Surjective Function

A surjective function, also called a surjection or an onto function, is a function f such that for every element y of its codomain there is at least one element x in its domain with f(x) equal to y, so that the image of the domain completely covers the codomain; x need not be unique, since f may send more than one element of the domain to the same element of the codomain. The terms surjective, injective and bijective were introduced by Nicolas Bourbaki, the pseudonym of a group of mainly French twentieth-century mathematicians who wrote an influential series of books on modern advanced mathematics beginning in 1935; the French word sur, meaning over or above, reflects how the image of the domain lies over the whole codomain. Any function can be turned into a surjection by restricting its codomain to the image of its domain, every surjective function has a right inverse under the axiom of choice, the composition of two surjective functions is always surjective, and any function can be decomposed into a surjection followed by an injection. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/