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=31682
Functional relation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Functional_relation&oldid=31682
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article