The equivalence relation R on a set or class (taking a set as an example) refers to a reflexive, symmetric and transitive binary relation, which can be divided into equivalence classes in the set that defines equivalence relations (that is, two elements belong to the same equivalence class as long as they have xRy), that is, a set composed of some subsets of the set. It is easy to prove that these subsets are disjoint in pairs and their sum is equal to the original set. An application: define an equivalence relation R on the true class V of all sets. If there is a one-to-one correspondence between two sets X and Y, xRy is divided into equivalence classes according to this equivalence relation, and then a representative element is extracted from each equivalence class by using the axiom of choice on the class, that is, the definition of the potential of the set based on AC.