empty set

An empty set is a set $\mathrm{\varnothing }$ 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 $X$ and then applying the axiom of separation to form the empty set $\mathrm{\varnothing }:=\{x\in X\mid x\ne x\}$.

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 $\mathrm{\varnothing }$.

Title	empty set
Canonical name	EmptySet
Date of creation	2013-03-22 11:49:55
Last modified on	2013-03-22 11:49:55
Owner	djao (24)
Last modified by	djao (24)
Numerical id	8
Author	djao (24)
Entry type	Definition
Classification	msc 03-00
Classification	msc 65H05
Classification	msc 65H10
Synonym	null set