Difference between revisions of "Empty set"
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In [[set theory]], the '''empty set''', usually denoted <math>\emptyset</math>, 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. More generally, the union of any set with the empty set is the original set, while the intersection of any set with the empty set is itself the empty set. | In [[set theory]], the '''empty set''', usually denoted <math>\emptyset</math>, 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. More generally, the union of any set with the empty set is the original set, while the intersection of any set with the empty set is itself the empty set. | ||
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[[Category: set theory]] | [[Category: set theory]] | ||
Revision as of 00:07, September 3, 2009
In set theory, the empty set, usually denoted 
, 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. More generally, the union of any set with the empty set is the original set, while the intersection of any set with the empty set is itself the empty set.
