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How An Infinite Hotel Ran Out Of Room

A 6-minute video by Veritasium about mathematical reasoning, on the Mathematics shelf. It came up in r/math, in a thread called “Absolute gorgeous mathematics channel like 3blue1brown”.

Veritasium, Video, 6 min, 2021, on the Mathematics shelf

If there's a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The surprising answer is yes -- this is important to know if you're the manager of the Hilbert Hotel.