You are here: irt.org | FOLDOC | 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.
Nearby terms: well-behaved « well-connected « well-known port « well-ordered set » WEP » Wesley Clark » Western Digital Corporation
FOLDOC, Topics, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, ?, ALL
©2018 Martin Webb