Finite Space is Sequentially Compact

Theorem
Let $T = \left({S, \vartheta}\right)$ be a topological space where $S$ is a finite set.

Then $T$ is sequentially compact.

Proof
We have that:
 * A Finite Topological Space is Compact.
 * A Compact Space is Countably Compact.
 * A Finite Space is Second-Countable.
 * A Second-Countable Space is First-Countable and Separable.
 * In a first-countable space, sequential compactness is equivalent to countable compactness.

Hence the result.