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

On Monday, 19 December 2022 at 12:04:58 UTC+2, 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?

Of course, it is not possible, but the morons who you waste your time with, will tell you it is. Like I've said to you before:

You cannot reason with religious fundamentalists.

HiIlbert was such a fucking moron. Nothing he said or did deserves the attention it got. An incorrigible crank after the order of the delusional fuckwad Georg Cantor.

>
> Regards, WM

On Monday, December 19, 2022 at 11:04:58 AM 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?
>
> Regards, WM

Maybe in Mückenhausen you can find an old, discarded, beaten up natural number lying around.
Then, if you are as confused about 'each', 'all' and 'every' as Prefosser Mückenheim from Mückenhausen,
you might be able to smuggle that into the complete set of natural numbers, making it even more
complete than it already was.

But if you really want to confuse Mücke Mückenheim:
Add a room or two to the Hilbert's Hotel or - horribile dictu - remove
some of the rooms - say every second one? How many homeless numbers
does that leave? And how many empty rooms?

Given another decade, do you think Mücke can learn to distinguish an object and its name?
An abstract concept, and its name? Its name and its category? And the name of the category?

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.

On Monday, December 19, 2022 at 1:12:14 PM UTC+1, FromTheRafters wrote:
> 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.

Or suppose we divide every room in two by wall, and
in each new room we put an exact duplicate of the natural number in
the original neighboring room, i.e. room n+1. Now what do we have?
And suppose we put an O an every new door and an X on every old door.
Obviously that proves Hilbert was an idiot and Mücke is the Prince
of pseudo-mathematical polemics.

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>

HTH, somebody, somewhere...

Julio

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.

>
> Regards, WM

On Monday, December 19, 2022 at 11:04:58 AM UTC+1, WM wrote:

> Is it possible to add a natural number to the set ℕ?

Hint: In the context of set theory we have:

natural_number(x) =df x e IN.

So (using symbols) your question is:

Ex e IN: IN u {x} =/= IN ?

The answer is no, since we can prove the theorem:

~Ex e IN & IN u {x} =/= IN ,
"There is no natural number x such the union of IN and {x} differs from IN."

(Actually, Ax e IN: IN u {x} = IN is a trivial theorem, since for all sets A and all elements a e A: A u {a} = A.)

On Monday, December 19, 2022 at 11:04:58 AM UTC+1, WM wrote:

> Is it possible to add a natural number to the set ℕ?

Hint: In the context of set theory we have:

natural_number(x) =df x e IN.

So (using symbols) your question is:

Ex e IN: IN u {x} =/= IN ?

The answer is no, since we can prove the theorem:

~Ex e IN: IN u {x} =/= IN ,
"There is no natural number x such the union of IN and {x} differs from IN."

(Actually, Ax e IN: IN u {x} = IN is a trivial theorem, since for all sets A and all elements a e A: A u {a} = A.)

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.

Regards, WM

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.

Regards, WM

Fritz Feldhase schrieb am Montag, 19. Dezember 2022 um 18:26:15 UTC+1:

> Ex e IN: IN u {x} =/= IN ?
>
> The answer is no, since we can prove the theorem:
>
> ~Ex e IN: IN u {x} =/= IN ,
> "There is no natural number x such the union of IN and {x} differs from IN."
>
But with the set of rooms things are different?

Regards, WM

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.

Julio

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?

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?
>
> Regards, WM
any message from WM that contains the word "complete" can be ignored. He is unable to define this word

William explained on 12/19/2022 :
> 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?
>>
>> Regards, WM
> any message from WM that contains the word "complete" can be ignored. He is
> unable to define this word

He also means |N = {1, 2, 3,...} instead of what almost everyone else
uses.

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!)

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. Spammers...

Julio

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.

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...

On 12/19/2022 2:16 AM, Eram semper recta wrote:
> On Monday, 19 December 2022 at 12:04:58 UTC+2, 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?
>
> Of course, it is not possible, but the morons who you waste your time with, will tell you it is. Like I've said to you before:

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

>
> You cannot reason with religious fundamentalists.
>
> HiIlbert was such a fucking moron. Nothing he said or did deserves the attention it got. An incorrigible crank after the order of the delusional fuckwad Georg Cantor.

On 12/19/2022 7:44 PM, Chris M. Thomasson wrote:
> On 12/19/2022 2:16 AM, Eram semper recta wrote:
>> On Monday, 19 December 2022 at 12:04:58 UTC+2, 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?
>>
>> Of course, it is not possible, but the morons who you waste your time
>> with, will tell you it is. Like I've said to you before:
>
> Why would one need to add something into an infinite pool?

Basically, adding a gallon of water to an infinite pool of water is not
going to increase it's volume.

>
>
>>
>> You cannot reason with religious fundamentalists.
>>
>> HiIlbert was such a fucking moron. Nothing he said or did deserves the
>> attention it got. An incorrigible crank after the order of the
>> delusional fuckwad Georg Cantor.
>
>
>

On 12/19/2022 10:29 AM, 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.

There is no such thing as a full infinite pool.

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...

On 12/19/2022 8:43 PM, Chris M. Thomasson wrote:
> 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...
>

Saying full means finite.