PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
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 (236)
Orphanage
Unclass'd (1)
Unproven (540)
Corrections (49)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Copyright
About
Owner confidence rating: Very low Entry average rating: No information on entry rating
cardinality of the rationals (Theorem)

The set of rational numbers $\mathbb{Q}$ is countable, and therefore its cardinality is $\aleph_0$



"cardinality of the rationals" is owned by quadrate.
(view preamble | get metadata)

View style:

See Also: countable, rational number, irrational, algebraic numbers are countable, the Cartesian product of a finite number of countable sets is countable

Other names:  power of the rationals
Keywords:  countable, rational number, cardinality

Attachments:
proof that the rationals are countable (Proof) by alozano
another proof of cardinality of the rationals (Proof) by Mathprof
Log in to rate this entry.
(view current ratings)

Cross-references: cardinality, countable, rational numbers
There are 2 references to this entry.

This is version 2 of cardinality of the rationals, born on 2001-11-16, modified 2002-02-25.
Object id is 921, canonical name is CardinalityOfTheRationals.
Accessed 4930 times total.

Classification:
AMS MSC: 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

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