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:
“Your mind was wrought in cosmic solitude,
Through which careered an undulous pageantry
Of fiends and suns, darkness and boiling sea,
All held in ordered sway by beauty’s mood.”
—Allen Tate (1899–1979)
“[My mother told me:] “You must decide whether you want to get married someday, or have a career.”... I set my sights on the career. I thought, what does any man really have to offer me?”
—Annie Elizabeth Delany (b. 1891)