adj. (of a function, relation, etc.) associating two sets in such a way that every member of the codomain, T, is the image of at least one member of the domain, S, although there may be members of the domain that are not mapped into any element of the codomain, as in the diagram below. The range of a surjective mapping is thus its entire codomain; that is, f(S) = T. For example, the mapping from the set of all men to the set of married women that takes each man into his own wife is a surjection. Compare injective, bijective. See also epimorphism.
Surjective. A surjective mapping.