The Grand Hotel

An infinitely large hotel (a truly Grand hotel) with infinitely many guests (a “full” hotel, by finitist standards) can always fit one more guest in, by moving each of the guests already occupying a room to the room next to it (thereby leaving room one free for the newcomer). In fact, it can fit infinitely many new guests in (by, this time, moving each guest to a room with a room-number twice as large as the one they were occupying, thereby leaving all the odd-numbered rooms free for the infinitely many newcomers). And, if infinitely many guests move out – it will still be full.

William Lane Craig (1991) “The Existence of God and the Beginning of the Universe.” Truth: A Journal of Modern Thought. Volume 3.


Two morals:
(1) The [physical, macroscopic] real makes an unsuitable host for actual infinity, because
(2) Even when it comes to infinity, our intuitions are modelled on the finite

Rather a simple solution: Infinite sets are a different kind of sets, than finite sets. They have radically different properties. (Georg Cantor, 1932)

Interesa? http://en.wikipedia.org/wiki/Georg_Cantor