> Sampling uniformly such that each distance is equally likely across the line gives at least a 90% chance of choosing a rational.
Let's say the numbers are targets on the line. Your distribution implies the range 1-9 is less dense with targets than the range 9-10. Doesn't that mean you're less than 90% likely to hit something between 1-9?
> You are NOT more likely to throw a dart that lands in 9+ just because you have magically introduced an infinitely tense series of irrationals in that range.
If we turn this around, by forbidding a bunch of values in the 1-9 range from being hit, then won't the probabilities get skewed towards the 9-10 range?
Let's say the numbers are targets on the line. Your distribution implies the range 1-9 is less dense with targets than the range 9-10. Doesn't that mean you're less than 90% likely to hit something between 1-9?
> You are NOT more likely to throw a dart that lands in 9+ just because you have magically introduced an infinitely tense series of irrationals in that range.
If we turn this around, by forbidding a bunch of values in the 1-9 range from being hit, then won't the probabilities get skewed towards the 9-10 range?