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"# Question about the Continuum Hypothesis
The Continuum Hypothesis hypothesises
There is no set whose cardinality is strictly between that of the integers and the real numbers.
Clearly this is either true or false - there ... | college_math |
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"# Probability Example Question
I'm reading my book on probability and I don't understand the example problem:
Question: Suppose that n + m balls, of which n are red and m are blue, are arranged in a linear order in such a w... | college_math |
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"## The intersection of two monomial ideals is a monomial ideal
Let $F$ be a field, let $R = F[x_1, \ldots, x_t]$, and let $M = (m_i \ |\ i \in I)$ and $N = (n_j \ |\ j \in J)$ be monomial ideals in $R$ (not necessarily finit... | college_math |
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"# Lesson 5Be There or Be SquarePractice Understanding
## Jump Start
Graph each function with at least two precise points on either side of the line of symmetry.
## Learning Focus
Use completing the square to change the fo... | college_math |
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"# Hexagonal sum filling
Q1: Fill this hexagon with numbers 1-19 (no repetition) such that the sum of every vertical and diagonal row is the same. (This should be easy)
Q2: Assume that one of these pre-solved cells was not g... | college_math |
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"TheInfoList
OR:
In
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. T... | college_math |
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"1,183 Pages
A total derivative of a multivariable function of several variables, each of which is a function of another argument, is the derivative of the function with respect to said argument. it is equal to the sum of the... | college_math |
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"Find Equivalence Classes for the relation $S$ on the set $\mathbb{R}^*$ is definied as $aSb \iff ab > 0$
I am trying to understand how to determine the equivalence classes. I have this question in the book
The relation $$S$... | college_math |
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"# Convex set
(Redirected from Convex subset)
A convex set.
A non-convex set, with a line-segment outside the set.
In Euclidean space, an object is convex if for every pair of points within the object, every point on the str... | college_math |
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"# The Next Permutation
Time Limit: 1000MS
Memory Limit: 65536K
## Description
For this problem, you will write a program that takes a (possibly long) string of decimal digits, and outputs the permutation of those decimal ... | college_math |
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"# Relationship of a planet's mass, size, and acceleration due to gravity
#### yoosnb
Homework Statement
Planet A and Planet B have the same mass, but planet A is twice larger than planet B. A ball dropped above the surface ... | college_math |
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"# Defining the rank for a finitely generated abelian group
So first some definitions. Let $G$ be an abelian group, a basis for $G$ is a linearly independant subset that generates $G$. We say that $G$ is finitely generated if... | college_math |
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"# 3d coordinate angles α β γ
1. Feb 8, 2014
### Tiven white
1. The problem statement, all variables and given/known data[/
In 3-D coordinate space, any two of the coordinate angles must …
Select one:
a. sum to less than 1
... | college_math |
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"# Question on data compression
Suppose we have some text as a series of a number of characters and a dictionary consisting of some words that are sub-strings of the text, $D=\{w_1,w_2,\dots,w_n\}$. The dictionary is rich eno... | college_math |
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"# Finding Smiley
The questions below are due on Monday May 17, 2021; 10:00:00 PM.
You are not logged in.
Note that this link will take you to an external site (https://shimmer.csail.mit.edu) to authenticate, and then you w... | college_math |
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"# subsemigroup of a cyclic semigroup
It is a well-known fact that the subgroup of a cyclic group is cyclic. Is this true for semigroups? The answer is clearly no. For example, take the cyclic semigroup of positive integers u... | college_math |
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"# Model of theory of real closed field
I heard somewhere that models of theory of real closed field are isomorphic.
However, there is also a statement in Internet which seems to say the opposite.
Are the models of theory o... | college_math |
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"# Could the sum of an even number of distinct positive odd numbers be divisible by each of the odd numbers?
Could the sum of an even number of distinct odd numbers be divisible by each of the odd numbers ?
Let $k\geq 4$ be ... | college_math |
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"# Subgroup of a Finite Group
Let $G$ be a finite group, and let $S$ be a nonempty subset of $G$. Suppose $S$ is closed with respect to multiplication. Prove that $S$ is a subgroup of $G$. (Hint: It remains to prove that $S$ ... | college_math |
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"# Fill in numbers on the cube!
You are given a cube. You are told to fill in each vertex with the numbers $$4,5,6,...,11$$, with no repetition. What is the probability that for each two vertices that are connected by a commo... | college_math |
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"# Probability of a shuffled deck having two adjacent cards that are same suit and numerically adjacent (with A-K looping)
The question is: what is the probability that a shuffled deck will have two position-adjacent cards th... | college_math |
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"# Radius Of Convergence Complex Power Series Problems
Continuity Abel's elementary proof that complex power series are termwise di erentiable in their disk of convergence incidentally shows that they are continuous there as ... | college_math |
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"# Homework Help: Area between curves
1. Feb 3, 2010
### hover
1. The problem statement, all variables and given/known data
Find the area of the bounded region enclosed by the curves: 6x+y^2=13, x=2y
2. Relevant equations
... | college_math |
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"# prove that $n$ is divisible by $8$
If $2n+1$ is a square number and $3n+1$ is a square number also, where $n \in \mathbb{N}$, prove that $n$ is divisible by $8$.
I know the solution already. just for sharing new ideas.
•... | college_math |
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"# Math Help - Needs some help with some calculus word problems
1. ## Needs some help with some calculus word problems
5. When powder or granular solids are piled up, the powder forms a conical pile. The edge of the pile rea... | college_math |
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"# Prove that in a field $F$ of characteristic $p$, $f(x)=x^p −x−a$ is either irreducible or splits over
I have seen some quite related qustions $x^p-x+a$ irreducible for nonzero $a\in K$ a field of characteristic $p$ prime
... | college_math |
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"# Complex Analysis Proof Review
1. Dec 12, 2011
### Poopsilon
Let D ⊂ ℂ be a domain and let f be analytic on D. Show that if there is an a ∈ D such that the kth derivative of f at a is zero for k=n, n+1, n+2,..., then f is... | college_math |
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"# Find sub-matrix with the given sum in C++
In this problem, we are given a 2D matrix of size N*N and two variables sum and size. Our task is to find a sub-matrix with the given sum.
We need to find a sub-matrix of size*siz... | college_math |
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"# Thread: Can the grid be filled?
1. ## Can the grid be filled?
Given binary sequences of equal length, let the "distance" between them be defined as the number of bits that would need to be flipped to convert one binary se... | college_math |
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"Math Help - cyclic function proof..
1. cyclic function proof..
prove that function f(x)=sinx +sinax
is cyclic if and only if "a" is rational
??
2. Originally Posted by transgalactic
prove that function f(x)=sinx +sinax
is ... | college_math |
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"# Non Invertable matrix
## Homework Statement
Let A be an nxn matrix. If A is row equivalent to a matrix B and there is a non-zero column matrix C such that BC=0, prove that A is singular
## The Attempt at a Solution
Im n... | college_math |
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"## Data Sufficiency
##### This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 15
Joined: 23 Jun 2020
### Data Sufficiency
by deep319933 » Wed Jun 24, 2020 12:31 am
x is a 4-digit positive integer whose digits... | college_math |
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"# For which $n$, can we find a sequence of $n+1$ distinct points s.t. the interpolating polynomial of every +ve continuous function is itself +ve
Fix an interval $$[a,b]$$. For which integers $$n>1$$, does there exist $$n+1$... | college_math |
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"/*
Diamond free sequence (CSPLib #50) in Picat.
http://www.csplib.org/Problems/prob050/
"""
Proposed by Alice Miller, Patrick Prosser
Given a simple undirected graph G=(V,E), where V is the set of vertices and E the set of... | college_math |
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"Definition. Let $R$ be a commutative ring with 1. The Heisenberg group $H(R)$ is defined by
$H(R) = \left \{ \begin{pmatrix} 1 & a & c \\ 0 & 1 & b \\ 0 & 0 & 1 \end{pmatrix}: \ \ a,b,c \in R \right \}.$
Clearly $H(R)$ is a... | college_math |
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"Prove that the inverse of a bijective function is also bijective. Your defintion of bijective is okay, yet we could continually say "the function" is the two surjective and injective, no longer "the two contraptions are". Acc... | college_math |
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"Negative numbers and absolute value
# Multiplying and dividing negative numbers
## Multiplying positive and negative numbers
Learn some rules of thumb for multiplying positive and negative numbers.
Back
## Multiplying pos... | college_math |
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"Proof by Strong Induction: every natural a product of an odd and a power of 2
Can someone guide me in the right direction on this question?
Prove that every $n$ in $\mathbb{N}$ can be written as a product of an odd integer ... | college_math |
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"Precalculus (6th Edition) Blitzer
The new matrix is, $\left[ \begin{matrix} 1 & -1 & 1 & 1 & 3 \\ 0 & 1 & -2 & -1 & 0 \\ 0 & 2 & 1 & 2 & 5 \\ 0 & 6 & -3 & -1 & -9 \\ \end{matrix} \right]$
Consider the given matrix, $\left[ \... | college_math |
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"# Recent questions tagged binary-tree
1
Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ ... | college_math |
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"KONECT
KONECT > Plots > Hop plot
## Hop plot
The hop plot is a visualization of the distribution of pairwise distances in a network. The distance between two nodes in a network is defined as the number of edges in the short... | college_math |
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"]> 3.8 Digression on Length and Distance in Vector Spaces
## 3.8 Digression on Length and Distance in Vector Spaces
The distance between two vectors $v ⟶$ and $w ⟶$ is the length of the difference vector $v ⟶ − w ⟶$ .
The... | college_math |
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"12 questions linked to/from Functions that are their own inversion.
1k views
Some examples of functions that are their own inverse? [duplicate]
I'm looking for the name and some examples of functions $f$ with the following ... | college_math |
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"## A community for students. Sign up today
Here's the question you clicked on:
## wannabegurl 2 years ago Can somebody explian to me dependent and independent probability
• This Question is Closed
1. wio
Independent event... | college_math |
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"# Two-Point Form: Examples
This lesson will cover a few examples involving the two-point form of the equation of a straight line.
Q1. Find the equation of the line passing through (2,4) and (4,2).
Sol. No need for much exp... | college_math |
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"# countably infinite
## English
countably infinite (not comparable)
1. (set theory, of a set) That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection ... | college_math |
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"# Closed Form Expression
matrices how to calculate closed form expression for r simplex .
syntax fibonaccis closed form expression in haskell stack overflow .
solved derive simple closed form expression for the follo .
so... | college_math |
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"A Appendix:
# On k-Total Dominating Graphs
## Abstract
For a graph , the -total dominating graph is the graph whose vertices correspond to the total dominating sets of that have cardinality at most ; two vertices of are ad... | college_math |
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"# A Lemma of Equal Areas
Bui Quang Tuan came up with a simple but surprisingly useful lemma:
Let $[X]$ denote the area of shape $X.$
Let $A,$ $B,$ $C$ be three collinear points. $D,$ $E$ are two points on one side with res... | college_math |
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"# Three-Cornered Deltoids
[This is the third and final post in this series on triangle geometry. See the previous posts on Morley’s theorem and the 9-point circle.]
For our final exploration in this series, let’s again begi... | college_math |
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"# Calculating air drag for a massive rocket
1. Sep 26, 2006
### Noone1982
Not just a little rocket that goes a 1000 feet in the air, but one that can get into space. How does one take into account that the air density grow... | college_math |
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"# A variation of Fermat’s little theorem in the form $a^{n-d}\equiv a$ (mod $p$).
Fermat’s little theorem states that for $n$ prime,
$$a^n \equiv a \pmod{n}.$$
The values of $n$ for which this holds are the primes and the ... | college_math |
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"# Can extreme points always be projected to be extreme points?
Consider a bounded polyhedron $P$, and a dimension reducing projection $\Omega$ (ie a linear operator $\Omega$ such that $\Omega^2 = \Omega$), claim: if $u$ is a... | college_math |
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"# Existence of analytic function with certain conditions
$$1$$. Does there exists an analytic function $$f: \mathbb{C} \rightarrow \mathbb{C}$$ such that $$f(z)=z$$ for all $$|z|=1$$ and $$f(z)=z^2$$ for all $$|z|=2$$.
$$2$... | college_math |
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"## Finding the repetend length of a decimal expansion
We’re still trying to find the prefix length $k$ and repetend length $n$ of the decimal expansion of a fraction $a/b$, that is, the length of the part before it starts re... | college_math |
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"109.26 Hilbert functions
Definition 109.26.1. A numerical polynomial is a polynomial $f(x) \in {\mathbf Q}[x]$ such that $f(n) \in {\mathbf Z}$ for every integer $n$.
Definition 109.26.2. A graded module $M$ over a ring $A$... | college_math |
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"# CF977A Wrong Subtraction
• 285通过
• 370提交
• 题目来源
• 评测方式 RemoteJudge
• 标签 字符串 模拟
• 难度 入门难度
• 时空限制 1000ms / 256MB
• 提示：收藏到任务计划后，可在首页查看。
## 题意翻译
已知一个数 $n$ ，你要对它进行 $k$ 次操作。对于每一次操作，如果 $n$ 的最后一位数字不为零，则将它减1，否则将它除以10（即删除最后一位数字）。
... | college_math |
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"# Metric spaces question
$$P = \{f \in\ C ( \mathbb{R}, \mathbb{R}) \mid f(x+2 \pi ) = f(x)\}$$ be the set of $2\pi$-periodic function.
1) Show that $P$ is a subspace of $C( \mathbb{R}, \mathbb{R})$
2) Let $\|F\| = \sup_{x... | college_math |
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"# Does there exist a non-empty set that is a subset of its power set?
While working through Velleman, I proved that if $A \subseteq P(A)$, then $P(A) \subseteq P(P(A))$.
One example where this may be the case is when $A = \... | college_math |
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"# Simplest way to get the real solutions for $x^{4}-2x+1=0$?
What is the simplest way to get the real solutions for this equation?
$$x^{4}-2x+1=0$$
I can do it and also ask for a step-by-step solution to Wolfram Alpha, but... | college_math |
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"# Shape of a Gaussian surface
• B
Why doesn't the flux through a Gaussian surface change, when the shape is changed? (while keeping the net charge inside it the same)
Flux is the dot product of electric field and surface are... | college_math |
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"Emerging E Expanded
Subscribe!
My latest posts can be found here:
Previous blog posts:
Start with 10 10.00000... Take the square root 3.162278... Take the square root of that 1.778279... Take the square root of that 1.3335... | college_math |
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"# Absorbing Markov chains
The preceding two posts are devoted to solving the problem of determining mean time to absorption and the problem of determining the probability of absorption (using first step analysis here and usi... | college_math |
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"# $M$ is a point in an equalateral $ABC$ of area $S$. $S'$ is the area of the triangle with sides $MA,MB,MC$. Prove that $S'\leq \frac{1}{3}S$.
$$M$$ is a point in an equilateral triangle $$ABC$$ with the area $$S$$. Prove t... | college_math |
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"# I want to prove a property of confocal conics
Prove that if a circle centred at the focus of a confocal ellipse and hyperbola touches the ellipse internally, it touches the hyperbola at its vertex.
This question can be so... | college_math |
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"# diagonalization
Let $V$ be a finite-dimensional linear space over a field $K$, and $T:V\rightarrow V$ a linear transformation. To diagonalize $T$ is to find a basis of $V$ that consists of eigenvectors. The transformation ... | college_math |
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"# Bagging - Size of the aggregate bags?
I'm reading up on bagging (boostrap aggregation), and several sources seem to state that the size of the bags (consist of random sampling from our training set with replacement) is typ... | college_math |
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"# 1673. GauB in Elementary School
Johann Carl Friedrich GauB (1777 – 1855) was one of the most important German mathematicians. For those of you who remember the Deutsche Mark, a picture of him was printed on the 10 – DM bil... | college_math |
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"# Entire function which equals exponential on real axis
I need to find all entire functions $f$ such that $f(x) = e^x$ on $\mathbb{R}$.
At first it seems that, since the function $f$ will be real analytic on $\mathbb{R}$ an... | college_math |
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"Linear decomposition of positive semi-definite matrices
It is true that the vector space of $n\times n$ Hermitian matrices is an $n^2-$dimensional real vector space and that one can find a basis for this space consisting exc... | college_math |
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"The probability to match pair of socks [closed]
There is $n$ pairs of socks that each sock having one mate,each pair is different from another pair .
There is $2$ drawers: left drawer and right drawer.
All the left socks a... | college_math |
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"# Sum-product number
Sum-product number
A sum-product number is an integer that in a given base is equal to the sum of its digits times the product of its digits. Or, to put it algebraically, given an integer "n" that is ... | college_math |
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"# How to just show a part of lines inside a tabular
I am drawing a matrix as follows:
$\begin{tabular}{l|lllll|ll} & 0 & i & j & k & \ldots & x & y \\ \hline 0 & 0 & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots\\ i &... | college_math |
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"# Point set proof
1. Sep 14, 2012
### Zondrina
1. The problem statement, all variables and given/known data
Let A and B be subsets of ℝn with A0, B0 denoting the sets of interior points for A and B respectively. Prove tha... | college_math |
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"# Divisibility rule for 22
Divisibility rule for 22: Under what conditions a natural number $N$ is divisible by $22$ ?
My thought is
The divisibility rule for $22$ is that the number is divisible by $2$ and by $11$. Divisi... | college_math |
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"# Math Help - !Cluster Point <=> Convergent
1. ## !Cluster Point <=> Convergent
Suppose that the sequence $\{ x_n \}$ is in $\mathbb {R}$.
Prove that $\{ x_n \}$ converges if and only if it has a unique cluster point.
My ... | college_math |
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"# How to Solve Complicated Summations ?
As you all know the of sum of first $$n$$ natural numbers is given by the formula $$\dfrac{n(n + 1)}{2}$$, the sum of their squares is given by the formula $$\dfrac{n(n + 1)(2n + 1)}{6... | college_math |
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"The midpoint of line segment AB is (5,-3). The coordinates of point A are (m,n) and those of point B are (r,s). What is the value of m+n+r+s?
• The midpoint of line segment AB is (5,-3). The coordinates of point A are (m,n) ... | college_math |
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"## Hitting Baseballs and Blocking Swords
###Learning to Fight
When I was an undergraduate student, I used to fight with the Society of Creative Anachronism (SCA). I remember when I was first learning how to strike with a ra... | college_math |
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"# 8.2: Altitudes and orthocenter
An altitude of a triangle is a line thru a vertex and perpendicular to the line containing the opposite side. The term altitude may also be used for the distance from the vertex to its foot ... | college_math |
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"# Halmos Naive Set Theory - Set Inclusion Antisymmetric
In Chapter 1 of Halmos's Naive Set Theory, he mentions that
If $$A$$ and $$B$$ are sets such that $$A \subset B$$ and $$B \subset A$$, then A and B have the same eleme... | college_math |
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"Math Help - continuity question
1. continuity question
Show that $f(x)=x^n$ where $n \in \mathbb{N}$ is continuous on the interval $[a,b]$.
using the $\delta \ \varepsilon$ yields:
$\forall \ \delta>0, \ \varepsilon >0 \ ... | college_math |
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"# How many significant figures are there in the number 1008500?
Aug 20, 2016
$5$ significant figures
#### Explanation:
The first thing to look for when deciding how many significant figures you have in a value is the numb... | college_math |
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"# Contraharmonic mean
In mathematics, a contraharmonic mean is a function complementary to the harmonic mean. The contraharmonic mean is a special case of the Lehmer mean, $L_p$, where p=2.
## Definition
The contraharmonic... | college_math |
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"# Prove that sup(ST) = sup(S)sup(T)
Mr Davis 97
## Homework Statement
Prove the following: Suppose S and T are non-empty, bounded subsets of (0,+∞) and let ST be the set, ST = {st: s∈S and t∈T}. Then sup(ST) = sup(S) sup(T... | college_math |
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"Definitions
# Graph isomorphism
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H
$f colon V\left(G\right) to V\left(H\right) ,!$
such that any two vertices u and v of G are... | college_math |
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"# Definition:Axis of Solid Figure
## Definition
### Axis of Cone
Let $K$ be a right circular cone.
Let point $A$ be the apex of $K$.
Let point $O$ be the center of the base of $K$.
Then the line $AO$ is the axis of $K$.... | college_math |
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"To find the circumcenter of an acute triangle, we use the following definition of a circumcenter. The point where they intersect is the circumcenter. So, the slope of the perpendicular bisector = 1. Step 1 : The point of conc... | college_math |
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"Preliminaries Next: Constructing the Octonions Up: Introduction Previous: Introduction
## 1.1 Preliminaries
Before our tour begins, let us settle on some definitions. For us a vector space will always be a finite-dimensiona... | college_math |
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"# Basic conceptual question about angle between two vectors
1. Jun 26, 2013
### anniecvc
I know to find the angle between two vectors you would take the arccosine of the dot product of the two vectors divided by the magnit... | college_math |
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"However, your example is very nice. Transitive Closure – Let be a relation on set . That wouldn't be the transitive closure of the set then would it? site design / logo © 2020 Stack Exchange Inc; user contributions licensed u... | college_math |
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"# Divisible by 7
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• Aug 21st 2010, 04:09 PM
Plato
I might as well add to this.
Suppose that it is true for $K$, i.e. $3^{2K+1}+2^{K+2}}$ is divisible by $7$.
L... | college_math |
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"# Finding the point that maximizes a linear function
Consider $$N$$ two-dimensional points of the form $$(x_i, y_i)$$ where all $$x_i, y_i > 0$$ are positive integers. We will be given a workload of queries $$Q = \{c_1, \dot... | college_math |
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"# Geometric interpretation of the ratio of the sides of a triangle.
In right triangle trigonometry, the sine of an angle $A$ is defined as the ratio of two lengths, the opposite leg $a$ and the hypotenuse $c$, that's to say,... | college_math |
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"# Find an example of metric space
I need to find an example of a metric space , in which
${lim}_{n→∞} (1/n)$ it's different from $0$.
I took the set of real numbers with the discrete metric space $(R,d)$ in which this limi... | college_math |
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"# What's the fewest weights you need to balance any weight from 1 to 40 pounds?
Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a two-sided scale b... | college_math |
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"Time Limit : sec, Memory Limit : KB
English
## Estimating the Flood Risk
Mr. Boat is the owner of a vast extent of land. As many typhoons have struck Japan this year, he became concerned of flood risk of his estate and he w... | college_math |
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"# Thread: Geometric Proof
1. ## Geometric Proof
1. The vertex E of a square EFGH is inside a square ABCD. The vertices F, G and H are outside the square ABCD. The side EF meets the side CD at X and the side EH meets the sid... | college_math |
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"# Module homomorphism explained
In algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring R, then a function
f:M\toN
is called... | college_math |
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"You will also learn how to find the complex conjugate of a complex number. Its magnitude or length, denoted by $${\displaystyle \|x\|}$$, is most commonly defined as its Euclidean norm (or Euclidean length): 1 Parameters; 2 R... | college_math |
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