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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.
[[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]]