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The Hilbert Hotel is a hypothetical hotel with infinite rooms, each occupied by one guest. When a new guest arrives, the manager accommodates them by asking current guests to move down one room, freeing up room one for the newcomer. This method illustrates the concept of infinity; even when fully occupied, the hotel can still accommodate more guests. If a bus with a hundred people arrives, the manager simply shifts each guest down a hundred rooms, making space for the new arrivals. This demonstrates how infinity can accommodate additional guests without limit.
