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[ser-jek-shuh n] /sərˈdʒɛk ʃən/
noun, Mathematics
Origin of surjection
1960-65; sur-1 + -jection, as in injection, projection, etc. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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British Dictionary definitions for surjection


a mathematical function or mapping for which every element of the image space is a value for some members of the domain See also injection (sense 5), bijection
Derived Forms
surjective, adjective
Word Origin
C20: from sur-1 + -jection, on the model of projection
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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surjection in Science
A function such that each member of its range is mapped onto by a member of the domain. Compare bijection, injection.

The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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surjection in Technology
A function f : A -> B is surjective or onto or a surjection if f A = B. I.e. f can return any value in B. This means that its image is its codomain.
Only surjections have right inverses, f' : B -> A where f (f' x) = x since if f were not a surjection there would be elements of B for which f' was not defined.
See also bijection, injection.
The Free On-line Dictionary of Computing, © Denis Howe 2010
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