est. 1924 at 1 Countable Way

The Hilbert Grand Hotel

No vacancy, Always vacancy.

The amenities

Breakfast
Served 6 to 10 a.m. on every floor. There are infinitely many floors.
The elevator
Stops at every floor. Please allow additional time if your room number contains several thousand digits.
Room service
Delivered promptly to any room whose number you can name.
The pool
Heated to a comfortable temperature. Disclaimer: the pool is not infinite, but is large enough for any number of guests who can swim.
Coach parking
Accepts any number of coaches. Infinite tour groups should call ahead.
Housekeeping
Every room is cleaned daily. Please do not ask us how many maids are on staff; the answer is infinite.
Quiet hours
From 10 p.m., please keep noise to a minimum. Somewhere, inevitably, someone is still checking in?
The night manager
Available throughout the night and capable of finding a room for every guest. This has been mathematically proven but personally exhausting.

I have stayed here since opening night. I like it except they keep asking me to move every so often.

G. Cantor @ Room 1 (formerly). Currently room 8.

I asked the front desk whether the hotel was full. They said yes. I asked whether I could have a room. They said certainly. Hmm?

K. Gödel @ Room 17

I arrived at midnight with infinitely many passengers, all of them tired. By a quarter past, every one of them had a bed. A remarkable operation!

A coach operator @ Coach No. 3

A grand hotel with infinitely many rooms, all of them occupied, and one ready for you.