Definition:Square/Mapping/Element

Definition

Let $\struct {S, \circ}$ be an algebraic structure.

Let $f: S \to S$ be the square mapping from $S$ to $S$:

$\forall x \in S: \map f x := x \circ x = x^2$

A square (element of $S$) is an element $y$ of $S$ for which:

$\exists x \in S: y = x^2$

Such a $y = x^2$ is referred to as the square of $x$.