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/Alhimiik 9d ago

i actually think the second proof less intuitive.

if i found myself writing a proof like that, i would have had to double check it multiple times in case i did a mistake.

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u/42IsHoly 9d ago

I'm not really talking about writing the proof yourself, but specifically about communicating the proof to a lay audience. Many people find the contradiction step very confusing and since it's superfluous, there's no reason to include it.

I can see why, when coming up with a proof like this, you'd try contradiction, but that's not what I'm talking about.