You will pick an irrational number "almost surely" or "with probability 1". It's a somewhat counterintuitive* concept, but very well defined mathematically. ht

You will pick an irrational number "almost surely" or "with probability 1". It's a somewhat counterintuitive* concept, but very well defined mathematically. https://en.wikipedia.org/wiki/Almost_surely https://en.wikipedia.org/wiki/Almost_surely [*] (For example, any individual number has probability 0 of being picked (exactly, not approximately), yet one is being picked. Or: there are infinitely many rational numbers between 0 and 1, but the probability that any one of them is picked is 0. Thus, the probability that one of the remaining ones is being picked (an irrational number), is 1.)