Your equation included more operations than just addition, subtraction, multiplication and division, under which the set of rationals is indeed closed. It included the operation of infinite summation under which the set of rationals is most definitely NOT closed. Any infinite, nonrepeating decimal is an example of an infinite summation of rationals that yields an irrational result, for example.
That is no more different than the probability of a needle touching a line as I have described. That has been my point all along. You can't "stop".