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EDIT: I THINK I STAND CORRECTED (lemmy.zip)

submitted 8 months ago* (last edited 8 months ago) by [email protected] to c/[email protected]

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I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!

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[–] [email protected] 2 points 8 months ago (1 children)

But clearly, if we add up all the infinite fractions between 0 and 1, they would add up to 1.

0.9 and 0.8 are in that set, so they would add up to at least 1.7. In fact if you give me any positive number I can give you a (finite!) set of (distinct) fractions less than 1 which sum to more than that number. In other words, the sum is infinite.

[–] [email protected] 3 points 8 months ago* (last edited 8 months ago)

I meant to say that we can infinitely divide the numbers between 0 and 1 and then match each with an integer. But I realized that the former wouldn't be rational numbers, they would be real numbers.

That aside, I see now that the original idea behind the meme was mistaken.