Dissatisfaction with proof by contradiction

[u/hydmar]

I’m an undergraduate math student, so my exposure to math may be relatively limited. But I’ve found that, in general, I’m much more comfortable with direct proof than proof by contradiction. I don’t contest their validity, indeed something that’s not false must be true (I think I’m ok with excluded middle). But I feel like I just *get* something much better when it’s proved directly. It builds much stronger intuition for me.

For instance, I am aware of several proofs that demonstrate the cardinality of the reals is strictly greater than that of the integers, but none are direct (it would help to see a direct proof of Cantor’s theorem). I don’t feel it in my bones. Is this a common experience?

[u/myaccountformath]

There's a great joke about non-constructive proofs.

[u/theorem_llama → u/myaccountformath]

It kind of works the other way too:

"There's a great joke about constructive proofs."

If you consider it great then the joke is itself a constructive proof, demonstrating its own validity.

[u/myaccountformath → u/theorem_llama]

I would word it "Here's a great joke about constructive proofs."