Hi Zen,
If 0.̅9̅ were not equal to 1, there would have to be a difference d.
For any value d you can find an exponent n, so that 1/10^(n) >= d > 1/10^(n+1)
e.g. d = 0.0002
0.001 >= d > 0.0001
But if that value d were the difference, then it is obvious that
(1 - d) < 1 - 10^(n+1) < 0.̅9̅
e.g. 0.9998 < 0.9999 < 0.̅9̅
So, obviously the difference is less than d=0.0002 or any d you choose.
