Question

Proof of $\bigcup_{i\in I}A_i=\bigcup_{X\in\mathcal F}(\bigcup_{i\in X}A_i)$ and similar statements.

score 391 · Answer 1 · 2026-04-13 01:06:47

391

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Proof of $\bigcup_{i\in I}A_i=\bigcup_{X\in\mathcal F}(\bigcup_{i\in X}A_i)$ and similar statements.

Published on 13 Apr 2026 - 1:06

score 119 · Answer 2 · 2026-04-10 20:31:19

119

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Better methods to approximate $2^{2\over 3}$

Published on 10 Apr 2026 - 20:31

score 31 · Answer 3 · 2026-03-30 11:38:46

31

Views

A bound on the maximal singular value of a linear map which preserves an ellipse

Published on 30 Mar 2026 - 11:38

score 80 · Answer 4 · 2020-08-03 08:26:51

80

Views

Proving that $\int_{-1}^{1} \frac{\{x^3\}(x^4+1)}{(x^6+1)} dx=\frac{\pi}{3}$, where $\{.\}$ is positive fractional part

Published on 03 Aug 2020 - 8:26

score 278 · Answer 5 · 2020-08-03 11:21:56

278

Views

How to prove that $\frac{\cos(x)-\cos(2x)}{\sin(x)+\sin(2x)} = \frac{1-\cos(x)}{\sin(x)}$ in a simpler way.

Published on 03 Aug 2020 - 11:21

score 186 · Answer 6 · 2026-03-29 19:14:26

186

Views

Prove $( xy+2x+2y+1 ) ^{2} ( x+y+2 ) ^{2}\geqslant \frac14 [xy(x+y)+2(x^2+y^2)-18xy+5(x+y)+2 ] ^{2}+144xy ( {x}^{2}+{y}^{2}+2) $

Published on 29 Mar 2026 - 19:14

score 158 · Answer 7 · 2026-03-25 22:11:24

158

Views

Little result using RCF theorem and an inequality by Vasile Cirtoaje

Published on 25 Mar 2026 - 22:11

score 404 · Answer 8 · 2026-04-13 02:01:31

404

Views

Angular coefficient of the straight line tangent to the parabola at one of its points: alternative proof

Published on 13 Apr 2026 - 2:01

score 503 · Answer 9 · 2026-04-13 12:00:25

503

Views

$(\forall n \in \mathbb{Z}):n^{3} \equiv n$ (mod $6$)

Published on 13 Apr 2026 - 12:00

score 72 · Answer 10 · 2026-03-25 23:42:43

72

Views

Question about convexity: how do we prove that $\displaystyle \sum_{i=1}^{k}p_{i}b_{i}\geq\prod_{i=1}^{k}b^{p_{i}}_{i}$?

Published on 25 Mar 2026 - 23:42

score 497 · Answer 11 · 2026-04-12 16:49:22

497

Views

Proof of Cauchy-Schwarz in $\mathbb{R}^n$ using Law of Cosines

Published on 12 Apr 2026 - 16:49

score 172 · Answer 12 · 2026-03-29 12:41:17

172

Views

Visualising the sum of the first $n$ positive odd integers

Published on 29 Mar 2026 - 12:41

score 407 · Answer 13 · 2026-04-12 18:52:57

407

Views

Prove that there are no tournament with exactly two champions.

Published on 12 Apr 2026 - 18:52

score 93 · Answer 14 · 2026-04-13 12:44:04

93

Views

Normalizer of normalizer of Sylow p-subgroup

Published on 13 Apr 2026 - 12:44

score 570 · Answer 15 · 2020-08-14 10:17:26

570

Views

Proving that $\mathbb R$ is a regular topological space

Published on 14 Aug 2020 - 10:17

List Question

Proof of $\bigcup_{i\in I}A_i=\bigcup_{X\in\mathcal F}(\bigcup_{i\in X}A_i)$ and similar statements.

Better methods to approximate $2^{2\over 3}$

A bound on the maximal singular value of a linear map which preserves an ellipse

Proving that $\int_{-1}^{1} \frac{\{x^3\}(x^4+1)}{(x^6+1)} dx=\frac{\pi}{3}$, where $\{.\}$ is positive fractional part

How to prove that $\frac{\cos(x)-\cos(2x)}{\sin(x)+\sin(2x)} = \frac{1-\cos(x)}{\sin(x)}$ in a simpler way.

Prove $( xy+2x+2y+1 ) ^{2} ( x+y+2 ) ^{2}\geqslant \frac14 [xy(x+y)+2(x^2+y^2)-18xy+5(x+y)+2 ] ^{2}+144xy ( {x}^{2}+{y}^{2}+2) $

Little result using RCF theorem and an inequality by Vasile Cirtoaje

Angular coefficient of the straight line tangent to the parabola at one of its points: alternative proof

$(\forall n \in \mathbb{Z}):n^{3} \equiv n$ (mod $6$)

Question about convexity: how do we prove that $\displaystyle \sum_{i=1}^{k}p_{i}b_{i}\geq\prod_{i=1}^{k}b^{p_{i}}_{i}$?

Proof of Cauchy-Schwarz in $\mathbb{R}^n$ using Law of Cosines

Visualising the sum of the first $n$ positive odd integers

Prove that there are no tournament with exactly two champions.

Normalizer of normalizer of Sylow p-subgroup

Proving that $\mathbb R$ is a regular topological space

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