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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 http://en.wikipedia.org/wiki/Ultrametric_space#Formal_definition2011-05-03
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    @lhf: Thanks a lot. That was eating me up.2011-05-03

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