Surjection

A function (or mapping) is called surjective if the image of its domain coincides with its range.

In other words, a function $ f : A \to B $ from a set $A$ to a set $B$ is

a surjective function or a surjection or a function onto $A$

iff

$ f(A)=B $, i.e., for each $ b \in B $ there is an $ a \in A $ such that $ f(a)=b $.

A function that is both surjective and injective is called bijective (or, if domain and range coincide, in some contexts, a permutation).