The Wayback Machine - https://web.archive.org/web/20060925041144/http://planetmath.org/encyclopedia/Union.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 (296)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

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

The union of two sets $ A$ and $ B$ is the set which contains all $ x \in A$ and all $ x \in B$, denoted $ A \cup B$. We can extend this to any (finite or infinite) family $ (A_i)_{i\in I}$, writing $ \bigcup_{i\in I}A_i$ for the union of this family. Formally, for a family $ (A_i)_{i\in I}$ of sets:

$\displaystyle x \in \bigcup_{i\in I}A_i\; \Leftrightarrow \;\bigvee_{i\in I}\, (x\in A_i) $

From an axiomatic point of view, the existence of the union is guaranteed by the axiom of union.



"union" is owned by Cosmin. [ full author list (2) | owner history (1) ]
(view preamble)


See Also: intersection


Cross-references: point, infinite, finite, contains
There are 105 references to this entry.

This is version 3 of union, born on 2002-01-26, modified 2005-06-11.
Object id is 1619, canonical name is Union.
Accessed 5443 times total.

Classification:
AMS MSC: 03E30 (Mathematical logic and foundations :: Set theory :: Axiomatics of classical set theory and its fragments)
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
forum policy

No messages.

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