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  2. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusion–exclusion...

    Inclusion–exclusion illustrated by a Venn diagram for three sets. Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections.

  3. Venn diagram - Wikipedia

    en.wikipedia.org/wiki/Venn_diagram

    A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.

  4. König's theorem (set theory) - Wikipedia

    en.wikipedia.org/wiki/König's_theorem_(set_theory)

    In set theory, KÅ‘nig's theorem states that if the axiom of choice holds, I is a set, and are cardinal numbers for every i in I, and < for every i in I, then <. The sum here is the cardinality of the disjoint union of the sets m i, and the product is the cardinality of the Cartesian product.

  5. Cardinal assignment - Wikipedia

    en.wikipedia.org/wiki/Cardinal_assignment

    The goal of a cardinal assignment is to assign to every set A a specific, unique set that is only dependent on the cardinality of A. This is in accordance with Cantor 's original vision of cardinals: to take a set and abstract its elements into canonical "units" and collect these units into another set, such that the only thing special about ...

  6. Cantor's theorem - Wikipedia

    en.wikipedia.org/wiki/Cantor's_theorem

    As a consequence, the cardinality of the real numbers, which is the same as that of the power set of the integers, is strictly larger than the cardinality of the integers; see Cardinality of the continuum for details. The theorem is named for Georg Cantor, who first stated and proved it at the end of the 19th century.

  7. Cardinality - Wikipedia

    en.wikipedia.org/wiki/Cardinality

    The cardinality of the natural numbers is denoted aleph-null (), while the cardinality of the real numbers is denoted by "" (a lowercase fraktur script "c"), and is also referred to as the cardinality of the continuum.

  8. 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.

  9. Finite set - Wikipedia

    en.wikipedia.org/wiki/Finite_set

    That is, the power set ℘ of a finite set S is finite, with cardinality | |. Any subset of a finite set is finite. The set of values of a function when applied to elements of a finite set is finite. All finite sets are countable, but not all countable sets are finite. (Some authors, however, use "countable" to mean "countably infinite", so do ...