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( Surjective function)
In mathematics, a function f is said to be surjective or onto, if its values span its whole codomain; that is, for every y in the codomain, there is at least one x in the domain such that f(x) = y . Said another way, a function f&_160;X&_160;?&_160;Y is surjective if and only if its range f(X) is equal to its codomain Y. A surjective function is called a surjection. Every function with a right inverse is a surjection. The converse is equivalent to the axiom of choice. That is, assuming the axiom of choice, a function f&_160;X&_160;?&_160;Y is surjective if and only if there exists a function g&_160;Y&_160;?&_160;X such that, for every  that is a function g such that f&_160;o&_160;g equals the identity function on Y (cf. with definition of inverse function).
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