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 …

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 …

I've seen this proof, however it's too advanced for me as it involves metric spaces - I'd like a simple proof using the known and simple triangle inequality I wrote in the question, thanks.

Explore related questions real-analysis inequality absolute-value triangle-inequality See similar questions with these tags.

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Jul 2, 2012 · How many proofs of the Cauchy-Schwarz inequality are there? Is there some kind of reference that lists all of these proofs?

Nov 10, 2015 · Prove Euclidean norm satisfies the triangle inequality Ask Question Asked 10 years, 1 month ago Modified 2 years, 11 months ago

Proof of Triangle Inequality on $ (\mathbb {R}^n, d_p)$ Ask Question Asked 14 years, 11 months ago Modified 2 years, 11 months ago

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.

May 9, 2020 · I don't know if you find that fact intuitive or not, but it is just a restatement of the fact that "the sum of two sides of a triangle is always greater (or equal to) the third side", which is …