>>14312768Suppose x has two or more representations, (a_k) and (b_k) where the kth terms are the kth digits of the representations of x.
There is some least j where a_j != b_j. WLOG, let a_j > b_j. It can be seen that a_j = b_j + 1, as the number represented by (b_{j+k}) is at most 10^{-j}. Particularly, (b_{j+k}) is a constant sequence of 9s. Correspondingly, (a_{j+k}) is a constant sequence of 0s. We have fixed the form of (a_k), so for any other decimal representation (c_k), we can repeat this process to see (b_k) = (c_k).
By its representation in (a_k), we can see that x = m / 10^n for some integers m, n.
