Definition:Inversion Mapping

Definition
Let $\struct {G, \circ}$ be a group.

The inversion mapping on $G$ is the mapping $\iota: G \to G$ defined by:


 * $\forall g \in G: \map \iota g = g^{-1}$

That is, $\iota$ assigns to an element of $G$ its inverse.

Also known as
Other notations for $\iota$ are $i$ and $(-)^{-1}$.

Also see

 * Definition:Group


 * Inversion Mapping is Mapping