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empty set

File:Nullset.svg · Wikimedia Commons · See Wikimedia Commons

EntityQ226183· pop 76· linked from 903 articles

empty set

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Also known as null set

set (in mathematics) containing no elements

AI overview

An empty set is a collection that contains nothing at all — no items, no members, no elements inside it. It matters in mathematics because it serves as a foundation for building logical systems and helps mathematicians precisely define and reason about collections of things.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

Instance of
finite set
Image
Empty set symbol.svg
Show 8 more facts
set cardinality
zero
different from
null set
TeX string
\varnothing
opposite of
non-empty set
Commons category
Nested set V4
on focus list of Wikimedia project
Wikipedia:Vital articles/Level/4
notation
Q87524418
maintained by WikiProject
WikiProject Mathematics
Sources (1)

via Wikidata · CC0

~14 min read

Encyclopedic overview

The empty set is the set containing no elements. In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. 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.

Excerpted from Wikipedia’s “empty set” article, available under the CC BY-SA 4.0 licence.

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