# All Questions

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### Prove that $G$ is finite and $|G|$ is prime.

Suppose $G\neq\{e\}$ is a group whose only subgroups are $\{e\}$ and G. Prove that $G$ is finite and $|G|$ is prime. In regards to the prime part, I believe that we can simply apply Lagrange's ...
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### Triangle rotating freely around origo, need to calculate corners.

Lets say I have a triangle with corners $(-1, -2)$, $(0, 2)$ and $(1, -2)$. I specify a line that is exactly one side of the triangle, for example $(-1, -2)$, $(0, 2)$. Now, I rotate the triangle ...
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### Binomial PMF not working! (real world application)

So I calculated the probability of an event k to be p(k) = (s+.005/n + 2), where s is number of times k has happened, n is number of trials that have happened I try to determine what the chances of ...
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### Do we need to formally teach the Greek Alphabet? [closed]

This is a question that I am purely interested in because I think we never thought about this before in Mathematics education... or even so was not discussed. When did we learn the Greek alphabets ...
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### Given two matrices to find one way to write a determinant

Given two matrices (2X2) with AB=BA,I was wondering if there is a way to decompose this expression $$xA^2+yAB+zB^2$$
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### Cardinality for all rational strongly increasing sequences

What is the cardinality for all rational strongly increasing sequences? Using diagonalization, I can show easily that for each list $f_n$ of sequnces, we can present a sequence which is not in ...
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### PDE characteristics.

I have solved the following equation using characteristics: $$u_{xx}+2u_{xy}-3u_{yy}=0$$ and obtained the characteristics: $$\xi=x+y$$ $$\eta=x-\frac{1}{3}y$$ I have determined the general solution to ...
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### what is the probability of a couple who has four girls and is trying again for a boy. what is the probability that the next kid will be a girl?

A couple has four kids already, all girls. the couple would like to have a son and would like to give it another try. what is the probability that the next kid will be a girl?
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### Let $A\subset X$; let $f:A\to Y$ be continuous; let $Y$ be Hausdorff. Is there an example where there is no continuous function for $g$?

Let $A\subset X$; let $f:A\to Y$ be continuous; let $Y$ be Hausdorff. Show that if $f$ may be extended to a continuous function $g:\mathrm{cl}(A)\to Y$, then $g$ is uniquely determined by $f$. Is ...
### Let $V$ be a vector space over a field $\mathbb F$. Show $0 \in \mathbb F$ is the only element : $\alpha v = 0 \in V, \alpha \in \mathbb F, v \neq 0$
Let $V$ be a vector space over a field $\mathbb F$. Show $0 \in \mathbb F$ is the only element : $\alpha v = 0 \in V, \alpha \in \mathbb F, v \neq 0$. Is this statement true ? I know in a field ...