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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. 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 ...

  4. Cardinality (data modeling) - Wikipedia

    en.wikipedia.org/wiki/Cardinality_(data_modeling)

    Within data modelling, cardinality is the numerical relationship between rows of one table and rows in another. Common cardinalities include one-to-one , one-to-many , and many-to-many . Cardinality can be used to define data models as well as analyze entities within datasets.

  5. Inclusion–exclusion principle - Wikipedia

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

    where is the multiset for which () =, and μ(S) = 1 if S is a set (i.e. a multiset without double elements) of even cardinality. μ(S) = −1 if S is a set (i.e. a multiset without double elements) of odd cardinality. μ(S) = 0 if S is a proper multiset (i.e. S has double elements).

  6. Flajolet–Martin algorithm - Wikipedia

    en.wikipedia.org/wiki/Flajolet–Martin_algorithm

    Estimate the cardinality of as /, where . The idea is that if n {\displaystyle n} is the number of distinct elements in the multiset M {\displaystyle M} , then B I T M A P [ 0 ] {\displaystyle \mathrm {BITMAP} [0]} is accessed approximately n / 2 {\displaystyle n/2} times, B I T M A P [ 1 ] {\displaystyle \mathrm {BITMAP} [1]} is accessed ...

  7. Paradoxes of set theory - Wikipedia

    en.wikipedia.org/wiki/Paradoxes_of_set_theory

    The root of this seeming paradox is that the countability or noncountability of a set is not always absolute, but can depend on the model in which the cardinality is measured. It is possible for a set to be uncountable in one model of set theory but countable in a larger model (because the bijections that establish countability are in the ...

  8. Löwenheim–Skolem theorem - Wikipedia

    en.wikipedia.org/wiki/Löwenheim–Skolem_theorem

    It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism. As a consequence, first-order theories are unable to control the cardinality of their infinite models.

  9. 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 ...