>>13718992>Any advice?If you're an absolute noob (or not) and you're struggling with proving stuff, learn the way by studying solved problems. The way they "summon" concepts to achieve the proof.
You will often find yourself in the "how am I supposed to know that I had to make that specific step here?" and the short answer is you don't, you don't "have to know" to do that specific thing. Proving is a 'creative' process where you have to use what you know or what you have seen before in order to do something new. That's why my "best" advice is to study another's proofs. Maybe it's like cheating but it works, and with enough study and practicing on your own you'll gain intuition to make your own proofs.
And when you think you're done solving a specific problem, try to generalize it a little further (if possible and if your intuition permits you to glimpse a sort of result). For example, a few days ago I was doing this complex analysis exercise:
Compute the value of
And came up with the result:
Then I was wondering, that maybe there's a general case where instead of in the denominator of the integrand maybe I can put a with being a positive number (why positive? because in the original problem it was a positive, so that was my initial guess). Then I worked the general case problem to come up with:
All following the same argument and reasoning as in the original problem. This time it worked, sometimes it doesn't, but it's a good way to practice if you change a little thing in some problem to come up with your own results.
