Hello fellow math enthusiasts, I am currently in a proof based class but am struggling to even understand how to write a proof. Whenever the teacher or fellow classmates write proofs none of the things they write or say make sense. This entire subject of math does not make sense to me but I am very good at computational mathematics. I am currently in the process of writing two different proofs one of them is in a previous post I made and the other one is for the proposition
Let $f: A \to B$ be a surjection. Then $f$ has a right inverse.
I do not get where to start or what to do. It seems that when the teacher does it they just write random stuff on the board and boom there is a proof, it would be much appreciated if I could get your guys' help. Thank you for your time!!!