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...
15 KB (2,181 words) - 10:50, 28 May 2024
set theory, the axiom of empty set, also called the axiom of null set and the axiom of existence, is a statement that asserts the existence of a set with...
6 KB (798 words) - 18:40, 23 August 2024
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...
41 KB (4,747 words) - 09:15, 3 July 2024
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...
12 KB (1,737 words) - 23:16, 26 December 2023
of the empty product we must take the decategorification of the empty product in the category of finite sets. Dually, the coproduct of an empty family...
10 KB (1,467 words) - 09:22, 22 March 2024
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...
20 KB (2,425 words) - 23:34, 3 April 2024
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...
27 KB (4,359 words) - 16:11, 15 August 2024
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...
11 KB (1,730 words) - 15:02, 24 June 2024
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,...
25 KB (3,037 words) - 22:51, 6 July 2024
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...
14 KB (1,881 words) - 12:46, 26 August 2024