If A is a subset of B, and at least one element in B does not belong to A, then the set A is called the proper subset of the set B, for example, the set of all Asian countries is the set of all countries on earth in proper subset. The set of all natural numbers is the proper subset of the set of all integers. { 1, 3} ? 6? 3 { 1, 2, 3, 4} { 1, 2, 3, 4} ? 6? The difference between 7 {1, 2,3,4} proper subset and subset is that all elements in one set are elements in another set, which may be equal to another set. Proper subset means that all elements in one set are elements in another set, but there is no equivalent editing. The examples of proper subset and subset in this paragraph are larger than those in proper subset, and there can be complete works in the subset, not in proper subset. Also, pay attention to the non-empty proper subset and proper subset. For example, the complete set I is {1, 2,3}, and its subsets are {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3}. Proper subset is {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3}, plus an empty set, excluding the complete I itself. Non-empty proper subset is {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3}, excluding complete I and empty sets. Let the number of complete set I be n, the number of its subsets be 2 to the n power, the number of proper subset be 2-1 to the n power, and the number of nonempty proper subset be 2 -2 to the n power.