\begin{definition}[Definition:Limit Point/Real Analysis]
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 $S$ {{iff}} $\xi$ is at zero distance from $S_\xi$.
\end{definition}