Question

Show that $\rho$ satisfies triangle inequality.

score 92 · Answer 1 · 2021-07-13 06:14:03

92

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Show that $\rho$ satisfies triangle inequality.

Published on 13 Jul 2021 - 6:14

score 1.8k · Answer 2 · 2021-07-20 22:27:20

1.8k

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Parallelogram equality implies norm is induced by inner product

Published on 20 Jul 2021 - 22:27

score 305 · Answer 3 · 2021-07-21 12:01:16

305

Views

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 21 Jul 2021 - 12:01

score 299 · Answer 4 · 2021-07-24 21:22:44

299

Views

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

Published on 24 Jul 2021 - 21:22

score 49 · Answer 5 · 2021-07-29 08:42:17

49

Views

Why does this inequality involving norms hold?

Published on 29 Jul 2021 - 8:42

score 135 · Answer 6 · 2021-08-08 07:50:21

135

Views

Geometry Problem from Olympiad book

Published on 08 Aug 2021 - 7:50

score 28 · Answer 7 · 2021-08-12 11:19:43

28

Views

Metric of a sequence (triangle inequality)

Published on 12 Aug 2021 - 11:19

score 261 · Answer 8 · 2021-08-12 11:52:37

261

Views

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

Published on 12 Aug 2021 - 11:52

score 104 · Answer 9 · 2021-08-16 12:11:33

104

Views

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

Published on 16 Aug 2021 - 12:11

score 76 · Answer 10 · 2021-08-23 13:39:38

76

Views

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

Published on 23 Aug 2021 - 13:39

score 68 · Answer 11 · 2021-08-29 17:19:35

68

Views

How does the triangle inequality prove continuous?

Published on 29 Aug 2021 - 17:19

score 22 · Answer 12 · 2021-09-07 17:31:03

22

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 07 Sep 2021 - 17:31

score 271 · Answer 13 · 2021-09-09 06:51:00

271

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 09 Sep 2021 - 6:51

score 470 · Answer 14 · 2021-09-10 00:59:26

470

Views

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

Published on 10 Sep 2021 - 0:59

score 69 · Answer 15 · 2026-02-23 08:00:09

69

Views

Bounding an integral involving tail probabilities

Published on 23 Feb 2026 - 8:00

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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