Limit points and isolated points (of sets of reals), definition

Limit points

Let $X$ be a subset of the real line. We say that $x$ is a limit point (or cluster point) of $X$ if [...].

Not to be confused with limit points of sequences.

Isolated points

Let $X$ be a subset of the real line. We say that $x$ is an isolated point of $X$ if $x\in X$ and [...].