Julio Di Egidio wrote: > "Consider a hypothetical hotel with a countably infinite number of > rooms, all of which are occupied." (*) > > The nature of countable infinity is such that there cannot be a last > room, and that's fundamental to the fact that new guests can be > accommodated in an infinite hotel at will, itself an illustration of the > fact that we can count endlessly. But, if there is no last room, it can > never be the case that *all* rooms are occupied, hence the whole > argument, for how informal, falls apart since inception.
Nonsense. If there is a way to tell whether something is one of the rooms in Hilbert's Hotel or not, and a way to tell if one of those rooms is occupied or not, those ways define a set of them which are not occupied, which can be tested for emptiness. --