An extension of the concept of a set. A multiset is an unordered collection of elements where the same element may appear more than once. Two multisets are equal if and only if they contain the same elements in the same multiplicities.

For example, A={1,2,3} and B={1,2,2,3} are distinct multisets (since the element 2 appears only once in A, but twice in B). On the other hand, C = {3,3,1,2} and D = {1,2,3,3} are equal as multisets.

If all the elements of a multiset A are drawn from some universal set U, then we can extend the notion of characterisitc function to multisets. The characteristic function of A (usually written), χA: U → N (where N is the set of natural numbers {0,1,2,...}) such that for all x in U, if x is an element of A, and appears with multiplicity n then χA(x)=n, and 0 otherwise.

It's easy to see that two multisets A and B are equal iff χA = χB as functions.

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