Finite Space is Sequentially Compact

Theorem
Let $T = \left({S, \vartheta}\right)$ be a topological space where $\vartheta$ is the discrete topology on $S$.

Let $S$ be an finite set, thereby making $\vartheta$ the finite discrete topology on $S$.

Then $T$ is sequentially compact.

Proof
We have that a Finite Topological Space is Countably Compact.

Then we have that in a first-countable space, sequential compactness is equivalent to countable compactness.

Then we have that a Discrete Space is First-Countable.

Hence the result.