On Thursday, 22 December 2022 at 00:17:01 UTC+1, Julio Di Egidio wrote:
> On Wednesday, 21 December 2022 at 20:05:11 UTC+1, WM wrote:
> > Dan Christensen schrieb am Mittwoch, 21. Dezember 2022 um 18:04:02 UTC+1:
>
> > > Forget Hilbert's Hotel. If you want to understand the infinite, start with the finite.
>
> Sure, and war is piece and freedom is having a job.
>
> > That is correct for potential infinity only, which is never complete. Actual infinity
> > cannot start from the finite. A complete set is complete. Nothing can be added
> > without changing the set. Same with pairs of rooms and guest. If the set is complete,
> > then adding a pair of guest and room changes the set.
>
> Actual infinity cannot be built from the finite because we need a *limit* to get
> there, i.e. an element that is primitively and intrinsically *infinite*, meaning
> greater than and unreachable from, by a finitary procedure, any other element.
>
> Your talk of "complete" just doesn't cut it: adding an element to |N is in fact still
> |N up to relabelling, indeed the cardinality stays the same (assuming |N is a set
> which it properly isn't). But exactly the same holds for the actually infinite set of
> extended natural numbers! Indeed, in *that* sense, they are simply both "infinite".
> The relevant difference, again, is that one forms a simple, finitary, simply endless,
> sequence of finite elements, forming a potentially infinite set, while the other does
> have a (non-finite) *maximum*.

Up 3. Frauds and spammers...

Julio

FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:18:46 UTC+1:

> *All* of the natural numbers are 'included' and none are
> 'excluded' from the *set* of natural numbers. It is an infinite set,
> not a semi-infinite collection.

Therefore: The set of guests = natural numbers ℕ is complete, i.e.., none can be added.
The set ℕ of room numbers of Hilbert's hotel is complete too.
The bijection between guests and room numbers has |ℕ| pairs.
If another guest arrives and is accomodated, then the bijection has one more pair. The natural room numbers contained therein have one more element. Contradiction.

Regards, WM

FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:25:10 UTC+1:
> WM explained on 12/22/2022 :
> > FromTheRafters schrieb am Mittwoch, 21. Dezember 2022 um 22:12:29 UTC+1:
> >> WM formulated the question :
> >
> >>> That is correct for potential infinity only, which is never complete.
> >>> Actual infinity cannot start from the finite. A complete set is complete.
> >>> Nothing can be added without changing the set. Same with pairs of rooms
> >>> and guest. If the set is complete, then adding a pair of guest and room
> >>> changes the set.
> >> Countably many rooms can only accomodate countably many guests in
> >> infinite hotel theory.
> >
> > The set of guests = natural numbers ℕ is complete, i.e., none can be added.
> > The set ℕ of room numbers of Hilbert's hotel is complete too.
> > The bijection between guests and room numbers has |ℕ| pairs.
> > If another guest arrives and is accomodated
> Impossible! Since you claimed that the *set* of guests was already
> "complete", arrivals make no sense.

The set of *accomodated* guests 1, 2, 3, ... is complete. Another guest 0 can arrive.

Regards, WM

FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:26:04 UTC+1:
> WM wrote on 12/22/2022 :
> > FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 08:57:34 UTC+1:
> >
> >> Is "up" supposed to be some kind of insult?
> >
> > Upvote, I assume.
> Good one. How about "plonk", he uses that one out of context too.

He wishes to veil his secret discoveries.
Please Let Others Not Know.

Regards, WM

William schrieb am Donnerstag, 22. Dezember 2022 um 19:17:29 UTC+1:
> On Thursday, December 22, 2022 at 5:39:38 AM UTC-4, WM wrote:
> > William schrieb am Donnerstag, 22. Dezember 2022 um 02:11:35 UTC+1:
> > > On Wednesday, December 21, 2022 at 3:01:14 PM UTC-4, WM wrote:
> > >
> > > > But all infinite sets which have not a fixed number of members are potentially infinite.
> > > Potentially infinite sets are nonsense. All sets are fixed.
> > Then call it collection.
> Nope, N is a set.

Well, may be.
|ℕ \ {1, 2, 3, ...}| = 0 .
But ℕ_def is only a collection:
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo

Regards, WM

On Friday, 23 December 2022 at 09:59:15 UTC+1, WM wrote:
> FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:26:04 UTC+1:
> > WM wrote on 12/22/2022 :
> > > FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 08:57:34 UTC+1:
> > >
> > >> Is "up" supposed to be some kind of insult?
> > >
> > > Upvote, I assume.

Assume you are an idiot and you're gonna be right all the time.

> > Good one. How about "plonk", he uses that one out of context too.
>
> He wishes to veil his secret discoveries.
> Please Let Others Not Know.

The Pencho Valev of mathematics.

Indeed BECAUSE OF YOU and then those who
play your game it is not been possible to have
a decent discussion about infinity around here
for the last couple of decades...

Congratulations, spammer and fraud.

Julio

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?
>
> Regards, WM

My message was deleted, but not by me! The sci.math cranks and trolls are at it again.

The fools you engage will tell you that it is possible to add a natural number to the set N because they do not view completeness in a sensible way. Their minds are filled with decay and rot of the delusional Cantor's garbage that was perpetrated by that stupid fuckwad David Hilbert, a NON-MATHEMATICIAN.

On Friday, 23 December 2022 at 12:50:42 UTC+2, 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?
> >
> > Regards, WM
>
> My message was deleted, but not by me! The sci.math cranks and trolls are at it again.
>
> The fools you engage will tell you that it is possible to add a natural number to the set N because they do not view completeness in a sensible way. Their minds are filled with decay and rot of the delusional Cantor's garbage that was perpetrated by that stupid fuckwad David Hilbert, a NON-MATHEMATICIAN.

Read fast as the bastards who have been deleting my comments will waste no time deleting this one as well.

On Monday, 19 December 2022 at 16:45:49 UTC+2, ju...@diegidio.name wrote:
> 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!

If the answer is NO, then you admit infinity is possible and that indeed a greatest natural number exists, you ridiculous, pompous ass!

Yeah, that's how syphilitic your fucked up brain is.

And don't try to say that "infinite set" is merely a way of talking about the properties of a particular set because one can do this without talking at all about infinity.

<PLONK>

Julio Idioto!

>
> And here is an analysis:
> <http://seprogrammo.blogspot.com/2014/02/hilberts-impossible-hotel.html>
>
> HTH, somebody, somewhere...
>
> Julio

On Thursday, 22 December 2022 at 20:17:29 UTC+2, William wrote:
> On Thursday, December 22, 2022 at 5:39:38 AM UTC-4, WM wrote:
> > William schrieb am Donnerstag, 22. Dezember 2022 um 02:11:35 UTC+1:
> > > On Wednesday, December 21, 2022 at 3:01:14 PM UTC-4, WM wrote:
> > >
> > > > But all infinite sets which have not a fixed number of members are potentially infinite.
> > > Potentially infinite sets are nonsense. All sets are fixed.
> > Then call it collection.
> Nope, N is a set.

A set is a "collection", you pretentious piece of shit!

On Friday, 23 December 2022 at 12:56:05 UTC+2, Eram semper recta wrote:
> On Thursday, 22 December 2022 at 20:17:29 UTC+2, William wrote:
> > On Thursday, December 22, 2022 at 5:39:38 AM UTC-4, WM wrote:
> > > William schrieb am Donnerstag, 22. Dezember 2022 um 02:11:35 UTC+1:
> > > > On Wednesday, December 21, 2022 at 3:01:14 PM UTC-4, WM wrote:
> > > >
> > > > > But all infinite sets which have not a fixed number of members are potentially infinite.
> > > > Potentially infinite sets are nonsense. All sets are fixed.
> > > Then call it collection.
> > Nope, N is a set.
> A set is a "collection", you pretentious piece of shit!

Since there is no formal definition of set, I propose we call it a "shet". Chuckle.

WM has brought this to us :
> FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:18:46 UTC+1:
>
>> *All* of the natural numbers are 'included' and none are
>> 'excluded' from the *set* of natural numbers. It is an infinite set,
>> not a semi-infinite collection.
>
> Therefore: The set of guests = natural numbers ℕ is complete, i.e., none can
> be added.

No, I am not saying that "complete" means "nothing can be added"
because one can add, subtract, multiply, divide, and raise to finite
powers without affecting the *size* of infinite sets.

WM was thinking very hard :
> FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:25:10 UTC+1:
>> WM explained on 12/22/2022 :
>>> FromTheRafters schrieb am Mittwoch, 21. Dezember 2022 um 22:12:29 UTC+1:
>>>> WM formulated the question :
>>>
>>>>> That is correct for potential infinity only, which is never complete.
>>>>> Actual infinity cannot start from the finite. A complete set is complete.
>>>>> Nothing can be added without changing the set. Same with pairs of rooms
>>>>> and guest. If the set is complete, then adding a pair of guest and room
>>>>> changes the set.
>>>> Countably many rooms can only accomodate countably many guests in
>>>> infinite hotel theory.
>>>
>>> The set of guests = natural numbers ℕ is complete, i.e., none can be added.
>>> The set ℕ of room numbers of Hilbert's hotel is complete too.
>>> The bijection between guests and room numbers has |ℕ| pairs.
>>> If another guest arrives and is accomodated
>> Impossible! Since you claimed that the *set* of guests was already
>> "complete", arrivals make no sense.
>
> The set of *accomodated* guests 1, 2, 3, ... is complete.

Whatever that means.

> Another guest 0 can arrive.

You switch between The positive integers and the non-negative integers
to add confusion. Those are different sets.

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?

Such a question only serves a purpose if there is a definition for "set". A definition was purposely left out and supplanted by the 9 beliefs, because when you argue with beliefs, you make up the "rules" as you go along. Truth and sensibility have nothing to do with the fake mathematics called "Set theory". Any time you encounter a contradiction or paradox, no problem! Simply issue another decree. Set theory is compiled from decrees. In sound mathematics there are NO decrees - religion and mythology have no place.

>
> Regards, WM

On Friday, 23 December 2022 at 13:07:56 UTC+2, FromTheRafters wrote:
> WM was thinking very hard :
> > FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:25:10 UTC+1:
> >> WM explained on 12/22/2022 :
> >>> FromTheRafters schrieb am Mittwoch, 21. Dezember 2022 um 22:12:29 UTC+1:
> >>>> WM formulated the question :
> >>>
> >>>>> That is correct for potential infinity only, which is never complete.
> >>>>> Actual infinity cannot start from the finite. A complete set is complete.
> >>>>> Nothing can be added without changing the set. Same with pairs of rooms
> >>>>> and guest. If the set is complete, then adding a pair of guest and room
> >>>>> changes the set.
> >>>> Countably many rooms can only accomodate countably many guests in
> >>>> infinite hotel theory.
> >>>
> >>> The set of guests = natural numbers ℕ is complete, i.e., none can be added.
> >>> The set ℕ of room numbers of Hilbert's hotel is complete too.
> >>> The bijection between guests and room numbers has |ℕ| pairs.
> >>> If another guest arrives and is accomodated
> >> Impossible! Since you claimed that the *set* of guests was already
> >> "complete", arrivals make no sense.
> >
> > The set of *accomodated* guests 1, 2, 3, ... is complete.
> Whatever that means.
> > Another guest 0 can arrive.
> You switch between The positive integers and the non-negative integers
> to add confusion. Those are different sets.

WM: Verstehst du die Bedeutung des Wortes "crank"?

Ein „Crank“ ist jemand, der angesichts überwältigender Beweise nicht überzeugt werden kann.

On Friday, 23 December 2022 at 14:05:51 UTC+2, Eram semper recta wrote:
> On Friday, 23 December 2022 at 13:07:56 UTC+2, FromTheRafters wrote:
> > WM was thinking very hard :
> > > FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:25:10 UTC+1:
> > >> WM explained on 12/22/2022 :
> > >>> FromTheRafters schrieb am Mittwoch, 21. Dezember 2022 um 22:12:29 UTC+1:
> > >>>> WM formulated the question :
> > >>>
> > >>>>> That is correct for potential infinity only, which is never complete.
> > >>>>> Actual infinity cannot start from the finite. A complete set is complete.
> > >>>>> Nothing can be added without changing the set. Same with pairs of rooms
> > >>>>> and guest. If the set is complete, then adding a pair of guest and room
> > >>>>> changes the set.
> > >>>> Countably many rooms can only accomodate countably many guests in
> > >>>> infinite hotel theory.
> > >>>
> > >>> The set of guests = natural numbers ℕ is complete, i.e., none can be added.
> > >>> The set ℕ of room numbers of Hilbert's hotel is complete too.
> > >>> The bijection between guests and room numbers has |ℕ| pairs..
> > >>> If another guest arrives and is accomodated
> > >> Impossible! Since you claimed that the *set* of guests was already
> > >> "complete", arrivals make no sense.
> > >
> > > The set of *accomodated* guests 1, 2, 3, ... is complete.
> > Whatever that means.
> > > Another guest 0 can arrive.
> > You switch between The positive integers and the non-negative integers
> > to add confusion. Those are different sets.
> WM: Verstehst du die Bedeutung des Wortes "crank"?
>
> Ein „Crank“ ist jemand, der angesichts überwältigender Beweise nicht überzeugt werden kann.

And here you are not only dealing with cranks, but with reprobate minds, meaning "no hope or salvation is possible". Such people are worthy only to be burnt and disposed of.

On 12/23/2022 3:00 AM, WM wrote:
> William schrieb am Donnerstag, 22. Dezember 2022 um 19:17:29 UTC+1:
>> On Thursday, December 22, 2022 at 5:39:38 AM UTC-4, WM wrote:
>>> William schrieb am Donnerstag, 22. Dezember 2022 um 02:11:35 UTC+1:
>>>> On Wednesday, December 21, 2022 at 3:01:14 PM UTC-4, WM wrote:
>>>>
>>>>> But all infinite sets which have not a fixed number of members are potentially infinite.
>>>> Potentially infinite sets are nonsense. All sets are fixed.
>>> Then call it collection.
>> Nope, N is a set.
>
> Well, may be.
> |ℕ \ {1, 2, 3, ...}| = 0 .
> But ℕ_def is only a collection:
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo

no, ℕ_def is bullshit IAW your daffynition where numbers are "defined" by rapping on a table, blinking a light, OR a color of a rainbow.

now, QuACk off troll !!

>
> Regards, WM
>

On 12/23/2022 5:07 AM, FromTheRafters wrote:
> WM was thinking very hard :
>> FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:25:10 UTC+1:
>>> WM explained on 12/22/2022 :
>>>> FromTheRafters schrieb am Mittwoch, 21. Dezember 2022 um 22:12:29 UTC+1:
>>>>> WM formulated the question :
>>>>
>>>>>> That is correct for potential infinity only, which is never complete. Actual infinity cannot start from the finite. A complete set is complete.
>>>>>> Nothing can be added without changing the set. Same with pairs of rooms and guest. If the set is complete, then adding a pair of guest and room
>>>>>> changes the set.
>>>>> Countably many rooms can only accomodate countably many guests in infinite hotel theory.
>>>>
>>>> The set of guests = natural numbers ℕ is complete, i.e., none can be added. The set ℕ of room numbers of Hilbert's hotel is complete too. The
>>>> bijection between guests and room numbers has |ℕ| pairs. If another guest arrives and is accomodated
>>> Impossible! Since you claimed that the *set* of guests was already "complete", arrivals make no sense.
>>
>> The set of *accomodated* guests 1, 2, 3, ... is complete.
>
> Whatever that means.

Accommodated Ants
Ants with Existing Accommodations
Accommodated Ants wanting more Complete Accommodations

>
>> Another guest 0 can arrive.

Guest Ant 0 not a member of club ℕ

>
> You switch between The positive integers and the non-negative integers to add confusion. Those are different sets.

On Friday, December 23, 2022 at 11:50:42 AM UTC+1, Eram semper recta wrote:
> On Monday, 19 December 2022 at 12:04:58 UTC+2, WM wrote:
> >
> > Is it possible to add a natural number to the set ℕ?

No, it's not possible. Sets are fixed, they dont grow. IN = {1, 2, 3, ...}

But we may conisder the set IN u {0} which comprises all natural numbers in IN _and_ the element 0: {0, 1, 2, 3, ...}.

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?

No, it's not possible. Sets are fixed, they don't grow. IN = {1, 2, 3, ....}

But we may conisder the set IN u {0} which comprises all natural numbers in IN _and_ the element 0: {0, 1, 2, 3, ...}.

On Friday, December 23, 2022 at 11:56:05 AM UTC+1, Eram semper recta wrote:
> On Thursday, 22 December 2022 at 20:17:29 UTC+2, William wrote:
> > On Thursday, December 22, 2022 at 5:39:38 AM UTC-4, WM wrote:
> > > William schrieb am Donnerstag, 22. Dezember 2022 um 02:11:35 UTC+1:
> > > >
> > > > "Potentially infinite sets" are nonsense. All sets are fixed.
> > > >
> > > Then call it collection.
> > >
> > Nope, N is a set.
> >
> A set is a "collection", you pretentious piece of shit!

Not for WM, it seems.

And right, in set theory sets are also called "collections", etc.

"A set may also be called a /collection/ or /family/, especially when its elements are themselves sets." (Wikipedia)

WE -except Mückenheim of course- know that.

On Friday, December 23, 2022 at 1:08:09 PM UTC+1, Eram semper recta wrote:

> [...] here you are not only dealing with cranks, but with reprobate minds, meaning "no hope or salvation is possible". Such people are worthy only to be burnt and disposed of.

Oh right, AH had such ideas too.

FromTheRafters schrieb am Freitag, 23. Dezember 2022 um 12:03:24 UTC+1:
> WM has brought this to us :
> > FromTheRafters schrieb am Donnerstag, 22. Dezember 2022 um 13:18:46 UTC+1:
> >
> >> *All* of the natural numbers are 'included' and none are
> >> 'excluded' from the *set* of natural numbers. It is an infinite set,
> >> not a semi-infinite collection.
> >
> > Therefore: The set of guests = natural numbers ℕ is complete, i.e., none can
> > be added.
> No, I am not saying that "complete" means "nothing can be added"

If the set of natural numbers is a set, i.e., complete, then no natural number can be added.
The set of room numbers is complete. If another guest arrives, then he cannot get a room number.

Regards, WM

Eram semper recta schrieb am Freitag, 23. Dezember 2022 um 12:24:49 UTC+1:
> 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?
> Such a question only serves a purpose if there is a definition for "set".

Here I accept that all natural numbers are in the set ℕ of room numbers.
If also all natural numbers are as guests in the rooms and another guest arrives, then he cannot get a room. I use this example only in order to show that set theorists argue inconsistently.

Regards, WM

Eram semper recta schrieb am Freitag, 23. Dezember 2022 um 13:05:51 UTC+1:

> WM: Verstehst du die Bedeutung des Wortes "crank"?
>
> Ein „Crank“ ist jemand, der angesichts überwältigender Beweise nicht überzeugt werden kann.

Yes, most set theorists are cranks, in German: Spinner.

Regards, WM