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"Only the hypocrite is really rotten to the core." -- Hannah Arendt.

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 - Mon, 25 Jul 2022 19:14 UTC

On Monday, 25 July 2022 at 14:09:44 UTC-3, WM wrote:
[...]
> If every endsegment contains a number, then, by inclusion monotony, all endsegments contain the same number. This is unavoidable.

Good grief. This again? You have no clue what inclusion monotony means for infinite collections. How FUCKING stupid can you be before you are allowed to teach at Augsburg Technical? You are a braindead moron. And now piss off.

Re: Natural numbers and vases III

<tbmq4l$j59$2@gioia.aioe.org>

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Subject: Re: Natural numbers and vases III
Date: Mon, 25 Jul 2022 14:15:32 -0500
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by: Sergio - Mon, 25 Jul 2022 19:15 UTC

On 7/25/2022 12:12 PM, WM wrote:
> Fritz Feldhase schrieb am Montag, 25. Juli 2022 um 17:19:10 UTC+2:
>> On Monday, July 25, 2022 at 3:00:01 PM UTC+2, WM wrote:
>>
>>> If there are infinitely many successors [...] it is also possible to remove all these [successors].
>>
>> Of course it is possible, with the appropriate notions.
>
> For all definable numers it is possible using \.
>
>> That's why I devised the "\\" operation.
>>
>> This way we can state
>>
>> IN \\ {{s(n)} : n e IN} = IN \\ {{2}, {3}, {4}, ...} = {1}
>>
>> This can be written as
>>
>> IN \ {2} \ {3} \ {4} \ ... = {1}.
>>
> For every {n} infinitely many successors provably are not subtracted.

having trouble reading equations ?

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Tue, 26 Jul 2022 05:23 UTC

måndag 25 juli 2022 kl. 19:06:00 UTC+2 skrev WM:
> William schrieb am Montag, 25. Juli 2022 um 16:53:30 UTC+2:
> > On Monday, July 25, 2022 at 9:55:31 AM UTC-3, WM wrote:
> > > ... removing "all elements which have infinitely many successors" leaves nothing.
> > > Why can the numbers not be removed individually?
> > A stepwise process, "removed individually", will not reach a final state.
> But you can define it by induction. Every definable number will be removed. But almost all will remain This is provable by induction.
>
> Regards, WM
Nope, it is not.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Tue, 26 Jul 2022 05:24 UTC

måndag 25 juli 2022 kl. 19:13:03 UTC+2 skrev WM:
> Fritz Feldhase schrieb am Montag, 25. Juli 2022 um 17:19:10 UTC+2:
> > On Monday, July 25, 2022 at 3:00:01 PM UTC+2, WM wrote:
> >
> > > If there are infinitely many successors [...] it is also possible to remove all these [successors].
> >
> > Of course it is possible, with the appropriate notions.
> For all definable numers it is possible using \.
> > That's why I devised the "\\" operation.
> >
> > This way we can state
> >
> > IN \\ {{s(n)} : n e IN} = IN \\ {{2}, {3}, {4}, ...} = {1}
> >
> > This can be written as
> >
> > IN \ {2} \ {3} \ {4} \ ... = {1}.
> >
> For every {n} infinitely many successors provably are not subtracted.
>
> Regards, WM
Can you please stop with these stupidities?

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 - Tue, 26 Jul 2022 11:01 UTC

Gus Gassmann schrieb am Montag, 25. Juli 2022 um 21:14:36 UTC+2:
> On Monday, 25 July 2022 at 14:09:44 UTC-3, WM wrote:
> [...]
> > If every endsegment contains a number, then, by inclusion monotony, all endsegments contain the same number. This is unavoidable.
> Good grief. This again? You have no clue what inclusion monotony means for infinite collections.

It means the same as for finite collections. A simple example is the sequence 1 + 1/n.

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 - Tue, 26 Jul 2022 11:06 UTC

William schrieb am Montag, 25. Juli 2022 um 19:28:19 UTC+2:
> On Monday, July 25, 2022 at 2:06:00 PM UTC-3, WM wrote:
> > William schrieb am Montag, 25. Juli 2022 um 16:53:30 UTC+2:
> > > On Monday, July 25, 2022 at 9:55:31 AM UTC-3, WM wrote:
> > > > ... removing "all elements which have infinitely many successors" leaves nothing.
> > > > Why can the numbers not be removed individually?
> > > A stepwise process, "removed individually", will not reach a final state.
> > But you can define it by induction.
> Nope. You can define a final state but not by induction.

You can define the removal of all natural numbers by induction. Very simple: If you have removed n then remove n+1. That will remove all natural numbers whh are subject to induction. But it will never remove all natural numbers because dark numbers are not subject ti induction.

> And the stepwise process will not reach a final state.

Nevertheless you cannot define a natural number which would remain, can you?.

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 - Tue, 26 Jul 2022 11:10 UTC

Sergio schrieb am Montag, 25. Juli 2022 um 21:14:36 UTC+2:
> On 7/25/2022 12:09 PM, WM wrote:

> > If every endsegment contains a number,
> each endsegment contains an infinity of numbers.
> > then, by inclusion monotony, all endsegments contain the same number.
> > This is unavoidable.
>
> no, it is not possible.

Take a leaking bathtub. As long as it contains a drop, this drop is the same for all states.
As long as it contains many drops, at least one drop is the same for all states.

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 - Tue, 26 Jul 2022 11:16 UTC

On Tuesday, 26 July 2022 at 08:01:53 UTC-3, WM wrote:
> Gus Gassmann schrieb am Montag, 25. Juli 2022 um 21:14:36 UTC+2:
> > Good grief. This again? You have no clue what inclusion monotony means for infinite collections.
> It means the same as for finite collections. A simple example is the sequence 1 + 1/n.

You have truly lost your mind! In what universe do you live where a sequence of real numbers is *inclusion monotone*?

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 - Tue, 26 Jul 2022 11:20 UTC

On Tuesday, 26 July 2022 at 08:10:31 UTC-3, WM wrote:
[...]
> Take a leaking bathtub. As long as it contains a drop, this drop is the same for all states.

And what states might those be? The state where this drop is *in* the tub, as opposed to all the other states where it is not? You are a dangerously demented person. I hope you have enough of a support system to help persuade you to hand in your driver's license before you kill somebody.

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by: Sergio - Tue, 26 Jul 2022 12:12 UTC

On 7/26/2022 6:06 AM, WM wrote:
> William schrieb am Montag, 25. Juli 2022 um 19:28:19 UTC+2:
>> On Monday, July 25, 2022 at 2:06:00 PM UTC-3, WM wrote:
>>> William schrieb am Montag, 25. Juli 2022 um 16:53:30 UTC+2:
>>>> On Monday, July 25, 2022 at 9:55:31 AM UTC-3, WM wrote:
>>>>> ... removing "all elements which have infinitely many successors" leaves nothing.
>>>>> Why can the numbers not be removed individually?
>>>> A stepwise process, "removed individually", will not reach a final state.
>>> But you can define it by induction.
>> Nope. You can define a final state but not by induction.
>
> You can define the removal of all natural numbers by induction. Very simple: If you have removed n then remove n+1. That will remove all natural numbers whh are subject to induction. But it will never remove all natural numbers because dark numbers are not subject ti induction.

Gad, you try so hard for your Darkies, even lie, but you are Still Wrong.

>
>> And the stepwise process will not reach a final state.
>
> Nevertheless you cannot define a natural number which would remain, can you?.

you are the one claiming that, so prove it.

>
> Regards, WM

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
Date: Tue, 26 Jul 2022 07:13:26 -0500
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by: Sergio - Tue, 26 Jul 2022 12:13 UTC

On 7/26/2022 6:10 AM, WM wrote:
> Sergio schrieb am Montag, 25. Juli 2022 um 21:14:36 UTC+2:
>> On 7/25/2022 12:09 PM, WM wrote:
>
>>> If every endsegment contains a number,
>> each endsegment contains an infinity of numbers.
>>> then, by inclusion monotony, all endsegments contain the same number.
>>> This is unavoidable.
>>
>> no, it is not possible.
>
> Take a leaking bathtub. As long as it contains a drop, this drop is the same for all states.
> As long as it contains many drops, at least one drop is the same for all states.
>
> Regards, WM

Bathtubs are finite, and do not apply to infinite sets.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Tue, 26 Jul 2022 07:16:09 -0500
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by: Sergio - Tue, 26 Jul 2022 12:16 UTC

On 7/26/2022 6:01 AM, WM wrote:
> Gus Gassmann schrieb am Montag, 25. Juli 2022 um 21:14:36 UTC+2:
>> On Monday, 25 July 2022 at 14:09:44 UTC-3, WM wrote:
>> [...]
>>> If every endsegment contains a number, then, by inclusion monotony, all endsegments contain the same number. This is unavoidable.
>> Good grief. This again? You have no clue what inclusion monotony means for infinite collections.
>
> It means the same as for finite collections. A simple example is the sequence 1 + 1/n.
>
> Regards, WM
>

You have no clue what inclusion monotony means for infinite collections.

so you are saying 1 + 1/n is included in 1 + 1/(n+1) ?

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Tue, 26 Jul 2022 12:26 UTC

On Tuesday, July 26, 2022 at 1:06:49 PM UTC+2, WM wrote:
>
> dark numbers are not subject to induction.

This implies that dark numbers aren't natural numbers, since ALL natural numbers "are subject to induction".

Proof (by induction). 1 is subject to induction. If a natural number n is subject to induction then n+1 is subject to induction too. Hence (by induction) all natural numbers are subject to induction. qed

So there are no "dark" natural numbers. Great you made that clear.

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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 - Tue, 26 Jul 2022 13:25 UTC

On Tuesday, 26 July 2022 at 09:26:53 UTC-3, Fritz Feldhase wrote:
> [...] ALL natural numbers "are subject to induction".
>
> Proof (by induction). 1 is subject to induction. If a natural number n is subject to induction then n+1 is subject to induction too. Hence (by induction) all natural numbers are subject to induction. qed

Hate to say it, but that is the same "proof by intimidation" that we accuse the great confuser of all the time. "[S]ubject to induction" is undefined (by wittle Mucki, of course), and the induction step is not a proof.

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by: FromTheRafters - Tue, 26 Jul 2022 13:41 UTC

on 7/26/2022, WM supposed :
> William schrieb am Montag, 25. Juli 2022 um 19:28:19 UTC+2:
>> On Monday, July 25, 2022 at 2:06:00 PM UTC-3, WM wrote:
>>> William schrieb am Montag, 25. Juli 2022 um 16:53:30 UTC+2:
>>>> On Monday, July 25, 2022 at 9:55:31 AM UTC-3, WM wrote:
>>>>> ... removing "all elements which have infinitely many successors" leaves
>>>>> nothing. Why can the numbers not be removed individually?
>>>> A stepwise process, "removed individually", will not reach a final state.
>>> But you can define it by induction.
>> Nope. You can define a final state but not by induction.
>
> You can define the removal of all natural numbers by induction.

What do you think proof by induction is?

BTW, you are not removing anything except possibly removing some
elements from consideration in the new set you are creating. IOW they
all remain where they were.

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 - Tue, 26 Jul 2022 13:45 UTC

> That will remove all natural numbers whh are subject to induction.

That is all elements of |N

> But it will never remove all natural numbers because dark numbers are not subject ti induction.

Piffle. |N is a Peano set and does not contain "dark numbers"

>
> > And the stepwise process will not reach a final state.

>
> Nevertheless

So what? A stepwise process will not reach a final state.

--
William Hughes

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 - Tue, 26 Jul 2022 15:35 UTC

Sergio schrieb am Dienstag, 26. Juli 2022 um 14:13:38 UTC+2:
> On 7/26/2022 6:10 AM, WM wrote:
> > Sergio schrieb am Montag, 25. Juli 2022 um 21:14:36 UTC+2:
> >> On 7/25/2022 12:09 PM, WM wrote:
> >
> >>> If every endsegment contains a number,
> >> each endsegment contains an infinity of numbers.
> >>> then, by inclusion monotony, all endsegments contain the same number.
> >>> This is unavoidable.
> >>
> >> no, it is not possible.
> >
> > Take a leaking bathtub. As long as it contains a drop, this drop is the same for all states.
> > As long as it contains many drops, at least one drop is the same for all states.
> >
> Bathtubs are finite, and do not apply to infinite sets.

In mathematics drops can halve their size every time.

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 - Tue, 26 Jul 2022 15:40 UTC

Fritz Feldhase schrieb am Dienstag, 26. Juli 2022 um 14:26:53 UTC+2:
> On Tuesday, July 26, 2022 at 1:06:49 PM UTC+2, WM wrote:
> >
> > dark numbers are not subject to induction.
>
> This implies that dark numbers aren't natural numbers, since ALL natural numbers "are subject to induction".
>
> Proof (by induction). 1 is subject to induction. If a natural number n is subject to induction then n+1 is subject to induction too.

Of course.

> Hence (by induction) all natural numbers are subject to induction. qed

Hence Elvis is alive?

No. By induction: After every n there remain infintely many natural numbers. Nevertheless you cannot define a natural number which would remain, can you?

Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 26 Jul 2022 15:41 UTC

William schrieb am Dienstag, 26. Juli 2022 um 15:45:38 UTC+2:

> A stepwise process will not reach a final state.

Nevertheless you cannot define a natural number which would remain, can you?.

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 - Tue, 26 Jul 2022 15:45 UTC

Gus Gassmann schrieb am Dienstag, 26. Juli 2022 um 13:16:42 UTC+2:
> On Tuesday, 26 July 2022 at 08:01:53 UTC-3, WM wrote:
> > A simple example is the sequence 1 + 1/n.
> In what universe do you live where a sequence of real numbers is *inclusion monotone*?

If you can't understand the abstract meaning, try to visualize it with geometric lengths.

Regards, WM

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 - Tue, 26 Jul 2022 16:12 UTC

On Tuesday, 26 July 2022 at 12:45:54 UTC-3, WM wrote:
[...]
> If you can't understand the abstract meaning, try to visualize it with geometric lengths.

If you can't express yourself in an understandable manner, then please piss off.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Tue, 26 Jul 2022 16:32 UTC

On Tuesday, July 26, 2022 at 3:25:41 PM UTC+2, Gus Gassmann wrote:
> On Tuesday, 26 July 2022 at 09:26:53 UTC-3, Fritz Feldhase wrote:
> >
> > [...] ALL natural numbers "are subject to induction".
> >
> > Proof (by induction). 1 is subject to induction. If a natural number n is subject to induction then n+1 is subject to induction too. Hence (by induction) all natural numbers are subject to induction. qed
> >
> Hate to say it, but that is the same "proof by intimidation" that we accuse the great confuser of all the time. "[S]ubject to induction" is undefined (by wittle Mucki, of course), and the induction step is not a proof.

Hell, and *I* thought no one would notice! :-P

Actually, I really don't know what "is subject to induction" could mean. My best guess: is a natural number.

Now my proof reads:

Proof (by induction). 1 is a natural number (by a Peano Axiom). If n is a natural number then n+1 is a natural number too (by a Peano Axiom and n + 1 = s(n)). Hence (by induction, another Peano Axiom) all natural numbers are natural numbers. qed

Ok? :-)

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 - Tue, 26 Jul 2022 16:39 UTC

On Tuesday, July 26, 2022 at 12:41:46 PM UTC-3, WM wrote:
> William schrieb am Dienstag, 26. Juli 2022 um 15:45:38 UTC+2:
>
> > A stepwise process will not reach a final state.
> Nevertheless you cannot define a natural number which would remain, can you?.

So What? This does not mean the stepwise process reaches a final state.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Tue, 26 Jul 2022 16:44 UTC

On Tuesday, July 26, 2022 at 5:45:54 PM UTC+2, WM wrote:
> Gus Gassmann schrieb am Dienstag, 26. Juli 2022 um 13:16:42 UTC+2:
> > On Tuesday, 26 July 2022 at 08:01:53 UTC-3, WM wrote:
> > >
> > > A simple example is the sequence 1 + 1/n.

Better use a sequence of sets, say the sequence of intervalls (I_n) with I_n = (1, 1 + 1/n] for all n e IN.

This sequence is inclusion monotonic (since I_(n+1) c I_n for all n e IN).The Intersection of the terms of this sequence is empty. INTERSECTION_(n e IN) I_n = { }.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Sergio - Tue, 26 Jul 2022 18:30 UTC

On 7/26/2022 10:40 AM, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 26. Juli 2022 um 14:26:53 UTC+2:
>> On Tuesday, July 26, 2022 at 1:06:49 PM UTC+2, WM wrote:
>>>
>>> dark numbers are not subject to induction.
>>
>> This implies that dark numbers aren't natural numbers, since ALL natural numbers "are subject to induction".
>>
>> Proof (by induction). 1 is subject to induction. If a natural number n is subject to induction then n+1 is subject to induction too.
>
> Of course.

Wrong => if n is subject to post-induction than n+1 is is subject to post-induction too, and if n is subject to pre-induction then n-1 is subject to
pre-induction.

>
>> Hence (by induction) all natural numbers are subject to induction. qed
>
> Hence Elvis is alive?

Yes! he goes by Dark Elvis now, yet no one has seen him.

>
> Regards, WM
>

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

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