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bender2
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Homework Statement
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.
Homework Equations
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.