\begin{definition}[Definition:Power of Element/Magma with Identity]
Let $\struct {S, \circ}$ be a magma with an identity element $e$.
Let $a \in S$.
Let the mapping $\circ^n a: \N \to S$ be recursively defined as:
:$\forall n \in S: \circ^n a = \begin{cases}
e & : n = 0 \\
\paren {\circ^r a} \circ a & : n = r + 1
\end{cases}$
The mapping $\circ^n a$ is known as the '''$n$th power of $a$ (under $\circ$)'''.
\end{definition}