I found this question in a book. Q-Suppose you own a hotel with a countable number of rooms. One night a traveler wishes to stay in your hotel, but all the rooms are occupied. Can you give him a room without kicking anybody out of the hotel? What if a tour bus shows up with countably many passengers, all wanting a room? (Assume each room only accommodates one person.) I would assume the answer is no since the hotel is completely occupied but something tells me thats not right.