Definition: A function \(f: D \to C\) is onto (or surjective) means for every \(b\) in the codomain, there is an element \(a\) in the domain with \(f(a) = b\). Formally, \(f: D \to C\) is onto means \(\underline{\phantom{\forall b \in C \exists a \in D ( f(a) = b)}}\).