symmetric relation


In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.In mathematical notation, this is: Note: symmetry is not the exact opposite of antisymmetry (aRb and bRa implies b = a). There are relations which are both symmetric and antisymmetric (equality and its subrelations, including, vacuously, the empty relation), there are relations which are neither symmetric nor antisymmetric (divisibility), there are relations which are symmetric and not antisymmetric (congruence modulo n), and there are relations which are not symmetric but are antisymmetric ("is less than or equal to").

Properties containing the symmetric relation

equivalence relation - A symmetric relation that is also transitive and reflexive.

Examples

• "is married to" is a symmetric relation, while "is less than" is not.
• "is equal to" (equality)
• "... is odd and ... is odd too":

See also

• Symmetry in mathematics
• Asymmetric relation
• Antisymmetric relation

Symetrická relaceSymmetrie (Mengenlehre)Relación simétricaRelazione simmetricaיחס סימטריSzimmetrikus reláció対称関係Relacja symetrycznaСимметричностьSymetrická reláciaSymmetrisk relationСиметричне відношення对称关系

(...as imported from WP)

home | about | policy | newsfeed