Originally Posted by Seltzer

Look, I know it seems counter-intuitive to believe that 0.9 recurring = 1, but you have to trust me on this one Your reasoning follows on from this:

2 - 1.9 = 0.1 = 10^-1 (which is more than 0)
2 - 1.99 = 0.01 = 10^-2 (ditto)
2 - 1.999 = 0.001 = 10^-3 (ditto)

General Form:
2 - 1.9{n} = 10^-n where 9 is repeated n times (which is more than 0)

That reasoning is fine for a finite n. But as n tends towards infinity, limit(10^-n) = 0. In other words, that 0.000...001 number you quoted is basically 1/∞ which is considered to be zero, meaning that 2 - 1.999... = 0 (which makes sense since 2 is 1.999...)