(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

prove that the given function is a metric, or give a counterexample to show how it fails to be a metric: d(x,y)=|x^{3}-y^{3}|

2. Relevant equations

ok, out of the 3 requirements to be a metric, 2 are trivial. The third is to prove the triangle inequality holds: d(x,y)[tex]\leq[/tex]d(x,z)+d(z,y)

should i just go through the different cases of x<y<z , x<z<y , z<x<y?? and if the inequality holds true for all of them I am done? I feel like there must be a better way to take care of this... Oh, and please don't spoil the question for me. Thanks

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# Homework Help: Is it a metric space?

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