Why are rationals special? They represent an exactness in a similarly unphysical way as the integers. The rationals are infinitely precise. 1/3 is not the same as 0.33333 or 0.33333333 or 0.3.
The real numbers exist and are approximable, either by rationals or by decimal expansion. The idea of approximability and computability are the critical things, not the specific representation.
The real numbers exist and are approximable, either by rationals or by decimal expansion. The idea of approximability and computability are the critical things, not the specific representation.