Yes, and that's a case of "you don't understand mathematics, you get used to it." Which applies exactly to notation and related conventions.

Edit:

More specifically, if we let a_k=9/10^k, and let s_n be the sum from k=1 to n of a_k, then the limit of s_n as n goes to infinity will be 1, but 1 won't be in {s_n|n in R}.

When somebody who is used to calculus sees ".99..." What they are thinking of is the limit, which is 1.

But before you get used to that, most likely what you think of is some member of {s_n|n in R} with an n that's large enough that you can't be bothered to write all the nines, but which is still finite.