What is "multiset"

n. (context set theory English) A generalization of a set: a container, in which, unlike for set, an element can be present multiple times.

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. For example, and are different multisets although they are the same set. However, order does not matter, so and are the same multiset.

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.