Ok, I posted this in another thread but then the thread died, so I'm going to try it here:
Something that I was wondering, not sure I know the answer - if you have 2 different sized infinite groups, and then choose 1 element from one of the groups at random relative to all members, what is the probability of choosing an element from either group?
Obviously we can have different sizes of infinity - say Natural and Real. So if I choose a number at random from all numbers, is it more likely to be only real or natural (and real)?
is it 50:50? Is it more likely to be only real? Does the question even make sense? If the question can't be answered, then how does probabilistic reasoning cope with infinity?
Thanks!
Something that I was wondering, not sure I know the answer - if you have 2 different sized infinite groups, and then choose 1 element from one of the groups at random relative to all members, what is the probability of choosing an element from either group?
Obviously we can have different sizes of infinity - say Natural and Real. So if I choose a number at random from all numbers, is it more likely to be only real or natural (and real)?
is it 50:50? Is it more likely to be only real? Does the question even make sense? If the question can't be answered, then how does probabilistic reasoning cope with infinity?
Thanks!
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