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 $x$.

Also see

 * Definition:Square Number