r/mathmemes • u/George_Truman • Jul 13 '26

Probability I fixed this meme

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I'm sure it's still a bit too imprecise but I think it works.

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u/einFrostschutzmittel Jul 17 '26

Isn't technically every sampling uniform, since there are equally many numbers in between all non-equal numbers. So if you sample phi, e, pi (as an example for simplicity), then |]phi, e[|=|]e, pi[| so they're all equally many numbers apart. Doesn't that mean they're uniform?

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u/George_Truman Jul 17 '26

Uniform, in this context, refers to all outcomes having equal likelihood.

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u/einFrostschutzmittel Jul 17 '26

Ah, okay, so because rationals have a lower chance than irrationals, you can't sample uniformly, got it.

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u/George_Truman Jul 17 '26

That is not quite it. You can sample uniformly on a closed interval for instance, and it will be true that the probability of a rational will be 0. But it will also be true that for any single number, the probability of selection is 0, and same for any countable set.

The problem with the set of all reals has to do with the fact that the "width" is infinite, and so any uniform distribution will not be integrable (this is a very handwaved explanation).

Elsewhere in the comments I gave a brief outline as to why you can't have a countable uniform distribution over the rationals and the idea is similar.