Computing Dictionary
well-ordered set definition
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)
