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It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Operations on sets" The following 11 pages are in this category, out of 11 ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
Just as arithmetic features binary operations on numbers, set theory features binary operations on sets. [9] The following is a partial list of them: Union of the sets A and B, denoted A ∪ B, is the set of all objects that are a member of A, or B, or both. [10] For example, the union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4}.
In mathematical set theory, a set of Gödel operations is a finite collection of operations on sets that can be used to construct the constructible sets from ordinals. Gödel ( 1940 ) introduced the original set of 8 Gödel operations 𝔉 1 ,...,𝔉 8 under the name fundamental operations .
[6] [7] [8] Operations on functions include composition and convolution. [9] [10] Operations may not be defined for every possible value of its domain. For example, in the real numbers one cannot divide by zero [11] or take square roots of negative numbers. The values for which an operation is defined form a set called its domain of definition ...
Download as PDF; Printable version; ... Operations on sets (1 C, 11 P) P. Predicate logic (2 C, 36 P) Pages in category "Basic concepts in set theory"
Since relations are sets, they can be manipulated using set operations, including union, intersection, and complementation, leading to the algebra of sets. Furthermore, the calculus of relations includes the operations of taking the converse and composing relations. [7] [8] [9]