Point in Closure of Subset of Metric Space iff Limit of Sequence

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

Let $H \subseteq A$ be a subset of $A$.

Let $H^-$ denote the closure of $H$.

Let $a \in A$.

Then $a \in H^-$ iff there exists a sequence $\left\langle{x_n}\right\rangle$ of points of $H$ which converges to the limit $a$.