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.

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