Definition:Injection/Definition 1 a

Definition
A mapping $f$ is an injection, or injective :
 * $\forall x_1, x_2 \in \Dom f: x_1 \ne x_2 \implies \map f {x_1} \ne \map f {x_2}$

That is, distinct elements of the domain are mapped to distinct elements of the image.

Also see

 * Equivalence of Definitions of Injection