It just means that the irrational number k = 0.9999~ is infinitely close to 1. By definition, this means nothing is closer to 1 than k. That doesn't mean k = 1.
You can prove the contrary through induction:
k = lim(n->+∞) ∑(n=1) 9*10^n
Take nmax = 1: k1 = 0.9
Take nmax = 2: k2 = 0.9+x = 0.99 where x=0.09 and x < 1-k1
Take nmax = 3: k3 = 0.99+x = 0.999 where x=0.009 and x < 1-k2.
If you see k as an arithmetic series, for every rank, the number added is always inferior to 1-k(n-1) where k(n-1) is the previous rank. Therefore it will grow infinitely close to 1, without ever reaching it, ever.
>>30 was therefore wrong. He was just playing with the misrepresentation that (0.99999~ * 10) - 9 is still 0.9999~, which is a circular proof.
>>47 is therefore correct, but should have provided us with the above truth instead of saging.
Good, you all have it now, you can all let the thread die.