Editing Total relation (section)

{{Short description|Type of logical relation}}
{{for|relations ''R'' where ''<nowiki>x=y</nowiki>'' or ''xRy'' or ''yRx'' for all ''x'' and ''y''|connected relation}}

In [[mathematics]], a [[binary relation]] ''R'' ⊆ ''X''×''Y'' between two sets ''X'' and ''Y'' is '''total''' (or '''left total''') if the source set ''X'' equals the domain {''x'' : there is a ''y'' with ''xRy'' }. Conversely, ''R'' is called '''right total''' if ''Y'' equals the range {''y'' : there is an ''x'' with ''xRy'' }.

When ''f'': ''X'' → ''Y'' is a [[function (mathematics)|function]], the domain of ''f'' is all of ''X'', hence ''f'' is a total relation. On the other hand, if ''f'' is a [[partial function]], then the domain may be a proper subset of ''X'', in which case ''f'' is not a total relation.

"A binary relation is said to be total with respect  to a universe of discourse just in case everything in that universe of discourse stands in that relation to something else."<ref>[http://caae.phil.cmu.edu/projects/logicandproofs/alpha/htmltest/m15_functions/chapter15.html Functions] from [[Carnegie Mellon University]]</ref>