I disagree with the notion that if you question your solution then your solution isn’t correct.
A beginner could easily fool herself onto thinking she has correct understanding, but actually her proof is buggy. Without feedback, she wouldn’t know.
A beginner could easily fool herself onto thinking she has correct understanding, but actually her proof is buggy. Without feedback, she wouldn’t know.
BTW, I didn't mention this earlier, but for verifying solutions to exercises which ask to prove something, I've never found it useful to see a solution that is simply a proof. The only way to get more confidence that you've proved something correctly is to find someone adversarial (e.g. a friend with similar or greater mathematical maturity) and try to prove it to them while they keep say “why” or “I'm not convinced”. (A proof is a social process; you cannot get feedback on your proof from a static, non-interactive source like a book.) One's proof may be superficially similar to what's in the book and yet not be a proof, while it can be very different and still be fine.
What provided proofs can help with is getting you unstuck when you've been unsuccessful at proving something. So they help with frustration and motivation, as I mentioned earlier (feedback not so much).