by wendy » Sun Mar 02, 2014 7:18 am
There is no paradox, since the 100% is an approximation. While there are more positive numbers greater than any given X, it is by no means 100%, and that you can't simply remove the possibility of picking a lesser number by pretending that some small n/N tends to 0, it must be 0 absolute.
I ran a program along this sort of line, where you generated what amounts to p random numbers less than p^2. (the actual property is that if b were chosen, then p^2 | b^(p-1). But by accepting a value you had to soot it into your hand of known numbers. We were only looking for the smallest 40, so we passed any value that was something like > 60p. p ran into the millions.