
Re: The selfcontradictory infinite hotel
Posted:
Feb 23, 2014 12:47 PM


On Sunday, 23 February 2014 19:29:20 UTC+2, Julio Di Egidio wrote: > "Julio Di Egidio" <julio@diegidio.name> wrote in message > > 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.
You can never have *all* the natural numbers. So, the second part of your statement is predicated on the assumption in your first sentence.
> If, for all n, room n+1 is occupied already, the hotel is just full and no > more guests can be accommodated.
Not true. A proposition about n does not say anything about a proposition involving infinity.
> If, conversely, the hotel is never fully occupied, there always exists n > such that n+1 is not occupied.
Your argument would be sound if you accepted that finite propositions can be used to establish results about an illformed and nonexistent concept  infinity. There is no such thing as infinity. It is a myth.

