Definition:Injection/Definition 1 a

Definition
A mapping $f$ is an injection, or injective :
 * $\forall x_1, x_2 \in \operatorname{Dom} \left({f}\right): x_1 \ne x_2 \implies f \left({x_1}\right) \ne f \left({x_2}\right)$

Also see

 * Equivalence of Definitions of Injection