I remember sitting in a topology class many years ago, listening to the professor carefully explaining how some sets of numbers are open, while others are closed. He went on to say that many sets are neither, and that the sets that are both open and closed play an especially interesting role. “How can a set be both open and closed?” I asked. He turned, glared at me for a long second, and said in his heavily accented English, “Eez not a door.” Turning back to the board, he resumed lecturing.