In mathematics, a "bag" is an unordered list. A bag differs from a set in that it can contain the same value more than once. A bag differs from a list in that its elements are not ordered. For example, $~$\operatorname{Bag}(1, 1, 2, 3) = \operatorname{Bag}(2, 1, 3, 1) \neq \operatorname{Bag}(1, 2, 3).$~$