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

Prove that if [itex] (X,\rho) [/itex]is a metric space then so is [itex](X,\bar\rho)[/itex], where

[itex]

\bar\rho:X \times X \Rightarrow R_{0}^{+}, (x,y) \Rightarrow \frac{\rho(x,y)}{1+\rho(x,y)}.

[/itex]

2. Relevant equations

I'm trying to prove the axiom that a metric space is positive definate.

3. The attempt at a solution

because given [itex] (X,\rho) [/itex] is a metric space is it enough to say that [itex](X,\bar\rho)[/itex], cannot be [itex]< 0 [/itex] because [itex] (X,\rho) [/itex] cannot be [itex]< 0 [/itex] ? ie the limit of [itex](X,\bar\rho)[/itex] is 0 as [itex] (X,\rho) [/itex] tends to zero ?

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# Homework Help: Metric space proof

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