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:
“Then he rang the bell and ordered a ham sandwich. When the maid placed the plate on the table, he deliberately looked away but as soon as the door had shut, he grabbed the sandwich with both hands, immediately soiled his fingers and chin with the hanging margin of fat and, grunting greedily, began to much.”
—Vladimir Nabokov (1899–1977)
“Unfortunately, many things have been omitted which should have been recorded in our journal; for though we made it a rule to set down all our experiences therein, yet such a resolution is very hard to keep, for the important experience rarely allows us to remember such obligations, and so indifferent things get recorded, while that is frequently neglected. It is not easy to write in a journal what interests us at any time, because to write it is not what interests us.”
—Henry David Thoreau (1817–1862)