Question

Proving Altitudes of Triangle can never form a Triangle

score 189 · Answer 1 · 2026-03-27 10:34:19

189

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Proving Altitudes of Triangle can never form a Triangle

Published on 27 Mar 2026 - 10:34

score 285 · Answer 2 · 2026-03-30 09:45:11

285

Views

Elementwise inequality to norm inequality

Published on 30 Mar 2026 - 9:45

score 59 · Answer 3 · 2018-09-14 14:56:24

59

Views

Simple sum inequality proof

Published on 14 Sep 2018 - 14:56

score 85 · Answer 4 · 2026-03-25 23:40:28

85

Views

Prove that if $\ |x-x_0| < \frac ε2$ and $|y-y_0| < \frac ε2 $ then $|(x+y) - (x_0 + y_0)| < ε$ and $|(x-y) - (x_0 - y_0)| < ε$

Published on 25 Mar 2026 - 23:40

score 62 · Answer 5 · 2018-09-15 11:57:29

62

Views

Prove that $n (3^{1/n} - 1) > 1$ for $n \in \mathbb{N}$!

Published on 15 Sep 2018 - 11:57

score 159 · Answer 6 · 2026-03-25 04:42:38

159

Views

Why does proving inductively $n < 2^n$ for $n \geq 1$ imply it is true for real values of $n$?

Published on 25 Mar 2026 - 4:42

score 584 · Answer 7 · 2018-09-15 14:34:24

584

Views

Solving an inequality with multiple cases

Published on 15 Sep 2018 - 14:34

score 30 · Answer 8 · 2026-03-26 08:02:31

30

Views

Is it sufficient to show the following inequality holds to prove $2^{2^n} \in \Omega(n!)$?

Published on 26 Mar 2026 - 8:02

score 196 · Answer 9 · 2026-03-25 07:46:29

196

Views

$\frac {x_1^3}{y_1}+\frac {x_2^3}{y_3}+\ldots+\frac {x_n^3}{y_n}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x_1^2+x_2^2+\ldots+x_n^2) $

Published on 25 Mar 2026 - 7:46

score 75 · Answer 10 · 2026-03-25 19:11:22

75

Views

Using Supremum to prove $|x+y| \leq |x|+|y|$ vs. my proof

Published on 25 Mar 2026 - 19:11

score 77 · Answer 11 · 2018-09-15 19:38:52

77

Views

Triangle inequality with a condition

Published on 15 Sep 2018 - 19:38

score 71 · Answer 12 · 2026-03-25 23:36:30

71

Views

How to solve this rational inequality?

Published on 25 Mar 2026 - 23:36

score 48 · Answer 13 · 2026-03-27 17:06:26

48

Views

Difficulty in understanding a derivation : Asymptotic behaviour of binomial coeeficients

Published on 27 Mar 2026 - 17:06

score 162 · Answer 14 · 2026-03-25 21:49:35

162

Views

Comparing $\frac{(x+n)!}{x!}$ to $n!$

Published on 25 Mar 2026 - 21:49

score 127 · Answer 15 · 2026-03-25 01:40:04

127

Views

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

Published on 25 Mar 2026 - 1:40

List Question

Proving Altitudes of Triangle can never form a Triangle

Elementwise inequality to norm inequality

Simple sum inequality proof

Prove that if $\ |x-x_0| < \frac ε2$ and $|y-y_0| < \frac ε2 $ then $|(x+y) - (x_0 + y_0)| < ε$ and $|(x-y) - (x_0 - y_0)| < ε$

Prove that $n (3^{1/n} - 1) > 1$ for $n \in \mathbb{N}$!

Why does proving inductively $n < 2^n$ for $n \geq 1$ imply it is true for real values of $n$?

Solving an inequality with multiple cases

Is it sufficient to show the following inequality holds to prove $2^{2^n} \in \Omega(n!)$?

$\frac {x_1^3}{y_1}+\frac {x_2^3}{y_3}+\ldots+\frac {x_n^3}{y_n}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x_1^2+x_2^2+\ldots+x_n^2) $

Using Supremum to prove $|x+y| \leq |x|+|y|$ vs. my proof

Triangle inequality with a condition

How to solve this rational inequality?

Difficulty in understanding a derivation : Asymptotic behaviour of binomial coeeficients

Comparing $\frac{(x+n)!}{x!}$ to $n!$

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

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