>>53 has attacked one terminological point in the post, without attacking the rest. He has not even tried to refute the proof. In fact, the point he attacked has nothing to do with the proof as
>>52 could well have just posted:
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.
QFT.
>>53 doesn't know shit about what he's talking about, and is probably the same person as
>>30.