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[[File:Nullset.svg|thumb|upright=0.6|The empty set is the set containing no elements.]]
In [[mathematics]], the '''empty set''' or "'''void set"''' is the unique [[Set (mathematics)|set]] having no [[Element (mathematics)|elements]]; its size or [[cardinality]] (count of elements in a set) is [[0|zero]].<ref name=":1">{{Cite web|last=Weisstein|first=Eric W.|title=Empty Set|url=https://mathworld.wolfram.com/EmptySet.html|access-date=2020-08-11|website=mathworld.wolfram.com|language=en}}</ref> Some [[axiomatic set theories]] ensure that the empty set exists by including an [[axiom of empty set]], while in other theories, its existence can be deduced. Many possible properties of sets are [[vacuously true]] for the empty set.
Any set other than the empty set is called non-empty.
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==Notation==
{{Main|Null sign}}
[[Image:Empty set symbol.svg|thumb|upright=0.6|A symbol for the empty set]]
Common notations for the empty set include "{ }", "<math>\emptyset</math>", and "[[Null sign|∅]]". The latter two symbols were introduced by the [[Bourbaki group]] (specifically [[André Weil]]) in 1939, inspired by the letter [[Ø]] ({{unichar|d8|LATIN CAPITAL LETTER O WITH STROKE}}) in the [[Danish orthography|Danish]] and [[Norwegian orthography|Norwegian]] alphabets.<ref>{{cite web| url = http://jeff560.tripod.com/set.html| title = Earliest Uses of Symbols of Set Theory and Logic.}}</ref> In the past, "0" (the numeral [[zero]]) was occasionally used as a symbol for the empty set, but this is now considered to be an improper use of notation.<ref>{{Cite book|url=https://archive.org/details/1979RudinW|title=Principles of Mathematical Analysis|last=Rudin|first=Walter|publisher=McGraw-Hill|year=1976|isbn=007054235X|edition=3rd|pages=300}}</ref>
The symbol ∅ is available at [[Unicode]] point {{unichar|2205|EMPTY SET}}.<ref>{{cite web| url = https://www.unicode.org/charts/PDF/U2200.pdf| title = Unicode Standard 5.2}}</ref> It can be coded in [[HTML]] as {{code|∅}} and as {{code|∅}} or as {{code|∅}}. It can be coded in [[LaTeX]] as {{code|\varnothing}}. The symbol <math>\emptyset</math> is coded in LaTeX as {{code|\emptyset}}.
