[hypersoar]

We can't really pick "random real numbers" in any practical sense, so this is pretty much a theoretical distinction. It's essentially a matter of definition. The rational numbers have probability zero of being drawn, but they still lie in the sample space.

One way to see it is this: The probability of picking any particular point in the interval is 0. But that doesn't mean that picking that point is impossible. _Some_ point has to show up when you pick one at random.