a totally ordered set in which every nonempty subset has a smallest element with the property that there is no element in the subset less than this smallest element.
mathematics A set with a total ordering and no infinite descending chains. A total ordering "x x x x x = y for all x, y: x In addition, if a set W is well-ordered then all non-empty subsets A of W have a least element, i.e. there exists x in A such that for all y in A, x Ordinals are isomorphism classes of well-ordered sets, just as integers are isomorphism classes of finite sets. (1995-04-19)