Is a multiset an element of itself?

Question

I know that a set cannot be an element of itself, but I don’t find anything about multisets. So, my question is: is a multiset an element of itself?

Answer 1

No. Mathematical objects cannot contain themselves under ZFC (which also tells us that a set cannot be a member of a set which is a member of itself or a member of a set which is a member of a set which is a member of itself, and so on), because they are also defined in terms of sets.

For example, the multiset is a set of order pairs $\{(A,c),\ldots\}$ where $A$ is the element they contain and $c$ is the number of that element the multiset contains.