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$} \end{cases}$