Notice, however, that it can’t possibly be the first entry on the list, since it differs from that entry at least in the first decimal place. It can’t be the second entry either, differing as it does from it in at least the second decimal place; nor the third, for the analogous reason, nor the fourth—nor the nth. It cannot, in fact, be anywhere on this list that was supposed to contain all of the reals in (0,1) because it differs from every entry on it in at least one decimal place—and that is the contradiction.
