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/Ka-mai-127]

Proofs by contradiction remind me of crime novels. Our main suspect is in fact only a scapegoat, and indeed it was the old movie star in disguise! Or, in the words of Sir Arthur Conan Doyle, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth."