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  2. Union (set theory) - Wikipedia

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

    One can take the union of several sets simultaneously. For example, the union of three sets A, B, and C contains all elements of A, all elements of B, and all elements of C, and nothing else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C.

  3. Relation (mathematics) - Wikipedia

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

    Union [e] If R and S are relations over X then R ∪ S = { (x, y) | xRy or xSy} is the union relation of R and S. The identity element of this operation is the empty relation. For example, ≤ is the union of < and =, and ≥ is the union of > and =. Intersection [e] If R and S are relations over X then R ∩ S = { (x, y) | xRy and xSy} is the ...

  4. List of set identities and relations - Wikipedia

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

    A universe set is an absorbing element of binary union . The empty set ∅ {\displaystyle \varnothing } is an absorbing element of binary intersection ∩ {\displaystyle \cap } and binary Cartesian product × , {\displaystyle \times ,} and it is also a left absorbing element of set subtraction ∖ : {\displaystyle \,\setminus :}

  5. 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".

  6. Category of sets - Wikipedia

    en.wikipedia.org/wiki/Category_of_sets

    Every set is a projective object in Set (assuming the axiom of choice). The finitely presentable objects in Set are the finite sets. Since every set is a direct limit of its finite subsets, the category Set is a locally finitely presentable category. If C is an arbitrary category, the contravariant functors from C to Set are often an important ...

  7. Set theory - Wikipedia

    en.wikipedia.org/wiki/Set_theory

    Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.

  8. Lévy hierarchy - Wikipedia

    en.wikipedia.org/wiki/Lévy_hierarchy

    The second entry of the ordered pair x is b [7] p. 14; f is a function. x is the domain/range of the function f. y is the value of f on x [7] p. 14; The Cartesian product of two sets. x is the union of y [8] x is a member of the αth level of Godel's L [9] R is a relation with domain/range/field a [7] p. 14

  9. Glossary of set theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_set_theory

    6. Cantor's absolute is a somewhat unclear concept sometimes used to mean the class of all sets 7. Cantor's theorem states that the powerset operation increases cardinalities Card The cardinality of a set Cartesian product The set of all ordered pairs obtained from two sets, where each pair consists of one element from each set. cardinal 1.