> We don't have access to unbounded quantities, so any discussion of them is necessarily going to be more abstract than the notions we're used to dealing with.

> We don't have access to unbounded quantities, so any discussion of them is necessarily going to be more abstract than the notions we're used to dealing with. I've always thought of infinite as very concrete unbounded processes, rather than quantities (but then, I'm a computer scientist, not a mathematician). You cannot count the size of an infinite set because you can never stop counting; the process goes on and on. So the way to compare infinities is to map things between them. If you can map all elements from the first infinite to the second, but not the other way around, the second is larger than the first. It makes sense as to define this process as the way to compare sizes, since actually counting all their items is ruled out. "Almost all" elements of an infinite set could be defined similarly, if for each item without a particular property you can create a limitless variety of different items with it.