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]].
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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]]. 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 17:11, 11 April 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.