well-ordered set

mathematics 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)