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  2. Cardinality - Wikipedia

    en.wikipedia.org/wiki/Cardinality

    There are two ways to define the "cardinality of a set": The cardinality of a set A is defined as its equivalence class under equinumerosity. A representative set is designated for each equivalence class. The most common choice is the initial ordinal in that class. This is usually taken as the definition of cardinal number in axiomatic set theory.

  3. Set cover problem - Wikipedia

    en.wikipedia.org/wiki/Set_cover_problem

    The task is then to find a minimum cardinality subset of left-vertices that has a non-trivial intersection with each of the right-vertices, which is precisely the hitting set problem. In the field of computational geometry, a hitting set for a collection of geometrical objects is also called a stabbing set or piercing set. [5]

  4. Cardinal number - Wikipedia

    en.wikipedia.org/wiki/Cardinal_number

    The notion of cardinality, as now understood, was formulated by Georg Cantor, the originator of set theory, in 1874–1884. Cardinality can be used to compare an aspect of finite sets. For example, the sets {1,2,3} and {4,5,6} are not equal, but have the same cardinality, namely three.

  5. Count-distinct problem - Wikipedia

    en.wikipedia.org/wiki/Count-distinct_problem

    In computer science, the count-distinct problem [1] (also known in applied mathematics as the cardinality estimation problem) is the problem of finding the number of distinct elements in a data stream with repeated elements. This is a well-known problem with numerous applications.

  6. Equinumerosity - Wikipedia

    en.wikipedia.org/wiki/Equinumerosity

    In some other systems of axiomatic set theory, for example in Von Neumann–Bernays–Gödel set theory and Morse–Kelley set theory, relations are extended to classes. A set A is said to have cardinality smaller than or equal to the cardinality of a set B, if there exists a one-to-one function (an injection) from A into B.

  7. 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.

  8. Aleph number - Wikipedia

    en.wikipedia.org/wiki/Aleph_number

    A set has cardinality ℵ 0 if and only if it is countably infinite, that is, there is a bijection (one-to-one correspondence) between it and the natural numbers. Examples of such sets are the set of natural numbers, irrespective of including or excluding zero, the set of all integers,

  9. Cardinal assignment - Wikipedia

    en.wikipedia.org/wiki/Cardinal_assignment

    In set theory, the concept of cardinality is significantly developable without recourse to actually defining cardinal numbers as objects in the theory itself (this is in fact a viewpoint taken by Frege; Frege cardinals are basically equivalence classes on the entire universe of sets, by equinumerosity).