empty set

An empty setMathworldPlanetmath is a set that contains no elements. The Zermelo-Fraenkel AxiomsMathworldPlanetmath of set theoryMathworldPlanetmath 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 :={xXxx}.

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

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