User blog comment:Edwin Shade/There is No Limit To Googology/@comment-32783837-20171129023530

We are not an all-knowing species. We have finite space and finite time to describe such things. If there is no limit, then we would be able to reach through all the finite numbers eventually. That would imply one of two things:

1: there is a largest finite number ψ such that ψ+n = ω  where n can be any positive number of arbitrarily small size (also implying there is a smallest number?), which doesn't make sense--there is no largest number.

2: we are capable of processing and holding an infinite amount of information, which is obviously false.

Eventually, as we create more and more powerful systems, we will not approach infinity, but merely approach the fabled K(n) systems, which cannot output an infinite number with a finite number of symbols.