What I said was any given natural number. Unbounded and infinite are not the same thing.
I do understand that you're talking about any given natural number. Surely you understand that if there are theorems that require more steps (to prove) than any given natural number, then it follows that there are theorems that require an infinite number of steps. Of course, infinite and unbounded aren't the same in the case of convergence! But here you clearly have divergence.
Kindly just give me the name of the theorem you're quoting, please. I'd really like to take a look at it and can't find it on Google using the keywords and phrases I'd expect to find in any description or discussion of it. Thx.