An ordered set - in order theory of mathematics - is an ambiguous term referring to a Set (mathematics)|set that is either a partially ordered set or a totally ordered set. A set with a binary relation R on its elements that is reflexive relation|reflexive (for all a in the set, aRa), antisymmetric relation|antisymmetric (if aRb and bRa, then a = b) and transitive relation|transitive (if aRb and bRc, then aRc) is described as a partially ordered set or poset. If the binary relation is antisymmetric, transitive and also total (for all a and b in the set, aRb or bRa), then the set is a totally ordered set. If every non-empty subset has a least element, then the set is a Well-order|well-ordered set.
In information theory, an ordered set is a non-data carrying set of bits as used in 8b/10b encoding.