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No. Your answer has absolutely nothing to do with infinity nor is it paradoxical.
The paradox is saying that for every number N there is an occupied room in the infinite hotel. But that there is still vacancy.
That's it.
We take every guest in their room N, and ask them to move to room N+1, and now room 1 is vacant.
So the infinite hotel is always full but always has vacancy. That's what makes it a paradox.
Why not ask them to move to room 2N+1? Then you could accommodate an infinite number of new guests (all the rooms 2N are now empty) before having to ask anyone to move again.
As I understand, that works too, and leads down that path to exploring the multiple 'levels' of infinity.
That's how you handle an infinite number of people showing up and needing rooms.
It was probably 50 years ago but I loved Hotel Infinity movie.
wikipedia - Hilbert's paradox of the Grand Hotel Hilbert imagines a hypothetical hotel with rooms numbered 1, 2, 3, and so on with no upper limit. This is called a countably infinite number of rooms. Initially every room is occupied, and yet new visitors arrive, each expecting their own room. A normal, finite hotel could not accommodate new guests once every room is full. However, it can be shown that the existing guests and newcomers – even an infinite number of them – can each have their own room in the infinite hotel.
As for the one i wrote what do you think?