Hilbert’s Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodate additional guests. But our analyze finds that this is not true. Let us illustrate Hilbert’s Grand Hotel in Figure 1 where each square is a room and is occupied. Suppose that the rooms of the hotel are numbered 1, 2,...

Cambridge ; New York, NY : Cambridge University Press, 2024.

The Grand Hotel was built in 1875. It's known as the White Palace but its huge lobby and even bigger main dining room had a cruise feel and there were children running around.