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

Let (X,ρ) and (Y,σ) be metric spaces.

Define a metric d on X x Y by d((x1,y1),(x2,y2))=max(ρ(x1,x2),σ(y1,y2)).

Verify that d is a metric.

2. Relevant equations

3. The attempt at a solution

I proved positive definiteness and symmetry, but I am not sure how to prove the "triangle inequality" property of a metric. How many cases do we need in total, and how can we prove it?

Any help is appreciated!

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# Homework Help: Prove that d is a METRIC

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