Point in Finite Metric Space is Isolated/Proof 2

Theorem

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

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

Let $x \in X$.

Then $x$ is isolated in $X$.

Proof

A Metric Space is Hausdorff.

Therefore Point in Finite Hausdorff Space is Isolated‎ can be applied.

Hence the result.

$\blacksquare$