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
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