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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 - Sun, 15 May 2022 13:53 UTC

Jim Burns schrieb am Samstag, 14. Mai 2022 um 23:08:19 UTC+2:
> On 5/14/2022 4:20 PM, WM wrote:

> > Never all swaps are completed.
> All swaps are described, right at the beginning.

There is not enough ink to decribe more than the unjustified belief.

> 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.

All that happens in a distance of ℵo from ω. Uninteresting.
>
>
> 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.

All that happens in a distance of ℵo from ω. Uninteresting.
>
> If k is a place that Bob can get to,

Then it is in a distance of ℵo from ω. Uninteresting.

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

If he can disappear in your theory, then your theory is without value.

> However,
> even though each swap conserves Bob,
> all swaps do not conserve Bob.

Bob cannot be dissolved or eliminated. What you cannot observe and cannot know is simply dark.

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

In the darkness.

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 - Sun, 15 May 2022 14:00 UTC

Jim Burns schrieb am Sonntag, 15. Mai 2022 um 00:30:42 UTC+2:
> 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.

I wrote: "For each place with a swap into it, there is a swap out of it. Never all swaps are completed."This means potential infinity.

> 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.

In potential infinity!

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

If Bob cannot be eliminated then he can only be in the dark.

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 - Sun, 15 May 2022 14:01 UTC

William schrieb am Sonntag, 15. Mai 2022 um 13:28:29 UTC+2:
> On Saturday, May 14, 2022 at 5:22:04 PM UTC-3, WM wrote:
>
> > Infinite sets change
>
> Piffle

Found in the internet:

What if countability is inconsistent? (adopted from Mueckenheim):

If the fractions m/n are enumerated by the natural numbers k according to Cantor's function
k = (m + n - 1)(m + n - 2)/2 + m
then all the fractions of the sequence
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
are enumerated.

But if the natural numbers first are in bijection with the integer fractions of the first column of the matrix

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

then they must be distributed over the matrix such that no fraction remains without index. That means, there is a permutation such that the X of the first column

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

by being exchanged with the O's cover all matrix positions. All O's will vanish. This is obviously impossible because exchanging cannot reduce them. The number of not indexed fractions, represented by O's, will remain constant forever, in infinity. Why do mathematicians believe in Cantor yet?

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: sergio - Sun, 15 May 2022 15:03 UTC

On 5/15/2022 9:01 AM, WM wrote:
> William schrieb am Sonntag, 15. Mai 2022 um 13:28:29 UTC+2:
>> On Saturday, May 14, 2022 at 5:22:04 PM UTC-3, WM wrote:
>>
>>> Infinite sets change
>>
>> Piffle
>

>
> If the fractions m/n are enumerated by the natural numbers k according to Cantor's function
> k = (m + n - 1)(m + n - 2)/2 + m
> then all the fractions of the sequence
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> are enumerated.
>

>
> Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 10:29:32 -0500
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 by: sergio - Sun, 15 May 2022 15:29 UTC

On 5/15/2022 8:53 AM, WM wrote:
> Jim Burns schrieb am Samstag, 14. Mai 2022 um 23:08:19 UTC+2:
>> On 5/14/2022 4:20 PM, WM wrote:
>
>>> Never all swaps are completed.
>> All swaps are described, right at the beginning.
>
>
>> 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.
>
> All that happens in a distance of ℵo from ω. Uninteresting.
>>
>> If k is a place that Bob can get to,
>
>
>> Where is Bob?
>> After all swaps, nowhere.
>
>> However,
>> even though each swap conserves Bob,
>> all swaps do not conserve Bob.
>
>
>> Where is Bob?
>> Nowhere with a swap out of it.
>
> In the darkness.

wrong, your swaparoofest to deceive shows you are entirely out of math.

>
> Regards, WM
>
>

google Cantors Enumeration that is the correct way to do it.

*by your own admission your way always fails*.

Re: Natural numbers and vases

<t5r6e2$5sv$2@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 10:32:17 -0500
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 by: sergio - Sun, 15 May 2022 15:32 UTC

On 5/15/2022 9:00 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 15. Mai 2022 um 00:30:42 UTC+2:
>> 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.
>
> I wrote: "For each place with a swap into it, there is a swap out of it. Never all swaps are completed."This means potential infinity.

wrong, you stopped at k again.

>
>> 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.
>
> In potential infinity!

now you say you are working with finite sets.

>
>> This is the heart of the proof that
>> not all collections have Bob-conservation.
>
> If Bob cannot be eliminated then he can only be in the dark.

dark to you, vast regions of math are dark to you.

>
> Regards, WM

Re: Natural numbers and vases

<t5r84e$313$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 09:01:17 -0700
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 by: FromTheRafters - Sun, 15 May 2022 16:01 UTC

WM was thinking very hard :
> William schrieb am Sonntag, 15. Mai 2022 um 13:28:29 UTC+2:
>> On Saturday, May 14, 2022 at 5:22:04 PM UTC-3, WM wrote:
>>
>>> Infinite sets change
>>
>> Piffle
>
> Found in the internet:
>
> What if countability is inconsistent? (adopted from Mueckenheim):

Sockenheim?

Re: Natural numbers and vases

<t5r8p4$16ph$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 11:12:18 -0500
Organization: Aioe.org NNTP Server
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 by: sergio - Sun, 15 May 2022 16:12 UTC

On 5/15/2022 11:01 AM, FromTheRafters wrote:
> WM was thinking very hard :
>> William schrieb am Sonntag, 15. Mai 2022 um 13:28:29 UTC+2:
>>> On Saturday, May 14, 2022 at 5:22:04 PM UTC-3, WM wrote:
>>>> Infinite sets change
>>>
>>> Piffle
>>
>> Found in the internet:
>>
>> What if countability is inconsistent? (adopted from Mueckenheim):
>
> Sockenheim?

Sockenheim Switcharoofestivuster (?)

Re: Natural numbers and vases

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 12:13:45 -0400
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 by: Jim Burns - Sun, 15 May 2022 16:13 UTC

On 5/15/2022 10:00 AM, WM wrote:
> Jim Burns schrieb
> am Sonntag, 15. Mai 2022 um 00:30:42 UTC+2:
>> 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.
>
> I wrote:
> "For each place with a swap into it,
> there is a swap out of it.

We, including you, know that.

From knowing that, we also know
all the swaps of k, k+1 leave out one of the swapped.
Thus Bob is not conserved.

> Never all swaps are completed."

We can claim of each swap k, k+1 that,
for each split BEFORE and AFTER of =< k,
some j ends BEFORE, and j+1 begins AFTER.

This is complete when we state it.
There are no other swaps we consider.

Of those swaps, we know that Bob is not conserved.

> This means potential infinity.

And what does "potential infinity" mean when
you use it?
From context, you mean "Cantor was correct".

>> 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.
>
> In potential infinity!

"Cantor was correct!"

>> This is the heart of the proof that
>> not all collections have Bob-conservation.
>
> If Bob cannot be eliminated
> then he can only be in the dark.

Getting to the dark requires a TARDIS.
What if Bob is not a Time Lord?

The places that non-Time-Lord Bob can get to
do not conserve Bob.

Re: Natural numbers and vases

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 12:42:24 -0400
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 by: Jim Burns - Sun, 15 May 2022 16:42 UTC

On 5/15/2022 9:53 AM, WM wrote:
> Jim Burns schrieb
> am Samstag, 14. Mai 2022 um 23:08:19 UTC+2:

>> However,
>> even though each swap conserves Bob,
>> all swaps do not conserve Bob.
>
> Bob cannot be dissolved or eliminated.

Each swap conserves Bob. Nonetheless...

> What you cannot observe and cannot know
> is simply dark.

What we know is what we are talking about.

We are talking about a swap k, k+1 such that
for each BEFORE and AFTER =< k,
some j ends BEFORE and j+1 begins AFTER.

Even though each swap conserves Bob,
all swaps do not conserve Bob.

>> Where is Bob?
>> Nowhere with a swap out of it.
>
> In the darkness.

Without a TARDIS? There's no way to get there.

You claim that Time-Lord Bob is conserved.
But what if Bob is not a Time Lord?

With no TARDIS, after all swaps,
Bob isn't anywhere with a swap into it,
Bob isn't anywhere with no swap into it.

Non-Time-Lord Bob is not conserved by all swaps.

Re: Natural numbers and vases

<t5rkbg$40c$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 14:29:50 -0500
Organization: Aioe.org NNTP Server
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 by: sergio - Sun, 15 May 2022 19:29 UTC

On 5/15/2022 11:13 AM, Jim Burns wrote:
> On 5/15/2022 10:00 AM, WM wrote:
>> Jim Burns schrieb
>> am Sonntag, 15. Mai 2022 um 00:30:42 UTC+2:
>>> 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.
>>
>> I wrote:
>> "For each place with a swap into it,
>> there is a swap out of it.
>
> We, including you, know that.
>
> From knowing that, we also know
> all the swaps of k, k+1 leave out one of the swapped.
> Thus Bob is not conserved.
>
>> Never all swaps are completed."
>
> We can claim of each swap k, k+1 that,
> for each split BEFORE and AFTER of =< k,
> some j ends BEFORE, and j+1 begins AFTER.
>
> This is complete when we state it.
> There are no other swaps we consider.
>
> Of those swaps, we know that Bob is not conserved.
>
>> This means potential infinity.
>
> And what does "potential infinity" mean when
> you use it?
> From context, you mean "Cantor was correct".
>
>>> 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.
>>
>> In potential infinity!
>
> "Cantor was correct!"
>
>>> This is the heart of the proof that
>>> not all collections have Bob-conservation.
>>
>> If Bob cannot be eliminated
>> then he can only be in the dark.
>
> Getting to the dark requires a TARDIS.
> What if Bob is not a Time Lord?
>
> The places that non-Time-Lord Bob can get to
> do not conserve Bob.
>

to conserve, freeze-dry King Bob. Re-hydrate when needed.

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 - Sun, 15 May 2022 20:16 UTC

sergio schrieb am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
> On 5/15/2022 9:00 AM, WM wrote:

> > I wrote: "For each place with a swap into it, there is a swap out of it. Never all swaps are completed."This means potential infinity.
> wrong, you stopped at k again.

At which k?

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 - Sun, 15 May 2022 20:24 UTC

Jim Burns schrieb am Sonntag, 15. Mai 2022 um 18:13:56 UTC+2:
> On 5/15/2022 10:00 AM, WM wrote:

> And what does "potential infinity" mean when
> you use it?

Cantor thought: By
k = (m + n - 1)(m + n - 2)/2 + m
all the fractions of the sequence
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
are enumerated. In fact we cannot find an exception.

Alas almost all fractions are not enumerated because for every indexed fraction another fraction must be stripped off its index because the index is required for further indexing.

So we have two facts: All fractions of the sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will become indexed. Almost all fractions will not become indexed.

The sequence must be potentially infinite.

> From context, you mean "Cantor was correct".

No, Cantor thought that his sequence contains all fractions.

> > In potential infinity!
> "Cantor was correct!"

Cantor refused to use potential infinity:

"In spite of significant difference between the notions of the potential and actual infinite, where the former is a variable finite magnitude, growing above all limits, the latter a constant quantity fixed in itself but beyond all finite magnitudes, it happens deplorably often that the one is confused with the other." [Cantor, p. 374]

Regards, WM

Re: Natural numbers and vases

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 by: Jim Burns - Sun, 15 May 2022 20:29 UTC

On 5/15/2022 4:16 PM, WM wrote:
> sergio schrieb
> am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
>> On 5/15/2022 9:00 AM, WM wrote:

>>> I wrote:
>>> "For each place with a swap into it,
>>> there is a swap out of it.
>>> Never all swaps are completed."
>>> This means potential infinity.
>>
>> wrong, you stopped at k again.
>
> At which k?

We know that,
for each BEFORE and AFTER of places =< k,
some j ends BEFORE and j+1 begins AFTER.

Can you answer your question from that?

If you can't, too bad.

But we still know that,
for each BEFORE and AFTER of places =< k,
some j ends BEFORE and j+1 begins AFTER.

And we know the answers to other questions.

Re: Natural numbers and vases

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 by: Jim Burns - Sun, 15 May 2022 21:01 UTC

On 5/15/2022 4:24 PM, WM wrote:
> Jim Burns schrieb
> am Sonntag, 15. Mai 2022 um 18:13:56 UTC+2:

>> And what does "potential infinity" mean when
>> you use it?
>
> Cantor thought: By
> k = (m + n - 1)(m + n - 2)/2 + m
> all the fractions of the sequence
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> are enumerated.
> In fact we cannot find an exception.

We know that no exceptions exist.
Therefore, it is A Good Thing that we can't find them.

> Alas almost all fractions are not enumerated because
> for every indexed fraction another fraction must be
> stripped off its index because the index is required
> for further indexing.

No.
There is no requirement keeping numerators and
denominators from also being indexes.

Your fantasy-argument would make ⟨0,0⟩ impossible,
since 0 is both the abscissa and the ordinate.
No.

> So we have two facts:
> All fractions of the sequence
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> will become indexed.

All fractions of the sequences are indexed by
k = (m+n-1)(m+n-2)/2+m

> Almost all fractions will not become indexed.

No.
Also, ⟨0,0⟩ is possible.
0 can be both the abscissa and the ordinate.

> The sequence must be potentially infinite.
>
>> From context, you mean "Cantor was correct".
>
> No, Cantor thought that his sequence
> contains all fractions.

Do you think that, when you state the following,
you disagree with Cantor?

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

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Sun, 15 May 2022 21:27:00 +0000
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 by: William - Sun, 15 May 2022 21:26 UTC

On Sunday, May 15, 2022 at 11:01:49 AM UTC-3, WM wrote:
> William schrieb am Sonntag, 15. Mai 2022 um 13:28:29 UTC+2:
> > On Saturday, May 14, 2022 at 5:22:04 PM UTC-3, WM wrote:
> >
> > > Infinite sets change
> >
> > Piffle
> Found in the internet:

The internet is full of piffile.

--
Willliam Hughes

Re: Natural numbers and vases

<t5sd31$rqb$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 21:32:00 -0500
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 by: sergio - Mon, 16 May 2022 02:32 UTC

On 5/15/2022 3:24 PM, WM wrote:
> Jim Burns schrieb am Sonntag, 15. Mai 2022 um 18:13:56 UTC+2:
>> On 5/15/2022 10:00 AM, WM wrote:
>
>> And what does "potential infinity" mean when
>> you use it?
>
> Cantor thought: By
> k = (m + n - 1)(m + n - 2)/2 + m
> all the fractions of the sequence
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> are enumerated. In fact we cannot find an exception.

Finally you agree that Cantors enumeration is 100% correct.

>
> Alas almost all fractions are not enumerated because for every indexed fraction another fraction must be stripped off its index because the index is required for further indexing.

what???

False!

We do not re-use indexes here, we always use a fresh set, you can buy them on eBay $15.99

m and n and k are ALL indexes. m is column, n is row, k is sequence number.

>
> So we have two facts: All fractions of the sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will become indexed.

True.

> Almost all fractions will not become indexed.

False

>
> The sequence must be potentially infinite.

False.

>
>> From context, you mean "Cantor was correct".
>
> No, Cantor thought that his sequence contains all fractions.

Wrong. Cantor proved the rationals have a one to one mapping to the natural numbers.

>
>>> In potential infinity!
>> "Cantor was correct!"
>
> Cantor refused to use potential infinity:

Cantor was not talking about finite sets, gumby.

>
> "In spite of significant difference between the notions of the potential and actual infinite, where the former is a variable finite magnitude, growing above all limits, the latter a constant quantity fixed in itself but beyond all finite magnitudes, it happens deplorably often that the one is confused with the other." [Cantor, p. 374]

your quote proves my point.

>
> Regards, WM

Re: Natural numbers and vases

<t5sd67$rqb$2@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 15 May 2022 21:33:43 -0500
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 by: sergio - Mon, 16 May 2022 02:33 UTC

On 5/15/2022 3:16 PM, WM wrote:
> sergio schrieb am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
>> On 5/15/2022 9:00 AM, WM wrote:
>
>>> I wrote: "For each place with a swap into it, there is a swap out of it. Never all swaps are completed."This means potential infinity.
>> wrong, you stopped at k again.
>
> At which k?
>
> Regards, WM

FISON(k)

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Mon, 16 May 2022 14:52:22 +0000
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 by: WM - Mon, 16 May 2022 14:52 UTC

Jim Burns schrieb am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
> On 5/15/2022 4:24 PM, WM wrote:
> > Jim Burns schrieb
> > am Sonntag, 15. Mai 2022 um 18:13:56 UTC+2:
> >> And what does "potential infinity" mean when
> >> you use it?
> >
> > Cantor thought: By
> > k = (m + n - 1)(m + n - 2)/2 + m
> > all the fractions of the sequence
> > 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> > are enumerated.
> > In fact we cannot find an exception.
> We know that no exceptions exist.

Wrong. We know that every index used to index a non-integer fraction or an integer fraction has to be taken from an integer fraction.

> There is no requirement keeping numerators and
> denominators from also being indexes.

That is not claimed by me. Try to understand that every index used to index a non-integer fraction or an integer fraction has to be taken from an integer fraction.

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

Here the first column carries natural indexes X.

XOOO...
XOOO...
XOOO...
XOOO...
....

They are taken from their fractions in order to index other fractions:

XXOO...
OOOO...
XOOO...
XOOO...
....

XXOO...
XOOO...
OOOO...
XOOO...
....

XXXO...
XOOO...
OOOO...
OOOO...
....

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 - Mon, 16 May 2022 14:54 UTC

sergio schrieb am Montag, 16. Mai 2022 um 04:33:52 UTC+2:
> On 5/15/2022 3:16 PM, WM wrote:
> > sergio schrieb am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
> >> On 5/15/2022 9:00 AM, WM wrote:
> >
> >>> I wrote: "For each place with a swap into it, there is a swap out of it. Never all swaps are completed."This means potential infinity.
> >> wrong, you stopped at k again.
> >
> > At which k?

> FISON(k)

At which k? k is not a number and therefore not finite. It is only a variable where infinitely many numbers can be inserted, for every number also its successor.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Mon, 16 May 2022 14:56:26 +0000
Content-Type: text/plain; charset="UTF-8"
 by: WM - Mon, 16 May 2022 14:56 UTC

William schrieb am Sonntag, 15. Mai 2022 um 23:27:04 UTC+2:
> On Sunday, May 15, 2022 at 11:01:49 AM UTC-3, WM wrote:

> The internet is full of piffile.

But empty of piffle compared to set theory.

Try to understand that every index used to index a non-integer fraction or an integer fraction has to be taken from an integer fraction.

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

Here the first column carries all natural indexes X.

XOOO...
XOOO...
XOOO...
XOOO...
....

They are taken from their fractions in order to index other fractions:

XXOO...
OOOO...
XOOO...
XOOO...
....

XXOO...
XOOO...
OOOO...
XOOO...
....

XXXO...
XOOO...
OOOO...
OOOO...
....

Regards, WM

Re: Natural numbers and vases

<t5ts8q$14sh$2@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 10:57:12 -0500
Organization: Aioe.org NNTP Server
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 by: sergio - Mon, 16 May 2022 15:57 UTC

On 5/16/2022 9:56 AM, WM wrote:
> William schrieb am Sonntag, 15. Mai 2022 um 23:27:04 UTC+2:
>> On Sunday, May 15, 2022 at 11:01:49 AM UTC-3, WM wrote:
>
>> The internet is full of piffile.
>
> But empty of piffle compared to set theory.
>
> Try to understand that every index used to index a non-integer fraction or an integer fraction has to be taken from an integer fraction.
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>
> Here the first column carries all natural indexes X.
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> They are taken from their fractions in order to index other fractions:
>
> XXOO...
> OOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> XOOO...
> OOOO...
> XOOO...
> ...
>
> XXXO...
> XOOO...
> OOOO...
> OOOO...
> ...
>
> Regards, WM

well, that is meaningless.

Re: Natural numbers and vases

<t5tsho$1b2e$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 11:01:59 -0500
Organization: Aioe.org NNTP Server
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 by: sergio - Mon, 16 May 2022 16:01 UTC

On 5/16/2022 9:54 AM, WM wrote:
> sergio schrieb am Montag, 16. Mai 2022 um 04:33:52 UTC+2:
>> On 5/15/2022 3:16 PM, WM wrote:
>>> sergio schrieb am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
>>>> On 5/15/2022 9:00 AM, WM wrote:
>>>
>>>>> I wrote: "For each place with a swap into it, there is a swap out of it. Never all swaps are completed."This means potential infinity.
>>>> wrong, you stopped at k again.
>>>
>>> At which k?
>
>> FISON(k)
>
> At which k? k is not a number and therefore not finite.

wrong, k represents a natural number and is always finite, it ends a FISON.

your diversion does not work.

Why do you always stop at some number ? So you can say there are dark numbers out beyond that point.

> It is only a variable where infinitely many numbers can be inserted, for every number also its successor.

so why do you say "never all swaps are completed" ? It is because you stopped somewhere, call your stopping place k.

>
> Regards, WM

Re: Natural numbers and vases

<t5tsm0$1b2e$2@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=100232&group=sci.math#100232

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 11:04:14 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t5tsm0$1b2e$2@gioia.aioe.org>
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 by: sergio - Mon, 16 May 2022 16:04 UTC

On 5/16/2022 9:52 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
>> On 5/15/2022 4:24 PM, WM wrote:
>>> Jim Burns schrieb
>>> am Sonntag, 15. Mai 2022 um 18:13:56 UTC+2:
>>>> And what does "potential infinity" mean when
>>>> you use it?
>>>
>>> Cantor thought: By
>>> k = (m + n - 1)(m + n - 2)/2 + m
>>> all the fractions of the sequence
>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>>> are enumerated.
>>> In fact we cannot find an exception.
>> We know that no exceptions exist.
>
> Wrong. We know that every index used to index a non-integer fraction or an integer fraction has to be taken from an integer fraction.

Wrong. this is stupid wrong.

>
>> There is no requirement keeping numerators and
>> denominators from also being indexes.
>

> Regards, WM
>
>
>

Re: Natural numbers and vases

<b58c00b8-f00f-55db-72a8-a107d3652596@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 12:12:13 -0400
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 by: Jim Burns - Mon, 16 May 2022 16:12 UTC

On 5/16/2022 10:52 AM, WM wrote:
> Jim Burns schrieb
> am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
>> On 5/15/2022 4:24 PM, WM wrote:

>>> Cantor thought: By
>>> k = (m + n - 1)(m + n - 2)/2 + m
>>> all the fractions of the sequence
>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>>> are enumerated.
>>> In fact we cannot find an exception.
>>
>> We know that no exceptions exist.
>
> Wrong.
> We know that every index used to index a non-integer
> fraction or an integer fraction has to be taken from
> an integer fraction.

We know that,
for each index k,
for each split BEFORE and AFTER of indices =< k,
some j ends BEFORE, and j+1 begins AFTER.

We know that,
for each index k,
there is a unique _fraction_ m/n,
(m/m ≠ 2m/2n), such that
m+n = ceiling((sqrt(8*k+1)+1)/2)
m = k - (m+n-1)*(m+n-2)/2
n = m+n - m

and, for that m,n,
k = (m+n-1)*(m+n-2)/2+m
and
for each split BEFORE and AFTER of indices =< m and
for each split BEFORE and AFTER of indices =< n,
some j ends BEFORE, and j+1 begins AFTER.

We know that,
for each fraction m/n,
for each split BEFORE and AFTER of indices =< m and
for each split BEFORE and AFTER of indices =< n,
some j ends BEFORE, and j+1 begins AFTER.

We know that,
for each fraction m/n,
there is a unique k such that,
k = (m+n-1)*(m+n-2)/2+m

and, for that k,
m+n = ceiling((sqrt(8*k+1)+1)/2)
m = k - (m+n-1)*(m+n-2)/2
n = m+n - m
and
for each split BEFORE and AFTER of indices =< k,
some j ends BEFORE, and j+1 begins AFTER.

The most important part of how we know these things
is that, for the numerators and denominators and indices
we are talking about,for each split BEFORE and AFTER of
indices =< m, n, or k,
some j ends BEFORE, and j+1 begins AFTER.

>> There is no requirement keeping numerators and
>> denominators from also being indexes.
>
> That is not claimed by me.

Are you pointing out that the collection of index/1
is a proper sub-collection of the collection of
numerator/denominator?

So it is.

That's the reason that we spend time on this argument.
It shows that some collections match some of their
proper sub-collections.

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server_pubkey.txt

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