Difference between revisions of "Empty set"
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| − | + | [[File:Empty set symbol.png|thumbnail|170px|right|'''Empty set''' symbol]] | |
| + | In [[set theory]], the '''empty set''', usually denoted <math>\emptyset</math>, is the set without any members. For example, the "set of all blue-eyed lions," the "set of all mermaids," and the "set of all people born in 1700 who are still alive" are all empty sets. | ||
| − | [[Category: | + | The empty set is unique, since any two empty sets have precisely the same members (that is, none) and is a [[subset]] of every other set. |
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| + | 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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| + | == Empty Set as a symbol for atheism == | ||
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| + | ''See also:'' [[Atheism symbols]] | ||
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| + | The empty set symbol, ∅, was originally suggested by Wayne Otero as a [[Atheism symbols|symbol to represent atheism]] and was derived from a letter in the Norwegian and Danish alphabet. It asserts the idea that there is no God and shows the obvious spiritual emptiness of atheists. A zero is another similar symbol that's been used. | ||
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| + | [[Category:Set Theory]] | ||
Latest revision as of 23:14, May 8, 2017
In set theory, the empty set, usually denoted 
, is the set without any members. For example, the "set of all blue-eyed lions," the "set of all mermaids," and the "set of all people born in 1700 who are still alive" are all empty sets.
The empty set is unique, since any two empty sets have precisely the same members (that is, none) 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.
Empty Set as a symbol for atheism
See also: Atheism symbols
The empty set symbol, ∅, was originally suggested by Wayne Otero as a symbol to represent atheism and was derived from a letter in the Norwegian and Danish alphabet. It asserts the idea that there is no God and shows the obvious spiritual emptiness of atheists. A zero is another similar symbol that's been used.
