Question

Show that $\rho$ satisfies triangle inequality.

score 94 · Answer 1 · 2026-04-10 08:56:58

94

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Show that $\rho$ satisfies triangle inequality.

Published on 10 Apr 2026 - 8:56

score 1.8k · Answer 2 · 2026-02-24 01:49:44

1.8k

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Parallelogram equality implies norm is induced by inner product

Published on 24 Feb 2026 - 1:49

score 306 · Answer 3 · 2026-02-24 01:54:40

306

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Prove that if $a,b,c$ are sides of a triangle and $s$ is the semi-perimeter, then $a^2+b^2+c^2 \geq \dfrac{36}{35}\bigg(s^2 + \dfrac{abc}{s}\bigg)$

Published on 24 Feb 2026 - 1:54

score 300 · Answer 4 · 2026-02-24 01:52:08

300

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Is the triangle inequality preserved when taking the minimum of both sides?

Published on 24 Feb 2026 - 1:52

score 52 · Answer 5 · 2026-04-11 11:48:08

52

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Why does this inequality involving norms hold?

Published on 11 Apr 2026 - 11:48

score 138 · Answer 6 · 2026-04-09 04:52:38

138

Views

Geometry Problem from Olympiad book

Published on 09 Apr 2026 - 4:52

score 30 · Answer 7 · 2026-04-11 03:23:21

30

Views

Metric of a sequence (triangle inequality)

Published on 11 Apr 2026 - 3:23

score 263 · Answer 8 · 2026-04-10 21:28:17

263

Views

Prove the metric of $\ell_2$ satisfies the triangle-inequality

Published on 10 Apr 2026 - 21:28

score 105 · Answer 9 · 2026-02-24 01:53:52

105

Views

$2\sum_{i,j} |x_i-y_j| \geq \sum_{i,j} (|x_i-x_j| + |y_i-y_j|)$?

Published on 24 Feb 2026 - 1:53

score 77 · Answer 10 · 2026-02-24 01:50:38

77

Views

Is there an inequality that involves $\|x+y\|$ and $\|x\|\|y\|$?

Published on 24 Feb 2026 - 1:50

score 71 · Answer 11 · 2026-04-09 01:30:06

71

Views

How does the triangle inequality prove continuous?

Published on 09 Apr 2026 - 1:30

score 23 · Answer 12 · 2026-02-24 01:55:15

23

Views

In a direction iterative method $x^{k+1}=x^k + d^k$ can one conclude that there is no limit point if $d^k$ is bounded away from zero?

Published on 24 Feb 2026 - 1:55

score 272 · Answer 13 · 2026-02-24 01:54:40

272

Views

Let $z_1,z_2$ be complex numbers with $|z_1|=|z_2|=1$. Prove that $|z_1 + 1| + |z_2 + 1| + |z_1z_2 + 1| \geq 2$

Published on 24 Feb 2026 - 1:54

score 472 · Answer 14 · 2026-04-11 19:04:02

472

Views

When does the norm of the sum of $n$ vectors equal the sum of the norms of the vectors?

Published on 11 Apr 2026 - 19:04

score 70 · Answer 15 · 2026-04-09 12:08:37

70

Views

Bounding an integral involving tail probabilities

Published on 09 Apr 2026 - 12:08

List Question

Show that $\rho$ satisfies triangle inequality.

Parallelogram equality implies norm is induced by inner product

Prove that if $a,b,c$ are sides of a triangle and $s$ is the semi-perimeter, then $a^2+b^2+c^2 \geq \dfrac{36}{35}\bigg(s^2 + \dfrac{abc}{s}\bigg)$

Is the triangle inequality preserved when taking the minimum of both sides?

Why does this inequality involving norms hold?

Geometry Problem from Olympiad book

Metric of a sequence (triangle inequality)

Prove the metric of $\ell_2$ satisfies the triangle-inequality

$2\sum_{i,j} |x_i-y_j| \geq \sum_{i,j} (|x_i-x_j| + |y_i-y_j|)$?

Is there an inequality that involves $\|x+y\|$ and $\|x\|\|y\|$?

How does the triangle inequality prove continuous?

In a direction iterative method $x^{k+1}=x^k + d^k$ can one conclude that there is no limit point if $d^k$ is bounded away from zero?

Let $z_1,z_2$ be complex numbers with $|z_1|=|z_2|=1$. Prove that $|z_1 + 1| + |z_2 + 1| + |z_1z_2 + 1| \geq 2$

When does the norm of the sum of $n$ vectors equal the sum of the norms of the vectors?

Bounding an integral involving tail probabilities

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