User:Jshflynn/Definition:Subalphabet power

Definition

Let $\Sigma$ be an alphabet.

Let $V$ be a subalphabet of $\Sigma$.

Then the $n$th power of $V$, where $n \in \mathbb{N}_0$, is denoted $V^{n}$ and defined inductively:

$

V^{n} = \begin{cases} \{\lambda\} & \text{if }n=0 \\ V^{n-1}V & \text{if }n > 0 \end{cases} $