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 case-by-case proof …

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 …

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.

Nov 10, 2015 · Prove Euclidean norm satisfies the triangle inequality Ask Question Asked 10 years, 3 months ago Modified 3 years, 1 month ago

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

Jul 4, 2024 · 1 I recently stumbled upon an idea for a proof for the sum of two sides of a triangle inequality. Note that I am just a high school student and feel free to correct me wherever if I am …

Jan 18, 2019 · In one dimension, the formula states that the length of one side of a triangle is less than or equal to the sum of the lengths of the other two sides.

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

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.