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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
|      |  |   | +- 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 IIIFritz Feldhase
|      |  |   | +- 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 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 IIIFritz Feldhase
|      |  |   | +- 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
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- 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 IIIGus Gassmann
|      |  |   | +- 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 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 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 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 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 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 IIIzelos...@gmail.com
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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
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
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|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
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|      |  |   | +- 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 IIIzelos...@gmail.com
|      |  |   | +- 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 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
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- 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
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- 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 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

<tcgkob$14gn$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 4 Aug 2022 09:23:05 -0500
Organization: Aioe.org NNTP Server
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 by: Sergio - Thu, 4 Aug 2022 14:23 UTC

On 8/4/2022 6:18 AM, WM wrote:
> William schrieb am Donnerstag, 4. August 2022 um 00:41:42 UTC+2:
>> On Wednesday, August 3, 2022 at 6:56:00 PM UTC-3, WM wrote:
>>> The property that a number can be written down (independent of time and ressources) is not a property of these numbers.
>> Piffle.
>>
>> 1 can be written down.
>> if n can be written down then n+1 can be written down (independent of time and resources)
>>
>> Hence each element of |N (without exception) can be written down (independent of time and resources).
>
> No.

Wrong. google Mathematical Induction

>>
>>> .. For instance you cannot name a number n the endsegment E(n) of which cannot removed from ∩{E(k) : k ∈ ℕ} = { } in order to maintain the empty result. [Each] endsegment which you can name can be removed.
>>
>> Indeed, Any finite set of endsegments, S, (whether or not S contains elements such that you cannot write down the first element) can be "removed".
>
> In order to remove a finite set, you have to give the last element.

Wrong. You must name all the elements.

again you argue over math nomenclature, this is not math, dummy.

>
>>> That means the endsegments which cause the empty intersection cannot be defined, not even in principle.
>> Piffle. "the endsegments which cause the empty intersection",T, is an infinite set of endsegments. T does not have every property that each of its elements has. In particular T cannot be "removed".
>
> It can be removed collectively. But none of its elements can be defined. They are dark.

wrong.

>
> Regards, WM

Re: Natural numbers and vases III

<tcgkr4$14gn$2@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 4 Aug 2022 09:24:34 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tcgkr4$14gn$2@gioia.aioe.org>
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 by: Sergio - Thu, 4 Aug 2022 14:24 UTC

On 8/4/2022 8:40 AM, WM wrote:
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 15:06:03 UTC+2:
>> WM pretended :
>>> In order to remove a finite set, you have to give the last element.
>> Sets don't change, you create a new set.
>
> That is a matter of language and taste.

wrong. It is called Math.

>>
>> The set of all natural numbers with fewer than 444 digits in base ten
>> notation. I did not give you the last element, you need a theorem.
>
>
> Regards, WM

Re: Natural numbers and vases III

<tcgmeh$2r7lm$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: Thu, 04 Aug 2022 10:51:56 -0400
Organization: Peripheral Visions
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 by: FromTheRafters - Thu, 4 Aug 2022 14:51 UTC

WM laid this down on his screen :
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 14:57:23 UTC+2:
>> WM presented the following explanation :
>>> zelos...@gmail.com schrieb am Donnerstag, 4. August 2022 um 13:41:58 UTC+2:
>>>
>>>>> All definable endsegments can be removed without changing the result.
>>>>> Therefore the required endegments are undefinable.
>>>> Your "definable" is still UNDEFINED!
>>>
>>> Definition: An endsegment is called definable, if it can be omitted,
>>> together with all its predecessors,
>> Endsegments don't have predecessors.
>
> Wrong. E(1) is the predecessor of E(2).

In a *sequence* of endsegements. *An* endsegemnt is merely *an*
endsegment.

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: Thu, 04 Aug 2022 11:00:47 -0400
Organization: Peripheral Visions
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 by: FromTheRafters - Thu, 4 Aug 2022 15:00 UTC

WM formulated on Thursday :
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 15:06:03 UTC+2:
>> WM pretended :
>>> In order to remove a finite set, you have to give the last element.
>> Sets don't change, you create a new set.
>
> That is a matter of language and taste.

No, it is a matter of understanding.

>> The set of all natural numbers with fewer than 444 digits in base ten
>> notation. I did not give you the last element, you need a theorem.
>
> You gave the last number.

No, I didn't. I gave only a larger number to start a countably infinite
range. I essentially gave the first 444 digit number, which begins your
endsegment, and you have to use the inverse of the successor function,
which is not given by axiom, to determine the last element of the
associated FISON.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 15:17 UTC

On Thursday, August 4, 2022 at 3:41:00 PM UTC+2, WM wrote:
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 15:06:03 UTC+2:
> >
> > Sets don't change, you create a new set.
> >
> That is a matter of language and taste.

No, that's a matter of knowledge and brains.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 15:19 UTC

On Thursday, August 4, 2022 at 3:48:05 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 4. August 2022 um 14:13:18 UTC+2:
> >
> > definable(E) :<-> En e IN: E = E(n) & ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(n)}) = { }
> >
> > Great. Then we get the result:
> >
> > AX e {E(k) : k ∈ ℕ}: definable(X)
> > or:
> > Ak e IN: definable(E(k))
> >
> > "All endsegments are definable."
> >
> Your claim is nonsense.

Nope. In contrast to YOUR brain dead NONSENSE it can be proved.

Hint: "[WM’s] conclusions are based on the sloppiness of his notions, his inability of giving precise definitions, his fundamental misunderstanding of elementary mathematical concepts, and sometimes, as the late Dik Winter remarked [...], on nothing at all."

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 15:27 UTC

On Thursday, August 4, 2022 at 5:01:03 PM UTC+2, FromTheRafters wrote:

WM wrote the following nonsense:

> > In order to remove a finite set, you have to give the last element.

The last element of what? Of the finite set?

What a blithering idiot!

Let /a/ be a number from IN, and let /b/ be a number from IN \ {a}.

Now I can consider the set difference IN \ {a, b} WITHOUT "giving" the last element.

Of course each and every nonempty finite set of numbers HAS a maximal/last element, but in this case I/we do _not know_ if /a/ is the maximum or /b/.

BUT we (except Mückenheim that is) DO know that EITHER a = b, OR a < b, OR b < a.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 15:49 UTC

On Thursday, August 4, 2022 at 3:44:02 PM UTC+2, WM wrote:

> There are many dark numbers in IN [...]. They cannot be distinguished. They are dark.

Yeah, "[WM’s] conclusions are based on the sloppiness of his notions, his inability of giving precise definitions, his fundamental misunderstanding of elementary mathematical concepts, and sometimes, as the late Dik Winter remarked [...], on nothing at all."

Hint: IN is a totally ordered set. For any element x e IN and any element y e IN:

EITHER x = y, OR x < y, OR y < x. (*)

Now from LOGIC we know for any element x e IN and any element y e IN: EITHER x = y, OR x =/= y.

IF x = y, we are just talking about ONE natural number, hence there is nothing to "distinguish".

IF x =/= y, then from (*) we get that EITHER x < y OR y < x. IF x < y then x is the smaller number and y is the larger. IF y < x then y is the smaller number and x is the larger. IN ANY CASE I can "distinguish" between these _two numbers_ "x" and "y" are referrig to by considering min({x, y)} vs.. max{(x, y)}. We than may state, say, min({x, y)} < max{(x, y)}.

It's just your mind, that is "dark".

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 15:53 UTC

On Thursday, August 4, 2022 at 5:49:32 PM UTC+2, Fritz Feldhase wrote:
> On Thursday, August 4, 2022 at 3:44:02 PM UTC+2, WM wrote:
> >
> > There are many dark numbers in IN [...]. They cannot be distinguished. They are dark.
> >
> Yeah, "[WM’s] conclusions are based on the sloppiness of his notions, his inability of giving precise definitions, his fundamental misunderstanding of elementary mathematical concepts, and sometimes, as the late Dik Winter remarked [...], on nothing at all."
>
> Hint: IN is a totally ordered set. For any element x e IN and any element y e IN:
>
> EITHER x = y, OR x < y, OR y < x. (*)
>
> Now from LOGIC we know for any element x e IN and any element y e IN: EITHER x = y, OR x =/= y.
>
> IF x = y, we are just talking about ONE natural number, hence there is nothing to "distinguish".
>
> IF x =/= y, then from (*) we get that EITHER x < y OR y < x. IF x < y then x is the smaller number and y is the larger. IF y < x then y is the smaller number and x is the larger. IN ANY CASE I can "distinguish" between these _two numbers_ "x" and "y" are referrig to by considering min({x, y)} vs. max{(x, y)}.

I mean, one is /the smaller of these two numbers/ while the other is /the larger of these two numbers/.

> We than may state, say, min({x, y)} < max{(x, y)}.
>
> It's just your mind, that is "dark".

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: monteu...@t-online.de (WM)
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 by: WM - Thu, 4 Aug 2022 16:28 UTC

William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
> On Thursday, August 4, 2022 at 8:18:43 AM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 4. August 2022 um 00:41:42 UTC+2:
> > > On Wednesday, August 3, 2022 at 6:56:00 PM UTC-3, WM wrote:
> > > > The property that a number can be written down (independent of time and ressources) is not a property of these numbers.
> > > Piffle.
> > >
> > > 1 can be written down.
> > > if n can be written down then n+1 can be written down (independent of time and resources)
> > >
> > > Hence each element of |N (without exception) can be written down (independent of time and resources).
> > No.
> He said, staring at the proof.

All endsegments together have an empty intersection
∩{E(k) : k ∈ ℕ} = { } .
All individually definable endsegments have an infinite intersection
|∩{E(k) : k ∈ ℕ_def}| = ℵ₀ .
Therefore the empty intersection is brought about by dark endsegments.
Or can you individually define endsegments which have an empty intersection?
Can you remove from the set of endsegments {E(1), E(2), ...} so many endsegments that the intersection is empty
∩({E(1), E(2), E(3), ...} \ {E(1), E(2), ..., E(X)}) = { }
but removing another definable endsegment E(X+1) would change the result. Can you define X?

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: monteu...@t-online.de (WM)
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 by: WM - Thu, 4 Aug 2022 16:33 UTC

Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 16:23:03 UTC+2:
> On Thursday, 4 August 2022 at 10:44:02 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 14:30:10 UTC+2:
> > > On Thursday, 4 August 2022 at 08:18:43 UTC-3, WM wrote:
> >
> > > Let E be the set of even natural numbers and O be the set of odd natural numbers.
> > > Then ∩({E(k) : k ∈ E} = ∩({E(k) : k ∈ O} = {}. Since E ∩ O = {} as well, this shows that *NO* natural number in and of itself has any influence on the intersection of the remaining end segments.
> > There are many dark numbers in |N and in E and in O. They cannot be distinguished. They are dark.
> So are you now saying that you do not know whether the intersection of E and O is empty or not?
The intersection of even and odd numbers is empty. But that is irrelevant. All definable endsegments have an infinite intersection. Proof: Define endsegments which have not. Fail.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: monteu...@t-online.de (WM)
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 by: WM - Thu, 4 Aug 2022 16:38 UTC

FromTheRafters schrieb am Donnerstag, 4. August 2022 um 16:52:11 UTC+2:
> WM laid this down on his screen :
> > FromTheRafters schrieb am Donnerstag, 4. August 2022 um 14:57:23 UTC+2:
> >> WM presented the following explanation :
> >>> zelos...@gmail.com schrieb am Donnerstag, 4. August 2022 um 13:41:58 UTC+2:
> >>>
> >>>>> All definable endsegments can be removed without changing the result.
> >>>>> Therefore the required endegments are undefinable.
> >>>> Your "definable" is still UNDEFINED!
> >>>
> >>> Definition: An endsegment is called definable, if it can be omitted,
> >>> together with all its predecessors,
> >> Endsegments don't have predecessors.
> >
> > Wrong. E(1) is the predecessor of E(2).
> In a *sequence* of endsegements. *An* endsegemnt is merely *an*
> endsegment.

Here we talk about the sequence. An endsegment is not of interest.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: monteu...@t-online.de (WM)
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 by: WM - Thu, 4 Aug 2022 16:40 UTC

FromTheRafters schrieb am Donnerstag, 4. August 2022 um 17:01:03 UTC+2:
> WM formulated on Thursday :

> >> The set of all natural numbers with fewer than 444 digits in base ten
> >> notation. I did not give you the last element, you need a theorem.

It is the numer with 443 nines.

Regards, WM

Re: Natural numbers and vases III

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Date: Thu, 4 Aug 2022 09:42:22 -0700 (PDT)
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Subject: Re: Natural numbers and vases III
From: monteu...@t-online.de (WM)
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 by: WM - Thu, 4 Aug 2022 16:42 UTC

Fritz Feldhase schrieb am Donnerstag, 4. August 2022 um 17:19:29 UTC+2:
> On Thursday, August 4, 2022 at 3:48:05 PM UTC+2, WM wrote:

> > > "All endsegments are definable."
> > >
> > Your claim is nonsense.
>
> it can be proved.

Your proofs are ninsense. Tho see it try to define enough endsegments to get an empty intersection.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 17:12 UTC

On Thursday, August 4, 2022 at 6:28:11 PM UTC+2, WM wrote:

> All endsegments together have an empty intersection
> ∩{E(k) : k ∈ ℕ} = { } .

Indeed. :-)

> All individually definable

Mumbo-Jumbo. READ: "Finitely many"

> endsegments have an infinite intersection
> |∩{E(k) : k ∈ ℕ_def}| = ℵ₀ .

Right. [ This implies that N_def is finite. ] But how is your N_def actually DEFINED?

> [...] the empty intersection is brought about by

sets of endsegments which are infinite.

Indeed!

> Or can you [state a finite set of] endsegments which ha[s] an empty intersection?

No, we can't.

> Can you remove from the set of endsegments {E(1), E(2), ...} [infinitely] many endsegments [such] that the intersection is empty

Sure:

> ∩({E(1), E(2), E(3), ...} \ {E(1), E(3), E(5), ...}) = { }

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 17:17 UTC

On Thursday, August 4, 2022 at 6:34:03 PM UTC+2, WM wrote:

> All definable endsegments have an infinite intersection.

Mumbo-Jumbo. READ: "Finitely many [but more than 0]"

| Finitely many [but more than 0] endsegments have an infinite intersection.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 4 Aug 2022 17:22 UTC

On Thursday, August 4, 2022 at 6:42:27 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 4. August 2022 um 17:19:29 UTC+2:
> > On Thursday, August 4, 2022 at 3:48:05 PM UTC+2, WM wrote:
> > > >
> > > > "All endsegments are definable."
> > > >
> > > Your claim is nonsense.
> > >
> > it can be proved.

BASED on the definition of "definable" you provided for endsegments. Don't you remember? Huh?!

> [...] proofs are nonsense. To see it <bla>

Man, we do not prove theorems in math by just "seeing things", but by formulating PROOFS, you know.

Learn some math, learn some logic, Mückenheim!

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: Thu, 4 Aug 2022 12:28:02 -0500
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 by: Sergio - Thu, 4 Aug 2022 17:28 UTC

On 8/4/2022 6:47 AM, WM wrote:
> zelos...@gmail.com schrieb am Donnerstag, 4. August 2022 um 13:41:58 UTC+2:
>
>>> All definable endsegments can be removed without changing the result. Therefore the required endegments are undefinable.
>> Your "definable" is still UNDEFINED!
>
> Definition: An endsegment is called definable, if it can be omitted, together with all its predecessors, from the intersection of all endsegments without changing the result empty set.

QUacK!!! "defined" by "omission"

>>
>> You think the finite rules holds for infinite, IT DOES NOT!
>
> In particular the individual definability does not.

In potentially particular the defined individual definablility potentially does not, not. GOT THAT ?

>
> Regards, WM

WM, the Math Omissionator

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: Thu, 4 Aug 2022 12:31:06 -0500
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 by: Sergio - Thu, 4 Aug 2022 17:31 UTC

On 8/4/2022 11:38 AM, WM wrote:
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 16:52:11 UTC+2:
>> WM laid this down on his screen :
>>> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 14:57:23 UTC+2:
>>>> WM presented the following explanation :
>>>>> zelos...@gmail.com schrieb am Donnerstag, 4. August 2022 um 13:41:58 UTC+2:
>>>>>
>>>>>>> All definable endsegments can be removed without changing the result.
>>>>>>> Therefore the required endegments are undefinable.
>>>>>> Your "definable" is still UNDEFINED!
>>>>>
>>>>> Definition: An endsegment is called definable, if it can be omitted,
>>>>> together with all its predecessors,
>>>> Endsegments don't have predecessors.
>>>
>>> Wrong. E(1) is the predecessor of E(2).
>> In a *sequence* of endsegements. *An* endsegemnt is merely *an*
>> endsegment.
>
> Here we talk about the sequence. An endsegment is not of interest.
>
> Regards, WM

WM trying to change the subject, after losing the battle

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: Thu, 4 Aug 2022 12:33:08 -0500
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 by: Sergio - Thu, 4 Aug 2022 17:33 UTC

On 8/4/2022 11:33 AM, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 16:23:03 UTC+2:
>> On Thursday, 4 August 2022 at 10:44:02 UTC-3, WM wrote:
>>> Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 14:30:10 UTC+2:
>>>> On Thursday, 4 August 2022 at 08:18:43 UTC-3, WM wrote:
>>>
>>>> Let E be the set of even natural numbers and O be the set of odd natural numbers.
>>>> Then ∩({E(k) : k ∈ E} = ∩({E(k) : k ∈ O} = {}. Since E ∩ O = {} as well, this shows that *NO* natural number in and of itself has any influence on the intersection of the remaining end segments.
>>> There are many dark numbers in |N and in E and in O. They cannot be distinguished. They are dark.
>> So are you now saying that you do not know whether the intersection of E and O is empty or not?
> The intersection of even and odd numbers is empty. But that is irrelevant. All definable endsegments have an infinite intersection. Proof: Define endsegments which have not. Fail.

Wrong and irrelevant.

>
> 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 - Thu, 4 Aug 2022 17:35 UTC

On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
> > On Thursday, August 4, 2022 at 8:18:43 AM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 4. August 2022 um 00:41:42 UTC+2:
> > > > On Wednesday, August 3, 2022 at 6:56:00 PM UTC-3, WM wrote:
> > > > > The property that a number can be written down (independent of time and ressources) is not a property of these numbers.
> > > > Piffle.
> > > >
> > > > 1 can be written down.
> > > > if n can be written down then n+1 can be written down (independent of time and resources)
> > > >
> > > > Hence each element of |N (without exception) can be written down (independent of time and resources).
> > > No.
> > He said, staring at the proof.
> ,,, All individually definable endsegments have infinite intersection.
Nope. You are staring at a proof that each endsegment is "individually definable", i.e the first element can be written down (independent of time and resources) "All individually definable endsegments" is the set of endsegments. So the interesction of "All individually definable endsegments" is empty. (The intersection of a *finite subset* of "All individually definable endsegments" is infinite, so
|∩{E(k) : k ∈ ℕ_def}| = ℵ₀ . )

--
William Hughes

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 - Thu, 4 Aug 2022 17:35 UTC

On Thursday, 4 August 2022 at 12:27:20 UTC-3, Fritz Feldhase wrote:
> On Thursday, August 4, 2022 at 5:01:03 PM UTC+2, FromTheRafters wrote:
>
> WM wrote the following nonsense:
> > > In order to remove a finite set, you have to give the last element.
> The last element of what? Of the finite set?
>
> What a blithering idiot!
>
> Let /a/ be a number from IN, and let /b/ be a number from IN \ {a}.
>
> Now I can consider the set difference IN \ {a, b} WITHOUT "giving" the last element.
>
> Of course each and every nonempty finite set of numbers HAS a maximal/last element, but in this case I/we do _not know_ if /a/ is the maximum or /b/..
>
> BUT we (except Mückenheim that is) DO know that EITHER a = b, OR a < b, OR b < a.

Again, without putting too fine a point to it, we (except Mückenheim that is) do know from your constraint b in ( IN \ {a} ) that a =/= b...

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 - Thu, 4 Aug 2022 17:38 UTC

On Thursday, 4 August 2022 at 13:34:03 UTC-3, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 16:23:03 UTC+2:
> > On Thursday, 4 August 2022 at 10:44:02 UTC-3, WM wrote:
> > > Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 14:30:10 UTC+2:
> > > > On Thursday, 4 August 2022 at 08:18:43 UTC-3, WM wrote:
> > >
> > > > Let E be the set of even natural numbers and O be the set of odd natural numbers.
> > > > Then ∩({E(k) : k ∈ E} = ∩({E(k) : k ∈ O} = {}. Since E ∩ O = {} as well, this shows that *NO* natural number in and of itself has any influence on the intersection of the remaining end segments.
> > > There are many dark numbers in |N and in E and in O. They cannot be distinguished. They are dark.
> > So are you now saying that you do not know whether the intersection of E and O is empty or not?
> The intersection of even and odd numbers is empty. But that is irrelevant..

Of course it is irrelevant, but for a reason entirely different from what you imagine in that little bird brain of yours. What matters is that the set of even naturals has cardinality aleph_0 (or, more precisely, does not contain a maximum), as does the set of odd naturals. And now, please take your stinking shit elsewhere.

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 - Thu, 4 Aug 2022 17:39 UTC

On Thursday, 4 August 2022 at 13:40:23 UTC-3, WM wrote:
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 17:01:03 UTC+2:
> > WM formulated on Thursday :
> > >> The set of all natural numbers with fewer than 444 digits in base ten
> > >> notation. I did not give you the last element, you need a theorem.
> It is the numer with 443 nines.

"numer"?

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 - Thu, 4 Aug 2022 17:40 UTC

On Thursday, 4 August 2022 at 13:42:27 UTC-3, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 4. August 2022 um 17:19:29 UTC+2:
> > On Thursday, August 4, 2022 at 3:48:05 PM UTC+2, WM wrote:
>
> > > > "All endsegments are definable."
> > > >
> > > Your claim is nonsense.
> >
> > it can be proved.
>
> Your proofs are ninsense. Tho see it try to define enough endsegments to get an empty intersection.

"ninsense"?


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

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