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:
“The case of Andrews is really a very bad one, as appears by the record already before me. Yet before receiving this I had ordered his punishment commuted to imprisonment ... and had so telegraphed. I did this, not on any merit in the case, but because I am trying to evade the butchering business lately.”
—Abraham Lincoln (1809–1865)
“I believe entertainment can aspire to be art, and can become art, but if you set out to make art you’re an idiot.”
—Steve Martin (b. 1945)