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 (210)
Orphanage
Unclass'd (1)
Unproven (472)
Corrections (37)
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
Cartesian product (Definition)

For any sets $ A$ and $ B$, the Cartesian product $ A \times B$ is the set consisting of all ordered pairs $ (a,b)$ where $ a \in A$ and $ b \in B$.

The Cartesian product satisfies the following properties, for all sets $ A$, $ B$, $ C$, and $ D$:

  • $ A\times \emptyset = \emptyset$
  • $ (A \times B) \cap (C \times D) = (A\cap C) \times (B\cap D)$
  • $ (A \times B)^\complement = (A^\complement \times B^\complement) \cup (A^\complement \times B) \cup (A \times B^\complement)$

Here $ \emptyset$ denotes the empty set, $ \cap$ denotes intersection, $ \cup$ denotes union, and $ {}^\complement$ denotes complement with respect to some universal set $ U$ containing $ A$ and $ B$.



"Cartesian product" is owned by djao.
(view preamble)

View style:

See Also: generalized Cartesian product
Log in to rate this entry.
(view current ratings)

Cross-references: universal, complement, union, intersection, empty set, properties, satisfies, ordered pairs
There are 46 references to this entry.

This is version 5 of Cartesian product, born on 2001-10-19, modified 2006-10-12.
Object id is 359, canonical name is CartesianProduct.
Accessed 21895 times total.

Classification:
AMS MSC: 03-00 (Mathematical logic and foundations :: General reference works )
Pending Errata and Addenda
None.
[ View all 6 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)