Hello everyone, I am currently working through Loomis and Sternberg's Advanced Calculus, and am having difficulty with rather simple proofs. Despite this, I am NOT having much difficultly with proofs that require more sophisticated mathematics. For instance, I am trying to prove that if ab = 0, then either a = 0 or b = 0. I have tried to add zero in manifold ways, yet have not been successful in proving this claim. I have two questions: could someone provide me with some hints; and is this an early indication of my failure as a mathematician? To me, problems of this sort are not truly going to display your ability as a mathematician, as they require merely exhausting all possibilities. Does anyone else share this sentiment? Thank you.