PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (192)
Orphanage
Unclass'd (1)
Unproven (490)
Corrections (6)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Low Entry average rating: No information on entry rating
Zermelo's well-ordering theorem (Theorem)

If $ X$ is any set whatsoever, then there exists a well-ordering of $ X$. The well-ordering theorem is equivalent to the Axiom of Choice.



"Zermelo's well-ordering theorem" is owned by vypertd.
(view preamble)

View style:

See Also: Hausdorff's maximum principle, Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle, every vector space has a basis, Kuratowski's lemma, axiom of choice, well-ordering principle implies axiom of choice

Other names:  well-ordering principle

Attachments:
proof of Zermelo's well-ordering theorem (Proof) by Henry
Log in to rate this entry.
(view current ratings)

Cross-references: axiom of choice, equivalent, well-ordering
There are 11 references to this entry.

This is version 2 of Zermelo's well-ordering theorem, born on 2002-08-25, modified 2002-08-25.
Object id is 3354, canonical name is ZermelosWellOrderingTheorem.
Accessed 9368 times total.

Classification:
AMS MSC: 03E25 (Mathematical logic and foundations :: Set theory :: Axiom of choice and related propositions)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy
About Empty Set by slayerchange on 2004-06-12 06:10:10
What if X is empty set. If R well-orders X ,then any subset of emptyset is again an emptyset , and we get a contradiction .
[ reply | up ]
Interact
post | correct | update request | prove | add result | add corollary | add example | add (any)