The following inequality can easily be proved on ##ℝ## :(adsbygoogle = window.adsbygoogle || []).push({});

## ||x|-|y|| \leq |x-y| ##

I was wondering if it extends to arbitrary normed linear spaces, since I can't seem to prove it using the axioms for linear spaces. (I can however, prove it using the definition of the norm on ##ℝ## by using casework).

Suggestions? Hints?

BiP

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# Variation of the triangle inequality on arbitrary normed spaces

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