# bijection

Also found in: Dictionary, Wikipedia.

## bijection

[′bī‚jek·shən] (mathematics)

A mapping ƒ from a set

*A*onto a set*B*which is both an injection and a surjection; that is, for every element*b*of*B*there is a unique element*a*of*A*for which ƒ*(a)*=*b*. Also known as bijective mapping.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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.

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.

This article is provided by FOLDOC - Free Online Dictionary of Computing (

**foldoc.org**)Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

Link to this page: