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bijection - 4 dictionary results

bi⋅jec⋅tion

  [bahy-jek-shuhn]
Use bijection in a Sentence
–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
Based on the Random House Dictionary, © Random House, Inc. 2009.
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bi·jec·tion   (bī-jěk'shən)   
n.   Mathematics
A function that is both one-to-one and onto.

[bi-1 + (in)jection or (pro)jection.]
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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bijection   (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.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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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)

The Free On-line Dictionary of Computing, © 1993-2007 Denis Howe
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