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  2. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    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.

  3. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    The above concept of relation [a] has been generalized to admit relations between members of two different sets (heterogeneous relation, like "lies on" between the set of all points and that of all lines in geometry), relations between three or more sets (finitary relation, like "person x lives in town y at time z "), and relations between ...

  4. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    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".

  5. Transitive closure - Wikipedia

    en.wikipedia.org/wiki/Transitive_closure

    A relation R on a set X is transitive if, for all x, y, z in X, whenever x R y and y R z then x R z. Examples of transitive relations include the equality relation on any set, the "less than or equal" relation on any linearly ordered set, and the relation "x was born before y" on the set of all people.

  6. Union (set theory) - Wikipedia

    en.wikipedia.org/wiki/Union_(set_theory)

    The most general notion is the union of an arbitrary collection of sets, sometimes called an infinitary union. If M is a set or class whose elements are sets, then x is an element of the union of M if and only if there is at least one element A of M such that x is an element of A. [11] In symbols:

  7. Category of sets - Wikipedia

    en.wikipedia.org/wiki/Category_of_sets

    Set is the prototype of a concrete category; other categories are concrete if they are "built on" Set in some well-defined way. Every two-element set serves as a subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B.

  8. Integer set library - Wikipedia

    en.wikipedia.org/wiki/Integer_set_library

    isl (integer set library) is a portable C library for manipulating sets and relations of integer points bounded by linear constraints. [2] The following operations are supported: [3] intersection, union, set difference; emptiness check; convex hull (integer) affine hull; integer projection; computing the lexicographic minimum using parametric ...

  9. Serial relation - Wikipedia

    en.wikipedia.org/wiki/Serial_relation

    A serial relation R is an endorelation on a set U. As stated by Russell, , where the universal and existential quantifiers refer to U. In contemporary language of relations, this property defines a total relation. But a total relation may be heterogeneous. Serial relations are of historic interest.