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December 15th, 2016, 12:20 PM   #21
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scanning all these they all seem to stem from the same basic unease of infinite sets having zero measure.

I really like the argument in the xkcd comment. If you pick a random natural number, the next one you pick is almost surely greater than the one you picked. This right here precludes the idea of a uniform distribution on the naturals. The probability of picking any natural number we can represent given the matter available in the universe or less is 0 as there are infinitely many numbers greater than this.
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December 15th, 2016, 04:18 PM   #22
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Originally Posted by Maschke View Post
...I'll offer some perspectives I found regarding putting uniform probability distributions on the naturals.
It looks like I have my homework cut out for me.
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