Pi and E can be thought of because there are mathematical formulas and algorithms relating them and computing them. There are only countably many such formulas

Pi and E can be thought of because there are mathematical formulas and algorithms relating them and computing them. There are only countably many such formulas & algorithms. You can't think of an arbitrary real number, in the sense of distinguishing it every other real number(including nearby reals an ε away from it), and with no other constraints besides being a real number.