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 xn 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.