Here's what I wrote before:
The Cat in Numberland, by Ivar Ekeland (ages 5 to adult)
The cat who lives in the Hotel Infinity gets confused when the hotel is full, and the numbers are all able to move up one room to make room for zero. This story is charming enough to entertain young children, and deep enough to intrigue anyone.
David Hilbert, a mathematician interested in thinking carefully about how infinity works, and different sizes of infinities, first made up the basic story. Many others have embellished on it. In this version, Mr. and Mrs. Hilbert run the hotel, and with a little help, find rooms for all the guests who come to visit, even when the hotel is already full. Mr. Hilbert gets worried when the fractions show up (doesn't everyone?), and Zero helps him see a solution.
John O'Brien's illustrations are delightful.