Editing Empty set (section)

{{short description|Mathematical set containing no elements}}
{{Redirect|∅|similar symbols|Ø (disambiguation)}}
{{Other uses of|Empty}}

[[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''.

In some textbooks and popularizations, the empty set is referred to as the "null set".<ref name=":1" />  However, [[null set]] is a distinct notion within the context of [[measure theory]], in which it describes a set of measure zero (which is not necessarily empty).