noun Mathematics.
a map or function that is one-to-one and onto.

1965–70; bi-1 + -jection, as in projection Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
bijection (baɪˈdʒɛkʃən)
injection See also surjection a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
Science Dictionary
bijection  [%PREMIUM_LINK%]     (bī-jěk'shən)  Pronunciation Key 
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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Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Computing Dictionary

bijection definition

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.
See also injection, surjection, isomorphism, permutation.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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Example sentences for bijection
Two sets have the same cardinal number if and only if there is a bijection between them.
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