Feb 19, 2013 · The significance of the triangle inequality is not in some deep insight its proof requires, but rather in its usefulness and in its elegant formulation compared to the tedious case-by-case proof …

how about if we square both sides of reverse triangle inequality and end up with $|X||Y|\gt XY$? The same output as if we square triangle inequality.

Dec 14, 2011 · The Cauchy-Schwarz Inequality holds for any inner Product, so the triangle inequality holds irrespective of how you define the norm of the vector to be, i.e., the way you define scalar …

Dec 28, 2019 · A better title would be "when does equality holds in the triangle inequality? ". With the norm you considered, I don't know the answer. With any strictly convex norm, such as the $L^p$ …

Mar 20, 2015 · The triangle comes from the fact that if one considers the metric induced by $|\cdot|$, then this is the triangle inequality. In particular, it means that the the distance of going from $a$ to …

Sep 6, 2015 · Triangle Inequality Equality Conditions Ask Question Asked 10 years, 3 months ago Modified 10 years, 3 months ago

5 This question already has answers here: Equality holds in triangle inequality iff both numbers are positive, both are negative or one is zero (4 answers)

Jul 1, 2024 · Triangle inequality for $l^2$ norm Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 months ago

General Proof for the triangle inequality Ask Question Asked 13 years, 2 months ago Modified 5 years, 4 months ago

Jul 29, 2017 · Proof for triangle inequality generalized to integrals Ask Question Asked 8 years, 4 months ago Modified 8 years, 4 months ago