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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.
The unsorted multiset is standard as of C++11; previously SGI's STL provides the hash_multiset class, which was copied and eventually standardized. For Java, third-party libraries provide multiset functionality: Apache Commons Collections provides the Bag and SortedBag interfaces, with implementing classes like HashBag and TreeBag.
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 ...
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. [a] Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time ...
Throughout this article, capital letters (such as ,,,,, and ) will denote sets.On the left hand side of an identity, typically, will be the leftmost set, will be the middle set, and
Modern object-oriented languages, such as C++ and Java, support a form of abstract data types. When a class is used as a type, it is an abstract type that refers to a hidden representation. In this model, an ADT is typically implemented as a class, and each instance of the ADT is usually an object of that class.
In the object-oriented application programming paradigm, which is related to database structure design, UML class diagrams may be used for object modeling. In that case, object relationships are modeled using UML associations, and multiplicity is used on those associations to denote cardinality. Here are some examples: [5]
In computer programming, a collection is an abstract data type that is a grouping of items that can be used in a polymorphic way. Often, the items are of the same data type such as int or string. Sometimes the items derive from a common type; even deriving from the most general type of a programming language such as object or variant.