A function \(f\) from set \(A\) to set \(B\) is called a *surjection* and \(f\) is said to be *surjective* if every element in \(B\) is mapped onto by some element in \(A\).

In symbols, \(f\) is surjective if for every \(y\in B\), there is some \(x\in A\) with \(f(x)=y\). (There may be more than one \(x\in A\) with \(f(x)=y\).)

A surjective function is also known as an *onto* function.