- #1

chipotleaway

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## Homework Statement

Let (X,d) is a metric space. Show that [itex]d_1=log(1+d)[/itex] is a metric space.

## The Attempt at a Solution

(it's not stated what d is so I'm assumed d=|x-y|)

I've checked positivity and symmetry but am having trouble with showing the triangle inequality holds. i.e. [itex]log(1+|x-y|) \leq log(1+|x-z|)+log(1+|y-z|)[/itex].

It doesn't appear as though log(a+b)≤log(a)+log(b) is always true