What is Hilbert's Hotel (sorry, the title says Hibert's hotel). Hilbert's hotel is a hotel with infinity rooms.
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Let's say your hotel is full. It is not fully booked. If a new guest comes, the hotel manager would move the person in room m to room m + 1. Of course such a hotel would not be possible in the real world, but mathematics does not care. 10^10^10^10^10^10^10^10^10^100 years from now, the hotel will eat up The Void.