " طيب", "probability": 0.97998046875}, {"start": 892.84, "end": 893.12, "word": " هذه", "probability": 0.402587890625}, {"start": 893.12, "end": 893.5, "word": " طريقة", "probability": 0.9676106770833334}, {"start": 893.5, "end": 893.86, "word": " الطريقة", "probability": 0.7490234375}, {"start": 893.86, "end": 894.22, "word": " التانية", "probability": 0.9708658854166666}, {"start": 894.22, "end": 895.28, "word": " أحدد", "probability": 0.9568684895833334}, {"start": 895.28, "end": 897.98, "word": " ال", "probability": 0.95166015625}, {"start": 897.98, "end": 898.44, "word": " variable", "probability": 0.76220703125}, {"start": 898.44, "end": 899.5, "word": " داخل", "probability": 0.9807942708333334}, {"start": 899.5, "end": 899.82, "word": " universe", "probability": 0.48046875}, {"start": 899.82, "end": 900.02, "word": " of", "probability": 0.96533203125}, {"start": 900.02, "end": 900.34, "word": " discourse", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 37, "seek": 92973, "start": 900.85, "end": 929.73, "text": "فإذا إما أني أعرفه فانعطيه قيمة محددة أو أني أعمله quantification تحديد عن طريق حاجة هتسميها quantifier expressions أو quantifiers مجموعة ال quantifiers هنتكلم عنها فال quantifiers هذه بتسمحلي أني أعمل quantification تحديد أو counting أني أنا قعدت أعرف بالظبط قداش how many objects in the universe of discourse satisfying a given predicate", "tokens": [5172, 28814, 15730, 11933, 15042, 14739, 1829, 5551, 3615, 28480, 3224, 6156, 7649, 3615, 9566, 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"word": " برغم", "probability": 0.92626953125}, {"start": 1101.37, "end": 1101.49, "word": " أن", "probability": 0.413330078125}, {"start": 1101.49, "end": 1101.57, "word": " أنا", "probability": 0.822265625}, {"start": 1101.57, "end": 1101.81, "word": " عملت", "probability": 0.8909505208333334}, {"start": 1101.81, "end": 1102.19, "word": " تحديد", "probability": 0.83221435546875}, {"start": 1102.19, "end": 1102.33, "word": " بس", "probability": 0.95166015625}, {"start": 1102.33, "end": 1102.73, "word": " التحديد", "probability": 0.9833984375}, {"start": 1102.73, "end": 1102.93, "word": " هذا", "probability": 0.9140625}, {"start": 1102.93, "end": 1103.73, "word": " لواحد", "probability": 0.8531901041666666}, {"start": 1103.73, "end": 1103.95, "word": " أو", "probability": 0.7294921875}, {"start": 1103.95, "end": 1104.37, "word": " أكتر", "probability": 0.9615478515625}, {"start": 1104.37, "end": 1104.71, "word": " و", "probability": 0.634765625}, {"start": 1104.71, "end": 1105.01, "word": " أكتر", "probability": 0.9232177734375}, {"start": 1105.01, "end": 1105.17, "word": " هذه", "probability": 0.52587890625}, {"start": 1105.17, "end": 1105.41, "word": " ممكن", "probability": 0.9921875}, {"start": 1105.41, "end": 1105.73, "word": " تصل", "probability": 0.986328125}, {"start": 1105.73, "end": 1106.13, "word": " لمرحلة", "probability": 0.87109375}, {"start": 1106.13, "end": 1106.75, "word": " الشمولية", "probability": 0.975341796875}], "temperature": 1.0}, {"id": 45, "seek": 113453, "start": 1108.03, "end": 1134.53, "text": "إن ممكن تصل تضم معاها for all ممكن تضم معاها for all تمام فهي هذه الشمولية والوجودية تمام تعبيرين هدولة هنقدر من خلالهم او ال two quantifiers هدولة نقدر من خلالهم نحول ال predicate او نحدد ال predicate بحيث انها تصبح اس proposition تعطيني معنى واضح اقدر اترجمها كلام حقيقي language حقيقية مظبوطة", "tokens": [28814, 1863, 3714, 43020, 6055, 36520, 6055, 11242, 2304, 20449, 995, 11296, 337, 439, 3714, 43020, 6055, 11242, 2304, 20449, 995, 11296, 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"probability": 0.947265625}, {"start": 1722.09, "end": 1722.25, "word": " احنا", "probability": 0.827392578125}, {"start": 1722.25, "end": 1722.65, "word": " شايفينه", "probability": 0.97548828125}, {"start": 1722.65, "end": 1722.79, "word": " هنا", "probability": 0.91845703125}, {"start": 1722.79, "end": 1723.13, "word": " اتنين", "probability": 0.7969970703125}, {"start": 1723.13, "end": 1723.39, "word": " free", "probability": 0.841796875}], "temperature": 1.0}, {"id": 69, "seek": 175309, "start": 1724.71, "end": 1753.09, "text": "صحيح؟ فإذن هي عبارة عن radicate with two free variables الاتنين مش محددين لا حددنا هذا ولا حددنا هذا طيب لما أقول there exist y such that L of X and Y هذه معناها أنا حددت ال Y طيب بس ال Y محددينهم ومحددينهم إيش؟ there exist", "tokens": [9381, 5016, 1829, 5016, 22807, 6156, 28814, 8848, 1863, 39896, 6225, 3555, 9640, 3660, 18871, 2843, 8700, 365, 732, 1737, 9102, 2423, 9307, 1863, 9957, 37893, 3714, 24401, 3215, 9957, 20193, 11331, 3215, 3215, 8315, 23758, 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"end": 1742.29, "word": " and", "probability": 0.9482421875}, {"start": 1742.29, "end": 1742.61, "word": " Y", "probability": 0.98974609375}, {"start": 1742.61, "end": 1743.47, "word": " هذه", "probability": 0.428955078125}, {"start": 1743.47, "end": 1744.03, "word": " معناها", "probability": 0.9514973958333334}, {"start": 1744.03, "end": 1744.97, "word": " أنا", "probability": 0.6376953125}, {"start": 1744.97, "end": 1746.15, "word": " حددت", "probability": 0.8692626953125}, {"start": 1746.15, "end": 1746.35, "word": " ال", "probability": 0.9892578125}, {"start": 1746.35, "end": 1746.67, "word": " Y", "probability": 0.7646484375}, {"start": 1746.67, "end": 1748.23, "word": " طيب", "probability": 0.931640625}, {"start": 1748.23, "end": 1748.69, "word": " بس", "probability": 0.94287109375}, {"start": 1748.69, "end": 1748.89, "word": " ال", "probability": 0.99755859375}, {"start": 1748.89, "end": 1749.19, "word": " Y", "probability": 0.962890625}, {"start": 1749.19, "end": 1750.69, "word": " محددينهم", "probability": 0.89521484375}, {"start": 1750.69, "end": 1751.25, "word": " ومحددينهم", "probability": 0.794189453125}, {"start": 1751.25, "end": 1752.19, "word": " إيش؟", "probability": 0.8453369140625}, {"start": 1752.19, "end": 1752.57, "word": " there", "probability": 0.845703125}, {"start": 1752.57, "end": 1753.09, "word": " exist", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 70, "seek": 178103, "start": 1753.55, "end": 1781.03, "text": "و أنا بتكلم عن people معناته someone معناته أنا بتكلم هنا عن someone بعض .. بعض الناس بتكلم عن بعض الناس كويس بس بدنا ناخد بالنا قبل ما أبدأ أترجم قبل ما أبدأ أعمل و قبل ما أحط ال expression بتاعتنا هذه اللي اتحددت إيش موقع أصلا كانت في ال predicate؟ لاحظوا x likes y من ال subject؟", "tokens": [2407, 41850, 39894, 4117, 19528, 18871, 561, 20449, 8315, 47395, 1580, 20449, 8315, 47395, 41850, 39894, 4117, 19528, 34105, 18871, 1580, 45030, 11242, 4386, 45030, 11242, 2423, 8315, 3794, 39894, 4117, 19528, 18871, 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3167.59, "word": " فبيضل", "probability": 0.7354736328125}, {"start": 3167.59, "end": 3168.53, "word": " للي", "probability": 0.905029296875}, {"start": 3168.53, "end": 3168.99, "word": " بعده", "probability": 0.962646484375}, {"start": 3168.99, "end": 3169.55, "word": " ان", "probability": 0.6923828125}, {"start": 3169.55, "end": 3169.75, "word": " شاء", "probability": 0.96435546875}, {"start": 3169.75, "end": 3169.83, "word": " الله", "probability": 0.95556640625}, {"start": 3169.83, "end": 3170.43, "word": " تعالى،", "probability": 0.9422607421875}, {"start": 3170.43, "end": 3170.61, "word": " للي", "probability": 0.978515625}, {"start": 3170.61, "end": 3170.83, "word": " بعده", "probability": 0.963134765625}, {"start": 3170.83, "end": 3171.11, "word": " بإذن", "probability": 0.9530029296875}, {"start": 3171.11, "end": 3171.25, "word": " الله", "probability": 0.947265625}, {"start": 3171.25, "end": 3171.53, "word": " تعالى،", "probability": 0.973388671875}, {"start": 3171.53, "end": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c67392af97f6dc6562cc9409732789164c2a15c4
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/kaJj5ZAU3A0_raw.srt
@@ -0,0 +1,2720 @@
+1
+00:00:20,770 --> 00:00:23,230
+طيب بسم الله الرحمن الرحيم و الصلاة و السلام علي
+
+2
+00:00:23,230 --> 00:00:28,110
+أشرف الأنبياء سيدنا محمد وعليه وصحبه أجمعين وجفنا
+
+3
+00:00:28,110 --> 00:00:30,110
+المرة اللي فاتت عند موضوع ال predicate logic
+
+4
+00:00:30,110 --> 00:00:35,170
+وقولنا هنكمله اليوم ممكن اتكلمنا هيك بصورة مستعجلة
+
+5
+00:00:35,170 --> 00:00:38,290
+شوية عن إيش يعني ال predicate logic أو سميناها
+
+6
+00:00:38,290 --> 00:00:41,110
+propositional function سميناها propositional
+
+7
+00:00:41,110 --> 00:00:44,070
+function فهي فعلا a propositional function و الهدف
+
+8
+00:00:44,070 --> 00:00:48,010
+من ال .. من ال function أساسا أن أنا أقدر أو
+
+9
+00:00:48,010 --> 00:00:52,900
+يعطيني سماحية أني أعبر عن كذاobject بجملة واحدة ..
+
+10
+00:00:52,900 --> 00:00:57,820
+بجملة واحدة فبتسميها function في variable معين ال
+
+11
+00:00:57,820 --> 00:01:01,320
+variable هذا ممكن ياخد اكثر من قيمة .. اكثر من
+
+12
+00:01:01,320 --> 00:01:04,360
+قيمة ففي الحالة هذه ان بكون انا اقدرت اسمع لنفسي
+
+13
+00:01:04,360 --> 00:01:08,420
+ان اعمل مجموعة of propositions في جملة واحدة في
+
+14
+00:01:08,420 --> 00:01:11,220
+ايش؟ في جملة واحدة و هو هذا الموضوع اللي احنا بدا
+
+15
+00:01:11,220 --> 00:01:13,820
+نتكلم عنه و ناخده بالتفاصيل ان شاء الله تعالى
+
+16
+00:01:13,820 --> 00:01:19,000
+فاحنا متكلم عنهproposition أو propositional
+
+17
+00:01:19,000 --> 00:01:24,080
+function فيه إمكانية إن أنا أعبر عن مجموعة thanks
+
+18
+00:01:24,080 --> 00:01:28,920
+أو مجموعة classes بجملة واحدة ففي الآخر عشان أعبر
+
+19
+00:01:28,920 --> 00:01:34,180
+عنهم بجملة واحدة بقول إن f of x و ال x هذه قد تأخذ
+
+20
+00:01:34,180 --> 00:01:42,180
+مجموعة قيم فبدا أكون محدد إيش العينةبتاعتنا اللي
+
+21
+00:01:42,180 --> 00:01:45,180
+ممكن ناخد منها قيم main قيم x فأصبحت هذه بالنسبالي
+
+22
+00:01:45,180 --> 00:01:50,200
+لو قلنا مثلا واحد اتنين تلاتة اربعة هي كأنها أصبحت
+
+23
+00:01:50,200 --> 00:01:59,640
+if of واحد and if of اتنين and if of three and if
+
+24
+00:01:59,640 --> 00:02:04,840
+of four طب بدل مكتوب كلها الكمية من ال expressions
+
+25
+00:02:05,750 --> 00:02:08,530
+أو من ال propositions طب انا بكتبها بحاجة .. بحالة
+
+26
+00:02:08,530 --> 00:02:12,830
+واحدة و بتضل عندى معروف معرفة ال variable محددة بس
+
+27
+00:02:12,830 --> 00:02:16,070
+بيضل اسمها predicate اذا انا ماعرفتش ال variable
+
+28
+00:02:16,070 --> 00:02:20,270
+هدى هي بالنسبالى not proposition لإن ماقدرش اعطيها
+
+29
+00:02:20,970 --> 00:02:24,710
+true value بقدرش اعطيها قيمة اقول ان هي true or
+
+30
+00:02:24,710 --> 00:02:28,310
+false ففي الآخر ال propositional logic احنا
+
+31
+00:02:28,310 --> 00:02:31,890
+بنتعامل فيه ال propositional logic بتعامل فيه مع
+
+32
+00:02:31,890 --> 00:02:36,190
+مين؟ مع propositions او sentence ال sentence هذه
+
+33
+00:02:36,190 --> 00:02:39,530
+الجملة هذه لازم تكون لها معنى عشان تكون لها معنى
+
+34
+00:02:39,530 --> 00:02:41,930
+بقدر أقول الله انتوا قولتولي sentence معينة فانا
+
+35
+00:02:41,930 --> 00:02:44,710
+بقدر أقولكوا اه صح او خطأ بقولكوا اه والله
+
+36
+00:02:44,710 --> 00:02:48,840
+المعلومة صحية او خاطية بس مش تكون ناقصةتكون
+
+37
+00:02:48,840 --> 00:02:52,780
+incomplete sentence كويس هذه زي ما قلنا اتكلمنا
+
+38
+00:02:52,780 --> 00:02:57,360
+عنها وسمناها ال atomic proposition او atomic
+
+39
+00:02:57,360 --> 00:03:00,880
+entities في المقابل في حاجة اسمها ال predicate
+
+40
+00:03:00,880 --> 00:03:05,580
+logic وهذه distinguish the subject of a sentence
+
+41
+00:03:05,580 --> 00:03:09,860
+from its predicate هذه بتميزلي مجموعة ال subjects
+
+42
+00:03:09,860 --> 00:03:13,540
+تبعتنا مجموعة الفاعل او ممكن تكون object بصورة
+
+43
+00:03:13,540 --> 00:03:20,230
+عامة object مجموعة أشياءبقدر يعني نعبر عنهم ك
+
+44
+00:03:20,230 --> 00:03:26,050
+variable و بعدين بنشوف كيف ممكن أحددها ال
+
+45
+00:03:26,050 --> 00:03:30,730
+variables هذهعشان احددها محتاج احط ال .. ال .. ال
+
+46
+00:03:30,730 --> 00:03:33,950
+.. ال predicate او ال propositional function و
+
+47
+00:03:33,950 --> 00:03:38,310
+بعدين احط where x equal to كذا مثلا حولت لاقش هنا
+
+48
+00:03:38,310 --> 00:03:43,090
+ل proposition لانعرفت ال variable عرفنا ال
+
+49
+00:03:43,090 --> 00:03:46,290
+variable هذا طريقة من طرق تحويل ال predicate ال
+
+50
+00:03:46,290 --> 00:03:49,630
+predicate بتاعتنا لمين ل proposition ل proposition
+
+51
+00:03:49,630 --> 00:03:57,000
+ناخد مثال عشان نتكلم بك فيهنوضح منها هالوقت لو
+
+52
+00:03:57,000 --> 00:04:01,020
+قلنا ال sentence بتاعتنا the dog is animal روحنا
+
+53
+00:04:01,020 --> 00:04:05,140
+على حدكة الحيوان و قلنا the dog is animal طبعا
+
+54
+00:04:05,140 --> 00:04:07,780
+هتلاقي في حدكة الحيوان أو في الزوية اللي موجودة في
+
+55
+00:04:07,780 --> 00:04:11,600
+أكتر من one animal صحيح؟ في مجموعة animals كتيرة
+
+56
+00:04:11,600 --> 00:04:17,460
+مجموعة و كل واحد في قفصه ف the dog is نفسها هذي
+
+57
+00:04:17,460 --> 00:04:19,600
+اللي هي ال subject أو ال object اللي بتتعامل معاه
+
+58
+00:04:19,600 --> 00:04:24,000
+هذي الشيء فممكن أعبر عنه ب X لإنه ممكن يكون في هنا
+
+59
+00:04:25,640 --> 00:04:32,480
+شبك أو مكان ل dog جنبه cat جنبه lion فيه مجموعة لو
+
+60
+00:04:32,480 --> 00:04:35,780
+بدي أعمل generalization لل expression تبعي لل
+
+61
+00:04:35,780 --> 00:04:40,060
+proposition تبعتي بنحطها x و x بعدين تاخد أي قيمة
+
+62
+00:04:40,060 --> 00:04:44,780
+بس نحددلها أنا عن إيش بتكلم فعشان نحددلها هي هناخد
+
+63
+00:04:44,780 --> 00:04:48,450
+لاحقا حاجة هنسميها فضاء العينةفي الإحصان تبتاخدوا
+
+64
+00:04:48,450 --> 00:04:50,630
+حاجة اسمه فضاء العينة أنا من وين أختار القيم
+
+65
+00:04:50,630 --> 00:04:53,890
+تبعتي؟ هنتكلم عنها لاحقا ان شاء الله طيب is animal
+
+66
+00:04:53,890 --> 00:04:57,790
+هذه ال predicate بتاعتنا هذه ال predicate بتاعتنا
+
+67
+00:04:57,790 --> 00:05:02,550
+اللي هي الصفة المشتركة لكل ال X الممكنة الصفة
+
+68
+00:05:02,550 --> 00:05:08,190
+المشتركة هذا هو الفرضية predicate أو بمعنى الفرضية
+
+69
+00:05:08,190 --> 00:05:13,150
+لكل ال X الممكنة ال X زي ما قلنا ال object أو اللي
+
+70
+00:05:13,150 --> 00:05:16,170
+هو ممكن يكون subject للجملة تبعتنا فاحنا هنا نتكلم
+
+71
+00:05:16,170 --> 00:05:20,520
+عنPredicate logic طبعا اذا انا ماقي لحالها
+
+72
+00:05:20,520 --> 00:05:24,500
+predicate وهذه لا تعبر عن ال proposition لحدها
+
+73
+00:05:24,500 --> 00:05:29,380
+بهذا الشكل لا تعبر عن ال proposition كجملة
+
+74
+00:05:29,380 --> 00:05:34,060
+predicate لحالها طيب لازم تتعرف ال x عشان اقول هذا
+
+75
+00:05:34,060 --> 00:05:38,320
+فعلا proposition كاملة تمام في الآخر انا بعبر احنا
+
+76
+00:05:38,320 --> 00:05:42,910
+ك function P ofvariables بحط مجموعة ال variables
+
+77
+00:05:42,910 --> 00:05:45,310
+اللي بديها ممكن تكون one variable ممكن تكون أكتر
+
+78
+00:05:45,310 --> 00:05:51,250
+من one variable from objects to propositions for
+
+79
+00:05:51,250 --> 00:05:55,330
+example P للمثال اللي احنا اتكلمناه هنا قلنا P of
+
+80
+00:05:55,330 --> 00:06:04,410
+X equal to X is animal وال X هنا is an object من
+
+81
+00:06:04,410 --> 00:06:08,190
+وين؟ any object من مين؟ من فضاء العين اللي هنتكلم
+
+82
+00:06:08,190 --> 00:06:12,400
+عنه ال universe of discourseأنا بتكلم عن إيش
+
+83
+00:06:12,400 --> 00:06:14,540
+الاحتمالات أو إيش ال possibilities اللي ممكن أخد
+
+84
+00:06:14,540 --> 00:06:18,460
+منها قيمة X بنسميها فضاء العينة .. بنسميها فضاء
+
+85
+00:06:18,460 --> 00:06:21,420
+العينة و بدنا نكون محددينها إذا بدي برضه أحولها ل
+
+86
+00:06:21,420 --> 00:06:24,840
+proposition فهنتكلم عن الأجزايا دي بس اللي بدنا
+
+87
+00:06:24,840 --> 00:06:29,080
+نكون عارفينه أن ال predicate .. ال predicate نفسها
+
+88
+00:06:29,080 --> 00:06:33,280
+بحد ذاتها .. بحد ذاتها هي .. هي not proposition هي
+
+89
+00:06:33,280 --> 00:06:35,960
+not proposition ليش؟ لأنها تحتوي على variable free
+
+90
+00:06:35,960 --> 00:06:42,950
+variable variable لسه مش محدد فهذه بتكونitself not
+
+91
+00:06:42,950 --> 00:06:48,790
+a proposition طيب قبل هيك احنا أخدنا .. أخدتوها
+
+92
+00:06:48,790 --> 00:06:53,030
+سابقا ال variables بتاعتنا بنستعملها small letters
+
+93
+00:06:53,030 --> 00:06:59,610
+او lower case variables x, y, z بهذا الشكل بتكون
+
+94
+00:06:59,610 --> 00:07:03,390
+حروف صغيرة طيب في المقابل ال uppercase variables
+
+95
+00:07:03,390 --> 00:07:07,750
+P, Q, R هد اللي هي ال predicate نفسها اللي بسميها
+
+96
+00:07:07,750 --> 00:07:13,390
+لها ال predicate P of Xال P capital ال X small
+
+97
+00:07:13,390 --> 00:07:19,630
+تمام فهذه بتكون بتعبّر لنا عن مين propositional
+
+98
+00:07:19,630 --> 00:07:25,830
+functions او predicate او ال predicate طيب ال P هي
+
+99
+00:07:25,830 --> 00:07:30,610
+بحد ذاتها زي ما قلناnot proposition لأن ماقدرش
+
+100
+00:07:30,610 --> 00:07:37,730
+أحكم عليها true or false طيب لكن إذا استعملت V of
+
+101
+00:07:37,730 --> 00:07:44,350
+X وعرفنا ال X تعرفت ال X فعلا هي معرفة بشكل دقيق
+
+102
+00:07:44,350 --> 00:07:50,000
+هتصبح ال predicate مباشرة propositionهتصبح
+
+103
+00:07:50,000 --> 00:07:54,720
+proposition زي لو قلنا عندنا ال predicate P of X
+
+104
+00:07:54,720 --> 00:08:00,040
+equal to X is a prime number X is a prime number
+
+105
+00:08:00,040 --> 00:08:04,120
+بهذا الشكل هي not proposition لأن أنا مش محدد X
+
+106
+00:08:04,120 --> 00:08:09,120
+فممكن أختار واحد يحط من باله قيمة ل X تطلع true
+
+107
+00:08:09,120 --> 00:08:13,440
+واحد تاني يحط false بس أنا ماعنديش إشيء موحد ولكن
+
+108
+00:08:13,440 --> 00:08:17,900
+إذا قلت P of 3 أه صارت proposition لأن
+
+109
+00:08:18,250 --> 00:08:22,410
+automatically ال X هنا هحوولها لإيش؟ ل 3 فصارت 3
+
+110
+00:08:22,410 --> 00:08:26,630
+is a prime number proposition .. proposition واضح
+
+111
+00:08:26,630 --> 00:08:29,450
+أنه proposition هيك صارت تمام فإمتى بتكون ال
+
+112
+00:08:29,450 --> 00:08:33,610
+proposition إذا كان عندكوا في الجملة zero free
+
+113
+00:08:33,610 --> 00:08:37,670
+variable مافيش أي variables موجودين هنا .. هنا كان
+
+114
+00:08:37,670 --> 00:08:41,070
+في variable هيومدن موجود variable هي predicate
+
+115
+00:08:41,070 --> 00:08:45,970
+وليست proposition هنا مافيش اي x او اي y كلهم
+
+116
+00:08:45,970 --> 00:08:49,610
+الجملة مافيش فيها أي variable معناته proposition
+
+117
+00:08:49,610 --> 00:08:55,510
+zero في free variable propositional function يعبر
+
+118
+00:08:55,510 --> 00:09:00,350
+عنها P of X equalوبنحط هنا إيش قيمة ال predicate
+
+119
+00:09:00,350 --> 00:09:03,810
+تبعتنا أو إيش ال function نفسها فهنقول x greater
+
+120
+00:09:03,810 --> 00:09:10,770
+than 7 في الحالة بتاعتنا ال x variable اتفقنا ال x
+
+121
+00:09:10,770 --> 00:09:17,530
+هذه هي ال variable تبعتنا ال x greater than 7 هذه
+
+122
+00:09:17,530 --> 00:09:25,790
+ال predicate هذا الفرضية بتاعتنا بيظل P of x has
+
+123
+00:09:25,790 --> 00:09:30,230
+no valueصحيح؟ بقدرش أقول true، بقدرش أقول false،
+
+124
+00:09:30,230 --> 00:09:33,390
+فإذا هذه بقدرش أقول إنها proposition طيب P of
+
+125
+00:09:33,390 --> 00:09:39,310
+three أه proposition، بس إيش قيمته؟ false P of ..
+
+126
+00:09:39,310 --> 00:09:43,290
+إيه .. إيه .. true بقدر أقول إنه أه والله هذه
+
+127
+00:09:43,290 --> 00:09:49,120
+proposition وقيمته .. قيمة تبعته trueكمان
+
+128
+00:09:49,120 --> 00:09:53,080
+proposition أو propositional function تانية بأكثر
+
+129
+00:09:53,080 --> 00:09:56,520
+من one variable هنا هنتكلم عن ال three variables
+
+130
+00:09:56,520 --> 00:10:02,280
+زي لما نقول P of X Y Z equal to X plus Y greater
+
+131
+00:10:02,280 --> 00:10:10,440
+than Z لما أقول P of X threefive has no value هذه
+
+132
+00:10:10,440 --> 00:10:14,500
+has no value ليش؟ لأن في مزال عندي one free
+
+133
+00:10:14,500 --> 00:10:18,620
+variable لو عندكوا عشرة variables تسعة منهم معرفين
+
+134
+00:10:18,620 --> 00:10:23,640
+و واحد مش معرف predicate لأنه هيضل عندكوا واحد
+
+135
+00:10:23,640 --> 00:10:29,400
+free variable ممكن يغير في قيمة ال truth value
+
+136
+00:10:29,400 --> 00:10:32,560
+بتاعتكم ممكن يغير في قيمة ال truth value طيب P of
+
+137
+00:10:32,560 --> 00:10:37,630
+three, two, four predicateبتصير proposition عفوا
+
+138
+00:10:37,630 --> 00:10:41,550
+proposition إيش قيمته true بس بتعوضه بتشوف هو هل
+
+139
+00:10:41,550 --> 00:10:48,350
+هي true or false P 248 is false برضه بتعوضه بتشوفه
+
+140
+00:10:48,350 --> 00:10:52,050
+تنطبق مع ال .. ال predicate function بتاعتك أو لأ
+
+141
+00:10:52,050 --> 00:11:02,030
+طيب كمان example let P X Y Z ال .. ال predicate
+
+142
+00:11:02,030 --> 00:11:09,010
+نفسها X gave Y the gradeZ هنا ممكن نحدد لو قلنا
+
+143
+00:11:09,010 --> 00:11:14,090
+عرفناها ان ال X هذه هي المدرسين اللي بدرسوا في
+
+144
+00:11:14,090 --> 00:11:19,530
+مستوى تالت مثلا او تاني ال Y هم طلاب مستوى تاني او
+
+145
+00:11:19,530 --> 00:11:25,510
+تالت و Z ل gradeأو ال grades الممكنة حسب نظام
+
+146
+00:11:25,510 --> 00:11:30,690
+الجامعة a يمكن يكون في a minus او بي مباشرة بي سي
+
+147
+00:11:30,690 --> 00:11:36,790
+دي لقدر على F فبنحصرهم مدام حصرناهم حددنا فضاء
+
+148
+00:11:36,790 --> 00:11:39,810
+العين لكل واحدة منهم ممكن ناخد من فضاء العين اي
+
+149
+00:11:39,810 --> 00:11:43,530
+قيمة لو عرفناهم كلهم وقلنا x مثلا تسوى my و y تسوى
+
+150
+00:11:43,530 --> 00:11:48,700
+Mary و z تسوى a أصبحتproposition لأن لو جينا
+
+151
+00:11:48,700 --> 00:11:55,060
+ترجمناها كتبناها هنجد أن هي proposition بدون أي
+
+152
+00:11:55,060 --> 00:12:00,100
+free variable لاحظوا Mike gave Mary the grade A
+
+153
+00:12:00,100 --> 00:12:04,800
+جملة منطقية جملة صحيحة ابن بيجي نشوف Mary في
+
+154
+00:12:04,800 --> 00:12:09,720
+المصاقر اللي بدرسه Mike أخدت A isn't true ماخدتش A
+
+155
+00:12:09,720 --> 00:12:13,220
+false خلاص إلها قيمة يعني ان صار في عندنا
+
+156
+00:12:13,220 --> 00:12:18,300
+proposition تصريحأصبح في عندكم تصريح واضح بقدر
+
+157
+00:12:18,300 --> 00:12:24,220
+أحكم عليه أما فرضية predicate لأ لأن هي ما زالت
+
+158
+00:12:24,220 --> 00:12:28,520
+قيمتها تفترض معرفتي بال variables اللي موجودة فيها
+
+159
+00:12:28,520 --> 00:12:32,780
+بال variables اللي موجودة فيها okay زي ما قلنا
+
+160
+00:12:32,780 --> 00:12:36,460
+هنتكلم عن ال universe of discourseuniversal
+
+161
+00:12:36,460 --> 00:12:38,820
+discourse فضاء العينة انتوا كنتوا تاخدوا في
+
+162
+00:12:38,820 --> 00:12:42,100
+الإحصاء حاجة اسمها فضاء العينة إيش هي فضاء العينة؟
+
+163
+00:12:42,100 --> 00:12:46,780
+هي set مجموعة .. مجموعة من ال objects اللي بقدر
+
+164
+00:12:46,780 --> 00:12:50,720
+أختار منها قيمة ال variables بتاعتنا اللي بنقدر
+
+165
+00:12:50,720 --> 00:12:54,600
+نختار منها قيمة ال variables بتاعتنا طبعا الكلام
+
+166
+00:12:54,600 --> 00:12:58,000
+هذا لجدام هنفضه بمعاني أخرى بس احنا الواجهة تخلينا
+
+167
+00:12:58,000 --> 00:13:01,070
+..على universal discourse او universal discourse
+
+168
+00:13:01,070 --> 00:13:06,590
+لو قلنا و ايش الهدف منه الحقيقة هي الهدف الأساسي
+
+169
+00:13:06,590 --> 00:13:09,310
+منه انه يخدملي ال predicate function او ال
+
+170
+00:13:09,310 --> 00:13:12,190
+propositional function بحيث انه say في عندكو
+
+171
+00:13:12,190 --> 00:13:16,950
+distinguishing objects from predicates is that it
+
+172
+00:13:16,950 --> 00:13:21,350
+lets you state things about many objects at once
+
+173
+00:13:21,350 --> 00:13:26,340
+انا بقدر اعبر عن مجموعة objects كتيرة جدافي نفس
+
+174
+00:13:26,340 --> 00:13:31,880
+الوقت في نفس اللحظة بجملة واحدة بجملة واحدة نوضحها
+
+175
+00:13:31,880 --> 00:13:36,540
+لو قلنا P of X equal to X plus one greater than X
+
+176
+00:13:36,540 --> 00:13:42,000
+كتبتنا الجملة هذه وخلاص هذه تعبر عن أي رقم ممكن
+
+177
+00:13:42,000 --> 00:13:49,050
+يكون ل X بدل ما اكتب0 plus 1 أكبر من 0 and 1 plus
+
+178
+00:13:49,050 --> 00:13:55,450
+1 أكبر من 1 and 2 plus 1 أكبر من 2 and طب أنا هيك
+
+179
+00:13:55,450 --> 00:14:00,490
+مش هخلص مش هنخلص لأ احنا ممكن نختزلها كلها بجملة
+
+180
+00:14:00,490 --> 00:14:04,830
+واحدة predicate function هنقول إن هي x plus 1
+
+181
+00:14:04,830 --> 00:14:09,370
+greater than x خلاص اختزلناها ممكن بس بعدين أعرف
+
+182
+00:14:09,370 --> 00:14:12,850
+إيش الأرقام اللي أنا محتاجها ل xنعملها تعريف فإذا
+
+183
+00:14:12,850 --> 00:14:16,390
+عرفتها التعريف تبعي هذا هيكون لمجموعة numbers او
+
+184
+00:14:16,390 --> 00:14:20,810
+مجموعة قيم بحطها في set او في مجموعة بنسميها
+
+185
+00:14:20,810 --> 00:14:25,010
+universe of discourse بسميها فضاء العينة تبعتنا
+
+186
+00:14:25,010 --> 00:14:33,580
+فضاء العينة فهذه هي القيم اللي ممكن تُعطى ل Xهذه
+
+187
+00:14:33,580 --> 00:14:38,100
+كلها بتجمع في set مجموعة بنسميها universe of
+
+188
+00:14:38,100 --> 00:14:42,540
+discourse كويس قلنا إن أنا عشان أحول ل predicate
+
+189
+00:14:42,540 --> 00:14:48,220
+لأ proposition محتاج
+
+190
+00:14:48,220 --> 00:14:53,860
+أعرف ال variables صحيح؟ طيب هذه طريقة الطريقة
+
+191
+00:14:53,860 --> 00:15:00,020
+التانية أحدد ال variable داخل universe of
+
+192
+00:15:00,020 --> 00:15:04,530
+discourseفإذا إما أني أعرفه فانعطيه قيمة محددة أو
+
+193
+00:15:04,530 --> 00:15:09,890
+أني أعمله quantification تحديد عن طريق حاجة
+
+194
+00:15:09,890 --> 00:15:12,670
+هتسميها quantifier expressions أو quantifiers
+
+195
+00:15:12,670 --> 00:15:15,690
+مجموعة ال quantifiers هنتكلم عنها فال quantifiers
+
+196
+00:15:15,690 --> 00:15:20,930
+هذه بتسمحلي أني أعمل quantification تحديد أو
+
+197
+00:15:20,930 --> 00:15:25,330
+counting أني أنا قعدت أعرف بالظبط قداش how many
+
+198
+00:15:25,330 --> 00:15:28,950
+objects in the universe of discourse satisfying a
+
+199
+00:15:28,950 --> 00:15:33,080
+given predicateقداش عدد ال objects اللى موجودة فى
+
+200
+00:15:33,080 --> 00:15:36,980
+فضاء العينة اللى ينطبق عليها ال predicate اللى
+
+201
+00:15:36,980 --> 00:15:39,220
+ينطبق عليها ال predicate او ال predicate بتكون
+
+202
+00:15:39,220 --> 00:15:43,400
+true عندها طيب هناخد اتنين quantifiers two
+
+203
+00:15:43,400 --> 00:15:47,960
+quantifiers ال quantifier الأول for all و هتلاقيها
+
+204
+00:15:47,960 --> 00:15:52,680
+ال E مجلوقة فى هذه العلامة هنعرف ان هي معناها for
+
+205
+00:15:52,680 --> 00:15:59,870
+allfor all is the for all or universal quantifier
+
+206
+00:15:59,870 --> 00:16:06,150
+المحدد الشمولي لما اقول كل الطالبات اللي موجودين
+
+207
+00:16:06,150 --> 00:16:11,250
+في القاعة مسجلين discrete شمولية معناته انه اي
+
+208
+00:16:11,250 --> 00:16:14,690
+واحدة انتقائيا لو قلت اه انت مسجلة شفت رقمها
+
+209
+00:16:14,690 --> 00:16:17,690
+الجامعة وفتحت على ال .. اه عليكيها مسجلة معناته
+
+210
+00:16:17,690 --> 00:16:22,350
+انه كل for allهكذا عملنا تحديد أصبحنا نقدر نعبر
+
+211
+00:16:22,350 --> 00:16:26,090
+عنها أو خلّيني نقول إن ال X بطلت variable لأن
+
+212
+00:16:26,090 --> 00:16:30,530
+حكمنا عليها إنه للكل .. للكل .. كل اللي موجودين في
+
+213
+00:16:30,530 --> 00:16:34,090
+القاعة مسجلين discrete .. discrete mathematics فلس
+
+214
+00:16:34,090 --> 00:16:38,730
+.. للكل .. فإذا هذه هيكون معناها فوق ال for all X
+
+215
+00:16:38,730 --> 00:16:45,110
+P of X is true معناها for all X in the universe of
+
+216
+00:16:45,110 --> 00:16:51,780
+discourse P holds أو ال predicate هتحصلأو true ..
+
+217
+00:16:51,780 --> 00:16:56,000
+هتصير .. كويس .. ال quantifier التاني هم ال two
+
+218
+00:16:56,000 --> 00:17:00,100
+quantifiers هدول اللي هناخدهم ال there exist ..
+
+219
+00:17:00,100 --> 00:17:05,160
+usually .. usually .. و هد مش مقلوبة زي هد .. هد
+
+220
+00:17:05,160 --> 00:17:08,600
+معكوسة ال E بتاعة exist معكوسة هناخدها في هد
+
+221
+00:17:08,600 --> 00:17:10,880
+العلمة .. العلمة هد ال notation هد هنعرف إن أنا
+
+222
+00:17:10,880 --> 00:17:19,020
+بتكلم عن there existthere exist أو يوجد محدد
+
+223
+00:17:19,020 --> 00:17:24,740
+الوجودية محدد الوجودية there exist x such that p
+
+224
+00:17:24,740 --> 00:17:29,680
+of x معناها there exists an x in the universe of
+
+225
+00:17:29,680 --> 00:17:36,140
+the squares such that p of x is true وفي الحالة
+
+226
+00:17:36,140 --> 00:17:42,050
+هني هنتكلم عن x إما قيمة واحدة أو أكتريعني يكفي
+
+227
+00:17:42,050 --> 00:17:45,410
+قيمة واحدة من ال .. من .. من الكل تحققت عشان أقول
+
+228
+00:17:45,410 --> 00:17:49,450
+إن والله ال there exists هنا أو الجملة كلها is
+
+229
+00:17:49,450 --> 00:17:54,690
+true يكفيني واحد بس يكفي طالب واحد يعني ممكن نقول
+
+230
+00:17:54,690 --> 00:17:58,670
+من الطالبات اللي موجودين في واحدة هتجيب امتياز
+
+231
+00:17:58,670 --> 00:18:05,910
+ممكن تكون أكتر من واحدة ممكن تكون كله صح؟تمام؟
+
+232
+00:18:05,910 --> 00:18:07,670
+الحالة الوحيدة اللي ممكن تكون فيها ده ماحدش يجيب
+
+233
+00:18:07,670 --> 00:18:12,210
+امتياز بس إذا قلت يوجد طالبة هتجيب امتياز ما هنا
+
+234
+00:18:12,210 --> 00:18:14,830
+there exist معناته أنا بتكلم عن there exist ممكن
+
+235
+00:18:14,830 --> 00:18:18,570
+تكون واحدة وممكن تكونتان وممكن تكونوا خمسة عشرة
+
+236
+00:18:18,570 --> 00:18:22,930
+فإذا في هنا برغم أن أنا عملت تحديد بس التحديد هذا
+
+237
+00:18:22,930 --> 00:18:26,750
+لواحد أو أكتر و أكتر هذه ممكن تصل لمرحلة الشمولية
+
+238
+00:18:28,030 --> 00:18:32,630
+إن ممكن تصل تضم معاها for all ممكن تضم معاها for
+
+239
+00:18:32,630 --> 00:18:38,090
+all تمام فهي هذه الشمولية والوجودية تمام تعبيرين
+
+240
+00:18:38,090 --> 00:18:41,670
+هدولة هنقدر من خلالهم او ال two quantifiers هدولة
+
+241
+00:18:41,670 --> 00:18:45,930
+نقدر من خلالهم نحول ال predicate او نحدد ال
+
+242
+00:18:45,930 --> 00:18:49,350
+predicate بحيث انها تصبح اس proposition تعطيني
+
+243
+00:18:49,350 --> 00:18:54,030
+معنى واضح اقدر اترجمها كلام حقيقي language حقيقية
+
+244
+00:18:54,030 --> 00:18:58,420
+مظبوطةناخد examples و نبدأ بمين؟ بال .. ال
+
+245
+00:18:58,420 --> 00:19:01,640
+quantifier أو ال universal quantifier let the
+
+246
+00:19:01,640 --> 00:19:05,720
+universal discourse of X be parking spaces at
+
+247
+00:19:05,720 --> 00:19:08,620
+Islamic university of Gaza لو قولنا أن ال parking
+
+248
+00:19:08,620 --> 00:19:14,900
+spaces أو الأماكن صفة السيارات هذه اللي موجودةفي
+
+249
+00:19:14,900 --> 00:19:19,920
+الساحات في الجامعة موجود مجموعة spaces as a
+
+250
+00:19:19,920 --> 00:19:23,440
+parking يعني هي هذه الفضاء العينية تاعتنا هي هذه
+
+251
+00:19:23,440 --> 00:19:27,560
+ال universe of these cars okay let's say P of X او
+
+252
+00:19:27,560 --> 00:19:34,360
+لبنتكيت تاعتنا X is full لجيت الصبح لعبت لف لف مش
+
+253
+00:19:34,360 --> 00:19:38,620
+لاجي اي parking space مش لاجي اي parking space
+
+254
+00:19:38,620 --> 00:19:41,460
+فإذا كله هيكون full لو بتتكلم عن universal
+
+255
+00:19:41,460 --> 00:19:45,940
+quantifier كأني بقول كلهم مليانينلكن in general
+
+256
+00:19:45,940 --> 00:19:49,620
+بقول x is full ممكن تكون واحدة منهم أو تكون مجموعة
+
+257
+00:19:49,620 --> 00:19:52,460
+أو نصفهم أو تلتهم أو خمسمهم أو كلهم فهذه هي ال
+
+258
+00:19:52,460 --> 00:19:56,600
+predicate ان x is full x احنا عارفين ان ال mean ال
+
+259
+00:19:56,600 --> 00:20:00,660
+parking spaces وين اللي عندنا في الجامعة تمام فهنا
+
+260
+00:20:00,660 --> 00:20:05,880
+لما أجى أتكلم for all x P of x P of x is true هذه
+
+261
+00:20:05,880 --> 00:20:10,240
+ال seal is the propositionفهنا هذه أصبحت
+
+262
+00:20:10,240 --> 00:20:12,320
+proposition هيك .. ليش؟ لأن أنا عملت
+
+263
+00:20:12,320 --> 00:20:17,340
+quantification على ال variable الوحيد اللي فيها ال
+
+264
+00:20:17,340 --> 00:20:22,880
+variable كان free لأ خلته bound .. ربطناه ..
+
+265
+00:20:22,880 --> 00:20:26,340
+ربطناه بحاجة محددة .. ربطناه بشيء محدد .. فهنا
+
+266
+00:20:26,340 --> 00:20:35,220
+هقول ان allall parking spaces at ig are .. أو
+
+267
+00:20:35,220 --> 00:20:43,140
+every parking spaces at ig are full كلهم all أو
+
+268
+00:20:43,140 --> 00:20:47,960
+every parking space is full هذه ممكن تكون بالشكل
+
+269
+00:20:47,960 --> 00:20:53,560
+هذا أو every is fullأو for each part of Swiss at I
+
+270
+00:20:53,560 --> 00:20:58,280
+and J that space is full بالطريقة اللي بتبقوا
+
+271
+00:20:58,280 --> 00:21:01,520
+إياها كتبوها المهم في الآخر أعرف أنه كل ال spaces
+
+272
+00:21:01,520 --> 00:21:06,180
+full فلاحظوا
+
+273
+00:21:06,180 --> 00:21:11,460
+احنا كتبنا هاي واحدة تنتين تلاتة three sentences
+
+274
+00:21:11,460 --> 00:21:16,100
+بتعبر عن المعنى تبعنا هذا كلهم كتبناهم بدون ما
+
+275
+00:21:16,100 --> 00:21:22,050
+نضطر نكتب variables صحيح؟في اي x موجودة هنا او هنا
+
+276
+00:21:22,050 --> 00:21:26,010
+او هنا فإذا أصبحت proposition حولناها ل
+
+277
+00:21:26,010 --> 00:21:29,160
+propositionطبعا كل واحدة الترجمة هي الطريقة اللي
+
+278
+00:21:29,160 --> 00:21:31,140
+بدها هي .. هتترجم واحدة .. هتاخد الشكل هذا و واحد
+
+279
+00:21:31,140 --> 00:21:33,820
+هذا و واحد .. مش أشكال .. في جميع الأحوال أصبحنا
+
+280
+00:21:33,820 --> 00:21:38,600
+بنتعامل مع proposition .. مع proposition بطلت ..
+
+281
+00:21:38,600 --> 00:21:42,780
+predicate .. ليش؟ لإن عملت quantification ..
+
+282
+00:21:42,780 --> 00:21:47,920
+استعملت ال universal quantifier فحددلي ال X أو ال
+
+283
+00:21:47,920 --> 00:21:52,460
+free variable اللي كان موجود في الجملةطيب ال
+
+284
+00:21:52,460 --> 00:21:57,180
+existential quantifier أو محدد الوجودية زي ما قلنا
+
+285
+00:21:57,180 --> 00:22:02,420
+انه على الأقل يوجد .. يوجد object واحد يحقق ال
+
+286
+00:22:02,420 --> 00:22:06,340
+predicate برضه نفس ال example هو .. هو لو افترضنا
+
+287
+00:22:06,340 --> 00:22:09,440
+نقول ان ال universe of discourse of X هو ال
+
+288
+00:22:09,440 --> 00:22:13,860
+parking spaces at I وG فقلنا ال P of X او ال
+
+289
+00:22:13,860 --> 00:22:17,880
+predicate بتاعتنا ما زالت هي ال X is full هنا لما
+
+290
+00:22:17,880 --> 00:22:25,120
+نتكلم عن there existx such that p of x هتصبح انه
+
+291
+00:22:25,120 --> 00:22:30,600
+at least في one parking space is full صحيح؟ at
+
+292
+00:22:30,600 --> 00:22:38,520
+least في one او there is one parking space is full
+
+293
+00:22:38,520 --> 00:22:42,280
+فهنا ممكن نقول some parking space برضه some واحد
+
+294
+00:22:42,280 --> 00:22:46,980
+او اكتر واحد او اكتر او there is a parking space
+
+295
+00:22:46,980 --> 00:22:51,570
+at iog that is fullأو زي ما قلنا at least one
+
+296
+00:22:51,570 --> 00:22:56,630
+parking space on I and G is full كلهم في الآخر
+
+297
+00:22:56,630 --> 00:23:01,730
+عرفت منهم إيش إنه يوجد على الأقل واحد أو أكتر أو
+
+298
+00:23:01,730 --> 00:23:06,110
+أكتر أو أكتر كلهم هنا إحنا بنتعامل مع مين مع ان
+
+299
+00:23:06,110 --> 00:23:09,630
+they exist ال quantifiers تبعنا there exist فإذا
+
+300
+00:23:09,630 --> 00:23:13,670
+two quantifiers for all there exist عرفنا الفرق
+
+301
+00:23:13,670 --> 00:23:18,370
+بينهم بدنا نميزهم كويس عن بعضهذا quantifier أول و
+
+302
+00:23:18,370 --> 00:23:21,010
+quantifier تاني الاتنين أهميتهم انهم بيعملولي
+
+303
+00:23:21,010 --> 00:23:26,670
+quantification ل variable معين فبحاولوا من free ل
+
+304
+00:23:26,670 --> 00:23:32,930
+bound عشان ال predicate نفسه يحاولوا ل proposition
+
+305
+00:23:32,930 --> 00:23:38,010
+ل proposition طيب فهنا بنتكلم عن free bound
+
+306
+00:23:38,010 --> 00:23:41,590
+variables امتى بيكون free و امتى بيكون bound لو
+
+307
+00:23:41,590 --> 00:23:46,450
+قلنا ال expression تبعنا P of XP of X، X مافيش أي
+
+308
+00:23:46,450 --> 00:23:49,410
+quantification عليها، في أي quantifier قبلها فيش،
+
+309
+00:23:49,410 --> 00:23:53,190
+فإذا هذه معناته إن X undefined، X undefined،
+
+310
+00:23:53,190 --> 00:23:58,030
+معناته أنا بتكلم عن predicate، مش proposition، هنا
+
+311
+00:23:58,030 --> 00:24:02,330
+مش proposition، ليش؟ لإن ال X undefined، معناته ال
+
+312
+00:24:02,330 --> 00:24:07,190
+X هذه مزالة free variable، مزالة متغير حر،
+
+313
+00:24:07,190 --> 00:24:12,070
+ماعملتولش أي تقييد، ماعرفنهش، ماحددنهشكويسة a
+
+314
+00:24:12,070 --> 00:24:17,910
+quantifier either for all or exists operates on an
+
+315
+00:24:17,910 --> 00:24:20,950
+expression having one or more free variables and
+
+316
+00:24:20,950 --> 00:24:26,510
+binds one or more of these variables ليش؟ to
+
+317
+00:24:26,510 --> 00:24:30,370
+produce an expression having or or more bound
+
+318
+00:24:30,370 --> 00:24:34,030
+variables إيش يعني؟ بمعنى إن ال quantifier تبعنا
+
+319
+00:24:34,030 --> 00:24:41,610
+الهدف منه إن هو يعملنا ..طبعا احنا بنطبق اولا على
+
+320
+00:24:41,610 --> 00:24:47,910
+ايش؟ على expression موجود في free variables طب لو
+
+321
+00:24:47,910 --> 00:24:51,690
+مافيش free variables مالوش اي معنى اطبقه اولا فإذا
+
+322
+00:24:51,690 --> 00:24:56,090
+لعند الان لعند هنا هيك انا بطبقه على ايش على
+
+323
+00:24:56,090 --> 00:25:00,790
+expression فيها one او اكتر يعني فيها free
+
+324
+00:25:00,790 --> 00:25:04,000
+variable او اكترطب لو مافيش فيها free variable
+
+325
+00:25:04,000 --> 00:25:08,920
+مالوش معنى أطبقه هذا بداية طيب خلصنا and pins
+
+326
+00:25:08,920 --> 00:25:14,560
+وبيعمل تقييد تقييد ل one or more of these
+
+327
+00:25:14,560 --> 00:25:18,480
+variables بيقيدلي واحد أو أكتر من مجموعة ال
+
+328
+00:25:18,480 --> 00:25:22,920
+variables هذه ليش؟ برضه بنقيدهم ليش؟ to produce an
+
+329
+00:25:22,920 --> 00:25:27,220
+expression having one or more bound variable مدام
+
+330
+00:25:27,220 --> 00:25:32,560
+ربطته معناته صار في عندي expression مقيدةأو أصبح
+
+331
+00:25:32,560 --> 00:25:36,940
+ال variable مقيدة بقيم محددة، القيم المحددة دي
+
+332
+00:25:36,940 --> 00:25:45,580
+بقدر أكتبها إما all أو there exist ففي الآخر أنا
+
+333
+00:25:45,580 --> 00:25:50,300
+لغيت ال free variable من الجملة، لغينا ال free
+
+334
+00:25:50,300 --> 00:25:56,090
+variable تبعتنا من الجملة، كويسfor example ناخد
+
+335
+00:25:56,090 --> 00:26:00,830
+مجموعة examples لو قلنا P of X, Y has two free
+
+336
+00:26:00,830 --> 00:26:03,730
+variables طبيعي اللي هم ماشي هم two variables
+
+337
+00:26:03,730 --> 00:26:06,690
+دعونا ال X و ال Y الاتنين مافيش علم اي
+
+338
+00:26:06,690 --> 00:26:11,610
+quantification هد free و هد free فمزالوا الاتنين
+
+339
+00:26:11,610 --> 00:26:15,670
+free هد predicate صريحة هد predicate صريحة او
+
+340
+00:26:15,670 --> 00:26:20,750
+propositional function صريحة واضحة طيب for all X P
+
+341
+00:26:20,750 --> 00:26:29,290
+of X and Y is trueلحظة for all x فإذا x هنا bound
+
+342
+00:26:29,290 --> 00:26:35,090
+و y three و
+
+343
+00:26:35,090 --> 00:26:41,890
+x bound variable طيب P of x where x equal to three
+
+344
+00:26:41,890 --> 00:26:45,210
+احنا قلنا فيه طريقتين ان انا اعمل quantification
+
+345
+00:26:45,210 --> 00:26:49,750
+او ان انا اعمل definition ان اعرف ال variable هنا
+
+346
+00:26:49,750 --> 00:26:52,270
+احنا معرفين ال variable فبرضه proposition صارت
+
+347
+00:26:52,270 --> 00:26:56,130
+ليش؟ لأن هو أصلا فعلا أصبح bound variableهو بالعكس
+
+348
+00:26:56,130 --> 00:26:59,770
+هو محدد جدا حتى احنا قيدناه بتلاتة بس لإن قيمته
+
+349
+00:26:59,770 --> 00:27:03,210
+الوحيدة هي تلاتة فهنا أصبح انكوا zero free
+
+350
+00:27:03,210 --> 00:27:07,790
+variables هذي واضح جدا ان هي bona fide او actual
+
+351
+00:27:07,790 --> 00:27:13,970
+proposition proposition صريحة حقيقية واضحة
+
+352
+00:27:13,970 --> 00:27:19,930
+proposition أصيلة تمام an expression with one or
+
+353
+00:27:19,930 --> 00:27:24,400
+more free variables is still in the gameيعني لو
+
+354
+00:27:24,400 --> 00:27:27,240
+عندكوا عشرة variables تسعة منهم معمولة بال
+
+355
+00:27:27,240 --> 00:27:33,060
+qualifications ال quantifications واحدة ضالة free
+
+356
+00:27:33,060 --> 00:27:35,540
+مازلت أنا بتتكلم عن ال predicate بقدرش أقول إن هي
+
+357
+00:27:35,540 --> 00:27:43,380
+proposition still one free variable معناته أنا
+
+358
+00:27:43,380 --> 00:27:46,220
+مازلت بتحدث عن إيش predicate بقدرش أقول إن هي
+
+359
+00:27:46,220 --> 00:27:49,300
+proposition بقدرش أقول إن هي proposition زي النفال
+
+360
+00:27:49,300 --> 00:27:55,860
+اللي عندكوا for all x P of X is trueحددنا ال X بس
+
+361
+00:27:55,860 --> 00:28:01,520
+ال Y دلت free ال
+
+362
+00:28:01,520 --> 00:28:04,680
+listing
+
+363
+00:28:04,680 --> 00:28:08,400
+of qualifiers ممكن تكون أكتر من ال quantifier
+
+364
+00:28:08,400 --> 00:28:11,280
+عندكم بدأنا نتكلم إنه ممكن يكون يدي أكتر من
+
+365
+00:28:11,280 --> 00:28:14,560
+variables معناه ذلك إنه برضه بالضروري ممكن أكون
+
+366
+00:28:14,560 --> 00:28:19,770
+حاطط أكتر من ال quantifier كل واحد لا variableلو
+
+367
+00:28:19,770 --> 00:28:23,470
+أخدنا example let the universal discourse of x and
+
+368
+00:28:23,470 --> 00:28:28,010
+y be people لو أخدنا الناس هم ال universal
+
+369
+00:28:28,010 --> 00:28:33,550
+discourse بتاعتنا الناس العادية let L أو ال
+
+370
+00:28:33,550 --> 00:28:41,990
+predicate L of x and y عبارة عن x likes y بالشكل
+
+371
+00:28:41,990 --> 00:28:46,490
+اللي احنا شايفينه هنا اتنين freeصحيح؟ فإذن هي
+
+372
+00:28:46,490 --> 00:28:52,710
+عبارة عن radicate with two free variables
+
+373
+00:28:52,710 --> 00:28:56,530
+الاتنين مش محددين لا حددنا هذا ولا حددنا هذا طيب
+
+374
+00:28:56,530 --> 00:29:03,470
+لما أقول there exist y such that L of X and Y هذه
+
+375
+00:29:03,470 --> 00:29:10,690
+معناها أنا حددت ال Y طيب بس ال Y محددينهم
+
+376
+00:29:10,690 --> 00:29:14,710
+ومحددينهم إيش؟ there existو أنا بتكلم عن people
+
+377
+00:29:14,710 --> 00:29:20,190
+معناته someone معناته أنا بتكلم هنا عن someone بعض
+
+378
+00:29:20,190 --> 00:29:25,090
+.. بعض الناس بتكلم عن بعض الناس كويس بس بدنا ناخد
+
+379
+00:29:25,090 --> 00:29:27,570
+بالنا قبل ما أبدأ أترجم قبل ما أبدأ أعمل و قبل ما
+
+380
+00:29:27,570 --> 00:29:33,310
+أحط ال expression بتاعتنا هذه اللي اتحددت إيش موقع
+
+381
+00:29:33,310 --> 00:29:40,330
+أصلا كانت في ال predicate؟ لاحظوا x likes y من ال
+
+382
+00:29:40,330 --> 00:29:47,360
+subject؟مين ال object؟ why؟ بدنا نحافظ على إن ال
+
+383
+00:29:47,360 --> 00:29:51,380
+why هنا اللي أنا عرفتها ما زالت هي المفقول بيه في
+
+384
+00:29:51,380 --> 00:29:55,940
+الجملة، هي ليست الفاعل، فتاخدوا بالكم من ترتيب ال
+
+385
+00:29:55,940 --> 00:29:58,780
+predicate من أصله، عشان لما تيجي ترجمه هالوجه،
+
+386
+00:29:58,780 --> 00:30:02,940
+تنكتب صح، فهنا لاحظوا there exists someone، آه
+
+387
+00:30:02,940 --> 00:30:07,100
+بصدروا بالكم، بدنا نكمل هالوجه بحيث إنه فعلا، نعبر
+
+388
+00:30:07,100 --> 00:30:13,240
+إن ال someone هدولة مفقول به مش فاعل،home x likes
+
+389
+00:30:13,240 --> 00:30:17,060
+فإذا x ما زالت هي إيش الفاعل subject تبع الجملة
+
+390
+00:30:17,060 --> 00:30:22,660
+اللي بيعرفه أنه ال quantifier بتترجمه أول شغلة و
+
+391
+00:30:22,660 --> 00:30:30,400
+بعدين بتحوله ب who or whom هل هو مفعول به أو فاعل
+
+392
+00:30:30,400 --> 00:30:34,440
+ف there exist على طول بكتب مباشرة there exist أو
+
+393
+00:30:34,440 --> 00:30:37,500
+there is someone بدون بتكلم عن people بتصير
+
+394
+00:30:37,500 --> 00:30:42,580
+someoneكويس؟ طيب someone هدولة فاعل .. فاعل ولا
+
+395
+00:30:42,580 --> 00:30:48,180
+مفقول بيه؟ مفقول بيه هم .. و بحط الفاعل اللي x
+
+396
+00:30:48,180 --> 00:30:52,240
+بيعتمدوا عليهم .. بيفضلوهم فهدولة someone اللي x
+
+397
+00:30:52,240 --> 00:30:59,080
+بتفضلهم بس لاحظوا أنا عندي هنا ال .. ال x free
+
+398
+00:30:59,080 --> 00:31:04,600
+صحيح؟ x free ماقدرتش أعملها quantification مدام
+
+399
+00:31:04,600 --> 00:31:06,640
+ماقدرتش أعملها quantification لاحظوا إن هي دلت
+
+400
+00:31:06,640 --> 00:31:11,020
+variable في الجملةما زالت variable في الجملة معناه
+
+401
+00:31:11,020 --> 00:31:14,780
+ذلك أنا هنا بتعامل مع ما زالت predicate predicate
+
+402
+00:31:14,780 --> 00:31:17,740
+ما زالت هي هي أنا ماحولتش لسه ل composition
+
+403
+00:31:17,740 --> 00:31:22,140
+ماتحولتش معايا ل proposition فإذا a predicate with
+
+404
+00:31:22,140 --> 00:31:29,520
+one free variable اللي هو x طيب لو قلنا for all x
+
+405
+00:31:29,520 --> 00:31:37,040
+there exists y such thatL of X and Y طبعا واضح أنه
+
+406
+00:31:37,040 --> 00:31:40,260
+automatically هذي هتتحول لإيش ل proposition ليش
+
+407
+00:31:40,260 --> 00:31:43,320
+لأن ال two variables اللي موجودين كل واحدة في إلها
+
+408
+00:31:43,320 --> 00:31:46,580
+ال quantifier تبعها كل واحدة في إلها quantifier
+
+409
+00:31:46,580 --> 00:31:49,840
+فهنا أول ما هنبدأ مين اللي بدأت في الأول ال all
+
+410
+00:31:49,840 --> 00:31:54,460
+ولا ال there exist all بحطها في الأول في الجملة في
+
+411
+00:31:54,460 --> 00:31:58,290
+جملتنا بحطها أولما تقولوليش لأ احنا اللغة
+
+412
+00:31:58,290 --> 00:32:00,850
+الإنجليزية قوية و مش عارفش و بدى أغير و أشجلب
+
+413
+00:32:00,850 --> 00:32:04,830
+فيها، لأ رطبوها بالظبط حسب الصيغة الرياضية اللى
+
+414
+00:32:04,830 --> 00:32:09,110
+قدامكوا، تمام؟ عشان ماتضيعوش الموضوع لإنه هنا
+
+415
+00:32:09,110 --> 00:32:13,790
+هتتشبك معاكوا الجصص و هتلاقوا حالكوا ممكن تترجموها
+
+416
+00:32:13,790 --> 00:32:19,130
+بشكل there exist y for all x مثلا
+
+417
+00:32:22,060 --> 00:32:24,660
+لو بتقولتلكم أنه تشجل بيقولوا لأ أنا بدي أعملها
+
+418
+00:32:24,660 --> 00:32:26,380
+على كيف يمكن أن تروحوا وعملتوا ال expression هذا
+
+419
+00:32:26,380 --> 00:32:32,940
+بدل هذا صح لأنه لاحظوا هم نفسهم تجريبا بس رياضيا
+
+420
+00:32:32,940 --> 00:32:38,480
+لأ فبتكونوا تاخدوا بالكوا أنه نترجم بالظبط حسب
+
+421
+00:32:38,480 --> 00:32:42,640
+تبتيب ال expression اللي موجود بدأت بقول و أنا
+
+422
+00:32:42,640 --> 00:32:47,200
+بتكلم عن people everyone خلاص everyone تمام اللي
+
+423
+00:32:47,200 --> 00:32:51,790
+وراهاsomeone؟ طيب everyone ال everyone هدولة هم
+
+424
+00:32:51,790 --> 00:32:56,310
+الفاعل ولا المفروض بيه؟ فاعل فإذا everyone has
+
+425
+00:32:56,310 --> 00:33:04,390
+someone whom he like تمام؟ فإذا في الآخر حطينا بس
+
+426
+00:33:04,390 --> 00:33:08,970
+verb مساعد يوضح لإنه هذه subject وهذه object
+
+427
+00:33:08,970 --> 00:33:14,330
+المساعد هذا بعدين اللي هو الفعل المساعد حدد نقشه،
+
+428
+00:33:14,330 --> 00:33:18,630
+اتحدد بعدين اشهر، كويسفهنا واضح ان الجملة هنا صارت
+
+429
+00:33:18,630 --> 00:33:24,570
+as proposition ليش؟ لأنه عندي zero free variables
+
+430
+00:33:24,570 --> 00:33:30,090
+حددناهم فهذه proposition في zero free variables
+
+431
+00:33:30,090 --> 00:33:37,050
+طيب كويس ناخد كمان شوية أمثلة و ناخد بالنا من
+
+432
+00:33:37,050 --> 00:33:44,090
+الترتيب كمان مرة لحظوا هذه وهذه هنا all هي all
+
+433
+00:33:44,090 --> 00:33:49,140
+there existبس لاحظوا رغم ان هو ممكن تعطيكوا نفس
+
+434
+00:33:49,140 --> 00:33:51,540
+المعنى او انتوا biological algorithm هو نفس المعنى
+
+435
+00:33:51,540 --> 00:33:55,200
+اعطانى بس هذه الجملة هتنكتب غير هذه ليش؟ لأن انا
+
+436
+00:33:55,200 --> 00:33:58,900
+بترجم expression, mathematical expression، بدي
+
+437
+00:33:58,900 --> 00:34:02,580
+اترجمه زي ما هوخلّينا بس نحدد ال universe of the
+
+438
+00:34:02,580 --> 00:34:04,580
+scores بتاعتنا ال universe of the scores بتاعتنا
+
+439
+00:34:04,580 --> 00:34:11,400
+برضه ال people ال people كويس ال R أو realize upon
+
+440
+00:34:11,400 --> 00:34:18,180
+اللي هو يعتمد على يعتمد على فإذا X realize upon Y
+
+441
+00:34:18,180 --> 00:34:26,900
+هذه معناها إن X يعتمد على Yنكتب كل واحدة من الخمسة
+
+442
+00:34:26,900 --> 00:34:29,820
+.. من الخمس صيغ اللي موجودة عندنا .. من الخمس صيغ
+
+443
+00:34:29,820 --> 00:34:36,540
+نبدأ بمين؟ في الأول every .. تمام everyone has
+
+444
+00:34:36,540 --> 00:34:43,340
+someone rely on .. rely on على أساس أن هنا الفعل
+
+445
+00:34:43,340 --> 00:34:44,760
+هو اللي جاي في الأول .. الفعل عفوا اللي جاي في
+
+446
+00:34:44,760 --> 00:34:50,200
+الأول .. rely .. to rely onOkay everyone has
+
+447
+00:34:50,200 --> 00:34:53,800
+someone تمام منطقية جدا حتى مع الترتيب هاي ال
+
+448
+00:34:53,800 --> 00:34:56,820
+everyone جاي في الأول و ال someone جاي في التاني
+
+449
+00:34:56,820 --> 00:34:59,680
+بعدين انتوا كملوها زي ما بدكم اعطوا المعنى اللي
+
+450
+00:34:59,680 --> 00:35:02,460
+بدكوا يوضحوه بس تكون واضحة ال everyone و ال
+
+451
+00:35:02,460 --> 00:35:05,800
+someone ترتيبهم يكون ماشي مع مين مع ال
+
+452
+00:35:05,800 --> 00:35:09,260
+mathematical expression تبعنا طيب هنا لإن someone
+
+453
+00:35:09,260 --> 00:35:14,580
+someone whom everyone realize on .. upon
+
+454
+00:35:17,370 --> 00:35:21,890
+تمام فإذا there is someone who every فهي واضحة إن
+
+455
+00:35:21,890 --> 00:35:25,490
+فعلا أنا حطيت there exist في الأول و بعدين
+
+456
+00:35:25,490 --> 00:35:33,230
+everyone تمام؟ جويس ال .. okay الباقية أتصور صارت
+
+457
+00:35:33,230 --> 00:35:38,290
+واضحة برضه هتبدو هنا بإيش someone someone has
+
+458
+00:35:39,590 --> 00:35:44,650
+everyone بس لما .. okay someone هنا ممكن أنتوا
+
+459
+00:35:44,650 --> 00:35:48,150
+أحيانا أعتقد الجملة هنا بس مزود فيها ممكن أنتوا
+
+460
+00:35:48,150 --> 00:35:51,710
+تكتبوا someone مباشرة بدون الكلمة هذه someone و
+
+461
+00:35:51,710 --> 00:35:56,990
+تكملوا جملتكوا عادي، كويس هنا احنا ايش .. ليش
+
+462
+00:35:56,990 --> 00:35:59,330
+كتبناها بهذا الشكل؟ كتبناها بهذا الشكل على أساس
+
+463
+00:35:59,330 --> 00:36:06,560
+انه إذا كانall و هنا .. او someone realized على
+
+464
+00:36:06,560 --> 00:36:11,760
+الكل، معناته هو بطبعه محتاج يعني، هو شخص محتاج،
+
+465
+00:36:11,760 --> 00:36:14,780
+needy person، هذه مجرد بلاغة بتكون .. بتساودوها
+
+466
+00:36:14,780 --> 00:36:18,160
+أنتوا أحرار، بتكونش تساودوها بلاش، هذه يعني جملة
+
+467
+00:36:18,160 --> 00:36:21,680
+هيك استقراضية زيادة على أساس أنه مادام هو معتمد
+
+468
+00:36:21,680 --> 00:36:27,610
+على كل الناس، معناته هو محتاجفقط انه بدل ما سمناه
+
+469
+00:36:27,610 --> 00:36:31,550
+one لأ احنا سمنا ال one هذا اعطينا صفة اللي هو
+
+470
+00:36:31,550 --> 00:36:36,830
+needy person شخص محتاج some needy person مجرد انه
+
+471
+00:36:36,830 --> 00:36:39,970
+بس تعريف ممكن انتوا كلها تجيلوها و تخلوها some one
+
+472
+00:36:39,970 --> 00:36:43,670
+عادية و تكملوا جمعتكوا بدون .. بدون إشكال بس بدنا
+
+473
+00:36:43,670 --> 00:36:46,830
+نضلنا محافظين زي ما قلنا الأهم شغل على ترتيب ال
+
+474
+00:36:46,830 --> 00:36:50,350
+quantifiersال quantifiers بتاعتنا تكون مرتبة حسب
+
+475
+00:36:50,350 --> 00:36:54,370
+ظهورها فعلا في ال expression تبعنا التالتة الرابعة
+
+476
+00:36:54,370 --> 00:37:00,610
+الرابعة نفس اللي الصح everyone هتبدو everyone whom
+
+477
+00:37:00,610 --> 00:37:06,290
+someone realized on كويس
+
+478
+00:37:06,290 --> 00:37:11,150
+بالاخيرة every كلها every و every كلها everyone
+
+479
+00:37:11,150 --> 00:37:16,030
+everyone بالظبط ف everyone realized upon everyone
+
+480
+00:37:17,620 --> 00:37:22,680
+كله بيعتمد على كله .. كله معتمد على كله .. تمام ..
+
+481
+00:37:22,680 --> 00:37:26,400
+واضح الجزية هذه .. لما تيجي تترجمه .. ما .. سيبونا
+
+482
+00:37:26,400 --> 00:37:29,340
+من المهارات بتاعتكوا .. بتاعت الإنجليزي .. خلونا
+
+483
+00:37:29,340 --> 00:37:33,680
+على جد .. اللي موجود .. حطولياه بنفس الترتيب ..
+
+484
+00:37:33,680 --> 00:37:37,400
+ليش؟ مش لأنه أنا هيك بده .. ولكن عشان نكون حافظنا
+
+485
+00:37:37,400 --> 00:37:41,060
+على ال mathematical expression .. بحيث أن الجملة
+
+486
+00:37:41,060 --> 00:37:46,200
+هذه لو بدي أرجحها للرياضياتترجع نفسها مش أفاجأ ان
+
+487
+00:37:46,200 --> 00:37:52,300
+انتوا عملتوها بطريقتكم فترجعلي هذه لأن فعلا ممكن
+
+488
+00:37:52,300 --> 00:37:56,040
+هذه واحد يروح ترجمها بالشكل هذا صح؟ حسب فهمه انه
+
+489
+00:37:56,040 --> 00:37:58,920
+ما هو المهم انه المعنى لأ هو مش المهم المعنى جدب
+
+490
+00:37:58,920 --> 00:38:01,800
+بهمنا في ال mathematics هنا ترتيبها كمان كيف تكون
+
+491
+00:38:01,800 --> 00:38:05,440
+عشان لما نيجي نرجحها من ال language ل ال
+
+492
+00:38:05,440 --> 00:38:08,820
+mathematical expression ترجع نفس ما هي ترجع كما هي
+
+493
+00:38:08,820 --> 00:38:10,760
+okay
+
+494
+00:38:15,860 --> 00:38:18,080
+Okay sometimes the universe of discourse is
+
+495
+00:38:18,080 --> 00:38:22,000
+restricted within the quantification أنا ممكن أعمل
+
+496
+00:38:22,000 --> 00:38:27,140
+restriction كمان عليه ممكن نعمل restriction أو
+
+497
+00:38:27,140 --> 00:38:31,120
+restrictions على ال quantifier نفسه على ال
+
+498
+00:38:31,120 --> 00:38:34,940
+quantifier نفسه زي أن أقول for all x لأ و أحط كمان
+
+499
+00:38:34,940 --> 00:38:39,800
+condition من عندي for all x أكبر من zero طب ممكن x
+
+500
+00:38:39,800 --> 00:38:43,670
+تكون هذه أنا بيعطيها من minus five to five مثلاصح
+
+501
+00:38:43,670 --> 00:38:46,490
+ممكن تكون من minus five to five لكن لما أقول for
+
+502
+00:38:46,490 --> 00:38:50,870
+all x greater than zero لأ أنا كمان عملت تحديد
+
+503
+00:38:50,870 --> 00:38:54,390
+داخل التحديد اللي أنا عامله داخل ال quantifier
+
+504
+00:38:54,390 --> 00:38:57,670
+اللي احنا عاملينه عاملين restrictions زيادة قيود
+
+505
+00:38:57,670 --> 00:39:03,030
+زيادة for all p of x is true هذه معناه for all x
+
+506
+00:39:03,030 --> 00:39:09,110
+that are greater than zero p of x is true يعني
+
+507
+00:39:09,110 --> 00:39:13,440
+كأنههذه الجملة جايانة من ال condition اللي انا
+
+508
+00:39:13,440 --> 00:39:17,580
+اضفته جايانة من ال condition اللي احنا اضفناها هذه
+
+509
+00:39:17,580 --> 00:39:20,900
+ايش معناها؟ معناها تكون انا بقول for all x و بدنا
+
+510
+00:39:20,900 --> 00:39:27,300
+نفتح قصر if x greater than zero then p of x is
+
+511
+00:39:27,300 --> 00:39:31,860
+true فإذا رابطناها هنا ب condition تاني رابطناها ب
+
+512
+00:39:31,860 --> 00:39:38,240
+f جديدة اللي هي إذا كان x أكبر من zeroit's okay أو
+
+513
+00:39:38,240 --> 00:39:45,580
+p of x is true طيب نفس الكلام مدام استعملناه ل for
+
+514
+00:39:45,580 --> 00:39:49,940
+all ممكن نستعمل there exist فهنقول there exist x
+
+515
+00:39:49,940 --> 00:39:55,340
+greater than zero such that p of x is true هذه
+
+516
+00:39:55,340 --> 00:40:00,920
+ممكن نكتبها there is an x greater than zero such
+
+517
+00:40:00,920 --> 00:40:09,710
+that p of xis it true تمام معناها there exist x
+
+518
+00:40:09,710 --> 00:40:13,870
+هنفتح الأقوى ساعتنا عشان نحط ال condition تبعنا x
+
+519
+00:40:13,870 --> 00:40:19,730
+greater than zero and p of x is true and p of x is
+
+520
+00:40:19,730 --> 00:40:26,050
+true على الأقل واحد يحقق الشرط هذا بس لازم يتحقق
+
+521
+00:40:26,050 --> 00:40:30,880
+الشرط كامل لو واحد بس بيكفييعني واحد يكون أكبر من
+
+522
+00:40:30,880 --> 00:40:36,360
+صفر و يكون حققنا ال P of X فبكون there exist أنه
+
+523
+00:40:36,360 --> 00:40:40,820
+يكفي واحد بس عشان ذلك يجب يحقق الشرطين مع بعض يكفي
+
+524
+00:40:40,820 --> 00:40:45,660
+واحد يحقق الشرطين مع بعض اللي هي أكبر من صفر و P
+
+525
+00:40:45,660 --> 00:40:49,760
+of X is true فP of X is true عشان ذلك حطينا لها
+
+526
+00:40:49,760 --> 00:40:50,600
+and
+
+527
+00:41:02,210 --> 00:41:05,470
+Okay لو اتكلم .. هنتكلم اكتر على حكاية ال bending
+
+528
+00:41:05,470 --> 00:41:09,270
+و ال .. و ال bound variables بصورة اكبر و كيف ممكن
+
+529
+00:41:09,270 --> 00:41:14,050
+اقول ان هذه free or bound variables لو قولنا for
+
+530
+00:41:14,050 --> 00:41:20,270
+all x there exist xp of x بستلمزكم احنا كل اللي
+
+531
+00:41:20,270 --> 00:41:24,310
+عندنا variable واحد ليش عملنا اتنين quantifier؟ مش
+
+532
+00:41:24,310 --> 00:41:27,030
+في عندنا اتنين quantifier زي هال logic؟طبعا عنده
+
+533
+00:41:27,030 --> 00:41:30,310
+كله variable واحد بنفعش نستعمل two quantifiers
+
+534
+00:41:30,310 --> 00:41:34,470
+لنفس ال variable بناخد
+
+535
+00:41:34,470 --> 00:41:42,250
+مين منهم الأعامل الأكثر عمومية اللي بيشمل التاني
+
+536
+00:41:42,250 --> 00:41:47,070
+يعني لما أقول كل القيم داخل universe of scores
+
+537
+00:41:47,070 --> 00:41:52,030
+بيحققوا الشرط و بعدين أقولكوا لأ و واحد على الأقل
+
+538
+00:41:52,030 --> 00:41:56,710
+يحقق الشرطمعناته الأوضح و اللي هتكون أشمل إنه على
+
+539
+00:41:56,710 --> 00:42:00,310
+الأقل واحد يحقق الشرط لإنه هي نفسها بتشمل معها إنه
+
+540
+00:42:00,310 --> 00:42:03,590
+الكل يحقق نفس الشرط لإنه زي ما قلنا there exist
+
+541
+00:42:03,590 --> 00:42:09,050
+ممكن تكون واحد أو اتنين أو تلاتة أو all فإذن هي
+
+542
+00:42:09,050 --> 00:42:14,030
+شاملة معها ال all ها دي مالهاش معنى لإن هي فعليا
+
+543
+00:42:14,030 --> 00:42:18,830
+مشمولة مع there exist ففعليا
+
+544
+00:42:18,830 --> 00:42:24,510
+نكتبها إيش there exist such that U of Xدائما خدوا
+
+545
+00:42:24,510 --> 00:42:27,970
+بالكوا بحطش أننا تعرفين لنفس ال variable معناته
+
+546
+00:42:27,970 --> 00:42:31,510
+واحد بيتقاطع مع التاني أكيد واحد بيتقاطع مع التاني
+
+547
+00:42:31,510 --> 00:42:35,030
+بتكونوا تشوفوا مين الأشمل منهم اللي بيشمل ال
+
+548
+00:42:35,030 --> 00:42:37,570
+condition التاني عشان يظل condition واحد او
+
+549
+00:42:37,570 --> 00:42:41,350
+quantifier واحد بس بالنسبة لل all و ال there exist
+
+550
+00:42:41,350 --> 00:42:45,710
+ال there exist هو الأقوى هو اللي بيشمل مع all
+
+551
+00:42:45,710 --> 00:42:49,950
+فانتوا هنا فعليا كأنكوا شملين اتنين مع بعض there
+
+552
+00:42:49,950 --> 00:42:52,830
+exist كأنكوا شملين اتنين مع بعض تمام
+
+553
+00:42:56,880 --> 00:43:03,120
+هنا لو أخدنا الطريقة التانية for all x p of x and
+
+554
+00:43:03,120 --> 00:43:11,060
+q of x أه هذا في واحد free ضايق ليش لأن ال
+
+555
+00:43:11,060 --> 00:43:15,740
+quantifier هنا أنا محدده لميه لل function p أما ال
+
+556
+00:43:15,740 --> 00:43:20,420
+function x لأ ال function x لأ ماحددناش إيش لل
+
+557
+00:43:20,420 --> 00:43:28,360
+function xليش؟ هالوقت ممكن اقول هنا الطلاب
+
+558
+00:43:28,360 --> 00:43:31,740
+مثلا هنا الطلاب ال .. او كل الطلاب الطلبة اللي
+
+559
+00:43:31,740 --> 00:43:36,940
+موجودين اللي عندنا مسجلين مساق ال discrete و مساق
+
+560
+00:43:36,940 --> 00:43:42,010
+ال logicلأ ال logic أنا مش معرف عنه إشي أما اللي
+
+561
+00:43:42,010 --> 00:43:44,690
+بقدر أعرف إن كل اللي موجود هنا أه مسجلها ليش لإنه
+
+562
+00:43:44,690 --> 00:43:47,930
+بدليل إنه حاضر المحاضرة بدليل إنه حاضر المحاضرة
+
+563
+00:43:47,930 --> 00:43:51,910
+فهو فعلا مسجل مساقى discrete فهدول هم ال universe
+
+564
+00:43:51,910 --> 00:43:55,810
+of the scores بتاعون مين بتاعون ال P of X بس مش هم
+
+565
+00:43:55,810 --> 00:44:00,730
+بتاعون ال Q ممكن تكون فيه تباير يعني مش كلكم
+
+566
+00:44:00,730 --> 00:44:04,030
+مسجلين ال logic صح؟ مش كلكم، في بعض منكم مسجلها و
+
+567
+00:44:04,030 --> 00:44:07,400
+في بعض منكم لأ مش مسجلهافبقدرش أحكم فيها هذه مافيش
+
+568
+00:44:07,400 --> 00:44:10,460
+عليها quantifier هذه مافيش عليها quantifier تمام
+
+569
+00:44:10,460 --> 00:44:14,060
+فهذه هتبقى free رغم ان هي x رغم ان هي x و انا
+
+570
+00:44:14,060 --> 00:44:16,600
+بتكلم عن نفسي اللي موجودة قدامنا الطالبات اللي
+
+571
+00:44:16,600 --> 00:44:19,980
+موجودين قدامنا بس هنا انا معرفهم بطريقة و هنا اللي
+
+572
+00:44:19,980 --> 00:44:25,330
+هم تعرفيه بطريقة تانيةطيب فإذا ال .. ال outside of
+
+573
+00:44:25,330 --> 00:44:29,530
+the scope of the universe of this .. for all
+
+574
+00:44:29,530 --> 00:44:35,110
+quantifier هو بيضل free، هيضل عندكوا free فهد
+
+575
+00:44:35,110 --> 00:44:38,850
+بقدرش أقول إن هي proposition، بقدرش أقول إن هي
+
+576
+00:44:38,850 --> 00:44:42,530
+proposition، بعكس اللي فوق، بعكس اللي فوق اللي
+
+577
+00:44:42,530 --> 00:44:48,970
+كانت فعلا proposition فإذا هد bound variable، هد
+
+578
+00:44:48,970 --> 00:44:54,300
+لأ، هد freeمايغركمش إن أنا بتكلم عن نفس ال X تمام؟
+
+579
+00:44:54,300 --> 00:44:57,360
+دايما بهمني إن ال predicate نفسه فيه ال quantifier
+
+580
+00:44:57,360 --> 00:45:04,780
+أو لا واضح إن ال Q .. ال Q غير ال P ال P هذا
+
+581
+00:45:04,780 --> 00:45:09,260
+quantifier له تعريفه و ال Q إلها تعريف تاني هتكون
+
+582
+00:45:09,260 --> 00:45:12,560
+التعريفة مختلف تماما ال predicate function مختلفة
+
+583
+00:45:12,560 --> 00:45:15,780
+بغض النظر إن ال variable طلع واحد بغض النظر إن ال
+
+584
+00:45:15,780 --> 00:45:22,060
+variable نفسه طيب .. طيب ..أصح أنها تكون بالشكل
+
+585
+00:45:22,060 --> 00:45:26,160
+التالي كل واحدة لها التعريف أو لها ال quantifier
+
+586
+00:45:26,160 --> 00:45:30,900
+تبعها فأقول for all x p of x and there exists x
+
+587
+00:45:30,900 --> 00:45:35,680
+such that q of x okay it's okay الحالة هذه مافيش
+
+588
+00:45:35,680 --> 00:45:39,680
+فيها مشكلة و جيدة و تمام تمام و this is legal
+
+589
+00:45:39,680 --> 00:45:44,620
+كويسة على أساس أن الأتنين عندكم مختلفين عن بعض
+
+590
+00:45:44,620 --> 00:45:49,060
+الأتنين بيكونوا مختلفين عن بعض
+
+591
+00:45:55,400 --> 00:46:02,260
+فبتلاحظوا إن هنا ال X هذه مقيدة بس هذه لأ هذه خارج
+
+592
+00:46:02,260 --> 00:46:09,800
+ال quantifier ال
+
+593
+00:46:09,800 --> 00:46:14,480
+quantifier equivalence laws ال quantifiers هذه زي
+
+594
+00:46:14,480 --> 00:46:16,900
+ما كنا بنتكلم في ال propositional equivalence
+
+595
+00:46:16,900 --> 00:46:20,280
+المرة اللي فاتت برضه في ال quantifiers فيه لها
+
+596
+00:46:20,280 --> 00:46:26,310
+equivalence أو equivalent expressionfor all هي
+
+597
+00:46:26,310 --> 00:46:30,550
+فعليا تعبر عن for all x P of x هي فعليا كأن أنا
+
+598
+00:46:30,550 --> 00:46:38,030
+بقول P عارف تبعنا a number x is even number x is
+
+599
+00:46:38,030 --> 00:46:44,370
+even هقول E of x E عصاس أن هي جمن even للتقريب طيب
+
+600
+00:46:44,370 --> 00:46:49,710
+إمتى الكلمة بتحقق if and only if it's equal to two
+
+601
+00:46:49,710 --> 00:46:53,220
+times some other numberأحنا عارفين عشان تكون even
+
+602
+00:46:53,220 --> 00:46:57,400
+المفروض أن هي تساوي 2 في رقم تاني مظبوط؟ يعني أو
+
+603
+00:46:57,400 --> 00:47:02,720
+بمعنى أخر بتقسم على 2 بمعنى أخر أن هي رقم بيقسم
+
+604
+00:47:02,720 --> 00:47:06,820
+على 2 طيب هنتأكد من الكلمة ده هل هو فعلا في عندي
+
+605
+00:47:06,820 --> 00:47:10,280
+رقم بيقسم على 2 بمشي الكلمة ده؟ كيف ممكن أن أعبر
+
+606
+00:47:10,280 --> 00:47:18,610
+عنها رياضيا فهقول مدام even كل القيم كل xاللي ممكن
+
+607
+00:47:18,610 --> 00:47:21,710
+نعبر عنها إن هي even المفروض تحقيق لنا الشغل
+
+608
+00:47:21,710 --> 00:47:28,830
+التالي إن هي even by conditional there exist y
+
+609
+00:47:28,830 --> 00:47:36,470
+such that x equal to 2y معناته هي even إذا كان
+
+610
+00:47:36,470 --> 00:47:44,830
+موجود لكل قيمة ل x هتكون even إمتى إذا كانت يوجد y
+
+611
+00:47:44,830 --> 00:47:52,020
+نص xهي معناها، فمعناها ضامن أن X يُعتبر ضعف أي رقم
+
+612
+00:47:52,020 --> 00:47:56,560
+تاني، ضعف some number، ضعف أي رقم تاني، مدام ضعف
+
+613
+00:47:56,560 --> 00:48:00,100
+أي رقم تاني، بتجبل جسمها اتنين، مدام جبلت القسم مع
+
+614
+00:48:00,100 --> 00:48:05,100
+اتنين، اكيد even، اكيد even، اكيد even، زوجي، رقم
+
+615
+00:48:05,100 --> 00:48:09,840
+زوجي، اكيد هتكون رقم زوجي، كمان مرة، for all X،
+
+616
+00:48:09,840 --> 00:48:17,810
+لكل قيم Xال .. even .. x is even if and only if مش
+
+617
+00:48:17,810 --> 00:48:20,330
+هي دي ال if and only if ال by conditional هيها
+
+618
+00:48:20,330 --> 00:48:25,870
+لحظة هنترجمها هيها a number x is even فإذا for all
+
+619
+00:48:25,870 --> 00:48:31,690
+x a number x is even هيها if and only if if and
+
+620
+00:48:31,690 --> 00:48:37,620
+only ifis equal to two times some other number
+
+621
+00:48:37,620 --> 00:48:39,580
+some other number معناته بدي اعرف اللي ايش ال
+
+622
+00:48:39,580 --> 00:48:43,280
+other number هذا there exist y why other number عن
+
+623
+00:48:43,280 --> 00:48:47,980
+x ايش العلاقة بينهم two times معناته ال x هذي
+
+624
+00:48:47,980 --> 00:48:51,520
+تساوي two times of ال other number اللي عرفناه انه
+
+625
+00:48:51,520 --> 00:48:57,940
+موجود رقم تاني يمثل نص x موجود رقم تاني يمثل نص x
+
+626
+00:48:57,940 --> 00:49:04,140
+ففي الحالة هذي بيقول انه فعلاالرقم هذا even الرقم
+
+627
+00:49:04,140 --> 00:49:13,690
+even طيب آخر مثال a number is prime P of Xأمتى
+
+628
+00:49:13,690 --> 00:49:16,830
+بيكون بيكون فعلا prime if and only if it's greater
+
+629
+00:49:16,830 --> 00:49:19,830
+than one لازم يكون أكبر من واحد بقدرش أقول إن
+
+630
+00:49:19,830 --> 00:49:22,810
+الواحد هو prime إن عارف أحسس إن هو prime و خلاص و
+
+631
+00:49:22,810 --> 00:49:24,550
+يدخلوا أنا في التاريخ لازم يكون أكبر من ال prime
+
+632
+00:49:24,550 --> 00:49:30,230
+and it's not the product of two non unity of
+
+633
+00:49:30,230 --> 00:49:35,890
+numbers معناته بقدرش أجيب محصلته من ضرب رقمين
+
+634
+00:49:35,890 --> 00:49:40,470
+بقدرش أجيبه من حاصل ضرب رقمين و لازم نحدد هنا إن
+
+635
+00:49:40,470 --> 00:49:42,110
+الرقمين هدول مايكونش فيهم الواحد
+
+636
+00:49:44,710 --> 00:49:50,170
+لأنه سبعة prime .. prime صح؟ بس بقدر أقول إن هو
+
+637
+00:49:50,170 --> 00:49:54,330
+سبعة في واحد صحيح؟
+
+638
+00:49:54,330 --> 00:49:57,110
+أنتوا فاهمين إن هو .. بتنضربش هذه، بس ال computer
+
+639
+00:49:57,110 --> 00:50:00,090
+بيفهمش، الرياضة بتفهمش، لازم تكون ال expression
+
+640
+00:50:00,090 --> 00:50:03,310
+تبعكوا واضح وشامل، عشان هيك لازم نحدد إن هو
+
+641
+00:50:03,310 --> 00:50:10,390
+مايكونش فيهم الواحد، مايكونش فيهم الواحدخلاص
+
+642
+00:50:10,390 --> 00:50:13,730
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+643
+00:50:13,730 --> 00:50:19,850
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+644
+00:50:19,850 --> 00:50:23,130
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+645
+00:50:23,130 --> 00:50:23,170
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+646
+00:50:23,170 --> 00:50:24,030
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+647
+00:50:24,030 --> 00:50:26,170
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+648
+00:50:26,170 --> 00:50:26,870
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+649
+00:50:26,870 --> 00:50:28,930
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+650
+00:50:28,930 --> 00:50:32,630
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+651
+00:50:32,630 --> 00:50:33,770
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+652
+00:50:33,770 --> 00:50:37,850
+فيهم الواحد مايكونش فيx is prime فهي حقق لـ
+
+653
+00:50:37,850 --> 00:50:41,270
+predicate طيب عشان احققها فعلا امتى بتصير الكلمة
+
+654
+00:50:41,270 --> 00:50:46,250
+if and only if نبدأ نمسكهم شوية شوية و نفتح الأقوى
+
+655
+00:50:46,250 --> 00:50:52,750
+ساعتنا و لاحظوا انه هنا if and only if تمام
+
+656
+00:50:52,750 --> 00:50:57,410
+لاحظوا يعطينا condition يعطينا التاني يعطينا
+
+657
+00:50:57,410 --> 00:51:01,370
+التالت في three conditions حطينا لنا معناته بدنا
+
+658
+00:51:01,370 --> 00:51:07,230
+نربطهم بands فتحنا ال course تبعناهذه قصتنا وهذه
+
+659
+00:51:07,230 --> 00:51:10,130
+هنعمل and .. and .. and .. نشوف أشياء .. مجموعة
+
+660
+00:51:10,130 --> 00:51:12,410
+القيم ال .. ال .. ال .. ال .. ال exceptions اللي
+
+661
+00:51:12,410 --> 00:51:17,430
+أعطانا إياها firstly, greater than one x أكبر من
+
+662
+00:51:17,430 --> 00:51:25,650
+واحد and it's not the product هو مش جاي من مجموع
+
+663
+00:51:25,650 --> 00:51:32,350
+ضربين .. ضرب رقمين معناته لا يوجد is not لا يوجد
+
+664
+00:51:32,350 --> 00:51:34,230
+رقمين
+
+665
+00:51:37,460 --> 00:51:44,320
+X حصل ضربهم بس بدنا نحدد هنا and Y ليست واحد و Z
+
+666
+00:51:44,320 --> 00:51:48,520
+ليست واحد عشان مايروحش يفكر لإن السبعة ممكن تيجي
+
+667
+00:51:48,520 --> 00:51:53,500
+سبعة في واحد عشان ما ال computer و انت بتعملوله
+
+668
+00:51:53,500 --> 00:51:57,380
+code بال expression هذا مايروحش يعتبر ان هي هذه
+
+669
+00:51:57,380 --> 00:52:01,600
+واحد و هي حصل ضرب رقمين بمش الحال لأ بدنا نقوله ان
+
+670
+00:52:01,600 --> 00:52:07,640
+لأ دير بالك الواحدال y لازم لا تسوى واحد and زي لا
+
+671
+00:52:07,640 --> 00:52:14,920
+تسوى واحد تمام فلحظه صار بنقدر من الجملة إذا عندنا
+
+672
+00:52:14,920 --> 00:52:20,460
+تعريف لمجموعة معينة من ال numbers بنقدر نعرف منها
+
+673
+00:52:20,460 --> 00:52:24,760
+إيش ال expression تبعنا أو بنقدر نكتب ال
+
+674
+00:52:24,760 --> 00:52:28,940
+expression الرياضي تبعنا رجعوهم في البيت هتلاقيوا
+
+675
+00:52:28,940 --> 00:52:32,930
+إنه فعلا امسكوهم كلمة كلمةواحدة واحدة هتركبوهم ورا
+
+676
+00:52:32,930 --> 00:52:37,930
+بعض، هتركبوهم ورا بعض، تمام؟ هيك احنا نخلص ..
+
+677
+00:52:37,930 --> 00:52:43,610
+نخلصنا، كل عامة بخير، ال .. طبعا ال .. ال homework
+
+678
+00:52:43,610 --> 00:52:48,530
+مش هتسلمونا إياه للأحد الجاى، هيكون عيد، فبيضل للي
+
+679
+00:52:48,530 --> 00:52:51,530
+بعده ان شاء الله تعالى، للي بعده بإذن الله تعالى،
+
+680
+00:52:51,530 --> 00:52:52,090
+يطبخوا العافية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..76ac9bb710907ab5faadf418383c753916b7307b
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI.srt
@@ -0,0 +1,2180 @@
+1
+00:00:20,670 --> 00:00:22,770
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,770 --> 00:00:24,690
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:24,690 --> 00:00:27,790
+أجمعين. نبدأ اليوم، نحاول نخلص الجزئية اللي بدأنا
+
+4
+00:00:27,790 --> 00:00:29,590
+نتكلمنا فيها المرة اللي فاتت، اللي هي الـ functions
+
+5
+00:00:29,590 --> 00:00:34,330
+وقلنا.. تحدثنا عن تعريف الـ functions وبعدين..
+
+6
+00:00:36,840 --> 00:00:39,440
+اتكلمنا عن أنواع الـ functions، قلنا فيها نوعين
+
+7
+00:00:39,440 --> 00:00:42,580
+مهمين اللي اتكلمنا عنهم المرة اللي فاتت، الـ الـ
+
+8
+00:00:42,580 --> 00:00:47,760
+one-to-one، الـ one-to-one والـ onto، والـ onto. فـ الـ
+
+9
+00:00:47,760 --> 00:00:49,980
+one-to-one والـ onto، أخدنا example المرة اللي فاتت
+
+10
+00:00:49,980 --> 00:00:54,200
+عليها. خلينا بسرعة نراجع الـ function الأولى هنا، هذي
+
+11
+00:00:54,200 --> 00:00:58,200
+one-to-one ولا onto أو combination، يعني أعمل
+
+12
+00:00:58,200 --> 00:01:00,420
+combination one-to-one
+
+13
+00:01:02,470 --> 00:01:07,950
+one to one، قلنا إن كل element في الـ domain له
+
+14
+00:01:07,950 --> 00:01:14,530
+output واحد فقط، وكل output في الـ co-domain أو في
+
+15
+00:01:14,530 --> 00:01:18,550
+الـ range، عشان أكون أدق، في الـ range جاي من pre-
+
+16
+00:01:18,550 --> 00:01:24,330
+image واحدة فقط. فهنا واضح إن هنا في element جاي من
+
+17
+00:01:24,330 --> 00:01:29,870
+اثنين. هذه مش one-to-one. طب one-to.. one-to.. إيش
+
+18
+00:01:29,870 --> 00:01:33,210
+كان تعريف الـ one-to؟ الـ domain.. الـ co-domain و
+
+19
+00:01:33,210 --> 00:01:35,830
+الـ range نفس الـ cardinality.. نفس الـ cardinality.
+
+20
+00:01:35,830 --> 00:01:39,590
+فإذا الأولى هذه كانت onto ولكن مش one-to-one. طيب
+
+21
+00:01:39,590 --> 00:01:44,990
+الثانية one-to-one لأ، لأن في عندنا two elements
+
+22
+00:01:44,990 --> 00:01:50,550
+ليهم نفس الـ output، والـ co-domain فيه عنصر غير موجود
+
+23
+00:01:50,550 --> 00:01:54,690
+في الـ range. فإذا لا هيك ولا هيك. كويس؟ الثالثة
+
+24
+00:01:56,690 --> 00:02:01,330
+الرابعة one to one و onto. الرابعة one to one، هذه
+
+25
+00:02:01,330 --> 00:02:05,230
+one to one مظبوط، ولكن not onto، لأن في عندك هذا
+
+26
+00:02:05,230 --> 00:02:10,510
+element فوق موجود، هذا خارج الحساب طبعاً. طيب، من
+
+27
+00:02:10,510 --> 00:02:12,650
+الاثنين هذول، اتكلمنا برضه المرة اللي فاتت على الـ
+
+28
+00:02:12,650 --> 00:02:15,110
+bijection، الـ bijection أو الـ one to one
+
+29
+00:02:15,110 --> 00:02:17,730
+correspondence، أو الـ bijection، أو الـ reversible
+
+30
+00:02:17,730 --> 00:02:22,380
+invertible، وقلنا إن هذه بتحقق الشرطين. إذا تحقق الـ
+
+31
+00:02:22,380 --> 00:02:25,340
+two conditions في function واحدة، الـ two conditions
+
+32
+00:02:25,340 --> 00:02:28,340
+في function واحدة بنقول عنها إيش؟ bijection. فإيش
+
+33
+00:02:28,340 --> 00:02:31,740
+بتلزمنا؟ بتلزمنا إن إذا كانت الـ function bijection،
+
+34
+00:02:31,740 --> 00:02:34,700
+معناته بقدر أجيب لها الـ inverse تبعها. بنقدر نجيب
+
+35
+00:02:34,700 --> 00:02:37,960
+الـ inverse function لها، والـ inverse function
+
+36
+00:02:37,960 --> 00:02:41,580
+بتاعتها أكيد بتكون مكتوبة كالتالي: inverse function
+
+37
+00:02:41,580 --> 00:02:45,840
+أو f<sup>-1</sup> from B to A.
+
+38
+00:02:45,840 --> 00:02:51,320
+لأن هذه في اتجاه العكسي، جاية من B to A، بالاتجاه
+
+39
+00:02:51,320 --> 00:02:56,400
+العكسي، لأنها الـ inverse لـ f، فبتكون
+
+40
+00:02:56,400 --> 00:03:00,840
+جاية من الـ co-domain للـ domain بتاع الـ f، فأصبحت
+
+41
+00:03:00,840 --> 00:03:04,480
+الـ B هي الـ domain تبعها، والـ A هي الـ co-domain تبعها.
+
+42
+00:03:04,480 --> 00:03:08,420
+هي الـ co-domain تبعها. Okay؟ وهذا بتكون unique، بمعنى
+
+43
+00:03:08,420 --> 00:03:13,400
+أن كل function، إذا كانت bijection، لها inverse واحد
+
+44
+00:03:13,400 --> 00:03:16,640
+فقط. ما تتوقعوش أنه يكون لها أكثر من inverse واحد، فقط
+
+45
+00:03:16,640 --> 00:03:20,570
+كويس؟ الاثنين هدول في بعض، اللي هي الـ function في
+
+46
+00:03:20,570 --> 00:03:24,050
+الـ inverse بتاعها بيعطونا الـ identity. وضرب، قلنا
+
+47
+00:03:24,050 --> 00:03:27,870
+عليه المرة اللي فاتت، هذا اللي هو إيش؟ composition. فـ
+
+48
+00:03:27,870 --> 00:03:32,850
+f<sup>-1</sup> ∘ f = I.  والـ I هذه اللي هي إيش؟ الـ identity value أو الـ
+
+49
+00:03:32,850 --> 00:03:37,010
+identity function. identity function. هاي الـ
+
+50
+00:03:37,010 --> 00:03:39,530
+identity function، بنعرفها لأي domain A، على أساس إن الـ
+
+51
+00:03:39,530 --> 00:03:44,070
+identity function، I from A to A. from A to A. ليش من
+
+52
+00:03:50,990 --> 00:03:55,450
+A لـ A؟ لأن فعلياً الـ input تبعها هو نفس الـ output. الـ
+
+53
+00:03:55,450 --> 00:04:00,550
+input هو نفس الـ output. هي غير مؤثرة. الأصل، إذا كانت
+
+54
+00:04:00,550 --> 00:04:03,730
+ضرب، مثلاً، الـ function عملية ضرب، المفروض نضرب في
+
+55
+00:04:03,730 --> 00:04:09,190
+واحد. إذا كانت جمع، بنجمع مع صفر. إذا كانت مثلاً and،
+
+56
+00:04:09,190 --> 00:04:15,230
+بنعمل and مع true، مع true. فـ الـ input اللي بندخله،
+
+57
+00:04:15,230 --> 00:04:17,950
+إذا كان true، حيضل true، وإذا كان false، حيضل false.
+
+58
+00:04:17,950 --> 00:04:21,650
+فالقصد إن إحنا بنتعامل مع element أو مع function،
+
+59
+00:04:21,650 --> 00:04:25,910
+الـ input بتاعها هو هو، هيطلع هو هو. إحنا فبنقول من A
+
+60
+00:04:25,910 --> 00:04:34,060
+to A، بنكتبها I<sub>A</sub> مع الـ set A، لـ identity للـ set A، أو
+
+61
+00:04:34,060 --> 00:04:38,380
+بنكتبها واحد بهذا الشكل، واحد. كويس؟ أو واحد A، one
+
+62
+00:04:38,380 --> 00:04:42,780
+لـ الـ set A. وهذه زي ما قلنا، unique function، بحيث
+
+63
+00:04:42,780 --> 00:04:47,280
+إن for all elements داخل الـ set، لكل الـ elements
+
+64
+00:04:47,280 --> 00:04:49,400
+داخل الـ set A،
+
+65
+00:04:51,360 --> 00:04:55,760
+f(a) = a. فإذا هي function محايدة. هي function
+
+66
+00:04:55,760 --> 00:05:00,620
+محايدة. الـ input هو هو، زي الـ output، هو هو نفس الـ
+
+67
+00:05:00,620 --> 00:05:04,900
+output. وإحنا يعني اتعلمنا مجموعة functions بتقدر
+
+68
+00:05:04,900 --> 00:05:08,600
+نفس الغرض، هذا زي لما نقول الـ positive أو الـ
+
+69
+00:05:08,600 --> 00:05:13,790
+plus أو الـ adding. الـ adding مع الـ zero ما بأثرش، الـ
+
+70
+00:05:13,790 --> 00:05:18,010
+dotting مع الـ one، أو الـ multiplication with one،
+
+71
+00:05:18,010 --> 00:05:24,370
+ما بأثرش. الـ and مع الـ true ما بأثرش. الـ or مع الـ false
+
+72
+00:05:24,370 --> 00:05:30,030
+ما بأثرش. الـ union مع الـ  ∅، union مع  ∅ ما حدش هيضل نفس
+
+73
+00:05:30,030 --> 00:05:34,010
+الـ set. طيب، الـ intersection مع الـ universe of
+
+74
+00:05:34,010 --> 00:05:39,490
+discourse، مع الـ U، ما بتأثرش. كويس؟ هنلاحظ أنه في جميع
+
+75
+00:05:39,490 --> 00:05:42,970
+الأحوال، في جميع الظروف، دائماً الـ identity هي
+
+76
+00:05:42,970 --> 00:05:48,930
+bijective، أو one to one و onto مع بعض، function، فهي
+
+77
+00:05:48,930 --> 00:05:53,030
+bijection function، أو bijective function. Okay؟
+
+78
+00:05:54,780 --> 00:05:58,960
+كيف نوضحها؟ كيف نرسم الرسم تبعها؟ إما عن طريق الـ
+
+79
+00:05:58,960 --> 00:06:04,340
+Venn diagram بهذا الشكل. فهي عندنا الـ set A، فيها
+
+80
+00:06:04,340 --> 00:06:07,400
+مجموعة الـ elements بتاعتها. الـ elements داخل الـ
+
+81
+00:06:07,400 --> 00:06:11,720
+domain. كل element under the function هيعطينا نفس
+
+82
+00:06:11,720 --> 00:06:15,360
+الـ element. فالاتجاه للـ function من الـ element
+
+83
+00:06:15,360 --> 00:06:19,620
+لنفسها، لأن زي ما قلنا، identity هيطلع نفس القيمة للـ
+
+84
+00:06:19,620 --> 00:06:26,460
+element. فهنا الـ a<sub>1</sub> تحت تأثير f هيعطي a<sub>1</sub>. a<sub>2</sub>
+
+85
+00:06:26,460 --> 00:06:33,060
+تحت تأثير f هيعطي a<sub>2</sub>، وهكذا. أي عنصر تحت تأثير f
+
+86
+00:06:33,060 --> 00:06:39,320
+(a) هيعطينا نفس العنصر اللي هو a. نفس العنصر. بالـ
+
+87
+00:06:39,320 --> 00:06:46,170
+plot هتكون linear، والـ slope تبع الـ linear هذا واحد.
+
+88
+00:06:46,170 --> 00:06:51,330
+هو عبارة عن line linear، الـ slope تبعه بواحد، عشان
+
+89
+00:06:51,330 --> 00:06:56,650
+أضمن إن أي x هتطلع نفس قيمتها في الـ y. فإذا x خمسة،
+
+90
+00:06:56,650 --> 00:07:01,030
+الـ y هتطلع خمسة، اللي هي الـ f(x). فهنا الـ x، وهذا
+
+91
+00:07:01,030 --> 00:07:07,670
+الـ y اللي هي تساوي f(x). فدائماً f(x) بتساوي x.
+
+92
+00:07:07,670 --> 00:07:10,930
+دائماً f(x) بتساوي x.
+
+93
+00:07:32,550 --> 00:07:36,050
+عشان نرسم الـ graphs of functions، إحنا بدنا نوقعها
+
+94
+00:07:36,050 --> 00:07:38,530
+بمجموعة نقاط، زي الـ plot اللي توقعنا رسمياً، وكيف
+
+95
+00:07:38,530 --> 00:07:43,640
+بنعمله فعلياً؟ بهذا الشكل. إذا كان عندكم x و f(x)،
+
+96
+00:07:43,640 --> 00:07:50,580
+اللي هي y، أنتو عادة إيش بتسووا؟ بتحطوا نقاط عند الـ
+
+97
+00:07:50,580 --> 00:07:57,620
+x، عندكم f(x) معرفة بطريقة معينة، بتفرضوا قيم لـ x،
+
+98
+00:07:57,620 --> 00:08:03,220
+قيمة x مثلاً واحد، بتعوضوا هنا، بتطلع لكم رقم،
+
+99
+00:08:03,220 --> 00:08:07,740
+الرقم هذا بيصير هو قيمة y المقابلة للواحد، فبتحطوها
+
+100
+00:08:07,740 --> 00:08:13,700
+نقطة. قيمة ثانية، تحطوا كمان نقطة، ثالثة، كمان نقطة،
+
+101
+00:08:13,700 --> 00:08:17,880
+رابعة، كمان نقطة، خامسة، كمان نقطة. فبتوصلوا بينهم،
+
+102
+00:08:17,880 --> 00:08:21,820
+عشان يطلع معاكم شكل الـ function. بتطلع معاكم في
+
+103
+00:08:21,820 --> 00:08:24,260
+الآخر شكل الـ function. بتقولوا: آه والله هي الـ
+
+104
+00:08:24,260 --> 00:08:26,680
+function هذه linear، الـ function هذه تربيعية، الـ
+
+105
+00:08:26,680 --> 00:08:28,740
+function هذه تكعيبية، آه هذه شبيهة بالـ sinusoidal، هذه
+
+106
+00:08:28,740 --> 00:08:31,840
+شبيهة بالـ.. تقدروا لو قلنا مثلاً، طلعوا نقاط
+
+107
+00:08:31,840 --> 00:08:34,000
+بالشكل هذا، هتقولوا: آه والله هذه linear، واضح إن إحنا
+
+108
+00:08:34,000 --> 00:08:38,840
+بنتكلم عن خط. الخط هذا بيظل، عملية إنه ممكن يكون الـ
+
+109
+00:08:38,840 --> 00:08:41,660
+identity مثلاً. طب كيف أفحص إن هي identity ولا لأ؟
+
+110
+00:08:41,660 --> 00:08:43,660
+بالـ slope، بالـ slope، بتشوف إذا كان واحد، هي الـ
+
+111
+00:08:43,660 --> 00:08:47,650
+identity. مش واحد؟ لأ، خلاص هذه function مختلفة تمام؟
+
+112
+00:08:47,650 --> 00:08:52,390
+identity ممكن تكون مضروبة بس بـ factor معين، كويس؟
+
+113
+00:08:52,390 --> 00:08:56,590
+معنى ذلك، خلينا نرجع لمفهوم كيف رسمنا الرسم هذا.
+
+114
+00:08:56,590 --> 00:09:02,030
+رسمناه من نقطة بداية، الشغل كانت نقطة، النقطة إيش
+
+115
+00:09:02,030 --> 00:09:10,990
+تمثل؟ تمثل x و f(x)، صحيح؟
+
+116
+00:09:10,990 --> 00:09:18,020
+هي x و f(x) بتاعتها، فمثلناها بزوج مرتب، عبارة عن
+
+117
+00:09:18,020 --> 00:09:24,340
+الـ input والـ f(x) اللي هو الـ output، اللي هو الـ
+
+118
+00:09:24,340 --> 00:09:30,660
+output طبعاً. Okay؟ فبنرتبها كـ (a, f(a))، إذا كنا
+
+119
+00:09:30,660 --> 00:09:34,900
+معرفين الـ function على أساس أنها من A to B،
+
+120
+00:09:34,900 --> 00:09:41,400
+فبنعرفها كزوج مرتب (a, f(a))، و a ∈ A، الـ domain. فإحنا بنختار في الآخر قيم من الـ domain،
+
+121
+00:09:41,400 --> 00:09:45,060
+القيم بتاعتنا بنختارها من من؟ من الـ domain. مش حاجة
+
+122
+00:09:45,060 --> 00:09:48,060
+من الـ domain. تبقى من 0 لـ 10، أختار 11، أو أختار minus
+
+123
+00:09:48,060 --> 00:09:52,600
+one. نختار قيمنا من مين؟ من الـ domain، وبتحدد
+
+124
+00:09:52,600 --> 00:09:56,810
+النقطة.. النقطة زي ما قلنا في الآخر، (a, f(a))،
+
+125
+00:09:56,810 --> 00:10:01,790
+قيمة الـ function بتاعتها، أو (x, y) حسب ما أنتو
+
+126
+00:10:01,790 --> 00:10:06,550
+كنتو دارسين الـ الـ الـ independent variable x،
+
+127
+00:10:06,550 --> 00:10:10,250
+و dependent variable y. فهي هتكون عبارة عن زوج من
+
+128
+00:10:10,250 --> 00:10:13,890
+x و y. Okay؟ لما نتكلم عن الأرقام، بنمثلها بأرقام زي
+
+129
+00:10:20,220 --> 00:10:24,520
+ما قلنا، أنتو بتستعملوا الـ x و y، بتستعملوا عادة x
+
+130
+00:10:24,520 --> 00:10:28,560
+و y، زي الشكل اللي إحنا رسمناه، بهذا الشكل. هي x و y.
+
+131
+00:10:28,560 --> 00:10:35,420
+ليش؟ لأن y هي نفسها f(x)، فبنحددها كنقطة على الـ
+
+132
+00:10:35,420 --> 00:10:38,660
+plane بتاعنا، عشان نحط نقطة، وبعدين نجرب نقطة ثانية
+
+133
+00:10:38,660 --> 00:10:42,390
+لـ x، نقطة ثالثة، نقطة رابعة، نقطة خامسة، ونوصل، نوصلهم
+
+134
+00:10:42,390 --> 00:10:46,430
+بعض، بنوصلهم بعض. في الآخر، مجموعة النقاط هدول،
+
+135
+00:10:46,430 --> 00:10:51,130
+إيش صاروا؟ صاروا set of points. صاروا لكم مجموعة
+
+136
+00:10:51,130 --> 00:10:54,730
+نقاط. مجموعة النقاط هذه صارت set of points، فهذه
+
+137
+00:10:54,730 --> 00:10:58,390
+اللي بيعطونا relation بين y و x، بيعطونا
+
+138
+00:10:58,390 --> 00:11:03,590
+relation بين y و x، على أساس إن هم set of
+
+139
+00:11:03,590 --> 00:11:05,550
+points. Okay؟
+
+140
+00:11:07,200 --> 00:11:11,000
+من اللي فهمناه، لوجود في عملية الرسم والـ function
+
+141
+00:11:11,000 --> 00:11:15,500
+نفسها، نتكلم عن موضوع الـ couple of key functions.
+
+142
+00:11:15,500 --> 00:11:22,040
+هنا بنعمل عملية تقريب لأقرب integers، لأقرب integer
+
+143
+00:11:22,040 --> 00:11:26,740
+number. طيب، أقرب integer الأعلى ولا الأقل؟ فهنا إما
+
+144
+00:11:26,740 --> 00:11:35,130
+بنعمل floor أو ceiling of x. الـ floor نرسمها بهذا
+
+145
+00:11:35,130 --> 00:11:39,570
+الشكل. في عندنا floor واضحة، الأرضية واضحة، شمال
+
+146
+00:11:39,570 --> 00:11:44,740
+ويمين للـ x. الـ ceiling لأ، الأرضية واضحة، لل سقف. فعندنا
+
+147
+00:11:44,740 --> 00:11:47,900
+هنا الأرضية، وهنا فينا السقف. فإحنا النقطة اللي
+
+148
+00:11:47,900 --> 00:11:51,180
+موجودة داخل الغرفة، المعلقة داخل الغرفة، بتقربها للـ
+
+149
+00:11:51,180 --> 00:11:54,400
+floor ولا بتجربها للسقف؟ بدنا نسحب الخيط طبعاً،
+
+150
+00:11:54,400 --> 00:11:56,580
+هنوصلها للسقف، ولا بدنا نقطع الخيط وننزلها للـ
+
+151
+00:11:56,580 --> 00:12:00,560
+floor؟ هاي المعنى. فإحنا لما بقول floor، معناته لأقرب
+
+152
+00:12:00,560 --> 00:12:05,600
+قربناها لإيش؟ للـ floor، تمام؟ إحنا موجودين في الدور
+
+153
+00:12:05,600 --> 00:12:09,600
+الخامس، صحيح؟ دور الخامس، المفروض إنه معناته إحنا الـ
+
+154
+00:12:09,600 --> 00:12:13,600
+level تبع الأرضية هذا، اللي هو رقم أربعة، رقم أربعة.
+
+155
+00:12:13,600 --> 00:12:17,900
+رقم أربعة، صحيح؟ إحنا بنبدأ تحت بواحد، فهذا رقم أربعة.
+
+156
+00:12:17,900 --> 00:12:21,200
+لما بدي أقرب، أعمل floor، هقول إن النقطة هذه
+
+157
+00:12:21,200 --> 00:12:24,810
+قربناها لأربعة. بالنسبة للأرض اللي برة، بالنسبة
+
+158
+00:12:24,810 --> 00:12:27,230
+للشباك اللي طلعنا، هنقول إن إحنا قربنا النقطة لمين؟
+
+159
+00:12:27,230 --> 00:12:31,330
+لأربعة. طب لما عملنا ceiling، قربناها للمستوى خمسة.
+
+160
+00:12:31,330 --> 00:12:35,150
+بنقربها هنا للمستوى خمسة. معنى ذلك إن النقطة كانت
+
+161
+00:12:35,150 --> 00:12:40,370
+between أربعة وخمسة، كانت real number من أربعة
+
+162
+00:12:40,370 --> 00:12:44,550
+لخمسة. فإحنا قربناها لـ integer، بس إحنا حددنا الـ
+
+163
+00:12:44,550 --> 00:12:49,760
+integer هذا هو floor أو ceiling؟ هل هو الـ floor أو
+
+164
+00:12:49,760 --> 00:12:52,360
+الـ ceiling؟ طيب، لما نتكلم عن الـ floor، هو فعلياً الـ
+
+165
+00:12:52,360 --> 00:12:58,000
+floor بيقلل القيمة، يعني بس هي عبارة عن إيش؟ هي الـ
+
+166
+00:12:58,000 --> 00:13:05,580
+greatest أو الـ largest integer أقل من x. أكبر
+
+167
+00:13:05,580 --> 00:
+
+223
+00:17:28,590 --> 00:17:33,510
+أقل من واحد، أقل بكثير بكثير، يعني إحنا عشان هيك مش
+
+224
+00:17:33,510 --> 00:17:36,570
+عارفين بالضبط قد إيش القيمة هي، delta delta أكبر من
+
+225
+00:17:36,570 --> 00:17:41,390
+صفر، بس قليلة جدا جدا جدا. طيب عشان نحددها قد إيش بده
+
+226
+00:17:41,390 --> 00:17:46,950
+أحددها، أنا مش عارف أحددها، نكتبها للواحد ولكن
+
+227
+00:17:46,950 --> 00:17:54,910
+الواحد غير مشمول، مفتوحة، فبنعملها هذه circle بس open
+
+228
+00:17:54,910 --> 00:17:58,470
+circle، فبنكتبها open circle للواحد، و للواحد غير
+
+229
+00:17:58,470 --> 00:18:03,450
+مشمول، لو عملناها solid circle بتصير لأ، مشمولة، فها
+
+230
+00:18:03,450 --> 00:18:06,770
+بدنا يعني كل الموضوع هذا بدنا نؤكد على حكاية اللي
+
+231
+00:18:06,770 --> 00:18:12,230
+هي ال open و ال solid، كويسة. فمعنى ذلك ال function
+
+232
+00:18:12,230 --> 00:18:16,650
+هذه، أو ال points هذه صحيحة لكل الفترة اللي من a
+
+233
+00:18:16,650 --> 00:18:23,110
+أكبر من أو تساوي صفر، و a أقل منه و لا تساوي
+
+234
+00:18:23,110 --> 00:18:28,830
+ما حطيناش يساوي، و لا تساوي واحد، و الواحد لأ، but not
+
+235
+00:18:28,830 --> 00:18:35,090
+for a، ايه، a equal to، ليش؟ لأن a بتساوي واحد، صارت
+
+236
+00:18:35,090 --> 00:18:38,710
+مشمولة مع نقطة تانية، مع function تانية، ال output
+
+237
+00:18:38,710 --> 00:18:45,390
+بتصير بواحد، ال output تبعها واحد، فـ a و ال output واحد
+
+238
+00:18:45,390 --> 00:18:49,730
+بتشمل معها a بتساوي واحد، بتشمل معها a بتساوي واحد
+
+239
+00:18:49,730 --> 00:18:54,830
+فحناخد بالنا إن هنا بتصير ال واحد هذه open set، هنا
+
+240
+00:18:54,830 --> 00:18:57,290
+بنتكلم عن open sets، open sets اللي هي معناته عند
+
+241
+00:18:57,290 --> 00:19:00,310
+نقطة معينة غير مشمولة، النقطة بس أنا لازم أعرفها
+
+242
+00:19:00,310 --> 00:19:03,510
+بالنقطة، لأن أنا مش عارف قد إيش أقل من النقطة، أقل من
+
+243
+00:19:03,510 --> 00:19:08,620
+النقطة بقيمة كتير صغيرة، يعني لو واحد منكم كتب 0
+
+244
+00:19:08,620 --> 00:19:14,900
+.99999، المفروض دلتا انفينتي، طبعا مش منطقي إن إحنا
+
+245
+00:19:14,900 --> 00:19:17,940
+نعملها انفينتي، فلأ بنقول واحد، بس بدنا نحدد إن
+
+246
+00:19:17,940 --> 00:19:22,040
+الواحد نفسه كقيمة، واحد غير مشمول كقيمة، غير مشمول
+
+247
+00:19:22,040 --> 00:19:27,780
+فهذه بنشملها، أو بنعملها circle أو open circle،
+
+248
+00:19:27,780 --> 00:19:34,210
+نكتبها شكلها زي dot أو circle بس بتكون ال solid
+
+249
+00:19:34,210 --> 00:19:37,490
+زي ما قلنا، إذا كانت مشمولة في ال curve، خلّيني
+
+250
+00:19:37,490 --> 00:19:43,170
+أنطبق الكلام ده على example عشان الأمور توضح أكتر،
+
+251
+00:19:43,170 --> 00:19:49,790
+معناه لو مقلوب، نعمل plot of graph of function f of
+
+252
+00:19:49,790 --> 00:19:56,390
+x equal to floor x over 3، x over 3، وهنا بيعطيكوا
+
+253
+00:19:56,390 --> 00:20:02,800
+ال x على أساس إن هي ال integer numbers، integer
+
+254
+00:20:02,800 --> 00:20:05,840
+numbers، مثلا، أو حتى fractions مش مشكلة، يعني ممكن
+
+255
+00:20:05,840 --> 00:20:10,000
+تقولوا R أساسا من minus infinity to infinity، نبدأ
+
+256
+00:20:10,000 --> 00:20:13,640
+مثلا ناخد الصفر، خلينا نبدأ من الصفر عشان نوضح لكم،
+
+257
+00:20:13,640 --> 00:20:21,420
+لو أخدنا الصفر نفسها، صفر على تلاتة صفر، floor zero،
+
+258
+00:20:21,420 --> 00:20:24,440
+خلاص النقطة هي مكانها، و solid لأنها مشمولة في
+
+259
+00:20:24,440 --> 00:20:27,740
+المجموعة هذه، مشمولة في المجموعة هذه، بنحطها صفر هنا،
+
+260
+00:20:27,740 --> 00:20:36,740
+كويس، الواحد على تلاتة، واحد على تلاتة، تصير تلت، floor تلت زيرو برضه،
+
+261
+00:20:36,740 --> 00:20:44,380
+فإذا هنا نفس الكلام، هتصير عندك واحد وزيرو، طيب هنا،
+
+262
+00:20:44,380 --> 00:20:52,060
+اتنين وزيرو، ال input اتنين، ال output زيرو، طيب هنا،
+
+263
+00:20:52,060 --> 00:20:59,500
+عند التلاتة، واحد، floor الواحد، واحد، بحطه هنا open، و
+
+264
+00:20:59,500 --> 00:21:04,100
+فوق هنا بحط عند الواحد solid، نفسها عندها نفسها، هاي
+
+265
+00:21:04,100 --> 00:21:08,020
+تمام،
+
+266
+00:21:08,020 --> 00:21:12,720
+هاي بهذا الشكل، طيب هيك صارنا متفقين، حتى على أساس
+
+267
+00:21:12,720 --> 00:21:17,060
+أن هذه function، لأنه مش معقول نفس ال input يكون له
+
+268
+00:21:17,060 --> 00:21:21,170
+قيمتين، أو two outputs، صحيح؟ إحنا متفقين على كلام
+
+269
+00:21:21,170 --> 00:21:24,030
+هذا، بنقول إن هي مش function من أصله، ولكن هنا لأ،
+
+270
+00:21:24,030 --> 00:21:27,570
+إحنا متفقين على الموضوع هذا من عند الواحد بالضبط،
+
+271
+00:21:27,570 --> 00:21:33,290
+صرنا مع ال output one، كويس، عند التلاتة، عند الستة،
+
+272
+00:21:33,290 --> 00:21:38,990
+عفوا، عند الستة بتصير هنا اتنين، الستة غير مشمولة في
+
+273
+00:21:38,990 --> 00:21:43,630
+في ال line هذا، غير مشمولة، بس أقل من الستة بأقل
+
+274
+00:21:43,630 --> 00:21:49,620
+قيمة ممكنة، صارت مشمولة مع الواحد، الستة تحديدًا لأ،
+
+275
+00:21:49,620 --> 00:21:52,820
+صارت مشمولة مع الإثنين، ستة تحديدًا مشمولة مع
+
+276
+00:21:52,820 --> 00:21:56,780
+الإثنين، فهنا solid، هنا open، الكلام برضه مرة
+
+277
+00:21:56,780 --> 00:22:05,350
+عليكم، أتوقع في المجموعات، في ال open sets. Okay، فضليه،
+
+278
+00:22:32,330 --> 00:22:36,470
+ال function نفسها، حسب ال function نفسها، إذا كانت
+
+279
+00:22:36,470 --> 00:22:41,790
+ceiling، بده ينعكسه ال solid و ال open، هنا هدول
+
+280
+00:22:41,790 --> 00:22:45,970
+اثنين، تبدو ما هيشي يتغيروا، معناته okay، هاي كانت
+
+281
+00:22:45,970 --> 00:22:50,130
+الجزئية اللي كانت ضايلة منا من جزء ال function، عشان
+
+282
+00:22:50,130 --> 00:22:59,960
+نبدأ في موضوعنا الرسمي اليوم، اللي هو استكمالا كان
+
+283
+00:22:59,960 --> 00:23:02,940
+الموضوع ال sets، إحنا اتكلمنا في ال sets سابقا،
+
+284
+00:23:02,940 --> 00:23:08,320
+اتكلمنا عن ال set، و أعرجنا شوية، وإحنا بنحكي عن ال
+
+285
+00:23:08,320 --> 00:23:12,120
+set، على ال sequence، و قلنا إن ال sequence إيش
+
+286
+00:23:12,120 --> 00:23:16,740
+اللي بميزه عن ال set، ترتيب، ترتيب بالضبط، فال
+
+287
+00:23:16,740 --> 00:23:20,180
+sequence، إحنا ملزمين بالترتيب، sequence إحنا ملزمين
+
+288
+00:23:20,180 --> 00:23:23,680
+بترتيب ال elements بتاعتنا، ملزمين بترتيب ال
+
+289
+00:23:23,680 --> 00:23:27,740
+elements بتاعتنا، على أساس، في ال set أنا ما أفرقش
+
+290
+00:23:27,740 --> 00:23:30,900
+معايا ال elements كيف ترتيبها، كل اللي بهمه إنّه
+
+291
+00:23:30,900 --> 00:23:35,880
+ما يكونش فيه تكرار لل elements، صحيح؟ فكل التكرارات
+
+292
+00:23:35,880 --> 00:23:39,260
+تنشل من ال element، في ال في ال sets، و بنعود
+
+293
+00:23:39,260 --> 00:23:44,620
+عنها، أو بنكتبها داخل ال ال curly بتاعتها، ال
+
+294
+00:23:44,620 --> 00:23:49,680
+curly ال braces بتاعتها، قيم unique values، كل قيمة
+
+295
+00:23:49,680 --> 00:23:53,140
+لحالها بنكتبها، ما فيش تكرار لها، في ال sequence لأ،
+
+296
+00:23:53,140 --> 00:23:58,090
+في ال sequence أنا مهتم جدا بال الترتيب، و ما ده
+
+297
+00:23:58,090 --> 00:24:02,930
+مهتم بالترتيب، مش هيفرق معايا التكرار، بمعنى إنّه
+
+298
+00:24:02,930 --> 00:24:05,930
+التكرار بنسيبه زي ما هو، تكرار، ليش؟ لأن مرتبط
+
+299
+00:24:05,930 --> 00:24:10,190
+بالترتيب، و ما ده مرتبط بالترتيب، بقدر برضه ال
+
+300
+00:24:10,190 --> 00:24:13,290
+sequence ده يتعامل معاها as a function، إحنا لسه
+
+301
+00:24:13,290 --> 00:24:16,390
+بنحكي في ال function، كلنا، as a function، معنى ذلك
+
+302
+00:24:16,390 --> 00:24:24,230
+إنّه هتكون function في n، الشي n، هذا ال location، هذا
+
+303
+00:24:24,230 --> 00:24:27,470
+إيش ال location؟ المكان اللي أنا موجود فيه داخل ال
+
+304
+00:24:27,470 --> 00:24:31,230
+sequence، في ال element الأول ولا الثاني ولا الثالث
+
+305
+00:24:31,230 --> 00:24:36,230
+ولا الرابع ولا الخامس، هذا بتساوي A M، ال element
+
+306
+00:24:36,230 --> 00:24:40,790
+اللي موجود في ال location M، قد إيش قيمته؟ فممكن نعبر
+
+307
+00:24:40,790 --> 00:24:45,650
+عنها بهذا الشكل، نقول إن هي function، إيش قيم ال
+
+308
+00:24:45,650 --> 00:24:51,370
+elements داخلها، كل element هو ناتج function في ال
+
+309
+00:24:51,370 --> 00:24:54,400
+location تبع ال element، في ال location تبع ال
+
+310
+00:24:54,400 --> 00:24:57,260
+elements، مدام إحنا من الأساس حددنا إن هي ordered،
+
+311
+00:24:57,260 --> 00:25:01,880
+okay، sequence، مجموعة أرقام مرتبة، و discrete،
+
+312
+00:25:01,880 --> 00:25:07,300
+discrete، بمعنى إنّه ال location الأول، الثاني، ما فيش
+
+313
+00:25:07,300 --> 00:25:09,840
+ال location اتنين ونص، هو يا ال location الأول يا
+
+314
+00:25:09,840 --> 00:25:12,540
+الثاني، ما فيش ال location واحد ونص، فإحنا بنتكلم عن
+
+315
+00:25:12,540 --> 00:25:19,220
+elements، هي discrete objects، ممكن تتعامل مع
+
+316
+00:25:19,220 --> 00:25:23,600
+ما تكونش أرقام، ما تكون objects أحيانا، كويسة، فمجموعة
+
+317
+00:25:23,600 --> 00:25:27,980
+elements اللي بيحددها، أو اللي بنقدر نعرف فيه ال
+
+318
+00:25:27,980 --> 00:25:31,580
+element هذا، ال location تبعها، حسب ال location،
+
+319
+00:25:31,580 --> 00:25:34,320
+فبنقول والله ال sequence الفلانية، ال element
+
+320
+00:25:34,320 --> 00:25:37,280
+الثالث تبعها قيمته كذا، هذا دائما هنكون قيمته كذا،
+
+321
+00:25:37,280 --> 00:25:41,860
+دائما، مدام أنا عرفت ال sequence الفلانية، معناته
+
+322
+00:25:41,860 --> 00:25:44,400
+فيها تعريف، ال sequence هذه، ممكن نقول ال sequence
+
+323
+00:25:44,400 --> 00:25:48,000
+هذه اللي هي الأرقام الزوجية مثلا، لأكبر من صفر،
+
+324
+00:25:49,490 --> 00:25:52,270
+الأرقام الزوجية اللي أكبر من صفر، دائما أول element
+
+325
+00:25:52,270 --> 00:25:57,010
+فيها إيش؟ اثنين، هل ممكن تقولوا لأي واحد الأرقام
+
+326
+00:25:57,010 --> 00:26:00,210
+الزوجية اللي أكبر من صفر، يجي يقولكوا الأربعة؟ لأ،
+
+327
+00:26:00,210 --> 00:26:05,130
+يمكن، فأنتم هنا بتتكلموا عن sequence، دائما الترتيب
+
+328
+00:26:05,130 --> 00:26:08,950
+تبعها ثابت، بس بدكم تعرفوه مسبقا، تعرفوه بطريقة
+
+329
+00:26:08,950 --> 00:26:13,080
+صحيحة مسبقا، فبنتكلم عن sequence of discrete
+
+330
+00:26:13,080 --> 00:26:18,980
+structure used to represent an ordered list، إحنا
+
+331
+00:26:18,980 --> 00:26:22,500
+بنستعمله عشان نعرف، أو نعمل تمثيل لإيش؟ ل sequence
+
+332
+00:26:22,500 --> 00:26:27,920
+مرتّب، ل sequence، أو قائمة مرتبة، for example، one، two،
+
+333
+00:26:27,920 --> 00:26:33,560
+three، five، eight، هذه sequence، بتقدر تعرف الرقم
+
+334
+00:26:33,560 --> 00:26:39,220
+اللي بعده؟ كويس، هذه هتكون هتكون شغلنا، شطرتنا،
+
+335
+00:26:39,220 --> 00:26:41,680
+bagel course، في bagel course طبعا اليوم إحنا بس،
+
+336
+00:26:41,680 --> 00:26:44,780
+شغلنا، هنتعرف بس إنه إيش ال sequence، يعني ما
+
+337
+00:26:44,780 --> 00:26:48,500
+معنى ال sequence، في ال chapters اللي جاية، هنقول
+
+338
+00:26:48,500 --> 00:26:51,080
+إنّه لأ، عندنا sequence معين، أو series معينة،
+
+339
+00:26:51,080 --> 00:26:54,340
+series معينة، بدنا نعرف ال elements اللي جاية، عشان
+
+340
+00:26:54,340 --> 00:26:56,300
+تعرفوا ال elements، هذا طبعا في في معظم
+
+341
+00:26:56,300 --> 00:26:58,000
+إمتحانات الذكاء العقلي، والأمور اللي زي ذات،
+
+342
+00:26:58,000 --> 00:27:01,560
+بتلاقوا حاجة زي هي، أسئلة بهذا الشكل، كويس، هذه
+
+343
+00:27:01,560 --> 00:27:04,830
+عشان نجيبها، هنتكلم عنها بس لاحقا، فيها chapter،
+
+344
+00:27:04,830 --> 00:27:08,790
+chapter جاي، هنتكلم فيه، ونقولكم كيف نجيب الأرقام
+
+345
+00:27:08,790 --> 00:27:10,670
+اللي بعدها، طب عشان أجيب الأرقام اللي بعدها، أنا
+
+346
+00:27:10,670 --> 00:27:16,610
+محتاج formula إلها، محتاج المعادلة تاعتها، تلاتة عشر،
+
+347
+00:27:16,610 --> 00:27:19,970
+هاي ناس البنات عرفوها، هاي هاي البنات عرفوها،
+
+348
+00:27:19,970 --> 00:27:24,490
+تلاتة عشر، اثنين وثلاثة، خمسة، خمسة وثلاثة، ثمانية،
+
+349
+00:27:24,490 --> 00:27:27,490
+ثمانية، وثمانية وخمسة، تلاتة عشر، تلاتة عشر وثمانية و
+
+350
+00:27:27,490 --> 00:27:32,540
+واحد وعشرين، هذه fibonacci series، بيسموها، عالم
+
+351
+00:27:32,540 --> 00:27:35,520
+إيطالي، هنتكلم عنه لاحقا، فهذه مشهورة جدا من ال
+
+352
+00:27:35,520 --> 00:27:39,440
+sequence، المشهورة جدا، فهي واحدة من ال series أو ال
+
+353
+00:27:39,440 --> 00:27:42,360
+sequence اللي أنتم ممكن تتعاملوا معها، وبتجيكم
+
+354
+00:27:42,360 --> 00:27:45,740
+هي في أسئلة ال IQ، اللي هي الذكاء العقلي، والأمور
+
+355
+00:27:45,740 --> 00:27:48,000
+هذه اللي بتشوفوها على ال net، وبتحضروها، يمكن
+
+356
+00:27:48,000 --> 00:27:51,360
+تشاركتوا فيها كمان، عشان تقول والله اه، وين أنا
+
+357
+00:27:51,360 --> 00:27:56,080
+موجود في سلم الأذكياء، تمام، هي في إنكم مثلا term،
+
+358
+00:27:56,080 --> 00:27:59,000
+ثاني، أو ممكن نقوله بهذا الشكل، ال sequence نعرفه 1،
+
+359
+00:27:59,000 --> 00:28:05,820
+3، 9، 27، 81، و لحظه، نعرف تلاتة ضبار n، وبعدين،
+
+360
+00:28:05,820 --> 00:28:12,660
+ellipses، infinite sequence، لا نهائية، خلاص هذه،
+
+361
+00:28:12,660 --> 00:28:17,320
+مستمرة، فمجرد عملت تلات نقاط، أنا عارف إن هي مستمرة،
+
+362
+00:28:17,320 --> 00:28:21,520
+عارفين إن هي مستمرة، طيب هي دي، هو يعطيني هي،
+
+363
+00:28:21,520 --> 00:28:24,800
+المعادلة التابعة لها، بس أحيانا ممكن ما يعطيناش إياها،
+
+364
+00:28:24,800 --> 00:28:27,200
+ويقولنا، اعطوني المعادلة، أو قولولي إيش الرقم اللي
+
+365
+00:28:27,200 --> 00:28:31,360
+ورا، فهذه أنتم بتشوفوها لاحقا، هناخدها مش اليوم،
+
+366
+00:28:31,360 --> 00:28:34,800
+لاحقا هناخدها، كيف أطلع المعادلة هذه، لأن لو
+
+367
+00:28:34,800 --> 00:28:43,120
+عوضتوا بصفر، عوضنا بواحد، باثنين، بثلاثة، بأربعة، تقدر
+
+368
+00:28:43,120 --> 00:28:44,860
+تجيبوا الخامس، تقدر تجيبوا ال element اللي وراه،
+
+369
+00:28:44,860 --> 00:28:48,180
+تقدر تجيبوا ال element اللي وراه، طيب إحنا من هنا،
+
+370
+00:28:48,180 --> 00:28:52,500
+طلعنا بحاجة، إن ال location تبعنا، ال location،
+
+371
+00:28:52,500 --> 00:28:58,060
+بناخذه من ال natural number، ليش؟ لأن هنا ال
+
+372
+00:28:58,060 --> 00:29:03,590
+location هيبدا بصفر، فإحنا فعلا في بعض ال sequences،
+
+373
+00:29:03,590 --> 00:29:07,250
+بتبدأ بال natural number، وفي بعضها natural number،
+
+374
+00:29:07,250 --> 00:29:12,080
+minus zero، ببدأ بواحد، فهذا يجب أن يكون معرف، إما
+
+375
+00:29:12,080 --> 00:29:15,700
+natural number، فببدأ مباشرة، إذا عند المعادلة ببدأ،
+
+376
+00:29:15,700 --> 00:29:20,600
+أعوّض من ال zero، أو لأ، natural number minus one، أو
+
+377
+00:29:20,600 --> 00:29:26,180
+أكبر أو يساوي واحد، فبعرف نبدأ من الواحد، نعرف نبدأ،
+
+378
+00:29:26,180 --> 00:29:28,260
+من الواحد، ما نبقاش شيء ثاني، دائما يا صفر يا
+
+379
+00:29:28,260 --> 00:29:32,060
+الواحد، عادة اللي بنبدأ فيه ال sequence تبعنا، Okay،
+
+380
+00:29:32,060 --> 00:29:37,460
+okay، مدام عرفنا إن أنا بتعامل مع set، هي عبارة عن
+
+381
+00:29:37,460 --> 00:29:42,080
+function، و ال set هذه لازم أتعامل معاها كمرتبة، ك
+
+382
+00:29:42,080 --> 00:29:44,560
+sequence، مرتب، ف أنا بقدر أقول إن هذه عبارة عن
+
+383
+00:29:44,560 --> 00:29:49,760
+function، ال domain تبعها هو ال locations، ال
+
+384
+00:29:49,760 --> 00:29:52,100
+locations، ال location الأول، الثاني، الثالث، الرابع،
+
+385
+00:29:52,100 --> 00:29:56,930
+الخامس، العشر، كويسة، ال function معينة، ال function
+
+386
+00:29:56,930 --> 00:30:00,270
+اللي هتعرف لنا ال sequence، بقدر أجيب ال elements
+
+387
+00:30:00,270 --> 00:30:03,930
+تحت ال sequence، كل واحد في ال location تبعه، لأن كل
+
+388
+00:30:03,930 --> 00:30:08,170
+واحد لازم يكون function في ال location تبعه، فهذه
+
+389
+00:30:08,170 --> 00
+
+445
+00:34:30,790 --> 00:34:35,470
+من واحد، واحد على واحد، واحد على واحد، واحد على اتنين
+
+446
+00:34:35,470 --> 00:34:39,990
+واحد على تلاتة، فلحظوا بتطلع الـ sequence هذه مقابلة
+
+447
+00:34:39,990 --> 00:34:42,510
+لا، اسم تمام
+
+448
+00:34:44,330 --> 00:34:47,190
+Okay، الـ examples with repetitions، طبعا في الـ
+
+449
+00:34:47,190 --> 00:34:50,830
+repetitions، احنا قولنا في الـ sequence مسموح في الـ
+
+450
+00:34:50,830 --> 00:34:56,790
+series، مسموح، ولكن في الـ sets لأ، فإذا لما يكون
+
+451
+00:34:56,790 --> 00:35:04,690
+عندنا constant of the sequence P0، P1، P2، P3، ونقول
+
+452
+00:35:04,690 --> 00:35:09,490
+أن الـ Pn equal to minus one to the power n، هاي الـ
+
+453
+00:35:09,490 --> 00:35:13,430
+relation، الأوطانية مجرد أن بنعوض، بنبدأ بالـ zero لأن
+
+454
+00:35:13,430 --> 00:35:18,910
+هنا بدأنا احنا
+
+455
+00:35:18,910 --> 00:35:19,010
+احنا
+
+456
+00:35:19,010 --> 00:35:19,310
+احنا
+
+457
+00:35:19,310 --> 00:35:22,810
+احنا
+
+458
+00:35:22,810 --> 00:35:25,010
+احنا
+
+459
+00:35:25,010 --> 00:35:33,330
+احنا
+
+460
+00:35:34,960 --> 00:35:37,800
+أه، بالظبط، هذه هتكون isolating، تمام، عاملة زي sunny
+
+461
+00:35:37,800 --> 00:35:45,180
+soda، يعني مش sunny soda، زي .. إيش بتسميها الـ .. أو
+
+462
+00:35:45,180 --> 00:35:51,810
+.. إيش بتسموها السوتوث .. السوتوث زي أسنان المنشرة
+
+463
+00:35:51,810 --> 00:35:55,530
+الـ Suture، عارفينه؟ فهذه تطلع زي الـ Suture،
+
+464
+00:35:55,530 --> 00:35:58,910
+تمام، طيب، في الحالة اللي عندنا هنا، في الـ
+
+465
+00:35:58,910 --> 00:36:03,250
+sequence مقبولة، في الـ series مقبولة، بس في الـ
+
+466
+00:36:03,250 --> 00:36:06,090
+sets لأ، في الـ sets .. لو عندي set بهذا الشكل،
+
+467
+00:36:06,090 --> 00:36:08,990
+الطبيعي أن هي تكون two elements فقط، بقولش أن هي
+
+468
+00:36:08,990 --> 00:36:14,340
+to infinity، هنا to infinite sequence، هنا
+
+469
+00:36:14,340 --> 00:36:18,540
+لأ، لما بتكلم عنها as a set، بقول أن هي لأ، set الـ
+
+470
+00:36:18,540 --> 00:36:22,740
+cardinality بتاعتها اتنين فقط، one، minus one، و بس
+
+471
+00:36:22,740 --> 00:36:30,270
+one، minus one، okay، recognizing sequences، كيف ممكن
+
+472
+00:36:30,270 --> 00:36:36,430
+نعمل تمييز للـ sequence بتاعتنا، طب احنا زي ما
+
+473
+00:36:36,430 --> 00:36:42,450
+قلت لكم، مش هناخد علميا بالحل لاحقا، هناخد الحل، هنرجع
+
+474
+00:36:42,450 --> 00:36:47,210
+للموضوع هذا، و نتكلم عن sequence، و محتاجين احنا
+
+475
+00:36:47,210 --> 00:36:50,590
+نجيب elements ناقصة فيه، أو نجيب الـ relation تبعته
+
+476
+00:36:50,590 --> 00:36:54,970
+هناخده، ولكن احنا هنا by logic، هيك .. بدنا نشوف شوية
+
+477
+00:36:54,970 --> 00:36:59,150
+examples لكيف أنا أميز الـ sequence تبعتنا .. كيف
+
+478
+00:36:59,150 --> 00:37:02,430
+أميز .. أقول اه دي sequence بتاعة كذا، لو بدأنا
+
+479
+00:37:02,430 --> 00:37:08,110
+نقول والله إيش الـ next number لواحد، اتنين، تلاتة
+
+480
+00:37:08,110 --> 00:37:12,510
+اربعة .. خمسة .. خمسة .. ليش؟ بيمشي أنا .. لأن
+
+481
+00:37:12,510 --> 00:37:17,570
+احنا، أنا متعامل عن أرقام .. الأرقام الـ positive ..
+
+482
+00:37:17,570 --> 00:37:21,650
+الـ positive integers .. positive integers، واحد،
+
+483
+00:37:21,650 --> 00:37:26,170
+اتنين، تلاتة، فطبيعي خامس element أكبر من صفر هو
+
+484
+00:37:26,170 --> 00:37:32,130
+الخمسة، طيب، واحد، تلاتة،  ......
+
+485
+00:37:32,130 --> 00:37:34,310
+......
+
+486
+00:37:34,310 --> 00:37:39,470
+......
+
+487
+00:37:39,470 --> 00:37:44,030
+......
+
+488
+00:37:44,030 --> 00:37:47,610
+داش
+
+489
+00:37:48,070 --> 00:37:50,510
+sequence، أنتو بتقدروا تعرفوها و تميزوها لحاجة، و
+
+490
+00:37:50,510 --> 00:37:54,510
+مجرد ما شوفتوها بتقدروا تميزوها، بتقدروا تميزوها
+
+491
+00:37:54,510 --> 00:37:59,670
+okay، ولكن مع ذلك بيصير أحيانا trouble with
+
+492
+00:37:59,670 --> 00:38:03,190
+recognition، في التمييز أحيانا بيصير مشكلة أن أنا
+
+493
+00:38:03,190 --> 00:38:11,470
+ماعرفتهاش بالظبط، زي لو قلنا أخدنا تلاتة، خمسة، سبعة
+
+494
+00:38:11,470 --> 00:38:15,070
+و سكتت و قلت لكم، هتقولي الرقم اللي وراه ممكن يكون
+
+495
+00:38:15,070 --> 00:38:18,550
+تسعة مثلا، ممكن يكون، ممكن يكون تسعة، و ممكن يكون
+
+496
+00:38:18,550 --> 00:38:22,770
+أحد عشر .. ممكن يكون تسعة، و ممكن يكون أحد عشر .. لحظة
+
+497
+00:38:22,770 --> 00:38:28,170
+دولهم متمتفقين مع بعض .. فلاحظوا أنه ممكن جدا يكون
+
+498
+00:38:28,170 --> 00:38:31,250
+في صعوبة في تمييز أي .. أنا بتعني أي sequence
+
+499
+00:38:31,250 --> 00:38:34,790
+بحتكلم، أو بحكي .. فعشان أجيب الـ element اللي وراها
+
+500
+00:38:34,790 --> 00:38:37,890
+هتكون فيه صعوبة، إيش الـ element اللي وراها؟ أو
+
+501
+00:38:37,890 --> 00:38:41,690
+يقولنا إيش الـ element اللي قدامها؟ ففي صعوبة في
+
+502
+00:38:41,690 --> 00:38:44,070
+تمييز الـ sequence في بعض الأحيان بتصير، ففي مشاكل
+
+503
+00:38:44,070 --> 00:38:46,750
+ممكن تصير في التمييز، المشاكل هذا إذا صارت بتكون
+
+504
+00:38:46,750 --> 00:38:50,410
+نتيجة أن أنا ماعرفتش الـ الـ الـ initial elements صح
+
+505
+00:38:50,410 --> 00:38:53,910
+الـ initial elements، هدول مش معرفين بصورة صحية، هدول
+
+506
+00:38:53,910 --> 00:38:59,360
+intersection لـ two sequence، إيه، و بدك منهم؟ هدول
+
+507
+00:38:59,360 --> 00:39:03,640
+هيكون intersection لـ .. intersection set للـ prime
+
+508
+00:39:03,640 --> 00:39:07,860
+و للـ odd، أنت مين بدك منهم، مش معرف، فهنا، أو خليني
+
+509
+00:39:07,860 --> 00:39:12,160
+أقول not well defined، هو مش معرف بطريقة جيدة، يمكن
+
+510
+00:39:12,160 --> 00:39:14,920
+كنا محتاجين element قبل، أو element بعد، عشان تتضح
+
+511
+00:39:14,920 --> 00:39:18,480
+الـ sequence، هذا، إن و منهم، فإذا كان فعلا بهذا الشكل
+
+512
+00:39:18,480 --> 00:39:23,500
+مش معرفة بصورة جيدة، واضح أنه هيكون فينا مشكلة في
+
+513
+00:39:23,500 --> 00:39:29,160
+تمييز الصورة في الغالب .. في الغالب إذا .. ماعناش
+
+514
+00:39:29,160 --> 00:39:34,140
+واضحة الصورة بهذا الشكل، في الغالب الأبسط هي اللي
+
+515
+00:39:34,140 --> 00:39:37,860
+بناخدها، في الغالب الأبسط هي اللي بناخدها، إذا
+
+516
+00:39:37,860 --> 00:39:42,800
+طبعا ماعناش أي معلومة مسبقة، فالـ simplest هي من الـ
+
+517
+00:39:42,800 --> 00:39:44,840
+functions، من الـ two functions اللي بنتعامل معها، و
+
+518
+00:39:44,840 --> 00:39:49,440
+بناخدها، هذا إذا كان لابد أن احنا نختاره، بس في
+
+519
+00:39:49,440 --> 00:39:52,240
+حالة زي هذه لأ، هي لها كذا احتمال، هي لها كذا
+
+520
+00:39:52,240 --> 00:39:58,350
+احتمال للشغل، okay، كيف احنا نعرف الـ simplicity اصلا
+
+521
+00:39:58,350 --> 00:40:02,510
+of a function، كيف نعرف مين البسيطة منهم، أساسا ما
+
+522
+00:40:02,510 --> 00:40:04,650
+احنا عندنا الـ prime، و عندنا الـ .. الـ .. الـ odd
+
+523
+00:40:04,650 --> 00:40:06,650
+التنتين بساطين بالنسبالي، يعني بالنسبالنا على level
+
+524
+00:40:06,650 --> 00:40:09,670
+تبعنا، ماهم التنتين زي بعض، مش هتفرق كتير، هذه بسيطة
+
+525
+00:40:09,670 --> 00:40:12,250
+و هذه بسيطة، أنا عرفت هذه، و عرفت هذه، و هذه ممكن
+
+526
+00:40:12,250 --> 00:40:16,690
+يكون يا هذه يا هذه، مين اختار منهم، هذا مافيش
+
+527
+00:40:16,690 --> 00:40:22,590
+objective right answer، بقدرش أقول لكم والله لأ، لازم
+
+528
+00:40:22,590 --> 00:40:26,530
+يكون بهذا الشكل، هي من الأساس غير معرفة بصورة
+
+529
+00:40:26,530 --> 00:40:31,170
+جيدة، غير معرفة، الـ elements هذه بصورة جيدة، فهذه
+
+530
+00:40:31,170 --> 00:40:35,590
+بيبقى قائمة لإحتمالاتها، ممكن حد يجاوب إن هي odd، و
+
+531
+00:40:35,590 --> 00:40:39,120
+ممكن حد يجاوب إن هي prime، بقدرش أقول هذا غلط ولا
+
+532
+00:40:39,120 --> 00:40:43,580
+بقدر أقول هذا غلط، لأنه من الأساس تعريفها مش غلط
+
+533
+00:40:43,580 --> 00:40:49,100
+ولكن ماكانش، أو not well defined، مش محدد بصورة
+
+534
+00:40:49,100 --> 00:40:53,720
+جيدة، مش مميز بصورة محددة واضحة، هو مش محدد، مش
+
+535
+00:40:53,720 --> 00:40:59,580
+محدد أصلا، طيب، what are strings really؟ احنا كنا
+
+536
+00:40:59,580 --> 00:41:01,760
+بتكلم عن الـ sequence، الـ string، الحقيقة بقى في
+
+537
+00:41:01,760 --> 00:41:05,060
+تعريفات كتير فيها، يعني في اختلاف حتى فيها، أنه الـ
+
+538
+00:41:05,060 --> 00:41:07,980
+string، إيش بيميزه عن الـ sequence، فهي في ناس عرفوها
+
+539
+00:41:07,980 --> 00:41:11,840
+عساسة أن هي الـ finite sequences، إذا كانت finite
+
+540
+00:41:12,340 --> 00:41:16,400
+sequences، بنسميها string، فاحنا إذا كان محددة، بادية
+
+541
+00:41:16,400 --> 00:41:20,280
+من واحد، و منتهية، and n، و n هذا belong to natural
+
+542
+00:41:20,280 --> 00:41:24,960
+number، بقى قيمة محددة معروفة، and بتقولي لعند عشر
+
+543
+00:41:24,960 --> 00:41:28,240
+terms، أول عشر terms، أول عشرين terms، خلاص أنا عارف
+
+544
+00:41:28,240 --> 00:41:31,520
+أنه جداش عدد الـ terms، بقدر أحسب لها cardinality
+
+545
+00:41:31,520 --> 00:41:35,580
+نقدر نحسب لها cardinality، نعرف جداش عدد الـ elements
+
+546
+00:41:35,580 --> 00:41:40,260
+فيها، جاله على أساس إنه هذا اللي يكون الـ sequence
+
+547
+00:41:40,260 --> 00:41:45,620
+طيب، ولكن رغم ذلك في infinite strings، رغم إنه
+
+548
+00:41:45,620 --> 00:41:48,920
+الكتاب معرفه على أساس إنه finite sequence، ولكن
+
+549
+00:41:48,920 --> 00:41:54,060
+احنا بنعرف إنه في infinite strings، في strings ممكن
+
+550
+00:41:54,060 --> 00:41:58,160
+نتعامل معها كـ infinite، كويس، ولكن هذا تعريف، في
+
+551
+00:41:58,160 --> 00:42:01,440
+تعريف تاني، strings are often restricted to
+
+552
+00:42:01,440 --> 00:42:07,510
+sequences composed of symbols، بدل الـ numbers، إذا
+
+553
+00:42:07,510 --> 00:42:13,290
+كانت الـ .. الـ sequence يحتوي على symbols، على
+
+554
+00:42:13,290 --> 00:42:17,430
+elements، مش أرقام، الـ symbols هذه، و الـ objects ..
+
+555
+00:42:17,430 --> 00:42:19,990
+الـ objects هذه، الـ symbols زي .. زي الـ alphabet
+
+556
+00:42:19,990 --> 00:42:26,430
+مثلا الـ alphabet symbols، a، b، c، d، e، f، g، الـ .. الـ ..
+
+557
+00:42:26,430 --> 00:42:29,870
+الـ letters هذه، إذا كانت الـ sequence .. sequence من
+
+558
+00:42:29,870 --> 00:42:35,600
+letters، فبنسميها string، هذا برضه تعريف ممكن التعامل
+
+559
+00:42:35,600 --> 00:42:39,540
+.. التعامل معه عساس أن هي تعتمد على مجموعة symbols
+
+560
+00:42:39,540 --> 00:42:42,400
+بنعرفه finite، طبعا، لأن إذا كان ما اتكلم عن الـ
+
+561
+00:42:42,400 --> 00:42:45,900
+alphabet، فهي الـ alphabet محددة، الـ alphabet محددة
+
+562
+00:42:45,900 --> 00:42:48,820
+هي مش to infinity، يعني خلاص هي معروفة أنه .. أنه
+
+563
+00:42:48,820 --> 00:42:51,980
+كام حرف؟ ستة و عشرين حرف، خلاص هم معروفين، ستة و
+
+564
+00:42:51,980 --> 00:42:56,400
+عشرين، هم مش هيزيدوا، مش هيزيدوا، كويس، و الـ .. زي ما
+
+565
+00:42:56,400 --> 00:43:00,870
+قلنا الـ index من صفر ببدأ، أو من واحد، من صفر أو واحد
+
+566
+00:43:00,870 --> 00:43:03,590
+فاحنا متفقين على التعريف، مع الـ sequence هو هو، إما
+
+567
+00:43:03,590 --> 00:43:07,050
+بنبدأ من صفر أو من واحد، بأي طريقة من الطريقتين
+
+568
+00:43:07,050 --> 00:43:12,190
+احنا هنتعامل مع، length of a finite string is just
+
+569
+00:43:12,190 --> 00:43:16,970
+its number of terms، أو distinct indices، بمعنى أنه
+
+570
+00:43:16,970 --> 00:43:21,090
+لازم نكون عارفين عدد الـ numbers، أو الـ number of
+
+571
+00:43:21,090 --> 00:43:23,870
+terms، جداش عدد الـ units اللي جواها، جداش عدد الـ
+
+572
+00:43:23,870 --> 00:43:28,550
+elements داخلها، و بنكون محدد في الحالة هذه، جداش
+
+573
+00:43:28,550 --> 00:43:32,460
+عدد الـ indices اللي موجودة، مكتوبة هنا، أها، يعني الـ
+
+574
+00:43:32,460 --> 00:43:36,540
+index الأولى، واحد، index، index، هدولة مجموعة، هم اللي
+
+575
+00:43:36,540 --> 00:43:39,820
+هم الـ indices اللي هم محددين، معروفين، أنه والله اه
+
+576
+00:43:39,820 --> 00:43:43,220
+عندي عشرين، عندي خمسين indices، بمعنى عندي عشرين
+
+577
+00:43:43,220 --> 00:43:47,700
+location، عشرين، خمسة و عشرين location، معروفة و محددة
+
+578
+00:43:47,700 --> 00:43:50,900
+فهذه بنتعامل معها على أساس إن هي string، على أساس
+
+579
+00:43:50,900 --> 00:43:57,730
+إن هذا string، Okay، strings more formally، أكثر ..
+
+580
+00:43:57,730 --> 00:44:01,250
+نوضحها بصورة أكثر، فاحنا زي ما قلنا، إذا كان عرفناها
+
+581
+00:44:01,250 --> 00:44:05,270
+عساس أن هي symbols، مجموعة عناصر أو رموز، symbols
+
+582
+00:44:05,270 --> 00:44:09,310
+ممكن تكون زي ما قلنا الـ alphabet، letters، نتعامل
+
+583
+00:44:09,310 --> 00:44:13,070
+معها عساس أن هي alphabet مثلا، generally A, B, C, D, Z
+
+584
+00:44:13,070 --> 00:44:21,830
+to Z، A String S، الـ S هذه اللي هي الـ string، و لاحظوا
+
+585
+00:44:21,830 --> 00:44:24,670
+إن احنا كاتبينها small، لأن إذا كتبناها capital
+
+586
+00:44:24,670 --> 00:44:31,010
+ستصبح six، ستصبح six، فلأ small، فأنا عارف إن هذه الـ
+
+587
+00:44:31,010 --> 00:44:35,030
+small string over alphabet، بنسميها مثلا big sigma
+
+588
+00:44:35,030 --> 00:44:38,150
+الـ big sigma، في الحلقة هذه بيقول و الله فينا
+
+589
+00:44:38,150 --> 00:44:42,490
+string S هذا عبارة عن alpha alphabet string
+
+590
+00:44:44,860 --> 00:44:49,780
+لـ any sequence of symbols SI، والـ I هذي زي ما
+
+591
+00:44:49,780 --> 00:44:52,740
+قلنا اللي هو الـ index تبعنا، الـ .. الـ .. الـ
+
+592
+00:44:52,740 --> 00:44:56,430
+sequence من الـ element الأول إيش هو؟ A، الـ element
+
+593
+00:44:56,430 --> 00:44:59,710
+التاني B، الـ element التالت C، الـ element الرابع D، و
+
+594
+00:44:59,710 --> 00:45:08,130
+هكذا، of symbols، فبنقول هنا الـ SI belong to sigma
+
+595
+00:45:08,130 --> 00:45:14,590
+فمعنى ذلك أن الـ element اللي داخل الـ set، أو داخل
+
+596
+00:45:14,590 --> 00:45:18,350
+الـ sequence، أو الـ string، احنا بنتكلم عن string
+
+597
+00:45:19,740 --> 00:45:22,960
+string، هذا، هذا هيكون مجموعة elements، متفقين على
+
+598
+00:45:22,960 --> 00:45:29,460
+هيك، طيب، كل element جوا، إيش بسميه SI، لأن حسب قيمة I
+
+599
+00:45:29,460 --> 00:45:33,620
+هتتغير الـ elements اللي جوا هذه، فهنقول أن الـ SI، أي
+
+600
+00:45:33,620 --> 00:45:38,680
+واحدة منهم لازم تكون belong to سيجما، سيجما الشيء
+
+601
+00:45:38,680 --> 00:45:46,880
+هذه، كل الـ alphabet symbols، إذا بعرف symbols تانية
+
+602
+00:45:46,880 --> 00:45:49,060
+غير الـ alphabet، بدي أكون معرفها برضه، عساس أن هي الـ
+
+603
+00:45:49,060 --> 00:45:53,800
+big sigma، هدولة كل الحروف اللي موجودين هنا، لو
+
+604
+00:45:53,800 --> 00:45:56,100
+بنتكلم عن الطالبات اللي موجودين، معناته كل أسماء
+
+605
+00:45:56,100 --> 00:46:00,960
+الطالبات هدولة، بتحطهم عساس أن هم هدول الـ big sigma
+
+606
+00:46:00,960 --> 00:46:04,300
+تمام؟ ويمكن بعد ما نخلص الامتحان، بيضطروا حسب
+
+607
+00:46:04,300 --> 00:46:07,260
+درجاتهم، عساس أن هذا الـ year بتتغيرش، مش هنقول والله
+
+608
+00:46:07,260 --> 00:46:10,830
+زي الـ set، الـ set قابلة للتبديل، أي حد بيجي اسمه قبل
+
+609
+00:46:10,830 --> 00:46:14,210
+تاني مفرقش، بس لو قلنا لأ، حسب مثلا في التوجيه جد
+
+610
+00:46:14,210 --> 00:46:17,050
+الجوا مثلا، خلاص هذه ثابتة، هذه لازم الـ string
+
+611
+00:46:17,050 --> 00:46:21,310
+أنحدده، لازم تكون مرتبة، بينفعش حد يجي مكان حد،
+
+612
+00:46:21,310 --> 00:46:27,510
+صحيح؟ كويس، فهنا alphabet هذه بتكون تشتمل على جميع
+
+613
+00:46:27,510 --> 00:46:30,210
+الـ symbols اللي أنا بتعامل معها، جميع الـ symbols
+
+614
+00:46:30,210 --> 00:46:33,890
+اللي بتتعامل معها، فأي symbol داخل الـ string لازم
+
+615
+00:46:33,890 --> 00:46:38,930
+يكون موجود أصلا معرف من الأول في الـ big sigma، و
+
+616
+00:46:38,
+
+667
+00:50:28,710 --> 00:50:32,810
+من صفر معناته بإننا زائد واحد آخر index موجود  جدش
+
+668
+00:50:32,810 --> 00:50:35,190
+قيمته زائد واحد إذا بدأنا والله automatically من ال
+
+669
+00:50:35,190 --> 00:50:39,790
+positive natural numbers خلاص الأخر هو يمثل العدد
+
+670
+00:50:39,790 --> 00:50:44,110
+العدد ال elements في الحالة هذه بنقول أن ال S is a
+
+671
+00:50:44,110 --> 00:50:49,430
+finite string and belongs to natural numbers الآن
+
+672
+00:50:49,430 --> 00:50:52,090
+طبعا جدش ال cardinality جدش عدد ال elements
+
+673
+00:50:52,090 --> 00:50:56,310
+طبيعي بده يكون عدد طبيعي، عدد صحيح integer هيكون
+
+674
+00:50:56,310 --> 00:50:59,410
+integer عدد طبيعي، العدد الطبيعي هو العدد الواحد
+
+675
+00:50:59,410 --> 00:51:03,770
+اثنين، ثلاثة، أربعة، مافيش فيها fractions، okay then لما
+
+676
+00:51:03,770 --> 00:51:09,470
+نقول هل وجد s string to the power n هذه معناها
+
+677
+00:51:09,470 --> 00:51:15,870
+denotes the concatenation of n cubit  او cubits of
+
+678
+00:51:15,870 --> 00:51:23,770
+s هنا معناته ال S عملتيلها نسخ N مرة، هناك كنا بنقول
+
+679
+00:51:23,770 --> 00:51:29,070
+S في T هذا كان String وهذا String وحطيناهم ورا بعض
+
+680
+00:51:29,070 --> 00:51:35,930
+طب لما نقول S تربيع كأنها S في S، sequence S بنحطه
+
+681
+00:51:35,930 --> 00:51:42,270
+ورا مباشرة كمان مرة ال sequence نفسه S، طيب N مرة
+
+682
+00:51:42,270 --> 00:51:48,390
+بده يتكرر لعند ما نصل، هذه واحد، هذه اثنين، to S
+
+683
+00:51:48,390 --> 00:51:52,810
+المرة N، المرة أنه كله بصير هذا sequence ..
+
+684
+00:51:52,810 --> 00:51:55,370
+sequence واحد، فهذه عملية ال concatenation، لما تشوف
+
+685
+00:51:55,370 --> 00:51:57,090
+كلمة concatenation معناها أن أنتم تعرفون أن أنتم
+
+686
+00:51:57,090 --> 00:51:59,570
+بت... هتعملوا string من مجموعة strings ثانية
+
+687
+00:51:59,570 --> 00:52:04,030
+بترتبوهم ورا .. ورا بعضهم، بترتبوهم ورا بعضهم، okay
+
+688
+00:52:04,030 --> 00:52:10,870
+في عندنا ال epsilon أو double quotation  فاضيين بهذا
+
+689
+00:52:10,870 --> 00:52:16,710
+الشكل، هذه معناته أن أنا بتكلم عن empty string أو
+
+690
+00:52:16,710 --> 00:52:23,790
+string of length zero، string طوله صفر، string
+
+691
+00:52:23,790 --> 00:52:28,190
+طوله صفر، string فاضي، string فاضي، لما تيجوا تطلعوا
+
+692
+00:52:28,190 --> 00:52:30,590
+عليه هتلاقوا مافيش فيه أي elements، ففي الحالة هذه
+
+693
+00:52:30,590 --> 00:52:34,630
+بنسميه epsilon أو ال double quotation، بعض كتب
+
+694
+00:52:34,630 --> 00:52:40,490
+أحيانًا بسموه Lambda، بيعرفوها على أساس أنه Lambda، على
+
+695
+00:52:40,490 --> 00:52:43,410
+أساس أنه Lambda، فLambda ممكن برضه في بعض كتب
+
+696
+00:52:43,410 --> 00:52:46,610
+تلاقوها عبارة عن ال empty string، عبارة عن empty
+
+697
+00:52:46,610 --> 00:52:51,710
+string، خلاص هي ال summation اللي كنتوا تتكلموا فيه
+
+698
+00:52:51,710 --> 00:52:55,430
+المرة الجاية بنبدأ عندنا string أو عندنا sequence
+
+699
+00:52:55,430 --> 00:52:59,950
+معين أو series معينة، بدنا ال series بتاعتنا هذه
+
+700
+00:52:59,950 --> 00:53:03,090
+نجمعهم، نجمع ال elements داخلها، زي الحالة اللي كنتوا
+
+701
+00:53:03,090 --> 00:53:07,130
+اتكلمنا عنها، اللي كانت عبارة عن واحد على X، واحد
+
+702
+00:53:07,130 --> 00:53:10,030
+على X، ممكن نقول واحد على X، وبدنا نجمع كل ال
+
+703
+00:53:10,030 --> 00:53:13,500
+elements فيه، لها شوية نظريات، فيه لها شوية rules،
+
+704
+00:53:13,500 --> 00:53:17,400
+فيه لها شوية قواعد في التعامل، فبدنا ناخدها المرة
+
+705
+00:53:17,400 --> 00:53:20,180
+الجاية إن شاء الله تعالى، ونكمل موضوعنا المرة
+
+706
+00:53:20,180 --> 00:53:20,460
+الجاية
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..61bda0d0220d6fc1fe207769a12fb1f712d4d979
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_postprocess.srt
@@ -0,0 +1,2824 @@
+1
+00:00:20,670 --> 00:00:22,770
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,770 --> 00:00:24,690
+الأنبياء والمرسلين سيدنا محمد وعلى أهلي وصحابي
+
+3
+00:00:24,690 --> 00:00:27,790
+أجمعين نبدأ اليوم نحاول نخلص الجزئية اللي بدأنا
+
+4
+00:00:27,790 --> 00:00:29,590
+نتكلمنا فيها المرة اللي فاتت اللي هي ال functions
+
+5
+00:00:29,590 --> 00:00:34,330
+وقولنا .. تحدثنا عن تعريف ال functions و بعدين ..
+
+6
+00:00:36,840 --> 00:00:39,440
+اتكلمنا عن أنواع ال functions قلنا فيهم دي نوعين
+
+7
+00:00:39,440 --> 00:00:42,580
+مهمين اللي اتكلمنا عنهم المرة اللي فاتت ال .. ال
+
+8
+00:00:42,580 --> 00:00:47,760
+one-to-one ال one-to-one و ال onto و ال onto ف ال
+
+9
+00:00:47,760 --> 00:00:49,980
+one-to-one و ال onto أخدنا example المرة اللي فاتت
+
+10
+00:00:49,980 --> 00:00:54,200
+عليها خلينا بسرعة نراجع ال function الأولى هنا هذي
+
+11
+00:00:54,200 --> 00:00:58,200
+one-to-one و لا onto او combination يعني اعمل
+
+12
+00:00:58,200 --> 00:01:00,420
+combination one-to-one
+
+13
+00:01:02,470 --> 00:01:07,950
+one to one قلنا إن كل element في ال domain إله
+
+14
+00:01:07,950 --> 00:01:14,530
+output واحد فقط وكل output في ال code main أو في
+
+15
+00:01:14,530 --> 00:01:18,550
+ال range عشان أكون أدق في ال range جاي من pre
+
+16
+00:01:18,550 --> 00:01:24,330
+image واحدة فقط فهنا واضح إن هنا في element جاي من
+
+17
+00:01:24,330 --> 00:01:29,870
+اتنينهذه مش one-to-one طب one-to .. one-to .. إيش
+
+18
+00:01:29,870 --> 00:01:33,210
+كان تعريف ال one-to؟ ال domain .. ال co-domain و
+
+19
+00:01:33,210 --> 00:01:35,830
+ال range نفس ال cardinality .. نفس ال cardinality
+
+20
+00:01:35,830 --> 00:01:39,590
+فإذا الأولى هذه كانت one-to ولكن مش one-to-one طيب
+
+21
+00:01:39,590 --> 00:01:44,990
+التانية one-to-one لأ لأن في عندنا two elements
+
+22
+00:01:44,990 --> 00:01:50,550
+هيوم أخله بالشرط و ال co-domain في عنصر غير موجود
+
+23
+00:01:50,550 --> 00:01:54,690
+في ال range فإذا لا هيك ولا هيك كويس التالتة
+
+24
+00:01:56,690 --> 00:02:01,330
+التنتين one to one و onto الرابع one to one هذه
+
+25
+00:02:01,330 --> 00:02:05,230
+one to one مظبوط ولكن not onto لأن في عندك هاي
+
+26
+00:02:05,230 --> 00:02:10,510
+element فوق موجود هذا خارج الحساب طبعا طيب من
+
+27
+00:02:10,510 --> 00:02:12,650
+التنتين هذول اتكلمنا برضه المرة اللى فاتت على ال
+
+28
+00:02:12,650 --> 00:02:15,110
+bijection ال bijection او ال one to one
+
+29
+00:02:15,110 --> 00:02:17,730
+correspondence او ال bijection او ال reversible
+
+30
+00:02:17,730 --> 00:02:22,380
+invertible وقلناإن هذه بتحقق الشرطين إذا تحقق ال
+
+31
+00:02:22,380 --> 00:02:25,340
+two functions في function واحدة ال two conditions
+
+32
+00:02:25,340 --> 00:02:28,340
+في function واحدة بنقول عنها إيش؟ bijection فإيش
+
+33
+00:02:28,340 --> 00:02:31,740
+بتلزمنا؟ بتلزمنا إن إذا كانت ال function bijection
+
+34
+00:02:31,740 --> 00:02:34,700
+معناته بقدر أجيب لها ال inverse تبعها بنقدر نجيب
+
+35
+00:02:34,700 --> 00:02:37,960
+ال inverse function لها و ال inverse function
+
+36
+00:02:37,960 --> 00:02:41,580
+بتاعتها أكيد بتكون منكتوبة كتالة inverse function
+
+37
+00:02:41,580 --> 00:02:45,840
+أو f of minus to the power minus one from b to a
+
+38
+00:02:45,840 --> 00:02:51,320
+لإن هذه في اتجاه العكسي جاية من b to aبالاتجاه
+
+39
+00:02:51,320 --> 00:02:56,400
+العكسى لأنها ال inverse لاتل اف انفرس ال F فهتكون
+
+40
+00:02:56,400 --> 00:03:00,840
+جاية من ال codomain لل domain بتاعون ال F فأصبحت
+
+41
+00:03:00,840 --> 00:03:04,480
+ال B هي ال domain تبعها وال A هي ال codomain تبعها
+
+42
+00:03:04,480 --> 00:03:08,420
+هي ال codomain تبعها okay وهذا بتكون unique بمعنى
+
+43
+00:03:08,420 --> 00:03:13,400
+أن كل function إذا كانت bijection لها inverse واحد
+
+44
+00:03:13,400 --> 00:03:16,640
+فقط ماتتوقعوش أنه يكون لها أكتر من انفرس واحد فقط
+
+45
+00:03:16,640 --> 00:03:20,570
+كويس؟الاتنين هدولة في بعض اللي هي ال function في
+
+46
+00:03:20,570 --> 00:03:24,050
+ال inverse بحها بيعطونا ال identity وضرب قولنا
+
+47
+00:03:24,050 --> 00:03:27,870
+عليه المرة اللي فاتت هذا اللي هو ايش composition ف
+
+48
+00:03:27,870 --> 00:03:32,850
+F to the power minus one compose F equal to I to I
+
+49
+00:03:32,850 --> 00:03:37,010
+و ال I هذي اللي هي ايش ال identity value او ال
+
+50
+00:03:37,010 --> 00:03:39,530
+identity function identity function هاي ال
+
+51
+00:03:39,530 --> 00:03:44,070
+identity function بنعرفها لأي domain A عساس ان ال
+
+52
+00:03:44,070 --> 00:03:50,990
+identity function I from A to Afrom a to a ليش من
+
+53
+00:03:50,990 --> 00:03:55,450
+a ل a لأن فعليا ال input تبعها هو نفس ال output ال
+
+54
+00:03:55,450 --> 00:04:00,550
+input هو نفس ال output هي غير مؤثرة الأصل إذا كانت
+
+55
+00:04:00,550 --> 00:04:03,730
+ضرب مثلا ال function عملية ضرب المفروض نضرب في
+
+56
+00:04:03,730 --> 00:04:09,190
+واحد إذا كانت جمع بنجمع مع صفر إذا كانت مثلا and
+
+57
+00:04:09,190 --> 00:04:15,230
+بنعمل and مع trueمع true ف ال input اللي بندخله
+
+58
+00:04:15,230 --> 00:04:17,950
+إذا كان true حيضل true و إذا كان false حيضل false
+
+59
+00:04:17,950 --> 00:04:21,650
+فالقصد إن إحنا بنتعامل مع element أو مع function
+
+60
+00:04:21,650 --> 00:04:25,910
+ال input تبحه هو هو هيتلعب هو هو نحن فبنقول من a
+
+61
+00:04:25,910 --> 00:04:34,060
+thبنكتبها I A مع ال set A ل identity لل set A أو
+
+62
+00:04:34,060 --> 00:04:38,380
+بنكتبها واحد بهذا الشكل واحد كويس او واحد ايه one
+
+63
+00:04:38,380 --> 00:04:42,780
+ل ال set A وهذه زي ما قولنا unique function بحيث
+
+64
+00:04:42,780 --> 00:04:47,280
+انه for all elements داخل ال set لكل ال elements
+
+65
+00:04:47,280 --> 00:04:49,400
+داخل ال set A
+
+66
+00:04:51,360 --> 00:04:55,760
+of a بيساوي a فإذا هي function محايدة هي function
+
+67
+00:04:55,760 --> 00:05:00,620
+محايدة ال input هو هو زيه ال output هو هو نفس ال
+
+68
+00:05:00,620 --> 00:05:04,900
+output و احنا يعني اتعلمنا مجموعة functions بتقد
+
+69
+00:05:04,900 --> 00:05:08,600
+نفس الغرض هذا زي لما نقول ال positive او ال
+
+70
+00:05:08,600 --> 00:05:13,790
+plusing او ال adding ال adding مع ال zeroبأثرش ال
+
+71
+00:05:13,790 --> 00:05:18,010
+dotting مع ال one أو ال multiplication with one
+
+72
+00:05:18,010 --> 00:05:24,370
+بأثرش ال and مع ال true بأثرش ال or مع ال false
+
+73
+00:05:24,370 --> 00:05:30,030
+بأثرش ال union مع ال fiveunion مع فعل ماحد ضال نفس
+
+74
+00:05:30,030 --> 00:05:34,010
+الست طيب ال intersection مع ال universe of
+
+75
+00:05:34,010 --> 00:05:39,490
+discourse مع ال U تفرجش كويسة هنلاحظ أنه في جميع
+
+76
+00:05:39,490 --> 00:05:42,970
+الأحوال في جميع الظروف دايما ال identity هي
+
+77
+00:05:42,970 --> 00:05:48,930
+bijective او one to one و onto مع بعض function فهي
+
+78
+00:05:48,930 --> 00:05:53,030
+bijection function او bijective function okay
+
+79
+00:05:54,780 --> 00:05:58,960
+كيف نوضحها كيف نرسم الرسم تبعها اما عن طريق ال
+
+80
+00:05:58,960 --> 00:06:04,340
+Venn diagram بهذا الشكل فهي عندنا ال set A فيها
+
+81
+00:06:04,340 --> 00:06:07,400
+مجموعة ال elements بتاعتها ال elements داخل ال
+
+82
+00:06:07,400 --> 00:06:11,720
+domain كل element under the function هيعطينا نفس
+
+83
+00:06:11,720 --> 00:06:15,360
+ال element فالاتجاه لل function من ال element
+
+84
+00:06:15,360 --> 00:06:19,620
+لنفسه لأن زي ما قلنا identity هيطلع نفس القيمة لل
+
+85
+00:06:19,620 --> 00:06:26,460
+element فهنا ال A1تحت تأثير f هيعطي اي واحد اتنين
+
+86
+00:06:26,460 --> 00:06:33,060
+تحت تأثير f هيعطي اتنين وهكذا اي عنصر تحت تأثير f
+
+87
+00:06:33,060 --> 00:06:39,320
+of a هيعطينا نفس العنصر اللي هو a نفس العنصر بال
+
+88
+00:06:39,320 --> 00:06:46,170
+plot هتكون linearو ال slope تبع ال linear هذا واحد
+
+89
+00:06:46,170 --> 00:06:51,330
+هو عبارة عن line linear ال slope تبعه بواحد عشان
+
+90
+00:06:51,330 --> 00:06:56,650
+اضمن ان اي x هتطلع نفس قيمتها في ال y فإذا x خمسة
+
+91
+00:06:56,650 --> 00:07:01,030
+ال y هتطلع خمسة اللي هي ال f of x فهنا ال x وهذا
+
+92
+00:07:01,030 --> 00:07:07,670
+ال y اللي هي تساوي f of x فدائما f of x بتساوي x
+
+93
+00:07:07,670 --> 00:07:10,930
+دائما f of x بتساوي x
+
+94
+00:07:32,550 --> 00:07:36,050
+عشان نرسم ال graphs of functions احنا بدنا نوقعه
+
+95
+00:07:36,050 --> 00:07:38,530
+بمجموعة نقاط زي ال plot اللي توقعنا رسميا و كيف
+
+96
+00:07:38,530 --> 00:07:43,640
+بنعمله فعليابهذا الشكل إذا كان عندكم X و F of X
+
+97
+00:07:43,640 --> 00:07:50,580
+يلي هي Y انتوا عادة ايش بتسوواه بتحطوا نقاط عند ال
+
+98
+00:07:50,580 --> 00:07:57,620
+X عندكوا F of X معرفة بطريقة معينة بتفرضوا قيم ل X
+
+99
+00:07:57,620 --> 00:08:03,220
+صحيح قيمة مثلا واحد بتعودوا هنا بتطلعلكوا رقم
+
+100
+00:08:03,220 --> 00:08:07,740
+الرقم هذا بصير هو قيمة Y المقابلة للواحد فبتحطوها
+
+101
+00:08:07,740 --> 00:08:13,700
+نقطةقيمة تانية تحطوا كمان نقطة تالتة كمان نقطة
+
+102
+00:08:13,700 --> 00:08:17,880
+رابعة كمان نقطة خمسة كمان نقطة فبتواصلوا بينهم
+
+103
+00:08:17,880 --> 00:08:21,820
+عشان يطلع معاكمشكل ال function بتطلع معاكم في
+
+104
+00:08:21,820 --> 00:08:24,260
+الآخر شكل ال function بتقول اه والله هى ال
+
+105
+00:08:24,260 --> 00:08:26,680
+function هده linear ال function هده تربيعية ال
+
+106
+00:08:26,680 --> 00:08:28,740
+function هده تقعبية اه هد شبيهة بال sinusoidal هد
+
+107
+00:08:28,740 --> 00:08:31,840
+شبيهة بال .. تقدروا لو قولنا مثلا طلعوا نقاط
+
+108
+00:08:31,840 --> 00:08:34,000
+بالشكل هد هتقولوا اه والله هد linear واضح ان احنا
+
+109
+00:08:34,000 --> 00:08:38,840
+بنتكلم عن خط الخط هد بيضل عملية انه ممكن يكون ال
+
+110
+00:08:38,840 --> 00:08:41,660
+identity مثلا طب كيف افحص ان هي identity ولا لأ
+
+111
+00:08:41,660 --> 00:08:43,660
+بال slope بال slope تبحث اذا كان واحد هي ال
+
+112
+00:08:43,660 --> 00:08:47,650
+identity مش واحد لأ خلاص هد function مختلفةتمام؟
+
+113
+00:08:47,650 --> 00:08:52,390
+Identity ممكن تكون مضروبة بس ب factor معين كويس
+
+114
+00:08:52,390 --> 00:08:56,590
+معنى ذلك خلينا نرجع لمفهوم كيف رسمنا الرسم هذا
+
+115
+00:08:56,590 --> 00:09:02,030
+رسمناه من نقطة بداية الشغل كانت نقطة النقطة إيش
+
+116
+00:09:02,030 --> 00:09:10,990
+تمثل؟ تمثل X و F of X صحيح؟
+
+117
+00:09:10,990 --> 00:09:18,020
+هي Xو F of X بتاعتها فمثلناها بزوج مرتب عبارة عن
+
+118
+00:09:18,020 --> 00:09:24,340
+ال input وال F of X اللي هو ال output اللي هو ال
+
+119
+00:09:24,340 --> 00:09:30,660
+output طبعا okay فبنرتبها ك A و F of Aإذا كنا
+
+120
+00:09:30,660 --> 00:09:34,900
+معرفين الـ function على أساس أنها من A to B
+
+121
+00:09:34,900 --> 00:09:41,400
+فبنعرفها كزوج مرتب A و F of A و A belong to set A
+
+122
+00:09:41,400 --> 00:09:45,060
+ال domain فاحنا بنختار في الآخر قيم من ال domain
+
+123
+00:09:45,060 --> 00:09:48,060
+القيم بتاعتنا بنختارها من من؟ من ال domain مش حاجة
+
+124
+00:09:48,060 --> 00:09:52,600
+ال domain تبقى من 0 ل10 أختار 11 أو نختار minus
+
+125
+00:09:52,600 --> 00:09:56,810
+one نختار قيمنا من مين؟من ال domain و بتحدد
+
+126
+00:09:56,810 --> 00:10:01,790
+النقطتنا .. النقطتنا زي ما قولنا في الآخر a و f of
+
+127
+00:10:01,790 --> 00:10:06,550
+a قيمة ال function بتاعتها او x و y حسب ما انتوا
+
+128
+00:10:06,550 --> 00:10:10,250
+كنتوا دارسين ال .. ال .. ال independent variable x
+
+129
+00:10:10,250 --> 00:10:13,890
+و independent variable y فهي هتكون عبارة عن زوج من
+
+130
+00:10:13,890 --> 00:10:20,220
+x و yOkay لما نتكلم عن الأرقام بنمثلها بأرقام زي
+
+131
+00:10:20,220 --> 00:10:24,520
+ما قلنا انتوا بتستعملوا ال X و Y بتستعملوا عادة X
+
+132
+00:10:24,520 --> 00:10:28,560
+و Y زي الشكل اللي احنا رسمنا بهذا الشكل هي X و Y
+
+133
+00:10:28,560 --> 00:10:35,420
+ليش؟ لأن Y هي نفسها F of X فبنحددها كنقطة على ال
+
+134
+00:10:35,420 --> 00:10:38,660
+plane تبعنا عشان نحط نقطة و بعدين نجرب نقطة تانية
+
+135
+00:10:38,660 --> 00:10:42,390
+ل X نقطة تالتة نقطة رابعة نقطة خمسة و نوصلبنوصلهم
+
+136
+00:10:42,390 --> 00:10:46,430
+بعض .. بنوصلهم بعض في الآخر مجموعة النقاط هدولة
+
+137
+00:10:46,430 --> 00:10:51,130
+ايش صاروا؟ صاروا set of points صار لانكوا مجموعة
+
+138
+00:10:51,130 --> 00:10:54,730
+نقاط مجموعة النقاط هدى صارت set of points فهدولة
+
+139
+00:10:54,730 --> 00:10:58,390
+اللى بيعطونا relation between y و x بيعطونا
+
+140
+00:10:58,390 --> 00:11:03,590
+relation between y و x على أساس ان هم set of
+
+141
+00:11:03,590 --> 00:11:05,550
+points okay
+
+142
+00:11:07,200 --> 00:11:11,000
+من اللى فهمناها لوجود فى عملية الرسم و ال function
+
+143
+00:11:11,000 --> 00:11:15,500
+نفسها نتكلم عن موضوع ال couple of key functions
+
+144
+00:11:15,500 --> 00:11:22,040
+هنا بنعمل عملية تقريب لأقرب integers لأقرب integer
+
+145
+00:11:22,040 --> 00:11:26,740
+number طيب أقرب integer الأعلى ولا الأقل فهنا إما
+
+146
+00:11:26,740 --> 00:11:35,130
+بنعمل floorأو ceiling of X ال floor نرسمها بهذا
+
+147
+00:11:35,130 --> 00:11:39,570
+الشكل في عندنا floor واضحة الأرضية واضحة شمال
+
+148
+00:11:39,570 --> 00:11:44,740
+ويمين لل X ال ceiling لأ الأرضية واضحة للصقففعنا
+
+149
+00:11:44,740 --> 00:11:47,900
+هنا الأرضية و هنا فينا الصقف فانا النقطة اللى
+
+150
+00:11:47,900 --> 00:11:51,180
+موجودة داخل الغرفة المعلجة داخل الغرفة بتقربها لل
+
+151
+00:11:51,180 --> 00:11:54,400
+floor ولا بتجربها للسجف بدنا نسحب الخيط طبعا
+
+152
+00:11:54,400 --> 00:11:56,580
+هنوصلها للسجف ولا بدنا نقطع الخيط و ننزلها لل
+
+153
+00:11:56,580 --> 00:12:00,560
+floor هاي المعنى فانا لما بقول floor معناته لأ
+
+154
+00:12:00,560 --> 00:12:05,600
+جربتيها لإيش لل floor تمامأحنا هلوجد في الدور
+
+155
+00:12:05,600 --> 00:12:09,600
+الخامس صحيح دور الخامس المفروض أنه معناته احنا ال
+
+156
+00:12:09,600 --> 00:12:13,600
+level تبع الأرضية هذا اللي هو رقم أربعة رقم أربعة
+
+157
+00:12:13,600 --> 00:12:17,900
+رقم أربعة صحيح احنا بنبدأ تحت بواحد فهذا رقم أربعة
+
+158
+00:12:17,900 --> 00:12:21,200
+لما بداش أقرب أعمل floor هقول أن النقطة هذي
+
+159
+00:12:21,200 --> 00:12:24,810
+قربناها لاربعةبالنسبة للأرض اللى برا بالنسبة
+
+160
+00:12:24,810 --> 00:12:27,230
+للشباك اللى طلعنا هنقول ان احنا قربنا النقطة لمين؟
+
+161
+00:12:27,230 --> 00:12:31,330
+لأربعة طب لما عمل ceiling خربناها للمستوى خمسة
+
+162
+00:12:31,330 --> 00:12:35,150
+بنقربها هنا للمستوى خمسة معنى ذلك ان النقطة كانت
+
+163
+00:12:35,150 --> 00:12:40,370
+between أربعة وخمسة كانت real number من أربعة
+
+164
+00:12:40,370 --> 00:12:44,550
+لخمسة فاحنا قربناها ل integer بس احنا حددنا ال
+
+165
+00:12:44,550 --> 00:12:49,760
+integer هذا هو floorأو ceiling هل هو ال floor او
+
+166
+00:12:49,760 --> 00:12:52,360
+ال ceiling طيب لما نتكلم عن ال floor هو فعليا ال
+
+167
+00:12:52,360 --> 00:12:58,000
+floor بقل القيمتها يعني بس هي عبارة عن ايش هي ال
+
+168
+00:12:58,000 --> 00:13:05,580
+greatest او ال largest integer اقل من X اكبر
+
+169
+00:13:05,580 --> 00:13:11,420
+integer اقل من X لما نقول تلاتة و نص ماقدرش اقربها
+
+170
+00:13:11,420 --> 00:13:15,400
+لاثنين تلاتة بالظبط تلاتة ايش اللي بميز التلاتة ان
+
+171
+00:13:15,400 --> 00:13:20,240
+هي اكبر integerلحظة هى اكبر انتجر من كل ال
+
+172
+00:13:20,240 --> 00:13:27,660
+integers اللى هنا اقل من ال X اكبر انتجر موجود اقل
+
+173
+00:13:27,660 --> 00:13:31,000
+من مين من X هى التعريف طيب نفس الكلام فى ceiling
+
+174
+00:13:31,000 --> 00:13:37,470
+هى smallest انتجر لو نجربها الاربعةطب ليش مجرد
+
+175
+00:13:37,470 --> 00:13:41,810
+التاسعة للخمسة للسبعة للتسعة كل هدول integers أقل
+
+176
+00:13:41,810 --> 00:13:45,650
+integer فعشان هي كلمة أقل ماتلحبطكمش احنا جاعدين
+
+177
+00:13:45,650 --> 00:13:48,450
+بنكبر القيمة بس مش معناه ان احنا في تعريف smallest
+
+178
+00:13:48,450 --> 00:13:54,370
+يعني بنجلل للا هي أقل integer أكبر من ال X فأقل
+
+179
+00:13:54,370 --> 00:13:57,990
+integer أكبر من اللي هو ال X الأربعة فتقرر ال
+
+180
+00:13:57,990 --> 00:14:03,590
+seeing تبعتها لمين لأربعة okay visualization
+
+181
+00:14:04,930 --> 00:14:12,890
+للكلام اللي قلناه example لمجموعة fractions نعمل
+
+182
+00:14:12,890 --> 00:14:17,230
+لها floor و ceiling هكون فينا مثلا ال one point
+
+183
+00:14:17,230 --> 00:14:21,830
+six هذا بدنا نعملها ceiling هتروح لمين للاتنين
+
+184
+00:14:21,830 --> 00:14:26,170
+بدنا نعملها floor للواحد طيب هنعكس ناخد قيمة
+
+185
+00:14:26,170 --> 00:14:31,550
+negative خدوا بالكوالما أعمل لهذه الواجهة ceiling
+
+186
+00:14:31,550 --> 00:14:36,690
+سالف واحد .. سالف واحد .. سالف واحد .. سالف واحد
+
+187
+00:14:36,690 --> 00:14:41,810
+.. سالف واحد .. سالف واحد .. سالف واحد .. سالف
+
+188
+00:14:41,810 --> 00:14:43,450
+واحد .. سالف واحد .. سالف واحد .. سالف واحد ..
+
+189
+00:14:43,450 --> 00:14:43,570
+سالف واحد .. سالف واحد .. سالف واحد .. سالف واحد
+
+190
+00:14:43,570 --> 00:14:44,010
+.. سالف واحد .. سالف واحد .. سالف واحد .. سالف
+
+191
+00:14:44,010 --> 00:14:45,770
+واحد .. سالف واحد .. سالف واحد .. سالف واحد ..
+
+192
+00:14:45,770 --> 00:14:57,030
+سالف واحد .. سالف واحد ..
+
+193
+00:14:57,030 --> 00:15:01,130
+سبدنا نشغل على 1.6 ما هي نفسها هتطلع يعني القيم
+
+194
+00:15:01,130 --> 00:15:06,590
+هتظل نفسها لو قلنا غيرناها 1.6 1.6 1.6 تمام فهنا
+
+195
+00:15:06,590 --> 00:15:10,630
+كأن أنا عملت ceiling ولا floor هنا اي واحدة منهم
+
+196
+00:15:10,630 --> 00:15:14,970
+نشغل على ال ceiling و بنعمى بالكلام هي minus x
+
+197
+00:15:14,970 --> 00:15:19,630
+صحيح؟ معناه ان ال x بتاعتنا معرفة على اساس ان هي 1
+
+198
+00:15:19,630 --> 00:15:28,020
+.6 لو x 1.6هذه ايش طلعت بتساوي؟ سالب واحد طيب نفس
+
+199
+00:15:28,020 --> 00:15:35,580
+الكلام لو قلنا هي نفسها ceiling minus ceiling x
+
+200
+00:15:35,580 --> 00:15:41,400
+طلعت سالب اتنين سالب اتنين طب سالب واحد لا تساوي
+
+201
+00:15:41,400 --> 00:15:45,420
+سالب اتنين الكلام نفسه برضه بتقدر تطبقه على ال
+
+202
+00:15:45,420 --> 00:15:48,950
+ceiling على ال floorأحنا طبقناه هنا على ال ceiling
+
+203
+00:15:48,950 --> 00:15:53,610
+بتقدر تطبقه برضه على ال floor فواضح أنه ال minus
+
+204
+00:15:53,610 --> 00:15:58,390
+بقدرش أتعامل معاها على أساس أنه بدخلها داخل القوس
+
+205
+00:15:58,390 --> 00:16:02,330
+و خلاص هذه مش أقوس هذه عملنا احنا فيها تقريب و لما
+
+206
+00:16:02,330 --> 00:16:05,670
+أعكس .. لما أعكس الإشارة معناته أنا جلبت التقريب
+
+207
+00:16:05,670 --> 00:16:08,510
+كله المفروض بدل ما أعمل ceiling كان المفروض يعملنا
+
+208
+00:16:08,510 --> 00:16:12,890
+floor من الأساس فواضح أنه هذه لا يسووا بعض في
+
+209
+00:16:12,890 --> 00:16:18,420
+الحلقة طيب ملاحظة تانيةceiling x إذا طلعت بتساوي
+
+210
+00:16:18,420 --> 00:16:23,200
+floor x معناته انت فعليا عند integer معناته x ده
+
+211
+00:16:23,200 --> 00:16:26,040
+هو أساسا بحد ذاته integer ال ceiling تبعه بساوي ال
+
+212
+00:16:26,040 --> 00:16:33,500
+floor تبعه بمشي الحال بمشي الحال كويس ال plot أو
+
+213
+00:16:33,500 --> 00:16:38,260
+بدنا نبدأ نرسم نعمل plots ل ال floor و ال ceiling
+
+214
+00:16:38,260 --> 00:16:45,080
+كيف نرسمهم floor و ceiling بدنا ناخد بالناالنقاط
+
+215
+00:16:45,080 --> 00:16:49,820
+نفس احنا كيف عرفناها توي كيف عرفنا النقطة عرفنا ال
+
+216
+00:16:49,820 --> 00:16:54,800
+point بتاعتنا على اساس ان هي لحظه x و f of x هذي f
+
+217
+00:16:54,800 --> 00:17:05,520
+of x ال zero هذي x و f of x x و f of x اللي هي ال
+
+218
+00:17:05,520 --> 00:17:09,240
+y بالضبط ال y طيب ال function بتاعتنا اللي بتطلعنا
+
+219
+00:17:09,240 --> 00:17:14,510
+ال y او ال f of x هي عبارة عن floorما دام حددناها
+
+220
+00:17:14,510 --> 00:17:20,790
+zero ال output zero هذا يتفق مع مجموعة a's انما
+
+221
+00:17:20,790 --> 00:17:23,650
+a's هدولة اللي بيتفق معاهم ان ده output zero اللي
+
+222
+00:17:23,650 --> 00:17:28,590
+من zero لأقل من واحد تمام لأقل شوية من واحد جدش
+
+223
+00:17:28,590 --> 00:17:33,510
+أقل من واحدأقل بكتير بكتير يعني احنا عشان هيك مش
+
+224
+00:17:33,510 --> 00:17:36,570
+عارفين بالظبط جدش القيمة هي delta delta أكبر من
+
+225
+00:17:36,570 --> 00:17:41,390
+صفر بس قليلة جدا جدا جدا طيب عشان نحددها جدش بده
+
+226
+00:17:41,390 --> 00:17:46,950
+أحددها أنا مش عارف أحددها نكتبها للواحد ولكن
+
+227
+00:17:46,950 --> 00:17:54,910
+الواحد غير مشمولمفتوحة فبنعملها هذه circle بس open
+
+228
+00:17:54,910 --> 00:17:58,470
+circle فبنكتبها open circle للواحد و للواحد غير
+
+229
+00:17:58,470 --> 00:18:03,450
+مشمول لو عملناها solid circle بتصير لأ مشمولة فها
+
+230
+00:18:03,450 --> 00:18:06,770
+بدنا يعني كل الموضوع هذا بدنا نأكد على حكاية اللي
+
+231
+00:18:06,770 --> 00:18:12,230
+هي ال open و ال solid كويسة فمعنى ذلك ال function
+
+232
+00:18:12,230 --> 00:18:16,650
+هذه او ال points هذه صحيحة لكل الفترة اللي من a
+
+233
+00:18:16,650 --> 00:18:23,110
+أكبر من أو تساويصفر و a أقل منه و لا تساوي
+
+234
+00:18:23,110 --> 00:18:28,830
+ماحطيناش يساوي و لا تساوي واحد و الواحد لأ but not
+
+235
+00:18:28,830 --> 00:18:35,090
+for a ايه ايه equal to ليش لأن a بتساوي واحد صارت
+
+236
+00:18:35,090 --> 00:18:38,710
+مشمولة مع نقطة تانية مع function تانية ال output
+
+237
+00:18:38,710 --> 00:18:45,390
+تبح بواحدال output تبعها واحد ف a وال output واحد
+
+238
+00:18:45,390 --> 00:18:49,730
+بتشمل معها a بتساوي واحد بتشمل معها a بتساوي واحد
+
+239
+00:18:49,730 --> 00:18:54,830
+فحناخد بالنا ان هنا بتصير ال واحد هذه open set هنا
+
+240
+00:18:54,830 --> 00:18:57,290
+بنتكلم عن open sets open sets اللي هي معناته عند
+
+241
+00:18:57,290 --> 00:19:00,310
+نقطة معينة غير مشمولة النقطة بس انا لازم اعرفها
+
+242
+00:19:00,310 --> 00:19:03,510
+بالنقطة لان انا مش عارف جدش اقل من النقطة اقل من
+
+243
+00:19:03,510 --> 00:19:08,620
+النقطة بقيمة كتير صغيرة يعني لو واحد منكم كتب0
+
+244
+00:19:08,620 --> 00:19:14,900
+.99999 المفروض دلته infinity طبعا مش منطقي ان احنا
+
+245
+00:19:14,900 --> 00:19:17,940
+نعملها infinity فلأ بنقول واحد بس بدنا نحدد ان
+
+246
+00:19:17,940 --> 00:19:22,040
+الواحد نفسه كقيمة واحد غير مشمول كقيمة غير مشمول
+
+247
+00:19:22,040 --> 00:19:27,780
+فهذه بنشملها او بنعملها circle او open circle
+
+248
+00:19:27,780 --> 00:19:34,210
+نكتبها شكلها زي dot او circle بس بتكونو ال solid
+
+249
+00:19:34,210 --> 00:19:37,490
+زي ما قلنا إذا كانت مشمولة في ال curve خلّيني
+
+250
+00:19:37,490 --> 00:19:43,170
+أنطبخ الكلام ده على example عشان الأمور توضح أكتر
+
+251
+00:19:43,170 --> 00:19:49,790
+معناه لو مقلوب نعمل plot of graph of function f of
+
+252
+00:19:49,790 --> 00:19:56,390
+x equal to floor x over 3 x over 3 وهنا بيعطيكوا
+
+253
+00:19:56,390 --> 00:20:02,800
+ال x على أساس إن هي ال integer numbersinteger
+
+254
+00:20:02,800 --> 00:20:05,840
+numbers مثلا أو حتى fractions مش مشكلة يعني ممكن
+
+255
+00:20:05,840 --> 00:20:10,000
+تقولوا R أساسا من minus infinity to infinity نبدأ
+
+256
+00:20:10,000 --> 00:20:13,640
+مثلا ناخد الصفر خلينا نبدأ من الصفر عشان نوضح لكم
+
+257
+00:20:13,640 --> 00:20:21,420
+لو أخدنا الصفر نفسها صفر على تلاتة صفر floor zero
+
+258
+00:20:21,420 --> 00:20:24,440
+خلاص النقطة هي مكانها و solid لأنها مشمولة في
+
+259
+00:20:24,440 --> 00:20:27,740
+المجموعة هذه مشمولة في المجموعة هذه بنحطها صفر هنا
+
+260
+00:20:27,740 --> 00:20:36,740
+كويس الواحدتلت واحد تصير تلت floor تلت زيرو برضه
+
+261
+00:20:36,740 --> 00:20:44,380
+فإذا هنا نفس الكلام هتصير عندك واحد وزيرو طيب هنا
+
+262
+00:20:44,380 --> 00:20:52,060
+اتنين وزيرو ال input اتنين ال output زيرو طيب هنا
+
+263
+00:20:52,060 --> 00:20:59,500
+عند التلاتة واحد floor الواحدواحد بحطه هنا open و
+
+264
+00:20:59,500 --> 00:21:04,100
+فوق هنا بحط عند الواحد solid نفسها عندها نفسها هاي
+
+265
+00:21:04,100 --> 00:21:08,020
+تمام
+
+266
+00:21:08,020 --> 00:21:12,720
+هاي بهذا الشكل طيب هيك صارنا متفقين حتى على أساس
+
+267
+00:21:12,720 --> 00:21:17,060
+أن هذه function لأنه مش معقول نفس ال input يكون له
+
+268
+00:21:17,060 --> 00:21:21,170
+قيمتين أو two outputs صحيح؟أحنا متفقين على كلام
+
+269
+00:21:21,170 --> 00:21:24,030
+هذا بنقول إن هي مش function من أصله ولكن هنا لأ
+
+270
+00:21:24,030 --> 00:21:27,570
+احنا متفقين على الموضوع هذا من عند الواحد بالضبط
+
+271
+00:21:27,570 --> 00:21:33,290
+صرنا مع ال output one كويس عند التلاتة عند الستة
+
+272
+00:21:33,290 --> 00:21:38,990
+عفوا عند الستة بتصير هنا اتنين الستة غير مشمولة في
+
+273
+00:21:38,990 --> 00:21:43,630
+في ال line هذا غير مشمولة بس أقل من الستة بأقل
+
+274
+00:21:43,630 --> 00:21:49,620
+قيمة ممكنة صارت مشمولة مع الواحدالستة تحديدًا لأ
+
+275
+00:21:49,620 --> 00:21:52,820
+صارت مشمولة مع الإتنين، ستة تحديدًا مشمولة مع
+
+276
+00:21:52,820 --> 00:21:56,780
+الإتنين، فهنا solid، هنا open، الكلام برضه مرة
+
+277
+00:21:56,780 --> 00:22:05,350
+عليكم أتوقع في المجموعات في ال open setsOkay فضليه
+
+278
+00:22:32,330 --> 00:22:36,470
+ال function نفسها حسب ال function نفسها إذا كانت
+
+279
+00:22:36,470 --> 00:22:41,790
+ceiling بده ينعكسه ال solid و ال open هنا هدول
+
+280
+00:22:41,790 --> 00:22:45,970
+اتنين تبدو مياشي يتغيروا معناها okay هاي كانت
+
+281
+00:22:45,970 --> 00:22:50,130
+الجزئية اللي كانت ضيلالنا من جزء ال function عشان
+
+282
+00:22:50,130 --> 00:22:59,960
+نبدأ في موضوعنا الرسمية اليوماللي هو استكمالا كان
+
+283
+00:22:59,960 --> 00:23:02,940
+الموضوع ال sets احنا اتكلمنا في ال sets سابقا
+
+284
+00:23:02,940 --> 00:23:08,320
+اتكلمنا عن ال set و اعرجنا شوية و احنا بنحكي عن ال
+
+285
+00:23:08,320 --> 00:23:12,120
+set على ال sequence و قولنا ان ال sequence ايش
+
+286
+00:23:12,120 --> 00:23:16,740
+اللي بميزه عن ال set ترتيب ترتيب بالضبط فال
+
+287
+00:23:16,740 --> 00:23:20,180
+sequence احنا ملزمين بالترتيب sequence احنا ملزمين
+
+288
+00:23:20,180 --> 00:23:23,680
+بترتيب ال elements بتاعتنا ملزمين بترتيب ال
+
+289
+00:23:23,680 --> 00:23:27,740
+elements بتاعتنا على اساسفي ال set أنا مافرجش
+
+290
+00:23:27,740 --> 00:23:30,900
+معايا ال elements كيف ترتيبها كل اللي بهم انه
+
+291
+00:23:30,900 --> 00:23:35,880
+مايكونش فيه تكرار لل elements صحيح فكل التكرارات
+
+292
+00:23:35,880 --> 00:23:39,260
+تنشل من ال element في ال .. في ال sets و بنعود
+
+293
+00:23:39,260 --> 00:23:44,620
+عنها او بنكتبها داخل ال .. ال curly بتاعتها ال
+
+294
+00:23:44,620 --> 00:23:49,680
+curly ال braces بتاعتها قيم unique values كل قيمة
+
+295
+00:23:49,680 --> 00:23:53,140
+لحالها بنكتبها مافيش تكرار لها في ال sequence لأ
+
+296
+00:23:53,140 --> 00:23:58,090
+في ال sequence انا مهتم جدا بال ..الترتيب وما ده
+
+297
+00:23:58,090 --> 00:24:02,930
+مهتم بالترتيب مش هيفرج معايا التكرار بمعنى انه
+
+298
+00:24:02,930 --> 00:24:05,930
+التكرار بنسيبه زي ما هو تكرار ليش؟ لأنه مرتبط
+
+299
+00:24:05,930 --> 00:24:10,190
+بالترتيب وما ده مرتبط بالترتيب بقدر برضه ال
+
+300
+00:24:10,190 --> 00:24:13,290
+sequence ده يتعامل معاها as a function احنا لسه
+
+301
+00:24:13,290 --> 00:24:16,390
+بنحكي في ال function كلنا as a function معنى ذلك
+
+302
+00:24:16,390 --> 00:24:24,230
+انه هتكون function في n الشي n هدى ال location هدى
+
+303
+00:24:24,230 --> 00:24:27,470
+ايش ال locationالمكان اللي أنا موجود فيه داخل ال
+
+304
+00:24:27,470 --> 00:24:31,230
+sequence في ال element الأول ولا التاني ولا التالت
+
+305
+00:24:31,230 --> 00:24:36,230
+ولا الرابع ولا الخامس هذا بتساوي A M ال element
+
+306
+00:24:36,230 --> 00:24:40,790
+اللي موجود في ال location M جدش قيمته فممكن نعبر
+
+307
+00:24:40,790 --> 00:24:45,650
+عنها بهذا الشكل نقول ان هي function ايش قيم ال
+
+308
+00:24:45,650 --> 00:24:51,370
+elements داخلها كل element هو ناتج function في ال
+
+309
+00:24:51,370 --> 00:24:54,400
+location تبع ال elementفي ال location تبع ال
+
+310
+00:24:54,400 --> 00:24:57,260
+elements مدام احنا من الأساس حددنا ان هي ordered
+
+311
+00:24:57,260 --> 00:25:01,880
+okay sequence مجموعة أرقام مرتبة و discrete
+
+312
+00:25:01,880 --> 00:25:07,300
+discrete بمعنى انه ال location الأول التاني مافيش
+
+313
+00:25:07,300 --> 00:25:09,840
+ال location اتنين و نص هو يا ال location الأول يا
+
+314
+00:25:09,840 --> 00:25:12,540
+التاني مافيش ال location واحد و نص فاحنا بنتكلم عن
+
+315
+00:25:12,540 --> 00:25:19,220
+elements هي discrete objects ممكن تتعامل مع ..
+
+316
+00:25:19,220 --> 00:25:23,600
+ماتكونش أرقام ماتكون objects أحيانا كويسةفمجموعة
+
+317
+00:25:23,600 --> 00:25:27,980
+elements اللي بيحددها أو اللي بنقدر نعرف فيه ال
+
+318
+00:25:27,980 --> 00:25:31,580
+element هذا ال location تبعها حسب ال location
+
+319
+00:25:31,580 --> 00:25:34,320
+فبنقول والله ال sequence الفلانية ال element
+
+320
+00:25:34,320 --> 00:25:37,280
+التالت تبعها قيمته كذا هذا دائما هنكون قيمته كذا
+
+321
+00:25:37,280 --> 00:25:41,860
+دائما مدام أنا عرفت ال sequence الفلانية معناته
+
+322
+00:25:41,860 --> 00:25:44,400
+فيها تعريف ال sequence هذه ممكن نقول ال sequence
+
+323
+00:25:44,400 --> 00:25:48,000
+هذه اللي هي الأرقام الزوجية مثلا لأكبر من صفر
+
+324
+00:25:49,490 --> 00:25:52,270
+الأرقام الزوجية اللي أكبر من صفر دائما أول element
+
+325
+00:25:52,270 --> 00:25:57,010
+فيها إيش؟ إتنين هل ممكن تقولوا لأي واحد الأرقام
+
+326
+00:25:57,010 --> 00:26:00,210
+الزوجية اللي أكبر من صفر يجي يقولكوا الأربعة؟ لا
+
+327
+00:26:00,210 --> 00:26:05,130
+يمكن فإنتوا هنا بتتكلموا عن sequence دائما الترتيب
+
+328
+00:26:05,130 --> 00:26:08,950
+تبعها ثابت بس بدكوا تعرفوه مسبقا، تعرفوه طريقة
+
+329
+00:26:08,950 --> 00:26:13,080
+صحيحة مسبقافبنتكلم عن sequence of discrete
+
+330
+00:26:13,080 --> 00:26:18,980
+structure used to represent an ordered list احنا
+
+331
+00:26:18,980 --> 00:26:22,500
+بنستعمله عشان نعرف أو نعمل تمثيل لإيش ل sequence
+
+332
+00:26:22,500 --> 00:26:27,920
+مرتب ل sequence أو قائمة مرتبة for example one two
+
+333
+00:26:27,920 --> 00:26:33,560
+three five eight هدى sequence بتقدر تعرف الرقم
+
+334
+00:26:33,560 --> 00:26:39,220
+اللى بعده؟كويس هذه هتكون .. هتكون شغلنا شطرتنا
+
+335
+00:26:39,220 --> 00:26:41,680
+bagel course .. في bagel course طبعا اليوم احنا بس
+
+336
+00:26:41,680 --> 00:26:44,780
+.. شغلنا هنتعرف بس انه ايش ال sequence يعني ما
+
+337
+00:26:44,780 --> 00:26:48,500
+معنى ال sequence في ال chapters اللي جاية هنقول
+
+338
+00:26:48,500 --> 00:26:51,080
+انه لأ عندنا sequence معين او series معينة ..
+
+339
+00:26:51,080 --> 00:26:54,340
+series معينة بدنا نعرف ال elements اللي جاية عشان
+
+340
+00:26:54,340 --> 00:26:56,300
+تعرفوا ال elements .. هذا طبعا في .. في معظم
+
+341
+00:26:56,300 --> 00:26:58,000
+امتحانات الذكاء العقلي و الامور اللي زي ذات
+
+342
+00:26:58,000 --> 00:27:01,560
+بتلاقوا حاجة زي هي أسئلة بهذا الشكل .. كويس هذه
+
+343
+00:27:01,560 --> 00:27:04,830
+عشان نجيبها هنتكلم عنها بس لاحقافيها chapter ..
+
+344
+00:27:04,830 --> 00:27:08,790
+chapter جاي، هنتكلم فيه ونقولكوا كيف نجيب الأرقام
+
+345
+00:27:08,790 --> 00:27:10,670
+اللي بعدها طب عشان أجيب الأرقام اللي بعدها أنا
+
+346
+00:27:10,670 --> 00:27:16,610
+محتاج formula إلها، محتاج المعادلة تعتها تلتاش،
+
+347
+00:27:16,610 --> 00:27:19,970
+هاي ناس .. البنات عرفوها هاي .. هاي البنات عرفوها
+
+348
+00:27:19,970 --> 00:27:24,490
+تلتاش، اتنين و تلاتة، خمسة، خمسة و تلتة، تمانية،
+
+349
+00:27:24,490 --> 00:27:27,490
+تمانية و تمانية و خمسة، تلتاش، تلتاش و تمانية و
+
+350
+00:27:27,490 --> 00:27:32,540
+واحد و عشرينهذه fabinacci series بيسموها عالم
+
+351
+00:27:32,540 --> 00:27:35,520
+إيطالي هنتكلم عنه لاحقا فهذه مشهورة جدا من ال
+
+352
+00:27:35,520 --> 00:27:39,440
+sequence المشهورة جدا فهي واحدة من ال series او ال
+
+353
+00:27:39,440 --> 00:27:42,360
+sequence اللي انتوا ممكن تتعاملوا معها و بتجيكوا
+
+354
+00:27:42,360 --> 00:27:45,740
+هي في أسئلة ال IQ اللي هي الذكاء العقلي و الأمور
+
+355
+00:27:45,740 --> 00:27:48,000
+هذه اللي بتشوفوها على ال net و بتحضروها يمكن
+
+356
+00:27:48,000 --> 00:27:51,360
+تشاركتوا فيها كمان عشان تقول والله اه وين انا
+
+357
+00:27:51,360 --> 00:27:56,080
+موجود في سلم الأذكياءتمام هى فى أنكوا مثلا term
+
+358
+00:27:56,080 --> 00:27:59,000
+تانى أو ممكن نقوله بهذا الشكل ال sequence نعرفه 1
+
+359
+00:27:59,000 --> 00:28:05,820
+3 9 27 81 و لحظه نعرف تلاتة ضبار n و بعدين
+
+360
+00:28:05,820 --> 00:28:12,660
+ellipses infinite sequence لا نهائية خلاص هذه
+
+361
+00:28:12,660 --> 00:28:17,320
+مستمرة فمجرد عملت تلت نقاط أنا عارف ان هي مستمرة
+
+362
+00:28:17,320 --> 00:28:21,520
+عارفين ان هي مستمرة طيب هى دى هو يعطينى هى
+
+363
+00:28:21,520 --> 00:28:24,800
+المعادلة التي عتهابس أحيانا ممكن ماعطيناش إياها
+
+364
+00:28:24,800 --> 00:28:27,200
+ويقولنا اعطوني المعادلة او قولولي إيش الرقم اللي
+
+365
+00:28:27,200 --> 00:28:31,360
+ورا فهذه انتوا بتصوروا لاحقا هناخدها مش اليوم
+
+366
+00:28:31,360 --> 00:28:34,800
+لاحقا هناخدنا كيف اطلع المعادلة هذه لأنوا لو
+
+367
+00:28:34,800 --> 00:28:43,120
+عوضتوا بصفرعوضنا بواحد، بتنين، تلاتة، أربعة، تقدر
+
+368
+00:28:43,120 --> 00:28:44,860
+تجيبوا الخمسة تقدر تجيبوا ال element اللي وراك
+
+369
+00:28:44,860 --> 00:28:48,180
+تقدر تجيبوا ال element اللي وراك طيب احنا من هنا
+
+370
+00:28:48,180 --> 00:28:52,500
+طلعنا بحاجة ان ال location تبعنا ال location
+
+371
+00:28:52,500 --> 00:28:58,060
+بناخده من ال natural number ليش؟ لأن هنا ال
+
+372
+00:28:58,060 --> 00:29:03,590
+location هيبدا بصفرفإحنا فعلا في بعض ال sequences
+
+373
+00:29:03,590 --> 00:29:07,250
+بتبدأ بال natural number وفي بعضها natural number
+
+374
+00:29:07,250 --> 00:29:12,080
+minus zero ببدأ بواحدفهذا يجب أن يكون معرفن، إما
+
+375
+00:29:12,080 --> 00:29:15,700
+natural number فببدأ مباشرة إذا عند المعادلة ببدأ
+
+376
+00:29:15,700 --> 00:29:20,600
+أعوض من ال zero أو لأ natural number minus one أو
+
+377
+00:29:20,600 --> 00:29:26,180
+أكبر أو يساوي واحد فبعرف نبدأ من الواحد، نعرف نبدأ
+
+378
+00:29:26,180 --> 00:29:28,260
+من الواحد، مانبقاش أشي تاني، دائما يا صفر يا
+
+379
+00:29:28,260 --> 00:29:32,060
+الواحد عادة اللي بنبدأ فيهم ال sequence تبعناOkay
+
+380
+00:29:32,060 --> 00:29:37,460
+okay مدام عرفنا ان انا بتعامل مع set هي عبارة عن
+
+381
+00:29:37,460 --> 00:29:42,080
+function و ال set هذه لازم اتعامل معاها كمرتبة ك
+
+382
+00:29:42,080 --> 00:29:44,560
+sequence مرتب فانا بقدر اقول ان هذه عبارة عن
+
+383
+00:29:44,560 --> 00:29:49,760
+function ال domain تبعها هو ال locations ال
+
+384
+00:29:49,760 --> 00:29:52,100
+locations ال location الأول التاني التالت الرابع
+
+385
+00:29:52,100 --> 00:29:56,930
+الخامس العشر كويسةالـ function معينة الـ function
+
+386
+00:29:56,930 --> 00:30:00,270
+اللي هتعرفلنا ال sequence بقدر أجيب ال elements
+
+387
+00:30:00,270 --> 00:30:03,930
+تحت ال sequence كل واحد في ال location تبعه لأن كل
+
+388
+00:30:03,930 --> 00:30:08,170
+واحد لازم يكون function في ال location تبعه فهذه
+
+389
+00:30:08,170 --> 00:30:13,990
+بتكون مرتبة و لازم تكون مرتبة لازم تكون مرتبة عادة
+
+390
+00:30:13,990 --> 00:30:18,590
+زي ما قلنا ال sets اللي احنا بتاعة ال locations
+
+391
+00:30:18,590 --> 00:30:21,870
+ممكن تكون بدية من الصفرممكن تبدأ صفر واحد اتنين
+
+392
+00:30:21,870 --> 00:30:24,430
+تلاتة اربعة او تبدأ من الواحد اتنين تلاتة اربعة
+
+393
+00:30:24,430 --> 00:30:27,790
+فاما ال natural number فهي الأولى صفر واحد اتنين
+
+394
+00:30:27,790 --> 00:30:31,550
+تلاتة او natural number minus zero فببدأ من الواحد
+
+395
+00:30:31,550 --> 00:30:34,750
+كويس عشان نجيب ال elements ال elements اللى هى ال
+
+396
+00:30:34,750 --> 00:30:40,130
+a,n ال a,n و ال index تبعها ال n معناه ذلك ان ال a
+
+397
+00:30:40,130 --> 00:30:45,720
+,n هذه لازم تظهر في ال location Mهذا ال element
+
+398
+00:30:45,720 --> 00:30:49,100
+اللي لازم يظهر في ال location N في بعض الكتب
+
+399
+00:30:49,100 --> 00:30:57,400
+هتلاقوها I بدل N فبتجنك تبقى أحيانا AI ماتلحبطوش
+
+400
+00:30:57,400 --> 00:31:00,920
+في الكتاب عندنا كله N في الغالب إذا دورتوا في كتب
+
+401
+00:31:00,920 --> 00:31:04,680
+تانية يمكن تلاقوا I بس احنا كل شغل نحن هنشتغل عليه
+
+402
+00:31:04,680 --> 00:31:10,060
+على ال NOkay ellipses هذه زي ما قلنا معناها انه
+
+403
+00:31:10,060 --> 00:31:15,400
+infinite sequence انه ال sequence لانهائي و هيظل
+
+404
+00:31:15,400 --> 00:31:21,180
+مستمر مستمر for example لو قلنا ال sequence a n
+
+405
+00:31:21,180 --> 00:31:27,860
+لاحظوا a n بيساوي صفر واحد اربع تسعة ستاشر خمسة و
+
+406
+00:31:27,860 --> 00:31:31,740
+عشرين اتصور ستة و تلاتين و بتكمل تسعة و ربعين و
+
+407
+00:31:31,740 --> 00:31:38,700
+هكذا ليش انا بتعامل مع n تربيع صفرzero واحد اتنين
+
+408
+00:31:38,700 --> 00:31:43,900
+تلاتة و حكدا تمام بس ال ellipses احنا بنتركز عليها
+
+409
+00:31:43,900 --> 00:31:47,800
+هنا ان انا بتعمل dots معناه تلت نقاط هيكي معناته
+
+410
+00:31:47,800 --> 00:31:51,220
+ان انا ب .. to infinity to infinity هتظل لانهائية
+
+411
+00:31:51,220 --> 00:31:55,740
+ال sequence بتاعها تمام تقدر نعرفها بهذا الشكل for
+
+412
+00:31:55,740 --> 00:32:00,380
+all n belong to natural numberانا واضح ان انا
+
+413
+00:32:00,380 --> 00:32:02,540
+اتعملت مع ال natural number يعني انا بدأت من صفر
+
+414
+00:32:02,540 --> 00:32:06,600
+بالظبط معناته بدأنا من الصفر فلما اجى اعود في
+
+415
+00:32:06,600 --> 00:32:10,440
+المعادلة نبدأ بالصفر نبدأ بالصفر نبدأ بالصفر okay
+
+416
+00:32:10,440 --> 00:32:14,820
+a n equal to n تربيع بتبدو تشتغلوا عليها عساس ان
+
+417
+00:32:14,820 --> 00:32:17,740
+ال locations تبعتكم تبدأ من صفر باعتبار ان هي
+
+418
+00:32:17,740 --> 00:32:19,660
+belong to natural number اتفضل
+
+419
+00:32:22,580 --> 00:32:27,440
+لأن هنا هذه الست نطق شيل منها ال element zero ال
+
+420
+00:32:27,440 --> 00:32:30,340
+natural number بدون ال element zero شيل ال element
+
+421
+00:32:30,340 --> 00:32:35,860
+zero فصارت كأنه من واحد بتبدأ واحد اتنين تلاتة
+
+422
+00:32:35,860 --> 00:32:44,080
+بتشيل .. بتشيل اللولة ليش؟ لأن احنا قلنا السالب
+
+423
+00:32:44,080 --> 00:32:50,720
+هذي في الست إيش كانت عبارة عن إيه؟ difference إيش
+
+424
+00:32:50,720 --> 00:32:54,590
+كانت اسم ال difference؟Okay لما نعمل difference ال
+
+425
+00:32:54,590 --> 00:32:59,130
+6 هذه من صفر to infinity طيب إيش ال elements اللي
+
+426
+00:32:59,130 --> 00:33:03,610
+موجود في N و غير موجود هنا هو ال zero الوحيد اللي
+
+427
+00:33:03,610 --> 00:33:05,990
+موجود في التنتين فهذا هو ال eventual فقط يعني
+
+428
+00:33:05,990 --> 00:33:08,650
+أنتوا بتشوفوا إيش التقاطع بينهم و بتشيلوه الباقي
+
+429
+00:33:08,650 --> 00:33:12,530
+بيضل الباقي ضل معناته الباقي هو إيش من واحد من
+
+430
+00:33:12,530 --> 00:33:17,990
+الواحد okay sequence examplesناخد شوية examples
+
+431
+00:33:17,990 --> 00:33:23,110
+عليها طبعا احنا واضح ممكن نكتبها اما نعرفها ك set
+
+432
+00:33:23,110 --> 00:33:26,710
+بهذا الشكل و نقول ايش المعادلة بتاعتها ممكن تتعرف
+
+433
+00:33:26,710 --> 00:33:34,870
+بهذا الشكل او احيانا ممكن تكون اوضح ف ال indices
+
+434
+00:33:34,870 --> 00:33:39,270
+بتاعتنا اكثر وضوحا بدل ما اعملها ان و خلاص لأ ممكن
+
+435
+00:33:39,270 --> 00:33:43,270
+تكون اوضح لان يكتبلي اي واحد اتنين فبعرف انه بدأ
+
+436
+00:33:43,270 --> 00:33:48,640
+بواحد خلاصA1, A2, A3, A4 هنا بتكون تعريفها أكثر
+
+437
+00:33:48,640 --> 00:33:52,800
+وضوحا ومع
+
+438
+00:33:52,800 --> 00:33:58,980
+ذلك في الكتاب اللحظة اللي احنا بكتبناها كتير A, N,
+
+439
+00:33:59,300 --> 00:34:05,300
+A, N كويس؟ تمام ناخد شوية examples لو قلنا اللي
+
+440
+00:34:05,300 --> 00:34:10,960
+عندنا series sequence series بيه هي نفس ال A, N,
+
+441
+00:34:11,220 --> 00:34:17,790
+A1, A2, ellipseswhere for all n أكبر أو يسوى واحد
+
+442
+00:34:17,790 --> 00:34:21,370
+معناته أننا بتعامل مع ال natural minus zero ببدأ
+
+443
+00:34:21,370 --> 00:34:26,230
+من واحد يعني بدين من واحد a n equal to f of n
+
+444
+00:34:26,230 --> 00:34:30,790
+equal to واحد over n معناته بدنا نبدأ نعود من وين
+
+445
+00:34:30,790 --> 00:34:35,470
+من واحد واحد على واحد واحد على واحد واحد على اتنين
+
+446
+00:34:35,470 --> 00:34:39,990
+واحد على تلاتة فلحظوا بتطلع ال sequence هذه مقابلة
+
+447
+00:34:39,990 --> 00:34:42,510
+لا اسم تمام
+
+448
+00:34:44,330 --> 00:34:47,190
+Okay ال examples with repetitions طبعا في ال
+
+449
+00:34:47,190 --> 00:34:50,830
+repetitions احنا قولنا في ال sequence مسموح في ال
+
+450
+00:34:50,830 --> 00:34:56,790
+series مسموح ولكن في ال sets لأ فإذا لما يكون
+
+451
+00:34:56,790 --> 00:35:04,690
+عندنا constant of the sequence P0 P1 P2 P3 ونقول
+
+452
+00:35:04,690 --> 00:35:09,490
+ان ال Pn equal to minus one to the power n هاي ال
+
+453
+00:35:09,490 --> 00:35:13,430
+relation الأوطانية مجرد ان بنعوض بنبدأ بال zeroلأن
+
+454
+00:35:13,430 --> 00:35:18,910
+هنا بدين احنا احنا احنا احنا
+
+455
+00:35:18,910 --> 00:35:19,010
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+456
+00:35:19,010 --> 00:35:19,310
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+457
+00:35:19,310 --> 00:35:22,810
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+458
+00:35:22,810 --> 00:35:25,010
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+459
+00:35:25,010 --> 00:35:33,330
+احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+460
+00:35:34,960 --> 00:35:37,800
+أه بالظبط هذه هتكون isolating تمام عاملة زي sunny
+
+461
+00:35:37,800 --> 00:35:45,180
+soda يعني مش sunny soda زي .. إيش بتسميها ال .. او
+
+462
+00:35:45,180 --> 00:35:51,810
+.. إيش بتسموها السوتوث .. السوتوثزي أسنان المنشرة
+
+463
+00:35:51,810 --> 00:35:55,530
+الـ Suture، عارفينه؟ فهذه تطلع زي الـ Suture،
+
+464
+00:35:55,530 --> 00:35:58,910
+تمام، طيب، في الحالة اللي عندنا هنا، في ال
+
+465
+00:35:58,910 --> 00:36:03,250
+sequence مقبولة، في ال series مقبولة، بس في ال
+
+466
+00:36:03,250 --> 00:36:06,090
+sets لأ، في ال sets .. لو عندي set بهذا الشكل،
+
+467
+00:36:06,090 --> 00:36:08,990
+الطبيعي أن هي تكون two elements فقط، بقولش أن هي
+
+468
+00:36:08,990 --> 00:36:14,340
+to infinity، هنا to infinityinfinite sequence هنا
+
+469
+00:36:14,340 --> 00:36:18,540
+لأ لما بتكلم عنها as a set بقول ان هي لأ set ال
+
+470
+00:36:18,540 --> 00:36:22,740
+cardinality بتاعتها اتنين فقط one minus one و بس
+
+471
+00:36:22,740 --> 00:36:30,270
+one minus one okay recognizing sequencesكيف ممكن
+
+472
+00:36:30,270 --> 00:36:36,430
+نعمل تمييز لل sequence بتاعتنا طب احنا زى ما
+
+473
+00:36:36,430 --> 00:36:42,450
+قلتلكم مش هناخد علميا بالحل لاحقا هناخد الحل هنرجع
+
+474
+00:36:42,450 --> 00:36:47,210
+للموضوع هذا و نتكلم عن sequence و محتاجين احنا
+
+475
+00:36:47,210 --> 00:36:50,590
+نجيب elements ناقصة فيه او نجيب ال relation تبعته
+
+476
+00:36:50,590 --> 00:36:54,970
+هناخده ولكن احنا هناby logic هيك .. بدنا نشوف شوية
+
+477
+00:36:54,970 --> 00:36:59,150
+examples لكيف انا اميز ال sequence تبعتنا .. كيف
+
+478
+00:36:59,150 --> 00:37:02,430
+اميز .. اقول اه دي sequence بتاعة كذا لو بدأنا
+
+479
+00:37:02,430 --> 00:37:08,110
+نقول والله ايش ال next number لواحد اتنين تلاتة
+
+480
+00:37:08,110 --> 00:37:12,510
+اربعة .. خمسة .. خمسة .. ليش؟ بيمشي انا .. لأن
+
+481
+00:37:12,510 --> 00:37:17,570
+احنا انا متعامل عن أرقام .. الأرقام ال positive ..
+
+482
+00:37:17,570 --> 00:37:21,650
+ال positive integers .. positive integersواحد،
+
+483
+00:37:21,650 --> 00:37:26,170
+اتنين، تلاتة، فطبيعي خامس element أكبر من صفر هو
+
+484
+00:37:26,170 --> 00:37:32,130
+الخمسة طيب، واحد، تلاتة، داشت، داشت، داشت، داشت،
+
+485
+00:37:32,130 --> 00:37:34,310
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+486
+00:37:34,310 --> 00:37:39,470
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+487
+00:37:39,470 --> 00:37:44,030
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+488
+00:37:44,030 --> 00:37:47,610
+داش
+
+489
+00:37:48,070 --> 00:37:50,510
+sequence انتوا بتقدروا تعرفوها و تميزوها لحاجة و
+
+490
+00:37:50,510 --> 00:37:54,510
+مجرد ما شوفتوها بتقدروا تميزوها بتقدروا تميزوها
+
+491
+00:37:54,510 --> 00:37:59,670
+okay ولكن مع ذلك بصير احيانا trouble with
+
+492
+00:37:59,670 --> 00:38:03,190
+recognition في التمييز احيانا بصير مشكلة ان انا
+
+493
+00:38:03,190 --> 00:38:11,470
+ماعرفتهاش بالظبط زي لو قلنا أخدنا تلاتة خمسة سبعة
+
+494
+00:38:11,470 --> 00:38:15,070
+و سكتت و قلتلكوا هتقولي الرقم اللي ورا ممكن يكون
+
+495
+00:38:15,070 --> 00:38:18,550
+تسعة مثلا ممكن يكونممكن يكون تسعة و ممكن يكون
+
+496
+00:38:18,550 --> 00:38:22,770
+احداش .. ممكن يكون تسعة و ممكن يكون احداش .. لحظة
+
+497
+00:38:22,770 --> 00:38:28,170
+دولهم متمتفقين مع بعض .. فلاحظوا انه ممكن جدا يكون
+
+498
+00:38:28,170 --> 00:38:31,250
+في صعوبة في تمييز اي .. انا بتعني اي sequence
+
+499
+00:38:31,250 --> 00:38:34,790
+بحتكلم او بحكي .. فعشان اجيب ال element اللي وراها
+
+500
+00:38:34,790 --> 00:38:37,890
+هتكون فيه صعوبة، ايش ال element اللي وراها؟ او
+
+501
+00:38:37,890 --> 00:38:41,690
+يقولنا ايش ال element اللي قدامها؟ففي صعوبة في
+
+502
+00:38:41,690 --> 00:38:44,070
+تمييز ال sequence في بعض الأحيان بتصير ففي مشاكل
+
+503
+00:38:44,070 --> 00:38:46,750
+ممكن تصير في التمييز المشاكل هدا إذا صارت بتكون
+
+504
+00:38:46,750 --> 00:38:50,410
+نتيجة إن أنا ماعرفتش ال ال ال initial elements صح
+
+505
+00:38:50,410 --> 00:38:53,910
+ال initial elements هدول مش معرفين بصورة صحية هدول
+
+506
+00:38:53,910 --> 00:38:59,360
+intersection ل two sequence ايه و بدك منهم؟هدول
+
+507
+00:38:59,360 --> 00:39:03,640
+هيكون intersection ل .. intersection set لل prime
+
+508
+00:39:03,640 --> 00:39:07,860
+و لل odd انت مين بدك منهم مش معرف فهنا او خليني
+
+509
+00:39:07,860 --> 00:39:12,160
+اقول not well defined هو مش معرف بطريقة جيدة يمكن
+
+510
+00:39:12,160 --> 00:39:14,920
+كنا محتاجين element قبل او element بعد عشان تتضح
+
+511
+00:39:14,920 --> 00:39:18,480
+ال sequence هدا ان و منهم فإذا كان فعلا بهذا الشكل
+
+512
+00:39:18,480 --> 00:39:23,500
+مش معرفة بصورة جيدة واضح انه هيكون فينا مشكلة في
+
+513
+00:39:23,500 --> 00:39:29,160
+تمييز الصورة في الغالب .. في الغالب إذا ..ماعناش
+
+514
+00:39:29,160 --> 00:39:34,140
+واضحة الصورة بهذا الشكل، في الغالب الأبسط هي اللي
+
+515
+00:39:34,140 --> 00:39:37,860
+بناخدها، في الغالب الأبسط هي اللي بناخدها، إذا
+
+516
+00:39:37,860 --> 00:39:42,800
+طبعا ماعناش أي معلومة مسبقة، فال simplest هي من ال
+
+517
+00:39:42,800 --> 00:39:44,840
+functions، من ال two functions اللي بنتعامل معها و
+
+518
+00:39:44,840 --> 00:39:49,440
+بناخدها، هذا إذا كان لابد أن أحنا نختاره، بس في
+
+519
+00:39:49,440 --> 00:39:52,240
+حالة زي هذه لأ، هي لها كذا احتمال، هي لها كذا
+
+520
+00:39:52,240 --> 00:39:58,350
+احتمال للشغل، okayكيف احنا نعرف ال simplicity اصلا
+
+521
+00:39:58,350 --> 00:40:02,510
+of a function كيف نعرف مين البسيطة منهم أساسا ما
+
+522
+00:40:02,510 --> 00:40:04,650
+احنا عندنا ال prime و عندنا ال .. ال .. ال odd
+
+523
+00:40:04,650 --> 00:40:06,650
+التنتين بساطين بالنسبالي يعني بالنسبالنا على level
+
+524
+00:40:06,650 --> 00:40:09,670
+تبعنا ماهم التنتين زي بعض مش هتفرج كتير هذه بسيطة
+
+525
+00:40:09,670 --> 00:40:12,250
+و هذه بسيطة انا عرفت هذه و اعرفت هذه و هذه ممكن
+
+526
+00:40:12,250 --> 00:40:16,690
+يكون يا هذه يا هذه مين اختار منهم هذا مافيش
+
+527
+00:40:16,690 --> 00:40:22,590
+objective right answerبقدرش أقولكم والله لأ لازم
+
+528
+00:40:22,590 --> 00:40:26,530
+يكون بهذا الشكل، هي من الأساس غير معرفة بصورة
+
+529
+00:40:26,530 --> 00:40:31,170
+جيدة، غير معرفة، ال elements هذه بصورة جيدة، فهذه
+
+530
+00:40:31,170 --> 00:40:35,590
+بيبقى قائمة لإحتمالاتها، ممكن حد يجاوب إن هي odd و
+
+531
+00:40:35,590 --> 00:40:39,120
+ممكن حد يجاوب إن هي primeبقدرش أقول هذا غلط ولا
+
+532
+00:40:39,120 --> 00:40:43,580
+بقدر أقول هذا غلط لأنه من الأساس تعريفها مش غلط
+
+533
+00:40:43,580 --> 00:40:49,100
+ولكن ماكانش أو not well defined مش محدد بصورة
+
+534
+00:40:49,100 --> 00:40:53,720
+جيدة، مش مميز بصورة محددة واضحة، هو مش محدد، مش
+
+535
+00:40:53,720 --> 00:40:59,580
+محدد أصلا طيب what are strings really؟ احنا كنا
+
+536
+00:40:59,580 --> 00:41:01,760
+بتكلم عن ال sequenceال string الحقيقة بقى في
+
+537
+00:41:01,760 --> 00:41:05,060
+تعريفات كتير فيها يعني في اختلفة حتى فيها انه ال
+
+538
+00:41:05,060 --> 00:41:07,980
+string ايش بيميزه عن ال sequence فهي في ناس عرفوها
+
+539
+00:41:07,980 --> 00:41:11,840
+عساسة ان هي ال finite sequences اذا كانت finite
+
+540
+00:41:12,340 --> 00:41:16,400
+sequences بنسميها string فاحنا إذا كان محددة بادية
+
+541
+00:41:16,400 --> 00:41:20,280
+من واحد ومنتهية and n و n هذا belong to natural
+
+542
+00:41:20,280 --> 00:41:24,960
+number بقى قيمة محددة معروفة and بتقولي لعند عشر
+
+543
+00:41:24,960 --> 00:41:28,240
+terms أول عشر terms أول عشرين terms خلاص أنا عارف
+
+544
+00:41:28,240 --> 00:41:31,520
+إنه جداش عدد ال terms بقدر أحسبلها cardinality
+
+545
+00:41:31,520 --> 00:41:35,580
+نقدر نحسبلها cardinality نعرف جداش عدد ال elements
+
+546
+00:41:35,580 --> 00:41:40,260
+فيهاجاله على أساس إنه هذا اللي يكون ال sequence
+
+547
+00:41:40,260 --> 00:41:45,620
+طيب ولكن رغم ذلك في infinite strings رغم إنه
+
+548
+00:41:45,620 --> 00:41:48,920
+الكتاب معرفه على أساس إنه finite sequence ولكن
+
+549
+00:41:48,920 --> 00:41:54,060
+احنا بنعرف إنه في infinite strings في strings ممكن
+
+550
+00:41:54,060 --> 00:41:58,160
+نتعامل معها ك infinite كويس ولكن هذا تعريف في
+
+551
+00:41:58,160 --> 00:42:01,440
+تعريف تاني strings are often restricted to
+
+552
+00:42:01,440 --> 00:42:07,510
+sequencescomposed of symbols بدل ال numbers إذا
+
+553
+00:42:07,510 --> 00:42:13,290
+كانت ال .. ال sequence يحتوي على symbols على
+
+554
+00:42:13,290 --> 00:42:17,430
+elements مش أرقام ال symbols هذه و ال objects ..
+
+555
+00:42:17,430 --> 00:42:19,990
+ال objects هذه ال symbols زي .. زي ال alphabet
+
+556
+00:42:19,990 --> 00:42:26,430
+مثلا ال alphabet symbols a b c d e f g ال .. ال ..
+
+557
+00:42:26,430 --> 00:42:29,870
+ال letters هذه إذا كانت ال sequence .. sequence من
+
+558
+00:42:29,870 --> 00:42:35,600
+letters فبنسميها stringهذا برضه تعريف ممكن التعامل
+
+559
+00:42:35,600 --> 00:42:39,540
+.. التعامل معه عساس ان هي تعتمد على مجموعة symbols
+
+560
+00:42:39,540 --> 00:42:42,400
+بنعرفه finite طبعا لان اذا كان ماتكلم عن ال
+
+561
+00:42:42,400 --> 00:42:45,900
+alphabet فهي ال alphabet محددة ال alphabet محددة
+
+562
+00:42:45,900 --> 00:42:48,820
+هي مش تو infinity يعني خلاص هي معروفة انه .. انه
+
+563
+00:42:48,820 --> 00:42:51,980
+كام حرف؟ ستة و عشرين حرف خلاص هم معروفين ستة و
+
+564
+00:42:51,980 --> 00:42:56,400
+عشرين هم مش هزيلوا مش هزيلوا كويس و ال .. زي ما
+
+565
+00:42:56,400 --> 00:43:00,870
+قلنا ال index من صفر ببدأ او من واحدمن صفر أو واحد
+
+566
+00:43:00,870 --> 00:43:03,590
+فاحنا متفقين على التعريف مع ال sequence هو هو إما
+
+567
+00:43:03,590 --> 00:43:07,050
+بنبدأ من صفر أو من واحد بأي طريقة من الطريقتين
+
+568
+00:43:07,050 --> 00:43:12,190
+احنا هنتعامل مع length of a finite string is just
+
+569
+00:43:12,190 --> 00:43:16,970
+its number of terms أو distinct indices بمعنى أنه
+
+570
+00:43:16,970 --> 00:43:21,090
+لازم نكون عارفين عدد ال numbersأو ال number of
+
+571
+00:43:21,090 --> 00:43:23,870
+terms جدش عدد ال units اللي جواها، جدش عدد ال
+
+572
+00:43:23,870 --> 00:43:28,550
+elements داخلها، و بنكون محدد في الحالة هذه جدش
+
+573
+00:43:28,550 --> 00:43:32,460
+عدد ال indices اللي موجودةمكتوبة هنا اها يعني ال
+
+574
+00:43:32,460 --> 00:43:36,540
+index الأولى واحد index index هدولة مجموعة هم اللي
+
+575
+00:43:36,540 --> 00:43:39,820
+هم ال indices اللي هم محددين معروفين انه والله اه
+
+576
+00:43:39,820 --> 00:43:43,220
+عندي عشرين عندي خمسين indices بمعنى عندي عشرين
+
+577
+00:43:43,220 --> 00:43:47,700
+location عشرين خمسة وعشرين location معروفة ومحددة
+
+578
+00:43:47,700 --> 00:43:50,900
+فهذه بنتعامل معها على أساس إن هي string على أساس
+
+579
+00:43:50,900 --> 00:43:57,730
+إن هذا stringOkay, strings more formally أكثر ..
+
+580
+00:43:57,730 --> 00:44:01,250
+نوضحها بصورة أكثر فاحنا زي ما قلنا إذا كان عرفناها
+
+581
+00:44:01,250 --> 00:44:05,270
+عساس أن هي symbols، مجموعة عناصر أو رموز، symbols
+
+582
+00:44:05,270 --> 00:44:09,310
+ممكن تكون زي ما قلنا ال alphabet، letters، نتعامل
+
+583
+00:44:09,310 --> 00:44:13,070
+معها عساس أن هي alphabet مثلا، generally A,B,C,D,Z
+
+584
+00:44:13,070 --> 00:44:21,830
+to ZA String S ال S هذه اللي هي ال string و لاحظوا
+
+585
+00:44:21,830 --> 00:44:24,670
+إن إحنا كاتبينها small لإن إذا كتبناها capital
+
+586
+00:44:24,670 --> 00:44:31,010
+ستصبح six ستصبح six فلأ small فأنا عارف إن هذه ال
+
+587
+00:44:31,010 --> 00:44:35,030
+small string over alphabet بنسميها مثلا big sigma
+
+588
+00:44:35,030 --> 00:44:38,150
+ال big sigma في الحلقة هذه بيقول و الله فينا
+
+589
+00:44:38,150 --> 00:44:42,490
+string S هذا عبارة عن alpha alphabet string
+
+590
+00:44:44,860 --> 00:44:49,780
+لـ any sequence of symbols SI والـ I هذي زي ما
+
+591
+00:44:49,780 --> 00:44:52,740
+قلنا اللي هو ال index تبعنا ال .. ال .. ال
+
+592
+00:44:52,740 --> 00:44:56,430
+sequence منالـ element الأول ايش هو؟ A ال element
+
+593
+00:44:56,430 --> 00:44:59,710
+التاني B ال element التالق C ال element الرابع D و
+
+594
+00:44:59,710 --> 00:45:08,130
+هكذا of symbols فبنقول هنا ال S I belong to sigma
+
+595
+00:45:08,130 --> 00:45:14,590
+فمعنى ذلك ان ال element اللي داخل ال set او داخل
+
+596
+00:45:14,590 --> 00:45:18,350
+ال sequence او ال string احنا بنتكلم عن string
+
+597
+00:45:19,740 --> 00:45:22,960
+string هدا هدا هيكون مجموعة elements متفقين على
+
+598
+00:45:22,960 --> 00:45:29,460
+هيك طيب كل element جوا إيش بسميه SI لإن حسب قيمة I
+
+599
+00:45:29,460 --> 00:45:33,620
+هتتغير ال elements اللي جوا هذه فهنقول إن ال SI أي
+
+600
+00:45:33,620 --> 00:45:38,680
+واحدة منهم لازم تكون belong to سيجما، سيجما الشي
+
+601
+00:45:38,680 --> 00:45:46,880
+هذه كل ال alphabet symbolsإذا باعرف symbols تانية
+
+602
+00:45:46,880 --> 00:45:49,060
+غير ال alphabet بدي أكون معرفها برضه عساس ان هي ال
+
+603
+00:45:49,060 --> 00:45:53,800
+big sigma هدولة كل الحروف اللي موجودين هنا لو
+
+604
+00:45:53,800 --> 00:45:56,100
+بنتكلم عن الطالبات اللي موجودين معناته كل أسماء
+
+605
+00:45:56,100 --> 00:46:00,960
+الطالبات هدولة بتحطهم عساس ان هم هدول ال big sigma
+
+606
+00:46:00,960 --> 00:46:04,300
+تمام؟ ويمكن بعد ما نخلص الامتحان بيضطرهم حسب
+
+607
+00:46:04,300 --> 00:46:07,260
+درجاتهم عساس ان هذا ال year بتتغيرش مش هنقول والله
+
+608
+00:46:07,260 --> 00:46:10,830
+زي ال setال set قابلة للتبديل، أي حد بيجي اسمه قبل
+
+609
+00:46:10,830 --> 00:46:14,210
+تان مفرجش، بس لو قولنا لأ حسب مثلا في التوجيه جد
+
+610
+00:46:14,210 --> 00:46:17,050
+الجوا مثلا، خلاص هذه ثابتة، هذه لازم ال string
+
+611
+00:46:17,050 --> 00:46:21,310
+انحدده، لازم تكون مرتبة، بينفعش حد يجي مكان حد،
+
+612
+00:46:21,310 --> 00:46:27,510
+صحيح؟ كويس فهنا alphabet هذه بتكون تشتمل على جميع
+
+613
+00:46:27,510 --> 00:46:30,210
+ال symbols اللي انا بتتعامل معها، جميع ال symbols
+
+614
+00:46:30,210 --> 00:46:33,890
+اللي بتتعامل معها، فأي symbol داخل ال stringلازم
+
+615
+00:46:33,890 --> 00:46:38,930
+يكون موجود أصلا معرف من الأول في ال big sigma و
+
+616
+00:46:38,930 --> 00:46:44,690
+indexed by لحظة هى natural number او natural
+
+617
+00:46:44,690 --> 00:46:49,090
+number minus هى زى ما قولنا ال difference ل set
+
+618
+00:46:49,090 --> 00:46:53,910
+بشيل منها بس ال zero ل set بنشيل منها ال zero فهدى
+
+619
+00:46:53,910 --> 00:46:56,970
+ال minus اللى هنا هدى مش مجرد طريح عادي يعنى احنا
+
+620
+00:46:56,970 --> 00:47:00,870
+بنتكلم عن ال difference ال difference between ال
+
+621
+00:47:00,870 --> 00:47:06,180
+setsلو قلنا if a,b,c هي ال symbols تبعتنا فممكن
+
+622
+00:47:06,180 --> 00:47:10,600
+نقول ان ال string تبعنا عبارة عن a,b,c لو نكمل
+
+623
+00:47:10,600 --> 00:47:13,940
+هنكمل معنا ellipses هي نكمل ellipses ممكن نكتبها
+
+624
+00:47:13,940 --> 00:47:18,940
+مباشرة a,b,c بدون كوماز بدون الكوماز بدون كوماز
+
+625
+00:47:18,940 --> 00:47:24,780
+بمشي الحل بمشي الحل طيب إذا كانت ال string s هذه
+
+626
+00:47:24,780 --> 00:47:32,200
+is finite string andT برضه String تانية فصار عندنا
+
+627
+00:47:32,200 --> 00:47:36,600
+two strings String اسمها S و String اسمها T then
+
+628
+00:47:36,600 --> 00:47:44,520
+the concatenation of S with T بنكتبها ST كأنهم
+
+629
+00:47:44,520 --> 00:47:49,100
+مضربين في بعض ST هدول كيف بنعملهم؟ بنحط كل عناصر S
+
+630
+00:47:49,100 --> 00:47:53,720
+في الأول و بعدين عناصر T وراهم في sequence واحد في
+
+631
+00:47:53,720 --> 00:48:00,230
+String واحدة بنسميها concatenationسلسلة أو بنحطهم
+
+632
+00:48:00,230 --> 00:48:03,650
+يعني سلسلة ورا بعض بنحطهم سلسلة ورا بعض زي بالظبط
+
+633
+00:48:03,650 --> 00:48:09,470
+لما تجيب سنسال عندكم و تجيبوا سنسالين و تفتح عروض
+
+634
+00:48:09,470 --> 00:48:13,130
+واحدة منهم و تربطيها في التاني، string كامل صار،
+
+635
+00:48:13,130 --> 00:48:15,850
+صاروا كلهم مع بعض، مش هم عبارة عن حلقات في بعض
+
+636
+00:48:16,470 --> 00:48:20,330
+الحلقات هذه واحدة مثلا طولها عشرة صنطة لأ انا بدي
+
+637
+00:48:20,330 --> 00:48:23,350
+اوسع شوية جيبنا كمان واحد عشرة صنطة فتحنا اخر
+
+638
+00:48:23,350 --> 00:48:25,470
+حلقتين هنا واخر حلقتين هنا و بعدين رابطناهم في بعض
+
+639
+00:48:25,470 --> 00:48:29,070
+عملنا concatenation عملناهم ايش؟ concatenation
+
+640
+00:48:29,070 --> 00:48:33,590
+فهذه رابطنا تنتين في بعض فلما اجي اطلع حلوجة عليا
+
+641
+00:48:33,590 --> 00:48:37,650
+كله على بعضه هعرفوا ايش الحلقة الأولى اللي كانت من
+
+642
+00:48:37,650 --> 00:48:40,830
+S الحلقة التانية كانت من S الحلقة العشرة كانت من S
+
+643
+00:48:40,830 --> 00:48:44,370
+الحلقة أحداشر كانت من Tبس خلاص هالوقت صاروا في
+
+644
+00:48:44,370 --> 00:48:49,430
+إيه؟ في concatenation sequence أو في ال sequence
+
+645
+00:48:49,430 --> 00:48:55,130
+الجديد اللي هو ال S T simply the string contains
+
+646
+00:48:55,130 --> 00:49:01,470
+هنا في الحالة هذه the symbols in S and in sequence
+
+647
+00:49:01,470 --> 00:49:06,490
+followed by the symbols in T in sequenceمتبعين
+
+648
+00:49:06,490 --> 00:49:11,750
+مباشرة وراها لو في وراهم كمان V لو في وراهم V في
+
+649
+00:49:11,750 --> 00:49:15,510
+الحالة هذه ايش بيصير عندنا STV بنحط كمان العناصر
+
+650
+00:49:15,510 --> 00:49:21,010
+تبعت V معاهم بنحط عناصر V في الحالة هذه معاهم هذه
+
+651
+00:49:21,010 --> 00:49:26,030
+هي ال concatenation في الحالة اللي احنا بنحكي عنها
+
+652
+00:49:26,030 --> 00:49:30,130
+طيب
+
+653
+00:49:30,130 --> 00:49:35,880
+ال length لل stringهي بالظبط ال cardinality ال
+
+654
+00:49:35,880 --> 00:49:39,120
+cardinality نفس لما بنيجي نعمل absolute هنا ال
+
+655
+00:49:39,120 --> 00:49:41,220
+cardinality ايش معناه ال cardinality لما كنا نتكلم
+
+656
+00:49:41,220 --> 00:49:44,680
+في ال set عدد ال elements داخل ال set طيب في ال
+
+657
+00:49:44,680 --> 00:49:47,160
+sequence أو في ال string هي نفس الكلام عدد ال
+
+658
+00:49:47,160 --> 00:49:50,520
+elements داخل ال string و باعتبار ان احنا عرفنا ال
+
+659
+00:49:50,520 --> 00:49:54,120
+string عساس ان هي finite و بدنا نتعامل كل شغلنا مع
+
+660
+00:49:54,120 --> 00:49:57,000
+ال finite string as معناه ذلك ان هي number of
+
+661
+00:49:57,000 --> 00:50:02,700
+positions number of positionsلحظة number of
+
+662
+00:50:02,700 --> 00:50:07,480
+positions مش ال index لأن ال index ممكن يبدأ من
+
+663
+00:50:07,480 --> 00:50:14,080
+صفر صح؟ طب لو من صفر لعشرة ال maximum عشرة هل بقول
+
+664
+00:50:14,080 --> 00:50:18,580
+اني عندي عشرة elements؟ لأ عندي 11 زي ما قلنا ال
+
+665
+00:50:18,580 --> 00:50:21,940
+cardinality هذه سهلة هو عدد number of indices او
+
+666
+00:50:21,940 --> 00:50:28,710
+ال index values I كده عدد ال index numberإذا بدين
+
+667
+00:50:28,710 --> 00:50:32,810
+من صفر معناته بإننا زائد واحد آخر index موجود جدش
+
+668
+00:50:32,810 --> 00:50:35,190
+قيمته زائد واحد إذا بدين والله automatically من ال
+
+669
+00:50:35,190 --> 00:50:39,790
+positive natural numbers خلاص الأخر هو يمثل العدد
+
+670
+00:50:39,790 --> 00:50:44,110
+العدد ال elements في الحالة هذه بنقول أن ال S is a
+
+671
+00:50:44,110 --> 00:50:49,430
+finite string andbelong to natural number الان
+
+672
+00:50:49,430 --> 00:50:52,090
+طبعا جديش ال cardinality جديش عدد ال elements
+
+673
+00:50:52,090 --> 00:50:56,310
+طبيعي بده يكون عدد طبيعي عدد طبيعي integer هيكون
+
+674
+00:50:56,310 --> 00:50:59,410
+integer عدد طبيعي العدد الطبيعي هي العدد الواحد
+
+675
+00:50:59,410 --> 00:51:03,770
+اتنين تلات اربع مافيش فيها fractions okay then لما
+
+676
+00:51:03,770 --> 00:51:09,470
+نقول هل وجد s string to the power n هذه معناها
+
+677
+00:51:09,470 --> 00:51:15,870
+denotes the concatenation of n cubit او cubits of
+
+678
+00:51:15,870 --> 00:51:23,770
+sهنا معناته ال S عملتيلها نسخ N مرة هناك كنا بنقول
+
+679
+00:51:23,770 --> 00:51:29,070
+S في T هذا كان String وهذا String وحطيناهم ورا بعض
+
+680
+00:51:29,070 --> 00:51:35,930
+طب لما نقول S تربيع كأنها S في S sequence S بنحطه
+
+681
+00:51:35,930 --> 00:51:42,270
+و ورا مباشرة كمان مرة ال sequence نفسه Sطيب N مرة
+
+682
+00:51:42,270 --> 00:51:48,390
+بده يتكرر لعند ما نصل هذه واحد هذه اتنين to S
+
+683
+00:51:48,390 --> 00:51:52,810
+المرة N المرة انه كله بصير هذا sequence ..
+
+684
+00:51:52,810 --> 00:51:55,370
+sequence واحد فهذه عملية ال concatenation لما تشوف
+
+685
+00:51:55,370 --> 00:51:57,090
+كلمة concatenation معناه ان انتوا تعرفين ان انتوا
+
+686
+00:51:57,090 --> 00:51:59,570
+بت .. هتعملوا string من مجموعة strings تانين
+
+687
+00:51:59,570 --> 00:52:04,030
+بترتبوهم ورا .. ورا بعضهم بترتبوهم ورا بعضهم okay
+
+688
+00:52:04,030 --> 00:52:10,870
+في عندنا ال epsilonأو double quotation فاضيين بهذا
+
+689
+00:52:10,870 --> 00:52:16,710
+الشكل هذه معناته ان انا بتكلم عن empty string او
+
+690
+00:52:16,710 --> 00:52:23,790
+string of length zero string طوله زي صفر string
+
+691
+00:52:23,790 --> 00:52:28,190
+طوله صفر string فاضي string فاضي لما ديش تطلعوا
+
+692
+00:52:28,190 --> 00:52:30,590
+عليه هتلاجوا مافيش فيه أي elements ففي الحالة هذه
+
+693
+00:52:30,590 --> 00:52:34,630
+بنسميه epsilon أو ال double quotation بعض كتب
+
+694
+00:52:34,630 --> 00:52:40,490
+أحيان بسموهLambda بيعرفوها على أساس أنه Lambda على
+
+695
+00:52:40,490 --> 00:52:43,410
+أساس أنه Lambda فLambda ممكن برضه في بعض كتب
+
+696
+00:52:43,410 --> 00:52:46,610
+تلاقوها عبارة عن ال empty string عبارة عن empty
+
+697
+00:52:46,610 --> 00:52:51,710
+stringخلاص هى ال summation اللى كنتوا تتكلموا فيه
+
+698
+00:52:51,710 --> 00:52:55,430
+المرة الجاية بنبدأ عندنا string او عندنا sequence
+
+699
+00:52:55,430 --> 00:52:59,950
+معين او series معينة بدنا ال series بتاعتنا هدى
+
+700
+00:52:59,950 --> 00:53:03,090
+نجمعهم نجمع ال elements داخلها زى الحال اللى كنتوا
+
+701
+00:53:03,090 --> 00:53:07,130
+اتكلمنا عنها اللى كانت عبارة عن واحد على X واحد
+
+702
+00:53:07,130 --> 00:53:10,030
+على X ممكن نقول واحد على X و بدنا نجمع كل ال
+
+703
+00:53:10,030 --> 00:53:13,500
+elementsفيه لها شوية نظريات، فيه لها شوية rules،
+
+704
+00:53:13,500 --> 00:53:17,400
+فيه لها شوية قواعد في التعامل، فبدنا ناخدها المرة
+
+705
+00:53:17,400 --> 00:53:20,180
+الجاية ان شاء الله تعالى و نكمل موضوعنا المرة
+
+706
+00:53:20,180 --> 00:53:20,460
+الجاية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..bed4abc61fef86660088c6d51992e6c98f6f4a19
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3433, "start": 20.67, "end": 34.33, "text": "بسم الله الرحمن الرحيم الصلاة والسلام على أشرف الأنبياء والمرسلين سيدنا محمد وعلى أهلي وصحابي أجمعين نبدأ اليوم نحاول نخلص الجزئية اللي بدأنا نتكلمنا فيها المرة اللي فاتت اللي هي ال functions وقولنا .. تحدثنا عن تعريف ال functions و بعدين ..", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 31767, 15040, 3660, 16070, 3794, 37440, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 29973, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 20292, 4032, 9381, 5016, 16758, 1829, 5551, 7435, 2304, 3615, 9957, 8717, 44510, 10721, 45595, 20498, 8717, 5016, 995, 12610, 8717, 9778, 1211, 9381, 25724, 11622, 19986, 10632, 13672, 1829, 47525, 10721, 8315, 8717, 2655, 4117, 19528, 8315, 8978, 11296, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 13672, 1829, 39896, 2423, 6828, 4032, 39648, 8315, 4386, 6055, 24401, 12984, 8315, 18871, 37279, 16572, 5172, 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"temperature": 1.0}, {"id": 70, "seek": 173902, "start": 1717.34, "end": 1739.02, "text": "عوضنا بواحد، بتنين، تلاتة، أربعة، تقدر تجيبوا الخمسة تقدر تجيبوا ال element اللي وراك تقدر تجيبوا ال element اللي وراك طيب احنا من هنا طلعنا بحاجة ان ال location تبعنا ال location بناخده من ال natural number ليش؟ لأن هنا ال location هيبدا بصفر", "tokens": [3615, 2407, 11242, 8315, 4724, 14407, 24401, 12399, 39894, 1863, 9957, 12399, 6055, 1211, 9307, 3660, 12399, 5551, 25513, 27884, 12399, 6055, 28543, 2288, 6055, 7435, 1829, 3555, 14407, 33962, 2304, 3794, 3660, 6055, 28543, 2288, 6055, 7435, 1829, 3555, 14407, 2423, 4478, 13672, 1829, 4032, 23557, 4117, 6055, 28543, 2288, 6055, 7435, 1829, 3555, 14407, 2423, 4478, 13672, 1829, 4032, 23557, 4117, 23032, 1829, 3555, 1975, 5016, 8315, 9154, 34105, 23032, 1211, 3615, 8315, 4724, 5016, 26108, 3660, 16472, 2423, 4914, 6055, 3555, 3615, 8315, 2423, 4914, 44945, 47283, 3215, 3224, 9154, 2423, 3303, 1230, 32239, 8592, 22807, 5296, 33456, 34105, 2423, 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ال sequences بتبدأ بال natural number وفي بعضها natural number minus zero ببدأ بواحد", "tokens": [5172, 28814, 5016, 8315, 6156, 3615, 15040, 8978, 45030, 11242, 2423, 22978, 39894, 44510, 10721, 20666, 3303, 1230, 4032, 41185, 45030, 11242, 11296, 3303, 1230, 3175, 4018, 4724, 44510, 10721, 4724, 14407, 24401], "avg_logprob": -0.2555146936108084, "compression_ratio": 1.2654867256637168, "no_speech_prob": 4.112720489501953e-06, "words": [{"start": 1740.9699999999998, "end": 1741.87, "word": "فإحنا", "probability": 0.6859130859375}, {"start": 1741.87, "end": 1742.33, "word": " فعلا", "probability": 0.806640625}, {"start": 1742.33, "end": 1742.75, "word": " في", "probability": 0.89453125}, {"start": 1742.75, "end": 1743.01, "word": " بعض", "probability": 0.992431640625}, {"start": 1743.01, "end": 1743.11, "word": " ال", "probability": 0.9365234375}, {"start": 1743.11, "end": 1743.59, "word": " sequences", "probability": 0.68212890625}, {"start": 1743.59, "end": 1744.57, "word": " بتبدأ", 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177086, "start": 1750.48, "end": 1770.86, "text": "فهذا يجب أن يكون معرفن، إما natural number فببدأ مباشرة إذا عند المعادلة ببدأ أعوض من ال zero أو لأ natural number minus one أو أكبر أو يساوي واحد فبعرف نبدأ من الواحد، نعرف نبدأ من الواحد، مانبقاش أشي تاني، دائما يا صفر يا الواحد عادة اللي بنبدأ فيهم ال sequence تبعنا", "tokens": [5172, 3224, 15730, 7251, 7435, 3555, 14739, 7251, 30544, 20449, 28480, 1863, 12399, 11933, 15042, 3303, 1230, 6156, 3555, 44510, 10721, 3714, 3555, 33599, 25720, 11933, 15730, 43242, 9673, 3615, 18513, 37977, 4724, 44510, 10721, 5551, 3615, 2407, 11242, 9154, 2423, 4018, 34051, 5296, 10721, 3303, 1230, 3175, 472, 34051, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 36764, 24401, 6156, 3555, 3615, 28480, 8717, 44510, 10721, 9154, 2423, 14407, 24401, 12399, 8717, 3615, 28480, 8717, 44510, 10721, 9154, 2423, 14407, 24401, 12399, 3714, 7649, 3555, 4587, 33599, 5551, 8592, 1829, 6055, 7649, 1829, 12399, 11778, 16373, 15042, 35186, 20328, 5172, 2288, 35186, 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ال sequence كل واحد في ال location تبعه لأن كل واحد لازم يكون function في ال location تبعه فهذه بتكون مرتبة و لازم تكون مرتبة لازم تكون مرتبة عادة زي ما قلنا ال sets اللي احنا بتاعة ال locations ممكن تكون بدية من الصفر", "tokens": [6027, 39184, 2445, 20449, 9957, 3660, 2423, 39184, 2445, 13672, 1829, 8032, 2655, 3615, 28480, 1211, 8315, 2423, 8310, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 2423, 4959, 6055, 33753, 2423, 8310, 28242, 36764, 24401, 8978, 2423, 4914, 6055, 3555, 3615, 3224, 5296, 33456, 28242, 36764, 24401, 5296, 31377, 2304, 7251, 30544, 2445, 8978, 2423, 4914, 6055, 3555, 3615, 3224, 6156, 3224, 24192, 39894, 30544, 3714, 43500, 49401, 4032, 5296, 31377, 2304, 6055, 30544, 3714, 43500, 49401, 5296, 31377, 2304, 6055, 30544, 3714, 43500, 49401, 6225, 18513, 3660, 30767, 1829, 19446, 12174, 1211, 8315, 2423, 6352, 13672, 1829, 1975, 5016, 8315, 39894, 995, 27884, 2423, 9253, 3714, 43020, 6055, 30544, 47525, 10632, 9154, 31767, 5172, 2288], "avg_logprob": 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"temperature": 1.0}, {"id": 85, "seek": 211279, "start": 2084.33, "end": 2112.79, "text": "Okay ال examples with repetitions طبعا في ال repetitions احنا قولنا في ال sequence مسموح في ال series مسموح ولكن في ال sets لأ فإذا لما يكون عندنا constant of the sequence P0 P1 P2 P3 ونقول ان ال Pn equal to minus one to the power n هاي ال relation الأوطانية مجرد ان بنعوض بنبدأ بال zero", "tokens": [8297, 2423, 5110, 365, 13645, 2451, 23032, 3555, 3615, 995, 8978, 2423, 13645, 2451, 1975, 5016, 8315, 12174, 12610, 8315, 8978, 2423, 8310, 3714, 38251, 2407, 5016, 8978, 2423, 2638, 3714, 38251, 2407, 5016, 35525, 19452, 8978, 2423, 6352, 5296, 10721, 6156, 28814, 15730, 5296, 15042, 7251, 30544, 43242, 8315, 5754, 295, 264, 8310, 430, 15, 430, 16, 430, 17, 430, 18, 4032, 1863, 39648, 16472, 2423, 430, 77, 2681, 281, 3175, 472, 281, 264, 1347, 297, 8032, 47302, 2423, 9721, 16247, 2407, 9566, 7649, 10632, 3714, 7435, 2288, 3215, 16472, 44945, 3615, 2407, 11242, 44945, 44510, 10721, 20666, 4018], 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"temperature": 1.0}, {"id": 116, "seek": 282117, "start": 2793.47, "end": 2821.17, "text": "لازم يكون موجود أصلا معرف من الأول في ال big sigma و indexed by لحظة هى natural number او natural number minus هى زى ما قولنا ال difference ل set بشيل منها بس ال zero ل set بنشيل منها ال zero فهدى ال minus اللى هنا هدى مش مجرد طريح عادي يعنى احنا بنتكلم عن ال difference ال difference between ال sets", "tokens": [1211, 31377, 2304, 7251, 30544, 3714, 29245, 23328, 5551, 9381, 15040, 20449, 28480, 9154, 16247, 12610, 8978, 2423, 955, 12771, 4032, 8186, 292, 538, 5296, 5016, 19913, 3660, 8032, 7578, 3303, 1230, 1975, 2407, 3303, 1230, 3175, 8032, 7578, 30767, 7578, 19446, 12174, 12610, 8315, 2423, 2649, 5296, 992, 4724, 8592, 26895, 9154, 11296, 4724, 3794, 2423, 4018, 5296, 992, 44945, 8592, 26895, 9154, 11296, 2423, 4018, 6156, 3224, 3215, 7578, 2423, 3175, 13672, 7578, 34105, 8032, 3215, 7578, 37893, 3714, 7435, 2288, 3215, 23032, 16572, 5016, 6225, 995, 16254, 37495, 1863, 7578, 1975, 5016, 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"probability": 0.99072265625}, {"start": 3188.73, "end": 3188.83, "word": " و", "probability": 0.82421875}, {"start": 3188.83, "end": 3189.01, "word": " بدنا", "probability": 0.7244873046875}, {"start": 3189.01, "end": 3189.49, "word": " نجمع", "probability": 0.9962158203125}, {"start": 3189.49, "end": 3189.93, "word": " كل", "probability": 0.96728515625}, {"start": 3189.93, "end": 3190.03, "word": " ال", "probability": 0.98974609375}, {"start": 3190.03, "end": 3190.25, "word": " elements", "probability": 0.92138671875}], "temperature": 1.0}, {"id": 132, "seek": 320046, "start": 3190.5, "end": 3200.46, "text": "فيه لها شوية نظريات، فيه لها شوية rules، فيه لها شوية قواعد في التعامل، فبدنا ناخدها المرة الجاية ان شاء الله تعالى و نكمل موضوعنا المرة الجاية", "tokens": [41185, 3224, 5296, 11296, 13412, 2407, 10632, 8717, 19913, 16572, 9307, 12399, 8978, 3224, 5296, 11296, 13412, 2407, 10632, 4474, 12399, 8978, 3224, 5296, 11296, 13412, 2407, 10632, 12174, 14407, 22488, 8978, 16712, 3615, 10943, 1211, 12399, 6156, 44510, 8315, 8717, 47283, 3215, 11296, 9673, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 4032, 8717, 24793, 1211, 3714, 2407, 11242, 45367, 8315, 9673, 25720, 25724, 995, 10632], "avg_logprob": -0.15206866071257794, "compression_ratio": 1.8478260869565217, "no_speech_prob": 0.0, "words": [{"start": 3190.5, "end": 3190.78, "word": "فيه", "probability": 0.635498046875}, {"start": 3190.78, "end": 3191.08, "word": " لها", "probability": 0.62445068359375}, {"start": 3191.08, "end": 3191.56, "word": " شوية", "probability": 0.8470052083333334}, {"start": 3191.56, "end": 3192.18, "word": " نظريات،", "probability": 0.90546875}, {"start": 3192.18, "end": 3192.26, "word": " فيه", "probability": 0.929931640625}, {"start": 3192.26, "end": 3192.36, "word": " لها", "probability": 0.966552734375}, {"start": 3192.36, "end": 3192.62, "word": " شوية", "probability": 0.9744466145833334}, {"start": 3192.62, "end": 3193.5, "word": " rules،", "probability": 0.7744140625}, {"start": 3193.5, "end": 3193.64, "word": " فيه", "probability": 0.953857421875}, {"start": 3193.64, "end": 3193.76, "word": " لها", "probability": 0.945068359375}, {"start": 3193.76, "end": 3194.06, "word": " شوية", "probability": 0.98046875}, {"start": 3194.06, "end": 3194.48, "word": " قواعد", "probability": 0.8736979166666666}, {"start": 3194.48, "end": 3194.58, "word": " في", "probability": 0.93603515625}, {"start": 3194.58, "end": 3195.44, "word": " التعامل،", "probability": 0.8908203125}, {"start": 3195.44, "end": 3196.06, "word": " فبدنا", "probability": 0.9376627604166666}, {"start": 3196.06, "end": 3197.18, "word": " ناخدها", "probability": 0.9835205078125}, {"start": 3197.18, "end": 3197.4, "word": " المرة", "probability": 0.865234375}, {"start": 3197.4, "end": 3197.62, "word": " الجاية", "probability": 0.8211263020833334}, {"start": 3197.62, "end": 3197.72, "word": " ان", "probability": 0.5986328125}, {"start": 3197.72, "end": 3197.84, "word": " شاء", "probability": 0.96728515625}, {"start": 3197.84, "end": 3197.9, "word": " الله", "probability": 0.93798828125}, {"start": 3197.9, "end": 3198.3, "word": " تعالى", "probability": 0.96923828125}, {"start": 3198.3, "end": 3198.8, "word": " و", "probability": 0.83740234375}, {"start": 3198.8, "end": 3199.2, "word": " نكمل", "probability": 0.943359375}, {"start": 3199.2, "end": 3199.74, "word": " موضوعنا", "probability": 0.98974609375}, {"start": 3199.74, "end": 3200.18, "word": " المرة", "probability": 0.9814453125}, {"start": 3200.18, "end": 3200.46, "word": " الجاية", "probability": 0.8147786458333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3202.49625, "duration_after_vad": 3117.489999999985}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..57557a32003709a367bbc34aac7de853ccc9a3ff
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/npyzAF-vFvI_raw.srt
@@ -0,0 +1,2852 @@
+1
+00:00:20,670 --> 00:00:22,770
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:22,770 --> 00:00:24,690
+الأنبياء والمرسلين سيدنا محمد وعلى أهلي وصحابي
+
+3
+00:00:24,690 --> 00:00:27,790
+أجمعين نبدأ اليوم نحاول نخلص الجزئية اللي بدأنا
+
+4
+00:00:27,790 --> 00:00:29,590
+نتكلمنا فيها المرة اللي فاتت اللي هي ال functions
+
+5
+00:00:29,590 --> 00:00:34,330
+وقولنا .. تحدثنا عن تعريف ال functions و بعدين ..
+
+6
+00:00:36,840 --> 00:00:39,440
+اتكلمنا عن أنواع ال functions قلنا فيهم دي نوعين
+
+7
+00:00:39,440 --> 00:00:42,580
+مهمين اللي اتكلمنا عنهم المرة اللي فاتت ال .. ال
+
+8
+00:00:42,580 --> 00:00:47,760
+one-to-one ال one-to-one و ال onto و ال onto ف ال
+
+9
+00:00:47,760 --> 00:00:49,980
+one-to-one و ال onto أخدنا example المرة اللي فاتت
+
+10
+00:00:49,980 --> 00:00:54,200
+عليها خلينا بسرعة نراجع ال function الأولى هنا هذي
+
+11
+00:00:54,200 --> 00:00:58,200
+one-to-one و لا onto او combination يعني اعمل
+
+12
+00:00:58,200 --> 00:01:00,420
+combination one-to-one
+
+13
+00:01:02,470 --> 00:01:07,950
+one to one قلنا إن كل element في ال domain إله
+
+14
+00:01:07,950 --> 00:01:14,530
+output واحد فقط وكل output في ال code main أو في
+
+15
+00:01:14,530 --> 00:01:18,550
+ال range عشان أكون أدق في ال range جاي من pre
+
+16
+00:01:18,550 --> 00:01:24,330
+image واحدة فقط فهنا واضح إن هنا في element جاي من
+
+17
+00:01:24,330 --> 00:01:29,870
+اتنينهذه مش one-to-one طب one-to .. one-to .. إيش
+
+18
+00:01:29,870 --> 00:01:33,210
+كان تعريف ال one-to؟ ال domain .. ال co-domain و
+
+19
+00:01:33,210 --> 00:01:35,830
+ال range نفس ال cardinality .. نفس ال cardinality
+
+20
+00:01:35,830 --> 00:01:39,590
+فإذا الأولى هذه كانت one-to ولكن مش one-to-one طيب
+
+21
+00:01:39,590 --> 00:01:44,990
+التانية one-to-one لأ لأن في عندنا two elements
+
+22
+00:01:44,990 --> 00:01:50,550
+هيوم أخله بالشرط و ال co-domain في عنصر غير موجود
+
+23
+00:01:50,550 --> 00:01:54,690
+في ال range فإذا لا هيك ولا هيك كويس التالتة
+
+24
+00:01:56,690 --> 00:02:01,330
+التنتين one to one و onto الرابع one to one هذه
+
+25
+00:02:01,330 --> 00:02:05,230
+one to one مظبوط ولكن not onto لأن في عندك هاي
+
+26
+00:02:05,230 --> 00:02:10,510
+element فوق موجود هذا خارج الحساب طبعا طيب من
+
+27
+00:02:10,510 --> 00:02:12,650
+التنتين هذول اتكلمنا برضه المرة اللى فاتت على ال
+
+28
+00:02:12,650 --> 00:02:15,110
+bijection ال bijection او ال one to one
+
+29
+00:02:15,110 --> 00:02:17,730
+correspondence او ال bijection او ال reversible
+
+30
+00:02:17,730 --> 00:02:22,380
+invertible وقلناإن هذه بتحقق الشرطين إذا تحقق ال
+
+31
+00:02:22,380 --> 00:02:25,340
+two functions في function واحدة ال two conditions
+
+32
+00:02:25,340 --> 00:02:28,340
+في function واحدة بنقول عنها إيش؟ bijection فإيش
+
+33
+00:02:28,340 --> 00:02:31,740
+بتلزمنا؟ بتلزمنا إن إذا كانت ال function bijection
+
+34
+00:02:31,740 --> 00:02:34,700
+معناته بقدر أجيب لها ال inverse تبعها بنقدر نجيب
+
+35
+00:02:34,700 --> 00:02:37,960
+ال inverse function لها و ال inverse function
+
+36
+00:02:37,960 --> 00:02:41,580
+بتاعتها أكيد بتكون منكتوبة كتالة inverse function
+
+37
+00:02:41,580 --> 00:02:45,840
+أو f of minus to the power minus one from b to a
+
+38
+00:02:45,840 --> 00:02:51,320
+لإن هذه في اتجاه العكسي جاية من b to aبالاتجاه
+
+39
+00:02:51,320 --> 00:02:56,400
+العكسى لأنها ال inverse لاتل اف انفرس ال F فهتكون
+
+40
+00:02:56,400 --> 00:03:00,840
+جاية من ال codomain لل domain بتاعون ال F فأصبحت
+
+41
+00:03:00,840 --> 00:03:04,480
+ال B هي ال domain تبعها وال A هي ال codomain تبعها
+
+42
+00:03:04,480 --> 00:03:08,420
+هي ال codomain تبعها okay وهذا بتكون unique بمعنى
+
+43
+00:03:08,420 --> 00:03:13,400
+أن كل function إذا كانت bijection لها inverse واحد
+
+44
+00:03:13,400 --> 00:03:16,640
+فقط ماتتوقعوش أنه يكون لها أكتر من انفرس واحد فقط
+
+45
+00:03:16,640 --> 00:03:20,570
+كويس؟الاتنين هدولة في بعض اللي هي ال function في
+
+46
+00:03:20,570 --> 00:03:24,050
+ال inverse بحها بيعطونا ال identity وضرب قولنا
+
+47
+00:03:24,050 --> 00:03:27,870
+عليه المرة اللي فاتت هذا اللي هو ايش composition ف
+
+48
+00:03:27,870 --> 00:03:32,850
+F to the power minus one compose F equal to I to I
+
+49
+00:03:32,850 --> 00:03:37,010
+و ال I هذي اللي هي ايش ال identity value او ال
+
+50
+00:03:37,010 --> 00:03:39,530
+identity function identity function هاي ال
+
+51
+00:03:39,530 --> 00:03:44,070
+identity function بنعرفها لأي domain A عساس ان ال
+
+52
+00:03:44,070 --> 00:03:50,990
+identity function I from A to Afrom a to a ليش من
+
+53
+00:03:50,990 --> 00:03:55,450
+a ل a لأن فعليا ال input تبعها هو نفس ال output ال
+
+54
+00:03:55,450 --> 00:04:00,550
+input هو نفس ال output هي غير مؤثرة الأصل إذا كانت
+
+55
+00:04:00,550 --> 00:04:03,730
+ضرب مثلا ال function عملية ضرب المفروض نضرب في
+
+56
+00:04:03,730 --> 00:04:09,190
+واحد إذا كانت جمع بنجمع مع صفر إذا كانت مثلا and
+
+57
+00:04:09,190 --> 00:04:15,230
+بنعمل and مع trueمع true ف ال input اللي بندخله
+
+58
+00:04:15,230 --> 00:04:17,950
+إذا كان true حيضل true و إذا كان false حيضل false
+
+59
+00:04:17,950 --> 00:04:21,650
+فالقصد إن إحنا بنتعامل مع element أو مع function
+
+60
+00:04:21,650 --> 00:04:25,910
+ال input تبحه هو هو هيتلعب هو هو نحن فبنقول من a
+
+61
+00:04:25,910 --> 00:04:34,060
+thبنكتبها I A مع ال set A ل identity لل set A أو
+
+62
+00:04:34,060 --> 00:04:38,380
+بنكتبها واحد بهذا الشكل واحد كويس او واحد ايه one
+
+63
+00:04:38,380 --> 00:04:42,780
+ل ال set A وهذه زي ما قولنا unique function بحيث
+
+64
+00:04:42,780 --> 00:04:47,280
+انه for all elements داخل ال set لكل ال elements
+
+65
+00:04:47,280 --> 00:04:49,400
+داخل ال set A
+
+66
+00:04:51,360 --> 00:04:55,760
+of a بيساوي a فإذا هي function محايدة هي function
+
+67
+00:04:55,760 --> 00:05:00,620
+محايدة ال input هو هو زيه ال output هو هو نفس ال
+
+68
+00:05:00,620 --> 00:05:04,900
+output و احنا يعني اتعلمنا مجموعة functions بتقد
+
+69
+00:05:04,900 --> 00:05:08,600
+نفس الغرض هذا زي لما نقول ال positive او ال
+
+70
+00:05:08,600 --> 00:05:13,790
+plusing او ال adding ال adding مع ال zeroبأثرش ال
+
+71
+00:05:13,790 --> 00:05:18,010
+dotting مع ال one أو ال multiplication with one
+
+72
+00:05:18,010 --> 00:05:24,370
+بأثرش ال and مع ال true بأثرش ال or مع ال false
+
+73
+00:05:24,370 --> 00:05:30,030
+بأثرش ال union مع ال fiveunion مع فعل ماحد ضال نفس
+
+74
+00:05:30,030 --> 00:05:34,010
+الست طيب ال intersection مع ال universe of
+
+75
+00:05:34,010 --> 00:05:39,490
+discourse مع ال U تفرجش كويسة هنلاحظ أنه في جميع
+
+76
+00:05:39,490 --> 00:05:42,970
+الأحوال في جميع الظروف دايما ال identity هي
+
+77
+00:05:42,970 --> 00:05:48,930
+bijective او one to one و onto مع بعض function فهي
+
+78
+00:05:48,930 --> 00:05:53,030
+bijection function او bijective function okay
+
+79
+00:05:54,780 --> 00:05:58,960
+كيف نوضحها كيف نرسم الرسم تبعها اما عن طريق ال
+
+80
+00:05:58,960 --> 00:06:04,340
+Venn diagram بهذا الشكل فهي عندنا ال set A فيها
+
+81
+00:06:04,340 --> 00:06:07,400
+مجموعة ال elements بتاعتها ال elements داخل ال
+
+82
+00:06:07,400 --> 00:06:11,720
+domain كل element under the function هيعطينا نفس
+
+83
+00:06:11,720 --> 00:06:15,360
+ال element فالاتجاه لل function من ال element
+
+84
+00:06:15,360 --> 00:06:19,620
+لنفسه لأن زي ما قلنا identity هيطلع نفس القيمة لل
+
+85
+00:06:19,620 --> 00:06:26,460
+element فهنا ال A1تحت تأثير f هيعطي اي واحد اتنين
+
+86
+00:06:26,460 --> 00:06:33,060
+تحت تأثير f هيعطي اتنين وهكذا اي عنصر تحت تأثير f
+
+87
+00:06:33,060 --> 00:06:39,320
+of a هيعطينا نفس العنصر اللي هو a نفس العنصر بال
+
+88
+00:06:39,320 --> 00:06:46,170
+plot هتكون linearو ال slope تبع ال linear هذا واحد
+
+89
+00:06:46,170 --> 00:06:51,330
+هو عبارة عن line linear ال slope تبعه بواحد عشان
+
+90
+00:06:51,330 --> 00:06:56,650
+اضمن ان اي x هتطلع نفس قيمتها في ال y فإذا x خمسة
+
+91
+00:06:56,650 --> 00:07:01,030
+ال y هتطلع خمسة اللي هي ال f of x فهنا ال x وهذا
+
+92
+00:07:01,030 --> 00:07:07,670
+ال y اللي هي تساوي f of x فدائما f of x بتساوي x
+
+93
+00:07:07,670 --> 00:07:10,930
+دائما f of x بتساوي x
+
+94
+00:07:32,550 --> 00:07:36,050
+عشان نرسم ال graphs of functions احنا بدنا نوقعه
+
+95
+00:07:36,050 --> 00:07:38,530
+بمجموعة نقاط زي ال plot اللي توقعنا رسميا و كيف
+
+96
+00:07:38,530 --> 00:07:43,640
+بنعمله فعليابهذا الشكل إذا كان عندكم X و F of X
+
+97
+00:07:43,640 --> 00:07:50,580
+يلي هي Y انتوا عادة ايش بتسوواه بتحطوا نقاط عند ال
+
+98
+00:07:50,580 --> 00:07:57,620
+X عندكوا F of X معرفة بطريقة معينة بتفرضوا قيم ل X
+
+99
+00:07:57,620 --> 00:08:03,220
+صحيح قيمة مثلا واحد بتعودوا هنا بتطلعلكوا رقم
+
+100
+00:08:03,220 --> 00:08:07,740
+الرقم هذا بصير هو قيمة Y المقابلة للواحد فبتحطوها
+
+101
+00:08:07,740 --> 00:08:13,700
+نقطةقيمة تانية تحطوا كمان نقطة تالتة كمان نقطة
+
+102
+00:08:13,700 --> 00:08:17,880
+رابعة كمان نقطة خمسة كمان نقطة فبتواصلوا بينهم
+
+103
+00:08:17,880 --> 00:08:21,820
+عشان يطلع معاكمشكل ال function بتطلع معاكم في
+
+104
+00:08:21,820 --> 00:08:24,260
+الآخر شكل ال function بتقول اه والله هى ال
+
+105
+00:08:24,260 --> 00:08:26,680
+function هده linear ال function هده تربيعية ال
+
+106
+00:08:26,680 --> 00:08:28,740
+function هده تقعبية اه هد شبيهة بال sinusoidal هد
+
+107
+00:08:28,740 --> 00:08:31,840
+شبيهة بال .. تقدروا لو قولنا مثلا طلعوا نقاط
+
+108
+00:08:31,840 --> 00:08:34,000
+بالشكل هد هتقولوا اه والله هد linear واضح ان احنا
+
+109
+00:08:34,000 --> 00:08:38,840
+بنتكلم عن خط الخط هد بيضل عملية انه ممكن يكون ال
+
+110
+00:08:38,840 --> 00:08:41,660
+identity مثلا طب كيف افحص ان هي identity ولا لأ
+
+111
+00:08:41,660 --> 00:08:43,660
+بال slope بال slope تبحث اذا كان واحد هي ال
+
+112
+00:08:43,660 --> 00:08:47,650
+identity مش واحد لأ خلاص هد function مختلفةتمام؟
+
+113
+00:08:47,650 --> 00:08:52,390
+Identity ممكن تكون مضروبة بس ب factor معين كويس
+
+114
+00:08:52,390 --> 00:08:56,590
+معنى ذلك خلينا نرجع لمفهوم كيف رسمنا الرسم هذا
+
+115
+00:08:56,590 --> 00:09:02,030
+رسمناه من نقطة بداية الشغل كانت نقطة النقطة إيش
+
+116
+00:09:02,030 --> 00:09:10,990
+تمثل؟ تمثل X و F of X صحيح؟
+
+117
+00:09:10,990 --> 00:09:18,020
+هي Xو F of X بتاعتها فمثلناها بزوج مرتب عبارة عن
+
+118
+00:09:18,020 --> 00:09:24,340
+ال input وال F of X اللي هو ال output اللي هو ال
+
+119
+00:09:24,340 --> 00:09:30,660
+output طبعا okay فبنرتبها ك A و F of Aإذا كنا
+
+120
+00:09:30,660 --> 00:09:34,900
+معرفين الـ function على أساس أنها من A to B
+
+121
+00:09:34,900 --> 00:09:41,400
+فبنعرفها كزوج مرتب A و F of A و A belong to set A
+
+122
+00:09:41,400 --> 00:09:45,060
+ال domain فاحنا بنختار في الآخر قيم من ال domain
+
+123
+00:09:45,060 --> 00:09:48,060
+القيم بتاعتنا بنختارها من من؟ من ال domain مش حاجة
+
+124
+00:09:48,060 --> 00:09:52,600
+ال domain تبقى من 0 ل10 أختار 11 أو نختار minus
+
+125
+00:09:52,600 --> 00:09:56,810
+one نختار قيمنا من مين؟من ال domain و بتحدد
+
+126
+00:09:56,810 --> 00:10:01,790
+النقطتنا .. النقطتنا زي ما قولنا في الآخر a و f of
+
+127
+00:10:01,790 --> 00:10:06,550
+a قيمة ال function بتاعتها او x و y حسب ما انتوا
+
+128
+00:10:06,550 --> 00:10:10,250
+كنتوا دارسين ال .. ال .. ال independent variable x
+
+129
+00:10:10,250 --> 00:10:13,890
+و independent variable y فهي هتكون عبارة عن زوج من
+
+130
+00:10:13,890 --> 00:10:20,220
+x و yOkay لما نتكلم عن الأرقام بنمثلها بأرقام زي
+
+131
+00:10:20,220 --> 00:10:24,520
+ما قلنا انتوا بتستعملوا ال X و Y بتستعملوا عادة X
+
+132
+00:10:24,520 --> 00:10:28,560
+و Y زي الشكل اللي احنا رسمنا بهذا الشكل هي X و Y
+
+133
+00:10:28,560 --> 00:10:35,420
+ليش؟ لأن Y هي نفسها F of X فبنحددها كنقطة على ال
+
+134
+00:10:35,420 --> 00:10:38,660
+plane تبعنا عشان نحط نقطة و بعدين نجرب نقطة تانية
+
+135
+00:10:38,660 --> 00:10:42,390
+ل X نقطة تالتة نقطة رابعة نقطة خمسة و نوصلبنوصلهم
+
+136
+00:10:42,390 --> 00:10:46,430
+بعض .. بنوصلهم بعض في الآخر مجموعة النقاط هدولة
+
+137
+00:10:46,430 --> 00:10:51,130
+ايش صاروا؟ صاروا set of points صار لانكوا مجموعة
+
+138
+00:10:51,130 --> 00:10:54,730
+نقاط مجموعة النقاط هدى صارت set of points فهدولة
+
+139
+00:10:54,730 --> 00:10:58,390
+اللى بيعطونا relation between y و x بيعطونا
+
+140
+00:10:58,390 --> 00:11:03,590
+relation between y و x على أساس ان هم set of
+
+141
+00:11:03,590 --> 00:11:05,550
+points okay
+
+142
+00:11:07,200 --> 00:11:11,000
+من اللى فهمناها لوجود فى عملية الرسم و ال function
+
+143
+00:11:11,000 --> 00:11:15,500
+نفسها نتكلم عن موضوع ال couple of key functions
+
+144
+00:11:15,500 --> 00:11:22,040
+هنا بنعمل عملية تقريب لأقرب integers لأقرب integer
+
+145
+00:11:22,040 --> 00:11:26,740
+number طيب أقرب integer الأعلى ولا الأقل فهنا إما
+
+146
+00:11:26,740 --> 00:11:35,130
+بنعمل floorأو ceiling of X ال floor نرسمها بهذا
+
+147
+00:11:35,130 --> 00:11:39,570
+الشكل في عندنا floor واضحة الأرضية واضحة شمال
+
+148
+00:11:39,570 --> 00:11:44,740
+ويمين لل X ال ceiling لأ الأرضية واضحة للصقففعنا
+
+149
+00:11:44,740 --> 00:11:47,900
+هنا الأرضية و هنا فينا الصقف فانا النقطة اللى
+
+150
+00:11:47,900 --> 00:11:51,180
+موجودة داخل الغرفة المعلجة داخل الغرفة بتقربها لل
+
+151
+00:11:51,180 --> 00:11:54,400
+floor ولا بتجربها للسجف بدنا نسحب الخيط طبعا
+
+152
+00:11:54,400 --> 00:11:56,580
+هنوصلها للسجف ولا بدنا نقطع الخيط و ننزلها لل
+
+153
+00:11:56,580 --> 00:12:00,560
+floor هاي المعنى فانا لما بقول floor معناته لأ
+
+154
+00:12:00,560 --> 00:12:05,600
+جربتيها لإيش لل floor تمامأحنا هلوجد في الدور
+
+155
+00:12:05,600 --> 00:12:09,600
+الخامس صحيح دور الخامس المفروض أنه معناته احنا ال
+
+156
+00:12:09,600 --> 00:12:13,600
+level تبع الأرضية هذا اللي هو رقم أربعة رقم أربعة
+
+157
+00:12:13,600 --> 00:12:17,900
+رقم أربعة صحيح احنا بنبدأ تحت بواحد فهذا رقم أربعة
+
+158
+00:12:17,900 --> 00:12:21,200
+لما بداش أقرب أعمل floor هقول أن النقطة هذي
+
+159
+00:12:21,200 --> 00:12:24,810
+قربناها لاربعةبالنسبة للأرض اللى برا بالنسبة
+
+160
+00:12:24,810 --> 00:12:27,230
+للشباك اللى طلعنا هنقول ان احنا قربنا النقطة لمين؟
+
+161
+00:12:27,230 --> 00:12:31,330
+لأربعة طب لما عمل ceiling خربناها للمستوى خمسة
+
+162
+00:12:31,330 --> 00:12:35,150
+بنقربها هنا للمستوى خمسة معنى ذلك ان النقطة كانت
+
+163
+00:12:35,150 --> 00:12:40,370
+between أربعة وخمسة كانت real number من أربعة
+
+164
+00:12:40,370 --> 00:12:44,550
+لخمسة فاحنا قربناها ل integer بس احنا حددنا ال
+
+165
+00:12:44,550 --> 00:12:49,760
+integer هذا هو floorأو ceiling هل هو ال floor او
+
+166
+00:12:49,760 --> 00:12:52,360
+ال ceiling طيب لما نتكلم عن ال floor هو فعليا ال
+
+167
+00:12:52,360 --> 00:12:58,000
+floor بقل القيمتها يعني بس هي عبارة عن ايش هي ال
+
+168
+00:12:58,000 --> 00:13:05,580
+greatest او ال largest integer اقل من X اكبر
+
+169
+00:13:05,580 --> 00:13:11,420
+integer اقل من X لما نقول تلاتة و نص ماقدرش اقربها
+
+170
+00:13:11,420 --> 00:13:15,400
+لاثنين تلاتة بالظبط تلاتة ايش اللي بميز التلاتة ان
+
+171
+00:13:15,400 --> 00:13:20,240
+هي اكبر integerلحظة هى اكبر انتجر من كل ال
+
+172
+00:13:20,240 --> 00:13:27,660
+integers اللى هنا اقل من ال X اكبر انتجر موجود اقل
+
+173
+00:13:27,660 --> 00:13:31,000
+من مين من X هى التعريف طيب نفس الكلام فى ceiling
+
+174
+00:13:31,000 --> 00:13:37,470
+هى smallest انتجر لو نجربها الاربعةطب ليش مجرد
+
+175
+00:13:37,470 --> 00:13:41,810
+التاسعة للخمسة للسبعة للتسعة كل هدول integers أقل
+
+176
+00:13:41,810 --> 00:13:45,650
+integer فعشان هي كلمة أقل ماتلحبطكمش احنا جاعدين
+
+177
+00:13:45,650 --> 00:13:48,450
+بنكبر القيمة بس مش معناه ان احنا في تعريف smallest
+
+178
+00:13:48,450 --> 00:13:54,370
+يعني بنجلل للا هي أقل integer أكبر من ال X فأقل
+
+179
+00:13:54,370 --> 00:13:57,990
+integer أكبر من اللي هو ال X الأربعة فتقرر ال
+
+180
+00:13:57,990 --> 00:14:03,590
+seeing تبعتها لمين لأربعة okay visualization
+
+181
+00:14:04,930 --> 00:14:12,890
+للكلام اللي قلناه example لمجموعة fractions نعمل
+
+182
+00:14:12,890 --> 00:14:17,230
+لها floor و ceiling هكون فينا مثلا ال one point
+
+183
+00:14:17,230 --> 00:14:21,830
+six هذا بدنا نعملها ceiling هتروح لمين للاتنين
+
+184
+00:14:21,830 --> 00:14:26,170
+بدنا نعملها floor للواحد طيب هنعكس ناخد قيمة
+
+185
+00:14:26,170 --> 00:14:31,550
+negative خدوا بالكوالما أعمل لهذه الواجهة ceiling
+
+186
+00:14:31,550 --> 00:14:36,690
+سالف واحد .. سالف واحد .. سالف واحد .. سالف واحد
+
+187
+00:14:36,690 --> 00:14:41,810
+.. سالف واحد .. سالف واحد .. سالف واحد .. سالف
+
+188
+00:14:41,810 --> 00:14:43,450
+واحد .. سالف واحد .. سالف واحد .. سالف واحد ..
+
+189
+00:14:43,450 --> 00:14:43,570
+سالف واحد .. سالف واحد .. سالف واحد .. سالف واحد
+
+190
+00:14:43,570 --> 00:14:44,010
+.. سالف واحد .. سالف واحد .. سالف واحد .. سالف
+
+191
+00:14:44,010 --> 00:14:45,770
+واحد .. سالف واحد .. سالف واحد .. سالف واحد ..
+
+192
+00:14:45,770 --> 00:14:45,770
+سالف واحد .. سالف واحد .. سالف واحد .. سالف واحد
+
+193
+00:14:45,770 --> 00:14:45,770
+.. سالف واحد .. سالف واحد .. سالف واحد .. سالف
+
+194
+00:14:45,770 --> 00:14:45,770
+واحد .. سالف واحد .. سالف واحد .. سالف واحد ..
+
+195
+00:14:45,770 --> 00:14:57,030
+سالف واحد .. سالف واحد ..
+
+196
+00:14:57,030 --> 00:15:01,130
+سبدنا نشغل على 1.6 ما هي نفسها هتطلع يعني القيم
+
+197
+00:15:01,130 --> 00:15:06,590
+هتظل نفسها لو قلنا غيرناها 1.6 1.6 1.6 تمام فهنا
+
+198
+00:15:06,590 --> 00:15:10,630
+كأن أنا عملت ceiling ولا floor هنا اي واحدة منهم
+
+199
+00:15:10,630 --> 00:15:14,970
+نشغل على ال ceiling و بنعمى بالكلام هي minus x
+
+200
+00:15:14,970 --> 00:15:19,630
+صحيح؟ معناه ان ال x بتاعتنا معرفة على اساس ان هي 1
+
+201
+00:15:19,630 --> 00:15:28,020
+.6 لو x 1.6هذه ايش طلعت بتساوي؟ سالب واحد طيب نفس
+
+202
+00:15:28,020 --> 00:15:35,580
+الكلام لو قلنا هي نفسها ceiling minus ceiling x
+
+203
+00:15:35,580 --> 00:15:41,400
+طلعت سالب اتنين سالب اتنين طب سالب واحد لا تساوي
+
+204
+00:15:41,400 --> 00:15:45,420
+سالب اتنين الكلام نفسه برضه بتقدر تطبقه على ال
+
+205
+00:15:45,420 --> 00:15:48,950
+ceiling على ال floorأحنا طبقناه هنا على ال ceiling
+
+206
+00:15:48,950 --> 00:15:53,610
+بتقدر تطبقه برضه على ال floor فواضح أنه ال minus
+
+207
+00:15:53,610 --> 00:15:58,390
+بقدرش أتعامل معاها على أساس أنه بدخلها داخل القوس
+
+208
+00:15:58,390 --> 00:16:02,330
+و خلاص هذه مش أقوس هذه عملنا احنا فيها تقريب و لما
+
+209
+00:16:02,330 --> 00:16:05,670
+أعكس .. لما أعكس الإشارة معناته أنا جلبت التقريب
+
+210
+00:16:05,670 --> 00:16:08,510
+كله المفروض بدل ما أعمل ceiling كان المفروض يعملنا
+
+211
+00:16:08,510 --> 00:16:12,890
+floor من الأساس فواضح أنه هذه لا يسووا بعض في
+
+212
+00:16:12,890 --> 00:16:18,420
+الحلقة طيب ملاحظة تانيةceiling x إذا طلعت بتساوي
+
+213
+00:16:18,420 --> 00:16:23,200
+floor x معناته انت فعليا عند integer معناته x ده
+
+214
+00:16:23,200 --> 00:16:26,040
+هو أساسا بحد ذاته integer ال ceiling تبعه بساوي ال
+
+215
+00:16:26,040 --> 00:16:33,500
+floor تبعه بمشي الحال بمشي الحال كويس ال plot أو
+
+216
+00:16:33,500 --> 00:16:38,260
+بدنا نبدأ نرسم نعمل plots ل ال floor و ال ceiling
+
+217
+00:16:38,260 --> 00:16:45,080
+كيف نرسمهم floor و ceiling بدنا ناخد بالناالنقاط
+
+218
+00:16:45,080 --> 00:16:49,820
+نفس احنا كيف عرفناها توي كيف عرفنا النقطة عرفنا ال
+
+219
+00:16:49,820 --> 00:16:54,800
+point بتاعتنا على اساس ان هي لحظه x و f of x هذي f
+
+220
+00:16:54,800 --> 00:17:05,520
+of x ال zero هذي x و f of x x و f of x اللي هي ال
+
+221
+00:17:05,520 --> 00:17:09,240
+y بالضبط ال y طيب ال function بتاعتنا اللي بتطلعنا
+
+222
+00:17:09,240 --> 00:17:14,510
+ال y او ال f of x هي عبارة عن floorما دام حددناها
+
+223
+00:17:14,510 --> 00:17:20,790
+zero ال output zero هذا يتفق مع مجموعة a's انما
+
+224
+00:17:20,790 --> 00:17:23,650
+a's هدولة اللي بيتفق معاهم ان ده output zero اللي
+
+225
+00:17:23,650 --> 00:17:28,590
+من zero لأقل من واحد تمام لأقل شوية من واحد جدش
+
+226
+00:17:28,590 --> 00:17:33,510
+أقل من واحدأقل بكتير بكتير يعني احنا عشان هيك مش
+
+227
+00:17:33,510 --> 00:17:36,570
+عارفين بالظبط جدش القيمة هي delta delta أكبر من
+
+228
+00:17:36,570 --> 00:17:41,390
+صفر بس قليلة جدا جدا جدا طيب عشان نحددها جدش بده
+
+229
+00:17:41,390 --> 00:17:46,950
+أحددها أنا مش عارف أحددها نكتبها للواحد ولكن
+
+230
+00:17:46,950 --> 00:17:54,910
+الواحد غير مشمولمفتوحة فبنعملها هذه circle بس open
+
+231
+00:17:54,910 --> 00:17:58,470
+circle فبنكتبها open circle للواحد و للواحد غير
+
+232
+00:17:58,470 --> 00:18:03,450
+مشمول لو عملناها solid circle بتصير لأ مشمولة فها
+
+233
+00:18:03,450 --> 00:18:06,770
+بدنا يعني كل الموضوع هذا بدنا نأكد على حكاية اللي
+
+234
+00:18:06,770 --> 00:18:12,230
+هي ال open و ال solid كويسة فمعنى ذلك ال function
+
+235
+00:18:12,230 --> 00:18:16,650
+هذه او ال points هذه صحيحة لكل الفترة اللي من a
+
+236
+00:18:16,650 --> 00:18:23,110
+أكبر من أو تساويصفر و a أقل منه و لا تساوي
+
+237
+00:18:23,110 --> 00:18:28,830
+ماحطيناش يساوي و لا تساوي واحد و الواحد لأ but not
+
+238
+00:18:28,830 --> 00:18:35,090
+for a ايه ايه equal to ليش لأن a بتساوي واحد صارت
+
+239
+00:18:35,090 --> 00:18:38,710
+مشمولة مع نقطة تانية مع function تانية ال output
+
+240
+00:18:38,710 --> 00:18:45,390
+تبح بواحدال output تبعها واحد ف a وال output واحد
+
+241
+00:18:45,390 --> 00:18:49,730
+بتشمل معها a بتساوي واحد بتشمل معها a بتساوي واحد
+
+242
+00:18:49,730 --> 00:18:54,830
+فحناخد بالنا ان هنا بتصير ال واحد هذه open set هنا
+
+243
+00:18:54,830 --> 00:18:57,290
+بنتكلم عن open sets open sets اللي هي معناته عند
+
+244
+00:18:57,290 --> 00:19:00,310
+نقطة معينة غير مشمولة النقطة بس انا لازم اعرفها
+
+245
+00:19:00,310 --> 00:19:03,510
+بالنقطة لان انا مش عارف جدش اقل من النقطة اقل من
+
+246
+00:19:03,510 --> 00:19:08,620
+النقطة بقيمة كتير صغيرة يعني لو واحد منكم كتب0
+
+247
+00:19:08,620 --> 00:19:14,900
+.99999 المفروض دلته infinity طبعا مش منطقي ان احنا
+
+248
+00:19:14,900 --> 00:19:17,940
+نعملها infinity فلأ بنقول واحد بس بدنا نحدد ان
+
+249
+00:19:17,940 --> 00:19:22,040
+الواحد نفسه كقيمة واحد غير مشمول كقيمة غير مشمول
+
+250
+00:19:22,040 --> 00:19:27,780
+فهذه بنشملها او بنعملها circle او open circle
+
+251
+00:19:27,780 --> 00:19:34,210
+نكتبها شكلها زي dot او circle بس بتكونو ال solid
+
+252
+00:19:34,210 --> 00:19:37,490
+زي ما قلنا إذا كانت مشمولة في ال curve خلّيني
+
+253
+00:19:37,490 --> 00:19:43,170
+أنطبخ الكلام ده على example عشان الأمور توضح أكتر
+
+254
+00:19:43,170 --> 00:19:49,790
+معناه لو مقلوب نعمل plot of graph of function f of
+
+255
+00:19:49,790 --> 00:19:56,390
+x equal to floor x over 3 x over 3 وهنا بيعطيكوا
+
+256
+00:19:56,390 --> 00:20:02,800
+ال x على أساس إن هي ال integer numbersinteger
+
+257
+00:20:02,800 --> 00:20:05,840
+numbers مثلا أو حتى fractions مش مشكلة يعني ممكن
+
+258
+00:20:05,840 --> 00:20:10,000
+تقولوا R أساسا من minus infinity to infinity نبدأ
+
+259
+00:20:10,000 --> 00:20:13,640
+مثلا ناخد الصفر خلينا نبدأ من الصفر عشان نوضح لكم
+
+260
+00:20:13,640 --> 00:20:21,420
+لو أخدنا الصفر نفسها صفر على تلاتة صفر floor zero
+
+261
+00:20:21,420 --> 00:20:24,440
+خلاص النقطة هي مكانها و solid لأنها مشمولة في
+
+262
+00:20:24,440 --> 00:20:27,740
+المجموعة هذه مشمولة في المجموعة هذه بنحطها صفر هنا
+
+263
+00:20:27,740 --> 00:20:36,740
+كويس الواحدتلت واحد تصير تلت floor تلت زيرو برضه
+
+264
+00:20:36,740 --> 00:20:44,380
+فإذا هنا نفس الكلام هتصير عندك واحد وزيرو طيب هنا
+
+265
+00:20:44,380 --> 00:20:52,060
+اتنين وزيرو ال input اتنين ال output زيرو طيب هنا
+
+266
+00:20:52,060 --> 00:20:59,500
+عند التلاتة واحد floor الواحدواحد بحطه هنا open و
+
+267
+00:20:59,500 --> 00:21:04,100
+فوق هنا بحط عند الواحد solid نفسها عندها نفسها هاي
+
+268
+00:21:04,100 --> 00:21:08,020
+تمام
+
+269
+00:21:08,020 --> 00:21:12,720
+هاي بهذا الشكل طيب هيك صارنا متفقين حتى على أساس
+
+270
+00:21:12,720 --> 00:21:17,060
+أن هذه function لأنه مش معقول نفس ال input يكون له
+
+271
+00:21:17,060 --> 00:21:21,170
+قيمتين أو two outputs صحيح؟أحنا متفقين على كلام
+
+272
+00:21:21,170 --> 00:21:24,030
+هذا بنقول إن هي مش function من أصله ولكن هنا لأ
+
+273
+00:21:24,030 --> 00:21:27,570
+احنا متفقين على الموضوع هذا من عند الواحد بالضبط
+
+274
+00:21:27,570 --> 00:21:33,290
+صرنا مع ال output one كويس عند التلاتة عند الستة
+
+275
+00:21:33,290 --> 00:21:38,990
+عفوا عند الستة بتصير هنا اتنين الستة غير مشمولة في
+
+276
+00:21:38,990 --> 00:21:43,630
+في ال line هذا غير مشمولة بس أقل من الستة بأقل
+
+277
+00:21:43,630 --> 00:21:49,620
+قيمة ممكنة صارت مشمولة مع الواحدالستة تحديدًا لأ
+
+278
+00:21:49,620 --> 00:21:52,820
+صارت مشمولة مع الإتنين، ستة تحديدًا مشمولة مع
+
+279
+00:21:52,820 --> 00:21:56,780
+الإتنين، فهنا solid، هنا open، الكلام برضه مرة
+
+280
+00:21:56,780 --> 00:22:05,350
+عليكم أتوقع في المجموعات في ال open setsOkay فضليه
+
+281
+00:22:32,330 --> 00:22:36,470
+ال function نفسها حسب ال function نفسها إذا كانت
+
+282
+00:22:36,470 --> 00:22:41,790
+ceiling بده ينعكسه ال solid و ال open هنا هدول
+
+283
+00:22:41,790 --> 00:22:45,970
+اتنين تبدو مياشي يتغيروا معناها okay هاي كانت
+
+284
+00:22:45,970 --> 00:22:50,130
+الجزئية اللي كانت ضيلالنا من جزء ال function عشان
+
+285
+00:22:50,130 --> 00:22:59,960
+نبدأ في موضوعنا الرسمية اليوماللي هو استكمالا كان
+
+286
+00:22:59,960 --> 00:23:02,940
+الموضوع ال sets احنا اتكلمنا في ال sets سابقا
+
+287
+00:23:02,940 --> 00:23:08,320
+اتكلمنا عن ال set و اعرجنا شوية و احنا بنحكي عن ال
+
+288
+00:23:08,320 --> 00:23:12,120
+set على ال sequence و قولنا ان ال sequence ايش
+
+289
+00:23:12,120 --> 00:23:16,740
+اللي بميزه عن ال set ترتيب ترتيب بالضبط فال
+
+290
+00:23:16,740 --> 00:23:20,180
+sequence احنا ملزمين بالترتيب sequence احنا ملزمين
+
+291
+00:23:20,180 --> 00:23:23,680
+بترتيب ال elements بتاعتنا ملزمين بترتيب ال
+
+292
+00:23:23,680 --> 00:23:27,740
+elements بتاعتنا على اساسفي ال set أنا مافرجش
+
+293
+00:23:27,740 --> 00:23:30,900
+معايا ال elements كيف ترتيبها كل اللي بهم انه
+
+294
+00:23:30,900 --> 00:23:35,880
+مايكونش فيه تكرار لل elements صحيح فكل التكرارات
+
+295
+00:23:35,880 --> 00:23:39,260
+تنشل من ال element في ال .. في ال sets و بنعود
+
+296
+00:23:39,260 --> 00:23:44,620
+عنها او بنكتبها داخل ال .. ال curly بتاعتها ال
+
+297
+00:23:44,620 --> 00:23:49,680
+curly ال braces بتاعتها قيم unique values كل قيمة
+
+298
+00:23:49,680 --> 00:23:53,140
+لحالها بنكتبها مافيش تكرار لها في ال sequence لأ
+
+299
+00:23:53,140 --> 00:23:58,090
+في ال sequence انا مهتم جدا بال ..الترتيب وما ده
+
+300
+00:23:58,090 --> 00:24:02,930
+مهتم بالترتيب مش هيفرج معايا التكرار بمعنى انه
+
+301
+00:24:02,930 --> 00:24:05,930
+التكرار بنسيبه زي ما هو تكرار ليش؟ لأنه مرتبط
+
+302
+00:24:05,930 --> 00:24:10,190
+بالترتيب وما ده مرتبط بالترتيب بقدر برضه ال
+
+303
+00:24:10,190 --> 00:24:13,290
+sequence ده يتعامل معاها as a function احنا لسه
+
+304
+00:24:13,290 --> 00:24:16,390
+بنحكي في ال function كلنا as a function معنى ذلك
+
+305
+00:24:16,390 --> 00:24:24,230
+انه هتكون function في n الشي n هدى ال location هدى
+
+306
+00:24:24,230 --> 00:24:27,470
+ايش ال locationالمكان اللي أنا موجود فيه داخل ال
+
+307
+00:24:27,470 --> 00:24:31,230
+sequence في ال element الأول ولا التاني ولا التالت
+
+308
+00:24:31,230 --> 00:24:36,230
+ولا الرابع ولا الخامس هذا بتساوي A M ال element
+
+309
+00:24:36,230 --> 00:24:40,790
+اللي موجود في ال location M جدش قيمته فممكن نعبر
+
+310
+00:24:40,790 --> 00:24:45,650
+عنها بهذا الشكل نقول ان هي function ايش قيم ال
+
+311
+00:24:45,650 --> 00:24:51,370
+elements داخلها كل element هو ناتج function في ال
+
+312
+00:24:51,370 --> 00:24:54,400
+location تبع ال elementفي ال location تبع ال
+
+313
+00:24:54,400 --> 00:24:57,260
+elements مدام احنا من الأساس حددنا ان هي ordered
+
+314
+00:24:57,260 --> 00:25:01,880
+okay sequence مجموعة أرقام مرتبة و discrete
+
+315
+00:25:01,880 --> 00:25:07,300
+discrete بمعنى انه ال location الأول التاني مافيش
+
+316
+00:25:07,300 --> 00:25:09,840
+ال location اتنين و نص هو يا ال location الأول يا
+
+317
+00:25:09,840 --> 00:25:12,540
+التاني مافيش ال location واحد و نص فاحنا بنتكلم عن
+
+318
+00:25:12,540 --> 00:25:19,220
+elements هي discrete objects ممكن تتعامل مع ..
+
+319
+00:25:19,220 --> 00:25:23,600
+ماتكونش أرقام ماتكون objects أحيانا كويسةفمجموعة
+
+320
+00:25:23,600 --> 00:25:27,980
+elements اللي بيحددها أو اللي بنقدر نعرف فيه ال
+
+321
+00:25:27,980 --> 00:25:31,580
+element هذا ال location تبعها حسب ال location
+
+322
+00:25:31,580 --> 00:25:34,320
+فبنقول والله ال sequence الفلانية ال element
+
+323
+00:25:34,320 --> 00:25:37,280
+التالت تبعها قيمته كذا هذا دائما هنكون قيمته كذا
+
+324
+00:25:37,280 --> 00:25:41,860
+دائما مدام أنا عرفت ال sequence الفلانية معناته
+
+325
+00:25:41,860 --> 00:25:44,400
+فيها تعريف ال sequence هذه ممكن نقول ال sequence
+
+326
+00:25:44,400 --> 00:25:48,000
+هذه اللي هي الأرقام الزوجية مثلا لأكبر من صفر
+
+327
+00:25:49,490 --> 00:25:52,270
+الأرقام الزوجية اللي أكبر من صفر دائما أول element
+
+328
+00:25:52,270 --> 00:25:57,010
+فيها إيش؟ إتنين هل ممكن تقولوا لأي واحد الأرقام
+
+329
+00:25:57,010 --> 00:26:00,210
+الزوجية اللي أكبر من صفر يجي يقولكوا الأربعة؟ لا
+
+330
+00:26:00,210 --> 00:26:05,130
+يمكن فإنتوا هنا بتتكلموا عن sequence دائما الترتيب
+
+331
+00:26:05,130 --> 00:26:08,950
+تبعها ثابت بس بدكوا تعرفوه مسبقا، تعرفوه طريقة
+
+332
+00:26:08,950 --> 00:26:13,080
+صحيحة مسبقافبنتكلم عن sequence of discrete
+
+333
+00:26:13,080 --> 00:26:18,980
+structure used to represent an ordered list احنا
+
+334
+00:26:18,980 --> 00:26:22,500
+بنستعمله عشان نعرف أو نعمل تمثيل لإيش ل sequence
+
+335
+00:26:22,500 --> 00:26:27,920
+مرتب ل sequence أو قائمة مرتبة for example one two
+
+336
+00:26:27,920 --> 00:26:33,560
+three five eight هدى sequence بتقدر تعرف الرقم
+
+337
+00:26:33,560 --> 00:26:39,220
+اللى بعده؟كويس هذه هتكون .. هتكون شغلنا شطرتنا
+
+338
+00:26:39,220 --> 00:26:41,680
+bagel course .. في bagel course طبعا اليوم احنا بس
+
+339
+00:26:41,680 --> 00:26:44,780
+.. شغلنا هنتعرف بس انه ايش ال sequence يعني ما
+
+340
+00:26:44,780 --> 00:26:48,500
+معنى ال sequence في ال chapters اللي جاية هنقول
+
+341
+00:26:48,500 --> 00:26:51,080
+انه لأ عندنا sequence معين او series معينة ..
+
+342
+00:26:51,080 --> 00:26:54,340
+series معينة بدنا نعرف ال elements اللي جاية عشان
+
+343
+00:26:54,340 --> 00:26:56,300
+تعرفوا ال elements .. هذا طبعا في .. في معظم
+
+344
+00:26:56,300 --> 00:26:58,000
+امتحانات الذكاء العقلي و الامور اللي زي ذات
+
+345
+00:26:58,000 --> 00:27:01,560
+بتلاقوا حاجة زي هي أسئلة بهذا الشكل .. كويس هذه
+
+346
+00:27:01,560 --> 00:27:04,830
+عشان نجيبها هنتكلم عنها بس لاحقافيها chapter ..
+
+347
+00:27:04,830 --> 00:27:08,790
+chapter جاي، هنتكلم فيه ونقولكوا كيف نجيب الأرقام
+
+348
+00:27:08,790 --> 00:27:10,670
+اللي بعدها طب عشان أجيب الأرقام اللي بعدها أنا
+
+349
+00:27:10,670 --> 00:27:16,610
+محتاج formula إلها، محتاج المعادلة تعتها تلتاش،
+
+350
+00:27:16,610 --> 00:27:19,970
+هاي ناس .. البنات عرفوها هاي .. هاي البنات عرفوها
+
+351
+00:27:19,970 --> 00:27:24,490
+تلتاش، اتنين و تلاتة، خمسة، خمسة و تلتة، تمانية،
+
+352
+00:27:24,490 --> 00:27:27,490
+تمانية و تمانية و خمسة، تلتاش، تلتاش و تمانية و
+
+353
+00:27:27,490 --> 00:27:32,540
+واحد و عشرينهذه fabinacci series بيسموها عالم
+
+354
+00:27:32,540 --> 00:27:35,520
+إيطالي هنتكلم عنه لاحقا فهذه مشهورة جدا من ال
+
+355
+00:27:35,520 --> 00:27:39,440
+sequence المشهورة جدا فهي واحدة من ال series او ال
+
+356
+00:27:39,440 --> 00:27:42,360
+sequence اللي انتوا ممكن تتعاملوا معها و بتجيكوا
+
+357
+00:27:42,360 --> 00:27:45,740
+هي في أسئلة ال IQ اللي هي الذكاء العقلي و الأمور
+
+358
+00:27:45,740 --> 00:27:48,000
+هذه اللي بتشوفوها على ال net و بتحضروها يمكن
+
+359
+00:27:48,000 --> 00:27:51,360
+تشاركتوا فيها كمان عشان تقول والله اه وين انا
+
+360
+00:27:51,360 --> 00:27:56,080
+موجود في سلم الأذكياءتمام هى فى أنكوا مثلا term
+
+361
+00:27:56,080 --> 00:27:59,000
+تانى أو ممكن نقوله بهذا الشكل ال sequence نعرفه 1
+
+362
+00:27:59,000 --> 00:28:05,820
+3 9 27 81 و لحظه نعرف تلاتة ضبار n و بعدين
+
+363
+00:28:05,820 --> 00:28:12,660
+ellipses infinite sequence لا نهائية خلاص هذه
+
+364
+00:28:12,660 --> 00:28:17,320
+مستمرة فمجرد عملت تلت نقاط أنا عارف ان هي مستمرة
+
+365
+00:28:17,320 --> 00:28:21,520
+عارفين ان هي مستمرة طيب هى دى هو يعطينى هى
+
+366
+00:28:21,520 --> 00:28:24,800
+المعادلة التي عتهابس أحيانا ممكن ماعطيناش إياها
+
+367
+00:28:24,800 --> 00:28:27,200
+ويقولنا اعطوني المعادلة او قولولي إيش الرقم اللي
+
+368
+00:28:27,200 --> 00:28:31,360
+ورا فهذه انتوا بتصوروا لاحقا هناخدها مش اليوم
+
+369
+00:28:31,360 --> 00:28:34,800
+لاحقا هناخدنا كيف اطلع المعادلة هذه لأنوا لو
+
+370
+00:28:34,800 --> 00:28:43,120
+عوضتوا بصفرعوضنا بواحد، بتنين، تلاتة، أربعة، تقدر
+
+371
+00:28:43,120 --> 00:28:44,860
+تجيبوا الخمسة تقدر تجيبوا ال element اللي وراك
+
+372
+00:28:44,860 --> 00:28:48,180
+تقدر تجيبوا ال element اللي وراك طيب احنا من هنا
+
+373
+00:28:48,180 --> 00:28:52,500
+طلعنا بحاجة ان ال location تبعنا ال location
+
+374
+00:28:52,500 --> 00:28:58,060
+بناخده من ال natural number ليش؟ لأن هنا ال
+
+375
+00:28:58,060 --> 00:29:03,590
+location هيبدا بصفرفإحنا فعلا في بعض ال sequences
+
+376
+00:29:03,590 --> 00:29:07,250
+بتبدأ بال natural number وفي بعضها natural number
+
+377
+00:29:07,250 --> 00:29:12,080
+minus zero ببدأ بواحدفهذا يجب أن يكون معرفن، إما
+
+378
+00:29:12,080 --> 00:29:15,700
+natural number فببدأ مباشرة إذا عند المعادلة ببدأ
+
+379
+00:29:15,700 --> 00:29:20,600
+أعوض من ال zero أو لأ natural number minus one أو
+
+380
+00:29:20,600 --> 00:29:26,180
+أكبر أو يساوي واحد فبعرف نبدأ من الواحد، نعرف نبدأ
+
+381
+00:29:26,180 --> 00:29:28,260
+من الواحد، مانبقاش أشي تاني، دائما يا صفر يا
+
+382
+00:29:28,260 --> 00:29:32,060
+الواحد عادة اللي بنبدأ فيهم ال sequence تبعناOkay
+
+383
+00:29:32,060 --> 00:29:37,460
+okay مدام عرفنا ان انا بتعامل مع set هي عبارة عن
+
+384
+00:29:37,460 --> 00:29:42,080
+function و ال set هذه لازم اتعامل معاها كمرتبة ك
+
+385
+00:29:42,080 --> 00:29:44,560
+sequence مرتب فانا بقدر اقول ان هذه عبارة عن
+
+386
+00:29:44,560 --> 00:29:49,760
+function ال domain تبعها هو ال locations ال
+
+387
+00:29:49,760 --> 00:29:52,100
+locations ال location الأول التاني التالت الرابع
+
+388
+00:29:52,100 --> 00:29:56,930
+الخامس العشر كويسةالـ function معينة الـ function
+
+389
+00:29:56,930 --> 00:30:00,270
+اللي هتعرفلنا ال sequence بقدر أجيب ال elements
+
+390
+00:30:00,270 --> 00:30:03,930
+تحت ال sequence كل واحد في ال location تبعه لأن كل
+
+391
+00:30:03,930 --> 00:30:08,170
+واحد لازم يكون function في ال location تبعه فهذه
+
+392
+00:30:08,170 --> 00:30:13,990
+بتكون مرتبة و لازم تكون مرتبة لازم تكون مرتبة عادة
+
+393
+00:30:13,990 --> 00:30:18,590
+زي ما قلنا ال sets اللي احنا بتاعة ال locations
+
+394
+00:30:18,590 --> 00:30:21,870
+ممكن تكون بدية من الصفرممكن تبدأ صفر واحد اتنين
+
+395
+00:30:21,870 --> 00:30:24,430
+تلاتة اربعة او تبدأ من الواحد اتنين تلاتة اربعة
+
+396
+00:30:24,430 --> 00:30:27,790
+فاما ال natural number فهي الأولى صفر واحد اتنين
+
+397
+00:30:27,790 --> 00:30:31,550
+تلاتة او natural number minus zero فببدأ من الواحد
+
+398
+00:30:31,550 --> 00:30:34,750
+كويس عشان نجيب ال elements ال elements اللى هى ال
+
+399
+00:30:34,750 --> 00:30:40,130
+a,n ال a,n و ال index تبعها ال n معناه ذلك ان ال a
+
+400
+00:30:40,130 --> 00:30:45,720
+,n هذه لازم تظهر في ال location Mهذا ال element
+
+401
+00:30:45,720 --> 00:30:49,100
+اللي لازم يظهر في ال location N في بعض الكتب
+
+402
+00:30:49,100 --> 00:30:57,400
+هتلاقوها I بدل N فبتجنك تبقى أحيانا AI ماتلحبطوش
+
+403
+00:30:57,400 --> 00:31:00,920
+في الكتاب عندنا كله N في الغالب إذا دورتوا في كتب
+
+404
+00:31:00,920 --> 00:31:04,680
+تانية يمكن تلاقوا I بس احنا كل شغل نحن هنشتغل عليه
+
+405
+00:31:04,680 --> 00:31:10,060
+على ال NOkay ellipses هذه زي ما قلنا معناها انه
+
+406
+00:31:10,060 --> 00:31:15,400
+infinite sequence انه ال sequence لانهائي و هيظل
+
+407
+00:31:15,400 --> 00:31:21,180
+مستمر مستمر for example لو قلنا ال sequence a n
+
+408
+00:31:21,180 --> 00:31:27,860
+لاحظوا a n بيساوي صفر واحد اربع تسعة ستاشر خمسة و
+
+409
+00:31:27,860 --> 00:31:31,740
+عشرين اتصور ستة و تلاتين و بتكمل تسعة و ربعين و
+
+410
+00:31:31,740 --> 00:31:38,700
+هكذا ليش انا بتعامل مع n تربيع صفرzero واحد اتنين
+
+411
+00:31:38,700 --> 00:31:43,900
+تلاتة و حكدا تمام بس ال ellipses احنا بنتركز عليها
+
+412
+00:31:43,900 --> 00:31:47,800
+هنا ان انا بتعمل dots معناه تلت نقاط هيكي معناته
+
+413
+00:31:47,800 --> 00:31:51,220
+ان انا ب .. to infinity to infinity هتظل لانهائية
+
+414
+00:31:51,220 --> 00:31:55,740
+ال sequence بتاعها تمام تقدر نعرفها بهذا الشكل for
+
+415
+00:31:55,740 --> 00:32:00,380
+all n belong to natural numberانا واضح ان انا
+
+416
+00:32:00,380 --> 00:32:02,540
+اتعملت مع ال natural number يعني انا بدأت من صفر
+
+417
+00:32:02,540 --> 00:32:06,600
+بالظبط معناته بدأنا من الصفر فلما اجى اعود في
+
+418
+00:32:06,600 --> 00:32:10,440
+المعادلة نبدأ بالصفر نبدأ بالصفر نبدأ بالصفر okay
+
+419
+00:32:10,440 --> 00:32:14,820
+a n equal to n تربيع بتبدو تشتغلوا عليها عساس ان
+
+420
+00:32:14,820 --> 00:32:17,740
+ال locations تبعتكم تبدأ من صفر باعتبار ان هي
+
+421
+00:32:17,740 --> 00:32:19,660
+belong to natural number اتفضل
+
+422
+00:32:22,580 --> 00:32:27,440
+لأن هنا هذه الست نطق شيل منها ال element zero ال
+
+423
+00:32:27,440 --> 00:32:30,340
+natural number بدون ال element zero شيل ال element
+
+424
+00:32:30,340 --> 00:32:35,860
+zero فصارت كأنه من واحد بتبدأ واحد اتنين تلاتة
+
+425
+00:32:35,860 --> 00:32:44,080
+بتشيل .. بتشيل اللولة ليش؟ لأن احنا قلنا السالب
+
+426
+00:32:44,080 --> 00:32:50,720
+هذي في الست إيش كانت عبارة عن إيه؟ difference إيش
+
+427
+00:32:50,720 --> 00:32:54,590
+كانت اسم ال difference؟Okay لما نعمل difference ال
+
+428
+00:32:54,590 --> 00:32:59,130
+6 هذه من صفر to infinity طيب إيش ال elements اللي
+
+429
+00:32:59,130 --> 00:33:03,610
+موجود في N و غير موجود هنا هو ال zero الوحيد اللي
+
+430
+00:33:03,610 --> 00:33:05,990
+موجود في التنتين فهذا هو ال eventual فقط يعني
+
+431
+00:33:05,990 --> 00:33:08,650
+أنتوا بتشوفوا إيش التقاطع بينهم و بتشيلوه الباقي
+
+432
+00:33:08,650 --> 00:33:12,530
+بيضل الباقي ضل معناته الباقي هو إيش من واحد من
+
+433
+00:33:12,530 --> 00:33:17,990
+الواحد okay sequence examplesناخد شوية examples
+
+434
+00:33:17,990 --> 00:33:23,110
+عليها طبعا احنا واضح ممكن نكتبها اما نعرفها ك set
+
+435
+00:33:23,110 --> 00:33:26,710
+بهذا الشكل و نقول ايش المعادلة بتاعتها ممكن تتعرف
+
+436
+00:33:26,710 --> 00:33:34,870
+بهذا الشكل او احيانا ممكن تكون اوضح ف ال indices
+
+437
+00:33:34,870 --> 00:33:39,270
+بتاعتنا اكثر وضوحا بدل ما اعملها ان و خلاص لأ ممكن
+
+438
+00:33:39,270 --> 00:33:43,270
+تكون اوضح لان يكتبلي اي واحد اتنين فبعرف انه بدأ
+
+439
+00:33:43,270 --> 00:33:48,640
+بواحد خلاصA1, A2, A3, A4 هنا بتكون تعريفها أكثر
+
+440
+00:33:48,640 --> 00:33:52,800
+وضوحا ومع
+
+441
+00:33:52,800 --> 00:33:58,980
+ذلك في الكتاب اللحظة اللي احنا بكتبناها كتير A, N,
+
+442
+00:33:59,300 --> 00:34:05,300
+A, N كويس؟ تمام ناخد شوية examples لو قلنا اللي
+
+443
+00:34:05,300 --> 00:34:10,960
+عندنا series sequence series بيه هي نفس ال A, N,
+
+444
+00:34:11,220 --> 00:34:17,790
+A1, A2, ellipseswhere for all n أكبر أو يسوى واحد
+
+445
+00:34:17,790 --> 00:34:21,370
+معناته أننا بتعامل مع ال natural minus zero ببدأ
+
+446
+00:34:21,370 --> 00:34:26,230
+من واحد يعني بدين من واحد a n equal to f of n
+
+447
+00:34:26,230 --> 00:34:30,790
+equal to واحد over n معناته بدنا نبدأ نعود من وين
+
+448
+00:34:30,790 --> 00:34:35,470
+من واحد واحد على واحد واحد على واحد واحد على اتنين
+
+449
+00:34:35,470 --> 00:34:39,990
+واحد على تلاتة فلحظوا بتطلع ال sequence هذه مقابلة
+
+450
+00:34:39,990 --> 00:34:42,510
+لا اسم تمام
+
+451
+00:34:44,330 --> 00:34:47,190
+Okay ال examples with repetitions طبعا في ال
+
+452
+00:34:47,190 --> 00:34:50,830
+repetitions احنا قولنا في ال sequence مسموح في ال
+
+453
+00:34:50,830 --> 00:34:56,790
+series مسموح ولكن في ال sets لأ فإذا لما يكون
+
+454
+00:34:56,790 --> 00:35:04,690
+عندنا constant of the sequence P0 P1 P2 P3 ونقول
+
+455
+00:35:04,690 --> 00:35:09,490
+ان ال Pn equal to minus one to the power n هاي ال
+
+456
+00:35:09,490 --> 00:35:13,430
+relation الأوطانية مجرد ان بنعوض بنبدأ بال zeroلأن
+
+457
+00:35:13,430 --> 00:35:18,910
+هنا بدين احنا احنا احنا احنا
+
+458
+00:35:18,910 --> 00:35:19,010
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+459
+00:35:19,010 --> 00:35:19,310
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+460
+00:35:19,310 --> 00:35:22,810
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+461
+00:35:22,810 --> 00:35:25,010
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+462
+00:35:25,010 --> 00:35:25,010
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+463
+00:35:25,010 --> 00:35:25,010
+احنا احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+464
+00:35:25,010 --> 00:35:33,330
+احنا احنا احنا احنا احنا احنا احنا احنا احنا
+
+465
+00:35:34,960 --> 00:35:37,800
+أه بالظبط هذه هتكون isolating تمام عاملة زي sunny
+
+466
+00:35:37,800 --> 00:35:45,180
+soda يعني مش sunny soda زي .. إيش بتسميها ال .. او
+
+467
+00:35:45,180 --> 00:35:51,810
+.. إيش بتسموها السوتوث .. السوتوثزي أسنان المنشرة
+
+468
+00:35:51,810 --> 00:35:55,530
+الـ Suture، عارفينه؟ فهذه تطلع زي الـ Suture،
+
+469
+00:35:55,530 --> 00:35:58,910
+تمام، طيب، في الحالة اللي عندنا هنا، في ال
+
+470
+00:35:58,910 --> 00:36:03,250
+sequence مقبولة، في ال series مقبولة، بس في ال
+
+471
+00:36:03,250 --> 00:36:06,090
+sets لأ، في ال sets .. لو عندي set بهذا الشكل،
+
+472
+00:36:06,090 --> 00:36:08,990
+الطبيعي أن هي تكون two elements فقط، بقولش أن هي
+
+473
+00:36:08,990 --> 00:36:14,340
+to infinity، هنا to infinityinfinite sequence هنا
+
+474
+00:36:14,340 --> 00:36:18,540
+لأ لما بتكلم عنها as a set بقول ان هي لأ set ال
+
+475
+00:36:18,540 --> 00:36:22,740
+cardinality بتاعتها اتنين فقط one minus one و بس
+
+476
+00:36:22,740 --> 00:36:30,270
+one minus one okay recognizing sequencesكيف ممكن
+
+477
+00:36:30,270 --> 00:36:36,430
+نعمل تمييز لل sequence بتاعتنا طب احنا زى ما
+
+478
+00:36:36,430 --> 00:36:42,450
+قلتلكم مش هناخد علميا بالحل لاحقا هناخد الحل هنرجع
+
+479
+00:36:42,450 --> 00:36:47,210
+للموضوع هذا و نتكلم عن sequence و محتاجين احنا
+
+480
+00:36:47,210 --> 00:36:50,590
+نجيب elements ناقصة فيه او نجيب ال relation تبعته
+
+481
+00:36:50,590 --> 00:36:54,970
+هناخده ولكن احنا هناby logic هيك .. بدنا نشوف شوية
+
+482
+00:36:54,970 --> 00:36:59,150
+examples لكيف انا اميز ال sequence تبعتنا .. كيف
+
+483
+00:36:59,150 --> 00:37:02,430
+اميز .. اقول اه دي sequence بتاعة كذا لو بدأنا
+
+484
+00:37:02,430 --> 00:37:08,110
+نقول والله ايش ال next number لواحد اتنين تلاتة
+
+485
+00:37:08,110 --> 00:37:12,510
+اربعة .. خمسة .. خمسة .. ليش؟ بيمشي انا .. لأن
+
+486
+00:37:12,510 --> 00:37:17,570
+احنا انا متعامل عن أرقام .. الأرقام ال positive ..
+
+487
+00:37:17,570 --> 00:37:21,650
+ال positive integers .. positive integersواحد،
+
+488
+00:37:21,650 --> 00:37:26,170
+اتنين، تلاتة، فطبيعي خامس element أكبر من صفر هو
+
+489
+00:37:26,170 --> 00:37:32,130
+الخمسة طيب، واحد، تلاتة، داشت، داشت، داشت، داشت،
+
+490
+00:37:32,130 --> 00:37:34,310
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+491
+00:37:34,310 --> 00:37:39,470
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+492
+00:37:39,470 --> 00:37:39,470
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+493
+00:37:39,470 --> 00:37:39,470
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+494
+00:37:39,470 --> 00:37:44,030
+داشت، داشت، داشت، داشت، داشت، داشت، داشت، داشت،
+
+495
+00:37:44,030 --> 00:37:47,610
+داش
+
+496
+00:37:48,070 --> 00:37:50,510
+sequence انتوا بتقدروا تعرفوها و تميزوها لحاجة و
+
+497
+00:37:50,510 --> 00:37:54,510
+مجرد ما شوفتوها بتقدروا تميزوها بتقدروا تميزوها
+
+498
+00:37:54,510 --> 00:37:59,670
+okay ولكن مع ذلك بصير احيانا trouble with
+
+499
+00:37:59,670 --> 00:38:03,190
+recognition في التمييز احيانا بصير مشكلة ان انا
+
+500
+00:38:03,190 --> 00:38:11,470
+ماعرفتهاش بالظبط زي لو قلنا أخدنا تلاتة خمسة سبعة
+
+501
+00:38:11,470 --> 00:38:15,070
+و سكتت و قلتلكوا هتقولي الرقم اللي ورا ممكن يكون
+
+502
+00:38:15,070 --> 00:38:18,550
+تسعة مثلا ممكن يكونممكن يكون تسعة و ممكن يكون
+
+503
+00:38:18,550 --> 00:38:22,770
+احداش .. ممكن يكون تسعة و ممكن يكون احداش .. لحظة
+
+504
+00:38:22,770 --> 00:38:28,170
+دولهم متمتفقين مع بعض .. فلاحظوا انه ممكن جدا يكون
+
+505
+00:38:28,170 --> 00:38:31,250
+في صعوبة في تمييز اي .. انا بتعني اي sequence
+
+506
+00:38:31,250 --> 00:38:34,790
+بحتكلم او بحكي .. فعشان اجيب ال element اللي وراها
+
+507
+00:38:34,790 --> 00:38:37,890
+هتكون فيه صعوبة، ايش ال element اللي وراها؟ او
+
+508
+00:38:37,890 --> 00:38:41,690
+يقولنا ايش ال element اللي قدامها؟ففي صعوبة في
+
+509
+00:38:41,690 --> 00:38:44,070
+تمييز ال sequence في بعض الأحيان بتصير ففي مشاكل
+
+510
+00:38:44,070 --> 00:38:46,750
+ممكن تصير في التمييز المشاكل هدا إذا صارت بتكون
+
+511
+00:38:46,750 --> 00:38:50,410
+نتيجة إن أنا ماعرفتش ال ال ال initial elements صح
+
+512
+00:38:50,410 --> 00:38:53,910
+ال initial elements هدول مش معرفين بصورة صحية هدول
+
+513
+00:38:53,910 --> 00:38:59,360
+intersection ل two sequence ايه و بدك منهم؟هدول
+
+514
+00:38:59,360 --> 00:39:03,640
+هيكون intersection ل .. intersection set لل prime
+
+515
+00:39:03,640 --> 00:39:07,860
+و لل odd انت مين بدك منهم مش معرف فهنا او خليني
+
+516
+00:39:07,860 --> 00:39:12,160
+اقول not well defined هو مش معرف بطريقة جيدة يمكن
+
+517
+00:39:12,160 --> 00:39:14,920
+كنا محتاجين element قبل او element بعد عشان تتضح
+
+518
+00:39:14,920 --> 00:39:18,480
+ال sequence هدا ان و منهم فإذا كان فعلا بهذا الشكل
+
+519
+00:39:18,480 --> 00:39:23,500
+مش معرفة بصورة جيدة واضح انه هيكون فينا مشكلة في
+
+520
+00:39:23,500 --> 00:39:29,160
+تمييز الصورة في الغالب .. في الغالب إذا ..ماعناش
+
+521
+00:39:29,160 --> 00:39:34,140
+واضحة الصورة بهذا الشكل، في الغالب الأبسط هي اللي
+
+522
+00:39:34,140 --> 00:39:37,860
+بناخدها، في الغالب الأبسط هي اللي بناخدها، إذا
+
+523
+00:39:37,860 --> 00:39:42,800
+طبعا ماعناش أي معلومة مسبقة، فال simplest هي من ال
+
+524
+00:39:42,800 --> 00:39:44,840
+functions، من ال two functions اللي بنتعامل معها و
+
+525
+00:39:44,840 --> 00:39:49,440
+بناخدها، هذا إذا كان لابد أن أحنا نختاره، بس في
+
+526
+00:39:49,440 --> 00:39:52,240
+حالة زي هذه لأ، هي لها كذا احتمال، هي لها كذا
+
+527
+00:39:52,240 --> 00:39:58,350
+احتمال للشغل، okayكيف احنا نعرف ال simplicity اصلا
+
+528
+00:39:58,350 --> 00:40:02,510
+of a function كيف نعرف مين البسيطة منهم أساسا ما
+
+529
+00:40:02,510 --> 00:40:04,650
+احنا عندنا ال prime و عندنا ال .. ال .. ال odd
+
+530
+00:40:04,650 --> 00:40:06,650
+التنتين بساطين بالنسبالي يعني بالنسبالنا على level
+
+531
+00:40:06,650 --> 00:40:09,670
+تبعنا ماهم التنتين زي بعض مش هتفرج كتير هذه بسيطة
+
+532
+00:40:09,670 --> 00:40:12,250
+و هذه بسيطة انا عرفت هذه و اعرفت هذه و هذه ممكن
+
+533
+00:40:12,250 --> 00:40:16,690
+يكون يا هذه يا هذه مين اختار منهم هذا مافيش
+
+534
+00:40:16,690 --> 00:40:22,590
+objective right answerبقدرش أقولكم والله لأ لازم
+
+535
+00:40:22,590 --> 00:40:26,530
+يكون بهذا الشكل، هي من الأساس غير معرفة بصورة
+
+536
+00:40:26,530 --> 00:40:31,170
+جيدة، غير معرفة، ال elements هذه بصورة جيدة، فهذه
+
+537
+00:40:31,170 --> 00:40:35,590
+بيبقى قائمة لإحتمالاتها، ممكن حد يجاوب إن هي odd و
+
+538
+00:40:35,590 --> 00:40:39,120
+ممكن حد يجاوب إن هي primeبقدرش أقول هذا غلط ولا
+
+539
+00:40:39,120 --> 00:40:43,580
+بقدر أقول هذا غلط لأنه من الأساس تعريفها مش غلط
+
+540
+00:40:43,580 --> 00:40:49,100
+ولكن ماكانش أو not well defined مش محدد بصورة
+
+541
+00:40:49,100 --> 00:40:53,720
+جيدة، مش مميز بصورة محددة واضحة، هو مش محدد، مش
+
+542
+00:40:53,720 --> 00:40:59,580
+محدد أصلا طيب what are strings really؟ احنا كنا
+
+543
+00:40:59,580 --> 00:41:01,760
+بتكلم عن ال sequenceال string الحقيقة بقى في
+
+544
+00:41:01,760 --> 00:41:05,060
+تعريفات كتير فيها يعني في اختلفة حتى فيها انه ال
+
+545
+00:41:05,060 --> 00:41:07,980
+string ايش بيميزه عن ال sequence فهي في ناس عرفوها
+
+546
+00:41:07,980 --> 00:41:11,840
+عساسة ان هي ال finite sequences اذا كانت finite
+
+547
+00:41:12,340 --> 00:41:16,400
+sequences بنسميها string فاحنا إذا كان محددة بادية
+
+548
+00:41:16,400 --> 00:41:20,280
+من واحد ومنتهية and n و n هذا belong to natural
+
+549
+00:41:20,280 --> 00:41:24,960
+number بقى قيمة محددة معروفة and بتقولي لعند عشر
+
+550
+00:41:24,960 --> 00:41:28,240
+terms أول عشر terms أول عشرين terms خلاص أنا عارف
+
+551
+00:41:28,240 --> 00:41:31,520
+إنه جداش عدد ال terms بقدر أحسبلها cardinality
+
+552
+00:41:31,520 --> 00:41:35,580
+نقدر نحسبلها cardinality نعرف جداش عدد ال elements
+
+553
+00:41:35,580 --> 00:41:40,260
+فيهاجاله على أساس إنه هذا اللي يكون ال sequence
+
+554
+00:41:40,260 --> 00:41:45,620
+طيب ولكن رغم ذلك في infinite strings رغم إنه
+
+555
+00:41:45,620 --> 00:41:48,920
+الكتاب معرفه على أساس إنه finite sequence ولكن
+
+556
+00:41:48,920 --> 00:41:54,060
+احنا بنعرف إنه في infinite strings في strings ممكن
+
+557
+00:41:54,060 --> 00:41:58,160
+نتعامل معها ك infinite كويس ولكن هذا تعريف في
+
+558
+00:41:58,160 --> 00:42:01,440
+تعريف تاني strings are often restricted to
+
+559
+00:42:01,440 --> 00:42:07,510
+sequencescomposed of symbols بدل ال numbers إذا
+
+560
+00:42:07,510 --> 00:42:13,290
+كانت ال .. ال sequence يحتوي على symbols على
+
+561
+00:42:13,290 --> 00:42:17,430
+elements مش أرقام ال symbols هذه و ال objects ..
+
+562
+00:42:17,430 --> 00:42:19,990
+ال objects هذه ال symbols زي .. زي ال alphabet
+
+563
+00:42:19,990 --> 00:42:26,430
+مثلا ال alphabet symbols a b c d e f g ال .. ال ..
+
+564
+00:42:26,430 --> 00:42:29,870
+ال letters هذه إذا كانت ال sequence .. sequence من
+
+565
+00:42:29,870 --> 00:42:35,600
+letters فبنسميها stringهذا برضه تعريف ممكن التعامل
+
+566
+00:42:35,600 --> 00:42:39,540
+.. التعامل معه عساس ان هي تعتمد على مجموعة symbols
+
+567
+00:42:39,540 --> 00:42:42,400
+بنعرفه finite طبعا لان اذا كان ماتكلم عن ال
+
+568
+00:42:42,400 --> 00:42:45,900
+alphabet فهي ال alphabet محددة ال alphabet محددة
+
+569
+00:42:45,900 --> 00:42:48,820
+هي مش تو infinity يعني خلاص هي معروفة انه .. انه
+
+570
+00:42:48,820 --> 00:42:51,980
+كام حرف؟ ستة و عشرين حرف خلاص هم معروفين ستة و
+
+571
+00:42:51,980 --> 00:42:56,400
+عشرين هم مش هزيلوا مش هزيلوا كويس و ال .. زي ما
+
+572
+00:42:56,400 --> 00:43:00,870
+قلنا ال index من صفر ببدأ او من واحدمن صفر أو واحد
+
+573
+00:43:00,870 --> 00:43:03,590
+فاحنا متفقين على التعريف مع ال sequence هو هو إما
+
+574
+00:43:03,590 --> 00:43:07,050
+بنبدأ من صفر أو من واحد بأي طريقة من الطريقتين
+
+575
+00:43:07,050 --> 00:43:12,190
+احنا هنتعامل مع length of a finite string is just
+
+576
+00:43:12,190 --> 00:43:16,970
+its number of terms أو distinct indices بمعنى أنه
+
+577
+00:43:16,970 --> 00:43:21,090
+لازم نكون عارفين عدد ال numbersأو ال number of
+
+578
+00:43:21,090 --> 00:43:23,870
+terms جدش عدد ال units اللي جواها، جدش عدد ال
+
+579
+00:43:23,870 --> 00:43:28,550
+elements داخلها، و بنكون محدد في الحالة هذه جدش
+
+580
+00:43:28,550 --> 00:43:32,460
+عدد ال indices اللي موجودةمكتوبة هنا اها يعني ال
+
+581
+00:43:32,460 --> 00:43:36,540
+index الأولى واحد index index هدولة مجموعة هم اللي
+
+582
+00:43:36,540 --> 00:43:39,820
+هم ال indices اللي هم محددين معروفين انه والله اه
+
+583
+00:43:39,820 --> 00:43:43,220
+عندي عشرين عندي خمسين indices بمعنى عندي عشرين
+
+584
+00:43:43,220 --> 00:43:47,700
+location عشرين خمسة وعشرين location معروفة ومحددة
+
+585
+00:43:47,700 --> 00:43:50,900
+فهذه بنتعامل معها على أساس إن هي string على أساس
+
+586
+00:43:50,900 --> 00:43:57,730
+إن هذا stringOkay, strings more formally أكثر ..
+
+587
+00:43:57,730 --> 00:44:01,250
+نوضحها بصورة أكثر فاحنا زي ما قلنا إذا كان عرفناها
+
+588
+00:44:01,250 --> 00:44:05,270
+عساس أن هي symbols، مجموعة عناصر أو رموز، symbols
+
+589
+00:44:05,270 --> 00:44:09,310
+ممكن تكون زي ما قلنا ال alphabet، letters، نتعامل
+
+590
+00:44:09,310 --> 00:44:13,070
+معها عساس أن هي alphabet مثلا، generally A,B,C,D,Z
+
+591
+00:44:13,070 --> 00:44:21,830
+to ZA String S ال S هذه اللي هي ال string و لاحظوا
+
+592
+00:44:21,830 --> 00:44:24,670
+إن إحنا كاتبينها small لإن إذا كتبناها capital
+
+593
+00:44:24,670 --> 00:44:31,010
+ستصبح six ستصبح six فلأ small فأنا عارف إن هذه ال
+
+594
+00:44:31,010 --> 00:44:35,030
+small string over alphabet بنسميها مثلا big sigma
+
+595
+00:44:35,030 --> 00:44:38,150
+ال big sigma في الحلقة هذه بيقول و الله فينا
+
+596
+00:44:38,150 --> 00:44:42,490
+string S هذا عبارة عن alpha alphabet string
+
+597
+00:44:44,860 --> 00:44:49,780
+لـ any sequence of symbols SI والـ I هذي زي ما
+
+598
+00:44:49,780 --> 00:44:52,740
+قلنا اللي هو ال index تبعنا ال .. ال .. ال
+
+599
+00:44:52,740 --> 00:44:56,430
+sequence منالـ element الأول ايش هو؟ A ال element
+
+600
+00:44:56,430 --> 00:44:59,710
+التاني B ال element التالق C ال element الرابع D و
+
+601
+00:44:59,710 --> 00:45:08,130
+هكذا of symbols فبنقول هنا ال S I belong to sigma
+
+602
+00:45:08,130 --> 00:45:14,590
+فمعنى ذلك ان ال element اللي داخل ال set او داخل
+
+603
+00:45:14,590 --> 00:45:18,350
+ال sequence او ال string احنا بنتكلم عن string
+
+604
+00:45:19,740 --> 00:45:22,960
+string هدا هدا هيكون مجموعة elements متفقين على
+
+605
+00:45:22,960 --> 00:45:29,460
+هيك طيب كل element جوا إيش بسميه SI لإن حسب قيمة I
+
+606
+00:45:29,460 --> 00:45:33,620
+هتتغير ال elements اللي جوا هذه فهنقول إن ال SI أي
+
+607
+00:45:33,620 --> 00:45:38,680
+واحدة منهم لازم تكون belong to سيجما، سيجما الشي
+
+608
+00:45:38,680 --> 00:45:46,880
+هذه كل ال alphabet symbolsإذا باعرف symbols تانية
+
+609
+00:45:46,880 --> 00:45:49,060
+غير ال alphabet بدي أكون معرفها برضه عساس ان هي ال
+
+610
+00:45:49,060 --> 00:45:53,800
+big sigma هدولة كل الحروف اللي موجودين هنا لو
+
+611
+00:45:53,800 --> 00:45:56,100
+بنتكلم عن الطالبات اللي موجودين معناته كل أسماء
+
+612
+00:45:56,100 --> 00:46:00,960
+الطالبات هدولة بتحطهم عساس ان هم هدول ال big sigma
+
+613
+00:46:00,960 --> 00:46:04,300
+تمام؟ ويمكن بعد ما نخلص الامتحان بيضطرهم حسب
+
+614
+00:46:04,300 --> 00:46:07,260
+درجاتهم عساس ان هذا ال year بتتغيرش مش هنقول والله
+
+615
+00:46:07,260 --> 00:46:10,830
+زي ال setال set قابلة للتبديل، أي حد بيجي اسمه قبل
+
+616
+00:46:10,830 --> 00:46:14,210
+تان مفرجش، بس لو قولنا لأ حسب مثلا في التوجيه جد
+
+617
+00:46:14,210 --> 00:46:17,050
+الجوا مثلا، خلاص هذه ثابتة، هذه لازم ال string
+
+618
+00:46:17,050 --> 00:46:21,310
+انحدده، لازم تكون مرتبة، بينفعش حد يجي مكان حد،
+
+619
+00:46:21,310 --> 00:46:27,510
+صحيح؟ كويس فهنا alphabet هذه بتكون تشتمل على جميع
+
+620
+00:46:27,510 --> 00:46:30,210
+ال symbols اللي انا بتتعامل معها، جميع ال symbols
+
+621
+00:46:30,210 --> 00:46:33,890
+اللي بتتعامل معها، فأي symbol داخل ال stringلازم
+
+622
+00:46:33,890 --> 00:46:38,930
+يكون موجود أصلا معرف من الأول في ال big sigma و
+
+623
+00:46:38,930 --> 00:46:44,690
+indexed by لحظة هى natural number او natural
+
+624
+00:46:44,690 --> 00:46:49,090
+number minus هى زى ما قولنا ال difference ل set
+
+625
+00:46:49,090 --> 00:46:53,910
+بشيل منها بس ال zero ل set بنشيل منها ال zero فهدى
+
+626
+00:46:53,910 --> 00:46:56,970
+ال minus اللى هنا هدى مش مجرد طريح عادي يعنى احنا
+
+627
+00:46:56,970 --> 00:47:00,870
+بنتكلم عن ال difference ال difference between ال
+
+628
+00:47:00,870 --> 00:47:06,180
+setsلو قلنا if a,b,c هي ال symbols تبعتنا فممكن
+
+629
+00:47:06,180 --> 00:47:10,600
+نقول ان ال string تبعنا عبارة عن a,b,c لو نكمل
+
+630
+00:47:10,600 --> 00:47:13,940
+هنكمل معنا ellipses هي نكمل ellipses ممكن نكتبها
+
+631
+00:47:13,940 --> 00:47:18,940
+مباشرة a,b,c بدون كوماز بدون الكوماز بدون كوماز
+
+632
+00:47:18,940 --> 00:47:24,780
+بمشي الحل بمشي الحل طيب إذا كانت ال string s هذه
+
+633
+00:47:24,780 --> 00:47:32,200
+is finite string andT برضه String تانية فصار عندنا
+
+634
+00:47:32,200 --> 00:47:36,600
+two strings String اسمها S و String اسمها T then
+
+635
+00:47:36,600 --> 00:47:44,520
+the concatenation of S with T بنكتبها ST كأنهم
+
+636
+00:47:44,520 --> 00:47:49,100
+مضربين في بعض ST هدول كيف بنعملهم؟ بنحط كل عناصر S
+
+637
+00:47:49,100 --> 00:47:53,720
+في الأول و بعدين عناصر T وراهم في sequence واحد في
+
+638
+00:47:53,720 --> 00:48:00,230
+String واحدة بنسميها concatenationسلسلة أو بنحطهم
+
+639
+00:48:00,230 --> 00:48:03,650
+يعني سلسلة ورا بعض بنحطهم سلسلة ورا بعض زي بالظبط
+
+640
+00:48:03,650 --> 00:48:09,470
+لما تجيب سنسال عندكم و تجيبوا سنسالين و تفتح عروض
+
+641
+00:48:09,470 --> 00:48:13,130
+واحدة منهم و تربطيها في التاني، string كامل صار،
+
+642
+00:48:13,130 --> 00:48:15,850
+صاروا كلهم مع بعض، مش هم عبارة عن حلقات في بعض
+
+643
+00:48:16,470 --> 00:48:20,330
+الحلقات هذه واحدة مثلا طولها عشرة صنطة لأ انا بدي
+
+644
+00:48:20,330 --> 00:48:23,350
+اوسع شوية جيبنا كمان واحد عشرة صنطة فتحنا اخر
+
+645
+00:48:23,350 --> 00:48:25,470
+حلقتين هنا واخر حلقتين هنا و بعدين رابطناهم في بعض
+
+646
+00:48:25,470 --> 00:48:29,070
+عملنا concatenation عملناهم ايش؟ concatenation
+
+647
+00:48:29,070 --> 00:48:33,590
+فهذه رابطنا تنتين في بعض فلما اجي اطلع حلوجة عليا
+
+648
+00:48:33,590 --> 00:48:37,650
+كله على بعضه هعرفوا ايش الحلقة الأولى اللي كانت من
+
+649
+00:48:37,650 --> 00:48:40,830
+S الحلقة التانية كانت من S الحلقة العشرة كانت من S
+
+650
+00:48:40,830 --> 00:48:44,370
+الحلقة أحداشر كانت من Tبس خلاص هالوقت صاروا في
+
+651
+00:48:44,370 --> 00:48:49,430
+إيه؟ في concatenation sequence أو في ال sequence
+
+652
+00:48:49,430 --> 00:48:55,130
+الجديد اللي هو ال S T simply the string contains
+
+653
+00:48:55,130 --> 00:49:01,470
+هنا في الحالة هذه the symbols in S and in sequence
+
+654
+00:49:01,470 --> 00:49:06,490
+followed by the symbols in T in sequenceمتبعين
+
+655
+00:49:06,490 --> 00:49:11,750
+مباشرة وراها لو في وراهم كمان V لو في وراهم V في
+
+656
+00:49:11,750 --> 00:49:15,510
+الحالة هذه ايش بيصير عندنا STV بنحط كمان العناصر
+
+657
+00:49:15,510 --> 00:49:21,010
+تبعت V معاهم بنحط عناصر V في الحالة هذه معاهم هذه
+
+658
+00:49:21,010 --> 00:49:26,030
+هي ال concatenation في الحالة اللي احنا بنحكي عنها
+
+659
+00:49:26,030 --> 00:49:30,130
+طيب
+
+660
+00:49:30,130 --> 00:49:35,880
+ال length لل stringهي بالظبط ال cardinality ال
+
+661
+00:49:35,880 --> 00:49:39,120
+cardinality نفس لما بنيجي نعمل absolute هنا ال
+
+662
+00:49:39,120 --> 00:49:41,220
+cardinality ايش معناه ال cardinality لما كنا نتكلم
+
+663
+00:49:41,220 --> 00:49:44,680
+في ال set عدد ال elements داخل ال set طيب في ال
+
+664
+00:49:44,680 --> 00:49:47,160
+sequence أو في ال string هي نفس الكلام عدد ال
+
+665
+00:49:47,160 --> 00:49:50,520
+elements داخل ال string و باعتبار ان احنا عرفنا ال
+
+666
+00:49:50,520 --> 00:49:54,120
+string عساس ان هي finite و بدنا نتعامل كل شغلنا مع
+
+667
+00:49:54,120 --> 00:49:57,000
+ال finite string as معناه ذلك ان هي number of
+
+668
+00:49:57,000 --> 00:50:02,700
+positions number of positionsلحظة number of
+
+669
+00:50:02,700 --> 00:50:07,480
+positions مش ال index لأن ال index ممكن يبدأ من
+
+670
+00:50:07,480 --> 00:50:14,080
+صفر صح؟ طب لو من صفر لعشرة ال maximum عشرة هل بقول
+
+671
+00:50:14,080 --> 00:50:18,580
+اني عندي عشرة elements؟ لأ عندي 11 زي ما قلنا ال
+
+672
+00:50:18,580 --> 00:50:21,940
+cardinality هذه سهلة هو عدد number of indices او
+
+673
+00:50:21,940 --> 00:50:28,710
+ال index values I كده عدد ال index numberإذا بدين
+
+674
+00:50:28,710 --> 00:50:32,810
+من صفر معناته بإننا زائد واحد آخر index موجود جدش
+
+675
+00:50:32,810 --> 00:50:35,190
+قيمته زائد واحد إذا بدين والله automatically من ال
+
+676
+00:50:35,190 --> 00:50:39,790
+positive natural numbers خلاص الأخر هو يمثل العدد
+
+677
+00:50:39,790 --> 00:50:44,110
+العدد ال elements في الحالة هذه بنقول أن ال S is a
+
+678
+00:50:44,110 --> 00:50:49,430
+finite string andbelong to natural number الان
+
+679
+00:50:49,430 --> 00:50:52,090
+طبعا جديش ال cardinality جديش عدد ال elements
+
+680
+00:50:52,090 --> 00:50:56,310
+طبيعي بده يكون عدد طبيعي عدد طبيعي integer هيكون
+
+681
+00:50:56,310 --> 00:50:59,410
+integer عدد طبيعي العدد الطبيعي هي العدد الواحد
+
+682
+00:50:59,410 --> 00:51:03,770
+اتنين تلات اربع مافيش فيها fractions okay then لما
+
+683
+00:51:03,770 --> 00:51:09,470
+نقول هل وجد s string to the power n هذه معناها
+
+684
+00:51:09,470 --> 00:51:15,870
+denotes the concatenation of n cubit او cubits of
+
+685
+00:51:15,870 --> 00:51:23,770
+sهنا معناته ال S عملتيلها نسخ N مرة هناك كنا بنقول
+
+686
+00:51:23,770 --> 00:51:29,070
+S في T هذا كان String وهذا String وحطيناهم ورا بعض
+
+687
+00:51:29,070 --> 00:51:35,930
+طب لما نقول S تربيع كأنها S في S sequence S بنحطه
+
+688
+00:51:35,930 --> 00:51:42,270
+و ورا مباشرة كمان مرة ال sequence نفسه Sطيب N مرة
+
+689
+00:51:42,270 --> 00:51:48,390
+بده يتكرر لعند ما نصل هذه واحد هذه اتنين to S
+
+690
+00:51:48,390 --> 00:51:52,810
+المرة N المرة انه كله بصير هذا sequence ..
+
+691
+00:51:52,810 --> 00:51:55,370
+sequence واحد فهذه عملية ال concatenation لما تشوف
+
+692
+00:51:55,370 --> 00:51:57,090
+كلمة concatenation معناه ان انتوا تعرفين ان انتوا
+
+693
+00:51:57,090 --> 00:51:59,570
+بت .. هتعملوا string من مجموعة strings تانين
+
+694
+00:51:59,570 --> 00:52:04,030
+بترتبوهم ورا .. ورا بعضهم بترتبوهم ورا بعضهم okay
+
+695
+00:52:04,030 --> 00:52:10,870
+في عندنا ال epsilonأو double quotation فاضيين بهذا
+
+696
+00:52:10,870 --> 00:52:16,710
+الشكل هذه معناته ان انا بتكلم عن empty string او
+
+697
+00:52:16,710 --> 00:52:23,790
+string of length zero string طوله زي صفر string
+
+698
+00:52:23,790 --> 00:52:28,190
+طوله صفر string فاضي string فاضي لما ديش تطلعوا
+
+699
+00:52:28,190 --> 00:52:30,590
+عليه هتلاجوا مافيش فيه أي elements ففي الحالة هذه
+
+700
+00:52:30,590 --> 00:52:34,630
+بنسميه epsilon أو ال double quotation بعض كتب
+
+701
+00:52:34,630 --> 00:52:40,490
+أحيان بسموهLambda بيعرفوها على أساس أنه Lambda على
+
+702
+00:52:40,490 --> 00:52:43,410
+أساس أنه Lambda فLambda ممكن برضه في بعض كتب
+
+703
+00:52:43,410 --> 00:52:46,610
+تلاقوها عبارة عن ال empty string عبارة عن empty
+
+704
+00:52:46,610 --> 00:52:51,710
+stringخلاص هى ال summation اللى كنتوا تتكلموا فيه
+
+705
+00:52:51,710 --> 00:52:55,430
+المرة الجاية بنبدأ عندنا string او عندنا sequence
+
+706
+00:52:55,430 --> 00:52:59,950
+معين او series معينة بدنا ال series بتاعتنا هدى
+
+707
+00:52:59,950 --> 00:53:03,090
+نجمعهم نجمع ال elements داخلها زى الحال اللى كنتوا
+
+708
+00:53:03,090 --> 00:53:07,130
+اتكلمنا عنها اللى كانت عبارة عن واحد على X واحد
+
+709
+00:53:07,130 --> 00:53:10,030
+على X ممكن نقول واحد على X و بدنا نجمع كل ال
+
+710
+00:53:10,030 --> 00:53:13,500
+elementsفيه لها شوية نظريات، فيه لها شوية rules،
+
+711
+00:53:13,500 --> 00:53:17,400
+فيه لها شوية قواعد في التعامل، فبدنا ناخدها المرة
+
+712
+00:53:17,400 --> 00:53:20,180
+الجاية ان شاء الله تعالى و نكمل موضوعنا المرة
+
+713
+00:53:20,180 --> 00:53:20,460
+الجاية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4880ee7917dadcc84143ccab931dfe4584179285
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ.srt
@@ -0,0 +1,2313 @@
+1
+00:00:20,670 --> 00:00:22,730
+بسم الله الرحمن الرحيم الصلاة والسلام عليك ورحمة
+
+2
+00:00:22,730 --> 00:00:24,330
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+3
+00:00:24,330 --> 00:00:24,430
+ورحمة الله ورحمة الله ورحمة الله ورحمة الله ورحمة
+
+4
+00:00:24,430 --> 00:00:24,590
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+5
+00:00:24,590 --> 00:00:28,470
+ورحمة
+
+6
+00:00:28,470 --> 00:00:34,650
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+7
+00:00:34,650 --> 00:00:37,610
+ورحمة الله ورحمة الله ورحمة الله ورحمة الله ورحمة
+
+8
+00:00:37,610 --> 00:00:43,400
+الله ورحمة الله ورحمة الله ورحمة الله فأذكر أن أحنا
+
+9
+00:00:43,400 --> 00:00:47,540
+تحدثنا عن أربع قواعد أساسية اللي هنبدأ نشرحها واحدة
+
+10
+00:00:47,540 --> 00:00:53,100
+واحدة، وهنضيف لها خامسة ضمن واحدة من الأربع
+
+11
+00:00:53,100 --> 00:00:57,120
+categories. هدول بداية، اتكلمنا عن الـ direct proof
+
+12
+00:00:57,120 --> 00:01:00,860
+وهذه مباشرة، الـ implication تبعنا اللي هنشتغل عليه
+
+13
+00:01:00,860 --> 00:01:03,680
+واللي أحنا أساسا بنعمل منه الإثبات بيكون عندنا
+
+14
+00:01:03,680 --> 00:01:07,640
+premises معطيات، ومنها بنبدأ نثبت conclusion أو
+
+15
+00:01:07,640 --> 00:01:15,370
+استنتاج. إذا نتكلم عن P implies Q، تحقق P اللي هي الـ
+
+16
+00:01:15,370 --> 00:01:20,190
+premises، بنبني عليها، بدي أحاول أستنتج الـ Q، بدنا
+
+17
+00:01:20,190 --> 00:01:24,210
+نستنتج الـ Q، فهذه بالـ direct search، بناخدها بنفس
+
+18
+00:01:24,210 --> 00:01:27,450
+الطريق، بنفس الاتجاه بتاع الـ implication، بمعنى
+
+19
+00:01:27,450 --> 00:01:34,490
+أني بفرض P is true وبحاول منها بشوية rules of
+
+20
+00:01:34,490 --> 00:01:42,770
+inference أصل لمين؟ لـ Q is true، بحاول منها نصل لـ Q
+
+21
+00:01:42,770 --> 00:01:46,010
+is true، في هذه الـ direct ماشية مباشرة مع مين؟ مع
+
+22
+00:01:46,010 --> 00:01:49,230
+الاتجاه. تبعنا الـ indirect لأ، في الـ indirect
+
+23
+00:01:49,230 --> 00:01:55,540
+بنتعامل مع الموضوع بطريقة عكسية، بالـ contrapositive
+
+24
+00:01:55,540 --> 00:02:00,540
+على أساس أن أنا ممكن الـ P نفسها تكون complicated
+
+25
+00:02:00,540 --> 00:02:06,500
+أو complex proposition، ممكن تكون معقدة شوية، أن أنا
+
+26
+00:02:06,500 --> 00:02:09,200
+أبدأ أتعامل معاها، ممكن في بعض الحالات، هذا إذا
+
+27
+00:02:09,200 --> 00:02:11,860
+طبعا سيبنا لكم الخيار، أنتم في الحالة دي اللي
+
+28
+00:02:11,860 --> 00:02:14,920
+جيتوها صعبة، أنكم تبتدأوا منها وتحاولوا بشوية
+
+29
+00:02:14,920 --> 00:02:18,320
+rules تطبقوها عليها، بتبدأوا تشتغلوا بالعكس، يمكن الـ
+
+30
+00:02:18,320 --> 00:02:24,320
+Q تكون أسهل، فبنتعامل مع negation Q، بنفرض أن هذه هي
+
+31
+00:02:24,320 --> 00:02:28,280
+فرضية من عندنا، بنفرض أن هذه هي الـ true، ومنها بدي
+
+32
+00:02:28,280 --> 00:02:34,300
+أحسّ… بدي أجيب negation P، إذا تحقق الـ condition
+
+33
+00:02:34,300 --> 00:02:37,640
+هذا automatically، هذا يتبع، ليش؟ لأن عارف أن
+
+34
+00:02:37,640 --> 00:02:41,920
+الاثنين equivalent لبعض، ضمن relation نسميها الـ
+
+35
+00:02:41,920 --> 00:02:44,860
+contrapositive relation، contrapositive للـ
+
+36
+00:02:44,860 --> 00:02:48,980
+implication. بتذكروا لما اتكلمنا عن inverse؟ للـ
+
+37
+00:02:48,980 --> 00:02:52,120
+implication، واتكلمنا عن الـ converse، وكان الجزء
+
+38
+00:02:52,120 --> 00:02:54,600
+النظري اللي هو إيش الـ inverse والـ converse مع
+
+39
+00:02:54,600 --> 00:02:58,000
+بعض، وسميناها الـ contrapositive، اللي هو بالشكل…
+
+40
+00:02:58,000 --> 00:03:00,500
+بالشكل اللي قلنا إنه هذه مكافئة مباشرة للـ
+
+41
+00:03:00,500 --> 00:03:05,080
+implication الأصلي، فإذا… إذا قدرت أثبت الـ
+
+42
+00:03:05,080 --> 00:03:08,640
+contrapositive، automatically هذه صحيحة…
+
+43
+00:03:08,640 --> 00:03:11,260
+automatically هذه صحيحة، فهنا بنعمل assuming لـ
+
+44
+00:03:11,260 --> 00:03:16,470
+negation Q، ومنها بنثبت negation P، بتحقق الكلام هذا
+
+45
+00:03:16,470 --> 00:03:18,670
+automatically، يقولوا أنه إذا الـ relation الأولى
+
+46
+00:03:18,670 --> 00:03:22,590
+صحيحة، الـ relation الأولى المطلوب إثباتها صحيحة
+
+47
+00:03:22,590 --> 00:03:27,870
+بالقياس مع الـ contrapositive. طيب، في الـ vacuous
+
+48
+00:03:27,870 --> 00:03:34,890
+proof، وهذه اتكلمنا عليها، معناها بلا معنى، يعني الـ
+
+49
+00:03:34,890 --> 00:03:37,930
+proof لا معنى له… هذه أنت بتصير إذا كان أثبتنا
+
+50
+00:03:37,930 --> 00:03:41,690
+negation P by itself، إذا كان هو معطيني P، على أساس إن
+
+51
+00:03:41,690 --> 00:03:47,150
+هي معطى، أثبتنا إنه لأ، P is false، طب أنت كيف تقول
+
+52
+00:03:47,150 --> 00:03:49,770
+هي true وهي أساسا false، فأنا بتعامل معها أصبحت
+
+53
+00:03:49,770 --> 00:03:52,250
+على أساس إن هي false، لأن الـ authoritative عندي بال…
+
+54
+00:03:52,250 --> 00:03:55,070
+بالمنطق تبعنا، إنه هي false، مدام false
+
+55
+00:03:55,070 --> 00:03:58,970
+automatically الـ relation صح، بغض النظر إنه إيش الـ
+
+56
+00:03:58,970 --> 00:04:03,280
+Q، فإذا أنا مش مضطر أجيب الـ Q أو أعرف بالظبط Q
+
+57
+00:04:03,280 --> 00:04:07,020
+الشيء، ليش؟ لأنه لو ما تذكرتوا، أقول لكم احنا المفروض
+
+58
+00:04:07,020 --> 00:04:10,020
+الـ implication هذا نكتبه هنا وما نضيعهوش تاني
+
+59
+00:04:10,020 --> 00:04:13,780
+بالمرة، لأن معظم شغلنا على الـ truth table تبع مين؟
+
+60
+00:04:13,780 --> 00:04:19,780
+الـ implication، فخلينا نكتبه هنا، هي P Q والـ
+
+61
+00:04:19,780 --> 00:04:23,400
+implication قلنا فيه عندكم false, false, true,
+
+62
+00:04:24,480 --> 00:04:32,840
+false, true true، وفي عندكم true false false، وفي
+
+63
+00:04:32,840 --> 00:04:39,100
+عندكم true true true. طيب، لو هذه… هبوط منكم على
+
+64
+00:04:39,100 --> 00:04:43,740
+جد… لحظة، إذا كان الـ P أثبتنا إن هي negation، الـ
+
+65
+00:04:43,740 --> 00:04:51,440
+relation صحيحة، بغض النظر إيش قيمة الـ Q، فخلاص، فإذا
+
+66
+00:04:51,440 --> 00:04:57,460
+بطريقة لا معنى لها، الجملة صحيحة، أو الإثبات صحيح.
+
+67
+00:04:57,940 --> 00:05:01,000
+ولو إن احنا مش كتير مقتنعين بالطريقة، ولكن خلاص هي
+
+68
+00:05:01,000 --> 00:05:04,940
+طريقة من طرق الإثبات، طريقة من طرق الإثبات، إذا كان
+
+69
+00:05:04,940 --> 00:05:09,340
+أثبتنا رياضيا أن الـ negation P هي الـ true، معناه
+
+70
+00:05:09,340 --> 00:05:13,960
+أن P هي الـ false، فإذا الـ implication أو الـ
+
+71
+00:05:13,960 --> 00:05:19,100
+relation صحيحة، بغض النظر الـ Q هتطلع صح ولا هتطلع
+
+72
+00:05:19,100 --> 00:05:24,350
+خطأ، الـ Q تطلع صح، تطلع غلط، مش هتفرق كتير. ممكن
+
+73
+00:05:24,350 --> 00:05:27,890
+تتذكروا المجموعة الـ examples اللي أخدناها عن الـ
+
+74
+00:05:27,890 --> 00:05:32,450
+implication، لما اتكلمنا عن إذا كان الجبنة الخضراء
+
+75
+00:05:32,450 --> 00:05:37,090
+بتنعمل في الجمر، مش عارف even كذا، تتذكروا المثال؟
+
+76
+00:05:37,090 --> 00:05:40,910
+كويس، هو نفس الكلام هذا، احنا مجرد أن الـ P لقيناها
+
+77
+00:05:40,910 --> 00:05:44,830
+false، قلنا الجملة صح، خلاص، قلنا خلاص automatically
+
+78
+00:05:44,830 --> 00:05:48,590
+الجملة صح، بغض النظر النتيجة تحققت أو ماتحققتش، الـ
+
+79
+00:05:48,590 --> 00:05:52,660
+relation كلها صحيحة، خلاص تمام. بس لما تيجي تتكلم
+
+80
+00:05:52,660 --> 00:05:56,880
+عنها، طب هو مالوش معنى، الجمر بيعمل جبنة خضراء، طبعي
+
+81
+00:05:56,880 --> 00:06:00,240
+مالهاش أي معنى، فحتاج إن فعلا كلام بلا معنى، ولكن
+
+82
+00:06:00,240 --> 00:06:05,680
+أثبت إنه صحيح، أثبت إنه حسب الجملة أو الجملة
+
+83
+00:06:05,680 --> 00:06:08,900
+الرياضية بتاعتها اللي هي الـ implication صحيحة. طيب، الـ
+
+84
+00:06:08,900 --> 00:06:13,960
+trivial proof، هذه لأ، بتثبت Q من نفسها، بمعنى أنا مش
+
+85
+00:06:13,960 --> 00:06:21,100
+محتاج الـ P، صار الـ P مالوش لازمة، أنا مش محتاج
+
+86
+00:06:21,100 --> 00:06:25,380
+premises، أعطاني premise بس ما استفدتش منها، أثبتنا
+
+87
+00:06:25,380 --> 00:06:30,800
+Q من نفسها، Q أثبتت من نفسها، مش محتاجين الـ P
+
+88
+00:06:30,800 --> 00:06:34,000
+فيها، ففي الحالة هذه الـ trivial بتسميها، تافه، يعني
+
+89
+00:06:34,000 --> 00:06:36,720
+أعطاني شرط تافه، مالوش أي معنى، أو الـ condition
+
+90
+00:06:36,720 --> 00:06:42,140
+ما استفدتش منه. تمام. في الـ indirect هنكمل غير الـ
+
+91
+00:06:42,140 --> 00:06:45,360
+contrapositive، هناخد في الآخر طريقة هنسميها الـ
+
+92
+00:06:45,360 --> 00:06:49,380
+contradiction، برضه هي تعتبر من طرق الـ indirect
+
+93
+00:06:49,380 --> 00:06:53,060
+فبنكون خلصناها فعليا، هم ثلاثة اللي هنشتغل عليهم و
+
+94
+00:06:53,060 --> 00:06:56,770
+نركز عليهم، الـ direct والـ contrapositive والـ
+
+95
+00:06:56,770 --> 00:06:59,670
+contradiction، هم دول الثلاثة الأكثر أهمية، يعني في
+
+96
+00:06:59,670 --> 00:07:03,030
+شغلنا. طيب، نبدأ في الـ direct وناخد example على طول.
+
+97
+00:07:03,030 --> 00:07:05,630
+خلاص، الـ direct عرفنا إيش يعني الـ direct، هبدأ من
+
+98
+00:07:05,630 --> 00:07:12,430
+الـ P وأحاول أثبت منها الـ Q، تمام. فإذا محتاجين الـ
+
+99
+00:07:12,430 --> 00:07:15,750
+theorem بتاعتنا، وهناخد شوية hints، شوية hints هتكي
+
+100
+00:07:15,750 --> 00:07:18,210
+تساعدنا في الحل، بس هي الـ theorem اللي مطلوب مننا
+
+101
+00:07:18,210 --> 00:07:24,570
+نثبتها، for all numbers N، if N is all integers، فإذن
+
+102
+00:07:24,570 --> 00:07:31,550
+هي integer عدد صحيح وفردي، then N تربيع is a non
+
+103
+00:07:31,550 --> 00:07:36,410
+integer، فإذن برضه الـ N تربيع بتكون integer
+
+104
+00:07:36,410 --> 00:07:41,810
+عدد صحيح وبرضه فردي، أثبتوا لنا الكلام هذا. طيب، عشان
+
+105
+00:07:41,810 --> 00:07:44,710
+نثبت الكلام هذا، في عندنا definitions من الأول
+
+106
+00:07:44,710 --> 00:07:49,350
+بنعرفها، كيف نعرفهم؟ العدد الفردي، وكيف أعرف العدد
+
+107
+00:07:49,350 --> 00:07:54,090
+الزوجي؟ العدد الفردي بنعرفه كالتالي: an integer n is
+
+108
+00:07:54,090 --> 00:07:58,830
+called odd if and only if n equal to 2k plus one.
+
+109
+00:07:58,830 --> 00:08:07,070
+2k زوجي زائد واحد، على طول صار فردي. فإذا كان تحقق للـ
+
+110
+00:08:07,070 --> 00:08:11,530
+N، أني بقدر أمثله بهذا الشكل، بهذه المعادلة، فبقدر
+
+111
+00:08:11,530 --> 00:08:16,170
+أقول إن الـ N هذه إيش؟ عدد فردي، for إيش؟ some integer
+
+112
+00:08:16,170 --> 00:08:21,710
+K، بشرط إن الـ K هذه ما تكونش كسر، ما تكونش كسر، تكون
+
+113
+00:08:21,710 --> 00:08:25,030
+برضه integer. إذا قدرنا نمثلها بهذا الشكل فهي odd.
+
+114
+00:08:25,030 --> 00:08:31,450
+طيب، and N is even if and only if N equal to 2K بس
+
+115
+00:08:32,090 --> 00:08:35,250
+أنه بتقبل القسمة على اتنين، بس خارج القسمة لازم يكون
+
+116
+00:08:35,250 --> 00:08:42,430
+integer، ما يكونش كسر، تمام، برضه for some k أو some
+
+117
+00:08:42,430 --> 00:08:49,330
+integer k. طيب، الـ axiom أو الشيء البديهي، أن أي
+
+118
+00:08:49,330 --> 00:08:53,510
+integer number هو يا odd يا even، ما فيش احتمال ثالث.
+
+119
+00:08:53,510 --> 00:08:59,630
+فإذا every integer is either odd or even، معنى ذلك
+
+120
+00:08:59,630 --> 00:09:02,390
+إذا كان هذا، بنقول الكلام هذا باعتبار أنه لو
+
+121
+00:09:02,390 --> 00:09:06,030
+ما تحققش الـ odd، هي automatically even، والعكس صحيح.
+
+122
+00:09:06,030 --> 00:09:10,050
+لو ما تحققش أنه even، الـ integer هي automatically
+
+123
+00:09:10,050 --> 00:09:17,250
+odd، تمام. نمسك نرجع للسؤال، طبعا المطلوب إيش نعمل؟ if
+
+124
+00:09:17,250 --> 00:09:25,770
+N is odd،  عفوا، is odd، تمام، implies N تربيع is odd.
+
+125
+00:09:26,750 --> 00:09:32,970
+N تربيع is odd، فأوتوماتيك، هنبدأ من هنا، من الـ P
+
+126
+00:09:32,970 --> 00:09:37,650
+فبنبدأ شغلنا عادي من الـ P زي ما هي. طيب، هذه عشان
+
+127
+00:09:37,650 --> 00:09:41,310
+تكون odd، المفروض هي تكون بتساوي 2k plus one،
+
+128
+00:09:41,310 --> 00:09:46,410
+صحيح، وننطلق منها نحاول نثبت هذا الكلام. طب، عشان
+
+129
+00:09:46,410 --> 00:09:50,070
+أثبت الكلام هذا، بدي أجيب N تربيع، فإذا بدي أربع هذا
+
+130
+00:09:50,070 --> 00:09:55,870
+الـ theorem ونفك التربيع، ونشوف هل بتطلع معانا نفس
+
+131
+00:09:55,870 --> 00:10:00,950
+الـ form هذا، ولا تطلع لأ، 2 في integer ولا 2
+
+132
+00:10:00,950 --> 00:10:04,830
+في integer plus واحد، بنحاول نشوف لما نفك هدول و
+
+133
+00:10:04,830 --> 00:10:07,950
+نجمع ونظبطها كيف ممكن تطلع، فهو هي… بس هي الـ
+
+134
+00:10:07,950 --> 00:10:12,650
+proof هي الـ strategy بتاعتنا، كويس. N is odd، then N
+
+135
+00:10:12,650 --> 00:10:17,550
+equal to 2K plus one، كويس، for some integer K. N
+
+136
+00:10:17,550 --> 00:10:23,370
+تربيع هي الـ integer تبعنا، بالـ representation تبعته
+
+137
+00:10:23,370 --> 00:10:28,210
+تربيع، فكنا الأولى
+
+138
+00:10:28,210 --> 00:10:31,670
+تربيع زائد الثانية تربيع زائد الأولى في الثانية في
+
+139
+00:10:31,670 --> 00:10:35,130
+اتنين، مظبوط، تمام. هاي الـ term اللي قلناه، لاحظوا أن
+
+140
+00:10:35,130 --> 00:10:39,930
+هذا الـ term بقدر أطلع منه اتنين عامل مشترك، كويسة،
+
+141
+00:10:39,930 --> 00:10:45,490
+تصير عندكم اتنين في 2K تربيع plus 2K، كله
+
+142
+00:10:45,490 --> 00:10:52,320
+زائد واحد. طيب، هذا الـ term، الـ K هذه إيش؟ Integer.
+
+143
+00:10:52,360 --> 00:10:56,700
+Integer تربيع؟ Integer. فاتنين؟ Integer. يعني في
+
+144
+00:10:56,700 --> 00:10:59,240
+Integer… Integer في Integer؟ Integer. الـ plus
+
+145
+00:10:59,240 --> 00:11:03,360
+integer؟ Integer. فإذا كل الـ term هذا بقدر أقول إن
+
+146
+00:11:03,360 --> 00:11:08,960
+هو J، وJ أكيد integer، فإذا بقدر أمثلها 2J plus
+
+147
+00:11:08,960 --> 00:11:14,780
+واحد، برضه الـ J هتكون some integer.
+
+148
+00:11:17,780 --> 00:11:24,420
+كويس، في الحالة دي أصبحت الـ N تربيع is 2j plus 1، والـ
+
+149
+00:11:24,420 --> 00:11:29,260
+J… الـ J هذه أكيد integer… أكيد integer، فـ
+
+150
+00:11:29,260 --> 00:11:32,700
+automatically، مدام أكيد integer، فالـ N تربيع برضه
+
+151
+00:11:32,700 --> 00:11:37,320
+odd، لإنه حقق، لأنه شرط من الشرطات، شرط الـ odd حققه،
+
+152
+00:11:37,320 --> 00:11:43,380
+أنه شرط الـ odd. خلصنا بشكل direct… بشكل direct.
+
+153
+00:11:43,380 --> 00:11:51,690
+بدأنا من الـ P ووصلنا لليش؟ للـ Q. هذه أول طريقة،
+
+154
+00:11:51,690 --> 00:11:58,290
+اللي هي direct، وعادة ابدأوا فكروا فيها أول ما
+
+155
+00:11:58,290 --> 00:12:02,230
+تبدأوا تحلوا، إذا ما كانش عندكم خيار من إيش؟ لازم
+
+156
+00:12:02,230 --> 00:12:05,450
+تستعملوا طريقة، ابدأوا حاولوا فكروا فيها، بس
+
+157
+00:12:05,450 --> 00:12:08,390
+أحيانا مش دائما بتنفع، هنشوفها في حالات اللي
+
+158
+00:12:08,390 --> 00:12:11,950
+لاحقا، هنشتغل عليها، بس خليني آخد كمان example للـ
+
+159
+00:12:11,950 --> 00:12:17,350
+direct، عشان ناخد أكتر من مثل. طيب، لو قلنا if الـ
+
+160
+00:12:17,350 --> 00:12:21,490
+theorem بتاعتنا اللي بدنا نثبتها: if 6x plus 9y
+
+161
+00:12:21,490 --> 00:12:30,470
+equal to 101، then x or y is not integer. طيب كيف
+
+162
+00:12:30,470 --> 00:12:36,930
+نثبتها؟ هذه بسيطة، هذه P، وهذه بدنا نثبتها Q، هذه P
+
+163
+00:12:36,930 --> 00:12:41,110
+وهذه Q. طيب، هنبدأها direct، مدام إننا نتكلم عن
+
+164
+00:12:41,110 --> 00:12:46,210
+direct، هنبدأ من هنا، هذه لو قسمنا كلها على ثلاثة
+
+165
+00:12:46,210 --> 00:12:49,830
+هتطلع لكم
+
+166
+00:12:49,830 --> 00:12:57,130
+هنا 2x plus 3y بتساوي… طيب
+
+167
+00:12:57,130 --> 00:13:01,570
+هذا not integer، واضحة، باين تماما، هذه not integer،
+
+168
+00:13:01,570 --> 00:13:04,750
+بتطلع 33.6666…
+
+169
+00:13:04,750 --> 00:13:10,590
+ثلثين، كويسة، not integer، أقسمه على integer، not
+
+170
+00:13:10,
+
+223
+00:17:32,460 --> 00:17:36,020
+نبنمثلها بهذا الشكل، هنضرب الثلاثة في الاثنين
+
+224
+00:17:36,020 --> 00:17:39,460
+صار عندكم ستة، اه بقدر أطلع اثنين عامل مشترك، بنقدر
+
+225
+00:17:39,460 --> 00:17:45,060
+وبسيطة جدا وواضحة، two في three k plus one برضه
+
+226
+00:17:45,060 --> 00:17:50,200
+الكلام هذا كله، هذا بقدر أقول أن هو j لأنه
+
+227
+00:17:50,200 --> 00:17:53,360
+integer، أكيد integer لأنه جاي من integer في
+
+228
+00:17:53,360 --> 00:17:57,040
+integer plus integer في integer في integer، أكيد
+
+229
+00:17:57,040 --> 00:18:02,520
+integer في plus integer، أكيد integer minus integer
+
+230
+00:18:02,520 --> 00:18:08,580
+integer على integer، لأ لأ، ما ادانيش، لا خبطش، إذا كان
+
+231
+00:18:08,580 --> 00:18:13,640
+في لجته على وجهه، مش مضمون، ما بقدرش أحطها theorem
+
+232
+00:18:13,640 --> 00:18:19,520
+ما بقدرش أحطها theorem، تمام كويس، then three n plus
+
+233
+00:18:19,520 --> 00:18:26,660
+two is even، لما إيش؟ لما كانت n even، ففي الحالة هذه
+
+234
+00:18:26,660 --> 00:18:31,860
+بقدر أقول أن اتحقق الشرط، فإذا negation n is odd
+
+235
+00:18:31,860 --> 00:18:37,240
+يعني معناها أنه كانت even implies negation 3n plus
+
+236
+00:18:37,240 --> 00:18:44,020
+2 is odd، بالcontrapositive بنعكس، صارت إذا if 3n
+
+237
+00:18:44,020 --> 00:18:49,530
+plus 2 is odd then n is odd، اللي بدنا إياه، اللي
+
+238
+00:18:49,530 --> 00:18:52,970
+بدنا إياه، في الحالة هذه بنكون من ال
+
+239
+00:18:52,970 --> 00:18:56,150
+contrapositive، أثبتنا النظرية أو الـ theory بتاعتنا
+
+240
+00:18:56,150 --> 00:19:01,230
+وبطريقة أسهل من أني أجهد وأشغل على الـ .. الـ .. الـ
+
+241
+00:19:01,230 --> 00:19:03,750
+.. الـ premise بتاعتنا، أني أبدأ من الـ premise
+
+242
+00:19:03,750 --> 00:19:08,970
+بتاعتنا، تمام، هذه الـ in .. الـ indirect
+
+243
+00:19:13,340 --> 00:19:16,380
+خلّيني أكمل، هنشوف في الـ indirect كمان example ..
+
+244
+00:19:16,380 --> 00:19:20,720
+كمان example، الـ theorem اللي مطلوب نثبتها if x
+
+245
+00:19:20,720 --> 00:19:28,340
+plus y greater than 100 then x greater than 50 or
+
+246
+00:19:28,340 --> 00:19:32,840
+y greater than 50، فعلا، ممكن واحدة منهم لازم يكون
+
+247
+00:19:32,840 --> 00:19:37,070
+على الأقل، يمكن يكون الاثنين، or قلنا إنها تشمل
+
+248
+00:19:37,070 --> 00:19:41,390
+الاثنين، لإيش؟ لأن ممكن المئة منهم تجيبوهم، يعني كيف
+
+249
+00:19:41,390 --> 00:19:47,250
+بتجيبوا رقمين مجموعهم مئة؟ خمسين وخمسين، بس أنتم
+
+250
+00:19:47,250 --> 00:19:50,830
+greater than أكبر من مئة، لازم واحدة منهم، واحدة و
+
+251
+00:19:50,830 --> 00:19:56,110
+خمسين، فصارت أكبر، تمام؟ طيب ممكن تكون سبعين وواحدة
+
+252
+00:19:56,110 --> 00:20:00,090
+وثلاثين، واحدة منهم هنا، وممكن تكون ستين وستين
+
+253
+00:20:00,090 --> 00:20:05,540
+الاثنين أكبر، ففي جميع الأحوال بنجح، بس في الحالة
+
+254
+00:20:05,540 --> 00:20:09,080
+هذه، ما بقدرش أقعد أعمل أحط كل احتمالات x وكل احتمالات
+
+255
+00:20:09,080 --> 00:20:15,800
+y وأجرب الـ relation هذه عشان أشتغل direct، عشان
+
+256
+00:20:15,800 --> 00:20:19,200
+لازم أبدأ من هنا، طب لأ، ما ادانيش أبدأ من هنا، هذه صعبة
+
+257
+00:20:19,200 --> 00:20:22,640
+ليش؟ لأنه بدي أحط كل احتمالات الممكنة لـ x وكل
+
+258
+00:20:22,640 --> 00:20:25,940
+احتمالات الممكنة لـ y، والاحتمالات، تعالوا نطلع عليها
+
+259
+00:20:25,940 --> 00:20:31,760
+x أكبر من 50، وهذه or كمان، يعني معنى ذلك أنه حامل
+
+260
+00:20:31,760 --> 00:20:35,040
+عملية احتمالات كبيرة جدا عشان نشغل direct، لو كنت
+
+261
+00:20:35,040 --> 00:20:38,840
+تشغل direct فهذه أنسب لها إيش؟ الـ indirect، ليش؟ لأن
+
+262
+00:20:38,840 --> 00:20:44,640
+الـ indirect لو كده بتصير كالتالي، من الـ theorem اللي
+
+263
+00:20:44,640 --> 00:20:48,660
+بتثبتها بنحدد الـ p، الـ p كانت x plus y greater than
+
+264
+00:20:48,660 --> 00:20:54,620
+100، لـ q كان x أكبر من 50 أو y أكبر من 50، هنشتغل
+
+265
+00:20:54,620 --> 00:20:58,240
+على الـ negation عشان نجيب الـ contrapositive، لما
+
+266
+00:20:58,240 --> 00:21:00,280
+نعمل negation للـ term هذا
+
+267
+00:21:03,380 --> 00:21:09,260
+شيء بنعمله نجاسة هنا، صارت العكس، أكبر من، أقل من أو
+
+268
+00:21:09,260 --> 00:21:16,780
+يساوي، طيب، وهنا أقل من أو يساوي، والـ or and ما ننساش
+
+269
+00:21:16,780 --> 00:21:24,020
+هذه دي مورغان، في نجاسة، هندخله على connection
+
+270
+00:21:24,020 --> 00:21:28,440
+موجودة، فبدنا نعكسها، الـ or بدتصير and، وهذول بدنا
+
+271
+00:21:28,440 --> 00:21:33,680
+نعكسهم تماما، عكس أكبر من، أقل من أو يساوي، لأن
+
+272
+00:21:33,680 --> 00:21:40,080
+المساواة لم تكن مشمولة في أكبر منه، تمام، فانشطرنا
+
+273
+00:21:40,080 --> 00:21:45,200
+على negation q، عبارة عن x أقل من أو يساوي خمسين و
+
+274
+00:21:45,200 --> 00:21:49,140
+y أقل من أو يساوي خمسين، negation p اللي بدنا نثبتها
+
+275
+00:21:49,140 --> 00:21:54,300
+منها أن x زائد y أقل من أو يساوي مئة، هل الكلام هذا
+
+276
+00:21:54,300 --> 00:21:58,490
+متحقق؟ إذا عرفنا نحقق negation p، هذه
+
+277
+00:21:58,490 --> 00:22:02,190
+قدرنا نحققها من negation q، فإذا الـ relation صحيحة
+
+278
+00:22:02,190 --> 00:22:04,830
+مع أن ذلك الـ contrapositive تبعها صحيحة، اللي هي
+
+279
+00:22:04,830 --> 00:22:08,750
+النظرية اللي بدنا نستخدمها، طيب تعالوا نشوف هنا أقل
+
+280
+00:22:08,750 --> 00:22:13,130
+من أو يساوي خمسين، أكبر قيمة ممكنة هي احتمال واحد
+
+281
+00:22:13,130 --> 00:22:15,890
+أنها تكون بتساوي فعليا خمسين، أنها تكون بتساوي
+
+282
+00:22:15,890 --> 00:22:20,690
+خمسين، عشان هذه القصة تكون أقل من أو يساوي مئة
+
+283
+00:22:20,690 --> 00:22:24,570
+فبدنا نشوف أكبر قيمة، هل هتظل ضمن الـ range تبعنا
+
+284
+00:22:24,570 --> 00:22:30,840
+هنا ولا لأ، طيب x زائد y أقل من خمسين، والـ y خمسين
+
+285
+00:22:30,840 --> 00:22:34,860
+أكبر قيمة ممكنة بتساوي مئة، المئة تنطبق مع المعادلة
+
+286
+00:22:34,860 --> 00:22:41,620
+المئة ماشية، لأنه يساوي مئة، فهي فعلا تساوي مئة
+
+287
+00:22:41,620 --> 00:22:48,860
+معنى ذلك أن كل الأرقام اللي أقل صحيحة برضه، لاحظوا
+
+288
+00:22:48,860 --> 00:22:54,160
+إحنا شغلنا x أقل من أو تساوي خمسين، صح؟ بنعمل test
+
+289
+00:22:54,160 --> 00:22:57,480
+على أكبر رقم ممكن، إذا تحقق الـ test على أكبر رقم
+
+290
+00:22:57,480 --> 00:23:03,020
+فإذا كل اللي أقل منه برضه متحقق، هي
+
+291
+00:23:03,020 --> 00:23:07,900
+أكبر رقم للـ x، الشيء أنها تكون خمسين، وأكبر رقم لـ
+
+292
+00:23:07,900 --> 00:23:11,920
+y خمسين، عشان عوضنا هنا ووجدنا أنها تتفق مع المعادلة
+
+293
+00:23:11,920 --> 00:23:15,700
+طيب لو أخذنا أي رقم آخر أقل من الخمسين، هي ماشية
+
+294
+00:23:15,700 --> 00:23:19,940
+المعادلة برضه، المعادلة ماشية، فإذا إحنا أخذنا
+
+295
+00:23:19,940 --> 00:23:25,200
+الاحتمال الوحيد اللي ممكن يبعد، إنها تكون تساوي
+
+296
+00:23:25,200 --> 00:23:28,660
+الخمسين، أكبر رقم ممكن لـ x وأكبر رقم ممكن لـ y
+
+297
+00:23:28,660 --> 00:23:33,960
+عوضنا ووجدناها ما زالت ضمن أو بتحقق ليه الـ negation
+
+298
+00:23:33,960 --> 00:23:37,680
+p، ما زالت بتحقق negation p، فإذا الـ relation دائما
+
+299
+00:23:37,680 --> 00:23:41,500
+صحيحة، الـ relation دائما صحيحة لكل الأرقام الممكنة لـ
+
+300
+00:23:41,500 --> 00:23:48,860
+x و y، for all numbers، لمين؟ لـ x و y، ففي الحالة دي
+
+301
+00:23:48,860 --> 00:23:53,120
+بقدر أقول أن الـ relation صحيحة، كل هذا على بعضه من
+
+302
+00:23:53,120 --> 00:23:58,560
+هنا employs الـ term هذا، okay، relation صح، فإذا الـ
+
+303
+00:23:58,560 --> 00:24:06,780
+contrapositive بتاعتها أكيد صحيحة، اللي هي الـ
+
+304
+00:24:06,780 --> 00:24:09,840
+theorem المطلوبة، من غير ما أعمل احتمالات كل
+
+305
+00:24:09,840 --> 00:24:14,160
+احتمالات الممكنة لأكبر من 100، الأقل هنا وفرت عليها
+
+306
+00:24:14,160 --> 00:24:19,520
+أقل، بجيب أكبر قيمة ممكنة، وهل هي ما زالت ضمن أقل من
+
+307
+00:24:19,520 --> 00:24:22,680
+100 ولا لأ؟ اه ما زالت ضمن أقل من 100، معناته حتى
+
+308
+00:24:22,680 --> 00:24:27,140
+اللي أقل ضمن المعادلة، ضمن المعادلة المطلوبة في
+
+309
+00:24:27,140 --> 00:24:31,160
+جاتها، ففي الحالة هذه قدرنا نثبت negation q
+
+310
+00:24:31,160 --> 00:24:35,920
+implies negation p، ومنها مباشرة، فإذا p implies q
+
+311
+00:24:36,760 --> 00:24:40,140
+اللي هي المعادلة اللي فوق، هي الـ contrapositive
+
+312
+00:24:40,140 --> 00:24:46,560
+اللي اتكلمنا عنها، أو الـ indirect، indirect محددينها
+
+313
+00:24:46,560 --> 00:24:53,580
+تحديدا اللي هي الـ contrapositive، تمام، الـ .. الـ
+
+314
+00:24:53,580 --> 00:24:58,260
+vacuous to prove example، هذا اللي قلنا بلا معنى
+
+315
+00:24:58,260 --> 00:25:02,720
+بمعنى أنه هيعطيني premise وبعدين إحنا مثبتين أن هي
+
+316
+00:25:02,720 --> 00:25:06,680
+الـ premise غلط من أصله، فمعنى ذلك إيش الـ conclusion
+
+317
+00:25:06,680 --> 00:25:10,500
+يطلع زي ما يطلع، مش هتفرق، الـ relation كلها على بعض
+
+318
+00:25:10,500 --> 00:25:19,220
+دائما صح، ليش؟ false الـ premise false، فإذا بغض
+
+319
+00:25:19,220 --> 00:25:24,180
+النظر، إيش النتيجة؟ هي دائما الـ relation صحيحة، لحظة
+
+320
+00:25:24,180 --> 00:25:30,640
+إذا كان أثبت عندكم أن الـ premise false، فالـ
+
+321
+00:25:30,640 --> 00:25:34,320
+relation كلها صحيحة بغض النظر، والله فعلا هيتحقق
+
+322
+00:25:34,320 --> 00:25:38,840
+اللي طالبه أو لا، الـ conclusion تحققت أو ما تحققتش
+
+323
+00:25:38,840 --> 00:25:42,400
+بغض النظر، دائما الـ relation كلها على بعض الـ
+
+324
+00:25:42,400 --> 00:25:47,200
+implication صحيحة، true، فـ automatically بشكل لا
+
+325
+00:25:47,200 --> 00:25:52,700
+معنى له هي صحيحة، تمام؟ كويس، خلّيني أشوف for example
+
+326
+00:25:52,700 --> 00:25:57,420
+إذا كانت n is both odd and even، اتنين، ما فيش اللي
+
+327
+00:25:57,420 --> 00:26:01,160
+odd أو even، n إحنا عارفين إنه يا odd يا even
+
+328
+00:26:01,160 --> 00:26:05,000
+بس واحد يجي يقول ليه إذا كان n تحققت لك الشرطين يا
+
+329
+00:26:05,000 --> 00:26:09,080
+odd و even، ما فيش حاجة اسمها odd و even، ما فيش أي
+
+330
+00:26:09,080 --> 00:26:11,880
+رقم integer بقدر أقول إنه odd و even، فإذا هذه
+
+331
+00:26:11,880 --> 00:26:18,440
+negation على طول هذه false، فـ then تحققت أو ما تحققتش
+
+332
+00:26:18,440 --> 00:26:22,040
+مش هتفرق، هي فعلا هتلاقوها مرات بتتحقق ومرات لأ
+
+333
+00:26:22,040 --> 00:26:25,980
+بس أنا مش هتطلعها أصلا، أشوف هي بتتحقق أو بتتحققش
+
+334
+00:26:25,980 --> 00:26:31,100
+يعني مش هتفرق معايا تحققت فليكن، ما تحققتش فليكن
+
+335
+00:26:31,100 --> 00:26:34,620
+ما تفرقش، مش هي اللي هتعطيني القرار، القرار بدأ من
+
+336
+00:26:34,620 --> 00:26:38,640
+where، من negation، فيه الفرضية اللي أصلا غلط
+
+337
+00:26:38,640 --> 00:26:42,840
+الفرضية اللي أساسا بادية من الأساس غلط، فمدام
+
+338
+00:26:42,840 --> 00:26:47,260
+الفرضية غلط، فبقول أن هي الـ theory كلها على بعض
+
+339
+00:26:47,260 --> 00:26:54,100
+vacuously true، بشكل لا معنى له، حقيقية صحيحة بشكل
+
+340
+00:26:54,100 --> 00:27:02,180
+بدون معنى، هي حقيقية فعلا كـ relation كاملة على بعض
+
+341
+00:27:02,180 --> 00:27:05,280
+طيب
+
+342
+00:27:05,280 --> 00:27:09,660
+الـ trivial، لأ، الـ trivial مختلفة شوية، إحنا ما نتكلمش
+
+343
+00:27:09,660 --> 00:27:14,820
+عن الـ premise، بنتكلم عن مين؟ عن الـ conclusion، لذا
+
+344
+00:27:14,820 --> 00:27:19,350
+الـ conclusion بقدر أثبته من نفسه، بغض النظر إيش هي
+
+345
+00:27:19,350 --> 00:27:23,830
+الـ premise، الـ premise صح غلط مش فارقة كتير، أنا
+
+346
+00:27:23,830 --> 00:27:30,210
+عندي إمكانية أن أنا أثبت الـ q من نفسها، مش محتاج الـ
+
+347
+00:27:30,210 --> 00:27:34,370
+p، مش محتاج الـ premise، الـ premise ما تفرقش معايا، صح
+
+348
+00:27:34,370 --> 00:27:38,570
+ولا غلط، ولا كويسة ولا مش كويسة، ولا premises كتيرة
+
+349
+00:27:38,570 --> 00:27:42,630
+ولا واحدة، ولا ما فيش premise أصلا، مش هتفرق، مش فارقة
+
+350
+00:27:42,630 --> 00:27:49,300
+هنا if we know q is true then p implies q is
+
+351
+00:27:49,300 --> 00:27:53,320
+true، تمام،
+
+352
+00:27:53,320 --> 00:28:00,380
+لاحظوا كأنكم هنا بتتكلموا عن الحالة الـ q، الـ
+
+353
+00:28:00,380 --> 00:28:04,850
+q، إذا q is true، فهي الـ relation صحيحة بغض
+
+354
+00:28:04,850 --> 00:28:09,510
+النظر عن الـ p، الـ p false فليكن، false true فليكن
+
+355
+00:28:09,510 --> 00:28:13,790
+true، في الآخر أنا اللي حاكم على الشغل تبعي أن الـ q
+
+356
+00:28:13,790 --> 00:28:18,230
+أنا أثبت منها نفسها أن هي true، مدام أثبت نفسي أن
+
+357
+00:28:18,230 --> 00:28:22,890
+هي true، الـ relation كلها true، فالإثبات النظرية هي
+
+358
+00:28:22,890 --> 00:28:25,970
+صحيحة، ليش؟ لأن هي النظرية أصلا relation يعطيني
+
+359
+00:28:25,970 --> 00:28:29,870
+إياها if then، فإذا الـ if then اللي هي الـ
+
+360
+00:28:29,870 --> 00:28:34,560
+implication relation هذه صحيحة، فإذا النظرية صحيحة
+
+361
+00:28:34,560 --> 00:28:40,100
+زي لو قال if it's raining today then three is an
+
+362
+00:28:40,100 --> 00:28:43,840
+odd number، طب ما هي فعلا three is an odd number بغض
+
+363
+00:28:43,840 --> 00:28:47,960
+النظر شتاء ولا مش شتاء اليوم، مش هتفرق كتير، ليش؟ هي
+
+364
+00:28:47,960 --> 00:28:53,620
+أصلا odd، three odd، الـ q هي متحققة بدون ما أعرف إيش
+
+365
+00:28:53,620 --> 00:28:55,780
+الـ premise
+
+366
+00:28:57,130 --> 00:28:59,430
+الـ premise أو الـ premises كلها، إذا كانوا أكثر من
+
+367
+00:28:59,430 --> 00:29:02,110
+واحدة، تكون اللي تكون تكون force تكون true، مش هتفرق
+
+368
+00:29:02,110 --> 00:29:07,810
+كتير معانا، ليش؟ لأن الـ conclusion أصلا is true هو
+
+369
+00:29:07,810 --> 00:29:12,530
+true أصلا، فينطبق مع الحالة بتاعة الـ implication أو
+
+370
+00:29:12,530 --> 00:29:15,290
+الـ relation للـ theory، الـ relation للـ theory، هذا
+
+371
+00:29:15,290 --> 00:29:18,610
+طريقة إثبات برضه للـ relations بتاعتنا هذه true
+
+372
+00:29:18,610 --> 00:29:22,530
+وهذه true، الـ conclusion true بغض النظر إيش الـ ..
+
+373
+00:29:22,530 --> 00:29:26,440
+الـ .. الـ premise، هي دائما true الـ relation، فإذا
+
+374
+00:29:26,440 --> 00:29:33,600
+النظرية دي true، فإذا طريقة trivially true، بطريقة
+
+375
+00:29:33,600 --> 00:29:39,060
+.. كأنه هي trivial، بمعنى تافه أو ما لهوش يعني ..
+
+376
+00:29:39,060 --> 00:29:42,480
+ما لهوش قيمة، ما لهوش قيمة، فمعنى ذلك أنه أنا .. أنا
+
+377
+00:29:42,480 --> 00:29:44,700
+عندي هنا الـ premise ما لهاش تافه، ما لهاش معنى،
+
+378
+00:29:44,700 --> 00:29:49,140
+ما لهاش قيمة، لو ما عطتنيش يحصل، هاي معناها، لو
+
+379
+00:29:49,140 --> 00:29:53,840
+ما عطتنيش إياها، ما بديش إياها المعلومة، ما بدناش إياها
+
+380
+00:29:56,030 --> 00:29:59,370
+معلومة trivial بالنسبة لي هي الـ q مثبت حالة لحاله
+
+381
+00:29:59,370 --> 00:30:08,990
+الـ q مثبت حالة لحاله الـ
+
+382
+00:30:08,990 --> 00:30:14,690
+q مثبت حالة لحاله الـ q مثبت حالة لحاله الـ q مثبت
+
+383
+00:30:14,690 --> 00:30:15,170
+حالة لحاله الـ q مثبت حالة لحاله الـ q مثبت حالة
+
+384
+00:30:15,170 --> 00:30:18,350
+لحاله الـ q مثبت حالة لحاله الـ q مثبت حالة لحاله
+
+385
+00:30:18,350 --> 00:30:19,450
+الـ q مثبت حالة لحاله الـ q مثبت حالة لحاله الـ q
+
+386
+00:30:19,450 --> 00:30:21,690
+حالة لحاله الـ q مثبت حالة لحاله الـ q، بغض النظر أن
+
+387
+00:30:21,690 --> 00:30:25,270
+الـ integer n ده هو فعلا عبارة عن مجموع رقمين
+
+388
+00:30:25,270 --> 00:30:28,970
+أوليين أو لأ، فليكن مجموع رقمين أوليين، وليكن لأ،
+
+389
+00:30:28,970 --> 00:30:31,690
+ما يكونش، مش مجموع، مش ه
+
+445
+00:34:43,520 --> 00:34:47,850
+بعض بشكلين ال two integers في أبسط صورهم بقدر
+
+446
+00:34:47,850 --> 00:34:52,910
+اختصرهم مع بعض لا يتم اختصارهم مع بعض هدول الرقمين
+
+447
+00:34:52,910 --> 00:34:56,070
+لا يختصرون مع بعض والاتنين integer إذا تحقق الكلام
+
+448
+00:34:56,070 --> 00:35:01,670
+نسميها the X هذه بنسميها rational تمام هنا
+
+449
+00:35:01,670 --> 00:35:06,310
+لا احنا بدنا بالعكس احنا قاعدين بنقول root two جذر
+
+450
+00:35:06,310 --> 00:35:13,120
+الاثنين is irrational هي لا يوجد أي رقمين integers
+
+451
+00:35:13,120 --> 00:35:18,700
+حاصل قسمتهم على بعض بيعطيك root 2 هذه معناها هذا
+
+452
+00:35:18,700 --> 00:35:21,580
+معناها بدنا نشوف هل الكلام هذا بصير معناه هذا بصيرش
+
+453
+00:35:21,580 --> 00:35:28,100
+معناه طيب عشان نعمله هنفرض negation فيه بدنا نفرض
+
+454
+00:35:28,100 --> 00:35:35,860
+negation فيه أنه هي ليست rationalنفترض أن المعلومة
+
+455
+00:35:35,860 --> 00:35:39,320
+التي أعطتني إياها مش صح، أنا بفترض عكسها، وأبدأ
+
+456
+00:35:39,320 --> 00:35:42,440
+أثبت، أشتغل في الإثبات تبعي، سأُفاجأ في الإثبات أن
+
+457
+00:35:42,440 --> 00:35:47,080
+إثباتي غلط، أنه طلع لي خطأ، معناته الصح كان
+
+458
+00:35:47,080 --> 00:35:50,580
+الأول بدون ما أضطر أشتغل على الأول من الأول
+
+459
+00:35:50,580 --> 00:35:54,100
+بدون أن أضطر بطريقة direct اضطررنا نشتغل هنا by
+
+460
+00:35:54,100 --> 00:35:58,280
+a method  نسميها ال contradiction أو التعارض
+
+461
+00:35:58,280 --> 00:36:01,480
+لإجابتنا
+
+462
+00:36:01,480 --> 00:36:05,180
+أنا المفروض نتوقع شغلة وهيطلع شغلة ثانية تمام
+
+463
+00:36:05,180 --> 00:36:09,260
+فهنا هنقول two to the power نص  التي هي برضه
+
+464
+00:36:09,260 --> 00:36:13,000
+root اثنين to the power نص التي هي كأنها الجذر
+
+465
+00:36:13,000 --> 00:36:16,300
+تمام well  ليست rational هنا  أقول irrational
+
+466
+00:36:16,300 --> 00:36:21,880
+بدي أقول أن هي rationalهذا يعني أن يوجد two
+
+467
+00:36:21,880 --> 00:36:29,400
+integers I وJ بقدر بيكون  لا يوجد عوامل مشتركة بينهما بدون
+
+468
+00:36:29,400 --> 00:36:33,040
+عوامل مشتركة زي ما قلت لكم تكون ال A و ال B بأبسط
+
+469
+00:36:33,040 --> 00:36:35,840
+صورهم يعني أنا ما أقدرش اختصرهم مع بعض أكثر من هيك
+
+470
+00:36:35,840 --> 00:36:39,360
+لا يتم اختصارهم مع بعض ما يكونش اثنين على أربعة
+
+471
+00:36:39,360 --> 00:36:44,920
+تكون ثلاثة على تسعة لا لا يتم اختصارهم مع بعض
+
+472
+00:36:44,920 --> 00:36:51,120
+لا يوجد أي عامل مشترك بينهما والاثنين integers إذا حصل
+
+473
+00:36:51,120 --> 00:36:55,560
+قسمتهم مع بعض بيطلق لكم X بغض النظر X، يمكن X لا
+
+474
+00:36:55,560 --> 00:36:58,840
+تكون integer، يعني ليس مضطراً تكون integer X، X ليس
+
+475
+00:36:58,840 --> 00:37:01,700
+مضطراً تكون integer، يمكن خمسة على ثلاثة، ليس
+
+476
+00:37:01,700 --> 00:37:06,280
+integer، بس الرقم خمسة على ثلاثة هو rational، هنا
+
+477
+00:37:06,280 --> 00:37:09,380
+يسمى rational، تمام، هنا زي ما قلنا بنعمل ال
+
+478
+00:37:09,380 --> 00:37:13,100
+negation فيه وننطلق منها لإثبات الشغل تبعنا
+
+479
+00:37:14,060 --> 00:37:16,900
+فهاجولي العكس إثبات أن هي تكون rational مادام
+
+480
+00:37:16,900 --> 00:37:21,520
+rational يعني يوجد two integers اللذان هما I and J
+
+481
+00:37:21,520 --> 00:37:24,840
+ولا يوجد common بينهما common divisors لا يوجد أي عامل
+
+482
+00:37:24,840 --> 00:37:30,160
+بينهما بنقدر في الحالة هذه نقول أن هذين rational
+
+483
+00:37:30,160 --> 00:37:35,440
+ريشونال معناه ذلك أن two to the power نص أو جذر
+
+484
+00:37:35,440 --> 00:37:40,860
+سيلاحظون جذر نص جذر اثنين أقدر أقول أن هو I
+
+485
+00:37:40,860 --> 00:37:45,990
+over Jصحيح؟ ما هي  original هي عبارة عن two
+
+486
+00:37:45,990 --> 00:37:48,990
+terms لكن بدنا نحدد أن ال two terms هذان integers
+
+487
+00:37:48,990 --> 00:37:54,770
+ال I integer ال J integer جيد ولا يوجد عامل مشترك
+
+488
+00:37:54,770 --> 00:37:58,490
+بينهما خلاص هذان بأبسط صورة لهما طيب لو ربعنا
+
+489
+00:37:58,490 --> 00:38:04,210
+الطرفين لو ربعنا الطرفين في الحالة هذه ماذا تصير
+
+490
+00:38:04,210 --> 00:38:11,600
+عندكم؟ ستصير اثنين تربيع ال I over تربيع ال Jتمام
+
+491
+00:38:11,600 --> 00:38:17,360
+برضه نكمل مع بعض two هذه سنطلعها فوق يعني كل ال
+
+492
+00:38:17,360 --> 00:38:22,560
+two المعادلة كلها سنضربها في J تربيع ستصير اثنين
+
+493
+00:38:22,560 --> 00:38:29,560
+J تربيع تساوي I تربيع طيب خليني امسككم  شيء شيء
+
+494
+00:38:29,560 --> 00:38:33,460
+المعادلة هذه حلوة وبنقدر نطلع منها شوية معلومات
+
+495
+00:38:33,460 --> 00:38:39,360
+اثنين J تربيع تساوي I تربيع معناه ذلك أن I تربيع
+
+496
+00:38:39,360 --> 00:38:46,470
+evenلحظة اثنين في some integer اثنين في some
+
+497
+00:38:46,470 --> 00:38:50,390
+integer  وَ نحن أصلاً قلنا ال rational هما two
+
+498
+00:38:50,390 --> 00:38:54,630
+integers على بعض فأنا ضامن أن ال J integer تربيع ال
+
+499
+00:38:54,630 --> 00:38:59,490
+integer integer لحظة كأنها صارت تتكلم عن اثنين K و
+
+500
+00:38:59,490 --> 00:39:05,410
+ال K هذا هو J تربيع ممتاز معناه ذلك أن I تربيع
+
+501
+00:39:05,410 --> 00:39:11,260
+evenطيب نحن نعرف إذا كانت I تربيع even
+
+502
+00:39:11,260 --> 00:39:20,900
+معناته I even تمام فإذا ال I even جيد ال I even
+
+503
+00:39:20,900 --> 00:39:25,760
+يعني أقدر أمثلها ب two K أقدر أمثلها ب two K فإذا
+
+504
+00:39:25,760 --> 00:39:31,940
+ببساطة جداً أقدر أقول أن اثنين J تربيع تساوي اثنين K
+
+505
+00:39:31,940 --> 00:39:43,240
+تربيع 2k تربيع 2k تربيع هذه 4k تربيع طيب نقسم على 2
+
+506
+00:39:43,240 --> 00:39:49,780
+2k تربيع صار عندنا كل هذا ال term J تربيع تساوي 2k
+
+507
+00:39:49,780 --> 00:40:01,560
+تربيع ممتاز  طيب ما هذه اثنين اثنين R و R some
+
+508
+00:40:01,560 --> 00:40:11,110
+integerمعنى ذلك J² even even صحيح؟ معنى ذلك أن
+
+509
+00:40:11,110 --> 00:40:14,130
+هذا even هو اثنين في some integer some integer
+
+510
+00:40:14,130 --> 00:40:18,190
+هذا عبارة عن integer تربيع عبارة عن integer تربيع
+
+511
+00:40:18,190 --> 00:40:22,550
+فليكن ال integer في integer سيطلع integer جيد
+
+512
+00:40:22,550 --> 00:40:33,620
+مادام J تربيع is even أكيد J even طلع I evenو J
+
+513
+00:40:33,620 --> 00:40:39,400
+even even على even يوجد عامل مشترك هو الاثنين طيب
+
+514
+00:40:39,400 --> 00:40:43,780
+نحن نقول من الأساس no common divisor then
+
+515
+00:40:43,780 --> 00:40:48,620
+false لاحظنا وضعنا أنفسنا في موقف صعب من الأول نقول
+
+516
+00:40:48,620 --> 00:40:50,980
+نقول أن هي rational مع الإثبات ظهر أنها ليست
+
+517
+00:40:50,980 --> 00:40:54,060
+rational لماذا ليست rational لأنه يوجد عامل مشترك بينهما
+
+518
+00:40:58,840 --> 00:41:03,600
+لا سنعيدها كلها لن نعيد من هنا كلها  سنجعلكم
+
+519
+00:41:03,600 --> 00:41:10,160
+للبداية بتاعتها لحظة
+
+520
+00:41:10,160 --> 00:41:17,220
+هلو  بدأنا قلنا أن الفرضية بتاعتنا عكس ال given
+
+521
+00:41:17,220 --> 00:41:23,550
+ال given يقول لكم أن جذر اثنين is irrational نفهم
+
+522
+00:41:23,550 --> 00:41:26,630
+ماذا يعني irrational لنعرف نشتغل، ف irrational
+
+523
+00:41:26,630 --> 00:41:30,730
+معناه أنه أقدر .. rational أولاً أنه أقدر ..
+
+524
+00:41:30,730 --> 00:41:35,650
+أقدر .. يعني نعمل تمثيل للرقم على أساس أنه حاصل
+
+525
+00:41:35,650 --> 00:41:42,190
+قسمة رقمين integers integers وبدون أي عوامل مشتركة
+
+526
+00:41:42,190 --> 00:41:47,970
+بينهما فإذا no common divisors أو لا يوجد عامل مشترك
+
+527
+00:41:47,970 --> 00:41:51,870
+بينهما لا يوجد عامل مشترك بينهما قلنا okay خلاص
+
+528
+00:41:51,870 --> 00:41:55,590
+سنفرض الفرضية التي هي negation لما هو موجود أصلاً
+
+529
+00:41:55,590 --> 00:42:01,410
+فهيقول أن جذر اثنين ليست rational هو يقول لي are
+
+530
+00:42:01,410 --> 00:42:04,750
+rational أو are rational  عملت ال negation فتصير
+
+531
+00:42:04,750 --> 00:42:10,250
+عبارة مادام rational أقدر أقول أنها I over J I over
+
+532
+00:42:10,250 --> 00:42:13,450
+J والاثنين يجب أن يكونا integers ولا يوجد عامل مشترك
+
+533
+00:42:13,450 --> 00:42:17,450
+بينهما تمام جيد  لنمشي معها  نحن نعرف
+
+534
+00:42:17,450 --> 00:42:21,430
+أن هذه جذر يعني لو عملنا تربيع هنا تربيع هنا
+
+535
+00:42:21,430 --> 00:42:26,530
+بمشي الحل ربعنا الطرفين تمام  ربعنا الطرفين
+
+536
+00:42:26,530 --> 00:42:29,910
+ومشيت الأمور الطرفين هذين لما ربعناهما ماذا
+
+537
+00:42:29,910 --> 00:42:37,190
+سيظهر عندكم سيظهر عندكم أن الاثنين تساوي I و
+
+538
+00:42:37,190 --> 00:42:40,690
+لا J التي فوق كانت I تربيع فوق I و J
+
+539
+00:42:40,690 --> 00:42:48,690
+تربيع صحيح  من هذه أقدر أقول أن I تربيع
+
+540
+00:42:48,690 --> 00:42:55,770
+تساوي 2J تربيع كلام صحيح كلام صحيح طيب نحن نعرف
+
+541
+00:42:55,770 --> 00:43:03,320
+أن لنعمل test على odd أو evenندور ال odd ال
+
+542
+00:43:03,320 --> 00:43:10,220
+even تكون عبارة عن 2k الرقم 2 في some integer ال
+
+543
+00:43:10,220 --> 00:43:15,620
+odd 2k + 1 لا نحن سنمسك الجزء هذا لأنه
+
+544
+00:43:15,620 --> 00:43:20,660
+ينطبق عندنا هنا هو الذي ينطبق عندنا هنا فإذا J
+
+545
+00:43:20,660 --> 00:43:28,240
+تربيع هي كأنها K مثلاً أو كأنها أي symbol آخر
+
+546
+00:43:28,240 --> 00:43:36,380
+سأقول مثلاً كأنها R تساوي J تربيع ال J أساساً من
+
+547
+00:43:36,380 --> 00:43:39,660
+الفرضية التي نريد فرضيتنا فيها أنها integer طيب
+
+548
+00:43:39,660 --> 00:43:44,660
+integer تربيع يجب أن تكون integer رقم صحيح في نفسه
+
+549
+00:43:44,660 --> 00:43:48,820
+يجب أن يطلع رقم صحيح فإذا R هي رقم صحيح ولاحظوا
+
+550
+00:43:48,820 --> 00:43:53,280
+أن I تربيع طلعت كأنها تساوي 2 في رقم صحيح في
+
+551
+00:43:53,280 --> 00:43:58,300
+integer طيب هذا يتوافق تماماً مع even معنا ذلك أن
+
+552
+00:43:58,300 --> 00:44:05,630
+I تربيع evenفإذن أقدر أقول I تربيع is even ال I
+
+553
+00:44:05,630 --> 00:44:11,290
+تربيع even معناه ذلك أن I لحالها برضه even برضه
+
+554
+00:44:11,290 --> 00:44:18,610
+even فإذن I is even هذه الجزئية برضه إذا أنتم
+
+555
+00:44:18,610 --> 00:44:23,670
+تريدون تثبتوها تستطيعون تثبيتها ببساطة إذا ممكن
+
+556
+00:44:23,670 --> 00:44:27,670
+تُعطى بالطرف الثاني أنه given أن I is even و
+
+557
+00:44:27,670 --> 00:44:31,810
+أثبت أن I تربيع is evenأو تُعطى بهذا الشكل إذا
+
+558
+00:44:31,810 --> 00:44:35,370
+كانت I تربيع is even أثبتوا أن I is even إذا
+
+559
+00:44:35,370 --> 00:44:39,770
+أعطيت بهذا الشكل  ممكن تشتغلوا على ال indirect إذا
+
+560
+00:44:39,770 --> 00:44:44,710
+I is even اشتغلوا على ال direct عوضوا هذا ب 2
+
+561
+00:44:44,710 --> 00:44:47,810
+واعملوا تربيع  ستحصلون على 4  الأربعة تستطيعون أخذ
+
+562
+00:44:47,810 --> 00:44:52,650
+مشتقة 2 فستطلع برضه even تمام المهم أننا وصلنا
+
+563
+00:44:52,650 --> 00:44:56,810
+لإثبات أن I even سنضع مربع عند هذه النقطة
+
+564
+00:44:56,810 --> 00:45:01,750
+طيب إذا كانت هي أصلاً evenهي أساساً even معناه ذلك
+
+565
+00:45:01,750 --> 00:45:08,310
+أنه فعلياً هي تساوي  I تربيع تساوي 2J  كذا هي
+
+566
+00:45:08,310 --> 00:45:16,010
+نفسها أقدر أحطها ب2K  تستطيعون  نضعها بشكل 2K أو بطريقة
+
+567
+00:45:16,010 --> 00:45:21,110
+التي هي 2K تمام في الحالة هذه تستطيعون مباشرة نقول أن
+
+568
+00:45:21,110 --> 00:45:26,220
+I هي عبارة عن 2 some integer في أي some integer في
+
+569
+00:45:26,220 --> 00:45:30,220
+الحالة التي نتكلم عنها وهذا معناه أن I تربيع
+
+570
+00:45:30,220 --> 00:45:38,520
+برضه هذا تربيع عبارة عن two K نحن  اتفقنا integer
+
+571
+00:45:38,520 --> 00:45:46,760
+integer اجعلوه تربيع يساوي اثنين J تربيع نقسم على
+
+572
+00:45:46,760 --> 00:45:50,440
+اثنين  بقي
+
+573
+00:45:50,440 --> 00:45:55,560
+على اثنين ماذا يظهر؟ يصبح J تربيع تساوي two K
+
+574
+00:45:55,560 --> 00:46:01,340
+تربيع على اثنين  هذه على اثنين عفواً هذه أساساً
+
+575
+00:46:01,340 --> 00:46:06,740
+term هذا عبارة عن أربعة K تربيع  الأربعة مع الاثنين
+
+576
+00:46:06,740 --> 00:46:13,000
+فإذا J تربيع تساوي اثنين في K تربيع K تربيع هذه
+
+577
+00:46:13,000 --> 00:46:18,320
+integer هي أساساً integerصحيح؟ كلها مع بعضها integer
+
+578
+00:46:18,320 --> 00:46:22,720
+لأننا ضمنّا من الأساس K سنحصل عليها من عودة في
+
+579
+00:46:22,720 --> 00:46:28,760
+I قلنا أن I تساوي 2K لماذا؟ لأنها even طيب لكي
+
+580
+00:46:28,760 --> 00:46:31,640
+تكون even يجب أن تكون اثنين في integer فال K هي
+
+581
+00:46:31,640 --> 00:46:35,360
+integer ومادام K integer K تربيع برضه
+
+582
+00:46:35,360 --> 00:46:42,280
+بالضرورة ستكون integer تمام فصار لدينا J تربيع
+
+583
+00:46:42,280 --> 00:46:44,720
+even
+
+584
+00:46:46,830 --> 00:46:51,110
+J تربيع even ونرجع من نفس النظرية إذا الرقم
+
+585
+00:46:51,110 --> 00:46:56,990
+تربيع even فإذا الرقم نفسه J نفسه برضه ستكون even
+
+586
+00:46:56,990 --> 00:47:04,970
+فإذا J is even طيب نمسك هذه النقطة ونمسك هذه
+
+587
+00:47:04,970 --> 00:47:10,980
+النقطة النقطتين هذين هما أساساً حاصل قسمتهما على بعض
+
+588
+00:47:10,980 --> 00:47:15,140
+الذي حصلنا منه root 2 لأننا من أصل فرضيتنا
+
+589
+00:47:15,140 --> 00:47:23,890
+بادئين بها  أن جذر 2 تساوي I over J وفرضنا أنها
+
+590
+00:47:23,890 --> 00:47:27,190
+rational فإن rational لها شروط ال rational ال rational
+
+591
+00:47:27,190 --> 00:47:29,290
+لكي تكون شروطها هذه واضحة يجب أن يكون الاثنين
+
+592
+00:47:29,290 --> 00:47:32,370
+integers هما  يتحققان في  integers لا يوجد مشكلة الشرط
+
+593
+00:47:32,370 --> 00:47:37,590
+الثاني no common divisor لا يوجد عامل مشترك بينهما طيب
+
+594
+00:47:37,590 --> 00:47:41,770
+للأسف نحن نعرف أن even أساساً فيه هو مضروب
+
+595
+00:47:41,770 --> 00:47:45,210
+اثنين يعني هو رقم مضروب  اثنين يعني معنى ذلك
+
+596
+00:47:45,210 --> 00:47:50,530
+الاثنين عامل مشترك بينهما هذه يجب أن أقدر أمثلها أقدر
+
+597
+00:47:50,530 --> 00:47:56,520
+أمثلها 2k وهذه أقدر أمثلها برضه ب 2r مثلاً some
+
+598
+00:47:56,520 --> 00:48:01,500
+integer فإذا لاحظوا لا يوجد common فإذا ليست rational
+
+599
+00:48:01,500 --> 00:48:06,540
+طيب أنت فرضت من الأول rational طلعت ليست rational أنت
+
+600
+00:48:06,540 --> 00:48:09,280
+فرضت من الأساس rational طلعت ليست rational معناته
+
+601
+00:48:09,280 --> 00:48:13,300
+العكس هو الذي صح العكس هو الذي كان صحيح الذي هو
+
+602
+00:48:13,300 --> 00:48:17,800
+أنها irrational هي irrational وليست رقم
+
+603
+00:48:17,800 --> 00:48:20,400
+نسمي ليست رقم نسمي
+
+604
+00:48:22,730 --> 00:48:27,330
+نحن نقول ال EU أنها false على أي حالة؟ على هذه
+
+605
+00:48:27,330 --> 00:48:31,510
+وهذه؟ لا أحكي الفوضى هنا في الجدول آه آه في
+
+606
+00:48:31,510 --> 00:48:34,150
+الجدول أنت تتكلم هنا على لا نحن هنا نتكلم في
+
+607
+00:48:34,150 --> 00:48:38,130
+فرضية أنت تفرض فرضية وأنت تعمل ولما تجيء أن
+
+608
+00:48:38,130 --> 00:48:43,010
+الفرضية غلط الشغل أنه الفرضية غلط أنت بدأت تقول
+
+609
+00:48:43,010 --> 00:48:47,470
+أنها rational ال rational لها شروط أتينا ونحن
+
+610
+00:48:47,470 --> 00:48:50,030
+نعمل وقلنا أنها rational أتينا نحقق الشروط
+
+611
+00:48:50,030 --> 00:48:56,330
+وجدنا أنها لا تتحقق فطبيعي الفرضية التي فرضتها
+
+612
+00:48:56,330 --> 00:48:59,790
+غلط  لأنها لم تتحقق شروطها شروطها أن تكون
+
+613
+00:48:59,790 --> 00:49:03,210
+عبارة عن حاصل قسمة رقمين الرقمان هذان الشرط الأول أن
+
+614
+00:49:03,210 --> 00:49:06,190
+هما يكونا integers هذا integer وهذا integer
+
+615
+00:49:06,190 --> 00:49:10,350
+الشرط الثاني ألا يكون فيه أي عامل مشترك بينهما طيب
+
+616
+00:49:10,350 --> 00:49:13,610
+نحن مع الشغل أثبتنا أن الاثنين even ونحن نعرف
+
+617
+00:49:13,610 --> 00:49:18,180
+أن even يقبل القسمة على اثنين فالبسط يقبل
+
+618
+00:49:1
+
+667
+00:52:35,170 --> 00:52:41,710
+أولى أكبر واسمه P طيب ماشي سميناه P هل وجد اللي
+
+668
+00:52:41,710 --> 00:52:46,790
+بنقول المفروض معناته كل ال primes التانية أقل منه؟
+
+669
+00:52:46,790 --> 00:52:50,450
+مدام هو الأكبر، معناته كل ال primes التانية أقل
+
+670
+00:52:50,450 --> 00:52:55,430
+منه، كويسة. The set of all primes lie between one and
+
+671
+00:52:55,430 --> 00:53:00,830
+P. بنقدر نعبرها بالشكل التالي: أن R بتساوي اتنين
+
+672
+00:53:00,830 --> 00:53:05,570
+هحط كل primes: اتنين، تلاتة، خمسة، سبعة، أحد عشر، تلاتة عشر،
+
+673
+00:53:05,570 --> 00:53:10,590
+مش عارف، سبعة عشر، تسعة عشر، ثلاثة وعشرين... بتكملوا،
+
+674
+00:53:10,590 --> 00:53:14,910
+كويسة لعند ما تصلوا لمين؟ للـ P اللي أنتو بتدعوا و
+
+675
+00:53:14,910 --> 00:53:19,870
+اللي إحنا دعينا أنه أكبر رقم prime أو أكبر رقم
+
+676
+00:53:19,870 --> 00:53:25,370
+أولي. معناه ذلك أنه مافيش أي رقم بعده. حلو، كويس جداً،
+
+677
+00:53:25,370 --> 00:53:30,850
+ولكن هنفاجأ أن كل مجموعة الأرقام الأولية، ضربهم في
+
+678
+00:53:30,850 --> 00:53:36,170
+بعض زائد واحد، دائماً بيطلع رقم أول جديد. خليني
+
+679
+00:53:36,170 --> 00:53:43,930
+أمسكهم: اتنين في تلاتة، زائد واحد، سبعة، سبعة
+
+680
+00:53:43,930 --> 00:53:50,650
+prime. طيب، ستة في خمسة، تلاتين، زائد واحد، الواحد
+
+681
+00:53:50,650 --> 00:53:56,370
+والثلاثين، الـ prime. طيب، هنا صارت جدّاً. ثلاثين في سبعة،
+
+682
+00:53:56,370 --> 00:54:01,830
+ثلاثين، صح. ثلاثين في سبعة، مئتين وعشرة، مئتين و إحدى
+
+683
+00:54:01,830 --> 00:54:06,510
+عشرة is a prime. هذه طريقة بتقدر تعمل فيها
+
+684
+00:54:06,510 --> 00:54:10,770
+generation للـ primes، للـ primes. معنى ذلك أن لا
+
+685
+00:54:10,770 --> 00:54:14,480
+يوجد أكبر من هذا. ببساطة جداً، لو كلهم ضربتوهم في بعض،
+
+686
+00:54:14,480 --> 00:54:19,660
+وزودت واحد، أكيد هيطلع prime. ومدام الـ prime ناتج من
+
+687
+00:54:19,660 --> 00:54:23,980
+ضرب الـ P في رقم أكبر من واحد، أكيد هيكون أكبر من P.
+
+688
+00:54:23,980 --> 00:54:27,600
+أكيد هيكون أكبر من P. معناه ذلك أنه لا يوجد دائماً رقم
+
+689
+00:54:27,600 --> 00:54:32,760
+أكبر منه. دائماً هيكون في رقم أكبر منه، لأن R plus
+
+690
+00:54:32,760 --> 00:54:38,540
+واحد، و R هي حاصل ضربهم. جربوها، جربوها بهذه الطريقة،
+
+691
+00:54:38,540 --> 00:54:41,420
+دائماً هتطلقوا primes، دائماً هتبقوا تطلقوا primes
+
+692
+00:54:41,420 --> 00:54:47,780
+منها. R plus واحد is a prime larger than P، منطقي
+
+693
+00:54:47,780 --> 00:54:51,320
+جداً. ليش؟ لأن أنا ضربت فيه الـ P في integer أكبر من
+
+694
+00:54:51,320 --> 00:54:56,320
+واحد، فطبيعي جداً، بده يعطيكوا رقم أعلى من الـ P،
+
+695
+00:54:56,320 --> 00:54:59,500
+مضاعفات من الـ P. Why؟ لأنها زي ما قلنا ضربناها
+
+696
+00:54:59,500 --> 00:55:03,150
+برقم أكبر من واحد. فإذا automatically صار عندكوا
+
+697
+00:55:03,150 --> 00:55:06,430
+contradiction. صار عندكوا تعرض أنتو فرضين أنه أكبر
+
+698
+00:55:06,430 --> 00:55:09,950
+رقم، بس قدرتوا تعملوا منه generation لرقم أكبر منه.
+
+699
+00:55:09,950 --> 00:55:16,310
+فإذا صار العكس، أثبتنا العكس. معناه ذلك أن عكس الـ
+
+700
+00:55:16,310 --> 00:55:21,290
+negation true اللي هي من الأصل أنه no largest
+
+701
+00:55:21,290 --> 00:55:25,590
+prime number. طيب، واضحة. إيه؟ أنتو بتقدروا تتعاملوا معها
+
+702
+00:55:25,590 --> 00:55:28,050
+مع الـ contradiction لما أنتو ما يكونش عندكوا
+
+703
+00:55:28,050 --> 00:55:32,750
+premises، واضحة. ما يكونش عندكوا فرضيات واضحة، وأنتم
+
+704
+00:55:32,750 --> 00:55:36,030
+مضطرين تتعاملوا مع الـ... مع الـ... الـ contradiction.
+
+705
+00:55:36,030 --> 00:55:37,790
+تضطروا في الحالة اللي تشتغلوا معها الـ
+
+706
+00:55:37,790 --> 00:55:43,010
+contradiction، تفرضوا العكس، وأثناء الشغل هيظهر
+
+707
+00:55:43,010 --> 00:55:46,110
+معاكوا أو بتكونوا تحاولوا تثبتوا أن العكس
+
+708
+00:55:46,110 --> 00:55:49,190
+اللي أنتم فرضته false، أن العكس اللي أنتم فرضينه
+
+709
+00:55:49,190 --> 00:55:49,970
+false.
+
+710
+00:55:55,950 --> 00:56:00,210
+هذا example؟ لأ، مش example. لأ، هذا برضه نفس
+
+711
+00:56:00,210 --> 00:56:03,430
+الطريقة، مش مشكلة، مش example كويسة. في الحالة هذه،
+
+712
+00:56:03,430 --> 00:56:09,870
+إحنا أخذنا مجموعة methods مهمة جداً لـ proofs من
+
+713
+00:56:09,870 --> 00:56:13,870
+المواضيع اللي مافيش امتحان يخلو منها. فإذا دائماً
+
+714
+00:56:13,870 --> 00:56:16,730
+بتفكروا بالـ direct، indirect، indirect على طول
+
+715
+00:56:16,730 --> 00:56:20,970
+مخّكم مع مين؟ مع الـ contrapositive. indirect مخّكم دائماً
+
+716
+00:56:20,970 --> 00:56:23,050
+على طول مع الـ contrapositive، في الـ direct وفي الـ
+
+717
+00:56:23,050 --> 00:56:25,970
+indirect. هذا بتكونوا تكونوا حافظينه كويس. واضح أن الـ
+
+718
+00:56:25,970 --> 00:56:29,850
+implication بدنا نحفظه، لأن كل شغلنا عليه الـ
+
+719
+00:56:29,850 --> 00:56:32,130
+implication. كل شغلنا عليه، سواء تشتغلوا على direct
+
+720
+00:56:32,130 --> 00:56:37,270
+أو indirect. في كمان إيش كان معناه الـ vacuous والـ
+
+721
+00:56:37,270 --> 00:56:40,490
+trivial، برضه بتكونوا حافظينه، لأنه من هنا بتقدر
+
+722
+00:56:40,490 --> 00:56:44,230
+تقولوا إنه ما بطل له معنى الـ conclusion أو بطل لها
+
+723
+00:56:44,230 --> 00:56:49,020
+معنى الـ premises. والحاجة الأهم هاني بقولكوا كمان
+
+724
+00:56:49,020 --> 00:56:51,700
+مرة اللي هي إيه؟ الـ contradiction... الـ
+
+725
+00:56:51,700 --> 00:56:55,240
+contradiction، لأنه هذا بتكون... بتكون تثبتوا منها
+
+726
+00:56:55,240 --> 00:57:00,620
+النظرية بدون ما يكون لها premises، بدون ما... خلاص
+
+727
+00:57:00,620 --> 00:57:04,400
+given عندكوا، أثبتوا. طب أنا ما عنديش premises أنطلق
+
+728
+00:57:04,400 --> 00:57:07,880
+منها، أشتغل منها، فبتروحوا بتعكسوها وبتثبتوا أن
+
+729
+00:57:07,880 --> 00:57:13,460
+عكسها false، معناه ذلك أن الـ... الـ... الـ... الـ...
+
+730
+00:57:13,460 --> 00:57:15,280
+الـ... الـ affirmation تبعها، اللي هو التأكيد تبعها
+
+731
+00:57:15,280 --> 00:57:20,540
+الأصلي هو اللي true، هو اللي كان true. طيب، نكفي،
+
+732
+00:57:20,540 --> 00:57:22,900
+هيك نكون خلصنا الموضوع هذا. المرة الجاية إن شاء
+
+733
+00:57:22,900 --> 00:57:26,560
+الله بنبدأ في مين؟ بنبدأ مع الـ six إن شاء الله.
+
+734
+00:57:26,560 --> 00:57:26,960
+تعالى
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..32a9651ecb643ad02736245de5751d4bdc3b330e
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ_postprocess.srt
@@ -0,0 +1,2936 @@
+1
+00:00:20,670 --> 00:00:22,730
+بسم الله الرحمن الرحيم الصلاة والسلام عليك ورحمة
+
+2
+00:00:22,730 --> 00:00:24,330
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+3
+00:00:24,330 --> 00:00:24,430
+ورحمة الله ورحمة الله ورحمة الله ورحمة الله ورحمة
+
+4
+00:00:24,430 --> 00:00:24,590
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+5
+00:00:24,590 --> 00:00:28,470
+ورحمة
+
+6
+00:00:28,470 --> 00:00:34,650
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+7
+00:00:34,650 --> 00:00:37,610
+ورحمة الله ورحمة الله ورحمة الله ورحمة الله ورحمة
+
+8
+00:00:37,610 --> 00:00:43,400
+الله ورحمة الله ورحمة الله ورحمة اللهفأذكر أن أحنا
+
+9
+00:00:43,400 --> 00:00:47,540
+تحدثنا عن أربع قرق أساسية اللي هنبدأ نشرحها واحدة
+
+10
+00:00:47,540 --> 00:00:53,100
+واحدة و هنظفلها واحدة خامسة ضمن واحدة من الأربع
+
+11
+00:00:53,100 --> 00:00:57,120
+categories هدولة بداية اتكلمنا عن ال direct proof
+
+12
+00:00:57,120 --> 00:01:00,860
+وهدي مباشرة ال implication تبعنا اللي هنشتغل عليه
+
+13
+00:01:00,860 --> 00:01:03,680
+و اللي أحنا أساسا بنعمل منه الإثبات بيكون عندنا
+
+14
+00:01:03,680 --> 00:01:07,640
+premises معطيات و منها بدأ نثبت conclusion أو
+
+15
+00:01:07,640 --> 00:01:15,370
+استنتاجفإذا نتكلم عن P implies Q تحقق P اللي هي ال
+
+16
+00:01:15,370 --> 00:01:20,190
+premises، بنانا عليها بدي أحاول أستنتج ال Q، بدنا
+
+17
+00:01:20,190 --> 00:01:24,210
+نستنتج ال Q فهذه بال direct search بناخدها بنفس
+
+18
+00:01:24,210 --> 00:01:27,450
+الطريق، بنفس الاتجاه بتاع ال implication، بمعنى
+
+19
+00:01:27,450 --> 00:01:34,490
+أني بفرض P is trueوبحاول منها بشوية rules of
+
+20
+00:01:34,490 --> 00:01:42,770
+inference أصل لمين ل Q is true بحاول منها نصل ل Q
+
+21
+00:01:42,770 --> 00:01:46,010
+is true في هذه ال direct ماشية مباشرة مع مين مع
+
+22
+00:01:46,010 --> 00:01:49,230
+الاتجاه تبعنا ال indirect لأ في ال indirect
+
+23
+00:01:49,230 --> 00:01:55,540
+بنتعامل مع الموضوع بطريقة عكسيةبال contrapositive
+
+24
+00:01:55,540 --> 00:02:00,540
+على أساس ان انا ممكن ال D نفسها تكون complicated
+
+25
+00:02:00,540 --> 00:02:06,500
+او complex proposition ممكن تكون معقدة شوية ان انا
+
+26
+00:02:06,500 --> 00:02:09,200
+ابتدأ اتعامل معاها ممكن في بعض الحالات هذا اذا
+
+27
+00:02:09,200 --> 00:02:11,860
+طبعا سيبناكوا الخيار فانتوا في الحالة دي اللي
+
+28
+00:02:11,860 --> 00:02:14,920
+جيتوها صعبة انكوا تبتنطلقوا منها و تحاولوا بشوية
+
+29
+00:02:14,920 --> 00:02:18,320
+rules تطبقوها عليها بتبدأوا تشتغلوا بالعكس يمكن ال
+
+30
+00:02:18,320 --> 00:02:24,320
+Q تكون أسهل فبنتعامل مع negation Qبنفرض أن هذه هي
+
+31
+00:02:24,320 --> 00:02:28,280
+فرضية من عندنا بنفرض أن هذه هي ال true و منها بدي
+
+32
+00:02:28,280 --> 00:02:34,300
+أحس .. بدي أجيب negation فيه إذا تحقق ال condition
+
+33
+00:02:34,300 --> 00:02:37,640
+هذا automatically هذا يتبع ليش؟ لأن عارف أن
+
+34
+00:02:37,640 --> 00:02:41,920
+الأثنين equivalent لبعض ضمن relation سمنها ال
+
+35
+00:02:41,920 --> 00:02:44,860
+contrapositive relation contrapositive لل
+
+36
+00:02:44,860 --> 00:02:48,980
+implication بتذكرين لما اتكلمنا عن inverse؟للـ
+
+37
+00:02:48,980 --> 00:02:52,120
+implication واتكلمنا عن ال converse وكان الجزء
+
+38
+00:02:52,120 --> 00:02:54,600
+التاريخي اللي هو إيش ال inverse و ال converse مع
+
+39
+00:02:54,600 --> 00:02:58,000
+بعض و سمناها ال contrapositive اللي هو بالشكل ..
+
+40
+00:02:58,000 --> 00:03:00,500
+بالشكل اللي قولنا إنه هذه مكافئة مباشرة لل
+
+41
+00:03:00,500 --> 00:03:05,080
+implication الأصلي فإذا .. إذا قدرت أثبت ال
+
+42
+00:03:05,080 --> 00:03:08,640
+contrapositive automatically هده صحيحة ..
+
+43
+00:03:08,640 --> 00:03:11,260
+automatically هده صحيحة فهنا بنعمل assuming لـ
+
+44
+00:03:11,260 --> 00:03:16,470
+negation Q و منها بنثبتnegation بتحقق الكلام هذا
+
+45
+00:03:16,470 --> 00:03:18,670
+automatically يقولوا أنه إذا ال relation الأولى
+
+46
+00:03:18,670 --> 00:03:22,590
+صحيحة ال relation الأولى المطلوب اثبتها صحيحة
+
+47
+00:03:22,590 --> 00:03:27,870
+بالقياس مع ال contrapositive طيب في ال vacuous
+
+48
+00:03:27,870 --> 00:03:34,890
+proof وهدي اتكلمنا عليها معناها بلا معنىيعني ال
+
+49
+00:03:34,890 --> 00:03:37,930
+proof لا معنى له .. هدى إنت بتصير إذا كان أثبتنا
+
+50
+00:03:37,930 --> 00:03:41,690
+negation P by itself إذا كان هو معطيني P عساس إن
+
+51
+00:03:41,690 --> 00:03:47,150
+هي معطة أثبتنا إنه لأ P is false طب إنت كيف تقولي
+
+52
+00:03:47,150 --> 00:03:49,770
+هي true و هي أساسا false فانا بتعامل معها أصبحت
+
+53
+00:03:49,770 --> 00:03:52,250
+عساس إن هي false لإن ال authoritative عندى بال ..
+
+54
+00:03:52,250 --> 00:03:55,070
+بالمنطق تبعنا إنه هي false مدام false
+
+55
+00:03:55,070 --> 00:03:58,970
+automatically ال relation صح بغض النظر إنه إيش ال
+
+56
+00:03:58,970 --> 00:04:03,280
+Qفإذا أنا مش مضطر أجيب ال Q أو أعرف بالظبط Q
+
+57
+00:04:03,280 --> 00:04:07,020
+الشيية ليش؟ لأنه لو ماذكرين أقولكوا احنا المفروض
+
+58
+00:04:07,020 --> 00:04:10,020
+ال implication هذا نقطبه هنا و ما نضمن محاش تاني
+
+59
+00:04:10,020 --> 00:04:13,780
+بالمرة لأن معظم شغلنا على ال truth table تبع مين
+
+60
+00:04:13,780 --> 00:04:19,780
+ال implication فخلينا نقطبه هنا هي P Q و ال
+
+61
+00:04:19,780 --> 00:04:23,400
+implication قولنا في عندكوا false, false, true,
+
+62
+00:04:24,480 --> 00:04:32,840
+false, truetrue و في عندكوا true false false و في
+
+63
+00:04:32,840 --> 00:04:39,100
+عندكوا true true true طيب لو هده .. هبطه منك على
+
+64
+00:04:39,100 --> 00:04:43,740
+جد .. لحظه إذا كان ال P أثبت إن هي negation ال
+
+65
+00:04:43,740 --> 00:04:51,440
+relation صحيحة بغض النظر إيش قيمة ال Q فخلاص فإذا
+
+66
+00:04:51,440 --> 00:04:57,460
+بطريقة لا معنى لها الجملة صحيحة أو الإثبات صحيحة
+
+67
+00:04:57,940 --> 00:05:01,000
+ولو ان احنا مش كتير مقتنعين بالطريقة ولكن خلاص هي
+
+68
+00:05:01,000 --> 00:05:04,940
+طريقة من طرق الاثبات طريقة من طرق الاثبات اذا كان
+
+69
+00:05:04,940 --> 00:05:09,340
+اثبتنا رياضيا ان ال negation بيه هي ال true معناه
+
+70
+00:05:09,340 --> 00:05:13,960
+ان P هي ال false فإذا ال implication او ال
+
+71
+00:05:13,960 --> 00:05:19,100
+relation صحيحة بغض النظر ال Q هتطلع صح ولا هتطلع
+
+72
+00:05:19,100 --> 00:05:24,350
+خطأ ال Q تطلع صح تطلع غلط مش هتفرج كتيرممكن
+
+73
+00:05:24,350 --> 00:05:27,890
+تتذكروا المجموعة ال examples اللى أخدناها عن ال
+
+74
+00:05:27,890 --> 00:05:32,450
+implication لما اتكلمنا عن إذا كان الجبنة الخضراء
+
+75
+00:05:32,450 --> 00:05:37,090
+بتنعمل في الجمر مش عارف even كذا متذكرينه المثال؟
+
+76
+00:05:37,090 --> 00:05:40,910
+كويس هو نفس الكلام هذا احنا مجرد أن ال P لجناها
+
+77
+00:05:40,910 --> 00:05:44,830
+false قلنا الجملة صح خلاص قلنا خلاص automatically
+
+78
+00:05:44,830 --> 00:05:48,590
+الجملة صح بغض النظر النتيجة تحققت او ماتحققتش ال
+
+79
+00:05:48,590 --> 00:05:52,660
+relation كلها صحيحة خلاصتمام بس لما تيجي تتكلم
+
+80
+00:05:52,660 --> 00:05:56,880
+عنها طب هو مالهوش معنى الجمر بيعمل جبنة خضرة طبيعي
+
+81
+00:05:56,880 --> 00:06:00,240
+مالهاش أي معنى فحتاج انه فعلا كلام بلا معنى ولكن
+
+82
+00:06:00,240 --> 00:06:05,680
+اثبت انه صحيح اثبت انه حسب الجملة او الجملة
+
+83
+00:06:05,680 --> 00:06:08,900
+الرياضية بتاعة اللي هي ال implication صحيحة طيب ال
+
+84
+00:06:08,900 --> 00:06:13,960
+trivial proof هذي لأ بتثبت Q من نفسها بمعنى انا مش
+
+85
+00:06:13,960 --> 00:06:21,100
+محتاج ال P صارال P مالوش لازمة، انا مش محتاج
+
+86
+00:06:21,100 --> 00:06:25,380
+premises، اعطاني premise بس ماستفدتش منها، أثبتنا
+
+87
+00:06:25,380 --> 00:06:30,800
+Q من نفسها، Q أثبتت من نفسها، مش محتاجين ال P
+
+88
+00:06:30,800 --> 00:06:34,000
+فيها، ففي الحالة هذه ال trivia بتسميها، تافه، يعني
+
+89
+00:06:34,000 --> 00:06:36,720
+اعطاني شرط تافه مالوش أي معنى أو ال condition
+
+90
+00:06:36,720 --> 00:06:42,140
+ماستفدتش منهتمام في ال indirect هنكمل غير ال
+
+91
+00:06:42,140 --> 00:06:45,360
+contrapositive هناخد في الآخر طريقة هنسميها ال
+
+92
+00:06:45,360 --> 00:06:49,380
+contradiction برضه هي تعتبر من طرق ال indirect
+
+93
+00:06:49,380 --> 00:06:53,060
+فبنكون خلصناها فعليا هم تلاتة اللي هنشتغل عليهم و
+
+94
+00:06:53,060 --> 00:06:56,770
+نركز عليهم ال directو ال contrapositive و ال
+
+95
+00:06:56,770 --> 00:06:59,670
+contradiction هم دول التلاتة الأكثر أهمية يعني في
+
+96
+00:06:59,670 --> 00:07:03,030
+شغلنا طيب نبدأ في ال direct و ناخد example على طول
+
+97
+00:07:03,030 --> 00:07:05,630
+خلاص ال direct تعرفنا إيش يعني ال direct هبدأ من
+
+98
+00:07:05,630 --> 00:07:12,430
+ال P و أحاول أثبت منها ال Q تمام فإذا محتاجين ال
+
+99
+00:07:12,430 --> 00:07:15,750
+theorem بتاعتنا و هناخد شوية hints شوية hints هيكي
+
+100
+00:07:15,750 --> 00:07:18,210
+تساعدنا في الحل بس هي ال theorem اللي مطلوب مننا
+
+101
+00:07:18,210 --> 00:07:24,570
+نثبتها for all numbers N if N is all integersفإذن
+
+102
+00:07:24,570 --> 00:07:31,550
+هي integer عدد صحيح و فردي then انتربيع is a non
+
+103
+00:07:31,550 --> 00:07:36,410
+integer فإذن برضه الانتربيع بتاعتها بتكون integer
+
+104
+00:07:36,410 --> 00:07:41,810
+عدد صحيح و برضه فردي اثبتولنا الكلام هذا طيب عشان
+
+105
+00:07:41,810 --> 00:07:44,710
+نثبت الكلام هذا في عندنا definitions من الأول
+
+106
+00:07:44,710 --> 00:07:49,350
+بيناعرفها كيف أعرفهمالعدد الفردي و كيف اعرف العدد
+
+107
+00:07:49,350 --> 00:07:54,090
+الزوجي العدد الفردي بنعرفه كالتالي an integer n is
+
+108
+00:07:54,090 --> 00:07:58,830
+called odd if and only if n equal to 2k plus one
+
+109
+00:07:58,830 --> 00:08:07,070
+2k زوجيزائد واحد على طوط صار فردي فإذا كان تحقق ل
+
+110
+00:08:07,070 --> 00:08:11,530
+ال N أني بقدر أمثله بهذا الشكل بهذه المعادلة فبقدر
+
+111
+00:08:11,530 --> 00:08:16,170
+أقول إن ال N هذي إيش عدد فردي for إيش some integer
+
+112
+00:08:16,170 --> 00:08:21,710
+K بشرط إن ال K هذي ما تكونش كسر ما تكونش كسر تكون
+
+113
+00:08:21,710 --> 00:08:25,030
+برضه integer إذا قدرنا نمثلها بهذا الشكل فهي odd
+
+114
+00:08:25,030 --> 00:08:31,450
+طيب and N is even if and only if N equal to 2K بس
+
+115
+00:08:32,090 --> 00:08:35,250
+انه بتقبل القسم على اتنين بس خارج القسم لازم يكون
+
+116
+00:08:35,250 --> 00:08:42,430
+integer مايكونش كسر تمام برضه for some k او some
+
+117
+00:08:42,430 --> 00:08:49,330
+integer k طيب ال axiom او الشيء البديهي ان اي
+
+118
+00:08:49,330 --> 00:08:53,510
+integer number هو يا odd يا even مافيش احتمال تالف
+
+119
+00:08:53,510 --> 00:08:59,630
+فإذا every integer is either odd or evenمعنى ذلك
+
+120
+00:08:59,630 --> 00:09:02,390
+إذا كان هدرش بنقول الكلام هذا باعتبار أنه لو
+
+121
+00:09:02,390 --> 00:09:06,030
+ماتحققش ال odd هي automatically even و العكس صحيح
+
+122
+00:09:06,030 --> 00:09:10,050
+لو ماتحققش أنهية even ال integer هي automatically
+
+123
+00:09:10,050 --> 00:09:17,250
+odd تمام نمسك نرجع للسؤال طبعا المطلوب إيش نعمل if
+
+124
+00:09:17,250 --> 00:09:25,770
+in is even in is is odd عفوا is odd تمام employees
+
+125
+00:09:26,750 --> 00:09:32,970
+انتربيع is odd فاطوماتيك لببدأ من هنا من ال P
+
+126
+00:09:32,970 --> 00:09:37,650
+فبنبدأ شغلنا عادي من ال P زي ما هي طيب هد عشان
+
+127
+00:09:37,650 --> 00:09:41,310
+تكون odd المفروض هي تكون بتساوي two k plus one
+
+128
+00:09:41,310 --> 00:09:46,410
+صحيح و ننطلق منها نحاول نثبت هذا الكلام طب عشان
+
+129
+00:09:46,410 --> 00:09:50,070
+أثبت الكلام هد بدي أجيب انتربيع فإذا بدي أربع هذا
+
+130
+00:09:50,070 --> 00:09:55,870
+ال theorem و نفك التربيعونشوف هل بتطلع معانا نفس
+
+131
+00:09:55,870 --> 00:10:00,950
+ال form هذا و لا تطلع لأ two في integer و لا two
+
+132
+00:10:00,950 --> 00:10:04,830
+في integer plus واحد بنحاول نشوف لما نفك هدول و
+
+133
+00:10:04,830 --> 00:10:07,950
+نجمع و نظبطها كيف ممكن تطلع فهو هى .. بس هى ال
+
+134
+00:10:07,950 --> 00:10:12,650
+proof هى ال strategy بتاعتنا كويس N is odd then N
+
+135
+00:10:12,650 --> 00:10:17,550
+equal to two K plus one كويس for some integer K N
+
+136
+00:10:17,550 --> 00:10:23,370
+تربيةهي ال integer تبعنا بال representation تبعته
+
+137
+00:10:23,370 --> 00:10:28,210
+تربيع فكنا الأولى
+
+138
+00:10:28,210 --> 00:10:31,670
+تربيع زائد التانية تربيع زائد الأولى في التانية في
+
+139
+00:10:31,670 --> 00:10:35,130
+اتنين مظبوط تمام هاي ال term اللي قلناه لاحظوا ان
+
+140
+00:10:35,130 --> 00:10:39,930
+هذا ال term بقدر اطلع منه اتنين عامل مشترك كويسة
+
+141
+00:10:39,930 --> 00:10:45,490
+تصير عندكوا اتنين في اتنين كتربيع plus two k كله
+
+142
+00:10:45,490 --> 00:10:52,320
+زائد واحد طيب هذا ال termال K هدي إيش؟ Integer.
+
+143
+00:10:52,360 --> 00:10:56,700
+Integer تربيع؟ Integer. فإتنين؟ Integer. يعني في
+
+144
+00:10:56,700 --> 00:10:59,240
+Integer .. Integer في Integer؟ Integer. ال plus
+
+145
+00:10:59,240 --> 00:11:03,360
+integer؟ Integer. فإذا كل ال term هذا بقدر أقول إن
+
+146
+00:11:03,360 --> 00:11:08,960
+هو J و J أكيد integer فإذا بقدر أمثلها two J plus
+
+147
+00:11:08,960 --> 00:11:14,780
+واحد برضه ال J هتكون some integer
+
+148
+00:11:17,780 --> 00:11:24,420
+كويس في الحالة دي أصبحت ال n تربيع is 2j plus 1 و
+
+149
+00:11:24,420 --> 00:11:29,260
+ال j .. ال j هذه أكيد integer .. أكيد integer ف
+
+150
+00:11:29,260 --> 00:11:32,700
+automatically مدام أكيد integer فال n تربيع برضه
+
+151
+00:11:32,700 --> 00:11:37,320
+odd لإنه حققت لأنه شرط من الشرطات شرط ال odd حققت
+
+152
+00:11:37,320 --> 00:11:43,380
+إنه شرط ال odd خلصنا بشكل direct .. بشكل direct
+
+153
+00:11:43,380 --> 00:11:51,690
+بدأنا من ال P و وصلنا لليش .. لل Qهذه أول طريقة،
+
+154
+00:11:51,690 --> 00:11:58,290
+اللي هي direct، و عادة ابدوا فاكروا فيها أول ما
+
+155
+00:11:58,290 --> 00:12:02,230
+تبدوا تحلوا، إذا ما كانش عندكم خيار من إيش لازم
+
+156
+00:12:02,230 --> 00:12:05,450
+تستعملوا طريقة، ابدوا حاولوا فاكروا فيها، بس
+
+157
+00:12:05,450 --> 00:12:08,390
+أحيانا مش دايما بتصبط، هنشوفها لغة الحلات اللي
+
+158
+00:12:08,390 --> 00:12:11,950
+لاحقا هنشتغل عليها، بس خليني ناخد كمان example ليش
+
+159
+00:12:11,950 --> 00:12:17,350
+لات direct، عشان ناخد أكتر من مثلطيب لو قلنا if ال
+
+160
+00:12:17,350 --> 00:12:21,490
+theorem بتاعتنا اللي بدنا نثبتها if 6x plus 9y
+
+161
+00:12:21,490 --> 00:12:30,470
+equal to 101 then x or y is not integer طيب كيف
+
+162
+00:12:30,470 --> 00:12:36,930
+نثبتها هذه بسيطة هذه P وهذه بدنا نثبتها Q هذه P
+
+163
+00:12:36,930 --> 00:12:41,110
+وهذه Q طيب هنبدأها direct مدام اننا نتكلم عن
+
+164
+00:12:41,110 --> 00:12:46,210
+direct هنبدأ من هنا هذه لو قسمنا كلهعلى تلاتة
+
+165
+00:12:46,210 --> 00:12:49,830
+هاتلعنكوا
+
+166
+00:12:49,830 --> 00:12:57,130
+هنا اتنين X plus تلاتة Y بتساوي طيب
+
+167
+00:12:57,130 --> 00:13:01,570
+هذا not integer واضحة باين تماما هذه not integer
+
+168
+00:13:01,570 --> 00:13:04,750
+بتطلع تلاتة وتلاتين فاصلة ستة فاصلة ستة ستة ستة
+
+169
+00:13:04,750 --> 00:13:10,590
+تلتين كويسة not integer اقسمه على integernot
+
+170
+00:13:10,590 --> 00:13:18,330
+integer نفس الكلام بتطلع x not integer فواحدة منهم
+
+171
+00:13:18,330 --> 00:13:22,090
+على الأقل لازم تكون not integer لأنه not integer
+
+172
+00:13:22,090 --> 00:13:27,890
+أجسمه على integer برضه not integer أساسا مجرد أني
+
+173
+00:13:27,890 --> 00:13:30,730
+أقول integer على integer مش بالضرورة تكون integer
+
+174
+00:13:30,730 --> 00:13:35,970
+صح؟ مش بالضرورة تكون integer فلما تكون fraction
+
+175
+00:13:35,970 --> 00:13:40,400
+أساسا فالمنطق أنه برضه هيطلع fractionبتجسمه
+
+176
+00:13:40,400 --> 00:13:46,860
+fraction على integer أكيد fraction فإذا بما يضع
+
+177
+00:13:46,860 --> 00:13:52,420
+مشكلة الشك x او y او الاتنين not integer او
+
+178
+00:13:52,420 --> 00:13:55,880
+الاتنين أثبتناها بطريقة مباشرة بدينا من ال
+
+179
+00:13:55,880 --> 00:14:02,640
+premises تبعتنا ووصلنا لنتيجة المقروبةهنشتغل كتر
+
+180
+00:14:02,640 --> 00:14:06,780
+لإن كلها نجسمها على تلاتة فهيطلع المعادلة two x
+
+181
+00:14:06,780 --> 00:14:10,720
+plus three y equal to one hundred one three over
+
+182
+00:14:10,720 --> 00:14:14,700
+three هدى إمتى ممكن لأ يكونوا كلهم integer إذا كان
+
+183
+00:14:14,700 --> 00:14:19,360
+اقدرت أقسمهم كله و موصلت للمعامل one للاتنين و
+
+184
+00:14:19,360 --> 00:14:23,500
+مازال النتج النهائي integer بس هو لسه موصلناش يعني
+
+185
+00:14:23,500 --> 00:14:27,640
+احنا حتى موصلناش لل coefficient واحد لكل واحد منهم
+
+186
+00:14:27,640 --> 00:14:30,200
+موصلناش احنا لسه فيه coefficient قدامه و مع ذلك
+
+187
+00:14:30,200 --> 00:14:36,710
+ظهرتالـ fraction ظهر ك fractional number كويس ف
+
+188
+00:14:36,710 --> 00:14:41,150
+automatic ل 101 على 3 هو is not an integer وهذا
+
+189
+00:14:41,150 --> 00:14:47,070
+معناه أنه بالضرورة لا X .. X مش هتكون integer أو Y
+
+190
+00:14:47,070 --> 00:14:51,330
+مش هتكون integer واحدة منهم مش هتكون integer وممكن
+
+191
+00:14:51,330 --> 00:14:54,910
+يكونوا الاتنين مع بعض ممكن يكونوا الاتنين مع بعض
+
+192
+00:14:54,910 --> 00:15:00,080
+طبعا أثبتنا كلامك بمجرد ما ظهر عندكوا termnot
+
+193
+00:15:00,080 --> 00:15:03,040
+integer بجرد ما اظهر في المعادلة term not integer
+
+194
+00:15:03,040 --> 00:15:08,920
+في ال indirect ال indirect بقولنا لأ مختلف الموضوع
+
+195
+00:15:08,920 --> 00:15:14,020
+شوية في ال indirect theorem
+
+196
+00:15:14,020 --> 00:15:20,900
+زي ال theorem اللي عندنا هنا if three n
+
+197
+00:15:20,900 --> 00:15:26,760
+plus two is odd employs
+
+198
+00:15:28,870 --> 00:15:37,050
+implies إيش؟ إن n is odd طيب
+
+199
+00:15:37,050 --> 00:15:42,990
+إحنا عارفين إمتى بقدر أقول ال term هذا odd two k
+
+200
+00:15:42,990 --> 00:15:48,230
+plus واحد صحيح؟ two k plus one ولكن إذا بدى أحط
+
+201
+00:15:48,230 --> 00:15:51,890
+هذا بيساوي two k plus one صار عندكوا two variables
+
+202
+00:15:51,890 --> 00:15:56,760
+k وصار عندكوا nفواضح أن ال direct هيعملنا شوية
+
+203
+00:15:56,760 --> 00:16:00,940
+لخمة لإنه هيصير في عندكوا two variables في عندنا n
+
+204
+00:16:00,940 --> 00:16:04,340
+و في ال k موجودين في المعادلة إذا بدي أسيوم في بعض
+
+205
+00:16:04,340 --> 00:16:06,980
+و بدي أحاول أجد رتبهم حتى يكون صعب شوية الترتيب لأ
+
+206
+00:16:06,980 --> 00:16:11,960
+بصير تفكير أكتر أن أروح لمين لل indirect ليش لأنه
+
+207
+00:16:11,960 --> 00:16:17,320
+النتيجة ك proposition أصغر، proposition سهل، ل
+
+208
+00:16:17,320 --> 00:16:20,220
+proposition سهل فهذه بجيبها هنا بس بال إيش بال
+
+209
+00:16:20,220 --> 00:16:26,000
+negation بتاعتها فبقول n is evenلأن برضه احنا قلنا
+
+210
+00:16:26,000 --> 00:16:29,240
+اي رقم integer هو يا odd يا even، إذا ماكانش odd،
+
+211
+00:16:29,240 --> 00:16:34,840
+negation odd، automatically even employees three
+
+212
+00:16:34,840 --> 00:16:40,560
+and plus two is even، تمام، إذا كان أثبتنا هذه،
+
+213
+00:16:40,560 --> 00:16:44,400
+فإذا هذه بالضرورة صحيحةهذه هتكون بالضرورة صحيحة
+
+214
+00:16:44,400 --> 00:16:50,400
+نتيجة إيش الcontra positive فهنبدأ من هنا هنقول إن
+
+215
+00:16:50,400 --> 00:16:57,040
+N is even مدام even بقدر امثلها بإيش 2K تمام وخلاص
+
+216
+00:16:57,040 --> 00:17:03,420
+اعملولا تربيع .. مش تربيع بنعود في المعادلة كل N
+
+217
+00:17:03,420 --> 00:17:08,560
+بنحطها ب2K و بنرتبها بنشوف هل المعادلة كلها بتقبل
+
+218
+00:17:08,560 --> 00:17:12,370
+القسم ع 2إذا بتكبر القسم ع 2، معناته بدّر أقول إن
+
+219
+00:17:12,370 --> 00:17:17,890
+هي عبارة عن 2 في some integer j و خلاص أثبتنا من
+
+220
+00:17:17,890 --> 00:17:22,330
+كل الكلام هذا هنشتغل نشوف هنا، فهنشتغل على أساس إن
+
+221
+00:17:22,330 --> 00:17:26,510
+أنا بشتغل على n even ليش even؟ لأنها ال negation
+
+222
+00:17:26,510 --> 00:17:32,460
+بتاع oddكويس for some integer k فإذا three n plus
+
+223
+00:17:32,460 --> 00:17:36,020
+two بنمثلها بهذا الشكل هنضرب التلاتة في الأتنين
+
+224
+00:17:36,020 --> 00:17:39,460
+صار عندكوا ستة اه بقدر اطلع اتنين عامل مشترك بنقدر
+
+225
+00:17:39,460 --> 00:17:45,060
+وبسيطة جدا و واضحة two في three k plus one برضه
+
+226
+00:17:45,060 --> 00:17:50,200
+الكلام هذا كله هده بقدر اقول ان هو j لأنه و
+
+227
+00:17:50,200 --> 00:17:53,360
+integer اكيد integer لأنه جاي من integer في
+
+228
+00:17:53,360 --> 00:17:57,040
+integer plus integerفي integer في integer أكيد
+
+229
+00:17:57,040 --> 00:18:02,520
+integer في plus integer أكيد integer minus integer
+
+230
+00:18:02,520 --> 00:18:08,580
+integer على integer لأ لأ ماداني لا خبطش إذا كان
+
+231
+00:18:08,580 --> 00:18:13,640
+في لجته على وجهه مش مضمون بقدرش أحطها theorem
+
+232
+00:18:13,640 --> 00:18:19,520
+مقدرش نحطها theorem تمام كويس then three and plus
+
+233
+00:18:19,520 --> 00:18:26,660
+two is evenلما إيش؟ لما كانت n even ففي الحالة هذه
+
+234
+00:18:26,660 --> 00:18:31,860
+بقدر أقول إن اتحقق الشرط فإذا negation n is odd
+
+235
+00:18:31,860 --> 00:18:37,240
+يعني معناها إنه كانت even implies negation 3n plus
+
+236
+00:18:37,240 --> 00:18:44,020
+2 is odd بالcontrapositive بنعكس صارت إذا if 3n
+
+237
+00:18:44,020 --> 00:18:49,530
+plus 2 is odd then n is oddاللي بدنا إيها، اللي
+
+238
+00:18:49,530 --> 00:18:52,970
+بدنا إيها، في الحالة هذه بنكون من ال
+
+239
+00:18:52,970 --> 00:18:56,150
+contrapositive أثبتنا النظرية أو ال theory بتاعتنا
+
+240
+00:18:56,150 --> 00:19:01,230
+وبطريقة أسهل من أني أجلد أشغل على ال .. ال .. ال
+
+241
+00:19:01,230 --> 00:19:03,750
+.. ال premise تبعتنا، أني أبدأ من ال premise
+
+242
+00:19:03,750 --> 00:19:08,970
+بتاعتنا، تمام، هذه ال in .. ال indirect
+
+243
+00:19:13,340 --> 00:19:16,380
+خلّيني أكمل، هنشوف في الـ indirect كمان example ..
+
+244
+00:19:16,380 --> 00:19:20,720
+كمان example ال theorem اللي مطلوب نثبتها if x
+
+245
+00:19:20,720 --> 00:19:28,340
+plus y greater than 100 then x greater than 50 or
+
+246
+00:19:28,340 --> 00:19:32,840
+y greater than 50 فعلا ممكن واحدة منهم لازم يكون
+
+247
+00:19:32,840 --> 00:19:37,070
+على الأقل، يمكن يكون ال 10 تانيو or قلنا إنها تشمل
+
+248
+00:19:37,070 --> 00:19:41,390
+التنتين لإيش؟ لأن ممكن المية منهم تجيبوهم يعني كيف
+
+249
+00:19:41,390 --> 00:19:47,250
+بتجيبوا رقمين مجموحهم مية؟ خمسين و خمسين بس إنتوا
+
+250
+00:19:47,250 --> 00:19:50,830
+greater than أكبر من مية لازم واحدة منهم واحدة و
+
+251
+00:19:50,830 --> 00:19:56,110
+خمسين فصارت أكبر تمام؟ طيب ممكن تكون سبعين و واحدة
+
+252
+00:19:56,110 --> 00:20:00,090
+و تلاتين واحدة منهم هنا و ممكن تكون ستين و ستين
+
+253
+00:20:00,090 --> 00:20:05,540
+التنتين أكبر ففي جميع الأحوال بنجرحبس في الحالة
+
+254
+00:20:05,540 --> 00:20:09,080
+هذه بقدرش أقعد أعمل أحط كل احتمالات X وكل احتمالات
+
+255
+00:20:09,080 --> 00:20:15,800
+Y و أجرب ال relation هذه عشان أشتغل direct عشان
+
+256
+00:20:15,800 --> 00:20:19,200
+لازم أبدأ من هنا، طب لأ مديش أبدأ من هنا، هذي صعبة
+
+257
+00:20:19,200 --> 00:20:22,640
+ليش؟ لأنه بدي أحط كل احتمالة الممكن إلى X وكل
+
+258
+00:20:22,640 --> 00:20:25,940
+احتمالة الممكن إلى Y و الاحتمالة تعالى نطلع عليها
+
+259
+00:20:25,940 --> 00:20:31,760
+X أكبر من 50و هذه or كمان يعني معنى ذلك إنه حامل
+
+260
+00:20:31,760 --> 00:20:35,040
+عملية احتمالات كبيرة جدا عشان نشغل direct لو كنت
+
+261
+00:20:35,040 --> 00:20:38,840
+تشغل direct فهذه أنسبلها إيش؟ ال indirect ليش؟ لأن
+
+262
+00:20:38,840 --> 00:20:44,640
+ال indirect لو كده بتصير كالتاليمن ال theorem اللي
+
+263
+00:20:44,640 --> 00:20:48,660
+بتثبتها بنحدد ال P ال P كانت X plus Y greater than
+
+264
+00:20:48,660 --> 00:20:54,620
+100 ل Q كان X أكبر من 50 او Y أكبر من 50 هنشتغل
+
+265
+00:20:54,620 --> 00:20:58,240
+على ال negation عشان نجيب ال contrapositive لما
+
+266
+00:20:58,240 --> 00:21:00,280
+نعمل negation لل term هذا
+
+267
+00:21:03,380 --> 00:21:09,260
+شيوء بنعمله نجاشة هنا صارت العكس أكبر من أقل أو
+
+268
+00:21:09,260 --> 00:21:16,780
+يساوي طيب و هنا أقل أو يساوي و ال or and ما ننساش
+
+269
+00:21:16,780 --> 00:21:24,020
+هذه دي مورغان في نجاشة هندخله على connection
+
+270
+00:21:24,020 --> 00:21:28,440
+موجودة فبدنا نعكسها ال or بدتصير and وهدولة بدنا
+
+271
+00:21:28,440 --> 00:21:33,680
+نعكسهم تماما عكس أكبر من أقل من أو يساويلأن
+
+272
+00:21:33,680 --> 00:21:40,080
+المساوية لم تكن مشمولة في أكبر منه تمام فانشطرنا
+
+273
+00:21:40,080 --> 00:21:45,200
+على negation q عبارة عن x أقل من أو يساوي خمسين و
+
+274
+00:21:45,200 --> 00:21:49,140
+y أقل من أو يساوي خمسين نيجيشن بي اللي بدنا نثبتها
+
+275
+00:21:49,140 --> 00:21:54,300
+منها أن x زائد y أقل من أو يساوي مية هل الكلام هذا
+
+276
+00:21:54,300 --> 00:21:58,490
+متحقق إذا عرفنا نحقق نيجيشن بيnegation P هدى
+
+277
+00:21:58,490 --> 00:22:02,190
+اقدرنا نحققها من negation Q فإذا ال relation صحيحة
+
+278
+00:22:02,190 --> 00:22:04,830
+مع أن ذلك ال contract positive تبعها صحيحة اللي هي
+
+279
+00:22:04,830 --> 00:22:08,750
+النظرية اللي بدنا نستخدمها طيب تعالى نشوف هنا أقل
+
+280
+00:22:08,750 --> 00:22:13,130
+من أو يساوي خمسين أكبر قيمة ممكنة هي احتمال واحد
+
+281
+00:22:13,130 --> 00:22:15,890
+انها تكون بتساوي فعليا خمسين انها تكون بتساوي
+
+282
+00:22:15,890 --> 00:22:20,690
+خمسين عشان هذه القصة تكون أقل من أو يساوي خمية
+
+283
+00:22:20,690 --> 00:22:24,570
+فبدنا نشوف أكبر قيمة هل هتظل ضمن ال range تبعنا
+
+284
+00:22:24,570 --> 00:22:30,840
+هنا ولا لأطيب x زائد y أقل من خمسين و ال y خمسين
+
+285
+00:22:30,840 --> 00:22:34,860
+أكبر قيمة ممكنة بتساوي مية مية تنطبق مع المعادلة
+
+286
+00:22:34,860 --> 00:22:41,620
+المية ماشية لأنه يساوي مية فهي فعلا تساوي مية
+
+287
+00:22:41,620 --> 00:22:48,860
+معناه ذلك أن كل الأرقام اللي أقل صحيحة برضه لاحظوا
+
+288
+00:22:48,860 --> 00:22:54,160
+احنا اشعلنا x أقل من أو تساوي خمسينصح؟ بنعمل test
+
+289
+00:22:54,160 --> 00:22:57,480
+على أكبر رقم ممكن إذا تحقق ال test على أكبر رقم
+
+290
+00:22:57,480 --> 00:23:03,020
+فإذا كل اللي أقل منه برضه متحقق هي
+
+291
+00:23:03,020 --> 00:23:07,900
+أكبر رقم لل X الشيية أنها تكون خمسين و أكبر رقم ل
+
+292
+00:23:07,900 --> 00:23:11,920
+Y خمسين عشان عوضنا هنا وجدنا أنها تتفق مع المعادلة
+
+293
+00:23:11,920 --> 00:23:15,700
+طيب لو أخدنا أي رقم أخر أقل من الخمسين هي ماشية
+
+294
+00:23:15,700 --> 00:23:19,940
+المعادلة برضهالمعادلة ماشية فإذا احنا أخدنا
+
+295
+00:23:19,940 --> 00:23:25,200
+الاحتمال الوحيد اللي ممكن يبعد إنها تكون تساوى
+
+296
+00:23:25,200 --> 00:23:28,660
+الخمسين أكبر رقم ممكن ل X و أكبر رقم ممكن ل Y
+
+297
+00:23:28,660 --> 00:23:33,960
+عوضنا وجدناها ما زالت ضمن أو بتحقق ليه ال negation
+
+298
+00:23:33,960 --> 00:23:37,680
+P ما زالت بتحقق negation P فإذا ال relation دائما
+
+299
+00:23:37,680 --> 00:23:41,500
+صحيحةال relation دائما صحيحة لكل الأرقام الممكنة ل
+
+300
+00:23:41,500 --> 00:23:48,860
+x و y for all numbers لمين ل x و y ففي الحالة دي
+
+301
+00:23:48,860 --> 00:23:53,120
+بقدر أقول ان ال relation صحيحة كل هيك على بعض من
+
+302
+00:23:53,120 --> 00:23:58,560
+هنا employs ال term هذا okay relation صح فإذا ال
+
+303
+00:23:58,560 --> 00:24:06,780
+contrapositive بتاعتها أكيد صحيحة اللي هيالـ
+
+304
+00:24:06,780 --> 00:24:09,840
+Theorem المطلوبة من غير ما أعمل احتمالات كل
+
+305
+00:24:09,840 --> 00:24:14,160
+احتمالات الممكنة لأكبر من 100 الأقل هنا وفرت عليها
+
+306
+00:24:14,160 --> 00:24:19,520
+أقل بجيب أكبر قيمة ممكنة وهل هي ما زالت ضمن أقل من
+
+307
+00:24:19,520 --> 00:24:22,680
+100 ولا لأ؟ أه ما زالت ضمن أقل من 100 معناته حتى
+
+308
+00:24:22,680 --> 00:24:27,140
+اللي أقل ضمن المعادلة ضمن المعادلة المطلوبة في
+
+309
+00:24:27,140 --> 00:24:31,160
+باتها ففي الحالة هذه اقدرنا نثبت negation Q
+
+310
+00:24:31,160 --> 00:24:35,920
+implies negation P ومنها مباشرة فإذا P implies Q
+
+311
+00:24:36,760 --> 00:24:40,140
+اللي هي المعادلة اللي فوق، هي ال contrapositive
+
+312
+00:24:40,140 --> 00:24:46,560
+اللي اتكلمنا عنها أو ال indirect، indirect محددنها
+
+313
+00:24:46,560 --> 00:24:53,580
+تحديدا اللي هي ال contrapositive، تمامال .. ال
+
+314
+00:24:53,580 --> 00:24:58,260
+vacuous to prove example هذا اللي قلنا بلا معنى
+
+315
+00:24:58,260 --> 00:25:02,720
+بمعنى انه هيعطيني premise و بعدين احنا مثبت ان هي
+
+316
+00:25:02,720 --> 00:25:06,680
+ال premise غلط من أصله فمعنى ذلك ايش ال conclusion
+
+317
+00:25:06,680 --> 00:25:10,500
+يطلع زي ما يطلع مش هتفرق ال relation كلها على بعض
+
+318
+00:25:10,500 --> 00:25:19,220
+دايما صح ليش؟ false ال premise false فإذا بغض
+
+319
+00:25:19,220 --> 00:25:24,180
+النظر ايش النتيجة هي دايما ال relation صحيحةلحظة
+
+320
+00:25:24,180 --> 00:25:30,640
+إذا كان اثبت عندكم ان ال premise false فال
+
+321
+00:25:30,640 --> 00:25:34,320
+relation كلها صحيحة بغض النظر والله فعلا هيتحقق
+
+322
+00:25:34,320 --> 00:25:38,840
+اللي طالبه او لا ال conclusion تحققت او ماتحققتش
+
+323
+00:25:38,840 --> 00:25:42,400
+بغض النظر دائما ال relation كلها على بعض ال
+
+324
+00:25:42,400 --> 00:25:47,200
+implication صحيحة true ف automatically بشكل لا
+
+325
+00:25:47,200 --> 00:25:52,700
+معنى له هي صحيحةتمام؟ كويس خلّيني أشوف for example
+
+326
+00:25:52,700 --> 00:25:57,420
+إذا كانت in is both odd and even اتننى مافيش اللي
+
+327
+00:25:57,420 --> 00:26:01,160
+odd أو even in احنا عارفين إنه يا يا odd يا even
+
+328
+00:26:01,160 --> 00:26:05,000
+بس واحد يجي يقول ليه إذا كان in تحققتلك الشرطين يا
+
+329
+00:26:05,000 --> 00:26:09,080
+odd و even مافيش حاجة اسمها odd و even مافيش أي
+
+330
+00:26:09,080 --> 00:26:11,880
+رقم integer بقدر أقول إنه odd و even فإذا هذه
+
+331
+00:26:11,880 --> 00:26:18,440
+negation على طول هذه false فthen تحققت أو ماتحققتش
+
+332
+00:26:18,440 --> 00:26:22,040
+مش هتفرقو هي فعلا هتلاقوها مرات بتتحقق و مرات لأ
+
+333
+00:26:22,040 --> 00:26:25,980
+بس أنا مش هتطلعها أصلا أشوف هي بتتحقق أو بتتحققش
+
+334
+00:26:25,980 --> 00:26:31,100
+يعني مش هتفرج معايا تحققت فليكن ماتحققتش فليكن
+
+335
+00:26:31,100 --> 00:26:34,620
+ماتفرجش مش هي اللي هتعطيني القرار القرار بدأ من
+
+336
+00:26:34,620 --> 00:26:38,640
+where من negation فيه الفرضية اللي أصلا غلط
+
+337
+00:26:38,640 --> 00:26:42,840
+الفرضية اللي أساسا بادية من الأساسغلط فمدام
+
+338
+00:26:42,840 --> 00:26:47,260
+الفرضية غلط فبقول ان هي ال theory كلها على بعض
+
+339
+00:26:47,260 --> 00:26:54,100
+factiously true بشكل لا معنى له حقيقية صحيحة بشكل
+
+340
+00:26:54,100 --> 00:27:02,180
+بدون معنى هي حقيقية فعلا ك relation كامة على بعض
+
+341
+00:27:02,180 --> 00:27:05,280
+طيب
+
+342
+00:27:05,280 --> 00:27:09,660
+ال trivial لأ ال trivial مختلفة شوية احنا بنتكلمش
+
+343
+00:27:09,660 --> 00:27:14,820
+عنال premise، بنتكلم عن مين؟ عن ال conclusion، لذا
+
+344
+00:27:14,820 --> 00:27:19,350
+ال conclusion بقدر أثبته من نفسهبغض النظر إيش هي
+
+345
+00:27:19,350 --> 00:27:23,830
+ال premise ال premise صح غلط مش فارقة كتير أنا
+
+346
+00:27:23,830 --> 00:27:30,210
+عندي إمكانية إن أنا أثبت ال Q من نفسها مش محتاج ال
+
+347
+00:27:30,210 --> 00:27:34,370
+P مش محتاج ال premise ال premise بتفرجش معايا صح
+
+348
+00:27:34,370 --> 00:27:38,570
+ولا غلط ولا كويسة ولا مش كويسة ولا premises كتيرة
+
+349
+00:27:38,570 --> 00:27:42,630
+ولا واحدة ولا مافيش premise أصلا مش هتفرج مش فارقة
+
+350
+00:27:42,630 --> 00:27:49,300
+هنا if we know Q is true thenP employees queue is
+
+351
+00:27:49,300 --> 00:27:53,320
+true تمام،
+
+352
+00:27:53,320 --> 00:28:00,380
+لاحظوا كأنكوا هنا بتتكلموا عن الحالة ال queue، ال
+
+353
+00:28:00,380 --> 00:28:04,850
+queue، إذا queue is trueفهي ال relation صحيحة بغض
+
+354
+00:28:04,850 --> 00:28:09,510
+النظر عن ال P ال P false فليكن false true فليكن
+
+355
+00:28:09,510 --> 00:28:13,790
+true في الأخر أنا اللي حكم على الشغل تبعي ان ال Q
+
+356
+00:28:13,790 --> 00:28:18,230
+أنا أثبت منها نفسها أن هي true مدام أثبت نفسي أن
+
+357
+00:28:18,230 --> 00:28:22,890
+هي true ال relation كلها true فالإثبات النظرية هي
+
+358
+00:28:22,890 --> 00:28:25,970
+صحيحة ليش؟ لأن هي النظرية أصلا relation يعطيني
+
+359
+00:28:25,970 --> 00:28:29,870
+إياها if then فإذا ال if then اللي هي ال
+
+360
+00:28:29,870 --> 00:28:34,560
+implication relation هذه صحيحةفإذا النظرية صحيحة
+
+361
+00:28:34,560 --> 00:28:40,100
+زي لو قال if it's raining today then three is an
+
+362
+00:28:40,100 --> 00:28:43,840
+odd number طبما هي فعلا three is an odd number بغض
+
+363
+00:28:43,840 --> 00:28:47,960
+النظر شتيت ولا مش شتيتش اليوم مش هتفرج كتير ليش هي
+
+364
+00:28:47,960 --> 00:28:53,620
+أصلا odd three odd ال Q هي متحققة بدون ماعرف إيش
+
+365
+00:28:53,620 --> 00:28:55,780
+ال premise
+
+366
+00:28:57,130 --> 00:28:59,430
+ال premise أو ال premises كلها إذا كانوا أكتر من
+
+367
+00:28:59,430 --> 00:29:02,110
+واحدة تكون اللي تكون تكون force تكون true مش هتفرج
+
+368
+00:29:02,110 --> 00:29:07,810
+كتير معانا ليش لأن ال conclusion أصلا is true هو
+
+369
+00:29:07,810 --> 00:29:12,530
+true أصلا فينطبق مع الحالة بتاعة ال implication أو
+
+370
+00:29:12,530 --> 00:29:15,290
+ال relation للtheory ال relation للtheory فهذا
+
+371
+00:29:15,290 --> 00:29:18,610
+طريقة إثبات برضه لل relations بتاعتنا هذه true
+
+372
+00:29:18,610 --> 00:29:22,530
+وهذه true ال conclusion true بغض النظر إيش ال ..
+
+373
+00:29:22,530 --> 00:29:26,440
+ال .. ال premise هي دائما true ال relationفإذا
+
+374
+00:29:26,440 --> 00:29:33,600
+النظرية ده true فإذا طريقة trivially true بطريقة
+
+375
+00:29:33,600 --> 00:29:39,060
+.. كأنه هي trivial بمعنى تافه أو مالوش يعني ..
+
+376
+00:29:39,060 --> 00:29:42,480
+مالوش قيمة، مالوش قيمة فمعنى ذلك أنه أنا .. أنا
+
+377
+00:29:42,480 --> 00:29:44,700
+عندي هنا ال premise مالهاش تافه، مالهاش معنى،
+
+378
+00:29:44,700 --> 00:29:49,140
+مالهاش قيمة، لو ماعطتنيش يحصل، هاي معناها، لو
+
+379
+00:29:49,140 --> 00:29:53,840
+ماعطتنيش إياها، بديش إياها المعلومة، بدناش إياها
+
+380
+00:29:56,030 --> 00:29:59,370
+معلومة trivial بالنسبالي هي الـ Q مثبت حاله لحاله
+
+381
+00:29:59,370 --> 00:30:08,990
+الـ Q مثبت حاله لحاله الـ
+
+382
+00:30:08,990 --> 00:30:14,690
+Q مثبت حاله لحاله الـ Q مثبت حاله لحاله الـ Q مثبت
+
+383
+00:30:14,690 --> 00:30:15,170
+حاله لحاله الـ Q مثبت حاله لحاله الـ Q مثبت حاله
+
+384
+00:30:15,170 --> 00:30:18,350
+لحاله الـ Q مثبت حاله لحاله الـ Q مثبت حاله لحاله
+
+385
+00:30:18,350 --> 00:30:19,450
+الـ Q مثبت حاله لحاله الـ Q مثبت حاله لحاله الـ Q
+
+386
+00:30:19,450 --> 00:30:21,690
+حاله لحاله الـ Q مثبت حاله لحاله الـ Qبغض النظر ان
+
+387
+00:30:21,690 --> 00:30:25,270
+ال integer in ده هو فعلا عبارة عن مجموع رقمين
+
+388
+00:30:25,270 --> 00:30:28,970
+اولين او لأ، فليكن مجموع رقمين اولين، و ليكن لأ،
+
+389
+00:30:28,970 --> 00:30:31,690
+مايكنش مش مجموع، مش هتفرج كتير معايا، ليش؟ لأن
+
+390
+00:30:31,690 --> 00:30:37,330
+then ال Q اللي عندها هنا بيقولكوا ان ال in ده يا
+
+391
+00:30:37,330 --> 00:30:40,330
+او دي او ي، طب ما احنا عارفين ان اي integer هو
+
+392
+00:30:40,330 --> 00:30:45,480
+محدد هى for all integersلل integers odd or even طب
+
+393
+00:30:45,480 --> 00:30:47,620
+انا عارف ان في كل ال integers ما هي لازم تكون يا
+
+394
+00:30:47,620 --> 00:30:50,900
+odd يا even مافيش احتمال تالت هو ميعطين الاحتمالين
+
+395
+00:30:50,900 --> 00:30:54,780
+الاتنين اللي موجودين عنده فهي يا odd يا even فإذا
+
+396
+00:30:54,780 --> 00:30:58,400
+واحدة منهم لازم تكون true واحدة منهم لازم تكون
+
+397
+00:30:58,400 --> 00:31:06,160
+false مع ال or أكيد ال relation كلها true true
+
+398
+00:31:06,160 --> 00:31:11,380
+فإذا أنا بتكلم عن الحالتينالحالتين دائما ال
+
+399
+00:31:11,380 --> 00:31:16,080
+relation صح، بغض النظر هم فعلا مجموع two primes او
+
+400
+00:31:16,080 --> 00:31:21,480
+لابغض النظر، صحيح؟ فإذا automatically هي true
+
+401
+00:31:21,480 --> 00:31:25,700
+trivially أو صحيحة
+
+402
+00:31:25,700 --> 00:31:31,200
+بدون الاستفادة من ال premise، بدون الاستفادة من ال
+
+403
+00:31:31,200 --> 00:31:34,720
+premise الشغلة
+
+404
+00:31:34,720 --> 00:31:38,560
+المهمة كمان اللي هي برضه بتندرج معانا مع جزئية ال
+
+405
+00:31:38,560 --> 00:31:44,630
+indirect مع جزئية ال indirect strategiesاللي هي مش
+
+406
+00:31:44,630 --> 00:31:48,130
+Contrapositive، Contradiction Contradiction
+
+407
+00:31:48,130 --> 00:31:52,130
+التعارض التعارض، إيش التعارض؟ معناه إن أنا بدي
+
+408
+00:31:52,130 --> 00:31:57,460
+أفرض فرضية و أثبت تعارضهاتناقض او تعارض تناقض
+
+409
+00:31:57,460 --> 00:32:01,020
+اثبتها و افرض انها متناقضة مع نفسها او متعارضة مع
+
+410
+00:32:01,020 --> 00:32:06,140
+الفرضية مع الفرضية كيف نعملها a method for proving
+
+411
+00:32:06,140 --> 00:32:11,940
+P هنا بدثبت P فبنعمل assuming لمن؟ ل negation P و
+
+412
+00:32:11,940 --> 00:32:15,260
+prove منها يعني ال promise اللي معطيكوا إياها
+
+413
+00:32:15,260 --> 00:32:20,820
+بنفرض عكسهالحظة ال premise يعطيكوا premise معينة
+
+414
+00:32:20,820 --> 00:32:25,320
+يعطيكوا معلومة معينة بنفرض عكسها و بنحاول نشتغل
+
+415
+00:32:25,320 --> 00:32:29,600
+بنجد من عكسها أنه صار عندكم proof لمين ل q و
+
+416
+00:32:29,600 --> 00:32:35,440
+negation q إذا فعلا صار أنه بقدر أثبت الاستنتاج و
+
+417
+00:32:35,440 --> 00:32:39,100
+التعارض تبعه فإذا النظرية هذه كلها ال premise من
+
+418
+00:32:39,100 --> 00:32:42,240
+أصله كان غلط و مدام كان من الأول غلط معناته ال
+
+419
+00:32:42,240 --> 00:32:45,580
+negation تبعه اللي هو ال P أصلا هي ال true ال P
+
+420
+00:32:45,580 --> 00:32:48,770
+أساسا هي اللي كانت trueفبنكون أثبتناها بطريقة برضه
+
+421
+00:32:48,770 --> 00:32:53,530
+غير .. غير مباشرة فإذا كأني بفرض negation P
+
+422
+00:32:53,530 --> 00:32:58,550
+employs Q and negation Q طبعا هذا الكلام دائما
+
+423
+00:32:58,550 --> 00:33:04,630
+false .. دائما false في الحالة هذه فمدام دائما
+
+424
+00:33:04,630 --> 00:33:08,750
+false خلاص ال .. ال .. كلها هتكون مش صحيحة أو ال
+
+425
+00:33:08,750 --> 00:33:11,150
+.. ال negation P مش هتكون صحيحة وهذا معناه
+
+426
+00:33:11,150 --> 00:33:16,740
+automatically أنه Pis it true, p is it true فهي a
+
+427
+00:33:16,740 --> 00:33:19,160
+queue and ال negation a queue ال trivial
+
+428
+00:33:19,160 --> 00:33:25,040
+contradiction هي تعارض واضح، هتكون تعارض واضح كيف
+
+429
+00:33:25,040 --> 00:33:31,070
+انتوا بتقول المعلومة صحيحة و عكسها صحيحفي تعارض ..
+
+430
+00:33:31,070 --> 00:33:35,810
+في تعارض .. تعامل أو تناقض ..ماشي أو متناقضة يعني
+
+431
+00:33:35,810 --> 00:33:39,250
+المعلومتين مع بعض فإذا equal to false في الحالة
+
+432
+00:33:39,250 --> 00:33:44,150
+هذه negation P is false negation P is false وهذا
+
+433
+00:33:44,150 --> 00:33:52,030
+معناه أن P is true P is true هذه طريقة إثبات P هذه
+
+434
+00:33:52,030 --> 00:33:58,510
+الطريقة الإثبات mean إثبات P طيب زي ..ناخد two
+
+435
+00:33:58,510 --> 00:34:01,070
+examples من ال examples المشهورة جدا الحقيقة على
+
+436
+00:34:01,070 --> 00:34:04,350
+ال net مشهورة حتى في معظم الكتب مشهورة جدا جدا
+
+437
+00:34:04,350 --> 00:34:08,970
+هناخد two examples واحدة علاقة بال rational واحدة
+
+438
+00:34:08,970 --> 00:34:13,850
+علاقة بال prize من القوانين المشهورة جدا و قديمة
+
+439
+00:34:13,850 --> 00:34:19,060
+الحقيقة يعنيالإثباتين قديمين جدا جدا مش حديثين
+
+440
+00:34:19,060 --> 00:34:22,940
+يعني تم إثباتهم من زمان جدا بس مشهورين جدا ل ال
+
+441
+00:34:22,940 --> 00:34:28,300
+contradiction أول نظرية بدنا نثبت أنه root two is
+
+442
+00:34:28,300 --> 00:34:33,240
+rational rational إيش يعني rational rational نسبي
+
+443
+00:34:33,240 --> 00:34:38,140
+نسبي بمعنى بقول الرقم x rational إذا كان قدرت
+
+444
+00:34:38,140 --> 00:34:43,520
+أمثله ال two integers على بعض ال two integers على
+
+445
+00:34:43,520 --> 00:34:47,850
+بعض بشكلان ال two integers في أبسط صورهم بقدرش
+
+446
+00:34:47,850 --> 00:34:52,910
+اختصرهم مع بعض لا يتم اختصارهم مع بعض هدول الرقمين
+
+447
+00:34:52,910 --> 00:34:56,070
+لا يختصروا مع بعض والاتنين انتجر اذا تحقق كلام
+
+448
+00:34:56,070 --> 00:35:01,670
+نسميها rational ال X هذه بنسميه rational تمام هنا
+
+449
+00:35:01,670 --> 00:35:06,310
+لا احنا بدنا بالعكس احنا قاعدين بنقول root two جدر
+
+450
+00:35:06,310 --> 00:35:13,120
+الاتنين is irrational هي لا يوجد اي رقمينانتجارز
+
+451
+00:35:13,120 --> 00:35:18,700
+حاصل قسمتهم على بعض بيعطيك root 2 هاي معناها هذا
+
+452
+00:35:18,700 --> 00:35:21,580
+معناها بدنا نشوف هل الكلام ده بصير معناه ده بصيرش
+
+453
+00:35:21,580 --> 00:35:28,100
+معناه طيب عشان نعمله هنفرض negation فيه بدنا نفرض
+
+454
+00:35:28,100 --> 00:35:35,860
+negation فيه انه هي لأ rationalبتفترض أن المعلومة
+
+455
+00:35:35,860 --> 00:35:39,320
+اللي أعطتنيها مش صح، أنا بتفترض عكسها، و أبدأ
+
+456
+00:35:39,320 --> 00:35:42,440
+أثبت، أشتغل في الإثبات تبعي، هأفاجأ في الإثبات أن
+
+457
+00:35:42,440 --> 00:35:47,080
+إثباتي غلط، أنه طلّع لي خطأ، معناته الصح كان
+
+458
+00:35:47,080 --> 00:35:50,580
+الأولانيبدون ما أضطر أشتغل على الأولان من الأول
+
+459
+00:35:50,580 --> 00:35:54,100
+بدون أن أضطر بطريقة direct اضطرنا نشتغل هنا in
+
+460
+00:35:54,100 --> 00:35:58,280
+direct بطريقة نسميها ال contradiction أو التعارض
+
+461
+00:35:58,280 --> 00:36:01,480
+لإجابتنا
+
+462
+00:36:01,480 --> 00:36:05,180
+أنا المفروض نتوقع شغلة و هيطلع شغلة تانية تمام
+
+463
+00:36:05,180 --> 00:36:09,260
+فهنا هنقول لأ two to the power نص اللي هي برضه
+
+464
+00:36:09,260 --> 00:36:13,000
+root اثنين to the power نص اللي هي كانها الجدر
+
+465
+00:36:13,000 --> 00:36:16,300
+تمام well rational لأ هنا بتماشي أقول irrational
+
+466
+00:36:16,300 --> 00:36:21,880
+بدي أقول إن هي rationalهذا يعني أن يوجد two
+
+467
+00:36:21,880 --> 00:36:29,400
+integers I وJ بقدر بيكون عوامل مشتركة بينهم بدون
+
+468
+00:36:29,400 --> 00:36:33,040
+عوامل مشتركة زي ما قلت لكوا تكون ال A و ال B بأبسط
+
+469
+00:36:33,040 --> 00:36:35,840
+صورهم يعني أنا ماقدرش اختصرهم مع بعض اكتر من هيك
+
+470
+00:36:35,840 --> 00:36:39,360
+لا يتم اختصارهم مع بعض مايكونش اتنين على اربعة
+
+471
+00:36:39,360 --> 00:36:44,920
+بتكون تلاتة على تسعة لأ لايتم اختصارهم مع بعض
+
+472
+00:36:44,920 --> 00:36:51,120
+مافيش اي عامل مشترك بينهموالاتنين integers إذا حصل
+
+473
+00:36:51,120 --> 00:36:55,560
+قسمتهم مع بعض بيطلق لكم X بغض النظر X، يمكن X ما
+
+474
+00:36:55,560 --> 00:36:58,840
+تكونش integer، يعني مش مضرور تكون integer X، X مش
+
+475
+00:36:58,840 --> 00:37:01,700
+مضرور تكون integer، يمكن خمسة على تلاتة، مش
+
+476
+00:37:01,700 --> 00:37:06,280
+integer، بس الرقم خمسة على تلاتة هو rational، هنا
+
+477
+00:37:06,280 --> 00:37:09,380
+بيكون اسمه rational، تمام، هنا زي ما قلنا بنعمل ال
+
+478
+00:37:09,380 --> 00:37:13,100
+acts negation فيه وننطلق منها لإثبات الشغل تبعنا
+
+479
+00:37:14,060 --> 00:37:16,900
+فهاجولي العكس تباحة ان هي تكون rational مادام
+
+480
+00:37:16,900 --> 00:37:21,520
+rational يعني يوجد two integers اللي هم I and J
+
+481
+00:37:21,520 --> 00:37:24,840
+ومافيش common بينهم common divisors مافيش اي عامل
+
+482
+00:37:24,840 --> 00:37:30,160
+بينهم بنقدر في الحالة هذه نقول ان هدول rational
+
+483
+00:37:30,160 --> 00:37:35,440
+ريشونال معناه ذلك انه two to the power نص او جذر
+
+484
+00:37:35,440 --> 00:37:40,860
+هيلحظوا جذر نص جذر افن اتنين بقدر اقول ان هو I
+
+485
+00:37:40,860 --> 00:37:45,990
+over Jصحيح؟ ما هي original ان هي عبارة عن two
+
+486
+00:37:45,990 --> 00:37:48,990
+terms بس بدنا نحدد ان ال two terms هدولة integers
+
+487
+00:37:48,990 --> 00:37:54,770
+ال I integer ال J integer كويس و لايوجد عامل مشترك
+
+488
+00:37:54,770 --> 00:37:58,490
+بينهم خلاص هدول بأبسط صورة لهم طيب لو ربعنا
+
+489
+00:37:58,490 --> 00:38:04,210
+الطرفين لو ربعنا الطرفين في الحالة هذه ايش بتصير
+
+490
+00:38:04,210 --> 00:38:11,600
+عندكم؟ هتصير اتنين تربيع ال I over تربيع ال Jتمام
+
+491
+00:38:11,600 --> 00:38:17,360
+برضه نكمل مع بعض two هذي هنطلحها فوق يعني كل ال
+
+492
+00:38:17,360 --> 00:38:22,560
+two المعادلة كلها هنضربها في جه تربيع هصير اتنين
+
+493
+00:38:22,560 --> 00:38:29,560
+جه تربيع تساوي I تربيع طيب خليني امسككم حاجة حاجة
+
+494
+00:38:29,560 --> 00:38:33,460
+المعادلة هذي حلوة و بنقدر نطلع منها شوية معلومات
+
+495
+00:38:33,460 --> 00:38:39,360
+two جه تربيع تساوي I تربيع معناه ذلك ان ال I تربيع
+
+496
+00:38:39,360 --> 00:38:46,470
+evenلحظة اتنين في some integer اتنين في some
+
+497
+00:38:46,470 --> 00:38:50,390
+integer و احنا اصلا قولنا ال rational هما two
+
+498
+00:38:50,390 --> 00:38:54,630
+integers على بعض فانا ضامن ان ال J انتجر تربيع ال
+
+499
+00:38:54,630 --> 00:38:59,490
+integer انتجر لحظة كأنها صرت بتتكلم عن اتنين K و
+
+500
+00:38:59,490 --> 00:39:05,410
+ال K ده هي J تربيع ممتاز معناه ذلك انه I تربيع
+
+501
+00:39:05,410 --> 00:39:11,260
+evenطيب احنا عارفين اذا كانت ال I تربيع even
+
+502
+00:39:11,260 --> 00:39:20,900
+معناته I even تمام فإذا ال I even حلو ال I even
+
+503
+00:39:20,900 --> 00:39:25,760
+يعني بقدر امثلها ب two K بنقدر امثلها ب two K فإذا
+
+504
+00:39:25,760 --> 00:39:31,940
+ببساطة جدا بقدر اقول ان two J تربيع بتساوي two K
+
+505
+00:39:31,940 --> 00:39:43,240
+تربيع2k تربيع 2k تربيع هذه 4k تربيع طيب نقسم على 2
+
+506
+00:39:43,240 --> 00:39:49,780
+2k تربيع صار عندنا كل هذا ال term j تربيع بساوي 2k
+
+507
+00:39:49,780 --> 00:40:01,560
+تربيع ممتاز طب ما هذه اتنين اتنين R و R some
+
+508
+00:40:01,560 --> 00:40:11,110
+integerمعنى ذلك الـ j² even even صح؟ معنى ذلك أن
+
+509
+00:40:11,110 --> 00:40:14,130
+هذه even هي اتنين في some integer ال some integer
+
+510
+00:40:14,130 --> 00:40:18,190
+ده عبارة عن integer تربيع عبارة عن integer تربيع
+
+511
+00:40:18,190 --> 00:40:22,550
+فاليكن ال integer في integer رح يطلع integer كويس
+
+512
+00:40:22,550 --> 00:40:33,620
+مدام j تربيع is even أكيد j even طلع I evenو j
+
+513
+00:40:33,620 --> 00:40:39,400
+even even على even في عامل مشترك هو الاتنين طب
+
+514
+00:40:39,400 --> 00:40:43,780
+احنا قاعدين بيقول من الأساس no common divisor then
+
+515
+00:40:43,780 --> 00:40:48,620
+false لاحظنا عرضنا حالنا لحالنا من الأول قاعدين
+
+516
+00:40:48,620 --> 00:40:50,980
+بيقول إن هي rational مع الإثبات ظهر إن هي مش
+
+517
+00:40:50,980 --> 00:40:54,060
+rational ليش مش rational لأنه في عامل مشترك بينهم
+
+518
+00:40:58,840 --> 00:41:03,600
+لأ احنا هنعيدها كلها مش هنعيد من هنا كلها بنجعلكم
+
+519
+00:41:03,600 --> 00:41:10,160
+للبداية بتاعتها لحظة
+
+520
+00:41:10,160 --> 00:41:17,220
+هلوجت بدأنا قولنا أن الفرضية بتاعتنا عكس ال given
+
+521
+00:41:17,220 --> 00:41:23,550
+ال given بيقولكم أن جذر اتنين is irrationalنفهم
+
+522
+00:41:23,550 --> 00:41:26,630
+ايش يعني irrational عشان نعرف نشتغل، ف irrational
+
+523
+00:41:26,630 --> 00:41:30,730
+معناته انه بقدر .. rational أول انه بقدر اعو ..
+
+524
+00:41:30,730 --> 00:41:35,650
+اعو .. يعني نعمل تمثيل للرقم على أساس انه حاصل
+
+525
+00:41:35,650 --> 00:41:42,190
+قسمة رقمين integersintegers و بدون أي عوامل مشترك
+
+526
+00:41:42,190 --> 00:41:47,970
+بينهم فإذا no common divisors أو لايوجد عامل مشترك
+
+527
+00:41:47,970 --> 00:41:51,870
+بينهم لايوجد عامل مشترك بينهم قولنا okay خلاص
+
+528
+00:41:51,870 --> 00:41:55,590
+هنفرض الفرضية اللي هي negation للي موجود أصلا
+
+529
+00:41:55,590 --> 00:42:01,410
+فهيقول إن جدر اتنين لأ rational هو بيقولي are
+
+530
+00:42:01,410 --> 00:42:04,750
+rational او are rational عملت ال negation فبتصير
+
+531
+00:42:04,750 --> 00:42:10,250
+عبارة مدام rational بقدر أقول إن هي I over JI over
+
+532
+00:42:10,250 --> 00:42:13,450
+G والاتنين لازم يكونوا integers ومافيش عامل مشترك
+
+533
+00:42:13,450 --> 00:42:17,450
+بينهم تمام كويس خلنا نمشي معاها الوجد احنا عارفين
+
+534
+00:42:17,450 --> 00:42:21,430
+انه هادي جدر يعني لو عملنا تربيح هنا تربيح هنا
+
+535
+00:42:21,430 --> 00:42:26,530
+بمشي الحل ربعنا الطرفين تمام هاي ربعنا الطرفين
+
+536
+00:42:26,530 --> 00:42:29,910
+ومشيت الأمور الطرفين هادولة لما ربعناهم ايش اللي
+
+537
+00:42:29,910 --> 00:42:37,190
+هيظهر عندكم هيظهر عندكم انهالاتنين بتساوي ال I و
+
+538
+00:42:37,190 --> 00:42:40,690
+لا ال J اللي فوق كانت ال I تربيع فوقي ال I و J
+
+539
+00:42:40,690 --> 00:42:48,690
+تربيع صحيح هذه منها بقدر اقول انه ال I تربيع
+
+540
+00:42:48,690 --> 00:42:55,770
+بتساوي 2J تربيع كلام صح كلام صح طيب احنا عارفين
+
+541
+00:42:55,770 --> 00:43:03,320
+انه عشان اعمل test على odd او evenبدور ال odd ال
+
+542
+00:43:03,320 --> 00:43:10,220
+even بتكون عبارة عن 2k الرقم 2 في some integer ال
+
+543
+00:43:10,220 --> 00:43:15,620
+odd 2k plus 1 لأ احنا هنمسك الجزء هذا لإن هو اللي
+
+544
+00:43:15,620 --> 00:43:20,660
+ينطبق عندنا هنا هو اللي ينطبق عندنا هنا فإذا J
+
+545
+00:43:20,660 --> 00:43:28,240
+تربيع هي كأنها K مثلا أو كأنها أي symbol تاني
+
+546
+00:43:28,240 --> 00:43:36,380
+خليني أقول مثلا كأنها Rتساوي J تربيع ال J أساسا من
+
+547
+00:43:36,380 --> 00:43:39,660
+الفرضية اللي بدهين فرضيتنا فيها أنها integer طب
+
+548
+00:43:39,660 --> 00:43:44,660
+integer تربيع لازم تكون integer رقم صحيح في نفسه
+
+549
+00:43:44,660 --> 00:43:48,820
+لازم هتطلع رقم صحيح فإذا ال R هي رقم صحيح و لاحظوا
+
+550
+00:43:48,820 --> 00:43:53,280
+أن I تربيع طلعت كأنها بتساوي 2 في رقم صحيح في
+
+551
+00:43:53,280 --> 00:43:58,300
+integer طب هذا هي تماشي تماما مع even معنا ذلك أن
+
+552
+00:43:58,300 --> 00:44:05,630
+I تربيع evenفإذن بقدر أقول I تربيع is even ال I
+
+553
+00:44:05,630 --> 00:44:11,290
+تربيع even معناه ذلك إن ال I لحالها برضه even برضه
+
+554
+00:44:11,290 --> 00:44:18,610
+even فإذن I is even هذه الجزئية برضه إذا انتوا
+
+555
+00:44:18,610 --> 00:44:23,670
+حابين اثبتوها بتقدروا تثبتوها ببساطة إذا ممكن
+
+556
+00:44:23,670 --> 00:44:27,670
+تعتقلكوا بالطرف تاني إنه given إن ال I is even و
+
+557
+00:44:27,670 --> 00:44:31,810
+اثبته إن ال I تربيع is evenأو تُعطى بهذا الشكل إذا
+
+558
+00:44:31,810 --> 00:44:35,370
+كانت I تربية is even اثبتول إن ال I is even إذا
+
+559
+00:44:35,370 --> 00:44:39,770
+أُعطت بهذا الشكل ممكن تشتغلوا على ال indirect إذا
+
+560
+00:44:39,770 --> 00:44:44,710
+I is even اشتغلوا على ال direct عوضوا هذا ب 2
+
+561
+00:44:44,710 --> 00:44:47,810
+وعملوا لتربية حصين 4 الأربعة تقدروا تاخدوا منها
+
+562
+00:44:47,810 --> 00:44:52,650
+مشتقة 2 فهتطلع برضه even تمام المهم إن احنا وصلنا
+
+563
+00:44:52,650 --> 00:44:56,810
+لإثبات إن ال I even بدنا نحط مربع عند هذه النقطة
+
+564
+00:44:56,810 --> 00:45:01,750
+طيب إذا كان هي أصلا evenهي أساسا even معناه ذلك
+
+565
+00:45:01,750 --> 00:45:08,310
+إنه فعليا هي بتساوي هي I تربيع بتساوي 2J كذا هي
+
+566
+00:45:08,310 --> 00:45:16,010
+نفسها بقدر أحطها ب2K بتقدر نحطها بشكل 2K أو بطريقة
+
+567
+00:45:16,010 --> 00:45:21,110
+اللي هي 2K تمام في الحالة دي بتقدر مباشرة نقول إن
+
+568
+00:45:21,110 --> 00:45:26,220
+I هي عبارة عن 2some integer في أي some integer في
+
+569
+00:45:26,220 --> 00:45:30,220
+الحالة اللي بنتكلم عنها وهذا معناه ان ال I تربيع
+
+570
+00:45:30,220 --> 00:45:38,520
+برضه هذا تربيع عبارة عن two K احنا اتفجنا انتجر
+
+571
+00:45:38,520 --> 00:45:46,760
+انتجر اعملوله تربيع بيساوي اتنين J تربيع نقسم على
+
+572
+00:45:46,760 --> 00:45:50,440
+اتنين جسمنا
+
+573
+00:45:50,440 --> 00:45:55,560
+على اتنين ايش بيظهر؟يصير J تربيع بتساوي two K
+
+574
+00:45:55,560 --> 00:46:01,340
+تربيع على اتنين هذه على اتنين عفوا هذه أساسا ال
+
+575
+00:46:01,340 --> 00:46:06,740
+term هذا عبارة عن أربعة K تربيع الأربعة مع الأتنين
+
+576
+00:46:06,740 --> 00:46:13,000
+فإذا J تربيع بتساوي اتنين في K تربيع K تربيع هذه
+
+577
+00:46:13,000 --> 00:46:18,320
+integer هي أساسا integerصحيح؟ كلها على بعض integer
+
+578
+00:46:18,320 --> 00:46:22,720
+لأن احنا ضمنين من الأساس ال K هتجيبناها من تعود في
+
+579
+00:46:22,720 --> 00:46:28,760
+I قولنا ان I بتساوي 2K ليش؟ لأنها even طيب عشان
+
+580
+00:46:28,760 --> 00:46:31,640
+تكون even لازم تكون اتنين في integer فالK هي
+
+581
+00:46:31,640 --> 00:46:35,360
+integer ومدام ال K integer ال K تربيع برضه
+
+582
+00:46:35,360 --> 00:46:42,280
+بالضرورة هتكون integer تمام فإذا صار لنا J تربيع
+
+583
+00:46:42,280 --> 00:46:44,720
+even
+
+584
+00:46:46,830 --> 00:46:51,110
+J تربيع even و بنرجع من نفس النظرية إذا الرقم
+
+585
+00:46:51,110 --> 00:46:56,990
+تربيع even فإذا الرقم نفسه J نفسه برضه هتكون even
+
+586
+00:46:56,990 --> 00:47:04,970
+فإذا J is even طيب نمسك هذه النقطة و نمسك هذه
+
+587
+00:47:04,970 --> 00:47:10,980
+النقطةالنقطين هدولة هم أساسا حاصل قسمتهم على بعض
+
+588
+00:47:10,980 --> 00:47:15,140
+اللي جبت منها ال route 2 لإن احنا من أصل فرضيتنا
+
+589
+00:47:15,140 --> 00:47:23,890
+بادية بهيها بإن جذر 2 تساوي I over Jوفرضنا إن هي
+
+590
+00:47:23,890 --> 00:47:27,190
+rational فإن ريشونال إلها شروط الريشونال الريشونال
+
+591
+00:47:27,190 --> 00:47:29,290
+عشان تكون الشروطها دي واضحة لازم تكون الاتنين
+
+592
+00:47:29,290 --> 00:47:32,370
+integers هم بتحقق فين integers مافيش مشكلة الشرط
+
+593
+00:47:32,370 --> 00:47:37,590
+التاني no common divisor مافيش عامل مشترك بينهم طب
+
+594
+00:47:37,590 --> 00:47:41,770
+للأسف احنا عارفين إن ال even أساسا فيه هو مضروب
+
+595
+00:47:41,770 --> 00:47:45,210
+اتنين يعني هو رقم مضروف اتنين يعني معنى ذلك
+
+596
+00:47:45,210 --> 00:47:50,530
+الاتنين عامل مشترك بينهم هذه لازم أقدر أمثلها بقدر
+
+597
+00:47:50,530 --> 00:47:56,520
+أمثلها 2kو هذه بقدر امثلها برضه ب two r مثلا some
+
+598
+00:47:56,520 --> 00:48:01,500
+integer فإذا لاحظوا مافيه comment فإذا مش rational
+
+599
+00:48:01,500 --> 00:48:06,540
+طب انت فارض من الأول rational طلعت مش rational انت
+
+600
+00:48:06,540 --> 00:48:09,280
+فارض من الأساس rational طلعت مش rational معناته
+
+601
+00:48:09,280 --> 00:48:13,300
+العكس هو اللي صح العكس هو اللي كان صحيح اللي هو
+
+602
+00:48:13,300 --> 00:48:17,800
+عياش ان هي irrational هي irrational و ليست رقم
+
+603
+00:48:17,800 --> 00:48:20,400
+نسمي ليست رقم نسمي
+
+604
+00:48:22,730 --> 00:48:27,330
+أحنا بتقول ال EU انها false على اي حالة؟ على هادي
+
+605
+00:48:27,330 --> 00:48:31,510
+و هادي؟ لأ بحكي الفوضى هنا في الجدول اه اه في
+
+606
+00:48:31,510 --> 00:48:34,150
+الجدول انت بتتكلم هنا على لأ احنا هنا بتتكلم في
+
+607
+00:48:34,150 --> 00:48:38,130
+فرضية انت فارضة فرضية و انت بتشتغل و لاجيت انه
+
+608
+00:48:38,130 --> 00:48:43,010
+الفرضية غلط الشغل انه الفرضية غلط انت باديا بتقول
+
+609
+00:48:43,010 --> 00:48:47,470
+ان هي rational ال rational لها شروط اجينا و احنا
+
+610
+00:48:47,470 --> 00:48:50,030
+بنشتغل و قولنا ان هي rational اجينا نحقق الشروط
+
+611
+00:48:50,030 --> 00:48:56,330
+وجدنا انها مابتتحققشفانت طبيعي الفرضية اللى فرضها
+
+612
+00:48:56,330 --> 00:48:59,790
+غلط مدى ما اتحققتش الشروط بتاعتها شروطها ان تكون
+
+613
+00:48:59,790 --> 00:49:03,210
+عبارة عن حصل قسمة رقمين الرقمين هدول اول شرط ان
+
+614
+00:49:03,210 --> 00:49:06,190
+هما يكونوا integers هذا integer و هذا integer
+
+615
+00:49:06,190 --> 00:49:10,350
+الشرط التانى مايكونش فيه اي عامل مشترك بينهم طب
+
+616
+00:49:10,350 --> 00:49:13,610
+احنا مع الشغل اثبتنا ان الاتنين even واحنا عارفين
+
+617
+00:49:13,610 --> 00:49:18,180
+ان ال evenبيقبل القسم على اتنين فإذا البصد بيقبل
+
+618
+00:49:18,180 --> 00:49:21,180
+القسم على اتنين والمقان أو ال denominator بيقبل
+
+619
+00:49:21,180 --> 00:49:23,440
+القسم على اتنين فال numerator بيقبل و ال
+
+620
+00:49:23,440 --> 00:49:27,680
+denominator بيقبل على اتنين فإذا في عامل مشترك هذا
+
+621
+00:49:27,680 --> 00:49:30,760
+بيقبل على اتنين و هذا بيقبل على اتنين نفينا
+
+622
+00:49:30,760 --> 00:49:34,060
+الفرضية اللي أنا بديها ماتطلعتش ليها على ال truth
+
+623
+00:49:34,060 --> 00:49:36,080
+tables ولا غيرها في ال contrapositive أنا بفرض
+
+624
+00:49:36,080 --> 00:49:41,500
+فرضية و بثبت عدم صحيتها و بنثبت عدم صحيتها و غالبا
+
+625
+00:49:41,500 --> 00:49:47,340
+بفرضها عكس ال givenنفرضها بعكس ال given فإذا العكس
+
+626
+00:49:47,340 --> 00:49:51,900
+ال negation للمعلومة اللي مُعطاها طلع false فإذا
+
+627
+00:49:51,900 --> 00:49:55,260
+المعلومة اللي مُعطاها أكيد true هذا لما يعطيكوا
+
+628
+00:49:55,260 --> 00:49:59,020
+معلومة بالشكل هذا ويقول كوثيب طولية طب أنا كيف بدي
+
+629
+00:49:59,020 --> 00:50:02,380
+أثبتها ب direct و indirect الطرق التقليدية أو ال
+
+630
+00:50:02,380 --> 00:50:05,420
+contrapositive؟ مقدرش ليش؟ لأنه هي معلومة ميعطيني
+
+631
+00:50:05,420 --> 00:50:08,380
+هو بس بدي أنا أعرفها صح ولا غلط مش ميعطيني إش معها
+
+632
+00:50:08,380 --> 00:50:13,770
+فكل اللي بتعملوا انتوا بتكونوا تفرضوا عكسهاو أثناء
+
+633
+00:50:13,770 --> 00:50:20,510
+الحل بده يطلع إثبات عكسها false إذا عكس العكس هو
+
+634
+00:50:20,510 --> 00:50:23,330
+اللي كان صحيح فإذا عكس العكس هو اللي كان صحيح و
+
+635
+00:50:23,330 --> 00:50:27,830
+اللي هو كان أساسا given من الأول ناخد لنا كمان
+
+636
+00:50:27,830 --> 00:50:32,130
+مثال ناخد لنا كمان مثال في نفس السياق في الcontra
+
+637
+00:50:32,130 --> 00:50:42,250
+positive في ال contradiction الموضوع
+
+638
+00:50:42,250 --> 00:50:48,580
+مهمالموضوع مهم يعني لاحظوا أنا كنت بطيئ جدا معاكم
+
+639
+00:50:48,580 --> 00:50:51,460
+وعملناها كذا مرة لأنه أنا مستشعر أهميتها و بتيجي
+
+640
+00:50:51,460 --> 00:50:55,120
+كتير في امتحانات فنركز فيها و بنعمل الحاجات المهمة
+
+641
+00:50:55,120 --> 00:50:57,380
+كتير ليش؟ لأنه مش بالضروري أقولكوا .. أقولكوا
+
+642
+00:50:57,380 --> 00:51:01,280
+دايما if then إذا كان كذا اثبتولي كذا لو ممكن
+
+643
+00:51:01,280 --> 00:51:05,540
+أقولكوا أثبتولي إنه هذه صح وخلاص بدون معلومات زي
+
+644
+00:51:05,540 --> 00:51:08,200
+الحالة اللي تواخدناها أو زي الحالة اللي جاية هنا
+
+645
+00:51:08,200 --> 00:51:11,120
+there is no largest prime number
+
+646
+00:51:13,730 --> 00:51:19,970
+إن مافيش رقم أولي أكبر، يعني كل رقم أولي فيه رقم
+
+647
+00:51:19,970 --> 00:51:23,470
+أولي أكبر منه، هاي معناها، أبضلكوا to infinity،
+
+648
+00:51:23,470 --> 00:51:28,230
+هبضلكوا to infinity، هاي المعنى، إنوا أثبتولنا إن
+
+649
+00:51:28,230 --> 00:51:33,670
+مافيش رقم أولي هو الأكبر من كل الأرقام الأولية، لأ
+
+650
+00:51:33,670 --> 00:51:37,960
+دائما فيه اللي أكبر منهطب هاذي كيف بتكون تثبتوها؟
+
+651
+00:51:37,960 --> 00:51:40,760
+لا ال contrapositive بتظبطها ولا ال direct بظبطها
+
+652
+00:51:40,760 --> 00:51:43,160
+ولا إيش بظبطها ال contradiction .. ال
+
+653
+00:51:43,160 --> 00:51:45,260
+contradiction هي راح تظبطها .. ليش؟ لإن بدي أفرض
+
+654
+00:51:45,260 --> 00:51:51,020
+العكس .. بدي نفرض العكس .. إنه لأ في largest prime
+
+655
+00:51:51,020 --> 00:51:54,420
+number .. إنه لأ والله في رقم أكبر .. و نثبت بعدين
+
+656
+00:51:54,420 --> 00:51:58,040
+إنه لأ والله في طلع هي أكبر منه .. بتكوننا فينا
+
+657
+00:51:58,040 --> 00:52:01,100
+إننا في .. بتكوننا فينا إننا في .. وهي الطريقة
+
+658
+00:52:01,100 --> 00:52:04,850
+اللي نقدر منها نعمل أثباتنا .. ف ..في الحالة هذه
+
+659
+00:52:04,850 --> 00:52:09,970
+فعليا أنتم ماعندكم مش أي فرضية أصلية عندكم نتيجة
+
+660
+00:52:09,970 --> 00:52:13,730
+ومطلوب اثبتوها فالحالات المناسبة لل contradiction
+
+661
+00:52:13,730 --> 00:52:17,110
+أن ماعندكم مش انتم فرضية معلومة اثبتوها يا
+
+662
+00:52:17,110 --> 00:52:20,170
+بتثبتوها يا بتثبتوهااش اللي بنعمله هنا بنفرض ال
+
+663
+00:52:20,170 --> 00:52:23,010
+contradiction أو بنفرض ال conclusion there is no
+
+664
+00:52:23,010 --> 00:52:27,510
+largest prime هذا is false هنفرض ان هو false ايش
+
+665
+00:52:27,510 --> 00:52:29,890
+يعني false يعني معناه ان there is a largest prime
+
+666
+00:52:29,890 --> 00:52:35,170
+number وحنسميه Pسأقول لأ يا جماعة الخير في رقم
+
+667
+00:52:35,170 --> 00:52:41,710
+أولي أكبر واسمه P طيب ماشي سميناه P هل وجد اللي
+
+668
+00:52:41,710 --> 00:52:46,790
+بنقول المفروض معناته كل ال primes التانية أقل منه؟
+
+669
+00:52:46,790 --> 00:52:50,450
+مدام هو الأكبر، معناته كل ال primes التانية أقل
+
+670
+00:52:50,450 --> 00:52:55,430
+منه، كويسةthe set of all primes lie between one or
+
+671
+00:52:55,430 --> 00:53:00,830
+and P بنقدر نعبرها بالشكل التالي ان ر بتساوي اتنين
+
+672
+00:53:00,830 --> 00:53:05,570
+هحط كل primes اتنين تلاتة خمسة سبعة احداشر تلاتاشر
+
+673
+00:53:05,570 --> 00:53:10,590
+مش عارف سبعتاشر تسعتاشر تلاتة وعشرين بتكملوا،
+
+674
+00:53:10,590 --> 00:53:14,910
+كويسة لعند ما تصلوا لمين؟ لل P اللي انتوا بتدعوا و
+
+675
+00:53:14,910 --> 00:53:19,870
+اللي احنا دعينا ان هو اكبر رقم prime او اكبر رقم
+
+676
+00:53:19,870 --> 00:53:25,370
+اولي معناه ذلك انه مافيش اي رقم بعدهحلو، كويس جدا،
+
+677
+00:53:25,370 --> 00:53:30,850
+ولكن هنفاجأ أن كل مجموعة الأرقام الأولية ضربهم في
+
+678
+00:53:30,850 --> 00:53:36,170
+بعض زائد واحد دائما بطلع رقم أول جديد خليني
+
+679
+00:53:36,170 --> 00:53:43,930
+أمسكهم، اتنين في تلاتة، زائد واحد، سبعة، سبعة
+
+680
+00:53:43,930 --> 00:53:50,650
+prime طيب، ستة في خمسة، تلاتين، زائد واحد، الواحد
+
+681
+00:53:50,650 --> 00:53:56,370
+تلاتين ال primeطيب هنا صارت جدش تلاتين في سبعة
+
+682
+00:53:56,370 --> 00:54:01,830
+تلاتين صح تلاتين في سبعة متين و عشرة متين و إحدى
+
+683
+00:54:01,830 --> 00:54:06,510
+عشرة is a prime هذا طريقة بتقدر تعمل فيها
+
+684
+00:54:06,510 --> 00:54:10,770
+generation ل ال primes ل ال primes معنى ذلك أن لأ
+
+685
+00:54:10,770 --> 00:54:14,480
+في أكبر من هذاببساطة جدا، لو كلهم ضربتوا في بعض
+
+686
+00:54:14,480 --> 00:54:19,660
+وزودت واحد أكيد هيطلع prime ومدام ال prime ناتج من
+
+687
+00:54:19,660 --> 00:54:23,980
+ضرب ال P في رقم أكبر من واحد أكيد هيكون أكبر من P
+
+688
+00:54:23,980 --> 00:54:27,600
+أكيد هيكون أكبر من P معناه ذلك أنه لأ دائما في رقم
+
+689
+00:54:27,600 --> 00:54:32,760
+أكبر منه دائما هيكون في رقم أكبر منه لأن R plus
+
+690
+00:54:32,760 --> 00:54:38,540
+واحد وR هي حاصل ضربهمجربوها، جربوها بطريقة هذه،
+
+691
+00:54:38,540 --> 00:54:41,420
+دايما هتطلقوا primes، دايما هتبقوا تطلقوا primes
+
+692
+00:54:41,420 --> 00:54:47,780
+منها R plus واحد is a prime larger than P، منطقي
+
+693
+00:54:47,780 --> 00:54:51,320
+جدا، ليش؟ لأن أنا ضربت فيه ال P في integer أكبر من
+
+694
+00:54:51,320 --> 00:54:56,320
+واحد، فطبيعي جدا، بدو يعطيكوا رقم أعلى من ال P،
+
+695
+00:54:56,320 --> 00:54:59,500
+مضاعفات من ال P، why؟ لأنها زي ما قلنا ضربناها
+
+696
+00:54:59,500 --> 00:55:03,150
+برقم أكبر من واحدفإذا automatically صار عندكوا
+
+697
+00:55:03,150 --> 00:55:06,430
+contradiction صار عندكوا تعرض أنتوا فرضين أنه أكبر
+
+698
+00:55:06,430 --> 00:55:09,950
+رقم بس قدرتوا تعمله منه generation لرقم أكبر منه
+
+699
+00:55:09,950 --> 00:55:16,310
+فإذا صار العكس أثبتته العكس معناه ذلك أن عكس ال
+
+700
+00:55:16,310 --> 00:55:21,290
+negation true اللي هي من الأصل أنه no largest
+
+701
+00:55:21,290 --> 00:55:25,590
+prime numberطيب واضحة ايه انت بتقدر تتعاملوا معها
+
+702
+00:55:25,590 --> 00:55:28,050
+مع ال contradiction لما انتوا مايكونش عندكوا
+
+703
+00:55:28,050 --> 00:55:32,750
+premises واضحة مايكونش عندكوا فرضيات واضحة وانتوا
+
+704
+00:55:32,750 --> 00:55:36,030
+مضطرين تتعاملوا مع ال .. مع ال .. ال contradiction
+
+705
+00:55:36,030 --> 00:55:37,790
+تضطروا في الحالة اللي تشتغلوا معها ال
+
+706
+00:55:37,790 --> 00:55:43,010
+contradiction تفرضوا العكس و أثناء الشغل هيظهر
+
+707
+00:55:43,010 --> 00:55:46,110
+معاكوا او بتكونوا تحاولوا تشتهدوا تثبتوا ان العكس
+
+708
+00:55:46,110 --> 00:55:49,190
+اللي انتوا فرضته false ان العكس اللي انتوا فرضينه
+
+709
+00:55:49,190 --> 00:55:49,970
+false
+
+710
+00:55:55,950 --> 00:56:00,210
+هذا example؟ لأ مش example، لأ هذا برضه نفس
+
+711
+00:56:00,210 --> 00:56:03,430
+الطريقة مش مشكلة، مش example كويسة، في الحالة هذه
+
+712
+00:56:03,430 --> 00:56:09,870
+احنا أخدنا مجموعة methods مهمة جدا ل proofs من
+
+713
+00:56:09,870 --> 00:56:13,870
+المواضيع اللي مافيش امتحان يخلو منها، فإذا دايما
+
+714
+00:56:13,870 --> 00:56:16,730
+بتفكروا بال direct، indirect، indirect على طول
+
+715
+00:56:16,730 --> 00:56:20,970
+مخكم مع مين؟ مع ال contrapositiveindirect مخ دايما
+
+716
+00:56:20,970 --> 00:56:23,050
+على طول مع ال contrapositive في ال direct و في ال
+
+717
+00:56:23,050 --> 00:56:25,970
+indirect هذا بتكون تكونوا حافظينه كويس واضح أن ال
+
+718
+00:56:25,970 --> 00:56:29,850
+implication بدنا نحفظه لأن كل شغلنا عليه ال
+
+719
+00:56:29,850 --> 00:56:32,130
+implication كل شغلنا عليه سواء تشتغلوا على direct
+
+720
+00:56:32,130 --> 00:56:37,270
+أو indirect في كمان إيش كان معناه ال vacuous و ال
+
+721
+00:56:37,270 --> 00:56:40,490
+trivial برضه بتكونوا حافظينه لأنه من هنا بتقدر
+
+722
+00:56:40,490 --> 00:56:44,230
+تقول إنه ما بطل له معنى ال conclusion أو بطل لها
+
+723
+00:56:44,230 --> 00:56:49,020
+معنى ال premisesو الحاجة الأهم هاني بقولكوا كمان
+
+724
+00:56:49,020 --> 00:56:51,700
+مرة اللي هي إيه؟ ال contradiction .. ال
+
+725
+00:56:51,700 --> 00:56:55,240
+contradiction لأنه هاد بتكون .. بتكون تثبتوا منها
+
+726
+00:56:55,240 --> 00:57:00,620
+النظرية بدون ما يكون لها premises بدون ما .. خلاص
+
+727
+00:57:00,620 --> 00:57:04,400
+given عندكوا اثبتواطب أنا ماعنديش premises أنطلق
+
+728
+00:57:04,400 --> 00:57:07,880
+منها، أشتغل منها، فبتروحوا بتعكسوها و بتثبتوا أن
+
+729
+00:57:07,880 --> 00:57:13,460
+عكسها false، معناه ذلك أن ال .. ال .. ال .. ال ..
+
+730
+00:57:13,460 --> 00:57:15,280
+ال .. ال affirment تبعها، اللي هو التأكيد تبعها
+
+731
+00:57:15,280 --> 00:57:20,540
+الأصلي هو اللي true، هو اللي كان true طيب، نكفي،
+
+732
+00:57:20,540 --> 00:57:22,900
+هيك نكون خلصنا الموضوع هذا، المرة الجاية ان شاء
+
+733
+00:57:22,900 --> 00:57:26,560
+الله بنبدأ في مين؟ بنبدأ مع ال six ان شاء الله
+
+734
+00:57:26,560 --> 00:57:26,960
+تعالى
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..855cd35093ee124bf9b433f2456f1742d2fa9f1b
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/pj-Ycs2xYQQ_raw.srt
@@ -0,0 +1,2948 @@
+1
+00:00:20,670 --> 00:00:22,730
+بسم الله الرحمن الرحيم الصلاة والسلام عليك ورحمة
+
+2
+00:00:22,730 --> 00:00:24,330
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+3
+00:00:24,330 --> 00:00:24,430
+ورحمة الله ورحمة الله ورحمة الله ورحمة الله ورحمة
+
+4
+00:00:24,430 --> 00:00:24,590
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+5
+00:00:24,590 --> 00:00:28,470
+ورحمة
+
+6
+00:00:28,470 --> 00:00:34,650
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+7
+00:00:34,650 --> 00:00:34,650
+ورحمة الله ورحمة الله ورحمة الله ورحمة الله ورحمة
+
+8
+00:00:34,650 --> 00:00:34,650
+الله ورحمة الله ورحمة الله ورحمة الله ورحمة الله
+
+9
+00:00:34,650 --> 00:00:37,610
+ورحمة الله ورحمة الله ورحمة الله ورحمة الله ورحمة
+
+10
+00:00:37,610 --> 00:00:43,400
+الله ورحمة الله ورحمة الله ورحمة اللهفأذكر أن أحنا
+
+11
+00:00:43,400 --> 00:00:47,540
+تحدثنا عن أربع قرق أساسية اللي هنبدأ نشرحها واحدة
+
+12
+00:00:47,540 --> 00:00:53,100
+واحدة و هنظفلها واحدة خامسة ضمن واحدة من الأربع
+
+13
+00:00:53,100 --> 00:00:57,120
+categories هدولة بداية اتكلمنا عن ال direct proof
+
+14
+00:00:57,120 --> 00:01:00,860
+وهدي مباشرة ال implication تبعنا اللي هنشتغل عليه
+
+15
+00:01:00,860 --> 00:01:03,680
+و اللي أحنا أساسا بنعمل منه الإثبات بيكون عندنا
+
+16
+00:01:03,680 --> 00:01:07,640
+premises معطيات و منها بدأ نثبت conclusion أو
+
+17
+00:01:07,640 --> 00:01:15,370
+استنتاجفإذا نتكلم عن P implies Q تحقق P اللي هي ال
+
+18
+00:01:15,370 --> 00:01:20,190
+premises، بنانا عليها بدي أحاول أستنتج ال Q، بدنا
+
+19
+00:01:20,190 --> 00:01:24,210
+نستنتج ال Q فهذه بال direct search بناخدها بنفس
+
+20
+00:01:24,210 --> 00:01:27,450
+الطريق، بنفس الاتجاه بتاع ال implication، بمعنى
+
+21
+00:01:27,450 --> 00:01:34,490
+أني بفرض P is trueوبحاول منها بشوية rules of
+
+22
+00:01:34,490 --> 00:01:42,770
+inference أصل لمين ل Q is true بحاول منها نصل ل Q
+
+23
+00:01:42,770 --> 00:01:46,010
+is true في هذه ال direct ماشية مباشرة مع مين مع
+
+24
+00:01:46,010 --> 00:01:49,230
+الاتجاه تبعنا ال indirect لأ في ال indirect
+
+25
+00:01:49,230 --> 00:01:55,540
+بنتعامل مع الموضوع بطريقة عكسيةبال contrapositive
+
+26
+00:01:55,540 --> 00:02:00,540
+على أساس ان انا ممكن ال D نفسها تكون complicated
+
+27
+00:02:00,540 --> 00:02:06,500
+او complex proposition ممكن تكون معقدة شوية ان انا
+
+28
+00:02:06,500 --> 00:02:09,200
+ابتدأ اتعامل معاها ممكن في بعض الحالات هذا اذا
+
+29
+00:02:09,200 --> 00:02:11,860
+طبعا سيبناكوا الخيار فانتوا في الحالة دي اللي
+
+30
+00:02:11,860 --> 00:02:14,920
+جيتوها صعبة انكوا تبتنطلقوا منها و تحاولوا بشوية
+
+31
+00:02:14,920 --> 00:02:18,320
+rules تطبقوها عليها بتبدأوا تشتغلوا بالعكس يمكن ال
+
+32
+00:02:18,320 --> 00:02:24,320
+Q تكون أسهل فبنتعامل مع negation Qبنفرض أن هذه هي
+
+33
+00:02:24,320 --> 00:02:28,280
+فرضية من عندنا بنفرض أن هذه هي ال true و منها بدي
+
+34
+00:02:28,280 --> 00:02:34,300
+أحس .. بدي أجيب negation فيه إذا تحقق ال condition
+
+35
+00:02:34,300 --> 00:02:37,640
+هذا automatically هذا يتبع ليش؟ لأن عارف أن
+
+36
+00:02:37,640 --> 00:02:41,920
+الأثنين equivalent لبعض ضمن relation سمنها ال
+
+37
+00:02:41,920 --> 00:02:44,860
+contrapositive relation contrapositive لل
+
+38
+00:02:44,860 --> 00:02:48,980
+implication بتذكرين لما اتكلمنا عن inverse؟للـ
+
+39
+00:02:48,980 --> 00:02:52,120
+implication واتكلمنا عن ال converse وكان الجزء
+
+40
+00:02:52,120 --> 00:02:54,600
+التاريخي اللي هو إيش ال inverse و ال converse مع
+
+41
+00:02:54,600 --> 00:02:58,000
+بعض و سمناها ال contrapositive اللي هو بالشكل ..
+
+42
+00:02:58,000 --> 00:03:00,500
+بالشكل اللي قولنا إنه هذه مكافئة مباشرة لل
+
+43
+00:03:00,500 --> 00:03:05,080
+implication الأصلي فإذا .. إذا قدرت أثبت ال
+
+44
+00:03:05,080 --> 00:03:08,640
+contrapositive automatically هده صحيحة ..
+
+45
+00:03:08,640 --> 00:03:11,260
+automatically هده صحيحة فهنا بنعمل assuming لـ
+
+46
+00:03:11,260 --> 00:03:16,470
+negation Q و منها بنثبتnegation بتحقق الكلام هذا
+
+47
+00:03:16,470 --> 00:03:18,670
+automatically يقولوا أنه إذا ال relation الأولى
+
+48
+00:03:18,670 --> 00:03:22,590
+صحيحة ال relation الأولى المطلوب اثبتها صحيحة
+
+49
+00:03:22,590 --> 00:03:27,870
+بالقياس مع ال contrapositive طيب في ال vacuous
+
+50
+00:03:27,870 --> 00:03:34,890
+proof وهدي اتكلمنا عليها معناها بلا معنىيعني ال
+
+51
+00:03:34,890 --> 00:03:37,930
+proof لا معنى له .. هدى إنت بتصير إذا كان أثبتنا
+
+52
+00:03:37,930 --> 00:03:41,690
+negation P by itself إذا كان هو معطيني P عساس إن
+
+53
+00:03:41,690 --> 00:03:47,150
+هي معطة أثبتنا إنه لأ P is false طب إنت كيف تقولي
+
+54
+00:03:47,150 --> 00:03:49,770
+هي true و هي أساسا false فانا بتعامل معها أصبحت
+
+55
+00:03:49,770 --> 00:03:52,250
+عساس إن هي false لإن ال authoritative عندى بال ..
+
+56
+00:03:52,250 --> 00:03:55,070
+بالمنطق تبعنا إنه هي false مدام false
+
+57
+00:03:55,070 --> 00:03:58,970
+automatically ال relation صح بغض النظر إنه إيش ال
+
+58
+00:03:58,970 --> 00:04:03,280
+Qفإذا أنا مش مضطر أجيب ال Q أو أعرف بالظبط Q
+
+59
+00:04:03,280 --> 00:04:07,020
+الشيية ليش؟ لأنه لو ماذكرين أقولكوا احنا المفروض
+
+60
+00:04:07,020 --> 00:04:10,020
+ال implication هذا نقطبه هنا و ما نضمن محاش تاني
+
+61
+00:04:10,020 --> 00:04:13,780
+بالمرة لأن معظم شغلنا على ال truth table تبع مين
+
+62
+00:04:13,780 --> 00:04:19,780
+ال implication فخلينا نقطبه هنا هي P Q و ال
+
+63
+00:04:19,780 --> 00:04:23,400
+implication قولنا في عندكوا false, false, true,
+
+64
+00:04:24,480 --> 00:04:32,840
+false, truetrue و في عندكوا true false false و في
+
+65
+00:04:32,840 --> 00:04:39,100
+عندكوا true true true طيب لو هده .. هبطه منك على
+
+66
+00:04:39,100 --> 00:04:43,740
+جد .. لحظه إذا كان ال P أثبت إن هي negation ال
+
+67
+00:04:43,740 --> 00:04:51,440
+relation صحيحة بغض النظر إيش قيمة ال Q فخلاص فإذا
+
+68
+00:04:51,440 --> 00:04:57,460
+بطريقة لا معنى لها الجملة صحيحة أو الإثبات صحيحة
+
+69
+00:04:57,940 --> 00:05:01,000
+ولو ان احنا مش كتير مقتنعين بالطريقة ولكن خلاص هي
+
+70
+00:05:01,000 --> 00:05:04,940
+طريقة من طرق الاثبات طريقة من طرق الاثبات اذا كان
+
+71
+00:05:04,940 --> 00:05:09,340
+اثبتنا رياضيا ان ال negation بيه هي ال true معناه
+
+72
+00:05:09,340 --> 00:05:13,960
+ان P هي ال false فإذا ال implication او ال
+
+73
+00:05:13,960 --> 00:05:19,100
+relation صحيحة بغض النظر ال Q هتطلع صح ولا هتطلع
+
+74
+00:05:19,100 --> 00:05:24,350
+خطأ ال Q تطلع صح تطلع غلط مش هتفرج كتيرممكن
+
+75
+00:05:24,350 --> 00:05:27,890
+تتذكروا المجموعة ال examples اللى أخدناها عن ال
+
+76
+00:05:27,890 --> 00:05:32,450
+implication لما اتكلمنا عن إذا كان الجبنة الخضراء
+
+77
+00:05:32,450 --> 00:05:37,090
+بتنعمل في الجمر مش عارف even كذا متذكرينه المثال؟
+
+78
+00:05:37,090 --> 00:05:40,910
+كويس هو نفس الكلام هذا احنا مجرد أن ال P لجناها
+
+79
+00:05:40,910 --> 00:05:44,830
+false قلنا الجملة صح خلاص قلنا خلاص automatically
+
+80
+00:05:44,830 --> 00:05:48,590
+الجملة صح بغض النظر النتيجة تحققت او ماتحققتش ال
+
+81
+00:05:48,590 --> 00:05:52,660
+relation كلها صحيحة خلاصتمام بس لما تيجي تتكلم
+
+82
+00:05:52,660 --> 00:05:56,880
+عنها طب هو مالهوش معنى الجمر بيعمل جبنة خضرة طبيعي
+
+83
+00:05:56,880 --> 00:06:00,240
+مالهاش أي معنى فحتاج انه فعلا كلام بلا معنى ولكن
+
+84
+00:06:00,240 --> 00:06:05,680
+اثبت انه صحيح اثبت انه حسب الجملة او الجملة
+
+85
+00:06:05,680 --> 00:06:08,900
+الرياضية بتاعة اللي هي ال implication صحيحة طيب ال
+
+86
+00:06:08,900 --> 00:06:13,960
+trivial proof هذي لأ بتثبت Q من نفسها بمعنى انا مش
+
+87
+00:06:13,960 --> 00:06:21,100
+محتاج ال P صارال P مالوش لازمة، انا مش محتاج
+
+88
+00:06:21,100 --> 00:06:25,380
+premises، اعطاني premise بس ماستفدتش منها، أثبتنا
+
+89
+00:06:25,380 --> 00:06:30,800
+Q من نفسها، Q أثبتت من نفسها، مش محتاجين ال P
+
+90
+00:06:30,800 --> 00:06:34,000
+فيها، ففي الحالة هذه ال trivia بتسميها، تافه، يعني
+
+91
+00:06:34,000 --> 00:06:36,720
+اعطاني شرط تافه مالوش أي معنى أو ال condition
+
+92
+00:06:36,720 --> 00:06:42,140
+ماستفدتش منهتمام في ال indirect هنكمل غير ال
+
+93
+00:06:42,140 --> 00:06:45,360
+contrapositive هناخد في الآخر طريقة هنسميها ال
+
+94
+00:06:45,360 --> 00:06:49,380
+contradiction برضه هي تعتبر من طرق ال indirect
+
+95
+00:06:49,380 --> 00:06:53,060
+فبنكون خلصناها فعليا هم تلاتة اللي هنشتغل عليهم و
+
+96
+00:06:53,060 --> 00:06:56,770
+نركز عليهم ال directو ال contrapositive و ال
+
+97
+00:06:56,770 --> 00:06:59,670
+contradiction هم دول التلاتة الأكثر أهمية يعني في
+
+98
+00:06:59,670 --> 00:07:03,030
+شغلنا طيب نبدأ في ال direct و ناخد example على طول
+
+99
+00:07:03,030 --> 00:07:05,630
+خلاص ال direct تعرفنا إيش يعني ال direct هبدأ من
+
+100
+00:07:05,630 --> 00:07:12,430
+ال P و أحاول أثبت منها ال Q تمام فإذا محتاجين ال
+
+101
+00:07:12,430 --> 00:07:15,750
+theorem بتاعتنا و هناخد شوية hints شوية hints هيكي
+
+102
+00:07:15,750 --> 00:07:18,210
+تساعدنا في الحل بس هي ال theorem اللي مطلوب مننا
+
+103
+00:07:18,210 --> 00:07:24,570
+نثبتها for all numbers N if N is all integersفإذن
+
+104
+00:07:24,570 --> 00:07:31,550
+هي integer عدد صحيح و فردي then انتربيع is a non
+
+105
+00:07:31,550 --> 00:07:36,410
+integer فإذن برضه الانتربيع بتاعتها بتكون integer
+
+106
+00:07:36,410 --> 00:07:41,810
+عدد صحيح و برضه فردي اثبتولنا الكلام هذا طيب عشان
+
+107
+00:07:41,810 --> 00:07:44,710
+نثبت الكلام هذا في عندنا definitions من الأول
+
+108
+00:07:44,710 --> 00:07:49,350
+بيناعرفها كيف أعرفهمالعدد الفردي و كيف اعرف العدد
+
+109
+00:07:49,350 --> 00:07:54,090
+الزوجي العدد الفردي بنعرفه كالتالي an integer n is
+
+110
+00:07:54,090 --> 00:07:58,830
+called odd if and only if n equal to 2k plus one
+
+111
+00:07:58,830 --> 00:08:07,070
+2k زوجيزائد واحد على طوط صار فردي فإذا كان تحقق ل
+
+112
+00:08:07,070 --> 00:08:11,530
+ال N أني بقدر أمثله بهذا الشكل بهذه المعادلة فبقدر
+
+113
+00:08:11,530 --> 00:08:16,170
+أقول إن ال N هذي إيش عدد فردي for إيش some integer
+
+114
+00:08:16,170 --> 00:08:21,710
+K بشرط إن ال K هذي ما تكونش كسر ما تكونش كسر تكون
+
+115
+00:08:21,710 --> 00:08:25,030
+برضه integer إذا قدرنا نمثلها بهذا الشكل فهي odd
+
+116
+00:08:25,030 --> 00:08:31,450
+طيب and N is even if and only if N equal to 2K بس
+
+117
+00:08:32,090 --> 00:08:35,250
+انه بتقبل القسم على اتنين بس خارج القسم لازم يكون
+
+118
+00:08:35,250 --> 00:08:42,430
+integer مايكونش كسر تمام برضه for some k او some
+
+119
+00:08:42,430 --> 00:08:49,330
+integer k طيب ال axiom او الشيء البديهي ان اي
+
+120
+00:08:49,330 --> 00:08:53,510
+integer number هو يا odd يا even مافيش احتمال تالف
+
+121
+00:08:53,510 --> 00:08:59,630
+فإذا every integer is either odd or evenمعنى ذلك
+
+122
+00:08:59,630 --> 00:09:02,390
+إذا كان هدرش بنقول الكلام هذا باعتبار أنه لو
+
+123
+00:09:02,390 --> 00:09:06,030
+ماتحققش ال odd هي automatically even و العكس صحيح
+
+124
+00:09:06,030 --> 00:09:10,050
+لو ماتحققش أنهية even ال integer هي automatically
+
+125
+00:09:10,050 --> 00:09:17,250
+odd تمام نمسك نرجع للسؤال طبعا المطلوب إيش نعمل if
+
+126
+00:09:17,250 --> 00:09:25,770
+in is even in is is odd عفوا is odd تمام employees
+
+127
+00:09:26,750 --> 00:09:32,970
+انتربيع is odd فاطوماتيك لببدأ من هنا من ال P
+
+128
+00:09:32,970 --> 00:09:37,650
+فبنبدأ شغلنا عادي من ال P زي ما هي طيب هد عشان
+
+129
+00:09:37,650 --> 00:09:41,310
+تكون odd المفروض هي تكون بتساوي two k plus one
+
+130
+00:09:41,310 --> 00:09:46,410
+صحيح و ننطلق منها نحاول نثبت هذا الكلام طب عشان
+
+131
+00:09:46,410 --> 00:09:50,070
+أثبت الكلام هد بدي أجيب انتربيع فإذا بدي أربع هذا
+
+132
+00:09:50,070 --> 00:09:55,870
+ال theorem و نفك التربيعونشوف هل بتطلع معانا نفس
+
+133
+00:09:55,870 --> 00:10:00,950
+ال form هذا و لا تطلع لأ two في integer و لا two
+
+134
+00:10:00,950 --> 00:10:04,830
+في integer plus واحد بنحاول نشوف لما نفك هدول و
+
+135
+00:10:04,830 --> 00:10:07,950
+نجمع و نظبطها كيف ممكن تطلع فهو هى .. بس هى ال
+
+136
+00:10:07,950 --> 00:10:12,650
+proof هى ال strategy بتاعتنا كويس N is odd then N
+
+137
+00:10:12,650 --> 00:10:17,550
+equal to two K plus one كويس for some integer K N
+
+138
+00:10:17,550 --> 00:10:23,370
+تربيةهي ال integer تبعنا بال representation تبعته
+
+139
+00:10:23,370 --> 00:10:28,210
+تربيع فكنا الأولى
+
+140
+00:10:28,210 --> 00:10:31,670
+تربيع زائد التانية تربيع زائد الأولى في التانية في
+
+141
+00:10:31,670 --> 00:10:35,130
+اتنين مظبوط تمام هاي ال term اللي قلناه لاحظوا ان
+
+142
+00:10:35,130 --> 00:10:39,930
+هذا ال term بقدر اطلع منه اتنين عامل مشترك كويسة
+
+143
+00:10:39,930 --> 00:10:45,490
+تصير عندكوا اتنين في اتنين كتربيع plus two k كله
+
+144
+00:10:45,490 --> 00:10:52,320
+زائد واحد طيب هذا ال termال K هدي إيش؟ Integer.
+
+145
+00:10:52,360 --> 00:10:56,700
+Integer تربيع؟ Integer. فإتنين؟ Integer. يعني في
+
+146
+00:10:56,700 --> 00:10:59,240
+Integer .. Integer في Integer؟ Integer. ال plus
+
+147
+00:10:59,240 --> 00:11:03,360
+integer؟ Integer. فإذا كل ال term هذا بقدر أقول إن
+
+148
+00:11:03,360 --> 00:11:08,960
+هو J و J أكيد integer فإذا بقدر أمثلها two J plus
+
+149
+00:11:08,960 --> 00:11:14,780
+واحد برضه ال J هتكون some integer
+
+150
+00:11:17,780 --> 00:11:24,420
+كويس في الحالة دي أصبحت ال n تربيع is 2j plus 1 و
+
+151
+00:11:24,420 --> 00:11:29,260
+ال j .. ال j هذه أكيد integer .. أكيد integer ف
+
+152
+00:11:29,260 --> 00:11:32,700
+automatically مدام أكيد integer فال n تربيع برضه
+
+153
+00:11:32,700 --> 00:11:37,320
+odd لإنه حققت لأنه شرط من الشرطات شرط ال odd حققت
+
+154
+00:11:37,320 --> 00:11:43,380
+إنه شرط ال odd خلصنا بشكل direct .. بشكل direct
+
+155
+00:11:43,380 --> 00:11:51,690
+بدأنا من ال P و وصلنا لليش .. لل Qهذه أول طريقة،
+
+156
+00:11:51,690 --> 00:11:58,290
+اللي هي direct، و عادة ابدوا فاكروا فيها أول ما
+
+157
+00:11:58,290 --> 00:12:02,230
+تبدوا تحلوا، إذا ما كانش عندكم خيار من إيش لازم
+
+158
+00:12:02,230 --> 00:12:05,450
+تستعملوا طريقة، ابدوا حاولوا فاكروا فيها، بس
+
+159
+00:12:05,450 --> 00:12:08,390
+أحيانا مش دايما بتصبط، هنشوفها لغة الحلات اللي
+
+160
+00:12:08,390 --> 00:12:11,950
+لاحقا هنشتغل عليها، بس خليني ناخد كمان example ليش
+
+161
+00:12:11,950 --> 00:12:17,350
+لات direct، عشان ناخد أكتر من مثلطيب لو قلنا if ال
+
+162
+00:12:17,350 --> 00:12:21,490
+theorem بتاعتنا اللي بدنا نثبتها if 6x plus 9y
+
+163
+00:12:21,490 --> 00:12:30,470
+equal to 101 then x or y is not integer طيب كيف
+
+164
+00:12:30,470 --> 00:12:36,930
+نثبتها هذه بسيطة هذه P وهذه بدنا نثبتها Q هذه P
+
+165
+00:12:36,930 --> 00:12:41,110
+وهذه Q طيب هنبدأها direct مدام اننا نتكلم عن
+
+166
+00:12:41,110 --> 00:12:46,210
+direct هنبدأ من هنا هذه لو قسمنا كلهعلى تلاتة
+
+167
+00:12:46,210 --> 00:12:49,830
+هاتلعنكوا
+
+168
+00:12:49,830 --> 00:12:57,130
+هنا اتنين X plus تلاتة Y بتساوي طيب
+
+169
+00:12:57,130 --> 00:13:01,570
+هذا not integer واضحة باين تماما هذه not integer
+
+170
+00:13:01,570 --> 00:13:04,750
+بتطلع تلاتة وتلاتين فاصلة ستة فاصلة ستة ستة ستة
+
+171
+00:13:04,750 --> 00:13:10,590
+تلتين كويسة not integer اقسمه على integernot
+
+172
+00:13:10,590 --> 00:13:18,330
+integer نفس الكلام بتطلع x not integer فواحدة منهم
+
+173
+00:13:18,330 --> 00:13:22,090
+على الأقل لازم تكون not integer لأنه not integer
+
+174
+00:13:22,090 --> 00:13:27,890
+أجسمه على integer برضه not integer أساسا مجرد أني
+
+175
+00:13:27,890 --> 00:13:30,730
+أقول integer على integer مش بالضرورة تكون integer
+
+176
+00:13:30,730 --> 00:13:35,970
+صح؟ مش بالضرورة تكون integer فلما تكون fraction
+
+177
+00:13:35,970 --> 00:13:40,400
+أساسا فالمنطق أنه برضه هيطلع fractionبتجسمه
+
+178
+00:13:40,400 --> 00:13:46,860
+fraction على integer أكيد fraction فإذا بما يضع
+
+179
+00:13:46,860 --> 00:13:52,420
+مشكلة الشك x او y او الاتنين not integer او
+
+180
+00:13:52,420 --> 00:13:55,880
+الاتنين أثبتناها بطريقة مباشرة بدينا من ال
+
+181
+00:13:55,880 --> 00:14:02,640
+premises تبعتنا ووصلنا لنتيجة المقروبةهنشتغل كتر
+
+182
+00:14:02,640 --> 00:14:06,780
+لإن كلها نجسمها على تلاتة فهيطلع المعادلة two x
+
+183
+00:14:06,780 --> 00:14:10,720
+plus three y equal to one hundred one three over
+
+184
+00:14:10,720 --> 00:14:14,700
+three هدى إمتى ممكن لأ يكونوا كلهم integer إذا كان
+
+185
+00:14:14,700 --> 00:14:19,360
+اقدرت أقسمهم كله و موصلت للمعامل one للاتنين و
+
+186
+00:14:19,360 --> 00:14:23,500
+مازال النتج النهائي integer بس هو لسه موصلناش يعني
+
+187
+00:14:23,500 --> 00:14:27,640
+احنا حتى موصلناش لل coefficient واحد لكل واحد منهم
+
+188
+00:14:27,640 --> 00:14:30,200
+موصلناش احنا لسه فيه coefficient قدامه و مع ذلك
+
+189
+00:14:30,200 --> 00:14:36,710
+ظهرتالـ fraction ظهر ك fractional number كويس ف
+
+190
+00:14:36,710 --> 00:14:41,150
+automatic ل 101 على 3 هو is not an integer وهذا
+
+191
+00:14:41,150 --> 00:14:47,070
+معناه أنه بالضرورة لا X .. X مش هتكون integer أو Y
+
+192
+00:14:47,070 --> 00:14:51,330
+مش هتكون integer واحدة منهم مش هتكون integer وممكن
+
+193
+00:14:51,330 --> 00:14:54,910
+يكونوا الاتنين مع بعض ممكن يكونوا الاتنين مع بعض
+
+194
+00:14:54,910 --> 00:15:00,080
+طبعا أثبتنا كلامك بمجرد ما ظهر عندكوا termnot
+
+195
+00:15:00,080 --> 00:15:03,040
+integer بجرد ما اظهر في المعادلة term not integer
+
+196
+00:15:03,040 --> 00:15:08,920
+في ال indirect ال indirect بقولنا لأ مختلف الموضوع
+
+197
+00:15:08,920 --> 00:15:14,020
+شوية في ال indirect theorem
+
+198
+00:15:14,020 --> 00:15:20,900
+زي ال theorem اللي عندنا هنا if three n
+
+199
+00:15:20,900 --> 00:15:26,760
+plus two is odd employs
+
+200
+00:15:28,870 --> 00:15:37,050
+implies إيش؟ إن n is odd طيب
+
+201
+00:15:37,050 --> 00:15:42,990
+إحنا عارفين إمتى بقدر أقول ال term هذا odd two k
+
+202
+00:15:42,990 --> 00:15:48,230
+plus واحد صحيح؟ two k plus one ولكن إذا بدى أحط
+
+203
+00:15:48,230 --> 00:15:51,890
+هذا بيساوي two k plus one صار عندكوا two variables
+
+204
+00:15:51,890 --> 00:15:56,760
+k وصار عندكوا nفواضح أن ال direct هيعملنا شوية
+
+205
+00:15:56,760 --> 00:16:00,940
+لخمة لإنه هيصير في عندكوا two variables في عندنا n
+
+206
+00:16:00,940 --> 00:16:04,340
+و في ال k موجودين في المعادلة إذا بدي أسيوم في بعض
+
+207
+00:16:04,340 --> 00:16:06,980
+و بدي أحاول أجد رتبهم حتى يكون صعب شوية الترتيب لأ
+
+208
+00:16:06,980 --> 00:16:11,960
+بصير تفكير أكتر أن أروح لمين لل indirect ليش لأنه
+
+209
+00:16:11,960 --> 00:16:17,320
+النتيجة ك proposition أصغر، proposition سهل، ل
+
+210
+00:16:17,320 --> 00:16:20,220
+proposition سهل فهذه بجيبها هنا بس بال إيش بال
+
+211
+00:16:20,220 --> 00:16:26,000
+negation بتاعتها فبقول n is evenلأن برضه احنا قلنا
+
+212
+00:16:26,000 --> 00:16:29,240
+اي رقم integer هو يا odd يا even، إذا ماكانش odd،
+
+213
+00:16:29,240 --> 00:16:34,840
+negation odd، automatically even employees three
+
+214
+00:16:34,840 --> 00:16:40,560
+and plus two is even، تمام، إذا كان أثبتنا هذه،
+
+215
+00:16:40,560 --> 00:16:44,400
+فإذا هذه بالضرورة صحيحةهذه هتكون بالضرورة صحيحة
+
+216
+00:16:44,400 --> 00:16:50,400
+نتيجة إيش الcontra positive فهنبدأ من هنا هنقول إن
+
+217
+00:16:50,400 --> 00:16:57,040
+N is even مدام even بقدر امثلها بإيش 2K تمام وخلاص
+
+218
+00:16:57,040 --> 00:17:03,420
+اعملولا تربيع .. مش تربيع بنعود في المعادلة كل N
+
+219
+00:17:03,420 --> 00:17:08,560
+بنحطها ب2K و بنرتبها بنشوف هل المعادلة كلها بتقبل
+
+220
+00:17:08,560 --> 00:17:12,370
+القسم ع 2إذا بتكبر القسم ع 2، معناته بدّر أقول إن
+
+221
+00:17:12,370 --> 00:17:17,890
+هي عبارة عن 2 في some integer j و خلاص أثبتنا من
+
+222
+00:17:17,890 --> 00:17:22,330
+كل الكلام هذا هنشتغل نشوف هنا، فهنشتغل على أساس إن
+
+223
+00:17:22,330 --> 00:17:26,510
+أنا بشتغل على n even ليش even؟ لأنها ال negation
+
+224
+00:17:26,510 --> 00:17:32,460
+بتاع oddكويس for some integer k فإذا three n plus
+
+225
+00:17:32,460 --> 00:17:36,020
+two بنمثلها بهذا الشكل هنضرب التلاتة في الأتنين
+
+226
+00:17:36,020 --> 00:17:39,460
+صار عندكوا ستة اه بقدر اطلع اتنين عامل مشترك بنقدر
+
+227
+00:17:39,460 --> 00:17:45,060
+وبسيطة جدا و واضحة two في three k plus one برضه
+
+228
+00:17:45,060 --> 00:17:50,200
+الكلام هذا كله هده بقدر اقول ان هو j لأنه و
+
+229
+00:17:50,200 --> 00:17:53,360
+integer اكيد integer لأنه جاي من integer في
+
+230
+00:17:53,360 --> 00:17:57,040
+integer plus integerفي integer في integer أكيد
+
+231
+00:17:57,040 --> 00:18:02,520
+integer في plus integer أكيد integer minus integer
+
+232
+00:18:02,520 --> 00:18:08,580
+integer على integer لأ لأ ماداني لا خبطش إذا كان
+
+233
+00:18:08,580 --> 00:18:13,640
+في لجته على وجهه مش مضمون بقدرش أحطها theorem
+
+234
+00:18:13,640 --> 00:18:19,520
+مقدرش نحطها theorem تمام كويس then three and plus
+
+235
+00:18:19,520 --> 00:18:26,660
+two is evenلما إيش؟ لما كانت n even ففي الحالة هذه
+
+236
+00:18:26,660 --> 00:18:31,860
+بقدر أقول إن اتحقق الشرط فإذا negation n is odd
+
+237
+00:18:31,860 --> 00:18:37,240
+يعني معناها إنه كانت even implies negation 3n plus
+
+238
+00:18:37,240 --> 00:18:44,020
+2 is odd بالcontrapositive بنعكس صارت إذا if 3n
+
+239
+00:18:44,020 --> 00:18:49,530
+plus 2 is odd then n is oddاللي بدنا إيها، اللي
+
+240
+00:18:49,530 --> 00:18:52,970
+بدنا إيها، في الحالة هذه بنكون من ال
+
+241
+00:18:52,970 --> 00:18:56,150
+contrapositive أثبتنا النظرية أو ال theory بتاعتنا
+
+242
+00:18:56,150 --> 00:19:01,230
+وبطريقة أسهل من أني أجلد أشغل على ال .. ال .. ال
+
+243
+00:19:01,230 --> 00:19:03,750
+.. ال premise تبعتنا، أني أبدأ من ال premise
+
+244
+00:19:03,750 --> 00:19:08,970
+بتاعتنا، تمام، هذه ال in .. ال indirect
+
+245
+00:19:13,340 --> 00:19:16,380
+خلّيني أكمل، هنشوف في الـ indirect كمان example ..
+
+246
+00:19:16,380 --> 00:19:20,720
+كمان example ال theorem اللي مطلوب نثبتها if x
+
+247
+00:19:20,720 --> 00:19:28,340
+plus y greater than 100 then x greater than 50 or
+
+248
+00:19:28,340 --> 00:19:32,840
+y greater than 50 فعلا ممكن واحدة منهم لازم يكون
+
+249
+00:19:32,840 --> 00:19:37,070
+على الأقل، يمكن يكون ال 10 تانيو or قلنا إنها تشمل
+
+250
+00:19:37,070 --> 00:19:41,390
+التنتين لإيش؟ لأن ممكن المية منهم تجيبوهم يعني كيف
+
+251
+00:19:41,390 --> 00:19:47,250
+بتجيبوا رقمين مجموحهم مية؟ خمسين و خمسين بس إنتوا
+
+252
+00:19:47,250 --> 00:19:50,830
+greater than أكبر من مية لازم واحدة منهم واحدة و
+
+253
+00:19:50,830 --> 00:19:56,110
+خمسين فصارت أكبر تمام؟ طيب ممكن تكون سبعين و واحدة
+
+254
+00:19:56,110 --> 00:20:00,090
+و تلاتين واحدة منهم هنا و ممكن تكون ستين و ستين
+
+255
+00:20:00,090 --> 00:20:05,540
+التنتين أكبر ففي جميع الأحوال بنجرحبس في الحالة
+
+256
+00:20:05,540 --> 00:20:09,080
+هذه بقدرش أقعد أعمل أحط كل احتمالات X وكل احتمالات
+
+257
+00:20:09,080 --> 00:20:15,800
+Y و أجرب ال relation هذه عشان أشتغل direct عشان
+
+258
+00:20:15,800 --> 00:20:19,200
+لازم أبدأ من هنا، طب لأ مديش أبدأ من هنا، هذي صعبة
+
+259
+00:20:19,200 --> 00:20:22,640
+ليش؟ لأنه بدي أحط كل احتمالة الممكن إلى X وكل
+
+260
+00:20:22,640 --> 00:20:25,940
+احتمالة الممكن إلى Y و الاحتمالة تعالى نطلع عليها
+
+261
+00:20:25,940 --> 00:20:31,760
+X أكبر من 50و هذه or كمان يعني معنى ذلك إنه حامل
+
+262
+00:20:31,760 --> 00:20:35,040
+عملية احتمالات كبيرة جدا عشان نشغل direct لو كنت
+
+263
+00:20:35,040 --> 00:20:38,840
+تشغل direct فهذه أنسبلها إيش؟ ال indirect ليش؟ لأن
+
+264
+00:20:38,840 --> 00:20:44,640
+ال indirect لو كده بتصير كالتاليمن ال theorem اللي
+
+265
+00:20:44,640 --> 00:20:48,660
+بتثبتها بنحدد ال P ال P كانت X plus Y greater than
+
+266
+00:20:48,660 --> 00:20:54,620
+100 ل Q كان X أكبر من 50 او Y أكبر من 50 هنشتغل
+
+267
+00:20:54,620 --> 00:20:58,240
+على ال negation عشان نجيب ال contrapositive لما
+
+268
+00:20:58,240 --> 00:21:00,280
+نعمل negation لل term هذا
+
+269
+00:21:03,380 --> 00:21:09,260
+شيوء بنعمله نجاشة هنا صارت العكس أكبر من أقل أو
+
+270
+00:21:09,260 --> 00:21:16,780
+يساوي طيب و هنا أقل أو يساوي و ال or and ما ننساش
+
+271
+00:21:16,780 --> 00:21:24,020
+هذه دي مورغان في نجاشة هندخله على connection
+
+272
+00:21:24,020 --> 00:21:28,440
+موجودة فبدنا نعكسها ال or بدتصير and وهدولة بدنا
+
+273
+00:21:28,440 --> 00:21:33,680
+نعكسهم تماما عكس أكبر من أقل من أو يساويلأن
+
+274
+00:21:33,680 --> 00:21:40,080
+المساوية لم تكن مشمولة في أكبر منه تمام فانشطرنا
+
+275
+00:21:40,080 --> 00:21:45,200
+على negation q عبارة عن x أقل من أو يساوي خمسين و
+
+276
+00:21:45,200 --> 00:21:49,140
+y أقل من أو يساوي خمسين نيجيشن بي اللي بدنا نثبتها
+
+277
+00:21:49,140 --> 00:21:54,300
+منها أن x زائد y أقل من أو يساوي مية هل الكلام هذا
+
+278
+00:21:54,300 --> 00:21:58,490
+متحقق إذا عرفنا نحقق نيجيشن بيnegation P هدى
+
+279
+00:21:58,490 --> 00:22:02,190
+اقدرنا نحققها من negation Q فإذا ال relation صحيحة
+
+280
+00:22:02,190 --> 00:22:04,830
+مع أن ذلك ال contract positive تبعها صحيحة اللي هي
+
+281
+00:22:04,830 --> 00:22:08,750
+النظرية اللي بدنا نستخدمها طيب تعالى نشوف هنا أقل
+
+282
+00:22:08,750 --> 00:22:13,130
+من أو يساوي خمسين أكبر قيمة ممكنة هي احتمال واحد
+
+283
+00:22:13,130 --> 00:22:15,890
+انها تكون بتساوي فعليا خمسين انها تكون بتساوي
+
+284
+00:22:15,890 --> 00:22:20,690
+خمسين عشان هذه القصة تكون أقل من أو يساوي خمية
+
+285
+00:22:20,690 --> 00:22:24,570
+فبدنا نشوف أكبر قيمة هل هتظل ضمن ال range تبعنا
+
+286
+00:22:24,570 --> 00:22:30,840
+هنا ولا لأطيب x زائد y أقل من خمسين و ال y خمسين
+
+287
+00:22:30,840 --> 00:22:34,860
+أكبر قيمة ممكنة بتساوي مية مية تنطبق مع المعادلة
+
+288
+00:22:34,860 --> 00:22:41,620
+المية ماشية لأنه يساوي مية فهي فعلا تساوي مية
+
+289
+00:22:41,620 --> 00:22:48,860
+معناه ذلك أن كل الأرقام اللي أقل صحيحة برضه لاحظوا
+
+290
+00:22:48,860 --> 00:22:54,160
+احنا اشعلنا x أقل من أو تساوي خمسينصح؟ بنعمل test
+
+291
+00:22:54,160 --> 00:22:57,480
+على أكبر رقم ممكن إذا تحقق ال test على أكبر رقم
+
+292
+00:22:57,480 --> 00:23:03,020
+فإذا كل اللي أقل منه برضه متحقق هي
+
+293
+00:23:03,020 --> 00:23:07,900
+أكبر رقم لل X الشيية أنها تكون خمسين و أكبر رقم ل
+
+294
+00:23:07,900 --> 00:23:11,920
+Y خمسين عشان عوضنا هنا وجدنا أنها تتفق مع المعادلة
+
+295
+00:23:11,920 --> 00:23:15,700
+طيب لو أخدنا أي رقم أخر أقل من الخمسين هي ماشية
+
+296
+00:23:15,700 --> 00:23:19,940
+المعادلة برضهالمعادلة ماشية فإذا احنا أخدنا
+
+297
+00:23:19,940 --> 00:23:25,200
+الاحتمال الوحيد اللي ممكن يبعد إنها تكون تساوى
+
+298
+00:23:25,200 --> 00:23:28,660
+الخمسين أكبر رقم ممكن ل X و أكبر رقم ممكن ل Y
+
+299
+00:23:28,660 --> 00:23:33,960
+عوضنا وجدناها ما زالت ضمن أو بتحقق ليه ال negation
+
+300
+00:23:33,960 --> 00:23:37,680
+P ما زالت بتحقق negation P فإذا ال relation دائما
+
+301
+00:23:37,680 --> 00:23:41,500
+صحيحةال relation دائما صحيحة لكل الأرقام الممكنة ل
+
+302
+00:23:41,500 --> 00:23:48,860
+x و y for all numbers لمين ل x و y ففي الحالة دي
+
+303
+00:23:48,860 --> 00:23:53,120
+بقدر أقول ان ال relation صحيحة كل هيك على بعض من
+
+304
+00:23:53,120 --> 00:23:58,560
+هنا employs ال term هذا okay relation صح فإذا ال
+
+305
+00:23:58,560 --> 00:24:06,780
+contrapositive بتاعتها أكيد صحيحة اللي هيالـ
+
+306
+00:24:06,780 --> 00:24:09,840
+Theorem المطلوبة من غير ما أعمل احتمالات كل
+
+307
+00:24:09,840 --> 00:24:14,160
+احتمالات الممكنة لأكبر من 100 الأقل هنا وفرت عليها
+
+308
+00:24:14,160 --> 00:24:19,520
+أقل بجيب أكبر قيمة ممكنة وهل هي ما زالت ضمن أقل من
+
+309
+00:24:19,520 --> 00:24:22,680
+100 ولا لأ؟ أه ما زالت ضمن أقل من 100 معناته حتى
+
+310
+00:24:22,680 --> 00:24:27,140
+اللي أقل ضمن المعادلة ضمن المعادلة المطلوبة في
+
+311
+00:24:27,140 --> 00:24:31,160
+باتها ففي الحالة هذه اقدرنا نثبت negation Q
+
+312
+00:24:31,160 --> 00:24:35,920
+implies negation P ومنها مباشرة فإذا P implies Q
+
+313
+00:24:36,760 --> 00:24:40,140
+اللي هي المعادلة اللي فوق، هي ال contrapositive
+
+314
+00:24:40,140 --> 00:24:46,560
+اللي اتكلمنا عنها أو ال indirect، indirect محددنها
+
+315
+00:24:46,560 --> 00:24:53,580
+تحديدا اللي هي ال contrapositive، تمامال .. ال
+
+316
+00:24:53,580 --> 00:24:58,260
+vacuous to prove example هذا اللي قلنا بلا معنى
+
+317
+00:24:58,260 --> 00:25:02,720
+بمعنى انه هيعطيني premise و بعدين احنا مثبت ان هي
+
+318
+00:25:02,720 --> 00:25:06,680
+ال premise غلط من أصله فمعنى ذلك ايش ال conclusion
+
+319
+00:25:06,680 --> 00:25:10,500
+يطلع زي ما يطلع مش هتفرق ال relation كلها على بعض
+
+320
+00:25:10,500 --> 00:25:19,220
+دايما صح ليش؟ false ال premise false فإذا بغض
+
+321
+00:25:19,220 --> 00:25:24,180
+النظر ايش النتيجة هي دايما ال relation صحيحةلحظة
+
+322
+00:25:24,180 --> 00:25:30,640
+إذا كان اثبت عندكم ان ال premise false فال
+
+323
+00:25:30,640 --> 00:25:34,320
+relation كلها صحيحة بغض النظر والله فعلا هيتحقق
+
+324
+00:25:34,320 --> 00:25:38,840
+اللي طالبه او لا ال conclusion تحققت او ماتحققتش
+
+325
+00:25:38,840 --> 00:25:42,400
+بغض النظر دائما ال relation كلها على بعض ال
+
+326
+00:25:42,400 --> 00:25:47,200
+implication صحيحة true ف automatically بشكل لا
+
+327
+00:25:47,200 --> 00:25:52,700
+معنى له هي صحيحةتمام؟ كويس خلّيني أشوف for example
+
+328
+00:25:52,700 --> 00:25:57,420
+إذا كانت in is both odd and even اتننى مافيش اللي
+
+329
+00:25:57,420 --> 00:26:01,160
+odd أو even in احنا عارفين إنه يا يا odd يا even
+
+330
+00:26:01,160 --> 00:26:05,000
+بس واحد يجي يقول ليه إذا كان in تحققتلك الشرطين يا
+
+331
+00:26:05,000 --> 00:26:09,080
+odd و even مافيش حاجة اسمها odd و even مافيش أي
+
+332
+00:26:09,080 --> 00:26:11,880
+رقم integer بقدر أقول إنه odd و even فإذا هذه
+
+333
+00:26:11,880 --> 00:26:18,440
+negation على طول هذه false فthen تحققت أو ماتحققتش
+
+334
+00:26:18,440 --> 00:26:22,040
+مش هتفرقو هي فعلا هتلاقوها مرات بتتحقق و مرات لأ
+
+335
+00:26:22,040 --> 00:26:25,980
+بس أنا مش هتطلعها أصلا أشوف هي بتتحقق أو بتتحققش
+
+336
+00:26:25,980 --> 00:26:31,100
+يعني مش هتفرج معايا تحققت فليكن ماتحققتش فليكن
+
+337
+00:26:31,100 --> 00:26:34,620
+ماتفرجش مش هي اللي هتعطيني القرار القرار بدأ من
+
+338
+00:26:34,620 --> 00:26:38,640
+where من negation فيه الفرضية اللي أصلا غلط
+
+339
+00:26:38,640 --> 00:26:42,840
+الفرضية اللي أساسا بادية من الأساسغلط فمدام
+
+340
+00:26:42,840 --> 00:26:47,260
+الفرضية غلط فبقول ان هي ال theory كلها على بعض
+
+341
+00:26:47,260 --> 00:26:54,100
+factiously true بشكل لا معنى له حقيقية صحيحة بشكل
+
+342
+00:26:54,100 --> 00:27:02,180
+بدون معنى هي حقيقية فعلا ك relation كامة على بعض
+
+343
+00:27:02,180 --> 00:27:05,280
+طيب
+
+344
+00:27:05,280 --> 00:27:09,660
+ال trivial لأ ال trivial مختلفة شوية احنا بنتكلمش
+
+345
+00:27:09,660 --> 00:27:14,820
+عنال premise، بنتكلم عن مين؟ عن ال conclusion، لذا
+
+346
+00:27:14,820 --> 00:27:19,350
+ال conclusion بقدر أثبته من نفسهبغض النظر إيش هي
+
+347
+00:27:19,350 --> 00:27:23,830
+ال premise ال premise صح غلط مش فارقة كتير أنا
+
+348
+00:27:23,830 --> 00:27:30,210
+عندي إمكانية إن أنا أثبت ال Q من نفسها مش محتاج ال
+
+349
+00:27:30,210 --> 00:27:34,370
+P مش محتاج ال premise ال premise بتفرجش معايا صح
+
+350
+00:27:34,370 --> 00:27:38,570
+ولا غلط ولا كويسة ولا مش كويسة ولا premises كتيرة
+
+351
+00:27:38,570 --> 00:27:42,630
+ولا واحدة ولا مافيش premise أصلا مش هتفرج مش فارقة
+
+352
+00:27:42,630 --> 00:27:49,300
+هنا if we know Q is true thenP employees queue is
+
+353
+00:27:49,300 --> 00:27:53,320
+true تمام،
+
+354
+00:27:53,320 --> 00:28:00,380
+لاحظوا كأنكوا هنا بتتكلموا عن الحالة ال queue، ال
+
+355
+00:28:00,380 --> 00:28:04,850
+queue، إذا queue is trueفهي ال relation صحيحة بغض
+
+356
+00:28:04,850 --> 00:28:09,510
+النظر عن ال P ال P false فليكن false true فليكن
+
+357
+00:28:09,510 --> 00:28:13,790
+true في الأخر أنا اللي حكم على الشغل تبعي ان ال Q
+
+358
+00:28:13,790 --> 00:28:18,230
+أنا أثبت منها نفسها أن هي true مدام أثبت نفسي أن
+
+359
+00:28:18,230 --> 00:28:22,890
+هي true ال relation كلها true فالإثبات النظرية هي
+
+360
+00:28:22,890 --> 00:28:25,970
+صحيحة ليش؟ لأن هي النظرية أصلا relation يعطيني
+
+361
+00:28:25,970 --> 00:28:29,870
+إياها if then فإذا ال if then اللي هي ال
+
+362
+00:28:29,870 --> 00:28:34,560
+implication relation هذه صحيحةفإذا النظرية صحيحة
+
+363
+00:28:34,560 --> 00:28:40,100
+زي لو قال if it's raining today then three is an
+
+364
+00:28:40,100 --> 00:28:43,840
+odd number طبما هي فعلا three is an odd number بغض
+
+365
+00:28:43,840 --> 00:28:47,960
+النظر شتيت ولا مش شتيتش اليوم مش هتفرج كتير ليش هي
+
+366
+00:28:47,960 --> 00:28:53,620
+أصلا odd three odd ال Q هي متحققة بدون ماعرف إيش
+
+367
+00:28:53,620 --> 00:28:55,780
+ال premise
+
+368
+00:28:57,130 --> 00:28:59,430
+ال premise أو ال premises كلها إذا كانوا أكتر من
+
+369
+00:28:59,430 --> 00:29:02,110
+واحدة تكون اللي تكون تكون force تكون true مش هتفرج
+
+370
+00:29:02,110 --> 00:29:07,810
+كتير معانا ليش لأن ال conclusion أصلا is true هو
+
+371
+00:29:07,810 --> 00:29:12,530
+true أصلا فينطبق مع الحالة بتاعة ال implication أو
+
+372
+00:29:12,530 --> 00:29:15,290
+ال relation للtheory ال relation للtheory فهذا
+
+373
+00:29:15,290 --> 00:29:18,610
+طريقة إثبات برضه لل relations بتاعتنا هذه true
+
+374
+00:29:18,610 --> 00:29:22,530
+وهذه true ال conclusion true بغض النظر إيش ال ..
+
+375
+00:29:22,530 --> 00:29:26,440
+ال .. ال premise هي دائما true ال relationفإذا
+
+376
+00:29:26,440 --> 00:29:33,600
+النظرية ده true فإذا طريقة trivially true بطريقة
+
+377
+00:29:33,600 --> 00:29:39,060
+.. كأنه هي trivial بمعنى تافه أو مالوش يعني ..
+
+378
+00:29:39,060 --> 00:29:42,480
+مالوش قيمة، مالوش قيمة فمعنى ذلك أنه أنا .. أنا
+
+379
+00:29:42,480 --> 00:29:44,700
+عندي هنا ال premise مالهاش تافه، مالهاش معنى،
+
+380
+00:29:44,700 --> 00:29:49,140
+مالهاش قيمة، لو ماعطتنيش يحصل، هاي معناها، لو
+
+381
+00:29:49,140 --> 00:29:53,840
+ماعطتنيش إياها، بديش إياها المعلومة، بدناش إياها
+
+382
+00:29:56,030 --> 00:29:59,370
+معلومة trivial بالنسبالي هي الـ Q مثبت حاله لحاله
+
+383
+00:29:59,370 --> 00:30:08,990
+الـ Q مثبت حاله لحاله الـ
+
+384
+00:30:08,990 --> 00:30:14,690
+Q مثبت حاله لحاله الـ Q مثبت حاله لحاله الـ Q مثبت
+
+385
+00:30:14,690 --> 00:30:15,170
+حاله لحاله الـ Q مثبت حاله لحاله الـ Q مثبت حاله
+
+386
+00:30:15,170 --> 00:30:18,350
+لحاله الـ Q مثبت حاله لحاله الـ Q مثبت حاله لحاله
+
+387
+00:30:18,350 --> 00:30:19,450
+الـ Q مثبت حاله لحاله الـ Q مثبت حاله لحاله الـ Q
+
+388
+00:30:19,450 --> 00:30:19,450
+مثبت حاله لحاله الـ Q مثبت حاله لحاله الـ Q مثبت
+
+389
+00:30:19,450 --> 00:30:21,690
+حاله لحاله الـ Q مثبت حاله لحاله الـ Qبغض النظر ان
+
+390
+00:30:21,690 --> 00:30:25,270
+ال integer in ده هو فعلا عبارة عن مجموع رقمين
+
+391
+00:30:25,270 --> 00:30:28,970
+اولين او لأ، فليكن مجموع رقمين اولين، و ليكن لأ،
+
+392
+00:30:28,970 --> 00:30:31,690
+مايكنش مش مجموع، مش هتفرج كتير معايا، ليش؟ لأن
+
+393
+00:30:31,690 --> 00:30:37,330
+then ال Q اللي عندها هنا بيقولكوا ان ال in ده يا
+
+394
+00:30:37,330 --> 00:30:40,330
+او دي او ي، طب ما احنا عارفين ان اي integer هو
+
+395
+00:30:40,330 --> 00:30:45,480
+محدد هى for all integersلل integers odd or even طب
+
+396
+00:30:45,480 --> 00:30:47,620
+انا عارف ان في كل ال integers ما هي لازم تكون يا
+
+397
+00:30:47,620 --> 00:30:50,900
+odd يا even مافيش احتمال تالت هو ميعطين الاحتمالين
+
+398
+00:30:50,900 --> 00:30:54,780
+الاتنين اللي موجودين عنده فهي يا odd يا even فإذا
+
+399
+00:30:54,780 --> 00:30:58,400
+واحدة منهم لازم تكون true واحدة منهم لازم تكون
+
+400
+00:30:58,400 --> 00:31:06,160
+false مع ال or أكيد ال relation كلها true true
+
+401
+00:31:06,160 --> 00:31:11,380
+فإذا أنا بتكلم عن الحالتينالحالتين دائما ال
+
+402
+00:31:11,380 --> 00:31:16,080
+relation صح، بغض النظر هم فعلا مجموع two primes او
+
+403
+00:31:16,080 --> 00:31:21,480
+لابغض النظر، صحيح؟ فإذا automatically هي true
+
+404
+00:31:21,480 --> 00:31:25,700
+trivially أو صحيحة
+
+405
+00:31:25,700 --> 00:31:31,200
+بدون الاستفادة من ال premise، بدون الاستفادة من ال
+
+406
+00:31:31,200 --> 00:31:34,720
+premise الشغلة
+
+407
+00:31:34,720 --> 00:31:38,560
+المهمة كمان اللي هي برضه بتندرج معانا مع جزئية ال
+
+408
+00:31:38,560 --> 00:31:44,630
+indirect مع جزئية ال indirect strategiesاللي هي مش
+
+409
+00:31:44,630 --> 00:31:48,130
+Contrapositive، Contradiction Contradiction
+
+410
+00:31:48,130 --> 00:31:52,130
+التعارض التعارض، إيش التعارض؟ معناه إن أنا بدي
+
+411
+00:31:52,130 --> 00:31:57,460
+أفرض فرضية و أثبت تعارضهاتناقض او تعارض تناقض
+
+412
+00:31:57,460 --> 00:32:01,020
+اثبتها و افرض انها متناقضة مع نفسها او متعارضة مع
+
+413
+00:32:01,020 --> 00:32:06,140
+الفرضية مع الفرضية كيف نعملها a method for proving
+
+414
+00:32:06,140 --> 00:32:11,940
+P هنا بدثبت P فبنعمل assuming لمن؟ ل negation P و
+
+415
+00:32:11,940 --> 00:32:15,260
+prove منها يعني ال promise اللي معطيكوا إياها
+
+416
+00:32:15,260 --> 00:32:20,820
+بنفرض عكسهالحظة ال premise يعطيكوا premise معينة
+
+417
+00:32:20,820 --> 00:32:25,320
+يعطيكوا معلومة معينة بنفرض عكسها و بنحاول نشتغل
+
+418
+00:32:25,320 --> 00:32:29,600
+بنجد من عكسها أنه صار عندكم proof لمين ل q و
+
+419
+00:32:29,600 --> 00:32:35,440
+negation q إذا فعلا صار أنه بقدر أثبت الاستنتاج و
+
+420
+00:32:35,440 --> 00:32:39,100
+التعارض تبعه فإذا النظرية هذه كلها ال premise من
+
+421
+00:32:39,100 --> 00:32:42,240
+أصله كان غلط و مدام كان من الأول غلط معناته ال
+
+422
+00:32:42,240 --> 00:32:45,580
+negation تبعه اللي هو ال P أصلا هي ال true ال P
+
+423
+00:32:45,580 --> 00:32:48,770
+أساسا هي اللي كانت trueفبنكون أثبتناها بطريقة برضه
+
+424
+00:32:48,770 --> 00:32:53,530
+غير .. غير مباشرة فإذا كأني بفرض negation P
+
+425
+00:32:53,530 --> 00:32:58,550
+employs Q and negation Q طبعا هذا الكلام دائما
+
+426
+00:32:58,550 --> 00:33:04,630
+false .. دائما false في الحالة هذه فمدام دائما
+
+427
+00:33:04,630 --> 00:33:08,750
+false خلاص ال .. ال .. كلها هتكون مش صحيحة أو ال
+
+428
+00:33:08,750 --> 00:33:11,150
+.. ال negation P مش هتكون صحيحة وهذا معناه
+
+429
+00:33:11,150 --> 00:33:16,740
+automatically أنه Pis it true, p is it true فهي a
+
+430
+00:33:16,740 --> 00:33:19,160
+queue and ال negation a queue ال trivial
+
+431
+00:33:19,160 --> 00:33:25,040
+contradiction هي تعارض واضح، هتكون تعارض واضح كيف
+
+432
+00:33:25,040 --> 00:33:31,070
+انتوا بتقول المعلومة صحيحة و عكسها صحيحفي تعارض ..
+
+433
+00:33:31,070 --> 00:33:35,810
+في تعارض .. تعامل أو تناقض ..ماشي أو متناقضة يعني
+
+434
+00:33:35,810 --> 00:33:39,250
+المعلومتين مع بعض فإذا equal to false في الحالة
+
+435
+00:33:39,250 --> 00:33:44,150
+هذه negation P is false negation P is false وهذا
+
+436
+00:33:44,150 --> 00:33:52,030
+معناه أن P is true P is true هذه طريقة إثبات P هذه
+
+437
+00:33:52,030 --> 00:33:58,510
+الطريقة الإثبات mean إثبات P طيب زي ..ناخد two
+
+438
+00:33:58,510 --> 00:34:01,070
+examples من ال examples المشهورة جدا الحقيقة على
+
+439
+00:34:01,070 --> 00:34:04,350
+ال net مشهورة حتى في معظم الكتب مشهورة جدا جدا
+
+440
+00:34:04,350 --> 00:34:08,970
+هناخد two examples واحدة علاقة بال rational واحدة
+
+441
+00:34:08,970 --> 00:34:13,850
+علاقة بال prize من القوانين المشهورة جدا و قديمة
+
+442
+00:34:13,850 --> 00:34:19,060
+الحقيقة يعنيالإثباتين قديمين جدا جدا مش حديثين
+
+443
+00:34:19,060 --> 00:34:22,940
+يعني تم إثباتهم من زمان جدا بس مشهورين جدا ل ال
+
+444
+00:34:22,940 --> 00:34:28,300
+contradiction أول نظرية بدنا نثبت أنه root two is
+
+445
+00:34:28,300 --> 00:34:33,240
+rational rational إيش يعني rational rational نسبي
+
+446
+00:34:33,240 --> 00:34:38,140
+نسبي بمعنى بقول الرقم x rational إذا كان قدرت
+
+447
+00:34:38,140 --> 00:34:43,520
+أمثله ال two integers على بعض ال two integers على
+
+448
+00:34:43,520 --> 00:34:47,850
+بعض بشكلان ال two integers في أبسط صورهم بقدرش
+
+449
+00:34:47,850 --> 00:34:52,910
+اختصرهم مع بعض لا يتم اختصارهم مع بعض هدول الرقمين
+
+450
+00:34:52,910 --> 00:34:56,070
+لا يختصروا مع بعض والاتنين انتجر اذا تحقق كلام
+
+451
+00:34:56,070 --> 00:35:01,670
+نسميها rational ال X هذه بنسميه rational تمام هنا
+
+452
+00:35:01,670 --> 00:35:06,310
+لا احنا بدنا بالعكس احنا قاعدين بنقول root two جدر
+
+453
+00:35:06,310 --> 00:35:13,120
+الاتنين is irrational هي لا يوجد اي رقمينانتجارز
+
+454
+00:35:13,120 --> 00:35:18,700
+حاصل قسمتهم على بعض بيعطيك root 2 هاي معناها هذا
+
+455
+00:35:18,700 --> 00:35:21,580
+معناها بدنا نشوف هل الكلام ده بصير معناه ده بصيرش
+
+456
+00:35:21,580 --> 00:35:28,100
+معناه طيب عشان نعمله هنفرض negation فيه بدنا نفرض
+
+457
+00:35:28,100 --> 00:35:35,860
+negation فيه انه هي لأ rationalبتفترض أن المعلومة
+
+458
+00:35:35,860 --> 00:35:39,320
+اللي أعطتنيها مش صح، أنا بتفترض عكسها، و أبدأ
+
+459
+00:35:39,320 --> 00:35:42,440
+أثبت، أشتغل في الإثبات تبعي، هأفاجأ في الإثبات أن
+
+460
+00:35:42,440 --> 00:35:47,080
+إثباتي غلط، أنه طلّع لي خطأ، معناته الصح كان
+
+461
+00:35:47,080 --> 00:35:50,580
+الأولانيبدون ما أضطر أشتغل على الأولان من الأول
+
+462
+00:35:50,580 --> 00:35:54,100
+بدون أن أضطر بطريقة direct اضطرنا نشتغل هنا in
+
+463
+00:35:54,100 --> 00:35:58,280
+direct بطريقة نسميها ال contradiction أو التعارض
+
+464
+00:35:58,280 --> 00:36:01,480
+لإجابتنا
+
+465
+00:36:01,480 --> 00:36:05,180
+أنا المفروض نتوقع شغلة و هيطلع شغلة تانية تمام
+
+466
+00:36:05,180 --> 00:36:09,260
+فهنا هنقول لأ two to the power نص اللي هي برضه
+
+467
+00:36:09,260 --> 00:36:13,000
+root اثنين to the power نص اللي هي كانها الجدر
+
+468
+00:36:13,000 --> 00:36:16,300
+تمام well rational لأ هنا بتماشي أقول irrational
+
+469
+00:36:16,300 --> 00:36:21,880
+بدي أقول إن هي rationalهذا يعني أن يوجد two
+
+470
+00:36:21,880 --> 00:36:29,400
+integers I وJ بقدر بيكون عوامل مشتركة بينهم بدون
+
+471
+00:36:29,400 --> 00:36:33,040
+عوامل مشتركة زي ما قلت لكوا تكون ال A و ال B بأبسط
+
+472
+00:36:33,040 --> 00:36:35,840
+صورهم يعني أنا ماقدرش اختصرهم مع بعض اكتر من هيك
+
+473
+00:36:35,840 --> 00:36:39,360
+لا يتم اختصارهم مع بعض مايكونش اتنين على اربعة
+
+474
+00:36:39,360 --> 00:36:44,920
+بتكون تلاتة على تسعة لأ لايتم اختصارهم مع بعض
+
+475
+00:36:44,920 --> 00:36:51,120
+مافيش اي عامل مشترك بينهموالاتنين integers إذا حصل
+
+476
+00:36:51,120 --> 00:36:55,560
+قسمتهم مع بعض بيطلق لكم X بغض النظر X، يمكن X ما
+
+477
+00:36:55,560 --> 00:36:58,840
+تكونش integer، يعني مش مضرور تكون integer X، X مش
+
+478
+00:36:58,840 --> 00:37:01,700
+مضرور تكون integer، يمكن خمسة على تلاتة، مش
+
+479
+00:37:01,700 --> 00:37:06,280
+integer، بس الرقم خمسة على تلاتة هو rational، هنا
+
+480
+00:37:06,280 --> 00:37:09,380
+بيكون اسمه rational، تمام، هنا زي ما قلنا بنعمل ال
+
+481
+00:37:09,380 --> 00:37:13,100
+acts negation فيه وننطلق منها لإثبات الشغل تبعنا
+
+482
+00:37:14,060 --> 00:37:16,900
+فهاجولي العكس تباحة ان هي تكون rational مادام
+
+483
+00:37:16,900 --> 00:37:21,520
+rational يعني يوجد two integers اللي هم I and J
+
+484
+00:37:21,520 --> 00:37:24,840
+ومافيش common بينهم common divisors مافيش اي عامل
+
+485
+00:37:24,840 --> 00:37:30,160
+بينهم بنقدر في الحالة هذه نقول ان هدول rational
+
+486
+00:37:30,160 --> 00:37:35,440
+ريشونال معناه ذلك انه two to the power نص او جذر
+
+487
+00:37:35,440 --> 00:37:40,860
+هيلحظوا جذر نص جذر افن اتنين بقدر اقول ان هو I
+
+488
+00:37:40,860 --> 00:37:45,990
+over Jصحيح؟ ما هي original ان هي عبارة عن two
+
+489
+00:37:45,990 --> 00:37:48,990
+terms بس بدنا نحدد ان ال two terms هدولة integers
+
+490
+00:37:48,990 --> 00:37:54,770
+ال I integer ال J integer كويس و لايوجد عامل مشترك
+
+491
+00:37:54,770 --> 00:37:58,490
+بينهم خلاص هدول بأبسط صورة لهم طيب لو ربعنا
+
+492
+00:37:58,490 --> 00:38:04,210
+الطرفين لو ربعنا الطرفين في الحالة هذه ايش بتصير
+
+493
+00:38:04,210 --> 00:38:11,600
+عندكم؟ هتصير اتنين تربيع ال I over تربيع ال Jتمام
+
+494
+00:38:11,600 --> 00:38:17,360
+برضه نكمل مع بعض two هذي هنطلحها فوق يعني كل ال
+
+495
+00:38:17,360 --> 00:38:22,560
+two المعادلة كلها هنضربها في جه تربيع هصير اتنين
+
+496
+00:38:22,560 --> 00:38:29,560
+جه تربيع تساوي I تربيع طيب خليني امسككم حاجة حاجة
+
+497
+00:38:29,560 --> 00:38:33,460
+المعادلة هذي حلوة و بنقدر نطلع منها شوية معلومات
+
+498
+00:38:33,460 --> 00:38:39,360
+two جه تربيع تساوي I تربيع معناه ذلك ان ال I تربيع
+
+499
+00:38:39,360 --> 00:38:46,470
+evenلحظة اتنين في some integer اتنين في some
+
+500
+00:38:46,470 --> 00:38:50,390
+integer و احنا اصلا قولنا ال rational هما two
+
+501
+00:38:50,390 --> 00:38:54,630
+integers على بعض فانا ضامن ان ال J انتجر تربيع ال
+
+502
+00:38:54,630 --> 00:38:59,490
+integer انتجر لحظة كأنها صرت بتتكلم عن اتنين K و
+
+503
+00:38:59,490 --> 00:39:05,410
+ال K ده هي J تربيع ممتاز معناه ذلك انه I تربيع
+
+504
+00:39:05,410 --> 00:39:11,260
+evenطيب احنا عارفين اذا كانت ال I تربيع even
+
+505
+00:39:11,260 --> 00:39:20,900
+معناته I even تمام فإذا ال I even حلو ال I even
+
+506
+00:39:20,900 --> 00:39:25,760
+يعني بقدر امثلها ب two K بنقدر امثلها ب two K فإذا
+
+507
+00:39:25,760 --> 00:39:31,940
+ببساطة جدا بقدر اقول ان two J تربيع بتساوي two K
+
+508
+00:39:31,940 --> 00:39:43,240
+تربيع2k تربيع 2k تربيع هذه 4k تربيع طيب نقسم على 2
+
+509
+00:39:43,240 --> 00:39:49,780
+2k تربيع صار عندنا كل هذا ال term j تربيع بساوي 2k
+
+510
+00:39:49,780 --> 00:40:01,560
+تربيع ممتاز طب ما هذه اتنين اتنين R و R some
+
+511
+00:40:01,560 --> 00:40:11,110
+integerمعنى ذلك الـ j² even even صح؟ معنى ذلك أن
+
+512
+00:40:11,110 --> 00:40:14,130
+هذه even هي اتنين في some integer ال some integer
+
+513
+00:40:14,130 --> 00:40:18,190
+ده عبارة عن integer تربيع عبارة عن integer تربيع
+
+514
+00:40:18,190 --> 00:40:22,550
+فاليكن ال integer في integer رح يطلع integer كويس
+
+515
+00:40:22,550 --> 00:40:33,620
+مدام j تربيع is even أكيد j even طلع I evenو j
+
+516
+00:40:33,620 --> 00:40:39,400
+even even على even في عامل مشترك هو الاتنين طب
+
+517
+00:40:39,400 --> 00:40:43,780
+احنا قاعدين بيقول من الأساس no common divisor then
+
+518
+00:40:43,780 --> 00:40:48,620
+false لاحظنا عرضنا حالنا لحالنا من الأول قاعدين
+
+519
+00:40:48,620 --> 00:40:50,980
+بيقول إن هي rational مع الإثبات ظهر إن هي مش
+
+520
+00:40:50,980 --> 00:40:54,060
+rational ليش مش rational لأنه في عامل مشترك بينهم
+
+521
+00:40:58,840 --> 00:41:03,600
+لأ احنا هنعيدها كلها مش هنعيد من هنا كلها بنجعلكم
+
+522
+00:41:03,600 --> 00:41:10,160
+للبداية بتاعتها لحظة
+
+523
+00:41:10,160 --> 00:41:17,220
+هلوجت بدأنا قولنا أن الفرضية بتاعتنا عكس ال given
+
+524
+00:41:17,220 --> 00:41:23,550
+ال given بيقولكم أن جذر اتنين is irrationalنفهم
+
+525
+00:41:23,550 --> 00:41:26,630
+ايش يعني irrational عشان نعرف نشتغل، ف irrational
+
+526
+00:41:26,630 --> 00:41:30,730
+معناته انه بقدر .. rational أول انه بقدر اعو ..
+
+527
+00:41:30,730 --> 00:41:35,650
+اعو .. يعني نعمل تمثيل للرقم على أساس انه حاصل
+
+528
+00:41:35,650 --> 00:41:42,190
+قسمة رقمين integersintegers و بدون أي عوامل مشترك
+
+529
+00:41:42,190 --> 00:41:47,970
+بينهم فإذا no common divisors أو لايوجد عامل مشترك
+
+530
+00:41:47,970 --> 00:41:51,870
+بينهم لايوجد عامل مشترك بينهم قولنا okay خلاص
+
+531
+00:41:51,870 --> 00:41:55,590
+هنفرض الفرضية اللي هي negation للي موجود أصلا
+
+532
+00:41:55,590 --> 00:42:01,410
+فهيقول إن جدر اتنين لأ rational هو بيقولي are
+
+533
+00:42:01,410 --> 00:42:04,750
+rational او are rational عملت ال negation فبتصير
+
+534
+00:42:04,750 --> 00:42:10,250
+عبارة مدام rational بقدر أقول إن هي I over JI over
+
+535
+00:42:10,250 --> 00:42:13,450
+G والاتنين لازم يكونوا integers ومافيش عامل مشترك
+
+536
+00:42:13,450 --> 00:42:17,450
+بينهم تمام كويس خلنا نمشي معاها الوجد احنا عارفين
+
+537
+00:42:17,450 --> 00:42:21,430
+انه هادي جدر يعني لو عملنا تربيح هنا تربيح هنا
+
+538
+00:42:21,430 --> 00:42:26,530
+بمشي الحل ربعنا الطرفين تمام هاي ربعنا الطرفين
+
+539
+00:42:26,530 --> 00:42:29,910
+ومشيت الأمور الطرفين هادولة لما ربعناهم ايش اللي
+
+540
+00:42:29,910 --> 00:42:37,190
+هيظهر عندكم هيظهر عندكم انهالاتنين بتساوي ال I و
+
+541
+00:42:37,190 --> 00:42:40,690
+لا ال J اللي فوق كانت ال I تربيع فوقي ال I و J
+
+542
+00:42:40,690 --> 00:42:48,690
+تربيع صحيح هذه منها بقدر اقول انه ال I تربيع
+
+543
+00:42:48,690 --> 00:42:55,770
+بتساوي 2J تربيع كلام صح كلام صح طيب احنا عارفين
+
+544
+00:42:55,770 --> 00:43:03,320
+انه عشان اعمل test على odd او evenبدور ال odd ال
+
+545
+00:43:03,320 --> 00:43:10,220
+even بتكون عبارة عن 2k الرقم 2 في some integer ال
+
+546
+00:43:10,220 --> 00:43:15,620
+odd 2k plus 1 لأ احنا هنمسك الجزء هذا لإن هو اللي
+
+547
+00:43:15,620 --> 00:43:20,660
+ينطبق عندنا هنا هو اللي ينطبق عندنا هنا فإذا J
+
+548
+00:43:20,660 --> 00:43:28,240
+تربيع هي كأنها K مثلا أو كأنها أي symbol تاني
+
+549
+00:43:28,240 --> 00:43:36,380
+خليني أقول مثلا كأنها Rتساوي J تربيع ال J أساسا من
+
+550
+00:43:36,380 --> 00:43:39,660
+الفرضية اللي بدهين فرضيتنا فيها أنها integer طب
+
+551
+00:43:39,660 --> 00:43:44,660
+integer تربيع لازم تكون integer رقم صحيح في نفسه
+
+552
+00:43:44,660 --> 00:43:48,820
+لازم هتطلع رقم صحيح فإذا ال R هي رقم صحيح و لاحظوا
+
+553
+00:43:48,820 --> 00:43:53,280
+أن I تربيع طلعت كأنها بتساوي 2 في رقم صحيح في
+
+554
+00:43:53,280 --> 00:43:58,300
+integer طب هذا هي تماشي تماما مع even معنا ذلك أن
+
+555
+00:43:58,300 --> 00:44:05,630
+I تربيع evenفإذن بقدر أقول I تربيع is even ال I
+
+556
+00:44:05,630 --> 00:44:11,290
+تربيع even معناه ذلك إن ال I لحالها برضه even برضه
+
+557
+00:44:11,290 --> 00:44:18,610
+even فإذن I is even هذه الجزئية برضه إذا انتوا
+
+558
+00:44:18,610 --> 00:44:23,670
+حابين اثبتوها بتقدروا تثبتوها ببساطة إذا ممكن
+
+559
+00:44:23,670 --> 00:44:27,670
+تعتقلكوا بالطرف تاني إنه given إن ال I is even و
+
+560
+00:44:27,670 --> 00:44:31,810
+اثبته إن ال I تربيع is evenأو تُعطى بهذا الشكل إذا
+
+561
+00:44:31,810 --> 00:44:35,370
+كانت I تربية is even اثبتول إن ال I is even إذا
+
+562
+00:44:35,370 --> 00:44:39,770
+أُعطت بهذا الشكل ممكن تشتغلوا على ال indirect إذا
+
+563
+00:44:39,770 --> 00:44:44,710
+I is even اشتغلوا على ال direct عوضوا هذا ب 2
+
+564
+00:44:44,710 --> 00:44:47,810
+وعملوا لتربية حصين 4 الأربعة تقدروا تاخدوا منها
+
+565
+00:44:47,810 --> 00:44:52,650
+مشتقة 2 فهتطلع برضه even تمام المهم إن احنا وصلنا
+
+566
+00:44:52,650 --> 00:44:56,810
+لإثبات إن ال I even بدنا نحط مربع عند هذه النقطة
+
+567
+00:44:56,810 --> 00:45:01,750
+طيب إذا كان هي أصلا evenهي أساسا even معناه ذلك
+
+568
+00:45:01,750 --> 00:45:08,310
+إنه فعليا هي بتساوي هي I تربيع بتساوي 2J كذا هي
+
+569
+00:45:08,310 --> 00:45:16,010
+نفسها بقدر أحطها ب2K بتقدر نحطها بشكل 2K أو بطريقة
+
+570
+00:45:16,010 --> 00:45:21,110
+اللي هي 2K تمام في الحالة دي بتقدر مباشرة نقول إن
+
+571
+00:45:21,110 --> 00:45:26,220
+I هي عبارة عن 2some integer في أي some integer في
+
+572
+00:45:26,220 --> 00:45:30,220
+الحالة اللي بنتكلم عنها وهذا معناه ان ال I تربيع
+
+573
+00:45:30,220 --> 00:45:38,520
+برضه هذا تربيع عبارة عن two K احنا اتفجنا انتجر
+
+574
+00:45:38,520 --> 00:45:46,760
+انتجر اعملوله تربيع بيساوي اتنين J تربيع نقسم على
+
+575
+00:45:46,760 --> 00:45:50,440
+اتنين جسمنا
+
+576
+00:45:50,440 --> 00:45:55,560
+على اتنين ايش بيظهر؟يصير J تربيع بتساوي two K
+
+577
+00:45:55,560 --> 00:46:01,340
+تربيع على اتنين هذه على اتنين عفوا هذه أساسا ال
+
+578
+00:46:01,340 --> 00:46:06,740
+term هذا عبارة عن أربعة K تربيع الأربعة مع الأتنين
+
+579
+00:46:06,740 --> 00:46:13,000
+فإذا J تربيع بتساوي اتنين في K تربيع K تربيع هذه
+
+580
+00:46:13,000 --> 00:46:18,320
+integer هي أساسا integerصحيح؟ كلها على بعض integer
+
+581
+00:46:18,320 --> 00:46:22,720
+لأن احنا ضمنين من الأساس ال K هتجيبناها من تعود في
+
+582
+00:46:22,720 --> 00:46:28,760
+I قولنا ان I بتساوي 2K ليش؟ لأنها even طيب عشان
+
+583
+00:46:28,760 --> 00:46:31,640
+تكون even لازم تكون اتنين في integer فالK هي
+
+584
+00:46:31,640 --> 00:46:35,360
+integer ومدام ال K integer ال K تربيع برضه
+
+585
+00:46:35,360 --> 00:46:42,280
+بالضرورة هتكون integer تمام فإذا صار لنا J تربيع
+
+586
+00:46:42,280 --> 00:46:44,720
+even
+
+587
+00:46:46,830 --> 00:46:51,110
+J تربيع even و بنرجع من نفس النظرية إذا الرقم
+
+588
+00:46:51,110 --> 00:46:56,990
+تربيع even فإذا الرقم نفسه J نفسه برضه هتكون even
+
+589
+00:46:56,990 --> 00:47:04,970
+فإذا J is even طيب نمسك هذه النقطة و نمسك هذه
+
+590
+00:47:04,970 --> 00:47:10,980
+النقطةالنقطين هدولة هم أساسا حاصل قسمتهم على بعض
+
+591
+00:47:10,980 --> 00:47:15,140
+اللي جبت منها ال route 2 لإن احنا من أصل فرضيتنا
+
+592
+00:47:15,140 --> 00:47:23,890
+بادية بهيها بإن جذر 2 تساوي I over Jوفرضنا إن هي
+
+593
+00:47:23,890 --> 00:47:27,190
+rational فإن ريشونال إلها شروط الريشونال الريشونال
+
+594
+00:47:27,190 --> 00:47:29,290
+عشان تكون الشروطها دي واضحة لازم تكون الاتنين
+
+595
+00:47:29,290 --> 00:47:32,370
+integers هم بتحقق فين integers مافيش مشكلة الشرط
+
+596
+00:47:32,370 --> 00:47:37,590
+التاني no common divisor مافيش عامل مشترك بينهم طب
+
+597
+00:47:37,590 --> 00:47:41,770
+للأسف احنا عارفين إن ال even أساسا فيه هو مضروب
+
+598
+00:47:41,770 --> 00:47:45,210
+اتنين يعني هو رقم مضروف اتنين يعني معنى ذلك
+
+599
+00:47:45,210 --> 00:47:50,530
+الاتنين عامل مشترك بينهم هذه لازم أقدر أمثلها بقدر
+
+600
+00:47:50,530 --> 00:47:56,520
+أمثلها 2kو هذه بقدر امثلها برضه ب two r مثلا some
+
+601
+00:47:56,520 --> 00:48:01,500
+integer فإذا لاحظوا مافيه comment فإذا مش rational
+
+602
+00:48:01,500 --> 00:48:06,540
+طب انت فارض من الأول rational طلعت مش rational انت
+
+603
+00:48:06,540 --> 00:48:09,280
+فارض من الأساس rational طلعت مش rational معناته
+
+604
+00:48:09,280 --> 00:48:13,300
+العكس هو اللي صح العكس هو اللي كان صحيح اللي هو
+
+605
+00:48:13,300 --> 00:48:17,800
+عياش ان هي irrational هي irrational و ليست رقم
+
+606
+00:48:17,800 --> 00:48:20,400
+نسمي ليست رقم نسمي
+
+607
+00:48:22,730 --> 00:48:27,330
+أحنا بتقول ال EU انها false على اي حالة؟ على هادي
+
+608
+00:48:27,330 --> 00:48:31,510
+و هادي؟ لأ بحكي الفوضى هنا في الجدول اه اه في
+
+609
+00:48:31,510 --> 00:48:34,150
+الجدول انت بتتكلم هنا على لأ احنا هنا بتتكلم في
+
+610
+00:48:34,150 --> 00:48:38,130
+فرضية انت فارضة فرضية و انت بتشتغل و لاجيت انه
+
+611
+00:48:38,130 --> 00:48:43,010
+الفرضية غلط الشغل انه الفرضية غلط انت باديا بتقول
+
+612
+00:48:43,010 --> 00:48:47,470
+ان هي rational ال rational لها شروط اجينا و احنا
+
+613
+00:48:47,470 --> 00:48:50,030
+بنشتغل و قولنا ان هي rational اجينا نحقق الشروط
+
+614
+00:48:50,030 --> 00:48:56,330
+وجدنا انها مابتتحققشفانت طبيعي الفرضية اللى فرضها
+
+615
+00:48:56,330 --> 00:48:59,790
+غلط مدى ما اتحققتش الشروط بتاعتها شروطها ان تكون
+
+616
+00:48:59,790 --> 00:49:03,210
+عبارة عن حصل قسمة رقمين الرقمين هدول اول شرط ان
+
+617
+00:49:03,210 --> 00:49:06,190
+هما يكونوا integers هذا integer و هذا integer
+
+618
+00:49:06,190 --> 00:49:10,350
+الشرط التانى مايكونش فيه اي عامل مشترك بينهم طب
+
+619
+00:49:10,350 --> 00:49:13,610
+احنا مع الشغل اثبتنا ان الاتنين even واحنا عارفين
+
+620
+00:49:13,610 --> 00:49:18,180
+ان ال evenبيقبل القسم على اتنين فإذا البصد بيقبل
+
+621
+00:49:18,180 --> 00:49:21,180
+القسم على اتنين والمقان أو ال denominator بيقبل
+
+622
+00:49:21,180 --> 00:49:23,440
+القسم على اتنين فال numerator بيقبل و ال
+
+623
+00:49:23,440 --> 00:49:27,680
+denominator بيقبل على اتنين فإذا في عامل مشترك هذا
+
+624
+00:49:27,680 --> 00:49:30,760
+بيقبل على اتنين و هذا بيقبل على اتنين نفينا
+
+625
+00:49:30,760 --> 00:49:34,060
+الفرضية اللي أنا بديها ماتطلعتش ليها على ال truth
+
+626
+00:49:34,060 --> 00:49:36,080
+tables ولا غيرها في ال contrapositive أنا بفرض
+
+627
+00:49:36,080 --> 00:49:41,500
+فرضية و بثبت عدم صحيتها و بنثبت عدم صحيتها و غالبا
+
+628
+00:49:41,500 --> 00:49:47,340
+بفرضها عكس ال givenنفرضها بعكس ال given فإذا العكس
+
+629
+00:49:47,340 --> 00:49:51,900
+ال negation للمعلومة اللي مُعطاها طلع false فإذا
+
+630
+00:49:51,900 --> 00:49:55,260
+المعلومة اللي مُعطاها أكيد true هذا لما يعطيكوا
+
+631
+00:49:55,260 --> 00:49:59,020
+معلومة بالشكل هذا ويقول كوثيب طولية طب أنا كيف بدي
+
+632
+00:49:59,020 --> 00:50:02,380
+أثبتها ب direct و indirect الطرق التقليدية أو ال
+
+633
+00:50:02,380 --> 00:50:05,420
+contrapositive؟ مقدرش ليش؟ لأنه هي معلومة ميعطيني
+
+634
+00:50:05,420 --> 00:50:08,380
+هو بس بدي أنا أعرفها صح ولا غلط مش ميعطيني إش معها
+
+635
+00:50:08,380 --> 00:50:13,770
+فكل اللي بتعملوا انتوا بتكونوا تفرضوا عكسهاو أثناء
+
+636
+00:50:13,770 --> 00:50:20,510
+الحل بده يطلع إثبات عكسها false إذا عكس العكس هو
+
+637
+00:50:20,510 --> 00:50:23,330
+اللي كان صحيح فإذا عكس العكس هو اللي كان صحيح و
+
+638
+00:50:23,330 --> 00:50:27,830
+اللي هو كان أساسا given من الأول ناخد لنا كمان
+
+639
+00:50:27,830 --> 00:50:32,130
+مثال ناخد لنا كمان مثال في نفس السياق في الcontra
+
+640
+00:50:32,130 --> 00:50:42,250
+positive في ال contradiction الموضوع
+
+641
+00:50:42,250 --> 00:50:48,580
+مهمالموضوع مهم يعني لاحظوا أنا كنت بطيئ جدا معاكم
+
+642
+00:50:48,580 --> 00:50:51,460
+وعملناها كذا مرة لأنه أنا مستشعر أهميتها و بتيجي
+
+643
+00:50:51,460 --> 00:50:55,120
+كتير في امتحانات فنركز فيها و بنعمل الحاجات المهمة
+
+644
+00:50:55,120 --> 00:50:57,380
+كتير ليش؟ لأنه مش بالضروري أقولكوا .. أقولكوا
+
+645
+00:50:57,380 --> 00:51:01,280
+دايما if then إذا كان كذا اثبتولي كذا لو ممكن
+
+646
+00:51:01,280 --> 00:51:05,540
+أقولكوا أثبتولي إنه هذه صح وخلاص بدون معلومات زي
+
+647
+00:51:05,540 --> 00:51:08,200
+الحالة اللي تواخدناها أو زي الحالة اللي جاية هنا
+
+648
+00:51:08,200 --> 00:51:11,120
+there is no largest prime number
+
+649
+00:51:13,730 --> 00:51:19,970
+إن مافيش رقم أولي أكبر، يعني كل رقم أولي فيه رقم
+
+650
+00:51:19,970 --> 00:51:23,470
+أولي أكبر منه، هاي معناها، أبضلكوا to infinity،
+
+651
+00:51:23,470 --> 00:51:28,230
+هبضلكوا to infinity، هاي المعنى، إنوا أثبتولنا إن
+
+652
+00:51:28,230 --> 00:51:33,670
+مافيش رقم أولي هو الأكبر من كل الأرقام الأولية، لأ
+
+653
+00:51:33,670 --> 00:51:37,960
+دائما فيه اللي أكبر منهطب هاذي كيف بتكون تثبتوها؟
+
+654
+00:51:37,960 --> 00:51:40,760
+لا ال contrapositive بتظبطها ولا ال direct بظبطها
+
+655
+00:51:40,760 --> 00:51:43,160
+ولا إيش بظبطها ال contradiction .. ال
+
+656
+00:51:43,160 --> 00:51:45,260
+contradiction هي راح تظبطها .. ليش؟ لإن بدي أفرض
+
+657
+00:51:45,260 --> 00:51:51,020
+العكس .. بدي نفرض العكس .. إنه لأ في largest prime
+
+658
+00:51:51,020 --> 00:51:54,420
+number .. إنه لأ والله في رقم أكبر .. و نثبت بعدين
+
+659
+00:51:54,420 --> 00:51:58,040
+إنه لأ والله في طلع هي أكبر منه .. بتكوننا فينا
+
+660
+00:51:58,040 --> 00:52:01,100
+إننا في .. بتكوننا فينا إننا في .. وهي الطريقة
+
+661
+00:52:01,100 --> 00:52:04,850
+اللي نقدر منها نعمل أثباتنا .. ف ..في الحالة هذه
+
+662
+00:52:04,850 --> 00:52:09,970
+فعليا أنتم ماعندكم مش أي فرضية أصلية عندكم نتيجة
+
+663
+00:52:09,970 --> 00:52:13,730
+ومطلوب اثبتوها فالحالات المناسبة لل contradiction
+
+664
+00:52:13,730 --> 00:52:17,110
+أن ماعندكم مش انتم فرضية معلومة اثبتوها يا
+
+665
+00:52:17,110 --> 00:52:20,170
+بتثبتوها يا بتثبتوهااش اللي بنعمله هنا بنفرض ال
+
+666
+00:52:20,170 --> 00:52:23,010
+contradiction أو بنفرض ال conclusion there is no
+
+667
+00:52:23,010 --> 00:52:27,510
+largest prime هذا is false هنفرض ان هو false ايش
+
+668
+00:52:27,510 --> 00:52:29,890
+يعني false يعني معناه ان there is a largest prime
+
+669
+00:52:29,890 --> 00:52:35,170
+number وحنسميه Pسأقول لأ يا جماعة الخير في رقم
+
+670
+00:52:35,170 --> 00:52:41,710
+أولي أكبر واسمه P طيب ماشي سميناه P هل وجد اللي
+
+671
+00:52:41,710 --> 00:52:46,790
+بنقول المفروض معناته كل ال primes التانية أقل منه؟
+
+672
+00:52:46,790 --> 00:52:50,450
+مدام هو الأكبر، معناته كل ال primes التانية أقل
+
+673
+00:52:50,450 --> 00:52:55,430
+منه، كويسةthe set of all primes lie between one or
+
+674
+00:52:55,430 --> 00:53:00,830
+and P بنقدر نعبرها بالشكل التالي ان ر بتساوي اتنين
+
+675
+00:53:00,830 --> 00:53:05,570
+هحط كل primes اتنين تلاتة خمسة سبعة احداشر تلاتاشر
+
+676
+00:53:05,570 --> 00:53:10,590
+مش عارف سبعتاشر تسعتاشر تلاتة وعشرين بتكملوا،
+
+677
+00:53:10,590 --> 00:53:14,910
+كويسة لعند ما تصلوا لمين؟ لل P اللي انتوا بتدعوا و
+
+678
+00:53:14,910 --> 00:53:19,870
+اللي احنا دعينا ان هو اكبر رقم prime او اكبر رقم
+
+679
+00:53:19,870 --> 00:53:25,370
+اولي معناه ذلك انه مافيش اي رقم بعدهحلو، كويس جدا،
+
+680
+00:53:25,370 --> 00:53:30,850
+ولكن هنفاجأ أن كل مجموعة الأرقام الأولية ضربهم في
+
+681
+00:53:30,850 --> 00:53:36,170
+بعض زائد واحد دائما بطلع رقم أول جديد خليني
+
+682
+00:53:36,170 --> 00:53:43,930
+أمسكهم، اتنين في تلاتة، زائد واحد، سبعة، سبعة
+
+683
+00:53:43,930 --> 00:53:50,650
+prime طيب، ستة في خمسة، تلاتين، زائد واحد، الواحد
+
+684
+00:53:50,650 --> 00:53:56,370
+تلاتين ال primeطيب هنا صارت جدش تلاتين في سبعة
+
+685
+00:53:56,370 --> 00:54:01,830
+تلاتين صح تلاتين في سبعة متين و عشرة متين و إحدى
+
+686
+00:54:01,830 --> 00:54:06,510
+عشرة is a prime هذا طريقة بتقدر تعمل فيها
+
+687
+00:54:06,510 --> 00:54:10,770
+generation ل ال primes ل ال primes معنى ذلك أن لأ
+
+688
+00:54:10,770 --> 00:54:14,480
+في أكبر من هذاببساطة جدا، لو كلهم ضربتوا في بعض
+
+689
+00:54:14,480 --> 00:54:19,660
+وزودت واحد أكيد هيطلع prime ومدام ال prime ناتج من
+
+690
+00:54:19,660 --> 00:54:23,980
+ضرب ال P في رقم أكبر من واحد أكيد هيكون أكبر من P
+
+691
+00:54:23,980 --> 00:54:27,600
+أكيد هيكون أكبر من P معناه ذلك أنه لأ دائما في رقم
+
+692
+00:54:27,600 --> 00:54:32,760
+أكبر منه دائما هيكون في رقم أكبر منه لأن R plus
+
+693
+00:54:32,760 --> 00:54:38,540
+واحد وR هي حاصل ضربهمجربوها، جربوها بطريقة هذه،
+
+694
+00:54:38,540 --> 00:54:41,420
+دايما هتطلقوا primes، دايما هتبقوا تطلقوا primes
+
+695
+00:54:41,420 --> 00:54:47,780
+منها R plus واحد is a prime larger than P، منطقي
+
+696
+00:54:47,780 --> 00:54:51,320
+جدا، ليش؟ لأن أنا ضربت فيه ال P في integer أكبر من
+
+697
+00:54:51,320 --> 00:54:56,320
+واحد، فطبيعي جدا، بدو يعطيكوا رقم أعلى من ال P،
+
+698
+00:54:56,320 --> 00:54:59,500
+مضاعفات من ال P، why؟ لأنها زي ما قلنا ضربناها
+
+699
+00:54:59,500 --> 00:55:03,150
+برقم أكبر من واحدفإذا automatically صار عندكوا
+
+700
+00:55:03,150 --> 00:55:06,430
+contradiction صار عندكوا تعرض أنتوا فرضين أنه أكبر
+
+701
+00:55:06,430 --> 00:55:09,950
+رقم بس قدرتوا تعمله منه generation لرقم أكبر منه
+
+702
+00:55:09,950 --> 00:55:16,310
+فإذا صار العكس أثبتته العكس معناه ذلك أن عكس ال
+
+703
+00:55:16,310 --> 00:55:21,290
+negation true اللي هي من الأصل أنه no largest
+
+704
+00:55:21,290 --> 00:55:25,590
+prime numberطيب واضحة ايه انت بتقدر تتعاملوا معها
+
+705
+00:55:25,590 --> 00:55:28,050
+مع ال contradiction لما انتوا مايكونش عندكوا
+
+706
+00:55:28,050 --> 00:55:32,750
+premises واضحة مايكونش عندكوا فرضيات واضحة وانتوا
+
+707
+00:55:32,750 --> 00:55:36,030
+مضطرين تتعاملوا مع ال .. مع ال .. ال contradiction
+
+708
+00:55:36,030 --> 00:55:37,790
+تضطروا في الحالة اللي تشتغلوا معها ال
+
+709
+00:55:37,790 --> 00:55:43,010
+contradiction تفرضوا العكس و أثناء الشغل هيظهر
+
+710
+00:55:43,010 --> 00:55:46,110
+معاكوا او بتكونوا تحاولوا تشتهدوا تثبتوا ان العكس
+
+711
+00:55:46,110 --> 00:55:49,190
+اللي انتوا فرضته false ان العكس اللي انتوا فرضينه
+
+712
+00:55:49,190 --> 00:55:49,970
+false
+
+713
+00:55:55,950 --> 00:56:00,210
+هذا example؟ لأ مش example، لأ هذا برضه نفس
+
+714
+00:56:00,210 --> 00:56:03,430
+الطريقة مش مشكلة، مش example كويسة، في الحالة هذه
+
+715
+00:56:03,430 --> 00:56:09,870
+احنا أخدنا مجموعة methods مهمة جدا ل proofs من
+
+716
+00:56:09,870 --> 00:56:13,870
+المواضيع اللي مافيش امتحان يخلو منها، فإذا دايما
+
+717
+00:56:13,870 --> 00:56:16,730
+بتفكروا بال direct، indirect، indirect على طول
+
+718
+00:56:16,730 --> 00:56:20,970
+مخكم مع مين؟ مع ال contrapositiveindirect مخ دايما
+
+719
+00:56:20,970 --> 00:56:23,050
+على طول مع ال contrapositive في ال direct و في ال
+
+720
+00:56:23,050 --> 00:56:25,970
+indirect هذا بتكون تكونوا حافظينه كويس واضح أن ال
+
+721
+00:56:25,970 --> 00:56:29,850
+implication بدنا نحفظه لأن كل شغلنا عليه ال
+
+722
+00:56:29,850 --> 00:56:32,130
+implication كل شغلنا عليه سواء تشتغلوا على direct
+
+723
+00:56:32,130 --> 00:56:37,270
+أو indirect في كمان إيش كان معناه ال vacuous و ال
+
+724
+00:56:37,270 --> 00:56:40,490
+trivial برضه بتكونوا حافظينه لأنه من هنا بتقدر
+
+725
+00:56:40,490 --> 00:56:44,230
+تقول إنه ما بطل له معنى ال conclusion أو بطل لها
+
+726
+00:56:44,230 --> 00:56:49,020
+معنى ال premisesو الحاجة الأهم هاني بقولكوا كمان
+
+727
+00:56:49,020 --> 00:56:51,700
+مرة اللي هي إيه؟ ال contradiction .. ال
+
+728
+00:56:51,700 --> 00:56:55,240
+contradiction لأنه هاد بتكون .. بتكون تثبتوا منها
+
+729
+00:56:55,240 --> 00:57:00,620
+النظرية بدون ما يكون لها premises بدون ما .. خلاص
+
+730
+00:57:00,620 --> 00:57:04,400
+given عندكوا اثبتواطب أنا ماعنديش premises أنطلق
+
+731
+00:57:04,400 --> 00:57:07,880
+منها، أشتغل منها، فبتروحوا بتعكسوها و بتثبتوا أن
+
+732
+00:57:07,880 --> 00:57:13,460
+عكسها false، معناه ذلك أن ال .. ال .. ال .. ال ..
+
+733
+00:57:13,460 --> 00:57:15,280
+ال .. ال affirment تبعها، اللي هو التأكيد تبعها
+
+734
+00:57:15,280 --> 00:57:20,540
+الأصلي هو اللي true، هو اللي كان true طيب، نكفي،
+
+735
+00:57:20,540 --> 00:57:22,900
+هيك نكون خلصنا الموضوع هذا، المرة الجاية ان شاء
+
+736
+00:57:22,900 --> 00:57:26,560
+الله بنبدأ في مين؟ بنبدأ مع ال six ان شاء الله
+
+737
+00:57:26,560 --> 00:57:26,960
+تعالى
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync.srt
new file mode 100644
index 0000000000000000000000000000000000000000..37f76bed935c852d1025e729c3fcab7f9f0d887a
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync.srt
@@ -0,0 +1,2677 @@
+1
+00:00:20,690 --> 00:00:23,010
+بسم الله الرحمن الرحيم، أُصلُ تواصلهم على أشرف
+
+2
+00:00:23,010 --> 00:00:25,170
+الأنبياء والمسلمين، سيدنا محمد وعلى آلهِ وصحبه
+
+3
+00:00:25,170 --> 00:00:28,050
+أجمالي، بنبدأ اليوم إن شاء الله الأسبوع الثاني في
+
+4
+00:00:28,050 --> 00:00:31,510
+الـ course، الأسبوع الأول كنا أخذنا introduction في
+
+5
+00:00:31,510 --> 00:00:33,930
+أول محاضرة، أخذنا في الجزء الثاني مجموعة الـ
+
+6
+00:00:33,930 --> 00:00:36,870
+operators، اتكلمنا عن الـ propositions بالصفة العامة
+
+7
+00:00:36,870 --> 00:00:40,110
+وبعدين اتكلمنا عن مجموعة الـ operators، وأخذنا كيف
+
+8
+00:00:40,110 --> 00:00:44,500
+تشتغل الـ operators هذه، يمكن الـ .. هنا بنلخص مجموعة
+
+9
+00:00:44,500 --> 00:00:47,220
+الـ operators اللي اتكلمنا عنها سابقًا، اتكلمنا عن الـ
+
+10
+00:00:47,220 --> 00:00:50,160
+negation، اتكلمنا عن الـ conjunction، اتكلمنا عن الـ
+
+11
+00:00:50,160 --> 00:00:53,240
+disjunction، اتكلمنا عن الـ XOR والـ
+
+12
+00:00:53,240 --> 00:00:56,980
+implication، والـ biconditional، والـ biconditional
+
+13
+00:00:56,980 --> 00:01:02,440
+فاليوم بنكمل، بسمع جزئية هيك سريعة عن الـ bits and
+
+14
+00:01:02,440 --> 00:01:05,680
+bit operations، وبعدين بننتقل للـ equivalence، وهي
+
+15
+00:01:05,680 --> 00:01:07,460
+الجزء اللي .. اللي .. اللي أهم هيكون اليوم في
+
+16
+00:01:07,460 --> 00:01:11,720
+محاضرتنا، اللي هي الـ propositional equivalence في
+
+17
+00:01:11,720 --> 00:01:15,100
+شغلنا، فخلينا اليوم نبدأ بسريع هيك على الـ bits and
+
+18
+00:01:15,100 --> 00:01:19,760
+bit operations، الـ bit احنا التعامل اللي كله هيكون
+
+19
+00:01:19,760 --> 00:01:22,740
+مع الـ binary، مجموعة الـ bits هتكون binary، فـ binary
+
+20
+00:01:22,740 --> 00:01:28,300
+بتكلم عن الـ PS2، بمعنى أنه كل bit بقدر أمثلها بـ two
+
+21
+00:01:28,300 --> 00:01:32,560
+elements، اللي هم الـ zero والـ one، فعليًا احنا بنقدر
+
+22
+00:01:32,560 --> 00:01:35,980
+.. يعني الـ binary هذه بتمثل .. بتعبر لنا عن الـ logic
+
+23
+00:01:35,980 --> 00:01:39,280
+ليش؟ بتعبر لنا عن الـ logic لأن الـ zero represents
+
+24
+00:01:39,280 --> 00:01:43,500
+false، الـ one represents true، فأنا كأني بتعامل
+
+25
+00:01:43,500 --> 00:01:47,340
+معاها على أساس أنها false true، true false أو
+
+26
+00:01:47,340 --> 00:01:52,160
+false true، طيب هذه  مناظرة تمامًا للعمليات الحسابية
+
+27
+00:01:52,160 --> 00:01:56,260
+اللي كنتوا بتشتغلوها زمان في الجامعة، والضرب، ففعليًا الـ
+
+28
+00:01:56,260 --> 00:02:00,960
+or هي مقابلة للجمع، والـ and مقابلة لمين؟ لعملية
+
+29
+00:02:00,960 --> 00:02:06,840
+الضرب، طيب الـ bit strings، الـ bit strings هي مجموعة
+
+30
+00:02:06,840 --> 00:02:11,260
+bits متسلسلة حول بعضها بحيث أنها معطينا series
+
+31
+00:02:11,260 --> 00:02:17,500
+معينة أو sequence، معطينا سلسلة من الـ bits أو أرقام
+
+32
+00:02:17,500 --> 00:02:23,330
+متعاقبة، sequence of n، و n لازم تكون أكبر من صفر
+
+33
+00:02:23,330 --> 00:02:27,690
+أكبر من صفر، أكبر أو تساوي صفر، بحيث أن يكون فعلاً
+
+34
+00:02:27,690 --> 00:02:31,070
+فينا sequence، إذا كانت صفر، فالـ sequence هذا empty
+
+35
+00:02:31,070 --> 00:02:34,330
+sequence، بمعنى أو الـ string empty، بمعنى string
+
+36
+00:02:34,330 --> 00:02:37,730
+فاضي، زي لما كنا .. هناخدها لحظة طبعًا لما نتكلم عن
+
+37
+00:02:37,730 --> 00:02:43,600
+المجموعات الفارغة أو المجموعات الخالية، المهم، في
+
+38
+00:02:43,600 --> 00:02:46,320
+عندنا sequence، في عندنا مجموعة bits، الـ bits هذه
+
+39
+00:02:46,320 --> 00:02:52,060
+تمثل لنا sequence معين أو string معين، الـ string
+
+40
+00:02:52,060 --> 00:02:57,140
+هذا هنستخدمه عادة كمجموعة bits متقاربة أو متجاورة
+
+41
+00:02:57,140 --> 00:03:01,460
+مع بعض، المتجاورة هذه بنبدأ دائمًا من اليمين، بنبدأ
+
+42
+00:03:01,460 --> 00:03:04,120
+من اليمين، يعني للـ sequence اللي موجود قدامنا هنا
+
+43
+00:03:04,120 --> 00:03:07,000
+اللي هو one zero zero one one zero one zero one
+
+44
+00:03:07,000 --> 00:03:12,280
+zero، أول element أو bit فيه هي الـ one، فأنا بطلع
+
+45
+00:03:12,280 --> 00:03:17,220
+من الشمال لليمين، وفعليًا هي الـ most significant bit
+
+46
+00:03:17,220 --> 00:03:21,560
+هي الـ bit الأكبر قيمة فيهم، الـ bit الأكبر قيمة فيهم
+
+47
+00:03:21,560 --> 00:03:25,510
+في الـ decimal system، نفس الكلام موجود، احنا ممكن
+
+48
+00:03:25,510 --> 00:03:29,070
+نستعمل الرقم خمسة، الرقم خمسة هذا، وين الخانة تبعته
+
+49
+00:03:29,070 --> 00:03:34,150
+بيعطيني الـ significant تبعته، فلما بتكلم عن خمسة
+
+50
+00:03:34,150 --> 00:03:37,350
+بهذا
+
+51
+00:03:37,350 --> 00:03:41,310
+الشكل، مثلًا في خمسة وستين، هي الخمسة هنا تمثل الآحاد
+
+52
+00:03:41,310 --> 00:03:45,830
+فالخانة بتاعتها الآحاد، طيب لو الخمسة هنا لو موجودة
+
+53
+00:03:45,830 --> 00:03:50,170
+في العشرات، لأ، القيمة بتاعتها صارت أعلى، بمعنى أنه
+
+54
+00:03:50,170 --> 00:03:55,270
+لو اتغيرت، التغير كبير، حيصير، هنا نفس الكلام، الـ most
+
+55
+00:03:55,270 --> 00:03:58,810
+significant هي الـ bit اللي جاية على ناحية اليمين، و
+
+56
+00:03:58,810 --> 00:04:01,810
+عشان نوضح الموضوع هذا، أنتم برضه كنتوا تعملوا
+
+57
+00:04:01,810 --> 00:04:03,850
+conversion، أو كنتوا تعملوا تحويل من system لـ
+
+58
+00:04:03,850 --> 00:04:07,690
+system، من binary لـ decimal، ومن decimal لـ .. لـ hex
+
+59
+00:04:07,690 --> 00:04:11,130
+أو من hex، كنتوا تشتغلوها كتير، فلو قلنا أي .. أي ..
+
+60
+00:04:12,230 --> 00:04:16,650
+example بالشكل هذا، عشان نشوف من وين بتيجي الـ
+
+61
+00:04:16,650 --> 00:04:19,170
+significant بتاعتنا، الـ significant بنبدأها دائمًا
+
+62
+00:04:19,170 --> 00:04:22,790
+من اليمين، هي الأقل significant، ممكن أنا بتعامل هنا
+
+63
+00:04:22,790 --> 00:04:28,850
+أن كل bit لها قيمتين، إما zero أو one، فأنا بتعامل
+
+64
+00:04:28,850 --> 00:04:34,720
+على أساس أنها two، فهي two to the power zero، 2 to the
+
+65
+00:04:34,720 --> 00:04:38,300
+power of 1، 2 to the power of 2، 2 to the power of 3،
+
+66
+00:04:38,300 --> 00:04:42,780
+2 to the power of .. وهكذا، بقارن كل واحدة في أي
+
+67
+00:04:42,780 --> 00:04:45,840
+خانة، وهذا أنتم كنتوا تعملوه حتى في الأرقام
+
+68
+00:04:45,840 --> 00:04:48,680
+العشرية، في الأرقام العشرية، هي من وين جايّة الأرقام
+
+69
+00:04:48,680 --> 00:04:53,660
+العشرية؟ عند ما نقول 65، 5 و 6، الـ 65 هذه جاية من 10
+
+70
+00:04:53,660 --> 00:04:59,400
+to the power of 0 ضرب 5، و 10 to the power of 1 ضرب
+
+71
+00:04:59,400 --> 00:05:05,900
+6، و 10 to the power of 2 ضرب 3، فبيعطيني جدش القيمة
+
+72
+00:05:05,900 --> 00:05:09,060
+هذه .. بيعطيني جدش قيمة .. القيمة هذه تحديدًا ..
+
+73
+00:05:09,060 --> 00:05:14,300
+فهنا هيكون هذه كيلومتر واحد في خمسة، في خمسة عشر، في
+
+74
+00:05:14,300 --> 00:05:21,570
+ستّة، في ستين، مية، تلاتمئة، اجمعوهم بيطلع تلاتمئة
+
+75
+00:05:21,570 --> 00:05:26,150
+خمسة وستين، تمام، نفس الكلام بنستعمله في الـ other
+
+76
+00:05:26,150 --> 00:05:28,170
+systems، يعني في كل الـ systems الثانية اللي غير الـ
+
+77
+00:05:28,170 --> 00:05:30,490
+decimal، مش معناه أنه بتنعمل في الـ decimal، فنفس
+
+78
+00:05:30,490 --> 00:05:36,430
+الكلام هنا، هتلاقوا أن في عندكم one، في one، one plus
+
+79
+00:05:36,430 --> 00:05:48,420
+two، في zero، four، في zero، eight، في one، فهنا بتطلع
+
+80
+00:05:48,420 --> 00:05:53,580
+تسعة، هذا الرقم تمثل تسعة، فلاحظوا أن الـ bit الأخيرة
+
+81
+00:05:53,580 --> 00:05:57,720
+اللي هي جاية في الـ left، هي الأعلى قيمة، هي الأعلى
+
+82
+00:05:57,720 --> 00:06:01,940
+قيمة، ليش؟ لأنها مضروبة في أعلى coefficient، في 2 to
+
+83
+00:06:01,940 --> 00:06:06,620
+the power 3، بالنسبة للرقم تبعنا، 2 to the power 3،
+
+84
+00:06:06,620 --> 00:06:15,220
+فعليًا
+
+85
+00:06:16,400 --> 00:06:19,960
+العشر أصابع، كم رقم بقدر أعدّ فيه، أو لعند جد إيش
+
+86
+00:06:19,960 --> 00:06:24,020
+بقدر أعدّ فيه باستخدام الـ decimal؟ لعند عشرة، الولد
+
+87
+00:06:24,020 --> 00:06:26,840
+الصغير اللي بنعلمه، كل واحد، اثنين، ثلاثة، لعند عشرة،
+
+88
+00:06:26,840 --> 00:06:30,380
+فبقدر لعند عشرة، لأ، actually احنا بقدر نعدّ فيه لعند
+
+89
+00:06:30,380 --> 00:06:35,580
+ألف وثلاثة وعشرين، لو تعاملنا معه كـ bits، وبنتعامل
+
+90
+00:06:35,580 --> 00:06:39,180
+معه كـ binary، فممكن أقول، ببدأ دائمًا زي ما قلنا من
+
+91
+00:06:39,180 --> 00:06:43,500
+الشمال، بنبدأ، أو يعني بالنسبة لي أنا شمال هيكون
+
+92
+00:06:43,500 --> 00:06:45,700
+بالنسبة لي كان اليمين، يعني فعليًا نبدأ باليمين، من
+
+93
+00:06:45,700 --> 00:06:53,640
+الأقل significant، هيها، فبقول، كله صفر، هيك واحد، طب
+
+94
+00:06:53,640 --> 00:06:56,820
+عشان أغيّر، أعمل flip أو أغيّر، أعمل الـ count اللي
+
+95
+00:06:56,820 --> 00:07:02,800
+وراها، ببدأ برضه دائمًا يمين، إذا واجهت واحد صفر، و
+
+96
+00:07:02,800 --> 00:07:07,720
+بُعطِي واحد للي وراه، فصارت صفر واحد صفر واحد، تمثل
+
+97
+00:07:07,720 --> 00:07:13,840
+اثنين، مش يمثلوا رقم اثنين، لأن الباقي كله zeros، طيب
+
+98
+00:07:13,840 --> 00:07:19,880
+هاي اثنين، طيب عشان هالوجه أجيب الرقم اللي وراه، ببدأ
+
+99
+00:07:19,880 --> 00:07:23,200
+إذا كان لقيْت صفر، برضه من اليمين، لقيْت صفر، بحوّله
+
+100
+00:07:23,200 --> 00:07:30,320
+لواحد، وخلصنا، هاي صار رقم ثلاثة، طيب رقم أربعة، لقيْت
+
+101
+00:07:30,320 --> 00:07:34,400
+واحد، بأحوّله صفر، وبنتقل للي وراه، واحد برضه
+
+102
+00:07:34,400 --> 00:07:37,480
+بأحوّله صفر، وبنتقل للي وراه، فصارت إيه؟ صفر صفر
+
+103
+00:07:37,480 --> 00:07:45,540
+واحد صفر صفر واحد، أربعة، وهكذا، فهذه عملية الـ
+
+104
+00:07:45,540 --> 00:07:50,020
+counting، على باستخدام الـ binary، in binary، فهتلاقوا
+
+105
+00:07:50,020 --> 00:07:53,520
+دائمًا بتعملوا change من one to zero، من one to zero،
+
+106
+00:07:53,520 --> 00:07:57,800
+إذا كان لقيْت one، في وشّه من اليمين، من اليمين،
+
+107
+00:07:57,800 --> 00:08:02,420
+دائمًا بتبدأ العدّ من اليمين، من الأقل أهمية، عشان
+
+108
+00:08:02,420 --> 00:08:05,340
+تطلعوا فيه لـ .. لـ .. لـ .. لما تصلوا لـ الـ most
+
+109
+00:08:05,340 --> 00:08:12,180
+significant، فبتعملوا flip to the next bit، Okay، الـ
+
+110
+00:08:12,180 --> 00:08:15,480
+.. الـ bitwise .. bitwise operations، احنا قبل هيك
+
+111
+00:08:15,480 --> 00:08:19,300
+قلنا، أنه لما اتكلمنا المرة اللي فاتت، وقلنا أنه
+
+112
+00:08:19,300 --> 00:08:22,840
+في البرمجة، هتاخدوا حاجة اسمها wordwise أو bitwise
+
+113
+00:08:22,840 --> 00:08:26,060
+bitwise، أنا بتعامل معها الـ sequence تبعي bit by
+
+114
+00:08:26,060 --> 00:08:29,480
+bit، فإذا كل bit داخل الـ sequence، بتعامل معاها
+
+115
+00:08:29,480 --> 00:08:33,500
+كأنها مستقلة، بـ .. بقارنها بالـ bit المقابلة لها في
+
+116
+00:08:33,500 --> 00:08:36,380
+الـ sequence الثاني، وبأعمل الـ operation تبعيتي، بنعمل
+
+117
+00:08:36,380 --> 00:08:40,130
+الـ operation بتاعتنا، معنى ذلك، معنى ذلك إن لو بدنا
+
+118
+00:08:40,130 --> 00:08:42,690
+.. عندنا .. عندنا two sequences بالشكل اللي احنا
+
+119
+00:08:42,690 --> 00:08:47,230
+شايفينه هذا، وبدنا نشتغل bitwise، بمعنى أنا بعملش
+
+120
+00:08:47,230 --> 00:08:51,770
+للكلمة كلها على بعض، مع الكلمة كلها على بعض، لأ، لكل
+
+121
+00:08:51,770 --> 00:08:56,690
+bit مع الـ bit المقابلة لها، كويس، لو بدنا نعمل
+
+122
+00:08:56,690 --> 00:09:02,730
+operator or، bitwise or، بمسك كل واحدة مع الـ .. مع
+
+123
+00:09:02,730 --> 00:09:06,850
+ما يقابلها، مع ما يقابلها، طيب لو الـ sequence عندكم
+
+124
+00:09:06,850 --> 00:09:12,270
+أصلًا الـ n تبع كل واحد منهم مختلفة عن الثانية، الـ n
+
+125
+00:09:12,270 --> 00:09:15,590
+واحد، والـ n اثنين، الـ n الأولى، نفترض ستة، فهي فيها
+
+126
+00:09:15,590 --> 00:09:22,490
+ستة elements، والـ n الثانية خمسة، بنكمل بـ zeros، و
+
+127
+00:09:22,490 --> 00:09:26,410
+هتلاحظوا أننا فعلاً مكملينها هنا بـ zero، الـ element
+
+128
+00:09:26,410 --> 00:09:30,120
+الأول هذا، أو الـ sequence الأول، هو فعلاً هنا بسبع في
+
+129
+00:09:30,120 --> 00:09:34,500
+zero، بتكملوا، بتقدروا تعملوا الـ bit الـ string،
+
+130
+00:09:34,500 --> 00:09:45,020
+بتعملوا، طيب or zero or one one one one one one one
+
+131
+00:09:45,020 --> 00:09:45,200
+one one one one one one one one one one one one
+
+132
+00:09:45,200 --> 00:09:45,240
+one one one one one one one one one one one one
+
+133
+00:09:45,240 --> 00:09:47,100
+one one one one one one one one one one one one
+
+134
+00:09:47,100 --> 00:09:47,140
+one one one one one one one one one one one one
+
+135
+00:09:47,140 --> 00:09:47,400
+one one one one one one one one one one one one
+
+136
+00:09:47,400 --> 00:09:50,660
+one one one one one one
+
+137
+00:09:50,660 --> 00:09:50,680
+one one one one one one one one one one one one
+
+138
+00:09:50,680 --> 00:09:57,460
+one، اللي عندكم، عارفين، كله zero، باستثناء one and one،
+
+139
+00:09:57,460 --> 00:10:01,800
+one and one، هاي في عندي one and one، وهي one and
+
+140
+00:10:01,800 --> 00:10:07,340
+one، وهي one and one، otherwise zeros، otherwise
+
+141
+00:10:07,340 --> 00:10:16,000
+zeros، طيب x or one، امتى؟ إذا اختلفوا، إذا اختلفوا،
+
+142
+00:10:16,000 --> 00:10:20,220
+إذا اختلفوا، طيب إذا كان متشابهين، zeros، تعالوا نشوف
+
+143
+00:10:20,220 --> 00:10:24,550
+وين في متشابهين؟ هاي في عندي متشابه، واحدة zero، هي
+
+144
+00:10:24,550 --> 00:10:29,250
+متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة،
+
+145
+00:10:29,250 --> 00:10:35,490
+فهي متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة، فهي
+
+146
+00:10:35,490 --> 00:10:42,290
+متشابهة، فهي
+
+147
+00:10:42,290 --> 00:10:44,490
+متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة،
+
+148
+00:10:44,490 --> 00:10:47,730
+متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة،
+
+149
+00:10:47,730 --> 00:10:50,170
+فهي متشابهة، فهي متشابهة، فهي متشابهة، فهي متشابهة، فهي
+
+150
+00:10:50,170 --> 00:10:51,580
+متشابهة، فهي متشابهة، فهي متشابهة، فاللي احنا عملناه، طب
+
+151
+00:10:51,580 --> 00:10:54,220
+ممكن تجرّبوا operators ثانية كمان، ممكن تجرّبوا أي
+
+152
+00:10:54,220 --> 00:10:58,520
+operators ثانية، وخصوصًا أن أنتم مرّ عليكم يعني
+
+153
+00:10:58,520 --> 00:11:01,540
+ممكن تجرّبوها على فكرة باستخدام الـ java، لو اتعلّمتوا
+
+154
+00:11:01,540 --> 00:11:05,200
+الـ java، ويعملوا sequence معين عندكم، ويستعملوا الـ
+
+155
+00:11:05,200 --> 00:11:10,860
+bitwise، علامة الـ bitwise هذه، استعملوهم، هيتطلعوا
+
+156
+00:11:10,860 --> 00:11:17,940
+نفس الحلول اللي احنا اشتغلنا عليها، طيب، نقول
+
+157
+00:11:17,940 --> 00:11:24,450
+للموضوع بتاع اليوم، هذه الجزئية كملنا فيها محاضرة
+
+158
+00:11:24,450 --> 00:11:28,610
+اللي فاتت، نبدأ في جزء اليوم، اللي هو الـ
+
+159
+00:11:28,610 --> 00:11:34,330
+propositional equivalence، طيب لفظيًا أو معناها
+
+160
+00:11:34,330 --> 00:11:38,310
+textually، بالحرف، معناها بالحرف، different compound
+
+161
+00:11:38,310 --> 00:11:43,850
+propositions may be semantically identical، إيش
+
+162
+00:11:43,850 --> 00:11:46,710
+يعني identical؟ معنى ذلك أنه have the same
+
+163
+00:11:46,710 --> 00:11:50,850
+meaning، إيش يعني؟ برضه هنا معنى ذلك أنه حرفيًا
+
+164
+00:11:50,850 --> 00:11:56,600
+موجود عندنا two different compound propositions،
+
+165
+00:11:56,600 --> 00:12:02,240
+عندنا propositions أو تصريحين، two sentences، عندنا
+
+166
+00:12:02,240 --> 00:12:08,720
+فرضيتين مركبتين ومختلفتين، proposition الأول،
+
+167
+00:12:08,720 --> 00:12:13,890
+proposition الثاني، ولكن لهم نفس المعنى، اللي هم نفس
+
+168
+00:12:13,890 --> 00:12:17,
+
+223
+00:15:55,110 --> 00:15:59,770
+تمام؟ فهنا زي ما نقول P disjunction negation P هذه
+
+224
+00:15:59,770 --> 00:16:03,270
+دائما true جملة بالشكل هذا دائما أبدا هتظل true
+
+225
+00:16:03,270 --> 00:16:08,730
+بغض النظر عن هل الـ atomic هي الوحدة الواحدة منهم الـ
+
+226
+00:16:08,730 --> 00:16:13,290
+atomic هادي أو هادي true or false مش هتفرق
+
+227
+00:16:13,290 --> 00:16:17,090
+whatever يعني إيش ما تكون القيمة بتاعتها المحصلة
+
+228
+00:16:17,090 --> 00:16:20,170
+كلها على بعض دائما true طيب العكس في الـ
+
+229
+00:16:20,170 --> 00:16:24,370
+contradiction الـ contradiction is a compound
+
+230
+00:16:24,370 --> 00:16:30,510
+proposition that is false no matter what the truth
+
+231
+00:16:30,510 --> 00:16:37,220
+values of its atomic propositions كويس زي P and
+
+232
+00:16:37,220 --> 00:16:41,000
+negation P تصحي الصبح تقول والله اليوم بدي أروح
+
+233
+00:16:41,000 --> 00:16:44,440
+الجامعة و بديش أروح الجامعة طبعا إيش المعنى؟
+
+234
+00:16:44,440 --> 00:16:47,480
+مالهاش معنى يعني أنه غلط كله واضح أنه غلط يا بدك
+
+235
+00:16:47,480 --> 00:16:52,440
+تروح يا بدكيش تروحي أما بدي أروح و بديش أروح فهذه
+
+236
+00:16:52,440 --> 00:16:55,900
+دائما هتكون إيش؟ false استمرار false لأن واحدة
+
+237
+00:16:55,900 --> 00:16:59,840
+منهم هتكون false لازم واحدة منهم هتكون false وفي
+
+238
+00:16:59,840 --> 00:17:02,980
+حالة الـ conjunction لازم كلهم يكونوا true عشان
+
+239
+00:17:02,980 --> 00:17:06,490
+يكونوا true لأ هنا دائما في واحدة منهم false فإذا
+
+240
+00:17:06,490 --> 00:17:10,950
+المحصلة دائما هتكون false otherwise يعني هدول
+
+241
+00:17:10,950 --> 00:17:13,890
+الحالات اللي هم مؤكدين تماما تاتولوجيا والـ
+
+242
+00:17:13,890 --> 00:17:18,610
+contradiction اللي هي الـ proposition مع الـ
+
+243
+00:17:18,610 --> 00:17:23,010
+negation تبعه أو الـ negation تبعه كويس otherwise
+
+244
+00:17:23,010 --> 00:17:27,830
+ممكن تكون تحصل أحيانا بالـ by chance بالحظ يعني
+
+245
+00:17:27,830 --> 00:17:31,250
+ممكن تلاقوا أن والله في column طلع كله tautology
+
+246
+00:17:31,250 --> 00:17:35,130
+أو column طلع كله contradiction كله false ممكن تصير
+
+247
+00:17:35,130 --> 00:17:40,210
+بالحظ في حالات معينة طيب logical equivalence شوفنا
+
+248
+00:17:40,210 --> 00:17:42,390
+الـ tautology شوفنا الـ construction الـ compound ..
+
+249
+00:17:42,390 --> 00:17:45,350
+الـ compound proposition compound بدنا نعرفه خلاص
+
+250
+00:17:45,350 --> 00:17:48,950
+compound أنا بتكلم عن مجموعة atomic propositions
+
+251
+00:17:48,950 --> 00:17:53,230
+مربطة .. مربوطة مع بعض .. مربوطة مع بعض هي مش مجرد
+
+252
+00:17:53,230 --> 00:17:56,650
+atomic proposition لحالة بشكل هذا لأ هي ممكن تكون
+
+253
+00:17:56,650 --> 00:18:02,420
+or and مع أي q مثلا جملة، أبسط .. أبسط compound
+
+254
+00:18:02,420 --> 00:18:06,140
+proposition، فيها أكتر من atomic proposition،
+
+255
+00:18:06,140 --> 00:18:08,960
+تمام؟ فلما بتلاقوا كله compound أنا بتكلم عن
+
+256
+00:18:08,960 --> 00:18:15,190
+complicated proposition متكونة من مجموعة atomic طيب
+
+257
+00:18:15,190 --> 00:18:18,310
+compound of proposition P is logically equivalent
+
+258
+00:18:18,310 --> 00:18:22,530
+to compound proposition Q compound proposition مع
+
+259
+00:18:22,530 --> 00:18:25,430
+compound preposition إذا كانوا فعلا الإثنين
+
+260
+00:18:25,430 --> 00:18:30,710
+مكافئين لبعض فإذا بقدر أقول أن P by conditional Q
+
+261
+00:18:30,710 --> 00:18:36,550
+is true هيكون ليش؟ لأن واحدة بتضمن الثانية والثانية
+
+262
+00:18:36,550 --> 00:18:39,550
+بتضمن الأولى إذا بالظبط الإثنين وإحنا
+
+263
+00:18:39,550 --> 00:18:43,930
+عارفين أنه في الـ by conditional إمتى بيكونوا true
+
+264
+00:18:43,930 --> 00:18:48,330
+by conditional يعني إمتى بتكون true؟ إذا كانت false،
+
+265
+00:18:48,330 --> 00:18:53,270
+false أو true، true متشابهين، متشابهين، متشابهين،
+
+266
+00:18:53,270 --> 00:18:54,290
+متشابهين، متشابهين، متشابهين،
+
+267
+00:18:54,290 --> 00:18:54,650
+متشابهين، متشابهين، متشابهين، متشابهين
+
+268
+00:18:54,650 --> 00:18:55,870
+متشابهين متشابهين متشابهين متشابهين
+
+269
+00:18:55,870 --> 00:18:58,910
+متشابهين متشابهين متشابهين متشابهين
+
+270
+00:18:58,910 --> 00:19:02,570
+متشابهين
+
+271
+00:19:02,570 --> 00:19:05,730
+متشابهين
+
+272
+00:19:06,450 --> 00:19:10,330
+هذه الإثنين هيكونوا متكافئين علامة التكافؤ إذا كانوا
+
+273
+00:19:10,330 --> 00:19:14,870
+فعلا compound is a tautology معناه ذلك أنه لازم
+
+274
+00:19:14,870 --> 00:19:20,270
+دائما true طب إنت ممكن تكون true فعليا لما كل
+
+275
+00:19:20,270 --> 00:19:23,050
+واحدة منهم مساوية للثانية بغض النظر false false
+
+276
+00:19:23,050 --> 00:19:26,850
+true true بس لازم تكون مساوية لها بنفس .. لها نفس
+
+277
+00:19:26,850 --> 00:19:30,550
+الـ value نفس الـ value زي ما قلنا بغض النظر الـ
+
+278
+00:19:30,550 --> 00:19:37,030
+value هدي false or true false false okay true الـ by
+
+279
+00:19:37,030 --> 00:19:39,570
+conditional بتاعتهم true .. true true .. by
+
+280
+00:19:39,570 --> 00:19:42,110
+conditional true .. فإذا tautology .. tautology هنا
+
+281
+00:19:42,110 --> 00:19:46,090
+تحققت للـ by conditional معناه ذلك أن كل
+
+282
+00:19:46,090 --> 00:19:50,850
+proposition منهم مكافئ للثاني .. مكافئ للثاني ..
+
+283
+00:19:50,850 --> 00:19:56,170
+له نفس القيمة .. okay هذه ممكن برضه نعملها .. ممكن
+
+284
+00:19:56,170 --> 00:19:59,910
+تجربوها برضه باستخدام الـ truth value فهي بتحتوي الـ
+
+285
+00:19:59,910 --> 00:20:04,070
+truth table اللي ما بتيجوا تعملوها الـ column تبع الـ
+
+286
+00:20:04,070 --> 00:20:08,030
+compound proposition المفروض أنه يحتوي على مجموعة
+
+287
+00:20:08,030 --> 00:20:15,010
+.. مجموعة symbols مشابهة .. مشابهة هو مساوية تماما للـ
+
+288
+00:20:15,010 --> 00:20:18,350
+الـ column تبع الـ proposition الثانية اللي لازم
+
+289
+00:20:18,350 --> 00:20:22,250
+تكون مكافئة عليها هذه بتستخدم أساسا من the same
+
+290
+00:20:22,250 --> 00:20:27,330
+truth value لما بنستعمل truth table لما بنستعمل
+
+291
+00:20:27,330 --> 00:20:32,970
+truth table زي ما هنشوف لاحقا هنا مثلا لو بدي أثبت
+
+292
+00:20:32,970 --> 00:20:39,870
+أعمل prove that بيه disjunction Q equivalent to
+
+293
+00:20:39,870 --> 00:20:45,720
+negation نفترض negation P and negation Q إيش
+
+294
+00:20:45,720 --> 00:20:48,400
+بدنا نسوي؟ بدنا نستعمل الـ truth table باستخدام الـ
+
+295
+00:20:48,400 --> 00:20:52,840
+truth table كل اللي هنعمله كم atomic proposition
+
+296
+00:20:52,840 --> 00:20:57,440
+عندنا؟ إثنين، معناه زي اللي كأنه عرفنا أن أنا كم رو
+
+297
+00:20:57,440 --> 00:21:02,400
+يكون عندي؟ أربعة، إثنين وهذه الأساس هتظل دائما
+
+298
+00:21:02,400 --> 00:21:06,220
+ثابتة معايا to the power عدد الـ atomic proposition
+
+299
+00:21:06,220 --> 00:21:07,400
+اللي هم إثنين
+
+300
+00:21:11,590 --> 00:21:15,770
+فحنشتغل على أول compound proposition P disjunction
+
+301
+00:21:15,770 --> 00:21:20,750
+Q كويس الثانية آه لأ لسه الثانية عشان أعملها محتاج
+
+302
+00:21:20,750 --> 00:21:25,870
+أول negation P negation Q بعدين الـ two negations
+
+303
+00:21:25,870 --> 00:21:31,010
+مع بعض نعملهم conjunction بعدين negation للـ
+
+304
+00:21:31,010 --> 00:21:34,450
+conjunction كله على بعض كويس خليني أشوف هنا لما
+
+305
+00:21:34,450 --> 00:21:42,830
+نقوله or الـ O لأ false otherwise true طيب وبعدين
+
+306
+00:21:42,830 --> 00:21:48,810
+بتعمل negation لـ P و negation لـ Q كويس
+
+307
+00:21:48,810 --> 00:21:53,890
+بعدين هنا هتعمله and and لـ مين؟ لـ الـ two columns
+
+308
+00:21:53,890 --> 00:21:56,770
+هدول مع بعض لـ الـ two columns هدول فهيكون بس أول
+
+309
+00:21:56,770 --> 00:22:04,030
+term هو الـ true otherwise false طيب negation لـ الـ
+
+310
+00:22:04,030 --> 00:22:06,870
+column هذا يعكسه تماما
+
+311
+00:22:08,450 --> 00:22:12,390
+لحظة الـ column هذا والـ column هذا the same values
+
+312
+00:22:12,390 --> 00:22:18,070
+the same values فإذا عندكم false true true true
+
+313
+00:22:18,070 --> 00:22:22,490
+true true true true true true true true true true
+
+314
+00:22:22,490 --> 00:22:23,790
+true true true true true true true true true true
+
+315
+00:22:23,790 --> 00:22:27,150
+true true true true true true true true true true
+
+316
+00:22:27,150 --> 00:22:27,210
+true true true true true true true true true true
+
+317
+00:22:27,210 --> 00:22:27,490
+true true true true true true true true true true
+
+318
+00:22:27,490 --> 00:22:28,190
+true true true true true true true true true true
+
+319
+00:22:28,190 --> 00:22:28,310
+true true true true true true true true true true
+
+320
+00:22:28,310 --> 00:22:29,030
+true true true true true true true true true true
+
+321
+00:22:29,030 --> 00:22:29,210
+true true true true true true true true true true
+
+322
+00:22:29,210 --> 00:22:29,230
+true true true true true true true true true true
+
+323
+00:22:29,230 --> 00:22:29,350
+true true true true true true true true true true
+
+324
+00:22:29,350 --> 00:22:30,030
+true true true true true true true true
+
+325
+00:22:36,040 --> 00:22:39,540
+يعني عندكوا P عندكوا Q عندكوا R عندكوا S عندكوا T
+
+326
+00:22:39,540 --> 00:22:46,280
+إثنين أو خمسة إثنين أو ثلاثين row طيب لو افترضنا
+
+327
+00:22:46,280 --> 00:22:49,620
+كمان أن الـ compound هذا مش هيكون الإثنين مع بعض
+
+328
+00:22:49,620 --> 00:22:53,540
+طبعا هيكون الخمسة مع بعضهم يعني محتاجين كذا column
+
+329
+00:22:53,540 --> 00:22:57,200
+عشان تصلوا للي بدكوا ياه بدون ما يصير لخبطة معاكم
+
+330
+00:22:57,200 --> 00:23:01,420
+فلاحظوا الموضوع كبر صار كثير كبير فهنا بيصير أفضل أن
+
+331
+00:23:01,420 --> 00:23:05,060
+إحنا نشتغل على symbolic derivations هناخدها
+
+332
+00:23:05,060 --> 00:23:09,480
+باستخدام قوانين ومعادلات معينة أو rules معينة طيب
+
+333
+00:23:09,480 --> 00:23:14,480
+نبدأ بالـ rules هذه اللي ممكن نستعملها في أول
+
+334
+00:23:14,480 --> 00:23:19,540
+rule اللي هي زي المحايد الجمعي والمحايد
+
+335
+00:23:19,540 --> 00:23:23,120
+الضربي أخذتوهم قبل هيك لما بتشتغلوا في الأرقام
+
+336
+00:23:23,120 --> 00:23:27,260
+العادية كان في عندكم محايد جمعي اللي هو صفر والـ
+
+337
+00:23:27,260 --> 00:23:30,440
+.. وفي اللي في الضرب واحد تمام طيب إحنا
+
+338
+00:23:30,440 --> 00:23:32,360
+اتفقنا أن صفر
+
+339
+00:23:34,820 --> 00:23:42,120
+للفالس one للـ true طيب لما بعمل ضرب الضرب المفروض
+
+340
+00:23:42,120 --> 00:23:48,380
+المعاكس للضرب المحايد الضرب واحد true conjunction
+
+341
+00:23:48,380 --> 00:23:51,740
+مع أي term أو مع أي proposition هيطلع الـ
+
+342
+00:23:51,740 --> 00:23:55,540
+proposition فالـ true هي محايدة بالنسبة للـ
+
+343
+00:23:55,540 --> 00:24:00,480
+conjunction للـ conjunction تمام العكس بالنسبة للـ
+
+344
+00:24:00,480 --> 00:24:03,800
+disjunction أو اللي هي الجمع يعني اللي كانت مقابلة
+
+345
+00:24:03,800 --> 00:24:08,240
+للجمع الجمع المحايد الجمع تبعها أو الـ disjunction
+
+346
+00:24:08,240 --> 00:24:13,020
+هي الـ false هي الـ false الـ zero false مع أي
+
+347
+00:24:13,020 --> 00:24:17,240
+proposition النتيجة قيمة الـ proposition إذا كان true
+
+348
+00:24:17,240 --> 00:24:22,100
+هيطلع true إذا كان false هيطلع false ونفس الكلام
+
+349
+00:24:22,100 --> 00:24:27,320
+كانت بالنسبة لها الـ conjunction طيب طب في الهيمنة
+
+350
+00:24:28,210 --> 00:24:31,410
+لما تقول والله الـ zero مثلا يمكن أوضح الـ zero أكثر
+
+351
+00:24:31,410 --> 00:24:36,830
+من الـ واحد لما تقول الـ zero في أي قيمة zero معناته
+
+352
+00:24:36,830 --> 00:24:41,050
+هنا الـ zero هيمن هيمن على المعادلة بتاعتنا هي
+
+353
+00:24:41,050 --> 00:24:48,710
+false conjunction في false طيب الثالثة الثالثة
+
+354
+00:24:48,710 --> 00:24:55,760
+اللي هي مش زي الـ tautology  لأ هذه عديمة الفائدة
+
+355
+00:24:55,760 --> 00:25:03,660
+أحيانا بيسموها بمعنى أن الـ proposition مع نفسه، الـ
+
+356
+00:25:03,660 --> 00:25:07,140
+proposition مع نفسه مالوش معنى، مالوش معنى أن أنا
+
+357
+00:25:07,140 --> 00:25:09,700
+أقول اليوم بدي أصحى من النوم واليوم بدي أصحى من
+
+358
+00:25:09,700 --> 00:25:14,540
+النوم طب ما هي المحصلة أن اليوم بدي أصحى من النوم،
+
+359
+00:25:14,540 --> 00:25:20,640
+اليوم بدي أروح الجامعة أو أن اليوم أروح الجامعة طب
+
+360
+00:25:20,640 --> 00:25:22,800
+ما هي المحصلة أنه حاليا يوم هنروح الجامعة فالـ
+
+361
+00:25:22,800 --> 00:25:25,000
+proposition في الحالة اللي زيها دي الـ proposition
+
+362
+00:25:25,000 --> 00:25:29,400
+مع نفسه أو مضروب في نفسه بمعنى and أو or مع نفسه
+
+363
+00:25:29,400 --> 00:25:34,860
+هو نفسه هو نفسه لو true إنها هتطلع true لو false
+
+364
+00:25:34,860 --> 00:25:40,080
+هيكون false هيكون false في الحالتين فهذا يمثل نفسه
+
+365
+00:25:40,080 --> 00:25:46,460
+طيب الـ rule الرابعة الـ double negation اللي هي نفي
+
+366
+00:25:46,460 --> 00:25:51,550
+النفي if bad صحيح؟ طيب نفي النفي إثبات فإذا أنا
+
+367
+00:25:51,550 --> 00:25:57,090
+أقول negation of negation P تطلع
+
+368
+00:25:57,090 --> 00:26:01,510
+P طيب الثانية
+
+369
+00:26:01,510 --> 00:26:06,950
+الـ domination domination الهيمنة وهذي عشان أوضح
+
+370
+00:26:06,950 --> 00:26:10,750
+لكم إياها أكثر بالأرقام اللي أنتم عارفينها الصفر لما
+
+371
+00:26:10,750 --> 00:26:14,410
+تضربيه بأي رقم هو هيمن عليه ليش؟ لأنه أعطى ناتج
+
+372
+00:26:14,410 --> 00:26:21,140
+دائما صفر لما نقول صفر في مليون صفر هنا معناها أن
+
+373
+00:26:21,140 --> 00:26:25,620
+الـ true أو false هيمنوا على الـ proposition لغوا،
+
+374
+00:26:25,620 --> 00:26:30,180
+لغوا تأثيره، لغوا الـ effect تبعه، كيف لغوا؟ الـ
+
+375
+00:26:30,180 --> 00:26:34,100
+true بتلغي تأثير الـ proposition اللي معها إذا كانت
+
+376
+00:26:34,100 --> 00:26:38,500
+مع مين؟ disjunction، disjunction إحنا عارفين أو،
+
+377
+00:26:38,500 --> 00:26:45,470
+فأي term أو true، true لأن في أو فاعطيني سماحية أن
+
+378
+00:26:45,470 --> 00:26:48,310
+ممكن أي واحد منهم true وكل الباقي يطلع true ما
+
+379
+00:26:48,310 --> 00:26:51,230
+هو فعلا أكيد في واحد منهم true لأن أنا حاطط true
+
+380
+00:26:51,230 --> 00:26:56,550
+حاططينه أصلا true فعلا طيب نفس الكلام في إيش؟ مع الـ
+
+381
+00:26:56,550 --> 00:26:59,970
+and اللي هي عملية كأنها عملية ضرب تقابل ضرب في الـ
+
+382
+00:26:59,970 --> 00:27:07,930
+decimal system هذه مع صفر صفر ضرب أي قيمة صفر
+
+383
+00:27:07,930 --> 00:27:11,630
+فيمكن هذه بتخلي المفهوم أوضح a proposition
+
+384
+00:27:13,290 --> 00:27:17,170
+conjunction مع false أكيد false لأن الـ conjunction
+
+385
+00:27:17,170 --> 00:27:21,470
+عشان يختلف عن الـ false يكون true لازم يكونوا إثنين
+
+386
+00:27:21,470 --> 00:27:26,030
+atomic proposition true صح لازم إثنين يكونوا true
+
+387
+00:27:26,030 --> 00:27:30,430
+لأ إحنا أي واحد منهم مش true خلاص واحد منهم false
+
+388
+00:27:30,430 --> 00:27:33,830
+انتهى أي واحد منهم false فإذا النتيجة لازم يكون
+
+389
+00:27:33,830 --> 00:27:37,890
+not true فإذا not true ما عنديش الاحتمال أن هو يا
+
+390
+00:27:37,890 --> 00:27:43,300
+true يا false الـ not true تمثل false طيب، آه لسه ما
+
+391
+00:27:43,300 --> 00:27:46,920
+اتكلمنا عن commutative، الـ commutative تبادلي،
+
+392
+00:27:46,920 --> 00:27:50,120
+تبادلي، تبادلي بمعنى .. تبادل إمتى؟ إذا كانت هم
+
+393
+00:27:50,120 --> 00:27:52,800
+بتتكلموا عن نفس الـ junction هيها الـ .. الـ .. الـ
+
+394
+00:27:52,800 --> 00:27:55,140
+الـ junction بتاعتنا أو هنا بتتكلم عن disjunction
+
+395
+00:27:55,140 --> 00:27:59,840
+فإذا P disjunction Q هي نفسها Q disjunction P و P
+
+396
+00:27:59,840 --> 00:28:05,890
+conjunction Q هي نفسها Q conjunction P كويس
+
+397
+00:28:05,890 --> 00:28:10,050
+associative الـ associative المشاركة في الـ priority
+
+398
+00:28:10,050 --> 00:28:15,590
+في الأولوية هو فعليا إذا كان أنا بتعامل مع نفس الـ
+
+399
+00:28:15,590 --> 00:28:18,990
+conjunction أو الـ disjunction يعني نفس الـ .. الـ ..
+
+400
+00:28:18,990 --> 00:28:23,450
+الـ operator فالمفروض أن الأولوية متساوية صح
+
+401
+00:28:23,450 --> 00:28:26,450
+الأ
+
+445
+00:31:51,170 --> 00:31:57,390
+محصلة كلها false طيب اللي عندنا اللحظة كل اللي
+
+446
+00:31:57,390 --> 00:32:00,070
+اتكلمنا عنهم اتكلمنا عنهم على أساس أننا نتكلم عن
+
+447
+00:32:00,070 --> 00:32:03,970
+negation, conjunction, and disjunction. طب إحنا أخدنا
+
+448
+00:32:03,970 --> 00:32:07,930
+أكثر من هيك، كان في مجموعة operators أكثر من ذلك
+
+449
+00:32:07,930 --> 00:32:12,070
+إحنا خدنا الـ XOR، وخدنا الـ implication، وخدنا الـ
+
+450
+00:32:12,070 --> 00:32:17,050
+biconditional. فكل واحد منهم هناخده صيغة تمثله
+
+451
+00:32:17,050 --> 00:32:24,590
+عشان نتعامل معاه لاحقا. فهنبدأ بالـ XOR. XOR P XOR
+
+452
+00:32:24,590 --> 00:32:29,910
+Q equivalent to P conjunction Q كله conjunction مع
+
+453
+00:32:29,910 --> 00:32:35,450
+negation ب conjunction Q. تمام؟ أو في form ثاني، و
+
+454
+00:32:35,450 --> 00:32:38,470
+طبعا لاحظوا أن الواحد بتقدر تجيبه من الثاني بـ ... بده بس
+
+455
+00:32:38,470 --> 00:32:41,750
+شوية سلسلة عمليات بنقدر نجيبهم من بعض .. بنقدر
+
+456
+00:32:41,750 --> 00:32:45,970
+نجيبهم من بعض، ولاحقا بس تتعلموا الطريقة اللي جاية
+
+457
+00:32:45,970 --> 00:32:47,970
+هتصيروا بتقدروا تعملوها لحالكم .. يعني الـ .. الـ
+
+458
+00:32:47,970 --> 00:32:51,990
+.. أن كيف أجيب واحد من الثاني، إن واحد من الثاني
+
+459
+00:32:51,990 --> 00:32:55,110
+هتتعاملوا معاه إن هذا equivalent لهذا، بتكون ثبتوا
+
+460
+00:32:55,110 --> 00:32:58,370
+عملية إثبات أن هل اثنين دول equivalent لبعض أو لأ.
+
+461
+00:32:58,370 --> 00:33:02,410
+الثاني يمكن تكون أوضح شوية لإيه؟ لأن إحنا عادة ..
+
+462
+00:33:02,410 --> 00:33:09,170
+عادة بنعمل true امتى؟ true للـ X or لما واحدة منهم
+
+463
+00:33:09,170 --> 00:33:16,310
+تكون عكس الثانية. فلاحظوا واحدة عكس الثانية، أوأولى
+
+464
+00:33:16,310 --> 00:33:18,930
+الثانية مع عكس الأولى، يعني واحدة  مع العكس
+
+465
+00:33:18,930 --> 00:33:21,990
+الثانية، فيمكن أقرب إنها تنحفظ معاكم هذه الصورة
+
+466
+00:33:21,990 --> 00:33:29,210
+أسرع. فإذا P and negation Q or Q negation and
+
+467
+00:33:29,210 --> 00:33:29,890
+negation P
+
+468
+00:33:33,080 --> 00:33:39,220
+طيب الـ employees هي negation الأولى أو الثانية
+
+469
+00:33:39,220 --> 00:33:43,540
+negation الأولى أو الثانية، negation الأولى أو الثانية
+
+470
+00:33:43,540 --> 00:33:47,380
+على طول، يعني سهل لو مالهاش فورم واحد نستعمله خلال
+
+471
+00:33:47,380 --> 00:33:53,120
+الـ course اللي هي negation الأولى or الثانية. طيب
+
+472
+00:33:53,120 --> 00:33:56,060
+الـ biconditional، الـ biconditional اللي إحنا قلناه
+
+473
+00:33:56,060 --> 00:33:58,880
+قبلكم أن هي implication في الاتجاهين، بمعنى أن أنا
+
+474
+00:33:58,880 --> 00:34:06,000
+ممكن أقول أن هي employs q and q employs p. واحدة من
+
+475
+00:34:06,000 --> 00:34:09,620
+الثانية أو الاستنتاج اللي استنتجناه أيام ما
+
+476
+00:34:09,620 --> 00:34:14,840
+اتكلمنا عنها أن هي عكس الـ X or، لأن هذه واحدة امتى؟
+
+477
+00:34:14,840 --> 00:34:20,280
+إذا تشابه الـ propositions بتعطيني one، بعكس الـ X or.
+
+478
+00:34:20,280 --> 00:34:24,400
+الـ X or إذا اختلفوا بتعطيني one، صحيح. تذكروا دول، إذا
+
+479
+00:34:24,400 --> 00:34:31,160
+هذه الـ negation ده بالـ X or. تمام؟ for example، خلينا
+
+480
+00:34:31,160 --> 00:34:34,660
+ناخد example. طيب لما يكون في عندكم example، و
+
+481
+00:34:34,660 --> 00:34:37,540
+بتشتغلوا عليه بالشكل اللي إحنا جايين، عندنا هنا طبعا
+
+482
+00:34:37,540 --> 00:34:40,680
+الأسئلة هتكون هيك طبيعتها، المفروض إن تعملوا check
+
+483
+00:34:40,680 --> 00:34:46,300
+على الـ .. إذا كانوا equivalent ولا لأ، إذا كانوا
+
+484
+00:34:46,300 --> 00:34:49,700
+فعلا اثنين equivalent، أو تعملوا proof إن هما فعلا
+
+485
+00:34:49,700 --> 00:34:54,060
+equivalent لبعض. طيب بكون عطيكم two compound
+
+486
+00:34:54,060 --> 00:34:57,100
+propositions. هذه أول compound proposition، وهذه
+
+487
+00:34:57,100 --> 00:35:00,940
+الثانية، والمطلوب نثبت إن هم equivalent لبعض.
+
+488
+00:35:00,940 --> 00:35:08,060
+firstly بتطلعوا عليهم، اللي بتلاقوه في operators صعبة
+
+489
+00:35:08,060 --> 00:35:12,640
+الشيء اللي هو الـ operators الصعبة، عادة الـ XOR، الـ
+
+490
+00:35:12,640 --> 00:35:15,980
+implication، و الـ biconditional. دول دايما بيهمنّا
+
+491
+00:35:15,980 --> 00:35:18,930
+نفكّهم فوق في الأول، بيهمنّا نفكّهم في الأول لإنه ماقدرش
+
+492
+00:35:18,930 --> 00:35:22,970
+أتعامل معهم مع الـ rules اللي أخدناهم قبل شوية، لازم
+
+493
+00:35:22,970 --> 00:35:25,710
+نفكّهم بواحدة من القوانين بتاعتهم، كل واحد أخدنا له
+
+494
+00:35:25,710 --> 00:35:29,210
+قانون، قانون، قانون، بنفكّهم في الأول، وبعدين نبدا
+
+495
+00:35:29,210 --> 00:35:32,550
+نستعمل الـ rules بتاعتنا أو الـ laws بتاعتنا اللي
+
+496
+00:35:32,550 --> 00:35:35,490
+منها دي مرجن ودي مرجن والـ competitive والـ
+
+497
+00:35:35,490 --> 00:35:39,630
+associative والأمور دي كلها. ما نقدرش نستعملهم مباشرة
+
+498
+00:35:39,630 --> 00:35:44,050
+عليهم. فإذ لما نيجي نطلع على الـ proof بالشكل اللي
+
+499
+00:35:44,050 --> 00:35:47,170
+إحنا شايفين، وهذا مطلوب مننا. أول ما بتطلع، بتطلع على
+
+500
+00:35:47,170 --> 00:35:52,190
+الـ left hand side، آه، هذا واضح أنه complicated أكثر
+
+501
+00:35:52,190 --> 00:35:56,290
+من الثاني، معناه بشتغل على هذا. نبدا نفكّه، نحلّله
+
+502
+00:35:56,290 --> 00:35:59,510
+نحلّله ليه؟ لأن في عندكم XOR، في عندكم complication
+
+503
+00:35:59,510 --> 00:36:04,250
+وفي عندكم XOR. عادة هي بداية الحل، دورّوا على الـ
+
+504
+00:36:04,250 --> 00:36:09,050
+implication، فكّوها في الأول، وبعدين نشوف إيه بيصير
+
+505
+00:36:09,050 --> 00:36:12,070
+معناه خلينا نبدا نفكّها ونشوف إيه بيصير، معناها و
+
+506
+00:36:12,070 --> 00:36:14,830
+خلينا تتوارد لنا الأفكار إيه اللي لازم نعمله لاحقا.
+
+507
+00:36:14,830 --> 00:36:23,430
+تمام، فإذا firstly بفكّ هذا ولا هذا في الأول؟ الأكبر
+
+508
+00:36:23,430 --> 00:36:28,020
+هو الـ implication، هو الـ implication لإنه بيربط الـ co
+
+509
+00:36:28,020 --> 00:36:31,580
+باتنين مع بعض، فهذا الكبير يعتبر هذا الـ operator
+
+510
+00:36:31,580 --> 00:36:36,840
+الثاني الأكبر، كويس. فبنبدأ فيها، في الـ implication.
+
+511
+00:36:36,840 --> 00:36:40,260
+الـ implication قلنا إن هي negation الأولى and
+
+512
+00:36:40,260 --> 00:36:44,640
+الثانية، negation الأولى عفوا or، or الثانية
+
+513
+00:36:44,640 --> 00:36:48,920
+disjunction or الثانية. فإذا بتعامل مع هذه كلها كده
+
+514
+00:36:48,920 --> 00:36:53,770
+كأنها proposition أولى، افترض إنها كأنها K، وهذه
+
+515
+00:36:53,770 --> 00:36:59,390
+كأنها كده على بعض، في عندنا R زد، فبتبقى تصير كأنه
+
+516
+00:36:59,390 --> 00:37:07,090
+negation K disjunction زد. هذا حطّه مكانها، حطّه
+
+517
+00:37:07,090 --> 00:37:09,810
+الـ القصّ نزل زي ما هو، وده نزل زي ما هو، وخلصنا من
+
+518
+00:37:09,810 --> 00:37:15,370
+مين؟ من الـ implication.  هكذا خلصنا أول جزئية، بالظبط،
+
+519
+00:37:15,370 --> 00:37:19,250
+بعدين نبدا نشوف، ضبط هذه الجزئية عشان نفك اللي في
+
+520
+00:37:19,250 --> 00:37:23,030
+جوابها، تمام؟ عشان ما تتلخبطوش، بس ما تـ .. الأقواس
+
+521
+00:37:23,030 --> 00:37:25,630
+ده ما تلخـ .. ما تلخبطكمش، بتعاملوا معاها بالشكل
+
+522
+00:37:25,630 --> 00:37:28,110
+هذا، خلاص الـ implication هذا بيربط إيه؟ آه، بيربط
+
+523
+00:37:28,110 --> 00:37:30,150
+قوس، معناه تلقوا القوس هذا كله على بعض، ومن المفروض ما
+
+524
+00:37:30,150 --> 00:37:33,810
+تتحركوش ولا تفكّوه، عشان ما تلخبطوش حالكم، زي ما
+
+525
+00:37:33,810 --> 00:37:37,330
+هو بتنقلّوه تحت حسب القانون تبع الـ implication.
+
+526
+00:37:38,210 --> 00:37:41,370
+implication negation k، فالـ negation بتطلعوها برّا.
+
+527
+00:37:41,370 --> 00:37:44,630
+ما تفكروش تعملوا خطّين ثلاثة في بعض، أنتم لسه
+
+528
+00:37:44,630 --> 00:37:47,950
+بتبدأوا تتعلموا الـ derivations، ما تلخبطوش حالكم.
+
+529
+00:37:47,950 --> 00:37:50,390
+تعملوا خطّين تلاتة في بعض، عشان بتكونوا تختصروا.
+
+530
+00:37:50,390 --> 00:37:54,530
+هتلاقوا حالكم الـ negation وجعت معاكم في النص، الـ
+
+531
+00:37:54,530 --> 00:37:58,070
+and صارت or، أو الـ or صارت and، وأنتم مش داريين.
+
+532
+00:37:58,070 --> 00:38:01,070
+فطبعا مش هتصيروا لحالكم، هتلاقوا حالكم ضيعتوا حالكم.
+
+533
+00:38:01,070 --> 00:38:09,850
+تمام؟ كويس، فهي الـ implication الأولى، عملنا
+
+534
+00:38:09,850 --> 00:38:17,790
+negation الأولى، هي or الثانية. نمسك من الـ XOR، كان
+
+535
+00:38:17,790 --> 00:38:21,730
+فين اللي كان لها قانونين؟ هستعمل أول قانون منهم
+
+536
+00:38:21,730 --> 00:38:24,710
+اللي كان فيه اتنين and، وواحدة or.
+
+537
+00:38:29,020 --> 00:38:32,340
+والواحدة آخر، فدول أنتم بتكونوا تحفظوهم، يعني هم
+
+538
+00:38:32,340 --> 00:38:34,960
+تلاتة أربعة قوانين، دول بتكونوا تحفظوهم، الباقيين بتكونوا
+
+539
+00:38:34,960 --> 00:38:37,740
+فاهمينهم، الباقيين الـ rules اللي إحنا خدناهم في
+
+540
+00:38:37,740 --> 00:38:40,220
+الأول، الـ laws دول اللي في الأول. لأ، أنتم بتكونوا
+
+541
+00:38:40,220 --> 00:38:43,260
+فاهمينهم، competitive. خلاص، أنا فاهم التبادل
+
+542
+00:38:43,260 --> 00:38:47,000
+التبادلية، إذا كان نفس الشيء، نفس الـ operator، خلاص
+
+543
+00:38:47,000 --> 00:38:49,880
+بفهمه، هكذا. distribution، عارفين distribution؟ إحنا
+
+544
+00:38:49,880 --> 00:38:52,940
+عارفين إنه بوزّع الأرقام على بعض، لما يكون فيه
+
+545
+00:38:52,940 --> 00:38:55,420
+أقواس، خلاص نفس الفكرة بنعملها .. نفس الفكرة
+
+546
+00:38:55,420 --> 00:38:59,340
+بنعملها .. دول فهم .. فيه على إنكم على اللي
+
+547
+00:38:59,340 --> 00:39:01,640
+بدكم .. في التلاتة الأربعة دول، اللي هي بتاعة الـ
+
+548
+00:39:01,640 --> 00:39:04,930
+XOR، الـ implication، والـ biconditional .. مع إنّ الـ
+
+549
+00:39:04,930 --> 00:39:08,490
+biconditional مش محتاجة أصلا، لأن هي اللي كتبناها
+
+550
+00:39:08,490 --> 00:39:12,170
+إياها كانت بدلالة الـ implication، وبدلالة الـ XOR.
+
+551
+00:39:12,170 --> 00:39:14,870
+فأنتم هتحفظوا بس الاثنين، الـ XOR، والـ implication، و
+
+552
+00:39:14,870 --> 00:39:18,150
+تكونوا فاهمين إنّ الـ biconditional ما هي إلا
+
+553
+00:39:18,150 --> 00:39:24,770
+negation XOR أو implication في الاتجاهين بس ..
+
+554
+00:39:24,770 --> 00:39:32,670
+كويس. طيب وصلنا لهنا، ما بدناش نحفظ، إحنا متفقين، ما بدناش
+
+555
+00:39:32,670 --> 00:39:36,330
+نحفظ رياضيات، ما هي مش قصة حفظ، هذا واجد، بدي أجيب كده
+
+556
+00:39:36,330 --> 00:39:41,730
+وأصف الحالات، وأطلع أنا إيه؟ بدنا نفكّ، ونصل
+
+557
+00:39:41,730 --> 00:39:46,790
+هذه. طيب، عشان أفكّ وأصل هذه، بدي أجي أطلع كده
+
+558
+00:39:46,790 --> 00:39:52,030
+حلاجات، إن والله في عندي هنا P، وهنا في P، وهنا في P
+
+559
+00:39:52,030 --> 00:39:56,830
+لو بقدر أجمّعهم مع بعض، بحيث إن أحصل على tautology أو
+
+560
+00:39:56,830 --> 00:40:01,310
+contradiction، أختصرهم. ليه؟ لأنّ دول tautology والـ
+
+561
+00:40:01,310 --> 00:40:03,930
+contradiction إيه بيعطوني؟ بيعطوني true و false. الـ
+
+562
+00:40:03,930 --> 00:40:08,190
+true و false دول أكيد هيختزلوا، هيشي. طيب كيف أعمل
+
+563
+00:40:08,190 --> 00:40:13,510
+الكلام هذا؟ firstly أنا ما أقدرش أدخل الأقواس دول كـ
+
+564
+00:40:13,510 --> 00:40:20,030
+competitive. ليه؟ لأنّ هذه and وهذه or، ما أقدرش أبدّلهم
+
+565
+00:40:20,030 --> 00:40:24,540
+مع بعض، آه. بس لحظة، استنوا. فيه negation، طب الـ negation
+
+566
+00:40:24,540 --> 00:40:29,380
+اللي دخلناها جوا الأقواس، هترجّع هذه لإيه؟ تمام.
+
+567
+00:40:29,380 --> 00:40:33,680
+فلاحظوا التفكير، إن أنا بدي أخفّف الشغل اللي عندي
+
+568
+00:40:33,680 --> 00:40:37,780
+عشان أخفّفه، فيه negation. بعد ما دخل الـ negation هذه
+
+569
+00:40:37,780 --> 00:40:40,820
+صار عند كل اثنين دول بيشابهوا بعض، صار في إمكاني أن
+
+570
+00:40:40,820 --> 00:40:45,880
+أحط واحدة مكان الثانية. في عملية associative، الـ
+
+571
+00:40:45,880 --> 00:40:48,260
+associative هذه بعدين هنستعملها لو جت كمان شوية
+
+572
+00:40:48,260 --> 00:40:52,880
+associative مع competitive عشان ندخل الـ P على
+
+573
+00:40:52,880 --> 00:40:55,020
+الأقواس تانية. خلونا ناخدها واحدة واحدة. في عندنا
+
+574
+00:40:55,020 --> 00:40:58,440
+مبدئيا اتفاجأنا إن فيه عندنا negation هذه، بنستعملها
+
+575
+00:40:58,440 --> 00:41:04,160
+دي مورغان، هي دي مورغان، دي مورغان. هندخلها هنا، يصير
+
+576
+00:41:04,160 --> 00:41:12,640
+negation P or Q، هي negation P or Q، تمام. هي كده
+
+577
+00:41:12,640 --> 00:41:16,420
+خلصنا عملية دي مورغان. هل وجد الجزء الثاني هنا؟ صارت
+
+578
+00:41:16,420 --> 00:41:23,240
+إيه؟ or or، بقدر أستعمل الـ associative، الأقواس أحطها
+
+579
+00:41:23,240 --> 00:41:27,140
+زي ما بدي، ما دام الاثنين هيوم or، or، الاثنين or، أنا
+
+580
+00:41:27,140 --> 00:41:35,080
+كل .. هتعامل معاها .. هتعامل معايا قوس هذا القوس
+
+581
+00:41:35,080 --> 00:41:44,200
+هذا مع .. مع القوس هذا. اعتبروها إن كلها دي ضبط. تمام؟
+
+582
+00:41:44,200 --> 00:41:47,100
+عشان ذي بقول لكم خلي عيونكم كويس واضحة تماما على
+
+583
+00:41:47,100 --> 00:41:50,640
+الأقواس، الأقواس. وقعوا يضيعوا منكم قوس، هتلقى تحت
+
+584
+00:41:50,640 --> 00:41:55,240
+عيونكم يروح قوس ما تعدّوش، كويس. هتلاقوا حالكم
+
+585
+00:41:55,240 --> 00:41:58,180
+صرتوا في expression مختلف تماما عن إن أنتم
+
+586
+00:41:58,180 --> 00:42:02,140
+بتشتغلوا عليه. تمام. لو تعاملنا مع هذه، فإذا
+
+587
+00:42:02,140 --> 00:42:05,300
+الأقواس هذه، ممكن أغيّر فيها زي ما بدي، أقول لكم
+
+588
+00:42:05,300 --> 00:42:11,480
+ممكن أشيلها، لو شلناها حاجة هتش؟ مش حاجة هتش. ليه؟
+
+589
+00:42:11,480 --> 00:42:17,140
+لأنه or or نفس الـ operator، فمافيش مشكلة. بدون نفس الـ
+
+590
+00:42:17,140 --> 00:42:21,640
+operator ما فيش أشكال. تمام. هي غيرنا، عملنا اللي
+
+591
+00:42:21,640 --> 00:42:25,500
+بدنا إياه. بعد هيك الـ competitive، التبديل بمعنى أن مين
+
+592
+00:42:25,500 --> 00:42:35,780
+قبل الثانية، مش هتفرق. negation P or Q هي نفسها Q or
+
+593
+00:42:35,780 --> 00:42:39,040
+negation P. يعني مين قبل مين مش هتفرق كتير.
+
+594
+00:42:39,040 --> 00:42:46,400
+competitive. كويس. هذه الجزئية هتخليني أحط الـ Q هنا، و
+
+595
+00:42:46,400 --> 00:42:50,620
+الـ P هنا. ليه؟ أجيبها للقوس لأن محتاج أعمل operation.
+
+596
+00:42:50,620 --> 00:42:55,260
+لأن أنا أصلا كل شغل أول ما بدأت أفكر من هنا، فكرت
+
+597
+00:42:55,260 --> 00:43:00,540
+إن كل الـ terms فيها P، طب الـ P هذه كلها لو قدرنا
+
+598
+00:43:00,540 --> 00:43:04,240
+بطريقة أو بأخرى نختزلها بعامل مشترك، طب هنا ما فيش
+
+599
+00:43:04,240 --> 00:43:08,040
+حاجة اسمها عامل مشترك. فعشان أعملها محتاج أدخلها جوا
+
+600
+00:43:08,040 --> 00:43:10,700
+على القوس. طب هل في إمكانية؟ آه في إمكانية. وجدنا إنّ
+
+601
+00:43:10,700 --> 00:43:15,020
+دي مورغان هتنفع، هل الإمكانية بعدين وجدنا لما صاروا
+
+602
+00:43:15,020 --> 00:43:19,000
+اثنين زي بعض، آه، صار في إمكانية. أو أوضح، وبينت أنا
+
+603
+00:43:19,000 --> 00:43:23,240
+بالنسبة لي كده بينت إن آه خلاص الـ P دخلت، خلصنا الـ P
+
+604
+00:43:23,240 --> 00:43:26,600
+الـ negation P هذه اللي برّا داخلة، خلاص ما فيش مشكلة
+
+605
+00:43:26,600 --> 00:43:35,200
+باين إن هي خلاص حتى دخلت الأقواس، فهي
+
+606
+00:43:35,200 --> 00:43:40,200
+الشغل، الجزء اللي تبعنا كان كده بالشكل هذا، عكسنا
+
+607
+00:43:42,560 --> 00:43:46,440
+لحظة، أخدنا كل واحدة منهم لحالها، competitive يعمل لنا
+
+608
+00:43:46,440 --> 00:43:51,240
+competitive. بعدين هنعمل الـ .. هذه، خلصنا كل اللي
+
+609
+00:43:51,240 --> 00:43:55,940
+هنعمله. associative بيعني إن القوس هذا وإحنا
+
+610
+00:43:55
+
+667
+00:49:00,260 --> 00:49:03,120
+proposition لو كان ال proposition false فالنتيجة
+
+668
+00:49:03,120 --> 00:49:07,720
+هتكون false لو كان ال proposition true هتكون true
+
+669
+00:49:07,720 --> 00:49:12,320
+لو قلنا ال negation P هذه بتساوي true معناه ذلك
+
+670
+00:49:12,320 --> 00:49:13,460
+أنا بتكلم عن true
+
+671
+00:49:16,130 --> 00:49:20,810
+or true هتكون true طيب لو كانت false .. false مع
+
+672
+00:49:20,810 --> 00:49:25,310
+false هتكون false فإذا قيمتها .. قيمة الناتج هي
+
+673
+00:49:25,310 --> 00:49:28,710
+نفس قيمة مين؟ ال proposition نفسه ال proposition
+
+674
+00:49:28,710 --> 00:49:32,790
+أنا إيش عندي اسمه؟ اسمه negation P فإذا بختزل
+
+675
+00:49:32,790 --> 00:49:36,830
+التنتين negation P هدول ب negation P واحدة بس
+
+676
+00:49:36,830 --> 00:49:42,830
+negation P واحدة فأصبح عندي هاي negation P واحدة
+
+677
+00:49:42,830 --> 00:49:46,590
+عندنا الأقوسة ده بقدر أفكها إذا فكيناها عيدوا
+
+678
+00:49:46,590 --> 00:49:49,170
+ترتيبهم زي ما بدكوا، ليش نقدر نعيد ترتيبهم زي ما
+
+679
+00:49:49,170 --> 00:49:53,590
+بدنا؟ لأنه في عندكوا or مع or ال priority هي هي،
+
+680
+00:49:53,590 --> 00:49:56,890
+مين جاب المين مش هي .. مش هيفرق معانا، هتكون
+
+681
+00:49:56,890 --> 00:50:03,470
+عندكوا competitive في شغلكوا، مين جاب المين، في
+
+682
+00:50:03,470 --> 00:50:06,830
+الآخر بترجعوا لمين، لـ ال expression اللي أساسا
+
+683
+00:50:06,830 --> 00:50:11,110
+مطلوب منكوا من الأول، تعملوله prove، تشوفوا كيف
+
+684
+00:50:11,110 --> 00:50:14,270
+كان ترتيبه، بترتبوا زي ما بدكوا، فإذا لو أطلعنا
+
+685
+00:50:15,240 --> 00:50:20,160
+هنقش اللي بديها بالظبط، بدي negation هي تشوفوا
+
+686
+00:50:20,160 --> 00:50:25,080
+اللي هنا كان هذا
+
+687
+00:50:25,080 --> 00:50:34,540
+negation P or Q or negation R فبنعيد من عندنا
+
+688
+00:50:34,540 --> 00:50:41,340
+النقطة اللي كنا وصلناها بنعيد نرتب شغلنا زي ما
+
+689
+00:50:41,340 --> 00:50:41,920
+احنا بدنا
+
+690
+00:50:46,680 --> 00:50:50,040
+كويس فهنا هنا فكناها نرجع بنرتبها زي ما احنا بنحط
+
+691
+00:50:50,040 --> 00:50:54,500
+هذه في الأول هذه في الثانية و بننزل هذه زي ما هي
+
+692
+00:50:54,500 --> 00:51:00,040
+لأن بينهم نفس ال operator تمام نفس ال
+
+693
+00:51:00,040 --> 00:51:03,400
+operator هو اللي بينهم فبقدر مباشرة اقول انه
+
+694
+00:51:03,400 --> 00:51:06,680
+الترتيب مش هيفرق معانا الترتيب مش هيفرق معانا و
+
+695
+00:51:06,680 --> 00:51:11,780
+نكون وصلنا لإثبات اللي احنا محتاجينه في الشغل طبعا
+
+696
+00:51:11,780 --> 00:51:17,560
+و بنكون وصلنا زي ما قلنا للي احنا بدنا إياه مع نهاية
+
+697
+00:51:17,560 --> 00:51:23,140
+ال example تبعنا بنكون عرفنا ال atomic .. ال
+
+698
+00:51:23,140 --> 00:51:26,420
+.. ال .. ال atomic propositions قلنا ان احنا
+
+699
+00:51:26,420 --> 00:51:30,180
+بنسميها بال .. بال .. بال lowercase letters او بال
+
+700
+00:51:30,180 --> 00:51:34,320
+small letters PQR بنعبر عليهم بهالشكل فهذه
+
+701
+00:51:34,320 --> 00:51:38,940
+عبارة عن propositions ال boolean algebra operators
+
+702
+00:51:38,940 --> 00:51:44,360
+أخدناها negation conjunction disjunction XOR ال
+
+703
+00:51:44,360 --> 00:51:47,980
+implication و biconditional او اللي قلنا عبارة
+
+704
+00:51:47,980 --> 00:51:51,410
+عنه ب if and only if اتكلمنا عن ال compound
+
+705
+00:51:51,410 --> 00:51:56,270
+propositions لما بتكلم عن compound propositions أنا
+
+706
+00:51:56,270 --> 00:52:00,710
+بتكلم عن expression لمجموعة propositions مرتبطة
+
+707
+00:52:00,710 --> 00:52:05,470
+ب operators مربوطة بمجموعة operators زي الشكل اللي
+
+708
+00:52:05,470 --> 00:52:08,970
+احنا شايفينه هنا كويس ال equivalence برضه اتكلمنا
+
+709
+00:52:08,970 --> 00:52:11,810
+عن ال equivalence وكيف ممكن استعمل ال equivalence
+
+710
+00:52:11,810 --> 00:52:16,730
+لإثبات اي expression معين فممكن اقول في حالة زي
+
+711
+00:52:16,730 --> 00:52:19,070
+الحلقة اللي عندنا وهذا الرمز أخدناها علامة
+
+712
+00:52:19,070 --> 00:52:22,910
+equivalence و أتكلمنا عن أمثلة منهم و قلنا كيف ممكن
+
+713
+00:52:22,910 --> 00:52:28,390
+أثبت ال equivalence اتكلمنا عن ال truth table ممكن
+
+714
+00:52:28,390 --> 00:52:33,430
+نستخدم ال truth tables أساسا أجيب ال truth value
+
+715
+00:52:33,430 --> 00:52:38,030
+لكل compound proposition منهم و نقارنهم مع بعض
+
+716
+00:52:38,030 --> 00:52:41,330
+فلازم كل element في ال row يساوي ال element في نفس
+
+717
+00:52:41,330 --> 00:52:44,350
+ال row لل expression الثاني إذا كان الكلام ده
+
+718
+00:52:44,350 --> 00:52:47,650
+ينطبق على جميع ال rows بقدر أقول ان ال two
+
+719
+00:52:47,650 --> 00:52:51,320
+compound propositions are equivalent كل واحدة منها
+
+720
+00:52:51,320 --> 00:52:55,400
+equivalent للثانية او symbolic derivations زي ال
+
+721
+00:52:55,400 --> 00:53:00,680
+example اللي أخدناه اللي هو آخر example كويسة
+
+722
+00:53:00,680 --> 00:53:03,520
+المرة الجاية إن شاء الله هنتكلم عن ال predicate
+
+723
+00:53:03,520 --> 00:53:07,540
+logic و هنتكلم نقول ان هذه ليست proposition هي
+
+724
+00:53:07,540 --> 00:53:12,140
+propositional function propositional function عشان
+
+725
+00:53:12,140 --> 00:53:16,140
+نسيبها لكم للمرة الجاية بتوضيح خفيف احنا أحيانا
+
+726
+00:53:16,140 --> 00:53:20,860
+نضطر نعبر عن مجموعة of propositions مجموعة كبيرة
+
+727
+00:53:20,860 --> 00:53:23,600
+ممكن تكون من ال propositions بس بتعبّر عنها ب
+
+728
+00:53:23,600 --> 00:53:28,620
+expression واحد فمعنى ذلك بستعمل variables  مشابه
+
+729
+00:53:28,620 --> 00:53:32,120
+تمامًا لفكرة ال function لما يكون في عندكوا
+
+730
+00:53:32,120 --> 00:53:36,620
+function و بحط لها ال variable x فال variable x ده
+
+731
+00:53:36,620 --> 00:53:42,200
+ممكن ياخد قيم متعددة أو مختلفة بناء على القيم
+
+732
+00:53:42,200 --> 00:53:46,580
+المختلفة كإن بقول إنه عند مجموعة propositions إيش
+
+733
+00:53:46,580 --> 00:53:53,060
+يعني؟ يعني لو قلنا ال x هذه جاية من من ست أو
+
+734
+00:53:53,060 --> 00:53:57,740
+مجموعة واحد اتنين تلاتة بيكفي نفترض انه تلاتة طبعا
+
+735
+00:53:57,740 --> 00:54:05,680
+تلاتة متواضعة جدا ككست عبارة عن if one and if two
+
+736
+00:54:05,680 --> 00:54:11,000
+and if three طبعا لو أكثر معناته هناخد وسعة كتير
+
+737
+00:54:11,000 --> 00:54:17,660
+لأ احنا كدا ممكن نكتبها if of x ونعرف لاحقا الـ
+
+738
+00:54:17,660 --> 00:54:22,220
+universe of discourse هنسميها أو فضاء العينة هنا
+
+739
+00:54:22,220 --> 00:54:25,420
+بنسيب الموضوع اللي predicated هذا نخليه للمرة
+
+740
+00:54:25,420 --> 00:54:29,920
+الجاية إن شاء الله بنشرحه بالتفصيل و بننهي جزئية
+
+741
+00:54:29,920 --> 00:54:33,260
+ال equivalence او ال propositional equivalence
+
+742
+00:54:33,260 --> 00:54:36,180
+بتاعتنا يعطيكم العافية و بارك الله فيكم للمرة
+
+743
+00:54:36,180 --> 00:54:38,560
+الجاية إن شاء الله تعالى و السلام عليكم و رحمة
+
+744
+00:54:38,560 --> 00:54:45,260
+الله تعالى و بركاته و بدنا نعرف هنا أول التعريف
+
+745
+00:54:45,260 --> 00:54:45,620
+تبعنا
+
+746
+00:55:04,220 --> 00:55:08,160
+عشان تكون even المفروض ان هي تساوي اتنين في رقم
+
+747
+00:55:08,160 --> 00:55:14,950
+ثاني بمعنى آخر بتقسم على اتنين بمعنى آخر ان هي رقم
+
+748
+00:55:14,950 --> 00:55:18,530
+بيقسم على اتنين طيب هنتأكد من الكلام ده هل هو فعلا
+
+749
+00:55:18,530 --> 00:55:22,630
+في عنده رقم بيقسم على اتنين بيمشي الكلام ده كيف
+
+750
+00:55:22,630 --> 00:55:29,170
+ممكن نعبر عنها رياضيا فهقول مدام even كل القيم كل
+
+751
+00:55:29,170 --> 00:55:34,430
+x اللي ممكن نعبر عنها ان هي even المفروض تحقق لنا
+
+752
+00:55:34,430 --> 00:55:41,170
+الشغل التالي ان هي even by conditional there exist
+
+753
+00:55:41,170 --> 00:55:49,390
+y such that x equal to 2y معناته هي even إذا كان
+
+754
+00:55:49,390 --> 00:55:57,750
+موجود لكل قيمة ل x هتكون even امتى إذا كانت يوجد y
+
+755
+00:55:57,750 --> 00:56:04,230
+نص x هاي معناها فمعناه ذاك ضامن إن x هي تعتبر ضعف
+
+756
+00:56:04,230 --> 00:56:09,190
+أي رقم ثاني ضعف some number ضعف أي رقم ثاني مدام
+
+757
+00:56:09,190 --> 00:56:12,890
+ضعف أي رقم ثاني بتقبل القسمة على اتنين مدام قبلت القسمة
+
+758
+00:56:12,890 --> 00:56:17,810
+على اتنين أكيد even .. أكيد even .. أكيد even زوجي ..
+
+759
+00:56:17,810 --> 00:56:21,110
+رقم زوجي .. أكيد هتكون رقم زوجي .. كمان مرة for
+
+760
+00:56:21,110 --> 00:56:29,430
+all x لكل قيم x ال .. even .. x is even if and
+
+761
+00:56:29,430 --> 00:56:32,510
+only if مش هاد ال if and only if .. by conditional
+
+762
+00:56:32,510 --> 00:56:37,610
+.. هيها لاحظوا هنترجمها هيها a number x is even
+
+763
+00:56:37,610 --> 00:56:43,830
+فإذا for all x a number x is even هيها if and only
+
+764
+00:56:43,830 --> 00:56:50,770
+if it's equal to two times some other number some
+
+765
+00:56:50,770 --> 00:56:53,010
+other number معناته بدي أعرف إيش ال other number
+
+766
+00:56:53,010 --> 00:56:57,590
+هذا there exists y y other number عن x إيش العلاقة
+
+767
+00:56:57,590 --> 00:57:02,210
+بينهم two times معناته ال x هذه تساوي two times of
+
+768
+00:57:02,210 --> 00:57:06,050
+ال other number اللي عرفناها إنه موجود رقم ثاني
+
+769
+00:57:06,050 --> 00:57:11,840
+يمثل نص x موجود رقم ثاني يمثل نص x ففي الحالة دي
+
+770
+00:57:11,840 --> 00:57:20,660
+بنقول إنه فعلا الرقم هذا even الرقم even طيب آخر
+
+771
+00:57:20,660 --> 00:57:27,760
+مثال a number is prime P of X أنت بيكون فعلا prime
+
+772
+00:57:27,760 --> 00:57:31,280
+if and only if it's greater than one لازم يكون
+
+773
+00:57:31,280 --> 00:57:34,180
+أكبر من واحد ما بقدرش أقول إن الواحد هو prime إن عارف
+
+774
+00:57:34,180 --> 00:57:36,380
+أحسس إن هو prime و خلاص و يدخل معناه في التاريخ
+
+775
+00:57:36,380 --> 00:57:40,080
+لازم يكون أكبر من ال one and it's not the
+
+776
+00:57:40,080 --> 00:57:47,260
+product of two non unity numbers معناته ما بقدرش أجيب
+
+777
+00:57:47,260 --> 00:57:51,640
+محصلته من ضرب رقمين ما بقدرش أجيبه من حاصل ضرب رقمين
+
+778
+00:57:51,640 --> 00:57:54,560
+و لازم نحدد هنا إن الرقمين هدول ما يكونش فيهم
+
+779
+00:57:54,560 --> 00:57:55,040
+الواحد
+
+780
+00:57:57,630 --> 00:58:03,090
+لأن سبعة prime .. prime صح؟ بس بقدر أقول إن هو
+
+781
+00:58:03,090 --> 00:58:07,250
+سبعة في واحد صحيح؟
+
+782
+00:58:07,250 --> 00:58:10,030
+أنتم فاهمين إن هو .. ما بتنضربش هذه، بس ال computer
+
+783
+00:58:10,030 --> 00:58:13,010
+ما بيفهمش، الرياضيات ما بتفهمش، لازم تكون ال expression
+
+784
+00:58:13,010 --> 00:58:16,230
+تبعكم واضح وشامل، عشان هيك لازم نحدد إن هو
+
+785
+00:58:16,230 --> 00:58:23,310
+مايكونش فيهم الواحد، مايكونش فيهم الواحد خلاص
+
+786
+00:58:23,310 --> 00:58:26,650
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+787
+00:58:26,650 --> 00:58:32,770
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+788
+00:58:32,770 --> 00:58:36,050
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+789
+00:58:36,050 --> 00:58:36,190
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+790
+00:58:36,190 --> 00:58:37,650
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+791
+00:58:37,650 --> 00:58:39,090
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+792
+00:58:39,090 --> 00:58:39,810
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+793
+00:58:39,810 --> 00:58:41,850
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+794
+00:58:41,850 --> 00:58:45,550
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+795
+00:58:45,550 --> 00:58:47,510
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+796
+00:58:47,510 --> 00:58:50,300
+فيهم الواحد مايكونش في x is prime فهي حققت الـ
+
+797
+00:58:50,300 --> 00:58:54,180
+predicate طيب عشان أحققها فعلا امتى بتصير الكلمة
+
+798
+00:58:54,180 --> 00:58:59,180
+if and only if نبدأ نمسكهم شوية شوية و نفتح الأقواس
+
+799
+00:58:59,180 --> 00:59:05,660
+ساعتنا و لاحظوا انه هنا if and only if تمام
+
+800
+00:59:05,660 --> 00:59:10,320
+لاحظوا يعطينا condition يعطينا الثاني يعطينا
+
+801
+00:59:10,320 --> 00:59:14,280
+الثالث في three conditions حط لنا معناته بدنا
+
+802
+00:59:14,280 --> 00:59:18,990
+نربطهم ب ands فتحنا ال course تبعنا هي ال cause
+
+803
+00:59:18,990 --> 00:59:23,050
+تبعنا وهي هنعمل and and and نشوف أشياء مجموعة
+
+804
+00:59:23,050 --> 00:59:25,610
+القيم ال .. ال .. ال .. ال exceptions اللي أعطانا
+
+805
+00:59:25,610 --> 00:59:30,770
+إياها firstly greater than one اه x أكبر من واحد
+
+806
+00:59:30,770 --> 00:59:38,570
+and it's not the product اه هو مش جاي من مجموع
+
+807
+00:59:38,570 --> 00:59:47,170
+ضرب رقمين يعني لا يوجد is not لا يوجد رقمين
+
+808
+00:59:50,300 --> 00:59:57,200
+x حاصل ضربهم بس بدنا نحدد هنا and y ليست واحد و z
+
+809
+00:59:57,200 --> 01:00:01,440
+ليست واحد عشان ما يروحش يفكر لأن السبعة ممكن تيجي
+
+810
+01:00:01,440 --> 01:00:06,420
+سبعة في واحد عشان ما ال computer و أنت بتعمل له
+
+811
+01:00:06,420 --> 01:00:10,300
+code بال expression هذا ما يروحش يعتبر ان هي هذه
+
+812
+01:00:10,300 --> 01:00:14,520
+واحد و هي حاصل ضرب رقمين  بمشكلة لا بدنا نقوله ان
+
+813
+01:00:14,520 --> 01:00:20,580
+لأ  دير بالك الواحد الـ y لازم لا تساوي واحد and z لا
+
+814
+01:00:20,580 --> 01:00:27,840
+تساوي واحد طبعا فلحظة صار بنقدر من الجملة إذا عندنا
+
+815
+01:00:27,840 --> 01:00:33,380
+تعريف لمجموعة معينة من ال numbers بنقدر نعرف منها
+
+816
+01:00:33,380 --> 01:00:37,680
+إيش ال expression تبعنا أو بنقدر نكتب ال
+
+817
+01:00:37,680 --> 01:00:41,860
+expression الرياضي تبعنا ارجعوا في البيت هتلاقوا
+
+818
+01:00:41,860 --> 01:00:45,690
+إن فعلا إن مسكناهم كلمة كلمة واحدة واحدة هتركبوهم
+
+819
+01:00:45,690 --> 01:00:50,930
+وراء بعض، هتركبوهم وراء بعض، تمام؟ هيك احنا نتخلص و
+
+820
+01:00:50,930 --> 01:00:56,530
+نخلصنا، كل عام بخير، ال .. طبعا ال .. ال homework
+
+821
+01:00:56,530 --> 01:01:01,450
+مش هتسلمونه إياه  لليوم الأحد القادم، هيكون عيد، فبيضل للي
+
+822
+01:01:01,450 --> 01:01:04,470
+بعده إن شاء الله تعالى، للي بعده بإذن الله تعالى،
+
+823
+01:01:04,470 --> 01:01:05,010
+يطيب لكم العافية
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8ee52621e9a114ad1857844872dea9032afa6e72
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_postprocess.srt
@@ -0,0 +1,3292 @@
+1
+00:00:20,690 --> 00:00:23,010
+بسم الله الرحمن الرحيم أُصل أتواصلهم على أشرف
+
+2
+00:00:23,010 --> 00:00:25,170
+الأنبياء والمسلمين سيدنا محمد وعلى أقلي هو صاحبي
+
+3
+00:00:25,170 --> 00:00:28,050
+أجمالي بنبدأ اليوم ان شاء الله الأسبوع التاني في
+
+4
+00:00:28,050 --> 00:00:31,510
+ال course الأسبوع الأول كنا أخدنا introduction في
+
+5
+00:00:31,510 --> 00:00:33,930
+أول محاضرة أخدنا في الجزء التاني مجموعة ال
+
+6
+00:00:33,930 --> 00:00:36,870
+operators اتكلمنا عن ال propositions بالصفة العامة
+
+7
+00:00:36,870 --> 00:00:40,110
+و بعدين اتكلمنا عن مجموعة operators و أخدنا كيف
+
+8
+00:00:40,110 --> 00:00:44,500
+تشتغل ال operators هذهيمكن ال .. هنا بنلخص مجموعة
+
+9
+00:00:44,500 --> 00:00:47,220
+ال operators اللي اتكلمنا عنها سابقا اتكلمنا عن ال
+
+10
+00:00:47,220 --> 00:00:50,160
+negation اتكلمنا عن ال conjunction اتكلمنا عن ال
+
+11
+00:00:50,160 --> 00:00:53,240
+dis على ال disjunction اتكلمنا عن ال XOR و ال
+
+12
+00:00:53,240 --> 00:00:56,980
+implication و ال biconditional و ال biconditional
+
+13
+00:00:56,980 --> 00:01:02,440
+فاليوم بنكمل بسمع جزئية هيك سريعة عن ال bits and
+
+14
+00:01:02,440 --> 00:01:05,680
+bit operations و بعدين بننجل لل equivalence و هي
+
+15
+00:01:05,680 --> 00:01:07,460
+الجزء اللي .. اللي .. اللي اهم هيكون اليوم في
+
+16
+00:01:07,460 --> 00:01:11,720
+محاضرتنا اللي هيال propositional equivalence في
+
+17
+00:01:11,720 --> 00:01:15,100
+شغلنا فخلينا اليوم نبدأ بسريع هيك على ال bits and
+
+18
+00:01:15,100 --> 00:01:19,760
+bit operations ال bit احنا التعامل اللي كله هيكون
+
+19
+00:01:19,760 --> 00:01:22,740
+مع ال binary مجموعة bits هتكون binary فbinary
+
+20
+00:01:22,740 --> 00:01:28,300
+بتكلم عن ال PS2بمعنى انه كل bit بقدر امثلها two
+
+21
+00:01:28,300 --> 00:01:32,560
+elements اللي هم ال zero و ال one فعليا احنا بنقدر
+
+22
+00:01:32,560 --> 00:01:35,980
+.. يعني ال binary هذه بتمثل .. بتعبرنا عن ال logic
+
+23
+00:01:35,980 --> 00:01:39,280
+ليش؟ بتعبرنا عن ال logic لإن ال zero represents
+
+24
+00:01:39,280 --> 00:01:43,500
+false ال one represents true فانا كأني بتعامل
+
+25
+00:01:43,500 --> 00:01:47,340
+معاها على أساس ان هي false true true false أو
+
+26
+00:01:47,340 --> 00:01:52,160
+false true طيب هذه مناضرة تماما للعمليات الحسابية
+
+27
+00:01:52,160 --> 00:01:56,260
+اللي كنتوا بتشتغلوها زمان الجامعةوالضرب ففعليا ال
+
+28
+00:01:56,260 --> 00:02:00,960
+or هي مقابلة للجمع وال and مقابلة لمين لعملية
+
+29
+00:02:00,960 --> 00:02:06,840
+الضرب طيب ال bit strings ال bit strings هي مجموعة
+
+30
+00:02:06,840 --> 00:02:11,260
+bits متسلسلة حوالين بعضها بحيث ان هي معطينا series
+
+31
+00:02:11,260 --> 00:02:17,500
+معينة او sequence معطينا سلسلة من ال bits او ارقام
+
+32
+00:02:17,500 --> 00:02:23,330
+متعاقبة sequenceof n و n لازم تكون اكبر من صفر
+
+33
+00:02:23,330 --> 00:02:27,690
+اكبر من صفر اكبر او تساوي صفر بحيث ان يكون فعلا
+
+34
+00:02:27,690 --> 00:02:31,070
+فينا sequence اذا كانت صفر فال sequence هذا empty
+
+35
+00:02:31,070 --> 00:02:34,330
+sequence بمعنى او ال string empty بمعنى string
+
+36
+00:02:34,330 --> 00:02:37,730
+فاضي زي لما كنا .. هناخدها لحظة طبعا لما نتكلم عن
+
+37
+00:02:37,730 --> 00:02:43,600
+المجموعات الفارغة او المجموعات الخالية المهمفي
+
+38
+00:02:43,600 --> 00:02:46,320
+عندنا sequence، في عندنا مجموعة bits، ال bits هذه
+
+39
+00:02:46,320 --> 00:02:52,060
+تمثل لنا sequence معين أو string معين، ال string
+
+40
+00:02:52,060 --> 00:02:57,140
+هذا هنستخدمه عادة كمجموعة bits متقاربة أو متجاورة
+
+41
+00:02:57,140 --> 00:03:01,460
+مع بعض، المتجاورة هذه بنبدأ دايما من اليمينبنبدأ
+
+42
+00:03:01,460 --> 00:03:04,120
+من اليمين يعني لل sequence اللي موجود قدامنا هنا
+
+43
+00:03:04,120 --> 00:03:07,000
+اللي هو one zero zero one one zero one zero one
+
+44
+00:03:07,000 --> 00:03:12,280
+zero اول element او bit فيه هي ال one فانا بتطلع
+
+45
+00:03:12,280 --> 00:03:17,220
+من الشمال لليمين وفعلا هي ال most significant bit
+
+46
+00:03:17,220 --> 00:03:21,560
+هي ال bit الاكبر قيمة فيهم ال bit الاكبر قيمة فيهم
+
+47
+00:03:21,560 --> 00:03:25,510
+في ال decimal system نفس الكلام موجود احناممكن
+
+48
+00:03:25,510 --> 00:03:29,070
+استعمل الرقم خمسة الرقم خمسة هذا وين الخانة تبعته
+
+49
+00:03:29,070 --> 00:03:34,150
+بيعطيني ال significant تبعته فلما بتكلم عن خمسة
+
+50
+00:03:34,150 --> 00:03:37,350
+بهذا
+
+51
+00:03:37,350 --> 00:03:41,310
+الشكل مثلا في خمسة وستين هي الخمسة هنا تمثل أحد
+
+52
+00:03:41,310 --> 00:03:45,830
+فالخانة بتاعتها الأحد طيب لو الخمسة هنا لأ موجودة
+
+53
+00:03:45,830 --> 00:03:50,170
+في العشرات لأ القيمة بتاعتها صارت أعلى بمعنى أنه
+
+54
+00:03:50,170 --> 00:03:55,270
+لو اتغيرت التغير كبير هيصيرفهنا نفس الكلام ال most
+
+55
+00:03:55,270 --> 00:03:58,810
+significant هي ال bit اللي جاية على ناحية اليمين و
+
+56
+00:03:58,810 --> 00:04:01,810
+عشان نوضح الموضوع هذا انتوا برضه كنتوا تعملوا
+
+57
+00:04:01,810 --> 00:04:03,850
+conversion او كنتوا تعملوا تحويل من system ل
+
+58
+00:04:03,850 --> 00:04:07,690
+system من binary ل decimal و من decimal ل .. ل hex
+
+59
+00:04:07,690 --> 00:04:11,130
+أو من hex كنتوا تشتغلوها كتير فلو قلنا اي .. اي ..
+
+60
+00:04:12,230 --> 00:04:16,650
+Example بالشكل هذا عشان نشعر من وين تليجي ال
+
+61
+00:04:16,650 --> 00:04:19,170
+significant بتبعتنا ال significant بنبدأها دايما
+
+62
+00:04:19,170 --> 00:04:22,790
+من اليمين هي الأقل significant ممكن انا بتعامل هنا
+
+63
+00:04:22,790 --> 00:04:28,850
+ان كل pet لها قيمتين اما zero او one فانا بتعامل
+
+64
+00:04:28,850 --> 00:04:34,720
+على ال path two فهي two to the power zero2 to the
+
+65
+00:04:34,720 --> 00:04:38,300
+power of 1 2 to the power of 2 2 to the power of 3
+
+66
+00:04:38,300 --> 00:04:42,780
+2 to the power of .. و هكذا بقارن كل واحدة في أي
+
+67
+00:04:42,780 --> 00:04:45,840
+خانة وهذا انتوا كنتوا تعملوه حتى في الأرقام
+
+68
+00:04:45,840 --> 00:04:48,680
+العشرية في الأرقام العشرية هي من وين جاي الأرقام
+
+69
+00:04:48,680 --> 00:04:53,660
+العشرية عند ما نقول 65 5 و 6 ال 65 هذه جاية من 10
+
+70
+00:04:53,660 --> 00:04:59,400
+to the power of 0 ضرب 5 و 10 to the power of 1 ضرب
+
+71
+00:04:59,400 --> 00:05:05,900
+6 و 10 to the power of 2 ضرب 3فبيعطييني جدش القيمة
+
+72
+00:05:05,900 --> 00:05:09,060
+هذه .. بيعطييني جدش قيمة .. القيمة هذه تحديدا ..
+
+73
+00:05:09,060 --> 00:05:14,300
+فهنا هيكون هذه كيلومتر واحد في خمسة في خمسة عشرة
+
+74
+00:05:14,300 --> 00:05:21,570
+في ستة في ستين مية تلات ميةاجمعوهم بيطلع تلاتمية
+
+75
+00:05:21,570 --> 00:05:26,150
+خمسة وستين تمام نفس الكلام بنستعمله في ال other
+
+76
+00:05:26,150 --> 00:05:28,170
+systems يعني في كل ال systems التانية اللي غير ال
+
+77
+00:05:28,170 --> 00:05:30,490
+decimal مش معناه ان بتنعمل في ال decimal فنفس
+
+78
+00:05:30,490 --> 00:05:36,430
+الكلام هنا هتلاقوا ان في عندكم one في one one plus
+
+79
+00:05:36,430 --> 00:05:48,420
+two في zero four في zero eight في oneفهنا بتطلع
+
+80
+00:05:48,420 --> 00:05:53,580
+تسعة هذا الرقم تمثل تسعة فلاحظوا ان ال bet الأخيرة
+
+81
+00:05:53,580 --> 00:05:57,720
+اللي هي جاية في ال left هي الأعلى قيمة هي الأعلى
+
+82
+00:05:57,720 --> 00:06:01,940
+قيمة ليش؟ لأنهم ضربت في أعلى coefficient في 2 to
+
+83
+00:06:01,940 --> 00:06:06,620
+the power 3 بالنسبة للرقم تبعنا 2 to the power 3
+
+84
+00:06:06,620 --> 00:06:15,220
+فعليا
+
+85
+00:06:16,400 --> 00:06:19,960
+العشر قصابيع أكم برقم بقدر أعد فيهم أو لعند جد إيش
+
+86
+00:06:19,960 --> 00:06:24,020
+بقدر أعد فيهم باستخدام ال decimal لعند عشرة الولد
+
+87
+00:06:24,020 --> 00:06:26,840
+الصغير اللي مابنعلمه كل واحد اتنين تلاتة لعند عشرة
+
+88
+00:06:26,840 --> 00:06:30,380
+فبقدر لعند عشرة لأ actually احنا بقدر نعد فيه لعند
+
+89
+00:06:30,380 --> 00:06:35,580
+الف تلاتة وعشرين لو أتعاملنا معاه ك bits و بنتعامل
+
+90
+00:06:35,580 --> 00:06:39,180
+معاه ك binary فممكن أقول ببدأ دايما زي ما قلنا من
+
+91
+00:06:39,180 --> 00:06:43,500
+الشمالبنبدأ او يعني بالنسبالي انا شمال حيكون
+
+92
+00:06:43,500 --> 00:06:45,700
+بالنسبالي كنت اليمين يعني فعليا نبدأ بيمين من
+
+93
+00:06:45,700 --> 00:06:53,640
+الأقل significant هيها فهقول كله صفر هيك واحد طب
+
+94
+00:06:53,640 --> 00:06:56,820
+عشان اغير اعمل flip او اغير اعمل ال count اللي
+
+95
+00:06:56,820 --> 00:07:02,800
+وراه ببدأ برضه دايما يمين اذا و جابلت واحد صفر و
+
+96
+00:07:02,800 --> 00:07:07,720
+بعطي واحد للي وراه فصارت صفر واحد صفر واحد تمثل
+
+97
+00:07:07,720 --> 00:07:13,840
+اتنينمش يمثلوا رقم اتنين لأن الباقي كل zeros طيب
+
+98
+00:07:13,840 --> 00:07:19,880
+هاي اتنين طيب عشان هالوجه اجيب الرقم اللي ورا ببدأ
+
+99
+00:07:19,880 --> 00:07:23,200
+اذا كان لجيت صفر برضه من اليمين لجيت صفر بحاوله
+
+100
+00:07:23,200 --> 00:07:30,320
+لواحد وخلصنا هاي صار رقم تلاتة طيب رقم اربعة لجيت
+
+101
+00:07:30,320 --> 00:07:34,400
+واحد باجلبها صفر و بنجل ع اللي ورا واحد برضه
+
+102
+00:07:34,400 --> 00:07:37,480
+باجلبها صفر و بنجل ع اللي ورا فصارت ايه صفر صفر
+
+103
+00:07:37,480 --> 00:07:45,540
+واحد صفر صفر واحدأربعة وهكذا فهذه عملية ال
+
+104
+00:07:45,540 --> 00:07:50,020
+counting على باستخدام ال binary in binary فهتلاجوا
+
+105
+00:07:50,020 --> 00:07:53,520
+دايما بتعملوا change من one to zero من one to zero
+
+106
+00:07:53,520 --> 00:07:57,800
+إذا كان جبل to one في وشكه من اليمين من اليمين
+
+107
+00:07:57,800 --> 00:08:02,420
+دايما بتبدو العدل من اليمين من الأقل أهمية عشان
+
+108
+00:08:02,420 --> 00:08:05,340
+تطلعوا فيها ل .. ل .. ل .. لما تصلوا ل ال most
+
+109
+00:08:05,340 --> 00:08:12,180
+significant فبتعملوا flip to the next bitOkay ال
+
+110
+00:08:12,180 --> 00:08:15,480
+.. ال bitwise .. bitwise operations احنا قبل هيك
+
+111
+00:08:15,480 --> 00:08:19,300
+تقولنا انه لما اتكلمنا المرة اللي فاتت و قولنا انه
+
+112
+00:08:19,300 --> 00:08:22,840
+في البرمجة هتاخدوا حاجة اسمها wordwise او bitwise
+
+113
+00:08:22,840 --> 00:08:26,060
+bitwise انا بتعامل معها ال sequence تبعي bit by
+
+114
+00:08:26,060 --> 00:08:29,480
+bit فإذا كل bit داخل ال sequence بتعامل معاها
+
+115
+00:08:29,480 --> 00:08:33,500
+كأنها مستقلة ب .. بقارنها بال bit المقابلة لها في
+
+116
+00:08:33,500 --> 00:08:36,380
+ال sequence التاني و بعمل ال operation تبعتي بنعمل
+
+117
+00:08:36,380 --> 00:08:40,130
+ال operation بتاعتنا معنى ذلكمعنى ذلك إن لو بدنا
+
+118
+00:08:40,130 --> 00:08:42,690
+.. عنا .. عنا two sequence بالشكل اللي احنا
+
+119
+00:08:42,690 --> 00:08:47,230
+شايفينه هذا و بدنا نشتغل bitwise بمعنى أنا بعملش
+
+120
+00:08:47,230 --> 00:08:51,770
+للكلمة كلها على بعض مع الكلمة كلها على بعض لأ لكل
+
+121
+00:08:51,770 --> 00:08:56,690
+bit مع ال bit المقابلة لها، كويس لو بدنا نعمل
+
+122
+00:08:56,690 --> 00:09:02,730
+operator or, bitwise or بمسك كل واحدة مع الم .. مع
+
+123
+00:09:02,730 --> 00:09:06,850
+ما يقابلهامع ما يقابلها طيب لو ال sequence عندكم
+
+124
+00:09:06,850 --> 00:09:12,270
+أصلا ال n تبعد كل واحد منهم مختلف عن التانية ال n
+
+125
+00:09:12,270 --> 00:09:15,590
+واحد و ال n اتنين ال n الأولى نفترض ستة فهي فيها
+
+126
+00:09:15,590 --> 00:09:22,490
+ستة elements و ال n التانية خمسة نكمل ب zeros و
+
+127
+00:09:22,490 --> 00:09:26,410
+هتلاحظوا أننا فعلا مكملينها هنا ب zero ال element
+
+128
+00:09:26,410 --> 00:09:30,120
+الأول هذا او ال sequence الأول هو فعلا هنا بسبس في
+
+129
+00:09:30,120 --> 00:09:34,500
+zero بتكملوا بتقدروا تعملوا ال bit ال string
+
+130
+00:09:34,500 --> 00:09:45,020
+بتعملوا طيب or zero or one one one one one one one
+
+131
+00:09:45,020 --> 00:09:45,200
+one one one one one one one one one one one one
+
+132
+00:09:45,200 --> 00:09:45,240
+one one one one one one one one one one one one
+
+133
+00:09:45,240 --> 00:09:47,100
+one one one one one one one one one one one one
+
+134
+00:09:47,100 --> 00:09:47,140
+one one one one one one one one one one one one
+
+135
+00:09:47,140 --> 00:09:47,400
+one one one one one one one one one one one one
+
+136
+00:09:47,400 --> 00:09:50,660
+one one one one one one
+
+137
+00:09:50,660 --> 00:09:50,680
+one one one one one one one one one one one one
+
+138
+00:09:50,680 --> 00:09:57,460
+oneاللي عندك عارفين كله zero باستثناء one and one
+
+139
+00:09:57,460 --> 00:10:01,800
+one and one هاي في عندي one and one وهي one and
+
+140
+00:10:01,800 --> 00:10:07,340
+one وهي one and one otherwise zeros otherwise
+
+141
+00:10:07,340 --> 00:10:16,000
+zeros طيب x or one امتى اذا اختلفوا اذا اختلفوا
+
+142
+00:10:16,000 --> 00:10:20,220
+اذا اختلفوا طيب اذا كان متشابهين zeros تعالى نشوف
+
+143
+00:10:20,220 --> 00:10:24,550
+وين في متشابهين هاي في عندي متشابه واحدة zeroهي
+
+144
+00:10:24,550 --> 00:10:29,250
+متشابه فهي متشابه فهي متشابه فهي متشابه فهي متشابه
+
+145
+00:10:29,250 --> 00:10:35,490
+فهي متشابه فهي متشابه فهي متشابه فهي متشابه فهي
+
+146
+00:10:35,490 --> 00:10:42,290
+متشابه فهي متشابه فهي
+
+147
+00:10:42,290 --> 00:10:44,490
+متشابه فهي متشابه فهي متشابه فهي متشابه فهي متشابه
+
+148
+00:10:44,490 --> 00:10:47,730
+متشابه فهي متشابه فهي متشابه فهي متشابه فهي متشابه
+
+149
+00:10:47,730 --> 00:10:50,170
+فهي متشابه فهي متشابه فهي متشابه فهي متشابه فهي
+
+150
+00:10:50,170 --> 00:10:51,580
+متشابه فهي متشابه فهي متشابه فاللي احنا عملناها طب
+
+151
+00:10:51,580 --> 00:10:54,220
+ممكن تجربوا operators تانية كمان ممكن تجربوا أي
+
+152
+00:10:54,220 --> 00:10:58,520
+operators تانية و خصوصا ان انتوا مر عليكوا يعني
+
+153
+00:10:58,520 --> 00:11:01,540
+ممكن تجربوها على فكرة باستخدام ال java لو اتعلمتوا
+
+154
+00:11:01,540 --> 00:11:05,200
+ال java و يعملوا sequence معين عندكم واستعملوا ال
+
+155
+00:11:05,200 --> 00:11:10,860
+bitwise علامة ال bitwise هذه استعملوهم هيتطلعوا
+
+156
+00:11:10,860 --> 00:11:17,940
+نفس الحلول اللي احنا اشتغلنا عليها طيب نقول
+
+157
+00:11:17,940 --> 00:11:24,450
+لموضوعنابتاع اليوم هذه الجزئية كملنا فيها محاضرة
+
+158
+00:11:24,450 --> 00:11:28,610
+المرة اللي فاتت نبدأ في جزء اليوماللي هو ال
+
+159
+00:11:28,610 --> 00:11:34,330
+propositional equivalence طيب لفظيا او معناها
+
+160
+00:11:34,330 --> 00:11:38,310
+textually بالحرف معناها بالحرف different compound
+
+161
+00:11:38,310 --> 00:11:43,850
+propositions may be the semantically identical إيش
+
+162
+00:11:43,850 --> 00:11:46,710
+يعني identical؟ معناه ذلك إنه have the same
+
+163
+00:11:46,710 --> 00:11:50,850
+meaning إيش يعني؟ برضه هنا معناه ذلك إنه حرفيا
+
+164
+00:11:50,850 --> 00:11:56,600
+موجود عندنا twodifferent compound prepositions
+
+165
+00:11:56,600 --> 00:12:02,240
+عندنا prepositions او تصريحين two sentences عندنا
+
+166
+00:12:02,240 --> 00:12:08,720
+فرضيتين مركبات و مختلفات preposition اول
+
+167
+00:12:08,720 --> 00:12:13,890
+preposition تاني ولكن لهم نفسالمعنى اللي هم نفس
+
+168
+00:12:13,890 --> 00:12:17,250
+المعنى فهدول المفروض اللي هم identical معنى ذلك
+
+169
+00:12:17,250 --> 00:12:20,030
+انه في equivalent between them او equivalence
+
+170
+00:12:20,030 --> 00:12:22,430
+between them كل واحدة equivalent للتانية كل واحدة
+
+171
+00:12:22,430 --> 00:12:27,050
+منهم هتكون equivalent للتانية ال .. و بدنا نركز بس
+
+172
+00:12:27,050 --> 00:12:29,590
+هنا على compound لأن معظم شغلنا هيشتغل على
+
+173
+00:12:29,590 --> 00:12:33,730
+compound ال compound هي فعليا proposition متكونة
+
+174
+00:12:33,730 --> 00:12:40,350
+من مجموعة atomic propositions لما بقول P هي atomic
+
+175
+00:12:40,350 --> 00:12:45,390
+propositionP في الفرضية بتاعتنا هي P خلاص هي
+
+176
+00:12:45,390 --> 00:12:48,810
+proposition ال proposition هذا atomic proposition
+
+177
+00:12:48,810 --> 00:12:54,390
+بنسميه طيب نفترض employees Q هذه هي كلها على بعض
+
+178
+00:12:54,390 --> 00:12:59,590
+compound proposition compound proposition طيب هذه
+
+179
+00:12:59,590 --> 00:13:04,490
+بدنا نعمل check هل هي مكافئة لحظه ولا لأ ل
+
+180
+00:13:04,490 --> 00:13:09,690
+whatever يعني هل هي مكافئة مثلا ل Q employees P
+
+181
+00:13:11,790 --> 00:13:16,230
+ولّا لأ؟ فلاحظوا هنا صارت compound preposition ..
+
+182
+00:13:16,230 --> 00:13:20,350
+compound preposition فصارت compound prepositions
+
+183
+00:13:20,350 --> 00:13:24,990
+هل هم .. لهم نفس ال meaning .. نفس .. have the
+
+184
+00:13:24,990 --> 00:13:28,570
+same meaning ولا لأ؟ the same meaning هناخدها بشكل
+
+185
+00:13:28,570 --> 00:13:33,430
+..رياضة بشكل اثبتة proof معينة و هنعرف هل هما فعلا
+
+186
+00:13:33,430 --> 00:13:36,410
+مثل الطباطة طبعا هي لا تثبت لا يكافئوا بعض في
+
+187
+00:13:36,410 --> 00:13:38,870
+الحالة اللي هنتكلم عليها هنا لا يكافئوا بعض ولكن
+
+188
+00:13:38,870 --> 00:13:42,850
+بدنا نعمل test نشوف كيف الموضوع فهذه هيك compound
+
+189
+00:13:42,850 --> 00:13:46,310
+proposition لأنه متكونة من اكتر من ال proposition
+
+190
+00:13:46,310 --> 00:13:49,390
+هي متكونة من مجموعة ايه اش atomic atomic
+
+191
+00:13:49,390 --> 00:13:52,030
+propositions كل واحدة من هدولة اللي هي اقل
+
+192
+00:13:52,030 --> 00:13:56,210
+proposition ممكن اقل جملة لها معنى اقل جملة لها
+
+193
+00:13:56,210 --> 00:14:01,880
+معنى atomic propositionطبعا هنستعمل مجموعة
+
+194
+00:14:01,880 --> 00:14:07,480
+equivalence rules and laws مجموعة قوانين وقواعد لل
+
+195
+00:14:07,480 --> 00:14:11,920
+equivalence عساس ان نمثل فيها او نعمل ال proof ..
+
+196
+00:14:11,920 --> 00:14:16,840
+ال proof سبعتنا ال proof سبعتنا هنستعمل حتين
+
+197
+00:14:16,840 --> 00:14:20,140
+الحقيقة اليوم هنشتغل على ال truth table باستخدام
+
+198
+00:14:20,140 --> 00:14:23,760
+truth table جدول الحقيقة و هنستعمل ال symbolic
+
+199
+00:14:23,760 --> 00:14:28,050
+derivations .. نستعمل ال symbolicneurovisions طيب
+
+200
+00:14:28,050 --> 00:14:30,570
+عشان نشتغل علي الموضوع هذا و نشوف هل اتنهى ال
+
+201
+00:14:30,570 --> 00:14:33,710
+covenant لبعض ولا لأ ممكن نشتغل علي حاجة يعني في
+
+202
+00:14:33,710 --> 00:14:37,470
+مصطلحين مهمين جدا بدنا نشتغل عليهم tautologies و
+
+203
+00:14:37,470 --> 00:14:40,790
+ال contradictions tautologies و ال contradictions
+
+204
+00:14:40,790 --> 00:14:44,830
+ال tautologies لما أقول tautology معناته حشو كلام
+
+205
+00:14:44,830 --> 00:14:49,330
+ع الفاضي رغي رغي سواء انجلوا ولا ما انجلش المعنى
+
+206
+00:14:49,330 --> 00:14:53,770
+واضح خلاص يعني زيادة على الفاضي زيادة هيك هذه
+
+207
+00:14:53,770 --> 00:14:57,880
+معناتهزي ما هو في التعريف الـ tautology is a
+
+208
+00:14:57,880 --> 00:15:00,680
+compound proposition that's true no matter what
+
+209
+00:15:00,680 --> 00:15:04,480
+the truth values of its atomic propositions are
+
+210
+00:15:04,480 --> 00:15:08,380
+بغض النظر جدش قيمة ال atomic لكل واحد ال atomic
+
+211
+00:15:08,380 --> 00:15:10,920
+propositions بتاعة كل واحدة منهم بغض النظر false
+
+212
+00:15:10,920 --> 00:15:14,320
+or true هتلاقوا إن ال compound كله على بعضه دائما
+
+213
+00:15:14,320 --> 00:15:20,120
+true مدام هيك معناته صح دائما صح مدام دائما صح طب
+
+214
+00:15:20,120 --> 00:15:23,640
+ليش بتقول ليه؟ خلاص يعني أشي مسلم فيه زي لما نقول
+
+215
+00:15:23,640 --> 00:15:31,550
+Pdisjunction negation P بنفع هذه دايما هتلاقوا ان
+
+216
+00:15:31,550 --> 00:15:34,870
+هي دايما true زي لما تصحي الصبح تقول والله اليوم
+
+217
+00:15:34,870 --> 00:15:39,670
+بدي اروح الجامعة او ماروحش الجامعةطب احنا عارفين
+
+218
+00:15:39,670 --> 00:15:42,690
+انك يا هتروح و يا مش هتروحه يعني إيش لجديد في ال
+
+219
+00:15:42,690 --> 00:15:45,810
+.. يعني وين ال .. ال .. الجملة المفيدة وين المعنى
+
+220
+00:15:45,810 --> 00:15:49,570
+الإضافي اللي ضفته في المعنى مفيش ليش؟ لأنه طبيعي
+
+221
+00:15:49,570 --> 00:15:51,690
+يا الواحد بصحى الصبح يا هيروح الجامعة يا مش هيروح
+
+222
+00:15:51,690 --> 00:15:55,110
+الجامعة مافيش احتمال تالد يا هيروح يا مش هيروح
+
+223
+00:15:55,110 --> 00:15:59,770
+تمام؟ فهنا زي ما نقول P disjunction negation P هذه
+
+224
+00:15:59,770 --> 00:16:03,270
+دائما true جملة بالشكل هذا دائما أبدا هتظل true
+
+225
+00:16:03,270 --> 00:16:08,730
+بغض النظر عن هل ال atomic هي الوحدةالواحدة منهم ال
+
+226
+00:16:08,730 --> 00:16:13,290
+atomic هادي او هادي true or false مش هتفرج
+
+227
+00:16:13,290 --> 00:16:17,090
+whatever يعني ايش ما تكون القيمة بتاعتها المحصلة
+
+228
+00:16:17,090 --> 00:16:20,170
+كلها على بعض دائما true طيب العكس في ال
+
+229
+00:16:20,170 --> 00:16:24,370
+contradiction ال contradiction is a compound
+
+230
+00:16:24,370 --> 00:16:30,510
+proposition that is false no matter what the truth
+
+231
+00:16:30,510 --> 00:16:37,220
+values of its atomic propositions كويس زيP and
+
+232
+00:16:37,220 --> 00:16:41,000
+negation P تصحي الصبح تقول والله اليوم بدي أروح
+
+233
+00:16:41,000 --> 00:16:44,440
+الجامعة و بديش أروح الجامعة طبعا إيش المعنى؟
+
+234
+00:16:44,440 --> 00:16:47,480
+مالهاش معنى يعني أنه غلط كله واضح أنه غلط يا بدك
+
+235
+00:16:47,480 --> 00:16:52,440
+تروح يا بدكيش تروحي أما بدي أروح و بديش أروح فهذه
+
+236
+00:16:52,440 --> 00:16:55,900
+دائما هتكون إيش؟ false استمرار false لأن واحدة
+
+237
+00:16:55,900 --> 00:16:59,840
+منهم هتكون false لازم واحدة منهم هتكون false وفي
+
+238
+00:16:59,840 --> 00:17:02,980
+حالة ال conjunction لازم كلهم يكونوا true عشان
+
+239
+00:17:02,980 --> 00:17:06,490
+يكونوا true لأ هنا دائما في واحدة منهمfalse فإذا
+
+240
+00:17:06,490 --> 00:17:10,950
+المحصلة دائما هتكون false otherwise يعني هدول
+
+241
+00:17:10,950 --> 00:17:13,890
+الحالات اللي هم مؤكدين تماما تاتولوجيا و ال
+
+242
+00:17:13,890 --> 00:17:18,610
+contradiction اللي هي ال proposition مع ال
+
+243
+00:17:18,610 --> 00:17:23,010
+negation تبعه أو ال negation تبعه كويس otherwise
+
+244
+00:17:23,010 --> 00:17:27,830
+ممكن تكون تحصل أحيانا بال by chance بالحظ يعني
+
+245
+00:17:27,830 --> 00:17:31,250
+ممكن تلاقوا ان والله في column طلع كله tautology
+
+246
+00:17:31,250 --> 00:17:35,130
+او column طلع كله contradiction كله falseممكن تصير
+
+247
+00:17:35,130 --> 00:17:40,210
+بالحظ في حالات معينة طيب logical equivalence شوفنا
+
+248
+00:17:40,210 --> 00:17:42,390
+ال totology شوفنا ال construction ال compound ..
+
+249
+00:17:42,390 --> 00:17:45,350
+ال compound proposition compound بدنا نعرفه خلاص
+
+250
+00:17:45,350 --> 00:17:48,950
+compound أنا بتكلم عن مجموعة atomic propositions
+
+251
+00:17:48,950 --> 00:17:53,230
+مربطة .. مربوطة مع بعض .. مربوطة مع بعض هي مش مجرد
+
+252
+00:17:53,230 --> 00:17:56,650
+atomic proposition لحالة بشكل هذا لأ هي ممكن تكون
+
+253
+00:17:56,650 --> 00:18:02,420
+or and مع أي q مثلاجملة، أبسط .. أبسط compound
+
+254
+00:18:02,420 --> 00:18:06,140
+preposition، فيها أكتر من atomic preposition،
+
+255
+00:18:06,140 --> 00:18:08,960
+تمام؟ فلما بتلاقوا كله compound أنا بتكلم عن
+
+256
+00:18:08,960 --> 00:18:15,190
+complicated prepositionمتكون من مجموعة atomic طيب
+
+257
+00:18:15,190 --> 00:18:18,310
+compound of preposition P is logically equivalent
+
+258
+00:18:18,310 --> 00:18:22,530
+to compound preposition Q compound preposition مع
+
+259
+00:18:22,530 --> 00:18:25,430
+compound preposition إذا كانوا فعلا الأتنين
+
+260
+00:18:25,430 --> 00:18:30,710
+مكافئين لبعض فإذا بقدر أقول أن P by conditional Q
+
+261
+00:18:30,710 --> 00:18:36,550
+is true هيكون ليش لأن واحدة بتضمن التانية و
+
+262
+00:18:36,550 --> 00:18:39,550
+التانية بتضمن الأولى إذا بالظبط التنتين و احنا
+
+263
+00:18:39,550 --> 00:18:43,930
+عارفين أنه في ال by conditional أمتى بيكونواtrue
+
+264
+00:18:43,930 --> 00:18:48,330
+by condition يعني إمتى بتكون true؟ إذا كانت false،
+
+265
+00:18:48,330 --> 00:18:53,270
+false أو true، true متشابهين، متشابهين، متشابهين،
+
+266
+00:18:53,270 --> 00:18:54,290
+متشابهين، متشابهين، متشابهين، متشابهين، متشابهين،
+
+267
+00:18:54,290 --> 00:18:54,650
+متشابهين، متشابهين، متشابهين، متشابهين متشابهين
+
+268
+00:18:54,650 --> 00:18:55,870
+متشابهين متشابهين متشابهين متشابهين متشابهين
+
+269
+00:18:55,870 --> 00:18:58,910
+متشابهين متشابهين متشابهين متشابهين متشابهين
+
+270
+00:18:58,910 --> 00:19:02,570
+متشابهين
+
+271
+00:19:02,570 --> 00:19:05,730
+متشابهين
+
+272
+00:19:06,450 --> 00:19:10,330
+هذه التنتين هكون متكافئين علامة التكافؤ إذا كانوا
+
+273
+00:19:10,330 --> 00:19:14,870
+فعلا compound is a tautology معناه ذلك إنه لازم
+
+274
+00:19:14,870 --> 00:19:20,270
+دايما true طب إنت ممكن تكون true فعليا لما كل
+
+275
+00:19:20,270 --> 00:19:23,050
+واحدة منهم مساوية للتانية بغض النظر false false
+
+276
+00:19:23,050 --> 00:19:26,850
+true true بس لازم تكون مساوية لها بنفس .. لها نفس
+
+277
+00:19:26,850 --> 00:19:30,550
+ال value نفس ال value زي ما قلنا بغض النظر ال
+
+278
+00:19:30,550 --> 00:19:37,030
+value هدي false or true false false okay trueال by
+
+279
+00:19:37,030 --> 00:19:39,570
+conditional بتاعتهم true .. true true .. by
+
+280
+00:19:39,570 --> 00:19:42,110
+conditional true .. فإذا تاتولوجي .. تاتولوجي هنا
+
+281
+00:19:42,110 --> 00:19:46,090
+تحققت لل by conditional معناه ذلك إن كل
+
+282
+00:19:46,090 --> 00:19:50,850
+proposition منهم مكافئ للتاني .. مكافئ للتاني ..
+
+283
+00:19:50,850 --> 00:19:56,170
+له نفس القيمة .. okayهذه ممكن برضه نعملها .. ممكن
+
+284
+00:19:56,170 --> 00:19:59,910
+تجربوها برضه باستخدام ال truth value فهي بتحتوي ال
+
+285
+00:19:59,910 --> 00:20:04,070
+truth table اللي مابتيجوا تعملوها ال column تبع ال
+
+286
+00:20:04,070 --> 00:20:08,030
+compound proposition المفروض انه يحتوي على مجموعة
+
+287
+00:20:08,030 --> 00:20:15,010
+.. مجموعة symbols مشابه .. مشابه هو مساوية تماما ل
+
+288
+00:20:15,010 --> 00:20:18,350
+ال column تبع ال proposition التانية اللي لازم
+
+289
+00:20:18,350 --> 00:20:22,250
+تكون مكافئة عليهاهذه بتستخدم عساس من the same
+
+290
+00:20:22,250 --> 00:20:27,330
+truth value لما بنستعمل truth table لما بنستعمل
+
+291
+00:20:27,330 --> 00:20:32,970
+truth table زى ما هنشوف لاحقا هنا مثلا لو بدى اثبت
+
+292
+00:20:32,970 --> 00:20:39,870
+اعمل prove that بيه disjunction Q equivalent to
+
+293
+00:20:39,870 --> 00:20:45,720
+negationنفتح قصر Negation P and Negation Q إيش
+
+294
+00:20:45,720 --> 00:20:48,400
+بدنا نسوي؟ بدنا نستعمل ال truth table باستخدام ال
+
+295
+00:20:48,400 --> 00:20:52,840
+truth table كل اللي هنعمله أكم atomic proposition
+
+296
+00:20:52,840 --> 00:20:57,440
+عندنا؟ اتنين، معناه زي اللي كأعرفت أن أنا أكم روح
+
+297
+00:20:57,440 --> 00:21:02,400
+يكون عندى؟ أربعة، اتنين وهذه الأساس هتظل دايما
+
+298
+00:21:02,400 --> 00:21:06,220
+ثابتة معايا to the power عدد ال atomic proposition
+
+299
+00:21:06,220 --> 00:21:07,400
+اللي هم اتنين
+
+300
+00:21:11,590 --> 00:21:15,770
+فحنشتغل على اول compound preposition P disjunction
+
+301
+00:21:15,770 --> 00:21:20,750
+Q كويس التانية اه لأ لسه التانية عشان اعملها محتاج
+
+302
+00:21:20,750 --> 00:21:25,870
+اول negation P negation Q بعدين ال two negations
+
+303
+00:21:25,870 --> 00:21:31,010
+مع بعض نعملهم conjunction بعدين negation لل
+
+304
+00:21:31,010 --> 00:21:34,450
+conjunction كله على بعض كويس خليني اشوف هنا لما
+
+305
+00:21:34,450 --> 00:21:42,830
+نقوله orالـ O لأ false otherwise true طيب و بعدين
+
+306
+00:21:42,830 --> 00:21:48,810
+بتعمله negation ل ال P و negation ل ال Q كويس
+
+307
+00:21:48,810 --> 00:21:53,890
+بعدين هنا هتعمله and and ل مين ل ال two columns
+
+308
+00:21:53,890 --> 00:21:56,770
+هدول مع بعض ل ال two columns هدول فهيكون بس أول
+
+309
+00:21:56,770 --> 00:22:04,030
+term هو ال true otherwise false طيب negation ل ال
+
+310
+00:22:04,030 --> 00:22:06,870
+column هذا يعكسوه تمازك
+
+311
+00:22:08,450 --> 00:22:12,390
+لحظة ال column هذا و ال column هذا the same values
+
+312
+00:22:12,390 --> 00:22:18,070
+the same values فإذا عندكم false true true true
+
+313
+00:22:18,070 --> 00:22:22,490
+true true true true true true true true true true
+
+314
+00:22:22,490 --> 00:22:23,790
+true true true true true true true true true true
+
+315
+00:22:23,790 --> 00:22:27,150
+true true true true true true true true true true
+
+316
+00:22:27,150 --> 00:22:27,210
+true true true true true true true true true true
+
+317
+00:22:27,210 --> 00:22:27,490
+true true true true true true true true true true
+
+318
+00:22:27,490 --> 00:22:28,190
+true true true true true true true true true true
+
+319
+00:22:28,190 --> 00:22:28,310
+true true true true true true true true true true
+
+320
+00:22:28,310 --> 00:22:29,030
+true true true true true true true true true true
+
+321
+00:22:29,030 --> 00:22:29,210
+true true true true true true true true true true
+
+322
+00:22:29,210 --> 00:22:29,230
+true true true true true true true true true true
+
+323
+00:22:29,230 --> 00:22:29,350
+true true true true true true true true true true
+
+324
+00:22:29,350 --> 00:22:30,030
+true true true true true true true true
+
+325
+00:22:36,040 --> 00:22:39,540
+يعني عندكوا P عندكوا Q عندكوا R عندكوا S عندكوا T
+
+326
+00:22:39,540 --> 00:22:46,280
+اتنين او خمس اتنين او تلاتين روه طيب لو افترضنا
+
+327
+00:22:46,280 --> 00:22:49,620
+كمان ان ال compound هذا مش هيكون الاتنين مع بعض
+
+328
+00:22:49,620 --> 00:22:53,540
+طبعا هيكون الخمسة مع بعضهم يعني محتاجين كذا column
+
+329
+00:22:53,540 --> 00:22:57,200
+عشان تصلوا للي بدكوا ياه بدون ما يصير لخبط معاكم
+
+330
+00:22:57,200 --> 00:23:01,420
+فلحظوا الموضوع كبر صار كتير كبير فهنا بصير افضل ان
+
+331
+00:23:01,420 --> 00:23:05,060
+احنا نشتغل علىsymbolic derivations هناخدها
+
+332
+00:23:05,060 --> 00:23:09,480
+باستخدام قوانين ومعادلة معينة أو rules معينة طيب
+
+333
+00:23:09,480 --> 00:23:14,480
+نبدأ الشيه rules هذه اللي ممكن نستعملها في أول
+
+334
+00:23:14,480 --> 00:23:19,540
+rule اللي هي زي المحايد المحايد الجامعي و المحايد
+
+335
+00:23:19,540 --> 00:23:23,120
+الضربي أخدتهم قبل هيك لما بتشتغلوا في الأرقام
+
+336
+00:23:23,120 --> 00:23:27,260
+العادية كان في عندكم محايد جامعي اللي هو صفر و ال
+
+337
+00:23:27,260 --> 00:23:30,440
+.. و في اللي جاء في الضرب واحد تمام طيب احنا
+
+338
+00:23:30,440 --> 00:23:32,360
+اتفجنا انه صفر
+
+339
+00:23:34,820 --> 00:23:42,120
+للفالس one لل true طيب لما بعمل ضرب الضرب المفروض
+
+340
+00:23:42,120 --> 00:23:48,380
+المعامل الضرب المحايد الضرب واحد true conjunction
+
+341
+00:23:48,380 --> 00:23:51,740
+مع أي term او مع أي proposition هيطلع ال
+
+342
+00:23:51,740 --> 00:23:55,540
+proposition فال true هي محايدة بالنسبة لل
+
+343
+00:23:55,540 --> 00:24:00,480
+conjunction لل conjunctionتمام العكس بالنسبة لل
+
+344
+00:24:00,480 --> 00:24:03,800
+disjunction أو اللي هي الجمع يعني اللي كانت مقابلة
+
+345
+00:24:03,800 --> 00:24:08,240
+للجمع الجمع المحيد الجمع تبعها او ال disjunction
+
+346
+00:24:08,240 --> 00:24:13,020
+هي ال false هي ال false ال zero false مع أي
+
+347
+00:24:13,020 --> 00:24:17,240
+proposition النتج قيمة ال proposition إذا كان true
+
+348
+00:24:17,240 --> 00:24:22,100
+هيطلع true إذا كان false هيطلع false و نفس الكلام
+
+349
+00:24:22,100 --> 00:24:27,320
+كانت بالنسبة لها ال conjunction طيب طب في الهيمنة
+
+350
+00:24:28,210 --> 00:24:31,410
+لما تقول والله ال zero مثلا يمكن اوضح ال zero اكتر
+
+351
+00:24:31,410 --> 00:24:36,830
+من ال واحد لما تقول ال zero في اي قيمة zero معناته
+
+352
+00:24:36,830 --> 00:24:41,050
+هنا ال zero هيمن هيمن على المعادلة بتاعتنا هي
+
+353
+00:24:41,050 --> 00:24:48,710
+false conjunction في false طيب التالتة التالتة
+
+354
+00:24:48,710 --> 00:24:55,760
+اللي هي مش زي ال tautology حشه لأ هذهعدمة الفائدة
+
+355
+00:24:55,760 --> 00:25:03,660
+أحيان بيسموها بمعنى أنه ال proposition مع نفسه، ال
+
+356
+00:25:03,660 --> 00:25:07,140
+proposition مع نفسه مالوش معنى، مالوش معنى أن أنا
+
+357
+00:25:07,140 --> 00:25:09,700
+أقول اليوم بدي أصحى من النوم و اليوم بدي أصحى من
+
+358
+00:25:09,700 --> 00:25:14,540
+النوم طب ما هي المحصلة أن اليوم بدي أصحى من النوم،
+
+359
+00:25:14,540 --> 00:25:20,640
+اليوم بدي أروح الجامعة أو أن اليوم أروح الجامعةطب
+
+360
+00:25:20,640 --> 00:25:22,800
+ما هي المحصلة إنه حالي يوم هنروح الجامعة فال
+
+361
+00:25:22,800 --> 00:25:25,000
+proposition في الحالة اللي زيها دي ال proposition
+
+362
+00:25:25,000 --> 00:25:29,400
+مع نفسه أو مضروب في نفسه بمعنى and أو or مع نفسه
+
+363
+00:25:29,400 --> 00:25:34,860
+هو نفسه هو نفسه لو true إنها هتطلع true لو false
+
+364
+00:25:34,860 --> 00:25:40,080
+هيكون false هيكون false في الحالتين فهذا يمثل نفسه
+
+365
+00:25:40,080 --> 00:25:46,460
+طيب ال rule الرابعة ال double negation اللي هي نفي
+
+366
+00:25:46,460 --> 00:25:51,550
+النفي if bad صحيح؟طيب نفي النفي اثبات فإذا أنا
+
+367
+00:25:51,550 --> 00:25:57,090
+أقول negation of negation P تطلع
+
+368
+00:25:57,090 --> 00:26:01,510
+P طيب التانية
+
+369
+00:26:01,510 --> 00:26:06,950
+ال domination domination الهيمنة و هذي عشان اوضح
+
+370
+00:26:06,950 --> 00:26:10,750
+لكيها أكتر بالأرقام اللي أنتوا عارفينها الصفر لما
+
+371
+00:26:10,750 --> 00:26:14,410
+تضربيه بأي رقم هو هيمن عليه ليش لأنه أعطى ناتج
+
+372
+00:26:14,410 --> 00:26:21,140
+دايما صفر لما نقول صفر في مليون صفرفهنا معناها أن
+
+373
+00:26:21,140 --> 00:26:25,620
+ال true or false هيمنوا على ال proposition لغوا،
+
+374
+00:26:25,620 --> 00:26:30,180
+لغوا تأثيره، لغوا ال effect تبعه، كيف لغوا؟ ال
+
+375
+00:26:30,180 --> 00:26:34,100
+true بتلغ تأثير ال proposition اللي معها إذا كانت
+
+376
+00:26:34,100 --> 00:26:38,500
+مع مين؟ disjunction، disjunction احنا عارفين أو،
+
+377
+00:26:38,500 --> 00:26:45,470
+فأي term أو true، trueلأن في او فاعتطنى سماحية ان
+
+378
+00:26:45,470 --> 00:26:48,310
+ممكن اي واحد منهم true و الكل الباقي يطلع true ما
+
+379
+00:26:48,310 --> 00:26:51,230
+هو فعلا اكيد في واحد منهم true لان انا حاط true
+
+380
+00:26:51,230 --> 00:26:56,550
+حاطينه اصلا true فعلا طيب نفس الكلام في اش مع ال
+
+381
+00:26:56,550 --> 00:26:59,970
+and اللى هى عملية كأنها عملية ضرب تقابل ضرب في ال
+
+382
+00:26:59,970 --> 00:27:07,930
+decimal system هذه مع صفر صفر ضرب اى قيمة صفر
+
+383
+00:27:07,930 --> 00:27:11,630
+فيمكن هذه بتجرب المفهوم اوضح a proposition
+
+384
+00:27:13,290 --> 00:27:17,170
+conjunction مع false أكيد false لأن ال conjunction
+
+385
+00:27:17,170 --> 00:27:21,470
+عشان يختلف عن ال false يكون true لازم يكونوا اتنين
+
+386
+00:27:21,470 --> 00:27:26,030
+atomic proposition true صح لازم لاتنين يكونوا true
+
+387
+00:27:26,030 --> 00:27:30,430
+لأ احنا اي واحد منهم مش true خلاص واحد منهم false
+
+388
+00:27:30,430 --> 00:27:33,830
+انتهى اي واحد منهم false فإذا النتيجة لازم يكون
+
+389
+00:27:33,830 --> 00:27:37,890
+not true فإذا not true ماعنديش الاحتمال ان هو يا
+
+390
+00:27:37,890 --> 00:27:43,300
+true يا false ال not true تمثل falseطيب، آه لسه ما
+
+391
+00:27:43,300 --> 00:27:46,920
+اتكلمنش عن competitive، ال competitive تباديل،
+
+392
+00:27:46,920 --> 00:27:50,120
+تبادلي، تبادلي بمعنى .. تبادل امتى؟ إذا كانت هم
+
+393
+00:27:50,120 --> 00:27:52,800
+بتتكلم عن نفس ال junction هيها ال .. ال .. ال ..
+
+394
+00:27:52,800 --> 00:27:55,140
+ال junction بتاعتنا أو هنا بتتكلم عن disjunction
+
+395
+00:27:55,140 --> 00:27:59,840
+فإذا P disjunction Q هي نفسها Q disjunction P و P
+
+396
+00:27:59,840 --> 00:28:05,890
+conjunction Q هي نفسها Q conjunction Pكويس
+
+397
+00:28:05,890 --> 00:28:10,050
+associative ال associative المشاركة في ال priority
+
+398
+00:28:10,050 --> 00:28:15,590
+في الأولوية هو فعليا إذا كان أنا بتعامل مع نفس ال
+
+399
+00:28:15,590 --> 00:28:18,990
+conjunction أو ال disjunction يعني نفس ال .. ال ..
+
+400
+00:28:18,990 --> 00:28:23,450
+ال operator فالمفروض أن الأولوية متساوية صح
+
+401
+00:28:23,450 --> 00:28:26,450
+الأولوية متساوية أنا بتعامل مع نفس ال .. ال .. ال
+
+402
+00:28:26,450 --> 00:28:32,440
+operator لما نقول خمسة زائد تلاتة زائد أربعةهتفرق
+
+403
+00:28:32,440 --> 00:28:36,640
+كثير لو قلت طبعا هنا خلّيني أقوص بالشكل هذا إن
+
+404
+00:28:36,640 --> 00:28:40,580
+أحسب 3 زاد 4 الأول و بعدين أجمحها على 5 ولا أقول
+
+405
+00:28:40,580 --> 00:28:45,520
+لأ 5 زاد 3 في الأول و بعدين 4 فهنا أنا بيعطي
+
+406
+00:28:45,520 --> 00:28:48,820
+priority لمين لل 3 زاد 4 في الأول هنا لأ اعطيت
+
+407
+00:28:48,820 --> 00:28:53,200
+priority أكتر لل 5 زاد 3 في الأول مش هتفرق في
+
+408
+00:28:53,200 --> 00:28:56,560
+الحالتين هيطلع نفس النتجةفي الحلتين هيطلع نفس
+
+409
+00:28:56,560 --> 00:29:01,260
+النتج في هذه associative مشاركة ال priority ان
+
+410
+00:29:01,260 --> 00:29:05,280
+الاتنين لهم نفس ال priority او ان هم اتنين انا
+
+411
+00:29:05,280 --> 00:29:08,960
+بتكلم هنا عن ال operator بتكلم عن ال operator ال
+
+412
+00:29:08,960 --> 00:29:11,120
+operator هذا مساوي لهذا لأن هم نفس ال operator
+
+413
+00:29:11,120 --> 00:29:14,440
+اصلا فمدام نفس ال operator تفرجش من احط الأحواص
+
+414
+00:29:14,440 --> 00:29:18,740
+تفرجش مين هعمل يا بالمين الكلام ينطبق سواء على ال
+
+415
+00:29:18,740 --> 00:29:23,800
+disjunction او conjunction طيب ال rule ال ..
+
+416
+00:29:24,130 --> 00:29:28,830
+السادسة يمكن او سادسة تقريبا ال distributive وهذه
+
+417
+00:29:28,830 --> 00:29:34,850
+مهمة جدا طيب اذا كانوا مش نفس ال operator لحظه مش
+
+418
+00:29:34,850 --> 00:29:38,930
+نفس ال operator طب ما هذا بخليني ارجع لنفس ال
+
+419
+00:29:38,930 --> 00:29:44,850
+decimal number تبعتنا لما اقول خمسة في اربعة زائد
+
+420
+00:29:44,850 --> 00:29:45,910
+تلاتة
+
+421
+00:29:51,040 --> 00:29:56,160
+هل كنا .. كان ممكن نعملها مثلا خمسة في أربعة زائد
+
+422
+00:29:56,160 --> 00:30:01,740
+تلاتة بهذا الشكل؟ طبعا غلط طب ها إيش كنا نعمل؟ كنا
+
+423
+00:30:01,740 --> 00:30:05,300
+نعمل توزيع كنا نعمل .. بالظبط كنا نعمل توزيع خمسة
+
+424
+00:30:05,300 --> 00:30:14,290
+في أربعة زائد خمسة في تلاتةنفسه تماما بدنا نعمله
+
+425
+00:30:14,290 --> 00:30:18,330
+مع ال operators اللي احنا بنشتغل عليها لاحظوا
+
+426
+00:30:18,330 --> 00:30:22,710
+disjunction افتحه قواص مع ال conjunction ال
+
+427
+00:30:22,710 --> 00:30:27,550
+disjunction هيها هنوزحها P disjunction Q و هدول
+
+428
+00:30:27,550 --> 00:30:32,650
+هنسكر عليهم قواص و بعدين P disjunction مع R و نسكر
+
+429
+00:30:32,650 --> 00:30:34,790
+عليها قواص و نخلي ال N بين القوسين
+
+430
+00:30:37,750 --> 00:30:44,930
+نفس الكلام لو عكسناه نفس الشيء لو عكسناه فهنكون
+
+431
+00:30:44,930 --> 00:30:47,830
+احنا فعلا حققنا عملية ال distribution أو التوزيع
+
+432
+00:30:47,830 --> 00:30:54,070
+التوزيع اللى كنا بتشتغلها عادة دي مارجانز عملنا
+
+433
+00:30:54,070 --> 00:30:57,410
+عملية توزيع بس عملها لمين اثبتها لمين لل negation
+
+434
+00:30:57,410 --> 00:31:01,850
+بحيث انه بيدخل ال negation بيدخل ال cost وبيعكس ال
+
+435
+00:31:01,850 --> 00:31:08,990
+operator بيعكس ال operatorand بيعكسها or إذا كانت
+
+436
+00:31:08,990 --> 00:31:15,370
+or أو disjunction بيعكسها and أو conjunction طيب
+
+437
+00:31:15,370 --> 00:31:18,350
+trivial, tautology or contradiction وهدا اللي
+
+438
+00:31:18,350 --> 00:31:22,890
+خدناها أول ما بدنا كلامنا قولنا إنه دائما الاصغر
+
+439
+00:31:22,890 --> 00:31:27,950
+هذه هتكون true اللي هي ال P disjunction negation P
+
+440
+00:31:27,950 --> 00:31:33,930
+ال proposition و عكسه ال proposition عفوا أو عكسه
+
+441
+00:31:35,010 --> 00:31:38,910
+أو عكسه ما هو طبيعي واحد منهم هيكون صح منطقي واحد
+
+442
+00:31:38,910 --> 00:31:43,130
+منهم يكون صح طيب ال proposition هو عكسه طبيعي واحد
+
+443
+00:31:43,130 --> 00:31:46,650
+منهم هيكون غلط واحد هيكون صح و واحد هيكون غلط
+
+444
+00:31:46,650 --> 00:31:51,170
+فيكفر ان واحد غلط عشان يقول ان المحصلة كلها false
+
+445
+00:31:51,170 --> 00:31:57,390
+محصلة كلها false طيب اللي عندنا اللحظة كل اللي
+
+446
+00:31:57,390 --> 00:32:00,070
+اتكلمنا عنهم اتكلمنا عنهم على اساس ان انا بتكلم عن
+
+447
+00:32:00,070 --> 00:32:03,970
+negation conjunction and disjunction طب احنا أخدنا
+
+448
+00:32:03,970 --> 00:32:07,930
+اكتر من هيككان في مجموعة operators أكتر من ذلك
+
+449
+00:32:07,930 --> 00:32:12,070
+احنا خدنا ال XOR وخدنا ال implication وخدنا ال
+
+450
+00:32:12,070 --> 00:32:17,050
+biconditional فكل واحد منهم هناخدله صيغة تمثله
+
+451
+00:32:17,050 --> 00:32:24,590
+عساس ان نتعامل معاه لاحقا فهنبدأ بال XOR XOR P XOR
+
+452
+00:32:24,590 --> 00:32:29,910
+Q equivalent to P conjunction Q كله conjunction مع
+
+453
+00:32:29,910 --> 00:32:35,450
+negation ب conjunction Qتمام؟ او في form تاني و
+
+454
+00:32:35,450 --> 00:32:38,470
+طبعا لاحظوا ان واحد بتقدر تجيبه من التاني بده بس
+
+455
+00:32:38,470 --> 00:32:41,750
+شوية سلسلة عمليات بنقدر نجيبهم من بعض .. بنقدر
+
+456
+00:32:41,750 --> 00:32:45,970
+نجيبهم من بعض و لاحقا بس تتعلموا الطريقة اللي جاية
+
+457
+00:32:45,970 --> 00:32:47,970
+هتصيروا بتقدروا تعملوها لحالكوا .. يعني ال .. ال
+
+458
+00:32:47,970 --> 00:32:51,990
+.. ان كيف اجيب واحد من التانيإن واحد من التاني
+
+459
+00:32:51,990 --> 00:32:55,110
+هتتعاملوا معاه إن هذا equivalent لهذا بتكون ثبته
+
+460
+00:32:55,110 --> 00:32:58,370
+عملية إثبات إن هل اتنين هذول equivalent لبعض أو لأ
+
+461
+00:32:58,370 --> 00:33:02,410
+التاني يمكن تكون أوضح شوية لإيش لإن احنا عادة ..
+
+462
+00:33:02,410 --> 00:33:09,170
+عادة بنعمل true امتى true لل X or لما واحدة منهم
+
+463
+00:33:09,170 --> 00:33:16,310
+تكون عكس التانية فلاحظوا واحدة عكس التانية أوأولة
+
+464
+00:33:16,310 --> 00:33:18,930
+التانية مع عكس الأولى يعني واحدة ده مع العكس
+
+465
+00:33:18,930 --> 00:33:21,990
+التانية فيمكن أقرب انها تنحفظ معاكم هذه الصورة
+
+466
+00:33:21,990 --> 00:33:29,210
+أسرع فإذا P and negation Q or Q negation and
+
+467
+00:33:29,210 --> 00:33:29,890
+negation P
+
+468
+00:33:33,080 --> 00:33:39,220
+طيب ال employees هي negation الأولى او التانية
+
+469
+00:33:39,220 --> 00:33:43,540
+نجاشن الأولى أو التانية نجاشن الأولى أو التانية
+
+470
+00:33:43,540 --> 00:33:47,380
+على طول يعني سهل لو مالهاش فورم واحد نستعمله خلال
+
+471
+00:33:47,380 --> 00:33:53,120
+ال course اللي هي negation الأولى or التانية طيب
+
+472
+00:33:53,120 --> 00:33:56,060
+ال biconditional ال biconditional اللي احنا قلناه
+
+473
+00:33:56,060 --> 00:33:58,880
+قبلك ان هي implication في الاتجاهين بمعنى ان انا
+
+474
+00:33:58,880 --> 00:34:06,000
+ممكن اقول ان هيemploys q and q employs p واحدة من
+
+475
+00:34:06,000 --> 00:34:09,620
+التانية او الاستنتاج اللى استنتجناه ايام ما
+
+476
+00:34:09,620 --> 00:34:14,840
+اتكلمنا عنها ان هي عكس ال X or لان هذه واحد امتى
+
+477
+00:34:14,840 --> 00:34:20,280
+اذا تشابه ال propositions بتعطيني one بعكس ال X or
+
+478
+00:34:20,280 --> 00:34:24,400
+ال X or اذا اختلفوا بتعطيني one صحيح تذكرينهم فاذا
+
+479
+00:34:24,400 --> 00:34:31,160
+هذه ال negation ده بال X orتمام for example خلينا
+
+480
+00:34:31,160 --> 00:34:34,660
+ناخد example طيب لما يكون في عندكوا example و
+
+481
+00:34:34,660 --> 00:34:37,540
+بتشتغلوا عليه بالشكل اللي احنا جاي عندنا هنا طبعا
+
+482
+00:34:37,540 --> 00:34:40,680
+الأسئلة هتكون هيك طبيعتها المفروض ان تعملوا check
+
+483
+00:34:40,680 --> 00:34:46,300
+على ال .. اذا كانوا equivalent ولا لأ اذا كانوا
+
+484
+00:34:46,300 --> 00:34:49,700
+فعلا اتنين equivalent او تعملوا proof ان هما فعلا
+
+485
+00:34:49,700 --> 00:34:54,060
+equivalent ببعض طيب بكون اعطيكواtwo compound
+
+486
+00:34:54,060 --> 00:34:57,100
+propositions هدى أول compound proposition و هدى
+
+487
+00:34:57,100 --> 00:35:00,940
+التانية و المطلوب نثبت ان هم equivalent لمين لبعض
+
+488
+00:35:00,940 --> 00:35:08,060
+firstly بتطلع عليهم اللى بتلاقوه فى operators صعبة
+
+489
+00:35:08,060 --> 00:35:12,640
+الشىء اللى هو ال operators الصعبة عادة ال XOR ال
+
+490
+00:35:12,640 --> 00:35:15,980
+implication و ال by condition هدولة دايما بهمنا
+
+491
+00:35:15,980 --> 00:35:18,930
+فوقكم فى الأولبهمنا نفكهم في الأول لإنه ماقدرش
+
+492
+00:35:18,930 --> 00:35:22,970
+أتعامل معهم مع ال rules اللي أخدناهم قبل شوية لازم
+
+493
+00:35:22,970 --> 00:35:25,710
+نفكهم بواحدة من القوانين بتاعتهم، كل واحد أخدناله
+
+494
+00:35:25,710 --> 00:35:29,210
+قانون قانون قانون، بنفكهم في الأول و بعدين بدبنا
+
+495
+00:35:29,210 --> 00:35:32,550
+نستعمل ال rules بتاعتنا أو ال laws بتاعتنا اللي
+
+496
+00:35:32,550 --> 00:35:35,490
+منهم دي مرجن و ما دي مرجن و ال competitive و ال
+
+497
+00:35:35,490 --> 00:35:39,630
+associative و الأمور دي كلهابتقدرش نستعملهم مباشرة
+
+498
+00:35:39,630 --> 00:35:44,050
+عليهم فإذا لما نيجي نطلع على ال proof بالشكل اللي
+
+499
+00:35:44,050 --> 00:35:47,170
+احنا شايفين وهذا مطلوب مننا اول ما بتطلع بتطلع على
+
+500
+00:35:47,170 --> 00:35:52,190
+ال left hand side اه هذا واضح انه complicated اكتر
+
+501
+00:35:52,190 --> 00:35:56,290
+من التاني معناته بشتغل على هذا نبدأ نفكه نحلله
+
+502
+00:35:56,290 --> 00:35:59,510
+نحلله ليش لأن في عندكوا XOR في عندكوا complication
+
+503
+00:35:59,510 --> 00:36:04,250
+و في عندكوا XORفعادة هاي بداية الحل دوروا على ال
+
+504
+00:36:04,250 --> 00:36:09,050
+implication يفقوها في الأول و بعدين نشوف أش بيصير
+
+505
+00:36:09,050 --> 00:36:12,070
+معناه خلينا نبدأ نفكها و نشوف أش بيصير معناها و
+
+506
+00:36:12,070 --> 00:36:14,830
+خلينا تتوارد لنا الأفكار إيش اللي لازم نعمله لاحقا
+
+507
+00:36:14,830 --> 00:36:23,430
+تمام فإذا firstly بفك هذا ولا هذا في الأول ال أكبر
+
+508
+00:36:23,430 --> 00:36:28,020
+هو ال implicationهو ال implication لأنه بربط ال co
+
+509
+00:36:28,020 --> 00:36:31,580
+باتنين مع بعض فهذا الكبير يعتبر هذا ال operator
+
+510
+00:36:31,580 --> 00:36:36,840
+التاني الأكبر كويس فبنبدأ فيها في ال implication
+
+511
+00:36:36,840 --> 00:36:40,260
+ال implication قلنا ان هي negation الأولى and
+
+512
+00:36:40,260 --> 00:36:44,640
+التانية negation الأولى عفوا or or التانية
+
+513
+00:36:44,640 --> 00:36:48,920
+disjunction or التانية فإذا بتعامل مع هذه كلها هيك
+
+514
+00:36:48,920 --> 00:36:53,770
+كأنها proposition أولى افترض أنها كأنها Kو هذه
+
+515
+00:36:53,770 --> 00:36:59,390
+كأنها هيك على بعض فى عندنا R زد فبتح تصير كأنه
+
+516
+00:36:59,390 --> 00:37:07,090
+negation K this junction زد هذا حطه مكانها حطه
+
+517
+00:37:07,090 --> 00:37:09,810
+القص نزله زي ما هو و ده نزله زي ما هو و خلصنا من
+
+518
+00:37:09,810 --> 00:37:15,370
+مين؟ من ال implicationهك خلصنا أول جزئية، بالظبط،
+
+519
+00:37:15,370 --> 00:37:19,250
+بعدين نبدأ نشوف الذبط هذه الشيعة عشان نفك اللي في
+
+520
+00:37:19,250 --> 00:37:23,030
+جلبها، تمام؟ عشان ما تتلخبطوش، بس ما ت .. الأقوسة
+
+521
+00:37:23,030 --> 00:37:25,630
+ده ما تلخم .. ما تلخمكمش، بتعاملوا معاها بالشكل
+
+522
+00:37:25,630 --> 00:37:28,110
+هذا، خلاص ال implication هذا بتربط إيش؟ أه بتربط
+
+523
+00:37:28,110 --> 00:37:30,150
+قوس، معناه تلقوس هذا كله على بعض و من المفروض ما
+
+524
+00:37:30,150 --> 00:37:33,810
+تتحركوش ولا تفكوه، عشان ما تلخمطوش حالكوا، زي ما
+
+525
+00:37:33,810 --> 00:37:37,330
+هو بتنقلوه تحت حسب القانون تبع ال implication
+
+526
+00:37:38,210 --> 00:37:41,370
+implication negation k فال negation بتطلعوها برا
+
+527
+00:37:41,370 --> 00:37:44,630
+ماتفكروش تعملولكوا خطوطين هوية واحدة انتوا لسه
+
+528
+00:37:44,630 --> 00:37:47,950
+يدوكوا بتتعلموا ال derivations ماتلخبطوش حالكوا
+
+529
+00:37:47,950 --> 00:37:50,390
+تعملولكوا خطوطين تلاتة في بعض عشان بتكونوا تختصروا
+
+530
+00:37:50,390 --> 00:37:54,530
+هتلاقوا حالكوا ال negation وجعت معاكوا في النص ال
+
+531
+00:37:54,530 --> 00:37:58,070
+and صارت or او ال or صارت and وانتوا مش دارينه
+
+532
+00:37:58,070 --> 00:38:01,070
+فطبعا مش هتصروا لحالة هتلاقوا حالكوا ضيعتوا حالته
+
+533
+00:38:01,070 --> 00:38:09,850
+تمام؟ كويس فهي ال implication الأولىفعملنا
+
+534
+00:38:09,850 --> 00:38:17,790
+negation الأولى هي or التانية نمسك من ال XOR كان
+
+535
+00:38:17,790 --> 00:38:21,730
+فين اللي كان لها قانونين هستعمل أول قانون منهم
+
+536
+00:38:21,730 --> 00:38:24,710
+اللي كان فيه اتنين and واحدة or
+
+537
+00:38:29,020 --> 00:38:32,340
+و الواحدة اخر فهدول انتوا بتكون تحفظوهم يعني هم
+
+538
+00:38:32,340 --> 00:38:34,960
+تلت اربع قوانين هدول بتكون تحفظوهم الباجين بتكون
+
+539
+00:38:34,960 --> 00:38:37,740
+فاهمينهم الباجين ال rules اللي احنا خدناهم في
+
+540
+00:38:37,740 --> 00:38:40,220
+الأول ال laws هدول اللي في الأول لأ انتوا بتكونوا
+
+541
+00:38:40,220 --> 00:38:43,260
+فاهمينهم competitive خلاص انا فاهم التبادل
+
+542
+00:38:43,260 --> 00:38:47,000
+التبادلية اذا كان نفس الاش نفس ال operator خلاص
+
+543
+00:38:47,000 --> 00:38:49,880
+بفهمه هيك distribution عارفين distributionأحنا
+
+544
+00:38:49,880 --> 00:38:52,940
+عارفين أنه بوزع الأرقام علي بعض لما يكون في
+
+545
+00:38:52,940 --> 00:38:55,420
+أقواتنا خلاص نفس الفكرة بعملها .. نفس الفكرة
+
+546
+00:38:55,420 --> 00:38:59,340
+بنعملها .. هدولة فهم .. في علي أنكوا علي اللي
+
+547
+00:38:59,340 --> 00:39:01,640
+بدكوا .. في هالتلت أربعة هدولة اللي هي بتاعة ال
+
+548
+00:39:01,640 --> 00:39:04,930
+XORال implication و ال biconditional .. مع أن ال
+
+549
+00:39:04,930 --> 00:39:08,490
+biconditional مش محتاجة أصلا لأن هي اللي كتبناهم
+
+550
+00:39:08,490 --> 00:39:12,170
+إياها كانت بدلالة ال implication و بدلالة ال XOR
+
+551
+00:39:12,170 --> 00:39:14,870
+فانتوا هتحفظوا بس لتنتين ال XOR و ال implication و
+
+552
+00:39:14,870 --> 00:39:18,150
+تكونوا فاهمين أن ال biconditional ما هي إلا
+
+553
+00:39:18,150 --> 00:39:24,770
+negation XOR أو implication في الاتجاهين بس ..
+
+554
+00:39:24,770 --> 00:39:32,670
+كويس طيب وصلنا لهنابدناش نحفظ احنا متفقين بدناش
+
+555
+00:39:32,670 --> 00:39:36,330
+نحفظ رياضيات ما هي مش قصة حفظ هل واجد بدي أجف هيك
+
+556
+00:39:36,330 --> 00:39:41,730
+و أصف المحالي و أطلع أنا إيش بدي؟ بدنا نفك و نصل
+
+557
+00:39:41,730 --> 00:39:46,790
+هادي طيب عشان أفك و أصل هادي بدي أجي أطلع هيك
+
+558
+00:39:46,790 --> 00:39:52,030
+حلاجي إن والله في عندي هنا P و هنا في P و هنا في P
+
+559
+00:39:52,030 --> 00:39:56,830
+لو بقدر أجمحهم مع بعضبحيث ان احصل على tautology او
+
+560
+00:39:56,830 --> 00:40:01,310
+contradiction اختزلهم ليش لان هدولة tautology و ال
+
+561
+00:40:01,310 --> 00:40:03,930
+contradiction ايش بيعطوني بيعطوني true و false ال
+
+562
+00:40:03,930 --> 00:40:08,190
+true و false هدولة اكيد هيختزلوا هيشي طيب كيف اعمل
+
+563
+00:40:08,190 --> 00:40:13,510
+الكلام هذا firstly انا مقدرش ادخل الأقواص هدولة ك
+
+564
+00:40:13,510 --> 00:40:20,030
+competitive ليش لان هذه and وهذه or مقدرش ابدلهم
+
+565
+00:40:20,030 --> 00:40:24,540
+مع بعض اه بس لحظةاستنوا في negation طب ال negation
+
+566
+00:40:24,540 --> 00:40:29,380
+اللي دخلناها جوا الأقواس هتركز هذه لإيش؟ تمام
+
+567
+00:40:29,380 --> 00:40:33,680
+فلحظوا التفكير إن أنا بدي أخفف الشغل اللي عندي
+
+568
+00:40:33,680 --> 00:40:37,780
+عشان أخففه فيه negation بعد دخل ال negation هذه
+
+569
+00:40:37,780 --> 00:40:40,820
+فصار عند كل اتنين هذول بيشابه بعض صار في إمكاني أن
+
+570
+00:40:40,820 --> 00:40:45,880
+أحط واحدة مكان التانيةفي عملية associative ال
+
+571
+00:40:45,880 --> 00:40:48,260
+associative هذه بعدين هنستعملها لو جت كمان شوية
+
+572
+00:40:48,260 --> 00:40:52,880
+associative مع competitive عشان ندخل ال P على
+
+573
+00:40:52,880 --> 00:40:55,020
+الأقواس تانية خلونا ناخدها واحدة واحدة في عندنا
+
+574
+00:40:55,020 --> 00:40:58,440
+مبدأيا اتفاجنا ان في عندنا negation هذه بستعملها
+
+575
+00:40:58,440 --> 00:41:04,160
+دي مورغان هاي دي مورغان دي مورغان هندخلها هنا بصيب
+
+576
+00:41:04,160 --> 00:41:12,640
+negation P or Q هاي negation P or Q تمامهي هيك
+
+577
+00:41:12,640 --> 00:41:16,420
+خلصنا عملية دي مورغان هل وجد الجزء التاني هنا صارت
+
+578
+00:41:16,420 --> 00:41:23,240
+إيش or or بقدر استعمل ال associative الأقواص أحطها
+
+579
+00:41:23,240 --> 00:41:27,140
+زي ما بدي مادام الإتنين هيوم or or الإتنين or أنا
+
+580
+00:41:27,140 --> 00:41:35,080
+كل .. هتعامل معاها .. هتعامل معايا قص هذا القص
+
+581
+00:41:35,080 --> 00:41:44,200
+هذا مع .. مع القص هذا اعتبروها إن كلها دي زبطتمام؟
+
+582
+00:41:44,200 --> 00:41:47,100
+عشان ذيك بقولكوا خلّي عينيكوا كويس واضحة تماما على
+
+583
+00:41:47,100 --> 00:41:50,640
+الأقواص الأقواص قوعوا يضيعوا منكوا قوس هيكي تحت
+
+584
+00:41:50,640 --> 00:41:55,240
+عينيكوا يروحوا قوس ماتعدوهوش كويس يتلاقوا حالكوا
+
+585
+00:41:55,240 --> 00:41:58,180
+صرتوا في expression مختلف تماما عن أن انتوا
+
+586
+00:41:58,180 --> 00:42:02,140
+بتشطروا عليه تمام لو أتعاملنا مع حد زده فإذا
+
+587
+00:42:02,140 --> 00:42:05,300
+الأقواص هذه ممكن أغير فيها غيرها زي ما بدي أقولكوا
+
+588
+00:42:05,300 --> 00:42:11,480
+ممكن أشيلها لو شيلناها حاسي رشة؟ مش حاسي رشة ليش؟
+
+589
+00:42:11,480 --> 00:42:17,140
+لأنهor or نفس ال operator فمافيش مشكلة بدون نفس ال
+
+590
+00:42:17,140 --> 00:42:21,640
+operator مافيش أشكال تمام هاي غيرنا عملنا اللي
+
+591
+00:42:21,640 --> 00:42:25,500
+بدناها بعد هيك ال competitive التبديل بمعنى أن مين
+
+592
+00:42:25,500 --> 00:42:35,780
+قبل التانية مش هتفرج negation P or Q هي نفسها Q or
+
+593
+00:42:35,780 --> 00:42:39,040
+negation P يعني مين قبل مين مش هتفرج كتير
+
+594
+00:42:39,040 --> 00:42:46,400
+competitiveكويس هذه الجزئية هتخليني احط ال Q هنا و
+
+595
+00:42:46,400 --> 00:42:50,620
+ال P هنا ليش اجرب للقوس لان محتاج اعمل operation
+
+596
+00:42:50,620 --> 00:42:55,260
+لان انا اصلا كل شغل اول ما بديت افكر من هنا فكرت
+
+597
+00:42:55,260 --> 00:43:00,540
+ان كل ال terms فيها P طب ال P هذه كلها لو اقدرنا
+
+598
+00:43:00,540 --> 00:43:04,240
+بطريقة او باخر نختزلها بعمل مشترك طب هنا مافيش
+
+599
+00:43:04,240 --> 00:43:08,040
+حاجة اسمها عمل مشترك فعشان اعملها محتاج ادخلها جوا
+
+600
+00:43:08,040 --> 00:43:10,700
+على القوس طب هل في إمكانية اه في إمكانية وجدنا ان
+
+601
+00:43:10,700 --> 00:43:15,020
+دي مورغان هينحكسهل الإمكانية بعدين وجدنا لما صاروا
+
+602
+00:43:15,020 --> 00:43:19,000
+تنتين زي بعض اه صار في إمكانية او اوضح و بينت انا
+
+603
+00:43:19,000 --> 00:43:23,240
+بالنسبالي هيك بينت ان اه خلاص ال P دخلت خلصنا ال P
+
+604
+00:43:23,240 --> 00:43:26,600
+ال negation P هذه اللي برا داخلة خلاص مافيش مشكلة
+
+605
+00:43:26,600 --> 00:43:35,200
+باين ان هي خلاص حتى دخلت الأقواس فهي
+
+606
+00:43:35,200 --> 00:43:40,200
+الشغل الجزء اللي تبعنا كان هيك بالشكل هذا عكسنا
+
+607
+00:43:42,560 --> 00:43:46,440
+لحظة أخدنا كل واحدة منهم لحال competitive يعملنا
+
+608
+00:43:46,440 --> 00:43:51,240
+competitive بعدين هنعمل ال .. هذه خلصنا كل اللي
+
+609
+00:43:51,240 --> 00:43:55,940
+هنعمله associative بيعني أن القوس هذا و احنا
+
+610
+00:43:55,940 --> 00:44:04,020
+متفقين أن هذه كلها هيك K مع أن ذلك بقدر أقول Q or
+
+611
+00:44:04,020 --> 00:44:08,700
+أفتح قوس negation P or K
+
+612
+00:44:11,900 --> 00:44:17,160
+بس وشية لإيش لإن التنتيه الأور فمافيش مشكلة مدام
+
+613
+00:44:17,160 --> 00:44:20,000
+التنتيه الأور مافيش مشكلة عندنا بنقدر نتحرك فيهم
+
+614
+00:44:20,000 --> 00:44:25,060
+تمام هذا هيقودنا أنه هالوجد الأقواص هذه هتروح
+
+615
+00:44:25,060 --> 00:44:31,980
+هينفتح قسم هنا وكمان يسكر قسم هنا هاي الأقواص
+
+616
+00:44:31,980 --> 00:44:38,140
+بتاعتنا كويس لسه بدنا ندخل ال negation P لسه برضه
+
+617
+00:44:38,140 --> 00:44:42,000
+مادخلتش على الأقواص جوا ماوصلتش لل P بتاعتهاكيف
+
+618
+00:44:42,000 --> 00:44:46,080
+ندخل على ال P بتاعتنا؟ خدوا بالك احنا وصلنا لوين ل
+
+619
+00:44:46,080 --> 00:44:54,080
+عند Q or هنفتح أقواص negation P or برضه هنفتح قوس
+
+620
+00:44:54,080 --> 00:44:58,600
+هنلاحظ ناخد بان من الأقواص بتاعتنا الأقواص اللي
+
+621
+00:44:58,600 --> 00:45:04,870
+موجودة عندنا فإذا هناnegation P بقدرش أتعامل معاها
+
+622
+00:45:04,870 --> 00:45:09,470
+مباشرة أو ال or الأولى، بقدرش أتعامل معاها مع ال
+
+623
+00:45:09,470 --> 00:45:13,790
+or اللي داخل الأقواس، ليش؟ لأنه بمجرد ما أفك
+
+624
+00:45:13,790 --> 00:45:17,170
+القواس اللي قدامي مباشرة، أنا هتعامل مع مين؟ مع ال
+
+625
+00:45:17,170 --> 00:45:21,330
+or في الأول، هنتعامل مع or جبل ما نتعامل نبدأ ندخل
+
+626
+00:45:21,330 --> 00:45:27,460
+على ال ..or بتاعتنا فهنتعامل مع جزئية ال and عشان
+
+627
+00:45:27,460 --> 00:45:31,940
+نتعامل or مع and كنا بنعمل ايش distribution او
+
+628
+00:45:31,940 --> 00:45:37,040
+distributive rule distributive rule بتاعتنا
+
+629
+00:45:37,040 --> 00:45:46,160
+automatically هتحول ل negation ب or القوس هذا كله
+
+630
+00:45:46,160 --> 00:45:53,690
+and negation ب or القوس التاني فهتصبحبهذا .. بهذا
+
+631
+00:45:53,690 --> 00:45:56,890
+الشكل اللي احنا شايفينه هنا بنقدر نقول انه ارتحت
+
+632
+00:45:56,890 --> 00:46:01,930
+.. ارتحنا ليش؟ لأنه صارت عندنا or مع or بنقدر
+
+633
+00:46:01,930 --> 00:46:07,230
+القواص هذا نفكه و نعمل associative .. associative
+
+634
+00:46:07,230 --> 00:46:10,670
+الأقواص نحطها و .. و .. ايه؟ وين بدنا ياها؟ فبنحطه
+
+635
+00:46:10,670 --> 00:46:15,430
+هنا، ممكن نحطه بهذا الشكل عساس ان استغل negationP
+
+636
+00:46:15,430 --> 00:46:20,510
+or negation P طيب كيف حيصير الكلام هذا؟ حيصير إنه
+
+637
+00:46:20,510 --> 00:46:26,470
+فعلا صار عندنا negation P مع P automatically مدام
+
+638
+00:46:26,470 --> 00:46:32,470
+or هذه هتكون true دائما ال true لما بيقول negation
+
+639
+00:46:32,470 --> 00:46:36,850
+P مع P أو negation ال proposition مع ال
+
+640
+00:46:36,850 --> 00:46:41,230
+proposition دائما مع بعض or as a or connection
+
+641
+00:46:41,230 --> 00:46:45,510
+بيكونوا trueكون true لأن واحدة منهم لازم تكون true
+
+642
+00:46:45,510 --> 00:46:52,390
+في الحالة هذه مع لما نقول or are مع أي proposition
+
+643
+00:46:52,390 --> 00:46:58,330
+آخر true مع أي proposition آخر أكيد هيطلع ايش true
+
+644
+00:46:58,330 --> 00:47:02,610
+true لأن ال or يكفي أن يكون في عندنا proposition
+
+645
+00:47:02,610 --> 00:47:08,470
+true عشان كل النتيجة تكون true فإذا كل الجزء هذا
+
+646
+00:47:08,470 --> 00:47:16,340
+trueتمام طيب true and ونفترض أنه كل ال term هذا
+
+647
+00:47:16,340 --> 00:47:22,660
+هيك هنسميه K صار عندنا true and K and proposition
+
+648
+00:47:22,660 --> 00:47:28,720
+K طيب فإذا إذا ال K هذه true كله true إذا كان
+
+649
+00:47:28,720 --> 00:47:35,730
+false كله false فإذا المحصلة كلها true andany
+
+650
+00:47:35,730 --> 00:47:39,290
+proposition هيعطينا ال value لل proposition، فإذا
+
+651
+00:47:39,290 --> 00:47:46,130
+الجزء هذا هو اللي يعبر عن كل ال term هذا، تمام؟
+
+652
+00:47:46,130 --> 00:47:51,370
+تمام، كويس، فأصبح عندنا true true كل الكلام اللي
+
+653
+00:47:51,370 --> 00:47:56,910
+احنا قولناه وصلنا للنتيجة النهائيةإنه فعلا هي ال
+
+654
+00:47:56,910 --> 00:48:00,090
+proposition هذا كله على بعض اللي بين القصين نزل
+
+655
+00:48:00,090 --> 00:48:03,890
+كما هو عندي هنا مع ال Q اللي احنا بديد كل شغلنا
+
+656
+00:48:03,890 --> 00:48:08,730
+فيها تمام هنا لاحظوا برضه في عندكم negation و في
+
+657
+00:48:08,730 --> 00:48:12,970
+في جوا بدنا نحاول ندخلهم مع بعض جاب ما أبدأ أدخلهم
+
+658
+00:48:12,970 --> 00:48:19,090
+مع بعض لاحظوا إن هذه or هذه and بركبوش مع بعضطيب و
+
+659
+00:48:19,090 --> 00:48:23,630
+لكن في negation برا دي مورغان ممكن يحلللي الموضوع
+
+660
+00:48:23,630 --> 00:48:29,550
+هذا أني أدخل negation جوا مع ال P و ال R فعكسنا ال
+
+661
+00:48:29,550 --> 00:48:36,510
+and لإيش ل or لما تنعكس ل or هتكون بهذا الشكل
+
+662
+00:48:36,510 --> 00:48:41,070
+دخلنا ال negation جوا و عكسناها or صار بقدر أشتغل
+
+663
+00:48:41,070 --> 00:48:44,350
+على ال associative associative أنه القوس هذا بلغي
+
+664
+00:48:44,350 --> 00:48:52,520
+من هنا و بنحطه بهذا الشكلطيب negation P or
+
+665
+00:48:52,520 --> 00:48:56,360
+negation P او proposition معناه انه بتكلم عن ال
+
+666
+00:48:56,360 --> 00:49:00,260
+proposition or نفس ال proposition هيعطينا ال
+
+667
+00:49:00,260 --> 00:49:03,120
+proposition لو كان ال proposition false فالنتيجة
+
+668
+00:49:03,120 --> 00:49:07,720
+هتكون false لو كان ال proposition true هتكون true
+
+669
+00:49:07,720 --> 00:49:12,320
+لو قلنا ال negation P هذه بتساوي true معناه ذلك
+
+670
+00:49:12,320 --> 00:49:13,460
+انا بتكلم عن true
+
+671
+00:49:16,130 --> 00:49:20,810
+or true هتكون true طيب لو كانت false .. false مع
+
+672
+00:49:20,810 --> 00:49:25,310
+false هتكون false فإذا قيمتها .. قيمة الناتج هي
+
+673
+00:49:25,310 --> 00:49:28,710
+نفس قيمة مين؟ ال proposition نفسه ال proposition
+
+674
+00:49:28,710 --> 00:49:32,790
+أنا إيش عندي اسمه؟ اسمه negation P فإذا بختزل
+
+675
+00:49:32,790 --> 00:49:36,830
+التنتين negation P هدول ب negation P واحدة بس
+
+676
+00:49:36,830 --> 00:49:42,830
+negation P واحدة فأصبح عندي هاي negation P واحدة
+
+677
+00:49:42,830 --> 00:49:46,590
+عندنا الأقوسة ده بقدر أفكهاإذا فقناها عيدوا
+
+678
+00:49:46,590 --> 00:49:49,170
+ترتيبهم زي ما بدكوا، ليش نقدر نعيد ترتيبهم زي ما
+
+679
+00:49:49,170 --> 00:49:53,590
+بدنا؟ لأنه في عندكوا or مع or ال priority هي هي،
+
+680
+00:49:53,590 --> 00:49:56,890
+مين جاب المين مش هي .. مش هيفرج معانا، هتكون
+
+681
+00:49:56,890 --> 00:50:03,470
+عندكوا competitive في شغلكوا، مين جاب المين، في
+
+682
+00:50:03,470 --> 00:50:06,830
+الآخر بترجعوا لمين، ل ال expression اللي أساسا
+
+683
+00:50:06,830 --> 00:50:11,110
+مطلوب منكوا من الأول، تعملوله prove، تشوفوا كيف
+
+684
+00:50:11,110 --> 00:50:14,270
+كان ترتيبه، بترتبوا زي ما بدكوا، فإذا لو أطلعنا
+
+685
+00:50:15,240 --> 00:50:20,160
+هنقش اللي بديها بالظبط، بدي negation هي تشوفوا
+
+686
+00:50:20,160 --> 00:50:25,080
+اللي هنا كان هذا
+
+687
+00:50:25,080 --> 00:50:34,540
+negation P or Q or negation R فبنعيد من عندنا
+
+688
+00:50:34,540 --> 00:50:41,340
+النقطة اللي كنا وصلناها بنعيد نرتب شغلنا زي ما
+
+689
+00:50:41,340 --> 00:50:41,920
+احنا بدنايا
+
+690
+00:50:46,680 --> 00:50:50,040
+كويس فهنا هنا فكناها نرجع بنرتبها زي ما احنا بنحط
+
+691
+00:50:50,040 --> 00:50:54,500
+هذه في الأول هذه في التانية و بننزل هذه زي ما هي
+
+692
+00:50:54,500 --> 00:51:00,040
+delta ليش؟ لأن بينهم نفس ال operator تمام نفس ال
+
+693
+00:51:00,040 --> 00:51:03,400
+operator هو اللي بينهم فبقدر مباشرة اقول انه
+
+694
+00:51:03,400 --> 00:51:06,680
+الترتيب مش هيفرج معانا الترتيب مش هيفرج معانا و
+
+695
+00:51:06,680 --> 00:51:11,780
+نكون وصلنا لإثبات اللي احنا محتاجينه في الشغل طبعا
+
+696
+00:51:11,780 --> 00:51:17,560
+و بنكون وصلنا زي ما قلنا للي احنا بدناهامع نهاية
+
+697
+00:51:17,560 --> 00:51:23,140
+ال example تبعنا بنكونتعرفنا على ال atomic .. ال
+
+698
+00:51:23,140 --> 00:51:26,420
+.. ال .. ال atomic propositions قولنا ان احنا
+
+699
+00:51:26,420 --> 00:51:30,180
+بنسميها بال .. بال .. بال lowercase letters او بال
+
+700
+00:51:30,180 --> 00:51:34,320
+small letters PQR بنعبر عليهم بشهد الشكل فهذه
+
+701
+00:51:34,320 --> 00:51:38,940
+عبارة عن propositions ال pollen algebra operator
+
+702
+00:51:38,940 --> 00:51:44,360
+أخدناها negation conjunction disjunction XOR ال
+
+703
+00:51:44,360 --> 00:51:47,980
+implication و biconditional او اللي قولنا عبارنا
+
+704
+00:51:47,980 --> 00:51:51,410
+عنه ب if and only ifاتكلمنا عن ال compound
+
+705
+00:51:51,410 --> 00:51:56,270
+prepositionsلما بتكلم عن compound propositions أنا
+
+706
+00:51:56,270 --> 00:52:00,710
+بتكلم عن expression لمجموعة propositions مرتبطة
+
+707
+00:52:00,710 --> 00:52:05,470
+بoperators مربوطة بمجموعة operators زي الشكل اللي
+
+708
+00:52:05,470 --> 00:52:08,970
+احنا شايفينه هنا كويس ال equivalence برضه اتكلمنا
+
+709
+00:52:08,970 --> 00:52:11,810
+عن ال equivalence وكيف ممكن استعمل ال equivalence
+
+710
+00:52:11,810 --> 00:52:16,730
+لإثبات اي expression معين فممكن اقول في حالة زي
+
+711
+00:52:16,730 --> 00:52:19,070
+الحلقة اللي عندنا وهذا العلامة أخدناها علامة
+
+712
+00:52:19,070 --> 00:52:22,910
+equivalenceو أتكلمنا عن أجمع منهم و قولنا كيف ممكن
+
+713
+00:52:22,910 --> 00:52:28,390
+أثبت ال equivalence اتكلمنا عن ال truth table ممكن
+
+714
+00:52:28,390 --> 00:52:33,430
+نستخدم ال truth tables عساس أجيب ال truth value
+
+715
+00:52:33,430 --> 00:52:38,030
+لكل compound proposition منهم و نقارنهم مع بعض
+
+716
+00:52:38,030 --> 00:52:41,330
+فلازم كل element في ال row يساوي ال element في نفس
+
+717
+00:52:41,330 --> 00:52:44,350
+ال row لل expression التاني إذا كان الكلام ده
+
+718
+00:52:44,350 --> 00:52:47,650
+ينطبق على جميع ال rows بقدر أقول ان ال two
+
+719
+00:52:47,650 --> 00:52:51,320
+compound propositions isequivalent كل واحدة منها
+
+720
+00:52:51,320 --> 00:52:55,400
+equivalent لتانية او symbolic derivations زي ال
+
+721
+00:52:55,400 --> 00:53:00,680
+example اللى اخدناه اللى هو اخر example كويسة
+
+722
+00:53:00,680 --> 00:53:03,520
+المرة الجاية ان شاء الله هنتكلم عن ال predicate
+
+723
+00:53:03,520 --> 00:53:07,540
+logic و هنتكلم نقول ان هده هي مش proposition هي
+
+724
+00:53:07,540 --> 00:53:12,140
+propositional function propositional function عشان
+
+725
+00:53:12,140 --> 00:53:16,140
+نسيبكوا إياها للمرة الجاية بتوضيح خفيف احنا أحيانا
+
+726
+00:53:16,140 --> 00:53:20,860
+نضطر نعبر عن مجموعة of propositionsمجموعة كبيرة
+
+727
+00:53:20,860 --> 00:53:23,600
+ممكن تكون من ال propositions بس بتعبّر عنها ب
+
+728
+00:53:23,600 --> 00:53:28,620
+expression واحد فمعنى ذلك بستعمل variables فمشابه
+
+729
+00:53:28,620 --> 00:53:32,120
+تماما لفكرة ال function لما يكون في عندكوا
+
+730
+00:53:32,120 --> 00:53:36,620
+function و بحطلها ال variable x فال variable x ده
+
+731
+00:53:36,620 --> 00:53:42,200
+ممكن ياخد قيم متعددة أو مختلفة بناء على القيم
+
+732
+00:53:42,200 --> 00:53:46,580
+المختلفة كإن بقول إنه عند مجموعة propositions إيش
+
+733
+00:53:46,580 --> 00:53:53,060
+يعني؟ يعني لو قولنا ال x هذهجاية من من ست او
+
+734
+00:53:53,060 --> 00:53:57,740
+مجموعة واحد اتنين تلتة بيكفي نفترض انه تلتة طبعا
+
+735
+00:53:57,740 --> 00:54:05,680
+تلتة متواضعة جدا ككست عبارة عن if one and if two
+
+736
+00:54:05,680 --> 00:54:11,000
+and if three طبعا لو اكتر معناته هناخد وسعة كتير
+
+737
+00:54:11,000 --> 00:54:17,660
+لأ احنا كدا ممكن نكتبها if of x ونعرف لاحقا الال
+
+738
+00:54:17,660 --> 00:54:22,220
+universe of discourse هنسميها أو فضاء العينة لهنا
+
+739
+00:54:22,220 --> 00:54:25,420
+بنسيب الموضوع اللي predicated هذا نخليه للمرة
+
+740
+00:54:25,420 --> 00:54:29,920
+الجاية ان شاء الله بنشرحه بالتفصيل و بننهيه جزئية
+
+741
+00:54:29,920 --> 00:54:33,260
+ال equivalence او ال propositional equivalence
+
+742
+00:54:33,260 --> 00:54:36,180
+بتاعتنا فيعطيكوا العافية و بارك الله فيكوا للمرة
+
+743
+00:54:36,180 --> 00:54:38,560
+الجاية ان شاء الله تعالى و السلام عليكم و رحمة
+
+744
+00:54:38,560 --> 00:54:45,260
+الله تعالى و بركاته و بدنا نعرف هنا أول التعريف
+
+745
+00:54:45,260 --> 00:54:45,620
+تبعنا
+
+746
+00:55:04,220 --> 00:55:08,160
+عشان تكون even المفروض ان هي تساوي اتنين في رقم
+
+747
+00:55:08,160 --> 00:55:14,950
+تاني بمعنى اخر بتقسم على اتنينبمعنى اخر ان هي رقم
+
+748
+00:55:14,950 --> 00:55:18,530
+بيقسم على اتنين طيب هنتأكد من الكلام ده هل هو فعلا
+
+749
+00:55:18,530 --> 00:55:22,630
+في عنده رقم بيقسم على اتنين بيمشي الكلام ده كيف
+
+750
+00:55:22,630 --> 00:55:29,170
+ممكن نعبر عنها رياضيا فهقول مدام even كل القيم كل
+
+751
+00:55:29,170 --> 00:55:34,430
+x اللي ممكن نعبر عنها ان هي even المفروض تحقيق لنا
+
+752
+00:55:34,430 --> 00:55:41,170
+الشغل التالي ان هي even by conditional there exist
+
+753
+00:55:41,170 --> 00:55:49,390
+ysuch that x equal to 2y معناته هي even إذا كان
+
+754
+00:55:49,390 --> 00:55:57,750
+موجود لكل قيمة ل x هتكون even امتى إذا كانت يوجد y
+
+755
+00:55:57,750 --> 00:56:04,230
+نص x هاي معناها فمعناه ذاك ضامن إن x هي تعتبر ضعف
+
+756
+00:56:04,230 --> 00:56:09,190
+أي رقم تاني ضعف some number ضعف أي رقم تاني مدام
+
+757
+00:56:09,190 --> 00:56:12,890
+ضعف أي رقم تاني بتجبل جسمها اتنين مدام جبلت القسم
+
+758
+00:56:12,890 --> 00:56:17,810
+ع اتنينأكيد even .. اكيد even .. اكيد even زوجي ..
+
+759
+00:56:17,810 --> 00:56:21,110
+رقم زوجي .. اكيد هتكون رقم زوجي .. كمان مرة for
+
+760
+00:56:21,110 --> 00:56:29,430
+all x لكل قيم x ال .. even .. x is even if and
+
+761
+00:56:29,430 --> 00:56:32,510
+only if مش هاد ال if and only if .. by conditional
+
+762
+00:56:32,510 --> 00:56:37,610
+.. هيها لاحظوا هنترجمها هيها a number x is even
+
+763
+00:56:37,610 --> 00:56:43,830
+فإذا for all x a number x is even هيهاif and only
+
+764
+00:56:43,830 --> 00:56:50,770
+if it's equal to two times some other number some
+
+765
+00:56:50,770 --> 00:56:53,010
+other number معناته بدي اعرف إيش ال other number
+
+766
+00:56:53,010 --> 00:56:57,590
+هذا there exists y y other number عن x إيش العلاقة
+
+767
+00:56:57,590 --> 00:57:02,210
+بينهم two times معناته ال x هذه تساوي two times of
+
+768
+00:57:02,210 --> 00:57:06,050
+ال other number اللي عرفناها إنه موجود رقم تاني
+
+769
+00:57:06,050 --> 00:57:11,840
+يمثل نص x موجود رقم تاني يمثل نص xففي الحالة دي
+
+770
+00:57:11,840 --> 00:57:20,660
+بنقول إنه فعلا الرقم هذا even الرقم even طيب آخر
+
+771
+00:57:20,660 --> 00:57:27,760
+مثال a number is prime P of Xأنت بيكون فعلا prime
+
+772
+00:57:27,760 --> 00:57:31,280
+if and only if it's greater than one لازم يكون
+
+773
+00:57:31,280 --> 00:57:34,180
+أكبر من واحد بقدرش أقول إن الواحد هو prime إن عارف
+
+774
+00:57:34,180 --> 00:57:36,380
+أحسس إن هو prime و خلاص و يدخل معناه في التاريخ
+
+775
+00:57:36,380 --> 00:57:40,080
+لازم يكون أكبر من ال prime and it's not the
+
+776
+00:57:40,080 --> 00:57:47,260
+product of two non unity numbers معناته بقدرش أجيب
+
+777
+00:57:47,260 --> 00:57:51,640
+محصلته من ضرب رقمين بقدرش أجيبه من حاصل ضرب رقمين
+
+778
+00:57:51,640 --> 00:57:54,560
+و لازم نحدد هنا إن الرقمين هدول مايكونش فيهم
+
+779
+00:57:54,560 --> 00:57:55,040
+الواحد
+
+780
+00:57:57,630 --> 00:58:03,090
+لأنه سبعة prime .. prime صح؟ بس بقدر أقول إن هو
+
+781
+00:58:03,090 --> 00:58:07,250
+سبعة في واحد صحيح؟
+
+782
+00:58:07,250 --> 00:58:10,030
+أنتوا فاهمين إن هو .. بتنضربش هذه، بس ال computer
+
+783
+00:58:10,030 --> 00:58:13,010
+بيفهمش، الرياضات بتفهمش، لازم تكون ال expression
+
+784
+00:58:13,010 --> 00:58:16,230
+تبعكوا واضح وشامل، عشان هيك لازم نحدد إن هو
+
+785
+00:58:16,230 --> 00:58:23,310
+مايكونش فيهم الواحد، مايكونش فيهم الواحدخلاص
+
+786
+00:58:23,310 --> 00:58:26,650
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+787
+00:58:26,650 --> 00:58:32,770
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+788
+00:58:32,770 --> 00:58:36,050
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+789
+00:58:36,050 --> 00:58:36,190
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+790
+00:58:36,190 --> 00:58:37,650
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+791
+00:58:37,650 --> 00:58:39,090
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+792
+00:58:39,090 --> 00:58:39,810
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+793
+00:58:39,810 --> 00:58:41,850
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+794
+00:58:41,850 --> 00:58:45,550
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+795
+00:58:45,550 --> 00:58:47,510
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+796
+00:58:47,510 --> 00:58:50,300
+فيهم الواحد مايكونش فيx is prime فهي حقق لـ
+
+797
+00:58:50,300 --> 00:58:54,180
+predicate طيب عشان احققها فعلا امتى بتصير الكلمة
+
+798
+00:58:54,180 --> 00:58:59,180
+if and only if نبدأ نمسكهم شوية شوية و نفتح الأقوى
+
+799
+00:58:59,180 --> 00:59:05,660
+ساعتنا و لاحظوا انه هنا if and only if تمام
+
+800
+00:59:05,660 --> 00:59:10,320
+لاحظوا يعطينا condition يعطينا التاني يعطينا
+
+801
+00:59:10,320 --> 00:59:14,280
+التالت في three conditions حطينا لنا معناته بدنا
+
+802
+00:59:14,280 --> 00:59:18,990
+نربطهم بands فتحنا ال course تبعناهي ال cause
+
+803
+00:59:18,990 --> 00:59:23,050
+تبعنا وهي هنعمل and and and نشوف أشياء مجموعة
+
+804
+00:59:23,050 --> 00:59:25,610
+القيم ال .. ال .. ال .. ال exceptions اللي أعطانا
+
+805
+00:59:25,610 --> 00:59:30,770
+إياها firstly greater than one اه x أكبر من واحد
+
+806
+00:59:30,770 --> 00:59:38,570
+and it's not the product اه هو مش جاي من مجموع
+
+807
+00:59:38,570 --> 00:59:47,170
+ضربين ضرب رقمين معناه لا يوجد is not لا يوجد رقمين
+
+808
+00:59:50,300 --> 00:59:57,200
+X حصل ضربهم بس بدنا نحدد هنا and Y ليست واحد و Z
+
+809
+00:59:57,200 --> 01:00:01,440
+ليست واحد عشان مايروحش يفكر لإن السبعة ممكن تيجي
+
+810
+01:00:01,440 --> 01:00:06,420
+سبعة في واحد عشان ما ال computer و انت بتعملوله
+
+811
+01:00:06,420 --> 01:00:10,300
+code بال expression هذا مايروحش يعتبر ان هي هذه
+
+812
+01:00:10,300 --> 01:00:14,520
+واحد و هي حصل ضرب رقمين بمش الحال لأ بدنا نقوله ان
+
+813
+01:00:14,520 --> 01:00:20,580
+لأ دير بالك الواحدالـ y لازم لا تسوى واحد and z لا
+
+814
+01:00:20,580 --> 01:00:27,840
+تسوى واحد طبعا فلحظه صار بنقدر من الجملة إذا عندنا
+
+815
+01:00:27,840 --> 01:00:33,380
+تعريف لمجموعة معينة من ال numbers بنقدر نعرف منها
+
+816
+01:00:33,380 --> 01:00:37,680
+إيش ال expression تبعنا أو بنقدر نكتب ال
+
+817
+01:00:37,680 --> 01:00:41,860
+expression الرياضي تبعنا رجعوهم في البيت هتلاقيوا
+
+818
+01:00:41,860 --> 01:00:45,690
+إن فعلا إن مسكوهم كلمة كلمةواحدة واحدة هتركبوهم
+
+819
+01:00:45,690 --> 01:00:50,930
+ورا بعض، هتركبوهم ورا بعض، تمام؟ هيك احنا نتخلص و
+
+820
+01:00:50,930 --> 01:00:56,530
+نخلصنا، كل عامة بخير، ال .. طبعا ال .. ال homework
+
+821
+01:00:56,530 --> 01:01:01,450
+مش هتسلمونا إياه للأحد الجاى، هيكون عيد، فبيضل للي
+
+822
+01:01:01,450 --> 01:01:04,470
+بعده ان شاء الله تعالى، للي بعده بإذن الله تعالى،
+
+823
+01:01:04,470 --> 01:01:05,010
+يطبخوا العافية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f01799b9ee01cee6d3dcaf224ac28f07ae7cd66a
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4133, "start": 20.69, "end": 41.33, "text": "بسم الله الرحمن الرحيم أُصل أتواصلهم على أشرف الأنبياء والمسلمين سيدنا محمد وعلى أقلي هو صاحبي أجمالي بنبدأ اليوم ان شاء الله الأسبوع التاني في ال course الأسبوع الأول كنا أخدنا introduction في أول محاضرة أخدنا في الجزء التاني مجموعة ال operators اتكلمنا عن ال propositions بالصفة العامة و بعدين اتكلمنا عن مجموعة operators و أخدنا كيف تشتغل ال operators هذه", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 5551, 10859, 36520, 5551, 2655, 2407, 33546, 1211, 16095, 15844, 5551, 8592, 28480, 16247, 1863, 21292, 16606, 16070, 2304, 3794, 19528, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 4587, 20292, 31439, 20328, 39319, 21292, 5551, 7435, 2304, 6027, 1829, 44945, 44510, 10721, 45595, 20498, 16472, 13412, 16606, 21984, 16247, 35457, 45367, 16712, 7649, 1829, 8978, 2423, 1164, 16247, 35457, 45367, 16247, 12610, 9122, 8315, 5551, 9778, 3215, 8315, 9339, 8978, 5551, 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5172, 3615, 29538, 11778, 47302, 15042, 8032, 2655, 15040, 4587, 14407, 16472, 39896, 11778, 47302, 15042, 2074, 30767, 1829, 5296, 15042, 6055, 9381, 5016, 1829, 31767, 49628, 6055, 39648, 16070, 43761, 45595, 20498, 4724, 16254, 1975, 32887, 5016, 25724, 10943, 27884, 1975, 2407, 3714, 9640, 2407, 5016, 8592, 25724, 10943, 27884], "avg_logprob": -0.20590571932873483, "compression_ratio": 1.4662162162162162, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 924.93, "end": 925.65, "word": "disjunction", "probability": 0.802734375}, {"start": 925.65, "end": 926.31, "word": " negation", "probability": 0.87158203125}, {"start": 926.31, "end": 926.73, "word": " P", "probability": 0.634765625}, {"start": 926.73, "end": 928.91, "word": " بنفع", "probability": 0.7418619791666666}, {"start": 928.91, "end": 930.79, "word": " هذه", "probability": 0.4755859375}, {"start": 930.79, "end": 931.07, "word": " دايما", "probability": 0.7923177083333334}, {"start": 931.07, "end": 931.47, "word": " هتلاقوا", "probability": 0.714794921875}, {"start": 931.47, "end": 931.55, "word": " ان", "probability": 0.5693359375}, {"start": 931.55, "end": 931.71, "word": " هي", "probability": 0.82763671875}, {"start": 931.71, "end": 932.07, "word": " دايما", "probability": 0.8917643229166666}, {"start": 932.07, "end": 932.53, "word": " true", "probability": 0.94482421875}, {"start": 932.53, "end": 932.89, "word": " زي", "probability": 0.91357421875}, {"start": 932.89, "end": 933.01, "word": " لما", "probability": 0.934326171875}, {"start": 933.01, "end": 933.29, "word": " تصحي", "probability": 0.8177490234375}, {"start": 933.29, "end": 933.53, "word": " الصبح", "probability": 0.987548828125}, {"start": 933.53, "end": 933.79, "word": " تقول", "probability": 0.727294921875}, {"start": 933.79, "end": 934.15, "word": " والله", "probability": 0.8984375}, {"start": 934.15, "end": 934.87, "word": " اليوم", "probability": 0.951416015625}, {"start": 934.87, "end": 935.95, "word": " بدي", "probability": 0.775390625}, {"start": 935.95, "end": 936.17, "word": " اروح", "probability": 0.8282063802083334}, {"start": 936.17, "end": 936.71, "word": " الجامعة", "probability": 0.9903971354166666}, {"start": 936.71, "end": 937.11, "word": " او", "probability": 0.915283203125}, {"start": 937.11, "end": 937.43, "word": " ماروحش", "probability": 0.9013671875}, {"start": 937.43, "end": 937.89, "word": " الجامعة", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 38, "seek": 96685, "start": 938.97, "end": 966.85, "text": "طب احنا عارفين انك يا هتروح و يا مش هتروحه يعني إيش لجديد في ال .. يعني وين ال .. ال .. الجملة المفيدة وين المعنى الإضافي اللي ضفته في المعنى مفيش ليش؟ لأنه طبيعي يا الواحد بصحى الصبح يا هيروح الجامعة يا مش هيروح الجامعة مافيش احتمال تالد يا هيروح يا مش هيروح تمام؟ فهنا زي ما نقول P disjunction negation P هذه دائما true جملة بالشكل هذا دائما أبدا هتظل true بغض النظر عن هل ال atomic هي الوحدة", "tokens": [9566, 3555, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 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هو", "probability": 0.25439453125}, {"start": 1213.51, "end": 1213.97, "word": " مساوية", "probability": 0.874755859375}, {"start": 1213.97, "end": 1214.51, "word": " تماما", "probability": 0.99072265625}, {"start": 1214.51, "end": 1215.01, "word": " ل", "probability": 0.7998046875}, {"start": 1215.01, "end": 1215.69, "word": " ال", "probability": 0.470703125}, {"start": 1215.69, "end": 1216.05, "word": " column", "probability": 0.96923828125}, {"start": 1216.05, "end": 1216.63, "word": " تبع", "probability": 0.9840494791666666}, {"start": 1216.63, "end": 1216.75, "word": " ال", "probability": 0.98583984375}, {"start": 1216.75, "end": 1217.13, "word": " proposition", "probability": 0.84619140625}, {"start": 1217.13, "end": 1217.63, "word": " التانية", "probability": 0.8889973958333334}, {"start": 1217.63, "end": 1217.75, "word": " اللي", "probability": 0.904052734375}, {"start": 1217.75, "end": 1218.35, "word": " لازم", "probability": 0.9514973958333334}, {"start": 1218.35, "end": 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{"id": 63, "seek": 163163, "start": 1603.33, "end": 1631.63, "text": "لأن في او فاعتطنى سماحية ان ممكن اي واحد منهم true و الكل الباقي يطلع true ما هو فعلا اكيد في واحد منهم true لان انا حاط true حاطينه اصلا true فعلا طيب نفس الكلام في اش مع ال and اللى هى عملية كأنها عملية ضرب تقابل ضرب في ال decimal system هذه مع صفر صفر ضرب اى قيمة صفر فيمكن هذه بتجرب المفهوم اوضح a proposition", "tokens": [1211, 33456, 8978, 1975, 2407, 6156, 995, 34268, 9566, 1863, 7578, 8608, 15042, 5016, 10632, 16472, 3714, 43020, 1975, 1829, 36764, 24401, 9154, 16095, 2074, 4032, 2423, 28820, 29739, 995, 38436, 7251, 9566, 1211, 3615, 2074, 19446, 31439, 6156, 3615, 15040, 1975, 4117, 25708, 8978, 36764, 24401, 9154, 16095, 2074, 5296, 7649, 1975, 8315, 11331, 41193, 2074, 11331, 41193, 9957, 3224, 1975, 9381, 15040, 2074, 6156, 3615, 15040, 23032, 1829, 3555, 8717, 36178, 2423, 28820, 10943, 8978, 1975, 8592, 20449, 2423, 293, 13672, 7578, 8032, 7578, 6225, 42213, 10632, 9122, 33456, 11296, 6225, 42213, 10632, 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{"start": 2179.05, "end": 2179.37, "word": " الأول", "probability": 0.990478515625}, {"start": 2179.37, "end": 2182.21, "word": " ال", "probability": 0.394775390625}, {"start": 2182.21, "end": 2183.43, "word": " أكبر", "probability": 0.7142333984375}, {"start": 2183.43, "end": 2184.61, "word": " هو", "probability": 0.422119140625}, {"start": 2184.61, "end": 2184.83, "word": " ال", "probability": 0.83349609375}, {"start": 2184.83, "end": 2185.27, "word": " implication", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 86, "seek": 221232, "start": 2186.36, "end": 2212.32, "text": "هو ال implication لأنه بربط ال co باتنين مع بعض فهذا الكبير يعتبر هذا ال operator التاني الأكبر كويس فبنبدأ فيها في ال implication ال implication قلنا ان هي negation الأولى and التانية negation الأولى عفوا or or التانية disjunction or التانية فإذا بتعامل مع هذه كلها هيك كأنها proposition أولى افترض أنها كأنها K", "tokens": [3224, 2407, 2423, 37814, 5296, 33456, 3224, 4724, 25513, 9566, 2423, 598, 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"word": " التانية", "probability": 0.96484375}, {"start": 2204.64, "end": 2205.78, "word": " disjunction", "probability": 0.697998046875}, {"start": 2205.78, "end": 2206.3, "word": " or", "probability": 0.80712890625}, {"start": 2206.3, "end": 2206.86, "word": " التانية", "probability": 0.9656575520833334}, {"start": 2206.86, "end": 2207.32, "word": " فإذا", "probability": 0.8326822916666666}, {"start": 2207.32, "end": 2207.78, "word": " بتعامل", "probability": 0.8477783203125}, {"start": 2207.78, "end": 2207.9, "word": " مع", "probability": 0.9853515625}, {"start": 2207.9, "end": 2208.2, "word": " هذه", "probability": 0.86865234375}, {"start": 2208.2, "end": 2208.58, "word": " كلها", "probability": 0.986572265625}, {"start": 2208.58, "end": 2208.92, "word": " هيك", "probability": 0.8876953125}, {"start": 2208.92, "end": 2209.44, "word": " كأنها", "probability": 0.711669921875}, {"start": 2209.44, "end": 2210.1, "word": " proposition", "probability": 0.623046875}, {"start": 2210.1, 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compound prepositions", "tokens": [9307, 4117, 19528, 8315, 18871, 2423, 14154, 2666, 329, 2451], "avg_logprob": -0.2933238582177596, "compression_ratio": 0.8070175438596491, "no_speech_prob": 0.0, "words": [{"start": 3110.25, "end": 3110.77, "word": "اتكلمنا", "probability": 0.79052734375}, {"start": 3110.77, "end": 3110.87, "word": " عن", "probability": 0.98828125}, {"start": 3110.87, "end": 3110.97, "word": " ال", "probability": 0.91162109375}, {"start": 3110.97, "end": 3111.41, "word": " compound", "probability": 0.61474609375}, {"start": 3111.41, "end": 3112.69, "word": " prepositions", "probability": 0.7084147135416666}], "temperature": 1.0}, {"id": 123, "seek": 313963, "start": 3113.73, "end": 3139.63, "text": "لما بتكلم عن compound propositions أنا بتكلم عن expression لمجموعة propositions مرتبطة بoperators مربوطة بمجموعة operators زي الشكل اللي احنا شايفينه هنا كويس ال equivalence برضه اتكلمنا عن ال equivalence وكيف ممكن استعمل ال equivalence لإثبات اي expression معين فممكن اقول في حالة زي الحلقة اللي عندنا وهذا العلامة أخدناها علامة equivalence", "tokens": [1211, 15042, 39894, 4117, 19528, 18871, 14154, 7532, 2451, 41850, 39894, 4117, 19528, 18871, 6114, 32767, 7435, 2304, 2407, 27884, 7532, 2451, 3714, 43500, 3555, 9566, 3660, 4724, 7192, 3391, 3714, 25513, 2407, 9566, 3660, 4724, 2304, 7435, 2304, 2407, 27884, 19077, 30767, 1829, 25124, 28820, 13672, 1829, 1975, 5016, 8315, 13412, 995, 33911, 9957, 3224, 34105, 9122, 45865, 3794, 2423, 9052, 655, 4724, 43042, 3224, 1975, 2655, 4117, 19528, 8315, 18871, 2423, 9052, 655, 4032, 4117, 33911, 3714, 43020, 44713, 25957, 1211, 2423, 9052, 655, 5296, 28814, 12984, 3555, 9307, 1975, 1829, 6114, 20449, 9957, 6156, 2304, 43020, 1975, 39648, 8978, 11331, 6027, 3660, 30767, 1829, 21542, 1211, 28671, 13672, 1829, 43242, 8315, 37037, 15730, 18863, 37440, 3660, 5551, 9778, 3215, 8315, 11296, 11203, 10943, 3660, 9052, 655], "avg_logprob": -0.15384615327303225, "compression_ratio": 1.9732824427480915, "no_speech_prob": 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"probability": 0.99560546875}, {"start": 3399.17, "end": 3399.83, "word": " a", "probability": 0.80908203125}, {"start": 3399.83, "end": 3400.21, "word": " number", "probability": 0.96044921875}, {"start": 3400.21, "end": 3400.81, "word": " x", "probability": 0.9833984375}, {"start": 3400.81, "end": 3401.05, "word": " is", "probability": 0.97119140625}, {"start": 3401.05, "end": 3401.37, "word": " even", "probability": 0.90771484375}, {"start": 3401.37, "end": 3401.77, "word": " هيها", "probability": 0.903076171875}], "temperature": 1.0}, {"id": 133, "seek": 343083, "start": 3402.99, "end": 3430.83, "text": "if and only if it's equal to two times some other number some other number معناته بدي اعرف إيش ال other number هذا there exists y y other number عن x إيش العلاقة بينهم two times معناته ال x هذه تساوي two times of ال other number اللي عرفناها إنه موجود رقم تاني يمثل نص x موجود رقم تاني يمثل نص x", "tokens": [351, 293, 787, 498, 309, 311, 2681, 281, 732, 1413, 512, 661, 1230, 512, 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طيب آخر مثال a number is prime P of X", "tokens": [5172, 41185, 21542, 6027, 3660, 11778, 1829, 44945, 39648, 36145, 3224, 6156, 3615, 15040, 34892, 4587, 2304, 23758, 754, 34892, 4587, 2304, 754, 23032, 1829, 3555, 19753, 34740, 50113, 6027, 257, 1230, 307, 5835, 430, 295, 1783], "avg_logprob": -0.21319901394216637, "compression_ratio": 1.1794871794871795, "no_speech_prob": 0.0, "words": [{"start": 3431.18, "end": 3431.44, "word": "ففي", "probability": 0.760009765625}, {"start": 3431.44, "end": 3431.7, "word": " الحالة", "probability": 0.9505208333333334}, {"start": 3431.7, "end": 3431.84, "word": " دي", "probability": 0.576416015625}, {"start": 3431.84, "end": 3432.1, "word": " بنقول", "probability": 0.73779296875}, {"start": 3432.1, "end": 3432.28, "word": " إنه", "probability": 0.6707763671875}, {"start": 3432.28, "end": 3432.6, "word": " فعلا", "probability": 0.8421223958333334}, {"start": 3432.6, "end": 3433.96, "word": " الرقم", "probability": 0.9344075520833334}, {"start": 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"word": " بعده", "probability": 0.961669921875}, {"start": 3661.93, "end": 3662.47, "word": " ان", "probability": 0.70361328125}, {"start": 3662.47, "end": 3662.67, "word": " شاء", "probability": 0.962646484375}, {"start": 3662.67, "end": 3662.75, "word": " الله", "probability": 0.9501953125}, {"start": 3662.75, "end": 3663.35, "word": " تعالى،", "probability": 0.9500732421875}, {"start": 3663.35, "end": 3663.53, "word": " للي", "probability": 0.977783203125}, {"start": 3663.53, "end": 3663.75, "word": " بعده", "probability": 0.960205078125}, {"start": 3663.75, "end": 3664.03, "word": " بإذن", "probability": 0.947265625}, {"start": 3664.03, "end": 3664.17, "word": " الله", "probability": 0.95263671875}, {"start": 3664.17, "end": 3664.47, "word": " تعالى،", "probability": 0.97607421875}, {"start": 3664.47, "end": 3664.69, "word": " يطبخوا", "probability": 0.6158203125}, {"start": 3664.69, "end": 3665.01, "word": " العافية", "probability": 0.6457112630208334}], "temperature": 1.0}], 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3fa830287b9714470610aabb629ce1c989732e99
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/uuf30_Y1Ync_raw.srt
@@ -0,0 +1,3364 @@
+1
+00:00:20,690 --> 00:00:23,010
+بسم الله الرحمن الرحيم أُصل أتواصلهم على أشرف
+
+2
+00:00:23,010 --> 00:00:25,170
+الأنبياء والمسلمين سيدنا محمد وعلى أقلي هو صاحبي
+
+3
+00:00:25,170 --> 00:00:28,050
+أجمالي بنبدأ اليوم ان شاء الله الأسبوع التاني في
+
+4
+00:00:28,050 --> 00:00:31,510
+ال course الأسبوع الأول كنا أخدنا introduction في
+
+5
+00:00:31,510 --> 00:00:33,930
+أول محاضرة أخدنا في الجزء التاني مجموعة ال
+
+6
+00:00:33,930 --> 00:00:36,870
+operators اتكلمنا عن ال propositions بالصفة العامة
+
+7
+00:00:36,870 --> 00:00:40,110
+و بعدين اتكلمنا عن مجموعة operators و أخدنا كيف
+
+8
+00:00:40,110 --> 00:00:44,500
+تشتغل ال operators هذهيمكن ال .. هنا بنلخص مجموعة
+
+9
+00:00:44,500 --> 00:00:47,220
+ال operators اللي اتكلمنا عنها سابقا اتكلمنا عن ال
+
+10
+00:00:47,220 --> 00:00:50,160
+negation اتكلمنا عن ال conjunction اتكلمنا عن ال
+
+11
+00:00:50,160 --> 00:00:53,240
+dis على ال disjunction اتكلمنا عن ال XOR و ال
+
+12
+00:00:53,240 --> 00:00:56,980
+implication و ال biconditional و ال biconditional
+
+13
+00:00:56,980 --> 00:01:02,440
+فاليوم بنكمل بسمع جزئية هيك سريعة عن ال bits and
+
+14
+00:01:02,440 --> 00:01:05,680
+bit operations و بعدين بننجل لل equivalence و هي
+
+15
+00:01:05,680 --> 00:01:07,460
+الجزء اللي .. اللي .. اللي اهم هيكون اليوم في
+
+16
+00:01:07,460 --> 00:01:11,720
+محاضرتنا اللي هيال propositional equivalence في
+
+17
+00:01:11,720 --> 00:01:15,100
+شغلنا فخلينا اليوم نبدأ بسريع هيك على ال bits and
+
+18
+00:01:15,100 --> 00:01:19,760
+bit operations ال bit احنا التعامل اللي كله هيكون
+
+19
+00:01:19,760 --> 00:01:22,740
+مع ال binary مجموعة bits هتكون binary فbinary
+
+20
+00:01:22,740 --> 00:01:28,300
+بتكلم عن ال PS2بمعنى انه كل bit بقدر امثلها two
+
+21
+00:01:28,300 --> 00:01:32,560
+elements اللي هم ال zero و ال one فعليا احنا بنقدر
+
+22
+00:01:32,560 --> 00:01:35,980
+.. يعني ال binary هذه بتمثل .. بتعبرنا عن ال logic
+
+23
+00:01:35,980 --> 00:01:39,280
+ليش؟ بتعبرنا عن ال logic لإن ال zero represents
+
+24
+00:01:39,280 --> 00:01:43,500
+false ال one represents true فانا كأني بتعامل
+
+25
+00:01:43,500 --> 00:01:47,340
+معاها على أساس ان هي false true true false أو
+
+26
+00:01:47,340 --> 00:01:52,160
+false true طيب هذه مناضرة تماما للعمليات الحسابية
+
+27
+00:01:52,160 --> 00:01:56,260
+اللي كنتوا بتشتغلوها زمان الجامعةوالضرب ففعليا ال
+
+28
+00:01:56,260 --> 00:02:00,960
+or هي مقابلة للجمع وال and مقابلة لمين لعملية
+
+29
+00:02:00,960 --> 00:02:06,840
+الضرب طيب ال bit strings ال bit strings هي مجموعة
+
+30
+00:02:06,840 --> 00:02:11,260
+bits متسلسلة حوالين بعضها بحيث ان هي معطينا series
+
+31
+00:02:11,260 --> 00:02:17,500
+معينة او sequence معطينا سلسلة من ال bits او ارقام
+
+32
+00:02:17,500 --> 00:02:23,330
+متعاقبة sequenceof n و n لازم تكون اكبر من صفر
+
+33
+00:02:23,330 --> 00:02:27,690
+اكبر من صفر اكبر او تساوي صفر بحيث ان يكون فعلا
+
+34
+00:02:27,690 --> 00:02:31,070
+فينا sequence اذا كانت صفر فال sequence هذا empty
+
+35
+00:02:31,070 --> 00:02:34,330
+sequence بمعنى او ال string empty بمعنى string
+
+36
+00:02:34,330 --> 00:02:37,730
+فاضي زي لما كنا .. هناخدها لحظة طبعا لما نتكلم عن
+
+37
+00:02:37,730 --> 00:02:43,600
+المجموعات الفارغة او المجموعات الخالية المهمفي
+
+38
+00:02:43,600 --> 00:02:46,320
+عندنا sequence، في عندنا مجموعة bits، ال bits هذه
+
+39
+00:02:46,320 --> 00:02:52,060
+تمثل لنا sequence معين أو string معين، ال string
+
+40
+00:02:52,060 --> 00:02:57,140
+هذا هنستخدمه عادة كمجموعة bits متقاربة أو متجاورة
+
+41
+00:02:57,140 --> 00:03:01,460
+مع بعض، المتجاورة هذه بنبدأ دايما من اليمينبنبدأ
+
+42
+00:03:01,460 --> 00:03:04,120
+من اليمين يعني لل sequence اللي موجود قدامنا هنا
+
+43
+00:03:04,120 --> 00:03:07,000
+اللي هو one zero zero one one zero one zero one
+
+44
+00:03:07,000 --> 00:03:12,280
+zero اول element او bit فيه هي ال one فانا بتطلع
+
+45
+00:03:12,280 --> 00:03:17,220
+من الشمال لليمين وفعلا هي ال most significant bit
+
+46
+00:03:17,220 --> 00:03:21,560
+هي ال bit الاكبر قيمة فيهم ال bit الاكبر قيمة فيهم
+
+47
+00:03:21,560 --> 00:03:25,510
+في ال decimal system نفس الكلام موجود احناممكن
+
+48
+00:03:25,510 --> 00:03:29,070
+استعمل الرقم خمسة الرقم خمسة هذا وين الخانة تبعته
+
+49
+00:03:29,070 --> 00:03:34,150
+بيعطيني ال significant تبعته فلما بتكلم عن خمسة
+
+50
+00:03:34,150 --> 00:03:37,350
+بهذا
+
+51
+00:03:37,350 --> 00:03:41,310
+الشكل مثلا في خمسة وستين هي الخمسة هنا تمثل أحد
+
+52
+00:03:41,310 --> 00:03:45,830
+فالخانة بتاعتها الأحد طيب لو الخمسة هنا لأ موجودة
+
+53
+00:03:45,830 --> 00:03:50,170
+في العشرات لأ القيمة بتاعتها صارت أعلى بمعنى أنه
+
+54
+00:03:50,170 --> 00:03:55,270
+لو اتغيرت التغير كبير هيصيرفهنا نفس الكلام ال most
+
+55
+00:03:55,270 --> 00:03:58,810
+significant هي ال bit اللي جاية على ناحية اليمين و
+
+56
+00:03:58,810 --> 00:04:01,810
+عشان نوضح الموضوع هذا انتوا برضه كنتوا تعملوا
+
+57
+00:04:01,810 --> 00:04:03,850
+conversion او كنتوا تعملوا تحويل من system ل
+
+58
+00:04:03,850 --> 00:04:07,690
+system من binary ل decimal و من decimal ل .. ل hex
+
+59
+00:04:07,690 --> 00:04:11,130
+أو من hex كنتوا تشتغلوها كتير فلو قلنا اي .. اي ..
+
+60
+00:04:12,230 --> 00:04:16,650
+Example بالشكل هذا عشان نشعر من وين تليجي ال
+
+61
+00:04:16,650 --> 00:04:19,170
+significant بتبعتنا ال significant بنبدأها دايما
+
+62
+00:04:19,170 --> 00:04:22,790
+من اليمين هي الأقل significant ممكن انا بتعامل هنا
+
+63
+00:04:22,790 --> 00:04:28,850
+ان كل pet لها قيمتين اما zero او one فانا بتعامل
+
+64
+00:04:28,850 --> 00:04:34,720
+على ال path two فهي two to the power zero2 to the
+
+65
+00:04:34,720 --> 00:04:38,300
+power of 1 2 to the power of 2 2 to the power of 3
+
+66
+00:04:38,300 --> 00:04:42,780
+2 to the power of .. و هكذا بقارن كل واحدة في أي
+
+67
+00:04:42,780 --> 00:04:45,840
+خانة وهذا انتوا كنتوا تعملوه حتى في الأرقام
+
+68
+00:04:45,840 --> 00:04:48,680
+العشرية في الأرقام العشرية هي من وين جاي الأرقام
+
+69
+00:04:48,680 --> 00:04:53,660
+العشرية عند ما نقول 65 5 و 6 ال 65 هذه جاية من 10
+
+70
+00:04:53,660 --> 00:04:59,400
+to the power of 0 ضرب 5 و 10 to the power of 1 ضرب
+
+71
+00:04:59,400 --> 00:05:05,900
+6 و 10 to the power of 2 ضرب 3فبيعطييني جدش القيمة
+
+72
+00:05:05,900 --> 00:05:09,060
+هذه .. بيعطييني جدش قيمة .. القيمة هذه تحديدا ..
+
+73
+00:05:09,060 --> 00:05:14,300
+فهنا هيكون هذه كيلومتر واحد في خمسة في خمسة عشرة
+
+74
+00:05:14,300 --> 00:05:21,570
+في ستة في ستين مية تلات ميةاجمعوهم بيطلع تلاتمية
+
+75
+00:05:21,570 --> 00:05:26,150
+خمسة وستين تمام نفس الكلام بنستعمله في ال other
+
+76
+00:05:26,150 --> 00:05:28,170
+systems يعني في كل ال systems التانية اللي غير ال
+
+77
+00:05:28,170 --> 00:05:30,490
+decimal مش معناه ان بتنعمل في ال decimal فنفس
+
+78
+00:05:30,490 --> 00:05:36,430
+الكلام هنا هتلاقوا ان في عندكم one في one one plus
+
+79
+00:05:36,430 --> 00:05:48,420
+two في zero four في zero eight في oneفهنا بتطلع
+
+80
+00:05:48,420 --> 00:05:53,580
+تسعة هذا الرقم تمثل تسعة فلاحظوا ان ال bet الأخيرة
+
+81
+00:05:53,580 --> 00:05:57,720
+اللي هي جاية في ال left هي الأعلى قيمة هي الأعلى
+
+82
+00:05:57,720 --> 00:06:01,940
+قيمة ليش؟ لأنهم ضربت في أعلى coefficient في 2 to
+
+83
+00:06:01,940 --> 00:06:06,620
+the power 3 بالنسبة للرقم تبعنا 2 to the power 3
+
+84
+00:06:06,620 --> 00:06:15,220
+فعليا
+
+85
+00:06:16,400 --> 00:06:19,960
+العشر قصابيع أكم برقم بقدر أعد فيهم أو لعند جد إيش
+
+86
+00:06:19,960 --> 00:06:24,020
+بقدر أعد فيهم باستخدام ال decimal لعند عشرة الولد
+
+87
+00:06:24,020 --> 00:06:26,840
+الصغير اللي مابنعلمه كل واحد اتنين تلاتة لعند عشرة
+
+88
+00:06:26,840 --> 00:06:30,380
+فبقدر لعند عشرة لأ actually احنا بقدر نعد فيه لعند
+
+89
+00:06:30,380 --> 00:06:35,580
+الف تلاتة وعشرين لو أتعاملنا معاه ك bits و بنتعامل
+
+90
+00:06:35,580 --> 00:06:39,180
+معاه ك binary فممكن أقول ببدأ دايما زي ما قلنا من
+
+91
+00:06:39,180 --> 00:06:43,500
+الشمالبنبدأ او يعني بالنسبالي انا شمال حيكون
+
+92
+00:06:43,500 --> 00:06:45,700
+بالنسبالي كنت اليمين يعني فعليا نبدأ بيمين من
+
+93
+00:06:45,700 --> 00:06:53,640
+الأقل significant هيها فهقول كله صفر هيك واحد طب
+
+94
+00:06:53,640 --> 00:06:56,820
+عشان اغير اعمل flip او اغير اعمل ال count اللي
+
+95
+00:06:56,820 --> 00:07:02,800
+وراه ببدأ برضه دايما يمين اذا و جابلت واحد صفر و
+
+96
+00:07:02,800 --> 00:07:07,720
+بعطي واحد للي وراه فصارت صفر واحد صفر واحد تمثل
+
+97
+00:07:07,720 --> 00:07:13,840
+اتنينمش يمثلوا رقم اتنين لأن الباقي كل zeros طيب
+
+98
+00:07:13,840 --> 00:07:19,880
+هاي اتنين طيب عشان هالوجه اجيب الرقم اللي ورا ببدأ
+
+99
+00:07:19,880 --> 00:07:23,200
+اذا كان لجيت صفر برضه من اليمين لجيت صفر بحاوله
+
+100
+00:07:23,200 --> 00:07:30,320
+لواحد وخلصنا هاي صار رقم تلاتة طيب رقم اربعة لجيت
+
+101
+00:07:30,320 --> 00:07:34,400
+واحد باجلبها صفر و بنجل ع اللي ورا واحد برضه
+
+102
+00:07:34,400 --> 00:07:37,480
+باجلبها صفر و بنجل ع اللي ورا فصارت ايه صفر صفر
+
+103
+00:07:37,480 --> 00:07:45,540
+واحد صفر صفر واحدأربعة وهكذا فهذه عملية ال
+
+104
+00:07:45,540 --> 00:07:50,020
+counting على باستخدام ال binary in binary فهتلاجوا
+
+105
+00:07:50,020 --> 00:07:53,520
+دايما بتعملوا change من one to zero من one to zero
+
+106
+00:07:53,520 --> 00:07:57,800
+إذا كان جبل to one في وشكه من اليمين من اليمين
+
+107
+00:07:57,800 --> 00:08:02,420
+دايما بتبدو العدل من اليمين من الأقل أهمية عشان
+
+108
+00:08:02,420 --> 00:08:05,340
+تطلعوا فيها ل .. ل .. ل .. لما تصلوا ل ال most
+
+109
+00:08:05,340 --> 00:08:12,180
+significant فبتعملوا flip to the next bitOkay ال
+
+110
+00:08:12,180 --> 00:08:15,480
+.. ال bitwise .. bitwise operations احنا قبل هيك
+
+111
+00:08:15,480 --> 00:08:19,300
+تقولنا انه لما اتكلمنا المرة اللي فاتت و قولنا انه
+
+112
+00:08:19,300 --> 00:08:22,840
+في البرمجة هتاخدوا حاجة اسمها wordwise او bitwise
+
+113
+00:08:22,840 --> 00:08:26,060
+bitwise انا بتعامل معها ال sequence تبعي bit by
+
+114
+00:08:26,060 --> 00:08:29,480
+bit فإذا كل bit داخل ال sequence بتعامل معاها
+
+115
+00:08:29,480 --> 00:08:33,500
+كأنها مستقلة ب .. بقارنها بال bit المقابلة لها في
+
+116
+00:08:33,500 --> 00:08:36,380
+ال sequence التاني و بعمل ال operation تبعتي بنعمل
+
+117
+00:08:36,380 --> 00:08:40,130
+ال operation بتاعتنا معنى ذلكمعنى ذلك إن لو بدنا
+
+118
+00:08:40,130 --> 00:08:42,690
+.. عنا .. عنا two sequence بالشكل اللي احنا
+
+119
+00:08:42,690 --> 00:08:47,230
+شايفينه هذا و بدنا نشتغل bitwise بمعنى أنا بعملش
+
+120
+00:08:47,230 --> 00:08:51,770
+للكلمة كلها على بعض مع الكلمة كلها على بعض لأ لكل
+
+121
+00:08:51,770 --> 00:08:56,690
+bit مع ال bit المقابلة لها، كويس لو بدنا نعمل
+
+122
+00:08:56,690 --> 00:09:02,730
+operator or, bitwise or بمسك كل واحدة مع الم .. مع
+
+123
+00:09:02,730 --> 00:09:06,850
+ما يقابلهامع ما يقابلها طيب لو ال sequence عندكم
+
+124
+00:09:06,850 --> 00:09:12,270
+أصلا ال n تبعد كل واحد منهم مختلف عن التانية ال n
+
+125
+00:09:12,270 --> 00:09:15,590
+واحد و ال n اتنين ال n الأولى نفترض ستة فهي فيها
+
+126
+00:09:15,590 --> 00:09:22,490
+ستة elements و ال n التانية خمسة نكمل ب zeros و
+
+127
+00:09:22,490 --> 00:09:26,410
+هتلاحظوا أننا فعلا مكملينها هنا ب zero ال element
+
+128
+00:09:26,410 --> 00:09:30,120
+الأول هذا او ال sequence الأول هو فعلا هنا بسبس في
+
+129
+00:09:30,120 --> 00:09:34,500
+zero بتكملوا بتقدروا تعملوا ال bit ال string
+
+130
+00:09:34,500 --> 00:09:45,020
+بتعملوا طيب or zero or one one one one one one one
+
+131
+00:09:45,020 --> 00:09:45,200
+one one one one one one one one one one one one
+
+132
+00:09:45,200 --> 00:09:45,200
+one one one one one one one one one one one one
+
+133
+00:09:45,200 --> 00:09:45,240
+one one one one one one one one one one one one
+
+134
+00:09:45,240 --> 00:09:47,100
+one one one one one one one one one one one one
+
+135
+00:09:47,100 --> 00:09:47,100
+one one one one one one one one one one one one
+
+136
+00:09:47,100 --> 00:09:47,100
+one one one one one one one one one one one one
+
+137
+00:09:47,100 --> 00:09:47,140
+one one one one one one one one one one one one
+
+138
+00:09:47,140 --> 00:09:47,400
+one one one one one one one one one one one one
+
+139
+00:09:47,400 --> 00:09:50,660
+one one one one one one
+
+140
+00:09:50,660 --> 00:09:50,680
+one one one one one one one one one one one one
+
+141
+00:09:50,680 --> 00:09:50,680
+one one one one one one one one one one one one
+
+142
+00:09:50,680 --> 00:09:50,680
+one one one one one one one one one one one one
+
+143
+00:09:50,680 --> 00:09:50,680
+one one one one one one one one one one one one
+
+144
+00:09:50,680 --> 00:09:50,680
+one one one one one one one one one one one one
+
+145
+00:09:50,680 --> 00:09:50,680
+one one one one one one one one one one one one
+
+146
+00:09:50,680 --> 00:09:50,680
+one one one one one one one one one one one one
+
+147
+00:09:50,680 --> 00:09:57,460
+oneاللي عندك عارفين كله zero باستثناء one and one
+
+148
+00:09:57,460 --> 00:10:01,800
+one and one هاي في عندي one and one وهي one and
+
+149
+00:10:01,800 --> 00:10:07,340
+one وهي one and one otherwise zeros otherwise
+
+150
+00:10:07,340 --> 00:10:16,000
+zeros طيب x or one امتى اذا اختلفوا اذا اختلفوا
+
+151
+00:10:16,000 --> 00:10:20,220
+اذا اختلفوا طيب اذا كان متشابهين zeros تعالى نشوف
+
+152
+00:10:20,220 --> 00:10:24,550
+وين في متشابهين هاي في عندي متشابه واحدة zeroهي
+
+153
+00:10:24,550 --> 00:10:29,250
+متشابه فهي متشابه فهي متشابه فهي متشابه فهي متشابه
+
+154
+00:10:29,250 --> 00:10:35,490
+فهي متشابه فهي متشابه فهي متشابه فهي متشابه فهي
+
+155
+00:10:35,490 --> 00:10:42,290
+متشابه فهي متشابه فهي
+
+156
+00:10:42,290 --> 00:10:44,490
+متشابه فهي متشابه فهي متشابه فهي متشابه فهي متشابه
+
+157
+00:10:44,490 --> 00:10:44,490
+فهي متشابه فهي متشابه فهي متشابه فهي متشابه فهي
+
+158
+00:10:44,490 --> 00:10:47,730
+متشابه فهي متشابه فهي متشابه فهي متشابه فهي متشابه
+
+159
+00:10:47,730 --> 00:10:50,170
+فهي متشابه فهي متشابه فهي متشابه فهي متشابه فهي
+
+160
+00:10:50,170 --> 00:10:51,580
+متشابه فهي متشابه فهي متشابه فاللي احنا عملناها طب
+
+161
+00:10:51,580 --> 00:10:54,220
+ممكن تجربوا operators تانية كمان ممكن تجربوا أي
+
+162
+00:10:54,220 --> 00:10:58,520
+operators تانية و خصوصا ان انتوا مر عليكوا يعني
+
+163
+00:10:58,520 --> 00:11:01,540
+ممكن تجربوها على فكرة باستخدام ال java لو اتعلمتوا
+
+164
+00:11:01,540 --> 00:11:05,200
+ال java و يعملوا sequence معين عندكم واستعملوا ال
+
+165
+00:11:05,200 --> 00:11:10,860
+bitwise علامة ال bitwise هذه استعملوهم هيتطلعوا
+
+166
+00:11:10,860 --> 00:11:17,940
+نفس الحلول اللي احنا اشتغلنا عليها طيب نقول
+
+167
+00:11:17,940 --> 00:11:24,450
+لموضوعنابتاع اليوم هذه الجزئية كملنا فيها محاضرة
+
+168
+00:11:24,450 --> 00:11:28,610
+المرة اللي فاتت نبدأ في جزء اليوماللي هو ال
+
+169
+00:11:28,610 --> 00:11:34,330
+propositional equivalence طيب لفظيا او معناها
+
+170
+00:11:34,330 --> 00:11:38,310
+textually بالحرف معناها بالحرف different compound
+
+171
+00:11:38,310 --> 00:11:43,850
+propositions may be the semantically identical إيش
+
+172
+00:11:43,850 --> 00:11:46,710
+يعني identical؟ معناه ذلك إنه have the same
+
+173
+00:11:46,710 --> 00:11:50,850
+meaning إيش يعني؟ برضه هنا معناه ذلك إنه حرفيا
+
+174
+00:11:50,850 --> 00:11:56,600
+موجود عندنا twodifferent compound prepositions
+
+175
+00:11:56,600 --> 00:12:02,240
+عندنا prepositions او تصريحين two sentences عندنا
+
+176
+00:12:02,240 --> 00:12:08,720
+فرضيتين مركبات و مختلفات preposition اول
+
+177
+00:12:08,720 --> 00:12:13,890
+preposition تاني ولكن لهم نفسالمعنى اللي هم نفس
+
+178
+00:12:13,890 --> 00:12:17,250
+المعنى فهدول المفروض اللي هم identical معنى ذلك
+
+179
+00:12:17,250 --> 00:12:20,030
+انه في equivalent between them او equivalence
+
+180
+00:12:20,030 --> 00:12:22,430
+between them كل واحدة equivalent للتانية كل واحدة
+
+181
+00:12:22,430 --> 00:12:27,050
+منهم هتكون equivalent للتانية ال .. و بدنا نركز بس
+
+182
+00:12:27,050 --> 00:12:29,590
+هنا على compound لأن معظم شغلنا هيشتغل على
+
+183
+00:12:29,590 --> 00:12:33,730
+compound ال compound هي فعليا proposition متكونة
+
+184
+00:12:33,730 --> 00:12:40,350
+من مجموعة atomic propositions لما بقول P هي atomic
+
+185
+00:12:40,350 --> 00:12:45,390
+propositionP في الفرضية بتاعتنا هي P خلاص هي
+
+186
+00:12:45,390 --> 00:12:48,810
+proposition ال proposition هذا atomic proposition
+
+187
+00:12:48,810 --> 00:12:54,390
+بنسميه طيب نفترض employees Q هذه هي كلها على بعض
+
+188
+00:12:54,390 --> 00:12:59,590
+compound proposition compound proposition طيب هذه
+
+189
+00:12:59,590 --> 00:13:04,490
+بدنا نعمل check هل هي مكافئة لحظه ولا لأ ل
+
+190
+00:13:04,490 --> 00:13:09,690
+whatever يعني هل هي مكافئة مثلا ل Q employees P
+
+191
+00:13:11,790 --> 00:13:16,230
+ولّا لأ؟ فلاحظوا هنا صارت compound preposition ..
+
+192
+00:13:16,230 --> 00:13:20,350
+compound preposition فصارت compound prepositions
+
+193
+00:13:20,350 --> 00:13:24,990
+هل هم .. لهم نفس ال meaning .. نفس .. have the
+
+194
+00:13:24,990 --> 00:13:28,570
+same meaning ولا لأ؟ the same meaning هناخدها بشكل
+
+195
+00:13:28,570 --> 00:13:33,430
+..رياضة بشكل اثبتة proof معينة و هنعرف هل هما فعلا
+
+196
+00:13:33,430 --> 00:13:36,410
+مثل الطباطة طبعا هي لا تثبت لا يكافئوا بعض في
+
+197
+00:13:36,410 --> 00:13:38,870
+الحالة اللي هنتكلم عليها هنا لا يكافئوا بعض ولكن
+
+198
+00:13:38,870 --> 00:13:42,850
+بدنا نعمل test نشوف كيف الموضوع فهذه هيك compound
+
+199
+00:13:42,850 --> 00:13:46,310
+proposition لأنه متكونة من اكتر من ال proposition
+
+200
+00:13:46,310 --> 00:13:49,390
+هي متكونة من مجموعة ايه اش atomic atomic
+
+201
+00:13:49,390 --> 00:13:52,030
+propositions كل واحدة من هدولة اللي هي اقل
+
+202
+00:13:52,030 --> 00:13:56,210
+proposition ممكن اقل جملة لها معنى اقل جملة لها
+
+203
+00:13:56,210 --> 00:14:01,880
+معنى atomic propositionطبعا هنستعمل مجموعة
+
+204
+00:14:01,880 --> 00:14:07,480
+equivalence rules and laws مجموعة قوانين وقواعد لل
+
+205
+00:14:07,480 --> 00:14:11,920
+equivalence عساس ان نمثل فيها او نعمل ال proof ..
+
+206
+00:14:11,920 --> 00:14:16,840
+ال proof سبعتنا ال proof سبعتنا هنستعمل حتين
+
+207
+00:14:16,840 --> 00:14:20,140
+الحقيقة اليوم هنشتغل على ال truth table باستخدام
+
+208
+00:14:20,140 --> 00:14:23,760
+truth table جدول الحقيقة و هنستعمل ال symbolic
+
+209
+00:14:23,760 --> 00:14:28,050
+derivations .. نستعمل ال symbolicneurovisions طيب
+
+210
+00:14:28,050 --> 00:14:30,570
+عشان نشتغل علي الموضوع هذا و نشوف هل اتنهى ال
+
+211
+00:14:30,570 --> 00:14:33,710
+covenant لبعض ولا لأ ممكن نشتغل علي حاجة يعني في
+
+212
+00:14:33,710 --> 00:14:37,470
+مصطلحين مهمين جدا بدنا نشتغل عليهم tautologies و
+
+213
+00:14:37,470 --> 00:14:40,790
+ال contradictions tautologies و ال contradictions
+
+214
+00:14:40,790 --> 00:14:44,830
+ال tautologies لما أقول tautology معناته حشو كلام
+
+215
+00:14:44,830 --> 00:14:49,330
+ع الفاضي رغي رغي سواء انجلوا ولا ما انجلش المعنى
+
+216
+00:14:49,330 --> 00:14:53,770
+واضح خلاص يعني زيادة على الفاضي زيادة هيك هذه
+
+217
+00:14:53,770 --> 00:14:57,880
+معناتهزي ما هو في التعريف الـ tautology is a
+
+218
+00:14:57,880 --> 00:15:00,680
+compound proposition that's true no matter what
+
+219
+00:15:00,680 --> 00:15:04,480
+the truth values of its atomic propositions are
+
+220
+00:15:04,480 --> 00:15:08,380
+بغض النظر جدش قيمة ال atomic لكل واحد ال atomic
+
+221
+00:15:08,380 --> 00:15:10,920
+propositions بتاعة كل واحدة منهم بغض النظر false
+
+222
+00:15:10,920 --> 00:15:14,320
+or true هتلاقوا إن ال compound كله على بعضه دائما
+
+223
+00:15:14,320 --> 00:15:20,120
+true مدام هيك معناته صح دائما صح مدام دائما صح طب
+
+224
+00:15:20,120 --> 00:15:23,640
+ليش بتقول ليه؟ خلاص يعني أشي مسلم فيه زي لما نقول
+
+225
+00:15:23,640 --> 00:15:31,550
+Pdisjunction negation P بنفع هذه دايما هتلاقوا ان
+
+226
+00:15:31,550 --> 00:15:34,870
+هي دايما true زي لما تصحي الصبح تقول والله اليوم
+
+227
+00:15:34,870 --> 00:15:39,670
+بدي اروح الجامعة او ماروحش الجامعةطب احنا عارفين
+
+228
+00:15:39,670 --> 00:15:42,690
+انك يا هتروح و يا مش هتروحه يعني إيش لجديد في ال
+
+229
+00:15:42,690 --> 00:15:45,810
+.. يعني وين ال .. ال .. الجملة المفيدة وين المعنى
+
+230
+00:15:45,810 --> 00:15:49,570
+الإضافي اللي ضفته في المعنى مفيش ليش؟ لأنه طبيعي
+
+231
+00:15:49,570 --> 00:15:51,690
+يا الواحد بصحى الصبح يا هيروح الجامعة يا مش هيروح
+
+232
+00:15:51,690 --> 00:15:55,110
+الجامعة مافيش احتمال تالد يا هيروح يا مش هيروح
+
+233
+00:15:55,110 --> 00:15:59,770
+تمام؟ فهنا زي ما نقول P disjunction negation P هذه
+
+234
+00:15:59,770 --> 00:16:03,270
+دائما true جملة بالشكل هذا دائما أبدا هتظل true
+
+235
+00:16:03,270 --> 00:16:08,730
+بغض النظر عن هل ال atomic هي الوحدةالواحدة منهم ال
+
+236
+00:16:08,730 --> 00:16:13,290
+atomic هادي او هادي true or false مش هتفرج
+
+237
+00:16:13,290 --> 00:16:17,090
+whatever يعني ايش ما تكون القيمة بتاعتها المحصلة
+
+238
+00:16:17,090 --> 00:16:20,170
+كلها على بعض دائما true طيب العكس في ال
+
+239
+00:16:20,170 --> 00:16:24,370
+contradiction ال contradiction is a compound
+
+240
+00:16:24,370 --> 00:16:30,510
+proposition that is false no matter what the truth
+
+241
+00:16:30,510 --> 00:16:37,220
+values of its atomic propositions كويس زيP and
+
+242
+00:16:37,220 --> 00:16:41,000
+negation P تصحي الصبح تقول والله اليوم بدي أروح
+
+243
+00:16:41,000 --> 00:16:44,440
+الجامعة و بديش أروح الجامعة طبعا إيش المعنى؟
+
+244
+00:16:44,440 --> 00:16:47,480
+مالهاش معنى يعني أنه غلط كله واضح أنه غلط يا بدك
+
+245
+00:16:47,480 --> 00:16:52,440
+تروح يا بدكيش تروحي أما بدي أروح و بديش أروح فهذه
+
+246
+00:16:52,440 --> 00:16:55,900
+دائما هتكون إيش؟ false استمرار false لأن واحدة
+
+247
+00:16:55,900 --> 00:16:59,840
+منهم هتكون false لازم واحدة منهم هتكون false وفي
+
+248
+00:16:59,840 --> 00:17:02,980
+حالة ال conjunction لازم كلهم يكونوا true عشان
+
+249
+00:17:02,980 --> 00:17:06,490
+يكونوا true لأ هنا دائما في واحدة منهمfalse فإذا
+
+250
+00:17:06,490 --> 00:17:10,950
+المحصلة دائما هتكون false otherwise يعني هدول
+
+251
+00:17:10,950 --> 00:17:13,890
+الحالات اللي هم مؤكدين تماما تاتولوجيا و ال
+
+252
+00:17:13,890 --> 00:17:18,610
+contradiction اللي هي ال proposition مع ال
+
+253
+00:17:18,610 --> 00:17:23,010
+negation تبعه أو ال negation تبعه كويس otherwise
+
+254
+00:17:23,010 --> 00:17:27,830
+ممكن تكون تحصل أحيانا بال by chance بالحظ يعني
+
+255
+00:17:27,830 --> 00:17:31,250
+ممكن تلاقوا ان والله في column طلع كله tautology
+
+256
+00:17:31,250 --> 00:17:35,130
+او column طلع كله contradiction كله falseممكن تصير
+
+257
+00:17:35,130 --> 00:17:40,210
+بالحظ في حالات معينة طيب logical equivalence شوفنا
+
+258
+00:17:40,210 --> 00:17:42,390
+ال totology شوفنا ال construction ال compound ..
+
+259
+00:17:42,390 --> 00:17:45,350
+ال compound proposition compound بدنا نعرفه خلاص
+
+260
+00:17:45,350 --> 00:17:48,950
+compound أنا بتكلم عن مجموعة atomic propositions
+
+261
+00:17:48,950 --> 00:17:53,230
+مربطة .. مربوطة مع بعض .. مربوطة مع بعض هي مش مجرد
+
+262
+00:17:53,230 --> 00:17:56,650
+atomic proposition لحالة بشكل هذا لأ هي ممكن تكون
+
+263
+00:17:56,650 --> 00:18:02,420
+or and مع أي q مثلاجملة، أبسط .. أبسط compound
+
+264
+00:18:02,420 --> 00:18:06,140
+preposition، فيها أكتر من atomic preposition،
+
+265
+00:18:06,140 --> 00:18:08,960
+تمام؟ فلما بتلاقوا كله compound أنا بتكلم عن
+
+266
+00:18:08,960 --> 00:18:15,190
+complicated prepositionمتكون من مجموعة atomic طيب
+
+267
+00:18:15,190 --> 00:18:18,310
+compound of preposition P is logically equivalent
+
+268
+00:18:18,310 --> 00:18:22,530
+to compound preposition Q compound preposition مع
+
+269
+00:18:22,530 --> 00:18:25,430
+compound preposition إذا كانوا فعلا الأتنين
+
+270
+00:18:25,430 --> 00:18:30,710
+مكافئين لبعض فإذا بقدر أقول أن P by conditional Q
+
+271
+00:18:30,710 --> 00:18:36,550
+is true هيكون ليش لأن واحدة بتضمن التانية و
+
+272
+00:18:36,550 --> 00:18:39,550
+التانية بتضمن الأولى إذا بالظبط التنتين و احنا
+
+273
+00:18:39,550 --> 00:18:43,930
+عارفين أنه في ال by conditional أمتى بيكونواtrue
+
+274
+00:18:43,930 --> 00:18:48,330
+by condition يعني إمتى بتكون true؟ إذا كانت false،
+
+275
+00:18:48,330 --> 00:18:53,270
+false أو true، true متشابهين، متشابهين، متشابهين،
+
+276
+00:18:53,270 --> 00:18:54,290
+متشابهين، متشابهين، متشابهين، متشابهين، متشابهين،
+
+277
+00:18:54,290 --> 00:18:54,650
+متشابهين، متشابهين، متشابهين، متشابهين متشابهين
+
+278
+00:18:54,650 --> 00:18:55,870
+متشابهين متشابهين متشابهين متشابهين متشابهين
+
+279
+00:18:55,870 --> 00:18:58,910
+متشابهين متشابهين متشابهين متشابهين متشابهين
+
+280
+00:18:58,910 --> 00:19:02,570
+متشابهين
+
+281
+00:19:02,570 --> 00:19:05,730
+متشابهين
+
+282
+00:19:06,450 --> 00:19:10,330
+هذه التنتين هكون متكافئين علامة التكافؤ إذا كانوا
+
+283
+00:19:10,330 --> 00:19:14,870
+فعلا compound is a tautology معناه ذلك إنه لازم
+
+284
+00:19:14,870 --> 00:19:20,270
+دايما true طب إنت ممكن تكون true فعليا لما كل
+
+285
+00:19:20,270 --> 00:19:23,050
+واحدة منهم مساوية للتانية بغض النظر false false
+
+286
+00:19:23,050 --> 00:19:26,850
+true true بس لازم تكون مساوية لها بنفس .. لها نفس
+
+287
+00:19:26,850 --> 00:19:30,550
+ال value نفس ال value زي ما قلنا بغض النظر ال
+
+288
+00:19:30,550 --> 00:19:37,030
+value هدي false or true false false okay trueال by
+
+289
+00:19:37,030 --> 00:19:39,570
+conditional بتاعتهم true .. true true .. by
+
+290
+00:19:39,570 --> 00:19:42,110
+conditional true .. فإذا تاتولوجي .. تاتولوجي هنا
+
+291
+00:19:42,110 --> 00:19:46,090
+تحققت لل by conditional معناه ذلك إن كل
+
+292
+00:19:46,090 --> 00:19:50,850
+proposition منهم مكافئ للتاني .. مكافئ للتاني ..
+
+293
+00:19:50,850 --> 00:19:56,170
+له نفس القيمة .. okayهذه ممكن برضه نعملها .. ممكن
+
+294
+00:19:56,170 --> 00:19:59,910
+تجربوها برضه باستخدام ال truth value فهي بتحتوي ال
+
+295
+00:19:59,910 --> 00:20:04,070
+truth table اللي مابتيجوا تعملوها ال column تبع ال
+
+296
+00:20:04,070 --> 00:20:08,030
+compound proposition المفروض انه يحتوي على مجموعة
+
+297
+00:20:08,030 --> 00:20:15,010
+.. مجموعة symbols مشابه .. مشابه هو مساوية تماما ل
+
+298
+00:20:15,010 --> 00:20:18,350
+ال column تبع ال proposition التانية اللي لازم
+
+299
+00:20:18,350 --> 00:20:22,250
+تكون مكافئة عليهاهذه بتستخدم عساس من the same
+
+300
+00:20:22,250 --> 00:20:27,330
+truth value لما بنستعمل truth table لما بنستعمل
+
+301
+00:20:27,330 --> 00:20:32,970
+truth table زى ما هنشوف لاحقا هنا مثلا لو بدى اثبت
+
+302
+00:20:32,970 --> 00:20:39,870
+اعمل prove that بيه disjunction Q equivalent to
+
+303
+00:20:39,870 --> 00:20:45,720
+negationنفتح قصر Negation P and Negation Q إيش
+
+304
+00:20:45,720 --> 00:20:48,400
+بدنا نسوي؟ بدنا نستعمل ال truth table باستخدام ال
+
+305
+00:20:48,400 --> 00:20:52,840
+truth table كل اللي هنعمله أكم atomic proposition
+
+306
+00:20:52,840 --> 00:20:57,440
+عندنا؟ اتنين، معناه زي اللي كأعرفت أن أنا أكم روح
+
+307
+00:20:57,440 --> 00:21:02,400
+يكون عندى؟ أربعة، اتنين وهذه الأساس هتظل دايما
+
+308
+00:21:02,400 --> 00:21:06,220
+ثابتة معايا to the power عدد ال atomic proposition
+
+309
+00:21:06,220 --> 00:21:07,400
+اللي هم اتنين
+
+310
+00:21:11,590 --> 00:21:15,770
+فحنشتغل على اول compound preposition P disjunction
+
+311
+00:21:15,770 --> 00:21:20,750
+Q كويس التانية اه لأ لسه التانية عشان اعملها محتاج
+
+312
+00:21:20,750 --> 00:21:25,870
+اول negation P negation Q بعدين ال two negations
+
+313
+00:21:25,870 --> 00:21:31,010
+مع بعض نعملهم conjunction بعدين negation لل
+
+314
+00:21:31,010 --> 00:21:34,450
+conjunction كله على بعض كويس خليني اشوف هنا لما
+
+315
+00:21:34,450 --> 00:21:42,830
+نقوله orالـ O لأ false otherwise true طيب و بعدين
+
+316
+00:21:42,830 --> 00:21:48,810
+بتعمله negation ل ال P و negation ل ال Q كويس
+
+317
+00:21:48,810 --> 00:21:53,890
+بعدين هنا هتعمله and and ل مين ل ال two columns
+
+318
+00:21:53,890 --> 00:21:56,770
+هدول مع بعض ل ال two columns هدول فهيكون بس أول
+
+319
+00:21:56,770 --> 00:22:04,030
+term هو ال true otherwise false طيب negation ل ال
+
+320
+00:22:04,030 --> 00:22:06,870
+column هذا يعكسوه تمازك
+
+321
+00:22:08,450 --> 00:22:12,390
+لحظة ال column هذا و ال column هذا the same values
+
+322
+00:22:12,390 --> 00:22:18,070
+the same values فإذا عندكم false true true true
+
+323
+00:22:18,070 --> 00:22:22,490
+true true true true true true true true true true
+
+324
+00:22:22,490 --> 00:22:23,790
+true true true true true true true true true true
+
+325
+00:22:23,790 --> 00:22:23,790
+true true true true true true true true true true
+
+326
+00:22:23,790 --> 00:22:27,150
+true true true true true true true true true true
+
+327
+00:22:27,150 --> 00:22:27,150
+true true true true true true true true true true
+
+328
+00:22:27,150 --> 00:22:27,150
+true true true true true true true true true true
+
+329
+00:22:27,150 --> 00:22:27,210
+true true true true true true true true true true
+
+330
+00:22:27,210 --> 00:22:27,210
+true true true true true true true true true true
+
+331
+00:22:27,210 --> 00:22:27,210
+true true true true true true true true true true
+
+332
+00:22:27,210 --> 00:22:27,490
+true true true true true true true true true true
+
+333
+00:22:27,490 --> 00:22:28,190
+true true true true true true true true true true
+
+334
+00:22:28,190 --> 00:22:28,310
+true true true true true true true true true true
+
+335
+00:22:28,310 --> 00:22:29,030
+true true true true true true true true true true
+
+336
+00:22:29,030 --> 00:22:29,210
+true true true true true true true true true true
+
+337
+00:22:29,210 --> 00:22:29,230
+true true true true true true true true true true
+
+338
+00:22:29,230 --> 00:22:29,350
+true true true true true true true true true true
+
+339
+00:22:29,350 --> 00:22:29,350
+true true true true true true true true true true
+
+340
+00:22:29,350 --> 00:22:29,350
+true true true true true true true true true true
+
+341
+00:22:29,350 --> 00:22:29,350
+true true true true true true true true true true
+
+342
+00:22:29,350 --> 00:22:30,030
+true true true true true true true true
+
+343
+00:22:36,040 --> 00:22:39,540
+يعني عندكوا P عندكوا Q عندكوا R عندكوا S عندكوا T
+
+344
+00:22:39,540 --> 00:22:46,280
+اتنين او خمس اتنين او تلاتين روه طيب لو افترضنا
+
+345
+00:22:46,280 --> 00:22:49,620
+كمان ان ال compound هذا مش هيكون الاتنين مع بعض
+
+346
+00:22:49,620 --> 00:22:53,540
+طبعا هيكون الخمسة مع بعضهم يعني محتاجين كذا column
+
+347
+00:22:53,540 --> 00:22:57,200
+عشان تصلوا للي بدكوا ياه بدون ما يصير لخبط معاكم
+
+348
+00:22:57,200 --> 00:23:01,420
+فلحظوا الموضوع كبر صار كتير كبير فهنا بصير افضل ان
+
+349
+00:23:01,420 --> 00:23:05,060
+احنا نشتغل علىsymbolic derivations هناخدها
+
+350
+00:23:05,060 --> 00:23:09,480
+باستخدام قوانين ومعادلة معينة أو rules معينة طيب
+
+351
+00:23:09,480 --> 00:23:14,480
+نبدأ الشيه rules هذه اللي ممكن نستعملها في أول
+
+352
+00:23:14,480 --> 00:23:19,540
+rule اللي هي زي المحايد المحايد الجامعي و المحايد
+
+353
+00:23:19,540 --> 00:23:23,120
+الضربي أخدتهم قبل هيك لما بتشتغلوا في الأرقام
+
+354
+00:23:23,120 --> 00:23:27,260
+العادية كان في عندكم محايد جامعي اللي هو صفر و ال
+
+355
+00:23:27,260 --> 00:23:30,440
+.. و في اللي جاء في الضرب واحد تمام طيب احنا
+
+356
+00:23:30,440 --> 00:23:32,360
+اتفجنا انه صفر
+
+357
+00:23:34,820 --> 00:23:42,120
+للفالس one لل true طيب لما بعمل ضرب الضرب المفروض
+
+358
+00:23:42,120 --> 00:23:48,380
+المعامل الضرب المحايد الضرب واحد true conjunction
+
+359
+00:23:48,380 --> 00:23:51,740
+مع أي term او مع أي proposition هيطلع ال
+
+360
+00:23:51,740 --> 00:23:55,540
+proposition فال true هي محايدة بالنسبة لل
+
+361
+00:23:55,540 --> 00:24:00,480
+conjunction لل conjunctionتمام العكس بالنسبة لل
+
+362
+00:24:00,480 --> 00:24:03,800
+disjunction أو اللي هي الجمع يعني اللي كانت مقابلة
+
+363
+00:24:03,800 --> 00:24:08,240
+للجمع الجمع المحيد الجمع تبعها او ال disjunction
+
+364
+00:24:08,240 --> 00:24:13,020
+هي ال false هي ال false ال zero false مع أي
+
+365
+00:24:13,020 --> 00:24:17,240
+proposition النتج قيمة ال proposition إذا كان true
+
+366
+00:24:17,240 --> 00:24:22,100
+هيطلع true إذا كان false هيطلع false و نفس الكلام
+
+367
+00:24:22,100 --> 00:24:27,320
+كانت بالنسبة لها ال conjunction طيب طب في الهيمنة
+
+368
+00:24:28,210 --> 00:24:31,410
+لما تقول والله ال zero مثلا يمكن اوضح ال zero اكتر
+
+369
+00:24:31,410 --> 00:24:36,830
+من ال واحد لما تقول ال zero في اي قيمة zero معناته
+
+370
+00:24:36,830 --> 00:24:41,050
+هنا ال zero هيمن هيمن على المعادلة بتاعتنا هي
+
+371
+00:24:41,050 --> 00:24:48,710
+false conjunction في false طيب التالتة التالتة
+
+372
+00:24:48,710 --> 00:24:55,760
+اللي هي مش زي ال tautology حشه لأ هذهعدمة الفائدة
+
+373
+00:24:55,760 --> 00:25:03,660
+أحيان بيسموها بمعنى أنه ال proposition مع نفسه، ال
+
+374
+00:25:03,660 --> 00:25:07,140
+proposition مع نفسه مالوش معنى، مالوش معنى أن أنا
+
+375
+00:25:07,140 --> 00:25:09,700
+أقول اليوم بدي أصحى من النوم و اليوم بدي أصحى من
+
+376
+00:25:09,700 --> 00:25:14,540
+النوم طب ما هي المحصلة أن اليوم بدي أصحى من النوم،
+
+377
+00:25:14,540 --> 00:25:20,640
+اليوم بدي أروح الجامعة أو أن اليوم أروح الجامعةطب
+
+378
+00:25:20,640 --> 00:25:22,800
+ما هي المحصلة إنه حالي يوم هنروح الجامعة فال
+
+379
+00:25:22,800 --> 00:25:25,000
+proposition في الحالة اللي زيها دي ال proposition
+
+380
+00:25:25,000 --> 00:25:29,400
+مع نفسه أو مضروب في نفسه بمعنى and أو or مع نفسه
+
+381
+00:25:29,400 --> 00:25:34,860
+هو نفسه هو نفسه لو true إنها هتطلع true لو false
+
+382
+00:25:34,860 --> 00:25:40,080
+هيكون false هيكون false في الحالتين فهذا يمثل نفسه
+
+383
+00:25:40,080 --> 00:25:46,460
+طيب ال rule الرابعة ال double negation اللي هي نفي
+
+384
+00:25:46,460 --> 00:25:51,550
+النفي if bad صحيح؟طيب نفي النفي اثبات فإذا أنا
+
+385
+00:25:51,550 --> 00:25:57,090
+أقول negation of negation P تطلع
+
+386
+00:25:57,090 --> 00:26:01,510
+P طيب التانية
+
+387
+00:26:01,510 --> 00:26:06,950
+ال domination domination الهيمنة و هذي عشان اوضح
+
+388
+00:26:06,950 --> 00:26:10,750
+لكيها أكتر بالأرقام اللي أنتوا عارفينها الصفر لما
+
+389
+00:26:10,750 --> 00:26:14,410
+تضربيه بأي رقم هو هيمن عليه ليش لأنه أعطى ناتج
+
+390
+00:26:14,410 --> 00:26:21,140
+دايما صفر لما نقول صفر في مليون صفرفهنا معناها أن
+
+391
+00:26:21,140 --> 00:26:25,620
+ال true or false هيمنوا على ال proposition لغوا،
+
+392
+00:26:25,620 --> 00:26:30,180
+لغوا تأثيره، لغوا ال effect تبعه، كيف لغوا؟ ال
+
+393
+00:26:30,180 --> 00:26:34,100
+true بتلغ تأثير ال proposition اللي معها إذا كانت
+
+394
+00:26:34,100 --> 00:26:38,500
+مع مين؟ disjunction، disjunction احنا عارفين أو،
+
+395
+00:26:38,500 --> 00:26:45,470
+فأي term أو true، trueلأن في او فاعتطنى سماحية ان
+
+396
+00:26:45,470 --> 00:26:48,310
+ممكن اي واحد منهم true و الكل الباقي يطلع true ما
+
+397
+00:26:48,310 --> 00:26:51,230
+هو فعلا اكيد في واحد منهم true لان انا حاط true
+
+398
+00:26:51,230 --> 00:26:56,550
+حاطينه اصلا true فعلا طيب نفس الكلام في اش مع ال
+
+399
+00:26:56,550 --> 00:26:59,970
+and اللى هى عملية كأنها عملية ضرب تقابل ضرب في ال
+
+400
+00:26:59,970 --> 00:27:07,930
+decimal system هذه مع صفر صفر ضرب اى قيمة صفر
+
+401
+00:27:07,930 --> 00:27:11,630
+فيمكن هذه بتجرب المفهوم اوضح a proposition
+
+402
+00:27:13,290 --> 00:27:17,170
+conjunction مع false أكيد false لأن ال conjunction
+
+403
+00:27:17,170 --> 00:27:21,470
+عشان يختلف عن ال false يكون true لازم يكونوا اتنين
+
+404
+00:27:21,470 --> 00:27:26,030
+atomic proposition true صح لازم لاتنين يكونوا true
+
+405
+00:27:26,030 --> 00:27:30,430
+لأ احنا اي واحد منهم مش true خلاص واحد منهم false
+
+406
+00:27:30,430 --> 00:27:33,830
+انتهى اي واحد منهم false فإذا النتيجة لازم يكون
+
+407
+00:27:33,830 --> 00:27:37,890
+not true فإذا not true ماعنديش الاحتمال ان هو يا
+
+408
+00:27:37,890 --> 00:27:43,300
+true يا false ال not true تمثل falseطيب، آه لسه ما
+
+409
+00:27:43,300 --> 00:27:46,920
+اتكلمنش عن competitive، ال competitive تباديل،
+
+410
+00:27:46,920 --> 00:27:50,120
+تبادلي، تبادلي بمعنى .. تبادل امتى؟ إذا كانت هم
+
+411
+00:27:50,120 --> 00:27:52,800
+بتتكلم عن نفس ال junction هيها ال .. ال .. ال ..
+
+412
+00:27:52,800 --> 00:27:55,140
+ال junction بتاعتنا أو هنا بتتكلم عن disjunction
+
+413
+00:27:55,140 --> 00:27:59,840
+فإذا P disjunction Q هي نفسها Q disjunction P و P
+
+414
+00:27:59,840 --> 00:28:05,890
+conjunction Q هي نفسها Q conjunction Pكويس
+
+415
+00:28:05,890 --> 00:28:10,050
+associative ال associative المشاركة في ال priority
+
+416
+00:28:10,050 --> 00:28:15,590
+في الأولوية هو فعليا إذا كان أنا بتعامل مع نفس ال
+
+417
+00:28:15,590 --> 00:28:18,990
+conjunction أو ال disjunction يعني نفس ال .. ال ..
+
+418
+00:28:18,990 --> 00:28:23,450
+ال operator فالمفروض أن الأولوية متساوية صح
+
+419
+00:28:23,450 --> 00:28:26,450
+الأولوية متساوية أنا بتعامل مع نفس ال .. ال .. ال
+
+420
+00:28:26,450 --> 00:28:32,440
+operator لما نقول خمسة زائد تلاتة زائد أربعةهتفرق
+
+421
+00:28:32,440 --> 00:28:36,640
+كثير لو قلت طبعا هنا خلّيني أقوص بالشكل هذا إن
+
+422
+00:28:36,640 --> 00:28:40,580
+أحسب 3 زاد 4 الأول و بعدين أجمحها على 5 ولا أقول
+
+423
+00:28:40,580 --> 00:28:45,520
+لأ 5 زاد 3 في الأول و بعدين 4 فهنا أنا بيعطي
+
+424
+00:28:45,520 --> 00:28:48,820
+priority لمين لل 3 زاد 4 في الأول هنا لأ اعطيت
+
+425
+00:28:48,820 --> 00:28:53,200
+priority أكتر لل 5 زاد 3 في الأول مش هتفرق في
+
+426
+00:28:53,200 --> 00:28:56,560
+الحالتين هيطلع نفس النتجةفي الحلتين هيطلع نفس
+
+427
+00:28:56,560 --> 00:29:01,260
+النتج في هذه associative مشاركة ال priority ان
+
+428
+00:29:01,260 --> 00:29:05,280
+الاتنين لهم نفس ال priority او ان هم اتنين انا
+
+429
+00:29:05,280 --> 00:29:08,960
+بتكلم هنا عن ال operator بتكلم عن ال operator ال
+
+430
+00:29:08,960 --> 00:29:11,120
+operator هذا مساوي لهذا لأن هم نفس ال operator
+
+431
+00:29:11,120 --> 00:29:14,440
+اصلا فمدام نفس ال operator تفرجش من احط الأحواص
+
+432
+00:29:14,440 --> 00:29:18,740
+تفرجش مين هعمل يا بالمين الكلام ينطبق سواء على ال
+
+433
+00:29:18,740 --> 00:29:23,800
+disjunction او conjunction طيب ال rule ال ..
+
+434
+00:29:24,130 --> 00:29:28,830
+السادسة يمكن او سادسة تقريبا ال distributive وهذه
+
+435
+00:29:28,830 --> 00:29:34,850
+مهمة جدا طيب اذا كانوا مش نفس ال operator لحظه مش
+
+436
+00:29:34,850 --> 00:29:38,930
+نفس ال operator طب ما هذا بخليني ارجع لنفس ال
+
+437
+00:29:38,930 --> 00:29:44,850
+decimal number تبعتنا لما اقول خمسة في اربعة زائد
+
+438
+00:29:44,850 --> 00:29:45,910
+تلاتة
+
+439
+00:29:51,040 --> 00:29:56,160
+هل كنا .. كان ممكن نعملها مثلا خمسة في أربعة زائد
+
+440
+00:29:56,160 --> 00:30:01,740
+تلاتة بهذا الشكل؟ طبعا غلط طب ها إيش كنا نعمل؟ كنا
+
+441
+00:30:01,740 --> 00:30:05,300
+نعمل توزيع كنا نعمل .. بالظبط كنا نعمل توزيع خمسة
+
+442
+00:30:05,300 --> 00:30:14,290
+في أربعة زائد خمسة في تلاتةنفسه تماما بدنا نعمله
+
+443
+00:30:14,290 --> 00:30:18,330
+مع ال operators اللي احنا بنشتغل عليها لاحظوا
+
+444
+00:30:18,330 --> 00:30:22,710
+disjunction افتحه قواص مع ال conjunction ال
+
+445
+00:30:22,710 --> 00:30:27,550
+disjunction هيها هنوزحها P disjunction Q و هدول
+
+446
+00:30:27,550 --> 00:30:32,650
+هنسكر عليهم قواص و بعدين P disjunction مع R و نسكر
+
+447
+00:30:32,650 --> 00:30:34,790
+عليها قواص و نخلي ال N بين القوسين
+
+448
+00:30:37,750 --> 00:30:44,930
+نفس الكلام لو عكسناه نفس الشيء لو عكسناه فهنكون
+
+449
+00:30:44,930 --> 00:30:47,830
+احنا فعلا حققنا عملية ال distribution أو التوزيع
+
+450
+00:30:47,830 --> 00:30:54,070
+التوزيع اللى كنا بتشتغلها عادة دي مارجانز عملنا
+
+451
+00:30:54,070 --> 00:30:57,410
+عملية توزيع بس عملها لمين اثبتها لمين لل negation
+
+452
+00:30:57,410 --> 00:31:01,850
+بحيث انه بيدخل ال negation بيدخل ال cost وبيعكس ال
+
+453
+00:31:01,850 --> 00:31:08,990
+operator بيعكس ال operatorand بيعكسها or إذا كانت
+
+454
+00:31:08,990 --> 00:31:15,370
+or أو disjunction بيعكسها and أو conjunction طيب
+
+455
+00:31:15,370 --> 00:31:18,350
+trivial, tautology or contradiction وهدا اللي
+
+456
+00:31:18,350 --> 00:31:22,890
+خدناها أول ما بدنا كلامنا قولنا إنه دائما الاصغر
+
+457
+00:31:22,890 --> 00:31:27,950
+هذه هتكون true اللي هي ال P disjunction negation P
+
+458
+00:31:27,950 --> 00:31:33,930
+ال proposition و عكسه ال proposition عفوا أو عكسه
+
+459
+00:31:35,010 --> 00:31:38,910
+أو عكسه ما هو طبيعي واحد منهم هيكون صح منطقي واحد
+
+460
+00:31:38,910 --> 00:31:43,130
+منهم يكون صح طيب ال proposition هو عكسه طبيعي واحد
+
+461
+00:31:43,130 --> 00:31:46,650
+منهم هيكون غلط واحد هيكون صح و واحد هيكون غلط
+
+462
+00:31:46,650 --> 00:31:51,170
+فيكفر ان واحد غلط عشان يقول ان المحصلة كلها false
+
+463
+00:31:51,170 --> 00:31:57,390
+محصلة كلها false طيب اللي عندنا اللحظة كل اللي
+
+464
+00:31:57,390 --> 00:32:00,070
+اتكلمنا عنهم اتكلمنا عنهم على اساس ان انا بتكلم عن
+
+465
+00:32:00,070 --> 00:32:03,970
+negation conjunction and disjunction طب احنا أخدنا
+
+466
+00:32:03,970 --> 00:32:07,930
+اكتر من هيككان في مجموعة operators أكتر من ذلك
+
+467
+00:32:07,930 --> 00:32:12,070
+احنا خدنا ال XOR وخدنا ال implication وخدنا ال
+
+468
+00:32:12,070 --> 00:32:17,050
+biconditional فكل واحد منهم هناخدله صيغة تمثله
+
+469
+00:32:17,050 --> 00:32:24,590
+عساس ان نتعامل معاه لاحقا فهنبدأ بال XOR XOR P XOR
+
+470
+00:32:24,590 --> 00:32:29,910
+Q equivalent to P conjunction Q كله conjunction مع
+
+471
+00:32:29,910 --> 00:32:35,450
+negation ب conjunction Qتمام؟ او في form تاني و
+
+472
+00:32:35,450 --> 00:32:38,470
+طبعا لاحظوا ان واحد بتقدر تجيبه من التاني بده بس
+
+473
+00:32:38,470 --> 00:32:41,750
+شوية سلسلة عمليات بنقدر نجيبهم من بعض .. بنقدر
+
+474
+00:32:41,750 --> 00:32:45,970
+نجيبهم من بعض و لاحقا بس تتعلموا الطريقة اللي جاية
+
+475
+00:32:45,970 --> 00:32:47,970
+هتصيروا بتقدروا تعملوها لحالكوا .. يعني ال .. ال
+
+476
+00:32:47,970 --> 00:32:51,990
+.. ان كيف اجيب واحد من التانيإن واحد من التاني
+
+477
+00:32:51,990 --> 00:32:55,110
+هتتعاملوا معاه إن هذا equivalent لهذا بتكون ثبته
+
+478
+00:32:55,110 --> 00:32:58,370
+عملية إثبات إن هل اتنين هذول equivalent لبعض أو لأ
+
+479
+00:32:58,370 --> 00:33:02,410
+التاني يمكن تكون أوضح شوية لإيش لإن احنا عادة ..
+
+480
+00:33:02,410 --> 00:33:09,170
+عادة بنعمل true امتى true لل X or لما واحدة منهم
+
+481
+00:33:09,170 --> 00:33:16,310
+تكون عكس التانية فلاحظوا واحدة عكس التانية أوأولة
+
+482
+00:33:16,310 --> 00:33:18,930
+التانية مع عكس الأولى يعني واحدة ده مع العكس
+
+483
+00:33:18,930 --> 00:33:21,990
+التانية فيمكن أقرب انها تنحفظ معاكم هذه الصورة
+
+484
+00:33:21,990 --> 00:33:29,210
+أسرع فإذا P and negation Q or Q negation and
+
+485
+00:33:29,210 --> 00:33:29,890
+negation P
+
+486
+00:33:33,080 --> 00:33:39,220
+طيب ال employees هي negation الأولى او التانية
+
+487
+00:33:39,220 --> 00:33:43,540
+نجاشن الأولى أو التانية نجاشن الأولى أو التانية
+
+488
+00:33:43,540 --> 00:33:47,380
+على طول يعني سهل لو مالهاش فورم واحد نستعمله خلال
+
+489
+00:33:47,380 --> 00:33:53,120
+ال course اللي هي negation الأولى or التانية طيب
+
+490
+00:33:53,120 --> 00:33:56,060
+ال biconditional ال biconditional اللي احنا قلناه
+
+491
+00:33:56,060 --> 00:33:58,880
+قبلك ان هي implication في الاتجاهين بمعنى ان انا
+
+492
+00:33:58,880 --> 00:34:06,000
+ممكن اقول ان هيemploys q and q employs p واحدة من
+
+493
+00:34:06,000 --> 00:34:09,620
+التانية او الاستنتاج اللى استنتجناه ايام ما
+
+494
+00:34:09,620 --> 00:34:14,840
+اتكلمنا عنها ان هي عكس ال X or لان هذه واحد امتى
+
+495
+00:34:14,840 --> 00:34:20,280
+اذا تشابه ال propositions بتعطيني one بعكس ال X or
+
+496
+00:34:20,280 --> 00:34:24,400
+ال X or اذا اختلفوا بتعطيني one صحيح تذكرينهم فاذا
+
+497
+00:34:24,400 --> 00:34:31,160
+هذه ال negation ده بال X orتمام for example خلينا
+
+498
+00:34:31,160 --> 00:34:34,660
+ناخد example طيب لما يكون في عندكوا example و
+
+499
+00:34:34,660 --> 00:34:37,540
+بتشتغلوا عليه بالشكل اللي احنا جاي عندنا هنا طبعا
+
+500
+00:34:37,540 --> 00:34:40,680
+الأسئلة هتكون هيك طبيعتها المفروض ان تعملوا check
+
+501
+00:34:40,680 --> 00:34:46,300
+على ال .. اذا كانوا equivalent ولا لأ اذا كانوا
+
+502
+00:34:46,300 --> 00:34:49,700
+فعلا اتنين equivalent او تعملوا proof ان هما فعلا
+
+503
+00:34:49,700 --> 00:34:54,060
+equivalent ببعض طيب بكون اعطيكواtwo compound
+
+504
+00:34:54,060 --> 00:34:57,100
+propositions هدى أول compound proposition و هدى
+
+505
+00:34:57,100 --> 00:35:00,940
+التانية و المطلوب نثبت ان هم equivalent لمين لبعض
+
+506
+00:35:00,940 --> 00:35:08,060
+firstly بتطلع عليهم اللى بتلاقوه فى operators صعبة
+
+507
+00:35:08,060 --> 00:35:12,640
+الشىء اللى هو ال operators الصعبة عادة ال XOR ال
+
+508
+00:35:12,640 --> 00:35:15,980
+implication و ال by condition هدولة دايما بهمنا
+
+509
+00:35:15,980 --> 00:35:18,930
+فوقكم فى الأولبهمنا نفكهم في الأول لإنه ماقدرش
+
+510
+00:35:18,930 --> 00:35:22,970
+أتعامل معهم مع ال rules اللي أخدناهم قبل شوية لازم
+
+511
+00:35:22,970 --> 00:35:25,710
+نفكهم بواحدة من القوانين بتاعتهم، كل واحد أخدناله
+
+512
+00:35:25,710 --> 00:35:29,210
+قانون قانون قانون، بنفكهم في الأول و بعدين بدبنا
+
+513
+00:35:29,210 --> 00:35:32,550
+نستعمل ال rules بتاعتنا أو ال laws بتاعتنا اللي
+
+514
+00:35:32,550 --> 00:35:35,490
+منهم دي مرجن و ما دي مرجن و ال competitive و ال
+
+515
+00:35:35,490 --> 00:35:39,630
+associative و الأمور دي كلهابتقدرش نستعملهم مباشرة
+
+516
+00:35:39,630 --> 00:35:44,050
+عليهم فإذا لما نيجي نطلع على ال proof بالشكل اللي
+
+517
+00:35:44,050 --> 00:35:47,170
+احنا شايفين وهذا مطلوب مننا اول ما بتطلع بتطلع على
+
+518
+00:35:47,170 --> 00:35:52,190
+ال left hand side اه هذا واضح انه complicated اكتر
+
+519
+00:35:52,190 --> 00:35:56,290
+من التاني معناته بشتغل على هذا نبدأ نفكه نحلله
+
+520
+00:35:56,290 --> 00:35:59,510
+نحلله ليش لأن في عندكوا XOR في عندكوا complication
+
+521
+00:35:59,510 --> 00:36:04,250
+و في عندكوا XORفعادة هاي بداية الحل دوروا على ال
+
+522
+00:36:04,250 --> 00:36:09,050
+implication يفقوها في الأول و بعدين نشوف أش بيصير
+
+523
+00:36:09,050 --> 00:36:12,070
+معناه خلينا نبدأ نفكها و نشوف أش بيصير معناها و
+
+524
+00:36:12,070 --> 00:36:14,830
+خلينا تتوارد لنا الأفكار إيش اللي لازم نعمله لاحقا
+
+525
+00:36:14,830 --> 00:36:23,430
+تمام فإذا firstly بفك هذا ولا هذا في الأول ال أكبر
+
+526
+00:36:23,430 --> 00:36:28,020
+هو ال implicationهو ال implication لأنه بربط ال co
+
+527
+00:36:28,020 --> 00:36:31,580
+باتنين مع بعض فهذا الكبير يعتبر هذا ال operator
+
+528
+00:36:31,580 --> 00:36:36,840
+التاني الأكبر كويس فبنبدأ فيها في ال implication
+
+529
+00:36:36,840 --> 00:36:40,260
+ال implication قلنا ان هي negation الأولى and
+
+530
+00:36:40,260 --> 00:36:44,640
+التانية negation الأولى عفوا or or التانية
+
+531
+00:36:44,640 --> 00:36:48,920
+disjunction or التانية فإذا بتعامل مع هذه كلها هيك
+
+532
+00:36:48,920 --> 00:36:53,770
+كأنها proposition أولى افترض أنها كأنها Kو هذه
+
+533
+00:36:53,770 --> 00:36:59,390
+كأنها هيك على بعض فى عندنا R زد فبتح تصير كأنه
+
+534
+00:36:59,390 --> 00:37:07,090
+negation K this junction زد هذا حطه مكانها حطه
+
+535
+00:37:07,090 --> 00:37:09,810
+القص نزله زي ما هو و ده نزله زي ما هو و خلصنا من
+
+536
+00:37:09,810 --> 00:37:15,370
+مين؟ من ال implicationهك خلصنا أول جزئية، بالظبط،
+
+537
+00:37:15,370 --> 00:37:19,250
+بعدين نبدأ نشوف الذبط هذه الشيعة عشان نفك اللي في
+
+538
+00:37:19,250 --> 00:37:23,030
+جلبها، تمام؟ عشان ما تتلخبطوش، بس ما ت .. الأقوسة
+
+539
+00:37:23,030 --> 00:37:25,630
+ده ما تلخم .. ما تلخمكمش، بتعاملوا معاها بالشكل
+
+540
+00:37:25,630 --> 00:37:28,110
+هذا، خلاص ال implication هذا بتربط إيش؟ أه بتربط
+
+541
+00:37:28,110 --> 00:37:30,150
+قوس، معناه تلقوس هذا كله على بعض و من المفروض ما
+
+542
+00:37:30,150 --> 00:37:33,810
+تتحركوش ولا تفكوه، عشان ما تلخمطوش حالكوا، زي ما
+
+543
+00:37:33,810 --> 00:37:37,330
+هو بتنقلوه تحت حسب القانون تبع ال implication
+
+544
+00:37:38,210 --> 00:37:41,370
+implication negation k فال negation بتطلعوها برا
+
+545
+00:37:41,370 --> 00:37:44,630
+ماتفكروش تعملولكوا خطوطين هوية واحدة انتوا لسه
+
+546
+00:37:44,630 --> 00:37:47,950
+يدوكوا بتتعلموا ال derivations ماتلخبطوش حالكوا
+
+547
+00:37:47,950 --> 00:37:50,390
+تعملولكوا خطوطين تلاتة في بعض عشان بتكونوا تختصروا
+
+548
+00:37:50,390 --> 00:37:54,530
+هتلاقوا حالكوا ال negation وجعت معاكوا في النص ال
+
+549
+00:37:54,530 --> 00:37:58,070
+and صارت or او ال or صارت and وانتوا مش دارينه
+
+550
+00:37:58,070 --> 00:38:01,070
+فطبعا مش هتصروا لحالة هتلاقوا حالكوا ضيعتوا حالته
+
+551
+00:38:01,070 --> 00:38:09,850
+تمام؟ كويس فهي ال implication الأولىفعملنا
+
+552
+00:38:09,850 --> 00:38:17,790
+negation الأولى هي or التانية نمسك من ال XOR كان
+
+553
+00:38:17,790 --> 00:38:21,730
+فين اللي كان لها قانونين هستعمل أول قانون منهم
+
+554
+00:38:21,730 --> 00:38:24,710
+اللي كان فيه اتنين and واحدة or
+
+555
+00:38:29,020 --> 00:38:32,340
+و الواحدة اخر فهدول انتوا بتكون تحفظوهم يعني هم
+
+556
+00:38:32,340 --> 00:38:34,960
+تلت اربع قوانين هدول بتكون تحفظوهم الباجين بتكون
+
+557
+00:38:34,960 --> 00:38:37,740
+فاهمينهم الباجين ال rules اللي احنا خدناهم في
+
+558
+00:38:37,740 --> 00:38:40,220
+الأول ال laws هدول اللي في الأول لأ انتوا بتكونوا
+
+559
+00:38:40,220 --> 00:38:43,260
+فاهمينهم competitive خلاص انا فاهم التبادل
+
+560
+00:38:43,260 --> 00:38:47,000
+التبادلية اذا كان نفس الاش نفس ال operator خلاص
+
+561
+00:38:47,000 --> 00:38:49,880
+بفهمه هيك distribution عارفين distributionأحنا
+
+562
+00:38:49,880 --> 00:38:52,940
+عارفين أنه بوزع الأرقام علي بعض لما يكون في
+
+563
+00:38:52,940 --> 00:38:55,420
+أقواتنا خلاص نفس الفكرة بعملها .. نفس الفكرة
+
+564
+00:38:55,420 --> 00:38:59,340
+بنعملها .. هدولة فهم .. في علي أنكوا علي اللي
+
+565
+00:38:59,340 --> 00:39:01,640
+بدكوا .. في هالتلت أربعة هدولة اللي هي بتاعة ال
+
+566
+00:39:01,640 --> 00:39:04,930
+XORال implication و ال biconditional .. مع أن ال
+
+567
+00:39:04,930 --> 00:39:08,490
+biconditional مش محتاجة أصلا لأن هي اللي كتبناهم
+
+568
+00:39:08,490 --> 00:39:12,170
+إياها كانت بدلالة ال implication و بدلالة ال XOR
+
+569
+00:39:12,170 --> 00:39:14,870
+فانتوا هتحفظوا بس لتنتين ال XOR و ال implication و
+
+570
+00:39:14,870 --> 00:39:18,150
+تكونوا فاهمين أن ال biconditional ما هي إلا
+
+571
+00:39:18,150 --> 00:39:24,770
+negation XOR أو implication في الاتجاهين بس ..
+
+572
+00:39:24,770 --> 00:39:32,670
+كويس طيب وصلنا لهنابدناش نحفظ احنا متفقين بدناش
+
+573
+00:39:32,670 --> 00:39:36,330
+نحفظ رياضيات ما هي مش قصة حفظ هل واجد بدي أجف هيك
+
+574
+00:39:36,330 --> 00:39:41,730
+و أصف المحالي و أطلع أنا إيش بدي؟ بدنا نفك و نصل
+
+575
+00:39:41,730 --> 00:39:46,790
+هادي طيب عشان أفك و أصل هادي بدي أجي أطلع هيك
+
+576
+00:39:46,790 --> 00:39:52,030
+حلاجي إن والله في عندي هنا P و هنا في P و هنا في P
+
+577
+00:39:52,030 --> 00:39:56,830
+لو بقدر أجمحهم مع بعضبحيث ان احصل على tautology او
+
+578
+00:39:56,830 --> 00:40:01,310
+contradiction اختزلهم ليش لان هدولة tautology و ال
+
+579
+00:40:01,310 --> 00:40:03,930
+contradiction ايش بيعطوني بيعطوني true و false ال
+
+580
+00:40:03,930 --> 00:40:08,190
+true و false هدولة اكيد هيختزلوا هيشي طيب كيف اعمل
+
+581
+00:40:08,190 --> 00:40:13,510
+الكلام هذا firstly انا مقدرش ادخل الأقواص هدولة ك
+
+582
+00:40:13,510 --> 00:40:20,030
+competitive ليش لان هذه and وهذه or مقدرش ابدلهم
+
+583
+00:40:20,030 --> 00:40:24,540
+مع بعض اه بس لحظةاستنوا في negation طب ال negation
+
+584
+00:40:24,540 --> 00:40:29,380
+اللي دخلناها جوا الأقواس هتركز هذه لإيش؟ تمام
+
+585
+00:40:29,380 --> 00:40:33,680
+فلحظوا التفكير إن أنا بدي أخفف الشغل اللي عندي
+
+586
+00:40:33,680 --> 00:40:37,780
+عشان أخففه فيه negation بعد دخل ال negation هذه
+
+587
+00:40:37,780 --> 00:40:40,820
+فصار عند كل اتنين هذول بيشابه بعض صار في إمكاني أن
+
+588
+00:40:40,820 --> 00:40:45,880
+أحط واحدة مكان التانيةفي عملية associative ال
+
+589
+00:40:45,880 --> 00:40:48,260
+associative هذه بعدين هنستعملها لو جت كمان شوية
+
+590
+00:40:48,260 --> 00:40:52,880
+associative مع competitive عشان ندخل ال P على
+
+591
+00:40:52,880 --> 00:40:55,020
+الأقواس تانية خلونا ناخدها واحدة واحدة في عندنا
+
+592
+00:40:55,020 --> 00:40:58,440
+مبدأيا اتفاجنا ان في عندنا negation هذه بستعملها
+
+593
+00:40:58,440 --> 00:41:04,160
+دي مورغان هاي دي مورغان دي مورغان هندخلها هنا بصيب
+
+594
+00:41:04,160 --> 00:41:12,640
+negation P or Q هاي negation P or Q تمامهي هيك
+
+595
+00:41:12,640 --> 00:41:16,420
+خلصنا عملية دي مورغان هل وجد الجزء التاني هنا صارت
+
+596
+00:41:16,420 --> 00:41:23,240
+إيش or or بقدر استعمل ال associative الأقواص أحطها
+
+597
+00:41:23,240 --> 00:41:27,140
+زي ما بدي مادام الإتنين هيوم or or الإتنين or أنا
+
+598
+00:41:27,140 --> 00:41:35,080
+كل .. هتعامل معاها .. هتعامل معايا قص هذا القص
+
+599
+00:41:35,080 --> 00:41:44,200
+هذا مع .. مع القص هذا اعتبروها إن كلها دي زبطتمام؟
+
+600
+00:41:44,200 --> 00:41:47,100
+عشان ذيك بقولكوا خلّي عينيكوا كويس واضحة تماما على
+
+601
+00:41:47,100 --> 00:41:50,640
+الأقواص الأقواص قوعوا يضيعوا منكوا قوس هيكي تحت
+
+602
+00:41:50,640 --> 00:41:55,240
+عينيكوا يروحوا قوس ماتعدوهوش كويس يتلاقوا حالكوا
+
+603
+00:41:55,240 --> 00:41:58,180
+صرتوا في expression مختلف تماما عن أن انتوا
+
+604
+00:41:58,180 --> 00:42:02,140
+بتشطروا عليه تمام لو أتعاملنا مع حد زده فإذا
+
+605
+00:42:02,140 --> 00:42:05,300
+الأقواص هذه ممكن أغير فيها غيرها زي ما بدي أقولكوا
+
+606
+00:42:05,300 --> 00:42:11,480
+ممكن أشيلها لو شيلناها حاسي رشة؟ مش حاسي رشة ليش؟
+
+607
+00:42:11,480 --> 00:42:17,140
+لأنهor or نفس ال operator فمافيش مشكلة بدون نفس ال
+
+608
+00:42:17,140 --> 00:42:21,640
+operator مافيش أشكال تمام هاي غيرنا عملنا اللي
+
+609
+00:42:21,640 --> 00:42:25,500
+بدناها بعد هيك ال competitive التبديل بمعنى أن مين
+
+610
+00:42:25,500 --> 00:42:35,780
+قبل التانية مش هتفرج negation P or Q هي نفسها Q or
+
+611
+00:42:35,780 --> 00:42:39,040
+negation P يعني مين قبل مين مش هتفرج كتير
+
+612
+00:42:39,040 --> 00:42:46,400
+competitiveكويس هذه الجزئية هتخليني احط ال Q هنا و
+
+613
+00:42:46,400 --> 00:42:50,620
+ال P هنا ليش اجرب للقوس لان محتاج اعمل operation
+
+614
+00:42:50,620 --> 00:42:55,260
+لان انا اصلا كل شغل اول ما بديت افكر من هنا فكرت
+
+615
+00:42:55,260 --> 00:43:00,540
+ان كل ال terms فيها P طب ال P هذه كلها لو اقدرنا
+
+616
+00:43:00,540 --> 00:43:04,240
+بطريقة او باخر نختزلها بعمل مشترك طب هنا مافيش
+
+617
+00:43:04,240 --> 00:43:08,040
+حاجة اسمها عمل مشترك فعشان اعملها محتاج ادخلها جوا
+
+618
+00:43:08,040 --> 00:43:10,700
+على القوس طب هل في إمكانية اه في إمكانية وجدنا ان
+
+619
+00:43:10,700 --> 00:43:15,020
+دي مورغان هينحكسهل الإمكانية بعدين وجدنا لما صاروا
+
+620
+00:43:15,020 --> 00:43:19,000
+تنتين زي بعض اه صار في إمكانية او اوضح و بينت انا
+
+621
+00:43:19,000 --> 00:43:23,240
+بالنسبالي هيك بينت ان اه خلاص ال P دخلت خلصنا ال P
+
+622
+00:43:23,240 --> 00:43:26,600
+ال negation P هذه اللي برا داخلة خلاص مافيش مشكلة
+
+623
+00:43:26,600 --> 00:43:35,200
+باين ان هي خلاص حتى دخلت الأقواس فهي
+
+624
+00:43:35,200 --> 00:43:40,200
+الشغل الجزء اللي تبعنا كان هيك بالشكل هذا عكسنا
+
+625
+00:43:42,560 --> 00:43:46,440
+لحظة أخدنا كل واحدة منهم لحال competitive يعملنا
+
+626
+00:43:46,440 --> 00:43:51,240
+competitive بعدين هنعمل ال .. هذه خلصنا كل اللي
+
+627
+00:43:51,240 --> 00:43:55,940
+هنعمله associative بيعني أن القوس هذا و احنا
+
+628
+00:43:55,940 --> 00:44:04,020
+متفقين أن هذه كلها هيك K مع أن ذلك بقدر أقول Q or
+
+629
+00:44:04,020 --> 00:44:08,700
+أفتح قوس negation P or K
+
+630
+00:44:11,900 --> 00:44:17,160
+بس وشية لإيش لإن التنتيه الأور فمافيش مشكلة مدام
+
+631
+00:44:17,160 --> 00:44:20,000
+التنتيه الأور مافيش مشكلة عندنا بنقدر نتحرك فيهم
+
+632
+00:44:20,000 --> 00:44:25,060
+تمام هذا هيقودنا أنه هالوجد الأقواص هذه هتروح
+
+633
+00:44:25,060 --> 00:44:31,980
+هينفتح قسم هنا وكمان يسكر قسم هنا هاي الأقواص
+
+634
+00:44:31,980 --> 00:44:38,140
+بتاعتنا كويس لسه بدنا ندخل ال negation P لسه برضه
+
+635
+00:44:38,140 --> 00:44:42,000
+مادخلتش على الأقواص جوا ماوصلتش لل P بتاعتهاكيف
+
+636
+00:44:42,000 --> 00:44:46,080
+ندخل على ال P بتاعتنا؟ خدوا بالك احنا وصلنا لوين ل
+
+637
+00:44:46,080 --> 00:44:54,080
+عند Q or هنفتح أقواص negation P or برضه هنفتح قوس
+
+638
+00:44:54,080 --> 00:44:58,600
+هنلاحظ ناخد بان من الأقواص بتاعتنا الأقواص اللي
+
+639
+00:44:58,600 --> 00:45:04,870
+موجودة عندنا فإذا هناnegation P بقدرش أتعامل معاها
+
+640
+00:45:04,870 --> 00:45:09,470
+مباشرة أو ال or الأولى، بقدرش أتعامل معاها مع ال
+
+641
+00:45:09,470 --> 00:45:13,790
+or اللي داخل الأقواس، ليش؟ لأنه بمجرد ما أفك
+
+642
+00:45:13,790 --> 00:45:17,170
+القواس اللي قدامي مباشرة، أنا هتعامل مع مين؟ مع ال
+
+643
+00:45:17,170 --> 00:45:21,330
+or في الأول، هنتعامل مع or جبل ما نتعامل نبدأ ندخل
+
+644
+00:45:21,330 --> 00:45:27,460
+على ال ..or بتاعتنا فهنتعامل مع جزئية ال and عشان
+
+645
+00:45:27,460 --> 00:45:31,940
+نتعامل or مع and كنا بنعمل ايش distribution او
+
+646
+00:45:31,940 --> 00:45:37,040
+distributive rule distributive rule بتاعتنا
+
+647
+00:45:37,040 --> 00:45:46,160
+automatically هتحول ل negation ب or القوس هذا كله
+
+648
+00:45:46,160 --> 00:45:53,690
+and negation ب or القوس التاني فهتصبحبهذا .. بهذا
+
+649
+00:45:53,690 --> 00:45:56,890
+الشكل اللي احنا شايفينه هنا بنقدر نقول انه ارتحت
+
+650
+00:45:56,890 --> 00:46:01,930
+.. ارتحنا ليش؟ لأنه صارت عندنا or مع or بنقدر
+
+651
+00:46:01,930 --> 00:46:07,230
+القواص هذا نفكه و نعمل associative .. associative
+
+652
+00:46:07,230 --> 00:46:10,670
+الأقواص نحطها و .. و .. ايه؟ وين بدنا ياها؟ فبنحطه
+
+653
+00:46:10,670 --> 00:46:15,430
+هنا، ممكن نحطه بهذا الشكل عساس ان استغل negationP
+
+654
+00:46:15,430 --> 00:46:20,510
+or negation P طيب كيف حيصير الكلام هذا؟ حيصير إنه
+
+655
+00:46:20,510 --> 00:46:26,470
+فعلا صار عندنا negation P مع P automatically مدام
+
+656
+00:46:26,470 --> 00:46:32,470
+or هذه هتكون true دائما ال true لما بيقول negation
+
+657
+00:46:32,470 --> 00:46:36,850
+P مع P أو negation ال proposition مع ال
+
+658
+00:46:36,850 --> 00:46:41,230
+proposition دائما مع بعض or as a or connection
+
+659
+00:46:41,230 --> 00:46:45,510
+بيكونوا trueكون true لأن واحدة منهم لازم تكون true
+
+660
+00:46:45,510 --> 00:46:52,390
+في الحالة هذه مع لما نقول or are مع أي proposition
+
+661
+00:46:52,390 --> 00:46:58,330
+آخر true مع أي proposition آخر أكيد هيطلع ايش true
+
+662
+00:46:58,330 --> 00:47:02,610
+true لأن ال or يكفي أن يكون في عندنا proposition
+
+663
+00:47:02,610 --> 00:47:08,470
+true عشان كل النتيجة تكون true فإذا كل الجزء هذا
+
+664
+00:47:08,470 --> 00:47:16,340
+trueتمام طيب true and ونفترض أنه كل ال term هذا
+
+665
+00:47:16,340 --> 00:47:22,660
+هيك هنسميه K صار عندنا true and K and proposition
+
+666
+00:47:22,660 --> 00:47:28,720
+K طيب فإذا إذا ال K هذه true كله true إذا كان
+
+667
+00:47:28,720 --> 00:47:35,730
+false كله false فإذا المحصلة كلها true andany
+
+668
+00:47:35,730 --> 00:47:39,290
+proposition هيعطينا ال value لل proposition، فإذا
+
+669
+00:47:39,290 --> 00:47:46,130
+الجزء هذا هو اللي يعبر عن كل ال term هذا، تمام؟
+
+670
+00:47:46,130 --> 00:47:51,370
+تمام، كويس، فأصبح عندنا true true كل الكلام اللي
+
+671
+00:47:51,370 --> 00:47:56,910
+احنا قولناه وصلنا للنتيجة النهائيةإنه فعلا هي ال
+
+672
+00:47:56,910 --> 00:48:00,090
+proposition هذا كله على بعض اللي بين القصين نزل
+
+673
+00:48:00,090 --> 00:48:03,890
+كما هو عندي هنا مع ال Q اللي احنا بديد كل شغلنا
+
+674
+00:48:03,890 --> 00:48:08,730
+فيها تمام هنا لاحظوا برضه في عندكم negation و في
+
+675
+00:48:08,730 --> 00:48:12,970
+في جوا بدنا نحاول ندخلهم مع بعض جاب ما أبدأ أدخلهم
+
+676
+00:48:12,970 --> 00:48:19,090
+مع بعض لاحظوا إن هذه or هذه and بركبوش مع بعضطيب و
+
+677
+00:48:19,090 --> 00:48:23,630
+لكن في negation برا دي مورغان ممكن يحلللي الموضوع
+
+678
+00:48:23,630 --> 00:48:29,550
+هذا أني أدخل negation جوا مع ال P و ال R فعكسنا ال
+
+679
+00:48:29,550 --> 00:48:36,510
+and لإيش ل or لما تنعكس ل or هتكون بهذا الشكل
+
+680
+00:48:36,510 --> 00:48:41,070
+دخلنا ال negation جوا و عكسناها or صار بقدر أشتغل
+
+681
+00:48:41,070 --> 00:48:44,350
+على ال associative associative أنه القوس هذا بلغي
+
+682
+00:48:44,350 --> 00:48:52,520
+من هنا و بنحطه بهذا الشكلطيب negation P or
+
+683
+00:48:52,520 --> 00:48:56,360
+negation P او proposition معناه انه بتكلم عن ال
+
+684
+00:48:56,360 --> 00:49:00,260
+proposition or نفس ال proposition هيعطينا ال
+
+685
+00:49:00,260 --> 00:49:03,120
+proposition لو كان ال proposition false فالنتيجة
+
+686
+00:49:03,120 --> 00:49:07,720
+هتكون false لو كان ال proposition true هتكون true
+
+687
+00:49:07,720 --> 00:49:12,320
+لو قلنا ال negation P هذه بتساوي true معناه ذلك
+
+688
+00:49:12,320 --> 00:49:13,460
+انا بتكلم عن true
+
+689
+00:49:16,130 --> 00:49:20,810
+or true هتكون true طيب لو كانت false .. false مع
+
+690
+00:49:20,810 --> 00:49:25,310
+false هتكون false فإذا قيمتها .. قيمة الناتج هي
+
+691
+00:49:25,310 --> 00:49:28,710
+نفس قيمة مين؟ ال proposition نفسه ال proposition
+
+692
+00:49:28,710 --> 00:49:32,790
+أنا إيش عندي اسمه؟ اسمه negation P فإذا بختزل
+
+693
+00:49:32,790 --> 00:49:36,830
+التنتين negation P هدول ب negation P واحدة بس
+
+694
+00:49:36,830 --> 00:49:42,830
+negation P واحدة فأصبح عندي هاي negation P واحدة
+
+695
+00:49:42,830 --> 00:49:46,590
+عندنا الأقوسة ده بقدر أفكهاإذا فقناها عيدوا
+
+696
+00:49:46,590 --> 00:49:49,170
+ترتيبهم زي ما بدكوا، ليش نقدر نعيد ترتيبهم زي ما
+
+697
+00:49:49,170 --> 00:49:53,590
+بدنا؟ لأنه في عندكوا or مع or ال priority هي هي،
+
+698
+00:49:53,590 --> 00:49:56,890
+مين جاب المين مش هي .. مش هيفرج معانا، هتكون
+
+699
+00:49:56,890 --> 00:50:03,470
+عندكوا competitive في شغلكوا، مين جاب المين، في
+
+700
+00:50:03,470 --> 00:50:06,830
+الآخر بترجعوا لمين، ل ال expression اللي أساسا
+
+701
+00:50:06,830 --> 00:50:11,110
+مطلوب منكوا من الأول، تعملوله prove، تشوفوا كيف
+
+702
+00:50:11,110 --> 00:50:14,270
+كان ترتيبه، بترتبوا زي ما بدكوا، فإذا لو أطلعنا
+
+703
+00:50:15,240 --> 00:50:20,160
+هنقش اللي بديها بالظبط، بدي negation هي تشوفوا
+
+704
+00:50:20,160 --> 00:50:25,080
+اللي هنا كان هذا
+
+705
+00:50:25,080 --> 00:50:34,540
+negation P or Q or negation R فبنعيد من عندنا
+
+706
+00:50:34,540 --> 00:50:41,340
+النقطة اللي كنا وصلناها بنعيد نرتب شغلنا زي ما
+
+707
+00:50:41,340 --> 00:50:41,920
+احنا بدنايا
+
+708
+00:50:46,680 --> 00:50:50,040
+كويس فهنا هنا فكناها نرجع بنرتبها زي ما احنا بنحط
+
+709
+00:50:50,040 --> 00:50:54,500
+هذه في الأول هذه في التانية و بننزل هذه زي ما هي
+
+710
+00:50:54,500 --> 00:51:00,040
+delta ليش؟ لأن بينهم نفس ال operator تمام نفس ال
+
+711
+00:51:00,040 --> 00:51:03,400
+operator هو اللي بينهم فبقدر مباشرة اقول انه
+
+712
+00:51:03,400 --> 00:51:06,680
+الترتيب مش هيفرج معانا الترتيب مش هيفرج معانا و
+
+713
+00:51:06,680 --> 00:51:11,780
+نكون وصلنا لإثبات اللي احنا محتاجينه في الشغل طبعا
+
+714
+00:51:11,780 --> 00:51:17,560
+و بنكون وصلنا زي ما قلنا للي احنا بدناهامع نهاية
+
+715
+00:51:17,560 --> 00:51:23,140
+ال example تبعنا بنكونتعرفنا على ال atomic .. ال
+
+716
+00:51:23,140 --> 00:51:26,420
+.. ال .. ال atomic propositions قولنا ان احنا
+
+717
+00:51:26,420 --> 00:51:30,180
+بنسميها بال .. بال .. بال lowercase letters او بال
+
+718
+00:51:30,180 --> 00:51:34,320
+small letters PQR بنعبر عليهم بشهد الشكل فهذه
+
+719
+00:51:34,320 --> 00:51:38,940
+عبارة عن propositions ال pollen algebra operator
+
+720
+00:51:38,940 --> 00:51:44,360
+أخدناها negation conjunction disjunction XOR ال
+
+721
+00:51:44,360 --> 00:51:47,980
+implication و biconditional او اللي قولنا عبارنا
+
+722
+00:51:47,980 --> 00:51:51,410
+عنه ب if and only ifاتكلمنا عن ال compound
+
+723
+00:51:51,410 --> 00:51:56,270
+prepositionsلما بتكلم عن compound propositions أنا
+
+724
+00:51:56,270 --> 00:52:00,710
+بتكلم عن expression لمجموعة propositions مرتبطة
+
+725
+00:52:00,710 --> 00:52:05,470
+بoperators مربوطة بمجموعة operators زي الشكل اللي
+
+726
+00:52:05,470 --> 00:52:08,970
+احنا شايفينه هنا كويس ال equivalence برضه اتكلمنا
+
+727
+00:52:08,970 --> 00:52:11,810
+عن ال equivalence وكيف ممكن استعمل ال equivalence
+
+728
+00:52:11,810 --> 00:52:16,730
+لإثبات اي expression معين فممكن اقول في حالة زي
+
+729
+00:52:16,730 --> 00:52:19,070
+الحلقة اللي عندنا وهذا العلامة أخدناها علامة
+
+730
+00:52:19,070 --> 00:52:22,910
+equivalenceو أتكلمنا عن أجمع منهم و قولنا كيف ممكن
+
+731
+00:52:22,910 --> 00:52:28,390
+أثبت ال equivalence اتكلمنا عن ال truth table ممكن
+
+732
+00:52:28,390 --> 00:52:33,430
+نستخدم ال truth tables عساس أجيب ال truth value
+
+733
+00:52:33,430 --> 00:52:38,030
+لكل compound proposition منهم و نقارنهم مع بعض
+
+734
+00:52:38,030 --> 00:52:41,330
+فلازم كل element في ال row يساوي ال element في نفس
+
+735
+00:52:41,330 --> 00:52:44,350
+ال row لل expression التاني إذا كان الكلام ده
+
+736
+00:52:44,350 --> 00:52:47,650
+ينطبق على جميع ال rows بقدر أقول ان ال two
+
+737
+00:52:47,650 --> 00:52:51,320
+compound propositions isequivalent كل واحدة منها
+
+738
+00:52:51,320 --> 00:52:55,400
+equivalent لتانية او symbolic derivations زي ال
+
+739
+00:52:55,400 --> 00:53:00,680
+example اللى اخدناه اللى هو اخر example كويسة
+
+740
+00:53:00,680 --> 00:53:03,520
+المرة الجاية ان شاء الله هنتكلم عن ال predicate
+
+741
+00:53:03,520 --> 00:53:07,540
+logic و هنتكلم نقول ان هده هي مش proposition هي
+
+742
+00:53:07,540 --> 00:53:12,140
+propositional function propositional function عشان
+
+743
+00:53:12,140 --> 00:53:16,140
+نسيبكوا إياها للمرة الجاية بتوضيح خفيف احنا أحيانا
+
+744
+00:53:16,140 --> 00:53:20,860
+نضطر نعبر عن مجموعة of propositionsمجموعة كبيرة
+
+745
+00:53:20,860 --> 00:53:23,600
+ممكن تكون من ال propositions بس بتعبّر عنها ب
+
+746
+00:53:23,600 --> 00:53:28,620
+expression واحد فمعنى ذلك بستعمل variables فمشابه
+
+747
+00:53:28,620 --> 00:53:32,120
+تماما لفكرة ال function لما يكون في عندكوا
+
+748
+00:53:32,120 --> 00:53:36,620
+function و بحطلها ال variable x فال variable x ده
+
+749
+00:53:36,620 --> 00:53:42,200
+ممكن ياخد قيم متعددة أو مختلفة بناء على القيم
+
+750
+00:53:42,200 --> 00:53:46,580
+المختلفة كإن بقول إنه عند مجموعة propositions إيش
+
+751
+00:53:46,580 --> 00:53:53,060
+يعني؟ يعني لو قولنا ال x هذهجاية من من ست او
+
+752
+00:53:53,060 --> 00:53:57,740
+مجموعة واحد اتنين تلتة بيكفي نفترض انه تلتة طبعا
+
+753
+00:53:57,740 --> 00:54:05,680
+تلتة متواضعة جدا ككست عبارة عن if one and if two
+
+754
+00:54:05,680 --> 00:54:11,000
+and if three طبعا لو اكتر معناته هناخد وسعة كتير
+
+755
+00:54:11,000 --> 00:54:17,660
+لأ احنا كدا ممكن نكتبها if of x ونعرف لاحقا الال
+
+756
+00:54:17,660 --> 00:54:22,220
+universe of discourse هنسميها أو فضاء العينة لهنا
+
+757
+00:54:22,220 --> 00:54:25,420
+بنسيب الموضوع اللي predicated هذا نخليه للمرة
+
+758
+00:54:25,420 --> 00:54:29,920
+الجاية ان شاء الله بنشرحه بالتفصيل و بننهيه جزئية
+
+759
+00:54:29,920 --> 00:54:33,260
+ال equivalence او ال propositional equivalence
+
+760
+00:54:33,260 --> 00:54:36,180
+بتاعتنا فيعطيكوا العافية و بارك الله فيكوا للمرة
+
+761
+00:54:36,180 --> 00:54:38,560
+الجاية ان شاء الله تعالى و السلام عليكم و رحمة
+
+762
+00:54:38,560 --> 00:54:45,260
+الله تعالى و بركاته و بدنا نعرف هنا أول التعريف
+
+763
+00:54:45,260 --> 00:54:45,620
+تبعنا
+
+764
+00:55:04,220 --> 00:55:08,160
+عشان تكون even المفروض ان هي تساوي اتنين في رقم
+
+765
+00:55:08,160 --> 00:55:14,950
+تاني بمعنى اخر بتقسم على اتنينبمعنى اخر ان هي رقم
+
+766
+00:55:14,950 --> 00:55:18,530
+بيقسم على اتنين طيب هنتأكد من الكلام ده هل هو فعلا
+
+767
+00:55:18,530 --> 00:55:22,630
+في عنده رقم بيقسم على اتنين بيمشي الكلام ده كيف
+
+768
+00:55:22,630 --> 00:55:29,170
+ممكن نعبر عنها رياضيا فهقول مدام even كل القيم كل
+
+769
+00:55:29,170 --> 00:55:34,430
+x اللي ممكن نعبر عنها ان هي even المفروض تحقيق لنا
+
+770
+00:55:34,430 --> 00:55:41,170
+الشغل التالي ان هي even by conditional there exist
+
+771
+00:55:41,170 --> 00:55:49,390
+ysuch that x equal to 2y معناته هي even إذا كان
+
+772
+00:55:49,390 --> 00:55:57,750
+موجود لكل قيمة ل x هتكون even امتى إذا كانت يوجد y
+
+773
+00:55:57,750 --> 00:56:04,230
+نص x هاي معناها فمعناه ذاك ضامن إن x هي تعتبر ضعف
+
+774
+00:56:04,230 --> 00:56:09,190
+أي رقم تاني ضعف some number ضعف أي رقم تاني مدام
+
+775
+00:56:09,190 --> 00:56:12,890
+ضعف أي رقم تاني بتجبل جسمها اتنين مدام جبلت القسم
+
+776
+00:56:12,890 --> 00:56:17,810
+ع اتنينأكيد even .. اكيد even .. اكيد even زوجي ..
+
+777
+00:56:17,810 --> 00:56:21,110
+رقم زوجي .. اكيد هتكون رقم زوجي .. كمان مرة for
+
+778
+00:56:21,110 --> 00:56:29,430
+all x لكل قيم x ال .. even .. x is even if and
+
+779
+00:56:29,430 --> 00:56:32,510
+only if مش هاد ال if and only if .. by conditional
+
+780
+00:56:32,510 --> 00:56:37,610
+.. هيها لاحظوا هنترجمها هيها a number x is even
+
+781
+00:56:37,610 --> 00:56:43,830
+فإذا for all x a number x is even هيهاif and only
+
+782
+00:56:43,830 --> 00:56:50,770
+if it's equal to two times some other number some
+
+783
+00:56:50,770 --> 00:56:53,010
+other number معناته بدي اعرف إيش ال other number
+
+784
+00:56:53,010 --> 00:56:57,590
+هذا there exists y y other number عن x إيش العلاقة
+
+785
+00:56:57,590 --> 00:57:02,210
+بينهم two times معناته ال x هذه تساوي two times of
+
+786
+00:57:02,210 --> 00:57:06,050
+ال other number اللي عرفناها إنه موجود رقم تاني
+
+787
+00:57:06,050 --> 00:57:11,840
+يمثل نص x موجود رقم تاني يمثل نص xففي الحالة دي
+
+788
+00:57:11,840 --> 00:57:20,660
+بنقول إنه فعلا الرقم هذا even الرقم even طيب آخر
+
+789
+00:57:20,660 --> 00:57:27,760
+مثال a number is prime P of Xأنت بيكون فعلا prime
+
+790
+00:57:27,760 --> 00:57:31,280
+if and only if it's greater than one لازم يكون
+
+791
+00:57:31,280 --> 00:57:34,180
+أكبر من واحد بقدرش أقول إن الواحد هو prime إن عارف
+
+792
+00:57:34,180 --> 00:57:36,380
+أحسس إن هو prime و خلاص و يدخل معناه في التاريخ
+
+793
+00:57:36,380 --> 00:57:40,080
+لازم يكون أكبر من ال prime and it's not the
+
+794
+00:57:40,080 --> 00:57:47,260
+product of two non unity numbers معناته بقدرش أجيب
+
+795
+00:57:47,260 --> 00:57:51,640
+محصلته من ضرب رقمين بقدرش أجيبه من حاصل ضرب رقمين
+
+796
+00:57:51,640 --> 00:57:54,560
+و لازم نحدد هنا إن الرقمين هدول مايكونش فيهم
+
+797
+00:57:54,560 --> 00:57:55,040
+الواحد
+
+798
+00:57:57,630 --> 00:58:03,090
+لأنه سبعة prime .. prime صح؟ بس بقدر أقول إن هو
+
+799
+00:58:03,090 --> 00:58:07,250
+سبعة في واحد صحيح؟
+
+800
+00:58:07,250 --> 00:58:10,030
+أنتوا فاهمين إن هو .. بتنضربش هذه، بس ال computer
+
+801
+00:58:10,030 --> 00:58:13,010
+بيفهمش، الرياضات بتفهمش، لازم تكون ال expression
+
+802
+00:58:13,010 --> 00:58:16,230
+تبعكوا واضح وشامل، عشان هيك لازم نحدد إن هو
+
+803
+00:58:16,230 --> 00:58:23,310
+مايكونش فيهم الواحد، مايكونش فيهم الواحدخلاص
+
+804
+00:58:23,310 --> 00:58:26,650
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+805
+00:58:26,650 --> 00:58:32,770
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+806
+00:58:32,770 --> 00:58:36,050
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+807
+00:58:36,050 --> 00:58:36,190
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+808
+00:58:36,190 --> 00:58:37,650
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+809
+00:58:37,650 --> 00:58:39,090
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+810
+00:58:39,090 --> 00:58:39,810
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+811
+00:58:39,810 --> 00:58:41,850
+فيهم الواحد مايكونش فيهم الواحد مايكونش فيهم
+
+812
+00:58:41,850 --> 00:58:45,550
+الواحد مايكونش فيهم الواحد مايكونش فيهم الواحد
+
+813
+00:58:45,550 --> 00:58:47,510
+مايكونش فيهم الواحد مايكونش فيهم الواحد مايكونش
+
+814
+00:58:47,510 --> 00:58:50,300
+فيهم الواحد مايكونش فيx is prime فهي حقق لـ
+
+815
+00:58:50,300 --> 00:58:54,180
+predicate طيب عشان احققها فعلا امتى بتصير الكلمة
+
+816
+00:58:54,180 --> 00:58:59,180
+if and only if نبدأ نمسكهم شوية شوية و نفتح الأقوى
+
+817
+00:58:59,180 --> 00:59:05,660
+ساعتنا و لاحظوا انه هنا if and only if تمام
+
+818
+00:59:05,660 --> 00:59:10,320
+لاحظوا يعطينا condition يعطينا التاني يعطينا
+
+819
+00:59:10,320 --> 00:59:14,280
+التالت في three conditions حطينا لنا معناته بدنا
+
+820
+00:59:14,280 --> 00:59:18,990
+نربطهم بands فتحنا ال course تبعناهي ال cause
+
+821
+00:59:18,990 --> 00:59:23,050
+تبعنا وهي هنعمل and and and نشوف أشياء مجموعة
+
+822
+00:59:23,050 --> 00:59:25,610
+القيم ال .. ال .. ال .. ال exceptions اللي أعطانا
+
+823
+00:59:25,610 --> 00:59:30,770
+إياها firstly greater than one اه x أكبر من واحد
+
+824
+00:59:30,770 --> 00:59:38,570
+and it's not the product اه هو مش جاي من مجموع
+
+825
+00:59:38,570 --> 00:59:47,170
+ضربين ضرب رقمين معناه لا يوجد is not لا يوجد رقمين
+
+826
+00:59:50,300 --> 00:59:57,200
+X حصل ضربهم بس بدنا نحدد هنا and Y ليست واحد و Z
+
+827
+00:59:57,200 --> 01:00:01,440
+ليست واحد عشان مايروحش يفكر لإن السبعة ممكن تيجي
+
+828
+01:00:01,440 --> 01:00:06,420
+سبعة في واحد عشان ما ال computer و انت بتعملوله
+
+829
+01:00:06,420 --> 01:00:10,300
+code بال expression هذا مايروحش يعتبر ان هي هذه
+
+830
+01:00:10,300 --> 01:00:14,520
+واحد و هي حصل ضرب رقمين بمش الحال لأ بدنا نقوله ان
+
+831
+01:00:14,520 --> 01:00:20,580
+لأ دير بالك الواحدالـ y لازم لا تسوى واحد and z لا
+
+832
+01:00:20,580 --> 01:00:27,840
+تسوى واحد طبعا فلحظه صار بنقدر من الجملة إذا عندنا
+
+833
+01:00:27,840 --> 01:00:33,380
+تعريف لمجموعة معينة من ال numbers بنقدر نعرف منها
+
+834
+01:00:33,380 --> 01:00:37,680
+إيش ال expression تبعنا أو بنقدر نكتب ال
+
+835
+01:00:37,680 --> 01:00:41,860
+expression الرياضي تبعنا رجعوهم في البيت هتلاقيوا
+
+836
+01:00:41,860 --> 01:00:45,690
+إن فعلا إن مسكوهم كلمة كلمةواحدة واحدة هتركبوهم
+
+837
+01:00:45,690 --> 01:00:50,930
+ورا بعض، هتركبوهم ورا بعض، تمام؟ هيك احنا نتخلص و
+
+838
+01:00:50,930 --> 01:00:56,530
+نخلصنا، كل عامة بخير، ال .. طبعا ال .. ال homework
+
+839
+01:00:56,530 --> 01:01:01,450
+مش هتسلمونا إياه للأحد الجاى، هيكون عيد، فبيضل للي
+
+840
+01:01:01,450 --> 01:01:04,470
+بعده ان شاء الله تعالى، للي بعده بإذن الله تعالى،
+
+841
+01:01:04,470 --> 01:01:05,010
+يطبخوا العافية
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..19a754477544d215be67937d1d3cfa68b323b265
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_postprocess.srt
@@ -0,0 +1,2644 @@
+1
+00:00:20,670 --> 00:00:22,930
+بسم الله الرحمن الرحيم والصلاة والسلام علي أشرف
+
+2
+00:00:22,930 --> 00:00:25,290
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحابي
+
+3
+00:00:25,290 --> 00:00:29,870
+أجمعين نكمل اليوم في ال set operations وناخد شوية
+
+4
+00:00:29,870 --> 00:00:35,130
+operators جديدة وشوية functions ونشوف شوية حاجات
+
+5
+00:00:35,130 --> 00:00:38,570
+إضافية على موضوع ال sets اللي كنا بدأنا فيه المرة
+
+6
+00:00:38,570 --> 00:00:42,230
+السابقة فبنتكلم عن ال disjoint أو ال disjointed
+
+7
+00:00:42,230 --> 00:00:49,030
+less اللي هي التفكك أو عدم التقاطعاللي هو ان ال
+
+8
+00:00:49,030 --> 00:00:52,090
+sets لايوجد بينهم اي تقاطع فهد امتى بنقدر نقول
+
+9
+00:00:52,090 --> 00:00:55,870
+الكلام هد اذا كان عندنا two sets a and b بنسميهم
+
+10
+00:00:55,870 --> 00:00:59,850
+disjoint او unjointed if and only if their
+
+11
+00:00:59,850 --> 00:01:04,790
+intersection is empty بمعنى انه a intersection b
+
+12
+00:01:04,790 --> 00:01:11,570
+equal to ايش؟ to set five ففي الحالة هد بنقدر نقول
+
+13
+00:01:11,570 --> 00:01:16,790
+ان هم disjoint من الحاجات المشهورة جدا لو قولنا ال
+
+14
+00:01:16,790 --> 00:01:23,170
+setاللي بتحتوي على ال odd integers واضح إن هي مع
+
+15
+00:01:23,170 --> 00:01:27,610
+ال even integers disjointed لإن مافيش أي علاقة
+
+16
+00:01:27,610 --> 00:01:30,790
+بينهم مستحيل تلاقوا element موجود في ال odd وموجود
+
+17
+00:01:30,790 --> 00:01:37,050
+في ال even sets كويس فهذه الأمور واضحة مش فيها
+
+18
+00:01:37,050 --> 00:01:41,030
+مشكلة هذه بتخلينا نصل أو نرجع رجوع شوية لل union
+
+19
+00:01:41,030 --> 00:01:44,130
+اللي أخدناها المرة اللي فاتت عشان نتكلم عن ال
+
+20
+00:01:44,130 --> 00:01:50,250
+inclusion و ال exclusion principleفي جزئية ال
+
+21
+00:01:50,250 --> 00:01:53,870
+union لما اتكلمنا عن ال union وعرفناها ان هي
+
+22
+00:01:53,870 --> 00:01:56,410
+مجموعة ال elements اللي موجودة في ال two sets مع
+
+23
+00:01:56,410 --> 00:02:01,090
+بعض يعني لازم تكون موجودة في ال set A او set B
+
+24
+00:02:01,090 --> 00:02:04,250
+معناه ذلك ان انا جمعت كل ال elements اللي موجودة
+
+25
+00:02:04,250 --> 00:02:07,630
+في ال two sets طبعا طيب لما ننشط نتكلم عن ال
+
+26
+00:02:07,630 --> 00:02:09,810
+cardinality و المرة اللي فاتت قلنا ايش يعني
+
+27
+00:02:09,810 --> 00:02:12,870
+cardinality قلنا ان هي عدد ال elements داخل ال set
+
+28
+00:02:12,870 --> 00:02:18,250
+فإذا لما اقولها لوجد cardinality ل A union Bهي
+
+29
+00:02:18,250 --> 00:02:21,290
+فعليا by logic أن هي العناصر اللي موجودة في A
+
+30
+00:02:21,290 --> 00:02:24,910
+والعناصر اللي موجودة في B فإذا ال cardinality ل A
+
+31
+00:02:24,910 --> 00:02:29,130
+زائد ال cardinality اللي موجودة في B بس ناخد بالنا
+
+32
+00:02:29,130 --> 00:02:33,870
+أنه في exclusion لازم نعمل لمين لل intersection
+
+33
+00:02:33,870 --> 00:02:37,050
+ليش لل intersection لأن ال intersection هنا هيتكرر
+
+34
+00:02:37,050 --> 00:02:42,070
+معاكم هيتكرر معاكم for example لو قلنا عندنا واحد
+
+35
+00:02:42,070 --> 00:02:48,730
+اتنين تلاتة هذه ستة Aو هنقول إن في عندنا ستة تانية
+
+36
+00:02:48,730 --> 00:02:55,890
+تلاتة أربعة خمسة هذه B لو بدنا نقول ال cardinality
+
+37
+00:02:55,890 --> 00:03:03,810
+ل A union B بعد ما نحسبها هنحسبها كالتالي إن كل
+
+38
+00:03:03,810 --> 00:03:10,450
+عناصر A مع كل عناصر B طيب عناصر A فعليا واحد اتنين
+
+39
+00:03:10,450 --> 00:03:17,500
+تلاتة عناصر B تلاتة أربعة خمسةلحظوا إنه إذا بدّي
+
+40
+00:03:17,500 --> 00:03:20,900
+أشباحهم بهذا الشكل هتطلع واحد، اتنين، تلاتة،
+
+41
+00:03:20,900 --> 00:03:26,400
+أربعة، خمسة، ستة، هتطلع ستة طيب فإذا هذا بيساوي ال
+
+42
+00:03:26,400 --> 00:03:31,120
+cardinality ل A اللي هي تساوي تلاتة plus
+
+43
+00:03:31,120 --> 00:03:36,360
+cardinality ب تلاتة هذا بيساوي الستة بس هذا مش صح
+
+44
+00:03:36,360 --> 00:03:41,200
+هذا مش صح لأنه فعليا ال A union B لا تحتوي على ست
+
+45
+00:03:41,200 --> 00:03:45,350
+عناصر أو six elementsفي element مشترك طب إيش اللي
+
+46
+00:03:45,350 --> 00:03:48,510
+بيميز ال element المشترك هذا عشان نشيله أن هو ال
+
+47
+00:03:48,510 --> 00:03:55,270
+intersection تبعهم فإذا minus ال intersection a و
+
+48
+00:03:55,270 --> 00:03:58,690
+b طب a و b وين ال intersection تبعتهم اللي هي
+
+49
+00:03:58,690 --> 00:04:05,150
+تلاتة هذا تمثل ست تحتوي على العنصر تلاتة فجدش ال
+
+50
+00:04:05,150 --> 00:04:09,310
+cardinality بتاعتها واحد فإذا هذا المفروض تكون ستة
+
+51
+00:04:09,310 --> 00:04:15,240
+ناقص واحدخمسة okay خمسة بتصير صح لأنه المفروض أنه
+
+52
+00:04:15,240 --> 00:04:19,380
+عندنا عنصر واحد فقط للتلاتة اذا واحد اتنين تلاتة
+
+53
+00:04:19,380 --> 00:04:26,780
+اربعة خمسة هو الصح هو الإجابة الصحية طيب خليني
+
+54
+00:04:26,780 --> 00:04:30,620
+اقول for example how many students are on our
+
+55
+00:04:30,620 --> 00:04:34,740
+class email list جداش عدد الطلاب اللي موجودين في
+
+56
+00:04:34,740 --> 00:04:38,770
+ال email list اللي موجود عندى الطلاب والطالباتأنا
+
+57
+00:04:38,770 --> 00:04:43,490
+بقدر أستقيهم هدولة من وين؟ من مصدرين، إما إن أقول
+
+58
+00:04:43,490 --> 00:04:48,070
+والله هم ال emails اللي واصليني من ال information
+
+59
+00:04:48,070 --> 00:04:51,030
+sheet، هقول والله واصليني من ال model، دخلت على ال
+
+60
+00:04:51,030 --> 00:04:52,850
+model، اللي مسجل منكوا ال model أنا عارف ال email
+
+61
+00:04:52,850 --> 00:04:56,490
+تبعه، بمجرد ما أنتوا سجلتوا ال model معلوماتكم
+
+62
+00:04:56,490 --> 00:05:00,570
+معظمها عنديفبعرف ال email تبعكم، كويس، ليش؟ لأن
+
+63
+00:05:00,570 --> 00:05:03,630
+ممكن أبعد email لكل المجموع اللي موجود عنده، إن
+
+64
+00:05:03,630 --> 00:05:07,010
+والله في موقع امتحان، في موقع كذا، في إشي بقدر من
+
+65
+00:05:07,010 --> 00:05:10,030
+عندي أتواصل معاكم، هدول مجموعة، طيب، هل كل
+
+66
+00:05:10,030 --> 00:05:13,370
+المسجلين المصاق موجودين عنده على ال model؟ يمكن مش
+
+67
+00:05:13,370 --> 00:05:16,850
+بالضروري كلهممش بالضروري كلهم طيب في نفس الوجد في
+
+68
+00:05:16,850 --> 00:05:19,850
+عندي مصدر آخر هدى هنسميها I اللى هو تعوين ال
+
+69
+00:05:19,850 --> 00:05:24,570
+information sheet اللى هم I عبارة عن set of S ال S
+
+70
+00:05:24,570 --> 00:05:26,930
+هدى من وين جايين ال students هدوله جايين من ال
+
+71
+00:05:26,930 --> 00:05:31,350
+information sheet طيب عندي مصدر آخر اللى هو ال
+
+72
+00:05:31,350 --> 00:05:35,490
+mail نفسه ال email نفسه مين اللى بعتلى email فممكن
+
+73
+00:05:35,490 --> 00:05:38,030
+يكونوا مجموعة ال students اللى بعتوا ل teaching
+
+74
+00:05:38,030 --> 00:05:42,740
+assistantemails فانا هروح اقول للمناس تبعتكم مين
+
+75
+00:05:42,740 --> 00:05:46,480
+اللي بعتلك emails عندك كشوف بدرجات ان البنات اللي
+
+76
+00:05:46,480 --> 00:05:48,600
+بعتولك اه هتقولي والله في بنتين بعتولي كانوا
+
+77
+00:05:48,600 --> 00:05:52,000
+بيسألوا عن كذا هاخد منها القائمة اللي عندها فصار
+
+78
+00:05:52,000 --> 00:05:55,240
+عندى قائمتين القائمتين هدولة منهم بدي احد اتجدش
+
+79
+00:05:55,240 --> 00:05:58,940
+عدد ال emails اللي اتحوشوا عندى اتجدش عدد ال
+
+80
+00:05:58,940 --> 00:06:01,720
+emails اللي اتحوشوا عندى كيف بدي اعملها بدي اعملها
+
+81
+00:06:01,720 --> 00:06:06,870
+على اساس ان هي ال union بتاعة Iunion m وبشوف ال
+
+82
+00:06:06,870 --> 00:06:09,250
+cardinality بتاعك تبجيب عدد الطلاب اللي انا عندي
+
+83
+00:06:09,250 --> 00:06:14,180
+ال email تبعهم اللي عندنا email هم صحيح تمامهدول
+
+84
+00:06:14,180 --> 00:06:16,840
+من وين بتجيب ال cardinality؟ عدد الطلاب اللي أنا
+
+85
+00:06:16,840 --> 00:06:20,740
+جبتهم عن طريق ال model زائد عدد الطلاب اللي أصلا
+
+86
+00:06:20,740 --> 00:06:23,900
+بعتولنا email فاحنا شفنا ال email اللي مابعتلنا
+
+87
+00:06:23,900 --> 00:06:26,140
+إما أنه بعتولنا يقولولنا و الله عندنا مشكلة في ال
+
+88
+00:06:26,140 --> 00:06:29,580
+model أو بعتولنا يقولولي احنا أخدنا ال homework
+
+89
+00:06:29,580 --> 00:06:32,380
+اللي على صفحتك ماخدناش اللي على ال model إيش نسوي
+
+90
+00:06:32,380 --> 00:06:35,640
+أو بعتولنا و الله إيش الكتاب اللي بنشتغل منه المهم
+
+91
+00:06:35,640 --> 00:06:38,340
+لا أي استفسار لا أي حاجة لا أي معلومة بعتولنا
+
+92
+00:06:38,340 --> 00:06:42,260
+email أخدناها من ال email list اللي موجودة كويس
+
+93
+00:06:42,260 --> 00:06:46,030
+هدول اللي هم ال cardinalityطب ناخد بالنا ما هو
+
+94
+00:06:46,030 --> 00:06:48,710
+ممكن اللي بعتولي بال emails هم نفسهم موجودين على
+
+95
+00:06:48,710 --> 00:06:51,970
+ال model موجودين في ال information sheet صحيح؟
+
+96
+00:06:51,970 --> 00:06:54,930
+معنى ذلك إذا بدي أجمحهم هدول و هدول مباشرة أنا في
+
+97
+00:06:54,930 --> 00:06:58,630
+ناس عديتهم مرتين هيك في ناس عديناهم مرتين فلازم
+
+98
+00:06:58,630 --> 00:07:02,630
+نطرح ال intersection تبعهم لازم نطرح ال
+
+99
+00:07:02,630 --> 00:07:04,830
+intersection تبعهم ال intersection طبعا أنا بكون
+
+100
+00:07:04,830 --> 00:07:08,010
+حسبته مرة واحدة يعني العنصر بكون عديته مرة واحدة
+
+101
+00:07:08,010 --> 00:07:12,870
+هنا هنكون عديناه مرتينبنخصم المرة من المرتين بيظل
+
+102
+00:07:12,870 --> 00:07:17,430
+المرة معدود فبكون كل element عدنا فقط مرة واحدة بس
+
+103
+00:07:17,430 --> 00:07:21,010
+وهو ده المطلوب برغم أنه اتكرر في ال two lasts بس
+
+104
+00:07:21,010 --> 00:07:24,510
+أنا عدته مرة واحدةفهذه مهمة جدا لما تيجوا ينطلب
+
+105
+00:07:24,510 --> 00:07:27,310
+منكوا ال cardinality لل union خدوا بالكوا من ال
+
+106
+00:07:27,310 --> 00:07:30,230
+intersection بتاعته ال two sets هذول تاخدوا بالكوا
+
+107
+00:07:30,230 --> 00:07:33,990
+من ال intersection طيب ال set difference ال set
+
+108
+00:07:33,990 --> 00:07:36,290
+difference احنا هم نتكلم عن two sets و بدنا نجيب
+
+109
+00:07:36,290 --> 00:07:39,010
+ال difference between them انه انقول ال difference
+
+110
+00:07:39,010 --> 00:07:43,290
+of a and b كأنه بقول a minus b هذه عبارة عن ال
+
+111
+00:07:43,290 --> 00:07:47,410
+elements اللي موجودة في a و غير موجودة في bهذه
+
+112
+00:07:47,410 --> 00:07:52,370
+معناها انا بتكلم عن كل عنصر موجود في a و غير موجود
+
+113
+00:07:52,370 --> 00:07:58,610
+في b هو ناتج ل a minus b فإذا هي set of x و x such
+
+114
+00:07:58,610 --> 00:08:01,710
+that او ال condition ل x ايش اللي لازم يتحقق ل x
+
+115
+00:08:01,710 --> 00:08:06,890
+ان x belong to a and x not belong to mean to b هذه
+
+116
+00:08:06,890 --> 00:08:11,250
+معناها negation x belong to a implies x belong to
+
+117
+00:08:11,250 --> 00:08:17,570
+b خلينا ننسى اللي فات هذي ايش معناها ان اذا xتنتمي
+
+118
+00:08:17,570 --> 00:08:21,830
+ل a then هي تنتمي ل b لأ إحنا بدنا ننفيها إذا x
+
+119
+00:08:21,830 --> 00:08:25,850
+تنتمي ل a لا تنتمي ل b نعكس ال implication فهنقول
+
+120
+00:08:25,850 --> 00:08:29,770
+negation جابلها هنحط لها negation فإما هذه أو هذه
+
+121
+00:08:29,770 --> 00:08:33,750
+بتعبر عن a minus b أحيانا بنسميها complement of b
+
+122
+00:08:33,750 --> 00:08:39,270
+with respect to a with respect to a فأنا كأني بقول
+
+123
+00:08:39,270 --> 00:08:46,410
+بدي أجيب المكمل ل b بالنسبة لمين ل a بالنسبة ل a
+
+124
+00:08:47,260 --> 00:08:52,100
+هذه هناخدها لما نجي نتكلم حاليا .. لاحقا عن a
+
+125
+00:08:52,100 --> 00:08:55,540
+محددة ال a هذه هنسميها universe of discourse فضاء
+
+126
+00:08:55,540 --> 00:08:59,600
+العينة و نبدأ نعمل complement داخلها هنشوفها في ال
+
+127
+00:08:59,600 --> 00:09:02,820
+slide الجاية بس ناخدلنا أكام من مثال على ال
+
+128
+00:09:02,820 --> 00:09:07,700
+difference أو ال set difference لو قلنا عندنا two
+
+129
+00:09:07,700 --> 00:09:10,420
+sets بدنا نجيب ال difference between them الأولى
+
+130
+00:09:10,420 --> 00:09:13,260
+من واحد لستة التانية الأعداد
+
+131
+00:09:16,350 --> 00:09:20,270
+لأ مش الأولية لإن في عندك تسعة لسه فإتنين تلاتة
+
+132
+00:09:20,270 --> 00:09:26,030
+خمسة سبعة تسعة احداشر من واحد لستة minus الست اللي
+
+133
+00:09:26,030 --> 00:09:29,950
+عرفناها إيش بدنا نسوي بدنا ندور على ال element
+
+134
+00:09:29,950 --> 00:09:32,770
+اللي موجود في الأولى و غير موجود في التانية خليني
+
+135
+00:09:32,770 --> 00:09:38,010
+أمسكهم واحد واحد الواحد بمشي الحالة الإتنين لأ
+
+136
+00:09:38,010 --> 00:09:45,330
+الإتنين موجودة فهذه بشيلها تلاتة موجودة بنشيلهاطيب
+
+137
+00:09:45,330 --> 00:09:49,010
+الأربعة .. الأربعة مش موجودة okay هذا بدنا نحسبها
+
+138
+00:09:49,010 --> 00:09:54,510
+الخامسة موجودة بنشيلها ستة غير موجودة فإذا صار
+
+139
+00:09:54,510 --> 00:10:00,230
+عندك واحد أربعة وستة هم هدولة ناتج ال difference
+
+140
+00:10:00,230 --> 00:10:06,170
+اللي بنتكلم عنه تمام فبتصير عندنا واحد أربعة ستة
+
+141
+00:10:06,170 --> 00:10:11,470
+واحد أربعة ستة طيب example تاني ل infinite sets لو
+
+142
+00:10:11,470 --> 00:10:16,140
+قلنا z minus nالـ integers minus الـ natural
+
+143
+00:10:16,140 --> 00:10:21,340
+numbers ايش بيعطينا؟ هيعطينا الـ negative integers
+
+144
+00:10:21,340 --> 00:10:24,780
+هيعطينا الـ negative integers بالظبط أو هيكون كتار
+
+145
+00:10:24,780 --> 00:10:28,780
+من minus infinity to infinity minus من صفر to
+
+146
+00:10:28,780 --> 00:10:33,340
+infinity كويس، هذه عبارة عن set of x such that x
+
+147
+00:10:33,340 --> 00:10:38,140
+is an integer but not a natural number أو هي عبارة
+
+148
+00:10:38,140 --> 00:10:43,150
+عن set of xو X ايش الشرط تبعها ان هي negative
+
+149
+00:10:43,150 --> 00:10:46,230
+integer تمام او نقدر نمثلها من minus infinity
+
+150
+00:10:46,230 --> 00:10:50,470
+بالنقطة دولة معناته من ال minus infinity to minus
+
+151
+00:10:50,470 --> 00:10:56,590
+one فانا بتكلم عن ال negative integer number okay
+
+152
+00:10:56,590 --> 00:11:00,970
+بال .. بال Venn diagram كيف نقدر نمثلها؟ بنمثلها
+
+153
+00:11:00,970 --> 00:11:06,870
+انه هي عبارة عن ال 6A مطروح منها ال intersection
+
+154
+00:11:08,700 --> 00:11:11,280
+مطروح منها ال intersection ليش؟ عشان أضمن إن هي
+
+155
+00:11:11,280 --> 00:11:16,120
+موجودة في A و غير موجودة في B موجودة في A و غير
+
+156
+00:11:16,120 --> 00:11:22,600
+موجودة في B فكأنه هنا B أكلت أو قضمت من Aجزء
+
+157
+00:11:22,600 --> 00:11:26,720
+التقاطع كأنه خصمت منها جزء التقاطع أو أخدت منها
+
+158
+00:11:26,720 --> 00:11:31,200
+جزء التقاطع فهي بيظل ال 6 تمثيلا بال Venn Diagram
+
+159
+00:11:31,200 --> 00:11:34,320
+بيكون ال 6 اللي ضايلة او ال 6 اللي بنقدر نعرفها a
+
+160
+00:11:34,320 --> 00:11:38,800
+minus b فهذه بتكون كأنها أكلت منها طيب ال
+
+161
+00:11:38,800 --> 00:11:41,980
+compliment نشتر على ال compliment علشان نشتر على
+
+162
+00:11:41,980 --> 00:11:44,560
+ال compliment لازم يكون واضح عند ال universe of
+
+163
+00:11:44,560 --> 00:11:47,560
+discourse الشيء ال universe of discourse بتاعتنا
+
+164
+00:11:47,560 --> 00:11:49,860
+فال universe of discourse بتاعتنا هنا هنقول أن هي
+
+165
+00:11:49,860 --> 00:11:50,180
+ال U
+
+166
+00:11:53,480 --> 00:11:56,960
+كويس؟ هنسميها you فبصير واضح لازم يكون طبعا في ال
+
+167
+00:11:56,960 --> 00:12:01,380
+context تبعنا واضح بشكل معرف أو معرف بشكل واضح ال
+
+168
+00:12:01,380 --> 00:12:04,020
+you بتاعتكم اللي هي ال universe of discourse انتوا
+
+169
+00:12:04,020 --> 00:12:07,820
+بتتكلموا عن فضع عينة مين بالظبط عشان لما أحدد ست
+
+170
+00:12:07,820 --> 00:12:11,280
+وبدي أعمل ال compliment داخلها أكون عارف أنا بعمل
+
+171
+00:12:11,280 --> 00:12:16,280
+with respect to إيش فلازم لما بجيب ال compliment ل
+
+172
+00:12:16,280 --> 00:12:21,620
+awith respect to you فلازم يكون محدد أصلا you و
+
+173
+00:12:21,620 --> 00:12:25,780
+معرف you بتاعتنا، كويس فهنا بنقدر نقول ان a لازم
+
+174
+00:12:25,780 --> 00:12:29,360
+تكون subset من you هي جزء من you عشان نجيب لها
+
+175
+00:12:29,360 --> 00:12:32,960
+compliment with respect to you with respect to you
+
+176
+00:12:32,960 --> 00:12:36,900
+the compliment of a هتكون عبارة عن ايش؟ a bar
+
+177
+00:12:36,900 --> 00:12:42,440
+بنسميها او a compliment a بنعملها علامة bar وبنكمل
+
+178
+00:12:42,440 --> 00:12:44,520
+عليها، ايه كويس في الحالة هذي بتكون عبارة عن
+
+179
+00:12:44,520 --> 00:12:49,380
+compliment a with respect to youA with respect to
+
+180
+00:12:49,380 --> 00:12:52,060
+U لازم تكون معرفين أصلا U بطريقة جيدة من الأساس
+
+181
+00:12:52,060 --> 00:12:54,680
+معرفين ال universe of discourse أو فضاء العينة
+
+182
+00:12:54,680 --> 00:12:59,900
+اللي بتحكوا عنه كويسة هنا بنكتبها U minus Aهي
+
+183
+00:12:59,900 --> 00:13:04,600
+عبارة عن u minus a فهي فعلا لو جينا عرفنا كمان مرة
+
+184
+00:13:04,600 --> 00:13:07,500
+ال difference اللي اتكلمنا عنه كل عنصر موجود في u
+
+185
+00:13:07,500 --> 00:13:10,620
+و غير موجود في a فهو ال complement ل a with
+
+186
+00:13:10,620 --> 00:13:14,720
+respect to u with respect to u for example لو
+
+187
+00:13:14,720 --> 00:13:17,500
+أخدنا ال u او ال universe of discourse بتاعتنا
+
+188
+00:13:17,500 --> 00:13:22,160
+natural number من صفر to infinity وقولنا بدنا ال
+
+189
+00:13:22,160 --> 00:13:29,790
+complement ل 6 3 5 فبنكتبها 6 3 5 complementبنحط
+
+190
+00:13:29,790 --> 00:13:33,510
+لها الbar هذي equal لإيش كل ال natural numbers بلا
+
+191
+00:13:33,510 --> 00:13:38,170
+استثناء باستثناء بس العنصرين هدول اللي موجودين في
+
+192
+00:13:38,170 --> 00:13:42,810
+ال A أو اللي هي التلاتة أو الخمسة فبنكتب صفر واحد
+
+193
+00:13:42,810 --> 00:13:48,690
+اتنين تلاتة لأ اربعة خمسة لأ طيب لو قلنا ال U
+
+194
+00:13:48,690 --> 00:13:51,750
+عندنا هنا جدلة نقولنا لأ ال U تبعتنا احنا معرفينها
+
+195
+00:13:51,750 --> 00:13:57,850
+عساس ان هي ال positive integers اقل من عشرةأقل من
+
+196
+00:13:57,850 --> 00:14:00,990
+عشرة في الحالة هذه هيكون ال set او ال compliment
+
+197
+00:14:00,990 --> 00:14:06,890
+بتاعتنا ايش واحد integer و positive integer مافيهم
+
+198
+00:14:06,890 --> 00:14:09,990
+صفر فعشانك لازم تكون ال u معرفة عننا عارفين ال
+
+199
+00:14:09,990 --> 00:14:13,810
+shia ال u بتاعتنا فتكون واحد اتنين تلتة لأ اربعة
+
+200
+00:14:13,810 --> 00:14:20,470
+ستة سبعة تمانية تسعة و بنسكر القصة تبعنا خلاص أنا
+
+201
+00:14:20,470 --> 00:14:24,370
+عارف ال universe of discourse تبعتيفاحنا ناخد بنا
+
+202
+00:14:24,370 --> 00:14:30,530
+with respect to إيش؟ لست اللي بدنا نطرح منها ال
+
+203
+00:14:30,530 --> 00:14:32,190
+إيه؟
+
+204
+00:14:37,030 --> 00:14:39,970
+كمان مرة بنعرفه A complement على اساس ان هو set of
+
+205
+00:14:39,970 --> 00:14:44,170
+X و X not belong to mean to A فإذا لو عندنا A بال
+
+206
+00:14:44,170 --> 00:14:48,690
+Venn .. بال Venn diagram A بالشكل هذا هنشيلها و
+
+207
+00:14:48,690 --> 00:14:52,850
+الباقي هو ال complement ل A هو ال complement ل A
+
+208
+00:14:52,850 --> 00:14:58,730
+هذه غير موجودة هذه غير موجودة هذه فاضية فإذا كل
+
+209
+00:14:58,730 --> 00:15:04,010
+اللون الأخضر هذا هو ال A ال A complement تمام ناخد
+
+210
+00:15:04,010 --> 00:15:10,150
+شوية setidentities او شوية rules شوية rules من ال
+
+211
+00:15:10,150 --> 00:15:14,430
+rules هذه المحايد اول شغل كنا ناخدها دايما في ال
+
+212
+00:15:14,430 --> 00:15:17,350
+rules ساعتنا اللي هو المحايد المحايد سواء لل union
+
+213
+00:15:17,350 --> 00:15:20,030
+او لل intersection لل union او لل ايش لل
+
+214
+00:15:20,030 --> 00:15:22,490
+intersection زي المحايد الجمعي و المحايد الضربي في
+
+215
+00:15:22,490 --> 00:15:25,310
+الأرقام في ال .. في ال .. في ال numbers هنا برضه
+
+216
+00:15:25,310 --> 00:15:31,970
+نفس الكلام a union phi a ماأثرتش طيب a
+
+217
+00:15:31,970 --> 00:15:36,510
+intersection uA هدا intersection و احنا عارفين ان
+
+218
+00:15:36,510 --> 00:15:40,650
+ال A subset of U لان ال U هنا universe of
+
+219
+00:15:40,650 --> 00:15:46,030
+discourse الفضاء كله فضاء العينة كله طيب بالعكس
+
+220
+00:15:46,030 --> 00:15:49,290
+لما تيجوا تعملوا ضرب في الصفر مثلا عملية الضرب
+
+221
+00:15:49,290 --> 00:15:52,110
+بتخلف عن عملية الجامعة عملية الجامعة كان محايد بس
+
+222
+00:15:52,110 --> 00:15:56,330
+في الضرب مهيمن ليش؟ لان أيش بتضربوا فيه هيحاول
+
+223
+00:15:56,330 --> 00:16:02,060
+كوية صفر هيتحول ليش؟ ل zero زيA intersection Phi
+
+224
+00:16:02,060 --> 00:16:07,460
+هيطلع Phi طيب نفس الكلام A union U أي اش اتحاد مع
+
+225
+00:16:07,460 --> 00:16:10,820
+ال universe of discourse كلها هي نفسها هتظل مش
+
+226
+00:16:10,820 --> 00:16:14,100
+هيأثر فيها فهتظل universe of discourse طيب
+
+227
+00:16:14,100 --> 00:16:19,520
+العمليات على نفس ال set ال set على نفسها ف set
+
+228
+00:16:19,520 --> 00:16:24,900
+union A هي نفسها ال set intersection مع نفسهاهي
+
+229
+00:16:24,900 --> 00:16:28,520
+نفسها ال a نفسها ف a intersection مع نفسها او
+
+230
+00:16:28,520 --> 00:16:33,580
+union مع نفسها هي هي اي set مش بدلول اي set مع
+
+231
+00:16:33,580 --> 00:16:40,220
+نفسها بتأثرش طيب ال double complement نفسها مكمل
+
+232
+00:16:40,220 --> 00:16:45,140
+المكمل هو نفسه رجعنا لل a فإذا مكمل مكمل ال a هي
+
+233
+00:16:45,140 --> 00:16:53,540
+نفسها ال a ال computative او تبديل a union b هي
+
+234
+00:16:53,540 --> 00:16:57,830
+نفس b union aنفس الكلام بالنسبة لل intersection A
+
+235
+00:16:57,830 --> 00:17:02,510
+intersection B هي نفسها B intersection A مش هتفرج
+
+236
+00:17:02,510 --> 00:17:09,830
+معناه كتير كويس ال associative A union B union C
+
+237
+00:17:09,830 --> 00:17:13,250
+مين جاب التاني بتفرجش مدام أنا بتعامل مع نفس ال
+
+238
+00:17:13,250 --> 00:17:17,530
+operator مع U هنا U و هنا U انتوا بتتعاملوا مع نفس
+
+239
+00:17:17,530 --> 00:17:21,550
+ال operator مين جاب المين ماتفرجش معناه طيبفممكن
+
+240
+00:17:21,550 --> 00:17:27,110
+اقول A مع B في الأول و بعدين الناتج مع C فليكن ال
+
+241
+00:17:27,110 --> 00:17:29,690
+intersection نفس الجثة نفس الكلام بس خدوا بأكوا
+
+242
+00:17:29,690 --> 00:17:32,850
+انه intersection مع intersection مايكونش في واحدة
+
+243
+00:17:32,850 --> 00:17:36,850
+intersection و واحدة unionمع بعض لأ مدام نفس ال
+
+244
+00:17:36,850 --> 00:17:42,190
+operator الكلام صحيح و ال associative تحققت دي
+
+245
+00:17:42,190 --> 00:17:46,030
+مورغان ورانا ورانا هيعطينا برضه نفس القانون اللي
+
+246
+00:17:46,030 --> 00:17:49,010
+عمله لل negation في ال proposition هيعطينا يا برضه
+
+247
+00:17:49,010 --> 00:17:52,510
+لل set بس let me ال compliment فبقول ال compliment
+
+248
+00:17:52,510 --> 00:17:57,150
+ل a union b تساوي a compliment intersection b
+
+249
+00:17:57,150 --> 00:18:00,850
+compliment تمام؟ كويس نفس الكلام في ال
+
+250
+00:18:00,850 --> 00:18:05,390
+intersectionال complement لل A intersection B هي
+
+251
+00:18:05,390 --> 00:18:09,730
+نفس ال complement A union complement لحظة عكسناها
+
+252
+00:18:09,730 --> 00:18:13,870
+بنعكسها و بنوزع ال complement جوا نفس اللي كنا
+
+253
+00:18:13,870 --> 00:18:16,650
+بنعمله في ال negation نفس كلام ال negation هو هو
+
+254
+00:18:16,650 --> 00:18:21,450
+طيب بعد ما قولنا الكلام هذا بدنا نعمل proving ل ال
+
+255
+00:18:21,450 --> 00:18:25,470
+set identities امتى بقول ان ال set او two sets
+
+256
+00:18:25,470 --> 00:18:29,600
+بيسوا بعض equivalent ل بعض identities مع بعضأمتى
+
+257
+00:18:29,600 --> 00:18:31,760
+بقدر أقول إن ال set هذه تساوي ال set هذه؟ في
+
+258
+00:18:31,760 --> 00:18:34,640
+الحقيقة عندنا three strategies أو three methods
+
+259
+00:18:34,640 --> 00:18:38,960
+نستخدمها الطريقة الأولى إن أنا أستعمل ال subset و
+
+260
+00:18:38,960 --> 00:18:43,820
+بنسميها mutual subset ال subset المتبادل يعني لو
+
+261
+00:18:43,820 --> 00:18:48,320
+قلنا المجموعة الأولى subset من المجموعة التانية و
+
+262
+00:18:48,320 --> 00:18:50,600
+المجموعة التانية برضه subset من المجموعة الأولى
+
+263
+00:18:50,600 --> 00:18:57,500
+فإنها متساويات بمعنى إنهE1 هي subset من E2 و هي
+
+264
+00:18:57,500 --> 00:19:01,940
+superset of E2 فهي subset و superset في نفس الوجد
+
+265
+00:19:01,940 --> 00:19:06,400
+معناته تساويها، مظبوط؟ هذا إذا كدرنا نثبت الكلام
+
+266
+00:19:06,400 --> 00:19:10,480
+هذا، بكون أثبت أن E1 و E2 equivalent أو
+
+267
+00:19:10,480 --> 00:19:14,800
+identities، كويس الطريقة التانية باستخدام ال
+
+268
+00:19:14,800 --> 00:19:17,760
+builder notation و بنعمل عليها ال logical
+
+269
+00:19:17,760 --> 00:19:21,740
+equivalence القوانين اللي توا اتكلمنا عنهابنحددها
+
+270
+00:19:21,740 --> 00:19:25,800
+بنكتبها as a builder notation تعريف بين أقواس
+
+271
+00:19:25,800 --> 00:19:29,640
+بنقول set of x و بنحط ال condition تبعناها such
+
+272
+00:19:29,640 --> 00:19:32,960
+that x equal to h و بعدين بنبدأ نشتغل على القوانين
+
+273
+00:19:32,960 --> 00:19:35,700
+اللي طوى اشتغلناها اللي طوى لسه صردناها و قولناها
+
+274
+00:19:35,700 --> 00:19:39,500
+كويس و بنثبت الإثبات اللي بيكون مطلوب منها النوع
+
+275
+00:19:39,500 --> 00:19:43,780
+التالت use a membership table truth table الذاكرين
+
+276
+00:19:43,780 --> 00:19:47,840
+truth table بنشتغله هو هو نفسه بنشتغله هذا برضه
+
+277
+00:19:47,840 --> 00:19:53,670
+طريقةطريقة تالتة و بشوف ايش ال columns تبعتنا اللي
+
+278
+00:19:53,670 --> 00:19:59,230
+ممكن نشتغل عليها طيب ناخد اول طريقة اللي هو ال
+
+279
+00:19:59,230 --> 00:20:03,230
+mutual subset mutual subset و ناخد example و اوضح
+
+280
+00:20:03,230 --> 00:20:06,470
+لنا الموضوع خلاص احنا متفقين ان كل اللي بديه ان ال
+
+281
+00:20:06,470 --> 00:20:10,930
+two expressions اللي هيكون معاكم معاهم ال two
+
+282
+00:20:10,930 --> 00:20:17,610
+compound set هنا تساوي المساوي لل set اللي هناكيف؟
+
+283
+00:20:17,610 --> 00:20:21,830
+إذا كانت الأولى subset من التانية و التانية subset
+
+284
+00:20:21,830 --> 00:20:25,050
+من الأولى فبنمسكهم واحدة واحدة و بدنا نعمل أول
+
+285
+00:20:25,050 --> 00:20:30,310
+إثبات إن الأولى subset من التانية بمعنى إن أي عنصر
+
+286
+00:20:30,310 --> 00:20:37,210
+ينتمي للست هذه ككل هو لازم ينتمي للست التانية
+
+287
+00:20:37,210 --> 00:20:40,690
+بالضرورة لازم ينتمي للست التانية كويس، بنكون خلصنا
+
+288
+00:20:40,690 --> 00:20:44,630
+أول جزء الجزء التاني إن أي عنصر ينتمي للست التانية
+
+289
+00:20:44,630 --> 00:20:48,100
+بالضرورة لازم ينتمي للست الأولىإذا أثبتنا
+
+290
+00:20:48,100 --> 00:20:51,180
+الطريقتين هدولة، بنكون أثبتنا إن الاتين equivalent
+
+291
+00:20:51,180 --> 00:20:54,780
+لبعض أو كل واحدة منهم equivalent للتانية نبدأ بأول
+
+292
+00:20:54,780 --> 00:21:00,680
+جزء إنه الأولى subset للتانية فبدنا عنصر نفترض إن
+
+293
+00:21:00,680 --> 00:21:05,620
+هو belong to set number one ومنه أحاول أثبت إن هو
+
+294
+00:21:05,620 --> 00:21:10,120
+لازم بالضرورة يكون موجود في إيش أو belong to set
+
+295
+00:21:10,120 --> 00:21:15,280
+number two هنقول إنه X ف X belong لست الأولى، هي
+
+296
+00:21:15,280 --> 00:21:20,110
+الست الأولىتمام إذا فعلًا belonged ل A
+
+297
+00:21:20,110 --> 00:21:25,070
+intersection B union C فهو بالضروري لازم يكون
+
+298
+00:21:25,070 --> 00:21:32,610
+belonged ل A لحالها و belonged ل ال union بتاعت ال
+
+299
+00:21:32,610 --> 00:21:35,050
+two sets دولة بالضروري لإن في بينهم intersection
+
+300
+00:21:36,130 --> 00:21:39,830
+هذه تمثل ال end هذه مشابهة تماما لل end اللي
+
+301
+00:21:39,830 --> 00:21:44,350
+أخدتوها مدام ال expression تاع end كله true فإذا
+
+302
+00:21:44,350 --> 00:21:49,450
+كل proposition كل proposition على حدة true صحيح؟
+
+303
+00:21:49,450 --> 00:21:52,350
+هو نفس الكلام اللي قلناه مدام intersection فإذا
+
+304
+00:21:52,350 --> 00:21:57,210
+الأولى هو ال X belong ل A و هو belong ل B union A
+
+305
+00:21:57,210 --> 00:22:02,730
+تمام؟ فإذا أول حاجة A ال X هذا belong ل A هذا
+
+306
+00:22:02,730 --> 00:22:09,920
+المفروض منههذا أكيد بيظل هنا ممكن يكون لأن هذا
+
+307
+00:22:09,920 --> 00:22:16,140
+union ممكن يكون مع a مع b أو مع c انا مش عارف
+
+308
+00:22:16,140 --> 00:22:18,940
+بالظبط او يمكن الاتنين مع بعض بس كل احتمالات
+
+309
+00:22:18,940 --> 00:22:22,440
+الاحتمال الأسوأ انه مايكنش في الاتنين مع بعض ان
+
+310
+00:22:22,440 --> 00:22:26,260
+يكون في واحدة منهم بس ابن مسكل احتمال هذا فبنقول
+
+311
+00:22:26,260 --> 00:22:33,240
+اما case number one انه ممكن يكون مع b x belong to
+
+312
+00:22:33,240 --> 00:22:40,040
+bهذه حالة أولى ممكن لأن او هذه الحالة التانية اللى
+
+313
+00:22:40,040 --> 00:22:46,100
+هنجربها لاحقا انه يكون belong لمن ل C بس هو لازم
+
+314
+00:22:46,100 --> 00:22:50,560
+يحقق واحدة من التنتين على الأقل لازم يحقق واحدة من
+
+315
+00:22:50,560 --> 00:22:53,700
+التنتين على الأقل عشان يحقق ال expression كله على
+
+316
+00:22:53,700 --> 00:22:58,340
+بعضه كويس خليني أخدها حالة حالة نفترض ان هو لأ مع
+
+317
+00:22:58,340 --> 00:23:04,250
+B مدان مع B معنى ذلك ان هو ينتمي لإيه؟وينتمي ل B
+
+318
+00:23:04,250 --> 00:23:09,270
+معناه ذلك أنه بالضرورة لازم ينتمي ل A intersection
+
+319
+00:23:09,270 --> 00:23:16,130
+B بالضرورة لازم ينتمي ل A مدام ينتمي ل كل set من
+
+320
+00:23:16,130 --> 00:23:19,830
+ال two sets دولة معناته ال intersection تبعهم أكيد
+
+321
+00:23:19,830 --> 00:23:23,510
+هو belong لل intersection تمام مدام belong لل
+
+322
+00:23:23,510 --> 00:23:28,170
+intersection union مع أي إشي أكيد هو هيكون belong
+
+323
+00:23:28,170 --> 00:23:37,290
+لل union صح هو موجود هناطب لما عملوا union مع أي
+
+324
+00:23:37,290 --> 00:23:40,910
+إشي مع أي شغلة ما هو لازم يكون موجود لأنه واحد من
+
+325
+00:23:40,910 --> 00:23:47,430
+الأطراف هي موجود لأن ال union تمثل or ال or يكفي
+
+326
+00:23:47,430 --> 00:23:51,490
+أن يكون ال proposition واحد true عشان ال or كلها
+
+327
+00:23:51,490 --> 00:23:56,670
+تكون true مظبوط خلاص و احنا هيتحقق الواحد منهم
+
+328
+00:23:56,670 --> 00:23:59,850
+فإذا union مع أي term تاني ال term التاني خليني
+
+329
+00:23:59,850 --> 00:24:07,060
+نقول A intersection Cفهو أكيد belonged للterm هذا
+
+330
+00:24:07,060 --> 00:24:10,200
+هاي
+
+331
+00:24:10,200 --> 00:24:17,260
+أول أثبات أثبتنا أن a intersection b union c هي
+
+332
+00:24:17,260 --> 00:24:21,740
+subset of a intersection b union مع a intersection
+
+333
+00:24:21,740 --> 00:24:28,070
+cهذه خلصناها و مكتوب طبعا الشرح والاحتمالات
+
+334
+00:24:28,070 --> 00:24:32,310
+الممكنة طبعا الكلام هو نفسه نفسه لو قلت case
+
+335
+00:24:32,310 --> 00:24:35,370
+number two لان احنا سبقنا يمكن يقولنا case number
+
+336
+00:24:35,370 --> 00:24:39,110
+two هتحققلنا الجزء التانيفنفس الكلام هتكون حققتكوا
+
+337
+00:24:39,110 --> 00:24:42,970
+الطرف التاني لل or هتكون حققت الطرف التاني لل or
+
+338
+00:24:42,970 --> 00:24:47,490
+كويس كل هذا الإثبات حتى الآن بس عشان نثبت أن
+
+339
+00:24:47,490 --> 00:24:50,370
+الأولى subset للتانية طب ما احنا لسه بدنا نكمل
+
+340
+00:24:50,370 --> 00:24:56,210
+التانية subset للأولى التانية subset للأولى ممكن
+
+341
+00:24:56,210 --> 00:25:00,230
+هذه مش موجودة في ال slides فناخدها لو قلنا term
+
+342
+00:25:00,230 --> 00:25:07,000
+هذا x belong لل term الأولو لاحظوا إن إحنا إيش في
+
+343
+00:25:07,000 --> 00:25:11,100
+عندنا هنا هدي
+
+344
+00:25:11,100 --> 00:25:15,000
+إيش union union معناته أنا مش ضامن إما إنها مع ال
+
+345
+00:25:15,000 --> 00:25:18,340
+term الأول أو ال term التاني برضه في عندنا
+
+346
+00:25:18,340 --> 00:25:26,080
+احتمالين فإذا إما x نقول case number one x belong
+
+347
+00:25:26,080 --> 00:25:33,770
+to A intersection Bناخد الحالة الأولى ال case
+
+348
+00:25:33,770 --> 00:25:39,370
+الأولى انه ممكن تكون مع هذا ال term في الحالة هذه
+
+349
+00:25:39,370 --> 00:25:48,490
+X belong to A و X belong to B بالضرورة مدام هو
+
+350
+00:25:48,490 --> 00:25:52,870
+belong ل ال intersection كله فهي بالضرورة ينتمي
+
+351
+00:25:52,870 --> 00:25:57,270
+لكل ستة على حدة لكل ستة على حدة طيب ببساطة جدا
+
+352
+00:25:57,270 --> 00:26:06,450
+بقدر اقول ان X belong to Bunion أي إشي صح union أي
+
+353
+00:26:06,450 --> 00:26:12,250
+إشي اللي هي ال C و
+
+354
+00:26:12,250 --> 00:26:15,110
+هاد ال C طلعت D طلعت F طلعت إش ما تكون تكون اللي
+
+355
+00:26:15,110 --> 00:26:20,400
+هو أنا عارف إن ال element belong to Bunion مع أي
+
+356
+00:26:20,400 --> 00:26:25,780
+شيء هو هيكون ضمن ال set تعطي ال union ال set ال
+
+357
+00:26:25,780 --> 00:26:30,400
+union كويس في الآخر هنلاقي ان x belong to a لإن هى
+
+358
+00:26:30,400 --> 00:26:37,680
+أصلا belong to a intersection ب union c لإن هى
+
+359
+00:26:37,680 --> 00:26:41,440
+belong لهذا ال term وbelong لهذا ال term فهى
+
+360
+00:26:41,440 --> 00:26:44,900
+belong لل intersection تبعهم طيب case number two
+
+361
+00:26:44,900 --> 00:26:49,120
+انه يكون belong لل term التانى
+
+362
+00:26:52,270 --> 00:26:59,890
+فإذا X belong ل A intersection C فإذا X بالضرورة
+
+363
+00:26:59,890 --> 00:27:06,950
+لازم تكون belong to A و X belong to C و نفس الكلام
+
+364
+00:27:06,950 --> 00:27:10,830
+اللي قلناه سابقا مدام هي belong to C هتكون belong
+
+365
+00:27:10,830 --> 00:27:16,410
+لاتحاد C مع أي إشي تاني اتحاد C مع أي إشي تاني مع
+
+366
+00:27:16,410 --> 00:27:21,020
+أي set تانية أكيد هيكون أحد العناصر للاتحادفإذن
+
+367
+00:27:21,020 --> 00:27:28,520
+بقدر أقول إن X belong to B union C لأن هو ينتمي
+
+368
+00:27:28,520 --> 00:27:33,980
+لأحد الطرفين اللي هي الـC كويسة هذه اتحققت وهي هذه
+
+369
+00:27:33,980 --> 00:27:38,940
+متحققة فإذن هو موجود في ال intersection بتاع
+
+370
+00:27:38,940 --> 00:27:43,400
+الأثنين هذولة فبالضرورة X هتكون belong to A
+
+371
+00:27:43,400 --> 00:27:47,000
+intersection B union C
+
+372
+00:27:51,230 --> 00:27:56,910
+فما دام أي element belong to A intersection B
+
+373
+00:27:56,910 --> 00:28:01,270
+union A intersection C أي element ينتمي لهذا ال
+
+374
+00:28:01,270 --> 00:28:05,690
+term بالضرورة هيكون ينتمي ل A intersection B union
+
+375
+00:28:05,690 --> 00:28:11,990
+C فإذا ال term هذا subset من ال term التاني طيب
+
+376
+00:28:11,990 --> 00:28:16,820
+احنا قبل شوية أثبتنا العكس طب ما دام العكسأثبت و
+
+377
+00:28:16,820 --> 00:28:20,260
+الأتنين أثبتوا مع بعض الأولى intersection للتانية
+
+378
+00:28:20,260 --> 00:28:23,560
+و التانية .. عفوا الأولى subset من التانية و
+
+379
+00:28:23,560 --> 00:28:26,700
+التانية subset من الأولى فإذا الأتنين بيسوا بعض ..
+
+380
+00:28:26,700 --> 00:28:29,380
+الأتنين بيسوا بعض و هذه طريقة إثبات .. هذه طريقة
+
+381
+00:28:29,380 --> 00:28:35,640
+إثبات ل ال sets ل ال sets equality تم .. أه
+
+382
+00:28:35,640 --> 00:28:41,900
+كتبتوهم؟ كيف؟ لأ واحدة لاتكفيش لأن مش هي اللى
+
+383
+00:28:41,900 --> 00:28:46,430
+بتعبّلك عن المساواة عن ال equality ال qualityلأ
+
+384
+00:28:46,430 --> 00:28:50,370
+مانت بدك تعمل كل احتمالات الاحتمالات كلها لازم
+
+385
+00:28:50,370 --> 00:28:52,350
+تكون واضحة case number one لازم تكون مكتوبة و case
+
+386
+00:28:52,350 --> 00:28:55,490
+number two لازم تكون مكتوبة عشان تقولوا فعلا
+
+387
+00:28:55,490 --> 00:29:00,150
+بيساووا بعض حقيقة انت بدك تضمني ال subset كيف بدك
+
+388
+00:29:00,150 --> 00:29:04,990
+تضمنيها بدك تضمني انه تحت كل الظروف مع كل احتمالات
+
+389
+00:29:04,990 --> 00:29:09,330
+اي element belonged to set number one بالضرورة
+
+390
+00:29:09,330 --> 00:29:13,960
+لازم يكون ينتمي ل set number twoطب إذا في أي
+
+391
+00:29:13,960 --> 00:29:18,540
+element أي احتمال أغفلته أو سبته معناته أنا بقدرش
+
+392
+00:29:18,540 --> 00:29:21,380
+أقول أنه لجميع الاحتمالات كل عنصر موجود هنا لازم
+
+393
+00:29:21,380 --> 00:29:24,380
+يكون بالضرورة موجود في ال set التانية بقدرش أقول
+
+394
+00:29:24,380 --> 00:29:28,860
+كل هذه for all elements لأ احنا بدنا يها for all
+
+395
+00:29:28,860 --> 00:29:32,740
+elements belonging to set number one بالضرورة ال
+
+396
+00:29:32,740 --> 00:29:35,700
+element هذا لازم يكون belonging to set number two
+
+397
+00:29:37,160 --> 00:29:41,840
+طيب الطريقة التانية ل .. ال .. ال quality ان انا
+
+398
+00:29:41,840 --> 00:29:44,060
+اعمل check على ال quality اللي هي ال builder
+
+399
+00:29:44,060 --> 00:29:48,480
+notation و ال logical equivalences كويس .. هنقول
+
+400
+00:29:48,480 --> 00:29:53,820
+بدنا نحقق قانون ال demorgan .. demorgan law ان a
+
+401
+00:29:53,820 --> 00:29:57,040
+.. ال complement ل a intersection b equal to
+
+402
+00:29:57,040 --> 00:30:01,580
+complement a union complement b بدنا نحققه هذا
+
+403
+00:30:01,580 --> 00:30:06,550
+فبنكتبه عن طريق ال builder notationهنقول ان ال
+
+404
+00:30:06,550 --> 00:30:10,470
+complement ل A intersection B عبارة عن set of X
+
+405
+00:30:10,470 --> 00:30:15,850
+such that ايش اللي لازم يحققه X ان X not belong to
+
+406
+00:30:15,850 --> 00:30:19,910
+A intersection B طيب تمام not belong معناته
+
+407
+00:30:19,910 --> 00:30:24,490
+negation ل ال belong معناته negation ل belong
+
+408
+00:30:24,490 --> 00:30:28,170
+belong notation ل belong notation كويس belong
+
+409
+00:30:28,170 --> 00:30:33,870
+notation معناه ذلك ان X belong to A and X belong
+
+410
+00:30:33,870 --> 00:30:40,160
+to Bصحيح؟ طيب دي مورجان هنا بندخل ال negation
+
+411
+00:30:40,160 --> 00:30:47,820
+بتصير هنا not belong x not belong to a or x not
+
+412
+00:30:47,820 --> 00:30:53,680
+belong to مين؟ to b تمام من هنا بنرجع ندخل ال
+
+413
+00:30:53,680 --> 00:30:58,690
+negation جوا بتصير not belongبنحطها العلمة not
+
+414
+00:30:58,690 --> 00:31:03,870
+belong هو نفس المعنى هو نفس المعنى، كويس طيب في
+
+415
+00:31:03,870 --> 00:31:07,550
+الحالة هذه بقدر اقول ان مدام not belong معناته هي
+
+416
+00:31:07,550 --> 00:31:13,930
+belong لل complement تعتها لما تقولوا x not belong
+
+417
+00:31:13,930 --> 00:31:20,690
+to a بالضروري هي x belong لمين؟ complement a هي
+
+418
+00:31:20,690 --> 00:31:28,710
+منتمية لل complement تبعهاتمام و نفس الكلام x not
+
+419
+00:31:28,710 --> 00:31:32,650
+belong معناته x belong to complement b طيب هنا
+
+420
+00:31:32,650 --> 00:31:37,990
+عندكوا or ال or بنمثلها بمين؟ بال union فإذا x
+
+421
+00:31:37,990 --> 00:31:42,810
+belong to ايش؟ complement a union complement b هو
+
+422
+00:31:42,810 --> 00:31:46,730
+نفس هذا الكلام اللي احنا فعلا بدنا نجيبه هو ده
+
+423
+00:31:46,730 --> 00:31:54,270
+اللي اتجيبه فهذه طريقة تانية هذه طريقة التانية
+
+424
+00:31:55,240 --> 00:31:58,900
+طريقة تالتة و اللي يمكن تكون الأسهل إذا كانت ال
+
+425
+00:31:58,900 --> 00:32:03,440
+expression تبعنا صغير مش كبير هتكون سهلة و بسيطة
+
+426
+00:32:03,440 --> 00:32:06,960
+اللي هي ال .. ال .. ال membership tables أو مقابلة
+
+427
+00:32:06,960 --> 00:32:09,180
+لل truth table اللي كنتوا بتاخدوه في ال
+
+428
+00:32:09,180 --> 00:32:12,920
+proposition هذه just إن أنا بستخدم ال truth table
+
+429
+00:32:12,920 --> 00:32:17,620
+بتاعة ال propositional logic و بنمثل belong to
+
+430
+00:32:17,620 --> 00:32:23,510
+بنمثل ب one not belong to بنمثل ب zeroفإذا كان ال
+
+431
+00:32:23,510 --> 00:32:28,210
+element ينتمي لل set بنحط قيمته ب 1 لا ينتمي لل
+
+432
+00:32:28,210 --> 00:32:33,850
+set بنحط قيمته ب 0 زي ال proof اللي مطلوب منها هنا
+
+433
+00:32:33,850 --> 00:32:40,250
+ف proof A union B minus كله minus B بدنا نشوف هل
+
+434
+00:32:40,250 --> 00:32:45,330
+هو equivalent ل A minus B ولا لأهنشوف هنحط ال a و
+
+435
+00:32:45,330 --> 00:32:47,970
+ال b و هنحط جميع الاحتمالات الممكنة ان هو not
+
+436
+00:32:47,970 --> 00:32:52,010
+belong not belong not belong belong to b هنا
+
+437
+00:32:52,010 --> 00:32:56,710
+belong to a not belong to b هنا belong ل a and b
+
+438
+00:32:56,710 --> 00:33:03,890
+مع بعض نبدأ بأول أول union عندنا a union b a union
+
+439
+00:33:03,890 --> 00:33:07,550
+b معناته يكفي أنه يكون موجود في واحد منهم هنا غير
+
+440
+00:33:07,550 --> 00:33:13,580
+موجود في أي واحدzero not belong ل ال union طيب
+
+441
+00:33:13,580 --> 00:33:18,080
+otherwise دايما في واحد اما في B او في A او في
+
+442
+00:33:18,080 --> 00:33:22,580
+كلاهما فبيعطينا دايما one بيعطينا دايما one كويس
+
+443
+00:33:22,580 --> 00:33:27,900
+لما نطرح منه B ناخد بالنا هنا لما بتكلم هنا عن B
+
+444
+00:33:27,900 --> 00:33:34,360
+بال minus معنا ذلك انه لازم يكون موجود هنا و غير
+
+445
+00:33:34,360 --> 00:33:39,850
+موجود هنامش احنا عرفنا a-b ان هو ال element اللي
+
+446
+00:33:39,850 --> 00:33:44,630
+موجود في a و غير موجود في b كويسة انا عند a union
+
+447
+00:33:44,630 --> 00:33:47,750
+b معناه ان انا بتكلم عن ال column هذا ايش ال
+
+448
+00:33:47,750 --> 00:33:53,190
+element اللي موجود هنا و غير موجود في b على طول
+
+449
+00:33:53,190 --> 00:33:57,970
+بيعطينا ال difference طبعا طيب خلينا نشوف غير
+
+450
+00:33:57,970 --> 00:34:03,330
+موجود لأ موجودو موجود، لأ مينفعش، موجود، غير
+
+451
+00:34:03,330 --> 00:34:07,810
+موجود، أه مظبوط، هذه حالة كويسة، طيب موجود، موجود،
+
+452
+00:34:07,810 --> 00:34:12,710
+لأ، فهذه الحالة الوحيدة ال one اللي هي فعلا تمثل
+
+453
+00:34:12,710 --> 00:34:16,930
+ال difference، تمثل difference، إن هي تكون موجودة
+
+454
+00:34:16,930 --> 00:34:21,550
+في ال term الأول و غير موجودة في ال term التانيو
+
+455
+00:34:21,550 --> 00:34:25,770
+غير موجودة في ايه؟ في ال term التاني كويس دل a
+
+456
+00:34:25,770 --> 00:34:30,430
+minus b برضه نفس المعنى موجودة في a و غير موجودة
+
+457
+00:34:30,430 --> 00:34:34,610
+في b لأ مش موجودة من أصله مش موجودة أصلا هي موجودة
+
+458
+00:34:34,610 --> 00:34:39,050
+و غير موجودة في a موجودة و موجودة لأ فإذا هو ال
+
+459
+00:34:39,050 --> 00:34:43,270
+term هذا الوحيد كويس
+
+460
+00:34:43,270 --> 00:34:46,170
+تعالوا نشوف ال two columns اللي بدنا نقارن بينهم
+
+461
+00:34:46,170 --> 00:34:48,890
+فعليا هم equivalent لبعض ولا لأ هي ال column الأول
+
+462
+00:34:48,890 --> 00:34:55,140
+وهي ال column التانيالاتنين بيساوي بعض في كل .. كل
+
+463
+00:34:55,140 --> 00:34:57,920
+role هنا يساوي .. او كل قيمة في ال role الأول
+
+464
+00:34:57,920 --> 00:35:02,200
+تساوي القيمة في ال role الأول هناك لاحظوا هنا و
+
+465
+00:35:02,200 --> 00:35:09,100
+هنا تمام هنسيبلكوا برضه مثال تشتغلوا هيك ..
+
+466
+00:35:09,100 --> 00:35:15,140
+تتدربوا عليه في البيت هذا ب .. ب three sets
+
+467
+00:35:16,070 --> 00:35:20,270
+هذا بال three sets فهيكون في عندكم مجموعة احتمالات
+
+468
+00:35:20,270 --> 00:35:22,770
+اكبر جداش عددهم ال possibilities تبعتكم تمانية
+
+469
+00:35:22,770 --> 00:35:26,430
+اتنين to the power عدد ال sets اللي موجودة او عدد
+
+470
+00:35:26,430 --> 00:35:30,510
+ال proposition لو بدنا نتكلم عن ال proposition ال
+
+471
+00:35:30,510 --> 00:35:35,970
+logic طيب نتكمل هتلاقوا في عندنا جزئية ال
+
+472
+00:35:35,970 --> 00:35:39,010
+generalization او generalized unions and
+
+473
+00:35:39,010 --> 00:35:42,010
+intersections المقصود هنا ان احنا مش بالضروري
+
+474
+00:35:42,010 --> 00:35:47,240
+نتعامل عن union ل two setsممكن يكون عندكوا أكتر من
+
+475
+00:35:47,240 --> 00:35:51,860
+two sets فهنا احنا بنتكلم عن n sets ممكن نعملهم
+
+476
+00:35:51,860 --> 00:35:55,400
+unions مع بعض فهنا بنكون عملنا generalized unions
+
+477
+00:35:55,400 --> 00:35:59,140
+فمعنى ذلك أنا بتكلم عن ال union operator لإيش؟
+
+478
+00:35:59,140 --> 00:36:03,860
+لأكتر من اتنين sets او لعدد كبير من ال sets اللي
+
+479
+00:36:03,860 --> 00:36:09,420
+موجود عندنا في الحالة بتاعتنا بشكل an ordered set
+
+480
+00:36:09,420 --> 00:36:14,910
+offset ليش؟ لأنه مش هتفرج معانا يقولنا جابنا هيكو
+
+481
+00:36:14,910 --> 00:36:17,650
+احنا بنتكلم في القوانين اللي اتكلمناها قولنا a
+
+482
+00:36:17,650 --> 00:36:24,090
+union b هي نفسها b union a فمين جاب المين مش هتفرج
+
+483
+00:36:24,090 --> 00:36:29,050
+كتير حتى و انا بتكلم عن اكثر من two sets حتى و انا
+
+484
+00:36:29,050 --> 00:36:35,950
+بتكلم عن اكثر من two sets okay نبدأ بال union لما
+
+485
+00:36:35,950 --> 00:36:39,390
+نقول ال binary union operator هذه binary union على
+
+486
+00:36:39,390 --> 00:36:43,730
+اساس ان انا بتكلم عنtwo sets فقط اللي مستعملهم فهي
+
+487
+00:36:43,730 --> 00:36:46,830
+binary union لأ انا ممكن اعمل generalization
+
+488
+00:36:46,830 --> 00:36:52,530
+للموضوع و اقول NRA union فانا موجود عندى N sets و
+
+489
+00:36:52,530 --> 00:36:56,670
+بدى اعملهم كلهم مع بعض union كلهم اتحاد مع بعض
+
+490
+00:36:56,670 --> 00:37:01,350
+كلهم اتحاد مع بعض تمام زى لما تقولوا والله في
+
+491
+00:37:01,350 --> 00:37:07,640
+عندكمبلدية غزة، بلدية خانونس، بلدية رفح، بلدية
+
+492
+00:37:07,640 --> 00:37:12,140
+الشمال بتحانون، بلدية .. كلهم اتحاد مع بعض بيعطونا
+
+493
+00:37:12,920 --> 00:37:16,360
+قطع غزة بيعطونا كل بلديات قطع غزة صحيح فبيعطوا قطع
+
+494
+00:37:16,360 --> 00:37:19,240
+غزة ليش هنعمل .. لأ لاتنتهي ممكن اعمل اتحاد للكل
+
+495
+00:37:19,240 --> 00:37:24,020
+فهنا قلت واحد في مؤتمر صحفي قال والله اتحاد خانونس
+
+496
+00:37:24,020 --> 00:37:27,880
+مع رفح واحد قال رفح مع خانونس هتفرج كتير مش هتفرج
+
+497
+00:37:27,880 --> 00:37:30,920
+كتير المهم ان اتحاد بلديات مع بعض مش هيفرج كتير
+
+498
+00:37:30,920 --> 00:37:34,560
+الترتيب هنا مش هيفرج الفكرة انه كأنه انا عملت
+
+499
+00:37:34,560 --> 00:37:40,430
+اتحادست أولى مع ست تانية الناتج مع الست التالتة
+
+500
+00:37:40,430 --> 00:37:43,850
+الناتج مع الرابعة لحد ما نخلص كل ال sets اللى بدنا
+
+501
+00:37:43,850 --> 00:37:47,630
+نعملهم union لكل ال sets اللى بدنا نعملهم union
+
+502
+00:37:47,630 --> 00:37:53,930
+بنعمل grouping هنا لكل ال sets بتاعتنا بنعطيها big
+
+503
+00:37:53,930 --> 00:38:01,690
+U فبقول I from one to N اذا أنا بتكلم عن N array
+
+504
+00:38:01,690 --> 00:38:08,020
+union او اننا N setsوبنحط ai فصار هذا عبارة عن ال
+
+505
+00:38:08,020 --> 00:38:13,240
+index لمين اللي بيعطينا indication لرقم ال set ال
+
+506
+00:38:13,240 --> 00:38:16,260
+set أولى، التانية، التالتة، الرابعة، الخمسة، تواش،
+
+507
+00:38:16,260 --> 00:38:22,260
+توان، بنحطها big U بتذكرنا ال summation بتذكرين ال
+
+508
+00:38:22,260 --> 00:38:25,040
+summation لما كنتوا رسموا ال summation طيب أو
+
+509
+00:38:25,040 --> 00:38:30,180
+infinite sets, sets of sets بنحطها U من واحدة to
+
+510
+00:38:30,180 --> 00:38:36,610
+infinity فبنحطها من واحدة to infinityكويسة نفس
+
+511
+00:38:36,610 --> 00:38:39,450
+الكلام نقدر نعمله لمن؟ لل intersection نعمله لل
+
+512
+00:38:39,450 --> 00:38:41,670
+intersection احنا في الاول كنا بتكلم عن binary
+
+513
+00:38:41,670 --> 00:38:45,570
+intersection operator كانت مجرد two sets بنشتغل
+
+514
+00:38:45,570 --> 00:38:48,150
+عليهم ممكن نعمل الموضوع على ال N array
+
+515
+00:38:48,150 --> 00:38:53,370
+intersection فبصير عندنا N sets بدنا نعملهم
+
+516
+00:38:53,370 --> 00:38:57,290
+intersection فبدنا تقاطعهم كلهم مع بعض بدنا نقاطع
+
+517
+00:38:57,290 --> 00:39:03,610
+الكل مع بعضكويس فهذه grouping او نقدر نعمل
+
+518
+00:39:03,610 --> 00:39:06,950
+grouping لل intersection بس هذه ممكن تكون مميزة
+
+519
+00:39:06,950 --> 00:39:10,710
+امتى او امتى بتقدروا تستفيدوا منها لما بتتكلموا
+
+520
+00:39:10,710 --> 00:39:15,920
+for example على خلط الألوانخلط الألوان مجموعة من
+
+521
+00:39:15,920 --> 00:39:19,060
+ال .. أو كل الألوان تقريبا ناخده من التلت ألوان
+
+522
+00:39:19,060 --> 00:39:21,580
+الرئيسية صحيح؟ موظفا لو ناخده من التلت ألوان
+
+523
+00:39:21,580 --> 00:39:25,200
+الرئيسية في لون لما بدنا ناخد ال intersection لتلت
+
+524
+00:39:25,200 --> 00:39:28,540
+مع بعض للتلت ألوان الرئيسية بناخد لون معين اللي هو
+
+525
+00:39:28,540 --> 00:39:35,240
+اللون الأسود اللي هيكون ناتج .. جمع التلتة صحيح؟ و
+
+526
+00:39:35,240 --> 00:39:40,610
+لا كان .. و لا الأبيض كان؟ اه انتوا مش عارفين؟ اهو
+
+527
+00:39:40,610 --> 00:39:44,650
+انا اتوقعت عندكم معلومة عنهم طيب مش اشكال مش اشكال
+
+528
+00:39:44,650 --> 00:39:48,770
+عندنا .. عندنا ناس خبيرة بالموضوع فالقصد انه ممكن
+
+529
+00:39:48,770 --> 00:39:52,810
+تنتج تلت ألوان رئيسية هي عبارة عن مجموعات هيك تلت
+
+530
+00:39:52,810 --> 00:39:55,770
+مجموعات من الألوان اعملتوا ال intersection فال
+
+531
+00:39:55,770 --> 00:39:59,610
+intersection هذا طلعلكوا intersection لكل
+
+532
+00:39:59,610 --> 00:40:02,550
+المجموعات بيعطيكوا indication لست جديدة الست
+
+533
+00:40:02,550 --> 00:40:07,450
+الجديدة دي بتعطي لون مزيج من الكل مزيج من الكلانا
+
+534
+00:40:07,450 --> 00:40:13,050
+اتوقع ان ال example هيكون يعني معروف يمكن او اشي
+
+535
+00:40:13,050 --> 00:40:20,910
+طيب بنمثلها كتالة big arch او قوس كبير big arch
+
+536
+00:40:20,910 --> 00:40:27,690
+from I ب equal to one to N AI تمام فاذا انا بتكلم
+
+537
+00:40:27,690 --> 00:40:34,590
+عن A1 intersection A2 intersection A3 to AN كويسأو
+
+538
+00:40:34,590 --> 00:40:38,730
+infinite set برضه من واحد و infinity و بنشتغل
+
+539
+00:40:38,730 --> 00:40:45,430
+عليها تمام طيب ال representations ل ال sets لما
+
+540
+00:40:45,430 --> 00:40:48,870
+نكون بدنا نعمل representation داخل set معينة كيف
+
+541
+00:40:48,870 --> 00:40:51,230
+ممكن أعمل representation لل elements اللي فيها
+
+542
+00:40:51,230 --> 00:40:55,770
+بحيث أن أنا أستفيد منها في ال operator اللي بنشتغل
+
+543
+00:40:55,770 --> 00:40:57,910
+عليها أنا في الآخر بتعامل مع ال sets هذه اللي
+
+544
+00:40:57,910 --> 00:41:01,240
+بتدخلها على ال pcفبدى محتاج طريقة ال
+
+545
+00:41:01,240 --> 00:41:04,300
+representation عشان نمثل فيها ال elements داخل ال
+
+546
+00:41:04,300 --> 00:41:10,800
+set فبنمثلها بال index تبعهابنمثلها وما جدقش رقمها
+
+547
+00:41:10,800 --> 00:41:15,600
+داخل ال set كترتيب فهنا بنتكلم عن ترتيبها لما نيجي
+
+548
+00:41:15,600 --> 00:41:19,040
+نعمل ال methods of representing indiscreet
+
+549
+00:41:19,040 --> 00:41:21,900
+structure using another discrete structure of a
+
+550
+00:41:21,900 --> 00:41:24,780
+different type خلينا ناخد ال type تبعنا اللي
+
+551
+00:41:24,780 --> 00:41:28,160
+بنشتغل عليه هو ال natural number و بدنا نعمله
+
+552
+00:41:28,160 --> 00:41:32,200
+representation عشان نوضح الموضوع هنقول zero عبارة
+
+553
+00:41:32,200 --> 00:41:37,090
+عن فيهذا بالنسبة لمن؟ لـ natural number فالـ zero
+
+554
+00:41:37,090 --> 00:41:40,290
+هذا أول element فيها مش هذا ال element الأول بنقدر
+
+555
+00:41:40,290 --> 00:41:44,350
+نعبر عنه كأنه هذا في ال element التاني بنعبر عليه
+
+556
+00:41:44,350 --> 00:41:48,450
+على أساس أن هذه ال six تحتوي على عنصر واحد أنه
+
+557
+00:41:48,450 --> 00:41:53,850
+عنصر؟ أول عنصر أول عنصر في ال natural number ال
+
+558
+00:41:53,850 --> 00:41:59,210
+zero اللي هو ال zero طيب اتنين مكافئة ل six تحتوي
+
+559
+00:41:59,210 --> 00:42:05,110
+علىتو elements اللي هم zero و one و هكذا و هكذا
+
+560
+00:42:05,110 --> 00:42:08,530
+تمام طيب الكلام هذا لما نيجي نعمل بال bit strings
+
+561
+00:42:08,530 --> 00:42:12,730
+او بال .. بال .. باستخدام ال bits ال bits ال zero
+
+562
+00:42:12,730 --> 00:42:17,070
+يمثل zero واحد يمثل واحد الأتنين لاحظوا هنا ال
+
+563
+00:42:17,070 --> 00:42:22,550
+zero يمثل في zero عشان نحول كلمة مجموعات هذه ال
+
+564
+00:42:22,550 --> 00:42:27,810
+sets ل bit strings ال zero يمثل zero هو هو طيب ال
+
+565
+00:42:27,810 --> 00:42:32,480
+oneيمثل جدش عدد ال elements انا هنا ال elements
+
+566
+00:42:32,480 --> 00:42:36,800
+الأول ال elements الأول فانا فعلا موجود عند ال
+
+567
+00:42:36,800 --> 00:42:43,680
+elements الأول طيب اتنين تمثل 01 01 في ال binary
+
+568
+00:42:43,680 --> 00:42:48,760
+هنا تمثل التلاتة تمثل 11 اربعة عارفين التمثيل هذا
+
+569
+00:42:48,760 --> 00:42:52,660
+طيب انا ايش بده استفيد منه يعني احنا بدنا هلوجد
+
+570
+00:42:52,660 --> 00:42:57,310
+كيف طريقة الاستفادةمن اللي فهمناها ده ان انا امثل
+
+571
+00:42:57,310 --> 00:43:00,910
+ال sets تبعت ب one و zeros عشان امثلهم ب one و
+
+572
+00:43:00,910 --> 00:43:05,930
+zeros الحقيقة هناخدمجموعة مثال نستفيد منه انا همثل
+
+573
+00:43:05,930 --> 00:43:09,910
+ال set ب one zeros بحيث نعمل عملية عملية ال
+
+574
+00:43:09,910 --> 00:43:14,610
+operations اللي احنا عارفينها سابقا ال or and و ال
+
+575
+00:43:14,610 --> 00:43:19,250
+negation او not و ال .. كل الأمور هذه خلينا نفرض
+
+576
+00:43:19,250 --> 00:43:21,450
+ان ال numerical universe of discourse بتاعتنا
+
+577
+00:43:21,450 --> 00:43:26,310
+اسمها U عبارة عن X1, X2, X3 هذا بنقدر نمثل فيها او
+
+578
+00:43:26,310 --> 00:43:31,530
+بتعمل represent a finite set S اللي هي subset of U
+
+579
+00:43:32,490 --> 00:43:37,550
+بنمثلها ك finite bit string لحظة ال set هذه
+
+580
+00:43:37,550 --> 00:43:43,310
+هنمثلها بيش ال bit string تمثل bit string هتكون
+
+581
+00:43:43,310 --> 00:43:47,230
+عندك set و فيها مجموعة elements مظبوط هنمثلهم bit
+
+582
+00:43:47,230 --> 00:43:50,770
+string ال bit string هذه اما one او zero مادام
+
+583
+00:43:50,770 --> 00:43:55,850
+بتكلم عن bit ال bit one or zero فهتكون بي one بي
+
+584
+00:43:55,850 --> 00:43:59,690
+two بي three بي two نكل واحدة من هدولا احتمالين
+
+585
+00:43:59,690 --> 00:44:04,190
+اما one او zero الاحتمالين هدولا one او zero بحطها
+
+586
+00:44:04,190 --> 00:44:08,170
+one اذا كان العنصر موجود في المجموعة و بحطها zero
+
+587
+00:44:08,170 --> 00:44:12,230
+اذا كان غير موجود في المجموعة هاي كل الموضوع بس
+
+588
+00:44:12,230 --> 00:44:17,520
+بدى اكون عارف مينال universe of discourse لأن كل
+
+589
+00:44:17,520 --> 00:44:20,060
+شغلنا على ال universe of discourse عندنا universe
+
+590
+00:44:20,060 --> 00:44:24,320
+of discourse فبقول الست هذى هل موجود العنصر هدى
+
+591
+00:44:24,320 --> 00:44:27,280
+فيها من ال universe of discourse او لأ موجود بحطه
+
+592
+00:44:27,280 --> 00:44:34,240
+one مش موجود بحطه zeroفهنا for all i xi أنا بتكلم
+
+593
+00:44:34,240 --> 00:44:37,540
+هنا اللحظة عن index belonging to S if and only if
+
+594
+00:44:37,540 --> 00:44:40,900
+i أقل من n لازم يكون هو ضمن ال universe of
+
+595
+00:44:40,900 --> 00:44:42,960
+discourse لما يقول ال universe of discourse فيها
+
+596
+00:44:42,960 --> 00:44:46,720
+عشرة elements أول عشرة elements مش معجول ال I تكون
+
+597
+00:44:46,720 --> 00:44:51,330
+رقم 11صحيح؟ مش ممكن انا بتكلم عن عشر elements و
+
+598
+00:44:51,330 --> 00:44:55,430
+بعدين احط i رقم 11 او اقول ان والله x 11 مافيش x
+
+599
+00:44:55,430 --> 00:45:01,230
+11 مش موجودة فهنا لازم تكون اقل من n and b i equal
+
+600
+00:45:01,230 --> 00:45:06,390
+to one عشان تكون belong to اذا not belong to equal
+
+601
+00:45:06,390 --> 00:45:12,510
+to zero equal to zero تمامنوضحها أكتر برضه بمثال
+
+602
+00:45:12,510 --> 00:45:16,030
+لأنه موضوحة بسيط جدا رغم أنه يمكن مش كتير واضحة لو
+
+603
+00:45:16,030 --> 00:45:20,610
+قلنا ال U ال natural number و ال S تبعته عبارة عن
+
+604
+00:45:20,610 --> 00:45:26,370
+اتنين، تلاتة، خمسة، سبعة، أحداشر الأعداد الأولية
+
+605
+00:45:26,370 --> 00:45:29,730
+ال primes كيف بمثلها هنا؟ أنا عارف أن ال universe
+
+606
+00:45:29,730 --> 00:45:32,890
+of discourse الشيية natural number طب ال natural
+
+607
+00:45:32,890 --> 00:45:40,060
+number خلينا نكتبهاصفر واحد اتنين تلاتة اربعة خمسة
+
+608
+00:45:40,060 --> 00:45:44,280
+شكة طيب
+
+609
+00:45:44,280 --> 00:45:52,900
+الصفر موجود في ال set بحطله zero الواحد مش موجود
+
+610
+00:45:52,900 --> 00:45:58,260
+الاتنين موجودة التلاتة واحد الاربعة
+
+611
+00:46:00,330 --> 00:46:05,530
+الخمسة واحد ستة مش موجودة سبعة واحد تمانية زيرو
+
+612
+00:46:05,530 --> 00:46:11,870
+تسعة خلاص عند ال 11 لأنه موجود واحد و بنوقف فانا
+
+613
+00:46:11,870 --> 00:46:16,490
+هيك عملت ايش representation لمي للست هذه و انا
+
+614
+00:46:16,490 --> 00:46:18,810
+عارف ان انا متكلم عن ال natural number احنا متكلم
+
+615
+00:46:18,810 --> 00:46:21,410
+عن ايش عن ال natural number في الحالة اللي متكلم
+
+616
+00:46:21,410 --> 00:46:26,320
+فيها طيب هنا بقدر اشتغل في الحالة هذهتمثيل ل set
+
+617
+00:46:26,320 --> 00:46:30,420
+تانية و نعمل intersection بينهم او نعمل union
+
+618
+00:46:30,420 --> 00:46:35,920
+باستخدام ال bitwise operator باستخدام bitwise
+
+619
+00:46:35,920 --> 00:46:39,320
+operator ان انا استعمل ال union او ال or اللي هي
+
+620
+00:46:39,320 --> 00:46:41,880
+ال union او ال intersection اللي كانت مكافئة على
+
+621
+00:46:41,880 --> 00:46:44,760
+ال or و ال and لان هالوقت لما بدي اشتغل على ال
+
+622
+00:46:44,760 --> 00:46:48,960
+bitwise هستخدم or و and فعليا ال complement هتصير
+
+623
+00:46:48,960 --> 00:46:53,960
+ال not او ال negation او ال negation تمام ناخد
+
+624
+00:46:53,960 --> 00:46:54,860
+مثال
+
+625
+00:46:59,400 --> 00:47:05,060
+عليهم ناخد مثال لو
+
+626
+00:47:05,060 --> 00:47:09,520
+معطينا هنا suppose that the universe set ال
+
+627
+00:47:09,520 --> 00:47:11,700
+universe of discourse متكلم عن ال universe of
+
+628
+00:47:11,700 --> 00:47:16,200
+discourse ال universe of discourse بتاعتنا U معرف
+
+629
+00:47:16,200 --> 00:47:20,270
+لنا هي واحد اتنين تلاتة اربعةخمسة، ستة، سبعة لعشرة
+
+630
+00:47:20,270 --> 00:47:22,930
+فإذا من واحد لعشرة خلاص حددلي ال universive
+
+631
+00:47:22,930 --> 00:47:27,330
+discourse تبعتنا حددلنا إيها كويس express each of
+
+632
+00:47:27,330 --> 00:47:32,890
+these sets with bit string where the ith bit in
+
+633
+00:47:32,890 --> 00:47:38,570
+the string is one if I is in the set and zero
+
+634
+00:47:38,570 --> 00:47:43,560
+otherwise إذا not in the set كويسفهي حتى معرّفلكوا
+
+635
+00:47:43,560 --> 00:47:46,020
+كمان إيش اللي بدكم تعمله، معرّفلكوا إيش بدكم تعمله
+
+636
+00:47:46,020 --> 00:47:49,340
+بيعطيكوا الست الأولى، three, four, five عشان
+
+637
+00:47:49,340 --> 00:47:54,280
+أمثلها احنا دايما بقالنا في مين؟ في ال universe of
+
+638
+00:47:54,280 --> 00:47:57,340
+discourse ال universe of discourse عندنا واحد،
+
+639
+00:47:57,340 --> 00:48:02,640
+اتنين، تلاتة، أربعة، خمسة، ستة، سبعة، تمانية،
+
+640
+00:48:02,640 --> 00:48:07,120
+تسعة، عشرة، كويس، هذه؟ zero
+
+641
+00:48:13,400 --> 00:48:17,840
+خلاص هاي تمثيلها بالإيش؟ بال bit string طريقة
+
+642
+00:48:17,840 --> 00:48:24,320
+تمثيلها بال bit string التانية واحد و واحد و واحد
+
+643
+00:48:24,320 --> 00:48:31,180
+و واحد و واحد و واحد و واحد و واحد و واحد و واحد
+
+644
+00:48:31,880 --> 00:48:38,300
+للعشرة للعشرة خمسة ستة عشرة مظبوط طيب الأخيرة one
+
+645
+00:48:38,300 --> 00:48:46,460
+one one zero zero one one one zero تمام نفس الكلام
+
+646
+00:48:46,460 --> 00:48:52,220
+بالعكس ال six هذه عبارة عن إيش؟ كلام بسيط يعني
+
+647
+00:48:52,220 --> 00:48:58,040
+حاسين أنه طبع ابتدائي هيك ولا طبع صحيح؟طيب، بس هي
+
+648
+00:48:58,040 --> 00:49:00,060
+طريقة التنفيذ، يعني أنتوا بتلاحظوا أنتوا فعلا
+
+649
+00:49:00,060 --> 00:49:03,940
+بتبنوا على معلومات خفيفة بسيطة و بتبنوا عليها علم،
+
+650
+00:49:03,940 --> 00:49:12,980
+تبنوا عليها العلم اللاحق طيب هذه .. تالي
+
+651
+00:49:12,980 --> 00:49:15,900
+واضحة الأمور مافيش مش محتاج يعني خليلكوا التنتين
+
+652
+00:49:15,900 --> 00:49:20,950
+التانية تتسلوا عليهم و ..بنكون هيك احنا اتوقع
+
+653
+00:49:20,950 --> 00:49:26,270
+خلصنا اخيرا ال set خلصنا ال set theory و خلصنا كل
+
+654
+00:49:26,270 --> 00:49:29,390
+معلوماتنا عن ال set theory بيضل المرة الجاية ان
+
+655
+00:49:29,390 --> 00:49:34,990
+شاء الله بنبدأ مع ال ال functions مع ال functions
+
+656
+00:49:34,990 --> 00:49:36,730
+عارفين ان ال function احنا بنتكلم فيها عن
+
+657
+00:49:36,730 --> 00:49:41,690
+dependent و independent variables صحيح؟ متذكرين ال
+
+658
+00:49:41,690 --> 00:49:46,290
+functions قبل هيك؟ولا انسوتوها؟ طيب راجعوا هيك
+
+659
+00:49:46,290 --> 00:49:49,230
+شوية معلومات خفيفة عنها عشان المرة الجاية نعرف
+
+660
+00:49:49,230 --> 00:49:52,270
+نتحرك سلاسة فيها بسرعة يعني ان شاء الله يالا
+
+661
+00:49:52,270 --> 00:49:53,410
+يعطيكوا العافية وبركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_raw.json b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2defe1e1bcb52ffadf305184214eb880e18b1a59
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_raw.json
@@ -0,0 +1 @@
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1.2516975402832031e-06, "words": [{"start": 107.99, "end": 108.55, "word": "في", "probability": 0.56201171875}, {"start": 108.55, "end": 109.11, "word": " جزئية", "probability": 0.9443359375}, {"start": 109.11, "end": 110.25, "word": " ال", "probability": 0.7705078125}, {"start": 110.25, "end": 110.87, "word": " union", "probability": 0.8828125}, {"start": 110.87, "end": 111.33, "word": " لما", "probability": 0.8759765625}, {"start": 111.33, "end": 111.75, "word": " اتكلمنا", "probability": 0.920703125}, {"start": 111.75, "end": 111.87, "word": " عن", "probability": 0.99169921875}, {"start": 111.87, "end": 111.99, "word": " ال", "probability": 0.98095703125}, {"start": 111.99, "end": 112.31, "word": " union", "probability": 0.96826171875}, {"start": 112.31, "end": 113.49, "word": " وعرفناها", "probability": 0.86904296875}, {"start": 113.49, "end": 113.65, "word": " ان", "probability": 0.6962890625}, {"start": 113.65, "end": 113.87, "word": " هي", "probability": 0.59814453125}, {"start": 113.87, "end": 114.33, "word": " مجموعة", "probability": 0.98017578125}, {"start": 114.33, "end": 114.53, "word": " ال", "probability": 0.93701171875}, {"start": 114.53, "end": 114.95, "word": " elements", "probability": 0.87890625}, {"start": 114.95, "end": 115.15, "word": " اللي", "probability": 0.7147216796875}, {"start": 115.15, "end": 115.57, "word": " موجودة", "probability": 0.9862060546875}, {"start": 115.57, "end": 115.67, "word": " في", "probability": 0.939453125}, {"start": 115.67, "end": 115.79, "word": " ال", "probability": 0.958984375}, {"start": 115.79, "end": 115.95, "word": " two", "probability": 0.92431640625}, {"start": 115.95, "end": 116.21, "word": " sets", "probability": 0.9365234375}, {"start": 116.21, "end": 116.41, "word": " مع", "probability": 0.9951171875}, {"start": 116.41, "end": 116.81, "word": " بعض", "probability": 0.99365234375}, {"start": 116.81, "end": 117.91, "word": " يعني", "probability": 0.838134765625}, {"start": 117.91, "end": 118.13, "word": " لازم", "probability": 0.97802734375}, {"start": 118.13, "end": 118.33, "word": " تكون", "probability": 0.9580078125}, {"start": 118.33, "end": 118.77, "word": " موجودة", "probability": 0.982666015625}, {"start": 118.77, "end": 119.15, "word": " في", "probability": 0.96337890625}, {"start": 119.15, "end": 119.27, "word": " ال", "probability": 0.81787109375}, {"start": 119.27, "end": 119.49, "word": " set", "probability": 0.982421875}, {"start": 119.49, "end": 119.83, "word": " A", "probability": 0.76708984375}, {"start": 119.83, "end": 120.47, "word": " او", "probability": 0.7578125}, {"start": 120.47, "end": 120.83, "word": " set", "probability": 0.6123046875}, {"start": 120.83, "end": 121.09, "word": " B", "probability": 0.96337890625}, {"start": 121.09, "end": 121.55, "word": " معناه", "probability": 0.8709309895833334}, {"start": 121.55, "end": 121.73, "word": " ذلك", "probability": 0.977783203125}, {"start": 121.73, "end": 121.87, "word": " ان", "probability": 0.849609375}, {"start": 121.87, "end": 122.01, "word": " انا", "probability": 0.8291015625}, {"start": 122.01, "end": 122.43, "word": " جمعت", "probability": 0.9734700520833334}, {"start": 122.43, "end": 122.89, "word": " كل", "probability": 0.95849609375}, {"start": 122.89, "end": 123.39, "word": " ال", "probability": 0.978515625}, {"start": 123.39, "end": 123.71, "word": " elements", "probability": 0.91162109375}, {"start": 123.71, "end": 123.89, "word": " اللي", "probability": 0.9794921875}, {"start": 123.89, "end": 124.25, "word": " موجودة", "probability": 0.9854736328125}, {"start": 124.25, "end": 124.35, "word": " في", "probability": 0.97216796875}, {"start": 124.35, "end": 124.49, "word": " ال", "probability": 0.97216796875}, {"start": 124.49, "end": 124.77, "word": " two", "probability": 0.931640625}, {"start": 124.77, "end": 125.51, "word": " sets", "probability": 0.91552734375}, {"start": 125.51, "end": 126.07, "word": " طبعا", "probability": 0.755615234375}, {"start": 126.07, "end": 126.55, "word": " طيب", "probability": 0.7986653645833334}, {"start": 126.55, "end": 126.69, "word": " لما", "probability": 0.7139892578125}, {"start": 126.69, "end": 126.91, "word": " ننشط", "probability": 0.5665740966796875}, {"start": 126.91, "end": 127.31, "word": " نتكلم", "probability": 0.9749755859375}, {"start": 127.31, "end": 127.51, "word": " عن", "probability": 0.9912109375}, {"start": 127.51, "end": 127.63, "word": " ال", "probability": 0.78857421875}, {"start": 127.63, "end": 128.29, "word": " cardinality", "probability": 0.931640625}, {"start": 128.29, "end": 128.71, "word": " و", "probability": 0.8076171875}, {"start": 128.71, "end": 128.91, "word": " المرة", "probability": 0.7213134765625}, {"start": 128.91, "end": 129.03, "word": " اللي", "probability": 0.6318359375}, {"start": 129.03, "end": 129.29, "word": " فاتت", "probability": 0.8756510416666666}, {"start": 129.29, "end": 129.51, "word": " قلنا", "probability": 0.7560221354166666}, {"start": 129.51, "end": 129.67, "word": " ايش", "probability": 0.7872721354166666}, {"start": 129.67, "end": 129.81, "word": " يعني", "probability": 0.92529296875}, {"start": 129.81, "end": 130.45, "word": " cardinality", "probability": 0.8995768229166666}, {"start": 130.45, "end": 131.05, "word": " قلنا", "probability": 0.8741861979166666}, {"start": 131.05, "end": 131.17, "word": " ان", "probability": 0.8486328125}, {"start": 131.17, "end": 131.33, "word": " هي", "probability": 0.8125}, {"start": 131.33, "end": 131.71, "word": " عدد", "probability": 0.9908854166666666}, {"start": 131.71, "end": 131.85, "word": " ال", "probability": 0.98681640625}, {"start": 131.85, "end": 132.15, "word": " elements", "probability": 0.93310546875}, {"start": 132.15, "end": 132.47, "word": " داخل", "probability": 0.9637044270833334}, {"start": 132.47, "end": 132.61, "word": " ال", "probability": 0.9638671875}, {"start": 132.61, "end": 132.87, "word": " set", "probability": 0.9833984375}, {"start": 132.87, "end": 133.65, "word": " فإذا", "probability": 0.8689778645833334}, {"start": 133.65, "end": 133.85, "word": " لما", "probability": 0.977294921875}, {"start": 133.85, "end": 134.13, "word": " اقولها", "probability": 0.8497721354166666}, {"start": 134.13, "end": 134.41, "word": " لوجد", "probability": 0.6842447916666666}, {"start": 134.41, "end": 135.53, "word": " cardinality", "probability": 0.8341471354166666}, {"start": 135.53, "end": 135.75, "word": " ل", "probability": 0.88134765625}, {"start": 135.75, "end": 136.03, "word": " A", "probability": 0.51806640625}, {"start": 136.03, "end": 136.57, "word": " union", "probability": 0.76708984375}, {"start": 136.57, "end": 136.99, "word": " B", "probability": 0.97265625}], "temperature": 1.0}, {"id": 5, "seek": 16483, "start": 137.97, "end": 164.83, "text": "هي فعليا by logic أن هي العناصر اللي موجودة في A والعناصر اللي موجودة في B فإذا ال cardinality ل A زائد ال cardinality اللي موجودة في B بس ناخد بالنا أنه في exclusion لازم نعمل لمين لل intersection ليش لل intersection لأن ال intersection هنا هيتكرر معاكم هيتكرر معاكم for example لو قلنا عندنا واحد اتنين تلاتة هذه ستة A", "tokens": [3224, 1829, 6156, 3615, 20292, 995, 538, 9952, 14739, 39896, 18863, 1863, 33546, 2288, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 316, 16070, 3615, 1863, 33546, 2288, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 363, 6156, 28814, 15730, 2423, 2920, 259, 1860, 5296, 316, 30767, 16373, 3215, 2423, 2920, 259, 1860, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 363, 4724, 3794, 8717, 47283, 3215, 20666, 8315, 14739, 3224, 8978, 33049, 5296, 31377, 2304, 8717, 25957, 1211, 5296, 2304, 9957, 24976, 15236, 32239, 8592, 24976, 15236, 5296, 33456, 2423, 15236, 34105, 8032, 36081, 37983, 2288, 20449, 995, 24793, 8032, 36081, 37983, 2288, 20449, 995, 24793, 337, 1365, 45164, 12174, 1211, 8315, 43242, 8315, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 29538, 8608, 2655, 3660, 316], "avg_logprob": -0.194702151697129, "compression_ratio": 1.9718875502008033, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 137.97, "end": 138.25, "word": "هي", "probability": 0.54144287109375}, {"start": 138.25, "end": 138.81, "word": " فعليا", "probability": 0.810546875}, {"start": 138.81, "end": 139.31, "word": " by", "probability": 0.12646484375}, {"start": 139.31, "end": 139.71, "word": " logic", "probability": 0.96826171875}, {"start": 139.71, "end": 139.93, "word": " أن", "probability": 0.56591796875}, {"start": 139.93, "end": 140.11, "word": " هي", "probability": 0.2490234375}, {"start": 140.11, "end": 140.57, "word": " العناصر", "probability": 0.9404296875}, {"start": 140.57, "end": 140.67, "word": " اللي", "probability": 0.69775390625}, {"start": 140.67, "end": 140.97, "word": " موجودة", "probability": 0.9830322265625}, {"start": 140.97, "end": 141.13, "word": " في", "probability": 0.9599609375}, {"start": 141.13, "end": 141.29, "word": " A", "probability": 0.476806640625}, {"start": 141.29, "end": 142.35, "word": " والعناصر", "probability": 0.88759765625}, {"start": 142.35, "end": 142.47, "word": " اللي", "probability": 0.985595703125}, {"start": 142.47, "end": 142.79, "word": " موجودة", "probability": 0.9886474609375}, {"start": 142.79, "end": 142.89, "word": " في", "probability": 0.9443359375}, {"start": 142.89, "end": 143.07, "word": " B", "probability": 0.96142578125}, {"start": 143.07, "end": 143.77, "word": " فإذا", "probability": 0.8367513020833334}, {"start": 143.77, "end": 143.95, "word": " ال", "probability": 0.7392578125}, {"start": 143.95, "end": 144.51, "word": " cardinality", "probability": 0.806640625}, {"start": 144.51, "end": 144.65, "word": " ل", "probability": 0.8759765625}, {"start": 144.65, "end": 144.91, "word": " A", "probability": 0.681640625}, {"start": 144.91, "end": 146.25, "word": " زائد", "probability": 0.7555338541666666}, {"start": 146.25, "end": 146.35, "word": " ال", "probability": 0.65771484375}, {"start": 146.35, "end": 146.83, "word": " cardinality", "probability": 0.9361979166666666}, {"start": 146.83, "end": 146.95, "word": " اللي", "probability": 0.97412109375}, {"start": 146.95, "end": 147.31, "word": " موجودة", "probability": 0.98974609375}, {"start": 147.31, "end": 147.41, "word": " في", "probability": 0.9228515625}, {"start": 147.41, "end": 147.65, "word": " B", "probability": 0.9609375}, {"start": 147.65, "end": 148.33, "word": " بس", "probability": 0.94482421875}, {"start": 148.33, "end": 148.65, "word": " ناخد", "probability": 0.9816080729166666}, {"start": 148.65, "end": 149.13, "word": " بالنا", "probability": 0.930908203125}, {"start": 149.13, "end": 149.89, "word": " أنه", "probability": 0.59375}, {"start": 149.89, "end": 150.03, "word": " في", "probability": 0.93310546875}, {"start": 150.03, "end": 151.11, "word": " exclusion", "probability": 0.93896484375}, {"start": 151.11, "end": 151.77, "word": " لازم", "probability": 0.9912109375}, {"start": 151.77, "end": 152.11, "word": " نعمل", "probability": 0.9000651041666666}, {"start": 152.11, "end": 152.55, "word": " لمين", "probability": 0.6525065104166666}, {"start": 152.55, "end": 153.23, "word": " لل", "probability": 0.58447265625}, {"start": 153.23, "end": 153.87, "word": " intersection", "probability": 0.8291015625}, {"start": 153.87, "end": 154.55, "word": " ليش", "probability": 0.82177734375}, {"start": 154.55, "end": 154.65, "word": " لل", "probability": 0.88671875}, {"start": 154.65, "end": 155.17, "word": " intersection", "probability": 0.9794921875}, {"start": 155.17, "end": 155.75, "word": " لأن", "probability": 0.736328125}, {"start": 155.75, "end": 155.83, "word": " ال", "probability": 0.74755859375}, {"start": 155.83, "end": 156.23, "word": " intersection", "probability": 0.98046875}, {"start": 156.23, "end": 156.49, "word": " هنا", "probability": 0.9052734375}, {"start": 156.49, "end": 157.05, "word": " هيتكرر", "probability": 0.8721923828125}, {"start": 157.05, "end": 157.45, "word": " معاكم", "probability": 0.9244791666666666}, {"start": 157.45, "end": 158.77, "word": " هيتكرر", "probability": 0.9014892578125}, {"start": 158.77, "end": 159.41, "word": " معاكم", "probability": 0.97802734375}, {"start": 159.41, "end": 160.27, "word": " for", "probability": 0.8720703125}, {"start": 160.27, "end": 160.69, "word": " example", "probability": 0.9638671875}, {"start": 160.69, "end": 161.17, "word": " لو", "probability": 0.97021484375}, {"start": 161.17, "end": 161.41, "word": " قلنا", "probability": 0.8743489583333334}, {"start": 161.41, "end": 161.71, "word": " عندنا", "probability": 0.7427978515625}, {"start": 161.71, "end": 162.07, "word": " واحد", "probability": 0.810791015625}, {"start": 162.07, "end": 162.87, "word": " اتنين", "probability": 0.943359375}, {"start": 162.87, "end": 163.41, "word": " تلاتة", "probability": 0.960205078125}, {"start": 163.41, "end": 163.67, "word": " هذه", "probability": 0.309326171875}, {"start": 163.67, "end": 164.67, "word": " ستة", "probability": 0.8566080729166666}, {"start": 164.67, "end": 164.83, "word": " A", "probability": 0.513671875}], "temperature": 1.0}, {"id": 6, "seek": 19539, "start": 166.25, "end": 195.39, "text": "و هنقول إن في عندنا ستة تانية تلاتة أربعة خمسة هذه B لو بدنا نقول ال cardinality ل A union B بعد ما نحسبها هنحسبها كالتالي إن كل عناصر A مع كل عناصر B طيب عناصر A فعليا واحد اتنين تلاتة عناصر B تلاتة أربعة خمسة", "tokens": [2407, 8032, 1863, 39648, 36145, 8978, 43242, 8315, 8608, 2655, 3660, 6055, 7649, 10632, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 16490, 2304, 3794, 3660, 29538, 363, 45164, 47525, 8315, 8717, 39648, 2423, 2920, 259, 1860, 5296, 316, 11671, 363, 39182, 19446, 8717, 5016, 35457, 11296, 8032, 1863, 5016, 35457, 11296, 9122, 6027, 2655, 6027, 1829, 36145, 28242, 18871, 33546, 2288, 316, 20449, 28242, 18871, 33546, 2288, 363, 23032, 1829, 3555, 18871, 33546, 2288, 316, 6156, 3615, 20292, 995, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 18871, 33546, 2288, 363, 6055, 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222.3, "text": "لحظوا إنه إذا بدّي أشباحهم بهذا الشكل هتطلع واحد، اتنين، تلاتة، أربعة، خمسة، ستة، هتطلع ستة طيب فإذا هذا بيساوي ال cardinality ل A اللي هي تساوي تلاتة plus cardinality ب تلاتة هذا بيساوي الستة بس هذا مش صح هذا مش صح لأنه فعليا ال A union B لا تحتوي على ست عناصر أو six elements", "tokens": [1211, 5016, 19913, 14407, 36145, 3224, 11933, 15730, 47525, 11703, 1829, 5551, 8592, 3555, 39319, 16095, 39627, 15730, 25124, 28820, 8032, 2655, 9566, 1211, 3615, 36764, 24401, 12399, 1975, 2655, 1863, 9957, 12399, 6055, 1211, 9307, 3660, 12399, 5551, 25513, 27884, 12399, 16490, 2304, 3794, 3660, 12399, 8608, 2655, 3660, 12399, 8032, 2655, 9566, 1211, 3615, 8608, 2655, 3660, 23032, 1829, 3555, 6156, 28814, 15730, 23758, 4724, 1829, 3794, 995, 45865, 2423, 2920, 259, 1860, 5296, 316, 13672, 1829, 39896, 6055, 3794, 995, 45865, 6055, 1211, 9307, 3660, 1804, 2920, 259, 1860, 4724, 6055, 1211, 9307, 3660, 23758, 4724, 1829, 3794, 995, 45865, 21136, 2655, 3660, 4724, 3794, 23758, 37893, 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"probability": 0.6566569010416666}, {"start": 200.38, "end": 200.56, "word": " اتنين،", "probability": 0.9166015625}, {"start": 200.56, "end": 200.9, "word": " تلاتة،", "probability": 0.9603515625}, {"start": 200.9, "end": 201.16, "word": " أربعة،", "probability": 0.9080810546875}, {"start": 201.16, "end": 201.48, "word": " خمسة،", "probability": 0.965625}, {"start": 201.48, "end": 201.94, "word": " ستة،", "probability": 0.899169921875}, {"start": 201.94, "end": 202.62, "word": " هتطلع", "probability": 0.96220703125}, {"start": 202.62, "end": 203.36, "word": " ستة", "probability": 0.9833984375}, {"start": 203.36, "end": 205.1, "word": " طيب", "probability": 0.8876953125}, {"start": 205.1, "end": 205.68, "word": " فإذا", "probability": 0.8094075520833334}, {"start": 205.68, "end": 205.9, "word": " هذا", "probability": 0.62451171875}, {"start": 205.9, "end": 206.28, "word": " بيساوي", "probability": 0.9267578125}, {"start": 206.28, "end": 206.4, "word": " ال", "probability": 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{"start": 214.3, "end": 214.64, "word": " بيساوي", "probability": 0.97587890625}, {"start": 214.64, "end": 215.32, "word": " الستة", "probability": 0.9251302083333334}, {"start": 215.32, "end": 215.76, "word": " بس", "probability": 0.8115234375}, {"start": 215.76, "end": 215.9, "word": " هذا", "probability": 0.9306640625}, {"start": 215.9, "end": 216.08, "word": " مش", "probability": 0.94921875}, {"start": 216.08, "end": 216.36, "word": " صح", "probability": 0.99560546875}, {"start": 216.36, "end": 217.88, "word": " هذا", "probability": 0.7939453125}, {"start": 217.88, "end": 218.06, "word": " مش", "probability": 0.9765625}, {"start": 218.06, "end": 218.28, "word": " صح", "probability": 0.994873046875}, {"start": 218.28, "end": 218.56, "word": " لأنه", "probability": 0.6910807291666666}, {"start": 218.56, "end": 219.02, "word": " فعليا", "probability": 0.8861083984375}, {"start": 219.02, "end": 219.14, "word": " ال", "probability": 0.9599609375}, {"start": 219.14, "end": 219.3, "word": " A", "probability": 0.86962890625}, {"start": 219.3, "end": 219.56, "word": " union", "probability": 0.7705078125}, {"start": 219.56, "end": 219.78, "word": " B", "probability": 0.80908203125}, {"start": 219.78, "end": 219.96, "word": " لا", "probability": 0.83837890625}, {"start": 219.96, "end": 220.32, "word": " تحتوي", "probability": 0.97265625}, {"start": 220.32, "end": 220.54, "word": " على", "probability": 0.9296875}, {"start": 220.54, "end": 221.2, "word": " ست", "probability": 0.927001953125}, {"start": 221.2, "end": 221.6, "word": " عناصر", "probability": 0.9803059895833334}, {"start": 221.6, "end": 221.7, "word": " أو", "probability": 0.93701171875}, {"start": 221.7, "end": 221.92, "word": " six", "probability": 0.72314453125}, {"start": 221.92, "end": 222.3, "word": " elements", "probability": 0.9208984375}], "temperature": 1.0}, {"id": 8, "seek": 25061, "start": 222.71, "end": 250.61, "text": "في element مشترك طب إيش اللي بيميز ال element المشترك هذا عشان نشيله أن هو ال intersection تبعهم فإذا minus ال intersection a و b طب a و b وين ال intersection تبعتهم اللي هي تلاتة هذا تمثل ست تحتوي على العنصر تلاتة فجدش ال cardinality بتاعتها واحد فإذا هذا المفروض تكون ستة ناقص واحد", "tokens": [41185, 4478, 37893, 2655, 31747, 23032, 3555, 11933, 1829, 8592, 13672, 1829, 4724, 32640, 1829, 11622, 2423, 4478, 9673, 8592, 2655, 31747, 23758, 6225, 8592, 7649, 8717, 8592, 26895, 3224, 14739, 31439, 2423, 15236, 6055, 3555, 3615, 16095, 6156, 28814, 15730, 3175, 2423, 15236, 257, 4032, 272, 23032, 3555, 257, 4032, 272, 4032, 9957, 2423, 15236, 6055, 3555, 34268, 16095, 13672, 1829, 39896, 6055, 1211, 9307, 3660, 23758, 46811, 12984, 1211, 8608, 2655, 6055, 33753, 45865, 15844, 18863, 1863, 9381, 2288, 6055, 1211, 9307, 3660, 6156, 7435, 3215, 8592, 2423, 2920, 259, 1860, 39894, 995, 34268, 11296, 36764, 24401, 6156, 28814, 15730, 23758, 9673, 5172, 32887, 11242, 6055, 30544, 8608, 2655, 3660, 8717, 995, 4587, 9381, 36764, 24401], "avg_logprob": -0.1821165948855777, 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"end": 247.75, "word": " فإذا", "probability": 0.9527994791666666}, {"start": 247.75, "end": 248.23, "word": " هذا", "probability": 0.6259765625}, {"start": 248.23, "end": 248.51, "word": " المفروض", "probability": 0.993408203125}, {"start": 248.51, "end": 248.73, "word": " تكون", "probability": 0.79931640625}, {"start": 248.73, "end": 249.31, "word": " ستة", "probability": 0.9405924479166666}, {"start": 249.31, "end": 250.13, "word": " ناقص", "probability": 0.969970703125}, {"start": 250.13, "end": 250.61, "word": " واحد", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 9, "seek": 27818, "start": 251.42, "end": 278.18, "text": "خمسة okay خمسة بتصير صح لأنه المفروض أنه عندنا عنصر واحد فقط للتلاتة اذا واحد اتنين تلاتة اربعة خمسة هو الصح هو الإجابة الصحية طيب خليني اقول for example how many students are on our class email list جداش عدد الطلاب اللي موجودين في ال email list اللي موجود عندى الطلاب والطالبات", "tokens": [9778, 2304, 3794, 3660, 1392, 16490, 2304, 3794, 3660, 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{"start": 1224.79, "end": 1225.05, "word": " أول", "probability": 0.932373046875}, {"start": 1225.05, "end": 1225.47, "word": " إثبات", "probability": 0.9033203125}, {"start": 1225.47, "end": 1225.95, "word": " إن", "probability": 0.454345703125}, {"start": 1225.95, "end": 1226.41, "word": " الأولى", "probability": 0.9451497395833334}, {"start": 1226.41, "end": 1227.09, "word": " subset", "probability": 0.9638671875}, {"start": 1227.09, "end": 1227.37, "word": " من", "probability": 0.99560546875}, {"start": 1227.37, "end": 1227.87, "word": " التانية", "probability": 0.9889322916666666}, {"start": 1227.87, "end": 1229.33, "word": " بمعنى", "probability": 0.9765625}, {"start": 1229.33, "end": 1229.71, "word": " إن", "probability": 0.82177734375}, {"start": 1229.71, "end": 1229.93, "word": " أي", "probability": 0.8583984375}, {"start": 1229.93, "end": 1230.31, "word": " عنصر", "probability": 0.96533203125}, {"start": 1230.31, "end": 1230.85, "word": " ينتمي", "probability": 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"probability": 0.942626953125}, {"start": 1239.07, "end": 1239.47, "word": " التانية", "probability": 0.9873046875}, {"start": 1239.47, "end": 1240.09, "word": " كويس،", "probability": 0.78082275390625}, {"start": 1240.09, "end": 1240.33, "word": " بنكون", "probability": 0.67041015625}, {"start": 1240.33, "end": 1240.69, "word": " خلصنا", "probability": 0.987548828125}, {"start": 1240.69, "end": 1240.95, "word": " أول", "probability": 0.974609375}, {"start": 1240.95, "end": 1241.27, "word": " جزء", "probability": 0.9959309895833334}, {"start": 1241.27, "end": 1241.95, "word": " الجزء", "probability": 0.9327799479166666}, {"start": 1241.95, "end": 1242.25, "word": " التاني", "probability": 0.94091796875}, {"start": 1242.25, "end": 1242.39, "word": " إن", "probability": 0.5185546875}, {"start": 1242.39, "end": 1242.61, "word": " أي", "probability": 0.87744140625}, {"start": 1242.61, "end": 1242.99, "word": " عنصر", "probability": 0.9905598958333334}, {"start": 1242.99, "end": 1243.41, "word": " ينتمي", "probability": 0.9913330078125}, {"start": 1243.41, "end": 1244.17, "word": " للست", "probability": 0.981689453125}, {"start": 1244.17, "end": 1244.63, "word": " التانية", "probability": 0.9900716145833334}, {"start": 1244.63, "end": 1245.43, "word": " بالضرورة", "probability": 0.965625}, {"start": 1245.43, "end": 1245.69, "word": " لازم", "probability": 0.9679361979166666}, {"start": 1245.69, "end": 1246.01, "word": " ينتمي", "probability": 0.9942626953125}, {"start": 1246.01, "end": 1246.29, "word": " للست", "probability": 0.95458984375}, {"start": 1246.29, "end": 1246.67, "word": " الأولى", "probability": 0.9768880208333334}], "temperature": 1.0}, {"id": 49, "seek": 127583, "start": 1247.38, "end": 1275.84, "text": "إذا أثبتنا الطريقتين هدولة، بنكون أثبتنا إن الاتين equivalent لبعض أو كل واحدة منهم equivalent للتانية نبدأ بأول جزء إنه الأولى subset للتانية فبدنا عنصر نفترض إن هو belong to set number one ومنه أحاول أثبت إن هو لازم بالضرورة يكون موجود في إيش أو belong to set number two هنقول إنه X ف X belong لست الأولى، هي الست الأولى", "tokens": [28814, 15730, 5551, 12984, 3555, 2655, 8315, 41950, 16572, 38149, 9957, 8032, 3215, 12610, 3660, 12399, 4724, 1863, 30544, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 9307, 9957, 10344, 5296, 3555, 3615, 11242, 34051, 28242, 36764, 24401, 3660, 9154, 16095, 10344, 24976, 2655, 7649, 10632, 8717, 44510, 10721, 4724, 10721, 12610, 10874, 11622, 38207, 36145, 3224, 16247, 12610, 7578, 25993, 24976, 2655, 7649, 10632, 6156, 44510, 8315, 18871, 9381, 2288, 8717, 5172, 2655, 43042, 36145, 31439, 5784, 281, 992, 1230, 472, 4032, 27842, 3224, 5551, 5016, 995, 12610, 5551, 12984, 3555, 2655, 36145, 31439, 5296, 31377, 2304, 20666, 11242, 2288, 13063, 3660, 7251, 30544, 3714, 29245, 23328, 8978, 11933, 1829, 8592, 34051, 5784, 281, 992, 1230, 732, 8032, 1863, 39648, 36145, 3224, 1783, 6156, 1783, 5784, 5296, 14851, 16247, 12610, 7578, 12399, 39896, 2423, 14851, 16247, 12610, 7578], "avg_logprob": 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"probability": 0.7978515625}, {"start": 1252.12, "end": 1252.52, "word": " كل", "probability": 0.95556640625}, {"start": 1252.52, "end": 1252.74, "word": " واحدة", "probability": 0.98046875}, {"start": 1252.74, "end": 1252.88, "word": " منهم", "probability": 0.978515625}, {"start": 1252.88, "end": 1253.2, "word": " equivalent", "probability": 0.96142578125}, {"start": 1253.2, "end": 1254.02, "word": " للتانية", "probability": 0.9306640625}, {"start": 1254.02, "end": 1254.34, "word": " نبدأ", "probability": 0.8844401041666666}, {"start": 1254.34, "end": 1254.78, "word": " بأول", "probability": 0.9697265625}, {"start": 1254.78, "end": 1255.52, "word": " جزء", "probability": 0.9895833333333334}, {"start": 1255.52, "end": 1256.16, "word": " إنه", "probability": 0.6024169921875}, {"start": 1256.16, "end": 1257.18, "word": " الأولى", "probability": 0.95703125}, {"start": 1257.18, "end": 1257.78, "word": " subset", "probability": 0.95947265625}, {"start": 1257.78, "end": 1258.56, "word": " للتانية", "probability": 0.86199951171875}, {"start": 1258.56, "end": 1259.34, "word": " فبدنا", "probability": 0.78857421875}, {"start": 1259.34, "end": 1260.0, "word": " عنصر", "probability": 0.978515625}, {"start": 1260.0, "end": 1260.52, "word": " نفترض", "probability": 0.9547119140625}, {"start": 1260.52, "end": 1260.68, "word": " إن", "probability": 0.59912109375}, {"start": 1260.68, "end": 1260.88, "word": " هو", "probability": 0.60595703125}, {"start": 1260.88, "end": 1261.7, "word": " belong", "probability": 0.294677734375}, {"start": 1261.7, "end": 1262.02, "word": " to", "probability": 0.97021484375}, {"start": 1262.02, "end": 1262.96, "word": " set", "probability": 0.9716796875}, {"start": 1262.96, "end": 1263.22, "word": " number", "probability": 0.89306640625}, {"start": 1263.22, "end": 1263.56, "word": " one", "probability": 0.7431640625}, {"start": 1263.56, "end": 1264.68, "word": " ومنه", "probability": 0.9352213541666666}, {"start": 1264.68, "end": 1265.08, "word": " أحاول", "probability": 0.91259765625}, {"start": 1265.08, "end": 1265.36, "word": " أثبت", "probability": 0.9925537109375}, {"start": 1265.36, "end": 1265.48, "word": " إن", "probability": 0.87451171875}, {"start": 1265.48, "end": 1265.62, "word": " هو", "probability": 0.85986328125}, {"start": 1265.62, "end": 1265.94, "word": " لازم", "probability": 0.9918619791666666}, {"start": 1265.94, "end": 1266.42, "word": " بالضرورة", "probability": 0.963671875}, {"start": 1266.42, "end": 1267.04, "word": " يكون", "probability": 0.98876953125}, {"start": 1267.04, "end": 1267.36, "word": " موجود", "probability": 0.9759114583333334}, {"start": 1267.36, "end": 1267.52, "word": " في", "probability": 0.9892578125}, {"start": 1267.52, "end": 1267.76, "word": " إيش", "probability": 0.741455078125}, {"start": 1267.76, "end": 1268.18, "word": " أو", "probability": 0.93896484375}, {"start": 1268.18, "end": 1268.5, "word": " belong", "probability": 0.8798828125}, {"start": 1268.5, "end": 1268.8, "word": " to", "probability": 0.98486328125}, {"start": 1268.8, "end": 1270.12, "word": " set", "probability": 0.96875}, {"start": 1270.12, "end": 1270.54, "word": " number", "probability": 0.96826171875}, {"start": 1270.54, "end": 1270.82, "word": " two", "probability": 0.888671875}, {"start": 1270.82, "end": 1271.96, "word": " هنقول", "probability": 0.8502604166666666}, {"start": 1271.96, "end": 1272.14, "word": " إنه", "probability": 0.971435546875}, {"start": 1272.14, "end": 1272.38, "word": " X", "probability": 0.50048828125}, {"start": 1272.38, "end": 1273.16, "word": " ف", "probability": 0.7978515625}, {"start": 1273.16, "end": 1273.36, "word": " X", "probability": 0.68408203125}, {"start": 1273.36, "end": 1273.7, "word": " belong", "probability": 0.72265625}, {"start": 1273.7, "end": 1274.46, "word": " لست", "probability": 0.6380615234375}, {"start": 1274.46, "end": 1275.22, "word": " الأولى،", "probability": 0.9161376953125}, {"start": 1275.22, "end": 1275.28, "word": " هي", "probability": 0.64404296875}, {"start": 1275.28, "end": 1275.5, "word": " الست", "probability": 0.723388671875}, {"start": 1275.5, "end": 1275.84, "word": " الأولى", "probability": 0.9850260416666666}], "temperature": 1.0}, {"id": 50, "seek": 129505, "start": 1277.77, "end": 1295.05, "text": "تمام إذا فعلًا belonged ل A intersection B union C فهو بالضروري لازم يكون belonged ل A لحالها و belonged ل ال union بتاعت ال two sets دولة بالضروري لإن في بينهم intersection", "tokens": [39237, 10943, 11933, 15730, 6156, 30241, 14111, 995, 28611, 5296, 316, 15236, 363, 11671, 383, 6156, 3224, 2407, 20666, 11242, 2288, 13063, 1829, 5296, 31377, 2304, 7251, 30544, 28611, 5296, 316, 5296, 5016, 6027, 11296, 4032, 28611, 5296, 2423, 11671, 39894, 995, 34268, 2423, 732, 6352, 11778, 12610, 3660, 20666, 11242, 2288, 13063, 1829, 5296, 28814, 1863, 8978, 49374, 16095, 15236], "avg_logprob": -0.24344757631901773, "compression_ratio": 1.5408805031446542, "no_speech_prob": 0.0, "words": [{"start": 1277.77, "end": 1278.19, "word": "تمام", "probability": 0.5982666015625}, {"start": 1278.19, "end": 1278.59, "word": " إذا", "probability": 0.7451171875}, {"start": 1278.59, "end": 1279.05, "word": " فعلًا", "probability": 0.6544189453125}, {"start": 1279.05, "end": 1279.43, "word": " belonged", "probability": 0.408935546875}, {"start": 1279.43, "end": 1279.69, "word": " ل", "probability": 0.84375}, {"start": 1279.69, "end": 1280.11, "word": " A", "probability": 0.429931640625}, {"start": 1280.11, "end": 1281.23, "word": " intersection", "probability": 0.87255859375}, {"start": 1281.23, "end": 1281.81, "word": " B", "probability": 0.89404296875}, {"start": 1281.81, "end": 1282.27, "word": " union", "probability": 0.7939453125}, {"start": 1282.27, "end": 1282.63, "word": " C", "probability": 0.97998046875}, {"start": 1282.63, "end": 1283.21, "word": " فهو", "probability": 0.9615885416666666}, {"start": 1283.21, "end": 1284.01, "word": " بالضروري", "probability": 0.88525390625}, {"start": 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معناته أنا بقدرش أقول أنه لجميع الاحتمالات كل عنصر موجود هنا لازم يكون بالضرورة موجود في ال set التانية بقدرش أقول كل هذه for all elements لأ احنا بدنا يها for all elements belonging to set number one بالضرورة ال element هذا لازم يكون belonging to set number two", "tokens": [9566, 3555, 11933, 15730, 8978, 36632, 4478, 36632, 1975, 33753, 2304, 6027, 5551, 17082, 5172, 1211, 47395, 34051, 8608, 3555, 47395, 20449, 8315, 47395, 41850, 4724, 28543, 2288, 8592, 5551, 39648, 14739, 3224, 5296, 7435, 2304, 40228, 42963, 33753, 2304, 6027, 9307, 28242, 18871, 9381, 2288, 3714, 29245, 23328, 34105, 5296, 31377, 2304, 7251, 30544, 20666, 11242, 2288, 13063, 3660, 3714, 29245, 23328, 8978, 2423, 992, 16712, 7649, 10632, 4724, 28543, 2288, 8592, 5551, 39648, 28242, 29538, 337, 439, 4959, 5296, 10721, 1975, 5016, 8315, 47525, 8315, 7251, 11296, 337, 439, 4959, 22957, 281, 992, 1230, 472, 20666, 11242, 2288, 13063, 3660, 2423, 4478, 23758, 5296, 31377, 2304, 7251, 30544, 22957, 281, 992, 1230, 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operator اللي بنشتغل عليها أنا في الآخر بتعامل مع ال sets هذه اللي بتدخلها على ال pc", "tokens": [10721, 2407, 13785, 992, 4724, 43042, 3224, 9154, 36764, 24401, 4032, 13202, 4032, 44945, 8592, 2655, 17082, 1211, 25894, 11296, 46811, 10943, 23032, 1829, 3555, 2423, 33358, 5296, 2423, 6352, 5296, 15042, 8717, 30544, 47525, 8315, 8717, 25957, 1211, 10290, 11778, 47283, 1211, 992, 20449, 9957, 3660, 9122, 33911, 3714, 43020, 5551, 25957, 1211, 10290, 24976, 4959, 13672, 1829, 8978, 11296, 4724, 5016, 1829, 12984, 14739, 41850, 5551, 14851, 5172, 25708, 9154, 11296, 8978, 2423, 12973, 13672, 1829, 44945, 8592, 2655, 17082, 1211, 25894, 11296, 41850, 8978, 6024, 95, 34740, 39894, 3615, 10943, 1211, 20449, 2423, 6352, 29538, 13672, 1829, 39894, 3215, 9778, 1211, 11296, 15844, 2423, 43451], "avg_logprob": -0.16829127729485888, "compression_ratio": 1.864, "no_speech_prob": 0.0, "words": [{"start": 2434.23, "end": 2434.59, "word": "أو", "probability": 0.8486328125}, {"start": 2434.59, "end": 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{"start": 2463.32, "end": 2463.42, "word": " ال", "probability": 0.93798828125}, {"start": 2463.42, "end": 2463.8, "word": " elements", "probability": 0.90283203125}, {"start": 2463.8, "end": 2464.16, "word": " داخل", "probability": 0.9801432291666666}, {"start": 2464.16, "end": 2464.3, "word": " ال", "probability": 0.9404296875}, {"start": 2464.3, "end": 2464.56, "word": " set", "probability": 0.9638671875}, {"start": 2464.56, "end": 2465.64, "word": " فبنمثلها", "probability": 0.9571707589285714}, {"start": 2465.64, "end": 2466.38, "word": " بال", "probability": 0.96533203125}, {"start": 2466.38, "end": 2466.78, "word": " index", "probability": 0.9384765625}, {"start": 2466.78, "end": 2467.24, "word": " تبعها", "probability": 0.933349609375}], "temperature": 1.0}, {"id": 97, "seek": 249260, "start": 2467.76, "end": 2492.6, "text": "بنمثلها وما جدقش رقمها داخل ال set كترتيب فهنا بنتكلم عن ترتيبها لما نيجي نعمل ال methods of representing indiscreet structure using another discrete structure of a different type خلينا ناخد ال type تبعنا اللي بنشتغل عليه هو ال natural number و بدنا نعمله representation عشان نوضح الموضوع هنقول zero عبارة عن في", "tokens": [3555, 1863, 2304, 12984, 1211, 11296, 4032, 15042, 10874, 3215, 4587, 8592, 12602, 4587, 2304, 11296, 11778, 47283, 1211, 2423, 992, 9122, 2655, 2288, 31371, 3555, 6156, 3224, 8315, 44945, 2655, 4117, 19528, 18871, 6055, 2288, 31371, 3555, 11296, 5296, 15042, 8717, 1829, 7435, 1829, 8717, 25957, 1211, 2423, 7150, 295, 13460, 1016, 5606, 4751, 3877, 1228, 1071, 27706, 3877, 295, 257, 819, 2010, 16490, 1211, 9957, 995, 8717, 47283, 3215, 2423, 2010, 6055, 3555, 3615, 8315, 13672, 1829, 44945, 8592, 2655, 17082, 1211, 47356, 31439, 2423, 3303, 1230, 4032, 47525, 8315, 8717, 25957, 43761, 10290, 6225, 8592, 7649, 8717, 2407, 11242, 5016, 9673, 2407, 11242, 45367, 8032, 1863, 39648, 4018, 6225, 3555, 9640, 3660, 18871, 8978], "avg_logprob": -0.1826006311733844, "compression_ratio": 1.6254545454545455, "no_speech_prob": 0.0, "words": [{"start": 2467.76, "end": 2468.44, "word": "بنمثلها", "probability": 0.8472493489583334}, {"start": 2468.44, "end": 2469.82, "word": " وما", "probability": 0.359954833984375}, {"start": 2469.82, "end": 2470.22, "word": " جدقش", "probability": 0.657867431640625}, {"start": 2470.22, "end": 2470.8, "word": " رقمها", "probability": 0.9615478515625}, {"start": 2470.8, "end": 2471.34, "word": " داخل", "probability": 0.935546875}, {"start": 2471.34, "end": 2471.48, "word": " ال", "probability": 0.94384765625}, {"start": 2471.48, "end": 2471.68, "word": " set", "probability": 0.82763671875}, {"start": 2471.68, "end": 2472.66, "word": " كترتيب", "probability": 0.94580078125}, {"start": 2472.66, "end": 2473.2, "word": " فهنا", "probability": 0.8986002604166666}, {"start": 2473.2, "end": 2473.68, "word": " بنتكلم", "probability": 0.83056640625}, {"start": 2473.68, "end": 2473.98, "word": " عن", "probability": 0.9912109375}, {"start": 2473.98, "end": 2474.86, "word": " ترتيبها", 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2485.16, "word": " بنشتغل", "probability": 0.98115234375}, {"start": 2485.16, "end": 2485.38, "word": " عليه", "probability": 0.98876953125}, {"start": 2485.38, "end": 2485.54, "word": " هو", "probability": 0.947265625}, {"start": 2485.54, "end": 2485.6, "word": " ال", "probability": 0.463623046875}, {"start": 2485.6, "end": 2485.9, "word": " natural", "probability": 0.91015625}, {"start": 2485.9, "end": 2487.34, "word": " number", "probability": 0.9853515625}, {"start": 2487.34, "end": 2487.68, "word": " و", "probability": 0.6357421875}, {"start": 2487.68, "end": 2487.84, "word": " بدنا", "probability": 0.7020263671875}, {"start": 2487.84, "end": 2488.16, "word": " نعمله", "probability": 0.98095703125}, {"start": 2488.16, "end": 2488.82, "word": " representation", "probability": 0.96240234375}, {"start": 2488.82, "end": 2489.16, "word": " عشان", "probability": 0.98388671875}, {"start": 2489.16, "end": 2489.54, "word": " نوضح", "probability": 0.987060546875}, {"start": 2489.54, "end": 2490.02, "word": " الموضوع", "probability": 0.99853515625}, {"start": 2490.02, "end": 2490.62, "word": " هنقول", "probability": 0.7965494791666666}, {"start": 2490.62, "end": 2491.04, "word": " zero", "probability": 0.67919921875}, {"start": 2491.04, "end": 2492.2, "word": " عبارة", "probability": 0.9891357421875}, {"start": 2492.2, "end": 2492.36, "word": " عن", "probability": 0.9970703125}, {"start": 2492.36, "end": 2492.6, "word": " في", "probability": 0.44677734375}], "temperature": 1.0}, {"id": 98, "seek": 251944, "start": 2493.23, "end": 2519.45, "text": "هذا بالنسبة لمن؟ لـ natural number فالـ zero هذا أول element فيها مش هذا ال element الأول بنقدر نعبر عنه كأنه هذا في ال element التاني بنعبر عليه على أساس أن هذه ال six تحتوي على عنصر واحد أنه عنصر؟ أول عنصر أول عنصر في ال natural number ال zero اللي هو ال zero طيب اتنين مكافئة ل six تحتوي على", "tokens": [3224, 15730, 20666, 1863, 35457, 3660, 5296, 27842, 22807, 5296, 39184, 3303, 1230, 6156, 6027, 39184, 4018, 23758, 5551, 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"word": " عبارة", "probability": 0.9901123046875}, {"start": 2720.47, "end": 2720.61, "word": " عن", "probability": 0.94677734375}, {"start": 2720.61, "end": 2721.17, "word": " اتنين،", "probability": 0.782275390625}, {"start": 2721.17, "end": 2721.97, "word": " تلاتة،", "probability": 0.96435546875}, {"start": 2721.97, "end": 2722.65, "word": " خمسة،", "probability": 0.97333984375}, {"start": 2722.65, "end": 2722.95, "word": " سبعة،", "probability": 0.9547119140625}, {"start": 2722.95, "end": 2723.67, "word": " أحداشر", "probability": 0.76263427734375}, {"start": 2723.67, "end": 2725.83, "word": " الأعداد", "probability": 0.73583984375}, {"start": 2725.83, "end": 2726.37, "word": " الأولية", "probability": 0.97216796875}, {"start": 2726.37, "end": 2727.13, "word": " ال", "probability": 0.85888671875}, {"start": 2727.13, "end": 2727.53, "word": " primes", "probability": 0.5821533203125}, {"start": 2727.53, "end": 2727.93, "word": " كيف", "probability": 0.901611328125}, {"start": 2727.93, "end": 2728.39, "word": " بمثلها", "probability": 0.8888671875}, {"start": 2728.39, "end": 2728.89, "word": " هنا؟", "probability": 0.807373046875}, {"start": 2728.89, "end": 2729.01, "word": " أنا", "probability": 0.775390625}, {"start": 2729.01, "end": 2729.27, "word": " عارف", "probability": 0.98681640625}, {"start": 2729.27, "end": 2729.37, "word": " أن", "probability": 0.5048828125}, {"start": 2729.37, "end": 2729.47, "word": " ال", "probability": 0.86328125}, {"start": 2729.47, "end": 2729.73, "word": " universe", "probability": 0.271484375}, {"start": 2729.73, "end": 2729.91, "word": " of", "probability": 0.966796875}, {"start": 2729.91, "end": 2730.27, "word": " discourse", "probability": 0.935546875}, {"start": 2730.27, "end": 2730.79, "word": " الشيية", "probability": 0.593994140625}, {"start": 2730.79, "end": 2731.69, "word": " natural", "probability": 0.6689453125}, {"start": 2731.69, "end": 2732.19, "word": " number", "probability": 0.9775390625}, {"start": 2732.19, "end": 2732.53, "word": " طب", "probability": 0.865478515625}, {"start": 2732.53, "end": 2732.63, "word": " ال", "probability": 0.9755859375}, {"start": 2732.63, "end": 2732.89, "word": " natural", "probability": 0.953125}, {"start": 2732.89, "end": 2733.27, "word": " number", "probability": 0.97607421875}, {"start": 2733.27, "end": 2733.97, "word": " خلينا", "probability": 0.73828125}, {"start": 2733.97, "end": 2734.43, "word": " نكتبها", "probability": 0.9939453125}], "temperature": 1.0}, {"id": 109, "seek": 275826, "start": 2735.08, "end": 2758.26, "text": "صفر واحد اتنين تلاتة اربعة خمسة شكة طيب الصفر موجود في ال set بحطله zero الواحد مش موجود الاتنين موجودة التلاتة واحد الاربعة", "tokens": [9381, 5172, 2288, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 16490, 2304, 3794, 3660, 13412, 4117, 3660, 23032, 1829, 3555, 31767, 5172, 2288, 3714, 29245, 23328, 8978, 2423, 992, 4724, 5016, 9566, 43761, 4018, 2423, 14407, 24401, 37893, 3714, 29245, 23328, 2423, 9307, 1863, 9957, 3714, 29245, 23328, 3660, 16712, 1211, 9307, 3660, 36764, 24401, 2423, 9640, 3555, 27884], "avg_logprob": -0.14287405506227957, "compression_ratio": 1.697674418604651, "no_speech_prob": 0.0, "words": [{"start": 2735.08, "end": 2735.64, "word": "صفر", "probability": 0.7891438802083334}, {"start": 2735.64, "end": 2736.72, "word": " واحد", "probability": 0.800537109375}, {"start": 2736.72, "end": 2737.42, "word": " اتنين", "probability": 0.9576416015625}, {"start": 2737.42, "end": 2738.34, "word": " تلاتة", "probability": 0.934814453125}, {"start": 2738.34, "end": 2739.14, "word": " اربعة", "probability": 0.87353515625}, {"start": 2739.14, "end": 2740.06, "word": " خمسة", "probability": 0.9468994140625}, {"start": 2740.06, "end": 2740.78, "word": " شكة", "probability": 0.5907389322916666}, {"start": 2740.78, "end": 2744.28, "word": " طيب", "probability": 0.75537109375}, {"start": 2744.28, "end": 2745.2, "word": " الصفر", "probability": 0.9736328125}, {"start": 2745.2, "end": 2746.86, "word": " موجود", "probability": 0.9860026041666666}, {"start": 2746.86, "end": 2747.28, "word": " في", "probability": 0.90869140625}, {"start": 2747.28, "end": 2747.42, "word": " ال", "probability": 0.86376953125}, {"start": 2747.42, "end": 2747.66, "word": " set", "probability": 0.88916015625}, {"start": 2747.66, "end": 2748.4, "word": " بحطله", "probability": 0.8660888671875}, {"start": 2748.4, "end": 2748.66, "word": " zero", "probability": 0.7685546875}, {"start": 2748.66, "end": 2750.12, "word": " الواحد", "probability": 0.9469401041666666}, {"start": 2750.12, "end": 2752.46, "word": " مش", "probability": 0.96826171875}, {"start": 2752.46, "end": 2752.9, "word": " موجود", "probability": 0.9899088541666666}, {"start": 2752.9, "end": 2753.76, "word": " الاتنين", "probability": 0.79742431640625}, {"start": 2753.76, "end": 2755.06, "word": " موجودة", "probability": 0.9888916015625}, {"start": 2755.06, "end": 2755.98, "word": " التلاتة", 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2776.49, "end": 2776.73, "word": " عارف", "probability": 0.9816080729166666}, {"start": 2776.73, "end": 2776.83, "word": " ان", "probability": 0.814453125}, {"start": 2776.83, "end": 2776.93, "word": " انا", "probability": 0.928955078125}, {"start": 2776.93, "end": 2777.17, "word": " متكلم", "probability": 0.7484537760416666}, {"start": 2777.17, "end": 2777.33, "word": " عن", "probability": 0.98486328125}, {"start": 2777.33, "end": 2777.45, "word": " ال", "probability": 0.50244140625}, {"start": 2777.45, "end": 2777.67, "word": " natural", "probability": 0.8232421875}, {"start": 2777.67, "end": 2778.11, "word": " number", "probability": 0.97314453125}, {"start": 2778.11, "end": 2778.53, "word": " احنا", "probability": 0.8331705729166666}, {"start": 2778.53, "end": 2778.81, "word": " متكلم", "probability": 0.92578125}, {"start": 2778.81, "end": 2778.97, "word": " عن", "probability": 0.9775390625}, {"start": 2778.97, "end": 2779.21, "word": " ايش", "probability": 0.808837890625}, 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اتوقع خلصنا اخيرا ال set خلصنا ال set theory و خلصنا كل معلوماتنا عن ال set theory بيضل المرة الجاية ان شاء الله بنبدأ مع ال ال functions مع ال functions عارفين ان ال function احنا بنتكلم فيها عن dependent و independent variables صحيح؟ متذكرين ال functions قبل هيك؟", "tokens": [3555, 1863, 30544, 39896, 4117, 1975, 5016, 8315, 1975, 2655, 30543, 3615, 16490, 1211, 9381, 8315, 1975, 9778, 13546, 995, 2423, 992, 16490, 1211, 9381, 8315, 2423, 992, 5261, 4032, 16490, 1211, 9381, 8315, 28242, 20449, 1211, 20498, 9307, 8315, 18871, 2423, 992, 5261, 4724, 1829, 11242, 1211, 9673, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 44945, 44510, 10721, 20449, 2423, 2423, 6828, 20449, 2423, 6828, 6225, 9640, 5172, 9957, 16472, 2423, 2445, 1975, 5016, 8315, 4724, 29399, 4117, 19528, 8978, 11296, 18871, 12334, 4032, 6695, 9102, 20328, 5016, 1829, 5016, 22807, 44650, 8848, 37983, 9957, 2423, 6828, 12174, 36150, 39896, 4117, 22807], "avg_logprob": -0.12500000454130628, "compression_ratio": 1.851528384279476, "no_speech_prob": 0.0, "words": [{"start": 2959.49, "end": 2959.99, "word": "بنكون", "probability": 0.9080403645833334}, {"start": 2959.99, "end": 2960.21, "word": " هيك", "probability": 0.693603515625}, {"start": 2960.21, "end": 2960.45, "word": " احنا", "probability": 0.9347330729166666}, {"start": 2960.45, "end": 2960.95, "word": " اتوقع", "probability": 0.8948974609375}, {"start": 2960.95, "end": 2961.67, "word": " خلصنا", "probability": 0.9715576171875}, {"start": 2961.67, "end": 2962.73, "word": " اخيرا", "probability": 0.8985595703125}, {"start": 2962.73, "end": 2962.97, "word": " ال", "probability": 0.95654296875}, {"start": 2962.97, "end": 2963.27, "word": " set", "probability": 0.931640625}, {"start": 2963.27, "end": 2964.33, "word": " خلصنا", "probability": 0.9356689453125}, {"start": 2964.33, "end": 2964.81, "word": " ال", "probability": 0.97802734375}, {"start": 2964.81, "end": 2964.97, "word": " set", "probability": 0.9658203125}, {"start": 2964.97, "end": 2965.31, "word": " theory", "probability": 0.73486328125}, {"start": 2965.31, "end": 2965.75, "word": " و", "probability": 0.9287109375}, {"start": 2965.75, "end": 2966.11, "word": " خلصنا", "probability": 0.958740234375}, {"start": 2966.11, "end": 2966.27, "word": " كل", "probability": 0.9833984375}, {"start": 2966.27, "end": 2966.71, "word": " معلوماتنا", "probability": 0.9126953125}, {"start": 2966.71, "end": 2966.83, "word": " عن", "probability": 0.99609375}, {"start": 2966.83, "end": 2966.95, "word": " ال", "probability": 0.982421875}, {"start": 2966.95, "end": 2967.11, "word": " set", "probability": 0.95947265625}, {"start": 2967.11, "end": 2967.39, "word": " theory", "probability": 0.82958984375}, {"start": 2967.39, "end": 2968.29, "word": " بيضل", "probability": 0.707763671875}, {"start": 2968.29, "end": 2969.01, "word": " المرة", "probability": 0.95849609375}, {"start": 2969.01, "end": 2969.25, "word": " الجاية", "probability": 0.8857421875}, {"start": 2969.25, "end": 2969.39, "word": " ان", "probability": 0.90380859375}, {"start": 2969.39, "end": 2969.49, "word": " شاء", "probability": 0.9287109375}, {"start": 2969.49, "end": 2969.55, "word": " الله", "probability": 0.939453125}, {"start": 2969.55, "end": 2970.13, "word": " بنبدأ", "probability": 0.9163411458333334}, {"start": 2970.13, "end": 2970.47, "word": " مع", "probability": 0.99169921875}, {"start": 2970.47, "end": 2971.11, "word": " ال", "probability": 0.9873046875}, {"start": 2971.11, "end": 2973.27, "word": " ال", "probability": 0.4453125}, {"start": 2973.27, "end": 2973.75, "word": " functions", "probability": 0.88427734375}, {"start": 2973.75, "end": 2974.29, "word": " مع", "probability": 0.85400390625}, {"start": 2974.29, "end": 2974.57, "word": " ال", "probability": 0.9658203125}, {"start": 2974.57, "end": 2974.99, "word": " functions", "probability": 0.92431640625}, {"start": 2974.99, "end": 2975.35, "word": " عارفين", "probability": 0.9747314453125}, {"start": 2975.35, "end": 2975.43, "word": " ان", "probability": 0.78515625}, {"start": 2975.43, "end": 2975.53, "word": " ال", "probability": 0.96875}, {"start": 2975.53, "end": 2975.83, "word": " function", "probability": 0.52978515625}, {"start": 2975.83, "end": 2975.95, "word": " احنا", "probability": 0.9303385416666666}, {"start": 2975.95, "end": 2976.27, "word": " بنتكلم", "probability": 0.8577880859375}, {"start": 2976.27, "end": 2976.55, "word": " فيها", "probability": 0.97216796875}, {"start": 2976.55, "end": 2976.73, "word": " عن", "probability": 0.95263671875}, {"start": 2976.73, "end": 2977.09, "word": " dependent", "probability": 0.84130859375}, {"start": 2977.09, "end": 2977.31, "word": " و", "probability": 0.98291015625}, {"start": 2977.31, "end": 2977.67, "word": " independent", "probability": 0.93896484375}, {"start": 2977.67, "end": 2979.21, "word": " variables", "probability": 0.94921875}, {"start": 2979.21, "end": 2981.13, "word": " صحيح؟", "probability": 0.89111328125}, {"start": 2981.13, "end": 2981.59, "word": " متذكرين", "probability": 0.76953125}, {"start": 2981.59, "end": 2981.69, "word": " ال", "probability": 0.982421875}, {"start": 2981.69, "end": 2981.99, "word": " functions", "probability": 0.9248046875}, {"start": 2981.99, "end": 2982.23, "word": " قبل", "probability": 0.850341796875}, {"start": 2982.23, "end": 2982.67, "word": " هيك؟", "probability": 0.9763997395833334}], "temperature": 1.0}, {"id": 119, "seek": 299341, "start": 2983.45, "end": 2993.41, "text": "ولا انسوتوها؟ طيب راجعوا هيك شوية معلومات خفيفة عنها عشان المرة الجاية نعرف نتحرك سلاسة فيها بسرعة يعني ان شاء الله يالا يعطيكوا العافية وبركة الله فيكم", "tokens": [12610, 995, 16472, 3794, 35473, 2407, 11296, 22807, 23032, 1829, 3555, 12602, 26108, 3615, 14407, 39896, 4117, 13412, 2407, 10632, 20449, 1211, 20498, 9307, 16490, 5172, 33911, 3660, 18871, 11296, 6225, 8592, 7649, 9673, 25720, 25724, 995, 10632, 8717, 3615, 28480, 8717, 2655, 5016, 31747, 8608, 15040, 3794, 3660, 8978, 11296, 4724, 3794, 2288, 27884, 37495, 22653, 16472, 13412, 16606, 21984, 7251, 6027, 995, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 4032, 26890, 4117, 3660, 21984, 8978, 24793], "avg_logprob": -0.17880859673023225, "compression_ratio": 1.7160493827160495, "no_speech_prob": 0.0010786056518554688, "words": [{"start": 2983.45, "end": 2983.75, "word": "ولا", "probability": 0.605224609375}, {"start": 2983.75, "end": 2984.67, "word": " انسوتوها؟", "probability": 0.7215169270833334}, {"start": 2984.67, "end": 2985.39, "word": " طيب", "probability": 0.9202473958333334}, {"start": 2985.39, "end": 2986.15, "word": " راجعوا", "probability": 0.827392578125}, {"start": 2986.15, "end": 2986.29, "word": " هيك", "probability": 0.808837890625}, {"start": 2986.29, "end": 2986.51, "word": " شوية", "probability": 0.8391927083333334}, {"start": 2986.51, "end": 2986.85, "word": " معلومات", "probability": 0.982177734375}, {"start": 2986.85, "end": 2987.19, "word": " خفيفة", "probability": 0.987548828125}, {"start": 2987.19, "end": 2987.35, "word": " عنها", "probability": 0.964111328125}, {"start": 2987.35, "end": 2987.55, "word": " عشان", "probability": 0.96044921875}, {"start": 2987.55, "end": 2987.79, "word": " المرة", "probability": 0.974609375}, {"start": 2987.79, "end": 2988.25, "word": " الجاية", "probability": 0.94482421875}, {"start": 2988.25, "end": 2989.23, "word": " نعرف", "probability": 0.9788411458333334}, {"start": 2989.23, "end": 2989.67, "word": " نتحرك", "probability": 0.9862060546875}, {"start": 2989.67, "end": 2990.85, "word": " سلاسة", "probability": 0.7916259765625}, {"start": 2990.85, "end": 2991.03, "word": " فيها", "probability": 0.9462890625}, {"start": 2991.03, "end": 2991.39, "word": " بسرعة", "probability": 0.9188232421875}, {"start": 2991.39, "end": 2991.59, "word": " يعني", "probability": 0.66552734375}, {"start": 2991.59, "end": 2991.71, "word": " ان", "probability": 0.6767578125}, {"start": 2991.71, "end": 2991.87, "word": " شاء", "probability": 0.987060546875}, {"start": 2991.87, "end": 2991.99, "word": " الله", "probability": 0.9521484375}, {"start": 2991.99, "end": 2992.27, "word": " يالا", "probability": 0.5030110677083334}, {"start": 2992.27, "end": 2992.53, "word": " يعطيكوا", "probability": 0.8529296875}, {"start": 2992.53, "end": 2992.81, "word": " العافية", "probability": 0.9166666666666666}, {"start": 2992.81, "end": 2993.13, "word": " وبركة", "probability": 0.8118896484375}, {"start": 2993.13, "end": 2993.21, "word": " الله", "probability": 0.80322265625}, {"start": 2993.21, "end": 2993.41, "word": " فيكم", "probability": 0.85986328125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2994.724, "duration_after_vad": 2896.0137499999864}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..19a754477544d215be67937d1d3cfa68b323b265
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yPkm4oT3FlY_raw.srt
@@ -0,0 +1,2644 @@
+1
+00:00:20,670 --> 00:00:22,930
+بسم الله الرحمن الرحيم والصلاة والسلام علي أشرف
+
+2
+00:00:22,930 --> 00:00:25,290
+الأنبياء والمرسلين سيدنا محمد وعلى آله وصحابي
+
+3
+00:00:25,290 --> 00:00:29,870
+أجمعين نكمل اليوم في ال set operations وناخد شوية
+
+4
+00:00:29,870 --> 00:00:35,130
+operators جديدة وشوية functions ونشوف شوية حاجات
+
+5
+00:00:35,130 --> 00:00:38,570
+إضافية على موضوع ال sets اللي كنا بدأنا فيه المرة
+
+6
+00:00:38,570 --> 00:00:42,230
+السابقة فبنتكلم عن ال disjoint أو ال disjointed
+
+7
+00:00:42,230 --> 00:00:49,030
+less اللي هي التفكك أو عدم التقاطعاللي هو ان ال
+
+8
+00:00:49,030 --> 00:00:52,090
+sets لايوجد بينهم اي تقاطع فهد امتى بنقدر نقول
+
+9
+00:00:52,090 --> 00:00:55,870
+الكلام هد اذا كان عندنا two sets a and b بنسميهم
+
+10
+00:00:55,870 --> 00:00:59,850
+disjoint او unjointed if and only if their
+
+11
+00:00:59,850 --> 00:01:04,790
+intersection is empty بمعنى انه a intersection b
+
+12
+00:01:04,790 --> 00:01:11,570
+equal to ايش؟ to set five ففي الحالة هد بنقدر نقول
+
+13
+00:01:11,570 --> 00:01:16,790
+ان هم disjoint من الحاجات المشهورة جدا لو قولنا ال
+
+14
+00:01:16,790 --> 00:01:23,170
+setاللي بتحتوي على ال odd integers واضح إن هي مع
+
+15
+00:01:23,170 --> 00:01:27,610
+ال even integers disjointed لإن مافيش أي علاقة
+
+16
+00:01:27,610 --> 00:01:30,790
+بينهم مستحيل تلاقوا element موجود في ال odd وموجود
+
+17
+00:01:30,790 --> 00:01:37,050
+في ال even sets كويس فهذه الأمور واضحة مش فيها
+
+18
+00:01:37,050 --> 00:01:41,030
+مشكلة هذه بتخلينا نصل أو نرجع رجوع شوية لل union
+
+19
+00:01:41,030 --> 00:01:44,130
+اللي أخدناها المرة اللي فاتت عشان نتكلم عن ال
+
+20
+00:01:44,130 --> 00:01:50,250
+inclusion و ال exclusion principleفي جزئية ال
+
+21
+00:01:50,250 --> 00:01:53,870
+union لما اتكلمنا عن ال union وعرفناها ان هي
+
+22
+00:01:53,870 --> 00:01:56,410
+مجموعة ال elements اللي موجودة في ال two sets مع
+
+23
+00:01:56,410 --> 00:02:01,090
+بعض يعني لازم تكون موجودة في ال set A او set B
+
+24
+00:02:01,090 --> 00:02:04,250
+معناه ذلك ان انا جمعت كل ال elements اللي موجودة
+
+25
+00:02:04,250 --> 00:02:07,630
+في ال two sets طبعا طيب لما ننشط نتكلم عن ال
+
+26
+00:02:07,630 --> 00:02:09,810
+cardinality و المرة اللي فاتت قلنا ايش يعني
+
+27
+00:02:09,810 --> 00:02:12,870
+cardinality قلنا ان هي عدد ال elements داخل ال set
+
+28
+00:02:12,870 --> 00:02:18,250
+فإذا لما اقولها لوجد cardinality ل A union Bهي
+
+29
+00:02:18,250 --> 00:02:21,290
+فعليا by logic أن هي العناصر اللي موجودة في A
+
+30
+00:02:21,290 --> 00:02:24,910
+والعناصر اللي موجودة في B فإذا ال cardinality ل A
+
+31
+00:02:24,910 --> 00:02:29,130
+زائد ال cardinality اللي موجودة في B بس ناخد بالنا
+
+32
+00:02:29,130 --> 00:02:33,870
+أنه في exclusion لازم نعمل لمين لل intersection
+
+33
+00:02:33,870 --> 00:02:37,050
+ليش لل intersection لأن ال intersection هنا هيتكرر
+
+34
+00:02:37,050 --> 00:02:42,070
+معاكم هيتكرر معاكم for example لو قلنا عندنا واحد
+
+35
+00:02:42,070 --> 00:02:48,730
+اتنين تلاتة هذه ستة Aو هنقول إن في عندنا ستة تانية
+
+36
+00:02:48,730 --> 00:02:55,890
+تلاتة أربعة خمسة هذه B لو بدنا نقول ال cardinality
+
+37
+00:02:55,890 --> 00:03:03,810
+ل A union B بعد ما نحسبها هنحسبها كالتالي إن كل
+
+38
+00:03:03,810 --> 00:03:10,450
+عناصر A مع كل عناصر B طيب عناصر A فعليا واحد اتنين
+
+39
+00:03:10,450 --> 00:03:17,500
+تلاتة عناصر B تلاتة أربعة خمسةلحظوا إنه إذا بدّي
+
+40
+00:03:17,500 --> 00:03:20,900
+أشباحهم بهذا الشكل هتطلع واحد، اتنين، تلاتة،
+
+41
+00:03:20,900 --> 00:03:26,400
+أربعة، خمسة، ستة، هتطلع ستة طيب فإذا هذا بيساوي ال
+
+42
+00:03:26,400 --> 00:03:31,120
+cardinality ل A اللي هي تساوي تلاتة plus
+
+43
+00:03:31,120 --> 00:03:36,360
+cardinality ب تلاتة هذا بيساوي الستة بس هذا مش صح
+
+44
+00:03:36,360 --> 00:03:41,200
+هذا مش صح لأنه فعليا ال A union B لا تحتوي على ست
+
+45
+00:03:41,200 --> 00:03:45,350
+عناصر أو six elementsفي element مشترك طب إيش اللي
+
+46
+00:03:45,350 --> 00:03:48,510
+بيميز ال element المشترك هذا عشان نشيله أن هو ال
+
+47
+00:03:48,510 --> 00:03:55,270
+intersection تبعهم فإذا minus ال intersection a و
+
+48
+00:03:55,270 --> 00:03:58,690
+b طب a و b وين ال intersection تبعتهم اللي هي
+
+49
+00:03:58,690 --> 00:04:05,150
+تلاتة هذا تمثل ست تحتوي على العنصر تلاتة فجدش ال
+
+50
+00:04:05,150 --> 00:04:09,310
+cardinality بتاعتها واحد فإذا هذا المفروض تكون ستة
+
+51
+00:04:09,310 --> 00:04:15,240
+ناقص واحدخمسة okay خمسة بتصير صح لأنه المفروض أنه
+
+52
+00:04:15,240 --> 00:04:19,380
+عندنا عنصر واحد فقط للتلاتة اذا واحد اتنين تلاتة
+
+53
+00:04:19,380 --> 00:04:26,780
+اربعة خمسة هو الصح هو الإجابة الصحية طيب خليني
+
+54
+00:04:26,780 --> 00:04:30,620
+اقول for example how many students are on our
+
+55
+00:04:30,620 --> 00:04:34,740
+class email list جداش عدد الطلاب اللي موجودين في
+
+56
+00:04:34,740 --> 00:04:38,770
+ال email list اللي موجود عندى الطلاب والطالباتأنا
+
+57
+00:04:38,770 --> 00:04:43,490
+بقدر أستقيهم هدولة من وين؟ من مصدرين، إما إن أقول
+
+58
+00:04:43,490 --> 00:04:48,070
+والله هم ال emails اللي واصليني من ال information
+
+59
+00:04:48,070 --> 00:04:51,030
+sheet، هقول والله واصليني من ال model، دخلت على ال
+
+60
+00:04:51,030 --> 00:04:52,850
+model، اللي مسجل منكوا ال model أنا عارف ال email
+
+61
+00:04:52,850 --> 00:04:56,490
+تبعه، بمجرد ما أنتوا سجلتوا ال model معلوماتكم
+
+62
+00:04:56,490 --> 00:05:00,570
+معظمها عنديفبعرف ال email تبعكم، كويس، ليش؟ لأن
+
+63
+00:05:00,570 --> 00:05:03,630
+ممكن أبعد email لكل المجموع اللي موجود عنده، إن
+
+64
+00:05:03,630 --> 00:05:07,010
+والله في موقع امتحان، في موقع كذا، في إشي بقدر من
+
+65
+00:05:07,010 --> 00:05:10,030
+عندي أتواصل معاكم، هدول مجموعة، طيب، هل كل
+
+66
+00:05:10,030 --> 00:05:13,370
+المسجلين المصاق موجودين عنده على ال model؟ يمكن مش
+
+67
+00:05:13,370 --> 00:05:16,850
+بالضروري كلهممش بالضروري كلهم طيب في نفس الوجد في
+
+68
+00:05:16,850 --> 00:05:19,850
+عندي مصدر آخر هدى هنسميها I اللى هو تعوين ال
+
+69
+00:05:19,850 --> 00:05:24,570
+information sheet اللى هم I عبارة عن set of S ال S
+
+70
+00:05:24,570 --> 00:05:26,930
+هدى من وين جايين ال students هدوله جايين من ال
+
+71
+00:05:26,930 --> 00:05:31,350
+information sheet طيب عندي مصدر آخر اللى هو ال
+
+72
+00:05:31,350 --> 00:05:35,490
+mail نفسه ال email نفسه مين اللى بعتلى email فممكن
+
+73
+00:05:35,490 --> 00:05:38,030
+يكونوا مجموعة ال students اللى بعتوا ل teaching
+
+74
+00:05:38,030 --> 00:05:42,740
+assistantemails فانا هروح اقول للمناس تبعتكم مين
+
+75
+00:05:42,740 --> 00:05:46,480
+اللي بعتلك emails عندك كشوف بدرجات ان البنات اللي
+
+76
+00:05:46,480 --> 00:05:48,600
+بعتولك اه هتقولي والله في بنتين بعتولي كانوا
+
+77
+00:05:48,600 --> 00:05:52,000
+بيسألوا عن كذا هاخد منها القائمة اللي عندها فصار
+
+78
+00:05:52,000 --> 00:05:55,240
+عندى قائمتين القائمتين هدولة منهم بدي احد اتجدش
+
+79
+00:05:55,240 --> 00:05:58,940
+عدد ال emails اللي اتحوشوا عندى اتجدش عدد ال
+
+80
+00:05:58,940 --> 00:06:01,720
+emails اللي اتحوشوا عندى كيف بدي اعملها بدي اعملها
+
+81
+00:06:01,720 --> 00:06:06,870
+على اساس ان هي ال union بتاعة Iunion m وبشوف ال
+
+82
+00:06:06,870 --> 00:06:09,250
+cardinality بتاعك تبجيب عدد الطلاب اللي انا عندي
+
+83
+00:06:09,250 --> 00:06:14,180
+ال email تبعهم اللي عندنا email هم صحيح تمامهدول
+
+84
+00:06:14,180 --> 00:06:16,840
+من وين بتجيب ال cardinality؟ عدد الطلاب اللي أنا
+
+85
+00:06:16,840 --> 00:06:20,740
+جبتهم عن طريق ال model زائد عدد الطلاب اللي أصلا
+
+86
+00:06:20,740 --> 00:06:23,900
+بعتولنا email فاحنا شفنا ال email اللي مابعتلنا
+
+87
+00:06:23,900 --> 00:06:26,140
+إما أنه بعتولنا يقولولنا و الله عندنا مشكلة في ال
+
+88
+00:06:26,140 --> 00:06:29,580
+model أو بعتولنا يقولولي احنا أخدنا ال homework
+
+89
+00:06:29,580 --> 00:06:32,380
+اللي على صفحتك ماخدناش اللي على ال model إيش نسوي
+
+90
+00:06:32,380 --> 00:06:35,640
+أو بعتولنا و الله إيش الكتاب اللي بنشتغل منه المهم
+
+91
+00:06:35,640 --> 00:06:38,340
+لا أي استفسار لا أي حاجة لا أي معلومة بعتولنا
+
+92
+00:06:38,340 --> 00:06:42,260
+email أخدناها من ال email list اللي موجودة كويس
+
+93
+00:06:42,260 --> 00:06:46,030
+هدول اللي هم ال cardinalityطب ناخد بالنا ما هو
+
+94
+00:06:46,030 --> 00:06:48,710
+ممكن اللي بعتولي بال emails هم نفسهم موجودين على
+
+95
+00:06:48,710 --> 00:06:51,970
+ال model موجودين في ال information sheet صحيح؟
+
+96
+00:06:51,970 --> 00:06:54,930
+معنى ذلك إذا بدي أجمحهم هدول و هدول مباشرة أنا في
+
+97
+00:06:54,930 --> 00:06:58,630
+ناس عديتهم مرتين هيك في ناس عديناهم مرتين فلازم
+
+98
+00:06:58,630 --> 00:07:02,630
+نطرح ال intersection تبعهم لازم نطرح ال
+
+99
+00:07:02,630 --> 00:07:04,830
+intersection تبعهم ال intersection طبعا أنا بكون
+
+100
+00:07:04,830 --> 00:07:08,010
+حسبته مرة واحدة يعني العنصر بكون عديته مرة واحدة
+
+101
+00:07:08,010 --> 00:07:12,870
+هنا هنكون عديناه مرتينبنخصم المرة من المرتين بيظل
+
+102
+00:07:12,870 --> 00:07:17,430
+المرة معدود فبكون كل element عدنا فقط مرة واحدة بس
+
+103
+00:07:17,430 --> 00:07:21,010
+وهو ده المطلوب برغم أنه اتكرر في ال two lasts بس
+
+104
+00:07:21,010 --> 00:07:24,510
+أنا عدته مرة واحدةفهذه مهمة جدا لما تيجوا ينطلب
+
+105
+00:07:24,510 --> 00:07:27,310
+منكوا ال cardinality لل union خدوا بالكوا من ال
+
+106
+00:07:27,310 --> 00:07:30,230
+intersection بتاعته ال two sets هذول تاخدوا بالكوا
+
+107
+00:07:30,230 --> 00:07:33,990
+من ال intersection طيب ال set difference ال set
+
+108
+00:07:33,990 --> 00:07:36,290
+difference احنا هم نتكلم عن two sets و بدنا نجيب
+
+109
+00:07:36,290 --> 00:07:39,010
+ال difference between them انه انقول ال difference
+
+110
+00:07:39,010 --> 00:07:43,290
+of a and b كأنه بقول a minus b هذه عبارة عن ال
+
+111
+00:07:43,290 --> 00:07:47,410
+elements اللي موجودة في a و غير موجودة في bهذه
+
+112
+00:07:47,410 --> 00:07:52,370
+معناها انا بتكلم عن كل عنصر موجود في a و غير موجود
+
+113
+00:07:52,370 --> 00:07:58,610
+في b هو ناتج ل a minus b فإذا هي set of x و x such
+
+114
+00:07:58,610 --> 00:08:01,710
+that او ال condition ل x ايش اللي لازم يتحقق ل x
+
+115
+00:08:01,710 --> 00:08:06,890
+ان x belong to a and x not belong to mean to b هذه
+
+116
+00:08:06,890 --> 00:08:11,250
+معناها negation x belong to a implies x belong to
+
+117
+00:08:11,250 --> 00:08:17,570
+b خلينا ننسى اللي فات هذي ايش معناها ان اذا xتنتمي
+
+118
+00:08:17,570 --> 00:08:21,830
+ل a then هي تنتمي ل b لأ إحنا بدنا ننفيها إذا x
+
+119
+00:08:21,830 --> 00:08:25,850
+تنتمي ل a لا تنتمي ل b نعكس ال implication فهنقول
+
+120
+00:08:25,850 --> 00:08:29,770
+negation جابلها هنحط لها negation فإما هذه أو هذه
+
+121
+00:08:29,770 --> 00:08:33,750
+بتعبر عن a minus b أحيانا بنسميها complement of b
+
+122
+00:08:33,750 --> 00:08:39,270
+with respect to a with respect to a فأنا كأني بقول
+
+123
+00:08:39,270 --> 00:08:46,410
+بدي أجيب المكمل ل b بالنسبة لمين ل a بالنسبة ل a
+
+124
+00:08:47,260 --> 00:08:52,100
+هذه هناخدها لما نجي نتكلم حاليا .. لاحقا عن a
+
+125
+00:08:52,100 --> 00:08:55,540
+محددة ال a هذه هنسميها universe of discourse فضاء
+
+126
+00:08:55,540 --> 00:08:59,600
+العينة و نبدأ نعمل complement داخلها هنشوفها في ال
+
+127
+00:08:59,600 --> 00:09:02,820
+slide الجاية بس ناخدلنا أكام من مثال على ال
+
+128
+00:09:02,820 --> 00:09:07,700
+difference أو ال set difference لو قلنا عندنا two
+
+129
+00:09:07,700 --> 00:09:10,420
+sets بدنا نجيب ال difference between them الأولى
+
+130
+00:09:10,420 --> 00:09:13,260
+من واحد لستة التانية الأعداد
+
+131
+00:09:16,350 --> 00:09:20,270
+لأ مش الأولية لإن في عندك تسعة لسه فإتنين تلاتة
+
+132
+00:09:20,270 --> 00:09:26,030
+خمسة سبعة تسعة احداشر من واحد لستة minus الست اللي
+
+133
+00:09:26,030 --> 00:09:29,950
+عرفناها إيش بدنا نسوي بدنا ندور على ال element
+
+134
+00:09:29,950 --> 00:09:32,770
+اللي موجود في الأولى و غير موجود في التانية خليني
+
+135
+00:09:32,770 --> 00:09:38,010
+أمسكهم واحد واحد الواحد بمشي الحالة الإتنين لأ
+
+136
+00:09:38,010 --> 00:09:45,330
+الإتنين موجودة فهذه بشيلها تلاتة موجودة بنشيلهاطيب
+
+137
+00:09:45,330 --> 00:09:49,010
+الأربعة .. الأربعة مش موجودة okay هذا بدنا نحسبها
+
+138
+00:09:49,010 --> 00:09:54,510
+الخامسة موجودة بنشيلها ستة غير موجودة فإذا صار
+
+139
+00:09:54,510 --> 00:10:00,230
+عندك واحد أربعة وستة هم هدولة ناتج ال difference
+
+140
+00:10:00,230 --> 00:10:06,170
+اللي بنتكلم عنه تمام فبتصير عندنا واحد أربعة ستة
+
+141
+00:10:06,170 --> 00:10:11,470
+واحد أربعة ستة طيب example تاني ل infinite sets لو
+
+142
+00:10:11,470 --> 00:10:16,140
+قلنا z minus nالـ integers minus الـ natural
+
+143
+00:10:16,140 --> 00:10:21,340
+numbers ايش بيعطينا؟ هيعطينا الـ negative integers
+
+144
+00:10:21,340 --> 00:10:24,780
+هيعطينا الـ negative integers بالظبط أو هيكون كتار
+
+145
+00:10:24,780 --> 00:10:28,780
+من minus infinity to infinity minus من صفر to
+
+146
+00:10:28,780 --> 00:10:33,340
+infinity كويس، هذه عبارة عن set of x such that x
+
+147
+00:10:33,340 --> 00:10:38,140
+is an integer but not a natural number أو هي عبارة
+
+148
+00:10:38,140 --> 00:10:43,150
+عن set of xو X ايش الشرط تبعها ان هي negative
+
+149
+00:10:43,150 --> 00:10:46,230
+integer تمام او نقدر نمثلها من minus infinity
+
+150
+00:10:46,230 --> 00:10:50,470
+بالنقطة دولة معناته من ال minus infinity to minus
+
+151
+00:10:50,470 --> 00:10:56,590
+one فانا بتكلم عن ال negative integer number okay
+
+152
+00:10:56,590 --> 00:11:00,970
+بال .. بال Venn diagram كيف نقدر نمثلها؟ بنمثلها
+
+153
+00:11:00,970 --> 00:11:06,870
+انه هي عبارة عن ال 6A مطروح منها ال intersection
+
+154
+00:11:08,700 --> 00:11:11,280
+مطروح منها ال intersection ليش؟ عشان أضمن إن هي
+
+155
+00:11:11,280 --> 00:11:16,120
+موجودة في A و غير موجودة في B موجودة في A و غير
+
+156
+00:11:16,120 --> 00:11:22,600
+موجودة في B فكأنه هنا B أكلت أو قضمت من Aجزء
+
+157
+00:11:22,600 --> 00:11:26,720
+التقاطع كأنه خصمت منها جزء التقاطع أو أخدت منها
+
+158
+00:11:26,720 --> 00:11:31,200
+جزء التقاطع فهي بيظل ال 6 تمثيلا بال Venn Diagram
+
+159
+00:11:31,200 --> 00:11:34,320
+بيكون ال 6 اللي ضايلة او ال 6 اللي بنقدر نعرفها a
+
+160
+00:11:34,320 --> 00:11:38,800
+minus b فهذه بتكون كأنها أكلت منها طيب ال
+
+161
+00:11:38,800 --> 00:11:41,980
+compliment نشتر على ال compliment علشان نشتر على
+
+162
+00:11:41,980 --> 00:11:44,560
+ال compliment لازم يكون واضح عند ال universe of
+
+163
+00:11:44,560 --> 00:11:47,560
+discourse الشيء ال universe of discourse بتاعتنا
+
+164
+00:11:47,560 --> 00:11:49,860
+فال universe of discourse بتاعتنا هنا هنقول أن هي
+
+165
+00:11:49,860 --> 00:11:50,180
+ال U
+
+166
+00:11:53,480 --> 00:11:56,960
+كويس؟ هنسميها you فبصير واضح لازم يكون طبعا في ال
+
+167
+00:11:56,960 --> 00:12:01,380
+context تبعنا واضح بشكل معرف أو معرف بشكل واضح ال
+
+168
+00:12:01,380 --> 00:12:04,020
+you بتاعتكم اللي هي ال universe of discourse انتوا
+
+169
+00:12:04,020 --> 00:12:07,820
+بتتكلموا عن فضع عينة مين بالظبط عشان لما أحدد ست
+
+170
+00:12:07,820 --> 00:12:11,280
+وبدي أعمل ال compliment داخلها أكون عارف أنا بعمل
+
+171
+00:12:11,280 --> 00:12:16,280
+with respect to إيش فلازم لما بجيب ال compliment ل
+
+172
+00:12:16,280 --> 00:12:21,620
+awith respect to you فلازم يكون محدد أصلا you و
+
+173
+00:12:21,620 --> 00:12:25,780
+معرف you بتاعتنا، كويس فهنا بنقدر نقول ان a لازم
+
+174
+00:12:25,780 --> 00:12:29,360
+تكون subset من you هي جزء من you عشان نجيب لها
+
+175
+00:12:29,360 --> 00:12:32,960
+compliment with respect to you with respect to you
+
+176
+00:12:32,960 --> 00:12:36,900
+the compliment of a هتكون عبارة عن ايش؟ a bar
+
+177
+00:12:36,900 --> 00:12:42,440
+بنسميها او a compliment a بنعملها علامة bar وبنكمل
+
+178
+00:12:42,440 --> 00:12:44,520
+عليها، ايه كويس في الحالة هذي بتكون عبارة عن
+
+179
+00:12:44,520 --> 00:12:49,380
+compliment a with respect to youA with respect to
+
+180
+00:12:49,380 --> 00:12:52,060
+U لازم تكون معرفين أصلا U بطريقة جيدة من الأساس
+
+181
+00:12:52,060 --> 00:12:54,680
+معرفين ال universe of discourse أو فضاء العينة
+
+182
+00:12:54,680 --> 00:12:59,900
+اللي بتحكوا عنه كويسة هنا بنكتبها U minus Aهي
+
+183
+00:12:59,900 --> 00:13:04,600
+عبارة عن u minus a فهي فعلا لو جينا عرفنا كمان مرة
+
+184
+00:13:04,600 --> 00:13:07,500
+ال difference اللي اتكلمنا عنه كل عنصر موجود في u
+
+185
+00:13:07,500 --> 00:13:10,620
+و غير موجود في a فهو ال complement ل a with
+
+186
+00:13:10,620 --> 00:13:14,720
+respect to u with respect to u for example لو
+
+187
+00:13:14,720 --> 00:13:17,500
+أخدنا ال u او ال universe of discourse بتاعتنا
+
+188
+00:13:17,500 --> 00:13:22,160
+natural number من صفر to infinity وقولنا بدنا ال
+
+189
+00:13:22,160 --> 00:13:29,790
+complement ل 6 3 5 فبنكتبها 6 3 5 complementبنحط
+
+190
+00:13:29,790 --> 00:13:33,510
+لها الbar هذي equal لإيش كل ال natural numbers بلا
+
+191
+00:13:33,510 --> 00:13:38,170
+استثناء باستثناء بس العنصرين هدول اللي موجودين في
+
+192
+00:13:38,170 --> 00:13:42,810
+ال A أو اللي هي التلاتة أو الخمسة فبنكتب صفر واحد
+
+193
+00:13:42,810 --> 00:13:48,690
+اتنين تلاتة لأ اربعة خمسة لأ طيب لو قلنا ال U
+
+194
+00:13:48,690 --> 00:13:51,750
+عندنا هنا جدلة نقولنا لأ ال U تبعتنا احنا معرفينها
+
+195
+00:13:51,750 --> 00:13:57,850
+عساس ان هي ال positive integers اقل من عشرةأقل من
+
+196
+00:13:57,850 --> 00:14:00,990
+عشرة في الحالة هذه هيكون ال set او ال compliment
+
+197
+00:14:00,990 --> 00:14:06,890
+بتاعتنا ايش واحد integer و positive integer مافيهم
+
+198
+00:14:06,890 --> 00:14:09,990
+صفر فعشانك لازم تكون ال u معرفة عننا عارفين ال
+
+199
+00:14:09,990 --> 00:14:13,810
+shia ال u بتاعتنا فتكون واحد اتنين تلتة لأ اربعة
+
+200
+00:14:13,810 --> 00:14:20,470
+ستة سبعة تمانية تسعة و بنسكر القصة تبعنا خلاص أنا
+
+201
+00:14:20,470 --> 00:14:24,370
+عارف ال universe of discourse تبعتيفاحنا ناخد بنا
+
+202
+00:14:24,370 --> 00:14:30,530
+with respect to إيش؟ لست اللي بدنا نطرح منها ال
+
+203
+00:14:30,530 --> 00:14:32,190
+إيه؟
+
+204
+00:14:37,030 --> 00:14:39,970
+كمان مرة بنعرفه A complement على اساس ان هو set of
+
+205
+00:14:39,970 --> 00:14:44,170
+X و X not belong to mean to A فإذا لو عندنا A بال
+
+206
+00:14:44,170 --> 00:14:48,690
+Venn .. بال Venn diagram A بالشكل هذا هنشيلها و
+
+207
+00:14:48,690 --> 00:14:52,850
+الباقي هو ال complement ل A هو ال complement ل A
+
+208
+00:14:52,850 --> 00:14:58,730
+هذه غير موجودة هذه غير موجودة هذه فاضية فإذا كل
+
+209
+00:14:58,730 --> 00:15:04,010
+اللون الأخضر هذا هو ال A ال A complement تمام ناخد
+
+210
+00:15:04,010 --> 00:15:10,150
+شوية setidentities او شوية rules شوية rules من ال
+
+211
+00:15:10,150 --> 00:15:14,430
+rules هذه المحايد اول شغل كنا ناخدها دايما في ال
+
+212
+00:15:14,430 --> 00:15:17,350
+rules ساعتنا اللي هو المحايد المحايد سواء لل union
+
+213
+00:15:17,350 --> 00:15:20,030
+او لل intersection لل union او لل ايش لل
+
+214
+00:15:20,030 --> 00:15:22,490
+intersection زي المحايد الجمعي و المحايد الضربي في
+
+215
+00:15:22,490 --> 00:15:25,310
+الأرقام في ال .. في ال .. في ال numbers هنا برضه
+
+216
+00:15:25,310 --> 00:15:31,970
+نفس الكلام a union phi a ماأثرتش طيب a
+
+217
+00:15:31,970 --> 00:15:36,510
+intersection uA هدا intersection و احنا عارفين ان
+
+218
+00:15:36,510 --> 00:15:40,650
+ال A subset of U لان ال U هنا universe of
+
+219
+00:15:40,650 --> 00:15:46,030
+discourse الفضاء كله فضاء العينة كله طيب بالعكس
+
+220
+00:15:46,030 --> 00:15:49,290
+لما تيجوا تعملوا ضرب في الصفر مثلا عملية الضرب
+
+221
+00:15:49,290 --> 00:15:52,110
+بتخلف عن عملية الجامعة عملية الجامعة كان محايد بس
+
+222
+00:15:52,110 --> 00:15:56,330
+في الضرب مهيمن ليش؟ لان أيش بتضربوا فيه هيحاول
+
+223
+00:15:56,330 --> 00:16:02,060
+كوية صفر هيتحول ليش؟ ل zero زيA intersection Phi
+
+224
+00:16:02,060 --> 00:16:07,460
+هيطلع Phi طيب نفس الكلام A union U أي اش اتحاد مع
+
+225
+00:16:07,460 --> 00:16:10,820
+ال universe of discourse كلها هي نفسها هتظل مش
+
+226
+00:16:10,820 --> 00:16:14,100
+هيأثر فيها فهتظل universe of discourse طيب
+
+227
+00:16:14,100 --> 00:16:19,520
+العمليات على نفس ال set ال set على نفسها ف set
+
+228
+00:16:19,520 --> 00:16:24,900
+union A هي نفسها ال set intersection مع نفسهاهي
+
+229
+00:16:24,900 --> 00:16:28,520
+نفسها ال a نفسها ف a intersection مع نفسها او
+
+230
+00:16:28,520 --> 00:16:33,580
+union مع نفسها هي هي اي set مش بدلول اي set مع
+
+231
+00:16:33,580 --> 00:16:40,220
+نفسها بتأثرش طيب ال double complement نفسها مكمل
+
+232
+00:16:40,220 --> 00:16:45,140
+المكمل هو نفسه رجعنا لل a فإذا مكمل مكمل ال a هي
+
+233
+00:16:45,140 --> 00:16:53,540
+نفسها ال a ال computative او تبديل a union b هي
+
+234
+00:16:53,540 --> 00:16:57,830
+نفس b union aنفس الكلام بالنسبة لل intersection A
+
+235
+00:16:57,830 --> 00:17:02,510
+intersection B هي نفسها B intersection A مش هتفرج
+
+236
+00:17:02,510 --> 00:17:09,830
+معناه كتير كويس ال associative A union B union C
+
+237
+00:17:09,830 --> 00:17:13,250
+مين جاب التاني بتفرجش مدام أنا بتعامل مع نفس ال
+
+238
+00:17:13,250 --> 00:17:17,530
+operator مع U هنا U و هنا U انتوا بتتعاملوا مع نفس
+
+239
+00:17:17,530 --> 00:17:21,550
+ال operator مين جاب المين ماتفرجش معناه طيبفممكن
+
+240
+00:17:21,550 --> 00:17:27,110
+اقول A مع B في الأول و بعدين الناتج مع C فليكن ال
+
+241
+00:17:27,110 --> 00:17:29,690
+intersection نفس الجثة نفس الكلام بس خدوا بأكوا
+
+242
+00:17:29,690 --> 00:17:32,850
+انه intersection مع intersection مايكونش في واحدة
+
+243
+00:17:32,850 --> 00:17:36,850
+intersection و واحدة unionمع بعض لأ مدام نفس ال
+
+244
+00:17:36,850 --> 00:17:42,190
+operator الكلام صحيح و ال associative تحققت دي
+
+245
+00:17:42,190 --> 00:17:46,030
+مورغان ورانا ورانا هيعطينا برضه نفس القانون اللي
+
+246
+00:17:46,030 --> 00:17:49,010
+عمله لل negation في ال proposition هيعطينا يا برضه
+
+247
+00:17:49,010 --> 00:17:52,510
+لل set بس let me ال compliment فبقول ال compliment
+
+248
+00:17:52,510 --> 00:17:57,150
+ل a union b تساوي a compliment intersection b
+
+249
+00:17:57,150 --> 00:18:00,850
+compliment تمام؟ كويس نفس الكلام في ال
+
+250
+00:18:00,850 --> 00:18:05,390
+intersectionال complement لل A intersection B هي
+
+251
+00:18:05,390 --> 00:18:09,730
+نفس ال complement A union complement لحظة عكسناها
+
+252
+00:18:09,730 --> 00:18:13,870
+بنعكسها و بنوزع ال complement جوا نفس اللي كنا
+
+253
+00:18:13,870 --> 00:18:16,650
+بنعمله في ال negation نفس كلام ال negation هو هو
+
+254
+00:18:16,650 --> 00:18:21,450
+طيب بعد ما قولنا الكلام هذا بدنا نعمل proving ل ال
+
+255
+00:18:21,450 --> 00:18:25,470
+set identities امتى بقول ان ال set او two sets
+
+256
+00:18:25,470 --> 00:18:29,600
+بيسوا بعض equivalent ل بعض identities مع بعضأمتى
+
+257
+00:18:29,600 --> 00:18:31,760
+بقدر أقول إن ال set هذه تساوي ال set هذه؟ في
+
+258
+00:18:31,760 --> 00:18:34,640
+الحقيقة عندنا three strategies أو three methods
+
+259
+00:18:34,640 --> 00:18:38,960
+نستخدمها الطريقة الأولى إن أنا أستعمل ال subset و
+
+260
+00:18:38,960 --> 00:18:43,820
+بنسميها mutual subset ال subset المتبادل يعني لو
+
+261
+00:18:43,820 --> 00:18:48,320
+قلنا المجموعة الأولى subset من المجموعة التانية و
+
+262
+00:18:48,320 --> 00:18:50,600
+المجموعة التانية برضه subset من المجموعة الأولى
+
+263
+00:18:50,600 --> 00:18:57,500
+فإنها متساويات بمعنى إنهE1 هي subset من E2 و هي
+
+264
+00:18:57,500 --> 00:19:01,940
+superset of E2 فهي subset و superset في نفس الوجد
+
+265
+00:19:01,940 --> 00:19:06,400
+معناته تساويها، مظبوط؟ هذا إذا كدرنا نثبت الكلام
+
+266
+00:19:06,400 --> 00:19:10,480
+هذا، بكون أثبت أن E1 و E2 equivalent أو
+
+267
+00:19:10,480 --> 00:19:14,800
+identities، كويس الطريقة التانية باستخدام ال
+
+268
+00:19:14,800 --> 00:19:17,760
+builder notation و بنعمل عليها ال logical
+
+269
+00:19:17,760 --> 00:19:21,740
+equivalence القوانين اللي توا اتكلمنا عنهابنحددها
+
+270
+00:19:21,740 --> 00:19:25,800
+بنكتبها as a builder notation تعريف بين أقواس
+
+271
+00:19:25,800 --> 00:19:29,640
+بنقول set of x و بنحط ال condition تبعناها such
+
+272
+00:19:29,640 --> 00:19:32,960
+that x equal to h و بعدين بنبدأ نشتغل على القوانين
+
+273
+00:19:32,960 --> 00:19:35,700
+اللي طوى اشتغلناها اللي طوى لسه صردناها و قولناها
+
+274
+00:19:35,700 --> 00:19:39,500
+كويس و بنثبت الإثبات اللي بيكون مطلوب منها النوع
+
+275
+00:19:39,500 --> 00:19:43,780
+التالت use a membership table truth table الذاكرين
+
+276
+00:19:43,780 --> 00:19:47,840
+truth table بنشتغله هو هو نفسه بنشتغله هذا برضه
+
+277
+00:19:47,840 --> 00:19:53,670
+طريقةطريقة تالتة و بشوف ايش ال columns تبعتنا اللي
+
+278
+00:19:53,670 --> 00:19:59,230
+ممكن نشتغل عليها طيب ناخد اول طريقة اللي هو ال
+
+279
+00:19:59,230 --> 00:20:03,230
+mutual subset mutual subset و ناخد example و اوضح
+
+280
+00:20:03,230 --> 00:20:06,470
+لنا الموضوع خلاص احنا متفقين ان كل اللي بديه ان ال
+
+281
+00:20:06,470 --> 00:20:10,930
+two expressions اللي هيكون معاكم معاهم ال two
+
+282
+00:20:10,930 --> 00:20:17,610
+compound set هنا تساوي المساوي لل set اللي هناكيف؟
+
+283
+00:20:17,610 --> 00:20:21,830
+إذا كانت الأولى subset من التانية و التانية subset
+
+284
+00:20:21,830 --> 00:20:25,050
+من الأولى فبنمسكهم واحدة واحدة و بدنا نعمل أول
+
+285
+00:20:25,050 --> 00:20:30,310
+إثبات إن الأولى subset من التانية بمعنى إن أي عنصر
+
+286
+00:20:30,310 --> 00:20:37,210
+ينتمي للست هذه ككل هو لازم ينتمي للست التانية
+
+287
+00:20:37,210 --> 00:20:40,690
+بالضرورة لازم ينتمي للست التانية كويس، بنكون خلصنا
+
+288
+00:20:40,690 --> 00:20:44,630
+أول جزء الجزء التاني إن أي عنصر ينتمي للست التانية
+
+289
+00:20:44,630 --> 00:20:48,100
+بالضرورة لازم ينتمي للست الأولىإذا أثبتنا
+
+290
+00:20:48,100 --> 00:20:51,180
+الطريقتين هدولة، بنكون أثبتنا إن الاتين equivalent
+
+291
+00:20:51,180 --> 00:20:54,780
+لبعض أو كل واحدة منهم equivalent للتانية نبدأ بأول
+
+292
+00:20:54,780 --> 00:21:00,680
+جزء إنه الأولى subset للتانية فبدنا عنصر نفترض إن
+
+293
+00:21:00,680 --> 00:21:05,620
+هو belong to set number one ومنه أحاول أثبت إن هو
+
+294
+00:21:05,620 --> 00:21:10,120
+لازم بالضرورة يكون موجود في إيش أو belong to set
+
+295
+00:21:10,120 --> 00:21:15,280
+number two هنقول إنه X ف X belong لست الأولى، هي
+
+296
+00:21:15,280 --> 00:21:20,110
+الست الأولىتمام إذا فعلًا belonged ل A
+
+297
+00:21:20,110 --> 00:21:25,070
+intersection B union C فهو بالضروري لازم يكون
+
+298
+00:21:25,070 --> 00:21:32,610
+belonged ل A لحالها و belonged ل ال union بتاعت ال
+
+299
+00:21:32,610 --> 00:21:35,050
+two sets دولة بالضروري لإن في بينهم intersection
+
+300
+00:21:36,130 --> 00:21:39,830
+هذه تمثل ال end هذه مشابهة تماما لل end اللي
+
+301
+00:21:39,830 --> 00:21:44,350
+أخدتوها مدام ال expression تاع end كله true فإذا
+
+302
+00:21:44,350 --> 00:21:49,450
+كل proposition كل proposition على حدة true صحيح؟
+
+303
+00:21:49,450 --> 00:21:52,350
+هو نفس الكلام اللي قلناه مدام intersection فإذا
+
+304
+00:21:52,350 --> 00:21:57,210
+الأولى هو ال X belong ل A و هو belong ل B union A
+
+305
+00:21:57,210 --> 00:22:02,730
+تمام؟ فإذا أول حاجة A ال X هذا belong ل A هذا
+
+306
+00:22:02,730 --> 00:22:09,920
+المفروض منههذا أكيد بيظل هنا ممكن يكون لأن هذا
+
+307
+00:22:09,920 --> 00:22:16,140
+union ممكن يكون مع a مع b أو مع c انا مش عارف
+
+308
+00:22:16,140 --> 00:22:18,940
+بالظبط او يمكن الاتنين مع بعض بس كل احتمالات
+
+309
+00:22:18,940 --> 00:22:22,440
+الاحتمال الأسوأ انه مايكنش في الاتنين مع بعض ان
+
+310
+00:22:22,440 --> 00:22:26,260
+يكون في واحدة منهم بس ابن مسكل احتمال هذا فبنقول
+
+311
+00:22:26,260 --> 00:22:33,240
+اما case number one انه ممكن يكون مع b x belong to
+
+312
+00:22:33,240 --> 00:22:40,040
+bهذه حالة أولى ممكن لأن او هذه الحالة التانية اللى
+
+313
+00:22:40,040 --> 00:22:46,100
+هنجربها لاحقا انه يكون belong لمن ل C بس هو لازم
+
+314
+00:22:46,100 --> 00:22:50,560
+يحقق واحدة من التنتين على الأقل لازم يحقق واحدة من
+
+315
+00:22:50,560 --> 00:22:53,700
+التنتين على الأقل عشان يحقق ال expression كله على
+
+316
+00:22:53,700 --> 00:22:58,340
+بعضه كويس خليني أخدها حالة حالة نفترض ان هو لأ مع
+
+317
+00:22:58,340 --> 00:23:04,250
+B مدان مع B معنى ذلك ان هو ينتمي لإيه؟وينتمي ل B
+
+318
+00:23:04,250 --> 00:23:09,270
+معناه ذلك أنه بالضرورة لازم ينتمي ل A intersection
+
+319
+00:23:09,270 --> 00:23:16,130
+B بالضرورة لازم ينتمي ل A مدام ينتمي ل كل set من
+
+320
+00:23:16,130 --> 00:23:19,830
+ال two sets دولة معناته ال intersection تبعهم أكيد
+
+321
+00:23:19,830 --> 00:23:23,510
+هو belong لل intersection تمام مدام belong لل
+
+322
+00:23:23,510 --> 00:23:28,170
+intersection union مع أي إشي أكيد هو هيكون belong
+
+323
+00:23:28,170 --> 00:23:37,290
+لل union صح هو موجود هناطب لما عملوا union مع أي
+
+324
+00:23:37,290 --> 00:23:40,910
+إشي مع أي شغلة ما هو لازم يكون موجود لأنه واحد من
+
+325
+00:23:40,910 --> 00:23:47,430
+الأطراف هي موجود لأن ال union تمثل or ال or يكفي
+
+326
+00:23:47,430 --> 00:23:51,490
+أن يكون ال proposition واحد true عشان ال or كلها
+
+327
+00:23:51,490 --> 00:23:56,670
+تكون true مظبوط خلاص و احنا هيتحقق الواحد منهم
+
+328
+00:23:56,670 --> 00:23:59,850
+فإذا union مع أي term تاني ال term التاني خليني
+
+329
+00:23:59,850 --> 00:24:07,060
+نقول A intersection Cفهو أكيد belonged للterm هذا
+
+330
+00:24:07,060 --> 00:24:10,200
+هاي
+
+331
+00:24:10,200 --> 00:24:17,260
+أول أثبات أثبتنا أن a intersection b union c هي
+
+332
+00:24:17,260 --> 00:24:21,740
+subset of a intersection b union مع a intersection
+
+333
+00:24:21,740 --> 00:24:28,070
+cهذه خلصناها و مكتوب طبعا الشرح والاحتمالات
+
+334
+00:24:28,070 --> 00:24:32,310
+الممكنة طبعا الكلام هو نفسه نفسه لو قلت case
+
+335
+00:24:32,310 --> 00:24:35,370
+number two لان احنا سبقنا يمكن يقولنا case number
+
+336
+00:24:35,370 --> 00:24:39,110
+two هتحققلنا الجزء التانيفنفس الكلام هتكون حققتكوا
+
+337
+00:24:39,110 --> 00:24:42,970
+الطرف التاني لل or هتكون حققت الطرف التاني لل or
+
+338
+00:24:42,970 --> 00:24:47,490
+كويس كل هذا الإثبات حتى الآن بس عشان نثبت أن
+
+339
+00:24:47,490 --> 00:24:50,370
+الأولى subset للتانية طب ما احنا لسه بدنا نكمل
+
+340
+00:24:50,370 --> 00:24:56,210
+التانية subset للأولى التانية subset للأولى ممكن
+
+341
+00:24:56,210 --> 00:25:00,230
+هذه مش موجودة في ال slides فناخدها لو قلنا term
+
+342
+00:25:00,230 --> 00:25:07,000
+هذا x belong لل term الأولو لاحظوا إن إحنا إيش في
+
+343
+00:25:07,000 --> 00:25:11,100
+عندنا هنا هدي
+
+344
+00:25:11,100 --> 00:25:15,000
+إيش union union معناته أنا مش ضامن إما إنها مع ال
+
+345
+00:25:15,000 --> 00:25:18,340
+term الأول أو ال term التاني برضه في عندنا
+
+346
+00:25:18,340 --> 00:25:26,080
+احتمالين فإذا إما x نقول case number one x belong
+
+347
+00:25:26,080 --> 00:25:33,770
+to A intersection Bناخد الحالة الأولى ال case
+
+348
+00:25:33,770 --> 00:25:39,370
+الأولى انه ممكن تكون مع هذا ال term في الحالة هذه
+
+349
+00:25:39,370 --> 00:25:48,490
+X belong to A و X belong to B بالضرورة مدام هو
+
+350
+00:25:48,490 --> 00:25:52,870
+belong ل ال intersection كله فهي بالضرورة ينتمي
+
+351
+00:25:52,870 --> 00:25:57,270
+لكل ستة على حدة لكل ستة على حدة طيب ببساطة جدا
+
+352
+00:25:57,270 --> 00:26:06,450
+بقدر اقول ان X belong to Bunion أي إشي صح union أي
+
+353
+00:26:06,450 --> 00:26:12,250
+إشي اللي هي ال C و
+
+354
+00:26:12,250 --> 00:26:15,110
+هاد ال C طلعت D طلعت F طلعت إش ما تكون تكون اللي
+
+355
+00:26:15,110 --> 00:26:20,400
+هو أنا عارف إن ال element belong to Bunion مع أي
+
+356
+00:26:20,400 --> 00:26:25,780
+شيء هو هيكون ضمن ال set تعطي ال union ال set ال
+
+357
+00:26:25,780 --> 00:26:30,400
+union كويس في الآخر هنلاقي ان x belong to a لإن هى
+
+358
+00:26:30,400 --> 00:26:37,680
+أصلا belong to a intersection ب union c لإن هى
+
+359
+00:26:37,680 --> 00:26:41,440
+belong لهذا ال term وbelong لهذا ال term فهى
+
+360
+00:26:41,440 --> 00:26:44,900
+belong لل intersection تبعهم طيب case number two
+
+361
+00:26:44,900 --> 00:26:49,120
+انه يكون belong لل term التانى
+
+362
+00:26:52,270 --> 00:26:59,890
+فإذا X belong ل A intersection C فإذا X بالضرورة
+
+363
+00:26:59,890 --> 00:27:06,950
+لازم تكون belong to A و X belong to C و نفس الكلام
+
+364
+00:27:06,950 --> 00:27:10,830
+اللي قلناه سابقا مدام هي belong to C هتكون belong
+
+365
+00:27:10,830 --> 00:27:16,410
+لاتحاد C مع أي إشي تاني اتحاد C مع أي إشي تاني مع
+
+366
+00:27:16,410 --> 00:27:21,020
+أي set تانية أكيد هيكون أحد العناصر للاتحادفإذن
+
+367
+00:27:21,020 --> 00:27:28,520
+بقدر أقول إن X belong to B union C لأن هو ينتمي
+
+368
+00:27:28,520 --> 00:27:33,980
+لأحد الطرفين اللي هي الـC كويسة هذه اتحققت وهي هذه
+
+369
+00:27:33,980 --> 00:27:38,940
+متحققة فإذن هو موجود في ال intersection بتاع
+
+370
+00:27:38,940 --> 00:27:43,400
+الأثنين هذولة فبالضرورة X هتكون belong to A
+
+371
+00:27:43,400 --> 00:27:47,000
+intersection B union C
+
+372
+00:27:51,230 --> 00:27:56,910
+فما دام أي element belong to A intersection B
+
+373
+00:27:56,910 --> 00:28:01,270
+union A intersection C أي element ينتمي لهذا ال
+
+374
+00:28:01,270 --> 00:28:05,690
+term بالضرورة هيكون ينتمي ل A intersection B union
+
+375
+00:28:05,690 --> 00:28:11,990
+C فإذا ال term هذا subset من ال term التاني طيب
+
+376
+00:28:11,990 --> 00:28:16,820
+احنا قبل شوية أثبتنا العكس طب ما دام العكسأثبت و
+
+377
+00:28:16,820 --> 00:28:20,260
+الأتنين أثبتوا مع بعض الأولى intersection للتانية
+
+378
+00:28:20,260 --> 00:28:23,560
+و التانية .. عفوا الأولى subset من التانية و
+
+379
+00:28:23,560 --> 00:28:26,700
+التانية subset من الأولى فإذا الأتنين بيسوا بعض ..
+
+380
+00:28:26,700 --> 00:28:29,380
+الأتنين بيسوا بعض و هذه طريقة إثبات .. هذه طريقة
+
+381
+00:28:29,380 --> 00:28:35,640
+إثبات ل ال sets ل ال sets equality تم .. أه
+
+382
+00:28:35,640 --> 00:28:41,900
+كتبتوهم؟ كيف؟ لأ واحدة لاتكفيش لأن مش هي اللى
+
+383
+00:28:41,900 --> 00:28:46,430
+بتعبّلك عن المساواة عن ال equality ال qualityلأ
+
+384
+00:28:46,430 --> 00:28:50,370
+مانت بدك تعمل كل احتمالات الاحتمالات كلها لازم
+
+385
+00:28:50,370 --> 00:28:52,350
+تكون واضحة case number one لازم تكون مكتوبة و case
+
+386
+00:28:52,350 --> 00:28:55,490
+number two لازم تكون مكتوبة عشان تقولوا فعلا
+
+387
+00:28:55,490 --> 00:29:00,150
+بيساووا بعض حقيقة انت بدك تضمني ال subset كيف بدك
+
+388
+00:29:00,150 --> 00:29:04,990
+تضمنيها بدك تضمني انه تحت كل الظروف مع كل احتمالات
+
+389
+00:29:04,990 --> 00:29:09,330
+اي element belonged to set number one بالضرورة
+
+390
+00:29:09,330 --> 00:29:13,960
+لازم يكون ينتمي ل set number twoطب إذا في أي
+
+391
+00:29:13,960 --> 00:29:18,540
+element أي احتمال أغفلته أو سبته معناته أنا بقدرش
+
+392
+00:29:18,540 --> 00:29:21,380
+أقول أنه لجميع الاحتمالات كل عنصر موجود هنا لازم
+
+393
+00:29:21,380 --> 00:29:24,380
+يكون بالضرورة موجود في ال set التانية بقدرش أقول
+
+394
+00:29:24,380 --> 00:29:28,860
+كل هذه for all elements لأ احنا بدنا يها for all
+
+395
+00:29:28,860 --> 00:29:32,740
+elements belonging to set number one بالضرورة ال
+
+396
+00:29:32,740 --> 00:29:35,700
+element هذا لازم يكون belonging to set number two
+
+397
+00:29:37,160 --> 00:29:41,840
+طيب الطريقة التانية ل .. ال .. ال quality ان انا
+
+398
+00:29:41,840 --> 00:29:44,060
+اعمل check على ال quality اللي هي ال builder
+
+399
+00:29:44,060 --> 00:29:48,480
+notation و ال logical equivalences كويس .. هنقول
+
+400
+00:29:48,480 --> 00:29:53,820
+بدنا نحقق قانون ال demorgan .. demorgan law ان a
+
+401
+00:29:53,820 --> 00:29:57,040
+.. ال complement ل a intersection b equal to
+
+402
+00:29:57,040 --> 00:30:01,580
+complement a union complement b بدنا نحققه هذا
+
+403
+00:30:01,580 --> 00:30:06,550
+فبنكتبه عن طريق ال builder notationهنقول ان ال
+
+404
+00:30:06,550 --> 00:30:10,470
+complement ل A intersection B عبارة عن set of X
+
+405
+00:30:10,470 --> 00:30:15,850
+such that ايش اللي لازم يحققه X ان X not belong to
+
+406
+00:30:15,850 --> 00:30:19,910
+A intersection B طيب تمام not belong معناته
+
+407
+00:30:19,910 --> 00:30:24,490
+negation ل ال belong معناته negation ل belong
+
+408
+00:30:24,490 --> 00:30:28,170
+belong notation ل belong notation كويس belong
+
+409
+00:30:28,170 --> 00:30:33,870
+notation معناه ذلك ان X belong to A and X belong
+
+410
+00:30:33,870 --> 00:30:40,160
+to Bصحيح؟ طيب دي مورجان هنا بندخل ال negation
+
+411
+00:30:40,160 --> 00:30:47,820
+بتصير هنا not belong x not belong to a or x not
+
+412
+00:30:47,820 --> 00:30:53,680
+belong to مين؟ to b تمام من هنا بنرجع ندخل ال
+
+413
+00:30:53,680 --> 00:30:58,690
+negation جوا بتصير not belongبنحطها العلمة not
+
+414
+00:30:58,690 --> 00:31:03,870
+belong هو نفس المعنى هو نفس المعنى، كويس طيب في
+
+415
+00:31:03,870 --> 00:31:07,550
+الحالة هذه بقدر اقول ان مدام not belong معناته هي
+
+416
+00:31:07,550 --> 00:31:13,930
+belong لل complement تعتها لما تقولوا x not belong
+
+417
+00:31:13,930 --> 00:31:20,690
+to a بالضروري هي x belong لمين؟ complement a هي
+
+418
+00:31:20,690 --> 00:31:28,710
+منتمية لل complement تبعهاتمام و نفس الكلام x not
+
+419
+00:31:28,710 --> 00:31:32,650
+belong معناته x belong to complement b طيب هنا
+
+420
+00:31:32,650 --> 00:31:37,990
+عندكوا or ال or بنمثلها بمين؟ بال union فإذا x
+
+421
+00:31:37,990 --> 00:31:42,810
+belong to ايش؟ complement a union complement b هو
+
+422
+00:31:42,810 --> 00:31:46,730
+نفس هذا الكلام اللي احنا فعلا بدنا نجيبه هو ده
+
+423
+00:31:46,730 --> 00:31:54,270
+اللي اتجيبه فهذه طريقة تانية هذه طريقة التانية
+
+424
+00:31:55,240 --> 00:31:58,900
+طريقة تالتة و اللي يمكن تكون الأسهل إذا كانت ال
+
+425
+00:31:58,900 --> 00:32:03,440
+expression تبعنا صغير مش كبير هتكون سهلة و بسيطة
+
+426
+00:32:03,440 --> 00:32:06,960
+اللي هي ال .. ال .. ال membership tables أو مقابلة
+
+427
+00:32:06,960 --> 00:32:09,180
+لل truth table اللي كنتوا بتاخدوه في ال
+
+428
+00:32:09,180 --> 00:32:12,920
+proposition هذه just إن أنا بستخدم ال truth table
+
+429
+00:32:12,920 --> 00:32:17,620
+بتاعة ال propositional logic و بنمثل belong to
+
+430
+00:32:17,620 --> 00:32:23,510
+بنمثل ب one not belong to بنمثل ب zeroفإذا كان ال
+
+431
+00:32:23,510 --> 00:32:28,210
+element ينتمي لل set بنحط قيمته ب 1 لا ينتمي لل
+
+432
+00:32:28,210 --> 00:32:33,850
+set بنحط قيمته ب 0 زي ال proof اللي مطلوب منها هنا
+
+433
+00:32:33,850 --> 00:32:40,250
+ف proof A union B minus كله minus B بدنا نشوف هل
+
+434
+00:32:40,250 --> 00:32:45,330
+هو equivalent ل A minus B ولا لأهنشوف هنحط ال a و
+
+435
+00:32:45,330 --> 00:32:47,970
+ال b و هنحط جميع الاحتمالات الممكنة ان هو not
+
+436
+00:32:47,970 --> 00:32:52,010
+belong not belong not belong belong to b هنا
+
+437
+00:32:52,010 --> 00:32:56,710
+belong to a not belong to b هنا belong ل a and b
+
+438
+00:32:56,710 --> 00:33:03,890
+مع بعض نبدأ بأول أول union عندنا a union b a union
+
+439
+00:33:03,890 --> 00:33:07,550
+b معناته يكفي أنه يكون موجود في واحد منهم هنا غير
+
+440
+00:33:07,550 --> 00:33:13,580
+موجود في أي واحدzero not belong ل ال union طيب
+
+441
+00:33:13,580 --> 00:33:18,080
+otherwise دايما في واحد اما في B او في A او في
+
+442
+00:33:18,080 --> 00:33:22,580
+كلاهما فبيعطينا دايما one بيعطينا دايما one كويس
+
+443
+00:33:22,580 --> 00:33:27,900
+لما نطرح منه B ناخد بالنا هنا لما بتكلم هنا عن B
+
+444
+00:33:27,900 --> 00:33:34,360
+بال minus معنا ذلك انه لازم يكون موجود هنا و غير
+
+445
+00:33:34,360 --> 00:33:39,850
+موجود هنامش احنا عرفنا a-b ان هو ال element اللي
+
+446
+00:33:39,850 --> 00:33:44,630
+موجود في a و غير موجود في b كويسة انا عند a union
+
+447
+00:33:44,630 --> 00:33:47,750
+b معناه ان انا بتكلم عن ال column هذا ايش ال
+
+448
+00:33:47,750 --> 00:33:53,190
+element اللي موجود هنا و غير موجود في b على طول
+
+449
+00:33:53,190 --> 00:33:57,970
+بيعطينا ال difference طبعا طيب خلينا نشوف غير
+
+450
+00:33:57,970 --> 00:34:03,330
+موجود لأ موجودو موجود، لأ مينفعش، موجود، غير
+
+451
+00:34:03,330 --> 00:34:07,810
+موجود، أه مظبوط، هذه حالة كويسة، طيب موجود، موجود،
+
+452
+00:34:07,810 --> 00:34:12,710
+لأ، فهذه الحالة الوحيدة ال one اللي هي فعلا تمثل
+
+453
+00:34:12,710 --> 00:34:16,930
+ال difference، تمثل difference، إن هي تكون موجودة
+
+454
+00:34:16,930 --> 00:34:21,550
+في ال term الأول و غير موجودة في ال term التانيو
+
+455
+00:34:21,550 --> 00:34:25,770
+غير موجودة في ايه؟ في ال term التاني كويس دل a
+
+456
+00:34:25,770 --> 00:34:30,430
+minus b برضه نفس المعنى موجودة في a و غير موجودة
+
+457
+00:34:30,430 --> 00:34:34,610
+في b لأ مش موجودة من أصله مش موجودة أصلا هي موجودة
+
+458
+00:34:34,610 --> 00:34:39,050
+و غير موجودة في a موجودة و موجودة لأ فإذا هو ال
+
+459
+00:34:39,050 --> 00:34:43,270
+term هذا الوحيد كويس
+
+460
+00:34:43,270 --> 00:34:46,170
+تعالوا نشوف ال two columns اللي بدنا نقارن بينهم
+
+461
+00:34:46,170 --> 00:34:48,890
+فعليا هم equivalent لبعض ولا لأ هي ال column الأول
+
+462
+00:34:48,890 --> 00:34:55,140
+وهي ال column التانيالاتنين بيساوي بعض في كل .. كل
+
+463
+00:34:55,140 --> 00:34:57,920
+role هنا يساوي .. او كل قيمة في ال role الأول
+
+464
+00:34:57,920 --> 00:35:02,200
+تساوي القيمة في ال role الأول هناك لاحظوا هنا و
+
+465
+00:35:02,200 --> 00:35:09,100
+هنا تمام هنسيبلكوا برضه مثال تشتغلوا هيك ..
+
+466
+00:35:09,100 --> 00:35:15,140
+تتدربوا عليه في البيت هذا ب .. ب three sets
+
+467
+00:35:16,070 --> 00:35:20,270
+هذا بال three sets فهيكون في عندكم مجموعة احتمالات
+
+468
+00:35:20,270 --> 00:35:22,770
+اكبر جداش عددهم ال possibilities تبعتكم تمانية
+
+469
+00:35:22,770 --> 00:35:26,430
+اتنين to the power عدد ال sets اللي موجودة او عدد
+
+470
+00:35:26,430 --> 00:35:30,510
+ال proposition لو بدنا نتكلم عن ال proposition ال
+
+471
+00:35:30,510 --> 00:35:35,970
+logic طيب نتكمل هتلاقوا في عندنا جزئية ال
+
+472
+00:35:35,970 --> 00:35:39,010
+generalization او generalized unions and
+
+473
+00:35:39,010 --> 00:35:42,010
+intersections المقصود هنا ان احنا مش بالضروري
+
+474
+00:35:42,010 --> 00:35:47,240
+نتعامل عن union ل two setsممكن يكون عندكوا أكتر من
+
+475
+00:35:47,240 --> 00:35:51,860
+two sets فهنا احنا بنتكلم عن n sets ممكن نعملهم
+
+476
+00:35:51,860 --> 00:35:55,400
+unions مع بعض فهنا بنكون عملنا generalized unions
+
+477
+00:35:55,400 --> 00:35:59,140
+فمعنى ذلك أنا بتكلم عن ال union operator لإيش؟
+
+478
+00:35:59,140 --> 00:36:03,860
+لأكتر من اتنين sets او لعدد كبير من ال sets اللي
+
+479
+00:36:03,860 --> 00:36:09,420
+موجود عندنا في الحالة بتاعتنا بشكل an ordered set
+
+480
+00:36:09,420 --> 00:36:14,910
+offset ليش؟ لأنه مش هتفرج معانا يقولنا جابنا هيكو
+
+481
+00:36:14,910 --> 00:36:17,650
+احنا بنتكلم في القوانين اللي اتكلمناها قولنا a
+
+482
+00:36:17,650 --> 00:36:24,090
+union b هي نفسها b union a فمين جاب المين مش هتفرج
+
+483
+00:36:24,090 --> 00:36:29,050
+كتير حتى و انا بتكلم عن اكثر من two sets حتى و انا
+
+484
+00:36:29,050 --> 00:36:35,950
+بتكلم عن اكثر من two sets okay نبدأ بال union لما
+
+485
+00:36:35,950 --> 00:36:39,390
+نقول ال binary union operator هذه binary union على
+
+486
+00:36:39,390 --> 00:36:43,730
+اساس ان انا بتكلم عنtwo sets فقط اللي مستعملهم فهي
+
+487
+00:36:43,730 --> 00:36:46,830
+binary union لأ انا ممكن اعمل generalization
+
+488
+00:36:46,830 --> 00:36:52,530
+للموضوع و اقول NRA union فانا موجود عندى N sets و
+
+489
+00:36:52,530 --> 00:36:56,670
+بدى اعملهم كلهم مع بعض union كلهم اتحاد مع بعض
+
+490
+00:36:56,670 --> 00:37:01,350
+كلهم اتحاد مع بعض تمام زى لما تقولوا والله في
+
+491
+00:37:01,350 --> 00:37:07,640
+عندكمبلدية غزة، بلدية خانونس، بلدية رفح، بلدية
+
+492
+00:37:07,640 --> 00:37:12,140
+الشمال بتحانون، بلدية .. كلهم اتحاد مع بعض بيعطونا
+
+493
+00:37:12,920 --> 00:37:16,360
+قطع غزة بيعطونا كل بلديات قطع غزة صحيح فبيعطوا قطع
+
+494
+00:37:16,360 --> 00:37:19,240
+غزة ليش هنعمل .. لأ لاتنتهي ممكن اعمل اتحاد للكل
+
+495
+00:37:19,240 --> 00:37:24,020
+فهنا قلت واحد في مؤتمر صحفي قال والله اتحاد خانونس
+
+496
+00:37:24,020 --> 00:37:27,880
+مع رفح واحد قال رفح مع خانونس هتفرج كتير مش هتفرج
+
+497
+00:37:27,880 --> 00:37:30,920
+كتير المهم ان اتحاد بلديات مع بعض مش هيفرج كتير
+
+498
+00:37:30,920 --> 00:37:34,560
+الترتيب هنا مش هيفرج الفكرة انه كأنه انا عملت
+
+499
+00:37:34,560 --> 00:37:40,430
+اتحادست أولى مع ست تانية الناتج مع الست التالتة
+
+500
+00:37:40,430 --> 00:37:43,850
+الناتج مع الرابعة لحد ما نخلص كل ال sets اللى بدنا
+
+501
+00:37:43,850 --> 00:37:47,630
+نعملهم union لكل ال sets اللى بدنا نعملهم union
+
+502
+00:37:47,630 --> 00:37:53,930
+بنعمل grouping هنا لكل ال sets بتاعتنا بنعطيها big
+
+503
+00:37:53,930 --> 00:38:01,690
+U فبقول I from one to N اذا أنا بتكلم عن N array
+
+504
+00:38:01,690 --> 00:38:08,020
+union او اننا N setsوبنحط ai فصار هذا عبارة عن ال
+
+505
+00:38:08,020 --> 00:38:13,240
+index لمين اللي بيعطينا indication لرقم ال set ال
+
+506
+00:38:13,240 --> 00:38:16,260
+set أولى، التانية، التالتة، الرابعة، الخمسة، تواش،
+
+507
+00:38:16,260 --> 00:38:22,260
+توان، بنحطها big U بتذكرنا ال summation بتذكرين ال
+
+508
+00:38:22,260 --> 00:38:25,040
+summation لما كنتوا رسموا ال summation طيب أو
+
+509
+00:38:25,040 --> 00:38:30,180
+infinite sets, sets of sets بنحطها U من واحدة to
+
+510
+00:38:30,180 --> 00:38:36,610
+infinity فبنحطها من واحدة to infinityكويسة نفس
+
+511
+00:38:36,610 --> 00:38:39,450
+الكلام نقدر نعمله لمن؟ لل intersection نعمله لل
+
+512
+00:38:39,450 --> 00:38:41,670
+intersection احنا في الاول كنا بتكلم عن binary
+
+513
+00:38:41,670 --> 00:38:45,570
+intersection operator كانت مجرد two sets بنشتغل
+
+514
+00:38:45,570 --> 00:38:48,150
+عليهم ممكن نعمل الموضوع على ال N array
+
+515
+00:38:48,150 --> 00:38:53,370
+intersection فبصير عندنا N sets بدنا نعملهم
+
+516
+00:38:53,370 --> 00:38:57,290
+intersection فبدنا تقاطعهم كلهم مع بعض بدنا نقاطع
+
+517
+00:38:57,290 --> 00:39:03,610
+الكل مع بعضكويس فهذه grouping او نقدر نعمل
+
+518
+00:39:03,610 --> 00:39:06,950
+grouping لل intersection بس هذه ممكن تكون مميزة
+
+519
+00:39:06,950 --> 00:39:10,710
+امتى او امتى بتقدروا تستفيدوا منها لما بتتكلموا
+
+520
+00:39:10,710 --> 00:39:15,920
+for example على خلط الألوانخلط الألوان مجموعة من
+
+521
+00:39:15,920 --> 00:39:19,060
+ال .. أو كل الألوان تقريبا ناخده من التلت ألوان
+
+522
+00:39:19,060 --> 00:39:21,580
+الرئيسية صحيح؟ موظفا لو ناخده من التلت ألوان
+
+523
+00:39:21,580 --> 00:39:25,200
+الرئيسية في لون لما بدنا ناخد ال intersection لتلت
+
+524
+00:39:25,200 --> 00:39:28,540
+مع بعض للتلت ألوان الرئيسية بناخد لون معين اللي هو
+
+525
+00:39:28,540 --> 00:39:35,240
+اللون الأسود اللي هيكون ناتج .. جمع التلتة صحيح؟ و
+
+526
+00:39:35,240 --> 00:39:40,610
+لا كان .. و لا الأبيض كان؟ اه انتوا مش عارفين؟ اهو
+
+527
+00:39:40,610 --> 00:39:44,650
+انا اتوقعت عندكم معلومة عنهم طيب مش اشكال مش اشكال
+
+528
+00:39:44,650 --> 00:39:48,770
+عندنا .. عندنا ناس خبيرة بالموضوع فالقصد انه ممكن
+
+529
+00:39:48,770 --> 00:39:52,810
+تنتج تلت ألوان رئيسية هي عبارة عن مجموعات هيك تلت
+
+530
+00:39:52,810 --> 00:39:55,770
+مجموعات من الألوان اعملتوا ال intersection فال
+
+531
+00:39:55,770 --> 00:39:59,610
+intersection هذا طلعلكوا intersection لكل
+
+532
+00:39:59,610 --> 00:40:02,550
+المجموعات بيعطيكوا indication لست جديدة الست
+
+533
+00:40:02,550 --> 00:40:07,450
+الجديدة دي بتعطي لون مزيج من الكل مزيج من الكلانا
+
+534
+00:40:07,450 --> 00:40:13,050
+اتوقع ان ال example هيكون يعني معروف يمكن او اشي
+
+535
+00:40:13,050 --> 00:40:20,910
+طيب بنمثلها كتالة big arch او قوس كبير big arch
+
+536
+00:40:20,910 --> 00:40:27,690
+from I ب equal to one to N AI تمام فاذا انا بتكلم
+
+537
+00:40:27,690 --> 00:40:34,590
+عن A1 intersection A2 intersection A3 to AN كويسأو
+
+538
+00:40:34,590 --> 00:40:38,730
+infinite set برضه من واحد و infinity و بنشتغل
+
+539
+00:40:38,730 --> 00:40:45,430
+عليها تمام طيب ال representations ل ال sets لما
+
+540
+00:40:45,430 --> 00:40:48,870
+نكون بدنا نعمل representation داخل set معينة كيف
+
+541
+00:40:48,870 --> 00:40:51,230
+ممكن أعمل representation لل elements اللي فيها
+
+542
+00:40:51,230 --> 00:40:55,770
+بحيث أن أنا أستفيد منها في ال operator اللي بنشتغل
+
+543
+00:40:55,770 --> 00:40:57,910
+عليها أنا في الآخر بتعامل مع ال sets هذه اللي
+
+544
+00:40:57,910 --> 00:41:01,240
+بتدخلها على ال pcفبدى محتاج طريقة ال
+
+545
+00:41:01,240 --> 00:41:04,300
+representation عشان نمثل فيها ال elements داخل ال
+
+546
+00:41:04,300 --> 00:41:10,800
+set فبنمثلها بال index تبعهابنمثلها وما جدقش رقمها
+
+547
+00:41:10,800 --> 00:41:15,600
+داخل ال set كترتيب فهنا بنتكلم عن ترتيبها لما نيجي
+
+548
+00:41:15,600 --> 00:41:19,040
+نعمل ال methods of representing indiscreet
+
+549
+00:41:19,040 --> 00:41:21,900
+structure using another discrete structure of a
+
+550
+00:41:21,900 --> 00:41:24,780
+different type خلينا ناخد ال type تبعنا اللي
+
+551
+00:41:24,780 --> 00:41:28,160
+بنشتغل عليه هو ال natural number و بدنا نعمله
+
+552
+00:41:28,160 --> 00:41:32,200
+representation عشان نوضح الموضوع هنقول zero عبارة
+
+553
+00:41:32,200 --> 00:41:37,090
+عن فيهذا بالنسبة لمن؟ لـ natural number فالـ zero
+
+554
+00:41:37,090 --> 00:41:40,290
+هذا أول element فيها مش هذا ال element الأول بنقدر
+
+555
+00:41:40,290 --> 00:41:44,350
+نعبر عنه كأنه هذا في ال element التاني بنعبر عليه
+
+556
+00:41:44,350 --> 00:41:48,450
+على أساس أن هذه ال six تحتوي على عنصر واحد أنه
+
+557
+00:41:48,450 --> 00:41:53,850
+عنصر؟ أول عنصر أول عنصر في ال natural number ال
+
+558
+00:41:53,850 --> 00:41:59,210
+zero اللي هو ال zero طيب اتنين مكافئة ل six تحتوي
+
+559
+00:41:59,210 --> 00:42:05,110
+علىتو elements اللي هم zero و one و هكذا و هكذا
+
+560
+00:42:05,110 --> 00:42:08,530
+تمام طيب الكلام هذا لما نيجي نعمل بال bit strings
+
+561
+00:42:08,530 --> 00:42:12,730
+او بال .. بال .. باستخدام ال bits ال bits ال zero
+
+562
+00:42:12,730 --> 00:42:17,070
+يمثل zero واحد يمثل واحد الأتنين لاحظوا هنا ال
+
+563
+00:42:17,070 --> 00:42:22,550
+zero يمثل في zero عشان نحول كلمة مجموعات هذه ال
+
+564
+00:42:22,550 --> 00:42:27,810
+sets ل bit strings ال zero يمثل zero هو هو طيب ال
+
+565
+00:42:27,810 --> 00:42:32,480
+oneيمثل جدش عدد ال elements انا هنا ال elements
+
+566
+00:42:32,480 --> 00:42:36,800
+الأول ال elements الأول فانا فعلا موجود عند ال
+
+567
+00:42:36,800 --> 00:42:43,680
+elements الأول طيب اتنين تمثل 01 01 في ال binary
+
+568
+00:42:43,680 --> 00:42:48,760
+هنا تمثل التلاتة تمثل 11 اربعة عارفين التمثيل هذا
+
+569
+00:42:48,760 --> 00:42:52,660
+طيب انا ايش بده استفيد منه يعني احنا بدنا هلوجد
+
+570
+00:42:52,660 --> 00:42:57,310
+كيف طريقة الاستفادةمن اللي فهمناها ده ان انا امثل
+
+571
+00:42:57,310 --> 00:43:00,910
+ال sets تبعت ب one و zeros عشان امثلهم ب one و
+
+572
+00:43:00,910 --> 00:43:05,930
+zeros الحقيقة هناخدمجموعة مثال نستفيد منه انا همثل
+
+573
+00:43:05,930 --> 00:43:09,910
+ال set ب one zeros بحيث نعمل عملية عملية ال
+
+574
+00:43:09,910 --> 00:43:14,610
+operations اللي احنا عارفينها سابقا ال or and و ال
+
+575
+00:43:14,610 --> 00:43:19,250
+negation او not و ال .. كل الأمور هذه خلينا نفرض
+
+576
+00:43:19,250 --> 00:43:21,450
+ان ال numerical universe of discourse بتاعتنا
+
+577
+00:43:21,450 --> 00:43:26,310
+اسمها U عبارة عن X1, X2, X3 هذا بنقدر نمثل فيها او
+
+578
+00:43:26,310 --> 00:43:31,530
+بتعمل represent a finite set S اللي هي subset of U
+
+579
+00:43:32,490 --> 00:43:37,550
+بنمثلها ك finite bit string لحظة ال set هذه
+
+580
+00:43:37,550 --> 00:43:43,310
+هنمثلها بيش ال bit string تمثل bit string هتكون
+
+581
+00:43:43,310 --> 00:43:47,230
+عندك set و فيها مجموعة elements مظبوط هنمثلهم bit
+
+582
+00:43:47,230 --> 00:43:50,770
+string ال bit string هذه اما one او zero مادام
+
+583
+00:43:50,770 --> 00:43:55,850
+بتكلم عن bit ال bit one or zero فهتكون بي one بي
+
+584
+00:43:55,850 --> 00:43:59,690
+two بي three بي two نكل واحدة من هدولا احتمالين
+
+585
+00:43:59,690 --> 00:44:04,190
+اما one او zero الاحتمالين هدولا one او zero بحطها
+
+586
+00:44:04,190 --> 00:44:08,170
+one اذا كان العنصر موجود في المجموعة و بحطها zero
+
+587
+00:44:08,170 --> 00:44:12,230
+اذا كان غير موجود في المجموعة هاي كل الموضوع بس
+
+588
+00:44:12,230 --> 00:44:17,520
+بدى اكون عارف مينال universe of discourse لأن كل
+
+589
+00:44:17,520 --> 00:44:20,060
+شغلنا على ال universe of discourse عندنا universe
+
+590
+00:44:20,060 --> 00:44:24,320
+of discourse فبقول الست هذى هل موجود العنصر هدى
+
+591
+00:44:24,320 --> 00:44:27,280
+فيها من ال universe of discourse او لأ موجود بحطه
+
+592
+00:44:27,280 --> 00:44:34,240
+one مش موجود بحطه zeroفهنا for all i xi أنا بتكلم
+
+593
+00:44:34,240 --> 00:44:37,540
+هنا اللحظة عن index belonging to S if and only if
+
+594
+00:44:37,540 --> 00:44:40,900
+i أقل من n لازم يكون هو ضمن ال universe of
+
+595
+00:44:40,900 --> 00:44:42,960
+discourse لما يقول ال universe of discourse فيها
+
+596
+00:44:42,960 --> 00:44:46,720
+عشرة elements أول عشرة elements مش معجول ال I تكون
+
+597
+00:44:46,720 --> 00:44:51,330
+رقم 11صحيح؟ مش ممكن انا بتكلم عن عشر elements و
+
+598
+00:44:51,330 --> 00:44:55,430
+بعدين احط i رقم 11 او اقول ان والله x 11 مافيش x
+
+599
+00:44:55,430 --> 00:45:01,230
+11 مش موجودة فهنا لازم تكون اقل من n and b i equal
+
+600
+00:45:01,230 --> 00:45:06,390
+to one عشان تكون belong to اذا not belong to equal
+
+601
+00:45:06,390 --> 00:45:12,510
+to zero equal to zero تمامنوضحها أكتر برضه بمثال
+
+602
+00:45:12,510 --> 00:45:16,030
+لأنه موضوحة بسيط جدا رغم أنه يمكن مش كتير واضحة لو
+
+603
+00:45:16,030 --> 00:45:20,610
+قلنا ال U ال natural number و ال S تبعته عبارة عن
+
+604
+00:45:20,610 --> 00:45:26,370
+اتنين، تلاتة، خمسة، سبعة، أحداشر الأعداد الأولية
+
+605
+00:45:26,370 --> 00:45:29,730
+ال primes كيف بمثلها هنا؟ أنا عارف أن ال universe
+
+606
+00:45:29,730 --> 00:45:32,890
+of discourse الشيية natural number طب ال natural
+
+607
+00:45:32,890 --> 00:45:40,060
+number خلينا نكتبهاصفر واحد اتنين تلاتة اربعة خمسة
+
+608
+00:45:40,060 --> 00:45:44,280
+شكة طيب
+
+609
+00:45:44,280 --> 00:45:52,900
+الصفر موجود في ال set بحطله zero الواحد مش موجود
+
+610
+00:45:52,900 --> 00:45:58,260
+الاتنين موجودة التلاتة واحد الاربعة
+
+611
+00:46:00,330 --> 00:46:05,530
+الخمسة واحد ستة مش موجودة سبعة واحد تمانية زيرو
+
+612
+00:46:05,530 --> 00:46:11,870
+تسعة خلاص عند ال 11 لأنه موجود واحد و بنوقف فانا
+
+613
+00:46:11,870 --> 00:46:16,490
+هيك عملت ايش representation لمي للست هذه و انا
+
+614
+00:46:16,490 --> 00:46:18,810
+عارف ان انا متكلم عن ال natural number احنا متكلم
+
+615
+00:46:18,810 --> 00:46:21,410
+عن ايش عن ال natural number في الحالة اللي متكلم
+
+616
+00:46:21,410 --> 00:46:26,320
+فيها طيب هنا بقدر اشتغل في الحالة هذهتمثيل ل set
+
+617
+00:46:26,320 --> 00:46:30,420
+تانية و نعمل intersection بينهم او نعمل union
+
+618
+00:46:30,420 --> 00:46:35,920
+باستخدام ال bitwise operator باستخدام bitwise
+
+619
+00:46:35,920 --> 00:46:39,320
+operator ان انا استعمل ال union او ال or اللي هي
+
+620
+00:46:39,320 --> 00:46:41,880
+ال union او ال intersection اللي كانت مكافئة على
+
+621
+00:46:41,880 --> 00:46:44,760
+ال or و ال and لان هالوقت لما بدي اشتغل على ال
+
+622
+00:46:44,760 --> 00:46:48,960
+bitwise هستخدم or و and فعليا ال complement هتصير
+
+623
+00:46:48,960 --> 00:46:53,960
+ال not او ال negation او ال negation تمام ناخد
+
+624
+00:46:53,960 --> 00:46:54,860
+مثال
+
+625
+00:46:59,400 --> 00:47:05,060
+عليهم ناخد مثال لو
+
+626
+00:47:05,060 --> 00:47:09,520
+معطينا هنا suppose that the universe set ال
+
+627
+00:47:09,520 --> 00:47:11,700
+universe of discourse متكلم عن ال universe of
+
+628
+00:47:11,700 --> 00:47:16,200
+discourse ال universe of discourse بتاعتنا U معرف
+
+629
+00:47:16,200 --> 00:47:20,270
+لنا هي واحد اتنين تلاتة اربعةخمسة، ستة، سبعة لعشرة
+
+630
+00:47:20,270 --> 00:47:22,930
+فإذا من واحد لعشرة خلاص حددلي ال universive
+
+631
+00:47:22,930 --> 00:47:27,330
+discourse تبعتنا حددلنا إيها كويس express each of
+
+632
+00:47:27,330 --> 00:47:32,890
+these sets with bit string where the ith bit in
+
+633
+00:47:32,890 --> 00:47:38,570
+the string is one if I is in the set and zero
+
+634
+00:47:38,570 --> 00:47:43,560
+otherwise إذا not in the set كويسفهي حتى معرّفلكوا
+
+635
+00:47:43,560 --> 00:47:46,020
+كمان إيش اللي بدكم تعمله، معرّفلكوا إيش بدكم تعمله
+
+636
+00:47:46,020 --> 00:47:49,340
+بيعطيكوا الست الأولى، three, four, five عشان
+
+637
+00:47:49,340 --> 00:47:54,280
+أمثلها احنا دايما بقالنا في مين؟ في ال universe of
+
+638
+00:47:54,280 --> 00:47:57,340
+discourse ال universe of discourse عندنا واحد،
+
+639
+00:47:57,340 --> 00:48:02,640
+اتنين، تلاتة، أربعة، خمسة، ستة، سبعة، تمانية،
+
+640
+00:48:02,640 --> 00:48:07,120
+تسعة، عشرة، كويس، هذه؟ zero
+
+641
+00:48:13,400 --> 00:48:17,840
+خلاص هاي تمثيلها بالإيش؟ بال bit string طريقة
+
+642
+00:48:17,840 --> 00:48:24,320
+تمثيلها بال bit string التانية واحد و واحد و واحد
+
+643
+00:48:24,320 --> 00:48:31,180
+و واحد و واحد و واحد و واحد و واحد و واحد و واحد
+
+644
+00:48:31,880 --> 00:48:38,300
+للعشرة للعشرة خمسة ستة عشرة مظبوط طيب الأخيرة one
+
+645
+00:48:38,300 --> 00:48:46,460
+one one zero zero one one one zero تمام نفس الكلام
+
+646
+00:48:46,460 --> 00:48:52,220
+بالعكس ال six هذه عبارة عن إيش؟ كلام بسيط يعني
+
+647
+00:48:52,220 --> 00:48:58,040
+حاسين أنه طبع ابتدائي هيك ولا طبع صحيح؟طيب، بس هي
+
+648
+00:48:58,040 --> 00:49:00,060
+طريقة التنفيذ، يعني أنتوا بتلاحظوا أنتوا فعلا
+
+649
+00:49:00,060 --> 00:49:03,940
+بتبنوا على معلومات خفيفة بسيطة و بتبنوا عليها علم،
+
+650
+00:49:03,940 --> 00:49:12,980
+تبنوا عليها العلم اللاحق طيب هذه .. تالي
+
+651
+00:49:12,980 --> 00:49:15,900
+واضحة الأمور مافيش مش محتاج يعني خليلكوا التنتين
+
+652
+00:49:15,900 --> 00:49:20,950
+التانية تتسلوا عليهم و ..بنكون هيك احنا اتوقع
+
+653
+00:49:20,950 --> 00:49:26,270
+خلصنا اخيرا ال set خلصنا ال set theory و خلصنا كل
+
+654
+00:49:26,270 --> 00:49:29,390
+معلوماتنا عن ال set theory بيضل المرة الجاية ان
+
+655
+00:49:29,390 --> 00:49:34,990
+شاء الله بنبدأ مع ال ال functions مع ال functions
+
+656
+00:49:34,990 --> 00:49:36,730
+عارفين ان ال function احنا بنتكلم فيها عن
+
+657
+00:49:36,730 --> 00:49:41,690
+dependent و independent variables صحيح؟ متذكرين ال
+
+658
+00:49:41,690 --> 00:49:46,290
+functions قبل هيك؟ولا انسوتوها؟ طيب راجعوا هيك
+
+659
+00:49:46,290 --> 00:49:49,230
+شوية معلومات خفيفة عنها عشان المرة الجاية نعرف
+
+660
+00:49:49,230 --> 00:49:52,270
+نتحرك سلاسة فيها بسرعة يعني ان شاء الله يالا
+
+661
+00:49:52,270 --> 00:49:53,410
+يعطيكوا العافية وبركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..71da83d265dbd709b8563cd2829ebda800ce68f1
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE.srt
@@ -0,0 +1,1878 @@
+1
+00:00:20,650 --> 00:00:22,810
+Okay, بسم الله الرحمن الرحيم، الصلاة والسلام علي
+
+2
+00:00:22,810 --> 00:00:25,210
+أشرف الأنبياء والمرسلين سيدنا محمد، وعلي آله
+
+3
+00:00:25,210 --> 00:00:28,350
+وصحبه أجمعين. طيب، المرة اللي فاتت احنا بدأنا
+
+4
+00:00:28,350 --> 00:00:32,210
+اتكلمنا في الـ... في حكاية الـ applications للـ
+
+5
+00:00:32,210 --> 00:00:34,770
+number theory، وقلنا إيش في applications ممكن
+
+6
+00:00:34,770 --> 00:00:39,390
+نعملها للـ numbers، وتطرقنا هيك بسرعة إن إيش اللي
+
+7
+00:00:39,390 --> 00:00:42,530
+هنشرحه المرة الجاية، اللي هي اليوم. قلنا هنتكلم عن
+
+8
+00:00:42,530 --> 00:00:46,650
+الـ pseudo random numbers، كيف ممكن نعمل sequence
+
+9
+00:00:46,650 --> 00:00:51,710
+بتهيألكوا إن هو random .. random sequence، ولكن هو
+
+10
+00:00:51,710 --> 00:00:54,990
+محسوب .. deterministic .. sequence، بمعنى أن أنا
+
+11
+00:00:54,990 --> 00:00:57,530
+بقدر أعمله regeneration .. بتقدروا أنتوا تعملوه
+
+12
+00:00:57,530 --> 00:01:00,250
+regeneration. الـ applications هذه كتيرة .. إلها
+
+13
+00:01:00,250 --> 00:01:02,790
+تطبيقات كتيرة، من أهمها يمكن الـ hash function،
+
+14
+00:01:02,790 --> 00:01:06,600
+من أهمها الـ games، الـ graphics، الـ simulations، الـ
+
+15
+00:01:06,600 --> 00:01:08,760
+.. الـ cryptographic، وأهم شغلها دي الـ
+
+16
+00:01:08,760 --> 00:01:11,440
+cryptographic اللي هناخدها مش .. طبعًا مش هنقدر
+
+17
+00:01:11,440 --> 00:01:14,280
+ناخدها اليوم، لأن زي ما قلتلكوا هناخد جزء اليوم
+
+18
+00:01:14,280 --> 00:01:19,120
+محاضرة، وعشان الامتحان فهنتكلم عن الـ cryptographic
+
+19
+00:01:19,120 --> 00:01:24,470
+وهنشوف كيف ممكن نعمل تشفير. علم التشفير كله مبني
+
+20
+00:01:24,470 --> 00:01:27,170
+علي حكايات الـ pseudorandom، علي حكايات الـ
+
+21
+00:01:27,170 --> 00:01:29,890
+pseudorandom، كيف بنعمل الحكايات الـ pseudorandom
+
+22
+00:01:29,890 --> 00:01:34,590
+هذه عن طريق الـ linear congruential method، و
+
+23
+00:01:34,590 --> 00:01:39,090
+هنستخدم فيها الـ modular اللي احنا خدناها سابقا،
+
+24
+00:01:39,090 --> 00:01:42,310
+عملية الـ modular operation اللي احنا خدناها سابقا،
+
+25
+00:01:42,310 --> 00:01:46,550
+طيب، إيش القصة بالظبط؟ إيش هو هذا الـ linear
+
+26
+00:01:46,550 --> 00:01:53,590
+congruential method؟ فعليًا هذه معادلة بنعمل فيها هذه
+
+27
+00:01:53,590 --> 00:01:57,610
+المعادلة محتاجة أربعة أرقام مهمة جدًا. الرقم الأول
+
+28
+00:01:57,610 --> 00:02:09,170
+هو الـ initial value.
+
+29
+00:02:09,940 --> 00:02:13,700
+الـ initial number اللي هنبدأ منه الشغل. فيه
+
+30
+00:02:13,700 --> 00:02:16,120
+دايمًا initial number نبدأ منه، نعمل numerical
+
+31
+00:02:16,120 --> 00:02:19,960
+generation، اللي هنسميه الـ X node أو X0. طيب، الـ A
+
+32
+00:02:19,960 --> 00:02:24,380
+هذه اللي هي الـ multiplier، بده يكون على الأقل بده
+
+33
+00:02:24,380 --> 00:02:28,460
+يكون اتنين. multiplier واحد مالوش معنى، معامل ضرب
+
+34
+00:02:28,460 --> 00:02:31,260
+واحد مالوش معنى، فبده يكون على الأقل اتنين، ويكون
+
+35
+00:02:31,260 --> 00:02:34,920
+أقل من الـ modulus. الـ modulus هذا الـ M، لازم تكون
+
+36
+00:02:34,920 --> 00:02:41,320
+أكبر رقم فيهم، لازم تكون أكبر رقم فيهم. فـ A بدها تكون
+
+37
+00:02:41,320 --> 00:02:44,760
+أقل من M، وأكبر من أو يساوي 2، على الأقل عشان نقول
+
+38
+00:02:44,760 --> 00:02:48,060
+إن آه والله في multiplier. طيب، الـ C، و .. اللي هي الـ
+
+39
+00:02:48,060 --> 00:02:51,220
+.. الـ increment، والـ seed، بدها تكون بين الصفر والـ
+
+40
+00:02:51,220 --> 00:02:54,840
+M، أقل من M طبعًا، أكيد هتكون أقل من M، بحيث برضه زي
+
+41
+00:02:54,840 --> 00:02:58,200
+اللي قلنا، الـ modulus يكون أكبر رقم موجود في الآخر.
+
+42
+00:02:58,200 --> 00:03:01,500
+هنعمل generation لـ sequence. الـ sequence ده هيبين
+
+43
+00:03:01,500 --> 00:03:06,580
+كأنه random، ولكن هو pseudorandom، شبيه العشوائي أو
+
+44
+00:03:06,580 --> 00:03:11,710
+شبه عشوائي sequence، أو شبه عشوائي. بيكون الأرقام
+
+45
+00:03:11,710 --> 00:03:15,130
+تبعته، كل الأرقام اللي موجودة فيها الـ Xn، تبعته كلها
+
+46
+00:03:15,130 --> 00:03:21,450
+من صفر أو أكبر to M. فإيش ولا رقم هيكون أكبر من مين؟
+
+47
+00:03:21,450 --> 00:03:25,930
+من الـ M، لأن هذا الـ modulus. أي رقم أكبر من M، طبيعي
+
+48
+00:03:25,930 --> 00:03:32,470
+الـ mod M هيرجعه لقيمة أقل من M. الـ Xn plus واحد
+
+49
+00:03:32,470 --> 00:03:36,810
+بمعنى أن الـ next value هتساوي الـ current value
+
+50
+00:03:37,410 --> 00:03:41,190
+current number، مضروب في الـ multiplier، مجموع عليه الـ
+
+51
+00:03:41,190 --> 00:03:46,230
+increment، كلهم ناتج طرحهم بنعمل mod أو modulo M.
+
+52
+00:03:46,230 --> 00:03:49,630
+طبعًا، هيطلع رقم جديد. الرقم الجديد بستعمله عشان أحسب
+
+53
+00:03:49,630 --> 00:03:52,390
+الرقم اللي وراه، اللي وراه بحسب اللي وراه، فبنكون
+
+54
+00:03:52,390 --> 00:03:56,790
+بنكون بنعمل sequence of pseudo random numbers. Okay؟
+
+55
+00:03:56,790 --> 00:04:01,290
+كويس جدًا عشان أقول والله الأرقام بتاعتنا عشوائية،
+
+56
+00:04:01,290 --> 00:04:06,360
+أو شكلها فعلاً عشوائي، وصعبة.. وصعب اكتشافها إن يكون
+
+57
+00:04:06,360 --> 00:04:11,060
+الـ a, c, m, primes، كل ما كانوا primes، كل ما كان
+
+58
+00:04:11,060 --> 00:04:16,740
+فيه إمكانية لعمل code صعب. عملية الـ regeneration
+
+59
+00:04:16,740 --> 00:04:20,580
+تبعته، أو صعب كسره، صعب إن حد غيركوا يعرفه. فأنتوا
+
+60
+00:04:20,580 --> 00:04:24,560
+بتعملوا generation بهذه الـ equation، عن طريق إن
+
+61
+00:04:24,560 --> 00:04:27,940
+أنتوا تحددوا بس إيش هي الـ a، إيش الـ c، إيش الـ m
+
+62
+00:04:27,940 --> 00:04:35,750
+بتاعتكم، وتحطوا الـ X الأولى .. أول قيمة بتحطوها
+
+63
+00:04:35,750 --> 00:04:38,710
+.. بتكونوا أنتوا عملتوا هنا generation، اللي هي الـ
+
+64
+00:04:38,710 --> 00:04:42,610
+sequence تبعكم أنتوا .. الأصل للأرقام هذه .. هذه
+
+65
+00:04:42,610 --> 00:04:47,710
+سرية .. هذه سرية .. اللي هيطلع مجموعة أرقام
+
+66
+00:04:47,710 --> 00:04:51,880
+عشوائية .. أنا لو شفتها المفروض ما أعرفهاش. أرقام لا
+
+67
+00:04:51,880 --> 00:04:55,180
+تحمل المعنى الحقيقي. أنا بالنسبة لي اللي هتطلع هيقول
+
+68
+00:04:55,180 --> 00:04:58,120
+إن هي random، أنا مش عارف كيف إن عملها الـ
+
+69
+00:04:58,120 --> 00:05:01,480
+generation. أنتوا اللي لازم تكونوا عارفين. طيب، مع
+
+70
+00:05:01,480 --> 00:05:06,120
+ذلك، ممكن يكسر الـ code تبعكوا هذا كيف؟ إذا كان الـ A
+
+71
+00:05:06,120 --> 00:05:08,780
+والـ C والـ M انعرفت. طيب، كيف أجل؟ الاحتمالية
+
+72
+00:05:08,780 --> 00:05:12,680
+معرفتها إن يكونوا prime، أو at least relatively
+
+73
+00:05:12,680 --> 00:05:18,790
+prime، يكونوا relatively prime لبعض. الـ A مع الـ C،  لجرد أكبر common divisor واحد. الـ C مع الـ M، لجرد أكبر common
+
+74
+00:05:18,790 --> 00:05:22,370
+divisor واحد. الـ A مع الـ M، لجرد أكبر common divisor
+
+75
+00:05:22,370 --> 00:05:25,770
+واحد. إذا كان هيك، معناته كل واحدة منهم relatively
+
+76
+00:05:29,670 --> 00:05:35,970
+prime للتانية، بتصير مناسبة. لو الـ C Zero، بتصير الـ a
+
+77
+00:05:35,970 --> 00:05:39,020
+pure multiplicative. بتصير هنا الـ sequence تبعكم
+
+78
+00:05:39,020 --> 00:05:43,040
+pure multiplicative، كله جاي من عملية ضرب مش أكثر.
+
+79
+00:05:43,040 --> 00:05:48,760
+مفيش أي جمع خالص، مفيش أي جمع. كويس. for example، لو
+
+80
+00:05:48,760 --> 00:05:54,220
+أخذنا الـ M بتساوي ألف، أخذنا الـ C بتساوي أربع مائة
+
+81
+00:05:54,220 --> 00:05:58,510
+سبعة وستة. رقم الـ prime، هي الـ multiplier برضه
+
+82
+00:05:58,510 --> 00:06:02,510
+prime، عبارة عن 293، والـ seed ممكن نختار أي رقم
+
+83
+00:06:02,510 --> 00:06:10,470
+اللي هي أول قيمة موجودة، 426. بنقدر من الـ 426 نعمل
+
+84
+00:06:10,470 --> 00:06:14,330
+generation للرقم اللي وراها، اللي هو الـ X1، عن
+
+85
+00:06:14,330 --> 00:06:19,990
+طريق المعادلة، طول ما بنحطها مباشرة في المعادلة، 285، 285
+
+86
+00:06:19,990 --> 00:06:26,650
+بستخدمها مكان X1 عشان نجيب X2، 972. بستخدمها عشان
+
+87
+00:06:26,650 --> 00:06:30,850
+تجيب X تلاتة. بتترسم وتشتغل، بتضايقوا، بتعملوا
+
+88
+00:06:30,850 --> 00:06:35,130
+generation. كود صغير، وبيفضل يطلع generation. طبعًا،
+
+89
+00:06:35,130 --> 00:06:40,530
+بعد فترة هيتكرر، بعد فترة هتلاقوه هيتكرر الأرقام.
+
+90
+00:06:40,530 --> 00:06:44,570
+اللي بيعملها generation هذه، هذه مرتبطة عددها بمين؟
+
+91
+00:06:44,570 --> 00:06:47,770
+بالـ modulus. الـ modulus ألف، معناه ذلك أن هذا بيقدر
+
+92
+00:06:47,770 --> 00:06:52,750
+يعملكوا generation من صفر لـ 999. الأرقام اللي بقدر
+
+93
+00:06:52,750 --> 00:06:55,890
+يعملها generation هي من صفر لتسعمائة وتسعة وتسعون.
+
+94
+00:06:55,890 --> 00:07:00,330
+Okay. فمعنى ذلك إن أنتَ هيصير repetition للأرقام
+
+95
+00:07:00,330 --> 00:07:05,230
+غالباً بعد عدد أقل من تسعمئة وتسعة وتسعون، أو يعني
+
+96
+00:07:05,230 --> 00:07:10,370
+بعد .. بعد أقل من ألف، بعد أقل من ألف number، هتلاقي
+
+97
+00:07:10,370 --> 00:07:13,710
+إن هيتكرر. ممكن يكون أجل من هيك كمان، ممكن يكون أجل
+
+98
+00:07:13,710 --> 00:07:17,030
+من هيك. امتى ممكن يكون أجل من هيك؟ إذا كانت الأرقام
+
+99
+00:07:17,030 --> 00:07:21,430
+اللي موجودة عندك، وهدي مش primes، فالاحتمالية إن
+
+100
+00:07:21,430 --> 00:07:25,230
+يصير الـ repetition أسرع بتصير أكبر، إن يصير أسرع.
+
+101
+00:07:25,230 --> 00:07:27,950
+طيب، إيش دخل الـ repetition؟ الـ repetition إنك كل ما
+
+102
+00:07:27,950 --> 00:07:32,450
+اتكررت في period صغيرة، كل ما كان إمكانية كسر الـ
+
+103
+00:07:32,450 --> 00:07:38,490
+code تبعك أسهل. معناه ذلك إن كل ما الـ period
+
+104
+00:07:38,490 --> 00:07:42,810
+تبعكم، أو تكرار الأرقام بتصير في مسافات قريبة من
+
+105
+00:07:42,810 --> 00:07:45,610
+بعض، معناه إن فيه إمكانية لكسر الـ code اللي أنتوا
+
+106
+00:07:45,610 --> 00:07:49,360
+عاملينه. هذا فيه إمكانية إن احنا نعرفه. فأنتوا بتبعتوا
+
+107
+00:07:49,360 --> 00:07:53,020
+معلومة مشفرة، فاكرين إن هي مشفرة، بس عاملين
+
+108
+00:07:53,020 --> 00:07:56,440
+regeneration باستخدام أرقام ممكن تكون زوجية مثلًا،
+
+109
+00:07:56,440 --> 00:08:00,920
+زوجية معروفة، لأن دايمًا فيه عوامل مشتركة بينهم. فمعنى
+
+110
+00:08:00,920 --> 00:08:04,850
+ذلك، هتلاقي إن سهلة إن نكسر الـ code، ونعرف إيش
+
+111
+00:08:04,850 --> 00:08:08,590
+الرسالة اللي أنتوا باعتينها. فبطلت مشفرة، فقدتوا
+
+112
+00:08:08,590 --> 00:08:10,950
+الهدف من، أصلاً من عملية التشفير اللي أنتوا بدكم
+
+113
+00:08:10,950 --> 00:08:14,750
+تستخدموها. فهذا مهم جدًا كمان. الأرقام جدًّا بتقدر تكون
+
+114
+00:08:14,750 --> 00:08:20,450
+prime، أو at least relatively prime. مثال ثاني، لو
+
+115
+00:08:20,450 --> 00:08:24,700
+أخذنا الـ M صغيرة،  قللناها، أخذناها قيمة أصغر بحيث
+
+116
+00:08:24,700 --> 00:08:29,860
+إن يكون التكرار سريعًا. الـ a سبعة، الـ c أربعة، الـ x
+
+117
+00:08:29,860 --> 00:08:34,580
+node تلاتة. لحظة بدأنا نعمل generation باستخدام الـ
+
+118
+00:08:34,580 --> 00:08:39,040
+x node اللي هي التلاتة، طلعت سبعة. السبعة استخدمناها
+
+119
+00:08:39,040 --> 00:08:42,700
+جبنا تمانية، بعد واحد، اتنين، تلاتة، أربعة، خمسة، ستة،
+
+120
+00:08:42,700 --> 00:08:51,850
+سبعة، تمانية. التاسعة، التاسعة بتكرر، ترجع تتكرر خلاص.
+
+121
+00:08:51,850 --> 00:08:55,150
+عرفت أنا في الحالة هذه إن التكرار هذا ممكن يعطيني
+
+122
+00:08:55,150 --> 00:09:00,210
+حق بمين؟ بالـ modulus. عرفنا رقم. يعني، هاي بدأت
+
+123
+00:09:00,210 --> 00:09:03,670
+عملية كسر الـ code تبعكم. بدأنا هنا نعرف مجموعة
+
+124
+00:09:03,670 --> 00:09:08,650
+أرقام. طيب، الهدف إن في الآخر تعملوا  سعي إن جدًا
+
+125
+00:09:08,650 --> 00:09:11,270
+ممكن تعملوا الأرقام بتاعتكم هذه تختاروها primes.
+
+126
+00:09:11,840 --> 00:09:14,800
+قدر الإمكان، ممكن تكون الـ M كبيرة حسب الـ application اللي
+
+127
+00:09:14,800 --> 00:09:19,020
+بتستخدموها، حسب لإيش بتكون الـ code تستخدموها، أو لإيش
+
+128
+00:09:19,020 --> 00:09:22,240
+بتكون الـ sequence هذه. طيب، أفضل sequence تم
+
+129
+00:09:22,240 --> 00:09:24,860
+استخدامه كان الـ pure multiplicative generator
+
+130
+00:09:24,860 --> 00:09:29,270
+باستخدام modulus 2 to the power of 31 minus
+
+131
+00:09:29,270 --> 00:09:33,230
+one. كان أفضل واحد على أساس إن هذا، والـ multiplier
+
+132
+00:09:33,230 --> 00:09:38,230
+تبعه كانت two primes،  متباعدين بعض. سبعة prime، متباعدين
+
+133
+00:09:38,230 --> 00:09:42,990
+خمسة متباعدين خمسة. كان مستخدم multiplier هذا is
+
+134
+00:09:42,990 --> 00:09:46,690
+widely used. الـ code هذا مستخدم جدًا وباستمرار،
+
+135
+00:09:46,690 --> 00:09:50,610
+بيستخدموه. بيطلع إن أو بيصير عملية تكرار بعد 2
+
+136
+00:09:51,420 --> 00:09:54,640
+to the power of 31 minus 2. هذه أنتَ بتتكلم عن عدد
+
+137
+00:09:54,640 --> 00:09:58,740
+كبير بالمليارات، يعني بعد كذا مليار، عبل ما الرقم
+
+138
+00:09:58,740 --> 00:10:01,920
+يبدأ يتكرر تاني. فطبعًا هذا بيكون صعب بالنسبة للـ
+
+139
+00:10:01,920 --> 00:10:05,480
+hacker، إن يقدر يتبع إيه؟ أنتَ بيصير التكرار إيه؟ أنتَ
+
+140
+00:10:05,480 --> 00:10:12,230
+بيصير عملية التكرار تبعه تمام. فخذ بالك من الأرقام
+
+141
+00:10:12,230 --> 00:10:15,850
+اللي احنا بنختارها كـ parameters. طيب، الأرقام هذه
+
+142
+00:10:15,850 --> 00:10:18,890
+برضه ممكن تفيدنا لما نيجي نتكلم عن linear
+
+143
+00:10:18,890 --> 00:10:24,110
+congruences، و inverses linear congruences. معناه
+
+144
+00:10:24,110 --> 00:10:29,150
+ذلك، أنا بتكلم عن معادلة في النهاية، AX congruent to
+
+145
+00:10:29,150 --> 00:10:36,250
+B، AX congruent to B under the modulo M. معناه ذلك
+
+146
+00:10:36,250 --> 00:10:40,150
+إن هدول اتنين مكافئين لبعض، وهدي عادة الفكرة اللي
+
+147
+00:10:40,150 --> 00:10:47,370
+بتستخدموها في حل المعادلات اللينية الخطية، لما يكون
+
+148
+00:10:47,370 --> 00:10:54,560
+عندكم A في X بيساوي B، وبتجيبوا X. ماذا كنتوا بتعملوا؟
+
+149
+00:10:54,560 --> 00:10:59,520
+تضربوا في الـ inverse لمين؟ للـ A. فتجيبوا A' في A
+
+150
+00:10:59,520 --> 00:11:05,720
+يساوي A' في B. فالمفروض الاتنين هذولة ضربهم واحد.
+
+151
+00:11:05,720 --> 00:11:11,820
+تمام، ضربهم بيساوي واحد. معناه ذلك إن أي رقم في الـ
+
+152
+00:11:11,820 --> 00:11:15,080
+inverse تبعه المفروض congruent to، main to one.
+
+153
+00:11:15,080 --> 00:11:19,380
+modulo one، بيساوي واحد. الاتنين هذول مفروض يساوي
+
+154
+00:11:19,380 --> 00:11:23,210
+واحد، بكون أقدر أجيب main X. هذه الطريقة اللي كنتوا
+
+155
+00:11:23,210 --> 00:11:26,330
+تستخدموها في ميد، في حالة المعادلات الخطية فعلاً.
+
+156
+00:11:26,330 --> 00:11:31,070
+هنستفيد منها برضه في الـ .. لو أنا بتكلم عن modulo
+
+157
+00:11:31,070 --> 00:11:36,110
+M، لو بنتكلم عن modulo M، المفروض إن الـ A prime في A
+
+158
+00:11:36,110 --> 00:11:41,570
+congruent to مين؟ to one. هدي بنقدر نشغلها، وعشان
+
+159
+00:11:41,570 --> 00:11:46,690
+نقول إن والله فعلاً في الـ modulo M، الـ A فيها إلها
+
+160
+00:11:46,690 --> 00:11:50,970
+inverse. الأصل إن يكونوا الاتنين relatively prime.
+
+161
+00:11:52,870 --> 00:11:56,550
+الـ greatest common divisor تبعهم واحد. فبقدر أقول
+
+162
+00:11:56,550 --> 00:12:03,850
+إيش؟ إن A إلها inverse وحيد داخل الموديلو السام، داخل
+
+163
+00:12:03,850 --> 00:12:07,550
+الموديلو السام، الموديلو
+
+164
+00:12:07,550 --> 00:12:09,390
+السام. هذا لو قلنا مثلًا سبعة.
+
+167
+00:12:21,250 --> 00:12:24,610
+افترضنا إن الاتنين أو التلاتة، وبدنا نجيب الـ
+
+168
+00:12:24,610 --> 00:12:28,710
+inverse للتلاتة، المفروض يكون إن هو رقم واحد أقل من
+
+169
+00:12:28,710 --> 00:12:33,230
+سبعة، هو الـ inverse تبعها، هو الـ inverse تبعها. الأصل
+
+170
+00:12:33,230 --> 00:12:39,050
+يكون unique
+
+223
+00:16:52,550 --> 00:16:54,670
+ففي الحالة هذه ال .. ال .. ال .. ال .. ال .. ال ..
+
+224
+00:16:54,670 --> 00:16:55,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+225
+00:16:55,730 --> 00:16:56,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+226
+00:16:56,290 --> 00:16:56,670
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+227
+00:16:56,670 --> 00:17:02,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+228
+00:17:02,610 --> 00:17:03,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+229
+00:17:03,430 --> 00:17:04,090
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+230
+00:17:04,090 --> 00:17:04,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+231
+00:17:04,130 --> 00:17:05,130
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+232
+00:17:05,130 --> 00:17:05,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+233
+00:17:05,730 --> 00:17:07,250
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+234
+00:17:07,250 --> 00:17:12,070
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+235
+00:17:12,070 --> 00:17:20,690
+ال .. ال ..
+
+236
+00:17:20,950 --> 00:17:26,150
+رقم congruent لها بس احنا نتكلم unique باعتبار أن
+
+237
+00:17:26,150 --> 00:17:31,290
+هو داخل ال cycle داخل أو أقل من سبعة هي ال minus
+
+238
+00:17:31,290 --> 00:17:39,190
+two أو الخمسة أو الخمسة صحيح؟ تعالوا نشوف لماذا
+
+239
+00:17:39,190 --> 00:17:45,370
+خمسة لأنها المكملة لل minus two كيف المكملة؟ مكملة
+
+240
+00:17:45,370 --> 00:17:49,690
+أنا أشتغل under modulo M  M هدفه سبعة ف minus two
+
+241
+00:17:49,690 --> 00:17:55,110
+إيش اللي بكملها السبعة؟  فيها أنها خمسة أن أمشي
+
+242
+00:17:55,110 --> 00:17:57,170
+خطوتين عكس عقارب الساعة
+
+243
+00:18:03,320 --> 00:18:07,820
+ممكن تكون minus 5 minus 2 أو 5 وكل رقم congruent
+
+244
+00:18:07,820 --> 00:18:13,360
+لهم كيف أجيب ال congruence تبعتهم minus 2 minus 7
+
+245
+00:18:13,360 --> 00:18:20,060
+minus 7 minus 7 minus 7 بتصير minus 19 كمان minus
+
+246
+00:18:20,060 --> 00:18:25,760
+7 بتصير minus 16 طيب هنا plus 7 plus 7 إذا كانت
+
+247
+00:18:25,760 --> 00:18:32,440
+جمع plus 7 أو طريقة  هلى minus 7 بتعطينا minus 2 هذه
+
+248
+00:18:32,440 --> 00:18:38,300
+زائد سبعة تعطينا خمسة زائد سبعة اثنا عشر زائد سبعة
+
+249
+00:18:38,300 --> 00:18:44,300
+تسعة عشر فمعنى ذلك ممكن تكون ال inverse للتلاتة
+
+250
+00:18:44,300 --> 00:18:50,620
+minus two أو خمسة أو minus تسعة أو اثنا عشر أو تسعة
+
+251
+00:18:50,620 --> 00:18:56,540
+عشر أو minus ستة عشر أي رقم أمشي أي رقم أمشي خلّيني
+
+252
+00:18:56,540 --> 00:19:00,470
+أنا آخذ مثلًا الخمسة خمسة في تلاتة محتاج أن نتأكد
+
+253
+00:19:00,470 --> 00:19:04,730
+هل فعلا ال A' هذه اللي هي خمسة في ال A اللي هي
+
+254
+00:19:04,730 --> 00:19:11,730
+تلاتة مد سبعة هيساوي فعلا واحد ولا لأ هدفي هدي
+
+255
+00:19:11,730 --> 00:19:20,730
+خمسة عشر مد سبعة واحد لو جربتوا أي رقم من الأرقام
+
+256
+00:19:20,730 --> 00:19:24,790
+هذه اللي هي كم كلها congruent كل واحدة congruent
+
+257
+00:19:24,790 --> 00:19:28,770
+لإنتاج اللي احنا طلعناه هو ال minus four أي واحدة
+
+258
+00:19:28,770 --> 00:19:35,190
+منهم اضربوا فيها تلاتة مود سبعة هيطلع واحد تمام
+
+259
+00:19:35,190 --> 00:19:39,770
+هي هذه الفكرة طبعًا لاحظوا أن احنا هنا استشفناها
+
+260
+00:19:39,770 --> 00:19:44,110
+مجرد script لأن الأرقام بسيطة سبعة جدًّا هتتكرر
+
+261
+00:19:44,110 --> 00:19:47,930
+تلاتة منها يطلع رقم اتنين كويسة مش دائمًا بتكون
+
+262
+00:19:47,930 --> 00:19:51,790
+الأرقام سهلة بهذا الشكل ممكن تكون أرقام كبيرة
+
+263
+00:19:51,790 --> 00:19:55,790
+الأرقام الكبيرة في لها طريقة ثانية الأرقام الكبيرة
+
+264
+00:19:55,790 --> 00:19:59,650
+بدنا نتأكد أولًا أن هي greatest common divisor equal
+
+265
+00:19:59,650 --> 00:20:02,910
+to one ولا لأ هل هم فعلا equal to one greatest
+
+266
+00:20:02,910 --> 00:20:06,930
+common divisor بينهم ولا لأ فلو قلنا بدنا ال
+
+267
+00:20:06,930 --> 00:20:14,430
+universe ل 101 مديوله 4620 أول شيء بدنا نتأكد هو هم
+
+268
+00:20:14,430 --> 00:20:18,670
+الاتنين هدول greatest common divisor equal to one
+
+269
+00:20:18,670 --> 00:20:22,030
+طيب أنا إيش بدي في ال one هذا تحديدا ال one هذا هو
+
+270
+00:20:22,030 --> 00:20:26,230
+ال congruent اللي أنا أشتغل عليه إذا فعلا ال
+
+271
+00:20:26,230 --> 00:20:35,570
+greatest common divisor ل 101 و 4620 فعلا واحد
+
+272
+00:20:35,570 --> 00:20:39,930
+الواحد هذا هو نفسه اللي أنا أشتغل عليه على اعتبار
+
+273
+00:20:39,930 --> 00:20:43,350
+أنه a في a equivalent to one
+
+274
+00:20:47,520 --> 00:20:49,800
+هو هذا اللي احنا بدنا ندور عليه إذا فعلا ال grade
+
+275
+00:20:49,800 --> 00:20:52,720
+of common divisor equal to one بضمن أن الاتنين
+
+276
+00:20:52,720 --> 00:20:59,540
+هدول ال congruent تبعهم واحد أقدر أجيب inverse أو
+
+277
+00:20:59,540 --> 00:21:04,340
+ال inverse في الحالة هذه للمية واحد موجود أو ممكن
+
+278
+00:21:04,340 --> 00:21:10,120
+في module 4620 عشان كده هنعمل grade of common divisor
+
+279
+00:21:10,120 --> 00:21:14,200
+اللي اتعودنا عليها باستخدام طريقة مين هذه؟
+
+280
+00:21:16,790 --> 00:21:24,790
+Euclid's algorithm في لحظة هاي 4620 هنا مضروبة
+
+281
+00:21:24,790 --> 00:21:29,530
+مكرر الألف والمية وواحد خمسة وأربعين مرة ال
+
+282
+00:21:29,530 --> 00:21:35,590
+remainder سبعة السبعة هذه لسة ما خلصناش احنا ما
+
+283
+00:21:35,590 --> 00:21:40,590
+خلصناش هذه ناتج في بعض الموديولو هذه أقل من B يعني
+
+284
+00:21:40,590 --> 00:21:43,790
+جاهز أعيد لكل ال algorithm نفسه أقل من B معناه ذلك
+
+285
+00:21:43,790 --> 00:21:52,220
+أنه صارت B كأنها B mod الناتج ال remainder R صحيح؟
+
+286
+00:21:52,220 --> 00:22:01,780
+كويس هاي B وهاي R طيب هذه برضه هتطلع ناتج R جديد
+
+287
+00:22:01,780 --> 00:22:09,320
+وصارت B جديدة ال B الجديدة 75 ف 75 مع ال R الجديدة ال
+
+288
+00:22:09,320 --> 00:22:11,240
+B الجديدة مع ال R الجديدة ال B الجديدة مع ال R
+
+289
+00:22:11,240 --> 00:22:15,950
+الجديدة لما نصل من لصفر لما كنا بنصل ل صفر الرقم
+
+290
+00:22:15,950 --> 00:22:19,830
+بيساوي صفر آخذ ال a هو ال greatest common divisor
+
+291
+00:22:19,830 --> 00:22:24,310
+هنا مش هيظهر عندكم صفر لأنه ما فيش أي عامل مشترك
+
+292
+00:22:24,310 --> 00:22:29,390
+بينهم الاتنين ال greatest common divisor تبعهم
+
+293
+00:22:29,390 --> 00:22:39,140
+واحد relatively prime فلاحظوا خلصت بواحد مش صفر مش
+
+294
+00:22:39,140 --> 00:22:42,220
+في صفر خلصت عندكم هنا بواحد هي آخر واحد هنا
+
+295
+00:22:42,220 --> 00:22:46,840
+تأكدنا منه جربنا هي هي خلاص بيظل واحد الواحد بيظل
+
+296
+00:22:46,840 --> 00:22:51,220
+زي ما هو الواحد فخلاص آخر مرحلة كانت هي هذه وكان
+
+297
+00:22:51,220 --> 00:22:54,680
+عندنا ال remainder آخر واحد واحد فمعنى ذلك أن هدول فعلا
+
+298
+00:22:54,680 --> 00:22:57,700
+relatively prime وهذا معناه أن مئة وواحد
+
+299
+00:22:57,700 --> 00:23:04,840
+يوجد inverse وحيد under modulo 4620 طيب إيش هو جدًّا
+
+300
+00:23:04,840 --> 00:23:11,680
+قيمته هذا ال inverse الوحيد؟ بدنا قيمته ال turn هذا
+
+301
+00:23:11,680 --> 00:23:15,240
+اللي كان يمثل لنا ال greatest common divisor هو هذا
+
+302
+00:23:15,240 --> 00:23:23,980
+اللي أنا بدي أنسب له طبعًا
+
+303
+00:23:23,980 --> 00:23:28,630
+واحد في M بهذا الشكل المفروض أنه يساوي مفروض أن هو
+
+304
+00:23:28,630 --> 00:23:31,130
+يساوي واحد زي الحالة بتاعة التلاتة عملناها في minus
+
+305
+00:23:31,130 --> 00:23:36,810
+اثنين تلاتة زائد واحد في سبعة زائد واحد طبعًا مش
+
+306
+00:23:36,810 --> 00:23:41,270
+مضروري واحد ممكن في النهاية تكون أي equivalent لل
+
+307
+00:23:41,270 --> 00:23:47,930
+M ف some K هنا صدف أن واحد لأن الأرقام كثير كانت
+
+308
+00:23:47,930 --> 00:23:51,270
+صغيرة وقريبة من بعض فهذا يساوي واحد فبدنا نبدأ من
+
+309
+00:23:51,270 --> 00:23:55,930
+الواحد هذا الواحد هذا أيه موجود عندكم؟ بدنا الواحد
+
+310
+00:23:55,930 --> 00:24:07,100
+يساوي some k أو some integer في 101 زائد
+
+311
+00:24:07,100 --> 00:24:16,720
+some integer في 4620 صحيح؟ إذا وصلنا لل form هذا
+
+312
+00:24:16,720 --> 00:24:21,420
+أقول أن هدول ال Bézout coefficients 101 إيش ال
+
+313
+00:24:21,420 --> 00:24:24,700
+coefficient اللي معها؟ هو هذا ال inverse تبعها هو
+
+314
+00:24:24,700 --> 00:24:27,880
+هذا ال إيش؟ ال inverse تبعها عشان نعمل الكلام هذا
+
+315
+00:24:27,880 --> 00:24:30,980
+هننطلق من نفس ال sequence اللي احنا مشيناه الواحد
+
+316
+00:24:30,980 --> 00:24:34,620
+هذا اللي بدنا نمسكه لأنه هذا اللي أنا بدي أساوي
+
+317
+00:24:34,620 --> 00:24:38,460
+فيه كل ال terms اللي  بعتمدها و هنلاحظ الواحد إيش
+
+318
+00:24:38,460 --> 00:24:44,440
+يساوي تلاتة ناقص واحد في اثنين تلاتة ناقص واحد في
+
+319
+00:24:44,440 --> 00:24:50,030
+اثنين طيب كويس الاثنين هذه كانت ال remainder
+
+320
+00:24:50,030 --> 00:24:54,570
+للمرحلة السابقة فبقدر آخذها بدلالة الاثنين السابقتين
+
+321
+00:24:54,570 --> 00:24:58,490
+فبتصير الاثنين عبارة عن تلاتة وعشرين ناقص سبعة في
+
+322
+00:24:58,490 --> 00:25:04,410
+تلاتة طيب تلاتة هي ستة وعشرين ناقص تلاتة تلاتة و
+
+323
+00:25:04,410 --> 00:25:09,950
+عشرين نزلنا نزول هلّوجد عشان نجيب greatest common
+
+324
+00:25:09,950 --> 00:25:13,130
+divisor عشان نجيب ال inverse بنطلع طلوع بالعكس
+
+325
+00:25:14,040 --> 00:25:17,360
+فكثير كويس وأنتم تحلّوا مسائل زي هذه تحطوا الاثنين
+
+326
+00:25:17,360 --> 00:25:20,280
+جنب بعض عشان تأخذوا معلوماتكم من بعض تأخذوا
+
+327
+00:25:20,280 --> 00:25:23,480
+المعلومات من بعض هاي أخذناها الأولى طيب اثنين قلنا
+
+328
+00:25:23,480 --> 00:25:26,500
+زي ما .. زي ما اتكلمنا هنا عبارة عن تلاتة وعشرين
+
+329
+00:25:26,500 --> 00:25:29,680
+ناقص سبعة في تلاتة تلاتة وعشرين ناقص سبعة في
+
+330
+00:25:29,680 --> 00:25:34,740
+تلاتة دائمًا هتلاقوا التلاتة اللي كانت هنا ال remainder
+
+331
+00:25:34,740 --> 00:25:39,240
+صارت هنا B ونفس الكلام التلاتة وعشرين هنا كانت
+
+332
+00:25:39,240 --> 00:25:44,370
+تتكرر هنا لأن كل B آخذها من ال R اللي قبلها مش
+
+333
+00:25:44,370 --> 00:25:46,950
+شكلة ال algorithm بيعطيني طيب ما هو نفس الكلام
+
+334
+00:25:46,950 --> 00:25:50,030
+هستفيد من الموضوع هذا أنه دائمًا هيكون في عندكم
+
+335
+00:25:50,030 --> 00:25:55,430
+common هنا في سبعة تلاتات هنا في تلاتة واحدة مجموعة
+
+336
+00:25:55,430 --> 00:26:00,130
+اللي بيصير في عندكم ثمان تلاتات ثمان تلاتات التلاتة هذه
+
+337
+00:26:00,130 --> 00:26:06,010
+بتعرضوا قيمتها من ال schedule اللي جايبكم من ال
+
+338
+00:26:06,010 --> 00:26:10,050
+schema اللي جايبكم كويسة لاحظوا هنا تلاتة وعشرين و
+
+339
+00:26:10,050 --> 00:26:13,830
+في تلاتة وعشرين ومنطق جدًّا أصلًا دائمًا يطلع فيه
+
+340
+00:26:13,830 --> 00:26:17,770
+أرقام متشابهة لأن هنا كانت ال B هنا كانت ال R وال
+
+341
+00:26:17,770 --> 00:26:22,390
+R هي نفسها ال B في المرحلة اللي بعدها احنا بناخذهم
+
+342
+00:26:22,390 --> 00:26:26,770
+من بعض أساسًا تمام فلاحظوا هنا minus one وهنا
+
+343
+00:26:26,770 --> 00:26:33,670
+minus ثمانية minus تسعة minus تسعة ال 23 عوضناها ب
+
+344
+00:26:33,670 --> 00:26:39,770
+75 ناقص 2 في 26 في 26 هنا في 26  بقى مع التجميع
+
+345
+00:26:39,770 --> 00:26:43,730
+هيطلع لكم 26 باعتبار أن ال 26 موجودة هنا بثمانية
+
+346
+00:26:43,730 --> 00:26:51,190
+ثمانية وهنا 18 ف 26 ب 26 26 برضه من هنا تقدر
+
+347
+00:26:51,190 --> 00:26:57,110
+تأخذوها على أساس أنها 101 ناقص 75 بدأ يظهر عند
+
+348
+00:26:57,110 --> 00:27:02,490
+أول term بديها في المعادلة مئة وواحد هي أول term
+
+349
+00:27:02,490 --> 00:27:07,190
+ظهر بدنا ال term الثاني ال 4620 عشان أربطهم
+
+350
+00:27:07,190 --> 00:27:09,850
+الاثنين في معادلة واحدة ولازم equal to one وأنا
+
+351
+00:27:09,850 --> 00:27:14,290
+ضمن أنه كله equal to one
+
+352
+00:27:15,830 --> 00:27:26,530
+وصلنا ل 75 برضه أوجد 4620 رتبنا المعادلة فالواحد
+
+353
+00:27:26,530 --> 00:27:29,530
+طلع بالساوي ماينص خمسة وثلاثين في أربعة ألاف
+
+354
+00:27:29,530 --> 00:27:35,170
+ستمائة وعشرين plus مئة ألف وستمائة وواحد في
+
+355
+00:27:35,170 --> 00:27:41,530
+مئة وواحد فإذا ال inverse تبعنا ألف وستمائة وواحد
+
+356
+00:27:42,890 --> 00:27:50,490
+إذا كانت ال A تساوي 101، then ال A' تساوي 1601
+
+357
+00:27:50,490 --> 00:27:58,970
+طبعًا هذا كله مود 4620
+
+358
+00:28:00,850 --> 00:28:06,550
+تمام؟ فهي طريقة الشغل في الحالة بتاعتنا لاحظوا أن
+
+359
+00:28:06,550 --> 00:28:09,990
+أنتم بتكونوا تعملوا grades of common divisors حتى
+
+360
+00:28:09,990 --> 00:28:13,830
+لو أنتم عارفين أنها primes بس بتسهل عليكم في ال
+
+361
+00:28:13,830 --> 00:28:17,050
+analysis هذا بتسهل عليكم لأن كل واحدة بتكونوا
+
+362
+00:28:17,050 --> 00:28:19,110
+عارفين إيش ال remainder اللي كان موجود وقداش
+
+363
+00:28:19,110 --> 00:28:25,600
+بتقدروه a minus some k في b A مضروبة في some K في B
+
+364
+00:28:25,600 --> 00:28:29,860
+تمام؟ تقدر تشتغل عليه بهذا الشكل أقدرنا هنا نجيب
+
+365
+00:28:29,860 --> 00:28:34,560
+greatest common divisor ومنها أقدرنا نجيب ال
+
+366
+00:28:34,560 --> 00:28:43,620
+inverse جئنا إليكم بسؤال بهذا الشكل حلّنا
+
+367
+00:28:43,620 --> 00:28:50,980
+قيمة X عندما تلاتة X congruent to 4 معادلة Linear هي
+
+368
+00:28:50,980 --> 00:28:53,520
+المعادلة Linear وبتجيبوا قيم ال variables اللي
+
+369
+00:28:53,520 --> 00:28:57,400
+فيها قيم ال variables احنا سابقًا اتكلمنا عن
+
+370
+00:28:57,400 --> 00:29:01,140
+الموضوع هذا باستخدام ال matrices لو متذكرين ال
+
+371
+00:29:01,140 --> 00:29:05,800
+matrices قلنا أن A في X بيساوي B فكنتم تقولون
+
+372
+00:29:05,800 --> 00:29:09,020
+ال vector الأول transpose طبعًا ال vector الأول
+
+373
+00:29:09,020 --> 00:29:12,880
+اللي أعمله transpose في ال X طبعًا ال A هذه كانت
+
+374
+00:29:12,880 --> 00:29:13,260
+Matrix
+
+375
+00:29:16,960 --> 00:29:19,800
+حسب جدًّا عدد المعادلات اللي موجودة عندكم وجدًّا عدد
+
+376
+00:29:19,800 --> 00:29:26,920
+ال variables بيساوي B كيف كنتم تحلونها؟
+
+377
+00:29:26,920 --> 00:29:32,360
+A inverse تضربوه في الأولى وتضربوه في الثانية،
+
+378
+00:29:32,360 --> 00:29:39,860
+صحيح؟ طيب ضربناه في الأولى وضربناه في الثانية طيب
+
+379
+00:29:39,860 --> 00:29:42,560
+هاي ال two inverses في بعض هدول ال two inverses
+
+380
+00:29:42,560 --> 00:29:47,220
+في بعض واحد فبيطلع لنا قيمة X على أساس أنها ال A
+
+381
+00:29:47,220 --> 00:29:51,580
+inverse في B فما هو نفس الكلام اللي بيحكيه فإذا
+
+382
+00:29:51,580 --> 00:29:54,580
+أنا مضطر أجيب ال inverse بتاعة ال matrix هنا وهنا
+
+383
+00:29:54,580 --> 00:29:57,360
+نفس الكلام عشان أحل المعادلة مضطر أجيب ال inverse
+
+384
+00:29:57,360 --> 00:30:02,260
+تبع ال A فمحتاج ال inverse prime عشان أجيب ال
+
+385
+00:30:02,260 --> 00:30:06,020
+inverse تبعها ال inverse تبعها بضمن لأن ال X  دلت
+
+386
+00:30:06,020 --> 00:30:11,210
+term لحالها فمنطقيًا هتساوي ال inverse للتلاتة ..
+
+387
+00:30:11,210 --> 00:30:14,550
+inverse للتلاتة هنا في أربعة .. inverse ل
+
+388
+00:30:14,550 --> 00:30:16,710
+التلاتة في أربعة هنشوف هل فعلا حد طبعًا الكلام ..
+
+389
+00:30:16,710 --> 00:30:24,750
+الكلام في غير شكل ولا لأ طيب مسبقًا احنا عرفنا أن
+
+390
+00:30:24,750 --> 00:30:29,530
+ال inverse للتلاتة module of seven يبقى لو
+
+391
+00:30:29,530 --> 00:30:33,070
+module ثاني بيختلف ديروا بالكم لو module ثاني ال
+
+392
+00:30:33,070 --> 00:30:36,500
+inverse للتلاتة هتختلف هذا إذا .. إذا فرضنا أنه
+
+393
+00:30:36,500 --> 00:30:41,040
+يوجد unique inverse إليها under modulo 3 .. under
+
+394
+00:30:41,
+
+445
+00:34:33,800 --> 00:34:38,340
+أنتم عاملين زي الساعة، لازم كل لفة بتلف لأنها عدد
+
+446
+00:34:38,340 --> 00:34:41,080
+لأنها من اللفات بتقدروا تقولوا الساعة هتلف قد إيش
+
+447
+00:34:41,080 --> 00:34:44,840
+عشان تحسبوا الزمن، هتلف باستمرار، هذا periodic
+
+448
+00:34:44,840 --> 00:34:48,360
+periodic معناها اتفقنا أنها هتتكرر، أنا بتكلم عن الـ
+
+449
+00:34:48,360 --> 00:34:51,940
+inverse داخل الدورة الواحدة، اللفة الواحدة، اللفة
+
+450
+00:34:51,940 --> 00:34:56,440
+الواحدة لها الستة فقط، طبعاً كل شيء يمثل ستة أو
+
+451
+00:34:56,440 --> 00:35:01,580
+بقدر قربه لستة، congruent to six، برضه يمشي الحال
+
+452
+00:35:01,580 --> 00:35:03,980
+ما أقدرش أقول إن هذا هو الرقم الـ standard تبعها
+
+453
+00:35:03,980 --> 00:35:12,600
+الزاوية 690، طبيعي لازم أجربها، أطرح منها 360، نطرح
+
+454
+00:35:12,600 --> 00:35:16,780
+منها 360، وهنا نفس الكلام، أي قيمة تجيكم، minus 15
+
+455
+00:35:16,780 --> 00:35:22,850
+طبيعي أنك تطرح منها 7، الأول نتشيل منها سبعة، شلنا
+
+456
+00:35:22,850 --> 00:35:26,810
+منها سبعة، فكأني جمعت عليها سبعة، فبتصير minus
+
+457
+00:35:26,810 --> 00:35:31,330
+ثمانية، طيب minus ثمانية لسه أكبر من minus سبعة
+
+458
+00:35:31,330 --> 00:35:35,530
+ثمان مرات، minus واحد، فإذا anti-clockwise لو بدنا
+
+459
+00:35:35,530 --> 00:35:39,770
+نختار anti-clockwise اللي هي مكافئة هي لتلاتين على
+
+460
+00:35:39,770 --> 00:35:46,270
+اعتبار ما كنتم تقولوا ناقص تلاتمية وتسعين، فإذا
+
+461
+00:35:46,270 --> 00:35:49,150
+clockwise إلها inverse واحد، anti-clockwise إلها
+
+462
+00:35:49,150 --> 00:35:54,060
+inverse واحد، فالـ two inverses تبقوا هنا minus 6 أو
+
+463
+00:35:54,060 --> 00:35:59,160
+minus 1، يعني عفواً الـ 6 أو الـ 1، والـ 6 أو الـ 1 في
+
+464
+00:35:59,160 --> 00:36:02,140
+الحالتين، اللي هي بتبقوا تمشوا من هنا 6 درجات
+
+465
+00:36:02,140 --> 00:36:06,980
+فبتوصلوا لهالنقطة، أو بالثانية درجة فبرضه هتوصلوا
+
+466
+00:36:06,980 --> 00:36:11,500
+لنفس النقطة، هي هي النقطة، واحدة يعني نقطة واحدة
+
+467
+00:36:11,500 --> 00:36:17,650
+داخل الـ cycle، نقطة واحدة داخل الـ cycle، واضح أن هنا
+
+468
+00:36:17,650 --> 00:36:21,250
+ما فيش مشكلة عندنا، مش أشكال طبعاً، لاحظوا إذا الأرقام
+
+469
+00:36:21,250 --> 00:36:28,130
+الكبيرة هنا، زي مثلاً المثلث، اعتمدوا هي 101، والـ
+
+470
+00:36:28,130 --> 00:36:32,370
+module أو الـ module تبعنا كان 4620 في الحالة هذه
+
+471
+00:36:32,370 --> 00:36:37,240
+تتحلوا من الأول، تعملوا greatest common divisor، و
+
+472
+00:36:37,240 --> 00:36:41,620
+بعدين تجيبوا الـ .. الـ .. الـ .. الـ Bézout الـ
+
+473
+00:36:41,620 --> 00:36:44,420
+coefficients تبعتكم، عشان تحسبوا الـ inverse، وبعدين
+
+474
+00:36:44,420 --> 00:36:47,740
+الـ inverse تجربوه، تضربوه هنا عشان تجيبوا قد إيش
+
+475
+00:36:47,740 --> 00:36:52,620
+القيم، قيمة x قد إيش، قيمة x الممكنة، قد إيش قيمة x
+
+476
+00:36:52,620 --> 00:36:58,560
+الممكنة، okay، pseudo primes، مدام كنا اتكلمنا عن
+
+477
+00:36:58,560 --> 00:37:01,580
+الـ random، طب ما فيه الـ primes كمان، فيه جزئية الـ
+
+478
+00:37:01,580 --> 00:37:05,900
+prime، الـ prime مش بالضروري دائماً يكون هو فعلاً الـ
+
+479
+00:37:05,900 --> 00:37:08,340
+prime، pure prime، مين اللي وضّح إنه جزئي هذا؟ مين
+
+480
+00:37:08,340 --> 00:37:11,060
+اللي خلّى الناس يفكروا في هذا الموضوع هذا؟ مجموعة
+
+481
+00:37:11,060 --> 00:37:14,520
+علماء صينيين قدماء جداً، يعني من قدماء الصينيين
+
+482
+00:37:14,520 --> 00:37:20,560
+طلعوا نظرية إنه إذا whenever n is prime، إذا كان n
+
+483
+00:37:20,560 --> 00:37:24,360
+is prime، فإذا two to the power n minus one
+
+484
+00:37:24,360 --> 00:37:29,950
+congruent to one mod n، هذا الكلام إذا كانت prime
+
+485
+00:37:29,950 --> 00:37:36,490
+ذهبوا في اعتقادهم لإثبات العكس، إيش هو؟ إنه إذا two
+
+486
+00:37:36,490 --> 00:37:39,550
+to the power of N minus one congruent to one mod N،
+
+487
+00:37:39,550 --> 00:37:44,790
+فإذا الـ N هذه is prime، للأسف
+
+488
+00:37:44,790 --> 00:37:49,850
+ادعاء العكس ما كان صحيح 100%، بعدهم كذا وقت، كذا
+
+489
+00:37:49,850 --> 00:37:57,640
+سنة، كذا عقد من السنوات، كذا قرن من القرون، طلعوا أن
+
+490
+00:37:57,640 --> 00:38:00,980
+لأ، والله ما تصدقش دائماً، هذا 2 to the power n
+
+491
+00:38:00,980 --> 00:38:05,800
+minus one equal to one mod n، مش بالضروري يتبع إنه
+
+492
+00:38:05,800 --> 00:38:11,240
+n is prime، كيف؟ لاحظوا المعادلة هذه؟ هي رقم تلاتمية
+
+493
+00:38:11,240 --> 00:38:14,980
+واحد وأربعين، هذه عبارة عن أحد عشر، واحدة، معناها مش
+
+494
+00:38:14,980 --> 00:38:20,160
+prime صحيح؟ مش prime، ومع ذلك 2 to the power n
+
+495
+00:38:20,160 --> 00:38:24,340
+minus one تساوي أو congruent to one mod تلاتمية
+
+496
+00:38:24,340 --> 00:38:29,530
+واحد وأربعين، طيب، كويس، هل معنى ذلك أن كلامهم كان
+
+497
+00:38:29,530 --> 00:38:33,670
+بالمجمل خطأ؟ لأ، استنوا لحظة، هم فتحوا علينا الـوجد
+
+498
+00:38:33,670 --> 00:38:38,670
+على حاجة ثانية، إن هذا okay، مش prime، بس أقدر أسميه
+
+499
+00:38:38,670 --> 00:38:41,710
+pseudo prime، ليش pseudo prime؟ لأنه لا يقبل
+
+500
+00:38:41,710 --> 00:38:50,090
+القسمة إلا على two primes، 11 و 31، فإذا الكلام هذا
+
+501
+00:38:50,090 --> 00:38:56,600
+صحيح، بس كان بده إضافة صغيرة، بدل ما أقول then M is
+
+502
+00:38:56,600 --> 00:39:03,480
+prime، كان ممكن أقول M at least pseudoprime، ممكن تكون
+
+503
+00:39:03,480 --> 00:39:06,580
+prime، وممكن تكون pseudoprime، إيش تعريف الـ pseudoprime؟
+
+504
+00:39:06,580 --> 00:39:12,340
+شبيه بالـ prime، مع اختلاف واحد، إنه ممكن يقسم على
+
+505
+00:39:12,340 --> 00:39:16,880
+عددين، اثنين primes، فهنا هذا فعلاً ما يقسمش إلا على
+
+506
+00:39:16,880 --> 00:39:19,300
+الرقمين هذول فقط، الرقمين هذول اللي شجعنا نطلع
+
+507
+00:39:19,300 --> 00:39:23,750
+عليهم، هي اثنين primes، الـ two primes هذا له خصوصية
+
+508
+00:39:23,750 --> 00:39:30,610
+هذا بنسميه pseudoprime، الـ 341 نسميه pseudoprime، ممكن
+
+509
+00:39:30,610 --> 00:39:34,410
+استخدامه لإني كنت بدور، بدّي primes، والـ prime
+
+510
+00:39:34,410 --> 00:39:37,170
+هذا، ليش احنا بندور عليه؟ الـ prime بندور عليه لأنه
+
+511
+00:39:37,170 --> 00:39:40,690
+بفيدنا في الـ security، اللحقة لما نجي نتكلم عن الـ
+
+512
+00:39:40,690 --> 00:39:45,200
+cryptographic أو الـ cryptography theory اللي هنتكلم
+
+513
+00:39:45,200 --> 00:39:49,340
+عنها، بلزمنا أنه نكون لما نعمل generation، حتى زي
+
+514
+00:39:49,340 --> 00:39:52,340
+توي، وأن أنا بدور على أرقام تكون prime، تكون أفضل
+
+515
+00:39:52,340 --> 00:39:56,400
+لما بدّي prime، أدور على prime، ورقمه كبير، يكون رقم
+
+516
+00:39:56,400 --> 00:40:01,100
+عالي كبير، هذه okay، ما نفعتش، بس هي هتكون، هتطلع لي two
+
+517
+00:40:01,100 --> 00:40:06,950
+primes بدل الواحد، إذا كانت تحقق الشرط هذا، فمعنى ذلك
+
+518
+00:40:06,950 --> 00:40:12,550
+أن هذه إما هي نفسها prime أو هي pseudoprime، هتطلع
+
+519
+00:40:12,550 --> 00:40:17,310
+two primes، هتطلع two primes، مش الـ prime واحد،
+
+520
+00:40:17,310 --> 00:40:22,210
+كويسة، فإذا النظرية هيك اتعدّلت شئ خفيف، بدل ما كنا
+
+521
+00:40:22,210 --> 00:40:27,910
+نقول الـ prime، بنقول إيش؟ بنقول pseudoprime، هتقولوا
+
+522
+00:40:27,910 --> 00:40:31,690
+ليه؟ مش بدنا فيها pseudoprime؟ لأ، الناس بعد ما وجدوا
+
+523
+00:40:31,690 --> 00:40:35,490
+أن هناك أرقام يعني نستفيد منها، إلها خصوصية، في
+
+524
+00:40:35,490 --> 00:40:40,490
+إلها ميزة، اللي هي pseudoprime، هذه إلها ميزة، ذهب في
+
+525
+00:40:40,490 --> 00:40:45,390
+الاعتقاد إنه مش بالضروري الـ base تبعتنا اثنين، لـ a,
+
+526
+00:40:45,510 --> 00:40:50,550
+b، الكلام صحيح، b to the power n minus one congruent
+
+527
+00:40:50,550 --> 00:40:55,130
+to one base n، اثنين أو أكثر، مش مشكلة، فاتعممت
+
+528
+00:40:55,130 --> 00:40:58,150
+القاعدة بهذا الشكل، على أساس أنه أي رقم بيحقق
+
+529
+00:40:58,150 --> 00:41:03,730
+المعادلة هذه، هنسميه pseudoprime Carmichael
+
+530
+00:41:03,730 --> 00:41:07,990
+Carmichael number، Carmichael مسك الموضوع هذا، ومسك
+
+531
+00:41:07,990 --> 00:41:11,870
+لنا كل الأرقام، بدأ يفحص الأرقام اللي ممكن نحطها
+
+532
+00:41:11,870 --> 00:41:17,410
+ضمن set، الـ set هنسميها pseudoprime، فلقينا أن هو في
+
+533
+00:41:17,410 --> 00:41:24,240
+الرقم بعد الرقم اللي احنا شغلناه، الـ 431، فيه 561، في
+
+534
+00:41:24,240 --> 00:41:30,260
+1105، في 1729، شكلهم كإنهم الـ prime، بس لأ، هم فعلياً
+
+535
+00:41:30,260 --> 00:41:33,260
+ما بينفعوش إلا إنه يكونوا حاصل ضرب two primes ثانية
+
+536
+00:41:33,260 --> 00:41:38,400
+يكونوا حاصل ضرب two primes ثانية فقط، يعني ما مجسموش
+
+537
+00:41:38,400 --> 00:41:41,480
+علاقة ثانية، إذا مجسموا علاقة ثانية بطلوا pseudoprime
+
+538
+00:41:41,480 --> 00:41:45,520
+فقط، مجسموا على رقمين، لإنه الرقمين هذول prime
+
+539
+00:41:45,520 --> 00:41:49,140
+فبدأ يعمل analysis، هيو بدأ يطلع فيهم لعام 29000، وفيه طبعة لهم تكملة،
+
+540
+00:41:49,140 --> 00:41:54,640
+طيب وبعدين؟ إيش بدنا فيهم
+
+541
+00:41:54,640 --> 00:42:01,000
+هذول؟ so what؟ who cares؟ مين الحق يعني؟ بعدين زي
+
+542
+00:42:01,000 --> 00:42:04,180
+ما أنتم، طب تقولوا طب، ولما نجيب الـ inverse؟
+
+543
+00:42:04,180 --> 00:42:07,040
+قلت لكم، لأ، اصبروا شوية، بنحل فيها المعادلة الـ
+
+544
+00:42:07,040 --> 00:42:10,900
+linear equation، الـ linear congruential، حلّيناها، طيب
+
+545
+00:42:10,900 --> 00:42:16,330
+هنا نفس الكلام، إيش بنهتم؟ هذا لكم، مع المرة الجاية
+
+546
+00:42:16,330 --> 00:42:22,110
+مع الواجب، بدي بس ورقة، ورقة A4 مرتبة ومنسقة، مش مزعة
+
+547
+00:42:22,110 --> 00:42:26,230
+أيك ورقة، اعملوا لنا بحث صغير، بس اكتبوا لنا على جوجل
+
+548
+00:42:26,230 --> 00:42:30,750
+ولا على أي search engine، Carmichael number
+
+549
+00:42:30,750 --> 00:42:34,990
+applications، كل واحدة لو جابت لي applications أو
+
+550
+00:42:34,990 --> 00:42:37,550
+application واحد، وقالت لنا كيف استخدمت فيه الرقم
+
+551
+00:42:37,550 --> 00:42:40,670
+تبعنا، عشان تحسوا بس أنه آه والله، إيش أهمية الرقم
+
+552
+00:42:41,690 --> 00:42:44,850
+تمام؟ على الأقل application واحد، مش بالضرورة
+
+553
+00:42:44,850 --> 00:42:47,630
+تفهموه كويس، بس إنك تحس إن والله الأرقام هذه لها
+
+554
+00:42:47,630 --> 00:42:52,410
+تطبيقات، لها تطبيقات، ورقة واحدة بدي بس، مش أكثر، ورقة
+
+555
+00:42:52,410 --> 00:42:58,790
+واحدة، اسمها كفو، Carmichael number applications أو
+
+556
+00:42:58,790 --> 00:43:01,590
+numbers applications، لأن هذه عدة أرقام كبيرة جداً
+
+557
+00:43:01,590 --> 00:43:06,470
+عددها كبير، شوفوا إن إيش التطبيقات اللي ممكن نستخدم
+
+558
+00:43:06,470 --> 00:43:11,560
+فيها، Carmichael، الـ Carmichael، مثلاً، okay، المرة
+
+559
+00:43:11,560 --> 00:43:15,760
+الجاية بنبدأ في الـ cryptography، لإنه مهمة برضه
+
+560
+00:43:15,760 --> 00:43:20,400
+كويسة، لأول واحد اشتغلها، اللي هو Caesar أو القيصر
+
+561
+00:43:20,400 --> 00:43:25,660
+اشتغل على الـ Caesar’s cypher أو شفرة Caesar، كان
+
+562
+00:43:25,660 --> 00:43:30,400
+بيبعت الرسائل تبعته للجيوش والقادة تبعونه مشفرة، كيف
+
+563
+00:43:30,400 --> 00:43:35,240
+كانت بشفرها؟ هنشوف طبعاً، بشفرها حرف by حرف، أو letter
+
+564
+00:43:35,240 --> 00:43:39,460
+by letter، كل حرف بعكسه وبيعمل له طريقة modification
+
+565
+00:43:39,460 --> 00:43:42,720
+وبيبعت الرسالة بطريقة معينة، هنتكلم عنها برضه
+
+566
+00:43:42,720 --> 00:43:46,040
+باستخدام الـ modulo، فالموديولو من زمان جداً أصلاً
+
+567
+00:43:46,040 --> 00:43:51,020
+مُقترح، ما عاملينه، طريقة كسر الـ code كمان هنتكلم
+
+568
+00:43:51,020 --> 00:43:54,180
+عنه، كيف ممكن نكسر الـ code ونعرف بالضبط هو إيش
+
+569
+00:43:54,180 --> 00:43:59,500
+اللي بعته، بعدين هنتكلم عن طريقة ثانية، وفي طريقة
+
+570
+00:43:59,500 --> 00:44:01,740
+ثالثة هنتكلم عنها لاحقاً، اللي هي ما زالت تستخدم
+
+571
+00:44:01,740 --> 00:44:04,320
+حتى الآن، ما زالت تستخدم حتى الآن، فبنخليها للمرة
+
+572
+00:44:04,320 --> 00:44:06,580
+الجاية إن شاء الله تعالى، عشان تلحقوا، تذاكروا أو
+
+573
+00:44:06,580 --> 00:44:10,180
+تراجعوا، إذا عندكم أي أسئلة، يعطيكم العفو وبركة
+
+574
+00:44:10,180 --> 00:44:10,600
+الله فيكم
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE_postprocess.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ff6b6f40dd139e14173445637fc156c6fa0fd5d5
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE_postprocess.srt
@@ -0,0 +1,2296 @@
+1
+00:00:20,650 --> 00:00:22,810
+Okay بسم الله الرحمن الرحيم الصلاة والسلام علي
+
+2
+00:00:22,810 --> 00:00:25,210
+أشرف الأنبياء والإنبسار لسيدنا محمد وعلي أهلا
+
+3
+00:00:25,210 --> 00:00:28,350
+وصحابي أجمال طيب المرة اللي فاتت احنا بدأنا
+
+4
+00:00:28,350 --> 00:00:32,210
+اتكلمنا في ال .. في حكاية ال applications لل
+
+5
+00:00:32,210 --> 00:00:34,770
+number theory وقلنا إيش في applications ممكن
+
+6
+00:00:34,770 --> 00:00:39,390
+نعملها لل numbers وتطرقنا هيك بسرعة إن إيش اللي
+
+7
+00:00:39,390 --> 00:00:42,530
+هنشرحه المرة الجاية اللي هي اليوم قلنا هنتكلم عن
+
+8
+00:00:42,530 --> 00:00:46,650
+ال pseudo random numbers كيك ممكن نعمل sequence
+
+9
+00:00:46,650 --> 00:00:51,710
+بتهيألكوا إن هوrandom .. random sequence ولكن هو
+
+10
+00:00:51,710 --> 00:00:54,990
+محسوب .. deterministic .. sequence بمعنى أن أنا
+
+11
+00:00:54,990 --> 00:00:57,530
+بقدر أعمله regeneration .. بتقدروا أنتوا تعملوه
+
+12
+00:00:57,530 --> 00:01:00,250
+regeneration .. ال applications هذه كتيرة .. إلو
+
+13
+00:01:00,250 --> 00:01:02,790
+تطبيقات كتيرة .. من أهمها يمكن ال hash function ..
+
+14
+00:01:02,790 --> 00:01:06,600
+من أهمها ال games .. ال graphicsال simulations ال
+
+15
+00:01:06,600 --> 00:01:08,760
+.. ال cryptographic و أهم شغلها دي ال
+
+16
+00:01:08,760 --> 00:01:11,440
+cryptographic اللي هناخدها مش .. طبعا مش هنقدر
+
+17
+00:01:11,440 --> 00:01:14,280
+ناخدها اليوم لأن زي ما قلتلكوا هناخد جزء اليوم
+
+18
+00:01:14,280 --> 00:01:19,120
+محاضر و عشان الامتحان فهنتكلم عن ال cryptographic
+
+19
+00:01:19,120 --> 00:01:24,470
+و هنشوف كيف ممكن نعمل تشفيهعلم التشفير كله مبني
+
+20
+00:01:24,470 --> 00:01:27,170
+على حكايات ال pseudorandom على حكايات ال
+
+21
+00:01:27,170 --> 00:01:29,890
+pseudorandom كيف بنعمل الحكايات ال pseudorandom
+
+22
+00:01:29,890 --> 00:01:34,590
+هذه عن طريق ال linear congruential method و
+
+23
+00:01:34,590 --> 00:01:39,090
+هنستخدم فيها ال modular اللي احنا خدناها سابقا
+
+24
+00:01:39,090 --> 00:01:42,310
+عملية ال modular operation اللي احنا خدناها سابقا
+
+25
+00:01:42,310 --> 00:01:46,550
+طيب ايش القلية بالظبط ايش هو هذا ال linear
+
+26
+00:01:46,550 --> 00:01:53,590
+congruential method فعليا هذه معادلة بنعمل فيهاهذه
+
+27
+00:01:53,590 --> 00:01:57,610
+المرحلة محتاجة أربع أرقام مهمية جدا الرقم الأول
+
+28
+00:01:57,610 --> 00:02:09,170
+مدلر مدلر مدلر مدلر مدلر مدلر مدلر مدلر مدلر مدلر
+
+29
+00:02:09,940 --> 00:02:13,700
+value ال initial number اللى هنبدأ منه الشغل ففيه
+
+30
+00:02:13,700 --> 00:02:16,120
+دايما initial number نبدأ منه نعمل numerical
+
+31
+00:02:16,120 --> 00:02:19,960
+generation اللى هبنسميه ال X node او X0 طيب ال A
+
+32
+00:02:19,960 --> 00:02:24,380
+هذه اللى هى ال multiplier بده يكون على الاقل بده
+
+33
+00:02:24,380 --> 00:02:28,460
+يكون اتنين multiplier واحد مالوش معناه معامل ضرب
+
+34
+00:02:28,460 --> 00:02:31,260
+واحد مالوش معناه فبده يكون على الاقل اتنين ويكون
+
+35
+00:02:31,260 --> 00:02:34,920
+اقل من ال modulus ال modulus هذا ال M لازم تكون
+
+36
+00:02:34,920 --> 00:02:41,320
+اكبر رقم فيهم لازم تكون اكبر رقم فيهم فA بدها تكون
+
+37
+00:02:41,320 --> 00:02:44,760
+أقل من M و أكبر من او يساوي 2 على الأقل عشان نقول
+
+38
+00:02:44,760 --> 00:02:48,060
+ان اه والله في multiplier طيب ال C و .. اللي هي ال
+
+39
+00:02:48,060 --> 00:02:51,220
+.. ال increment و ال seed بدها تكون بين الصفر و ال
+
+40
+00:02:51,220 --> 00:02:54,840
+M أقل من M طبعا أكيد هتكون أقل من M بحيث برضه زي
+
+41
+00:02:54,840 --> 00:02:58,200
+اللي قلنا ال modulus يكون أكبر رقم موجود في الآخر
+
+42
+00:02:58,200 --> 00:03:01,500
+هنعمل generation ل sequence ال sequence ده هيبين
+
+43
+00:03:01,500 --> 00:03:06,580
+كأنه random ولكن هو pseudorandom شبيه العشوائي أو
+
+44
+00:03:06,580 --> 00:03:11,710
+شبه عشوائيsequence أو شبه عشوائي بيكون الأرقام
+
+45
+00:03:11,710 --> 00:03:15,130
+تبعته كل الأرقام اللى موجودة فيها ال Xn تبعته كلها
+
+46
+00:03:15,130 --> 00:03:21,450
+من صفر او اكبر to M فاش ولا رقم هيكون اكبر من مين
+
+47
+00:03:21,450 --> 00:03:25,930
+من ال M لأن هذا ال modulus اي رقم اكبر من M طبيعي
+
+48
+00:03:25,930 --> 00:03:32,470
+ال mod M هيرجعه لقيمة اقل من M ال Xn plus واحد
+
+49
+00:03:32,470 --> 00:03:36,810
+بمعنى ان ال next value هتساوي ال current value
+
+50
+00:03:37,410 --> 00:03:41,190
+current number مضروف في ال multiplier مجموع على ال
+
+51
+00:03:41,190 --> 00:03:46,230
+increment كلهم ناتج تباحهم بنعمل mod أو modulo M
+
+52
+00:03:46,230 --> 00:03:49,630
+طبعا حيطلع رقم جديد الرقم الجديد بستعمله عشان أحسب
+
+53
+00:03:49,630 --> 00:03:52,390
+الرقم اللي وراه اللي وراه بحسب اللي وراه فبنكون
+
+54
+00:03:52,390 --> 00:03:56,790
+جاندي بنعمل sequence of pseudo random numbers okay
+
+55
+00:03:56,790 --> 00:04:01,290
+كويس جدا عشان أقول والله الأرقام بتاعتنا عشوائية
+
+56
+00:04:01,290 --> 00:04:06,360
+أو شكلها فعلا عشوائي وصعبةو صعب اكتشافها انه يكون
+
+57
+00:04:06,360 --> 00:04:11,060
+ال a, c, m, primes كل ما كانوا primes كل ما كان
+
+58
+00:04:11,060 --> 00:04:16,740
+فيه إمكانية لعمل code صعب عملية ال regeneration
+
+59
+00:04:16,740 --> 00:04:20,580
+تبعته او صعب كسره صعب انه حد غيركوا يعرفه فانتوا
+
+60
+00:04:20,580 --> 00:04:24,560
+بتعملوا generation بهذه ال equation عن طريق ان
+
+61
+00:04:24,560 --> 00:04:27,940
+انتوا تحددوا بس ايش هي ال a ايش ال c ايش ال m
+
+62
+00:04:27,940 --> 00:04:35,750
+بتاعتكم و اتحطواالـ X الأولى .. أول قيمة بتحطوها
+
+63
+00:04:35,750 --> 00:04:38,710
+.. بتكونوا انتوا عملتوا هنا generation اللي هي ال
+
+64
+00:04:38,710 --> 00:04:42,610
+sequence تبعكم انتوا .. الأصل للأرقام هذه .. هذه
+
+65
+00:04:42,610 --> 00:04:47,710
+سرية .. هذه سرية .. اللي هيطلع مجموعة أرقام
+
+66
+00:04:47,710 --> 00:04:51,880
+عشوائية .. أنا لو شفتها المفروض ماعرفهاشأرقام لا
+
+67
+00:04:51,880 --> 00:04:55,180
+تحمل المعنى الحقيقي أنا بالنسبة اللي هتطلع هيقول
+
+68
+00:04:55,180 --> 00:04:58,120
+ان هي random انا مش عارف كيف ان عملها ال
+
+69
+00:04:58,120 --> 00:05:01,480
+generation انتوا اللي لازم تكونوا عارفين طيب مع
+
+70
+00:05:01,480 --> 00:05:06,120
+ذلك ممكن يكسر ال code تبعكوا هذا كيف إذا كان ال A
+
+71
+00:05:06,120 --> 00:05:08,780
+و ال C و ال M انعرفت طيب كيف أجل الأحتمالية
+
+72
+00:05:08,780 --> 00:05:12,680
+معرفتها انه يكونوا prime أو at least relatively
+
+73
+00:05:12,680 --> 00:05:18,790
+primeيكونوا relative prime لبعض ال A مع ال C لجرد
+
+74
+00:05:18,790 --> 00:05:22,370
+اس common divisor واحد ال C مع ال M لجرد اس common
+
+75
+00:05:22,370 --> 00:05:25,770
+divisor واحد ال A مع ال M لجرد اس common divisor
+
+76
+00:05:25,770 --> 00:05:29,670
+واحد إذا كان هيك معناته كل واحدة منهم relative
+
+77
+00:05:29,670 --> 00:05:35,970
+prime للتانية بتصير مناسبة لو ال C Zero بتصير a
+
+78
+00:05:35,970 --> 00:05:39,020
+pure multiplicativeبتصير هنا ال sequence تبعكم
+
+79
+00:05:39,020 --> 00:05:43,040
+pure multiplicative كله جاي من عملية ضرب مش اكثر
+
+80
+00:05:43,040 --> 00:05:48,760
+مفيش اي جمع عالي مفيش اي جمع كويس for example لو
+
+81
+00:05:48,760 --> 00:05:54,220
+أخدنا ال M بتساوي الف أخدنا ال C بتساوي اربعمية
+
+82
+00:05:54,220 --> 00:05:58,510
+سبعة ستة primeرقم ال prime هيه ال multiplier برضه
+
+83
+00:05:58,510 --> 00:06:02,510
+prime عبارة عن 293 و ال seed ممكن نختار اي رقم
+
+84
+00:06:02,510 --> 00:06:10,470
+اللي هي اول قيمة موجودة 426 بنقدر من ال 426 نعمل
+
+85
+00:06:10,470 --> 00:06:14,330
+generation لمي للرقم اللي وراها اللي هو ال X1 عن
+
+86
+00:06:14,330 --> 00:06:19,990
+طريق المعادلة طول مباشرة في المعادلة 285 285
+
+87
+00:06:19,990 --> 00:06:26,650
+بستخدمها مكان X1 عشان نجيب X2972 972 بستخدمها عشان
+
+88
+00:06:26,650 --> 00:06:30,850
+تجيب X تلاتة بتترسم و تسوقن بتضايقوا بتعملوا
+
+89
+00:06:30,850 --> 00:06:35,130
+generation كود صغير و بيضل يطلع generation طبعا
+
+90
+00:06:35,130 --> 00:06:40,530
+بعد فترة هيتكرر بعد فترة هتلاقوه هيتكرر الأرقام
+
+91
+00:06:40,530 --> 00:06:44,570
+اللي بيعملها generation هذه هذه مرتبطة عددها بمين
+
+92
+00:06:44,570 --> 00:06:47,770
+بال modulus ال modulus الف معناه ذلك أن هذا بيقدر
+
+93
+00:06:47,770 --> 00:06:52,750
+يعملكوا generation من صفر ل999الأرقام اللى بقدر
+
+94
+00:06:52,750 --> 00:06:55,890
+يعملها generation هي من صفر تسعمية تسعة وتسعين
+
+95
+00:06:55,890 --> 00:07:00,330
+okay فمعنى ذلك انه انت هيصير reputation للأرقام
+
+96
+00:07:00,330 --> 00:07:05,230
+غالبا بعد عدد اقل من تسعمية تسعة وتسعين او يعني
+
+97
+00:07:05,230 --> 00:07:10,370
+بعد بعد اقل من الف بعد اقل من الف number هتلاقي
+
+98
+00:07:10,370 --> 00:07:13,710
+انه هيتكرر ممكن يكون اجل من هيك كمان ممكن يكون اجل
+
+99
+00:07:13,710 --> 00:07:17,030
+من هيك امتى ممكن يكون اجل من هيك اذا كانت الأرقام
+
+100
+00:07:17,030 --> 00:07:21,430
+اللى موجودة عندك و هدي مش primesفالاحتمالية انه
+
+101
+00:07:21,430 --> 00:07:25,230
+يصير ال repetition اسرع بتصير اكبر انه يصير اسرع
+
+102
+00:07:25,230 --> 00:07:27,950
+طيب ايش دخل ال repetition ال repetition انك كل ما
+
+103
+00:07:27,950 --> 00:07:32,450
+اتكررت في period صغيرة كل ما كان امكانية كسر ال
+
+104
+00:07:32,450 --> 00:07:38,490
+code تبعك أسهل معناه ذلك انه كل ما ال period
+
+105
+00:07:38,490 --> 00:07:42,810
+تبعتكم او التكرار الأرقام بتصير في مسافات جريبة من
+
+106
+00:07:42,810 --> 00:07:45,610
+بعض معناه انه في امكانية لكسر ال code اللي انتوا
+
+107
+00:07:45,610 --> 00:07:49,360
+عاملينه هذا في امكانية ان احنا نعرفهفانتوا بتبعتوا
+
+108
+00:07:49,360 --> 00:07:53,020
+معلومة مشفرة فاكرين ان هي مشفرة بس عاملين
+
+109
+00:07:53,020 --> 00:07:56,440
+regeneration باستخدام أرقام ممكن تكون زوجية مثلا
+
+110
+00:07:56,440 --> 00:08:00,920
+زوجية معروفة لأنه دائما في عوامل مشترك بينهم فمعنى
+
+111
+00:08:00,920 --> 00:08:04,850
+ذلك هتلاقي انه سهلانه نكسر ال code و اعرف ايش
+
+112
+00:08:04,850 --> 00:08:08,590
+الرسالة اللى انتوا باعطينها فبطلت مشفرة فقدتوا
+
+113
+00:08:08,590 --> 00:08:10,950
+الهدف من اصلا من عملية التشفير اللى انتوا بدكوا
+
+114
+00:08:10,950 --> 00:08:14,750
+تستخدموها فهذا مهم جدا كمان الارقام جدش بتقدر تكون
+
+115
+00:08:14,750 --> 00:08:20,450
+prime او at least relatively prime زمبل تانى لو
+
+116
+00:08:20,450 --> 00:08:24,700
+أخدنا ال M high not جللناهاأخدناها قيمة أصغر بحيث
+
+117
+00:08:24,700 --> 00:08:29,860
+أنه يكون تكرار معنا تسعة ال a سبعة ال c أربعة ال x
+
+118
+00:08:29,860 --> 00:08:34,580
+node تلاتة لحظة بدأنا نعمل generation باستخدام ال
+
+119
+00:08:34,580 --> 00:08:39,040
+x node اللي هي التلاتة طلعت سبعة السبعة استخدمناها
+
+120
+00:08:39,040 --> 00:08:42,700
+جبنا تمانية بعد واحد اتنين تلاتة أربعة خمسة ستة
+
+121
+00:08:42,700 --> 00:08:51,850
+سبعة تمانية التاسعة التاسعة تكررهترجع تتكرر خلاص
+
+122
+00:08:51,850 --> 00:08:55,150
+اعرفت انا في الحالة هذه ان التكرار هذا ممكن يعطيني
+
+123
+00:08:55,150 --> 00:09:00,210
+حق بال مين؟ بال modulus اعرفنا رقم يعني هاي بدت
+
+124
+00:09:00,210 --> 00:09:03,670
+عملية كسر ال code تبعكم بدأنا هنا نعرف مجموعة
+
+125
+00:09:03,670 --> 00:09:08,650
+أرقام طيب الهدف انه في الآخر تعملوا ساقوا انه جدش
+
+126
+00:09:08,650 --> 00:09:11,270
+ممكن تعملوا الأرقام بتاعتكم هذه تختاروها primes
+
+127
+00:09:11,840 --> 00:09:14,800
+قدرش ممكن تكون ال M كبيرة حسب ال application اللي
+
+128
+00:09:14,800 --> 00:09:19,020
+بتبقيها حسب لإيش بتكون ال code تستخدموها أو لإيش
+
+129
+00:09:19,020 --> 00:09:22,240
+بتكون ال sequence هذه طيب أفضل sequence تم
+
+130
+00:09:22,240 --> 00:09:24,860
+استخدامه كان ال pure multiplicative generator
+
+131
+00:09:24,860 --> 00:09:29,270
+باستخدام modulus 2 to the powerواحد ثلاثين minus
+
+132
+00:09:29,270 --> 00:09:33,230
+one كان أفضل واحد على أساس أنه هذا و ال multiplier
+
+133
+00:09:33,230 --> 00:09:38,230
+تبعه كانت two primes تتبار بعض سبعة prime تتبار
+
+134
+00:09:38,230 --> 00:09:42,990
+خمسة تتبار خمسة كان مستخدم multiplier هذا is
+
+135
+00:09:42,990 --> 00:09:46,690
+widely used ال code هذا مستخدم جدا و باستمرار
+
+136
+00:09:46,690 --> 00:09:50,610
+بيستخدموه بيطلع ان او بيصير عملية تكرار بعدي اتنين
+
+137
+00:09:51,420 --> 00:09:54,640
+to the power of 31 minus 2 هذه انت بتتكلم عن عدد
+
+138
+00:09:54,640 --> 00:09:58,740
+كبير بالمليارات يعني بعد كذا مليار عبل ما الرقم
+
+139
+00:09:58,740 --> 00:10:01,920
+يبدأ يتكرر تاني فطبعا هذا بيكون صعب بالنسبة لل
+
+140
+00:10:01,920 --> 00:10:05,480
+hacker ان يجوز يتبع ايه انت بيصير التكرار ايه انت
+
+141
+00:10:05,480 --> 00:10:12,230
+بيصير عملية التكرار تبعه تمامفناخد بالة من الأرقام
+
+142
+00:10:12,230 --> 00:10:15,850
+اللى احنا بنختارها كparameters طيب الأرقام هذه
+
+143
+00:10:15,850 --> 00:10:18,890
+برضه ممكن تفيدنا لما نيجي نتكلم عن linear
+
+144
+00:10:18,890 --> 00:10:24,110
+congruences و inverses linear congruences معناه
+
+145
+00:10:24,110 --> 00:10:29,150
+ذلك أنا بتكلم عن معادلة في النهايةAX congruent to
+
+146
+00:10:29,150 --> 00:10:36,250
+B AX congruent to B under the modulo M معناه ذلك
+
+147
+00:10:36,250 --> 00:10:40,150
+ان هدول اتنين مكافئين لبعض و هدى عادة الفكرة اللى
+
+148
+00:10:40,150 --> 00:10:47,370
+بتستخدموها في حل المعادلات اللينية الخطية لما يكون
+
+149
+00:10:47,370 --> 00:10:54,560
+عندكم A في X بيساوي B وبتجيبوا Xماذا كنتوا بتعمله؟
+
+150
+00:10:54,560 --> 00:10:59,520
+تضربوا في ال inverse لمن؟ لل A فتجيبوا A' في A
+
+151
+00:10:59,520 --> 00:11:05,720
+يساوي A' في B فالمفروض التنتين هذولة ضربهم واحد
+
+152
+00:11:05,720 --> 00:11:11,820
+تمام ضربهم بيساوي واحد معناه ذلك أنه أي رقم في ال
+
+153
+00:11:11,820 --> 00:11:15,080
+inverse تبعه المفروض congruent to main to one
+
+154
+00:11:15,080 --> 00:11:19,380
+modulo one بيساوي واحد الاتنين هذول مفروض يساوي
+
+155
+00:11:19,380 --> 00:11:23,210
+واحد بكون اقدر تجيب main Xهذه الطريقة اللى كنتوا
+
+156
+00:11:23,210 --> 00:11:26,330
+تستخدموها في ميد في حالة المعادلات الخطية فعلا
+
+157
+00:11:26,330 --> 00:11:31,070
+هنستفيد منها برضه في ال .. لو أنا بتكلم عن modulo
+
+158
+00:11:31,070 --> 00:11:36,110
+M لو بنتكلم عن modulo M المفروض ان ال A prime في A
+
+159
+00:11:36,110 --> 00:11:41,570
+congruent to مين to one هدى بنقدر نشغلها وعشان
+
+160
+00:11:41,570 --> 00:11:46,690
+نقول ان والله فعلا في ال modulo M ال A فيه إلها
+
+161
+00:11:46,690 --> 00:11:50,970
+inverse الأصل أن يكونوا الأتنين relatively prime
+
+162
+00:11:52,870 --> 00:11:56,550
+الـ greatest common divisor تبعهم واحد فبقدر أقول
+
+163
+00:11:56,550 --> 00:12:03,850
+إيش أنه A إلها inverse وحيد داخل الموضل السام داخل
+
+164
+00:12:03,850 --> 00:12:07,550
+الموضل السام الموضل
+
+165
+00:12:07,550 --> 00:12:09,390
+السام هذا لو قلنا مثلا سبعة
+
+166
+00:12:17,990 --> 00:12:21,250
+داخل المدلة السابعة لها المفروض يكون .. يعني لو
+
+167
+00:12:21,250 --> 00:12:24,610
+افترضنا انه الاتنين او التلاتة و بدنا نجيب ال
+
+168
+00:12:24,610 --> 00:12:28,710
+inverse للتلاتة المفروض يكون انها رقم واحد اقل من
+
+169
+00:12:28,710 --> 00:12:33,230
+سبعة هو ال inverse تبعها هو ال inverse تبعها الاصل
+
+170
+00:12:33,230 --> 00:12:39,050
+يكون unique inverse مايكونش اكتر من inverse واحد
+
+171
+00:12:39,050 --> 00:12:42,190
+ففي الحالة هذه اذا كان .. هنرجع نقول نفس الكلام
+
+172
+00:12:42,190 --> 00:12:46,730
+اذا كان ال GCD او ال greatest common divisor A و M
+
+173
+00:12:48,090 --> 00:12:55,970
+A و M ال A اللي احنا بنشتغل عليها و ال Mإذا كان
+
+174
+00:12:55,970 --> 00:12:58,310
+فعلًا الـ greatest common divisor تبعهم equal to
+
+175
+00:12:58,310 --> 00:13:01,770
+one و ال M طبعًا لازم يكون أكبر من واحد، يكون فيه
+
+176
+00:13:01,770 --> 00:13:05,170
+فعلا عندكم modulus، موجودة ال modulus، then A has
+
+177
+00:13:05,170 --> 00:13:11,330
+a unique inverse, A prime، إلها inverse وحيد أقل
+
+178
+00:13:11,330 --> 00:13:18,090
+من M طبعًا هذا الكلام ضمن modulo M، ضمن modulo M،
+
+179
+00:13:18,090 --> 00:13:21,830
+كيف الكلام هذا بتهم؟عشان نعمل هذا الكلام فعليا
+
+180
+00:13:21,830 --> 00:13:25,770
+بدنا ننطلق من نفس المعادلة أو بدنا نجيل للرقمين
+
+181
+00:13:25,770 --> 00:13:30,910
+هدولة ال .. ال bizot coefficient ال big
+
+182
+00:13:30,910 --> 00:13:33,010
+coefficients ال bizot coefficients هذه المفروضة
+
+183
+00:13:33,010 --> 00:13:38,190
+اللي هي تعطينا القيمة بالظبط تعطينا القيمة بتاعتنا
+
+184
+00:13:38,190 --> 00:13:45,050
+بحسب الاعتبار انه ال .. السبعةاللي هي ال modulus
+
+185
+00:13:45,050 --> 00:13:49,290
+طبعنا بنعملها analysis باستخدام باستخدام مين
+
+186
+00:13:49,290 --> 00:13:55,190
+باستخدام ال A طيب هتساوي تلاتة احنا بدنا نشتغل
+
+187
+00:13:55,190 --> 00:13:59,250
+فعليا هنا على بدنا نجيب ال inverse لتلاتة modulo
+
+188
+00:13:59,250 --> 00:14:05,170
+seven three modulo seven تلاتة في قداش المفروض
+
+189
+00:14:05,170 --> 00:14:14,210
+تكون في ايش في اتنين زائد واحد اتنين زائدالكلام
+
+190
+00:14:14,210 --> 00:14:17,150
+هذا احنا عشان نقول ان هم الاتنين congruent لبعض
+
+191
+00:14:17,150 --> 00:14:21,490
+المفروض انه كل مجموحهم نحطهم في term واحد equal to
+
+192
+00:14:21,490 --> 00:14:26,090
+one congruent to one احنا لسه قاعدين نتكلمين شوية
+
+193
+00:14:26,090 --> 00:14:32,350
+انه الاصل congruent to one to one فهذا نفس الكلام
+
+194
+00:14:32,350 --> 00:14:35,470
+كيف ممكن اعملهم الاتنين في term واحد congruent to
+
+195
+00:14:35,470 --> 00:14:42,180
+one هنقول واحدأو سبعة مانس تلاتة اتنين في تلاتة
+
+196
+00:14:42,180 --> 00:14:48,160
+بساوي واحد ناخد هذا على ناحية التالية طيب هذه
+
+197
+00:14:48,160 --> 00:14:53,860
+عبارة عن في واحد فال .. ال .. بزوت ال coefficients
+
+198
+00:14:53,860 --> 00:15:00,480
+هنا تبعتنا الواحد و minus اتنين و minus two فال
+
+199
+00:15:00,480 --> 00:15:03,740
+minus two هذه هذه ال coefficients تبعة اتنين بتاعة
+
+200
+00:15:03,740 --> 00:15:11,160
+ال a هي ال a primeباستخدام modulo 7 باستخدام
+
+201
+00:15:11,160 --> 00:15:15,060
+modulo 7 هي نفس المعادلة هي الواحد هذا هو اللي أنا
+
+202
+00:15:15,060 --> 00:15:18,900
+بديه لإن ال congruent له باخد ال term هذا عن ناحية
+
+203
+00:15:18,900 --> 00:15:22,300
+التانية بس ال term هذا بناخده عن ناحية التانية ال
+
+204
+00:15:22,300 --> 00:15:26,660
+coefficients تبعته هي ال inverse تبعت التلاتة هي
+
+205
+00:15:26,660 --> 00:15:30,900
+ال inverse على التلاتة كيف الكلام هذا خلينا نشوف
+
+206
+00:15:30,900 --> 00:15:36,430
+هل فعلا congruent oneالـ-2 هذه فعلا كتير one to
+
+207
+00:15:36,430 --> 00:15:42,550
+one ببساطة عشان تضربوا minus two في تلاتة صارت ال
+
+208
+00:15:42,550 --> 00:15:49,570
+a prime في ال a والمفروض تساوي واحد من seven مش
+
+209
+00:15:49,570 --> 00:15:52,530
+هذه العلاقة ال relation بتاعتنا طب خلينا نضربهم في
+
+210
+00:15:52,530 --> 00:15:58,610
+بعض كده اش بطلع minus 6 minus 6 معناته ان انا بمشي
+
+211
+00:15:58,610 --> 00:16:01,450
+ست خطوات anticlockwise
+
+212
+00:16:02,920 --> 00:16:07,200
+عكس اتجاه عقارب الساعة فاحنا ماشيين من هى واحد
+
+213
+00:16:07,200 --> 00:16:09,780
+اتنين تلاتة اربعة خمسة طيب لأ نمشيها بالعكس واحد
+
+214
+00:16:09,780 --> 00:16:17,280
+اتنين تلاتة اربعة خمسة ستة للواحد
+
+215
+00:16:17,280 --> 00:16:24,080
+فإذا فعلا تسوى واحد فعلا هتسوى واحد هذه المكملة
+
+216
+00:16:24,080 --> 00:16:30,410
+للواحدموديولو سبن هذه المكملة للواحد موديولو سبن
+
+217
+00:16:30,410 --> 00:16:36,130
+باعتبار أن واحد ناقص سبعة ناقص الموديولو ناقص
+
+218
+00:16:36,130 --> 00:16:40,270
+الموديولو
+
+219
+00:16:40,270 --> 00:16:43,790
+ناقص الموديولو ناقص
+
+220
+00:16:43,790 --> 00:16:45,370
+الموديولو ناقص الموديولو ناقص الموديولو ناقص
+
+221
+00:16:45,370 --> 00:16:47,690
+الموديولو ناقص الموديولو ناقص الموديولو ناقص
+
+222
+00:16:47,690 --> 00:16:48,610
+الموديولو ناقص الموديولو ناقص المو
+
+223
+00:16:52,550 --> 00:16:54,670
+ففي الحالة هذه ال .. ال .. ال .. ال .. ال .. ال ..
+
+224
+00:16:54,670 --> 00:16:55,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+225
+00:16:55,730 --> 00:16:56,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+226
+00:16:56,290 --> 00:16:56,670
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+227
+00:16:56,670 --> 00:17:02,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+228
+00:17:02,610 --> 00:17:03,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+229
+00:17:03,430 --> 00:17:04,090
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+230
+00:17:04,090 --> 00:17:04,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+231
+00:17:04,130 --> 00:17:05,130
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+232
+00:17:05,130 --> 00:17:05,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+233
+00:17:05,730 --> 00:17:07,250
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+234
+00:17:07,250 --> 00:17:12,070
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+235
+00:17:12,070 --> 00:17:20,690
+ال .. ال ..
+
+236
+00:17:20,950 --> 00:17:26,150
+رقم congruent لها بس احنا نتكلم unique باعتبار ان
+
+237
+00:17:26,150 --> 00:17:31,290
+هو داخل ال cycle داخل او اقل من سبعة هي ال minus
+
+238
+00:17:31,290 --> 00:17:39,190
+two او الخمسة او الخمسة صحيح؟ تعالوا نشوف لماذا
+
+239
+00:17:39,190 --> 00:17:45,370
+خمسة لأنها المكملة لل minus twoكيف المكملة؟ مكملة
+
+240
+00:17:45,370 --> 00:17:49,690
+انا بشتغل under modulo M M هدق سبعة ف minus two
+
+241
+00:17:49,690 --> 00:17:55,110
+ايش اللي بكملها السبعة؟ فيها انها خمسة ان امشي
+
+242
+00:17:55,110 --> 00:17:57,170
+خطوطين عكس عقارب الساعة
+
+243
+00:18:03,320 --> 00:18:07,820
+ممكن تكون minus 5 minus 2 أو 5 وكل رقم congruent
+
+244
+00:18:07,820 --> 00:18:13,360
+لهم كيف بجيب ال congruence تبعتهم minus 2 minus 7
+
+245
+00:18:13,360 --> 00:18:20,060
+minus 7 minus 7 minus 7 بتصير minus 19 كمان minus
+
+246
+00:18:20,060 --> 00:18:25,760
+7 بتصير minus 16 طيب هنا plus 7 plus 7 اذا كانت
+
+247
+00:18:25,760 --> 00:18:32,440
+جمع plus 7 او طريقة هلى minus 7 بتعطينا minus 2هذه
+
+248
+00:18:32,440 --> 00:18:38,300
+زائد سبعة تعطينا خمسة زائد سبعة اتناش زائد سبعة
+
+249
+00:18:38,300 --> 00:18:44,300
+تسعة عشر فمعنى ذلك ممكن تكون ال inverse للتلاتة
+
+250
+00:18:44,300 --> 00:18:50,620
+minus two أو خمسة أو minus تسعة او اتناش او تسعة
+
+251
+00:18:50,620 --> 00:18:56,540
+عشر او minus ستة عشر اي رقم بمشي اي رقم بمشي خليني
+
+252
+00:18:56,540 --> 00:19:00,470
+انا اخد مثلًا الخمسة خمسة في تلاتةمحتاج أن نتأكد
+
+253
+00:19:00,470 --> 00:19:04,730
+هل فعلا ال A' هذه اللي هي خمسة في ال A اللي هي
+
+254
+00:19:04,730 --> 00:19:11,730
+تلاتة مد سبعة هيساوي فعلا واحد ولا لأ هدفي هدي
+
+255
+00:19:11,730 --> 00:19:20,730
+خمستاشر مد سبعة واحد لو جربتوا أي رقم من الأرقام
+
+256
+00:19:20,730 --> 00:19:24,790
+هذه اللي هي كم كلها congruent كل واحدة congruent
+
+257
+00:19:24,790 --> 00:19:28,770
+لالنتج اللي احنا طلعناه هو ال minus fourأي واحدة
+
+258
+00:19:28,770 --> 00:19:35,190
+منهم اضربوها فيه تلاتة موت سبعة هيطلع واحد تمام
+
+259
+00:19:35,190 --> 00:19:39,770
+هي هذه الفكرة طبعا لاحظوا ان احنا هنا استشفناها
+
+260
+00:19:39,770 --> 00:19:44,110
+مجرد script لأن الأرقام بسيطة سبعة جداش هتتكرر
+
+261
+00:19:44,110 --> 00:19:47,930
+تلاتة منها يطلع رقم اتنين كويسة مش دايما بتكون
+
+262
+00:19:47,930 --> 00:19:51,790
+الأرقام سهلة بهذا الشكلفممكن تكون أرقام كبيرة
+
+263
+00:19:51,790 --> 00:19:55,790
+الأرقام الكبيرة في لها قلية تانية الأرقام الكبيرة
+
+264
+00:19:55,790 --> 00:19:59,650
+بدنا نتأكد أول أن هي greatest common divisor equal
+
+265
+00:19:59,650 --> 00:20:02,910
+to one ولا لأ هل هم فعلا equal to one greatest
+
+266
+00:20:02,910 --> 00:20:06,930
+common divisor بينهم ولا لأ فلو قلنا بدنا ال
+
+267
+00:20:06,930 --> 00:20:14,430
+universe ل 101 مديوله 4620 أول شي بدنا نتأكد هو هم
+
+268
+00:20:14,430 --> 00:20:18,670
+الاتنين هدولةgreatest common divisor equal to one
+
+269
+00:20:18,670 --> 00:20:22,030
+طب انا إيش بدي في ال one هذا تحديدا ال one هذا هو
+
+270
+00:20:22,030 --> 00:20:26,230
+ال congruent اللي أنا بشتغل عليه إذا فعلا ال
+
+271
+00:20:26,230 --> 00:20:35,570
+greatest common divisor ل 101 و 4620 فعلا واحد
+
+272
+00:20:35,570 --> 00:20:39,930
+الواحد هذا هو نفسه اللي أنا بشتغل عليه على اعتبار
+
+273
+00:20:39,930 --> 00:20:43,350
+انه a في a equivalent to one
+
+274
+00:20:47,520 --> 00:20:49,800
+هو هذا اللي احنا بدنا ندور عليه إذا فعلا ال grade
+
+275
+00:20:49,800 --> 00:20:52,720
+of common divisor equal to one بضمن ان الاتنين
+
+276
+00:20:52,720 --> 00:20:59,540
+هدول ال congruent تبعهم واحد بقدر أجيب inverse او
+
+277
+00:20:59,540 --> 00:21:04,340
+ال inverse في الحالة هذه للمية واحد موجود او ممكن
+
+278
+00:21:04,340 --> 00:21:10,120
+في module 4620 عشانك هنعمل grade of common divisor
+
+279
+00:21:10,120 --> 00:21:14,200
+اللي اتعودنا عليها باستخدام طريقة مين هذه؟
+
+280
+00:21:16,790 --> 00:21:24,790
+Euclid's algorithm في لحظة هاي 4620 هنا مضروبة
+
+281
+00:21:24,790 --> 00:21:29,530
+مكرر الألف والمية وواحد خمسة واربعين مرة ال
+
+282
+00:21:29,530 --> 00:21:35,590
+remainder سبعة السبعة هذه لسه ما خلصناش احنا ما
+
+283
+00:21:35,590 --> 00:21:40,590
+خلصناش هذه ناتج في بعض الموديولو هذه اقل من B يعني
+
+284
+00:21:40,590 --> 00:21:43,790
+جاهز بعيد لكل ال algorithm نفسه اقل من B معناه ذلك
+
+285
+00:21:43,790 --> 00:21:52,220
+انه صارت Bكأنها B mod الناتج ال remainder R صحيح؟
+
+286
+00:21:52,220 --> 00:22:01,780
+كويس هاي B وهاي R طيب هذه برضه هتطلع ناتج R جديد
+
+287
+00:22:01,780 --> 00:22:09,320
+وصرت B جديدة ال B جديدة 75 ف75 مع ال R الجديدة ال
+
+288
+00:22:09,320 --> 00:22:11,240
+B الجديدة مع ال R الجديدة ال B الجديدة مع ال R
+
+289
+00:22:11,240 --> 00:22:15,950
+الجديدة لما نصل مين لصفرلما كنا بنصل ل صفر الرقم
+
+290
+00:22:15,950 --> 00:22:19,830
+بيسوء صفر باخد ال a هو ال greatest common divisor
+
+291
+00:22:19,830 --> 00:22:24,310
+هنا مش هيظهر عندكوا صفر لأنه مافيش اي عامل مشترك
+
+292
+00:22:24,310 --> 00:22:29,390
+بينهم الاتنين ال greatest common divisor تبعهم
+
+293
+00:22:29,390 --> 00:22:39,140
+واحد relatively prime فلاحظوا خلصت بواحد مش صفرمش
+
+294
+00:22:39,140 --> 00:22:42,220
+في صفر خلصت عندكوا هنا بواحد هي اخر واحد هنا
+
+295
+00:22:42,220 --> 00:22:46,840
+اتاكدنا منه جربنا هي هي خلاص بيظل واحد الواحد بيظل
+
+296
+00:22:46,840 --> 00:22:51,220
+زي ما هو الواحد فخلاص اخر مرحلة كانت هي هذه وكان
+
+297
+00:22:51,220 --> 00:22:54,680
+عندنا الميدر اخر واحد واحد فمعنى ذلك ان هدول فعلا
+
+298
+00:22:54,680 --> 00:22:57,700
+relative to the prime وهدا معناه انه لمية واحد
+
+299
+00:22:57,700 --> 00:23:04,840
+يوجد inverse وحيد under modulo 4620 طب ايش هو جدش
+
+300
+00:23:04,840 --> 00:23:11,680
+قيمته هذا ال inverse الوحيد؟ بدنا قيمتهال turn هذا
+
+301
+00:23:11,680 --> 00:23:15,240
+اللى كان يمثلنا ل greatest common divisor هو هذا
+
+302
+00:23:15,240 --> 00:23:23,980
+اللى انا بدي أنسبله طبعا
+
+303
+00:23:23,980 --> 00:23:28,630
+واحد في M بهذا الشكل المفروض انه يسوىمفروض ان هو
+
+304
+00:23:28,630 --> 00:23:31,130
+يساوي واحد زي الحالة بتاع التولة عملناها في minus
+
+305
+00:23:31,130 --> 00:23:36,810
+اتنين تلاتة زائد واحد في سبعة زائد واحد طبعا مش
+
+306
+00:23:36,810 --> 00:23:41,270
+مضروري واحد ممكن في النهاية تكون اي equivalent لل
+
+307
+00:23:41,270 --> 00:23:47,930
+M ف some K هنا صدفت انه واحد لان الأرقام كتير كانت
+
+308
+00:23:47,930 --> 00:23:51,270
+صغيرة و جريبة من بعض فهذا يساوي واحد فبدنا نبدأ من
+
+309
+00:23:51,270 --> 00:23:55,930
+الواحد هذا الواحد هذا أيه موجود عندكم؟ بدنا الواحد
+
+310
+00:23:55,930 --> 00:24:07,100
+يساويsome k أو some integer في 101 زائد
+
+311
+00:24:07,100 --> 00:24:16,720
+some integer في 4620 صحيح؟ إذا وصلنا لل form هذا
+
+312
+00:24:16,720 --> 00:24:21,420
+بقول إن هدولة ال بيزوت coefficients 101 إيش ال
+
+313
+00:24:21,420 --> 00:24:24,700
+coefficient اللي معها؟ هو هذا ال inverse تبعها هو
+
+314
+00:24:24,700 --> 00:24:27,880
+هذا ال إيش؟ ال inverse تبعهاعشان نعمل الكلام هذا
+
+315
+00:24:27,880 --> 00:24:30,980
+هننطلق من نفس ال sequence اللي احنا مشيناه الواحد
+
+316
+00:24:30,980 --> 00:24:34,620
+هذا اللي بدنا نمسكها لأن هذا اللي انا بدي أساوي
+
+317
+00:24:34,620 --> 00:24:38,460
+فيه كل ال terms اللي بعتنا و هنلاحظ الواحد ايش
+
+318
+00:24:38,460 --> 00:24:44,440
+يساوي تلاتة ناقص واحد في اتنين تلاتة ناقص واحد في
+
+319
+00:24:44,440 --> 00:24:50,030
+اتنين طيب كويس الاتنينهذه كانت الـ remainder
+
+320
+00:24:50,030 --> 00:24:54,570
+للمرحلة السابقة فبقدر أخدها بدلالة الأتنين السابقة
+
+321
+00:24:54,570 --> 00:24:58,490
+فبتصير الأتنين عبارة عن تلاتة و عشرين ناقص سبعة و
+
+322
+00:24:58,490 --> 00:25:04,410
+تلاتة طيب تلاتة هي ستة و عشرين ناقص تلاتة تلاتة و
+
+323
+00:25:04,410 --> 00:25:09,950
+عشرين نزلنا نزول هلوجد عشان نجيب greatest common
+
+324
+00:25:09,950 --> 00:25:13,130
+divisor عشان نجيب ال inverse بنطلع طلوع بالعكس
+
+325
+00:25:14,040 --> 00:25:17,360
+فكثير كويس وانت بتحلوا مسائل زي هذه تحطوا الاتنين
+
+326
+00:25:17,360 --> 00:25:20,280
+جان بعض عشان تاخدوا معلومتكم من بعض تاخدوا
+
+327
+00:25:20,280 --> 00:25:23,480
+المعلومات من بعض هاي أخدناها الأولى طيب اتنين قلنا
+
+328
+00:25:23,480 --> 00:25:26,500
+زي ما .. زي ما اتكلمنا هنا عبارة عن تلاتة و عشرين
+
+329
+00:25:26,500 --> 00:25:29,680
+ناقص سبعة في تلاتة تلاتة و عشرين ناقص سبعة في
+
+330
+00:25:29,680 --> 00:25:34,740
+تلاتة دائما هتلاقوا التلاتة اللي كانت هنا الميندر
+
+331
+00:25:34,740 --> 00:25:39,240
+صارت هنا B و نفس الكلام التلاتة و عشرين هنا كانت
+
+332
+00:25:39,240 --> 00:25:44,370
+تتكرر هنا لأن كل B باخدها من ال R اللي جابلهامش
+
+333
+00:25:44,370 --> 00:25:46,950
+شكالة ال algorithm بيعطيني طب ما هو نفس الكلام
+
+334
+00:25:46,950 --> 00:25:50,030
+هستفيد من الموضوع هذا انه دايما هيكون في عندكم
+
+335
+00:25:50,030 --> 00:25:55,430
+common هنا في سبع تلتات هنا في تلتة واحدة مجموعة
+
+336
+00:25:55,430 --> 00:26:00,130
+اللي بصير في عندك تمان تلتات تمان تلتات التلتة هذه
+
+337
+00:26:00,130 --> 00:26:06,010
+بتعرضوا قيمتها من ال schedule اللي جامكم من ال
+
+338
+00:26:06,010 --> 00:26:10,050
+schema اللي جامكم كويسة لاحظوا هنا تلتة و عشرين و
+
+339
+00:26:10,050 --> 00:26:13,830
+في تلتة و عشرينو منطق جدا أصلا دايما يطلع فيه
+
+340
+00:26:13,830 --> 00:26:17,770
+أرقام متشابهة لأن هنا كانت ال B هنا كانت ال R و ال
+
+341
+00:26:17,770 --> 00:26:22,390
+R هي نفسها ال B في المرحلة اللي بعدها احنا بناخدهم
+
+342
+00:26:22,390 --> 00:26:26,770
+من بعض أساسا تمام فلاحظوا هنا minus one و هنا
+
+343
+00:26:26,770 --> 00:26:33,670
+minus تمانية minus تسعة minus تسعة ال 23 عوضناها ب
+
+344
+00:26:33,670 --> 00:26:39,770
+75 ناقص 2 في 26 في 26 هنا في 26بقى مع التجميع
+
+345
+00:26:39,770 --> 00:26:43,730
+هيطلع لكوا 26 باعتبار ان ال 26 موجودة هنا ب تمانية
+
+346
+00:26:43,730 --> 00:26:51,190
+تمانية و هنا 18 ف26 ب 26 26 برضه من هنا تقدر
+
+347
+00:26:51,190 --> 00:26:57,110
+تاخدوها على أساس ان هي 101 ناقص 75 بدا يظهر عند
+
+348
+00:26:57,110 --> 00:27:02,490
+أول tear بديها في المعادلةالمية واحد هي اول term
+
+349
+00:27:02,490 --> 00:27:07,190
+ظهر بدنا ال term التاني ال 4620 عشان اربطهم
+
+350
+00:27:07,190 --> 00:27:09,850
+الاتنين في معدلة واحدة و لازم equal to one و انا
+
+351
+00:27:09,850 --> 00:27:14,290
+ضمن انه كله equal to one
+
+352
+00:27:15,830 --> 00:27:26,530
+وصلنا لـ 75 برضه إيجد 4620 رتبنا المعادلة فالواحد
+
+353
+00:27:26,530 --> 00:27:29,530
+طلع بالساوي ماينوس خمسة و تلاتين في اش في الاربع
+
+354
+00:27:29,530 --> 00:27:35,170
+تلاف ستمية و عشرين plus مية الف و ستمية و واحد في
+
+355
+00:27:35,170 --> 00:27:41,530
+مية و واحد فإذا ال inverse تبعنا الف ستمية و واحد
+
+356
+00:27:42,890 --> 00:27:50,490
+إذا كانت ال A تساوي 101، then ال A' تساوي 1601
+
+357
+00:27:50,490 --> 00:27:58,970
+طبعا هذا كله مود 4620
+
+358
+00:28:00,850 --> 00:28:06,550
+تمام؟ فهي طريقة الشغل في الحالة بتاعتنا لاحظوا ان
+
+359
+00:28:06,550 --> 00:28:09,990
+انتوا بتكونوا تعملوا grades of common divisors حتى
+
+360
+00:28:09,990 --> 00:28:13,830
+لو انتوا عارفين ان هي primes بس بتسهل عليكوا في ال
+
+361
+00:28:13,830 --> 00:28:17,050
+analysis هذا بتسهل عليكوا لان كل واحدة بتكونوا
+
+362
+00:28:17,050 --> 00:28:19,110
+عارفين ايش ال remainder اللي كان موجود وقداش
+
+363
+00:28:19,110 --> 00:28:25,600
+بتقدروه a minus some k في bA مضروبة في sum K في B
+
+364
+00:28:25,600 --> 00:28:29,860
+تمام؟ تقدر تشتغله عليه بهذا الشكل اقدرنا هنا نجيب
+
+365
+00:28:29,860 --> 00:28:34,560
+greatest common divisor ومنها اقدرنا نجيب ال
+
+366
+00:28:34,560 --> 00:28:43,620
+inverse جينا إيجاكوا سؤال بهذا الشكل حلولنا
+
+367
+00:28:43,620 --> 00:28:50,980
+قيمة Xعندما تلاتة X congruent to 4 معدلة Linear هي
+
+368
+00:28:50,980 --> 00:28:53,520
+المعادلة Linear و بتجيبوا قيم ال variables اللي
+
+369
+00:28:53,520 --> 00:28:57,400
+فيها قيم ال variables احنا سابقا اتكلمنا عن
+
+370
+00:28:57,400 --> 00:29:01,140
+الموضوع هذا باستخدام ال matrices لو متذكرين ال
+
+371
+00:29:01,140 --> 00:29:05,800
+matrices قولنا انه A في X بساوي B فكنتوا بتقولوا
+
+372
+00:29:05,800 --> 00:29:09,020
+ال vector الأول transpose طبعا ال vector الأول
+
+373
+00:29:09,020 --> 00:29:12,880
+اللي اعمله transpose في ال X طبعا ال A هذه كانت
+
+374
+00:29:12,880 --> 00:29:13,260
+Matrix
+
+375
+00:29:16,960 --> 00:29:19,800
+حسب جداش عدد المعادلات اللي موجودة عندكم وجداش عدد
+
+376
+00:29:19,800 --> 00:29:26,920
+ال variables بساوي B كيف كنتوا تحلوها؟
+
+377
+00:29:26,920 --> 00:29:32,360
+A inverse تضربوه في الأولى و تضربوه في التانية،
+
+378
+00:29:32,360 --> 00:29:39,860
+صحيح؟ طيب ضربناه في الأولى و ضربناه في التانية طيب
+
+379
+00:29:39,860 --> 00:29:42,560
+هاي ال two inverses في بعض هدولة ال two inverses
+
+380
+00:29:42,560 --> 00:29:47,220
+في بعض واحد فبطلعنا قيمة Xعلى أساس إن هي ال A
+
+381
+00:29:47,220 --> 00:29:51,580
+inverse في B فما هو نفس الكلام اللي بيحكيه فإذا
+
+382
+00:29:51,580 --> 00:29:54,580
+أنا مضطر أجيب ال inverse بتاعة ال matrix هنا و هنا
+
+383
+00:29:54,580 --> 00:29:57,360
+نفس الكلام عشان أحل المعادلة مضطر أجيب ال inverse
+
+384
+00:29:57,360 --> 00:30:02,260
+تبع ال A فمحتاج ال inverse prime عشان أجيب ال
+
+385
+00:30:02,260 --> 00:30:06,020
+inverse تبعها ال inverse تبعها بضمن لإن ال X دلت
+
+386
+00:30:06,020 --> 00:30:11,210
+term لحالهافمنطقيا هتساوي ال inverse ل التلاتة ..
+
+387
+00:30:11,210 --> 00:30:14,550
+inverse ل التلاتة هنا في أربعة .. inverse ل
+
+388
+00:30:14,550 --> 00:30:16,710
+التلاتة في أربعة هنشوف هل فعلا حد طبعا الكلام ..
+
+389
+00:30:16,710 --> 00:30:24,750
+الكلام في غير شكل ولا لأ طيب مسبقا احنا عرفنا ان
+
+390
+00:30:24,750 --> 00:30:29,530
+ال inverse ل التلاتة module of seven يبقى لو
+
+391
+00:30:29,530 --> 00:30:33,070
+moduleه تاني بختلف ديروا بالكم لو moduleه تاني ال
+
+392
+00:30:33,070 --> 00:30:36,500
+inverse ل التلاتة هتختلفهذا إذا .. إذا فرضنا إنه
+
+393
+00:30:36,500 --> 00:30:41,040
+يوجد unique inverse إليها under modulo 3 .. under
+
+394
+00:30:41,040 --> 00:30:45,640
+modulo 7 طيب، قلنا إن هي فيه سالف 2، معناه ذلك إنه
+
+395
+00:30:45,640 --> 00:30:51,080
+بدروا الطرفين في سالف 2 الطرفين اللي ضربناهم في
+
+396
+00:30:51,080 --> 00:30:56,660
+سالف 2، هنا حصير فيه سالف 6 طيب، سالف 6 إحنا
+
+397
+00:30:56,660 --> 00:31:00,000
+عارفين مسبقا إنه سالف 6، هاي اللي حلناها جابت هاي
+
+398
+00:31:00,000 --> 00:31:01,260
+equivalent to 1
+
+399
+00:31:05,210 --> 00:31:08,110
+السالف ستة كانت equivalent to one فهنا كانت ال one
+
+400
+00:31:08,110 --> 00:31:12,370
+two three سالف ستة هاي واحد اتنين تلاتة اربع خمسة
+
+401
+00:31:12,370 --> 00:31:17,690
+ستة هاي سالف ستة equivalent لمين للواحد فهذه كأنها
+
+402
+00:31:17,690 --> 00:31:23,550
+واحد طبعا الكلام ده كله modulo seven modulo seven
+
+403
+00:31:23,550 --> 00:31:26,790
+لازم نحدد ان احنا نتكلم عن modulo seven طيب هنا
+
+404
+00:31:26,790 --> 00:31:31,870
+minus تمانين هذا صحيحمينوس تمانية فإذا المينوس
+
+405
+00:31:31,870 --> 00:31:36,090
+تمانية هذه برضه مكافئة لمين كأنك تتنشوا بالسالب
+
+406
+00:31:36,090 --> 00:31:40,970
+واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية
+
+407
+00:31:40,970 --> 00:31:46,770
+covenant لمن للستة فإذا سالب تمانية covenant للستة
+
+408
+00:31:46,770 --> 00:31:52,590
+covenant للستة فإذا x تساوي ممكن تقوله مينوس
+
+409
+00:31:52,590 --> 00:31:57,770
+تمانية بمش الحال أو ممكن تقوله ستةبالنسبة لكلمة ده
+
+410
+00:31:57,770 --> 00:32:03,410
+كله موديولو سبع طيب اتجربوا ممكن اتجربوا اتجربوا
+
+411
+00:32:03,410 --> 00:32:07,690
+اتجربوا اضربوا تلاتة في اكس شوفوا هل فعلا يكون في
+
+412
+00:32:07,690 --> 00:32:12,330
+الاربعة ولا لا هاي تلاتة في اكس وخلينا نقول انه
+
+413
+00:32:12,330 --> 00:32:16,310
+بدنا نستخدم الستة تمانتعش موديولو سبع اترحوا
+
+414
+00:32:16,310 --> 00:32:19,750
+اربعتاش على اعتبار ان اربعتاش اترحوا اربعتاش اتنين
+
+415
+00:32:19,750 --> 00:32:25,360
+في سبعة بيضل اربعةطبعا الكلام ده سواء استخدمته
+
+416
+00:32:25,360 --> 00:32:31,480
+minus 8 او 6 او المضاعفاتها ال congruences تبعتها
+
+417
+00:32:31,480 --> 00:32:36,720
+ال congruences بتاعتها هتكون 13 مثلا اشمعوا 7 13
+
+418
+00:32:36,720 --> 00:32:41,900
+ممكن تكون 20 ممكن يكون هنا بالثالث مع 7 minus 15
+
+419
+00:32:41,900 --> 00:32:47,190
+minus 1فلاحظوا ان كلهم اي واحدة منهم استخدموها
+
+420
+00:32:47,190 --> 00:32:51,450
+هتطلع معاكم .. اي واحدة منهم استخدموها هتطلع معاكم
+
+421
+00:32:51,450 --> 00:32:55,590
+لو ضرقتوها في .. في التلاتة لازم ال .. ال .. ال ..
+
+422
+00:32:55,590 --> 00:32:55,990
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+423
+00:32:55,990 --> 00:32:56,830
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+424
+00:32:56,830 --> 00:32:57,050
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+425
+00:32:57,050 --> 00:32:58,570
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+426
+00:32:58,570 --> 00:33:00,830
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+427
+00:33:00,830 --> 00:33:02,970
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+428
+00:33:02,970 --> 00:33:08,470
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+429
+00:33:11,010 --> 00:33:14,510
+unique inverse داخل ال cycle الواحدة باعتبار أنه
+
+430
+00:33:14,510 --> 00:33:20,930
+داخل one cycle له unique واحدة فإذا هنا في الحالة
+
+431
+00:33:20,930 --> 00:33:24,730
+اللي كنا نتكلم عنها في الحالة اللي عندنا داخل ال
+
+432
+00:33:24,730 --> 00:33:31,290
+cycle الواحدة clockwise فقط ال 6 مضاعفاتها هتكون
+
+433
+00:33:31,290 --> 00:33:34,490
+أكبر من ال cycle هتكون أكبر من ال cycle زي لما
+
+434
+00:33:34,490 --> 00:33:39,200
+كنتوامتذكرين كنتوا بتحكوا عن الزوايا لما تقولوا
+
+435
+00:33:39,200 --> 00:33:45,780
+سالب تلاتين درجة اللي هي قداش تلاتمية و تلاتين لأن
+
+436
+00:33:45,780 --> 00:33:50,180
+سالب تلاتين تمشي بالعكس كنتوا تمشي بالعكس تلاتين
+
+437
+00:33:50,180 --> 00:33:58,280
+درجة فهذه كأنها تلاتمية و تلاتين درجة تلاتمية و
+
+438
+00:33:58,280 --> 00:34:04,570
+تلاتين درجة طيب ممكن جدا تقولوا لأالزاوية 330 ممكن
+
+439
+00:34:04,570 --> 00:34:11,210
+تسمعها 360 ونقول و الله 690 690
+
+440
+00:34:11,210 --> 00:34:16,250
+ما هي equivalent لمين ل 330 ل 330 ولكن بقدرش اعتمد
+
+441
+00:34:16,250 --> 00:34:20,630
+على 300 على 690 واسيبها بهذا الشكل لازم اوحدها
+
+442
+00:34:20,630 --> 00:34:26,670
+دايما لمين ارجحها لقيمة مكافئة لها داخل ال cycle
+
+443
+00:34:26,670 --> 00:34:30,010
+الواحدة داخل ال one cycle فاحنا هنا بنقول انه لها
+
+444
+00:34:30,010 --> 00:34:33,800
+interest داخل ال cycleotherwise ما احنا عارفين ان
+
+445
+00:34:33,800 --> 00:34:38,340
+انتوا عاملين زي الساعة لازم كل لفة بتلف لأنها عدد
+
+446
+00:34:38,340 --> 00:34:41,080
+لانهية من اللفات بتقدر تقولوا الساعة هتلف جديش
+
+447
+00:34:41,080 --> 00:34:44,840
+عشان تحسب الزمن هتلف باستمرار هدي periodic
+
+448
+00:34:44,840 --> 00:34:48,360
+periodic معناته اتوحى انها هتتكرر انا بتكلم عن ال
+
+449
+00:34:48,360 --> 00:34:51,940
+inverse داخل الدورة الواحدة اللفة الواحدة اللفة
+
+450
+00:34:51,940 --> 00:34:56,440
+الواحدة الها الستة فقط طبعا كل شيء يمثل ستة او
+
+451
+00:34:56,440 --> 00:35:01,580
+بقدر قربه لستة congruent to six برضه يمشي الحقبس
+
+452
+00:35:01,580 --> 00:35:03,980
+بقدرش أقول إن هذا هو الرقم ال standard تبعها
+
+453
+00:35:03,980 --> 00:35:12,600
+الزاوية 690 طبيعي لازم أجربها أطرح منها 360 نطرح
+
+454
+00:35:12,600 --> 00:35:16,780
+منها 360 وهنا نفس الكلام أي قيمة تجيكوا minus 15
+
+455
+00:35:16,780 --> 00:35:22,850
+طبيعي أنك تطرح منها 7 الأولبتشيلوا منها سبعة شيلنا
+
+456
+00:35:22,850 --> 00:35:26,810
+منها سبعة فكأني جمعت عليها سبعة فبتصير minus
+
+457
+00:35:26,810 --> 00:35:31,330
+تمانية طيب minus تمانية لسه أكبر من minus سبعة
+
+458
+00:35:31,330 --> 00:35:35,530
+تمان مرة minus واحد فإذا anti-clockwise لو بدنا
+
+459
+00:35:35,530 --> 00:35:39,770
+نشتر anti-clockwise اللي هي مكافئة هي لتلاتين على
+
+460
+00:35:39,770 --> 00:35:46,270
+اعتبار ما كنتوا يقولوا ناقص تلاتمية وتسعين فإذا
+
+461
+00:35:46,270 --> 00:35:49,150
+clockwise إلها inverse واحد anti-clockwise إلها
+
+462
+00:35:49,150 --> 00:35:54,060
+inverse واحدفال two inverses تبقوا هنا minus 6 او
+
+463
+00:35:54,060 --> 00:35:59,160
+minus 1 يعني عفوا ال 6 او 1 و ال 6 او 1 في
+
+464
+00:35:59,160 --> 00:36:02,140
+الحالتين اللي هي بتبقوا تمشوا من هنا 6 درجات
+
+465
+00:36:02,140 --> 00:36:06,980
+فبتصلوا لهاد النقطة او بالثاني درجة فبرضه هتصلوا
+
+466
+00:36:06,980 --> 00:36:11,500
+لنفس النقطة هي هي النقطة واحدة يعني نقطة واحدة
+
+467
+00:36:11,500 --> 00:36:17,650
+داخل ال cycle نقطة واحدة داخل ال cycleواضح ان هنا
+
+468
+00:36:17,650 --> 00:36:21,250
+مافيش مشكلة عندنا مش أشكال طبعا لاحظوا إذا الأرقام
+
+469
+00:36:21,250 --> 00:36:28,130
+الكبيرة هنا زي مثلا المثلة تعتودي هي 101 و ال
+
+470
+00:36:28,130 --> 00:36:32,370
+module أو ال module تبعنا كان 4620 في الحالة هذه
+
+471
+00:36:32,370 --> 00:36:37,240
+تتحللوا من الأول تعملوا greatest common divisorو
+
+472
+00:36:37,240 --> 00:36:41,620
+بعدين تجيبوا ال .. ال .. ال .. ال بيزوت ال
+
+473
+00:36:41,620 --> 00:36:44,420
+coefficients تبعتكم عشان تحسبوا ال inverse و بعدين
+
+474
+00:36:44,420 --> 00:36:47,740
+ال inverse تجربوه .. تضربوه هنا عشان تجيبوا قداش
+
+475
+00:36:47,740 --> 00:36:52,620
+القيم .. قيمة x قداش قيمة x الممكنة .. قداش قيمة x
+
+476
+00:36:52,620 --> 00:36:58,560
+الممكنة okay pseudo primes مدام كنا .. اتكلمنا عن
+
+477
+00:36:58,560 --> 00:37:01,580
+ال random طب مافيه ال primes كمان فيه جزئية ال
+
+478
+00:37:01,580 --> 00:37:05,900
+primeالـ prime مش بالضروري دايما يكون هو فعلا الـ
+
+479
+00:37:05,900 --> 00:37:08,340
+prime, pure prime مين اللي وضّح إنه جزئي هذا؟ مين
+
+480
+00:37:08,340 --> 00:37:11,060
+اللي خلّى الناس يفكروا في هذا الموضوع هذا؟ مجموعة
+
+481
+00:37:11,060 --> 00:37:14,520
+علماء صينيين قدماء جدا، يعني من قدماء الصينيين
+
+482
+00:37:14,520 --> 00:37:20,560
+طلعوا نظرية إنه إذا whenever n is prime، إذا كان n
+
+483
+00:37:20,560 --> 00:37:24,360
+is prime، فإذا two to the power n minus one
+
+484
+00:37:24,360 --> 00:37:29,950
+congruent to one mod nهذا الكلام إذا كانت prime
+
+485
+00:37:29,950 --> 00:37:36,490
+ذهبوا في اعتقادهم لإثبات العكس إيش هو؟ إنه إذا two
+
+486
+00:37:36,490 --> 00:37:39,550
+to the power of N minus one congruent to one mod N
+
+487
+00:37:39,550 --> 00:37:44,790
+فإذا ال N هذي is prime للأسف
+
+488
+00:37:44,790 --> 00:37:49,850
+إدعاء العكس ماكنت صحيح 100% بعدهم كذا وقت، كذا
+
+489
+00:37:49,850 --> 00:37:57,640
+سنة، كذا عقد من السنوات، كذا قرن من القرونطلعوا ان
+
+490
+00:37:57,640 --> 00:38:00,980
+لأ و الله تصبتش دايما هدى اتنين to the power n
+
+491
+00:38:00,980 --> 00:38:05,800
+minus one equal to one mod n مش بالضرورى يتبحى انه
+
+492
+00:38:05,800 --> 00:38:11,240
+n is prime كيف؟ لحظوا المعادلة هدى؟ هى رقم تلاتمية
+
+493
+00:38:11,240 --> 00:38:14,980
+واحد واربعين هدى عبارة عن احداشه واحدة معناته مش
+
+494
+00:38:14,980 --> 00:38:20,160
+prime صحيح؟ مش prime ومع ذلك اتنين to the power n
+
+495
+00:38:20,160 --> 00:38:24,340
+minus one تساوي او congruent to one mod تلاتمية
+
+496
+00:38:24,340 --> 00:38:29,530
+واحد واربعينطيب، كويس، هل معنى ذلك أن كلامه كان
+
+497
+00:38:29,530 --> 00:38:33,670
+بالمجمل خطأ؟ لأ، استنوا لحظة، هم فتحوا علينا الوجد
+
+498
+00:38:33,670 --> 00:38:38,670
+على حاجة تانية إن هذا okay مش prime بس بقدر أسميه
+
+499
+00:38:38,670 --> 00:38:41,710
+pseudo prime ليش pseudo prime؟ لأن هو لا يقبل
+
+500
+00:38:41,710 --> 00:38:50,090
+القسمة إلا على two primes 11 و 31 فإذا الكلام هذا
+
+501
+00:38:50,090 --> 00:38:56,600
+صحيح بس كان بده إضافة صغيرة بدل ما أقول thenM is
+
+502
+00:38:56,600 --> 00:39:03,480
+prime كان ممكن اقول M at least Sodoprime ممكن تكون
+
+503
+00:39:03,480 --> 00:39:06,580
+prime و ممكن تكون Sodoprime ايش تعريف ال Sodoprime
+
+504
+00:39:06,580 --> 00:39:12,340
+شبيه بالprime مع اختلاف واحد انه ممكن يقسم على
+
+505
+00:39:12,340 --> 00:39:16,880
+اعدادين لاتنين primes فهنا هذا فعلا بقسمش الا على
+
+506
+00:39:16,880 --> 00:39:19,300
+الرقامين هدول فقط الرقامين هدول اللي شجعنا نطلع
+
+507
+00:39:19,300 --> 00:39:23,750
+عليهم هي اتنين primesالـ two primes هذا له خصوصية
+
+508
+00:39:23,750 --> 00:39:30,610
+هذا بنسميه Sodoprime الـ 341 نسميه Sodoprime ممكن
+
+509
+00:39:30,610 --> 00:39:34,410
+استخدامه لإن أنا كنت بدور بدّي Primes و ال Prim
+
+510
+00:39:34,410 --> 00:39:37,170
+هذا ليش احنا بندور عليه ال Prim بندور عليه لإن هذا
+
+511
+00:39:37,170 --> 00:39:40,690
+بفيدنا في ال security اللحقة لما نجي نتكلم عن ال
+
+512
+00:39:40,690 --> 00:39:45,200
+cryptographicأو ال cryptography theory اللي هنتكلم
+
+513
+00:39:45,200 --> 00:39:49,340
+عنها بلزمنا أنه نكون لما نعمل generation حتى زي
+
+514
+00:39:49,340 --> 00:39:52,340
+توي و أن أنا بدور على أرقام تكون برايم تكون أفضل
+
+515
+00:39:52,340 --> 00:39:56,400
+لما بدي برايم أدور على برايم و رقمه كبير تكون رقم
+
+516
+00:39:56,400 --> 00:40:01,100
+عالي كبير هذه okay مانفعتش بس هي هتكون هتطلعلي two
+
+517
+00:40:01,100 --> 00:40:06,950
+primes بدل الواحد إذا كانت تحقق الشرط هذافمعنى ذلك
+
+518
+00:40:06,950 --> 00:40:12,550
+أن هذه إما هي نفسها prime أو هي pseudo prime هتطلع
+
+519
+00:40:12,550 --> 00:40:17,310
+two primes، هتطلع two primes، مش ال prime واحد،
+
+520
+00:40:17,310 --> 00:40:22,210
+كويسة، فإذا النظرية هيك اتعدلت شئ خفيف بدل ما كنا
+
+521
+00:40:22,210 --> 00:40:27,910
+نقول ال prime، بنقول إيش؟بنقول Sodoprime هتقولوا
+
+522
+00:40:27,910 --> 00:40:31,690
+ليه؟ مش بدنا فيها Sodoprime لأ الناس بعد ما وجدوا
+
+523
+00:40:31,690 --> 00:40:35,490
+أن هناك أرقام يعني نستفيد منها، إلها خصوصية، في
+
+524
+00:40:35,490 --> 00:40:40,490
+إلها ميزة اللي هي Sodoprime هذه إلها ميزة ذهب في
+
+525
+00:40:40,490 --> 00:40:45,390
+الاعتقاد إنه مش بالضروري ال base تبعتنا اتنين ل a,
+
+526
+00:40:45,510 --> 00:40:50,550
+b الكلام صحيح b to the power n minus one congruent
+
+527
+00:40:50,550 --> 00:40:55,130
+to one base nأتنين او اكتر مش مشكلة فاتعممت
+
+528
+00:40:55,130 --> 00:40:58,150
+القاعدة بهذا الشكل على اساس انه اي رقم بيحقق
+
+529
+00:40:58,150 --> 00:41:03,730
+المعادلة هذه هنسميه pseudo prime Carmichael
+
+530
+00:41:03,730 --> 00:41:07,990
+Carmichael number Carmichael مسك الموضوع هذا ومسك
+
+531
+00:41:07,990 --> 00:41:11,870
+لنا كل الأرقام بدأ يفحص الأرقام اللي ممكن نحطها
+
+532
+00:41:11,870 --> 00:41:17,410
+ضمن set ال set هنسميها pseudo prime فجلنا ان هو في
+
+533
+00:41:17,410 --> 00:41:24,240
+الرقم بعد الرقم اللي احنا شغلناه ال 431 فيه561 في
+
+534
+00:41:24,240 --> 00:41:30,260
+1105 في 1729 شكلهم كإنهم ال prime بس لأ هم فعليا
+
+535
+00:41:30,260 --> 00:41:33,260
+بينفعوش إلا إنه يكونوا ضرب حاصل two prime ثانية
+
+536
+00:41:33,260 --> 00:41:38,400
+يكونوا حاصل ضرب two prime ثانية فقط يعني مجسموش
+
+537
+00:41:38,400 --> 00:41:41,480
+علاقش اتاني إذا مجسموا علاقش اتاني بطلوا pseudo
+
+538
+00:41:41,480 --> 00:41:45,520
+prime فقط مجسموا على رقمين لإن رقمين هدولة prime
+
+539
+00:41:45,520 --> 00:41:49,140
+فبدأ يعمل analysis هيو بدأ يطلع فيهم لعام موصل ل
+
+540
+00:41:49,140 --> 00:41:54,640
+29000 وفيه طبنة لهم تكملطيب و بعدين؟ إيش بدنا فيهم
+
+541
+00:41:54,640 --> 00:42:01,000
+هدولة؟ so what؟ who cares؟ مين الحق يعني؟ بعدين زي
+
+542
+00:42:01,000 --> 00:42:04,180
+ما انتوا طب تقولوا طب و لما نجيب ال inverse؟
+
+543
+00:42:04,180 --> 00:42:07,040
+قولتلكوا لأ أصبروا شوية بنحل فيها المعادلة ال
+
+544
+00:42:07,040 --> 00:42:10,900
+linear equation ال linear congruential حلناها طيب
+
+545
+00:42:10,900 --> 00:42:16,330
+هنا نفس الكلام إيش بنهتم؟ هدي إلكممع المرة الجاية
+
+546
+00:42:16,330 --> 00:42:22,110
+مع الواجب بدي بس ورقة ورقة A4 مرتبة ومنصقة مش مزعة
+
+547
+00:42:22,110 --> 00:42:26,230
+ايكى ورقة اعملولنا بحث صغير بس اكتبولنا على جوجل
+
+548
+00:42:26,230 --> 00:42:30,750
+ولا على اي search engine Carmichael number
+
+549
+00:42:30,750 --> 00:42:34,990
+applications كل واحدة لو جابتلي applications او
+
+550
+00:42:34,990 --> 00:42:37,550
+application واحد وجالتنا كيف استخدمت فيه الرقم
+
+551
+00:42:37,550 --> 00:42:40,670
+تبعنا عشان تحسوا بس انه اه والله ايش اهمية الرقم
+
+552
+00:42:41,690 --> 00:42:44,850
+تمام؟ على الأقل application واحد مش بالضرورة
+
+553
+00:42:44,850 --> 00:42:47,630
+تفهموه كويس بس انك تحس ان والله الأرقام هذه لها
+
+554
+00:42:47,630 --> 00:42:52,410
+تطبيقات لها تطبيقات ورقة واحدة بدي بس مش أكتر ورقة
+
+555
+00:42:52,410 --> 00:42:58,790
+واحدة اسم كفوغ Carmichael number applications او
+
+556
+00:42:58,790 --> 00:43:01,590
+numbers applications لأن هذه عدة أرقام كبيرة جدا
+
+557
+00:43:01,590 --> 00:43:06,470
+عددها كبير شوفوا ان ايش التطبيقات اللي ممكن نستخدم
+
+558
+00:43:06,470 --> 00:43:11,560
+فيها Carmichael ال Carmichael مثلاOkay المرة
+
+559
+00:43:11,560 --> 00:43:15,760
+الجاية بنبدأ في ال cryptography لإنه مهمة برضه
+
+560
+00:43:15,760 --> 00:43:20,400
+كويسة لأول واحد اشتغلها اللي هو Caesar او القيصر
+
+561
+00:43:20,400 --> 00:43:25,660
+اشتغل على ال Caesars cypher او شفرة Caesar كان
+
+562
+00:43:25,660 --> 00:43:30,400
+بيبعت الرسائل تبعته للجيوش والقادة تعونه مشفرةكيف
+
+563
+00:43:30,400 --> 00:43:35,240
+كانت بشفرها هنشوف طبعا بشفرها حرف by حرف أو letter
+
+564
+00:43:35,240 --> 00:43:39,460
+by letter كل حرف بعكسه و بيعمله طريقة modification
+
+565
+00:43:39,460 --> 00:43:42,720
+و بيبعت الرسالة بطريقة معينة هنتكلم عنها برضه
+
+566
+00:43:42,720 --> 00:43:46,040
+باستخدام ال modulo فالموديولو من زمان جدا اصلا
+
+567
+00:43:46,040 --> 00:43:51,020
+مقترعوا ما عاملينهطريقة كسر ال code كمان هنتكلم
+
+568
+00:43:51,020 --> 00:43:54,180
+عنه، كيف ممكن نكسر ال code و نعرف بالظبط هو إيش
+
+569
+00:43:54,180 --> 00:43:59,500
+اللي بعته، بعدين هنتكلم عن طريقة تانية و في طريقة
+
+570
+00:43:59,500 --> 00:44:01,740
+تالتة هنتكلم عنها لاحقا، اللي هي ما زالت تستخدم
+
+571
+00:44:01,740 --> 00:44:04,320
+حتى الآن، ما زالت تستخدم حتى الآن، فبنخليها للمرة
+
+572
+00:44:04,320 --> 00:44:06,580
+الجاية ان شاء الله تعالى عشان تلحقوا، تذاكروا أو
+
+573
+00:44:06,580 --> 00:44:10,180
+تترجعوا إذا عندكوا أي أسئلة، يعطيكم العفو و بركة
+
+574
+00:44:10,180 --> 00:44:10,600
+الله فيكم
+
diff --git a/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE_raw.srt b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ba818795508e30cddd6c85f8ee98a46908e7e97f
--- /dev/null
+++ b/PL9fwy3NUQKwZmc_eouW8jXyoWdwe0lOqs/yRm5oxxfkLE_raw.srt
@@ -0,0 +1,2320 @@
+1
+00:00:20,650 --> 00:00:22,810
+Okay بسم الله الرحمن الرحيم الصلاة والسلام علي
+
+2
+00:00:22,810 --> 00:00:25,210
+أشرف الأنبياء والإنبسار لسيدنا محمد وعلي أهلا
+
+3
+00:00:25,210 --> 00:00:28,350
+وصحابي أجمال طيب المرة اللي فاتت احنا بدأنا
+
+4
+00:00:28,350 --> 00:00:32,210
+اتكلمنا في ال .. في حكاية ال applications لل
+
+5
+00:00:32,210 --> 00:00:34,770
+number theory وقلنا إيش في applications ممكن
+
+6
+00:00:34,770 --> 00:00:39,390
+نعملها لل numbers وتطرقنا هيك بسرعة إن إيش اللي
+
+7
+00:00:39,390 --> 00:00:42,530
+هنشرحه المرة الجاية اللي هي اليوم قلنا هنتكلم عن
+
+8
+00:00:42,530 --> 00:00:46,650
+ال pseudo random numbers كيك ممكن نعمل sequence
+
+9
+00:00:46,650 --> 00:00:51,710
+بتهيألكوا إن هوrandom .. random sequence ولكن هو
+
+10
+00:00:51,710 --> 00:00:54,990
+محسوب .. deterministic .. sequence بمعنى أن أنا
+
+11
+00:00:54,990 --> 00:00:57,530
+بقدر أعمله regeneration .. بتقدروا أنتوا تعملوه
+
+12
+00:00:57,530 --> 00:01:00,250
+regeneration .. ال applications هذه كتيرة .. إلو
+
+13
+00:01:00,250 --> 00:01:02,790
+تطبيقات كتيرة .. من أهمها يمكن ال hash function ..
+
+14
+00:01:02,790 --> 00:01:06,600
+من أهمها ال games .. ال graphicsال simulations ال
+
+15
+00:01:06,600 --> 00:01:08,760
+.. ال cryptographic و أهم شغلها دي ال
+
+16
+00:01:08,760 --> 00:01:11,440
+cryptographic اللي هناخدها مش .. طبعا مش هنقدر
+
+17
+00:01:11,440 --> 00:01:14,280
+ناخدها اليوم لأن زي ما قلتلكوا هناخد جزء اليوم
+
+18
+00:01:14,280 --> 00:01:19,120
+محاضر و عشان الامتحان فهنتكلم عن ال cryptographic
+
+19
+00:01:19,120 --> 00:01:24,470
+و هنشوف كيف ممكن نعمل تشفيهعلم التشفير كله مبني
+
+20
+00:01:24,470 --> 00:01:27,170
+على حكايات ال pseudorandom على حكايات ال
+
+21
+00:01:27,170 --> 00:01:29,890
+pseudorandom كيف بنعمل الحكايات ال pseudorandom
+
+22
+00:01:29,890 --> 00:01:34,590
+هذه عن طريق ال linear congruential method و
+
+23
+00:01:34,590 --> 00:01:39,090
+هنستخدم فيها ال modular اللي احنا خدناها سابقا
+
+24
+00:01:39,090 --> 00:01:42,310
+عملية ال modular operation اللي احنا خدناها سابقا
+
+25
+00:01:42,310 --> 00:01:46,550
+طيب ايش القلية بالظبط ايش هو هذا ال linear
+
+26
+00:01:46,550 --> 00:01:53,590
+congruential method فعليا هذه معادلة بنعمل فيهاهذه
+
+27
+00:01:53,590 --> 00:01:57,610
+المرحلة محتاجة أربع أرقام مهمية جدا الرقم الأول
+
+28
+00:01:57,610 --> 00:02:09,170
+مدلر مدلر مدلر مدلر مدلر مدلر مدلر مدلر مدلر مدلر
+
+29
+00:02:09,940 --> 00:02:13,700
+value ال initial number اللى هنبدأ منه الشغل ففيه
+
+30
+00:02:13,700 --> 00:02:16,120
+دايما initial number نبدأ منه نعمل numerical
+
+31
+00:02:16,120 --> 00:02:19,960
+generation اللى هبنسميه ال X node او X0 طيب ال A
+
+32
+00:02:19,960 --> 00:02:24,380
+هذه اللى هى ال multiplier بده يكون على الاقل بده
+
+33
+00:02:24,380 --> 00:02:28,460
+يكون اتنين multiplier واحد مالوش معناه معامل ضرب
+
+34
+00:02:28,460 --> 00:02:31,260
+واحد مالوش معناه فبده يكون على الاقل اتنين ويكون
+
+35
+00:02:31,260 --> 00:02:34,920
+اقل من ال modulus ال modulus هذا ال M لازم تكون
+
+36
+00:02:34,920 --> 00:02:41,320
+اكبر رقم فيهم لازم تكون اكبر رقم فيهم فA بدها تكون
+
+37
+00:02:41,320 --> 00:02:44,760
+أقل من M و أكبر من او يساوي 2 على الأقل عشان نقول
+
+38
+00:02:44,760 --> 00:02:48,060
+ان اه والله في multiplier طيب ال C و .. اللي هي ال
+
+39
+00:02:48,060 --> 00:02:51,220
+.. ال increment و ال seed بدها تكون بين الصفر و ال
+
+40
+00:02:51,220 --> 00:02:54,840
+M أقل من M طبعا أكيد هتكون أقل من M بحيث برضه زي
+
+41
+00:02:54,840 --> 00:02:58,200
+اللي قلنا ال modulus يكون أكبر رقم موجود في الآخر
+
+42
+00:02:58,200 --> 00:03:01,500
+هنعمل generation ل sequence ال sequence ده هيبين
+
+43
+00:03:01,500 --> 00:03:06,580
+كأنه random ولكن هو pseudorandom شبيه العشوائي أو
+
+44
+00:03:06,580 --> 00:03:11,710
+شبه عشوائيsequence أو شبه عشوائي بيكون الأرقام
+
+45
+00:03:11,710 --> 00:03:15,130
+تبعته كل الأرقام اللى موجودة فيها ال Xn تبعته كلها
+
+46
+00:03:15,130 --> 00:03:21,450
+من صفر او اكبر to M فاش ولا رقم هيكون اكبر من مين
+
+47
+00:03:21,450 --> 00:03:25,930
+من ال M لأن هذا ال modulus اي رقم اكبر من M طبيعي
+
+48
+00:03:25,930 --> 00:03:32,470
+ال mod M هيرجعه لقيمة اقل من M ال Xn plus واحد
+
+49
+00:03:32,470 --> 00:03:36,810
+بمعنى ان ال next value هتساوي ال current value
+
+50
+00:03:37,410 --> 00:03:41,190
+current number مضروف في ال multiplier مجموع على ال
+
+51
+00:03:41,190 --> 00:03:46,230
+increment كلهم ناتج تباحهم بنعمل mod أو modulo M
+
+52
+00:03:46,230 --> 00:03:49,630
+طبعا حيطلع رقم جديد الرقم الجديد بستعمله عشان أحسب
+
+53
+00:03:49,630 --> 00:03:52,390
+الرقم اللي وراه اللي وراه بحسب اللي وراه فبنكون
+
+54
+00:03:52,390 --> 00:03:56,790
+جاندي بنعمل sequence of pseudo random numbers okay
+
+55
+00:03:56,790 --> 00:04:01,290
+كويس جدا عشان أقول والله الأرقام بتاعتنا عشوائية
+
+56
+00:04:01,290 --> 00:04:06,360
+أو شكلها فعلا عشوائي وصعبةو صعب اكتشافها انه يكون
+
+57
+00:04:06,360 --> 00:04:11,060
+ال a, c, m, primes كل ما كانوا primes كل ما كان
+
+58
+00:04:11,060 --> 00:04:16,740
+فيه إمكانية لعمل code صعب عملية ال regeneration
+
+59
+00:04:16,740 --> 00:04:20,580
+تبعته او صعب كسره صعب انه حد غيركوا يعرفه فانتوا
+
+60
+00:04:20,580 --> 00:04:24,560
+بتعملوا generation بهذه ال equation عن طريق ان
+
+61
+00:04:24,560 --> 00:04:27,940
+انتوا تحددوا بس ايش هي ال a ايش ال c ايش ال m
+
+62
+00:04:27,940 --> 00:04:35,750
+بتاعتكم و اتحطواالـ X الأولى .. أول قيمة بتحطوها
+
+63
+00:04:35,750 --> 00:04:38,710
+.. بتكونوا انتوا عملتوا هنا generation اللي هي ال
+
+64
+00:04:38,710 --> 00:04:42,610
+sequence تبعكم انتوا .. الأصل للأرقام هذه .. هذه
+
+65
+00:04:42,610 --> 00:04:47,710
+سرية .. هذه سرية .. اللي هيطلع مجموعة أرقام
+
+66
+00:04:47,710 --> 00:04:51,880
+عشوائية .. أنا لو شفتها المفروض ماعرفهاشأرقام لا
+
+67
+00:04:51,880 --> 00:04:55,180
+تحمل المعنى الحقيقي أنا بالنسبة اللي هتطلع هيقول
+
+68
+00:04:55,180 --> 00:04:58,120
+ان هي random انا مش عارف كيف ان عملها ال
+
+69
+00:04:58,120 --> 00:05:01,480
+generation انتوا اللي لازم تكونوا عارفين طيب مع
+
+70
+00:05:01,480 --> 00:05:06,120
+ذلك ممكن يكسر ال code تبعكوا هذا كيف إذا كان ال A
+
+71
+00:05:06,120 --> 00:05:08,780
+و ال C و ال M انعرفت طيب كيف أجل الأحتمالية
+
+72
+00:05:08,780 --> 00:05:12,680
+معرفتها انه يكونوا prime أو at least relatively
+
+73
+00:05:12,680 --> 00:05:18,790
+primeيكونوا relative prime لبعض ال A مع ال C لجرد
+
+74
+00:05:18,790 --> 00:05:22,370
+اس common divisor واحد ال C مع ال M لجرد اس common
+
+75
+00:05:22,370 --> 00:05:25,770
+divisor واحد ال A مع ال M لجرد اس common divisor
+
+76
+00:05:25,770 --> 00:05:29,670
+واحد إذا كان هيك معناته كل واحدة منهم relative
+
+77
+00:05:29,670 --> 00:05:35,970
+prime للتانية بتصير مناسبة لو ال C Zero بتصير a
+
+78
+00:05:35,970 --> 00:05:39,020
+pure multiplicativeبتصير هنا ال sequence تبعكم
+
+79
+00:05:39,020 --> 00:05:43,040
+pure multiplicative كله جاي من عملية ضرب مش اكثر
+
+80
+00:05:43,040 --> 00:05:48,760
+مفيش اي جمع عالي مفيش اي جمع كويس for example لو
+
+81
+00:05:48,760 --> 00:05:54,220
+أخدنا ال M بتساوي الف أخدنا ال C بتساوي اربعمية
+
+82
+00:05:54,220 --> 00:05:58,510
+سبعة ستة primeرقم ال prime هيه ال multiplier برضه
+
+83
+00:05:58,510 --> 00:06:02,510
+prime عبارة عن 293 و ال seed ممكن نختار اي رقم
+
+84
+00:06:02,510 --> 00:06:10,470
+اللي هي اول قيمة موجودة 426 بنقدر من ال 426 نعمل
+
+85
+00:06:10,470 --> 00:06:14,330
+generation لمي للرقم اللي وراها اللي هو ال X1 عن
+
+86
+00:06:14,330 --> 00:06:19,990
+طريق المعادلة طول مباشرة في المعادلة 285 285
+
+87
+00:06:19,990 --> 00:06:26,650
+بستخدمها مكان X1 عشان نجيب X2972 972 بستخدمها عشان
+
+88
+00:06:26,650 --> 00:06:30,850
+تجيب X تلاتة بتترسم و تسوقن بتضايقوا بتعملوا
+
+89
+00:06:30,850 --> 00:06:35,130
+generation كود صغير و بيضل يطلع generation طبعا
+
+90
+00:06:35,130 --> 00:06:40,530
+بعد فترة هيتكرر بعد فترة هتلاقوه هيتكرر الأرقام
+
+91
+00:06:40,530 --> 00:06:44,570
+اللي بيعملها generation هذه هذه مرتبطة عددها بمين
+
+92
+00:06:44,570 --> 00:06:47,770
+بال modulus ال modulus الف معناه ذلك أن هذا بيقدر
+
+93
+00:06:47,770 --> 00:06:52,750
+يعملكوا generation من صفر ل999الأرقام اللى بقدر
+
+94
+00:06:52,750 --> 00:06:55,890
+يعملها generation هي من صفر تسعمية تسعة وتسعين
+
+95
+00:06:55,890 --> 00:07:00,330
+okay فمعنى ذلك انه انت هيصير reputation للأرقام
+
+96
+00:07:00,330 --> 00:07:05,230
+غالبا بعد عدد اقل من تسعمية تسعة وتسعين او يعني
+
+97
+00:07:05,230 --> 00:07:10,370
+بعد بعد اقل من الف بعد اقل من الف number هتلاقي
+
+98
+00:07:10,370 --> 00:07:13,710
+انه هيتكرر ممكن يكون اجل من هيك كمان ممكن يكون اجل
+
+99
+00:07:13,710 --> 00:07:17,030
+من هيك امتى ممكن يكون اجل من هيك اذا كانت الأرقام
+
+100
+00:07:17,030 --> 00:07:21,430
+اللى موجودة عندك و هدي مش primesفالاحتمالية انه
+
+101
+00:07:21,430 --> 00:07:25,230
+يصير ال repetition اسرع بتصير اكبر انه يصير اسرع
+
+102
+00:07:25,230 --> 00:07:27,950
+طيب ايش دخل ال repetition ال repetition انك كل ما
+
+103
+00:07:27,950 --> 00:07:32,450
+اتكررت في period صغيرة كل ما كان امكانية كسر ال
+
+104
+00:07:32,450 --> 00:07:38,490
+code تبعك أسهل معناه ذلك انه كل ما ال period
+
+105
+00:07:38,490 --> 00:07:42,810
+تبعتكم او التكرار الأرقام بتصير في مسافات جريبة من
+
+106
+00:07:42,810 --> 00:07:45,610
+بعض معناه انه في امكانية لكسر ال code اللي انتوا
+
+107
+00:07:45,610 --> 00:07:49,360
+عاملينه هذا في امكانية ان احنا نعرفهفانتوا بتبعتوا
+
+108
+00:07:49,360 --> 00:07:53,020
+معلومة مشفرة فاكرين ان هي مشفرة بس عاملين
+
+109
+00:07:53,020 --> 00:07:56,440
+regeneration باستخدام أرقام ممكن تكون زوجية مثلا
+
+110
+00:07:56,440 --> 00:08:00,920
+زوجية معروفة لأنه دائما في عوامل مشترك بينهم فمعنى
+
+111
+00:08:00,920 --> 00:08:04,850
+ذلك هتلاقي انه سهلانه نكسر ال code و اعرف ايش
+
+112
+00:08:04,850 --> 00:08:08,590
+الرسالة اللى انتوا باعطينها فبطلت مشفرة فقدتوا
+
+113
+00:08:08,590 --> 00:08:10,950
+الهدف من اصلا من عملية التشفير اللى انتوا بدكوا
+
+114
+00:08:10,950 --> 00:08:14,750
+تستخدموها فهذا مهم جدا كمان الارقام جدش بتقدر تكون
+
+115
+00:08:14,750 --> 00:08:20,450
+prime او at least relatively prime زمبل تانى لو
+
+116
+00:08:20,450 --> 00:08:24,700
+أخدنا ال M high not جللناهاأخدناها قيمة أصغر بحيث
+
+117
+00:08:24,700 --> 00:08:29,860
+أنه يكون تكرار معنا تسعة ال a سبعة ال c أربعة ال x
+
+118
+00:08:29,860 --> 00:08:34,580
+node تلاتة لحظة بدأنا نعمل generation باستخدام ال
+
+119
+00:08:34,580 --> 00:08:39,040
+x node اللي هي التلاتة طلعت سبعة السبعة استخدمناها
+
+120
+00:08:39,040 --> 00:08:42,700
+جبنا تمانية بعد واحد اتنين تلاتة أربعة خمسة ستة
+
+121
+00:08:42,700 --> 00:08:51,850
+سبعة تمانية التاسعة التاسعة تكررهترجع تتكرر خلاص
+
+122
+00:08:51,850 --> 00:08:55,150
+اعرفت انا في الحالة هذه ان التكرار هذا ممكن يعطيني
+
+123
+00:08:55,150 --> 00:09:00,210
+حق بال مين؟ بال modulus اعرفنا رقم يعني هاي بدت
+
+124
+00:09:00,210 --> 00:09:03,670
+عملية كسر ال code تبعكم بدأنا هنا نعرف مجموعة
+
+125
+00:09:03,670 --> 00:09:08,650
+أرقام طيب الهدف انه في الآخر تعملوا ساقوا انه جدش
+
+126
+00:09:08,650 --> 00:09:11,270
+ممكن تعملوا الأرقام بتاعتكم هذه تختاروها primes
+
+127
+00:09:11,840 --> 00:09:14,800
+قدرش ممكن تكون ال M كبيرة حسب ال application اللي
+
+128
+00:09:14,800 --> 00:09:19,020
+بتبقيها حسب لإيش بتكون ال code تستخدموها أو لإيش
+
+129
+00:09:19,020 --> 00:09:22,240
+بتكون ال sequence هذه طيب أفضل sequence تم
+
+130
+00:09:22,240 --> 00:09:24,860
+استخدامه كان ال pure multiplicative generator
+
+131
+00:09:24,860 --> 00:09:29,270
+باستخدام modulus 2 to the powerواحد ثلاثين minus
+
+132
+00:09:29,270 --> 00:09:33,230
+one كان أفضل واحد على أساس أنه هذا و ال multiplier
+
+133
+00:09:33,230 --> 00:09:38,230
+تبعه كانت two primes تتبار بعض سبعة prime تتبار
+
+134
+00:09:38,230 --> 00:09:42,990
+خمسة تتبار خمسة كان مستخدم multiplier هذا is
+
+135
+00:09:42,990 --> 00:09:46,690
+widely used ال code هذا مستخدم جدا و باستمرار
+
+136
+00:09:46,690 --> 00:09:50,610
+بيستخدموه بيطلع ان او بيصير عملية تكرار بعدي اتنين
+
+137
+00:09:51,420 --> 00:09:54,640
+to the power of 31 minus 2 هذه انت بتتكلم عن عدد
+
+138
+00:09:54,640 --> 00:09:58,740
+كبير بالمليارات يعني بعد كذا مليار عبل ما الرقم
+
+139
+00:09:58,740 --> 00:10:01,920
+يبدأ يتكرر تاني فطبعا هذا بيكون صعب بالنسبة لل
+
+140
+00:10:01,920 --> 00:10:05,480
+hacker ان يجوز يتبع ايه انت بيصير التكرار ايه انت
+
+141
+00:10:05,480 --> 00:10:12,230
+بيصير عملية التكرار تبعه تمامفناخد بالة من الأرقام
+
+142
+00:10:12,230 --> 00:10:15,850
+اللى احنا بنختارها كparameters طيب الأرقام هذه
+
+143
+00:10:15,850 --> 00:10:18,890
+برضه ممكن تفيدنا لما نيجي نتكلم عن linear
+
+144
+00:10:18,890 --> 00:10:24,110
+congruences و inverses linear congruences معناه
+
+145
+00:10:24,110 --> 00:10:29,150
+ذلك أنا بتكلم عن معادلة في النهايةAX congruent to
+
+146
+00:10:29,150 --> 00:10:36,250
+B AX congruent to B under the modulo M معناه ذلك
+
+147
+00:10:36,250 --> 00:10:40,150
+ان هدول اتنين مكافئين لبعض و هدى عادة الفكرة اللى
+
+148
+00:10:40,150 --> 00:10:47,370
+بتستخدموها في حل المعادلات اللينية الخطية لما يكون
+
+149
+00:10:47,370 --> 00:10:54,560
+عندكم A في X بيساوي B وبتجيبوا Xماذا كنتوا بتعمله؟
+
+150
+00:10:54,560 --> 00:10:59,520
+تضربوا في ال inverse لمن؟ لل A فتجيبوا A' في A
+
+151
+00:10:59,520 --> 00:11:05,720
+يساوي A' في B فالمفروض التنتين هذولة ضربهم واحد
+
+152
+00:11:05,720 --> 00:11:11,820
+تمام ضربهم بيساوي واحد معناه ذلك أنه أي رقم في ال
+
+153
+00:11:11,820 --> 00:11:15,080
+inverse تبعه المفروض congruent to main to one
+
+154
+00:11:15,080 --> 00:11:19,380
+modulo one بيساوي واحد الاتنين هذول مفروض يساوي
+
+155
+00:11:19,380 --> 00:11:23,210
+واحد بكون اقدر تجيب main Xهذه الطريقة اللى كنتوا
+
+156
+00:11:23,210 --> 00:11:26,330
+تستخدموها في ميد في حالة المعادلات الخطية فعلا
+
+157
+00:11:26,330 --> 00:11:31,070
+هنستفيد منها برضه في ال .. لو أنا بتكلم عن modulo
+
+158
+00:11:31,070 --> 00:11:36,110
+M لو بنتكلم عن modulo M المفروض ان ال A prime في A
+
+159
+00:11:36,110 --> 00:11:41,570
+congruent to مين to one هدى بنقدر نشغلها وعشان
+
+160
+00:11:41,570 --> 00:11:46,690
+نقول ان والله فعلا في ال modulo M ال A فيه إلها
+
+161
+00:11:46,690 --> 00:11:50,970
+inverse الأصل أن يكونوا الأتنين relatively prime
+
+162
+00:11:52,870 --> 00:11:56,550
+الـ greatest common divisor تبعهم واحد فبقدر أقول
+
+163
+00:11:56,550 --> 00:12:03,850
+إيش أنه A إلها inverse وحيد داخل الموضل السام داخل
+
+164
+00:12:03,850 --> 00:12:07,550
+الموضل السام الموضل
+
+165
+00:12:07,550 --> 00:12:09,390
+السام هذا لو قلنا مثلا سبعة
+
+166
+00:12:17,990 --> 00:12:21,250
+داخل المدلة السابعة لها المفروض يكون .. يعني لو
+
+167
+00:12:21,250 --> 00:12:24,610
+افترضنا انه الاتنين او التلاتة و بدنا نجيب ال
+
+168
+00:12:24,610 --> 00:12:28,710
+inverse للتلاتة المفروض يكون انها رقم واحد اقل من
+
+169
+00:12:28,710 --> 00:12:33,230
+سبعة هو ال inverse تبعها هو ال inverse تبعها الاصل
+
+170
+00:12:33,230 --> 00:12:39,050
+يكون unique inverse مايكونش اكتر من inverse واحد
+
+171
+00:12:39,050 --> 00:12:42,190
+ففي الحالة هذه اذا كان .. هنرجع نقول نفس الكلام
+
+172
+00:12:42,190 --> 00:12:46,730
+اذا كان ال GCD او ال greatest common divisor A و M
+
+173
+00:12:48,090 --> 00:12:55,970
+A و M ال A اللي احنا بنشتغل عليها و ال Mإذا كان
+
+174
+00:12:55,970 --> 00:12:58,310
+فعلًا الـ greatest common divisor تبعهم equal to
+
+175
+00:12:58,310 --> 00:13:01,770
+one و ال M طبعًا لازم يكون أكبر من واحد، يكون فيه
+
+176
+00:13:01,770 --> 00:13:05,170
+فعلا عندكم modulus، موجودة ال modulus، then A has
+
+177
+00:13:05,170 --> 00:13:11,330
+a unique inverse, A prime، إلها inverse وحيد أقل
+
+178
+00:13:11,330 --> 00:13:18,090
+من M طبعًا هذا الكلام ضمن modulo M، ضمن modulo M،
+
+179
+00:13:18,090 --> 00:13:21,830
+كيف الكلام هذا بتهم؟عشان نعمل هذا الكلام فعليا
+
+180
+00:13:21,830 --> 00:13:25,770
+بدنا ننطلق من نفس المعادلة أو بدنا نجيل للرقمين
+
+181
+00:13:25,770 --> 00:13:30,910
+هدولة ال .. ال bizot coefficient ال big
+
+182
+00:13:30,910 --> 00:13:33,010
+coefficients ال bizot coefficients هذه المفروضة
+
+183
+00:13:33,010 --> 00:13:38,190
+اللي هي تعطينا القيمة بالظبط تعطينا القيمة بتاعتنا
+
+184
+00:13:38,190 --> 00:13:45,050
+بحسب الاعتبار انه ال .. السبعةاللي هي ال modulus
+
+185
+00:13:45,050 --> 00:13:49,290
+طبعنا بنعملها analysis باستخدام باستخدام مين
+
+186
+00:13:49,290 --> 00:13:55,190
+باستخدام ال A طيب هتساوي تلاتة احنا بدنا نشتغل
+
+187
+00:13:55,190 --> 00:13:59,250
+فعليا هنا على بدنا نجيب ال inverse لتلاتة modulo
+
+188
+00:13:59,250 --> 00:14:05,170
+seven three modulo seven تلاتة في قداش المفروض
+
+189
+00:14:05,170 --> 00:14:14,210
+تكون في ايش في اتنين زائد واحد اتنين زائدالكلام
+
+190
+00:14:14,210 --> 00:14:17,150
+هذا احنا عشان نقول ان هم الاتنين congruent لبعض
+
+191
+00:14:17,150 --> 00:14:21,490
+المفروض انه كل مجموحهم نحطهم في term واحد equal to
+
+192
+00:14:21,490 --> 00:14:26,090
+one congruent to one احنا لسه قاعدين نتكلمين شوية
+
+193
+00:14:26,090 --> 00:14:32,350
+انه الاصل congruent to one to one فهذا نفس الكلام
+
+194
+00:14:32,350 --> 00:14:35,470
+كيف ممكن اعملهم الاتنين في term واحد congruent to
+
+195
+00:14:35,470 --> 00:14:42,180
+one هنقول واحدأو سبعة مانس تلاتة اتنين في تلاتة
+
+196
+00:14:42,180 --> 00:14:48,160
+بساوي واحد ناخد هذا على ناحية التالية طيب هذه
+
+197
+00:14:48,160 --> 00:14:53,860
+عبارة عن في واحد فال .. ال .. بزوت ال coefficients
+
+198
+00:14:53,860 --> 00:15:00,480
+هنا تبعتنا الواحد و minus اتنين و minus two فال
+
+199
+00:15:00,480 --> 00:15:03,740
+minus two هذه هذه ال coefficients تبعة اتنين بتاعة
+
+200
+00:15:03,740 --> 00:15:11,160
+ال a هي ال a primeباستخدام modulo 7 باستخدام
+
+201
+00:15:11,160 --> 00:15:15,060
+modulo 7 هي نفس المعادلة هي الواحد هذا هو اللي أنا
+
+202
+00:15:15,060 --> 00:15:18,900
+بديه لإن ال congruent له باخد ال term هذا عن ناحية
+
+203
+00:15:18,900 --> 00:15:22,300
+التانية بس ال term هذا بناخده عن ناحية التانية ال
+
+204
+00:15:22,300 --> 00:15:26,660
+coefficients تبعته هي ال inverse تبعت التلاتة هي
+
+205
+00:15:26,660 --> 00:15:30,900
+ال inverse على التلاتة كيف الكلام هذا خلينا نشوف
+
+206
+00:15:30,900 --> 00:15:36,430
+هل فعلا congruent oneالـ-2 هذه فعلا كتير one to
+
+207
+00:15:36,430 --> 00:15:42,550
+one ببساطة عشان تضربوا minus two في تلاتة صارت ال
+
+208
+00:15:42,550 --> 00:15:49,570
+a prime في ال a والمفروض تساوي واحد من seven مش
+
+209
+00:15:49,570 --> 00:15:52,530
+هذه العلاقة ال relation بتاعتنا طب خلينا نضربهم في
+
+210
+00:15:52,530 --> 00:15:58,610
+بعض كده اش بطلع minus 6 minus 6 معناته ان انا بمشي
+
+211
+00:15:58,610 --> 00:16:01,450
+ست خطوات anticlockwise
+
+212
+00:16:02,920 --> 00:16:07,200
+عكس اتجاه عقارب الساعة فاحنا ماشيين من هى واحد
+
+213
+00:16:07,200 --> 00:16:09,780
+اتنين تلاتة اربعة خمسة طيب لأ نمشيها بالعكس واحد
+
+214
+00:16:09,780 --> 00:16:17,280
+اتنين تلاتة اربعة خمسة ستة للواحد
+
+215
+00:16:17,280 --> 00:16:24,080
+فإذا فعلا تسوى واحد فعلا هتسوى واحد هذه المكملة
+
+216
+00:16:24,080 --> 00:16:30,410
+للواحدموديولو سبن هذه المكملة للواحد موديولو سبن
+
+217
+00:16:30,410 --> 00:16:36,130
+باعتبار أن واحد ناقص سبعة ناقص الموديولو ناقص
+
+218
+00:16:36,130 --> 00:16:40,270
+الموديولو
+
+219
+00:16:40,270 --> 00:16:43,790
+ناقص الموديولو ناقص
+
+220
+00:16:43,790 --> 00:16:45,370
+الموديولو ناقص الموديولو ناقص الموديولو ناقص
+
+221
+00:16:45,370 --> 00:16:47,690
+الموديولو ناقص الموديولو ناقص الموديولو ناقص
+
+222
+00:16:47,690 --> 00:16:47,690
+الموديولو ناقص الموديولو ناقص الموديولو ناقص
+
+223
+00:16:47,690 --> 00:16:47,690
+الموديولو ناقص الموديولو ناقص الموديولو ناقص
+
+224
+00:16:47,690 --> 00:16:47,690
+الموديولو ناقص الموديولو ناقص الموديولو ناقص
+
+225
+00:16:47,690 --> 00:16:48,610
+الموديولو ناقص الموديولو ناقص المو
+
+226
+00:16:52,550 --> 00:16:54,670
+ففي الحالة هذه ال .. ال .. ال .. ال .. ال .. ال ..
+
+227
+00:16:54,670 --> 00:16:55,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+228
+00:16:55,730 --> 00:16:56,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+229
+00:16:56,290 --> 00:16:56,670
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+230
+00:16:56,670 --> 00:17:02,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+231
+00:17:02,610 --> 00:17:03,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+232
+00:17:03,430 --> 00:17:04,090
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+233
+00:17:04,090 --> 00:17:04,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+234
+00:17:04,130 --> 00:17:05,130
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+235
+00:17:05,130 --> 00:17:05,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+236
+00:17:05,730 --> 00:17:07,250
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+237
+00:17:07,250 --> 00:17:07,250
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+238
+00:17:07,250 --> 00:17:12,070
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+239
+00:17:12,070 --> 00:17:20,690
+ال .. ال ..
+
+240
+00:17:20,950 --> 00:17:26,150
+رقم congruent لها بس احنا نتكلم unique باعتبار ان
+
+241
+00:17:26,150 --> 00:17:31,290
+هو داخل ال cycle داخل او اقل من سبعة هي ال minus
+
+242
+00:17:31,290 --> 00:17:39,190
+two او الخمسة او الخمسة صحيح؟ تعالوا نشوف لماذا
+
+243
+00:17:39,190 --> 00:17:45,370
+خمسة لأنها المكملة لل minus twoكيف المكملة؟ مكملة
+
+244
+00:17:45,370 --> 00:17:49,690
+انا بشتغل under modulo M M هدق سبعة ف minus two
+
+245
+00:17:49,690 --> 00:17:55,110
+ايش اللي بكملها السبعة؟ فيها انها خمسة ان امشي
+
+246
+00:17:55,110 --> 00:17:57,170
+خطوطين عكس عقارب الساعة
+
+247
+00:18:03,320 --> 00:18:07,820
+ممكن تكون minus 5 minus 2 أو 5 وكل رقم congruent
+
+248
+00:18:07,820 --> 00:18:13,360
+لهم كيف بجيب ال congruence تبعتهم minus 2 minus 7
+
+249
+00:18:13,360 --> 00:18:20,060
+minus 7 minus 7 minus 7 بتصير minus 19 كمان minus
+
+250
+00:18:20,060 --> 00:18:25,760
+7 بتصير minus 16 طيب هنا plus 7 plus 7 اذا كانت
+
+251
+00:18:25,760 --> 00:18:32,440
+جمع plus 7 او طريقة هلى minus 7 بتعطينا minus 2هذه
+
+252
+00:18:32,440 --> 00:18:38,300
+زائد سبعة تعطينا خمسة زائد سبعة اتناش زائد سبعة
+
+253
+00:18:38,300 --> 00:18:44,300
+تسعة عشر فمعنى ذلك ممكن تكون ال inverse للتلاتة
+
+254
+00:18:44,300 --> 00:18:50,620
+minus two أو خمسة أو minus تسعة او اتناش او تسعة
+
+255
+00:18:50,620 --> 00:18:56,540
+عشر او minus ستة عشر اي رقم بمشي اي رقم بمشي خليني
+
+256
+00:18:56,540 --> 00:19:00,470
+انا اخد مثلًا الخمسة خمسة في تلاتةمحتاج أن نتأكد
+
+257
+00:19:00,470 --> 00:19:04,730
+هل فعلا ال A' هذه اللي هي خمسة في ال A اللي هي
+
+258
+00:19:04,730 --> 00:19:11,730
+تلاتة مد سبعة هيساوي فعلا واحد ولا لأ هدفي هدي
+
+259
+00:19:11,730 --> 00:19:20,730
+خمستاشر مد سبعة واحد لو جربتوا أي رقم من الأرقام
+
+260
+00:19:20,730 --> 00:19:24,790
+هذه اللي هي كم كلها congruent كل واحدة congruent
+
+261
+00:19:24,790 --> 00:19:28,770
+لالنتج اللي احنا طلعناه هو ال minus fourأي واحدة
+
+262
+00:19:28,770 --> 00:19:35,190
+منهم اضربوها فيه تلاتة موت سبعة هيطلع واحد تمام
+
+263
+00:19:35,190 --> 00:19:39,770
+هي هذه الفكرة طبعا لاحظوا ان احنا هنا استشفناها
+
+264
+00:19:39,770 --> 00:19:44,110
+مجرد script لأن الأرقام بسيطة سبعة جداش هتتكرر
+
+265
+00:19:44,110 --> 00:19:47,930
+تلاتة منها يطلع رقم اتنين كويسة مش دايما بتكون
+
+266
+00:19:47,930 --> 00:19:51,790
+الأرقام سهلة بهذا الشكلفممكن تكون أرقام كبيرة
+
+267
+00:19:51,790 --> 00:19:55,790
+الأرقام الكبيرة في لها قلية تانية الأرقام الكبيرة
+
+268
+00:19:55,790 --> 00:19:59,650
+بدنا نتأكد أول أن هي greatest common divisor equal
+
+269
+00:19:59,650 --> 00:20:02,910
+to one ولا لأ هل هم فعلا equal to one greatest
+
+270
+00:20:02,910 --> 00:20:06,930
+common divisor بينهم ولا لأ فلو قلنا بدنا ال
+
+271
+00:20:06,930 --> 00:20:14,430
+universe ل 101 مديوله 4620 أول شي بدنا نتأكد هو هم
+
+272
+00:20:14,430 --> 00:20:18,670
+الاتنين هدولةgreatest common divisor equal to one
+
+273
+00:20:18,670 --> 00:20:22,030
+طب انا إيش بدي في ال one هذا تحديدا ال one هذا هو
+
+274
+00:20:22,030 --> 00:20:26,230
+ال congruent اللي أنا بشتغل عليه إذا فعلا ال
+
+275
+00:20:26,230 --> 00:20:35,570
+greatest common divisor ل 101 و 4620 فعلا واحد
+
+276
+00:20:35,570 --> 00:20:39,930
+الواحد هذا هو نفسه اللي أنا بشتغل عليه على اعتبار
+
+277
+00:20:39,930 --> 00:20:43,350
+انه a في a equivalent to one
+
+278
+00:20:47,520 --> 00:20:49,800
+هو هذا اللي احنا بدنا ندور عليه إذا فعلا ال grade
+
+279
+00:20:49,800 --> 00:20:52,720
+of common divisor equal to one بضمن ان الاتنين
+
+280
+00:20:52,720 --> 00:20:59,540
+هدول ال congruent تبعهم واحد بقدر أجيب inverse او
+
+281
+00:20:59,540 --> 00:21:04,340
+ال inverse في الحالة هذه للمية واحد موجود او ممكن
+
+282
+00:21:04,340 --> 00:21:10,120
+في module 4620 عشانك هنعمل grade of common divisor
+
+283
+00:21:10,120 --> 00:21:14,200
+اللي اتعودنا عليها باستخدام طريقة مين هذه؟
+
+284
+00:21:16,790 --> 00:21:24,790
+Euclid's algorithm في لحظة هاي 4620 هنا مضروبة
+
+285
+00:21:24,790 --> 00:21:29,530
+مكرر الألف والمية وواحد خمسة واربعين مرة ال
+
+286
+00:21:29,530 --> 00:21:35,590
+remainder سبعة السبعة هذه لسه ما خلصناش احنا ما
+
+287
+00:21:35,590 --> 00:21:40,590
+خلصناش هذه ناتج في بعض الموديولو هذه اقل من B يعني
+
+288
+00:21:40,590 --> 00:21:43,790
+جاهز بعيد لكل ال algorithm نفسه اقل من B معناه ذلك
+
+289
+00:21:43,790 --> 00:21:52,220
+انه صارت Bكأنها B mod الناتج ال remainder R صحيح؟
+
+290
+00:21:52,220 --> 00:22:01,780
+كويس هاي B وهاي R طيب هذه برضه هتطلع ناتج R جديد
+
+291
+00:22:01,780 --> 00:22:09,320
+وصرت B جديدة ال B جديدة 75 ف75 مع ال R الجديدة ال
+
+292
+00:22:09,320 --> 00:22:11,240
+B الجديدة مع ال R الجديدة ال B الجديدة مع ال R
+
+293
+00:22:11,240 --> 00:22:15,950
+الجديدة لما نصل مين لصفرلما كنا بنصل ل صفر الرقم
+
+294
+00:22:15,950 --> 00:22:19,830
+بيسوء صفر باخد ال a هو ال greatest common divisor
+
+295
+00:22:19,830 --> 00:22:24,310
+هنا مش هيظهر عندكوا صفر لأنه مافيش اي عامل مشترك
+
+296
+00:22:24,310 --> 00:22:29,390
+بينهم الاتنين ال greatest common divisor تبعهم
+
+297
+00:22:29,390 --> 00:22:39,140
+واحد relatively prime فلاحظوا خلصت بواحد مش صفرمش
+
+298
+00:22:39,140 --> 00:22:42,220
+في صفر خلصت عندكوا هنا بواحد هي اخر واحد هنا
+
+299
+00:22:42,220 --> 00:22:46,840
+اتاكدنا منه جربنا هي هي خلاص بيظل واحد الواحد بيظل
+
+300
+00:22:46,840 --> 00:22:51,220
+زي ما هو الواحد فخلاص اخر مرحلة كانت هي هذه وكان
+
+301
+00:22:51,220 --> 00:22:54,680
+عندنا الميدر اخر واحد واحد فمعنى ذلك ان هدول فعلا
+
+302
+00:22:54,680 --> 00:22:57,700
+relative to the prime وهدا معناه انه لمية واحد
+
+303
+00:22:57,700 --> 00:23:04,840
+يوجد inverse وحيد under modulo 4620 طب ايش هو جدش
+
+304
+00:23:04,840 --> 00:23:11,680
+قيمته هذا ال inverse الوحيد؟ بدنا قيمتهال turn هذا
+
+305
+00:23:11,680 --> 00:23:15,240
+اللى كان يمثلنا ل greatest common divisor هو هذا
+
+306
+00:23:15,240 --> 00:23:23,980
+اللى انا بدي أنسبله طبعا
+
+307
+00:23:23,980 --> 00:23:28,630
+واحد في M بهذا الشكل المفروض انه يسوىمفروض ان هو
+
+308
+00:23:28,630 --> 00:23:31,130
+يساوي واحد زي الحالة بتاع التولة عملناها في minus
+
+309
+00:23:31,130 --> 00:23:36,810
+اتنين تلاتة زائد واحد في سبعة زائد واحد طبعا مش
+
+310
+00:23:36,810 --> 00:23:41,270
+مضروري واحد ممكن في النهاية تكون اي equivalent لل
+
+311
+00:23:41,270 --> 00:23:47,930
+M ف some K هنا صدفت انه واحد لان الأرقام كتير كانت
+
+312
+00:23:47,930 --> 00:23:51,270
+صغيرة و جريبة من بعض فهذا يساوي واحد فبدنا نبدأ من
+
+313
+00:23:51,270 --> 00:23:55,930
+الواحد هذا الواحد هذا أيه موجود عندكم؟ بدنا الواحد
+
+314
+00:23:55,930 --> 00:24:07,100
+يساويsome k أو some integer في 101 زائد
+
+315
+00:24:07,100 --> 00:24:16,720
+some integer في 4620 صحيح؟ إذا وصلنا لل form هذا
+
+316
+00:24:16,720 --> 00:24:21,420
+بقول إن هدولة ال بيزوت coefficients 101 إيش ال
+
+317
+00:24:21,420 --> 00:24:24,700
+coefficient اللي معها؟ هو هذا ال inverse تبعها هو
+
+318
+00:24:24,700 --> 00:24:27,880
+هذا ال إيش؟ ال inverse تبعهاعشان نعمل الكلام هذا
+
+319
+00:24:27,880 --> 00:24:30,980
+هننطلق من نفس ال sequence اللي احنا مشيناه الواحد
+
+320
+00:24:30,980 --> 00:24:34,620
+هذا اللي بدنا نمسكها لأن هذا اللي انا بدي أساوي
+
+321
+00:24:34,620 --> 00:24:38,460
+فيه كل ال terms اللي بعتنا و هنلاحظ الواحد ايش
+
+322
+00:24:38,460 --> 00:24:44,440
+يساوي تلاتة ناقص واحد في اتنين تلاتة ناقص واحد في
+
+323
+00:24:44,440 --> 00:24:50,030
+اتنين طيب كويس الاتنينهذه كانت الـ remainder
+
+324
+00:24:50,030 --> 00:24:54,570
+للمرحلة السابقة فبقدر أخدها بدلالة الأتنين السابقة
+
+325
+00:24:54,570 --> 00:24:58,490
+فبتصير الأتنين عبارة عن تلاتة و عشرين ناقص سبعة و
+
+326
+00:24:58,490 --> 00:25:04,410
+تلاتة طيب تلاتة هي ستة و عشرين ناقص تلاتة تلاتة و
+
+327
+00:25:04,410 --> 00:25:09,950
+عشرين نزلنا نزول هلوجد عشان نجيب greatest common
+
+328
+00:25:09,950 --> 00:25:13,130
+divisor عشان نجيب ال inverse بنطلع طلوع بالعكس
+
+329
+00:25:14,040 --> 00:25:17,360
+فكثير كويس وانت بتحلوا مسائل زي هذه تحطوا الاتنين
+
+330
+00:25:17,360 --> 00:25:20,280
+جان بعض عشان تاخدوا معلومتكم من بعض تاخدوا
+
+331
+00:25:20,280 --> 00:25:23,480
+المعلومات من بعض هاي أخدناها الأولى طيب اتنين قلنا
+
+332
+00:25:23,480 --> 00:25:26,500
+زي ما .. زي ما اتكلمنا هنا عبارة عن تلاتة و عشرين
+
+333
+00:25:26,500 --> 00:25:29,680
+ناقص سبعة في تلاتة تلاتة و عشرين ناقص سبعة في
+
+334
+00:25:29,680 --> 00:25:34,740
+تلاتة دائما هتلاقوا التلاتة اللي كانت هنا الميندر
+
+335
+00:25:34,740 --> 00:25:39,240
+صارت هنا B و نفس الكلام التلاتة و عشرين هنا كانت
+
+336
+00:25:39,240 --> 00:25:44,370
+تتكرر هنا لأن كل B باخدها من ال R اللي جابلهامش
+
+337
+00:25:44,370 --> 00:25:46,950
+شكالة ال algorithm بيعطيني طب ما هو نفس الكلام
+
+338
+00:25:46,950 --> 00:25:50,030
+هستفيد من الموضوع هذا انه دايما هيكون في عندكم
+
+339
+00:25:50,030 --> 00:25:55,430
+common هنا في سبع تلتات هنا في تلتة واحدة مجموعة
+
+340
+00:25:55,430 --> 00:26:00,130
+اللي بصير في عندك تمان تلتات تمان تلتات التلتة هذه
+
+341
+00:26:00,130 --> 00:26:06,010
+بتعرضوا قيمتها من ال schedule اللي جامكم من ال
+
+342
+00:26:06,010 --> 00:26:10,050
+schema اللي جامكم كويسة لاحظوا هنا تلتة و عشرين و
+
+343
+00:26:10,050 --> 00:26:13,830
+في تلتة و عشرينو منطق جدا أصلا دايما يطلع فيه
+
+344
+00:26:13,830 --> 00:26:17,770
+أرقام متشابهة لأن هنا كانت ال B هنا كانت ال R و ال
+
+345
+00:26:17,770 --> 00:26:22,390
+R هي نفسها ال B في المرحلة اللي بعدها احنا بناخدهم
+
+346
+00:26:22,390 --> 00:26:26,770
+من بعض أساسا تمام فلاحظوا هنا minus one و هنا
+
+347
+00:26:26,770 --> 00:26:33,670
+minus تمانية minus تسعة minus تسعة ال 23 عوضناها ب
+
+348
+00:26:33,670 --> 00:26:39,770
+75 ناقص 2 في 26 في 26 هنا في 26بقى مع التجميع
+
+349
+00:26:39,770 --> 00:26:43,730
+هيطلع لكوا 26 باعتبار ان ال 26 موجودة هنا ب تمانية
+
+350
+00:26:43,730 --> 00:26:51,190
+تمانية و هنا 18 ف26 ب 26 26 برضه من هنا تقدر
+
+351
+00:26:51,190 --> 00:26:57,110
+تاخدوها على أساس ان هي 101 ناقص 75 بدا يظهر عند
+
+352
+00:26:57,110 --> 00:27:02,490
+أول tear بديها في المعادلةالمية واحد هي اول term
+
+353
+00:27:02,490 --> 00:27:07,190
+ظهر بدنا ال term التاني ال 4620 عشان اربطهم
+
+354
+00:27:07,190 --> 00:27:09,850
+الاتنين في معدلة واحدة و لازم equal to one و انا
+
+355
+00:27:09,850 --> 00:27:14,290
+ضمن انه كله equal to one
+
+356
+00:27:15,830 --> 00:27:26,530
+وصلنا لـ 75 برضه إيجد 4620 رتبنا المعادلة فالواحد
+
+357
+00:27:26,530 --> 00:27:29,530
+طلع بالساوي ماينوس خمسة و تلاتين في اش في الاربع
+
+358
+00:27:29,530 --> 00:27:35,170
+تلاف ستمية و عشرين plus مية الف و ستمية و واحد في
+
+359
+00:27:35,170 --> 00:27:41,530
+مية و واحد فإذا ال inverse تبعنا الف ستمية و واحد
+
+360
+00:27:42,890 --> 00:27:50,490
+إذا كانت ال A تساوي 101، then ال A' تساوي 1601
+
+361
+00:27:50,490 --> 00:27:58,970
+طبعا هذا كله مود 4620
+
+362
+00:28:00,850 --> 00:28:06,550
+تمام؟ فهي طريقة الشغل في الحالة بتاعتنا لاحظوا ان
+
+363
+00:28:06,550 --> 00:28:09,990
+انتوا بتكونوا تعملوا grades of common divisors حتى
+
+364
+00:28:09,990 --> 00:28:13,830
+لو انتوا عارفين ان هي primes بس بتسهل عليكوا في ال
+
+365
+00:28:13,830 --> 00:28:17,050
+analysis هذا بتسهل عليكوا لان كل واحدة بتكونوا
+
+366
+00:28:17,050 --> 00:28:19,110
+عارفين ايش ال remainder اللي كان موجود وقداش
+
+367
+00:28:19,110 --> 00:28:25,600
+بتقدروه a minus some k في bA مضروبة في sum K في B
+
+368
+00:28:25,600 --> 00:28:29,860
+تمام؟ تقدر تشتغله عليه بهذا الشكل اقدرنا هنا نجيب
+
+369
+00:28:29,860 --> 00:28:34,560
+greatest common divisor ومنها اقدرنا نجيب ال
+
+370
+00:28:34,560 --> 00:28:43,620
+inverse جينا إيجاكوا سؤال بهذا الشكل حلولنا
+
+371
+00:28:43,620 --> 00:28:50,980
+قيمة Xعندما تلاتة X congruent to 4 معدلة Linear هي
+
+372
+00:28:50,980 --> 00:28:53,520
+المعادلة Linear و بتجيبوا قيم ال variables اللي
+
+373
+00:28:53,520 --> 00:28:57,400
+فيها قيم ال variables احنا سابقا اتكلمنا عن
+
+374
+00:28:57,400 --> 00:29:01,140
+الموضوع هذا باستخدام ال matrices لو متذكرين ال
+
+375
+00:29:01,140 --> 00:29:05,800
+matrices قولنا انه A في X بساوي B فكنتوا بتقولوا
+
+376
+00:29:05,800 --> 00:29:09,020
+ال vector الأول transpose طبعا ال vector الأول
+
+377
+00:29:09,020 --> 00:29:12,880
+اللي اعمله transpose في ال X طبعا ال A هذه كانت
+
+378
+00:29:12,880 --> 00:29:13,260
+Matrix
+
+379
+00:29:16,960 --> 00:29:19,800
+حسب جداش عدد المعادلات اللي موجودة عندكم وجداش عدد
+
+380
+00:29:19,800 --> 00:29:26,920
+ال variables بساوي B كيف كنتوا تحلوها؟
+
+381
+00:29:26,920 --> 00:29:32,360
+A inverse تضربوه في الأولى و تضربوه في التانية،
+
+382
+00:29:32,360 --> 00:29:39,860
+صحيح؟ طيب ضربناه في الأولى و ضربناه في التانية طيب
+
+383
+00:29:39,860 --> 00:29:42,560
+هاي ال two inverses في بعض هدولة ال two inverses
+
+384
+00:29:42,560 --> 00:29:47,220
+في بعض واحد فبطلعنا قيمة Xعلى أساس إن هي ال A
+
+385
+00:29:47,220 --> 00:29:51,580
+inverse في B فما هو نفس الكلام اللي بيحكيه فإذا
+
+386
+00:29:51,580 --> 00:29:54,580
+أنا مضطر أجيب ال inverse بتاعة ال matrix هنا و هنا
+
+387
+00:29:54,580 --> 00:29:57,360
+نفس الكلام عشان أحل المعادلة مضطر أجيب ال inverse
+
+388
+00:29:57,360 --> 00:30:02,260
+تبع ال A فمحتاج ال inverse prime عشان أجيب ال
+
+389
+00:30:02,260 --> 00:30:06,020
+inverse تبعها ال inverse تبعها بضمن لإن ال X دلت
+
+390
+00:30:06,020 --> 00:30:11,210
+term لحالهافمنطقيا هتساوي ال inverse ل التلاتة ..
+
+391
+00:30:11,210 --> 00:30:14,550
+inverse ل التلاتة هنا في أربعة .. inverse ل
+
+392
+00:30:14,550 --> 00:30:16,710
+التلاتة في أربعة هنشوف هل فعلا حد طبعا الكلام ..
+
+393
+00:30:16,710 --> 00:30:24,750
+الكلام في غير شكل ولا لأ طيب مسبقا احنا عرفنا ان
+
+394
+00:30:24,750 --> 00:30:29,530
+ال inverse ل التلاتة module of seven يبقى لو
+
+395
+00:30:29,530 --> 00:30:33,070
+moduleه تاني بختلف ديروا بالكم لو moduleه تاني ال
+
+396
+00:30:33,070 --> 00:30:36,500
+inverse ل التلاتة هتختلفهذا إذا .. إذا فرضنا إنه
+
+397
+00:30:36,500 --> 00:30:41,040
+يوجد unique inverse إليها under modulo 3 .. under
+
+398
+00:30:41,040 --> 00:30:45,640
+modulo 7 طيب، قلنا إن هي فيه سالف 2، معناه ذلك إنه
+
+399
+00:30:45,640 --> 00:30:51,080
+بدروا الطرفين في سالف 2 الطرفين اللي ضربناهم في
+
+400
+00:30:51,080 --> 00:30:56,660
+سالف 2، هنا حصير فيه سالف 6 طيب، سالف 6 إحنا
+
+401
+00:30:56,660 --> 00:31:00,000
+عارفين مسبقا إنه سالف 6، هاي اللي حلناها جابت هاي
+
+402
+00:31:00,000 --> 00:31:01,260
+equivalent to 1
+
+403
+00:31:05,210 --> 00:31:08,110
+السالف ستة كانت equivalent to one فهنا كانت ال one
+
+404
+00:31:08,110 --> 00:31:12,370
+two three سالف ستة هاي واحد اتنين تلاتة اربع خمسة
+
+405
+00:31:12,370 --> 00:31:17,690
+ستة هاي سالف ستة equivalent لمين للواحد فهذه كأنها
+
+406
+00:31:17,690 --> 00:31:23,550
+واحد طبعا الكلام ده كله modulo seven modulo seven
+
+407
+00:31:23,550 --> 00:31:26,790
+لازم نحدد ان احنا نتكلم عن modulo seven طيب هنا
+
+408
+00:31:26,790 --> 00:31:31,870
+minus تمانين هذا صحيحمينوس تمانية فإذا المينوس
+
+409
+00:31:31,870 --> 00:31:36,090
+تمانية هذه برضه مكافئة لمين كأنك تتنشوا بالسالب
+
+410
+00:31:36,090 --> 00:31:40,970
+واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية
+
+411
+00:31:40,970 --> 00:31:46,770
+covenant لمن للستة فإذا سالب تمانية covenant للستة
+
+412
+00:31:46,770 --> 00:31:52,590
+covenant للستة فإذا x تساوي ممكن تقوله مينوس
+
+413
+00:31:52,590 --> 00:31:57,770
+تمانية بمش الحال أو ممكن تقوله ستةبالنسبة لكلمة ده
+
+414
+00:31:57,770 --> 00:32:03,410
+كله موديولو سبع طيب اتجربوا ممكن اتجربوا اتجربوا
+
+415
+00:32:03,410 --> 00:32:07,690
+اتجربوا اضربوا تلاتة في اكس شوفوا هل فعلا يكون في
+
+416
+00:32:07,690 --> 00:32:12,330
+الاربعة ولا لا هاي تلاتة في اكس وخلينا نقول انه
+
+417
+00:32:12,330 --> 00:32:16,310
+بدنا نستخدم الستة تمانتعش موديولو سبع اترحوا
+
+418
+00:32:16,310 --> 00:32:19,750
+اربعتاش على اعتبار ان اربعتاش اترحوا اربعتاش اتنين
+
+419
+00:32:19,750 --> 00:32:25,360
+في سبعة بيضل اربعةطبعا الكلام ده سواء استخدمته
+
+420
+00:32:25,360 --> 00:32:31,480
+minus 8 او 6 او المضاعفاتها ال congruences تبعتها
+
+421
+00:32:31,480 --> 00:32:36,720
+ال congruences بتاعتها هتكون 13 مثلا اشمعوا 7 13
+
+422
+00:32:36,720 --> 00:32:41,900
+ممكن تكون 20 ممكن يكون هنا بالثالث مع 7 minus 15
+
+423
+00:32:41,900 --> 00:32:47,190
+minus 1فلاحظوا ان كلهم اي واحدة منهم استخدموها
+
+424
+00:32:47,190 --> 00:32:51,450
+هتطلع معاكم .. اي واحدة منهم استخدموها هتطلع معاكم
+
+425
+00:32:51,450 --> 00:32:55,590
+لو ضرقتوها في .. في التلاتة لازم ال .. ال .. ال ..
+
+426
+00:32:55,590 --> 00:32:55,990
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+427
+00:32:55,990 --> 00:32:56,830
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+428
+00:32:56,830 --> 00:32:57,050
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+429
+00:32:57,050 --> 00:32:58,570
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+430
+00:32:58,570 --> 00:33:00,830
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+431
+00:33:00,830 --> 00:33:02,970
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+432
+00:33:02,970 --> 00:33:02,970
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+433
+00:33:02,970 --> 00:33:02,970
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+434
+00:33:02,970 --> 00:33:08,470
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+435
+00:33:11,010 --> 00:33:14,510
+unique inverse داخل ال cycle الواحدة باعتبار أنه
+
+436
+00:33:14,510 --> 00:33:20,930
+داخل one cycle له unique واحدة فإذا هنا في الحالة
+
+437
+00:33:20,930 --> 00:33:24,730
+اللي كنا نتكلم عنها في الحالة اللي عندنا داخل ال
+
+438
+00:33:24,730 --> 00:33:31,290
+cycle الواحدة clockwise فقط ال 6 مضاعفاتها هتكون
+
+439
+00:33:31,290 --> 00:33:34,490
+أكبر من ال cycle هتكون أكبر من ال cycle زي لما
+
+440
+00:33:34,490 --> 00:33:39,200
+كنتوامتذكرين كنتوا بتحكوا عن الزوايا لما تقولوا
+
+441
+00:33:39,200 --> 00:33:45,780
+سالب تلاتين درجة اللي هي قداش تلاتمية و تلاتين لأن
+
+442
+00:33:45,780 --> 00:33:50,180
+سالب تلاتين تمشي بالعكس كنتوا تمشي بالعكس تلاتين
+
+443
+00:33:50,180 --> 00:33:58,280
+درجة فهذه كأنها تلاتمية و تلاتين درجة تلاتمية و
+
+444
+00:33:58,280 --> 00:34:04,570
+تلاتين درجة طيب ممكن جدا تقولوا لأالزاوية 330 ممكن
+
+445
+00:34:04,570 --> 00:34:11,210
+تسمعها 360 ونقول و الله 690 690
+
+446
+00:34:11,210 --> 00:34:16,250
+ما هي equivalent لمين ل 330 ل 330 ولكن بقدرش اعتمد
+
+447
+00:34:16,250 --> 00:34:20,630
+على 300 على 690 واسيبها بهذا الشكل لازم اوحدها
+
+448
+00:34:20,630 --> 00:34:26,670
+دايما لمين ارجحها لقيمة مكافئة لها داخل ال cycle
+
+449
+00:34:26,670 --> 00:34:30,010
+الواحدة داخل ال one cycle فاحنا هنا بنقول انه لها
+
+450
+00:34:30,010 --> 00:34:33,800
+interest داخل ال cycleotherwise ما احنا عارفين ان
+
+451
+00:34:33,800 --> 00:34:38,340
+انتوا عاملين زي الساعة لازم كل لفة بتلف لأنها عدد
+
+452
+00:34:38,340 --> 00:34:41,080
+لانهية من اللفات بتقدر تقولوا الساعة هتلف جديش
+
+453
+00:34:41,080 --> 00:34:44,840
+عشان تحسب الزمن هتلف باستمرار هدي periodic
+
+454
+00:34:44,840 --> 00:34:48,360
+periodic معناته اتوحى انها هتتكرر انا بتكلم عن ال
+
+455
+00:34:48,360 --> 00:34:51,940
+inverse داخل الدورة الواحدة اللفة الواحدة اللفة
+
+456
+00:34:51,940 --> 00:34:56,440
+الواحدة الها الستة فقط طبعا كل شيء يمثل ستة او
+
+457
+00:34:56,440 --> 00:35:01,580
+بقدر قربه لستة congruent to six برضه يمشي الحقبس
+
+458
+00:35:01,580 --> 00:35:03,980
+بقدرش أقول إن هذا هو الرقم ال standard تبعها
+
+459
+00:35:03,980 --> 00:35:12,600
+الزاوية 690 طبيعي لازم أجربها أطرح منها 360 نطرح
+
+460
+00:35:12,600 --> 00:35:16,780
+منها 360 وهنا نفس الكلام أي قيمة تجيكوا minus 15
+
+461
+00:35:16,780 --> 00:35:22,850
+طبيعي أنك تطرح منها 7 الأولبتشيلوا منها سبعة شيلنا
+
+462
+00:35:22,850 --> 00:35:26,810
+منها سبعة فكأني جمعت عليها سبعة فبتصير minus
+
+463
+00:35:26,810 --> 00:35:31,330
+تمانية طيب minus تمانية لسه أكبر من minus سبعة
+
+464
+00:35:31,330 --> 00:35:35,530
+تمان مرة minus واحد فإذا anti-clockwise لو بدنا
+
+465
+00:35:35,530 --> 00:35:39,770
+نشتر anti-clockwise اللي هي مكافئة هي لتلاتين على
+
+466
+00:35:39,770 --> 00:35:46,270
+اعتبار ما كنتوا يقولوا ناقص تلاتمية وتسعين فإذا
+
+467
+00:35:46,270 --> 00:35:49,150
+clockwise إلها inverse واحد anti-clockwise إلها
+
+468
+00:35:49,150 --> 00:35:54,060
+inverse واحدفال two inverses تبقوا هنا minus 6 او
+
+469
+00:35:54,060 --> 00:35:59,160
+minus 1 يعني عفوا ال 6 او 1 و ال 6 او 1 في
+
+470
+00:35:59,160 --> 00:36:02,140
+الحالتين اللي هي بتبقوا تمشوا من هنا 6 درجات
+
+471
+00:36:02,140 --> 00:36:06,980
+فبتصلوا لهاد النقطة او بالثاني درجة فبرضه هتصلوا
+
+472
+00:36:06,980 --> 00:36:11,500
+لنفس النقطة هي هي النقطة واحدة يعني نقطة واحدة
+
+473
+00:36:11,500 --> 00:36:17,650
+داخل ال cycle نقطة واحدة داخل ال cycleواضح ان هنا
+
+474
+00:36:17,650 --> 00:36:21,250
+مافيش مشكلة عندنا مش أشكال طبعا لاحظوا إذا الأرقام
+
+475
+00:36:21,250 --> 00:36:28,130
+الكبيرة هنا زي مثلا المثلة تعتودي هي 101 و ال
+
+476
+00:36:28,130 --> 00:36:32,370
+module أو ال module تبعنا كان 4620 في الحالة هذه
+
+477
+00:36:32,370 --> 00:36:37,240
+تتحللوا من الأول تعملوا greatest common divisorو
+
+478
+00:36:37,240 --> 00:36:41,620
+بعدين تجيبوا ال .. ال .. ال .. ال بيزوت ال
+
+479
+00:36:41,620 --> 00:36:44,420
+coefficients تبعتكم عشان تحسبوا ال inverse و بعدين
+
+480
+00:36:44,420 --> 00:36:47,740
+ال inverse تجربوه .. تضربوه هنا عشان تجيبوا قداش
+
+481
+00:36:47,740 --> 00:36:52,620
+القيم .. قيمة x قداش قيمة x الممكنة .. قداش قيمة x
+
+482
+00:36:52,620 --> 00:36:58,560
+الممكنة okay pseudo primes مدام كنا .. اتكلمنا عن
+
+483
+00:36:58,560 --> 00:37:01,580
+ال random طب مافيه ال primes كمان فيه جزئية ال
+
+484
+00:37:01,580 --> 00:37:05,900
+primeالـ prime مش بالضروري دايما يكون هو فعلا الـ
+
+485
+00:37:05,900 --> 00:37:08,340
+prime, pure prime مين اللي وضّح إنه جزئي هذا؟ مين
+
+486
+00:37:08,340 --> 00:37:11,060
+اللي خلّى الناس يفكروا في هذا الموضوع هذا؟ مجموعة
+
+487
+00:37:11,060 --> 00:37:14,520
+علماء صينيين قدماء جدا، يعني من قدماء الصينيين
+
+488
+00:37:14,520 --> 00:37:20,560
+طلعوا نظرية إنه إذا whenever n is prime، إذا كان n
+
+489
+00:37:20,560 --> 00:37:24,360
+is prime، فإذا two to the power n minus one
+
+490
+00:37:24,360 --> 00:37:29,950
+congruent to one mod nهذا الكلام إذا كانت prime
+
+491
+00:37:29,950 --> 00:37:36,490
+ذهبوا في اعتقادهم لإثبات العكس إيش هو؟ إنه إذا two
+
+492
+00:37:36,490 --> 00:37:39,550
+to the power of N minus one congruent to one mod N
+
+493
+00:37:39,550 --> 00:37:44,790
+فإذا ال N هذي is prime للأسف
+
+494
+00:37:44,790 --> 00:37:49,850
+إدعاء العكس ماكنت صحيح 100% بعدهم كذا وقت، كذا
+
+495
+00:37:49,850 --> 00:37:57,640
+سنة، كذا عقد من السنوات، كذا قرن من القرونطلعوا ان
+
+496
+00:37:57,640 --> 00:38:00,980
+لأ و الله تصبتش دايما هدى اتنين to the power n
+
+497
+00:38:00,980 --> 00:38:05,800
+minus one equal to one mod n مش بالضرورى يتبحى انه
+
+498
+00:38:05,800 --> 00:38:11,240
+n is prime كيف؟ لحظوا المعادلة هدى؟ هى رقم تلاتمية
+
+499
+00:38:11,240 --> 00:38:14,980
+واحد واربعين هدى عبارة عن احداشه واحدة معناته مش
+
+500
+00:38:14,980 --> 00:38:20,160
+prime صحيح؟ مش prime ومع ذلك اتنين to the power n
+
+501
+00:38:20,160 --> 00:38:24,340
+minus one تساوي او congruent to one mod تلاتمية
+
+502
+00:38:24,340 --> 00:38:29,530
+واحد واربعينطيب، كويس، هل معنى ذلك أن كلامه كان
+
+503
+00:38:29,530 --> 00:38:33,670
+بالمجمل خطأ؟ لأ، استنوا لحظة، هم فتحوا علينا الوجد
+
+504
+00:38:33,670 --> 00:38:38,670
+على حاجة تانية إن هذا okay مش prime بس بقدر أسميه
+
+505
+00:38:38,670 --> 00:38:41,710
+pseudo prime ليش pseudo prime؟ لأن هو لا يقبل
+
+506
+00:38:41,710 --> 00:38:50,090
+القسمة إلا على two primes 11 و 31 فإذا الكلام هذا
+
+507
+00:38:50,090 --> 00:38:56,600
+صحيح بس كان بده إضافة صغيرة بدل ما أقول thenM is
+
+508
+00:38:56,600 --> 00:39:03,480
+prime كان ممكن اقول M at least Sodoprime ممكن تكون
+
+509
+00:39:03,480 --> 00:39:06,580
+prime و ممكن تكون Sodoprime ايش تعريف ال Sodoprime
+
+510
+00:39:06,580 --> 00:39:12,340
+شبيه بالprime مع اختلاف واحد انه ممكن يقسم على
+
+511
+00:39:12,340 --> 00:39:16,880
+اعدادين لاتنين primes فهنا هذا فعلا بقسمش الا على
+
+512
+00:39:16,880 --> 00:39:19,300
+الرقامين هدول فقط الرقامين هدول اللي شجعنا نطلع
+
+513
+00:39:19,300 --> 00:39:23,750
+عليهم هي اتنين primesالـ two primes هذا له خصوصية
+
+514
+00:39:23,750 --> 00:39:30,610
+هذا بنسميه Sodoprime الـ 341 نسميه Sodoprime ممكن
+
+515
+00:39:30,610 --> 00:39:34,410
+استخدامه لإن أنا كنت بدور بدّي Primes و ال Prim
+
+516
+00:39:34,410 --> 00:39:37,170
+هذا ليش احنا بندور عليه ال Prim بندور عليه لإن هذا
+
+517
+00:39:37,170 --> 00:39:40,690
+بفيدنا في ال security اللحقة لما نجي نتكلم عن ال
+
+518
+00:39:40,690 --> 00:39:45,200
+cryptographicأو ال cryptography theory اللي هنتكلم
+
+519
+00:39:45,200 --> 00:39:49,340
+عنها بلزمنا أنه نكون لما نعمل generation حتى زي
+
+520
+00:39:49,340 --> 00:39:52,340
+توي و أن أنا بدور على أرقام تكون برايم تكون أفضل
+
+521
+00:39:52,340 --> 00:39:56,400
+لما بدي برايم أدور على برايم و رقمه كبير تكون رقم
+
+522
+00:39:56,400 --> 00:40:01,100
+عالي كبير هذه okay مانفعتش بس هي هتكون هتطلعلي two
+
+523
+00:40:01,100 --> 00:40:06,950
+primes بدل الواحد إذا كانت تحقق الشرط هذافمعنى ذلك
+
+524
+00:40:06,950 --> 00:40:12,550
+أن هذه إما هي نفسها prime أو هي pseudo prime هتطلع
+
+525
+00:40:12,550 --> 00:40:17,310
+two primes، هتطلع two primes، مش ال prime واحد،
+
+526
+00:40:17,310 --> 00:40:22,210
+كويسة، فإذا النظرية هيك اتعدلت شئ خفيف بدل ما كنا
+
+527
+00:40:22,210 --> 00:40:27,910
+نقول ال prime، بنقول إيش؟بنقول Sodoprime هتقولوا
+
+528
+00:40:27,910 --> 00:40:31,690
+ليه؟ مش بدنا فيها Sodoprime لأ الناس بعد ما وجدوا
+
+529
+00:40:31,690 --> 00:40:35,490
+أن هناك أرقام يعني نستفيد منها، إلها خصوصية، في
+
+530
+00:40:35,490 --> 00:40:40,490
+إلها ميزة اللي هي Sodoprime هذه إلها ميزة ذهب في
+
+531
+00:40:40,490 --> 00:40:45,390
+الاعتقاد إنه مش بالضروري ال base تبعتنا اتنين ل a,
+
+532
+00:40:45,510 --> 00:40:50,550
+b الكلام صحيح b to the power n minus one congruent
+
+533
+00:40:50,550 --> 00:40:55,130
+to one base nأتنين او اكتر مش مشكلة فاتعممت
+
+534
+00:40:55,130 --> 00:40:58,150
+القاعدة بهذا الشكل على اساس انه اي رقم بيحقق
+
+535
+00:40:58,150 --> 00:41:03,730
+المعادلة هذه هنسميه pseudo prime Carmichael
+
+536
+00:41:03,730 --> 00:41:07,990
+Carmichael number Carmichael مسك الموضوع هذا ومسك
+
+537
+00:41:07,990 --> 00:41:11,870
+لنا كل الأرقام بدأ يفحص الأرقام اللي ممكن نحطها
+
+538
+00:41:11,870 --> 00:41:17,410
+ضمن set ال set هنسميها pseudo prime فجلنا ان هو في
+
+539
+00:41:17,410 --> 00:41:24,240
+الرقم بعد الرقم اللي احنا شغلناه ال 431 فيه561 في
+
+540
+00:41:24,240 --> 00:41:30,260
+1105 في 1729 شكلهم كإنهم ال prime بس لأ هم فعليا
+
+541
+00:41:30,260 --> 00:41:33,260
+بينفعوش إلا إنه يكونوا ضرب حاصل two prime ثانية
+
+542
+00:41:33,260 --> 00:41:38,400
+يكونوا حاصل ضرب two prime ثانية فقط يعني مجسموش
+
+543
+00:41:38,400 --> 00:41:41,480
+علاقش اتاني إذا مجسموا علاقش اتاني بطلوا pseudo
+
+544
+00:41:41,480 --> 00:41:45,520
+prime فقط مجسموا على رقمين لإن رقمين هدولة prime
+
+545
+00:41:45,520 --> 00:41:49,140
+فبدأ يعمل analysis هيو بدأ يطلع فيهم لعام موصل ل
+
+546
+00:41:49,140 --> 00:41:54,640
+29000 وفيه طبنة لهم تكملطيب و بعدين؟ إيش بدنا فيهم
+
+547
+00:41:54,640 --> 00:42:01,000
+هدولة؟ so what؟ who cares؟ مين الحق يعني؟ بعدين زي
+
+548
+00:42:01,000 --> 00:42:04,180
+ما انتوا طب تقولوا طب و لما نجيب ال inverse؟
+
+549
+00:42:04,180 --> 00:42:07,040
+قولتلكوا لأ أصبروا شوية بنحل فيها المعادلة ال
+
+550
+00:42:07,040 --> 00:42:10,900
+linear equation ال linear congruential حلناها طيب
+
+551
+00:42:10,900 --> 00:42:16,330
+هنا نفس الكلام إيش بنهتم؟ هدي إلكممع المرة الجاية
+
+552
+00:42:16,330 --> 00:42:22,110
+مع الواجب بدي بس ورقة ورقة A4 مرتبة ومنصقة مش مزعة
+
+553
+00:42:22,110 --> 00:42:26,230
+ايكى ورقة اعملولنا بحث صغير بس اكتبولنا على جوجل
+
+554
+00:42:26,230 --> 00:42:30,750
+ولا على اي search engine Carmichael number
+
+555
+00:42:30,750 --> 00:42:34,990
+applications كل واحدة لو جابتلي applications او
+
+556
+00:42:34,990 --> 00:42:37,550
+application واحد وجالتنا كيف استخدمت فيه الرقم
+
+557
+00:42:37,550 --> 00:42:40,670
+تبعنا عشان تحسوا بس انه اه والله ايش اهمية الرقم
+
+558
+00:42:41,690 --> 00:42:44,850
+تمام؟ على الأقل application واحد مش بالضرورة
+
+559
+00:42:44,850 --> 00:42:47,630
+تفهموه كويس بس انك تحس ان والله الأرقام هذه لها
+
+560
+00:42:47,630 --> 00:42:52,410
+تطبيقات لها تطبيقات ورقة واحدة بدي بس مش أكتر ورقة
+
+561
+00:42:52,410 --> 00:42:58,790
+واحدة اسم كفوغ Carmichael number applications او
+
+562
+00:42:58,790 --> 00:43:01,590
+numbers applications لأن هذه عدة أرقام كبيرة جدا
+
+563
+00:43:01,590 --> 00:43:06,470
+عددها كبير شوفوا ان ايش التطبيقات اللي ممكن نستخدم
+
+564
+00:43:06,470 --> 00:43:11,560
+فيها Carmichael ال Carmichael مثلاOkay المرة
+
+565
+00:43:11,560 --> 00:43:15,760
+الجاية بنبدأ في ال cryptography لإنه مهمة برضه
+
+566
+00:43:15,760 --> 00:43:20,400
+كويسة لأول واحد اشتغلها اللي هو Caesar او القيصر
+
+567
+00:43:20,400 --> 00:43:25,660
+اشتغل على ال Caesars cypher او شفرة Caesar كان
+
+568
+00:43:25,660 --> 00:43:30,400
+بيبعت الرسائل تبعته للجيوش والقادة تعونه مشفرةكيف
+
+569
+00:43:30,400 --> 00:43:35,240
+كانت بشفرها هنشوف طبعا بشفرها حرف by حرف أو letter
+
+570
+00:43:35,240 --> 00:43:39,460
+by letter كل حرف بعكسه و بيعمله طريقة modification
+
+571
+00:43:39,460 --> 00:43:42,720
+و بيبعت الرسالة بطريقة معينة هنتكلم عنها برضه
+
+572
+00:43:42,720 --> 00:43:46,040
+باستخدام ال modulo فالموديولو من زمان جدا اصلا
+
+573
+00:43:46,040 --> 00:43:51,020
+مقترعوا ما عاملينهطريقة كسر ال code كمان هنتكلم
+
+574
+00:43:51,020 --> 00:43:54,180
+عنه، كيف ممكن نكسر ال code و نعرف بالظبط هو إيش
+
+575
+00:43:54,180 --> 00:43:59,500
+اللي بعته، بعدين هنتكلم عن طريقة تانية و في طريقة
+
+576
+00:43:59,500 --> 00:44:01,740
+تالتة هنتكلم عنها لاحقا، اللي هي ما زالت تستخدم
+
+577
+00:44:01,740 --> 00:44:04,320
+حتى الآن، ما زالت تستخدم حتى الآن، فبنخليها للمرة
+
+578
+00:44:04,320 --> 00:44:06,580
+الجاية ان شاء الله تعالى عشان تلحقوا، تذاكروا أو
+
+579
+00:44:06,580 --> 00:44:10,180
+تترجعوا إذا عندكوا أي أسئلة، يعطيكم العفو و بركة
+
+580
+00:44:10,180 --> 00:44:10,600
+الله فيكم
+