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 the result that All Points in Finite Metric Space are Isolated, and the definition of limit point.