# bijection

## bijection

[bahy-jek-shuhn]
noun Mathematics.
a map or function that is one-to-one and onto.

Origin:
1965–70; bi-1 + -jection, as in projection

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World English Dictionary
 bijection (baɪˈdʒɛkʃən) —n injection See also surjection a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse

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Science Dictionary
 bijection  [%PREMIUM_LINK%]     (bī-jěk'shən)  Pronunciation Key  Mathematics A function that is both an injection and a surjection. In a bijection, each member of the range corresponds to an element of the domain that is mapped onto it, and there is a one-to-one correspondence between the members of the domain and the range. All linear functions, such as y = x + 3, are bijections. Compare injection, surjection.
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Computing Dictionary

### bijection definition

mathematics
A function is bijective or a bijection or a one-to-one correspondence if it is both injective (no two values map to the same value) and surjective (for every element of the codomain there is some element of the domain which maps to it). I.e. there is exactly one element of the domain which maps to each element of the codomain.
For a general bijection f from the set A to the set B:
f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B.
A and B could be disjoint sets.