A set with a total ordering and no infinite descending chains. A total ordering "<=" satisfies X <= XX <= y <= z => X <= z X <= y <= X => X = y for all X, y: X <= y or 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 <= y. Ordinals are isomorphism classes of well-ordered sets, just as integers are isomorphism classes of finite sets. (1995-04-19)