well-ordered set
well-ordered set
[′wel ¦ȯr·dərd ′set]well-ordered set
(mathematics)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-emptysubsets A of W have a least element, i.e. there exists x in Asuch 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.