<Tr> <Td> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> </Td> </Tr> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f (x) = y . It is not required that x is unique; the function f may map one or more elements of X to the same element of Y . </P> <P> The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th - century mathematicians who under this pseudonym wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935 . The French prefix sur means over or above and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain . </P>

When is a function said to be onto