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The paradox is that, after picking a random number, you have just done a thing which has probability zero. Doing a thing that has zero probability shouldn't be
by Houshalter 9y ago
The paradox is that, after picking a random number, you have just done a thing which has probability zero. Doing a thing that has zero probability shouldn't be possible. Ever.
- dorgo 9y agoI would argue that the distribution you used to pick a random number was not uniform. Not all the real number were equaliy likely to be picked by you. Hence the probability for some numbers was > 0.
- marcosdumay 9y agoNon-countable sets defy intuition on several ways. The silver lining is that we don't have any evidence a non-countable thing exist on the real world. I don't think anybody even has a procedure for gathering that kind of evidence.
- dorgo 9y agoNo. Rational number are countable, but have the same property of zero probability for an item in a uniform distribution.
- pelario 9y agoWhy the downvotes? I think he is correct; and if someone think he is not, please elaborate
- marcosdumay 9y agoYes, no reason for the downvotes. Infinities are problematic too.
- rocqua 9y agoYou can't pick a random real number between 0 and 1. Heck, almost all reals between 0 and 1 can't ever be constructed let alone picked. The here is the non-constructive nature of the real numbers. That is not to say the reals are useless, but they are not much more than a formalism. It's rather useful though because it's hard to get numbers like pi or e. Its really nice that any real interval is compact, but that too is hard to replicate.
- bjl 9y agoYou can certainly pick a random real number from the unit interval.
- waqf 9y agoReally? Go on, then, pick one and tell us what it is (or at least tell us what your procedure was).
- Houshalter 9y agoOne example in a finite space and time setting would be selecting a random point on the ground. Say by dropping a ball there or something. The exact coordinates it lands is a random real number. But the probability that it landed on those exact coordinates is exactly 0, hence a paradox.
- deleted 9y ago[deleted]
- oh_sigh 9y agoIs it probability actually zero, or just infinitely close to zero?
- waqf 9y agoIf it's a random real then the probability is zero. If it's an arbitrarily close approximation to a random real then the probability is arbitrarily close to zero.
- oh_sigh 9y agoHow can the sum of infinitely many zero probabilities be 1? I can understand how the sum of infinitely many infinitely close to zero values can be 1, but not infinitely many exactly zero values
- Retra 9y agoThere's no such thing as a "sum of infinitely many" anything. What we are talking about is the limit of an infinite series, which behaves nothing at all like a sum.
- Retra 9y agoThose are the same thing. You're just calling them by different names.
- pelario 9y agoIt is possible! Actually I remember pointing out a similar concern in my probability class back in the day. The teacher's answer: that is precisely the difference between probablity and possibility :)