As Cyan pointed out, when you choose a number confined to a certain number of bits, you are actually choosing from among the rationals.
I don’t understand your reference to QM. I wasn’t objecting to the randomness aspect. I was simply pointing out that to actually receive that randomly chosen real, you will (almost certainly) need to receive an infinite number of bits, and assuming finite channel capacity, that will take an infinite amount of time. So that event you mentioned, the one with an infinitesimal probability (zero probability for all practical purposes) is not going to actually happen (i.e. finish happening).
It was a minor quibble, which I now regret making.
As Cyan pointed out, when you choose a number confined to a certain number of bits, you are actually choosing from among the rationals.
I don’t understand your reference to QM. I wasn’t objecting to the randomness aspect. I was simply pointing out that to actually receive that randomly chosen real, you will (almost certainly) need to receive an infinite number of bits, and assuming finite channel capacity, that will take an infinite amount of time. So that event you mentioned, the one with an infinitesimal probability (zero probability for all practical purposes) is not going to actually happen (i.e. finish happening).
It was a minor quibble, which I now regret making.