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This is NOT a homework, I am over homework stage ages ago :-)
What function draws semicircle?
$$y=f(x) = \text{something}$$
and I end up with a unit circle.
|
I have to prove this question:
$$2^{k} \,\left|\, {2k \choose 0} \cdot 3^{0} + {2k \choose 2} \cdot 3^{1} + \cdots + {2k \choose 2i} \cdot 3^{i} + \cdots + {2k \choose 2k} \cdot 3^{k}\right.$$
What i did was to get a closed form for this summation, and i haven't been able to get one. Any ideas, or is there any other me... |
I have $2$ perpendicular vectors in space. How can I determine the plane determined by the $2$ vectors?
|
Venn diagrams captured my attention a few years ago. One night I decided to see if I could come up with some new Venn Diagrams. After a few hours, this is what I came up with. I'm a web developer not a mathematician, so I'm quite proud of this little creation. I've searched the internet and several books to confirm tha... |
Are continuous functions always differentiable? Are there any examples in dimension $n > 1$?
|
I am learning about various signal processing methods in my university course, and I can't seem to grasp what 'energy' in signals represent. I mean, I know that it is the integral of the absolute value of energy squared (side question: why is absolute value needed?), but I don't know the meaning of what this energy is.... |
Notation question (I believe the notes that I'm reading uses pretty common notation):
Let $V $ be a vector space over a field $K$. What is $V^\mathbb{N}$? Is it a vector space of infinite dimensions? What are the elements of $V^\mathbb{N}$? Are they infinite length tuples?
|
in R3 (3d) , having a vector perpendicular with a plane ( so we know where is 'up') , how do we determine if a certain point is below our plane ?
Regards,
Alexandru Badescu
|
One observes that
\begin{equation*}
4!+1 =25=5^{2},~5!+1=121=11^{2}
\end{equation*}
is a perfect square. Similarly for $n=7$ also we see that $n!+1$ is a perfect square. So one can ask the truth of this question:
Is $n!+1$ a perfect square for infinitely many $n$? If yes, then how to prove.
|
I was trying to teach myself some basic Lie theory, and I came across this statement on Mathworld, relating the commutator of a group, $\alpha\beta\alpha^{-1}\beta^{-1}$, to the commutator of its Lie algebra, $[A,B] = AB-BA$:
For instance, let $A$ and $B$ be square matrices, and let $\alpha(s)$ and $\beta(t)$ be paths... |
Let $\mathbf C$ be an abelian category admitting projective limits. Let's consider the category whose objects are those of the form
$$
0\to A\to B\to C\to 0
$$
and whose morphisms are triples of morphisms of $\mathbf C$ such that the diagram
$$
\begin{array}{ccccc}
A&\hookrightarrow & B & \to & C & \newline
\downarrow ... |
If I have 5 students (A-E) that score 80%, 70%, 70%, 60% and 50% on a test what percentiles do they fall in?
A - 20th percentile (80%)
B - 40th percentile (70%)
C - 40th percentile (70%)
D - 80th percentile (60%)
E - 100th percentile (50%)
Is this correct?
Let me expand the question as I wasn't clear earlier: If A is... |
This is a question on the homework for my finite fields class. The beginning of the assignment defines the following notation:
For $i\geq1 $, define the following elements of $A=\mathbb{F}_{q}[T]$ :
$[i]=T^{q^{i}}-T$,
$L_{i}=[i][i-1]\cdots[1]$,
$D_{i}=[i][i-1]^{q}\cdots[1]^{q^{i-1}}$
and put $D_{0}=L_{0}=1$.
Let $... |
Let's assume we have a commutative ring with identity. Can the Nil-Radical and the Jacobson Radical be equal in a non-trivial case (i.e. not every nonzero prime ideal in said ring is maximal)?
Are there any interesting examples of this case?
|
Suppose for company A, there is a $60 \%$ chance that no claim is made in the coming year. If one or more claims are made, then the total amount is normally distributed with mean $1000$ and standard deviation $2000$.
Suppose for company B, there is a $70 \%$ chance that no claim is made during the coming year. If one o... |
I'm looking for a function that will replicate logical operators. In particular consider the AND operator. Then I am looking for a function z = f(x,y) such that
$$x,y,z \in \{0,1\}$$
f(0,0)=0
f(1,0)=0
f(0,1)=0
f(1,1)=1
More importantly I need to generalize over a space where Xi,Yi ∈ {0,1} and I need to do this for othe... |
I'm aware that one can use a Fast Fourier Transform (FFT) to take the cost of multiplication of two polynomials of degree N from O$(N^2)$ to O$(N \ln N)$ (which is an amazing reduction when dealing with large polynomials!). Does a similar transformation procedure exist for multinomials?
I'm interested in the special ca... |
What are good expositions of spectral sequences, which include a thorough introduction to the topic as well as the most important examples of applications - maybe with an emphasis an topological and/or operator algebraic uses.
I know that the wikipedia article is quite extensive, but I'd like to have something... nicer... |
I'm trying to sample a lot of points efficiently. I'm wondering if the following method is possible.
I sample points of a function (evaluate the function) mod $n$. I.e. I calculate f(element one), f(element 2)...f(element n). I do this for all of the points in a ring. Now I take a second ring (mod $m$, for instance)... |
Is there a succinct proof for the fact that the rank of a non-zero skew-symmetric matrix ($A = -A^T$) is at least 2? I can think of a proof by contradiction: Assume rank is 1. Then you express all other rows as multiple of the first row. Using skew-symmetric property, this matrix has to be a zero matrix.
Why does suc... |
I've read so much about it but none of it makes a lot of sense. Also, what's so unsolvable about it?
|
Suppose I have an optimization problem of the form:
$$\min \mathbf{d}^{T}\mathbf{y}$$
subject to
$$\mathbf{M}\mathbf{y} \geq \mathbf{d}, \qquad \mathbf{y} \geq 0$$
If a solution $\mathbf{s}$ which satisfies $\mathbf{M}\mathbf{s} = \mathbf{d}$ and $\mathbf{s} \geq 0$, how can it be shown $\mathbf{s}$ is optimal for th... |
"It is a profoundly erroneous truism, repeated by copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thin... |
So I feel a bit strange asking a Calculus question, but this came up today while teaching.
One can check that if you start with some integral, which can be see as an "obvious u-substitution problem", that you can instead use integration by parts, and wind up with the scenario where you have have the original integral o... |
I'm trying to describe a counterexample for a theorem which includes the figure eight or "infinity" symbol, but I'm having trouble finding a good piecewise function to draw it. I need it to be the symbol, except at the "crossing point" the function jumps (not continuous) so that we still have a manifold.
|
Let $R$ be a ring and $f(X) \in R[x]$ be a non-constant polynomial. We know that the number of roots, of $f(X)$ in $R$ has no relation, to its degree if $R$ is not commutative, or commutative but not a domain. But,
The number of roots, of a non-zero polynomial over commutative integral domain, is at most its degree.
... |
I manually arranged two complete latin squares from ordered pairs of 4 and 6 like so:
1 2 3 4
2 4 1 3
3 1 4 2
4 3 2 1
1 2 3 4 5 6
2 4 1 6 3 5
3 1 5 2 6 4
4 6 2 5 1 3
5 3 6 1 4 2
6 5 4 3 2 1
I like this kind of sequence, but can tell it is going to be more difficult to manually arrange as the number of pairs increase... |
Let $\varphi(n)$ be Euler's totient function, the number of positive integers less than or equal to $n$ and relatively prime to $n$.
Challenge: Prove
$$\sum_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}.$$
I have two proofs, one of which is partially combinatorial.
I'm posing this pr... |
I'm just starting to learn some basic topology, and I've mostly encountered definitions. For instance, I read that for a topological space $X$, for any $E\subseteq X$, define its closure $\overline{E}$ as the set of points $p\in X$ such that each neighborhood $N$ of $p$ has a nonempty intersection with $E$.
I wanted to... |
Just wondering if equations used as props in SG1, atlantis and most recently Universe are just random and cool looking, or real/meaningful and cool looking.
Most recent episode of Stargate Universe S02E04 has a "corridor of equations" where dr nick Rush is trying to decipher something. Has anyone familiar with the show... |
Given a set $S$, one can easily find a set with greater cardinality -- just take the power set of $S$. In this way, one can construct a sequence of sets, each with greater cardinality than the last. Hence there are at least countably infinite many orders of infinity.
But do there exist uncountably infinite orders of in... |
I'm looking for lightweight, free, Windows, Math software.
Something I can put an expression and get an answer, or graph it.
I tried Euler, but it is quiet complicated and HUGE.
Basic needs:
Expression Based
Supports Variables
Support Functions, User defined and auto loaded.
Supports graphs, 2D. Not really needing 3D... |
Well, in a previous post regarding the explanation of Riemann Hypothesis Matt answered that:
The prime number theorem states that the number of primes less than or equal to $x$ is approximately equal to $\int_2^x \dfrac{dt}{\log t}.$ The Riemann hypothesis gives a precise answer to how good this approximation is; name... |
Lots of people (including myself) face lot of problems in tackling Mathematical Problems, which appear as if we can solve it, but then writing out a solution becomes difficult.
Let us consider some examples:
I was asked this question, some time back in an exam. Give an example of a continuous function on $(a,b)$ which... |
See this question on applying probability theory principles in software design.
The question is generally the following: you design some system (say software) and rely on some well-known mathematical concept (say hash function). You know that when this concept is used without caution your system can sometimes fail, how... |
Problem with this question
$$f(x)=3\sin x\cos \frac x 2 \text{ around } a=1$$
I have been breaking up $f(x)$ into $g(x) = 3\sin x$ and $h(x)= \cos \frac x 2$, and then multiplying them back ($g(x)\cdot h(x)$) this was suggested to my by the lecturer. but for the life of me I cant get the answer.
Answer is: $y = 0.817x+... |
Statement:
There exist a polynomial $P$ such that $|P(x) - \cos(x)| \leq 10^{-6}$ for all (real) $x$.
My answer: False. All polynomials of a degree $n \geq 1$ are unbounded as $x$ tends to infinity. A polynomial of degree $n = 0$ is bounded only when it is in the form $y = a$ (horizontal line) but this will not help be... |
$$
\begin{pmatrix}
Y \\ Cb \\ Cr
\end{pmatrix}
=
\mathrm{Round}
\left\{
\begin{pmatrix}
0.2126\times\frac{219}{255} &
0.7152\times\frac{219}{255} &
0.0722\times\frac{219}{255} \\
-\frac{0.2126}{1.8556}\times\frac{224}{255} &
-\frac{0.7152}{1.8556}\times\frac{224}{255} &
0.5\times\frac{224}{255} \\
0.5\times\frac{224}{... |
Let $A$ be and $n\times n$ matrix over $\mathbb{R}$ or $\mathbb{C}$. Suppose $B$ is an $n\times n$ matrix over the same field as $A$ and $B\vec{x}=A\vec{x}$ for all $\vec{x} \in \mathbb{R}^n$. Prove that $A=B$, that is $a_{ij}=b_{ij}$, for all $i,j$.
|
I have a problem understanding this equation (I encountered it in a mechanics problem).
Given:
$x = x(t)$
$q = q(t)$
$v = dx/dt$
$w = dq/dt$
Then:
$\frac {\partial v}{ \partial w} = \frac{\partial x}{\partial q}$
Is that true? If yes, why is that true? How can I proof that?
EDIT:
Actually it's a passage in the derivati... |
How can I prove that for every positive integer $n$ we have
\begin{equation*}
\frac{n\pi}{4}−\frac{1}{\sqrt{8n}}<\frac{1}{2}+\sum_{k=1}^{n−1}\sqrt{1−\frac{k^2}{n^2}}?
\end{equation*}
|
I have made up this "fun" problem.
The first row of a 3x3 matrix is $(a_{11} a_{12} a_{13})$. The next row consists of the variables $h, g$ and $c$ in any order. The last row are distinct non-zero fixed scalars, such as $2, 1, 7$ or $-4$ etc. They could be any integer.
Given an expression for $det(A)$ for example:
$(-c... |
Wondering if my following question is an application of information theory:
Lets say we have a factory and ship boxes of stuff outside. If a competitor stands outside my factory, observes the stream of boxes coming out of a factory and note their sizes, he can get valuable information about my manufacturing process. So... |
In this formula for Euler numbers:
\begin{equation*}
A_n = i^{n+1}\sum _{k=1}^{n+1} \sum _{j=0}^k{k\choose{j}} \frac{(-1)^j(k-2j)^{n+1}}{2^ki^kk},
\end{equation*}
what is $i$? I have to generate the $n^{th}$ Euler number, and I don't have $i$.
It is not the imaginary unit, is it?
|
I know it is a very general question, but i'm not sure how to get started and improve number theory related skills related to ACM ICPC and other programming competitions.Any good way or book recommendations ?
|
What's the meaning of $\choose$ in this formula:
$$C_n=\frac1{n+1}\binom{2n}{n}=\frac{(2n)!}{n!(n+1)!}\qquad\mathrm{for}\;n\geq 0$$
Is it a division?
|
If $2 x^4 + x^3 - 11 x^2 + x + 2 = 0$, then find the value of $x + \frac{1}{x}$ ?
I would be very grateful if somebody show me how to factor this polynomial by hand, as of now I have used to Mathematica to get $(x-2) (2x - 1) (1 + 3x + x^2)$, but I am having trouble to factor this manually.
Best regards,
|
If a,b,c are in arithmetic progression., p,q,r in harmonic progression and ap,bq,cr are in geometric progression., then $\frac{p}{r}+\frac{r}{p} = $ ?
EDIT: I have tried to use the basic/standard properties of the respective progressions to get the desired result, but I am not yet successful.
|
Let $(X, d)$ be a metric space. Is the function $x\mapsto d(x, z)$ continuous? Is it uniformly continuous?
|
Solve $2x \equiv 1 \pmod{p}$ where $p$ is an odd prime.
I'm really stuck on this one.
|
At the Blizzcon 2010, StarCraft II multiplayer panel, this stuff was supposed to explain the ladder matchmaking system. I look at this and go eh? what!?
Is any of this real? or are they just messing with me, because I can't make heads or tails of this humongous equation. Can anyone break it down for me? or at least ex... |
I need to do a series expansion of this forumla
$$z = \sqrt{\frac{x+1}{y+1}}.$$
I need to get Zx Zxx and so on. but I really dont know where to start with this this.
just a push in the right direction should be enough.
|
I've got a function whose general form is
$f(x) = \frac{1}{x^\alpha}$
where $x > 0$ and $\alpha > 0$. I would like to show that if $0< \alpha < 1$ $f(x)$ has slow decay and if $\alpha > 1$ the $f(x)$ has rapid decay. (I've already verified these properties of $f(x)$ using a graphing application.)
|
Suppose $B \subset X$ where $X$ is a vector space. $B$ is called balanced if $\alpha B \subset B$ for every $\alpha \in \Phi$ with $|\alpha| \leq 1$. Note that $\Phi = \textbf{R}$ or $\Phi = \textbf{C}$. What is the intuition behind balanced sets? Why do we define them? Is it "good" for a vector space to have more bala... |
Does any compact subset belong to Borel Sigma Algebra?
Why?
Here Borel Sigma algebra is defined to be the sigma algebra generated by all open subsets in the topological space.
Thanks and regards!
UPDATE:
I found that there are two kinds of definitions for a Borel sigma algebra: one generated by all open subsets, and ... |
Suppose $A$ is a set of finite measure. Is it possible that $A$ can be an uncountable union of disjoint subsets of $A$, each of which has positive measure?
|
How is a Borel measure on Euclidean space defined?
I mean the Borel measure on the Borel sigma algebra generated by usual toplogy on an Euclidean space, which coincides with the normal definition of volume of subsets in the Euclidean space.
For Lebesgue measure on an Euclidean space, it is defined in terms of the oute... |
I am not a math expert nor a native English speaker, so maybe I am using wrong terminology... In this case, help me to improve my question :)
Part 1:
This is my set of equations, I have to calculate values $x_n$, $y_n$ and $z_n$. I know the values of $A, B, C$, Total and sums of parameters ($S_1$ = $x_1$ + $x_2$ + $x_... |
For each $n>0$, how do we prove that $$\Gamma'(n+1)> \log{n} \cdot \Gamma(n+1)$$
I had spent about half an hour on this question, but just could find any way of proceeding for the solution.
Wikipedia page gave me an interesting identity $$\Gamma'(n+1)= n! \cdot \Biggl( - \gamma + \sum\limits_{k=1}^{n} \frac{1}{k}\Big... |
Let $X$ be integral scheme and $\mathcal K$ sheaf of rational functions on $X$. For any
point $y\in X$ different of generic point we know that fiber of $\mathcal K$ (defined as usual as $\mathcal K _y / \mathcal m_y \mathcal K_y$) is zero. I'll be very gratefull if you explain intuitively why this is so, in language o... |
Given the octic group $G = \{e, \sigma, \sigma^2, \sigma^3, \beta, \gamma, \delta, t\}$.
Find a subgroup of $G$ that has order $2$ and is a normal subgroup of $G$.
Find a subgroup of $G$ that has order $2$ and is not a normal subgroup of $G$.
|
A polynomial $P$ with integral coefficients satisfies $P(n)>n$ for all positive integers $n$. Every positive integer $m$ is a factor of some number of the form $P(1),\, P(P(1)),\, P(P(P(1))),\dots $. Prove that $P(x)=x+1$.
|
If i have a standard LP problem:
$$\min \mathbf{d}^T \mathbf{x}$$
subject to
$$\mathbf{B}\mathbf{x}=\mathbf{f},\qquad \mathbf{x} \geq 0$$
$\mathbf{y}$ is the optimal solution and $\mathbf{z}$ is the optimal solution to the dual problem
Now, for the same cost function $\mathbf{d}$, if $\mathbf{f}$ is replaced by $\mathb... |
I'm quite positive that I saw before an encyclopedia (more accurately, dictionary/glossary) on Elsevier website. I remember I looked up the definition of a hyperplane there, few months ago. But I can't find it through Google anymore.
Does anyone know the link?
|
Imagine I have a company that makes widgets, where each widget costs me A dollars to make. Each month I can allocate money toward research and development with the aim of finding a new process that will allow me to build widgets for a cost of A/B dollars. Presume that I know that for each C dollars I spend on research ... |
Given three containers of specified volume, how many different volumes can you measure ?
For example, suppose we have cans with capacities 2, 3, 4 litres.
We can measure :
1 litre by filling the 3 litre can and pouring it in the 2 litre can.
2, 3, 4 litres are trivial.
5 litres by filling both the 2 and 3 litre can... |
Is there a short way to say $f(f(f(f(x))))$?
I know you can use recursion:
$g(x,y)=\begin{cases}
f(g(x,y-1)) & \text{if } y > 0, \
\newline x & \text{if } y = 0.
\end{cases}$
|
$1$.How many proper subset of $\{1,2,3,4,5,6,7\}$ contain the numbers $1$ and $7$ ?
Lets consider $\{1,7\}$ as a single element then the number of possible subset is $2^6$ and hence the number of proper subset is $62$.
$2$. A survey show that $63$% of the Americans like cheese where as $73$% like apples.If $x$% of Ame... |
I'm asking because numerical tests seem to give nonsensical answers, and I thought I would check if there was an analytic way of checking for divergence, but I couldn't think of one offhand.
|
A union of finite sets can always be converted to a union of finite disjoint sets.
I was wondering if a union of countable sets can always be converted to a union of countable disjoint sets? If yes how to do that?
Thanks!
Update with Paul's question:
"I wonder about the natural extension of this question to uncountabl... |
I'm trying to think of an example of a homomorphism of commutative rings $f:A\rightarrow B$ and ideals $I,J$ of $B$ such that $f^{-1}(I)+f^{-1}(J)$ is not a preimage of any ideal of $B$. I can't seem to come up with one... anyone know one?
Edit: To clear up some basic facts / head off some mistakes:
As Arturo points o... |
What is the easiest way to find the maximum of $9\cos(t) - 8\cos (3t)$?
|
Of course, Euler proved that the Riemann zeta function can be defined as the analytic continuation of a product over all primes.
$$\zeta(s) = \prod_{p \in \mathbb{P}}\frac1{1-p^{-s}}$$
It is well known (but not something I understand) that the positions of zeros of the zeta function allows one to make inferences abou... |
Let $z_1, z_2 \ldots z_m$ be complex numbers, $m \in \mathbb{N}$. Can anybody tell me how to prove the following inequality?
$| z_1 z_2 \ldots z_m - 1 | \leq e^{|z_1 - 1| + \ldots + |z_m - 1|} - 1$
In case you're wondering, this is asserted without proof in a paper by Von Neumann, about infinite tensor products of Hilb... |
Define the relation $\sim$ on $\mathbb{Z}$ by $a \sim b$ if and only if $5a \equiv 2b \pmod{3}$.
Prove that $\sim$ is an equivalence relation on $\mathbb{Z}$.
Identify the distinct equivalence classes on $\mathbb{Z}/\sim$.
How can I prove something like this? Do I need to prove something for reflexiveness, symmetry, a... |
I have a graph $G$ with a list of edges $E$, all the edges can form cycles, as shown below:
All the coordinates for the vertex $V$ are known.
Wat is the algorithm to find all the faces $F$? For the example above, there are 4 such faces, as indicated by the looping arrow.
Update: Why is it that the algorithm to find t... |
This animation from Wikipedia shows basically what I want to accomplish, however - I'm hoping to have it flipped around, where it starts progressing more towards the destination and "up" (in this image), and then arcs more directly to the end point. However, I only have access to a starting point and ending point, what... |
Let $C$ be a circle of radius $r$ with $n$ points. Prove that there is a point on the circle such that the product of the distances from this point to the other $n$ points is greater than $r^n$. So we seem to be looking at chords that are of length $\leq 2r$. To show the existence of such a point, would you use a const... |
How many distinct integral value of $n$ satisfies the equation $2^{2n} - 3 \cdot (2^{n+2}) + 32 = 0 $ ?
|
We know that the points of discontinuity of a monotone function on an interval $[a,b]$ are countable. Using this can we prov that:
Any bijection $f: \mathbb{R} \to [0,\infty)$ has infinitely many points of discontinuity.
If yes, how or otherwise how to prove the above result?
|
Is the localization of a reduced ring (no nilpotents) still reduced?
|
I want to write the equation of a line in $\mathbb C^n$ passing through a point $(z_1,z_2,...,z_n)$. Actually I have a set of points and I suspect they all lie on the same line which passes through this point and I want a convenient way to check it.
Thank you
|
If a set contain $(2n+1)$ elements and if the number of subsets which contain at most n elements is 4096, then what is the value of $n$?
|
In a compact hyperbolic Riemann surface without boundary tbe length minimizing geodesic between two points $p$ and $q$ is unique.
|
I'm trying to understand basic tensor analysis. I understand the basic concept that the valency of the tensor determines how it is transformed, but I am having trouble visualizing the difference between different valencies when it comes to higher order tensors.
I have this picture in my mind for the lower order tensor... |
What is an example of a lambda-system that is not a sigma algebra?
|
This is probably an obvious parallel that most people are aware of, but I only just noticed it the other day and it made me quite excited. The determinant in algebra has a lot in common with the integral in analysis. For example:
They are both applied to functions, the integral to integrable functions, the determinan... |
Can an element in the Kalman gain vector ever be over one?
|
I remember seeing something like the following problem in the past and would like to know if it has a solution (or if I can find a source for it).
Problem Given a finite set of points in the plane in general position (no three are collinear), does there exist a line that intersects no points?
|
It is well-known that given two primes $p$ and $q$, $pZ + qZ = Z$ where $Z$ stands for all integers.
It seems to me that the set of natural number multiples, i.e. $pN + qN$ also span all natural numbers that are large enough. That is, there exists some $K>0$, such that
$$pN + qN = [K,K+1,...).$$
My question is, given ... |
For a ring $R$, an $R$-right-module $M$, an $R$-left-module $N$, and an abelian group $P$, one can use the universal property of the tensor product to construct maps
$$
M\otimes_R N\to P.
$$
It concrete cases, it is often easy to see that the constructed map is surjective by just writing down pre-images.
It seems to be... |
Consider a function $f : \mathcal X \times \mathcal Y \mapsto \mathbb R$. I want to define $g_x(y) = f(x,y) : \mathcal Y \mapsto \mathbb R$. I want to say that
$g_x$ is a ___ of function $f$.
What is the appropriate word for _____
|
I have a function that is difficult to integrate. So I elect to work with power series representations. Suppose the power series representation for this function is the following:
$f(x) = \sum_{i=M}^N{c_i x^i}$
I attempt to integrate each term of the power series seperately. For instance, looking at a few terms, we ... |
Is it true that for all proofs $\forall x \exists y : R(x, y)$, then $y = y(x)$?
A while back I remember reading a book on functional programming that was leading into some questions about what exactly mathematical proofs were and how they were related to functions. In fact, I just found the book: link to PDF, page 16 ... |
Simple example in order to clarify what I mean:
Sequence - $\{2 , -1, 4, 2, 9 \}$
Sum and product combination: $\{ 16, -144 \}$
Question:
Is a combination of sum and product unique for any* sequence?
"any sequence" except that one which consists only of zeros.
UPD: The answer to my initial question is "no". Thanks.
B... |
Quick formulation of the problem:
Given two points: $(x_l, y_l)$ and $(x_u, y_u)$
with: $x_l < x_u$ and $y_l < y_u$,
and given lower asymptote=0 and higher asymptote=1,
what's the logistic function that passes through the two points?
Explanatory image:
Other details:
I'm given two points in the form of Pareto 90/10 (g... |
I am working on a game program.
I have an array of 8 points in 3d space $(X,Y,Z)$ that are the 8 corners of a cube whose $W=H=D$. The 8 points are listed in no particular order. For the sake of determining this algorithm, The cube's center is at the world origin, $(0,0,0)$ but the cube's orientation is not aligned with... |
This was suggested by a problem on FreeNode's #math a little while ago...
Construct a directed graph $\Gamma$ with vertex set the set of compact convex sets in $\mathbb R^2$, and an arrow $A\to B$ if $A$ and $B$ are disjoint and there is a point $a$ in $A$ and a $t>0$ such that $a+(t,0)$ is in $B$.
I guess there are no... |
How does one go about solving the following quadratic congruence?
$4x^2 \equiv 2 \ (\text{mod} \ 7)$
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In a survey of political preference, $78$% of those asked were in favor of at-least one of the proposals: I, II and III. $50$% of those asked favored proposal I, $30$% favored proposal II, and $20$% favored proposal III. If $5$% favored all the three proposals, what % of those asked favored more than one of the three p... |
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