Definition:Square/Mapping

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

Let $f: S \to S$ be the mapping from $S$ to $S$ defined as:
 * $\forall x \in S: \map f x := x \circ x$

This is usually denoted $x^2$:
 * $x^2 := x \circ x$

Square Function
The square mapping (or square function) is usually defined in the context of the standard number systems: