Question

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

score 239 · Answer 1 · 2020-08-17 14:06:28

239

Views

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

Published on 17 Aug 2020 - 14:06

score 46 · Answer 2 · 2020-08-28 18:32:48

46

Views

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

Published on 28 Aug 2020 - 18:32

score 205 · Answer 3 · 2020-08-29 16:31:41

205

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 29 Aug 2020 - 16:31

score 88 · Answer 4 · 2020-09-01 11:28:45

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

score 75 · Answer 5 · 2020-09-03 06:41:46

75

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 03 Sep 2020 - 6:41

score 67 · Answer 6 · 2020-09-05 03:55:43

67

Views

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

Published on 05 Sep 2020 - 3:55

score 288 · Answer 7 · 2020-09-06 14:50:07

288

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 06 Sep 2020 - 14:50

score 169 · Answer 8 · 2020-09-07 13:42:10

169

Views

Hamming distance triangle inequality

Published on 07 Sep 2020 - 13:42

score 88 · Answer 9 · 2020-09-09 20:22:16

88

Views

How do I prove triangle inequality for this metric?

Published on 09 Sep 2020 - 20:22

score 103 · Answer 10 · 2020-09-10 11:48:55

103

Views

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

Published on 10 Sep 2020 - 11:48

score 49 · Answer 11 · 2020-09-14 02:49:57

49

Views

How to prove the following using triangle inequality?

Published on 14 Sep 2020 - 2:49

score 360 · Answer 12 · 2020-09-15 06:49:34

360

Views

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

Published on 15 Sep 2020 - 6:49

score 103 · Answer 13 · 2020-09-23 18:30:41

103

Views

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

Published on 23 Sep 2020 - 18:30

score 44 · Answer 14 · 2020-09-24 16:42:00

44

Views

Triangle inequality for tensor products

Published on 24 Sep 2020 - 16:42

score 56 · Answer 15 · 2020-09-26 08:45:20

56

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 26 Sep 2020 - 8:45

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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