This hotel is 2 star at best, imagine having to pack up your stuff every time the hotel receives a new guest? I’ve decided to fix that. The hotel still has infinite rooms and guests but this time every other room is unoccupied which prepares the hotel for an infinite amount of new visitors without inconveniencing the current residence.
If the number of guests is countable (which is the usual assumption in Hilbert’s setup), then every guest will only have to travel a finite (albeit unboundedly long) distance before they reach their room.
Yes a very very long distance which I suppose means anyone who is booking in must not be planning on going anywhere else. This hotel could be the final destination, I hope they have a good room service.
Hilbert’s Motel improvement
This hotel is 2 star at best, imagine having to pack up your stuff every time the hotel receives a new guest? I’ve decided to fix that. The hotel still has infinite rooms and guests but this time every other room is unoccupied which prepares the hotel for an infinite amount of new visitors without inconveniencing the current residence.
But isn’t the whole point that the hotel is full initially, and yet can accept more guests?
Yeah, the hotel being always half full no matter how many guests it has doesn’t seem as cool.
As soon as one more guest shows up it’s more than half full.
But if an infinite number of guests show up, then they might have to travel an infinite distance to their hotel room.
If the number of guests is countable (which is the usual assumption in Hilbert’s setup), then every guest will only have to travel a finite (albeit unboundedly long) distance before they reach their room.
Yes a very very long distance which I suppose means anyone who is booking in must not be planning on going anywhere else. This hotel could be the final destination, I hope they have a good room service.