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Replies: 62   Last Post: Feb 24, 2014 10:17 PM

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 thenewcalculus@gmail.com Posts: 1,361 Registered: 11/1/13
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 ill-formed and non-existent concept - infinity. There is no such thing as infinity. It is a myth.