List questions from alternative-proof

Published on 09 May 2023 - 22:55

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Consider the region $R=\{(x,y):x^{2}+y^{2} \leq 100, \sin (x+y)>0\}.$ What is the area of $R$?

Published on 10 May 2023 - 7:17

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How prove that $AD$ and $BC$ of the given convex quadrilateral are parallel?

Published on 29 Mar 2026 - 6:33

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Brezis' exercise 5.25.6: weak convergence of Cesàro mean

Published on 14 May 2023 - 15:23

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If $\int_0^t f(s) \, \mathrm d s = 0$ for a.e. $t \in (0, 1)$, then $f=0$ a.e.

Published on 16 May 2023 - 21:25

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Brezis' Exercise 5.30.4: an orthonormal basis of $L^2(0, 1)$

Published on 17 May 2023 - 14:48

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If $X$ and $Y$ are equipotent then the bijections set of $X$ into $X$ is equipotent to the bijections set of $Y$ into $Y$.

Published on 01 Apr 2026 - 21:35

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If $X=\{0,1\}$ then for any set $A,$ prove that $|X^A|= |P(A)|.$

Published on 22 May 2023 - 6:45

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Suppose $A$ and $B$ are two sets with $B\subset A.$ Let $f:A\to B$ be injective. Then show that $\exists$ a bijection $h:A\to B.$

Published on 22 May 2023 - 7:32

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Solving a counting problem by correcting an estimate

Published on 23 May 2023 - 20:25

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Proof verification for $(2n)! ≥ 2^n (n!)^2$

Published on 24 May 2023 - 7:38

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Prove that $f(x) := e^{x^2/2}-x \ge 0$ for all $x$

Published on 27 May 2023 - 16:29

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Uniform convergence of heat kernel

Published on 28 May 2023 - 15:26

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Uniform convergence of the Laplacian of heat kernel

Published on 29 Mar 2026 - 3:35

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Trace of symmetric power of a matrix explanation

Published on 29 May 2023 - 9:17

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Proof for trick to multiply fast

Consider the region $R=\{(x,y):x^{2}+y^{2} \leq 100, \sin (x+y)>0\}.$ What is the area of $R$?

How prove that $AD$ and $BC$ of the given convex quadrilateral are parallel?

Brezis' exercise 5.25.6: weak convergence of Cesàro mean

If $\int_0^t f(s) \, \mathrm d s = 0$ for a.e. $t \in (0, 1)$, then $f=0$ a.e.

Brezis' Exercise 5.30.4: an orthonormal basis of $L^2(0, 1)$

If $X$ and $Y$ are equipotent then the bijections set of $X$ into $X$ is equipotent to the bijections set of $Y$ into $Y$.

If $X=\{0,1\}$ then for any set $A,$ prove that $|X^A|= |P(A)|.$

Suppose $A$ and $B$ are two sets with $B\subset A.$ Let $f:A\to B$ be injective. Then show that $\exists$ a bijection $h:A\to B.$

Solving a counting problem by correcting an estimate

Proof verification for $(2n)! ≥ 2^n (n!)^2$

Prove that $f(x) := e^{x^2/2}-x \ge 0$ for all $x$

Uniform convergence of heat kernel

Uniform convergence of the Laplacian of heat kernel

Trace of symmetric power of a matrix explanation

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