What One Be

Of course, A is true. $.9999\dots$ is essentially an informal way of writing $lim_{n\to\infty}1-10^n$ , and the limit is just 1.

With the second example, it is also clear that the limit of the sequence is 1. However, unlike the last case, every element of the set has a finite number of points after the decimal place, and thus is finitely far from 1. So we cannot simply look at the limit. In fact, the set has no maximal element, since for any value $n/(n+1)$ , there exists a greater value in the set, such as $(n+1)/(n+2)$ .