LudovicoVan
Posts:
3,785
From:
London
Registered:
2/8/08


Re: The selfcontradictory infinite hotel
Posted:
Feb 23, 2014 12:29 PM


"Julio Di Egidio" <julio@diegidio.name> wrote in message news:ledaon$1f2$1@dontemail.me... > > slightly more rigorously, if we have 1, 2, 3, etc. up to (allegedly) *all* > natural numbers, there is just no natural number missing that we can add > to the lot.
If, for all n, room n+1 is occupied already, the hotel is just full and no more guests can be accommodated.
If, conversely, the hotel is never fully occupied, there always exists n such that n+1 is not occupied.
Either one or the other, but not both.
Julio

