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:
“Twenty-four-hour room service generally refers to the length of time that it takes for the club sandwich to arrive. This is indeed disheartening, particularly when you’ve ordered scrambled eggs.”
—Fran Lebowitz (b. 1950)
“Surely, ‘tis one step towards acting well, to think worthily of our nature; and as in common life, the way to make a man honest, is, to suppose him so ... so here, to set some value upon ourselves, enables us to support the character ... of generosity and virtue.”
—Laurence Sterne (1713–1768)