Definition
Multiset
A multiset is a collection in which an object may occur more than once and its number of occurrences matters. Over a set
of possible objects, a multiset is described by its multiplicity function where
is the number of copies of in . Two multisets are equal precisely when every object has the same multiplicity: An ordinary set is the special case in which every multiplicity is either
or .
Support and Size
The support of a multiset is the set of objects that occur at least once:
For a finite multiset, its size counts occurrences rather than only distinct objects:
Example
Example
Consider
Its multiplicities are
Therefore