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Re: Natural numbers and vases III

Subject	Author
Natural numbers and vases III	WM
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Africani
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eduardo Faqtardo
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Archimedes Plutonium
Re: Natural numbers and vases III	Archimedes Plutonium

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Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Fri, 12 Aug 2022 13:16 UTC

On Friday, 12 August 2022 at 10:01:07 UTC-3, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 20:32:12 UTC+2:
> > On Thursday, August 11, 2022 at 7:55:16 PM UTC+2, WM wrote:
> > > Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
[...]
> > > > It's clear that Cantor DID NOT talk about a "stepwise process" here:
> > > >
> > > > "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen [....]" [Cantor, p. 119]
> > > >
> > > > Actually, he didn't talk about a process at all
> > IN THE QUOTE MENTIONED ABOVE!!!
> Element für Element defined a process.

It did not, you imbecile. It simply defined a one-to-one mapping. How *FUCKING* stupid does one have to be before the University of Implied Sciences offers one employment and cover to produce *SHIT* sold as "research"?

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Fri, 12 Aug 2022 13:30:13 +0000
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by: WM - Fri, 12 Aug 2022 13:30 UTC

Gus Gassmann schrieb am Freitag, 12. August 2022 um 15:16:39 UTC+2:
> On Friday, 12 August 2022 at 10:01:07 UTC-3, WM wrote:
> > Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 20:32:12 UTC+2:
> > > On Thursday, August 11, 2022 at 7:55:16 PM UTC+2, WM wrote:
> > > > Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
> [...]
> > > > > It's clear that Cantor DID NOT talk about a "stepwise process" here:
> > > > >
> > > > > "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen [...]" [Cantor, p. 119]
> > > > >
> > > > > Actually, he didn't talk about a process at all
> > > IN THE QUOTE MENTIONED ABOVE!!!
> > Element für Element defined a process.
> It did not,

It does.

> It simply defined a one-to-one mapping.

Yes, like here: und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.

Regards, WM

Re: Natural numbers and vases III

<td5n7m$idg$1@gioia.aioe.org>

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Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 09:14:13 -0500
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by: Sergio - Fri, 12 Aug 2022 14:14 UTC

On 8/12/2022 8:01 AM, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 20:32:12 UTC+2:
>> On Thursday, August 11, 2022 at 7:55:16 PM UTC+2, WM wrote:
>>> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
>>>> On Thursday, August 11, 2022 at 3:00:07 PM UTC+2, WM wrote:
>>>>
>>>>> Very correct! All must happen element by element, i.e., as steps of a super task.
>>>>
>>>> Du hast einen Riesensprung in der Schüssel.
>>>>
>>>> Please elaborate how this could be done for uncountable sets. (Say, [-1, 1] and IR.)
>>>>
>>>> See: https://en.wikipedia.org/wiki/Uncountable_set
>> NO ANSWER? WHY NOT?!
>
> 1) there are no uncountable sets.

Wrong, any set of real numbers is uncountable.

>
>>
>>>> It's clear that Cantor DID NOT talk about a "stepwise process" here:
>>>>
>>>> "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen [...]" [Cantor, p. 119]
>>>>
>>>> Actually, he didn't talk about a process at all
>> IN THE QUOTE MENTIONED ABOVE!!!
>
> Element für Element defined a process.

one to one mapping, which is not step by step. You remain confused.

>
> Regards, WM

Re: Natural numbers and vases III

<td5nct$idg$2@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 09:17:00 -0500
Organization: Aioe.org NNTP Server
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by: Sergio - Fri, 12 Aug 2022 14:17 UTC

On 8/12/2022 8:30 AM, WM wrote:
> Gus Gassmann schrieb am Freitag, 12. August 2022 um 15:16:39 UTC+2:
>> On Friday, 12 August 2022 at 10:01:07 UTC-3, WM wrote:
>>> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 20:32:12 UTC+2:
>>>> On Thursday, August 11, 2022 at 7:55:16 PM UTC+2, WM wrote:
>>>>> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
>> [...]
>>>>>> It's clear that Cantor DID NOT talk about a "stepwise process" here:
>>>>>>
>>>>>> "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen [...]" [Cantor, p. 119]
>>>>>>
>>>>>> Actually, he didn't talk about a process at all
>>>> IN THE QUOTE MENTIONED ABOVE!!!
>>> Element für Element defined a process.
>> It did not,
>
> It does.

Wrong, you make mistake.

>
>> It simply defined a one-to-one mapping.
>
> Yes, like here: und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.

can you provide a URL that has that snippet in full context ?

I cannot trust you to provide a truthful view.

>
> Regards, WM

Re: Natural numbers and vases III

<td5nen$idg$3@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 09:17:58 -0500
Organization: Aioe.org NNTP Server
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by: Sergio - Fri, 12 Aug 2022 14:17 UTC

On 8/12/2022 8:04 AM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 12. August 2022 um 07:46:52 UTC+2:
>> torsdag 11 augusti 2022 kl. 15:01:00 UTC+2 skrev WM:
>>> zelos...@gmail.com schrieb am Donnerstag, 11. August 2022 um 07:10:35 UTC+2:
>>>> onsdag 10 augusti 2022 kl. 17:41:55 UTC+2 skrev WM:
>>>>> zelos...@gmail.com schrieb am Mittwoch, 10. August 2022 um 07:52:19 UTC+2:
>>>>>> tisdag 9 augusti 2022 kl. 13:54:44 UTC+2 skrev WM:
>>>>>
>>>>>>> Of course. All intersections with definable endsegments are finite. The infinite intersection contains endsegments which are not individually definable.
>>>>>>>
>>>>>> Your "definable" is meaningless.
>>>>>
>>>>> The set can only be subtracted collectively.
>>>> your "collectively" is meaningless
>>> It means as a whole and not by successively omittig elements.
>>
>> which is meaningless as mathematics is not a process based thing.
>
> Bijecting with |N is a process. Up to every definable number it can be checked.

Wrong, and Wrong.

google Bijection

>>
>>>>
>>>>> |ℕ \ ℕ| = 0
>>>>
>>>> Correct
>>>>> Every element or FISON subtracted will leave almost all of the set remaining.
>>>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>>>>> Can you guess why?
>>>> Because that is how cardinal arithmetic fucking works.
>>> Why does it work that way and not other?
>>
>> Because of the fucking definitions. Why are you so retarded?
>
> Why do they say so?
>
> Regards, WM

Re: Natural numbers and vases III

<td5nm2$qpf$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 09:21:53 -0500
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by: Sergio - Fri, 12 Aug 2022 14:21 UTC

On 8/12/2022 8:15 AM, WM wrote:
> Gus Gassmann schrieb am Freitag, 12. August 2022 um 15:08:29 UTC+2:
>> On Friday, 12 August 2022 at 09:54:37 UTC-3, WM wrote:
>>> [...] What I wanted to say is this:
>>>
>>> |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>>>
>>> It proves that less than ℵo numbers are subject to induction.
>> It proves nothing of the sort. It proves that every FISON is finite, but it does not prove anything about the *number* of FISONs (which is ℵo), or the *set* of all FISONs or the *union* of all FISONs.
>
> No. Induction proves that ℵo numberws are not swubject toinduction.
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
>
> Regards, WM

WRONG!

It says |E(k+1)| = ℵo and then the next equation says |E(k+2)| = ℵo

Trivial, there is NO step by step, nor induction in either equation or the combination of equations.

you are really bad at math.

Or you like being a troll.

Re: Natural numbers and vases III

<d7992d1b-3d2d-43ad-bb04-d6f7675e74fan@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Fri, 12 Aug 2022 14:26 UTC

On Friday, August 12, 2022 at 9:54:37 AM UTC-3, WM wrote:
> |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>
> It proves that less than ℵo numbers are subject to induction.
>
Nope, the finite value k can be any *element* of |N, and the infinite *set* |N contains ℵo *elements*.

--
William Hughes

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 11:38:25 -0400
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by: FromTheRafters - Fri, 12 Aug 2022 15:38 UTC

WM expressed precisely :
> zelos...@gmail.com schrieb am Freitag, 12. August 2022 um 07:46:52 UTC+2:
>> torsdag 11 augusti 2022 kl. 15:01:00 UTC+2 skrev WM:
>>> zelos...@gmail.com schrieb am Donnerstag, 11. August 2022 um 07:10:35
>>> UTC+2:
>>>> onsdag 10 augusti 2022 kl. 17:41:55 UTC+2 skrev WM:
>>>>> zelos...@gmail.com schrieb am Mittwoch, 10. August 2022 um 07:52:19
>>>>> UTC+2:
>>>>>> tisdag 9 augusti 2022 kl. 13:54:44 UTC+2 skrev WM:
>>>>>>> Of course. All intersections with definable endsegments are finite. The
>>>>>>> infinite intersection contains endsegments which are not individually
>>>>>>> definable.
>>>>>>>
>>>>>> Your "definable" is meaningless.
>>>>>
>>>>> The set can only be subtracted collectively.
>>>> your "collectively" is meaningless
>>> It means as a whole and not by successively omittig elements.
>>
>> which is meaningless as mathematics is not a process based thing.
>
> Bijecting with |N is a process. Up to every definable number it can be

I suppose so, since bijecting is a verb, likened to an action, but we
instead speak of a bijection existing between two sets of the same
size. It is a state of existence, not a step-by-step process. Just
because it can be checked to some finite extent by such a process
doesn't mean its existence depends upon the aforementioned step-by-step
validation process.

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 11:43:41 -0400
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by: FromTheRafters - Fri, 12 Aug 2022 15:43 UTC

WM has brought this to us :
> William schrieb am Donnerstag, 11. August 2022 um 20:25:01 UTC+2:
>> On Thursday, August 11, 2022 at 2:57:49 PM UTC-3, WM wrote:
>>
>>> Does
>>>
>>>> ℕ \ {1, 2, 3, ..., k}| < omega ==> |ℕ \ {1, 2, 3, ..., k, k+1}| < omega
>>>
>>> mean that omega is subject to finite induction too?
>>>
>> Nope. k and k+1 are both elements of |N, and are both less than omega.
>
> That was a mistake. What I wanted to say is this:
>
>> {1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>
> It proves that less than ℵo numbers are subject to induction.

Two finite sets each being less than infinite somehow proves something
about inductive sets?

Tell us more.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Fri, 12 Aug 2022 16:38 UTC

FromTheRafters schrieb am Freitag, 12. August 2022 um 17:43:57 UTC+2:
> WM has brought this to us :
> > What I wanted to say is this:
> >
> >> {1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
> >
> > It proves that less than ℵo numbers are subject to induction.
> Two finite sets each being less than infinite somehow proves something
> about inductive sets?
>
> Tell us more.

All sets reachable by induction have a finite number of elements.
ℕ with its ℵo elements is not covered by induction:
|ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Fri, 12 Aug 2022 16:41 UTC

William schrieb am Freitag, 12. August 2022 um 16:26:30 UTC+2:
> On Friday, August 12, 2022 at 9:54:37 AM UTC-3, WM wrote:
>
> > |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
> >
> > It proves that less than ℵo numbers are subject to induction.
> >
> Nope, the finite value k can be any *element* of |N, and the infinite *set* |N contains ℵo *elements*.
>
The latter is true. But induction fails to cover ℕ. This is proved by

|ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo

where k can be any element subject to induction. In any case ℵo elements of ℕ are outside.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Fri, 12 Aug 2022 16:46 UTC

FromTheRafters schrieb am Freitag, 12. August 2022 um 17:38:41 UTC+2:
> WM expressed precisely :
> > zelos...@gmail.com schrieb am Freitag, 12. August 2022 um 07:46:52 UTC+2:
> >> torsdag 11 augusti 2022 kl. 15:01:00 UTC+2 skrev WM:
> >>> zelos...@gmail.com schrieb am Donnerstag, 11. August 2022 um 07:10:35
> >>> UTC+2:
> >>>> onsdag 10 augusti 2022 kl. 17:41:55 UTC+2 skrev WM:
> >>>>> zelos...@gmail.com schrieb am Mittwoch, 10. August 2022 um 07:52:19
> >>>>> UTC+2:
> >>>>>> tisdag 9 augusti 2022 kl. 13:54:44 UTC+2 skrev WM:
> >>>>>>> Of course. All intersections with definable endsegments are finite. The
> >>>>>>> infinite intersection contains endsegments which are not individually
> >>>>>>> definable.
> >>>>>>>
> >>>>>> Your "definable" is meaningless.
> >>>>>
> >>>>> The set can only be subtracted collectively.
> >>>> your "collectively" is meaningless
> >>> It means as a whole and not by successively omittig elements.
> >>
> >> which is meaningless as mathematics is not a process based thing.
> >
> > Bijecting with |N is a process. Up to every definable number it can be
> I suppose so, since bijecting is a verb, likened to an action, but we
> instead speak of a bijection existing between two sets of the same
> size.

But when following the process, which first has to establish this bijection, then it turns out that this claim is wrong.

> It is a state of existence, not a step-by-step process. Just
> because it can be checked to some finite extent by such a process
> doesn't mean its existence depends upon the aforementioned step-by-step
> validation process.

It does. Cantor knew that. And everybody honest enough will agree. Cantors opinion is proved by his statement: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand". It is a process and it does not halt. Something that can halt must be moving.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Fri, 12 Aug 2022 16:56 UTC

On Friday, August 12, 2022 at 1:41:21 PM UTC-3, WM wrote:
> William schrieb am Freitag, 12. August 2022 um 16:26:30 UTC+2:
> > On Friday, August 12, 2022 at 9:54:37 AM UTC-3, WM wrote:
> >
> > > |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
> > >
> > > It proves that less than ℵo numbers are subject to induction.
> > >
> > Nope, the finite value k can be any *element* of |N, and the infinite *set* |N contains ℵo *elements*.
> >
> The latter is true. But induction fails to cover ℕ.

Induction works for every *element* of |N and as you note, |N contains ℵo *elements*.

--
William Hughes

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 12:01:42 -0500
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by: Sergio - Fri, 12 Aug 2022 17:01 UTC

On 8/12/2022 11:46 AM, WM wrote:
> FromTheRafters schrieb am Freitag, 12. August 2022 um 17:38:41 UTC+2:
>> WM expressed precisely :
>>> zelos...@gmail.com schrieb am Freitag, 12. August 2022 um 07:46:52 UTC+2:
>>>> torsdag 11 augusti 2022 kl. 15:01:00 UTC+2 skrev WM:
>>>>> zelos...@gmail.com schrieb am Donnerstag, 11. August 2022 um 07:10:35
>>>>> UTC+2:
>>>>>> onsdag 10 augusti 2022 kl. 17:41:55 UTC+2 skrev WM:
>>>>>>> zelos...@gmail.com schrieb am Mittwoch, 10. August 2022 um 07:52:19
>>>>>>> UTC+2:
>>>>>>>> tisdag 9 augusti 2022 kl. 13:54:44 UTC+2 skrev WM:
>>>>>>>>> Of course. All intersections with definable endsegments are finite. The
>>>>>>>>> infinite intersection contains endsegments which are not individually
>>>>>>>>> definable.
>>>>>>>>>
>>>>>>>> Your "definable" is meaningless.
>>>>>>>
>>>>>>> The set can only be subtracted collectively.
>>>>>> your "collectively" is meaningless
>>>>> It means as a whole and not by successively omittig elements.
>>>>
>>>> which is meaningless as mathematics is not a process based thing.
>>>
>>> Bijecting with |N is a process. Up to every definable number it can be
>> I suppose so, since bijecting is a verb, likened to an action, but we
>> instead speak of a bijection existing between two sets of the same
>> size.
>
> But when following the process, which first has to establish this bijection, then it turns out that this claim is wrong.

so you are saying " = " is a process ?
>
>> It is a state of existence, not a step-by-step process. Just
>> because it can be checked to some finite extent by such a process
>> doesn't mean its existence depends upon the aforementioned step-by-step
>> validation process.
>
> It does. Cantor knew that. And everybody honest enough will agree. Cantors opinion is proved by his statement: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand". It is a process and it does not halt. Something that can halt must be moving.

that is out of context, you bad boy!

>
> Regards, WM

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 13:27:20 -0400
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by: FromTheRafters - Fri, 12 Aug 2022 17:27 UTC

WM formulated on Friday :
> FromTheRafters schrieb am Freitag, 12. August 2022 um 17:38:41 UTC+2:
>> WM expressed precisely :
>>> zelos...@gmail.com schrieb am Freitag, 12. August 2022 um 07:46:52 UTC+2:
>>>> torsdag 11 augusti 2022 kl. 15:01:00 UTC+2 skrev WM:
>>>>> zelos...@gmail.com schrieb am Donnerstag, 11. August 2022 um 07:10:35
>>>>> UTC+2:
>>>>>> onsdag 10 augusti 2022 kl. 17:41:55 UTC+2 skrev WM:
>>>>>>> zelos...@gmail.com schrieb am Mittwoch, 10. August 2022 um 07:52:19
>>>>>>> UTC+2:
>>>>>>>> tisdag 9 augusti 2022 kl. 13:54:44 UTC+2 skrev WM:
>>>>>>>>> Of course. All intersections with definable endsegments are finite.
>>>>>>>>> The infinite intersection contains endsegments which are not
>>>>>>>>> individually definable.
>>>>>>>>>
>>>>>>>> Your "definable" is meaningless.
>>>>>>>
>>>>>>> The set can only be subtracted collectively.
>>>>>> your "collectively" is meaningless
>>>>> It means as a whole and not by successively omittig elements.
>>>>
>>>> which is meaningless as mathematics is not a process based thing.
>>>
>>> Bijecting with |N is a process. Up to every definable number it can be
>> I suppose so, since bijecting is a verb, likened to an action, but we
>> instead speak of a bijection existing between two sets of the same
>> size.
>
> But when following the process, which first has to establish this bijection,
> then it turns out that this claim is wrong.

The 'process' does not establish the bijection, the bijection is
already there.

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 13:31:20 -0400
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by: FromTheRafters - Fri, 12 Aug 2022 17:31 UTC

WM has brought this to us :
> FromTheRafters schrieb am Freitag, 12. August 2022 um 17:43:57 UTC+2:
>> WM has brought this to us :
>>> What I wanted to say is this:
>>>
>>>> {1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>>>
>>> It proves that less than ℵo numbers are subject to induction.
>> Two finite sets each being less than infinite somehow proves something
>> about inductive sets?
>>
>> Tell us more.
>
> All sets reachable by induction have a finite number of elements.

No, inductive sets are not finite sets.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Fri, 12 Aug 2022 18:32 UTC

On Friday, 12 August 2022 at 11:14:28 UTC-3, Sergio wrote:
> On 8/12/2022 8:01 AM, WM wrote:
[...]
> > 1) there are no uncountable sets.
> Wrong, any set of real numbers is uncountable.

This, I think, needs to be qualified. First, there definitely are sets of real numbers that are countable, even finite, e.g., the set of roots of the equation x^2 = 5. But there is a bit more to it, and WM gave Cantor's quote (even though it is clear that he has no clue what Cantor meant).

> > 2) Alle Mengen sind daher in einem erweiterten Sinne "abzählbar", im besonderen alle "Kontinua". [Cantor]

("All sets are therefore in an extended sense "countable", especially all 'continua'".) This is what cardinality measures. If there is a bijection between a set and the natural numbers, the set has the same cardinality as |N --- that is, aleph_0. But if there is a bijection between the set and the real numbers, then the set has the same cardinality as the reals and could therefore be called "countable of type c" --- which of course nobody uses now (not sure what Cantor would have called it). If the continuum hypothesis is true, this would be the cardinality aleph_1, and so on.

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Fri, 12 Aug 2022 18:37 UTC

On Friday, 12 August 2022 at 10:15:17 UTC-3, WM wrote:
> Gus Gassmann schrieb am Freitag, 12. August 2022 um 15:08:29 UTC+2:
> > On Friday, 12 August 2022 at 09:54:37 UTC-3, WM wrote:
> > > [...] What I wanted to say is this:
> > >
> > > |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
> > >
> > > It proves that less than ℵo numbers are subject to induction.
> > It proves nothing of the sort. It proves that every FISON is finite, but it does not prove anything about the *number* of FISONs (which is ℵo), or the *set* of all FISONs or the *union* of all FISONs.
> No. Induction proves that ℵo numberws are not swubject toinduction.
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.

You have gone completely soft in the head. There is no other way to say it and no other way to explain this latest lunacy of yours. You even repeated it in a slightly different form that doesn't make it any less wrong. By now I would estimate that you have fewer than three synapses left that can still fire occasionally.

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 15:04:39 -0500
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by: Sergio - Fri, 12 Aug 2022 20:04 UTC

On 8/12/2022 11:41 AM, WM wrote:
> William schrieb am Freitag, 12. August 2022 um 16:26:30 UTC+2:
>> On Friday, August 12, 2022 at 9:54:37 AM UTC-3, WM wrote:
>>
>>> |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>>>
>>> It proves that less than ℵo numbers are subject to induction.
>>>
>> Nope, the finite value k can be any *element* of |N, and the infinite *set* |N contains ℵo *elements*.
>>
> The latter is true. But induction fails to cover ℕ. This is proved by
>
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo

WRONG!

It says |E(k+1)| = ℵo and then the next equation says |E(k+2)| = ℵo

Trivial, there is NO step by step, nor induction in either equation or the combination of equations.

your conclusion is QUACKERS!

you are really bad at math.

Or you like being a troll.

>
> Regards, WM

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 15:06:50 -0500
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by: Sergio - Fri, 12 Aug 2022 20:06 UTC

On 8/12/2022 11:38 AM, WM wrote:
> FromTheRafters schrieb am Freitag, 12. August 2022 um 17:43:57 UTC+2:
>> WM has brought this to us :
>>> What I wanted to say is this:
>>>
>>>> {1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>>>
>>> It proves that less than ℵo numbers are subject to induction.
>> Two finite sets each being less than infinite somehow proves something
>> about inductive sets?
>>
>> Tell us more.
>
> All sets reachable by induction have a finite number of elements.
> ℕ with its ℵo elements is not covered by induction:

You have no idea what Mathematical Induction is, it is obvious from you use of the word induction.

>
> Regards, WM

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 12 Aug 2022 19:28:23 -0500
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by: Sergio - Sat, 13 Aug 2022 00:28 UTC

On 8/12/2022 1:32 PM, Gus Gassmann wrote:
> On Friday, 12 August 2022 at 11:14:28 UTC-3, Sergio wrote:
>> On 8/12/2022 8:01 AM, WM wrote:
> [...]
>>> 1) there are no uncountable sets.
>> Wrong, any set of real numbers is uncountable.
>
> This, I think, needs to be qualified. First, there definitely are sets of real numbers that are countable, even finite, e.g., the set of roots of the equation x^2 = 5. But there is a bit more to it, and WM gave Cantor's quote (even though it is clear that he has no clue what Cantor meant).

agree, I was too general, I was thinking of a set partitioned out on the real line, some interval between A and B... like the set of reals between 0
and 1, [0,1]

>
>>> 2) Alle Mengen sind daher in einem erweiterten Sinne "abzählbar", im besonderen alle "Kontinua". [Cantor]
>
> ("All sets are therefore in an extended sense "countable", especially all 'continua'".) This is what cardinality measures. If there is a bijection between a set and the natural numbers, the set has the same cardinality as |N --- that is, aleph_0. But if there is a bijection between the set and the real numbers, then the set has the same cardinality as the reals and could therefore be called "countable of type c" --- which of course nobody uses now (not sure what Cantor would have called it). If the continuum hypothesis is true, this would be the cardinality aleph_1, and so on.

Re: Natural numbers and vases III

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From: reu...@hiaibhar.ab (Chau Barbieri)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Followup-To: sci.physics.relativity
Date: Sat, 13 Aug 2022 15:50:44 -0000 (UTC)
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by: Chau Barbieri - Sat, 13 Aug 2022 15:50 UTC

Sergio wrote:

> agree, I was too general, I was thinking of a set partitioned out on the
> real line, some interval between A and B... like the set of reals
> between 0 and 1, [0,1]

capitalist america, the bidans crime scene, is going other countries to
buy food for their families, to put on the table. *lol*

Bidenflation is so BAD that Americans are going to MEXICO for cheaper food
https://www.bitchute.com/video/lORA9Z9EMFIg/

the nazis, the rulers of the europe, don't want to work and pay for the
food thy eat. *lol*

Ukrainian refugees complain thatthey are forced to go to work and pay for
accommodationand food https://www.bitchute.com/video/MDr3pfFHaXHy/

roger waters is fucking up the mental retarded khazar, gay actor, cocaine
zelenske, badly. *lol*. You capitalist nazis are the next.

Roger Waters (Pink Floyd) on Zelensky and Minsk Accords
https://www.bitchute.com/video/g2zrKhFyXdM1/

watch you favorite khazar gay actor, "president" puppet, cocaine zelenske,
worse in words than his dementia hit puppeteers.

DEMENTED - Zelensky in today's address again called on the EU to close
entry for Russians https://www.bitchute.com/video/DHQmvjGcNNB2/

your corrupt parliament are still standing up in ovations, watching him
retarding on a screen.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Sat, 13 Aug 2022 16:03 UTC

William schrieb am Freitag, 12. August 2022 um 18:57:03 UTC+2:
> On Friday, August 12, 2022 at 1:41:21 PM UTC-3, WM wrote:
> > William schrieb am Freitag, 12. August 2022 um 16:26:30 UTC+2:
> > > On Friday, August 12, 2022 at 9:54:37 AM UTC-3, WM wrote:
> > >
> > > > |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
> > > >
> > > > It proves that less than ℵo numbers are subject to induction.
> > > >
> > > Nope, the finite value k can be any *element* of |N, and the infinite *set* |N contains ℵo *elements*.
> > >
> > The latter is true. But induction fails to cover ℕ.
> Induction works for every *element* of |N
>
You may proclaim that again and again. It is like proclaiming 2 + 2 = 7.
Every element of induction shows
|ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
and that will never change for any n subject to induction.

> and as you note, |N contains ℵo *elements*.

Yes. But most of them stay outside of induction because, according to Cantor, ω - n = ω.

Regards, WM

Re: Natural numbers and vases III

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by: WM - Sat, 13 Aug 2022 16:04 UTC

FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:

> > But when following the process, which first has to establish this bijection,
> > then it turns out that this claim is wrong.
> The 'process' does not establish the bijection, the bijection is
> already there.

In your delusions but not in mathematics.

Regards, WM

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Sat, 13 Aug 2022 16:09 UTC

On Saturday, 13 August 2022 at 13:03:30 UTC-3, WM wrote:
> William schrieb am Freitag, 12. August 2022 um 18:57:03 UTC+2:
[...]
> > Induction works for every *element* of |N
> >
> You may proclaim that again and again. It is like proclaiming 2 + 2 = 7..
> Every element of induction shows
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
> and that will never change for any n subject to induction.

You may proclaim that again and again. It is like proclaiming 2 + 2 = 7. That doesn't mean it makes any sense. In fact, it is your usual bullshit.

tech / sci.math / Re: Natural numbers and vases III

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