Dale, it's not the upper limit of all numbers, it's the upper limit on the answer to a specific mathematical question. I think G's number is G(63), but G's notation can be used on any integer. Surely G(99) > G(63), but G(63) is useful because it says that the answer to a specific question cannot be greater than that.

This kind of this is very useful in general in computer science and operations research, for example, although I've never had occasion to use any numbers quite this big. I just have a very vague awareness that there are people looking at much bigger problem spaces.