How An Infinite Hotel Ran Out Of Room

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.

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References: Ewald, W., & Sieg, W. (2013). David Hilbert’s Lectures on the Foundations of Arithmetic and Logic 1917-1933. Springer Berlin Heidelberg. — https://ve42.co/Ewald2013

Gamow, G. (1988). One, two, three–infinity: facts and speculations of science. Courier Corporation. — https://ve42.co/Gamow1947

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Animation by JD Pounds and Jonny Hyman
Thumbnail by Iván Tello
Music by Jonny Hyman and from Epidemic Sound and E’s Jammy Jams (Hotel Lavish – Radio Nights, Steps in Time – Golden Age Radio, What Now – Golden Age Radio, Book Bag – E’s Jammy Jams, Arabian Sand – E’s Jammy Jams, Firefly in a Fairytale – Gareth Coker)
Written By Derek Muller and Alex Kontorovich
Sound Design by Jonny Hyman

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