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Topic: Matheology § 264 Hilbert's Hotel: checking out.
Replies: 16   Last Post: May 13, 2013 3:29 AM

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Posts: 18,076
Registered: 1/29/05
Re: Matheology § 264 Hilbert's Hotel: checking out.
Posted: May 12, 2013 3:27 AM
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On 11 Mai, 22:16, Ralf Bader <> wrote:

> But no such limit procedure
> has been defined for Hilbert's hotel. To be sure, even the easy task of
> accomodating one additional guest if all rooms are occupied already
> requires a limit procedure (at least if it is seen as occurring in stages,
> where in stage i the guest from room i switches into room i+1) if the hotel
> wants a certification (as popular today) that it is working according to
> ZFC. But that is an unproblematic limit procedure (because in this case the
> guest in room j does not change any more after stage j,

The infinite limit is allowed? Changing of finite room-numbers however
is not allowed? Or is it allowed only finitely often? Is there an
upper limit for the number of those changes?

>and so this can be
> taken for the limit after running through all stages) and it is ignored in
> the popular fairy tale.

If n guest will have to be accomodated, then every guest will have to
change his room n times. How many times is allowed? Potential infinity
possible? Is that a better infinity than when leaving? There must be
very subtle differences in matheology, not immediately obvious to

No! It is simply nonsense to think that aleph_0 is "reached" somehow.
(Zermelo's axiom does not say that the complete set could be
manipulated. That's grwon out of the phantasy of matheologians.) And
this can best be seen by the fact, that from aleph_0 we never reach 0.

> In your nonsense story things are totally different
> (because now the guest in each room changes in each stage and there is
> nothing reached in a finite stage which can be taken for the limit after
> all finite stages)

Wrong. The final state is this: All guests are accomodated in Math's
Motel. That limit is as well defined as that of Hilbert's Hotel, ins't
it? And in the other story an enumeration of all algebraic
irrationals is "reached".

> But all this is only for readers which might fall prey to your nonsense; you
> have been told all this so often in the course of almost 10 years now
> without showing the least sign of understanding

If a fool tries to tell something, it is better not to listen and it
is dangerous to "understand" him because that would be a sign of own

Regards, WM

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