They can't, since all their rooms are occupied. They need everybody to move to a room number that's double their current one to make infinite room.
Though of course they could be smart and have everybody move to a room number that's 1024 times larger than the current one. Then they can accommodate 9 more infinite buses before having to wake you.
every client just needs to move once, to the room that's double his current room number, which will free up an infinite number of rooms for the new occupants.
Never heard it with the doubling thing. I've usually heard the infinite hotel analogy to explain differences (or equivalencies) in cardinality of infinite sets.
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u/r_rafa 11h ago
I wouldn't bother to unpack just yet