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]]. | + | 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]]. Though this seems counterintuitive, the empty set is a subset of the empty set, and the empty set is [[disjoint]] with itself. |
[[Category: set theory]] | [[Category: set theory]] | ||
Revision as of 23:11, April 11, 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. Though this seems counterintuitive, the empty set is a subset of the empty set, and the empty set is disjoint with itself.