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)
“Who shall set a limit to the influence of a human being? There are men, who, by their sympathetic attractions, carry nations with them, and lead the activity of the human race. And if there be such a tie, that, wherever the mind of man goes, nature will accompany him, perhaps there are men whose magnetisms are of that force to draw material and elemental powers, and, where they appear, immense instrumentalities organize around them.”
—Ralph Waldo Emerson (1803–1882)