TITLE: When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable?
QUESTION [47 upvotes]: When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable?

Often times I "feel" as if I can write a proof to an exercise but most of those times I do not feel confident that the proof that I am thinking of is good enough or even correct at all.  I can sort of think a proof in my head, but am not confident this is a correct proof.
Any input would be appreciated. Thanks.

REPLY [2 votes]: "Proof" is an argument, that strictly follows logical inferences.  That is all there is to it.  
Do not be intimidated by the term "logical inferences".  If you have trouble with them, practice on something like Sudoku.
In my opinion, Sudoku puzzles are great because they help introduce people to the concept of "proof".  Try a really hard Sudoku puzzle.  In the middle, you don't know the whole solution yet, but, you may be able to tell that this particular square "must" contain so-and-so number, so you can write it in.  You did not merely "try" this number, you wrote it in for sure.    How did you do that?  Well, you went through some precise argument.  That was a "proof".