It's counter-intuitive, but your algorithm actually only generate a subset of the rational numbers. That's because all of your numbers have a finite number of decimal digits. Most reals, like 1/3 or pi, will never appear in your list. (Though numbers close to them will.)

Most reals don't have a generating algorithm, since there is an uncountable number of reals, but only a countable number of algorithms. (Assuming an algorithm has to be a finite length program.)