Proving the singleton language {x} is regular for all x ∈ Σ*
$\Sigma^*$ is a set of finite strings. There are infinitely many of them, but each one is finite&nbsp;&ndash; just like there are infinitely many natural numbers but each one of them is finite.

So, for any $x\in\Sigma^*$, $\{x\}$ is a finite language (it contains one string) of finite strings (because everything in $\Sigma^*$ is finite), so it's regular.