mathematics, the empty 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...

axiomatic set theory, the axiom of empty set is a statement that asserts the existence of a set with no elements. It is an axiom of Kripke–Platek set theory...

other sets. A set may have a finite number of elements or be an infinite set. There is a unique set with no elements, called the empty set; a set with...

A\cap B=B\cap A.} The intersection of any set with the empty set results in the empty set; that is, that for any set A {\displaystyle A} , A ∩ ∅ = ∅ {\displaystyle...

mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed...

members, every finite intersection of its members, the empty set, and the whole set itself. A set in which such a collection is given is called a topological...

set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set,...

null set should not be confused with the empty set as defined in set theory. Although the empty set has Lebesgue measure zero, there are also non-empty sets...

In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one...

of real numbers and the empty set—the unique set containing no elements. The empty set is also occasionally called the null set, though this name is ambiguous...