Thank you for the response. I actually agree with you. The largest number equals infinity. But I think this whole game of large numbers has more of a psychological context than a scientific one.
I’m by no means saying that such exercises are useless—on the contrary, they develop mathematical skills (and Petrov's article even presents a very interesting modification of the Ackermann function). However, the key point here is that the human mind struggles to conceive abstract numbers or numbers that go beyond comparison with something physical. Yet, there is a constant drive toward the new and the peaks of the unknown.
We can easily imagine (albeit conditionally) a billion. Even the total number of atoms in the universe is still within the grasp of human understanding. But Graham's number is already something abstract. Petrov's Hypergiganton is even more abstract, although formally it is clearly defined and has a specific finite value.
My version, the "Super-Hypergiganton" (N = Ω(10)^{Ω(10)})—is an even larger number.
