I find this easy to accept: lim_{n->inf} 1 - 1/10^n = 1 But I'm not quite sure if I agree that 0.999... = lim 0.999... edit: according to Wikipedia, they'r

I find this easy to accept: lim_{n->inf} 1 - 1/10^n = 1 But I'm not quite sure if I agree that 0.999... = lim 0.999... edit: according to Wikipedia, they're today defined to be equal. While convenient, it's not obvious to me. edit2: ah-ha! I just remembered the proof that had once upon a time satisfied me: there is a number between any two distinct numbers. there isn't one between 0.999... and 1, so they aren't distinct.