Don't want to sound condescending, but I don't think that seeing this in layman's terms has any merit. All of mathematics, although often built out of some intu

Don't want to sound condescending, but I don't think that seeing this in layman's terms has any merit. All of mathematics, although often built out of some intuitive, natural notions, is about definition: describe an object and then see what follows from your description. The description is not, in general, something that's "out there" and can be deduced by common-sense. (Infinity, in fact, can be defined as a number and can be defined as a non-number in different contexts. But infinity is only something when it's part of a strictly defined mathematical universe with specific axioms.)