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In mathematics, a multiset (or bag) is a generalization of the concept of a set that, unlike a set, allows multiple instances of the multiset's elements. The multiplicity of an element is the number of instances of the element in a specific multiset. For example, an infinite number of multisets exist which contain elements and , varying only by multiplicity: * The unique set contains only elements and , each having multiplicity 1 * In multiset , has multiplicity 2 and has multiplicity 1 * In multiset , and both have multiplicity 3 Nicolaas Govert de Bruijn coined the word ''multiset'' in the 1970s, according to Donald Knuth. However, the use of multisets predates the word ''multiset'' by many centuries. Knuth attributes the first study of multisets to the Indian mathematician Bhāskarāchārya, who described permutations of multisets around 1150. Knuth also lists other names that were proposed or used for multisets, including ''list'', ''bunch'', ''bag'', ''heap'', ''sample'', ''weighted set'', ''collection'', and ''suite''.〔 ==Overview== The number of times an element belongs to the multiset is the multiplicity of that member. The total number of elements in a multiset, including repeated memberships, is the cardinality of the multiset. For example, in the multiset the multiplicities of the members , , and are respectively 2, 3, and 1, and the cardinality of the multiset is 6. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset can be represented as . In multisets, as in sets and in contrast to tuples, the order of elements is irrelevant: The multisets and are equal. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multiset」の詳細全文を読む スポンサード リンク
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