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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.
In mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, 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 ...
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Static sets allow only query operations on their elements — such as checking whether a given value is in the set, or enumerating the values in some arbitrary order. Other variants, called dynamic or mutable sets , allow also the insertion and deletion of elements from the set.
[2] [3] Primitives of imperative programming languages rely on assignment to do iteration. [4] At the lowest level, assignment is implemented using machine operations such as MOVE or STORE. [2] [4] Variables are containers for values. It is possible to put a value into a variable and later replace it with a new one.
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 .
Set operation may have one of the following meanings. Any operation with sets; Set operation (Boolean), Boolean set operations in the algebra of sets; Set operations (SQL), type of operation in SQL; Fuzzy set operations, a generalization of crisp sets for fuzzy sets
Venn diagram showing the union of sets A and B as everything not in white. In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as