Definition:Surjection/Definition 1

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

$f: S \to T$ is a surjection :
 * $\forall y \in T: \exists x \in \Dom f: \map f x = y$

That is, $f$ is right-total.

Thus a surjection is a relation which is:
 * Left-total
 * Many-to-one
 * Right-total.

Also see

 * Equivalence of Definitions of Surjection