I think the notion of continuity (and calculus) could not even exist without the idea of infinitely precise numbers. It is hard for me to say that something (real numbers) is "mythical" when it has independently driven so many to the same conclusions. My vote is that mathematics is the study of real numbers.
On Sep 5, 2012, at 11:38 AM, Joe Niederberger <email@example.com> wrote:
> Here's a debate. Do mathematicians actually study infinitely precise numbers, or do they merely play games in (hopefully) consistent systems whose semantics have traditionally been explained as studying such mythical objects? The games, in as much as they have been given precise rules, appear themselves to be computational games.