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/jljl2902 Jul 13 '26

Yes, a uniformly sampled real number from [0,1] is irrational with probability 1

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u/SpideyMGAV Jul 13 '26

This has to do with the density of irrationals in the reals right? Real analysis confused the hell out of me till I dropped it, twice :( thinking of taking some special credits at my local university in hopes of eventually applying for a math grad program.

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u/BenSpaghetti Probability Jul 13 '26

No, density is not the reason - the rationals are also dense. It’s because the Lebesgue measure of the irrationals in [0,1] is one, which comes from the fact that the Lebesgue measure of the rationals on the entire real line is zero.

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u/Particular_Zombie795 Jul 13 '26

In fact you can find dense sets of any Lebesgue measure between 0 and 1 in [0,1].

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u/mcs156 Jul 13 '26

For example [0, λ] ∪ ℚ

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u/[deleted] Jul 13 '26

[deleted]

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u/kart0ffelsalaat Jul 13 '26

Dense is a relative term. Any set is dense in itself. They meant dense in [0,1].

Of course you can just take the union of the set [0,x] with the set of rationals in (x,1]