Quote Originally Posted by Random_person View Post
Aleph-0 is, as far as I am aware, the lowest transfinite number, being defined as the cardinality of the set of natural numbers. It is the largest number which you can name, including by means of this process, with an arbitrary increase in size. It is about as close to infinity as you get while still being vaguely able to work with it sanely.
See, that I can agree with. I have no problem with this having a chance of reaching an arbitrarily high number. I even said it would do that. It's just when you start confusing an arbitrarily high number with infinity that the problems crop up.