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

let |e^{-x}-e^{-y}| be a metric, x,y over R.

let X=[0,infinity) be a metric space.

prove that X is closed, bounded but not compact.

2. Relevant equations

3. The attempt at a solution

there is no problem for me to show that X is closed and bounded. but how do I prove it's not compact?

I assume it must be done with the use of Cauchy sequence. if x_{n}is Cauchy but it's not convergent then X is not complete and then it's not compact. but how do I right it down in algebraical form?

thanks in advance.

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# Homework Help: Closed, bounded but not compact

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