On Sunday, 23 February 2014 05:11:06 UTC+2, 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. > > > > 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
You are very much on the right track! What I would like to do with Hilbert and his followers is kick their rear ends as hard as I can, so they can't get out of Cantor's fools' paradise. Thereafter, I would like to lock the door and throw the key away.
No one shall remove Cantor's fools from the paradise he has created for them.