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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. 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 ...

  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. 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. Paradoxes of set theory - Wikipedia

    en.wikipedia.org/wiki/Paradoxes_of_set_theory

    Then an ordinal number is, by definition, a class consisting of all well-ordered sets of the same order type. To have the same order type is an equivalence relation on the class of well-ordered sets, and the ordinal numbers are the equivalence classes. Two sets of the same order type have the same cardinality.

  7. Fuzzy set - Wikipedia

    en.wikipedia.org/wiki/Fuzzy_set

    A fuzzy set is a pair (,) where is a set (often required to be non-empty) and : [,] a membership function. The reference set (sometimes denoted by or ) is called universe of discourse, and for each , the value () is called the grade of membership of in (,).

  8. 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.

  9. 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 ...