On 12/19/2022 9:12 AM, Sergi o wrote:
> On 12/19/2022 4:04 AM, WM wrote:
>
>> Is it possible to add a natural number to the set ℕ?
>
> a trolling question...
>
> Or a question asked by a math moron.
>
> Or both.
I say, both?

On 12/19/2022 7:08 PM, Sergi o wrote:
> On 12/19/2022 6:38 PM, Fritz Feldhase wrote:
>> On Tuesday, December 20, 2022 at 12:49:00 AM UTC+1, FromTheRafters wrote:
>>> William explained on 12/19/2022 :
>>>>
>>>> any message from WM that contains the word "complete" can be
>>>> ignored. He is
>>>> unable to define this word
>>>>
>>> He also means IN = {1, 2, 3,...} instead of what almost everyone else
>>> uses.
>>
>> Yes, because due to Mückenheim "0 is not a natural number"! :-)
>>
>> (You see, for him this is not a question of definition but an
>> unshakeable fact. Don't ask!)
>
> counting numbers were in, started at 1.
>
> but when data bytes were born, we counted from 0 to 7 for 8bit, 0 to 3
> for 4 bit, etc
>
> so the use of 0 as a counting number has increased in the digital age.
>
> In the past, if you were a 0, you were left out, but not any more...

Pascal vs C. Indexing an array starts at one or zero? I think there is a
setting in Pascal to index at zero. I cannot remember right now. Sorry.

William schrieb am Dienstag, 20. Dezember 2022 um 00:26:24 UTC+1:
> On Monday, December 19, 2022 at 6:04:58 AM UTC-4, 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?
> >
> any message from WM that contains the word "complete" can be ignored. He is unable to define this word

I accept Cantor's use: "The infinite sequence thus defined has the peculiar property to contain the positive rational numbers completely, and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)], but here with natural instead of rational numbers.

Regards, WM

Chris M. Thomasson schrieb am Dienstag, 20. Dezember 2022 um 04:44:51 UTC+1:

> Why would one need to add something into an infinite pool?

Because it is complete.

Regards, WM

Chris M. Thomasson schrieb am Dienstag, 20. Dezember 2022 um 05:43:10 UTC+1:
> On 12/19/2022 10:29 AM, WM wrote:

> > Only a potentially infinite number of rooms can grow.
> There is no such thing as a full infinite pool.

Maybe. But Cantor's theory needs a full infinity pool.

Regards, WM

Sergi o was thinking very hard :
> On 12/19/2022 5:01 PM, FromTheRafters wrote:
>> WM expressed precisely :
>>> FromTheRafters schrieb am Montag, 19. Dezember 2022 um 13:12:14 UTC+1:
>>>> WM has brought this to us :
>>>>> 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?
>>>> Sure, you can adjoin a zero. Then it becomes the naturals with zero and
>>>> many will still insist that they are just the natural numbers.
>>>> If you start with the positive integers, adjoining a zero makes them the
>>>> non-negative integers -- so, no confusion of terminology in that case.
>>>
>>> But you cannot adjoin 10 rooms to the hotel if the set of rooms has been
>>> complete before.
>>
>> Adjoining zero only works because of the confusion over what is meant by
>> the natural numbers. Using non-ambiguous terminology is better.
>>
>> Did the hotel already have a room number zero?
>
>
> no, you cant count 0, if you did you would always be off by 1. HH uses
> counting numbers.

Yes, what used to be called the natural numbers.

Chris M. Thomasson pretended :
> On 12/19/2022 11:53 AM, Julio Di Egidio wrote:
>> On Monday, 19 December 2022 at 19:29:45 UTC+1, WM wrote:
>>> ju...@diegidio.name schrieb am Montag, 19. Dezember 2022 um 15:45:49
>>> UTC+1:
>>>> On Monday, 19 December 2022 at 11:04:58 UTC+1, 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?
>>>>
>>>> Good question and the valid and correct answer indeed is NO!
>>>>
>>>> And here is an analysis:
>>>> <http://seprogrammo.blogspot.com/2014/02/hilberts-impossible-hotel.html>
>>>
>>> A full hotel is just full. Hard to understand that so many mathematicians
>>> did not see that the actually infinite set of rooms is complete and cannot
>>> be extended. Only a potentially infinite number of rooms can grow.
>>
>> Nope, *finite or infinite*, a full hotel is just full !!
> [...]
>
> No, not a Hotel that has infinite rooms...

The rooms aren't that big, but there are infinitely many of them.

For every guest there is a next guest, for every room there is a next
room.

FromTheRafters schrieb am Dienstag, 20. Dezember 2022 um 10:16:30 UTC+1:

> For every guest there is a next guest, for every room there is a next
> room.

And none is without a guest.

Regards, WM

On Monday, 19 December 2022 at 20:53:57 UTC+1, Julio Di Egidio wrote:
> On Monday, 19 December 2022 at 19:29:45 UTC+1, WM wrote:
> > ju...@diegidio.name schrieb am Montag, 19. Dezember 2022 um 15:45:49 UTC+1:
> > > On Monday, 19 December 2022 at 11:04:58 UTC+1, 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?
> > >
> > > Good question and the valid and correct answer indeed is NO!
> > >
> > > And here is an analysis:
> > > <http://seprogrammo.blogspot.com/2014/02/hilberts-impossible-hotel.html>
> >
> > A full hotel is just full. Hard to understand that so many mathematicians
> > did not see that the actually infinite set of rooms is complete and cannot
> > be extended. Only a potentially infinite number of rooms can grow.
>
> Nope, *finite or infinite*, a full hotel is just full !!
> Which rather entails that there is no such thing
> as a potentially infinite set, e.g. a complete
> collection of all and only the finite naturals.
>
> Not per chance in finitary mathematics proper,
> not your botched version of it, the natural
> numbers rather form a proper class...
>
> HTH, somebody, etc.

Up. Liars and spammers...

Julio

WM used his keyboard to write :
> FromTheRafters schrieb am Dienstag, 20. Dezember 2022 um 10:16:30 UTC+1:
>
>> For every guest there is a next guest, for every room there is a next
>> room.
>
> And none is without a guest.

Correct, it's a bijection from guests to rooms.

On Tuesday, 20 December 2022 at 12:47:14 UTC+1, Julio Di Egidio wrote:
> On Monday, 19 December 2022 at 20:53:57 UTC+1, Julio Di Egidio wrote:
> > On Monday, 19 December 2022 at 19:29:45 UTC+1, WM wrote:
> > > ju...@diegidio.name schrieb am Montag, 19. Dezember 2022 um 15:45:49 UTC+1:
> > > > On Monday, 19 December 2022 at 11:04:58 UTC+1, 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?
> > > >
> > > > Good question and the valid and correct answer indeed is NO!
> > > >
> > > > And here is an analysis:
> > > > <http://seprogrammo.blogspot.com/2014/02/hilberts-impossible-hotel.html>
> > >
> > > A full hotel is just full. Hard to understand that so many mathematicians
> > > did not see that the actually infinite set of rooms is complete and cannot
> > > be extended. Only a potentially infinite number of rooms can grow.
> >
> > Nope, *finite or infinite*, a full hotel is just full !!
> > Which rather entails that there is no such thing
> > as a potentially infinite set, e.g. a complete
> > collection of all and only the finite naturals.
> >
> > Not per chance in finitary mathematics proper,
> > not your botched version of it, the natural
> > numbers rather form a proper class...
> >
> > HTH, somebody, etc.

Up, you pieces of fraudulent nazi-shit.

Julio

On Monday, December 19, 2022 at 2:29:45 PM UTC-4, WM wrote:

> A full hotel is just full. Hard to understand that so many mathematicians did not see that the actually infinite set of rooms is complete and cannot be extended.

Hard to understand because no one has suggested that an infinite set of rooms can be extended. However, an infinite set of rooms can be split into two sets, each of which has "just as many elements" as the original set.

On Tuesday, 20 December 2022 at 11:06:12 UTC-4, William wrote:
> On Monday, December 19, 2022 at 2:29:45 PM UTC-4, WM wrote:
>
> > A full hotel is just full. Hard to understand that so many mathematicians did not see that the actually infinite set of rooms is complete and cannot be extended.
> Hard to understand because no one has suggested that an infinite set of rooms can be extended.

Well, actually.... The rooms could, hypothetically, be indexed with the real numbers or sets of even higher cardinality. That has to count as an "extension". But, even though Muckenheim will never grasp that, the set {1, 2, 3, 4, ...} has the same cardinality as the set {0, 1, 2, 3, ...}

> However, an infinite set of rooms can be split into two sets, each of which has "just as many elements" as the original set.

Even countably many sets...

William schrieb am Dienstag, 20. Dezember 2022 um 16:06:12 UTC+1:
> On Monday, December 19, 2022 at 2:29:45 PM UTC-4, WM wrote:
>
> > A full hotel is just full. Hard to understand that so many mathematicians did not see that the actually infinite set of rooms is complete and cannot be extended.
> Hard to understand because no one has suggested that an infinite set of rooms can be extended.

If all rooms, enumerated by 1, 2, 3, ..., are occupied and another room is needed, the number of rooms must be extended. However that is not possible.

> However, an infinite set of rooms can be split into two sets, each of which has "just as many elements" as the original set.

That is nonsense. But you have no chance to understand it unless you study my proof eagerly: https://www.researchgate.net/publication/365605468_Proof_of_the_existence_of_dark_numbers_bilingual_version

Regards, WM

Gus Gassmann schrieb am Dienstag, 20. Dezember 2022 um 16:32:35 UTC+1:
> But, even though Muckenheim will never grasp that, the set {1, 2, 3, 4, ...} has the same cardinality as the set {0, 1, 2, 3, ...}

Nothing to grasp. I have proved the contrary.
https://www.researchgate.net/publication/365605468_Proof_of_the_existence_of_dark_numbers_bilingual_version

Regards, WM

On Tuesday, December 20, 2022 at 5:43:09 PM UTC+1, WM wrote:
> William schrieb am Dienstag, 20. Dezember 2022 um 16:06:12 UTC+1:
> > On Monday, December 19, 2022 at 2:29:45 PM UTC-4, WM wrote:
> >
> > > A full hotel is just full. Hard to understand that so many mathematicians did not see that the actually infinite set of rooms is complete and cannot be extended.
> > Hard to understand because no one has suggested that an infinite set of rooms can be extended.
> If all rooms, enumerated by 1, 2, 3, ..., are occupied and another room is needed, the number of rooms must be extended. However that is not possible.
> > However, an infinite set of rooms can be split into two sets, each of which has "just as many elements" as the original set.
> That is nonsense. But you have no chance to understand it unless you study my proof eagerly: https://www.researchgate.net/publication/365605468_Proof_of_the_existence_of_dark_numbers_bilingual_version
>
> Regards, WM

Now we have really reverted to the pre-Newtonian 17-th century.
Look up the meaning of "eagerly".

On 12/20/2022 6:11 AM, FromTheRafters wrote:
> WM used his keyboard to write :
>> FromTheRafters schrieb am Dienstag, 20. Dezember 2022 um 10:16:30 UTC+1:
>>
>>> For every guest there is a next guest, for every room there is a next room.
>>
>> And none is without a guest.
>
> Correct, it's a bijection from guests to rooms.

I would never get room numbered 0 at the Bates Motel

On 12/20/2022 10:44 AM, WM wrote:
> Gus Gassmann schrieb am Dienstag, 20. Dezember 2022 um 16:32:35 UTC+1:
>> But, even though Muckenheim will never grasp that, the set {1, 2, 3, 4, ...} has the same cardinality as the set {0, 1, 2, 3, ...}
>
> Nothing to grasp. I have proved the contrary.
> https://www.researchgate.net/publication/365605468_Proof_of_the_existence_of_dark_numbers_bilingual_version
>
> Regards, WM

that is troll food, or troll poop.

On Tuesday, December 20, 2022 at 12:43:09 PM UTC-4, WM wrote:
> William schrieb am Dienstag, 20. Dezember 2022 um 16:06:12 UTC+1:
> > On Monday, December 19, 2022 at 2:29:45 PM UTC-4, WM wrote:
> >
> > > A full hotel is just full. Hard to understand that so many mathematicians did not see that the actually infinite set of rooms is complete and cannot be extended.
> > Hard to understand because no one has suggested that an infinite set of rooms can be extended.
> If all rooms, enumerated by 1, 2, 3, ..., are occupied and another room is needed, the number of rooms must be extended.

Nope. This is not possible and not needed. A set of previously occupied rooms can be freed up by placing all the previous occupants in a proper subset of the rooms.

On Monday, 19 December 2022 at 20:53:57 UTC+1, Julio Di Egidio wrote:
> On Monday, 19 December 2022 at 19:29:45 UTC+1, WM wrote:
> > ju...@diegidio.name schrieb am Montag, 19. Dezember 2022 um 15:45:49 UTC+1:
> > > On Monday, 19 December 2022 at 11:04:58 UTC+1, 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?
> > >
> > > Good question and the valid and correct answer indeed is NO!
> > >
> > > And here is an analysis:
> > > <http://seprogrammo.blogspot.com/2014/02/hilberts-impossible-hotel.html>
> >
> > A full hotel is just full. Hard to understand that so many mathematicians
> > did not see that the actually infinite set of rooms is complete and cannot
> > be extended. Only a potentially infinite number of rooms can grow.
>
> Nope, *finite or infinite*, a full hotel is just full !!
> Which rather entails that there is no such thing
> as a potentially infinite set, e.g. a complete
> collection of all and only the finite naturals.
>
> Not per chance in finitary mathematics proper,
> not your botched version of it, the natural
> numbers rather form a proper class...
>
> HTH, somebody, etc.

Up, liars and spammers.

Julio

on 12/20/2022, Sergi o supposed :
> On 12/20/2022 6:11 AM, FromTheRafters wrote:
>> WM used his keyboard to write :
>>> FromTheRafters schrieb am Dienstag, 20. Dezember 2022 um 10:16:30 UTC+1:
>>>
>>>> For every guest there is a next guest, for every room there is a next
>>>> room.
>>>
>>> And none is without a guest.
>>
>> Correct, it's a bijection from guests to rooms.
>
>
>
> I would never get room numbered 0 at the Bates Motel

It would be 'curtains' for you if you did.

William schrieb am Dienstag, 20. Dezember 2022 um 18:36:28 UTC+1:
> On Tuesday, December 20, 2022 at 12:43:09 PM UTC-4, WM wrote:
> > William schrieb am Dienstag, 20. Dezember 2022 um 16:06:12 UTC+1:
> > > On Monday, December 19, 2022 at 2:29:45 PM UTC-4, WM wrote:
> > >
> > > > A full hotel is just full. Hard to understand that so many mathematicians did not see that the actually infinite set of rooms is complete and cannot be extended.
> > > Hard to understand because no one has suggested that an infinite set of rooms can be extended.
> > If all rooms, enumerated by 1, 2, 3, ..., are occupied and another room is needed, the number of rooms must be extended.
> Nope. This is not possible and not needed. A set of previously occupied rooms can be freed up by placing all the previous occupants in a proper subset of the rooms.

Set theory has damahed many brains. Your statement is a proof of that deplorable fact. Of course in completed infinity no Dedekind-mapping is possible. But you will not even understand this clear exposition:

https://www.researchgate.net/publication/365605468_Proof_of_the_existence_of_dark_numbers_bilingual_version

Alas you will not be able to find a mistake either.

Regards, WM

On 12/20/2022 3:16 AM, FromTheRafters wrote:
> Chris M. Thomasson pretended :
>> On 12/19/2022 11:53 AM, Julio Di Egidio wrote:
>>> On Monday, 19 December 2022 at 19:29:45 UTC+1, WM wrote:
>>>> ju...@diegidio.name schrieb am Montag, 19. Dezember 2022 um 15:45:49 UTC+1:
>>>>> On Monday, 19 December 2022 at 11:04:58 UTC+1, 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?
>>>>>
>>>>> Good question and the valid and correct answer indeed is NO!
>>>>>
>>>>> And here is an analysis:
>>>>> <http://seprogrammo.blogspot.com/2014/02/hilberts-impossible-hotel.html>
>>>>
>>>> A full hotel is just full. Hard to understand that so many mathematicians
>>>> did not see that the actually infinite set of rooms is complete and cannot
>>>> be extended.  Only a potentially infinite number of rooms can grow.
>>>
>>> Nope, *finite or infinite*, a full hotel is just full !!
>> [...]
>>
>> No, not a Hotel that has infinite rooms...
>
> The rooms aren't that big, but there are infinitely many of them.
>
> For every guest there is a next guest, for every room there is a next room.

had one of those, a hotel room in NYC downtown, it was 6" larger than the mattress on one side, no windows, the mattress was from the 30's, one 40W
light bulb from the ceiling in the middle, and the porter wanted a tip.

On 12/20/2022 12:47 PM, WM wrote:
> William schrieb am Dienstag, 20. Dezember 2022 um 18:36:28 UTC+1:
>> On Tuesday, December 20, 2022 at 12:43:09 PM UTC-4, WM wrote:
>>> William schrieb am Dienstag, 20. Dezember 2022 um 16:06:12 UTC+1:
>>>> On Monday, December 19, 2022 at 2:29:45 PM UTC-4, WM wrote:
>>>>
>>>>> A full hotel is just full. Hard to understand that so many mathematicians did not see that the actually infinite set of rooms is complete and cannot be extended.
>>>> Hard to understand because no one has suggested that an infinite set of rooms can be extended.
>>> If all rooms, enumerated by 1, 2, 3, ..., are occupied and another room is needed, the number of rooms must be extended.
>> Nope. This is not possible and not needed. A set of previously occupied rooms can be freed up by placing all the previous occupants in a proper subset of the rooms.
>
> Set theory has damahed many brains. Your statement is a proof of that deplorable fact. Of course in completed infinity no Dedekind-mapping is possible. But you will not even understand this clear exposition:
>
> https://www.researchgate.net/publication/365605468_Proof_of_the_existence_of_dark_numbers_bilingual_version
>
> Alas you will not be able to find a mistake either.

your not serious at all. your Spoof is a mistake, self published from this news group.

>
> Regards, WM

On Tuesday, December 20, 2022 at 2:47:44 PM UTC-4, WM wrote:

> no Dedekind-mapping is possible.

So you do understand what is being claimed but you dishonestly pretend something else is being claimed. The claim is that a bijection from the set to a proper subset exists. The claim is not that an "extention" exists

--
William Hughes