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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
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- 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 IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- 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 IIIFritz Feldhase
|      |  |   | +- 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 IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
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|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
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|      |  |   | +- 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
|      |  |   | +- 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
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- 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
|      |  |   | +- 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
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
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|      |  |   | +- 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 IIIzelos...@gmail.com
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|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
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|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
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|      |  |   | +* 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 IIIzelos...@gmail.com
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|      |  |   | +- 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 IIIGus Gassmann
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|      |  |   | +- 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 IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
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|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +* 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 IIIEram semper recta
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|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- 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 IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- 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 IIIFromTheRafters
|      |  `* Re: Natural numbers and vases IIIzelos...@gmail.com
|      `* Re: Natural numbers and vases IIIFritz Feldhase
+* Re: Natural numbers and vases IIIzelos...@gmail.com
+* 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: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Tue, 6 Sep 2022 10:26 UTC

On Tuesday, 6 September 2022 at 07:01:14 UTC-3, WM wrote:
> Gus Gassmann schrieb am Sonntag, 4. September 2022 um 16:27:38 UTC+2:
> > On Sunday, 4 September 2022 at 11:02:17 UTC-3, WM wrote:
> > [...]
> > > That does not matter. Any bathtub that is not empty will do.
> > > And possibly some logic: As long as it is not empty, it is not empty and was not empty before.
> > Correct.
> > > Therefore the intersection of its states is not empty.
> > Nope. I thought your entire point was that the bathtub _can_ empty. Unlike the intersection of an infinite number of end segments, however, the bathtub is guaranteed to empty in finite time
> No, it may happen that at every time only half of its contents is lost.

No, that may not happen, you fucking imbecile. Once you are down to a single H20 molecule, the bathtub process stops, with that molecule either in, or out.

> > The intersection of end segments is not empty for any finite collection of end segments, and is empty for any infinite collection.
> Wrong.

Right.

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 - Tue, 6 Sep 2022 11:40 UTC

Jim Burns schrieb am Sonntag, 4. September 2022 um 19:26:25 UTC+2:

> ๐ตโ‚– is NOT between all of ๐“” and โˆ…

There is nothing between all endsegments and โˆ….
There is infinitely many between all infinite endsegments and โˆ….

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 - Tue, 6 Sep 2022 11:44 UTC

Jim Burns schrieb am Sonntag, 4. September 2022 um 20:17:03 UTC+2:

> โˆ… is next[2] after all of ๐“”

Yes.

> No set exists which is after (โŠ‚) each ๐ธ โˆˆ ๐“”
> and before (โŠƒ) โˆ…

Yes.

But after all *infinite* endsegments there exist infinitely many endsegments because an endegment can lose only one natnumber:

โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

Regards, WM

Re: Natural numbers and vases III

<tf7db0$3tcp6$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 06 Sep 2022 08:10:04 -0400
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 by: FromTheRafters - Tue, 6 Sep 2022 12:10 UTC

WM submitted this idea :
> Jim Burns schrieb am Sonntag, 4. September 2022 um 20:17:03 UTC+2:
>
>> โˆ… is next[2] after all of ?
>
> Yes.
>
>> No set exists which is after (โŠ‚) each ? โˆˆ ?
>> and before (โŠƒ) โˆ…
>
> Yes.
>
> But after all *infinite* endsegments

The terms FISON and infinite endsegment are redundant. All Initial
Segments of Natural Numbers (ISONs) are Finite and all of their
associated endsegments are infinite and complementary to their ISONs.

Re: Natural numbers and vases III

<6c60045b-8b29-481c-bcd8-c70382e80641n@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 6 Sep 2022 12:33 UTC

FromTheRafters schrieb am Dienstag, 6. September 2022 um 14:10:17 UTC+2:
> WM submitted this idea :
> > Jim Burns schrieb am Sonntag, 4. September 2022 um 20:17:03 UTC+2:
> >
> >> โˆ… is next[2] after all of ?
> >
> > Yes.
> >
> >> No set exists which is after (โŠ‚) each ? โˆˆ ?
> >> and before (โŠƒ) โˆ…
> >
> > Yes.
> >
> > But after all *infinite* endsegments
> The terms FISON and infinite endsegment are redundant. All Initial
> Segments of Natural Numbers (ISONs) are Finite and all of their
> associated endsegments are infinite and complementary to their ISONs.

No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs. Finite endsegments are necessarily undefined and undefinable. But if all natural numbers are existing and can be exhausted, then, according to
โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}
finite endsegments must exist too.

Regards, WM

Re: Natural numbers and vases III

<a80097a0-773c-486c-a638-7c95a3807ff5n@googlegroups.com>

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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 - Tue, 6 Sep 2022 12:37 UTC

tisdag 6 september 2022 kl. 14:33:59 UTC+2 skrev WM:
> FromTheRafters schrieb am Dienstag, 6. September 2022 um 14:10:17 UTC+2:
> > WM submitted this idea :
> > > Jim Burns schrieb am Sonntag, 4. September 2022 um 20:17:03 UTC+2:
> > >
> > >> โˆ… is next[2] after all of ?
> > >
> > > Yes.
> > >
> > >> No set exists which is after (โŠ‚) each ? โˆˆ ?
> > >> and before (โŠƒ) โˆ…
> > >
> > > Yes.
> > >
> > > But after all *infinite* endsegments
> > The terms FISON and infinite endsegment are redundant. All Initial
> > Segments of Natural Numbers (ISONs) are Finite and all of their
> > associated endsegments are infinite and complementary to their ISONs.
> No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs. Finite endsegments are necessarily undefined and undefinable. But if all natural numbers are existing and can be exhausted, then, according to
> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}
> finite endsegments must exist too.
>
> Regards, WM
False, it means nothing of the sort

Re: Natural numbers and vases III

<tf7ik4$f3o$3@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 6 Sep 2022 08:40:19 -0500
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 by: Sergio - Tue, 6 Sep 2022 13:40 UTC

On 9/6/2022 6:40 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 4. September 2022 um 19:26:25 UTC+2:
>
>> ๐ตโ‚– is NOT between all of ๐“” and โˆ…
>
> There is nothing between all endsegments and โˆ….
> There is infinitely many between all infinite endsegments and โˆ….
>
> Regards, WM

try to follow his proof.

Re: Natural numbers and vases III

<tf7inn$f3o$4@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 6 Sep 2022 08:42:14 -0500
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 by: Sergio - Tue, 6 Sep 2022 13:42 UTC

On 9/6/2022 6:44 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 4. September 2022 um 20:17:03 UTC+2:
>
>> โˆ… is next[2] after all of ๐“”
>
> Yes.
>
>> No set exists which is after (โŠ‚) each ๐ธ โˆˆ ๐“”
>> and before (โŠƒ) โˆ…
>
> Yes.
>
> But after all *infinite* endsegments there exist infinitely many endsegments because an endegment can lose only one natnumber:
>
> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .
>
> Regards, WM

wrong, that does not make any sense. What do you mean by "after all" in terms of mathematics, use an equation please.

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 6 Sep 2022 08:43:15 -0500
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 by: Sergio - Tue, 6 Sep 2022 13:43 UTC

On 9/6/2022 7:33 AM, WM wrote:
> FromTheRafters schrieb am Dienstag, 6. September 2022 um 14:10:17 UTC+2:
>> WM submitted this idea :
>>> Jim Burns schrieb am Sonntag, 4. September 2022 um 20:17:03 UTC+2:
>>>
>>>> โˆ… is next[2] after all of ?
>>>
>>> Yes.
>>>
>>>> No set exists which is after (โŠ‚) each ? โˆˆ ?
>>>> and before (โŠƒ) โˆ…
>>>
>>> Yes.
>>>
>>> But after all *infinite* endsegments
>> The terms FISON and infinite endsegment are redundant. All Initial
>> Segments of Natural Numbers (ISONs) are Finite and all of their
>> associated endsegments are infinite and complementary to their ISONs.
>
> No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs. Finite endsegments are necessarily undefined and undefinable. But if all natural numbers are existing and can be exhausted, then, according to
> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}
> finite endsegments must exist too.
>
> Regards, WM

the cheese has slid off your cracker.

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 6 Sep 2022 08:44:45 -0500
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 by: Sergio - Tue, 6 Sep 2022 13:44 UTC

On 9/6/2022 5:26 AM, Gus Gassmann wrote:
> On Tuesday, 6 September 2022 at 07:01:14 UTC-3, WM wrote:
>> Gus Gassmann schrieb am Sonntag, 4. September 2022 um 16:27:38 UTC+2:
>>> On Sunday, 4 September 2022 at 11:02:17 UTC-3, WM wrote:
>>> [...]
>>>> That does not matter. Any bathtub that is not empty will do.
>>>> And possibly some logic: As long as it is not empty, it is not empty and was not empty before.
>>> Correct.
>>>> Therefore the intersection of its states is not empty.
>>> Nope. I thought your entire point was that the bathtub _can_ empty. Unlike the intersection of an infinite number of end segments, however, the bathtub is guaranteed to empty in finite time
>> No, it may happen that at every time only half of its contents is lost.
>
> No, that may not happen, you fucking imbecile. Once you are down to a single H20 molecule, the bathtub process stops, with that molecule either in, or out.
>
>>> The intersection of end segments is not empty for any finite collection of end segments, and is empty for any infinite collection.
>> Wrong.
>
> Right.

careful, WM will drag out Scrooge McDuck next

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 6 Sep 2022 08:45:51 -0500
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 by: Sergio - Tue, 6 Sep 2022 13:45 UTC

On 9/6/2022 5:07 AM, WM wrote:
> Jim Burns schrieb am Dienstag, 6. September 2022 um 00:24:09 UTC+2:
>
>> Remember that, for each ๐น,
>> ((โ‹ƒ๐“•)โŠ•๐”ป)\๐น โ‰  ๐”ป
>
> It is larger.
>>
>> If ๐”ป = โˆ…,
>> ((โ‹ƒ๐“•)โŠ•โˆ…)\๐น โ‰  โˆ…
>
> ๐”ป =/= โˆ…
>>
>> The bathtub is never empty.
>> And the intersection of bathtub-states
>> is empty.
>
> Wrong. Much ado before an unjustified conclusion.
>
> Regards WM
>

No, Jim was correct in his proof.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Tue, 6 Sep 2022 15:38 UTC

On Tuesday, 6 September 2022 at 09:33:59 UTC-3, WM wrote:
[...]
> No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs.

This is correct, since every end segment is infinite. In particular, every end segment has cardinality aleph_0.

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 06 Sep 2022 11:43:36 -0400
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 by: FromTheRafters - Tue, 6 Sep 2022 15:43 UTC

on 9/6/2022, WM supposed :
> FromTheRafters schrieb am Dienstag, 6. September 2022 um 14:10:17 UTC+2:
>> WM submitted this idea :
>>> Jim Burns schrieb am Sonntag, 4. September 2022 um 20:17:03 UTC+2:
>>>
>>>> โˆ… is next[2] after all of ?
>>>
>>> Yes.
>>>
>>>> No set exists which is after (โŠ‚) each ? โˆˆ ?
>>>> and before (โŠƒ) โˆ…
>>>
>>> Yes.
>>>
>>> But after all *infinite* endsegments
>> The terms FISON and infinite endsegment are redundant. All Initial
>> Segments of Natural Numbers (ISONs) are Finite and all of their
>> associated endsegments are infinite and complementary to their ISONs.
>
> No. A FISON defines all its numbers. Therefore finite endsegments

Finite endsegments of |N* (the non-zero natural numbers)?

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Tue, 6 Sep 2022 14:02:19 -0400
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 by: Jim Burns - Tue, 6 Sep 2022 18:02 UTC

On 9/6/2022 7:40 AM, WM wrote:
> Jim Burns schrieb am Sonntag,
> 4. September 2022 um 19:26:25 UTC+2:

>> ๐ตโ‚– is NOT between all of ๐“” and โˆ…
>
> There is nothing between
> all endsegments and โˆ….

๐“” is the set of all
infinite end segments of โ‹ƒ๐“•

> There is infinitely many between
> all infinite endsegments and โˆ….

No.

๐“”[โ‹ƒ๐“•,ฯ‰] is the set of all
infinite end segments of โ‹ƒ๐“•

No set exists between all of ๐“”[โ‹ƒ๐“•,ฯ‰] and โˆ…

โ‹ƒ๐“• is an infinite end segment of โ‹ƒ๐“•
โ‹ƒ๐“• โˆˆ ๐“”[โ‹ƒ๐“•,ฯ‰]

If
๐ตโ‚– is between all of ๐“”[โ‹ƒ๐“•,ฯ‰] and โˆ…
then
๐ตโ‚– is between โ‹ƒ๐“• and โˆ…
and
๐ตโ‚– is a non-empty subset of โ‹ƒ๐“•
and
for at least one k โˆˆ โ‹ƒ๐“•, k โˆˆ ๐ตโ‚–

For each k โˆˆ โ‹ƒ๐“•
there is at least one
infinite end segment ๐ธโ‚–โ‚Šโ‚ of โ‹ƒ๐“• without k
๐ธโ‚–โ‚Šโ‚ โˆˆ ๐“”[โ‹ƒ๐“•,ฯ‰] and k โˆ‰ ๐ธโ‚–โ‚Šโ‚

If
๐ตโ‚– is between all of ๐“”[โ‹ƒ๐“•,ฯ‰] and โˆ…
then
๐ตโ‚– is between ๐ธโ‚–โ‚Šโ‚ and โˆ…
and
๐ตโ‚– is a subset of ๐ธโ‚–โ‚Šโ‚

However,
๐ตโ‚– is NOT a subset of ๐ธโ‚–โ‚Šโ‚
k โˆˆ ๐ตโ‚– but k โˆ‰ ๐ธโ‚–โ‚Šโ‚
Contradiction.

Therefore,
๐ตโ‚– is NOT between all of ๐“”[โ‹ƒ๐“•,ฯ‰] and โˆ…

No set exists between all of ๐“”[โ‹ƒ๐“•,ฯ‰] and โˆ…

Re: Natural numbers and vases III

<67268ea8-d751-3d33-cf63-598359484759@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 6 Sep 2022 15:56:39 -0400
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 by: Jim Burns - Tue, 6 Sep 2022 19:56 UTC

On 9/6/2022 6:07 AM, WM wrote:
> Jim Burns schrieb am Dienstag,
> 6. September 2022 um 00:24:09 UTC+2:

>> Remember that, for each ๐น,
>> ((โ‹ƒ๐“•)โŠ•๐”ป)\๐น โ‰  ๐”ป
>
> It is larger.

When I see these hyper-vague sentences,
an image pops into my head of
a car thief filing serial numbers off
a car engine.

WHAT is larger than WHAT in WHAT sense?

>> If ๐”ป = โˆ…,
>> ((โ‹ƒ๐“•)โŠ•โˆ…)\๐น โ‰  โˆ…
>
> ๐”ป =/= โˆ…

๐”ป is the water that never leaks.

You (WM) claim that,
if
the intersection of bathtub-states
is empty,
then
one of the bathtub-states is empty.

If
๐”ป โ‰  โˆ…
then
the intersection of all bathtub-states
is not empty
but
none of the bathtub-states is empty

If
๐”ป โ‰  โˆ…
then
that "๐”ป โ‰  โˆ…" leaky bathtub
is irrelevant to your claim.

On the other hand,
we could consider a bathtub
from which all of its water leaks
๐”ป = โˆ…
in which all leaks are followed by more leaks
โˆ€๐น, โˆƒ๐น', ๐น โŠ‚ ๐น'

In each state, there is still more
water yet to be leaked.
That bathtub is never empty.

Any water in the bathtub leaks.
For that water, there is a state in which
it is not in the tub.
The intersection of bathtub-states is empty.

"All leaks are followed by more leaks"
isn't a bad way to think of all the FISONs.

Each FISON ๐นโ‚™ is followed by more FISONs.
In particular, ๐นโ‚™โˆชโŸจn+1โŸฉ is a FISON too.

And, of course, each FISON represents a leak.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: heeee198...@gmail.com (Kristjan Robam)
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 by: Kristjan Robam - Wed, 7 Sep 2022 08:12 UTC

Hey Jim......

Wazzzzaaaa ? Something interesting ?

Jim Burns kirjutas Kolmapรคev, 31. august 2022 kl 10:41:04 UTC-7:
> On 8/31/2022 9:02 AM, WM wrote:
> > Jim Burns schrieb am Dienstag,
> > Jim Burns schrieb am Dienstag,
> >> On 8/30/2022 3:51 PM, WM wrote:
>
> >>> What obstacle would hinder to collect
> >>> as many definable endsegments as possible?
> >>
> >> No obstacle. Say
> >> "This collection contains all and only
> >> (definable) end segments."
> >
> > and has an infinite intersection:
> > |โˆฉ{E(1), E(2), ..., E(k)}| = โ„ตโ‚€
>
> Your English and your Mathematics do not
> say the same thing.
>
> What your Mathematics says is
> | and ends (โŠ‡) an end-segment collection
> | which has an infinite intersection.
>
> The one collection of all and only end segments
> which are in the described collections
> is not any of those collections.
>
> Each of those intersections is infinite.
> This one collection's intersection is
> not infinite.
>
> This is not a contradiction.
> This is different things being different.
>
> >> Nothing can be added.
> >> Nothing can be removed.
> >
> > That is wrong.
>
> Call this collection ๐“”_def
>
> Each (definable) end segment which ends (โŠ‡)
> an end-segment collection which has
> an infinite intersection is in ๐“”_def
>
> Nothing can be added.
>
> Everything in ๐“”_def ends (โŠ‡)
> an end-segment collection which has
> an infinite intersection.
>
> Nothing can be removed.
>
> >>> Would their intersection be empty?
> >> Yes, empty.
> >>
> >> Do you see that this is a different question?
> >
> > No, it is not a question because
> > there is a definition:
> > Collect all endsegments which have
> > an infinite intersection.
>
> You mean the intersection of the collection
> which that end segment ends.
>
> >> No collection _up to_ an end segment
> >> is the collection of all end segments.
> >
> > Every definable endsegment can act as
> > the last one.
>
> ... of an end-segment collection.
>
> > An endsegment that cannot
> > act as a last one cannot be definable.
>
> None of those end segments is
> the last of all those end segments.
>
> Nothing else other than one of those
> end segments can be last of all those
> end segments.
>
> (omega is not the last natural number, etc.)
>
> >>> Collecting as many definable endsegments
> >>> as possible means swapping? Why?
> >>
> >> It is an invalid swap to step from
> >> | For each natural k,
> >> | there is an infinite set E,
> >> | all of E is after k
> >>
> >> to
> >> | There is an infinite set E,
> >> | for each natural k,
> >> | all of E is after k
>
> > There is no swap.
>
> | For each natural k,
> and
> | there is an infinite set E,
> are swapped.
> It is an invalid step.

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 - Wed, 7 Sep 2022 13:30 UTC

Gus Gassmann schrieb am Dienstag, 6. September 2022 um 17:38:53 UTC+2:
> On Tuesday, 6 September 2022 at 09:33:59 UTC-3, WM wrote:
> [...]
> > No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs.
> This is correct, since every end segment is infinite. In particular, every end segment has cardinality aleph_0.

And every intersection over infinite endsegments has not lost more than the infinite endsegments, namely only a finite set

โˆ€k โˆˆ โ„•_def: โˆฉ{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = โ„ตโ‚€ .

All definable endsegments E(n) are defined by the FISONs F(n).
As long as FISONs reach, the endsegments and their intersection are infinite.

โˆ€k โˆˆ โ„•_def: โˆฉ{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = โ„ตโ‚€ .

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 - Wed, 7 Sep 2022 13:34 UTC

Jim Burns schrieb am Dienstag, 6. September 2022 um 20:02:28 UTC+2:
> On 9/6/2022 7:40 AM, WM wrote:
> > Jim Burns schrieb am Sonntag,
> > 4. September 2022 um 19:26:25 UTC+2:
>
> >> ๐ตโ‚– is NOT between all of ๐“” and โˆ…

But there is much between all infinite endegments and โˆ… , namely the whole
staircase from infinity down to โˆ…

โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}.

Your long and winded arguments contradicts this equation. I stay to it.
> >
> > There is infinitely many between
> > all infinite endsegments and โˆ….
> No.

Your laconic denial contradicts the above equation. I'll stay to it.

Try to find the first instance where it fails. If you can't stop your "proofs".

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Wed, 7 Sep 2022 13:35 UTC

On Wednesday, 7 September 2022 at 10:30:32 UTC-3, WM wrote:
> Gus Gassmann schrieb am Dienstag, 6. September 2022 um 17:38:53 UTC+2:
> > On Tuesday, 6 September 2022 at 09:33:59 UTC-3, WM wrote:
> > [...]
> > > No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs.
> > This is correct, since every end segment is infinite. In particular, every end segment has cardinality aleph_0.
> And every intersection over infinite endsegments has not lost more than the infinite endsegments, namely only a finite set

This is circular. With every additional end segment in the intersection, at least one additional natural numbers is *NOT* in the intersection. What if you take an infinite intersection, oh benighted one? Why would you or ANYONE believe that only finitely many natural numbers could be missing from the intersection? You are so full of shit, you fucking moron. Why don't you take a hint from your "infinite endsegments", and get lost yourself?

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 - Wed, 7 Sep 2022 14:13 UTC

Jim Burns schrieb am Dienstag, 6. September 2022 um 21:56:47 UTC+2:
> On 9/6/2022 6:07 AM, WM wrote:

> On the other hand,
> we could consider a bathtub
> from which all of its water leaks
> ๐”ป = โˆ…

That is the same when the endsegments lose all elements.

> In each state, there is still more
> water yet to be leaked.
> That bathtub is never empty.

Then the intersection of its states is never empty.
>
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 - Wed, 7 Sep 2022 14:19 UTC

> Jim Burns kirjutas Kolmapรคev, 31. august 2022 kl 10:41:04 UTC-7:

> > | For each natural k,
> > and
> > | there is an infinite set E,
> > are swapped.
> > It is an invalid step.

As soon as there is no longer an infinite set, the next state of affairs is a finite set by the very definition of endsegments, i.e., simple mathematics: โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .
To deny it by the analogy that
โˆ€k โˆˆ โ„• โˆƒm โˆˆ โ„•: k < m ==> โˆƒm โˆˆ โ„• โˆ€k โˆˆ โ„•: k < m
is an invalid conclusion, is an invalid conclusion and shows naivety.

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 - Wed, 7 Sep 2022 14:26 UTC

Gus Gassmann schrieb am Mittwoch, 7. September 2022 um 15:36:02 UTC+2:
> On Wednesday, 7 September 2022 at 10:30:32 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Dienstag, 6. September 2022 um 17:38:53 UTC+2:
> > > On Tuesday, 6 September 2022 at 09:33:59 UTC-3, WM wrote:
> > > [...]
> > > > No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs.
> > > This is correct, since every end segment is infinite. In particular, every end segment has cardinality aleph_0.
> > And every intersection over infinite endsegments has not lost more than the infinite endsegments, namely only a finite set
> With every additional end segment in the intersection, at least one additional natural numbers is *NOT* in the intersection. What if you take an infinite intersection? Why would you or ANYONE believe that only finitely many natural numbers could be missing from the intersection?

Because every FISON is finite.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Wed, 7 Sep 2022 14:58 UTC

On Wednesday, 7 September 2022 at 11:26:16 UTC-3, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 7. September 2022 um 15:36:02 UTC+2:
> > On Wednesday, 7 September 2022 at 10:30:32 UTC-3, WM wrote:
> > > Gus Gassmann schrieb am Dienstag, 6. September 2022 um 17:38:53 UTC+2:
> > > > On Tuesday, 6 September 2022 at 09:33:59 UTC-3, WM wrote:
> > > > [...]
> > > > > No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs.
> > > > This is correct, since every end segment is infinite. In particular, every end segment has cardinality aleph_0.
> > > And every intersection over infinite endsegments has not lost more than the infinite endsegments, namely only a finite set
> > With every additional end segment in the intersection, at least one additional natural numbers is *NOT* in the intersection. What if you take an infinite intersection? Why would you or ANYONE believe that only finitely many natural numbers could be missing from the intersection?
>
> Because every FISON is finite.

Your stupidity and cluelessness are so vast, it is breathtaking. There are infinitely many FISONs, one for each natural number. Your quantifier switching may at one point have been cute, but now it is just tedious drivel. Go fuck yourself.

Re: Natural numbers and vases III

<tfabn6$1hus$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=111816&group=sci.math#111816

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 7 Sep 2022 10:00:52 -0500
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 by: Sergio - Wed, 7 Sep 2022 15:00 UTC

On 9/7/2022 8:34 AM, WM wrote:
> Jim Burns schrieb am Dienstag, 6. September 2022 um 20:02:28 UTC+2:
>> On 9/6/2022 7:40 AM, WM wrote:
>>> Jim Burns schrieb am Sonntag,
>>> 4. September 2022 um 19:26:25 UTC+2:
>>
>>>> ๐ตโ‚– is NOT between all of ๐“” and โˆ…
>
> But there is much between all infinite endegments and โˆ… , namely the whole
> staircase from infinity down to โˆ…
>
> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}.

the equation only states the relationship between two adjacent endsegments.
it is not step by step, it never gets to infinite.

You, WM are miss applying it.

you refuse to live withing the structures of Math.

>
> Your long and winded arguments contradicts this equation.

Wrong. You cannot except the fact that
1 he proved there are no dark numbers, and
2 you have not proved they exist.

>>>
>>> There is infinitely many between
>>> all infinite endsegments and โˆ….
>> No.
>
> Your laconic denial contradicts the above equation. I'll stay to it.

Your Ego prevents you from doing correct math.

>
> Try to find the first instance where it fails. If you can't stop your "proofs".

his proofs are correct.

>
> Regards, WM

Re: Natural numbers and vases III

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https://www.novabbs.com/tech/article-flat.php?id=111817&group=sci.math#111817

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 7 Sep 2022 10:03:30 -0500
Organization: Aioe.org NNTP Server
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 by: Sergio - Wed, 7 Sep 2022 15:03 UTC

On 9/7/2022 9:26 AM, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 7. September 2022 um 15:36:02 UTC+2:
>> On Wednesday, 7 September 2022 at 10:30:32 UTC-3, WM wrote:
>>> Gus Gassmann schrieb am Dienstag, 6. September 2022 um 17:38:53 UTC+2:
>>>> On Tuesday, 6 September 2022 at 09:33:59 UTC-3, WM wrote:
>>>> [...]
>>>>> No. A FISON defines all its numbers. Therefore finite endsegments cannot follow upon FISONs.
>>>> This is correct, since every end segment is infinite. In particular, every end segment has cardinality aleph_0.
>>> And every intersection over infinite endsegments has not lost more than the infinite endsegments, namely only a finite set
>> With every additional end segment in the intersection, at least one additional natural numbers is *NOT* in the intersection. What if you take an infinite intersection? Why would you or ANYONE believe that only finitely many natural numbers could be missing from the intersection?
>
> Because every FISON is finite.

red herring. fully Answer the specific question:

"Why would you or ANYONE believe that only finitely many natural numbers could be missing from the intersection?"

>
> Regards, WM

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

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