@dramforever what is real? what makes any number real?

the ability to talk about large numbers like 2^(2^64) (or a few powers of that) makes them, in my view, real. it's when you start getting into sizes that are so large that we can't even describe a single number, that i start to struggle. it's hard to imagine but almost all "large numbers" are of that form -- impossible to describe, even to just describe an upper bound.