15 ms·
> Probability-zero events happen all the time. The probability of getting any specific value selected uniformly at random from the unit interval (say, 0.232829)
by baduser 2y ago
> Probability-zero events happen all the time. The probability of getting any specific value selected uniformly at random from the unit interval (say, 0.232829) is zero.
I would strongly challenge that claim. First, you did not choose that number uniformly at random, you chose it from at best a countably infinite subset, or more realistically, from a finite subset. And secondly, I do not think you can describe a situation where a number is actually chosen uniformly and randomly from the unity interval.
- rbanffy 2y agoBut, if the set is infinite, won’t the odds of any individual number to be selected be effectively zero?
- 998244353 2y agoIt is, and if you choose the number uniformly at random, it's not just "effectively" zero, it is precisely zero. GP's point, as I understand it, is that it is not actually possible to choose a number from [0, 1] uniformly at random in "real life". I think you could argue that, e.g. in the dartboard thought experiment, the probability of choosing individual points doesn't really matter: only probabilities of measurable subsets with positive measure matter.
- baduser 2y agoI guess, but, the set is not even countably infinite. "Selecting at random" is something that happens in the real, non-infinite world, not in the mathematically rigorous would where infinities can exist. So, no, probability-zero events do not happen in either.
- rbanffy 2y agoNot necessarily - you might just come up with a number you know is in the set, say pi/4. I know it's in the set because it satisfies the conditions that define it. Still, the odds of that particular number being picked up are zero.
- baduser 2y agoIf you picked that, you did not pick uniformly from the unit interval. You picked from something else, which was much smaller.
- bryanrasmussen 2y agoso how does the random function selecting the number select the number before the last number in the infinite set?
- rbanffy 2y agoIt wouldn't "select" as if it were an infinite deck of cards, but rather generate a number we know is on the infinite set. It can very well take an infinite amount of time to come up with the digits though...
- shiandow 2y agoWhat last number?
- bryanrasmussen 2y agoexactly