well-ordered set | computing dictionary |

<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.

(01 Mar 1995)

well-differentiated lymphocytic lymphoma, wellingtenia, well-known port, well-liking < Prev | Next > Wells, G, Wells, Michael Vernon

Bookmark with: | word visualiser | Go and visit our forums |