# Bijection

From Encyclopedia of Mathematics

*bijective mapping, of a set into a set *

A mapping under which different elements in have different images in . In other words, is a one-to-one mapping of onto , i.e. a mapping that is both an injection and a surjection. A bijection establishes a one-to-one correspondence between the elements of the sets and . A bijection of a set onto itself is also called a permutation of .

**How to Cite This Entry:**

Bijection.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Bijection&oldid=18176

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article