# All Questions

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### Dense subset of the Cantor set

Prove that the set of endpoints of removed intervals in the Cantor middle thirds set is a dense subset of the Cantor set. Attempt at proof: Since each subinterval is of length $(1/3)^n$, any ...
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### Modular Arithmetic on Circle

On the unit circle, what does the set $\left \{ n \bmod{2\pi}:n \in \mathbb{N}\right \}$ represent? What is the subsequentieal limits of $\left \{ \sin(n) \right \}_{n\in \mathbb{N}}$? I am probably ...
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### characteristics proyections of a PDE

Let $u(x,y)$ by the integral surface of the equation: $a(x,y)u_x+b(x,y)u_y+u=0$ Where $a,b$ are positives differential function in the hole plane. Let $D=\{(x,y)||x|<1 ,|y|<1\}$ How do I ...
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### Maximum number of truths in an optimized truth table.

I have a math-related question: I have a set of predicates that need to be evaluated. These predicates can have two kinds of operators; AND/OR. When such an expression is constructed my code builds ...
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### Solutions of Diophantine equations ${x^y} = {y^x}$ [duplicate]

Possible Duplicate: $x^y = y^x$ for integers $x$ and $y$ How to prove that $(2,4)$ and $(4,2)$ are the only solutions of Diophantine equations ${x^y} = {y^x}$ for $x \ne y$?
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### $x^n-x$ and some irreducible factors properties over $K[x]$

Let $K$ be a field , $a\in K$ , let $d$ be the greatest common divisor, of all the irreducible factors of $x^n-a$ in $K[x]$. $i)$ Prove that $d|n$ , and there exist $b\in K$ , such that $a^d =b^n$. ...
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### Chracterizing quartic polynomials F such that $F, F',F''$ have only real rational roots.

When designing friendly problems for a calculus class one comes up with such a question. (The cubic case is relatively easy.) Of course one can generalize: Characterize degree $n$ polynomials such ...
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### How to show that this logical argument is valid?

I am asked to show the following argument is valid: I know you need to use the rules of inference like modus ponens/converse fallacy but I'm confused because it doesn't look like any of the forms ...
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### Epsilon Delta Limit Proofs at and going to infinity.

So I understand the concept of epsilon delta limit proofs with linear functions, easy enough, and I am still shaky about doing it with non linear but I am slowly understanding that. I don't quite ...
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### {Thinking}: Why equivalent percentage increase of A and decrease of B is not the same end result?

original post the examples here are, the most important word -- fundamentally -- the same. example1: the most abstract way to present this example. Why equivalent % increase of A in event1 and % ...
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### Unions and intersections of compact subsets

I'd really appreciate some input on these two proofs regarding unions and intersections of compact subsets (under additional necessary conditions). Namely, are my proofs valid? Could they be ...
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### Find an ellipse whose length is the same as the outer rim of the monkey saddle

Given the monkey saddle $z=x^3-3xy^2$ over the unit circle $x^2+y^2 \leq 1$, find an ellipse whose length is the same as the length of the outer edge of the monkey saddle. I've already found a ...
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### Simplex Tableaux Problem

I have the following LP which I need to solve using the simplex method. I know there are no feasible solutions as there are constricting constraints. How do I use the Tableaux method to show this? ...
### On the eigenvalues of the square of a real matrix $A$
I just read this snippet in a textbook "The eigenvalues of a symmetric real matrix are real (The proof follows by noting that if $A$ is symmetric, the eigenvalues of $A^TA$ are the ...
If $A\cap B = B\cap C$, then $(A-B)\cup C = A\cup (C-B)$. Are the two statements at the end equivalent?