User blog comment:Emlightened/Definition of Googology/@comment-28606698-20170709205728/@comment-30754445-20170709215357

I'm not sure what's the "problem" really is.

Why not simply state that:

"Googology is a branch of mathematics that studies the realm of really large numbers"?

Becaue that's what googology really is.

My point is, that studying "the realm of large numbers" includes much more than creating and naming large numbers. Saying otherwise is like believing that geometry is about drawing a bunch of random shapes and giving them names. It is utterly rediculous.

So yes, we need to study fast growing functions, because without them we can't even compare two googological numbers. We need ordinals because they connect our field of interest with well-developed structures from set theory. We need to study levels of uncomputability because they translate - quite directly - to different googological levels of numbers which can then be ordered by size.

Even the people who are more into the whimsical side of googology are benifiting from these studies. After all, the better our understanding of the playground is, the more fun we'll have playing in it.