In the proposal of Hilbert's Hotel you have a set of infinite rooms, each of which has an occupant. But then, from somewhere outside this described environment, a new potential customer is introduced and the continuous room switching commences. This outsider here is key. Please note that the new customer is introduced from outside the infinity and as the room switching takes place there must always be a customer outside a room. Hence, you will always have an occupant that is not an occupant in the mix. Something very much like Russel's paradox seems to have been introduced by setting the hotel occupancies in motion. The attempted manipulation of the infinte by an outsider generally always introduces paradox, when examined closely. Perhaps this is where Schroedinger and Bohr found the notion of observer-created reality to be remedial to wave-function collapse. The potential and the actualized are always in flux.
In the proposal of Hilbert's Hotel you have a set of infinite rooms, each of which has an occupant.
But then, from somewhere outside this described environment, a new potential customer is introduced and the continuous room switching commences. This outsider here is key.
Please note that the new customer is introduced from outside the infinity and as the room switching takes place there must always be a customer outside a room. Hence, you will always have an occupant that is not an occupant in the mix. Something very much like Russel's paradox seems to have been introduced by setting the hotel occupancies in motion.
The attempted manipulation of the infinte by an outsider generally always introduces paradox, when examined closely. Perhaps this is where Schroedinger and Bohr found the notion of observer-created reality to be remedial to wave-function collapse.
The potential and the actualized are always in flux.