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:

$S_\xi := \left\{{x: x \in S, x \ne \xi}\right\}$

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