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:
“Today everything is different. I can’t even get decent food. Right after I got here I ordered some spaghetti with marinara sauce and I got egg noodles and catsup. I’m an average nobody, I get to live the rest of my life like a schnook.”
—Nicholas Pileggi, U.S. screenwriter, and Martin Scorsese. Henry Hill (Ray Liotta)
“The political horizon looks dark and lowering; but the people, under Providence, will set all right.”
—Abraham Lincoln (1809–1865)