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Let A⊆(X,d) a metric space. Suppose there are an infinite number of elements in e1,e2,e3,...∈ A...

Let A⊆(X,d) a metric space. Suppose there are an infinite number of elements in e1,e2,e3,...∈ A such that d(ei,ej)=4 if i≠j and d(ei,ej)=0 if i=j for i,j=1,2,3...

Prove that A is not totally bounded.

(Please do not write in script and show all your steps and definitions used)

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