On Monday, January 30, 2023 at 2:22:07 PM UTC-5, Mostowski Collapse wrote:
> Dan Christensen schrieb am Montag, 30. Januar 2023 um 20:18:28 UTC+1:
> > On Monday, January 30, 2023 at 1:04:31 PM UTC-5, _ Olcott wrote:
> > > On 1/30/2023 11:38 AM, Dan Christensen wrote:
> > > > On Friday, January 27, 2023 at 2:43:32 PM UTC-5, _ Olcott wrote:
> > > >> On 12/19/2022 4:04 AM, WM wrote:
> > > >>> If the complete set ℕ of natural numbers exists, then it can be used to populate Hilbert's Hotel.
> > > >>> Is it possible to add a natural number to the set ℕ?
> > > >>>
> > > >>> Regards, WM
> > > >>
> > > >> You don't actually mean "add" as in arithmetic you actually mean append
> > > >> as in string concatenation.
> > > >>
> > > >>
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
> > > >>
> > > >> Hilbert's Hotel is incoherent in that all of the infinite number of
> > > >> rooms are occupied and a vacant room can be made for one more guest.
> > > >>
> > > >
> > > > This bizarre scenario can be avoided by first getting a handle on FINITE sets. Then an infinite set is just one that is not finite. See my blog posting on this topic:
https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> > > >
> > > > Dan
> > > >
> > > > Download my DC Proof 2.0 freeware at
http://www.dcproof.com
> > > > Visit my Math Blog at
http://www.dcproof.wordpress.com
> > > >
> >
> > > None-the-less if every room of a countably infinite set of rooms is
> > > filled, then each room is already associated with an element of N as
> > > its room number, leaving zero room numbers available for occupancy.
> > >
> > > Hilbert simply got this wrong.
> > I disagree. I think Hilbert's Hotel was simply a thought experiment to justify that, on an infinite set X, there exists a bijection from X to a proper subset of X (from Dedekind). It succeeds at this much.
> >
> > In my development, I start with a thought experiment to develop the notion of a Dedekind FINITE set. It avoids a lot of the supernatural silliness of Hilbert's Hotel.
> Hell No! A thought experiment. Please stick to Historical Facts,
> and not some Mathematical Fiction.
>
Maybe you didn't know, but there are actually no infinite hotels. Maybe there would if those unicorns of yours had existed, Mr. Collapse. HA, HA, HA!