Definition:Surjection/Definition 2

Definition
Let $S$ and $T$ be sets.

Let $f: S \to T$ be a mapping from $S$ to $T$.

$f: S \to T$ is a surjection iff:
 * $f \left[{S}\right] = T$

That is, $f$ is a surjection iff its image equals its codomain:
 * $\operatorname{Im} \left({f}\right) = \operatorname{Cdm} \left({f}\right)$

Also see

 * Equivalence of Definitions of Surjection