Finite Subset of Metric Space has no Limit Points

Theorem
Let $M = \left({A, d}\right)$ be a metric space.

Let $X \subseteq A$ such that $X$ is finite.

Then $X$ has no limit points.

Proof
Follows directly from:
 * Point in Finite Metric Space is Isolated
 * Point is Isolated iff not Limit Point.