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Multiset

Logic, Foundations and Set Theory

A multiset, also called a bag or mset, modifies the concept of a set by allowing multiple instances of each of its elements, with the number of instances of a given element called its multiplicity. The set {a, b} and the multisets {a, a, b} and {a, a, a, b, b, b} are all different as multisets, since they assign different multiplicities to a and b, even though they share the same underlying elements. As with ordinary sets, and unlike tuples, the order in which elements are listed does not matter, so {a, a, b} and {a, b, a} denote the same multiset. The cardinality of a multiset is the sum of the multiplicities of all its elements; Nicolaas Govert de Bruijn coined the word multiset in the 1970s.

Facts
Origin Year
1675 1
Dates the 1675 publication by Jean Prestet of a general rule for multiset permutations, the earliest precisely dated formal mathematical treatment named in the source; an earlier circa 1150 study by Bhaskaracharya is dated only approximately, and the word multiset itself was coined later still, by Nicolaas Govert de Bruijn in the 1970s.
Connections

Associated With

Combination, Concepts
Sets, Concepts

In Branch

Sources
1. Multiset (Wikipedia)
Wikimedia Foundation
  • Lead section
    In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements.
  • History section
    Jean Prestet published a general rule for multiset permutations in 1675.
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