1. Given a set, any element, whether it belongs to the set or not, must be one of them, and no ambiguity is allowed.

2. Any two elements in a set are considered different, that is, each element can only appear once. Sometimes it is necessary to describe the situation where the same element appears many times. You can use multiset, where elements are allowed to appear multiple times.

3. As an element of a set, it must be certain, that is to say, objects that cannot be determined cannot form a set, that is, given a set, whether any object is an element of this set is also certain.

4. For a given set, the elements in the set must be different (or different from each other), that is, any two elements in the set are different objects, and the same object can only be counted as one element in the set when it belongs to the same set.

5. A set with finite elements is called a finite set, and a set with infinite elements is called an infinite set.