In mathematics, a bijection, or a bijective function is a function f from a set X to a set Y with the property that, for every y in Y, there is exactly one x in X such that f(x) = y and no unmapped element exists in either X or Y.Alternatively, f is bijective if it is a one-to-one correspondence between those sets, both one-to-one (injective) and onto (surjective). (One-to-one function means one-to-one correspondence (i.e., bijection) to some authors, but injection to others.)For example, consider the function succ, defined from the set of integers Z to Z, that to each integer x associates the integer succ(x) = x + 1. For another example, consider the function sumdif that to each pair (x,y) of real numbers associates the pair sumdif(x,y) = (x + y, x ? y).

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