bijective

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.Alternatively, f is bijective if it is a one-to-one correspondence between those sets; i.e., both one-to-one (injective) and onto (surjective). (See also Bijection, injection and surjection.)For example, consider the function succ, defined from the set of integers  to , 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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In mathematics and related technical fields, the term map or mapping is often a synonym for function. Thus, for example, a partial map is a partial function, and a total map is a total function. Related terms like domain, codomain, injective, continuous, etc. can be applied equally to maps and functions, with the same meaning.
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