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.
