Ah, now I get it, thanks Klaus.
I'd never actually heard the term "limit transition" before, damn that book for not explaining the thing properly... Neglecting to mention that the authors didn't in fact consider the two things to be exactly the same made me doubt my whole understanding of the issue.
Now I don't, so I'll join the discussion. The series will not reach 2, it will only approach it. Likewise, 1 != 0,9999...
Let's do it with some finite numbers first:
Now, if you continue inserting a finite number of nines, the difference of 9-8,9...1 will still remain there preventing x from equaling 1, it'll just be smaller. Problem is, at infinity it'll be infinitely small, and you won't be able to manipulate it normally, which is why you can manage to prove 0,99...=1.
However, if you write it properly as lim(x->1) = 1, you won't. Limit transitions aside, that is
I hope that made any sense, it's just my interpretation based on normal schoolwork.