12.2 Injective and Surjective Functions

Functions

• A function $f:A\to B$ is:

Injective

• if for all $a,a\prime \in A$, $a\ne a\prime$ implies $f(a)\ne f(a\prime )$

Surjective

• if for every $b\in B$ there is an $a\in A$ with $f(a)=b$

Bijective

• if $f$ is both injective and surjective.