In article <email@example.com>, "Julio Di Egidio" <firstname.lastname@example.org> 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.
One can have a bijection between two infinite sets, such as between the odd natuals and the even naturals.
A bijection between rooms and occupants would leave no room unoccupied and no occupant unroomed.. --