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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 ...
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. Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth.
In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...
Sometimes the items derive from a common type; even deriving from the most general type of a programming language such as object or variant. Although easily confused with implementations in programming languages, collection, as an abstract concept, refers to mathematical concepts which can be misunderstood when the focus is on an implementation.
For example, C.J. will sometimes ask that gas with odd numbers be collected or gas with even numbers be collected, meaning that this game sometimes teaches mathematics. He will sometimes also ask things related to language arts/reading, such as asking the player to collect gas with words that have a blend in them or words with a digraph in them ...
A second distinction among sampling schemes is whether ordering matters. For example, if we have ten items, of which we choose two, then the choice (4, 7) is different from (7, 4) if ordering matters; on the other hand, if ordering does not matter, then the choices (4, 7) and (7, 4) are equivalent.
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