Real Analysis/Limit Points (Accumulation Points)

Definition
Let $$(X,d)$$ be a metric space, and let $$A \subset X$$. We call $$x \in X$$ a limit point of $$A$$ if for any $$\epsilon > 0$$ there exists some $$y \neq x$$ such that $$y \in B(x,\epsilon)\cap A$$.

We denote the set $$ lim(A) $$ the set of all $$x \in X$$ such that $$x$$ is a limit point of $$A$$.