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Proving that $\lVert x\rVert=\sqrt{\langle x,x \rangle}$ is a norm (triangle inequality).

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#linear-algebra #vector-spaces #inner-products #cauchy-schwarz-inequality #triangle-inequality
36
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Is there any simple way of proving triangle inequality for $d(x,y)= \dfrac{2|x-y|}{\sqrt{1+x^2}+\sqrt{1+y^2}}, \,\,x,y\in \mathbb{R}$

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#real-analysis #inequality #metric-spaces #a.m.-g.m.-inequality #triangle-inequality
110
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How many triangles can be formed so that the area of $\triangle ABC$ is 9 times $\triangle DEF$?

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#geometry #trigonometry #contest-math #triangle-inequality
41
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Lemma for the Bescicovitch covering lemma

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#inequality #angle #cauchy-schwarz-inequality #spheres #triangle-inequality
98
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Triangle Inequality for this metric

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#metric-spaces #supremum-and-infimum #triangle-inequality
45
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How to prove the triangle inequality in the case of an n-sided polygon?

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#geometry #triangle-inequality
81
Views

Alternative triangle inequality proof for complex numbers

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#complex-numbers #alternative-proof #triangle-inequality
160
Views

Does angle between vectors satisfy triangle inequality?

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#metric-spaces #vectors #triangle-inequality
83
Views

Does the reverse triangle inequality holds for Wasserstein-1 distance?

Published on
#optimal-transport #triangle-inequality #wasserstein
101
Views

proof of $\|a+b\|_2\le\|a\|_2+\|b\|_2$

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#analysis #inequality #reference-request #triangle-inequality
38
Views

Unclear passage in this triangle inequality $\cup$ Cauchy-Schwarz proof

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#inequality #proof-explanation #cauchy-schwarz-inequality #triangle-inequality
246
Views

Simrank distance triangle inequality

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#discrete-mathematics #graph-theory #triangle-inequality
38
Views

Simple inequality using density of rationals

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#real-analysis #inequality #triangle-inequality
110
Views

Case of equality in spectral norm matrix triangle inequality

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#matrices #matrix-decomposition #triangle-inequality #spectral-norm
124
Views

Prove that a triangle exists using the triangle inequality.

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#inequality #triangles #triangle-inequality

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