Question

$x^2+y^2-z^2=0$ is not a manifold in $\mathbb{R}^3$.

score 471 · Answer 1 · 2026-04-14 17:04:39

471

Views

$x^2+y^2-z^2=0$ is not a manifold in $\mathbb{R}^3$.

Published on 14 Apr 2026 - 17:04

score 530 · Answer 2 · 2026-04-15 22:39:17

530

Views

Prove that: $\sum\limits_{cyc}\frac{1}{\sqrt{2a^2+5ab+2b^2}} \geq\sqrt{\frac{3}{ab+ac+bc}}$

Published on 15 Apr 2026 - 22:39

score 85 · Answer 3 · 2026-04-12 13:36:32

85

Views

Largest dimension that the subspaces can have

Published on 12 Apr 2026 - 13:36

score 271 · Answer 4 · 2026-04-16 06:27:05

271

Views

Lemma 2.3. of Riemannian Geometry by do Carmo; Existence/Uniqueness of the Geodesic field $G$ on $TM$

Published on 16 Apr 2026 - 6:27

score 187 · Answer 5 · 2026-04-17 06:49:56

187

Views

If $f(x)=\frac{-8(1-\sqrt{1-x})^3}{x^2}$, then $f(f(x))=x$. Slick proof?

Published on 17 Apr 2026 - 6:49

score 306 · Answer 6 · 2026-04-13 16:58:38

306

Views

Union of collection of non-trivial intervals of $\mathbb{R}$ can be written as the union of a countable subset of that collection

Published on 13 Apr 2026 - 16:58

score 36 · Answer 7 · 2026-04-14 08:07:20

36

Views

Choose the right proof pattern

Published on 14 Apr 2026 - 8:07

score 61 · Answer 8 · 2026-04-14 00:51:03

61

Views

High school level proof for Euclid's GCD theorem

Published on 14 Apr 2026 - 0:51

score 124 · Answer 9 · 2026-04-09 02:33:45

124

Views

How to complete gcd number theory proof with induction?

Published on 09 Apr 2026 - 2:33

score 228 · Answer 10 · 2026-04-15 03:38:46

228

Views

Line segment in triangle is at most as long as the longest side

Published on 15 Apr 2026 - 3:38

score 77 · Answer 11 · 2026-04-10 04:13:34

77

Views

How to use Stewart theorem to prove this result?

Published on 10 Apr 2026 - 4:13

score 455 · Answer 12 · 2026-04-15 23:32:52

455

Views

Prove that $\sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} \ge ab + bc + ca$

Published on 15 Apr 2026 - 23:32

score 239 · Answer 13 · 2026-04-17 01:19:19

239

Views

Direct proof from AC that every vector space has a basis?

Published on 17 Apr 2026 - 1:19

score 348 · Answer 14 · 2026-04-14 14:33:12

348

Views

Prove $\displaystyle\sum_{-\infty}^0\text H(x)=\frac12\sum_0^\infty\frac{\text H_\frac x2-\text H_\frac{x-1}2}{x!}=\frac{\text{Ei}(2)-\text{Ei}(1)}e$

Published on 14 Apr 2026 - 14:33

score 134 · Answer 15 · 2026-04-16 05:52:42

134

Views

What is the proof for $\sqrt{mn} \neq \sqrt{m} \sqrt{n}$ for $m,n < 0$

Published on 16 Apr 2026 - 5:52

List Question

$x^2+y^2-z^2=0$ is not a manifold in $\mathbb{R}^3$.

Prove that: $\sum\limits_{cyc}\frac{1}{\sqrt{2a^2+5ab+2b^2}} \geq\sqrt{\frac{3}{ab+ac+bc}}$

Largest dimension that the subspaces can have

Lemma 2.3. of Riemannian Geometry by do Carmo; Existence/Uniqueness of the Geodesic field $G$ on $TM$

If $f(x)=\frac{-8(1-\sqrt{1-x})^3}{x^2}$, then $f(f(x))=x$. Slick proof?

Union of collection of non-trivial intervals of $\mathbb{R}$ can be written as the union of a countable subset of that collection

Choose the right proof pattern

High school level proof for Euclid's GCD theorem

How to complete gcd number theory proof with induction?

Line segment in triangle is at most as long as the longest side

How to use Stewart theorem to prove this result?

Prove that $\sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} \ge ab + bc + ca$

Direct proof from AC that every vector space has a basis?

Prove $\displaystyle\sum_{-\infty}^0\text H(x)=\frac12\sum_0^\infty\frac{\text H_\frac x2-\text H_\frac{x-1}2}{x!}=\frac{\text{Ei}(2)-\text{Ei}(1)}e$

What is the proof for $\sqrt{mn} \neq \sqrt{m} \sqrt{n}$ for $m,n < 0$

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