The Paradox of the Infinite Hotel

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Consider a hotel with an infinite number of rooms, each numbered consecutively from 1 onwards. The hotel is fully occupied, but a new guest arrives. To accommodate this guest, the manager decides to move the guest in Room 1 to Room 2, the guest in Room 2 to Room 3, and so on, shifting each existing guest to the room number that is one greater than their current room number.

After this rearrangement, in which room will the new guest be accommodated?

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