So just prove that they can't be equal.

Suppose the element {a, b, c, ...} is in x and the element {A, b, c, ...} is in P(X):

a - A，b-B， .......

It is only necessary to prove that this correspondence cannot exhaust P(X). Construct a subset of x, and the elements in u and u are selected as follows: if u has the above-mentioned one-to-one correspondence, the corresponding set is v; If u does not belong to v, then u belongs to u; If u belongs to v and u does not belong to u, the construction of this set is legal, because every element in x can be judged.

According to the assumption of one-to-one correspondence, there is a corresponding relationship between X and U in X.

If x does not belong to u, then the construction method according to u must contain x, which is contradictory.

If x belongs to u, the construction method of u does not contain x, which is contradictory.

So such an X does not exist, which proves to be complete.