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
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...
4 KB (648 words) - 07:18, 6 March 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) - 17:59, 3 June 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
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
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) - 14:19, 28 January 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...
28 KB (4,574 words) - 13:12, 16 April 2024
is a set with no members at all. Because a set is determined completely by its elements, there can be only one empty set. (See axiom of empty set.) Although...
34 KB (4,715 words) - 07:25, 14 February 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) - 10:42, 12 February 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) - 20:45, 11 May 2024