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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 2:25 AM

On Sunday, 23 February 2014 08:23:54 UTC+2, Virgil wrote:
> In article <lebotv\$fc7\$1@dont-email.me>,
>
> "Julio Di Egidio" <julio@diegidio.name> wrote:
>
>
>

> > "Consider a hypothetical hotel with a countably infinite number of rooms,
>
> > all of which are occupied." (*)
>
> >
>
> > The nature of countable infinity is such that there cannot be a last room,
>
> > and that's fundamental to the fact that new guests can be accommodated in an
>
> > infinite hotel at will, itself an illustration of the fact that we can count
>
> > endlessly. But, if there is no last room, it can never be the case that
>
> > *all* rooms are occupied, hence the whole argument, for how informal, falls
>
> > apart since inception.
>
>
>
> One can have a bijection between two infinite sets, such as between the
>
> odd natuals and the even naturals.
>
>
>
> A bijection between rooms and occupants would leave no room unoccupied
>
> and no occupant unroomed..
>
> --

Hogwash. A bijection does not lead to that conclusion at all.

A bijection exists iff a transformation is one-to-one and onto.
This means that f is a bijective function if f:x->y <=> finverse (y) = x for all x in the domain of f.

The catch: There is no such thing as f(oo) = k and finverse(k) = oo.