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:
“I am aware that I have been on many a man’s premises, and might have been legally ordered off, but I am not aware that I have been in many men’s houses.”
—Henry David Thoreau (1817–1862)
“Is it enough
That the dish of milk is set out at night,
That we think of him sometimes,
Sometimes and always, with mixed feelings?”
—John Ashbery (b. 1927)