The Infinite Regress of Infinity Hotel

A hotel has infinitely many staff. Several of them are assigned to look after each guest. But the staff themselves are treated as guests in the hotel, staying in numbered rooms and receiving exactly the same benefits as every other guest. The fallacious idea of delegating all one's work to other staff in hiere numbered rooms is called an infinite regress. It is one of the things that one cannot validly do with infinity. Infinity is not magic. It has logical rules. That is the whole point of the infinity hotel thought experiment.