Difference between revisions of "Empty set"
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| − | In [[mathematics]], and more specifically [[set theory]], the '''empty set''' is the unique [[Set (mathematics)|set]] having no [[Element (mathematics)|elements]]; its size or [[cardinality]] (count of elements in a set) is [[zero]]. | + | In [[mathematics]], and more specifically [[set theory]], the '''empty set''' is the unique [[Set (mathematics)|set]] having no [[Element (mathematics)|elements]]; its size or [[cardinality]] (count of elements in a set) is [[0 (number)|zero]]. |
== Description == | == Description == | ||
| Line 11: | Line 11: | ||
== See also == | == See also == | ||
| + | * [[0 (number)]] | ||
| + | * [[Cardinality]] | ||
| + | * [[Element (mathematics)]] | ||
* [[Inhabited set]] | * [[Inhabited set]] | ||
* [[Nothing]] | * [[Nothing]] | ||
* [[Null set]] | * [[Null set]] | ||
| + | * [[Set theory]] | ||
== External links == | == External links == | ||
Latest revision as of 13:03, 24 September 2016
In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
Description
Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set.
Null set was once a common synonym for "empty set", but is now a technical term in measure theory.
The empty set may also be called the void set.
See also
External links
- Empty set @ Wikipedia
