Question

Quick proof: orthogonal matrix commuting with special orthogonal matrix is special orthogonal

score 139 · Answer 1 · 2026-04-14 08:13:26

139

Views

Quick proof: orthogonal matrix commuting with special orthogonal matrix is special orthogonal

Published on 14 Apr 2026 - 8:13

score 150 · Answer 2 · 2026-04-15 23:27:31

150

Views

At least 3 points on the convex hull

Published on 15 Apr 2026 - 23:27

score 59 · Answer 3 · 2026-04-17 10:33:33

59

Views

Finding Subspaces $U, V, W < \mathbb{R}^4$ such that $\mathbb{R}^4 = U \oplus V = U \oplus W = V \oplus W$

Published on 17 Apr 2026 - 10:33

score 494 · Answer 4 · 2026-04-09 02:50:55

494

Views

is proof by contradiction essential for proving the Pigeonhole Principle?

Published on 09 Apr 2026 - 2:50

score 220 · Answer 5 · 2026-04-14 16:55:37

220

Views

$f$ is a polynomial and $f(0)\neq0$. Why is $fg+x$ a perfect square for some $g$?

Published on 14 Apr 2026 - 16:55

score 117 · Answer 6 · 2026-04-16 20:49:04

117

Views

(Dis)prove $f(2\sqrt{xy}+\frac{1}{3xy}(\exp(\frac{\ln(xy(x-y)^{2}+1)}{xy(x-y)^{2}+1})-1))-\frac{xy}{1-x-y}\ge 0$

Published on 16 Apr 2026 - 20:49

score 90 · Answer 7 · 2026-04-14 09:40:18

90

Views

For which values $k \in \mathbb{R}$ does $kz - \tan z$ have non-real roots?

Published on 14 Apr 2026 - 9:40

score 131 · Answer 8 · 2026-04-15 20:32:07

131

Views

Is there a valid proof of one-to-one correspondence b/n the real interval $(0, 1]$ and the nonterminating decimal expansions $0.d_1 d_2 d_3 …$?

Published on 15 Apr 2026 - 20:32

score 314 · Answer 9 · 2026-04-17 04:35:23

314

Views

Evaluating $\int_0^1\frac{\ln^2(1+x)+2\ln(x)\ln(1+x^2)}{1+x^2}dx$

Published on 17 Apr 2026 - 4:35

score 83 · Answer 10 · 2026-04-14 05:01:24

83

Views

Proof about concave decreasing function with some constraints

Published on 14 Apr 2026 - 5:01

score 71 · Answer 11 · 2026-04-13 15:06:49

71

Views

Is there a simplified 4-color proof for pixilated maps?

Published on 13 Apr 2026 - 15:06

score 946 · Answer 12 · 2026-04-10 16:27:12

946

Views

Is this alternative proof that $\sqrt 2$ is irrational sound?

Published on 10 Apr 2026 - 16:27

score 33 · Answer 13 · 2026-04-13 07:35:24

33

Views

Correctness of method - if $\{ y_n \} $ is unbounded, prove $\{ y_n z_n\} $ does not converge to $0$

Published on 13 Apr 2026 - 7:35

score 272 · Answer 14 · 2026-04-14 20:28:34

272

Views

Given a sequence with $a_1=1$ and $a_{n+1}=a_n-\frac13a_n^2$. Is there an easier way to get an upper bound of $1/a_{100}$?

Published on 14 Apr 2026 - 20:28

score 92 · Answer 15 · 2026-04-16 01:30:14

92

Views

What are some elementary ways to show that there's no solution to $\pm1 \pm 2 \pm 3\dots \pm n =0$ for $n \equiv 1,2 \ \, (\bmod 4\,)$?

Published on 16 Apr 2026 - 1:30

List Question

Quick proof: orthogonal matrix commuting with special orthogonal matrix is special orthogonal

At least 3 points on the convex hull

Finding Subspaces $U, V, W < \mathbb{R}^4$ such that $\mathbb{R}^4 = U \oplus V = U \oplus W = V \oplus W$

is proof by contradiction essential for proving the Pigeonhole Principle?

$f$ is a polynomial and $f(0)\neq0$. Why is $fg+x$ a perfect square for some $g$?

(Dis)prove $f(2\sqrt{xy}+\frac{1}{3xy}(\exp(\frac{\ln(xy(x-y)^{2}+1)}{xy(x-y)^{2}+1})-1))-\frac{xy}{1-x-y}\ge 0$

For which values $k \in \mathbb{R}$ does $kz - \tan z$ have non-real roots?

Is there a valid proof of one-to-one correspondence b/n the real interval $(0, 1]$ and the nonterminating decimal expansions $0.d_1 d_2 d_3 …$?

Evaluating $\int_0^1\frac{\ln^2(1+x)+2\ln(x)\ln(1+x^2)}{1+x^2}dx$

Proof about concave decreasing function with some constraints

Is there a simplified 4-color proof for pixilated maps?

Is this alternative proof that $\sqrt 2$ is irrational sound?

Correctness of method - if $\{ y_n \} $ is unbounded, prove $\{ y_n z_n\} $ does not converge to $0$

Given a sequence with $a_1=1$ and $a_{n+1}=a_n-\frac13a_n^2$. Is there an easier way to get an upper bound of $1/a_{100}$?

What are some elementary ways to show that there's no solution to $\pm1 \pm 2 \pm 3\dots \pm n =0$ for $n \equiv 1,2 \ \, (\bmod 4\,)$?

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