LudovicoVan
Posts:
4,025
From:
London
Registered:
2/8/08


Re: The selfcontradictory infinite hotel
Posted:
Feb 24, 2014 4:24 PM


"WizardOfOz" <somewhere@overtherainbow.com> wrote in message news:XnsA2DE594FBC0E6somewhereovertherain@94.75.214.39... > "Julio Di Egidio" <julio@diegidio.name> wrote in > news:ledb78$4c1$1@dontemail.me: >> "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 > > Badly expressed, as your condition fails if the first room is unoccupied.
I had assumed some context, pardon my naiveté: but even conceding the nitpick, the argument does not fail, one single room available is just not enough to salvage our hotel.
> You should have said that for all n, room n is occupied.
No, it's rather fundamental to the implied inductive argument that one talks of a situation at n+1 as a consequence of a situation at n... Never mind, you have a point: I will try and rewrite it more rigorously.
>> and no more guests can be accommodated. > > That's where you're wrong when the hotel has infinite rooms <snip>
That's rather where you start paraphrasing the usual thesis with no argument at all.
Julio

