Thread: Can sets have a repeating element?

In a set, the number of times an element (whether a number or a box) occurs does not matter. We have {1, 2, 2, 3} = {1, 2, 3}. In fact, the axiom of extensionality says that A = B as sets iff for all x. Now, the proposition does not count the number of times x occurs in A; x either occurs or it does not.

In contrast, in multisets the number of times an element occurs (multiplicity) matters.