Definition:Power (B-Algebra)

Definition
Let $\struct {X, \circ}$ be a $B$-algebra.

For any $x \in X$ and $n \in \N$, define the $n$th power of $x$, denoted $x^n$, inductively:


 * $x^n = \begin{cases}

0 & \text {if $n = 0$} \\ x^{n - 1} \circ \paren {0 \circ x} & \text {if $n \ge 1$} \end{cases}$

Also see

 * First Power of Element in $B$-Algebra, demonstrating $x^1 = x$