I am going to prove through logical steps the following statement:

"There are

either infinite or zero omnipotent beings."

Let's say P(n) is the claim we want to prove.

So P(n) is "For any number n (n>0 , n integer) there can't be exactly n omnipotent beings."

We are going to prove that P(1) is true:

Let's assume that there is

exactly one omnipotent being which we will call x, then:

Can x create another omnipotent being y?

- If no, then it is not omnipotent because there is something it can't do. Contradiction.

- If yes, then there are two omnipotent beings. Contradiction.

We arrive at contradiction in any case.

Therefore there can't be exactly one omnipotent being.

So P(1) is true.

Now we are going to assume that the same claim holds for exactly n omnipotent beings and we are going to prove that this claim is true for n+1 omnipotent beings.

Or in short:

We assume that P(n) is true and we are going to prove that if P(n) is true then P(n+1) is true.

With that said:

Assuming there are

exactly n+1 omnipotent beings, then:

Can any of the above entities create another omnipotent being?

- If yes, then there aren't exactly n+1 omnipotent beings (there are at least n+2). Contradiction.

- If no, then there is something that these beings can't do. Contradiction.

We arrive in contradiction in any case.

Therefore if P(n) is true then P(n+1) is also true.

Let's see what we proved so far:

- P(1) is true

- If P(n) is true then P(n+1) is true (1)

(1) => (for n = 1) if P(1) is true then P(2) is true and because P(1) is indeed true, P(2) is true.

but if P(2) is true then similary P(3) is true

but if P(3) is true then similary P(4) is true

and so on and the forth.

Therefore P(n) is true for every n.

The only cases left are if n=0 or n --> +∞

Q.E.D.

Prove me wrong