Definition:Injection/Definition 1

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

That is, an injection is a mapping such that the output uniquely determines its input.

Definition 1 a
This can otherwise be put:

Also see

 * Equivalence of Definitions of Injection