i am just starting to learn proofs on my own. this is probably a basic proof but i am having trouble with it. so far i am thinking of using induction to prove this. the problem is if a and b are in the set of integers, prove that ab is also in that set. so i'm letting a be a fixed integer and S be the set of all integers b such that ab is in the set of integers. its obvious that 1 is in the set S. i'm trying to show that b and b+1 are in the set as well. is this the correct method to prove the statement?