>>38
All real numbers are the limits of cauchy sequences of rationals.
Two cauchy sequences with the same limit represent the same number.
Lim (n->inf) [1] = 1
0.999... =(by definition) Lim (n->inf) [1-(1/10)^n] = 1
=>0.999...=1
You can classify the cauchy sequences representing 1 as much as you want, but that doesn't change the fact that 0.999... and 1 are one and the same object. The LIMIT of these sequences.