## Randomly Choosing Positive Integers

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### Randomly Choosing Positive Integers

If you could random choose a positive integer each positive integer had an equal chance of being selected then no matter which of the positive integers you choose 100% of all positive integers will be greater than the positive integer you selected and 0% of all positive integers will be less than the positive integer you selected because only a finite number of positive integers will be less than the positive integer you selected but an infinite number of positive integers will be greater than the positive integer you selected. If you select a 2nd positive integer then there will be a 100% chance that the 2nd positive integer you selected is greater than the 1st as 100% of all positive integers are greater than the 1st positive integer you selected. There will also be a 100% chance that the 1st positive integer you selected is greater than the 2nd positive integer you selected as 100% of all positive integers are also greater than the second positive integer you selected. So randomly selecting two positive integers results in a paradox in which for both selected positive integers there is a 100% chance that it is greater than the other selected positive integer.
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anderscolingustafson
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### Re: Randomly Choosing Positive Integers

There is no paradox, since the 100% is an approximation. While there are more positive numbers greater than any given X, it is by no means 100%, and that you can't simply remove the possibility of picking a lesser number by pretending that some small n/N tends to 0, it must be 0 absolute.

I ran a program along this sort of line, where you generated what amounts to p random numbers less than p^2. (the actual property is that if b were chosen, then p^2 | b^(p-1). But by accepting a value you had to soot it into your hand of known numbers. We were only looking for the smallest 40, so we passed any value that was something like > 60p. p ran into the millions.
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wendy
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### Re: Randomly Choosing Positive Integers

I suppose probability as we know it will not work when there are infinitely many outcomes
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Prashantkrishnan
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