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Killing is wrong. -- Losira, "That Which Survives", stardate unknown


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

SubjectAuthor
* Natural numbers and vasesWilliam
+- Re: Natural numbers and vasesRoss A. Finlayson
+* Re: Natural numbers and vasesWM
|+* Re: Natural numbers and vasesWilliam
||`* Re: Natural numbers and vasesWM
|| +- Re: Natural numbers and vasessergio
|| `* Re: Natural numbers and vasesWilliam
||  `* Re: Natural numbers and vasesWM
||   +- Re: Natural numbers and vasessergio
||   `* Re: Natural numbers and vasesWilliam
||    `* Re: Natural numbers and vasesWM
||     +- Re: Natural numbers and vasessergio
||     `* Re: Natural numbers and vasesWilliam
||      +- Re: Natural numbers and vasesFritz Feldhase
||      `* Re: Natural numbers and vasesWM
||       +* Re: Natural numbers and vasesWilliam
||       |+* Re: Natural numbers and vasesGus Gassmann
||       ||`* Re: Natural numbers and vasesFritz Feldhase
||       || `- Re: Natural numbers and vasesGus Gassmann
||       |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasesGus Gassmann
||       | +* Re: Natural numbers and vasesWilliam
||       | |+* Re: Natural numbers and vasesWM
||       | ||+* Re: Natural numbers and vasesWilliam
||       | |||`* Re: Natural numbers and vasesWM
||       | ||| `* Re: Natural numbers and vasesWilliam
||       | |||  +* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |`- Re: Natural numbers and vasessergio
||       | |||  +* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasesFromTheRafters
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChris M. Thomasson
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+* Re: Natural numbers and vasesJim Burns
||       | |||  |||`* Re: Natural numbers and vasesWM
||       | |||  ||| +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| |`* Re: Natural numbers and vasesWM
||       | |||  ||| | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | `- Re: Natural numbers and vasessergio
||       | |||  ||| `- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `* Re: Natural numbers and vasesWM
||       | |||  ||  `* Re: Natural numbers and vasessergio
||       | |||  ||   +* Re: Natural numbers and vasessergio
||       | |||  ||   |`* Re: Natural numbers and vasesFredJeffries
||       | |||  ||   | `- Re: Natural numbers and vasessergio
||       | |||  ||   `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||    `* Re: Natural numbers and vasessergio
||       | |||  ||     +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||     |`- Re: Natural numbers and vasessergio
||       | |||  ||     `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||      `* Re: Natural numbers and vasessergio
||       | |||  ||       `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        |`- Re: Natural numbers and vasessergio
||       | |||  ||        `- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  || +* Re: Natural numbers and vasesFromTheRafters
||       | |||  || `* Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |`* Re: Natural numbers and vasesWM
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  `- Re: Natural numbers and vaseszelos...@gmail.com
||       | ||`- Re: Natural numbers and vasessergio
||       | |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasessergio
||       | `* Re: Natural numbers and vasesJim Burns
||       `- Re: Natural numbers and vasessergio
|+- Re: Natural numbers and vasesRoss A. Finlayson
|`- Re: Natural numbers and vasesFritz Feldhase
+* Re: Natural numbers and vasesChris M. Thomasson
+* Re: Natural numbers and vasesMostowski Collapse
`- Re: Natural numbers and vasesSocratis T.n.p.

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Re: Natural numbers and vases

<e21ddb0b-8455-d969-34ff-57a08bf5170f@att.net>

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https://www.novabbs.com/tech/article-flat.php?id=99987&group=sci.math#99987

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 13 May 2022 17:06:45 -0400
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Message-ID: <e21ddb0b-8455-d969-34ff-57a08bf5170f@att.net>
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 by: Jim Burns - Fri, 13 May 2022 21:06 UTC

On 5/13/2022 4:41 PM, WM wrote:
> Jim Burns schrieb
> am Donnerstag, 12. Mai 2022 um 19:35:52 UTC+2:

>>> Describe a place which Bob can exchange into.[1]
>>> From that description, we will know that
>>> it is also a place Bob can exchange out of.
>
> There is no fixed border between definable nd dark.

Any place that Bob cannot swap _into_
is not where Bob is after all swaps.

Any place that Bob can swap _out of_
is not where Bob is after all swaps.

> There is no end to potential infinity.

Describe a place which Bob can swap into.

From that description, we know that
any place that Bob can swap into is also
a place that Bob can swap out of.

Therefore, we know that, after all swaps,
each place is not where Bob is.

No empty places created by swaps, but
there is no Bob-conservation for all swaps.

Re: Natural numbers and vases

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 13 May 2022 16:11:24 -0500
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 by: sergio - Fri, 13 May 2022 21:11 UTC

On 5/13/2022 3:41 PM, WM wrote:
> Jim Burns schrieb am Donnerstag, 12. Mai 2022 um 19:35:52 UTC+2:
>
>>> Describe a place which Bob can exchange into.[1]
>>> From that description, we will know that
>>> it is also a place Bob can exchange out of.
>
> There is no fixed border between definable nd dark.

there is! your beeps, flashes, raps daffynition of "definable" is the border

> There is no end to potential infinity.

wrong, potential infinity means finite, all finites have an end.

>
> Regards, WM

Re: Natural numbers and vases

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 13 May 2022 14:58:43 -0700
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 by: Chris M. Thomasson - Fri, 13 May 2022 21:58 UTC

On 5/13/2022 1:27 PM, WM wrote:
> horand....@gmail.com schrieb am Freitag, 13. Mai 2022 um 19:18:45 UTC+2:
>> On Friday, 13 May 2022 at 14:01:08 UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
>>>> On Thursday, May 12, 2022 at 10:07:27 AM UTC-3, WM wrote:
>>>> .>..[any single] element having an infinite set S(n) of successors can be removed.
>>>>
>>>> Indeed. Any single *element* of N_p can be removed.
>>> Together with all its predecessors!
>>>> (indeed any finite set of elements of N_p).
>>> There are no other sets defined by natural numbers. Every FISON is finite. No definable natural number is outside of a FISON.
>> *EVERY* natural number is an element of a FISON,
>
> No.

Why not? Infinite FISON's can handle infinite natural numbers... Right?

Re: Natural numbers and vases

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 13 May 2022 14:59:46 -0700
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 by: Chris M. Thomasson - Fri, 13 May 2022 21:59 UTC

On 5/13/2022 1:41 PM, WM wrote:
> Jim Burns schrieb am Donnerstag, 12. Mai 2022 um 19:35:52 UTC+2:
>
>>> Describe a place which Bob can exchange into.[1]
>>> From that description, we will know that
>>> it is also a place Bob can exchange out of.
>
> There is no fixed border between definable nd dark.
> There is no end to potential infinity.

Are you potentially wrong?

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 13 May 2022 15:41:00 -0700
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 by: FromTheRafters - Fri, 13 May 2022 22:41 UTC

After serious thinking Chris M. Thomasson wrote :
> On 5/13/2022 1:27 PM, WM wrote:
>> horand....@gmail.com schrieb am Freitag, 13. Mai 2022 um 19:18:45 UTC+2:
>>> On Friday, 13 May 2022 at 14:01:08 UTC-3, WM wrote:
>>>> William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
>>>>> On Thursday, May 12, 2022 at 10:07:27 AM UTC-3, WM wrote:
>>>>> .>..[any single] element having an infinite set S(n) of successors can
>>>>> be removed.
>>>>>
>>>>> Indeed. Any single *element* of N_p can be removed.
>>>> Together with all its predecessors!
>>>>> (indeed any finite set of elements of N_p).
>>>> There are no other sets defined by natural numbers. Every FISON is
>>>> finite. No definable natural number is outside of a FISON.
>>> *EVERY* natural number is an element of a FISON,
>>
>> No.
>
> Why not? Infinite FISON's can handle infinite natural numbers... Right?

Infinitely *many* FISONs can be indexed by the infinitely *many*
natural numbers. Don't fall into his trap about infinite finite things
and finitely infinite things. :)

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 13 May 2022 15:45:11 -0700
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 by: FromTheRafters - Fri, 13 May 2022 22:45 UTC

It happens that WM formulated :
> FromTheRafters schrieb am Freitag, 13. Mai 2022 um 21:29:14 UTC+2:
>> WM used his keyboard to write :
>>> William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
>>>> On Thursday, May 12, 2022 at 10:07:27 AM UTC-3, WM wrote:
>>>> .>..[any single] element having an infinite set S(n) of successors can be
>>>> removed.
>>>>
>>>> Indeed. Any single *element* of N_p can be removed.
>>>
>>> Together with all its predecessors!
>> That would be a proper subset, not a single element. You could use the
>> initial element to satisfy this trivially since it has no predecessor.
>>
>> Again, you are not removing them from a set
>
> I am removing elements from a set. A \ B is possible.

So, set difference is the same as subtraction? No wonder your set of
natural numbers is growing and shrinking so much.

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Sat, 14 May 2022 00:08 UTC

On Friday, May 13, 2022 at 2:01:08 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:

>Every FISON is finite. No definable natural number is outside of a FISON.

Indeed. every *element* of N_p is finite. The *set* N_p is infinite.

> > The *set* N_p cannot be removed.
> Which n would resist?

No single *element* of N_p. would "resist". So what? The fact that every *element* of N_p would not resist says nothing about whether the *set* N_p would "resist".

> ... potentially infinite.

Nonsense..

--
William Hughes

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 14 May 2022 13:24 UTC

Jim Burns schrieb am Freitag, 13. Mai 2022 um 23:06:57 UTC+2:
> On 5/13/2022 4:41 PM, WM wrote:

> > There is no fixed border between definable nd dark.
> Any place that Bob cannot swap _into_
> is not where Bob is after all swaps.

If you insist on this then there are never all swaps.
>
> Any place that Bob can swap _out of_
> is not where Bob is after all swaps.

If you insist on this then there are never all swaps.
Otherwise there are many dark places where Bob can hang around.

Look, If someone says that he is collecting all elements but when collecting one element always loses one element, then we would call him a fool. That's the common opinion of all people, even of matheologians - as long as they don't know that it describes Cantor's practice of enumerating all fractions.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 14 May 2022 13:44 UTC

Jim Burns schrieb am Freitag, 13. Mai 2022 um 23:06:57 UTC+2:

> Any place that Bob can swap

In order to release you from Bob, go the other way round. Let all integer fractions be indexed. Then distribute the indices according to Cantor over the whole matrix, staring at the upper left corner. Recognize that you must fail because for every indexed fraction you will lose an indexed fraction.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 14 May 2022 13:54 UTC

FromTheRafters schrieb am Samstag, 14. Mai 2022 um 00:45:26 UTC+2:
> It happens that WM formulated :
> > FromTheRafters schrieb am Freitag, 13. Mai 2022 um 21:29:14 UTC+2:
> >> WM used his keyboard to write :
> >>> William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
> >>>> On Thursday, May 12, 2022 at 10:07:27 AM UTC-3, WM wrote:
> >>>> .>..[any single] element having an infinite set S(n) of successors can be
> >>>> removed.
> >>>>
> >>>> Indeed. Any single *element* of N_p can be removed.
> >>>
> >>> Together with all its predecessors!
> >> That would be a proper subset, not a single element. You could use the
> >> initial element to satisfy this trivially since it has no predecessor.
> >>
> >> Again, you are not removing them from a set
> >
> > I am removing elements from a set. A \ B is possible.
> So, set difference is the same as subtraction?

Of course. The only difference is that the result cannot get negative.

> No wonder your set of
> natural numbers is growing and shrinking so much.

Semikontinua genannt habe, lassen sich gewissermaßen durch Addition und Subtraktion aus perfekten Punktmengen (Cantor)

Es sind dies die Operationen welche ich in einem Schreiben an Prof. Mittag-Leffler v. 20n Oct. mit Differenz, Cohärenz, Adhärenz, Inhärenz, Supplement und Residuum in Zeichen mit d, c, a, i, s, r bezeichnet habe; es stellt sich nämlich heraus, dass diese Operationen nicht nur an Punctmengen, sondern an Typen selbst vornehmbar sind. (Cantor)

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 14 May 2022 13:59 UTC

William schrieb am Samstag, 14. Mai 2022 um 02:08:09 UTC+2:
> On Friday, May 13, 2022 at 2:01:08 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
>
>
> >Every FISON is finite. No definable natural number is outside of a FISON..
> Indeed. every *element* of N_p is finite. The *set* N_p is infinite.

The set is finite (potentially infinite) because its complement is actually infinite. I know that you don't trust mathematics, but this is fact:

∀n ∈ ℕ_p: |ℕ \ {1, 2, 3, ..., n}| = ℵ₀.

And the set is not more than all its elements.

> > > The *set* N_p cannot be removed.
> > Which n would resist?
> No single *element* of N_p. would "resist". So what? The fact that every *element* of N_p would not resist says nothing about whether the *set* N_p would "resist".

That is irrational matheologial belief. The set is not more than all its elements. When all its elements have gone, then the set is gone too.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 14 May 2022 14:00 UTC

horand....@gmail.com schrieb am Samstag, 14. Mai 2022 um 14:25:08 UTC+2:
> On Friday, 13 May 2022 at 17:27:52 UTC-3, WM wrote:
> [..]
> > > *EVERY* natural number is an element of a FISON,
> > No.
> > > and *EVERY* natural number defines an end segment of cardinality aleph_0.
> > No.
> Yes and yes. This is getting too boring.

Then try mathematics: ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵ₀.

Regards, WM

Re: Natural numbers and vases

<t5oed3$1uu2$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 09:29:55 -0500
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 by: sergio - Sat, 14 May 2022 14:29 UTC

On 5/14/2022 9:00 AM, WM wrote:
> horand....@gmail.com schrieb am Samstag, 14. Mai 2022 um 14:25:08 UTC+2:
>> On Friday, 13 May 2022 at 17:27:52 UTC-3, WM wrote:
>> [..]
>>>> *EVERY* natural number is an element of a FISON,
>>> No.
>>>> and *EVERY* natural number defines an end segment of cardinality aleph_0.
>>> No.
>> Yes and yes. This is getting too boring.
>
> Then try mathematics: ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵ₀.
>
> Regards, WM

boring and trivial.

Re: Natural numbers and vases

<t5oemj$5ji$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
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Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 09:34:58 -0500
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 by: sergio - Sat, 14 May 2022 14:34 UTC

On 5/14/2022 8:54 AM, WM wrote:
> FromTheRafters schrieb am Samstag, 14. Mai 2022 um 00:45:26 UTC+2:
>> It happens that WM formulated :
>>> FromTheRafters schrieb am Freitag, 13. Mai 2022 um 21:29:14 UTC+2:
>>>> WM used his keyboard to write :
>>>>> William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
>>>>>> On Thursday, May 12, 2022 at 10:07:27 AM UTC-3, WM wrote:
>>>>>> .>..[any single] element having an infinite set S(n) of successors can be
>>>>>> removed.
>>>>>>
>>>>>> Indeed. Any single *element* of N_p can be removed.
>>>>>
>>>>> Together with all its predecessors!
>>>> That would be a proper subset, not a single element. You could use the
>>>> initial element to satisfy this trivially since it has no predecessor.
>>>>
>>>> Again, you are not removing them from a set
>>>
>>> I am removing elements from a set. A \ B is possible.
>> So, set difference is the same as subtraction?
>
> Of course. The only difference is that the result cannot get negative.

So you are saying *it is not the same as subtraction*.

>
>> No wonder your set of
>> natural numbers is growing and shrinking so much.
>
> Semikontinua genannt habe, lassen sich gewissermaßen durch Addition und Subtraktion aus perfekten Punktmengen (Cantor)

wrong quote, if you take a number out of a set of natural numbers, it is not the set of natural numbers anymore.

>
> Es sind dies die Operationen welche ich in einem Schreiben an Prof. Mittag-Leffler v. 20n Oct. mit Differenz, Cohärenz, Adhärenz, Inhärenz, Supplement und Residuum in Zeichen mit d, c, a, i, s, r bezeichnet habe; es stellt sich nämlich heraus, dass diese Operationen nicht nur an Punctmengen, sondern an Typen selbst vornehmbar sind. (Cantor)

which says if you change a set using an operator, it is not that set anymore. This is where you make your mistakes.

>
> Regards, WM
>

Re: Natural numbers and vases

<t5oet7$8ia$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
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Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 09:38:30 -0500
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 by: sergio - Sat, 14 May 2022 14:38 UTC

On 5/14/2022 8:59 AM, WM wrote:
> William schrieb am Samstag, 14. Mai 2022 um 02:08:09 UTC+2:
>> On Friday, May 13, 2022 at 2:01:08 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
>>
>>
>>> Every FISON is finite. No definable natural number is outside of a FISON.
>> Indeed. every *element* of N_p is finite. The *set* N_p is infinite.
>
> The set is finite (potentially infinite) because its complement is actually infinite.

Compliment of a set ?

what is the compliment of {1,2,17.31} ?

>
>>>> The *set* N_p cannot be removed.
>>> Which n would resist?
>> No single *element* of N_p. would "resist". So what? The fact that every *element* of N_p would not resist says nothing about whether the *set* N_p would "resist".
>
> That is irrational matheologial belief. The set is not more than all its elements. When all its elements have gone, then the set is gone too.

Wrong.

When one element is taken out, the set is gone.
It has been changed into a different set.

>
> Regards, WM

"always wrong" WM. (AWWM)

Re: Natural numbers and vases

<t5of4u$cnr$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 09:42:37 -0500
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 by: sergio - Sat, 14 May 2022 14:42 UTC

On 5/14/2022 8:44 AM, WM wrote:
> Jim Burns schrieb am Freitag, 13. Mai 2022 um 23:06:57 UTC+2:
>
>> Any place that Bob can swap
>
> In order to release you from Bob, go the other way round. Let all integer fractions be indexed. Then distribute the indices according to Cantor over the whole matrix, staring at the upper left corner. Recognize that you must fail because for every indexed fraction you will lose an indexed fraction.

totally wrong.

>
> Regards, WM

when you make a serious mistake, and everyone knows it, you should fess up, and admit your mistake. That is what honest men do.

Your ego cannot defend your bad math in refusing Cantors Enumeration.

You are wrong.

Re: Natural numbers and vases

<746e092d-1dc3-164b-0113-2fb44e43e084@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 13:57:27 -0400
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 by: Jim Burns - Sat, 14 May 2022 17:57 UTC

On 5/14/2022 9:24 AM, WM wrote:
> Jim Burns schrieb
> am Freitag, 13. Mai 2022 um 23:06:57 UTC+2:
>> On 5/13/2022 4:41 PM, WM wrote:

<WM<JB>>
>>>>>
>>>>>> "All matrix positions remain occupied" follows
>>>>>> from the assumption
>>>>>
>>>>> No it follows from the fact that
>>>>> only exchanges take place which
>>>>> never can empty a place.
>>>>>
</WM<JB>>

>>> There is no fixed border between definable nd dark.
>>
>> Any place that Bob cannot swap _into_
>> is not where Bob is after all swaps.
>
> If you insist on this then there are never all swaps.

Each swap that Bob makes never can empty a place.

For each place with a swap into it,
there is a swap out of it.

After all swaps, there are only
places Bob never came to, and
places Bob has left.

Where is Bob?
After all swaps, nowhere.

>> Any place that Bob can swap _out of_
>> is not where Bob is after all swaps.
>
> If you insist on this then there are never all swaps.

Each swap that Bob makes never can empty a place.

For each place with a swap into it,
there is a swap out of it.

After all swaps, there are only
places Bob never came to, and
places Bob has left.

Where is Bob?
After all swaps, nowhere.

> Otherwise there are many dark places where
> Bob can hang around.

How did Bob get there?

Is Bob a Time Lord, and his TARDIS dropped him
into a dark place without steps-between?

I think that you should mention it in your proof
if Bob and his buddies are Time Lords.[1]

However,
let's assume otherwise.
Let's assume that Bob is not a Time Lord,
and, anywhere Bob is after all swaps, he got there.

All swaps are between places j and j+1.
No swaps lose Bob or lose any X.

Assume that Bob gets to place k.
⟨1,...,k⟩ is the collection of k and of all the places
Bob is on the way to k.

Describe ⟨1,...,k⟩

Consider the split BEFORE and AFTER of ⟨1,...,k⟩
Each place in BEFORE is before each place in AFTER.

Since Bob gets from 1 to k,
we know that Bob gets from BEFORE to AFTER.
There must be some j such that
j ends BEFORE, and j+1 begins AFTER.

Assume that Bob gets to place k.
For each split of ⟨1,...,k⟩,
some j ends BEFORE, and j+1 begins AFTER.

Append k+1 after ⟨1,...,k⟩ == ⟨1,...,k+1⟩
For each split of ⟨1,...,k+1⟩,
some j ends BEFORE, and j+1 begins AFTER.

If k is a place that Bob can get to,
then k+1 is a place that Bob can get to, from k,
and k is not a place where Bob is, after all swaps.

After all swaps, there are only
places Bob never came to, and
places Bob has left.

Where is Bob?
After all swaps, nowhere.

> Look,
> If someone says that he is collecting all elements

I deny that Bob is a Time Lord.
Is that really the same thing?

I say that Bob is only at places he gets to.

From the description of places Bob gets to,
we know that any place Bob can get to
Bob can leave.

After all swaps -- each of which conserves Bob --
there is nowhere that Bob either has not left
or never gets to.

Perhaps Time Lords can be at places which
they didn't get to. I don't know.
However, consider a non-Time-Lord Bob.

> but when collecting one element always loses
> one element, then we would call him a fool.
> That's the common opinion of all people, even of
> matheologians - as long as they don't know that
> it describes Cantor's practice of enumerating
> all fractions.

----
[1]
I think that you should mention it in your proof
if Bob and his buddies are Time Lords.

I'm thinking of something along these lines:

Consider a matrix of X's and O's

XOOOO...
XOOOO...
XOOOO...
XOOOO...
....

Swap X's in the first column with X's or O's in
the full matrix - by Cantor's rule.

XXXXX...
XXXXX...
XXXXX...
XXXXX...
....

Yes, the first column covers the full matrix.
This proves that dark numbers exist, because
all the O's are Time Lords and they have gone in
their TARDIS to dark places outside the full matrix.

I think that this is a much better proof than any
you have offered. You're welcome.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Sat, 14 May 2022 19:20 UTC

On Saturday, May 14, 2022 at 10:59:17 AM UTC-3, WM wrote:
> William schrieb am Samstag, 14. Mai 2022 um 02:08:09 UTC+2:
> > On Friday, May 13, 2022 at 2:01:08 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 12. Mai 2022 um 21:23:05 UTC+2:
> >
> >
> > >Every FISON is finite. No definable natural number is outside of a FISON.
> > Indeed. every *element* of N_p is finite. The *set* N_p is infinite.
> The set is finite (potentially infinite)

Piffle, A "potentially infinite" set is nonsense. Sets do not change.

--
William Hughes

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 14 May 2022 20:20:45 +0000
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 by: WM - Sat, 14 May 2022 20:20 UTC

Jim Burns schrieb am Samstag, 14. Mai 2022 um 19:57:38 UTC+2:
> On 5/14/2022 9:24 AM, WM wrote:

> >> Any place that Bob cannot swap _into_
> >> is not where Bob is after all swaps.
> >
> > If you insist on this then there are never all swaps.
> Each swap that Bob makes never can empty a place.

And never can complete all swaps.
>
> For each place with a swap into it,
> there is a swap out of it.

And therefore it is not all swaps.
>
> After all swaps, there are only
> places Bob never came to, and
> places Bob has left.
>
> Where is Bob?
> After all swaps, nowhere.

For each place with a swap into it, there is a swap out of it. Never all swaps are completed.

> Where is Bob?
> After all swaps, nowhere.

But a state after "all swaps" doesn't exist.

> > Otherwise there are many dark places where
> > Bob can hang around.
> How did Bob get there?

In the same way as he can leave the matrix. Never.
>
> I say that Bob is only at places he gets to.

But he never gets out of the matrix.
>
> I'm thinking of something along these lines:
>
> Consider a matrix of X's and O's
>
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> ...
>
> Swap X's in the first column with X's or O's in
> the full matrix - by Cantor's rule.
>
> XXXXX...
> XXXXX...
> XXXXX...
> XXXXX...
> ...

But by mathematics the X's can never increase and the O's can never decrease --- *within the matrix* .

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 14 May 2022 20:21:59 +0000
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 by: WM - Sat, 14 May 2022 20:21 UTC

William schrieb am Samstag, 14. Mai 2022 um 21:20:08 UTC+2:
> On Saturday, May 14, 2022 at 10:59:17 AM UTC-3, WM wrote:

> > > >Every FISON is finite. No definable natural number is outside of a FISON.
> > > Indeed. every *element* of N_p is finite. The *set* N_p is infinite.
> > The set is finite (potentially infinite)
> Piffle, A "potentially infinite" set is nonsense. Sets do not change.

Infinite sets change unless they contain dark elements.

Regards, WM

Re: Natural numbers and vases

<1a6ed543-f405-434a-c519-57d38bea0494@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 17:08:07 -0400
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 by: Jim Burns - Sat, 14 May 2022 21:08 UTC

On 5/14/2022 4:20 PM, WM wrote:
> Jim Burns schrieb
> am Samstag, 14. Mai 2022 um 19:57:38 UTC+2:

>> After all swaps, there are only
>> places Bob never came to, and
>> places Bob has left.
>>
>> Where is Bob?
>> After all swaps, nowhere.
>
> For each place with a swap into it,
> there is a swap out of it.
> Never all swaps are completed.

All swaps are described, right at the beginning.
Then, all swaps are reasoned about.
Any conclusion applies to all swaps.

All swaps are between places j and j+1.
No swap loses Bob or loses any X.

Assume that Bob gets to place k.
⟨1,...,k⟩ is the collection of k and of all the places
Bob is at on the way to k.

Describe ⟨1,...,k⟩

Consider the split BEFORE and AFTER of ⟨1,...,k⟩
Each place in BEFORE is before each place in AFTER.

Since Bob gets from 1 to k,
we know that Bob gets from BEFORE to AFTER.
There must be some j such that
j ends BEFORE, and j+1 begins AFTER.

Assume that Bob gets to place k.
For each split of ⟨1,...,k⟩,
some j ends BEFORE, and j+1 begins AFTER.

Append k+1 after ⟨1,...,k⟩ == ⟨1,...,k+1⟩
For each split of ⟨1,...,k+1⟩,
some j ends BEFORE, and j+1 begins AFTER.

If k is a place that Bob can get to,
then k+1 is a place that Bob can get to, from k,
and k is not a place where Bob is, after all swaps.

After all swaps, there are only
places Bob never came to, and
places Bob came to and left.

Where is Bob?
After all swaps, nowhere.

>> Where is Bob?
>> After all swaps, nowhere.
>
> But a state after "all swaps" doesn't exist.

<WM<JB>>
>
>> "All matrix positions remain occupied" follows
>> from the assumption
>
> No it follows from the fact that
> only exchanges take place which
> never can empty a place.
>
</WM<JB>>
Date: Thu, 12 May 2022 06:06:24 -0700 (PDT)

Upthread, you described your own position incorrectly.
What does that say about you?

> But a state after "all swaps" doesn't exist.

Whatever your position is today,
Bob does not go anywhere which is after all swaps.
However,
even though each swap conserves Bob,
all swaps do not conserve Bob.

> For each place with a swap into it,
> there is a swap out of it.

You have given the reason why all the swaps
do not conserve Bob.

Where is Bob?
Nowhere with a swap out of it.

Re: Natural numbers and vases

<t5p83p$1f43$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 16:48:40 -0500
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 by: sergio - Sat, 14 May 2022 21:48 UTC

On 5/14/2022 3:21 PM, WM wrote:
> William schrieb am Samstag, 14. Mai 2022 um 21:20:08 UTC+2:
>> On Saturday, May 14, 2022 at 10:59:17 AM UTC-3, WM wrote:
>
>>>>> Every FISON is finite. No definable natural number is outside of a FISON.
>>>> Indeed. every *element* of N_p is finite. The *set* N_p is infinite.
>>> The set is finite (potentially infinite)
>> Piffle, A "potentially infinite" set is nonsense. Sets do not change.
>
> Infinite sets change

>
> Regards, WM

wrong. Sets do not change.

if you change one element, you have a different set.

finite or infinite doesn't matter, sets do not change.

you are outside of math.

Re: Natural numbers and vases

<t5p89r$1hqh$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 16:51:54 -0500
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 by: sergio - Sat, 14 May 2022 21:51 UTC

On 5/14/2022 3:20 PM, WM wrote:
> Jim Burns schrieb am Samstag, 14. Mai 2022 um 19:57:38 UTC+2:
>> On 5/14/2022 9:24 AM, WM wrote:
>
>>>> Any place that Bob cannot swap _into_
>>>> is not where Bob is after all swaps.
>>>
>>> If you insist on this then there are never all swaps.
>> Each swap that Bob makes never can empty a place.
>
> And never can complete all swaps.

you are out of math, with your swaparoo swapfestable nonsense.

use Equations, if you know math.

Re: Natural numbers and vases

<1fbcd173-4f35-d45f-5a6f-10873e59dd91@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 14 May 2022 18:30:31 -0400
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 by: Jim Burns - Sat, 14 May 2022 22:30 UTC

On 5/14/2022 4:20 PM, WM wrote:

> For each place with a swap into it,
> there is a swap out of it.

Yes.
For each place with a swap into it,
there is a swap out of it.

And, after all swaps,
Bob is not at any place with a swap out of it.

Where is Bob, after all swaps?

He's not at any place with a swap into it,
because there's a swap out of it.

He's not at any place with no swap into it,
because he doesn't have a TARDIS.

Where is Bob, after all swaps?

Nowhere.

----
My explanation is that
some collections have Bob-conservation.
These are the collections we are most familiar with.
Sheep. Pebbles. Sand grains. Stars.

However,
not all collections have Bob-conservation.
We call these collections "infinite" or some variation
on that, but, whatever we call them,
these other collections do not have Bob-conservation.

> For each place with a swap into it,
> there is a swap out of it.

This is the heart of the proof that
not all collections have Bob-conservation.

Re: Natural numbers and vases

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Path: i2pn2.org!i2pn.org!usenet.blueworldhosting.com!feed1.usenet.blueworldhosting.com!peer02.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: sci.math
Date: Sun, 15 May 2022 04:28:23 -0700 (PDT)
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Message-ID: <3c503871-597b-4d9e-8184-68259c58b2a8n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Sun, 15 May 2022 11:28:23 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 4220
 by: William - Sun, 15 May 2022 11:28 UTC

On Saturday, May 14, 2022 at 5:22:04 PM UTC-3, WM wrote:

> Infinite sets change

Piffle

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