Question

Finding some ideas $\frac{2(a+b+c)}{abc}+3\ge \sqrt{4+\frac{5}{a^2}}+\sqrt{4+\frac{5}{b^2}}+\sqrt{4+\frac{5}{c^2}}$

score 79 · Answer 1 · 2023-12-11 11:57:14

79

Views

Finding some ideas $\frac{2(a+b+c)}{abc}+3\ge \sqrt{4+\frac{5}{a^2}}+\sqrt{4+\frac{5}{b^2}}+\sqrt{4+\frac{5}{c^2}}$

Published on 11 Dec 2023 - 11:57

score 129 · Answer 2 · 2023-12-13 16:43:32

129

Views

A quick, more elementary way to show $(\mathbb{Z}/16 \mathbb{Z})^{\times} \cong C_4 \times C_2$

Published on 13 Dec 2023 - 16:43

score 59 · Answer 3 · 2026-04-03 18:22:39

59

Views

Calculate the transitive interior and the transitive closure.

Published on 03 Apr 2026 - 18:22

score 104 · Answer 4 · 2023-12-14 00:25:22

104

Views

$AB=A^2+A+I_n$ for real square matrices then $AB=BA$

Published on 14 Dec 2023 - 0:25

score 93 · Answer 5 · 2023-12-16 18:57:41

93

Views

If A is a non singular matrix show that $(xA)^{-1} = \frac{1}{x}A^{-1}$

Published on 16 Dec 2023 - 18:57

score 138 · Answer 6 · 2023-12-19 07:28:34

138

Views

How to rigorously prove that $e^x = \sum\limits_{n=0}^ \infty \frac{x^n}{n!}$ without defining derivatives?

Published on 19 Dec 2023 - 7:28

score 119 · Answer 7 · 2026-04-02 09:51:14

119

Views

Are there alternatives to Rudin's proof that $\sup \{ p\in\mathbb{ Q}^+\mid p^2<2 \} =\sqrt 2$?

Published on 02 Apr 2026 - 9:51

score 1.2k · Answer 8 · 2023-12-25 20:05:23

1.2k

Views

Alternative proof that ring of functions does not contain any nontrivial multiple of the exponential function

Published on 25 Dec 2023 - 20:05

score 194 · Answer 9 · 2026-03-25 14:36:51

194

Views

Show that if $A \in M_{2 \times 2}(\mathbb{R})$ then $A, A^T$ are similar.

Published on 25 Mar 2026 - 14:36

score 99 · Answer 10 · 2026-03-30 10:16:29

99

Views

$\epsilon$-proof for convergent infinite product

Published on 30 Mar 2026 - 10:16

score 110 · Answer 11 · 2024-01-07 12:36:42

110

Views

$f(S)=S^{-1}$ is continuous where $S:E\rightarrow E$ is an isomorphism between Banach spaces.

Published on 07 Jan 2024 - 12:36

score 140 · Answer 12 · 2026-03-28 11:25:44

140

Views

Confusion about proof statement by implication

Published on 28 Mar 2026 - 11:25

score 71 · Answer 13 · 2024-01-09 20:33:46

71

Views

Can my approach for this 'verification by Induction' be simplified?

Published on 09 Jan 2024 - 20:33

score 186 · Answer 14 · 2026-02-23 11:42:54

186

Views

Locus of centroid, given the slopes of the sides

Published on 23 Feb 2026 - 11:42

score 39 · Answer 15 · 2026-03-29 05:34:04

39

Views

H-spaces and universal covering space

Published on 29 Mar 2026 - 5:34

List Question

Finding some ideas $\frac{2(a+b+c)}{abc}+3\ge \sqrt{4+\frac{5}{a^2}}+\sqrt{4+\frac{5}{b^2}}+\sqrt{4+\frac{5}{c^2}}$

A quick, more elementary way to show $(\mathbb{Z}/16 \mathbb{Z})^{\times} \cong C_4 \times C_2$

Calculate the transitive interior and the transitive closure.

$AB=A^2+A+I_n$ for real square matrices then $AB=BA$

If A is a non singular matrix show that $(xA)^{-1} = \frac{1}{x}A^{-1}$

How to rigorously prove that $e^x = \sum\limits_{n=0}^ \infty \frac{x^n}{n!}$ without defining derivatives?

Are there alternatives to Rudin's proof that $\sup \{ p\in\mathbb{ Q}^+\mid p^2<2 \} =\sqrt 2$?

Alternative proof that ring of functions does not contain any nontrivial multiple of the exponential function

Show that if $A \in M_{2 \times 2}(\mathbb{R})$ then $A, A^T$ are similar.

$\epsilon$-proof for convergent infinite product

$f(S)=S^{-1}$ is continuous where $S:E\rightarrow E$ is an isomorphism between Banach spaces.

Confusion about proof statement by implication

Can my approach for this 'verification by Induction' be simplified?

Locus of centroid, given the slopes of the sides

H-spaces and universal covering space

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