Compactness and Sequential Compactness are Equivalent in Metric Spaces

Theorem
Let $\struct {X, d}$ be a metric space.

Then $\struct {X, d}$ is compact it is sequentially compact.

Necessary Condition
This is precisely Compact Subspace of Metric Space is Sequentially Compact in Itself.

Sufficient Condition
This is precisely Sequentially Compact Metric Space is Compact.