Definition:Square/Mapping/Element
< Definition:Square | Mapping(Redirected from Definition:Square Element)
Jump to navigation
Jump to search
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
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): square: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): square: 2.