You have a choice of three doors at a game show. One is a fabulous prize, but the other two are empty. Once you choose a door, the host opens one to reveal one of the empty rooms. You’re given the chance to switch your choice to the remaining door. Should you? Can you tell if “This statement is false.” is true or false? In arithmetic, we learn that dividing by zero does not work… most of the time. So, when can we? How big is infinity? We’ll answer the answerable questions and show why the unanswerable questions are impossible.