Why 0.999, ...=1 - also bashing OOP

A quote: "However, that leaves us reliant on an analytical concept: a limit. It’s true within mathematics as we use it. But is it inherently logically true?"

The answer is that there's no difference -- a mathematical theorem is also a logical one.

Also, the notion of a limit has been examined very carefully, and it passes muster with those who care about logical consistency. Not only that, but the idea of a limit can be replaced with the idea of infinitesimals, with no change in the outcome and no logical inconsistency:

http://en.wikipedia.org/wiki/Infinitesimal_calculus

Quote: "There are other mathematical regimes that have different rules."

Let's not allow post-modernism into mathematics, all right? Mathematical principles aren't -- shouldn't be -- a matter of opinion. There's one set of mathematical principles -- we don't get to roll out own.