An ordered set - in order theory of mathematics - is an ambiguous term referring to a 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 (for all a in the set, aRa), antisymmetric (if aRb and bRa, then a = b) and 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-ordered set.
In information theory, an ordered set is a non-data carrying set of bits as used in 8b/10b encoding.
Famous quotes containing the words ordered and/or set:
“The peace conference must not adjourn without the establishment of some ordered system of international government, backed by power enough to give authority to its decrees. ... Unless a league something like this results at our peace conference, we shall merely drop back into armed hostility and international anarchy. The war will have been fought in vain ...”
—Virginia Crocheron Gildersleeve (1877–1965)
“Those who want to row on the ocean of human knowledge do not get far, and the storm drives those out of their course who set sail.”
—Franz Grillparzer (1791–1872)