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 (198)
Orphanage
Unclass'd
Unproven (490)
Corrections (7)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: High Entry average rating: No information on entry rating
Zermelo's postulate (Theorem)

If $ \mathcal{F}$ is a disjoint family of nonempty sets, then there is a set $ C$ which has exactly one element of each $ A\in \mathcal{F}$ (i.e such that $ A\cap C$ is a singleton for each $ A\in \mathcal{F}$.)

This is one of the many propositions that are equivalent to the axiom of choice.



"Zermelo's postulate" is owned by Koro.
(view preamble)

View style:

See Also: axiom of choice, maximality principle, Tukey's lemma, Zorn's lemma, Kuratowski's lemma


Attachments:
proof of Zermelo's postulate (Proof) by Wkbj79
Log in to rate this entry.
(view current ratings)

Cross-references: axiom of choice, equivalent, propositions, singleton, disjoint
There are 3 references to this entry.

This is version 3 of Zermelo's postulate, born on 2002-12-09, modified 2006-09-13.
Object id is 3694, canonical name is ZermelosPostulate.
Accessed 2696 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

No messages.

Interact
post | correct | update request | prove | add result | add corollary | add example | add (any)