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In set theory, the intersection of two sets and , denoted by , [1] is the set containing all elements of that also belong to or equivalently, all elements of that also belong to . [2] Notation and terminology
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 computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set.
Two disjoint sets. In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two ...
From a spatial point of view, nearness (a.k.a. proximity) is considered a generalization of set intersection.For disjoint sets, a form of nearness set intersection is defined in terms of a set of objects (extracted from disjoint sets) that have similar features within some tolerance (see, e.g., §3 in).
TypeScript supports intersection types, [5] improving expressiveness of the type system and reducing potential class hierarchy size, demonstrated as follows.. The following program code defines the classes Chicken, Cow, and RandomNumberGenerator that each have a method produce returning an object of either type Egg, Milk, or number.
The second polygon set comprises the four large inward-pointing arrows. In each example, the areas resulting from the GPC operation between the two sets of polygons are rendered in colour. This example shows difference between the two sets: Example of GPC Difference. This example shows intersection between the two sets: Example of GPC Intersection
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".