The Wayback Machine - https://web.archive.org/web/20060925040029/http://planetmath.org/encyclopedia/Finite.html
PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (234)
Orphanage
Unclass'd
Unproven (392)
Corrections (292)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
finite (Definition)

A set $ S$ is finite if there exists a natural number $ n$ and a bijection from $ S$ to $ n$. Note that we are using the set theoretic definition of natural number, under which the natural number $ n$ equals the set $ \{0,1,2,\ldots,n-1\}$.

If there exists such an $ n$, then it is unique, and it is called the cardinality of $ S$.



"finite" is owned by djao.
(view preamble)



Cross-references: cardinality, bijection, natural number
There are 420 references to this entry.

This is version 3 of finite, born on 2001-10-25, modified 2004-02-22.
Object id is 500, canonical name is Finite.
Accessed 15066 times total.

Classification:
AMS MSC: 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers)
Pending Errata and Addenda
None.
[ View all 3 ]
Discussion
forum policy
Interact
rate | post | correct | update request | add derivation | add example | add (any)