Finite Subset of Metric Space has no Limit Points

Theorem
Let $M = \struct {A, d}$ be a metric space.

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

Then $X$ has no limit points.

Proof
Let $x \in X$.

From Point in Finite Metric Space is Isolated, $x$ is an isolated point.

The result follows by definition of isolated point:
 * $x$ is an isolated point $x$ is not a limit point.