Difference between revisions of "Empty set"
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| − | In [[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. | + | In [[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. Christian scientists and others hold that it is impossible to create something from nothing, casting doubt on the existence of the empty set. However, it remains an important tool among secular mathematicians. |
[[Category: set theory]] | [[Category: set theory]] | ||
Revision as of 04:30, February 23, 2009
In 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. Christian scientists and others hold that it is impossible to create something from nothing, casting doubt on the existence of the empty set. However, it remains an important tool among secular mathematicians.