Reflexive Relation

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Reflexive Relation

At least in this context, ''(binary) relation'' (on ''X'') always means a relation on ''X''×''X'', or in other words from a set ''X'' into itself.

A reflexive relation ''R'' on set ''X'' is one where for all ''a'' in ''X'', ''a'' is ''R''-related to itself. In Mathematical Notation , this is:

:

orall a \in X,\ a R a

.

An irreflexive (or '''aliorelative''') relation ''R'' is one where for all ''a'' in ''X'', ''a'' is never ''R''-related to itself. In mathematical notation, this is:

:

orall a \in X,\ \lnot (a R a)

.