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 (200)
Orphanage
Unclass'd
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: High Entry average rating: No information on entry rating
pigeonhole principle (Theorem)

For any natural number $ n$, there does not exist a bijection between $ n$ and a proper subset of $ n$.

The name of the theorem is based upon the observation that pigeons will not occupy a pigeonhole that already contains a pigeon, so there is no way to fit $ n$ pigeons in fewer than $ n$ pigeonholes.



"pigeonhole principle" is owned by djao.
(view preamble)

View style:

Other names:  box principle, Dirichlet principle

Attachments:
example of pigeonhole principle (Example) by Mathprof
proof of pigeonhole principle (Proof) by Wkbj79
another proof of pigeonhole principle (Proof) by ratboy
Log in to rate this entry.
(view current ratings)

Cross-references: contains, proper subset, bijection, natural number
There are 10 references to this entry.

This is version 6 of pigeonhole principle, born on 2001-10-25, modified 2003-04-03.
Object id is 502, canonical name is PigeonholePrinciple.
Accessed 11976 times total.

Classification:
AMS MSC: 03E05 (Mathematical logic and foundations :: Set theory :: Other combinatorial set theory)
Pending Errata and Addenda
None.
[ View all 3 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

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