Nearby Words
noun Mathematics.
a map or function that is one-to-one and onto.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2012.
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Based on the Random House Dictionary, © Random House, Inc. 2012.
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Link To Bijection
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Bijection
is always a great word to know.
So is precalculus. Does it mean:
| a number that is a multiple of all the numbers of a given set |
| pertaining to the mathematical prerequisites for the study of calculus, as algebra, analytical geometry, and trigonometry |
Collins
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 | |
Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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American Heritage
Science Dictionary
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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Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
Cite This Source
FOLDOC
Computing Dictionary
bijection definition
mathematicsA 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)
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