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Closed set in a metric space

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If A is a closed set in a metric space (X,d) and , show that d(x,A)>0.

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Solution Summary

This solution is comprised of a detailed explanation to show that d(x,A)>0.

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Proof:
We know, d(x,A)=inf{d(x,y):y in A}.
If d(x,A)=0, then for any e_n=1/n, we can find some y_n in A, such that d(x,y_n)<e_n. Otherwise, d(x,A)>=e_n>0 and this is a ...

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