Question

Show that if $a,b \in \mathbb{R}^n$, then $|||a|| - ||b||| \leqslant ||a+b||$

score 240 · Answer 1 · 2026-02-23 15:09:12

240

Views

Show that if $a,b \in \mathbb{R}^n$, then $|||a|| - ||b||| \leqslant ||a+b||$

Published on 23 Feb 2026 - 15:09

score 47 · Answer 2 · 2026-02-23 15:10:40

47

Views

Do these points lie on one line of this metric space?

Published on 23 Feb 2026 - 15:10

score 206 · Answer 3 · 2026-02-23 15:11:13

206

Views

Sides $\frac{|b - c|}{\sqrt{(b^2 + 1)(c^2 + 1)}}, \frac{|c - a|}{\sqrt{(c^2 + 1)(a^2 + 1)}}, \frac{|a - b|}{\sqrt{(a^2 + 1)(b^2 + 1)}}$ of a triangle.

Published on 23 Feb 2026 - 15:11

score 89 · Answer 4 · 2026-02-23 15:11:13

Alternate Triangle Inequality: Instead of $\Big|\,|x| - |y|\,\Big| \leq |x-y|$ can we use $|x| - |y| \leq |x-y|$?

score 76 · Answer 5 · 2026-02-23 15:09:44

76

Views

Show that $|a| + |b| + |c| \leq |a - |b - c|| + |b - |c - a|| + |c - |a - b||$ where $a, b, c \in \mathbb{R}$ and $a + b + c = 0$

Published on 23 Feb 2026 - 15:09

score 68 · Answer 6 · 2026-02-23 15:11:06

68

Views

$X$ is a subset of $\mathbb{R}$. Prove that $|x-2|<c$ for all $x$ that are elements of $X$.

Published on 23 Feb 2026 - 15:11

score 289 · Answer 7 · 2026-02-23 15:11:12

289

Views

Why did the text only check the case in which the sum of the lengths of the two shortest sides is jot greater than the length of the longest side?

Published on 23 Feb 2026 - 15:11

score 170 · Answer 8 · 2026-02-23 15:03:21

170

Views

Hamming distance triangle inequality

Published on 23 Feb 2026 - 15:03

score 90 · Answer 9 · 2026-04-11 10:15:08

90

Views

How do I prove triangle inequality for this metric?

Published on 11 Apr 2026 - 10:15

score 104 · Answer 10 · 2026-02-23 15:11:06

104

Views

If $P(z)$ is a polynomial, then $|P(z)|>\frac{1}{2}a_nR^n$ when $|z|>R$

Published on 23 Feb 2026 - 15:11

score 52 · Answer 11 · 2026-04-09 02:39:34

52

Views

How to prove the following using triangle inequality?

Published on 09 Apr 2026 - 2:39

score 361 · Answer 12 · 2026-02-23 15:09:22

361

Views

Find the smallest value for sum of square roots? (2008 AMC Senior)

Published on 23 Feb 2026 - 15:09

score 104 · Answer 13 · 2026-02-23 15:07:44

104

Views

Prove that $|x| + |y| \le |x-y| + |x+y| $

Published on 23 Feb 2026 - 15:07

score 47 · Answer 14 · 2026-04-08 19:43:19

47

Views

Triangle inequality for tensor products

Published on 08 Apr 2026 - 19:43

score 57 · Answer 15 · 2026-02-23 15:11:06

57

Views

Given $|b-c|\leq a\leq b+c$ show that $\frac{a}{1+a}\leq\frac{b}{1+b}+\frac{c}{1+c}$

Published on 23 Feb 2026 - 15:11

List Question

Show that if $a,b \in \mathbb{R}^n$, then $|||a|| - ||b||| \leqslant ||a+b||$

Do these points lie on one line of this metric space?

Sides $\frac{|b - c|}{\sqrt{(b^2 + 1)(c^2 + 1)}}, \frac{|c - a|}{\sqrt{(c^2 + 1)(a^2 + 1)}}, \frac{|a - b|}{\sqrt{(a^2 + 1)(b^2 + 1)}}$ of a triangle.

Alternate Triangle Inequality: Instead of $\Big|\,|x| - |y|\,\Big| \leq |x-y|$ can we use $|x| - |y| \leq |x-y|$?

Show that $|a| + |b| + |c| \leq |a - |b - c|| + |b - |c - a|| + |c - |a - b||$ where $a, b, c \in \mathbb{R}$ and $a + b + c = 0$

$X$ is a subset of $\mathbb{R}$. Prove that $|x-2|<c$ for all $x$ that are elements of $X$.

Why did the text only check the case in which the sum of the lengths of the two shortest sides is jot greater than the length of the longest side?

Hamming distance triangle inequality

How do I prove triangle inequality for this metric?

If $P(z)$ is a polynomial, then $|P(z)|>\frac{1}{2}a_nR^n$ when $|z|>R$

How to prove the following using triangle inequality?

Find the smallest value for sum of square roots? (2008 AMC Senior)

Prove that $|x| + |y| \le |x-y| + |x+y| $

Triangle inequality for tensor products

Given $|b-c|\leq a\leq b+c$ show that $\frac{a}{1+a}\leq\frac{b}{1+b}+\frac{c}{1+c}$

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