If you allow infinitely long descriptions, then I don't know what's the score. In the case of "descriptions" that amount to (potentially infinite) decimal expan

If you allow infinitely long descriptions, then I don't know what's the score. In the case of "descriptions" that amount to (potentially infinite) decimal expansions, I think an argument akin to Cantor's diagonal will show that you can't possibly describe all real numbers (or all numbers between 0 and 1), but I'm not confident I can assert this to be true.