The Hotel That's Always Full and Always Has Room

A hotel with infinite rooms, all occupied, can still fit a new guest — just shift everyone over by one room.

Why we kept this

A thought experiment simple enough to explain in one sentence that still makes infinity feel wrong in your stomach.

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If you liked that

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• The Walk That Invented a Math Field
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• The Pigeonhole Principle
• Conway's Game of Life
• The Gömböc
• The Four Color Theorem

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