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## Main Question or Discussion Point

Prove that a is a cluster point of E if and only if the set (E intersection (a-r,a+r))\{a} is nonempty for each r > 0.

I have the forward implication done but the backwards implication is giving me some trouble. Could you explain it to me.

I have the forward implication done but the backwards implication is giving me some trouble. Could you explain it to me.