The power set of {0, 1} is

{{}, {0}, {1}, {0, 1}}.

The power set of the power set of {0, 1} is

{{}, {{}}, {{0}}, {{1}}, {{0, 1}}, {{}, {0}}, {{}, {1}}, {{}, {0, 1}}, {{0}, {1}}, {{0}, {0, 1}}, {{1}, {0, 1}}, {{}, {0}, {1}}, {{}, {0}, {0, 1}}, {{}, {1}, {0, 1}}, {{0}, {1}, {0, 1}}, {{}, {0}, {1}, {0, 1}}}.

Note that {0} is not a member of the power set of the power set of {0, 1}.

No member of the power set of the power set of {0, 1} is a set of numbers, it is a set of sets.

Every member of the power set of the power set of any set S is a set of sets.

Consider the power set of the power set of the power set of {0, 1}.

How many members does it have?

It would be very difficult to type a representation of this set character by character.

It would be much easier to write a program to display a representation of this set.

I just wrote that program and the output is 5,668,866 characters.

You write your version.

If we let 0 represent {} and 1 represent {{}},

then {0, 1} is the power set of the power set of {}.

Consider the power set of the power set of the power set of N.