> [!NOTE] Definition (Surjection) > A [[Function|function]] $f: X \to Y$ is *surjective* if it has the following property $\forall y \in Y, \quad \exists x \in X \; \text{ s.t.} \; f(x)=y$ # Properties A surjection that is also [[Injection|injective]] is a [[Bijection|bijection]]. Relation to invertibility: [[Surjective iff right-invertible]].