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  2. Binary relation - Wikipedia

    en.wikipedia.org/wiki/Binary_relation

    A homogeneous relation over a set is a binary relation over and itself, i.e. it is a subset of the Cartesian product . [14] [32] [33] It is also simply called a (binary) relation over .

  3. List of set identities and relations - Wikipedia

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

    It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. The binary operations of set union and intersection satisfy many identities. Several of these identities or "laws" have well established names.

  4. 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 ...

  5. Set theory - Wikipedia

    en.wikipedia.org/wiki/Set_theory

    A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces { }. [5] Since sets are objects, the membership relation can relate sets as well, i.e., sets themselves can be members of other sets. A derived binary relation between two sets is the subset relation, also called set inclusion.

  6. Join and meet - Wikipedia

    en.wikipedia.org/wiki/Join_and_meet

    By definition, a binary operation on a set is a meet if it satisfies the three conditions a, b, and c. The pair ( A , ∧ ) {\displaystyle (A,\wedge )} is then a meet-semilattice . Moreover, we then may define a binary relation ≤ {\displaystyle \,\leq \,} on A , by stating that x ≤ y {\displaystyle x\leq y} if and only if x ∧ y = x ...

  7. Composition of relations - Wikipedia

    en.wikipedia.org/wiki/Composition_of_relations

    The set of binary relations on a set (that is, relations from to ) together with (left or right) relation composition forms a monoid with zero, where the identity map on is the neutral element, and the empty set is the zero element.

  8. Category of relations - Wikipedia

    en.wikipedia.org/wiki/Category_of_relations

    David Rydeheard and Rod Burstall consider Rel to have objects that are homogeneous relations. For example, A is a set and R ⊆ A × A is a binary relation on A.The morphisms of this category are functions between sets that preserve a relation: Say S ⊆ B × B is a second relation and f: A → B is a function such that () (), then f is a morphism.

  9. Transitive closure - Wikipedia

    en.wikipedia.org/wiki/Transitive_closure

    In mathematics, the transitive closure R + of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive.For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets R + is the unique minimal transitive superset of R.