Just put the boulder in the first room and tell the guest to deal with it. What are they gonna do? Sisyphus has a massive boulder and plenty of muscle mass to deal with an unfriendly hotel roommate.
this post was submitted on 11 Oct 2024
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And all the guests can just tell the guest in the next room do the same, so even when it's full, there's still space for it.
The heck is the grand Gilbert hotel?
Rephrased, for any countably infinite set, there exists a bijective function which maps the countably infinite set to the set of natural numbers, even if the countably infinite set contains the natural numbers.
Ah, but of course.
It's a thought experiment on infinity. If you have a hotel with infinite rooms, and an infinite number of guests, can you fit another guest? You can't just put them in any random room, because that room already has a guest. But if you shift all the existing guests to the next room in line (guest 1 to room 2, guest 2 to room 3, etc.) all the way to infinity, now you have an empty room 1.
If a bus with an infinite number of passengers shows up, you can fit them too. Guest 1 goes to room 2, guest 2 to room 4, guest 3 to room 6, etc. Now you have an infinite number of empty rooms.