User:Jshflynn/Definition:String power

Definition

Let $\Sigma$ be an alphabet.

Let $x$ be a word over $\Sigma$ and $\circ$ denoted concatenation.

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

$

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