Multiset

Common card · No. 226191

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 number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist that contain only elements a and b, but vary in the multiplicities 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 the multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1. In the 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, the order in which elements are listed does not matter in discriminating multisets, so {a, a, b} and {a, b, a} denote the same multiset. To distinguish...

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