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Surjective function

In mathematics, a surjective function (also known as surjection, or onto function) is a functionf such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x) = y. In other words, for a function f : X → Y, the codomain Y is the image of the function's domain X. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y. 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.

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