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Let's say you have to move to the infinite room. How can someone check out of the hotel?
There is no infinity room, but there is an infinity pool
You can check out any time you like
The only issue is that if I have to travel to an infinite distance to the lobby, I'll never check out.
Don't worry, you can never be put in a room with an infinite number, only an arbitrarily large one. That's the idea of the hotel; it has an infinite number of rooms, but every room has a finite number, since you can count forever without reaching infinity.
Whew, I was worried as the infinite passanger on that bus that I'd be put into an infinite room.
Just move halfway to the lobby, then again halfway to the lobby and...
...shit.
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