Countable Discrete Space is Sigma-Compact/Proof 1

Proof
We have that Singleton Set in Discrete Space is Compact.

We also have that $S$ is the union of all its singleton sets:
 * $\displaystyle S = \bigcup_{x \mathop \in S} \left\{{x}\right\}$

As $S$ is countable, it is the union of countably many compact sets.

Hence the result, by definition of $\sigma$-compact.