>>24
I'm not well known for being easy to understand, so I'll try again. First, limitations are not necessarily bad. It's a limitation of the rational numbers that it doesn't include pi. Pi is useful, so we create a new set of numbers, namely the real numbers, that does include it. In this case, it's a limitation of the real numbers that "infinitesimals" are not included. It's not that useful, so we usually neglect to construct a number system that does include "infinitesimals". I don't remember the details, but I recall a qualified friend saying that including "infinitesimals" causes problems with open/closed sets.
>>25
gj - any model of the real numbers cannot include "infinitesimals"