On Nov 26, 2013, at 1:38 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> I find that insight interesting. It seems to touch on the delightful "paradoxes" G. Chaitin like to point out in "How Real are Real Numbers" and his book "Meta Math". > I would suggest that by the very fact that the dart hits some number (one of the anonymous, invisible "reals") then by that very fact, that number instantly becomes very particular, and therefore, unhittable.
Yes, no number can ever be hit twice. Not an unreasonable result based on the probability argument this idea is founded on. I say we use "(pre) determined number" in place of "particular". The gist being that there are always infinitely more undetermined numbers than there are determined numbers or even sets of determined numbers and thus the odds of hitting a determined number is zero.
If the label hadn't already been taken I would have called the undetermined numbers "natural" and the determined numbers "unnatural".