On Sun, 23 Feb 2014 03:11:06 -0000, "Julio Di Egidio" <firstname.lastname@example.org> wrote:
>"Consider a hypothetical hotel with a countably infinite number of rooms, >all of which are occupied." (*) > >[...] But, if there is no last room, it can never be the case that >*all* rooms are occupied,
Why do you imagine that's so? We havve rooms R1, R2, etc. We have guests G1, G2, etc. Guest G1 is in room R1, etc. All the rooms are occupied.
>hence the whole argument, for how informal, falls >apart since inception. > >More logical seems to say that, while there can be ideal constructs such as >the actual infinities of super-tasks and corresponding "super-numbers", >there can be no such thing as the standard countable infinity, as that would >be something that at the same time is and is not exhausted, i.e. a >self-contradictory notion. Finite infinity is rather just that, the ever >unfinished. > >Julio > >(*) http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel >