>>2
The Calculus taught me that as long as the function converges, the limit is a value that is the same thing as other values. Hence, since 0.999... converges, it is equal to 1, which is the limit of its convergence.
A line has no area, yet is exists on a plane. I see the two situations being fairly similar. There is zero difference between a plane, and a plane with a line subtracted. Hence, there is zero difference between 1, and 1 with an infinitesimal subracted.