bijection - Definitions from Dictionary.com

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Dictionary.com Unabridged (v 1.1) - Cite This Source - Share This

bi·jec·tion

Audio Help [bahy-jek-shuh

n] Pronunciation Key

–noun Mathematics.

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

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

]

Dictionary.com Unabridged (v 1.1)
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.

Encyclopædia Britannica, Inc.
bijection

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American Heritage Dictionary - Cite This Source - Share This

bi·jec·tion Audio Help (bī-jěk'shən) Pronunciation Key
n. Mathematics
A function that is both one-to-one and onto.

[bi-¹ + (in)jection or (pro)jection.]

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The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.

The American Heritage Science Dictionary - Cite This Source - Share This

bijection Audio Help (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.

Free On-line Dictionary of Computing - Cite This Source - Share This

bijection 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.
See also injection, surjection, isomorphism, permutation.
(2001-05-10)