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bijection

[bahy-jek-shuh n] /baɪˈdʒɛk ʃən/
noun, Mathematics
1.
a map or function that is one-to-one and onto.
Origin
1965-1970
1965-70; bi-1 + -jection, as in projection
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Examples from the web for bijection
  • Two sets have the same cardinal number if and only if there is a bijection between them.
British Dictionary definitions for bijection

bijection

/baɪˈdʒɛkʃən/
noun
1.
a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse See also injection (sense 5), surjection
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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bijection in Science
bijection
  (bī-jěk'shən)   
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 in Technology

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, © Denis Howe 2010 http://foldoc.org
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