Question

If $\left|z+1\right|=3$, determine the greatest and least possible values for $|z|$

score 109 · Answer 1 · 2020-09-28 14:46:48

109

Views

If $\left|z+1\right|=3$, determine the greatest and least possible values for $|z|$

Published on 28 Sep 2020 - 14:46

score 70 · Answer 2 · 2020-10-01 17:35:13

70

Views

If $d(A,B) = \inf_{a \in A, b \in B}{d(a,b)}$ , does $d(A, B) ≤ d(A, C) + d(C, B)? $

Published on 01 Oct 2020 - 17:35

score 90 · Answer 3 · 2020-10-01 19:16:05

90

Views

Does $\left\lVert (x,y) \right\rVert := \sqrt{x^2+y^2+xy} \phantom{1}$ satisfy the triangular inequality?

Published on 01 Oct 2020 - 19:16

score 54 · Answer 4 · 2020-10-02 09:40:02

54

Views

If $d$ is a metric in $X$ and $A \subset X$, does $\lvert d(x,A) - d(y,A) \rvert \le d(x,y) \phantom{5} \forall x, y \in X$?

Published on 02 Oct 2020 - 9:40

score 417 · Answer 5 · 2020-10-13 18:26:05

417

Views

Can any norm be used in a product metric

Published on 13 Oct 2020 - 18:26

score 63 · Answer 6 · 2020-10-19 16:12:34

63

Views

Proof that $2(a^4+b^4+c^4)<(a^2+b^2+c^2)^2$ if and only if line segments of length $a$,$b$ and $c$ form a triangle

Published on 19 Oct 2020 - 16:12

score 35 · Answer 7 · 2020-10-19 16:41:07

35

Views

The proposition about metric space and limit

Published on 19 Oct 2020 - 16:41

score 218 · Answer 8 · 2020-10-21 13:29:15

218

Views

Integer length altitudes of a scalene triangle $ABC$

Published on 21 Oct 2020 - 13:29

score 55 · Answer 9 · 2020-10-24 06:12:40

55

Views

Check whether this function is a metric over $\mathbb{R}$ or not?

Published on 24 Oct 2020 - 6:12

score 55 · Answer 10 · 2020-10-29 21:07:23

55

Views

prove the following using the triangle inequality

Published on 29 Oct 2020 - 21:07

score 164 · Answer 11 · 2020-10-30 12:26:51

164

Views

How to prove that $\frac{|x+y+z|}{1+|x+y+z|} \le \frac{|x|}{1+|y|+|z|}+\frac{|y|}{|1+|x|+|z|}+\frac{|z|}{1+|x|+|y|}$

Published on 30 Oct 2020 - 12:26

score 91 · Answer 12 · 2020-10-30 19:11:38

91

Views

Proof reviewer needed

Published on 30 Oct 2020 - 19:11

score 308 · Answer 13 · 2020-11-10 04:45:35

308

Views

Find minimum value of $|z|+|z-e^{ix}|+|z-5e^{ix}|+|z-7e^{ix}|+|z-32e^{ix}|$ where $z$ is a complex number

Published on 10 Nov 2020 - 4:45

score 82 · Answer 14 · 2020-11-11 13:46:34

82

Views

Is it true that $|x + y| \geq |x| - |y|$?

Published on 11 Nov 2020 - 13:46

score 172 · Answer 15 · 2020-11-13 18:21:36

172

Views

Simple Triangle-like Inequality for a general norm

Published on 13 Nov 2020 - 18:21

List Question

If $\left|z+1\right|=3$, determine the greatest and least possible values for $|z|$

If $d(A,B) = \inf_{a \in A, b \in B}{d(a,b)}$ , does $d(A, B) ≤ d(A, C) + d(C, B)? $

Does $\left\lVert (x,y) \right\rVert := \sqrt{x^2+y^2+xy} \phantom{1}$ satisfy the triangular inequality?

If $d$ is a metric in $X$ and $A \subset X$, does $\lvert d(x,A) - d(y,A) \rvert \le d(x,y) \phantom{5} \forall x, y \in X$?

Can any norm be used in a product metric

Proof that $2(a^4+b^4+c^4)<(a^2+b^2+c^2)^2$ if and only if line segments of length $a$,$b$ and $c$ form a triangle

The proposition about metric space and limit

Integer length altitudes of a scalene triangle $ABC$

Check whether this function is a metric over $\mathbb{R}$ or not?

prove the following using the triangle inequality

How to prove that $\frac{|x+y+z|}{1+|x+y+z|} \le \frac{|x|}{1+|y|+|z|}+\frac{|y|}{|1+|x|+|z|}+\frac{|z|}{1+|x|+|y|}$

Proof reviewer needed

Find minimum value of $|z|+|z-e^{ix}|+|z-5e^{ix}|+|z-7e^{ix}|+|z-32e^{ix}|$ where $z$ is a complex number

Is it true that $|x + y| \geq |x| - |y|$?

Simple Triangle-like Inequality for a general norm

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