Difference between revisions of "Empty set"
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| − | The '''empty set''' is the unique set that contains no element and is a subset of every other set. Its existence is postulated by the [[Axiom of empty set]] in the axioms of [[Zermelo–Fraenkel set theory]]. Note that the empty set is not a subset of the empty set in Zermelo–Fraenkel [[set theory | + | The '''empty set''' is the unique set that contains no element and is a subset of every other set. Its existence is postulated by the [[Axiom of empty set]] in the axioms of [[Zermelo–Fraenkel set theory]]. Note that the empty set is not a subset of the empty set in Zermelo–Fraenkel [[set theory]]. |
[[Category: set theory]] | [[Category: set theory]] | ||
Revision as of 01:50, March 31, 2007
The empty set is the unique set that contains no element and is a subset of every other set. Its existence is postulated by the Axiom of empty set in the axioms of Zermelo–Fraenkel set theory. Note that the empty set is not a subset of the empty set in Zermelo–Fraenkel set theory.