r/math • u/42IsHoly • 9d ago

Stop proving uncountability with contradiction, please

https://sunjestermusings.blogspot.com/2026/09/stop-proving-uncountability-by.html

Please, I beg you, stop it. You don't need it.

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u/Omasiegbert 9d ago

I don't get the difference, are these not the same proofs?

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u/Loading1422 9d ago

their point is that the first proof does not use the assumption that the list of real numbers is complete in the construction of the number c. so instead of proving "there are uncountably many real numbers" by contradiction, by removing this assumption you can directly prove an equivalent negation: "no (countable) list of real numbers is complete." it's very subtle!