I'm not sure what you mean by "not every point is represented" but how can you say "they begin to accumulate around -1 and 1" and suggest that there are no accumulation points? For all even n, the subsequence is (1+ 1/n) which obviously converges to 1. For all odd n, the subsequence is -(1+ 1/n) which obviously converges to -1. The set of accumulation points is {-1, 1}.