Definition:Injection/Definition 1

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

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