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So far, I have:

Let [itex]A\subseteq\mathbb{R}[/itex]. I want to show that if every neighborhood of [itex]x\in A[/itex] has infinitely many points of A, there exists a [itex]y\in\mathbb{R}[/itex] such that [itex]y\in((x-\epsilon,x+\epsilon)\bigcap A[/itex]\{x}).

Am I on the right track?