A bag or multiset is a collection of object whose members need not be distinct (unlike a set , whose members are distinct).
So the bag [ a , b , c , c ] is the same as the bag [ c , a , b , c ] but distinct from the bag [ a , b , c ]. Contrast this with the set { a , b , c , c }, which is the same as the set { c , a , b , c }, and is also the same as the set { a , b , c }.
The number of repetitions of each member is the multiplicity of that member. For the bag [ a , b , c , c ], the multiplicity of a and of b is 1, and the multiplicity of c is 2.