On Nov 27, 2013, at 5:33 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> But -- now describe a process that "selects" that non-computable number. The best I could come up would be > a Geiger-counter driven digit generator. But it would never get to the end of that first number. That "dart" would never really reach the board! So saying "pick a random real ...." really hides quite a bit of sisyphean effort.
It's mathematics, not physics. This reminds me of a past discussion we had regarding imaginary numbers equal to SQRT(-1).
Computable and uncomputable numbers both have an infinite number of decimal digits. A more formal argument would probably look at these numbers using a finite precision, N and prove that as the number of digits increase without bound (N -> infinity) the probability (P) approaches zero. You are ok with limits, right? Or is analysis and calculus suspect because of the impossibility of ever actually reaching infinity?