In reply to:

If you don't believe that 0.9999999... is equal to 1, then please tell me how far from 1 it is. That is, what is 1 - 0.9999999... = ???? If you are right, the difference must be equal to some probably quite small but finite number

That is exactly what I am saying. 1- (0.999999...) is an infinitesimally small value not quite equal to zero. When we talk about 0.99999999... we are talking about the limit of x as x approaches 1, which is represented lim(x) x --> 1. This is understood to be infinitesimally close to 1 but not quite one.

The example I offered suffered from a lack of ellipses, but it holds true in differentiating 3.000...0001 from 2.9999999.... In fact, the more zeros or nines in the decimal point, the greater the difference between the two defined outcomes.