Infinitely More

Share this post

Hilbert's Grand Hotel

www.infinitelymore.xyz
The Book of Infinity

Hilbert's Grand Hotel

The hotel is full, yet nevertheless can accommodate new guests, even infinitely many new guests. Thus the parable of Hilbert's Grand Hotel illuminates the nature of countable infinity.

Joel David Hamkins
Feb 4, 2023
∙ Paid
6
Share this post

Hilbert's Grand Hotel

www.infinitelymore.xyz
2
Share

Hilbert's Grand Hotel

Let us hear the parable of Hilbert's Grand Hotel. The hotel has infinitely many rooms, each a luxurious full-floor suite, numbered like the natural numbers: room 0, room 1, room 2, and so on without end. Every room is occupied—the hotel is completely full with infinitely many guests.

A new guest arrives seeking a room. She inquires at the reception desk—is there any possibility of accommodating her? The manager replies coolly, “No problem, just a minute.”

Keep reading with a 7-day free trial

Subscribe to Infinitely More to keep reading this post and get 7 days of free access to the full post archives.

Already a paid subscriber? Sign in
Previous
Next
© 2023 Joel David Hamkins
Privacy ∙ Terms ∙ Collection notice
Start WritingGet the app
Substack is the home for great writing