"Wizard-Of-Oz" <email@example.com> wrote in message news:XnsA2DE594FBC0E6somewhereovertherain@126.96.36.199... > "Julio Di Egidio" <firstname.lastname@example.org> wrote in > news:email@example.com: >> "Julio Di Egidio" <firstname.lastname@example.org> wrote in message >> news:email@example.com... >>> >>> 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.