Proving the singleton language {x} is regular for all x ∈ Σ* So I'm aware that the singleton language is in fact regular for all x ∈ Σ*, but I do not understand why it is. A formal proof would help, but also getting some intuition as to why it is regular would also be appreciated! As of now I'm just aware of it as a property, but I don't have a good grasp on why it is regular.
$\Sigma^*$ 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.