@WalterPlinge wrote:
This is more-or-less because the concept of infinity is hard to grasp. There are "infinitely many" integers (i.e. whole numbers), "infinitely many" rationals, and "infinitely many" irrationals, however it is still possible to compare the "sizes" of these different collections of numbers. There is a certain sense in which there are "as many" integers as rationals, but there are far more irrationals (and hence more real numbers) than either. Infinitely more, in fact.
If you use the standard intuition for probability (number of favorable outcomes divided by number of total outcomes), taking into account that there are "infinitely more" reals than rationals, you would get that the probability of hitting a rational number is 0.
If you want a more rigorous explanation, then it would be a good idea to look up the concept of cardinality of a set. It gets pretty weird.
