Symmetry,

Transfer binary relations,

In the set where equivalence relation is defined, equivalence classes can be divided according to equivalence relation (that is, as long as two elements have xRy,

They belong to the same equivalence class),

That is, a set consisting of some subsets of a set,

It is easy to prove that these subsets are disjoint and equal to the original set.

Application:

Define the equivalence relation r on the true class v of all sets,

If two sets of x,

There is a one-to-one mapping between y and y,

Then xRy.

According to this equivalence relation, it is divided into equivalence classes,

Then a representative element is extracted from each equivalent class by using the axiom of choice on the class.

That is, the definition of the potential of the set based on AC.