Definition:Injection/Definition 3

Definition
Let $f$ be a mapping.

Then $f$ is an injection :
 * $f^{-1} {\restriction_{\operatorname{Im} \left({f}\right)}}: \operatorname{Im} \left({f}\right) \to \operatorname{Dom} \left({f}\right)$ is a mapping

where $f^{-1} {\restriction_{\operatorname{Im} \left({f}\right)}}$ is the restriction of the inverse of $f$ to the image set of $f$.

Also see

 * Equivalence of Definitions of Injection