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  2. Multiset - Wikipedia

    en.wikipedia.org/wiki/Multiset

    The cardinality or "size" of a multiset is the sum of the multiplicities of all its elements. For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6.

  3. Bose–Einstein statistics - Wikipedia

    en.wikipedia.org/wiki/Bose–Einstein_statistics

    More generally, each element of (,) is a multiset of cardinality (number of dice) with elements taken from the set {, …,} of cardinality (number of possible values of each die), and the number of such multisets, i.e., (,) is the multiset coefficient

  4. HyperLogLog - Wikipedia

    en.wikipedia.org/wiki/HyperLogLog

    HyperLogLog is an algorithm for the count-distinct problem, approximating the number of distinct elements in a multiset. [1] Calculating the exact cardinality of the distinct elements of a multiset requires an amount of memory proportional to the cardinality, which is impractical for very large data sets. Probabilistic cardinality estimators ...

  5. Set (abstract data type) - Wikipedia

    en.wikipedia.org/wiki/Set_(abstract_data_type)

    In some cases a multiset in this counting sense may be generalized to allow negative values, as in Python. C++'s Standard Template Library implements both sorted and unsorted multisets. It provides the multiset class for the sorted multiset, as a kind of associative container, which implements this multiset using a self-balancing binary search ...

  6. Glossary of set theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_set_theory

    2. An inductive definition is a definition that specifies how to construct members of a set based on members already known to be in the set, often used for defining recursively defined sequences, functions, and structures. 3. A poset is called inductive if every non-empty ordered subset has an upper bound infinity axiom See Axiom of infinity.

  7. Cardinal assignment - Wikipedia

    en.wikipedia.org/wiki/Cardinal_assignment

    The oldest definition of the cardinality of a set X (implicit in Cantor and explicit in Frege and Principia Mathematica) is as the set of all sets that are equinumerous with X: this does not work in ZFC or other related systems of axiomatic set theory because this collection is too large to be a set, but it does work in type theory and in New ...

  8. ‘A Complete Unknown’ Director James Mangold Says There’s ...

    www.aol.com/complete-unknown-director-james...

    James Mangold misses the era when movies weren’t embarrassed to make audiences feel something. The director of the Bob Dylan musical biopic “A Complete Unknown” and comic book adaptation ...

  9. Set-theoretic topology - Wikipedia

    en.wikipedia.org/wiki/Set-theoretic_topology

    Cardinal functions are widely used in topology as a tool for describing various topological properties. [4] [5] Below are some examples.(Note: some authors, arguing that "there are no finite cardinal numbers in general topology", [6] prefer to define the cardinal functions listed below so that they never take on finite cardinal numbers as values; this requires modifying some of the definitions ...