Originally Posted by Kestrel

So looking at this some more, I think the guy is right (as much of an arrogant prick he is), but his proofs are wrong. Two ways to look at it:
1) Calculus limit
0.99999..... = 1-1/10^x, where x goes to +inf.
lim x->inf (1-1/10^x) = 1

2) Geometric series
0.99999..... = 0.9 + 0.09 + 0.009 + ... + 0.9*1/10^x, where x goes to +inf
sum of a converging geometric series = a/(1-r)
=> 0.9/(1-1/10) = 1