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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)
Injection-Date: Thu, 19 May 2022 13:42:30 +0000
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 by: WM - Thu, 19 May 2022 13:42 UTC

Jim Burns schrieb am Mittwoch, 18. Mai 2022 um 20:15:26 UTC+2:
> On 5/18/2022 8:57 AM, WM wrote:

> > We check the number of indexes by bijecting them
> > with the fractions of the first column (we could use
> > every other column or line as well).
> >
> > 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, ...
> > ...
> >
> > When applying the indexes for indexing fractions
> > according to m/n gets the index k from
> >
> > k = (m + n - 1)(m + n - 2)/2 + m
> >
> > with the result
> >
> > 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> >
> > then the integer fractions have to supply these indexes.
> > They are stripped off these indexes.
> >
> Consider the first column of The Matrix.
> k/1
>
> 1/1
> 2/1
> 3/1
> 4/1
> 5/1
> 6/1
> 7/1
> 8/1
> 9/1
> 10/1
> 11/1
> ...
>
> For each numerator k,
> there is a _triangle number_ k*(k+1)/2
> k/1 k*(k+1)/2
>
> 1/1 1
> 2/1 3
> 3/1 6
> 4/1 10
> 5/1 15
> 6/1 21
> 7/1 28
> 8/1 36
> 9/1 45
> 10/1 55
> 11/1 66
> ...
>
> For each numerator k,
> there is a last triangle number < k
> there is m = k - (last triangle num < k)
> k/1 m
>
> 1/1 0 1
> 2/1 1 1
> 3/1 1 2
> 4/1 3 1
> 5/1 3 2
> 6/1 3 3
> 7/1 6 1
> 8/1 6 2
> 9/1 6 3
> 10/1 6 4
> 11/1 10 1
> ...
>
> For each numerator k,
> there is a last triangle number < k
> there is s = the index of (last triangle num < k)
> there is n = s + 2 - m
> k/1 s n
>
> 1/1 0 0 1
> 2/1 1 1 2
> 3/1 1 1 1
> 4/1 3 2 3
> 5/1 3 2 2
> 6/1 3 2 1
> 7/1 6 3 4
> 8/1 6 3 3
> 9/1 6 3 2
> 10/1 6 3 1
> 11/1 10 4 5
> ...
>
> For each numerator k,
> there is a fraction m/n
> k/1 m/n
>
> 1/1 1/1
> 2/1 1/2
> 3/1 2/1
> 4/1 1/3
> 5/1 2/2
> 6/1 3/1
> 7/1 1/4
> 8/1 2/3
> 9/1 3/2
> 10/1 4/1
> 11/1 1/5
> ...
>
> No exceptions.
>
> ----
> Consider The Matrix.
> 1/1 1/2 1/3 1/4 1/5 ...
> 2/1 2/2 2/3 2/4 2/5 ...
> 3/1 3/2 3/3 3/4 3/5 ...
> 4/1 4/2 4/3 4/4 4/5 ...
> 5/1 5/2 5/3 5/4 5/5 ...
> ...
>
> For each fraction m/n,
> there is s = m + n
> 2 3 4 5 6 ...
> 3 4 5 6 7 ...
> 4 5 6 7 8 ...
> 5 6 7 8 9 ...
> 6 7 8 9 10 ...
> ...
>
> For each fraction m/n,
> there is (s-1)*(s-2)/2
> 0 1 3 6 10 ...
> 1 3 6 10 15 ...
> 3 6 10 15 21 ...
> 6 10 15 21 28 ...
> 10 15 21 28 36 ...
> ...
>
> For each fraction m/n,
> there is k = m + (s-2)*(s-2)/2
> 1 2 4 7 11 ...
> 3 5 7 12 17 ...
> 6 8 13 18 24 ...
> 10 14 19 25 32 ...
> 15 20 26 33 41 ...
> ...
>
> No exceptions.
>
> ----
> > When applying the indexes for indexing fractions
> > according to m/n gets the index k from
> >
> > k = (m + n - 1)(m + n - 2)/2 + m
> >
> > with the result
> >
> > 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> >
> > then the integer fractions have to supply these indexes.
> > They are stripped off these indexes.
> >
> > No? This one is an exception?
> What are you asking if it might be an exception?
> An exception to what?

An exception of your claim that completely true claims do not _become_ true.

My claim *is* true: In spite of your triangle numbers it is clear that in my matrix the share of enumerated fractions is |N| and the share of not enumerated fractions is |N|^2 - |N|, and that will never change. It is a true claim for the whole mapping.

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, 19 May 2022 13:42:49 +0000
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 by: WM - Thu, 19 May 2022 13:42 UTC

Jim Burns schrieb am Mittwoch, 18. Mai 2022 um 21:16:16 UTC+2:

> I would very much like WM to read it,
> but I make no prediction in that regard.
>
> He's not my only possible reader, though.
> I imagine myself putting a light in the window
> for those trying to find their way out of WM's fog.
>
I have read it but I have not seen a refutation of my claim that in my matrix the share of enumerated fractions is |N| and the share of not enumerated fractions is |N|^2 - |N|, and that will never change. It is a true claim for the whole mapping.

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, 19 May 2022 13:56 UTC

William schrieb am Mittwoch, 18. Mai 2022 um 16:27:56 UTC+2:
> No *element* of N_p is infinite. The *set* N_p is infinite.

Potentially infinite, never actually infinite. For that sake it must have more than any natural number of numbers. This is impossible with definable natural numbers since they count them selves and never leave the finite domain.

You claim that every natural number of N_p has aleph_0 successors between itself and omega.
That implies that no natural number of N_p has less successors between itself and omega.

Do you agree?

That implies that between all elements of the the set N_p and omega there are aleph_0 successors.

Do you still agree?

That implies that between the set N_p and omega there are aleph_0 successors.

The latter can only be denied by believers in magic sets stretching farther than their elements reach.

Regards, WM

Re: Natural numbers and vases

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 by: sergi o - Thu, 19 May 2022 14:02 UTC

On 5/19/2022 8:41 AM, WM wrote:
> horand....@gmail.com schrieb am Mittwoch, 18. Mai 2022 um 18:24:37 UTC+2:
>> On Wednesday, 18 May 2022 at 13:04:51 UTC-3, FromTheRafters wrote:
>>> It happens that WM formulated :
>>>> my argument does not increase the taken set in the least such that
>>>> not-exhausting of the infinite set is matter of fact.
>>> What?
>> Well, in a sense he is right:

>
> Of course. The shares of enumerated and not enumerated fractions do never change.

wrong, all fractions are enumerated. case closed.

> That is the only important feature. Whether we can finish or not, is irrelevant.

wrong. all fractions are enumerated. case closed.

>
> 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, 19 May 2022 14:06 UTC

horand....@gmail.com schrieb am Mittwoch, 18. Mai 2022 um 16:45:45 UTC+2:
> On Wednesday, 18 May 2022 at 10:08:40 UTC-3, WM wrote:
> > horand....@gmail.com schrieb am Mittwoch, 18. Mai 2022 um 15:04:54 UTC+2:
> > > On Wednesday, 18 May 2022 at 09:52:21 UTC-3, WM wrote:
> >
> > > > Of course! But there is a slight difference. Taking a number of integers from an infinite set increases the taken set and raises the impression of some fools that finally the infinite set could be exhausted nevertheless. Contrary to that, my argument does not increase the taken set in the least such that [...]
> > >
> > > ...the only thing that is glaringly obvious is that the professor hasn't got a clue about limits.
> >
> > First: Limits are not relevant when enumerating elements. Second: The limit of a constant set is a constant set.
> What did I just say? Your sequence of matrices is decidedly *NOT* a constant set, at least not in any way that you seem to think of it.

The set of indices is |N, a constant set.
The set of missing indices is constant too and larger than |N.

Regards, WM

Re: Natural numbers and vases

<t65j23$dql$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=100495&group=sci.math#100495

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 19 May 2022 09:09:04 -0500
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 by: sergi o - Thu, 19 May 2022 14:09 UTC

On 5/19/2022 8:56 AM, WM wrote:
> William schrieb am Mittwoch, 18. Mai 2022 um 16:27:56 UTC+2:
>> No *element* of N_p is infinite. The *set* N_p is infinite.
>
> Potentially infinite, never actually infinite.

Wrong.

> For that sake it must have more than any natural number of numbers.

Wrong.

> This is impossible with definable natural numbers since they count them selves and never leave the finite domain.

Wrong, numbers do not count themselves

Your "definable" is only for stoners

>
> You claim that every natural number of N_p has aleph_0 successors between itself and omega.

do you disagree ?

> That implies that no natural number of N_p has less successors between itself and omega.

call the natural number k, so k has less successors between itself and omega.
obviously false

>
> That implies that between all elements of the the set N_p and omega there are aleph_0 successors.

Wrong, between the elements k and k+1 there are 0 successors.

>
> That implies that between the set N_p and omega there are aleph_0 successors.

Wrong. set N_p and omega are not numbers

>
> Regards, WM
>
>
>

7 wrongs, 1 right in one post, obviously in steep decline

Re: Natural numbers and vases

<t65j3d$dql$2@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100496&group=sci.math#100496

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 19 May 2022 09:09:49 -0500
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 by: sergi o - Thu, 19 May 2022 14:09 UTC

On 5/19/2022 8:42 AM, WM wrote:
> Jim Burns schrieb am Mittwoch, 18. Mai 2022 um 21:16:16 UTC+2:
>
>> I would very much like WM to read it,
>> but I make no prediction in that regard.
>>
>> He's not my only possible reader, though.
>> I imagine myself putting a light in the window
>> for those trying to find their way out of WM's fog.
>>
> I have read it but I have not seen a refutation of my claim that in my matrix the share of enumerated fractions is |N| and the share of not enumerated fractions is |N|^2 - |N|, and that will never change. It is a true claim for the whole mapping.
>
> Regards, WM

outright lie.

Re: Natural numbers and vases

<t65j5v$dql$3@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100498&group=sci.math#100498

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 19 May 2022 09:11:11 -0500
Organization: Aioe.org NNTP Server
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 by: sergi o - Thu, 19 May 2022 14:11 UTC

On 5/19/2022 8:42 AM, WM wrote:
> Jim Burns schrieb am Mittwoch, 18. Mai 2022 um 20:15:26 UTC+2:
>> On 5/18/2022 8:57 AM, WM wrote:
>
>>> We check the number of indexes by bijecting them
>>> with the fractions of the first column (we could use
>>> every other column or line as well).
>>>
>>> 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, ...
>>> ...
>>>
>>> When applying the indexes for indexing fractions
>>> according to m/n gets the index k from
>>>
>>> k = (m + n - 1)(m + n - 2)/2 + m
>>>
>>> with the result
>>>
>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>>>
>>> then the integer fractions have to supply these indexes.
>>> They are stripped off these indexes.
>>>
>> Consider the first column of The Matrix.
>> k/1
>>
>> 1/1
>> 2/1
>> 3/1
>> 4/1
>> 5/1
>> 6/1
>> 7/1
>> 8/1
>> 9/1
>> 10/1
>> 11/1
>> ...
>>
>> For each numerator k,
>> there is a _triangle number_ k*(k+1)/2
>> k/1 k*(k+1)/2
>>
>> 1/1 1
>> 2/1 3
>> 3/1 6
>> 4/1 10
>> 5/1 15
>> 6/1 21
>> 7/1 28
>> 8/1 36
>> 9/1 45
>> 10/1 55
>> 11/1 66
>> ...
>>
>> For each numerator k,
>> there is a last triangle number < k
>> there is m = k - (last triangle num < k)
>> k/1 m
>>
>> 1/1 0 1
>> 2/1 1 1
>> 3/1 1 2
>> 4/1 3 1
>> 5/1 3 2
>> 6/1 3 3
>> 7/1 6 1
>> 8/1 6 2
>> 9/1 6 3
>> 10/1 6 4
>> 11/1 10 1
>> ...
>>
>> For each numerator k,
>> there is a last triangle number < k
>> there is s = the index of (last triangle num < k)
>> there is n = s + 2 - m
>> k/1 s n
>>
>> 1/1 0 0 1
>> 2/1 1 1 2
>> 3/1 1 1 1
>> 4/1 3 2 3
>> 5/1 3 2 2
>> 6/1 3 2 1
>> 7/1 6 3 4
>> 8/1 6 3 3
>> 9/1 6 3 2
>> 10/1 6 3 1
>> 11/1 10 4 5
>> ...
>>
>> For each numerator k,
>> there is a fraction m/n
>> k/1 m/n
>>
>> 1/1 1/1
>> 2/1 1/2
>> 3/1 2/1
>> 4/1 1/3
>> 5/1 2/2
>> 6/1 3/1
>> 7/1 1/4
>> 8/1 2/3
>> 9/1 3/2
>> 10/1 4/1
>> 11/1 1/5
>> ...
>>
>> No exceptions.
>>
>> ----
>> Consider The Matrix.
>> 1/1 1/2 1/3 1/4 1/5 ...
>> 2/1 2/2 2/3 2/4 2/5 ...
>> 3/1 3/2 3/3 3/4 3/5 ...
>> 4/1 4/2 4/3 4/4 4/5 ...
>> 5/1 5/2 5/3 5/4 5/5 ...
>> ...
>>
>> For each fraction m/n,
>> there is s = m + n
>> 2 3 4 5 6 ...
>> 3 4 5 6 7 ...
>> 4 5 6 7 8 ...
>> 5 6 7 8 9 ...
>> 6 7 8 9 10 ...
>> ...
>>
>> For each fraction m/n,
>> there is (s-1)*(s-2)/2
>> 0 1 3 6 10 ...
>> 1 3 6 10 15 ...
>> 3 6 10 15 21 ...
>> 6 10 15 21 28 ...
>> 10 15 21 28 36 ...
>> ...
>>
>> For each fraction m/n,
>> there is k = m + (s-2)*(s-2)/2
>> 1 2 4 7 11 ...
>> 3 5 7 12 17 ...
>> 6 8 13 18 24 ...
>> 10 14 19 25 32 ...
>> 15 20 26 33 41 ...
>> ...
>>
>> No exceptions.
>>
>> ----
>>> When applying the indexes for indexing fractions
>>> according to m/n gets the index k from
>>>
>>> k = (m + n - 1)(m + n - 2)/2 + m
>>>
>>> with the result
>>>
>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>>>
>>> then the integer fractions have to supply these indexes.
>>> They are stripped off these indexes.
>>>
>>> No? This one is an exception?
>> What are you asking if it might be an exception?
>> An exception to what?
>
> An exception of your claim that completely true claims do not _become_ true.
>
> My claim *is* true: In spite of your triangle numbers it is clear that in my matrix the share of enumerated fractions is |N| and the share of not enumerated fractions is |N|^2 - |N|, and that will never change. It is a true claim for the whole mapping.
>
> Regards, WM

no, your claim is troll BS.

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, 19 May 2022 14:24 UTC

On Thursday, May 19, 2022 at 10:56:45 AM UTC-3, WM wrote:

> ... You claim that every natural number of N_p has aleph_0 successors between itself and omega.
> That implies that no natural number of N_p has less successors between itself and omega.
>
> Do you agree?
>

Indeed, between each element of the set N_p and omega there are aleph_0 successors

> That implies that between all elements of the the set N_p and omega there are aleph_0 successors.

Nope because the set, "all elements", can have a property that "each element" does not have. Each *element* of N_p is finite. The *set* N_p is infinite. "Potentially Infinite" is nonsense. Sets do not change.

--
William Hughes

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, 19 May 2022 14:25 UTC

On Thursday, 19 May 2022 at 10:41:38 UTC-3, WM wrote:
> horand....@gmail.com schrieb am Mittwoch, 18. Mai 2022 um 18:24:37 UTC+2:
> > On Wednesday, 18 May 2022 at 13:04:51 UTC-3, FromTheRafters wrote:
> > > It happens that WM formulated :
> > > > my argument does not increase the taken set in the least such that
> > > > not-exhausting of the infinite set is matter of fact.
> > > What?
> > Well, in a sense he is right:
> Of course. The shares of enumerated and not enumerated fractions do never change. That is the only important feature. Whether we can finish or not, is irrelevant.

Imaginative editing. Very funny!

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
Date: Thu, 19 May 2022 10:18:05 -0500
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 by: sergi o - Thu, 19 May 2022 15:18 UTC

On 5/19/2022 9:06 AM, WM wrote:
> horand....@gmail.com schrieb am Mittwoch, 18. Mai 2022 um 16:45:45 UTC+2:
>> On Wednesday, 18 May 2022 at 10:08:40 UTC-3, WM wrote:
>>> horand....@gmail.com schrieb am Mittwoch, 18. Mai 2022 um 15:04:54 UTC+2:
>>>> On Wednesday, 18 May 2022 at 09:52:21 UTC-3, WM wrote:
>>>
>>>>> Of course! But there is a slight difference. Taking a number of integers from an infinite set increases the taken set and raises the impression of some fools that finally the infinite set could be exhausted nevertheless. Contrary to that, my argument does not increase the taken set in the least such that [...]
>>>>
>>>> ...the only thing that is glaringly obvious is that the professor hasn't got a clue about limits.
>>>
>>> First: Limits are not relevant when enumerating elements. Second: The limit of a constant set is a constant set.
>> What did I just say? Your sequence of matrices is decidedly *NOT* a constant set, at least not in any way that you seem to think of it.
>
> The set of indices is |N, a constant set.

no, the set of natural numbers is an infinite set.

> The set of missing indices is constant too and larger than |N.

no, if they are missing, someone must have noticed that they are missing.

>
> Regards, WM

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, 19 May 2022 12:56:37 -0400
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 by: Jim Burns - Thu, 19 May 2022 16:56 UTC

On 5/19/2022 9:42 AM, WM wrote:
> Jim Burns schrieb
> am Mittwoch, 18. Mai 2022 um 20:15:26 UTC+2:
>> On 5/18/2022 8:57 AM, WM wrote:

>>> When applying the indexes for indexing fractions
>>> according to m/n gets the index k from
>>>
>>> k = (m + n - 1)(m + n - 2)/2 + m
>>>
>>> with the result
>>>
>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>>>
>>> then the integer fractions have to supply these indexes.
>>> They are stripped off these indexes.
>>>
>>> No? This one is an exception?
>>
>> What are you asking if it might be an exception?
>> An exception to what?
>
> An exception of your claim that
> completely true claims do not _become_ true.

1. Some claims are not completely true.
2. Some claims are completely true.

The method which I advocate
starts with type 2 claims
and proceeds to further claims _only_
by methods that can _only_ give a type 2 claim
from type 2 claims.

I speculate that you are calling type 1 claims
exceptions.

It's correct to say that I don't use type 1 claims
in the the method which I advocate.

This is intentional.
Not-using type 1 claims is a large part of
how we know further claims are type 2.

> My claim *is* true:
> In spite of your triangle numbers it is clear that
> in my matrix the share of enumerated fractions is |N|
> and the share of not enumerated fractions is
> |N|^2 - |N|, and that will never change.
> It is a true claim for the whole mapping.

This formula assigns a unique index to each fraction.
k = m+(m+n-1)*(m+n-2)/2

"k is the index of m/n" is type 2.

Type 2:
For each BEFORE and AFTER =< m,
some j ends BEFORE and j+1 begins AFTER.
For each BEFORE and AFTER =< n,
some j ends BEFORE and j+1 begins AFTER.

Those claims are type 2 essentially because we say so.
By saying so, we _beat the bounds_ of our discussion.

Type 2:
For each BEFORE and AFTER =< k,
some j ends BEFORE and j+1 begins AFTER.

That claim is type 2 because the earlier claims about
m and n are type 2.
The information we have about BEFORE and AFTER
=< m and =< n gives us a way to derive information
about BEFORE and AFTER =< k = m+(m+n-1)*(m+n-2)/2

That derivation holds for whatever the starting
claims hold for.
The starting claims hold for any natural number.
Thus, the derivation holds for any natural number.
Thus, we end with more type 2 claims.

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, 20 May 2022 11:02 UTC

horand....@gmail.com schrieb am Donnerstag, 19. Mai 2022 um 16:28:19 UTC+2:
> On Thursday, 19 May 2022 at 10:56:45 UTC-3, WM wrote:
> > William schrieb am Mittwoch, 18. Mai 2022 um 16:27:56 UTC+2:
> > > No *element* of N_p is infinite. The *set* N_p is infinite.
> > Potentially infinite, never actually infinite. For that sake it must have more than any natural number of numbers. This is impossible with definable natural numbers since they count them selves and never leave the finite domain.
> >
> > You claim that every natural number of N_p has aleph_0 successors between itself and omega.
> > That implies that no natural number of N_p has less successors between itself and omega.
> >
> > Do you agree?
> >
> > That implies that between all elements of the the set N_p and omega there are aleph_0 successors.
> Ah, the quantifier switch. Nice!

Here it is justified because the idea that no natural number of N_p has less successors between itself and omega but they all together cover these successors, is deepest medieval belief in black magic. And I dare to guess that not even the stupidest witch hunters would have believed that.

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, 20 May 2022 11:07 UTC

William schrieb am Donnerstag, 19. Mai 2022 um 16:25:02 UTC+2:
> On Thursday, May 19, 2022 at 10:56:45 AM UTC-3, WM wrote:
>
>
>
> > ... You claim that every natural number of N_p has aleph_0 successors between itself and omega.
> > That implies that no natural number of N_p has less successors between itself and omega.
> >
> > Do you agree?
> >
> Indeed, between each element of the set N_p and omega there are aleph_0 successors
> > That implies that between all elements of the the set N_p and omega there are aleph_0 successors.
> Nope because the set, "all elements", can have a property that "each element" does not have.

You are outside of logic. The set is nothing else but all its elements. If no natural number of N_p has less successors between itself and omega, then all natural numbers have not less successors. Note not any has less means all together have not less.

> Each *element* of N_p is finite. The *set* N_p is infinite. "Potentially Infinite" is nonsense. Sets do not change.

Your argument: Every line in Cantor's second diagonal argument does not contain the diagonal number. But nevertheless it can belong to the set of all lines.

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, 20 May 2022 11:15 UTC

Jim Burns schrieb am Donnerstag, 19. Mai 2022 um 18:56:49 UTC+2:
> On 5/19/2022 9:42 AM, WM wrote:
> > Jim Burns schrieb
> > am Mittwoch, 18. Mai 2022 um 20:15:26 UTC+2:
> >> On 5/18/2022 8:57 AM, WM wrote:
>
> >>> When applying the indexes for indexing fractions
> >>> according to m/n gets the index k from
> >>>
> >>> k = (m + n - 1)(m + n - 2)/2 + m
> >>>
> >>> with the result
> >>>
> >>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> >>>
> >>> then the integer fractions have to supply these indexes.
> >>> They are stripped off these indexes.
> >>>
> >>> No? This one is an exception?
> >>
> >> What are you asking if it might be an exception?
> >> An exception to what?
> >
> > An exception of your claim that
> > completely true claims do not _become_ true.
> 1. Some claims are not completely true.
> 2. Some claims are completely true.
>
> The method which I advocate
> starts with type 2 claims
> and proceeds to further claims _only_
> by methods that can _only_ give a type 2 claim
> from type 2 claims.
>
> I speculate that you are calling type 1 claims
> exceptions.

My claim is absolutely true because every index supplied to a fraction is taken from a fraction: the integer fractions have to supply these indexes.
>
> It's correct to say that I don't use type 1 claims
> in the the method which I advocate.

You do, because you deny that every index supplied to a fraction is taken from a fraction.
>
> > My claim *is* true:
> > In spite of your triangle numbers it is clear that
> > in my matrix the share of enumerated fractions is |N|
> > and the share of not enumerated fractions is
> > |N|^2 - |N|, and that will never change.
> > It is a true claim for the whole mapping.
> This formula assigns a unique index to each fraction.
> k = m+(m+n-1)*(m+n-2)/2

That does not contradict my claim.
>
> "k is the index of m/n" is type 2.

Yes, but every defined k has aleph_0 successors. Therefore your k do not cover all natnumbers. That is a type 2 recognition.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
Date: Fri, 20 May 2022 04:23:29 -0700
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 by: FromTheRafters - Fri, 20 May 2022 11:23 UTC

WM was thinking very hard :
> William schrieb am Donnerstag, 19. Mai 2022 um 16:25:02 UTC+2:
>> On Thursday, May 19, 2022 at 10:56:45 AM UTC-3, WM wrote:
>>
>>
>>
>>> ... You claim that every natural number of N_p has aleph_0 successors
>>> between itself and omega. That implies that no natural number of N_p has
>>> less successors between itself and omega.
>>>
>>> Do you agree?
>>> Indeed, between each element of the set N_p and omega there are aleph_0
>>> successors That implies that between all elements of the the set N_p and
>>> omega there are aleph_0 successors.
>> Nope because the set, "all elements", can have a property that "each
>> element" does not have.
>
> You are outside of logic. The set is nothing else but all its elements.

You have said this before, do you have a citation for that?

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 by: sergi o - Fri, 20 May 2022 13:30 UTC

On 5/20/2022 6:02 AM, WM wrote:
> horand....@gmail.com schrieb am Donnerstag, 19. Mai 2022 um 16:28:19 UTC+2:
>> On Thursday, 19 May 2022 at 10:56:45 UTC-3, WM wrote:
>>> William schrieb am Mittwoch, 18. Mai 2022 um 16:27:56 UTC+2:
>>>> No *element* of N_p is infinite. The *set* N_p is infinite.
>>> Potentially infinite, never actually infinite. For that sake it must have more than any natural number of numbers. This is impossible with definable natural numbers since they count them selves and never leave the finite domain.
>>>
>>> You claim that every natural number of N_p has aleph_0 successors between itself and omega.
>>> That implies that no natural number of N_p has less successors between itself and omega.
>>>
>>> Do you agree?
>>>
>>> That implies that between all elements of the the set N_p and omega there are aleph_0 successors.
>> Ah, the quantifier switch. Nice!
>
> Here it is justified because the idea that no natural number of N_p has less successors between itself and omega but they all together cover these successors, is deepest medieval belief in black magic. And I dare to guess that not even the stupidest witch hunters would have believed that.
>
> Regards, WM

you are outside of math, with your black numbers, magic math, it is stupid math.

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Subject: Re: Natural numbers and vases
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 by: sergi o - Fri, 20 May 2022 13:34 UTC

On 5/20/2022 6:15 AM, WM wrote:
> Jim Burns schrieb am Donnerstag, 19. Mai 2022 um 18:56:49 UTC+2:
>> On 5/19/2022 9:42 AM, WM wrote:
>>> Jim Burns schrieb
>>> am Mittwoch, 18. Mai 2022 um 20:15:26 UTC+2:
>>>> On 5/18/2022 8:57 AM, WM wrote:
>>
>>>>> When applying the indexes for indexing fractions
>>>>> according to m/n gets the index k from
>>>>>
>>>>> k = (m + n - 1)(m + n - 2)/2 + m
>>>>>
>>>>> with the result
>>>>>
>>>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>>>>>
>>>>> then the integer fractions have to supply these indexes.
>>>>> They are stripped off these indexes.
>>>>>
>>>>> No? This one is an exception?
>>>>
>>>> What are you asking if it might be an exception?
>>>> An exception to what?
>>>
>>> An exception of your claim that
>>> completely true claims do not _become_ true.
>> 1. Some claims are not completely true.
>> 2. Some claims are completely true.
>>
>> The method which I advocate
>> starts with type 2 claims
>> and proceeds to further claims _only_
>> by methods that can _only_ give a type 2 claim
>> from type 2 claims.
>>
>> I speculate that you are calling type 1 claims
>> exceptions.
>
> My claim is absolutely true because every index supplied to a fraction is taken from a fraction: the integer fractions have to supply these indexes.

no, your claim is absolutely stupid, and intentionally misleading.

>>
>> It's correct to say that I don't use type 1 claims
>> in the the method which I advocate.
>
> You do, because you deny that every index supplied to a fraction is taken from a fraction.
>>
>>> My claim *is* true:
>>> In spite of your triangle numbers it is clear that
>>> in my matrix the share of enumerated fractions is |N|
>>> and the share of not enumerated fractions is
>>> |N|^2 - |N|, and that will never change.
>>> It is a true claim for the whole mapping.
>> This formula assigns a unique index to each fraction.
>> k = m+(m+n-1)*(m+n-2)/2
>
> That does not contradict my claim.
>>
>> "k is the index of m/n" is type 2.
>
> Yes, but every defined k has aleph_0 successors. Therefore your k do not cover all natnumbers. That is a type 2 recognition.

if you believe that, you do not believe in equations.

>
> Regards, WM

Re: Natural numbers and vases

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 20 May 2022 11:51:42 -0700
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 by: Chris M. Thomasson - Fri, 20 May 2022 18:51 UTC

On 5/20/2022 6:30 AM, sergi o wrote:
> On 5/20/2022 6:02 AM, WM wrote:
>> horand....@gmail.com schrieb am Donnerstag, 19. Mai 2022 um 16:28:19
>> UTC+2:
>>> On Thursday, 19 May 2022 at 10:56:45 UTC-3, WM wrote:
>>>> William schrieb am Mittwoch, 18. Mai 2022 um 16:27:56 UTC+2:
>>>>> No *element* of N_p is infinite. The *set* N_p is infinite.
>>>> Potentially infinite, never actually infinite. For that sake it must
>>>> have more than any natural number of numbers. This is impossible
>>>> with definable natural numbers since they count them selves and
>>>> never leave the finite domain.
>>>>
>>>> You claim that every natural number of N_p has aleph_0 successors
>>>> between itself and omega.
>>>> That implies that no natural number of N_p has less successors
>>>> between itself and omega.
>>>>
>>>> Do you agree?
>>>>
>>>> That implies that between all elements of the the set N_p and omega
>>>> there are aleph_0 successors.
>>> Ah, the quantifier switch. Nice!
>>
>> Here it is justified because the idea that no natural number of N_p
>> has less successors between itself and omega but they all together
>> cover these successors, is deepest medieval belief in black magic. And
>> I dare to guess that not even the stupidest witch hunters would have
>> believed that.
>>
>> Regards, WM
>
> you are outside of math, with your black numbers, magic math, it is
> stupid math.

dark numbers written on a contrasting color of paper can be read?
Imaging using black ink to write on a piece of paper that is black. WM's
dark numbers... ;^)

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
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 by: Jim Burns - Fri, 20 May 2022 19:25 UTC

On 5/20/2022 2:51 PM, Chris M. Thomasson wrote:
> On 5/20/2022 6:30 AM, sergi o wrote:
>> On 5/20/2022 6:02 AM, WM wrote:

>>> Regards, WM
>>
>> you are outside of math, with your black numbers,
>> magic math, it is stupid math.
>
> dark numbers written on a contrasting color of paper
> can be read? Imaging using black ink to write on a piece
> of paper that is black. WM's dark numbers... ;^)

I heard somewhere that black panthers have spots --
black-on-black spots.

The problem with WM's dark numbers is that
he thinks it's impossible to talk about
only non-black-panther leopards.

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 by: Chris M. Thomasson - Fri, 20 May 2022 20:26 UTC

On 5/20/2022 12:25 PM, Jim Burns wrote:
> On 5/20/2022 2:51 PM, Chris M. Thomasson wrote:
>> On 5/20/2022 6:30 AM, sergi o wrote:
>>> On 5/20/2022 6:02 AM, WM wrote:
>
>>>> Regards, WM
>>>
>>> you are outside of math, with your black numbers,
>>> magic math, it is  stupid math.
>>
>> dark numbers written on a contrasting color of paper
>> can be read?  Imaging using black ink to write on a piece
>> of paper that is black. WM's  dark numbers... ;^)
>
> I heard somewhere that black panthers have spots --
> black-on-black spots.
>
> The problem with WM's dark numbers is that
> he thinks it's impossible to talk about
> only non-black-panther leopards.
>

Excellent response! A Jacuzzi is a spa... However, not all spas are a
jacuzzi, in a sense... ;^)

Did I pick up on your sense, in a sense... :^)

Re: Natural numbers and vases

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https://www.novabbs.com/tech/article-flat.php?id=100574&group=sci.math#100574

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 20 May 2022 13:30:15 -0700
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 by: Chris M. Thomasson - Fri, 20 May 2022 20:30 UTC

On 5/8/2022 6:39 PM, sergio wrote:
> On 5/8/2022 4:09 PM, Chris M. Thomasson wrote:
>> On 5/8/2022 2:05 PM, sergio wrote:
>>> On 5/8/2022 3:26 PM, Chris M. Thomasson wrote:
>>>> On 5/8/2022 5:40 AM, WM wrote:
>>>>> William schrieb am Samstag, 7. Mai 2022 um 22:13:39 UTC+2:
>>>>>> On Saturday, May 7, 2022 at 8:33:00 AM UTC-3, WM wrote:
>>>>>>> William schrieb am Freitag, 6. Mai 2022 um 23:28:16 UTC+2:
>>>>>>
>>>>>>>> There is no element of N_p between the set N_p and omega.
>>>>>>> You can claim this nonsense,
>>>>>> Piffle. It is not nonsense. How could an element of N_p be between
>>>>>> the set N_p and omega?
>>>>>
>>>>> There are infinitely many dark natnumbers between the set N_p and
>>>>> omega.
>>>>>
>>>>>   It would have to be between itself and omega. Recall, N_p is a
>>>>> Peano set and thus has no "dark elements".
>>>>>
>>>>> Then the dark elements are between it and omega.
>>>>>
>>>>>> Whatever, if anything, is between the set N_p and omega it is not
>>>>>> an element of N_p
>>>>>
>>>>> It is dark.
>>>>
>>>> I am wondering if you would consider 1/2 to be dark between the
>>>> interval 0 and 1?
>>>>
>>>
>>> heads or tails when flipping a coin, but the thin edge of the dark in
>>> between heads and tails...
>>>
>>> (LL => dont use Fat coins)
>>
>> Ahhh. So, perhaps 1/2 is not dark but, .50000123004100042 might be?
>> Well, not now because I just wrote it down?
>
>
> according to WM, if no one is looking at it, or thinking about it, it is
> dark.
>
> so, according to WM, your number was dark, then non dark when you
> finished typing it, but went dark again when you stopped looking at it.
>
> So it is not dark now, as I am looking at it occasionally, but it is
> lights out for that dude when I send this out.
>

Interesting. Humm... Well, shit. All numbers are dark to a baby? Humm...
Almost all?

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Fri, 20 May 2022 21:29:47 +0000
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 by: Fritz Feldhase - Fri, 20 May 2022 21:29 UTC

On Friday, May 20, 2022 at 1:07:53 PM UTC+2, WM wrote:
> William schrieb am Donnerstag, 19. Mai 2022 um 16:25:02 UTC+2:
> >
> > Nope because the set, "all elements", can have a property that "each element" does not have.
> >
> You are outside of logic.

Ach, halt Dich mal die Fresse, Du Troll!

> The set is nothing else but all its elements.

Nonsense. Hint: The set {} is empty. Which of its elements is empty too?

The set {{0, 1}} contains exactly ONE element, namely the set {0, 1}, but this element contains ZWO elements, namely 0 and 1.

_______________________________________________________

Now: The set IN = {{}, {{}}, {{}, {{}}}, ...} is INFINITE, while each and every of its elements is FINITE.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Fri, 20 May 2022 21:34:13 +0000
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 by: Fritz Feldhase - Fri, 20 May 2022 21:34 UTC

On Friday, May 20, 2022 at 1:07:53 PM UTC+2, WM wrote:
> William schrieb am Donnerstag, 19. Mai 2022 um 16:25:02 UTC+2:
> >
> > Nope because the set, "all elements", can have a property that "each element" does not have.
> >
> You are outside of logic.

Ach, halt doch mal die Fresse, Du Troll!

> The set is nothing else but all its elements.

Nonsense. Hint: The set {} is empty. Which of its elements is empty too?

The set {{0, 1}} contains exactly ONE element, namely the set {0, 1}, but this element contains ZWO elements, namely 0 and 1.

_______________________________________________________

Now: The set IN = {{}, {{}}, {{}, {{}}}, ...} is INFINITE, while each and every of its elements is FINITE.

Re: Natural numbers and vases

<t6932m$a80$1@dont-email.me>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100580&group=sci.math#100580

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 20 May 2022 15:00:47 -0700
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 by: FromTheRafters - Fri, 20 May 2022 22:00 UTC

Jim Burns formulated on Friday :
> On 5/20/2022 2:51 PM, Chris M. Thomasson wrote:
>> On 5/20/2022 6:30 AM, sergi o wrote:
>>> On 5/20/2022 6:02 AM, WM wrote:
>
>>>> Regards, WM
>>>
>>> you are outside of math, with your black numbers,
>>> magic math, it is stupid math.
>>
>> dark numbers written on a contrasting color of paper
>> can be read? Imaging using black ink to write on a piece
>> of paper that is black. WM's dark numbers... ;^)
>
> I heard somewhere that black panthers have spots --
> black-on-black spots.
>
> The problem with WM's dark numbers is that
> he thinks it's impossible to talk about
> only non-black-panther leopards.

https://www.forbes.com/sites/kionasmith/2017/06/24/alan-turing-described-natures-beauty-with-numbers/?sh=737a7dfc77ae

Might be a paywall.

https://www.bbcearth.com/news/the-maths-behind-a-leopards-spots

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