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Uncompensated overtime? Just Say No.

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

SubjectAuthor
* Natural numbers and vases IIIWM
+* Re: Natural numbers and vases IIIFritz Feldhase
|+- Re: Natural numbers and vases IIIGus Gassmann
|`* Re: Natural numbers and vases IIIWM
| `- Re: Natural numbers and vases IIIsergi o
+* Re: Natural numbers and vases IIIsergi o
|`* Re: Natural numbers and vases IIIFromTheRafters
| +- Re: Natural numbers and vases IIIsergi o
| `* Re: Natural numbers and vases IIIWM
|  `* Re: Natural numbers and vases IIIsergi o
|   `- Re: Natural numbers and vases IIIsergi o
+* Re: Natural numbers and vases IIIWilliam
|`* Re: Natural numbers and vases IIIWM
| `* Re: Natural numbers and vases IIIWilliam
|  `* Re: Natural numbers and vases IIIWM
|   `* Re: Natural numbers and vases IIIWilliam
|    `* Re: Natural numbers and vases IIIWM
|     `* Re: Natural numbers and vases IIIWilliam
|      +* Re: Natural numbers and vases IIIWM
|      |`* Re: Natural numbers and vases IIIWilliam
|      | `* Re: Natural numbers and vases IIIWM
|      |  +* Re: Natural numbers and vases IIIWilliam
|      |  |+- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |+- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |+* Re: Natural numbers and vases IIIFritz Feldhase
|      |  ||`* Re: Natural numbers and vases IIIWM
|      |  || `* Re: Natural numbers and vases IIIsergi o
|      |  ||  `* Re: Natural numbers and vases IIIEram semper recta
|      |  ||   `- Re: Natural numbers and vases IIIEram semper recta
|      |  |`* Re: Natural numbers and vases IIIWM
|      |  | +- Re: Natural numbers and vases IIIsergi o
|      |  | `* Re: Natural numbers and vases IIIWilliam
|      |  |  +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |  |`* Re: Natural numbers and vases IIIWM
|      |  |  | +- Re: Natural numbers and vases IIIFromTheRafters
|      |  |  | `* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |  |  +* Re: Natural numbers and vases IIIWM
|      |  |  |  |`- Re: Natural numbers and vases IIIFromTheRafters
|      |  |  |  +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |  |  `- Re: Natural numbers and vases IIIGus Gassmann
|      |  |  `* Re: Natural numbers and vases IIIWM
|      |  |   +* Re: Natural numbers and vases IIIWilliam
|      |  |   |`* Re: Natural numbers and vases IIIWM
|      |  |   | +* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIIFromTheRafters
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||+* Re: Natural numbers and vases IIIFromTheRafters
|      |  |   | |||`- Re: Natural numbers and vases IIISurgio
|      |  |   | ||`* Re: Natural numbers and vases IIIJim Burns
|      |  |   | || +* Re: Natural numbers and vases IIIWM
|      |  |   | || |+- Re: Natural numbers and vases IIISergio
|      |  |   | || |`* Re: Natural numbers and vases IIIJim Burns
|      |  |   | || | `* Re: Natural numbers and vases IIIWM
|      |  |   | || |  `* Re: Natural numbers and vases IIISergio
|      |  |   | || |   `- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | || +* Re: Natural numbers and vases IIIWM
|      |  |   | || |`- Re: Natural numbers and vases IIISergio
|      |  |   | || +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || `- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISurgio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISurgio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`* Re: Natural numbers and vases IIISergio
|      |  |   | || +* Re: Natural numbers and vases IIIWM
|      |  |   | || |`* Re: Natural numbers and vases IIISergio
|      |  |   | || | +* Re: Natural numbers and vases IIIWM
|      |  |   | || | |`* Re: Natural numbers and vases IIISergio
|      |  |   | || | | `- Re: Natural numbers and vases IIIJim Africani
|      |  |   | || | `- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || `- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIFredJeffries
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIFredJeffries
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIFredJeffries
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |`* Re: Natural numbers and vases IIIWM
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
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|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
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|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
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|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
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|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
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+* Re: Natural numbers and vases IIIEram semper recta
+- Re: Natural numbers and vases IIIEduardo Faqtardo
+- Re: Natural numbers and vases IIIEram semper recta
+- Re: Natural numbers and vases IIIArchimedes Plutonium
`- Re: Natural numbers and vases IIIArchimedes Plutonium

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Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Fri, 22 Jul 2022 19:22:43 +0000
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 by: WM - Fri, 22 Jul 2022 19:22 UTC

William schrieb am Freitag, 22. Juli 2022 um 17:36:49 UTC+2:
> On Friday, July 22, 2022 at 9:55:21 AM UTC-3, WM wrote:

> > If all elements of |N could be removed element by element, then no successors would remain.
> Correct.
> >But that is not possible.
> So what? A stepwise process cannot show |N\|N_s={}.

And that is provable in general. It does not depend on time or ressources.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Fri, 22 Jul 2022 20:30 UTC

On Friday, July 22, 2022 at 4:22:48 PM UTC-3, WM wrote:
> William schrieb am Freitag, 22. Juli 2022 um 17:36:49 UTC+2:
> > On Friday, July 22, 2022 at 9:55:21 AM UTC-3, WM wrote:
>
> > > If all elements of |N could be removed element by element, then no successors would remain.
> > Correct.
> > >But that is not possible.
> > So what? A stepwise process cannot show |N\|N_s={}.
> And that is provable in general.

So what? We know that |N\N_s={} from methods (e.g. induction) that do work

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 22 Jul 2022 21:02 UTC

William schrieb am Freitag, 22. Juli 2022 um 22:30:28 UTC+2:
> On Friday, July 22, 2022 at 4:22:48 PM UTC-3, WM wrote:
> > William schrieb am Freitag, 22. Juli 2022 um 17:36:49 UTC+2:
> > > On Friday, July 22, 2022 at 9:55:21 AM UTC-3, WM wrote:
> >
> > > > If all elements of |N could be removed element by element, then no successors would remain.
> > > Correct.
> > > >But that is not possible.
> > > So what? A stepwise process cannot show |N\|N_s={}.
> > And that is provable in general.
> So what? We know that |N\N_s={} from methods (e.g. induction) that do work
>
Induction does not work. I works for every finite set but not for the infinite set. Any other method?

Regards, WM

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Fri, 22 Jul 2022 21:19 UTC

> Induction does not work.

Piffle. Induction shows that each element of |N (without exception.e.g. elements that cannot be written down) is an element of |N_s.

--
William Hughes

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
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Subject: Re: Natural numbers and vases III
Date: Fri, 22 Jul 2022 20:02:28 -0400
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 by: FromTheRafters - Sat, 23 Jul 2022 00:02 UTC

WM has brought this to us :
> William schrieb am Freitag, 22. Juli 2022 um 22:30:28 UTC+2:
>> On Friday, July 22, 2022 at 4:22:48 PM UTC-3, WM wrote:
>>> William schrieb am Freitag, 22. Juli 2022 um 17:36:49 UTC+2:
>>>> On Friday, July 22, 2022 at 9:55:21 AM UTC-3, WM wrote:
>>>>> If all elements of |N could be removed element by element, then no
>>>>> successors would remain. Correct. But that is not possible.
>>>> So what? A stepwise process cannot show |N\|N_s={}.
>>> And that is provable in general.
>> So what? We know that |N\N_s={} from methods (e.g. induction) that do work
>>
> Induction does not work. I works for every finite set but not for the
> infinite set. Any other method?

That's a keeper.

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From: inva...@invalid.com (Surgio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 22 Jul 2022 19:43:42 -0500
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 by: Surgio - Sat, 23 Jul 2022 00:43 UTC

On 7/22/2022 7:02 PM, FromTheRafters wrote:
> WM has brought this to us :
>> William schrieb am Freitag, 22. Juli 2022 um 22:30:28 UTC+2:
>>> On Friday, July 22, 2022 at 4:22:48 PM UTC-3, WM wrote:
>>>> William schrieb am Freitag, 22. Juli 2022 um 17:36:49 UTC+2:
>>>>> On Friday, July 22, 2022 at 9:55:21 AM UTC-3, WM wrote:
>>>>>> If all elements of |N could be removed element by element, then no successors would remain.  Correct.  But that is not possible.
>>>>> So what? A stepwise process cannot show |N\|N_s={}.
>>>> And that is provable in general.
>>> So what? We know that |N\N_s={} from methods (e.g. induction) that do work
>> Induction does not work. I works for every finite set but not for the infinite set. Any other method?
>
> That's a keeper.

agree! a peek inside the mind of WM!

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Sat, 23 Jul 2022 10:02 UTC

onsdag 20 juli 2022 kl. 13:14:19 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Mittwoch, 20. Juli 2022 um 06:56:48 UTC+2:
> > tisdag 19 juli 2022 kl. 20:49:41 UTC+2 skrev WM:
> > > William schrieb am Dienstag, 19. Juli 2022 um 18:30:29 UTC+2:
> > >
> > > > WM: Defined = finite,
> > >
> > > as an abbreviation of: subset of defined elements = finite subset.
> > >
> > which means it has a largest element.
> Try to find it. I will give you a larger one.
>
> Regards, WM

If you can always find a larger one, then it is infinite. Contradiction.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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 by: zelos...@gmail.com - Sat, 23 Jul 2022 10:04 UTC

onsdag 20 juli 2022 kl. 13:25:23 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Mittwoch, 20. Juli 2022 um 06:55:20 UTC+2:
> > tisdag 19 juli 2022 kl. 14:21:25 UTC+2 skrev WM:
> > > Dark successors and definable elements are the elements of |N.
> > There is nothing "dark"
>
> Proof: ∩{E(k) : k ∈ ℕ} = { }

You don't give proofs, you give assertions.

> But apply the Minorantenkriterium for infinite sequences.
> There is a sequence (S(k)) where S(k) = |∩{E(1), E(2), ..., E(k)} = ℵ₀ .

Correct, noting how that is a finite collection of endsegments while previous was an infinite.

> This sequence has a minorante
> (M(k)) where M(k) = 10 for all k.
>
> According to mathematics, the limit of (S(k)) cannot be less than the limit of (M(k)), if (S(k)) has a limit at all.

and false. You are going from intersection to limits to random ass pulls, you are as always wrong.

> > > > > We don't remove the set but all its elements. If this is not the same, then something is wrong in Cantor-land.
>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 23 Jul 2022 13:04 UTC

William schrieb am Freitag, 22. Juli 2022 um 23:19:38 UTC+2:
> > Induction does not work.
>
> Piffle. Induction shows that each element of |N (without exception.e.g. elements that cannot be written down) is an element of |N_s.

Induction shows that induction cannot show anything about almost all natural numbers.

You said recently: Correct is to say "removing any element of |N_s leaves infinitely many successors". However "them", |N_s, is not an element of |N_s

That means you cannot handle all elements of |N_s individually but only as the set.
Why? Dark numbrs!

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Sat, 23 Jul 2022 09:40:20 -0500
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 by: Surgio - Sat, 23 Jul 2022 14:40 UTC

On 7/23/2022 8:04 AM, WM wrote:
> William schrieb am Freitag, 22. Juli 2022 um 23:19:38 UTC+2:
>>> Induction does not work.
>>
>> Piffle. Induction shows that each element of |N (without exception.e.g. elements that cannot be written down) is an element of |N_s.
>
> Induction shows that induction cannot show anything about almost all natural numbers.

Liar.

>
> You said recently: Correct is to say "removing any element of |N_s leaves infinitely many successors".

> However "them", |N_s, is not an element of |N_s

wrong.

>
> That means you cannot handle all elements of |N_s individually but only as the set.

still wrong.

> Why? Dark numbrs!

no such thing.

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Sat, 23 Jul 2022 15:08 UTC

On Saturday, July 23, 2022 at 10:04:51 AM UTC-3, WM wrote:

> ... You said recently: Correct is to say "removing any element of |N_s leaves infinitely many successors". However "them", |N_s, is not an element of |N_s

Correct. Induction does not prove the *set* |N has some property, it proves that each *element* of IN has some property. In particular: Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 23 Jul 2022 15:26 UTC

William schrieb am Samstag, 23. Juli 2022 um 17:08:36 UTC+2:
> Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.

Finally you see the difference between each individually definable element and all (mostly undefinable) elements?

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Sat, 23 Jul 2022 15:41 UTC

lördag 23 juli 2022 kl. 17:26:51 UTC+2 skrev WM:
> William schrieb am Samstag, 23. Juli 2022 um 17:08:36 UTC+2:
> > Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.
> Finally you see the difference between each individually definable element and all (mostly undefinable) elements?
>
> Regards, WM
you still have not defined any of those terms you retard

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Sat, 23 Jul 2022 16:22 UTC

On Saturday, July 23, 2022 at 12:26:51 PM UTC-3, WM wrote:
> William schrieb am Samstag, 23. Juli 2022 um 17:08:36 UTC+2:
> > Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.
> Finally
You acknowledge something I have said many times.
All or your "contradictions" are based on the false idea that the set |N is followed by an element of |N.
--
William Hughes

Re: Natural numbers and vases III

<tbh8e1$1pbc$1@gioia.aioe.org>

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From: inva...@invalid.com (Surgio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 23 Jul 2022 11:42:39 -0500
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 by: Surgio - Sat, 23 Jul 2022 16:42 UTC

On 7/23/2022 10:26 AM, WM wrote:
> William schrieb am Samstag, 23. Juli 2022 um 17:08:36 UTC+2:
>> Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.
>
> Finally you see the difference between each individually definable element and all (mostly undefinable) elements?
>
> Regards, WM
>
>

your definition of "definable" is ridiculous, and its use always signals the stop of real math, and direct return to your phony made up silly math.

"definable" => with its "colors of the rainbow", beeps, raps, flashes, and if you only have a duck available, then QuAcKs should work too !

Re: Natural numbers and vases III

<931c35be-36ea-53dc-e4c9-f8c6758c833b@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 23 Jul 2022 14:14:35 -0400
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 by: Jim Burns - Sat, 23 Jul 2022 18:14 UTC

On 7/22/2022 5:02 PM, WM wrote:
> William schrieb
> am Freitag, 22. Juli 2022 um 22:30:28 UTC+2:

>> We know that |N\N_s={}
>> from methods (e.g. induction) that do work
>
> Induction does not work.
> I works for every finite set
> but not for the infinite set.

No.

"Induction works for k"
can be derived from
"k is in some ⟨0⋯i,i+1⋯n⟩"

Induction works for each k in each ⟨0⋯i,i+1⋯n⟩
and each ⟨0⋯i,i+1⋯n⟩ is finite.
However,
no ⟨0⋯i,i+1⋯𝔊⟩ is possible which contains
each k for which induction works.

⋃{⟨0⋯i,i+1⋯?⟩} contains
each k in some ⟨0⋯i,i+1⋯n⟩ with any end n
⋃{⟨0⋯i,i+1⋯?⟩} is infinite.

No ⟨0⋯i,i+1⋯𝔊⟩ is possible such that
⟨0⋯i,i+1⋯𝔊⟩ = ⋃{⟨0⋯i,i+1⋯?⟩}

| Whatever 𝔊 could possibly be,
| ⟨0⋯i,i+1⋯𝔊⟩ ⊆ ⋃{⟨0⋯i,i+1⋯?⟩}
| | However
| 𝔊+1 ∉ ⟨0⋯i,i+1⋯𝔊⟩
| and also
| ⟨0⋯i,i+1⋯𝔊,𝔊+1⟩ ⊆ ⋃{⟨0⋯i,i+1⋯?⟩}
| | ⟨0⋯i,i+1⋯𝔊⟩ ≠ ⋃{⟨0⋯i,i+1⋯?⟩}

----
𝔊+1 ∉ ⟨0⋯i,i+1⋯𝔊⟩

| Assume otherwise.
| Assume 𝔊+1 ∈ ⟨0⋯i,i+1⋯𝔊⟩
| | ⟨0⋯i,i+1⋯𝔊⟩ is a collection such that
| for each split, a step i,i+1 exists such that
| i is last before and i+1 is first after,
| and
| the collection begins at 0
| and
| the collection ends somewhere.
| | In this case, its second end is 𝔊
| | If
| 𝔊+1 was in ⟨0⋯i,i+1⋯𝔊⟩
| then
| there would be a split {k=<𝔊},{𝔊+1=<k}
| with 𝔊 before the split,
| and
| 𝔊 would not be its second end.
| Contradiction.

----
"Induction works for k"
can be derived from
"k is in some ⟨0⋯i,i+1⋯n⟩"

| Assume that k is in some ⟨0⋯i,i+1⋯n⟩
| | Assume P(0) ∧ ~P(k)
| | Define a split BEFORE,AFTER of ⟨0⋯i,i+1⋯k⟩
| such that
| AFTER contains all j such that
| ∃jₚ, ~P(jₚ) ∧ jₚ =< j
| BEFORE contains all j not in AFTER
| | Because ⟨0⋯i,i+1⋯k⟩
| some step i,i+1 exists such that
| BEFORE ends at i
| AFTER begins at i+1
| | From the definition of BEFORE,AFTER
| ∃jₚ, ~P(jₚ) ∧ jₚ =< j
| we know that
| P(i) ∧ ~P(i+1)

Therefore,
if
∃k ∈ ⟨0⋯i,i+1⋯n⟩, P(0) & ~P(k)
then
∃i ∈ ⟨0⋯i,i+1⋯k⟩, P(i) & ~P(i+1)

Consider ⋃{⟨0⋯i,i+1⋯?⟩}

If we can prove
~∃i ∈ ⋃{⟨0⋯i,i+1⋯?⟩}, P(i) & ~P(i+1)
the we have proved
~∃k ∈ ⋃{⟨0⋯i,i+1⋯?⟩}, P(0) & ~P(k)

Then, if we can prove
P(0)
then we have proved
~∃k ∈ ⋃{⟨0⋯i,i+1⋯?⟩}, ~P(k)

That is induction:
If
P(0) and
~∃i ∈ ⋃{⟨0⋯i,i+1⋯?⟩}, P(i) & ~P(i+1)
then
~∃k ∈ ⋃{⟨0⋯i,i+1⋯?⟩}, ~P(k)

Induction is more often written,
with ℕ = ⋃{⟨0⋯i,i+1⋯?⟩}, as:
If
P(0) and
∀i ∈ ℕ, P(i) -> ~P(i+1)
then
∀k ∈ ℕ, P(k)

----
Different is not the same as contradictory.
Finite sets and infinite sets have different
properties. For example...

For each pair n,1 in ℕ = ⋃{⟨0⋯i,i+1⋯?⟩}
there is a unique pair p,q in ℕ
s = ⌈((⎷(8*n+1)+1)/2)⌉
p = n - (s-1)*(s-2)/2
q = s - p

For each pair p,q in ℕ = ⋃{⟨0⋯i,i+1⋯?⟩}
there is a unique pair n,1 in ℕ
s = p+q
n = (s-1)*(s-2)/2 + p

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 23 Jul 2022 20:59 UTC

William schrieb am Samstag, 23. Juli 2022 um 18:22:29 UTC+2:
> On Saturday, July 23, 2022 at 12:26:51 PM UTC-3, WM wrote:
> > William schrieb am Samstag, 23. Juli 2022 um 17:08:36 UTC+2:
> > > Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.
> > Finally
> You acknowledge something I have said many times.

With great pleasure!
But in addition I am asking why is that so?

> All or your "contradictions" are based on the false idea that the set |N is followed by an element of |N.

Not at all! The contradiction with the claim that all natnunbers can be individually defined is caused by the fact that not all natnumbers can be individually defined, but all individually defined natnumbers have more successors than predecessors. So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Sat, 23 Jul 2022 21:24 UTC

On Saturday, July 23, 2022 at 5:59:07 PM UTC-3, WM wrote:
> So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.

So what? Each element of |N (whether or not it has the property "can be individually defined (i.e. can be written down)") has the property that it has an infinite number of successors.

--
William Hughes

Re: Natural numbers and vases III

<tbid39$agu$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
Date: Sat, 23 Jul 2022 22:08:24 -0500
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 by: Sergio - Sun, 24 Jul 2022 03:08 UTC

On 7/23/2022 3:59 PM, WM wrote:
> William schrieb am Samstag, 23. Juli 2022 um 18:22:29 UTC+2:
>> On Saturday, July 23, 2022 at 12:26:51 PM UTC-3, WM wrote:
>>> William schrieb am Samstag, 23. Juli 2022 um 17:08:36 UTC+2:
>>>> Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.
>>> Finally
>> You acknowledge something I have said many times.
>
> With great pleasure!
> But in addition I am asking why is that so?
>
>> All or your "contradictions" are based on the false idea that the set |N is followed by an element of |N.
>
> Not at all! The contradiction with the claim that all natnunbers can be individually defined is caused by the fact that not all natnumbers can be individually defined, but all individually defined natnumbers have more successors than predecessors. So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.
>

You're just lost in the woods with this subject, and you do not know what you are talking about.

You built your math on your phoney daffynition of "defined" usings raps, taps, colors of the rainbow, so *it will never make sense to you* or anyone else.

Fact: Each and every natural number has more successors than predecessors, and that fact has noting to do with your smoke and mirrors of "individually"
or "defined"

your very rough estimation of half, underscores the fact that you do not know math involving infinite sets.

> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Sun, 24 Jul 2022 06:07 UTC

lördag 23 juli 2022 kl. 22:59:07 UTC+2 skrev WM:
> William schrieb am Samstag, 23. Juli 2022 um 18:22:29 UTC+2:
> > On Saturday, July 23, 2022 at 12:26:51 PM UTC-3, WM wrote:
> > > William schrieb am Samstag, 23. Juli 2022 um 17:08:36 UTC+2:
> > > > Each element of |N is followed by an infinite number of elements of |N, the set |N is not followed by an element of |N.
> > > Finally
> > You acknowledge something I have said many times.
> With great pleasure!
> But in addition I am asking why is that so?
> > All or your "contradictions" are based on the false idea that the set |N is followed by an element of |N.
> Not at all! The contradiction with the claim that all natnunbers can be individually defined is caused by the fact that not all natnumbers can be individually defined, but all individually defined natnumbers have more successors than predecessors. So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.
>
> Regards, WM
your "Individually defined" doesn't mean anything!

>but all individually defined natnumbers have more successors than predecessors

WHICH IS ALL OF THE NATURAL NUMBERS!

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sun, 24 Jul 2022 14:08 UTC

William schrieb am Samstag, 23. Juli 2022 um 23:24:40 UTC+2:
> On Saturday, July 23, 2022 at 5:59:07 PM UTC-3, WM wrote:
> > So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.
> So what? Each element of |N (whether or not it has the property "can be individually defined (i.e. can be written down)") has the property that it has an infinite number of successors.

So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.
Removing all elements which have infinitely many successors leaves these successors.
Removing the set |N leaves nothing.
What is the difference?

Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Date: Sun, 24 Jul 2022 07:08:44 -0700 (PDT)
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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sun, 24 Jul 2022 14:08 UTC

zelos...@gmail.com schrieb am Sonntag, 24. Juli 2022 um 08:07:21 UTC+2:

> >but all individually defined natnumbers have more successors than predecessors
> WHICH IS ALL OF THE NATURAL NUMBERS!

So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.
Removing all elements which have infinitely many successors leaves these successors.
Removing the set |N leaves nothing.
What is the difference?

Regards, WM

Re: Natural numbers and vases III

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

Jim Burns schrieb am Samstag, 23. Juli 2022 um 20:14:46 UTC+2:

> Induction works for each k in each ⟨0⋯i,i+1⋯n⟩

Yes.

> However,
> no ⟨0⋯i,i+1⋯𝔊⟩ is possible which contains
> each k for which induction works.

Induction shows that each k for which induction works has finitely many predecessors and by far mr successors.Therefore a rough estimation shows that induction works for less than half of all natnumbers.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Sun, 24 Jul 2022 14:40 UTC

On Sunday, July 24, 2022 at 11:08:40 AM UTC-3, WM wrote:

> Removing all elements which have infinitely many successors leaves these successors.

Piffle. "All elements which have infinitely many successors" is the set |N. Removing the set |N leaves nothing.
So removing "all elements which have infinitely many successors" leaves nothing.

--
William Hughes

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
Date: Sun, 24 Jul 2022 09:50:17 -0500
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 by: Sergio - Sun, 24 Jul 2022 14:50 UTC

On 7/24/2022 9:08 AM, WM wrote:
> zelos...@gmail.com schrieb am Sonntag, 24. Juli 2022 um 08:07:21 UTC+2:
>
>>> but all individually defined natnumbers have more successors than predecessors
>> WHICH IS ALL OF THE NATURAL NUMBERS!
>
> So a very rough estimation shows that at least half of all natnumbers cannot be individually defined.

liar.

> Removing all elements which have infinitely many successors leaves these successors.

each and every element of the set of natural numbers has an infinite number of successors.

each and every successor is an element of the set.

by remove each and every element, you have removed all successors too.

> Removing the set |N leaves nothing.
> What is the difference?

what do you mean by "removing" ?

>
> Regards, WM

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

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