Countable Discrete Space is Separable

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

Let $S$ be a countable set, thereby making $\tau$ the countable discrete topology on $S$.

Then $T$ is separable.

Also see

 * Uncountable Discrete Space is not Separable