Definition:Inversion Mapping

Definition
Let $\left({G, \circ}\right)$ be a group.

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


 * $\forall g \in G: \iota \left({g}\right) = g^{-1}$

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

By Inverses in Group are Unique, $\iota$ is well-defined.

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

Also see

 * Definition:Group