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. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements:

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• 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. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements: * The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset. * In multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1. * In multiset {a, a, a, b, b, b}, a and b both have multiplicity 3. These objects are all different, when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, order does not matter in discriminating multisets, so {a, a, b} and {a, b, a} denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset {a, a, b} can be denoted as [a, a, b]. The cardinality of a multiset is constructed by summing up 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. Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth.However, the use of the concept of multisets predates the coinage of word multiset by many centuries. Knuth himself 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 this concept, including list, bunch, bag, heap, sample, weighted set, collection, and suite. (en)
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• 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. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements: (en)
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• Multiset (en)
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