Definition:Power of Element/Notation/Semigroup

Notation for Power of Element of Semigroup
Let $\left({T, \oplus}\right)$ be a semigroup.

Let $a \in T$.

Thus the power of an element of a semigroup is defined recursively as:


 * $a^n = \begin{cases}

a : & n = 1 \\ a^x \circ a : & n = x + 1 \end{cases}$

... that is:
 * $a^n = \underbrace{a \circ a \circ \cdots \circ a}_{n \text{ copies of } a} = \circ^n \left({a}\right)$