# Functional relation

From Encyclopedia of Mathematics

A binary relation on a set satisfying , where is the diagonal of . This means that and imply that , that is, for each there is at most one such that . Thus, determines a function (perhaps not defined everywhere) on . When it satisfies this function is well-defined everywhere and is one-to-one.

#### Comments

A functional relation is more generally defined as a binary relation between sets and such that and imply .

**How to Cite This Entry:**

Functional relation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Functional_relation&oldid=13901

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