>>6 here
guys i really didn't want to mess things up. I just revised it again for uni short time ago so i was able to prove it.
As far as i know that proof is mathematically right and logically too.
Just think if it's wrong, by contradiction you should prove that it exists a number between .(9) and 1. Do it, then I'll say i'm wrong. No problem.
in b4 (.(9) + 1) / 2 :)