A SET with a total ordering and no infinite descending chains. A total ordering "<=" satisfies x <= x x <= 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)