Feb 18, 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 …

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.

May 9, 2020 · This is of course reflected in the fact that the reverse triangle inequality is a direct consequence of the 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 …

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

Sep 12, 2021 · I'm not sure what the precise statement of Cauchy-Schwarz is, at least relative to proving the triangle inequality for this metric, but this one appeared most natural.

Explore related questions solution-verification complex-numbers triangle-inequality See similar questions with these tags.

I was able to find several proofs of the "reverse triangle inequality", but they all start off with $|x-y|$ instead of $|x+y|$ like in the upper and lower bounds given.

Equality of triangle inequality in complex numbers Ask Question Asked 11 years, 9 months ago Modified 4 years, 1 month ago

In my opinion the proper way to prove the triangle inequality for $L_p$ spaces is via duality - I wish people taught it that way instead of those magical computational tricks.