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)