multiset

In a multiset, each element can appear an arbitrary number of times.

In mathematics, bag is another name for a multiset.

Certain items are either elements of that multiset, or they are not.

Thus any groupoid is equivalent to a multiset of unrelated groups.

However, multisets are different from sets: The same type of item can be in the multiset more than once.

A multiset is illustrated by means of a histogram.

If the multiset being represented is immutable, this is not an issue.

Python's standard library includes , which is similar to a multiset.

Let's define as one of the maximum of the multiset .

Another is the multiset of solutions of an algebraic equation.

The number of times an element belongs to the multiset is the multiplicity of that member.

Negative numbers are allowed in the multiset.

The below table would generate a multiset :

Grzymala-Busse (1987) introduced the concept of a rough multiset, using multirelations.

Not every multiset of positive integers has a partition into two halves with equal sum.

A multiset is a generalization of the notion of a set such that an element can occur more than once.

A multiset corresponds to an ordinary set if the multiplicity of every element is one (as opposed to some larger natural number).

Usual set theoretic notation is employed, though note that is a multiset.

The scalar multiplication of a multiset by a natural number n may be defined as:

The multiset of eigenvalues of this matrix is called the Seidel spectrum.

A multiset can also be considered an unordered tuple:

Suppose is a multiset and .

The concept of a multiset is a generalization of the concept of a set.

The size of an -biased set is the size of the multiset that generates the sample space.

The lattice of all sub-multisets of a multiset.