GridVids
Sign in with YouTube

How An Infinite Hotel Ran Out Of Room

Veritasium May 28, 2026 13:00
Create an account to hide videos, mark them watched, or save them to Don't Miss.
Don't Miss
Create an account to hide videos, mark them watched, or save them to Don't Miss.
Mark watched
Create an account to hide videos, mark them watched, or save them to Don't Miss.
Hide
Open in popup Open on YouTube
Share video

Share video

Copy the GridVids link or iframe code.

Video link
Iframe code
Iframe content

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.
Education
#veritasium #science #physics #infinite hotel paradox #hilbert #infinite #hilbert hotel #infinity #infinity paradox #infinity hotel #hilbert's hotel #math #mathematics #maths #david hilbert #what is infinity #countable infinity #how big is infinity #infinity hotel paradox #paradox #size of infinity #how to understand infinity #hilbert's grand hotel #hilbert's infinite hotel #banach–tarski paradox #axiom of choice