> [!NOTE] Definiton (Injection) > A [[Function|function]] $f: X \to Y$ is *injective* iff $\forall x,x' \in X, \quad f(x)=f(x') \implies x = x'$ # Properties **Relation to invertibility**: [[Injective iff left-invertible]] **Bijection**: An injection that is also [[Surjection|surjective]] is a [[Bijection|bijection]].