well-ordered set definition mathematics
A set with a total ordering
and no infinite descending chains
. A total ordering "x x x x x = y
for all x, 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 Ordinals
are isomorphism classes of well-ordered sets
, just as integers
are isomorphism classes of finite sets.