surjection

Meaning

A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y.

Synonyms

onto function

onto

onto mapping

epimorphism

Pronounced as (IPA)

/sɜː(ɹ)ˈd͡ʒɛk.ʃən/

Etymology

From French surjection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.
Ultimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).