Question

Show the $d_p(x,y)$ is not a metric on $\mathbb{R}^2$

score 350 · Answer 1 · 2021-09-27 20:04:28

350

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Show the $d_p(x,y)$ is not a metric on $\mathbb{R}^2$

Published on 27 Sep 2021 - 20:04

score 155 · Answer 2 · 2021-09-29 03:30:53

155

Views

How to Prove $\lim_{(x, y) \rightarrow (0, 0)}\frac{x^3-y^3}{x^2+y^2}=0$

Published on 29 Sep 2021 - 3:30

score 121 · Answer 3 · 2021-10-01 17:00:36

121

Views

Triangle Equality is Equal When...

Published on 01 Oct 2021 - 17:00

score 188 · Answer 4 · 2021-10-04 06:13:42

188

Views

How can we visualize $a^2+b^2-c^2$ for a triangle of sides $a$, $b$, $c$?

Published on 04 Oct 2021 - 6:13

score 177 · Answer 5 · 2021-10-11 10:59:24

177

Views

How to prove cosine distance does not satisfy triangle inequality metric in Euclidean space

Published on 11 Oct 2021 - 10:59

score 90 · Answer 6 · 2021-10-22 15:32:59

90

Views

Proving $|a| + |b| \leq |a+b| + |a-b|$ using the Triangle Inequality

Published on 22 Oct 2021 - 15:32

score 18 · Answer 7 · 2021-11-01 15:04:59

18

Views

Proving triangle inequality for general vectors.

Published on 01 Nov 2021 - 15:04

score 91 · Answer 8 · 2021-11-02 16:50:37

91

Views

Is $d(x, y)={(\sum_{i=1}^{n}{|{x_i} -{y_i}|}^p})^{1/p}$ , $x, y\in\mathbb{R^n}$, $0<p<1$ metric on $\mathbb{R^n}$?

Published on 02 Nov 2021 - 16:50

score 43 · Answer 9 · 2021-11-09 16:26:01

43

Views

Is the function $f(x) =(\sum_{i=1}^{2}{|x_i|^{1/2}})^2$ , where $x=(x_1, x_2)\in {\mathbb{R^2}}$ a norm on $\mathbb{R^2}$?

Published on 09 Nov 2021 - 16:26

score 63 · Answer 10 · 2021-11-16 21:54:38

63

Views

Find the greatest values of |z| such that |z-4/z|=2. Solution without triangle inequality

Published on 16 Nov 2021 - 21:54

score 492 · Answer 11 · 2021-11-20 15:20:05

492

Views

Is the proof $|d(x, A) - d(y, A) |\le d(x, y) $ in $(X, d) $ and $\emptyset \neq A \subset X$ and $x, y\in X$ logically perfect?

Published on 20 Nov 2021 - 15:20

score 101 · Answer 12 · 2021-11-26 15:56:22

101

Views

Is there a proof for triangle inequality in $\mathbb{R}$ by contradiction/absurd?

Published on 26 Nov 2021 - 15:56

score 112 · Answer 13 · 2021-12-17 02:11:05

112

Views

How do I prove that the inner product operator is a metric?

Published on 17 Dec 2021 - 2:11

score 597 · Answer 14 · 2022-01-04 09:05:56

597

Views

The Triangle Inequality implies that the shortest path between two points is a line segment. (in "Linear Algebra Done Right 3rd Edition" by Axler)

Published on 04 Jan 2022 - 9:05

score 31 · Answer 15 · 2022-01-24 14:28:32

31

Views

Inequality for two triangles with the same base

Published on 24 Jan 2022 - 14:28

List Question

Show the $d_p(x,y)$ is not a metric on $\mathbb{R}^2$

How to Prove $\lim_{(x, y) \rightarrow (0, 0)}\frac{x^3-y^3}{x^2+y^2}=0$

Triangle Equality is Equal When...

How can we visualize $a^2+b^2-c^2$ for a triangle of sides $a$, $b$, $c$?

How to prove cosine distance does not satisfy triangle inequality metric in Euclidean space

Proving $|a| + |b| \leq |a+b| + |a-b|$ using the Triangle Inequality

Proving triangle inequality for general vectors.

Is $d(x, y)={(\sum_{i=1}^{n}{|{x_i} -{y_i}|}^p})^{1/p}$ , $x, y\in\mathbb{R^n}$, $0<p<1$ metric on $\mathbb{R^n}$?

Is the function $f(x) =(\sum_{i=1}^{2}{|x_i|^{1/2}})^2$ , where $x=(x_1, x_2)\in {\mathbb{R^2}}$ a norm on $\mathbb{R^2}$?

Find the greatest values of |z| such that |z-4/z|=2. Solution without triangle inequality

Is the proof $|d(x, A) - d(y, A) |\le d(x, y) $ in $(X, d) $ and $\emptyset \neq A \subset X$ and $x, y\in X$ logically perfect?

Is there a proof for triangle inequality in $\mathbb{R}$ by contradiction/absurd?

How do I prove that the inner product operator is a metric?

The Triangle Inequality implies that the shortest path between two points is a line segment. (in "Linear Algebra Done Right 3rd Edition" by Axler)

Inequality for two triangles with the same base

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