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Your favourite application of the Baire Category Theorem

$\pi$ in arbitrary metric spaces

Cute Determinant Question

Mathematicians don't quit, they fade away [closed]

Differential equations and Fourier and Laplace transforms

How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$?

Tensors: Acting on Vectors vs Multilinear Maps

Sum of open/closed/compact sets in $\mathbb{R}^n$ open/closed/compact

How to evaluate $\sum_{\gcd (p,q)=1} \frac{1}{p^2q^2}$?

Proving $~\prod~\frac{\cosh\left(n^2+n+\frac12\right)+i\sinh\left(n+\frac12\right)}{\cosh\left(n^2+n+\frac12\right)-i\sinh\left(n+\frac12\right)}~=~i$

How do I solve this exponential equation? $5^{x}-4^{x}=3^{x}-2^{x}$ [closed]

Prove the following series $\sum\limits_{s=0}^\infty \frac{1}{(sn)!}$ [duplicate]

Let $f:[1,10]\to \Bbb{Q}$ be a continuous function and $f(1)=10,$then $f(10)=?$

Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$

Finite Messy Trigonometric Sum

Proving that $\sum_{i = 0}^{m}{\binom{k+i}{k} \binom{n-i}{n-m}} = \binom{n+k+1}{m}$

Determining the Jordan Canonical Form $18\times 18$ matrix

Is it possible to extend $f(z)=\frac{\Re(z)}{|z|}$ by continuity at $z=0$?

Extremizing a functional subject to an equality constraint

Convergence of the series: $\sum_{n=2}^{\infty}\frac{1}{n^2(\ln n)^2\left | \sin(n\pi\sqrt{2}) \right |}$

For $z=f(x,y)$ with $(x,y)=(r\cos\theta,r\sin\theta)$, show that $z_{xx}+z_{yy}=z_{rr}+ \frac{1}{r^2}z_{\theta \theta} + \frac{1}{r} z_r$

orthogonality for all even-ordered terms polynomial

Suppose $A,B\subseteq [0,1]$ are Lebesgue measurable with measure of at least $1/2$.

Question about a double summation

Approximating the number $e$ through computer simulation - mathematical background

what sample size is necessary for 95% CI?

Which of the choices solution of the Cauchy problem? [duplicate]

Consider the increasing, concave function $x^{0.5}$ on $[0, 1]$.

Shortest distance between $\frac{x^2}{25}+\frac{y^2}{16}+\frac{z^2}9=1$ and $x^2+y^2+z^2=4$ by the calculus of variations