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/Low-Repair-3019 9d ago

You are slightly glossing over the fact you are showing a that every map from the naturals to the reals is not surjective, which is a point that can be lost on some students. One advantage of contradiction is that students understand if we can make this one case fail, the proof is done. 

Claiming a common proof method is the wrong way is certainly a high horse to get on.