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  2. Union (set theory) - Wikipedia

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

    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. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set ...

  3. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.

  4. Intersection (set theory) - Wikipedia

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

    Intersections of the unaccented modern Greek, Latin, and Cyrillic scripts, considering only the shapes of the letters and ignoring their pronunciation Example of an intersection with sets The intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B {\displaystyle A\cap B} , [ 3 ] is the set of all objects that ...

  5. 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.

  6. Venn diagram - Wikipedia

    en.wikipedia.org/wiki/Venn_diagram

    The combined region of the two sets is called their union, denoted by A ∪ B, where A is the orange circle and B the blue. The union in this case contains all living creatures that either are two-legged or can fly (or both). The region included in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B.

  7. Ring of sets - Wikipedia

    en.wikipedia.org/wiki/Ring_of_sets

    A ring of sets in the order-theoretic sense forms a distributive lattice in which the intersection and union operations correspond to the lattice's meet and join operations, respectively. Conversely, every distributive lattice is isomorphic to a ring of sets; in the case of finite distributive lattices, this is Birkhoff's representation theorem ...

  8. Intersection - Wikipedia

    en.wikipedia.org/wiki/Intersection

    The intersection (red) of two disks (white and red with black boundaries). The circle (black) intersects the line (purple) in two points (red). The disk (yellow) intersects the line in the line segment between the two red points. The intersection of D and E is shown in grayish purple. The intersection of A with any of B, C, D, or E is the empty ...

  9. Borel set - Wikipedia

    en.wikipedia.org/wiki/Borel_set

    An example of a subset of the reals that is non-Borel, due to Lusin, [4] is described below. In contrast, an example of a non-measurable set cannot be exhibited, although the existence of such a set is implied, for example, by the axiom of choice. Every irrational number has a unique representation by an infinite simple continued fraction