Definition:Limit Point/Real Analysis

Definition
Let $S \subseteq \R$ be a subset of the real numbers.

Let $\xi \in \R$ and let $S_\xi$ be the set defined as:
 * $S_\xi := \set {x: x \in S, x \ne \xi}$

Then $\xi$ is a limit point of $S$ $\xi$ is at zero distance from $S_\xi$.