PlanetMath: empty set

(more info)

Math for the people, by the people.

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (210)
Orphanage
Unclass'd (1)
Unproven (473)
Corrections (38)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Legalese
About

Entry average rating: No information on entry rating

empty set

(Definition)

An empty set is a set $\emptyset$ that contains no elements. The Zermelo-Fraenkel Axioms of set theory imply that there exists an empty set. One constructs an empty set by starting with any set and then applying the axiom of separation to form the empty set $\emptyset := \{ x \in X \mid x \neq x\}$ .

An empty set is a subset of every other set, and any two empty sets are equal. Alternative notations for the empty set include $\{\}$ and $\varnothing$ .

"empty set" is owned by djao.

(view preamble)

Other names:

null set

Log in to rate this entry.
(view current ratings)

Cross-references: subset, axiom of separation, imply, set theory, Zermelo-Fraenkel axioms, contains
There are 90 references to this entry.

This is version 3 of empty set, born on 2001-10-19, modified 2004-04-05.
Object id is 382, canonical name is EmptySet.
Accessed 23358 times total.

Classification:

AMS MSC:

03-00 (Mathematical logic and foundations :: General reference works )

Pending Errata and Addenda

None.[ View all 2 ]

Discussion

forum policy

No messages.

Interact