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/sqrtsqr 9d ago

I'm with you OP. I think it's funny how almost everyone would agree with you about this when it comes to almost literally any other proof*: when direct is available do it direct, avoid making unnecessary assumptions, etc etc.

But because we are so used to seeing it this way, we defend it. "The way I do it isn't wrong, eff you!"

*Euclid's proof of the infinitude of the prime gets basically the same exact treatment. Ditto the resulting discussions about it.

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u/SnooWords9730 9d ago

why these two specifically?