Set of all Strings

languages

Definition

Set of all Strings

The set of all strings ${\Sigma }^{\ast }$ over an alphabet $\Sigma$ is the set of all possible string concatenations on $\Sigma$.

Monoid

The set of all strings ${\Sigma }^{\ast }$ (including the empty string) is a monoid:

$$⟨{\Sigma }^{\ast },\cdot ,\epsilon ⟩\text{ is a Monoid}$$

where $\epsilon$ is the empty string (the neutral element).