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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

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Thu, 26 May 2022 16:04 UTC

horand....@gmail.com schrieb am Donnerstag, 26. Mai 2022 um 17:38:58 UTC+2:
> On Thursday, 26 May 2022 at 11:58:39 UTC-3, WM wrote:
> > horand....@gmail.com schrieb am Mittwoch, 25. Mai 2022 um 16:39:46 UTC+2:
> > > On Wednesday, 25 May 2022 at 11:21:20 UTC-3, WM wrote:
> >
> > > > Before the "limit" there must
> > > ... be an understanding on your part what a limit actually is.
> > That is not of interest in this case because indexing is a matter of terms and not of any limit.
> Your insistence that there is no limit involved

Of course not. Every fraction has to be covered by an index. "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239] That is a clear denial of limit in case of Zuordnungsprozess. But in my example always and X and and O are exchanged. This cannot lead to an increase of X or O, not even in the limit. The process is fully symmetric. If the X's could increase also the O's increase and the X's could completely disappear. Why not??? Try to find one reasonable argument - once in your life.

> You have no clue about sequences and limits.

I have written about this topic more than you will ever be able to understand.
W. Mückenheim: "Sequences and Limits", Advances in Pure Mathematics 5, 2015, pp. 59 - 61
http://www.scirp.org/journal/Articles.aspx?searchCode=Mueckenheim&searchField=All&page=1&SKID=57296550

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: sergi o - Thu, 26 May 2022 16:04 UTC

On 5/26/2022 9:58 AM, WM wrote:
> horand....@gmail.com schrieb am Mittwoch, 25. Mai 2022 um 16:39:46 UTC+2:
>> On Wednesday, 25 May 2022 at 11:21:20 UTC-3, WM wrote:
>
>>> Before the "limit" there must
>> ... be an understanding on your part what a limit actually is.
>
> That is not of interest in this case because indexing is a matter of terms and not of any limit.

you dont know what a limit is or what to do with a limit.

You cant even do indexing!

FAIL, you get an F.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
Date: Thu, 26 May 2022 11:06:10 -0500
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 by: sergi o - Thu, 26 May 2022 16:06 UTC

On 5/26/2022 9:56 AM, WM wrote:
> William schrieb am Mittwoch, 25. Mai 2022 um 17:14:25 UTC+2:
>> On Wednesday, May 25, 2022 at 11:08:13 AM UTC-3, WM wrote:
>>>> ,,, more are not available.
>>
>>
>> Piffle. Using infinitely many indexes from a set of cardinality alpeh_0 does not mean "more are not available".
>
> Here precisely this has been proven:
>

that is not a proof at all it is a spoof, try googling for mathematical proof

your swaparoofest underscores the fact that you are unable to use Math.

>

> 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 - Thu, 26 May 2022 16:07 UTC

William schrieb am Donnerstag, 26. Mai 2022 um 18:02:06 UTC+2:
> On Thursday, May 26, 2022 at 11:56:11 AM UTC-3, WM wrote:
> > ...This is obviously impossible because exchanging cannot reduce them
>
> Piffle. An exchange takes you from one set of cardinality aleph_0 to another set of cardinality aleph_0. It is meaningless to say that the "number of elements" is or is not "reduced". There is no "number of elements", there is just cardinality.

On the contrary. But if you can't understand this argument, try to understand this one: Iin my example always and X and and O are exchanged. So much should be possible to say. The process is fully symmetric. If the X's could increase also the O's could increase and the X's could completely disappear. Why not?

Regards, WM

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 by: sergi o - Thu, 26 May 2022 16:10 UTC

On 5/26/2022 10:54 AM, WM wrote:
> Jim Burns schrieb am Mittwoch, 25. Mai 2022 um 19:21:30 UTC+2:
>> On 5/25/2022 9:51 AM, WM wrote:
>
>>> Then explain how the share of X can grow by
>>> simply moving them around.
>> Your experience of collections which cannot match
>> any of their proper subsets
>> is not universally applicable.
>
>

"My experience that by exchange of X and O never an X appears and never an O disappears is basic to all mathematics"- WM

a Keeper !!!

>>
>> Compare to:
>> Our experience, pre-Einstein, of moving objects
>> which do not experience time-dilation
>> is not universally applicable.
>
> There is no parallel. Always, in the whole sequence, only one X and one O are exchanged. But I note that you are in great despair.
>
> Regards, WM

Bla... you post nonsense, WM.

Re: Natural numbers and vases

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 26 May 2022 11:12:32 -0500
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 by: sergi o - Thu, 26 May 2022 16:12 UTC

On 5/26/2022 11:07 AM, WM wrote:
> William schrieb am Donnerstag, 26. Mai 2022 um 18:02:06 UTC+2:
>> On Thursday, May 26, 2022 at 11:56:11 AM UTC-3, WM wrote:
>>> ...This is obviously impossible because exchanging cannot reduce them
>>
>> Piffle. An exchange takes you from one set of cardinality aleph_0 to another set of cardinality aleph_0. It is meaningless to say that the "number of elements" is or is not "reduced". There is no "number of elements", there is just cardinality.
>
> On the contrary. But if you can't understand this argument, try to understand this one: Iin my example always and X and and O are exchanged. So much should be possible to say. The process is fully symmetric. If the X's could increase also the O's could increase and the X's could completely disappear. Why not?

reread your sentence, it is self conflicting.

>
> Regards, WM

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 - Thu, 26 May 2022 16:17 UTC

On Thursday, May 26, 2022 at 1:07:30 PM UTC-3, WM wrote:
>> The process is fully symmetric.

Piffle. The sequence of the sets of indexes of X's differs from the sequence of the sets of indexes of O's.

--
William Hughes

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: sergi o - Thu, 26 May 2022 16:28 UTC

On 5/26/2022 11:04 AM, WM wrote:
> horand....@gmail.com schrieb am Donnerstag, 26. Mai 2022 um 17:38:58 UTC+2:
>> On Thursday, 26 May 2022 at 11:58:39 UTC-3, WM wrote:
>>> horand....@gmail.com schrieb am Mittwoch, 25. Mai 2022 um 16:39:46 UTC+2:
>>>> On Wednesday, 25 May 2022 at 11:21:20 UTC-3, WM wrote:
>>>
>>>>> Before the "limit" there must
>>>> ... be an understanding on your part what a limit actually is.
>>> That is not of interest in this case because indexing is a matter of terms and not of any limit.
>> Your insistence that there is no limit involved
>
> Of course not. Every fraction has to be covered by an index.

no, in Cantors Enumeration every fraction has 3 indexes, m,n,k

fractions are not required to have an index either

what does 'covered' mean ?

"und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239]

that quote does not apply.

> But in my example always and X and and O are exchanged. This cannot lead to an increase of X or O, not even in the limit. The process is fully symmetric. If the X's could increase also the O's increase and the X's could completely disappear.
your sentence is self conflicting, correct it.

>
>> You have no clue about sequences and limits.
>
> I have written about this topic more than you will ever be able to understand.
> W. Mückenheim: "Sequences and Limits", Advances in Pure Mathematics 5, 2015, pp. 59 - 61
> http://www.scirp.org/journal/Articles.aspx?searchCode=Mueckenheim&searchField=All&page=1&SKID=57296550

another squirrelly useless troll paper in a non refereed paper

Abstract:
It is widely held that irrational numbers can be represented by infinite digit-sequences. We will
show that this is not possible. A digit sequence is only an abbreviated notation for an
infinite sequence of rational partial sums.

the editors should have never published it

>
> Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Thu, 26 May 2022 16:34:47 +0000
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 by: WM - Thu, 26 May 2022 16:34 UTC

William schrieb am Donnerstag, 26. Mai 2022 um 18:18:04 UTC+2:
> On Thursday, May 26, 2022 at 1:07:30 PM UTC-3, WM wrote:
> >> The process is fully symmetric.
> Piffle. The sequence of the sets of indexes of X's differs from the sequence of the sets of indexes of O's.

The *sequences* differ, but the *process* of exchanges is fully symmetric. An X leaves its place and occupies the place of an O while the O leaves its place and occupies the original place of the X. At every step 1 X and 1 O start and 1 X and 1 O end. Do you deny this? Do you believe that the not involved X's and O's will multiply or vanish during the encounter?

Regards, WM

Re: Natural numbers and vases

<1fbd8314-78bf-8437-cfb5-ddf782fcd7d5@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 26 May 2022 12:38:31 -0400
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 by: Jim Burns - Thu, 26 May 2022 16:38 UTC

On 5/26/2022 11:20 AM, WM wrote:
> Jim Burns schrieb
> am Donnerstag, 26. Mai 2022 um 11:14:17 UTC+2:

>> We can describe one of (what happens to be)
>> infinitely-many tasks.
>> We can reason about one of (what happens to be)
>> infinitely-many tasks,
>
> Of course you can describe and reason about every
> issued index.

We can describe and reason about each m/n such that,
for each BEFORE and AFTER =< m
and each BEFORE and AFTER =< n,
some j ends BEFORE and j+1 begins AFTER.

For each m/n _like that_
for each BEFORE and AFTER =< (m+n-1)*(m+n-2)/2+m
some j ends BEFORE and j+1 begin AFTER.

Define the matrix to be all m/n _like that_
Define the index k of each m/n to be
k = (m+n-1)*(m+n-2)/2+m

By describing and reasoning, we know that
each m/n has an index k, and
k/1 is in the first column of the matrix.

> But the distance to omega will always remain
> aleph_0.
> You like to forget that.

There is no last index after 1.
Therefore,
there is no last index after any index after 1.

Infinity is not a reallyreallyreallyreallyreallyreally
large number. It is a different kind of thing.

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 - Thu, 26 May 2022 17:00 UTC

> ... the *process* of exchanges is fully symmetric. An X leaves its place and occupies the place of an O

Piffle. The place that the X leaves and the place the the O leaves differ. Thus this is not "fully symmetric".

--
William Hughes

Re: Natural numbers and vases

<ef55b18e-0dbf-c13e-797e-bbe45fe35bae@att.net>

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Natural numbers and vases
Date: Thu, 26 May 2022 13:06:53 -0400
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 by: Jim Burns - Thu, 26 May 2022 17:06 UTC

On 5/26/2022 12:07 PM, WM wrote:

> If the X's could increase also the O's could increase
> and the X's could completely disappear. Why not?

Infinity is not a reallyreallyreallyreallyreallyreally
large number. It is a different kind of thing.

1/1:1/2 1/2:1/3 1/3:1/4 1/4:1/5 ...
2/1:2/2 2/2:2/3 2/3:2/4 2/4:2/5 ...
3/1:3/2 3/2:3/3 3/3:3/4 3/4:3/5 ...
4/1:4/2 4/2:4/3 4/3:4/4 4/4:4/5 ...
5/1:5/2 5/2:5/3 5/3:5/4 5/4:5/5 ...
6/1:6/2 6/2:6/3 6/3:6/4 6/4:6/5 ...
7/1:7/2 7/2:7/3 7/3:7/4 7/4:7/5 ...
8/1:8/2 8/2:8/3 8/3:8/4 8/4:8/5 ...
9/1:9/2 9/2:9/3 9/3:9/4 9/4:9/5 ...
.... ... ... ...

X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
X:O O:O O:O O:O ...
.... ... ... ...

Also, as noted earlier,
infinity is not a reallyreallyreallyreallyreallyreally
large number. It is a different kind of thing.

1/1:1/1 1/2:2/1 1/3:4/1 1/4:7/1 ...
2/1:3/1 2/2:5/1 2/3:8/1 2/4:12/1 ...
3/1:6/1 3/2:9/1 3/3:13/1 3/4:18/1 ...
4/1:10/1 4/2:14/1 4/3:19/1 4/4:25/1 ...
5/1:15/1 5/2:20/1 5/3:26/1 5/4:33/1 ...
6/1:21/1 6/2:27/1 6/3:34/1 6/4:42/1 ...
7/1:28/1 7/2:35/1 7/3:43/1 7/4:52/1 ...
8/1:36/1 8/2:44/1 8/3:53/1 8/4:63/1 ...
9/1:45/1 9/2:54/1 9/3:64/1 9/4:75/1 ...
.... ... ... ...

X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
.... ... ... ...

Re: Natural numbers and vases

<t6od0h$s5n$1@gioia.aioe.org>

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Subject: Re: Natural numbers and vases
Date: Thu, 26 May 2022 12:22:23 -0500
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 by: sergi o - Thu, 26 May 2022 17:22 UTC

On 5/26/2022 11:38 AM, Jim Burns wrote:
> On 5/26/2022 11:20 AM, WM wrote:
>> Jim Burns schrieb
>> am Donnerstag, 26. Mai 2022 um 11:14:17 UTC+2:
>
>>> We can describe one of (what happens to be)
>>> infinitely-many tasks.
>>> We can reason about one of (what happens to be)
>>> infinitely-many tasks,
>>
>> Of course you can describe and reason about every
>> issued index.
>
> We can describe and reason about each m/n such that,
> for each BEFORE and AFTER =< m
> and each BEFORE and AFTER =< n,
> some j ends BEFORE and j+1 begins AFTER.
>
> For each m/n _like that_
> for each BEFORE and AFTER =< (m+n-1)*(m+n-2)/2+m
> some j ends BEFORE and j+1 begin AFTER.
>
> Define the matrix to be all m/n _like that_
> Define the index k of each m/n to be
> k = (m+n-1)*(m+n-2)/2+m
>
> By describing and reasoning, we know that
> each m/n has an index k, and
> k/1 is in the first column of the matrix.
>
>> But the distance to omega will always remain
>> aleph_0.
>> You like to forget that.
>
> There is no last index after 1.
> Therefore,
> there is no last index after any index after 1.
>
> Infinity is not a reallyreallyreallyreallyreallyreally
> large number. It is a different kind of thing.
>
>

This is a very simple problem that WM refuses to understand, so he can keep bantering about in his pre-algebra way, but it is not math.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Thu, 26 May 2022 20:20 UTC

On Thursday, 26 May 2022 at 13:04:33 UTC-3, WM wrote:
> horand....@gmail.com schrieb am Donnerstag, 26. Mai 2022 um 17:38:58 UTC+2:
> > On Thursday, 26 May 2022 at 11:58:39 UTC-3, WM wrote:
> > > horand....@gmail.com schrieb am Mittwoch, 25. Mai 2022 um 16:39:46 UTC+2:
> > > > On Wednesday, 25 May 2022 at 11:21:20 UTC-3, WM wrote:
> > >
> > > > > Before the "limit" there must
> > > > ... be an understanding on your part what a limit actually is.
> > > That is not of interest in this case because indexing is a matter of terms and not of any limit.
> > Your insistence that there is no limit involved
> Of course not. Every fraction has to be covered by an index. "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239] That is a clear denial of limit in case of Zuordnungsprozess.

Now you no longer know how to process German terminology correctly!?! What the *FUCK* do you think a "Zuordnungsprozess" is? It sure as hell is not your moving X's and O's around in a matrix. That is a stepwise procedure. It also does not stop, but it needs to be analyzed differently. (Not that you have any clue about that, either.) Yes, a "Zuordnungsprozess" does not stop.. What do you think *that* means? And what do you think a *LIMIT* is, you fucking lunatic? There is no longer any point to arguing anything with you (well, there hasn't been for fifteen years --- your mind was going even then). So, go fuck yourself.

Re: Natural numbers and vases

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Natural numbers and vases
Date: Thu, 26 May 2022 17:39:26 -0400
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 by: Jim Burns - Thu, 26 May 2022 21:39 UTC

On 5/26/2022 11:54 AM, WM wrote:
> Jim Burns schrieb
> am Mittwoch, 25. Mai 2022 um 19:21:30 UTC+2:
>> On 5/25/2022 9:51 AM, WM wrote:

>>> Then explain how the share of X can grow by
>>> simply moving them around.
>>
>> Your experience of collections which cannot match
>> any of their proper subsets
>> is not universally applicable.
>
> My experience that by exchange of X and O
> never an X appears and never an O disappears
> is basic to all mathematics.

1/1:1/1 1/2:2/1 1/3:4/1 1/4:7/1 ...
2/1:3/1 2/2:5/1 2/3:8/1 2/4:12/1 ...
3/1:6/1 3/2:9/1 3/3:13/1 3/4:18/1 ...
4/1:10/1 4/2:14/1 4/3:19/1 4/4:25/1 ...
5/1:15/1 5/2:20/1 5/3:26/1 5/4:33/1 ...
6/1:21/1 6/2:27/1 6/3:34/1 6/4:42/1 ...
7/1:28/1 7/2:35/1 7/3:43/1 7/4:52/1 ...
8/1:36/1 8/2:44/1 8/3:53/1 8/4:63/1 ...
9/1:45/1 9/2:54/1 9/3:64/1 9/4:75/1 ...
.... ... ... ...

X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
X:X O:X O:X O:X ...
.... ... ... ...

>> Compare to:
>> Our experience, pre-Einstein, of moving objects
>> which do not experience time-dilation
>> is not universally applicable.
>
> There is no parallel.

Muons are sometimes created by cosmic rays hitting
the Earth's upper atmosphere.
Some of those travel down to the Earth's surface.
Some of those (a very, very few) trip a particle
detector in a muon-lifetime-measuring experiment,
and stop.
All of those decay a time between t and t+dt later
with a probability of exp(-t/tau)*dt
Some of those decay products trip particle detectors,
which gives us one measurement of a muon lifetime.
Enough measurements (running the experiment long
enough) allows us to draw an exponential curve
through our data very precisely.
This gives us tau, the muon lifetime: 2.197 us

Here's the problem:
These collisions occur about 15 km above the
Earth's surface.
*IF* the muons traveling near the speed of light
decay at the same rate as the ones stopped
in our apparatus,
*THEN* half of them decay every 460 meters.

With every 460 meters more of height,
there _should_ be twice as many muons.
However, that's not what we see.

----
If we solve this problem by the Mückenheim method,
we must refuse to admit that these muons exist.
No muons, no problem.

We must ask secondary-school student if they
seen any muons around.

We must look for silly names to call these
muon-measurers, and pretend that measuring muons
is a religion.

Or, on the other hand, we could try to understand
the wider world in which muons experience time
dilation but we, even running reallyreally fast,
do not.

Everyone get to choose.
(Not all choices are equal.)

> Always, in the whole sequence,
> only one X and one O are exchanged.
> But I note that you are in great despair.

It's true that I'm feeling great sadness these days,
but you deserve neither blame nor credit for that.

If it pleases you, know that you have convinced me
that you will not do better.
However, you are not the only person I am
writing for.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
Date: Thu, 26 May 2022 19:23:24 -0500
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 by: sergi o - Fri, 27 May 2022 00:23 UTC

On 5/26/2022 4:39 PM, Jim Burns wrote:
> On 5/26/2022 11:54 AM, WM wrote:
>> Jim Burns schrieb
>> am Mittwoch, 25. Mai 2022 um 19:21:30 UTC+2:
>>> On 5/25/2022 9:51 AM, WM wrote:
>
>>>> Then explain how the share of X can grow by
>>>> simply moving them around.
>>>
>>> Your experience of collections which cannot match
>>> any of their proper subsets
>>> is not universally applicable.
>>
>> My experience that by exchange of X and O
>> never an X appears and never an O disappears
>> is basic to all mathematics.
>
> 1/1:1/1   1/2:2/1   1/3:4/1   1/4:7/1   ...
> 2/1:3/1   2/2:5/1   2/3:8/1   2/4:12/1  ...
> 3/1:6/1   3/2:9/1   3/3:13/1  3/4:18/1  ...
> 4/1:10/1  4/2:14/1  4/3:19/1  4/4:25/1  ...
> 5/1:15/1  5/2:20/1  5/3:26/1  5/4:33/1  ...
> 6/1:21/1  6/2:27/1  6/3:34/1  6/4:42/1  ...
> 7/1:28/1  7/2:35/1  7/3:43/1  7/4:52/1  ...
> 8/1:36/1  8/2:44/1  8/3:53/1  8/4:63/1  ...
> 9/1:45/1  9/2:54/1  9/3:64/1  9/4:75/1  ...
> ...       ...       ...       ...
>
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> X:X       O:X       O:X       O:X       ...
> ...       ...       ...       ...
>
>>> Compare to:
>>> Our experience, pre-Einstein, of moving objects
>>> which do not experience time-dilation
>>> is not universally applicable.
>>
>> There is no parallel.
>
> Muons are sometimes created by cosmic rays hitting
> the Earth's upper atmosphere.
> Some of those travel down to the Earth's surface.
> Some of those (a very, very few) trip a particle
> detector in a muon-lifetime-measuring experiment,
> and stop.
> All of those decay a time between t and t+dt later
> with a probability of exp(-t/tau)*dt
> Some of those decay products trip particle detectors,
> which gives us one measurement of a muon lifetime.
> Enough measurements (running the experiment long
> enough) allows us to draw an exponential curve
> through our data very precisely.
> This gives us tau, the muon lifetime: 2.197 us
>
> Here's the problem:
> These collisions occur about 15 km above the
> Earth's surface.
> *IF* the muons traveling near the speed of light
> decay at the same rate as the ones stopped
> in our apparatus,
> *THEN* half of them decay every 460 meters.
>
> With every 460 meters more of height,
> there _should_ be twice as many muons.
> However, that's not what we see.
>
> ----
> If we solve this problem by the Mückenheim method,
> we must refuse to admit that these muons exist.
> No muons, no problem.
>
> We must ask secondary-school student if they
> seen any muons around.
>
> We must look for silly names to call these
> muon-measurers, and pretend that measuring muons
> is a religion.
>
>
> Or, on the other hand, we could try to understand
> the wider world in which muons experience time
> dilation but we, even running reallyreally fast,
> do not.
>
>
> Everyone get to choose.
> (Not all choices are equal.)
>
>> Always, in the whole sequence,
>> only one X and one O are exchanged.
>> But I note that you are in great despair.
>
> It's true that I'm feeling great sadness these days,
> but you deserve neither blame nor credit for that.
>
> If it pleases you, know that you have convinced me
> that you will not do better.
> However, you are not the only person I am
> writing for.
>

there is no despair anywhere.
WM continues his quest in confusitorium to generate his darkies without using math, because you can prove using math they do not exist.
I use simple math to disprove him, I hold very high regard for more advanced math, it is honorable, I will defend it.
You use very reasonable ways to show him the way. Perhaps he knew math many years ago, but that is gone.

I love your muon example, I have a few PMTs w plastic syntillator, and you can always tell when a muon come in, huge signal, which should not exist at
the surface of the earth, except for time dilation!

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 - Fri, 27 May 2022 19:31 UTC

William schrieb am Donnerstag, 26. Mai 2022 um 19:00:49 UTC+2:
> > ... the *process* of exchanges is fully symmetric. An X leaves its place and occupies the place of an O
>
> Piffle. The place that the X leaves and the place the the O leaves differ. Thus this is not "fully symmetric".
>
By the difference of place-numbers a deviation from the 1:1 parity can't happen, can it?

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 - Fri, 27 May 2022 19:34 UTC

Jim Burns schrieb am Donnerstag, 26. Mai 2022 um 18:38:43 UTC+2:

> Infinity is not a reallyreallyreallyreallyreallyreally
> large number. It is a different kind of thing.

Nevertheless every exchange of X and O happens in finite distance from the start.
Do you agree that in finite distance from start the 1:1 parity is guaranteed?

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 - Fri, 27 May 2022 19:39 UTC

horand....@gmail.com schrieb am Donnerstag, 26. Mai 2022 um 22:20:56 UTC+2:
> On Thursday, 26 May 2022 at 13:04:33 UTC-3, WM wrote:
> > horand....@gmail.com schrieb am Donnerstag, 26. Mai 2022 um 17:38:58 UTC+2:
> > > On Thursday, 26 May 2022 at 11:58:39 UTC-3, WM wrote:
> > > > horand....@gmail.com schrieb am Mittwoch, 25. Mai 2022 um 16:39:46 UTC+2:
> > > > > On Wednesday, 25 May 2022 at 11:21:20 UTC-3, WM wrote:
> > > >
> > > > > > Before the "limit" there must
> > > > > ... be an understanding on your part what a limit actually is.
> > > > That is not of interest in this case because indexing is a matter of terms and not of any limit.
> > > Your insistence that there is no limit involved
> > Of course not. Every fraction has to be covered by an index. "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239] That is a clear denial of limit in case of Zuordnungsprozess.
> What the *FUCK* do you think a "Zuordnungsprozess" is? It sure as hell is not your moving X's and O's around in a matrix. That is a stepwise procedure. It also does not stop, but it needs to be analyzed differently.

It is a process that goes on and on like Cantor's Zuordnungsprozess.

> Yes, a "Zuordnungsprozess" does not stop. What do you think *that* means?

It means that every exchange of X and O happens at a finite step. Never the 1:1 parity will be violated.

> And what do you think a *LIMIT* is,

Here no limit is involved but an ever lasting process. Never the 1:1 parity will be violated.

Regards, WM

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 - Fri, 27 May 2022 19:40 UTC

On Friday, May 27, 2022 at 4:31:58 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 26. Mai 2022 um 19:00:49 UTC+2:
> > > ... the *process* of exchanges is fully symmetric. An X leaves its place and occupies the place of an O
> >
> > Piffle. The place that the X leaves and the place the the O leaves differ. Thus this is not "fully symmetric".
> >
> By the difference of place-numbers a deviation from the 1:1 parity can't happen, can it?

Piffle. You said it was "fully symmetric". There here is one X and one Y but there are different two different sets.

--
Willism 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 - Fri, 27 May 2022 19:45 UTC

Jim Burns schrieb am Donnerstag, 26. Mai 2022 um 23:39:39 UTC+2:

> If we solve this problem by the Mückenheim method,
> we must refuse to admit that these muons exist.
> No muons, no problem.

I have explained this phenomeneon during 25 years of teaching physics. But that is not comparable with the present problem: There we have the 1:1 parity conservation for every finite step. And there are no infinite steps.
>
> Or, on the other hand, we could try to understand
> the wider world in which muons experience time
> dilation

Not with the fairy tale tools used to defend Cantor.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Fri, 27 May 2022 19:50:05 +0000
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 by: WM - Fri, 27 May 2022 19:50 UTC

William schrieb am Freitag, 27. Mai 2022 um 21:41:04 UTC+2:
> On Friday, May 27, 2022 at 4:31:58 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 26. Mai 2022 um 19:00:49 UTC+2:
> > > > ... the *process* of exchanges is fully symmetric. An X leaves its place and occupies the place of an O
> > >
> > > Piffle. The place that the X leaves and the place the the O leaves differ. Thus this is not "fully symmetric".
> > >
> > By the difference of place-numbers a deviation from the 1:1 parity can't happen, can it?
> Piffle. You said it was "fully symmetric".

By symmetry I addressed this: If the exchange of one X and one O can result in two X and no O, then it can as well result in two O and no X.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Fri, 27 May 2022 20:16:15 +0000
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 by: William - Fri, 27 May 2022 20:16 UTC

On Friday, May 27, 2022 at 4:50:10 PM UTC-3, WM wrote:
> William schrieb am Freitag, 27. Mai 2022 um 21:41:04 UTC+2:
> > On Friday, May 27, 2022 at 4:31:58 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 26. Mai 2022 um 19:00:49 UTC+2:
> > > > > ... the *process* of exchanges is fully symmetric. An X leaves its place and occupies the place of an O
> > > >
> > > > Piffle. The place that the X leaves and the place the the O leaves differ. Thus this is not "fully symmetric".
> > > >
> > > By the difference of place-numbers a deviation from the 1:1 parity can't happen, can it?
> > Piffle. You said it was "fully symmetric".
> By symmetry I addressed this: If the exchange of one X and one O can result in two X and no O,

It cannot. Before the exchange there is a set of coordintates of the X's with cardinality aleph_0 and a set of coordinates of the O'x with cardinality aleph_0. Performing the exchange does not change the cardinalities, but does change the sets. Since the sets and the changes to the sets are different the process is not "fully symmetric".

You have shown a result that is strongly counterintuitive. You have not shown a contradiction/

--
William Hughes

Re: Natural numbers and vases

<t6rcu7$ujd$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 27 May 2022 13:39:28 -0700
Organization: Peripheral Visions
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 by: FromTheRafters - Fri, 27 May 2022 20:39 UTC

WM pretended :
> horand....@gmail.com schrieb am Donnerstag, 26. Mai 2022 um 22:20:56 UTC+2:
>> On Thursday, 26 May 2022 at 13:04:33 UTC-3, WM wrote:
>>> horand....@gmail.com schrieb am Donnerstag, 26. Mai 2022 um 17:38:58 UTC+2:
>>>> On Thursday, 26 May 2022 at 11:58:39 UTC-3, WM wrote:
>>>>> horand....@gmail.com schrieb am Mittwoch, 25. Mai 2022 um 16:39:46 UTC+2:
>>>>>> On Wednesday, 25 May 2022 at 11:21:20 UTC-3, WM wrote:
>>>>>>> Before the "limit" there must
>>>>>> ... be an understanding on your part what a limit actually is.
>>>>> That is not of interest in this case because indexing is a matter of
>>>>> terms and not of any limit.
>>>> Your insistence that there is no limit involved
>>> Of course not. Every fraction has to be covered by an index. "und es
>>> erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen
>>> Stillstand." [Cantor, p. 239] That is a clear denial of limit in case of
>>> Zuordnungsprozess.
>> What the *FUCK* do you think a "Zuordnungsprozess" is? It sure as hell is
>> not your moving X's and O's around in a matrix. That is a stepwise
>> procedure. It also does not stop, but it needs to be analyzed differently.
>
> It is a process that goes on and on like Cantor's Zuordnungsprozess.
>
>> Yes, a "Zuordnungsprozess" does not stop. What do you think *that* means?
>
> It means that every exchange of X and O happens at a finite step. Never the
> 1:1 parity will be violated.
>
>> And what do you think a *LIMIT* is,
>
> Here no limit is involved but an ever lasting process. Never the 1:1 parity
> will be violated.

Parity? Is that how you avoid using 'bijection' these days. Your math
is more like parody.

Re: Natural numbers and vases

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Natural numbers and vases
Date: Fri, 27 May 2022 19:13:58 -0400
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 by: Jim Burns - Fri, 27 May 2022 23:13 UTC

On 5/27/2022 3:34 PM, WM wrote:
> Jim Burns schrieb
> am Donnerstag, 26. Mai 2022 um 18:38:43 UTC+2:

>> Infinity is not a reallyreallyreallyreallyreallyreally
>> large number. It is a different kind of thing.
>
> Nevertheless every exchange of X and O happens in
> finite distance from the start.

There is no finite distance in which
every exchange of X and O happens.

Each place with a swap in has a swap out.
This is possible because
there is no finite distance in which
every exchange of X and O happens.

When all the swaps have swapped,
no O is left in a place with a swap out.
This is possible because
each place with a swap in has a swap out.

When all swaps have been swapped,
no O is left.
No O is left in a place with a swap in and a swap out.
No O is left in a place with no swap in.

> Do you agree that in finite distance from start
> the 1:1 parity is guaranteed?

There is no finite distance in which
every exchange of X and O happens.

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