# Ultrametric inequality

I am having trouble seeing the following consequence of the ultrametric inequality, which is supposed to be immediate.

If $|x+y|\leq \max{\{|x|,|y|\}}$, then, equality holds when $|x|\neq |y|$.

I looked up three books/notes and all of them just say that this is immediate.

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The details are given in en.wikipedia.org/wiki/Ultrametric_space#Formal_definition –  lhf May 3 '11 at 15:02
@lhf: Thanks a lot. That was eating me up. –  Milo Kunis May 3 '11 at 15:08