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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
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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
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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 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 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

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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, 31 Aug 2022 15:04 UTC

On Wednesday, 31 August 2022 at 10:15:07 UTC-3, WM wrote:
[...]
> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersectiion?

Because, you fucking imbecile, the card() function is not continuous, the Peano axioms define *ALL* natural numbers, quantifiers cannot be thrown around arbitrarily, and the fucking *DEFINITION* of the intersection over all end segments proves that it is empty. That you can't understand that is really not anyone's problem other than yours and your employer's, that prestigious institution of higher learning called the "Augsburg University of Applied Sciences".

Re: Natural numbers and vases III

<tentat$1k97$2@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 10:05:01 -0500
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 by: Sergio - Wed, 31 Aug 2022 15:05 UTC

On 8/31/2022 8:10 AM, WM wrote:
> zelos...@gmail.com schrieb am Mittwoch, 31. August 2022 um 07:05:13 UTC+2:
>> tisdag 30 augusti 2022 kl. 15:42:23 UTC+2 skrev WM:
>>> Fritz Feldhase schrieb am Montag, 29. August 2022 um 16:07:22 UTC+2:
>>>> On Monday, August 29, 2022 at 3:27:52 PM UTC+2, WM wrote:
>>>>
>>>>> you are not aware of the fact that dark numbers exist and that your proofs are invalid for dark numbers.
>>>> Yeah, I have to admit that I'm indeed not aware of these "facts".
>>> But you need them to understand set theory correctly.
>>
>> We do not need "dark numbers" to understand them as they do not exist.
>
> You do not understand.

No, he does understand, and refutes your fictional "dark numbers". Got that ?

>>
>>> If no dark numbers would blow up the set ℕ to accomplish
>>
>> "blow up" is not a mathematical term.
>
> You do not know it.

perhaps you ment to use "inflate" instead of "blow up" ?

>>
>>> ∩{E(k) : k ∈ ℕ} = { }
>>> then only the elements of
>>> ∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀
>>> would exist and therefore
>>> ∩{E(k) : k ∈ ℕ} =/= { } .
>>>>
>> Non-sequiter galore.
>
> You cannot follow.

All aboard the Non-sense train!

>
> Regards, WM

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: Wed, 31 Aug 2022 10:06:49 -0500
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 by: Sergio - Wed, 31 Aug 2022 15:06 UTC

On 8/31/2022 7:47 AM, WM wrote:
>
> Jim Burns schrieb am Dienstag, 30. August 2022 um 22:09:23 UTC+2:
>> On 8/30/2022 3:25 PM, WM wrote:
>>> Jim Burns schrieb am Dienstag,
>>> 30. August 2022 um 20:43:01 UTC+2:
>
>>>> Whatever you call the set of all FISON-ends,
>>>> it remains the set of all FISON-ends.
>>>
>>> But it is not a set.
>> <WM<FromTheRafters>>
>>>>
>>>> Then what is a set?
>>>
>>> As I said:
>>> All elements are there,
>>> none can be added.
>
> And that is not so for the collection of FISONs.

collection or set ?

>
>> All the FISON-ends are in the collection of
>> FISON-ends. None can be added.
>
> The FISONs are counted by the content of FISONs.

self referencing definitions are wrong in most all cases

>
> 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 - Wed, 31 Aug 2022 15:08 UTC

On Wednesday, August 31, 2022 at 9:41:46 AM UTC-3, WM wrote:
> William schrieb am Dienstag, 30. August 2022 um 22:05:23 UTC+2:
> > On Tuesday, August 30, 2022 at 4:13:40 PM UTC-3, WM wrote:
> > > William schrieb am Dienstag, 30. August 2022 um 20:13:26 UTC+2:
> > > > On Tuesday, August 30, 2022 at 2:42:23 PM UTC-3, WM wrote:
> > > > > William schrieb am Dienstag, 30. August 2022 um 17:30:01 UTC+2:
> > >
> > > > > Show an infinite endsegment which has not infinitely many elements together with all infinite endsegments, predecessors as well as successors. If you can't, and it is clear that you can't,
> > > > So what? Each pair of endsegements (A,B), has infinite set S(A,B) of elements in common. However, there is no single unchanging set S that works for all pairs A,B.
> > > That is irrelevant. If every infinite endsegment E_m has infinitely many natnumbers in common with every infinite endsegment E(n),then there is no endsegment, which has only a finite number of endsegments in common with any infinite endsegment.
> > Correct. Note the infinite set can and does change.
> It decreases with increasing index but remains infinite.
> > >Inclusion monotony shows that all those endsegments have one and the same infinite set of natnumbers in common.,
> > Nope. It shows no such thing.
> An infinite set which decreases maintains infinitely many numbers.

So what? At each step infinitely many numbers are "maintained". This does not mean that there is a number x, which is "maintained" at every step.

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 17:41:47 +0200
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 by: Tom Bola - Wed, 31 Aug 2022 15:41 UTC

Gus Gassmann wrote:

> WM wrote:
> [...]
>> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersectiion?
>
> Because, you fucking imbecile, the card() function is not continuous, the Peano axioms define *ALL* natural numbers, quantifiers cannot be thrown around arbitrarily, and the fucking *DEFINITION* of the intersection over all end segments proves that it is empty. That you can't understand that is really not anyone's problem other than yours and your employer's, that prestigious institution of higher learning called the "Augsburg University of Applied Sciences".

Exactly.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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 by: Python - Wed, 31 Aug 2022 15:54 UTC

Tom Bola wrote:
> Gus Gassmann wrote:
>
>> WM wrote:
>> [...]
>>> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersectiion?
>>
>> Because, you fucking imbecile, the card() function is not continuous, the Peano axioms define *ALL* natural numbers, quantifiers cannot be thrown around arbitrarily, and the fucking *DEFINITION* of the intersection over all end segments proves that it is empty. That you can't understand that is really not anyone's problem other than yours and your employer's, that prestigious institution of higher learning called the "Augsburg University of Applied Sciences".
>
> Exactly.

BTW, it is definitely pointless to try to convince Pr. Mückenheim of
anything with rational arguments: he has permanent brain damage and
his lack of integrity is obvious.

Nevertheless he is likely to teach his crazy pseudo-mathematical stuff
to real student this academic year and his infamous books are still
sold as serious material by an established publisher in Germany.

This is definitely something that MUST be done in Germany, especially
in Augsburg (is anybody from the real Augsburg University aware of
this scandalous state of fact?) to stop this outrageous scandal.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 12:12:19 -0400
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 by: Jim Burns - Wed, 31 Aug 2022 16:12 UTC

On 8/31/2022 9:06 AM, WM wrote:
> Jim Burns schrieb am Mittwoch,
> 31. August 2022 um 01:45:01 UTC+2:
>> On 8/30/2022 3:58 PM, WM wrote:

>>> All sets of two infinite endsegments
>>> do not have a last endsegment.
>>
>> No.
>> All sets of two (infinite) end segments
>> have a last end segment.
>
> Each one has.

Good.

A set of two end segments has
a last (⊇) end segment.

The last end segment is their intersection.

No end segment is last (⊇) of all
end segments.

No end segment is the intersection of
all end segments.

All end segments are infinite and
the intersection of all end segments
is empty.

End segments and intersection are different.
So, this is not a contradiction.

> All together have not.

The union of all sets of two (infinite)
end segments is not
a set of two (infinite) end segments.

In other news...

The union of all FISONs is not a FISON.

The intersection of all (infinite)
end segments is not an (infinite)
end segment.

Re: Natural numbers and vases III

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 by: Archimedes Plutonium - Wed, 31 Aug 2022 16:55 UTC

Take this bullshit failed ignorance to sci.logic, you do not deserve to post in sci.math.
On Monday, July 18, 2022 at 4:29:37 PM UTC-5, WM wrote:

Take this bullshit over to sci.logic, for you are a math failure-- Your AND connector is subtraction with 2 OR 1 = 3. You do not even know a geometry proof of Fundamental Theorem of Calculus. You are a failure in geometry for your slant cut in cone is a ellipse when actually that is a oval. But worst of all-- your so stupid in science you cannot even ask the question which is the atom's true electron-- 0.5MeV particle or the muon stuck inside a 840 MeV proton torus.

You do not deserve to post in sci.math with your failed ignorance of math.

3rd published book

AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
by Archimedes Plutonium (Author)

Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.

Product details
• ASIN ‏ : ‎ B07PLSDQWC
• Publication date ‏ : ‎ March 11, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 1621 KB
• Text-to-Speech ‏ : ‎ Enabled
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Not Enabled
• Print length ‏ : ‎ 20 pages
• Lending ‏ : ‎ Enabled

Proofs Ellipse is never a Conic section, always a Cylinder section and a Well Defined Oval definition//Student teaches professor series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 14May2022. This is AP's 68th published book of science.

Preface: A similar book on single cone cut is a oval, never a ellipse was published in 11Mar2019 as AP's 3rd published book, but Amazon Kindle converted it to pdf file, and since then, I was never able to edit this pdf file, and decided rather than struggle and waste time, decided to leave it frozen as is in pdf format. Any new news or edition of ellipse is never a conic in single cone is now done in this book. The last thing a scientist wants to do is wade and waddle through format, when all a scientist ever wants to do is science itself. So all my new news and thoughts of Conic Sections is carried out in this 68th book of AP. And believe you me, I have plenty of new news.

In the course of 2019 through 2022, I have had to explain this proof often on Usenet, sci.math and sci.physics. And one thing that constant explaining does for a mind of science, is reduce the proof to its stripped down minimum format, to bare bones skeleton proof. I can prove the slant cut in single cone is a Oval, never the ellipse in just a one sentence proof. Proof-- A single cone and oval have just one axis of symmetry, while a ellipse requires 2 axes of symmetry, hence slant cut is always a oval, never the ellipse..

Product details
• ASIN ‏ : ‎ B081TWQ1G6
• Publication date ‏ : ‎ November 21, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 827 KB
• Simultaneous device usage ‏ : ‎ Unlimited
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Not Enabled
• Print length ‏ : ‎ 51 pages
• Lending ‏ : ‎ Enabled

#12-2, 11th published book

World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 15Dec2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.

Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". And very surprising that most math professors cannot tell the difference between a "proving something" and that of "analyzing something". As if an analysis is the same as a proof. We often analyze various things each and every day, but few if none of us consider a analysis as a proof. Yet that is what happened in the science of mathematics where they took an analysis and elevated it to the stature of being a proof, when it was never a proof.

To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?

Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.

Product details
ASIN ‏ : ‎ B07PQTNHMY
Publication date ‏ : ‎ March 14, 2019
Language ‏ : ‎ English
File size ‏ : ‎ 1309 KB
Text-to-Speech ‏ : ‎ Enabled
Screen Reader ‏ : ‎ Supported
Enhanced typesetting ‏ : ‎ Enabled
X-Ray ‏ : ‎ Not Enabled
Word Wise ‏ : ‎ Not Enabled
Print length ‏ : ‎ 154 pages
Lending ‏ : ‎ Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)

Re: Natural numbers and vases III

<c26d2b75-3f9c-7214-7169-94bc7f6de35d@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 13:40:56 -0400
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 by: Jim Burns - Wed, 31 Aug 2022 17:40 UTC

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:
> |∩{E(1), E(2), ..., E(k)}| = ℵ₀

Your English and your Mathematics do not
say the same thing.

What your Mathematics says is
| and ends (⊇) 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 𝓔_def

Each (definable) end segment which ends (⊇)
an end-segment collection which has
an infinite intersection is in 𝓔_def

Nothing can be added.

Everything in 𝓔_def ends (⊇)
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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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 13:43:59 -0500
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 by: Sergio - Wed, 31 Aug 2022 18:43 UTC

On 8/31/2022 11:12 AM, Jim Burns wrote:
> On 8/31/2022 9:06 AM, WM wrote:
>> Jim Burns schrieb am Mittwoch,
>> 31. August 2022 um 01:45:01 UTC+2:
>>> On 8/30/2022 3:58 PM, WM wrote:
>
>>>> All sets of two infinite endsegments
>>>> do not have a last endsegment.
>>>
>>> No.
>>> All sets of two (infinite) end segments
>>> have a last end segment.
>>
>> Each one has.
>
> Good.
>
> A set of two end segments has
> a last (⊇) end segment.
>
> The last end segment is their intersection.
>
> No end segment is last (⊇) of all
> end segments.
>
> No end segment is the intersection of
> all end segments.
>
>
> All end segments are infinite and
> the intersection of all end segments
> is empty.
>
> End segments and intersection are different.
> So, this is not a contradiction.
>
>> All together have not.
>
> The union of all sets of two (infinite)
> end segments is not
> a set of two (infinite) end segments.
>
> In other news...
>
> The union of all FISONs is not a FISON.

correctomundo!

[corollary: the "last" FISON is not a FISON]

>
> The intersection of all (infinite)
> end segments is not an (infinite)
> end segment.
>

correctomundo!

Re: Natural numbers and vases III

<teoatt$km$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=110986&group=sci.math#110986

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 13:57:00 -0500
Organization: Aioe.org NNTP Server
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 by: Sergio - Wed, 31 Aug 2022 18:57 UTC

On 8/31/2022 10:54 AM, Python wrote:
> Tom Bola wrote:
>> Gus Gassmann wrote:
>>
>>> WM wrote:
>>> [...]
>>>> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersectiion?
>>>
>>> Because, you fucking imbecile, the card() function is not continuous, the Peano axioms define *ALL* natural numbers, quantifiers cannot be thrown
>>> around arbitrarily, and the fucking *DEFINITION* of the intersection over all end segments proves that it is empty. That you can't understand that is
>>> really not anyone's problem other than yours and your employer's,  that prestigious institution of higher learning called the "Augsburg University of
>>> Applied Sciences".
>>
>> Exactly.
>
> BTW, it is definitely pointless to try to convince Pr. Mückenheim of
> anything with rational arguments: he has permanent brain damage and
> his lack of integrity is obvious.
>
> Nevertheless he is likely to teach his crazy pseudo-mathematical stuff
> to real student this academic year and his infamous books are still
> sold as serious material by an established publisher in Germany.
>
> This is definitely something that MUST be done in Germany, especially
> in Augsburg (is anybody from the real Augsburg University aware of
> this scandalous state of fact?) to stop this outrageous scandal.
>
>

https://zbmath.org/?q=an:1195.00004

Review of his book
Mückenheim, Wolfgang
The mathematics of infinity.

"In Chapter 9, the author sets out to prove that Cantor’s set theory is inconsistent, that his proof of the uncountability of the reals is incorrect,
and that “infinite numbers” cannot exist. The author’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 in his online review
of this book, on nothing at all."

"In his explanation why π does not exist, he denies the existence of ideal circles because a physical circle deforms Euclidean space and because the
wave character of matter prevents a sharp boundary."

Keywords:
pseudo-mathematics

Re: Natural numbers and vases III

<teocgj$mgt$1@gioia.aioe.org>

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From: Tom...@bolamail.etc (Tom Bola)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 21:24:02 +0200
Organization: Aioe.org NNTP Server
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 by: Tom Bola - Wed, 31 Aug 2022 19:24 UTC

Sergio schrieb:

> On 8/31/2022 10:54 AM, Python wrote:
>> Tom Bola wrote:
>>> Gus Gassmann wrote:
>>>
>>>> WM wrote:
>>>> [...]
>>>>> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersectiion?
>>>>
>>>> Because, you fucking imbecile, the card() function is not continuous, the Peano axioms define *ALL* natural numbers, quantifiers cannot be thrown
>>>> around arbitrarily, and the fucking *DEFINITION* of the intersection over all end segments proves that it is empty. That you can't understand that is
>>>> really not anyone's problem other than yours and your employer's,  that prestigious institution of higher learning called the "Augsburg University of
>>>> Applied Sciences".
>>>
>>> Exactly.
>>
>> BTW, it is definitely pointless to try to convince Pr. Mückenheim of
>> anything with rational arguments: he has permanent brain damage and
>> his lack of integrity is obvious.
>>
>> Nevertheless he is likely to teach his crazy pseudo-mathematical stuff
>> to real student this academic year and his infamous books are still
>> sold as serious material by an established publisher in Germany.
>>
>> This is definitely something that MUST be done in Germany, especially
>> in Augsburg (is anybody from the real Augsburg University aware of
>> this scandalous state of fact?) to stop this outrageous scandal.
>>
>>
>
> https://zbmath.org/?q=an:1195.00004
>
> Review of his book
> Mückenheim, Wolfgang
> The mathematics of infinity.
>
>
> "In Chapter 9, the author sets out to prove that Cantor’s set theory is inconsistent, that his proof of the uncountability of the reals is incorrect,
> and that “infinite numbers” cannot exist. The author’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 in his online review
> of this book, on nothing at all."

Yes, he doesn't want it to be ALLOWED to use "unnatural" infinite objects (and
thougts)...
> "In his explanation why π does not exist, he denies the existence of ideal circles because a physical circle deforms Euclidean space and because the
> wave character of matter prevents a sharp boundary."

ROTFL, that one has killed me almost...
> Keywords:
> pseudo-mathematics

He is an low IQ idiot and an abhoring kind of person...

Re: Natural numbers and vases III

<teojcq$1em9$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 31 Aug 2022 16:21:29 -0500
Organization: Aioe.org NNTP Server
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 by: Sergio - Wed, 31 Aug 2022 21:21 UTC

On 8/31/2022 2:24 PM, Tom Bola wrote:
> Sergio schrieb:
>
>> On 8/31/2022 10:54 AM, Python wrote:
>>> Tom Bola wrote:
>>>> Gus Gassmann wrote:
>>>>
>>>>> WM wrote:
>>>>> [...]
>>>>>> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersectiion?
>>>>>
>>>>> Because, you fucking imbecile, the card() function is not continuous, the Peano axioms define *ALL* natural numbers, quantifiers cannot be thrown
>>>>> around arbitrarily, and the fucking *DEFINITION* of the intersection over all end segments proves that it is empty. That you can't understand that is
>>>>> really not anyone's problem other than yours and your employer's,  that prestigious institution of higher learning called the "Augsburg University of
>>>>> Applied Sciences".
>>>>
>>>> Exactly.
>>>
>>> BTW, it is definitely pointless to try to convince Pr. Mückenheim of
>>> anything with rational arguments: he has permanent brain damage and
>>> his lack of integrity is obvious.
>>>
>>> Nevertheless he is likely to teach his crazy pseudo-mathematical stuff
>>> to real student this academic year and his infamous books are still
>>> sold as serious material by an established publisher in Germany.
>>>
>>> This is definitely something that MUST be done in Germany, especially
>>> in Augsburg (is anybody from the real Augsburg University aware of
>>> this scandalous state of fact?) to stop this outrageous scandal.
>>>
>>>
>>
>> https://zbmath.org/?q=an:1195.00004
>>
>> Review of his book
>> Mückenheim, Wolfgang
>> The mathematics of infinity.
>>
>>
>> "In Chapter 9, the author sets out to prove that Cantor’s set theory is inconsistent, that his proof of the uncountability of the reals is incorrect,
>> and that “infinite numbers” cannot exist. The author’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 in his online review
>> of this book, on nothing at all."
>
> Yes, he doesn't want it to be ALLOWED to use "unnatural" infinite objects (and
> thougts)...
>
>> "In his explanation why π does not exist, he denies the existence of ideal circles because a physical circle deforms Euclidean space and because the
>> wave character of matter prevents a sharp boundary."
>
> ROTFL, that one has killed me almost...
>
>> Keywords:
>> pseudo-mathematics
>
> He is an low IQ idiot and an abhoring kind of person...

I have worked with many phd,s in physics, 1/2 are geniuses, the other 1/2 are nuts.
Guess WM has crossed over

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, 31 Aug 2022 22:08 UTC

On Wednesday, 31 August 2022 at 18:21:40 UTC-3, Sergio wrote:
> I have worked with many phd,s in physics, 1/2 are geniuses, the other 1/2 are nuts.
> Guess WM has crossed over

Are you saying you think that he is a former genius? Do you have any basis for this astonishing pronouncement?

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: Wed, 31 Aug 2022 18:02:43 -0500
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 by: Sergio - Wed, 31 Aug 2022 23:02 UTC

On 8/31/2022 5:08 PM, Gus Gassmann wrote:
> On Wednesday, 31 August 2022 at 18:21:40 UTC-3, Sergio wrote:
>> I have worked with many phd,s in physics, 1/2 are geniuses, the other 1/2 are nuts.
>> Guess WM has crossed over
>
> Are you saying you think that he is a former genius? Do you have any basis for this astonishing pronouncement?

in this case, bad word choice, replace "geniuses" with "potentially good"

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Thu, 1 Sep 2022 08:51 UTC

onsdag 31 augusti 2022 kl. 15:10:29 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Mittwoch, 31. August 2022 um 07:05:13 UTC+2:
> > tisdag 30 augusti 2022 kl. 15:42:23 UTC+2 skrev WM:
> > > Fritz Feldhase schrieb am Montag, 29. August 2022 um 16:07:22 UTC+2:
> > > > On Monday, August 29, 2022 at 3:27:52 PM UTC+2, WM wrote:
> > > >
> > > > > you are not aware of the fact that dark numbers exist and that your proofs are invalid for dark numbers.
> > > > Yeah, I have to admit that I'm indeed not aware of these "facts".
> > > But you need them to understand set theory correctly.
> >
> > We do not need "dark numbers" to understand them as they do not exist.
> You do not understand.

Yes I do, you make shit up.

> >
> > > If no dark numbers would blow up the set ℕ to accomplish
> >
> > "blow up" is not a mathematical term.
> You do not know it.

I know mathematics better than you.

> >
> > > ∩{E(k) : k ∈ ℕ} = { }
> > > then only the elements of
> > > ∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀
> > > would exist and therefore
> > > ∩{E(k) : k ∈ ℕ} =/= { } .
> > > >
> > Non-sequiter galore.
>
> You cannot follow.

Because there is nothing to follow. You are spewing bullshit

>
> 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 - Thu, 1 Sep 2022 13:05 UTC

Gus Gassmann schrieb am Mittwoch, 31. August 2022 um 17:04:08 UTC+2:
> On Wednesday, 31 August 2022 at 10:15:07 UTC-3, WM wrote:
> [...]
> > So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersection?
> Because the card() function is not continuous,

Why is it not continuous?

Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Thu, 1 Sep 2022 13:09 UTC

William schrieb am Mittwoch, 31. August 2022 um 17:08:57 UTC+2:
> On Wednesday, August 31, 2022 at 9:41:46 AM UTC-3, WM wrote:

> > An infinite set which decreases maintains infinitely many numbers.
> So what? At each step infinitely many numbers are "maintained". This does not mean that there is a number x, which is "maintained" at every step.

It does mean exactly this as long as no endsegment has lost all its numbers.

But it is not only one number x because it could be defined. There must be infinitely many dark numbers.

If you argue that all numbers leave the intersection but infinitely many numbers do not leave the contributing endsegments, then you are outside of logic and reason.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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 by: Python - Thu, 1 Sep 2022 13:13 UTC

Crank Wolfgang Mückenheim, aka WM wrote:
> Gus Gassmann schrieb am Mittwoch, 31. August 2022 um 17:04:08 UTC+2:
>> On Wednesday, 31 August 2022 at 10:15:07 UTC-3, WM wrote:
>> [...]
>>> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersection?
>> Because the card() function is not continuous,
>
> Why is it not continuous?

http://bsb.me.uk/dd-wealth.pdf

Re: Natural numbers and vases III

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 by: WM - Thu, 1 Sep 2022 13:16 UTC

Jim Burns schrieb am Mittwoch, 31. August 2022 um 18:12:28 UTC+2:
> On 8/31/2022 9:06 AM, WM wrote:

> No end segment is last (⊇) of all
> end segments.

True. The reason is this: The infinite, definable endsegments are potentially infinite. The empty endsegment is not discernible among all infinite and finite dark endsegments.
>
> The intersection of all (infinite)
> end segments is not an (infinite)
> end segment.

Either the intersection is infinite or it is not existing.

In every case the states of a nonempty bathtub have a non-empty intersection. Likewise the intervals [0, 1+1/n] have a non-empty intersection. The existence of infinitely many states is not an argument for an empty intersection.

Regards, WM

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 1 Sep 2022 13:30:48 -0500
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 by: Sergio - Thu, 1 Sep 2022 18:30 UTC

On 9/1/2022 8:16 AM, WM wrote:
> Jim Burns schrieb am Mittwoch, 31. August 2022 um 18:12:28 UTC+2:
>> On 8/31/2022 9:06 AM, WM wrote:
>
>> No end segment is last (⊇) of all
>> end segments.
>
> True. The reason is this: The infinite, definable endsegments are potentially infinite.

no, your reason above does not apply at all.

> The empty endsegment is not discernible among all infinite and finite dark endsegments.

no, there are no empty endsegments, no finite endsegments, no finite dark endsegments, you talk about nothing.

>>
>> The intersection of all (infinite)
>> end segments is not an (infinite)
>> end segment.
>
> Either the intersection is infinite or it is not existing.

wrong, the intersection of all endsegments is empty.

your Marble that says "all endsegments are infinite", has left the building...

>
> In every case the states of a nonempty bathtub have a non-empty intersection.

no, what sets of non empty bathtubs are you talking about ?

> Likewise the intervals [0, 1+1/n] have a non-empty intersection.

no, what sets are you talking about? Do the homework, state all the conditions, sloppy math boy.

> The existence of infinitely many states is not an argument for an empty intersection.

states of what ?

>
> Regards, WM

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, 1 Sep 2022 13:34:02 -0500
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 by: Sergio - Thu, 1 Sep 2022 18:34 UTC

On 9/1/2022 8:09 AM, WM wrote:
> William schrieb am Mittwoch, 31. August 2022 um 17:08:57 UTC+2:
>> On Wednesday, August 31, 2022 at 9:41:46 AM UTC-3, WM wrote:
>
>>> An infinite set which decreases maintains infinitely many numbers.
>> So what? At each step infinitely many numbers are "maintained". This does not mean that there is a number x, which is "maintained" at every step.
>
> It does mean exactly this as long as no endsegment has lost all its numbers.

sets do not lose numbers.

> But it is not only one number x because it could be defined. There must be infinitely many dark numbers.

then prove it, you haven't so far, over decades of posting. Take a refresher course at night.

>
> If you argue that all numbers leave the intersection

did the numbers take a bus from the corner ? you are outta math.

> but infinitely many numbers do not leave the contributing endsegments, then you are outside of logic and reason.
>
> Regards, WM
>

agree that you are outside of logic and reason, and math, a long time ago too.

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, 1 Sep 2022 13:38:36 -0500
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 by: Sergio - Thu, 1 Sep 2022 18:38 UTC

On 9/1/2022 8:13 AM, Python wrote:
> Crank Wolfgang Mückenheim, aka WM wrote:
>> Gus Gassmann schrieb am Mittwoch, 31. August 2022 um 17:04:08 UTC+2:
>>> On Wednesday, 31 August 2022 at 10:15:07 UTC-3, WM wrote:
>>> [...]
>>>> So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersection?
>>> Because the card() function is not continuous,
>>
>> Why is it not continuous?
>
> http://bsb.me.uk/dd-wealth.pdf
>
>

that was from 2014. so far no progress for WM

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 1 Sep 2022 14:52:24 -0400
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 by: Jim Burns - Thu, 1 Sep 2022 18:52 UTC

On 9/1/2022 9:16 AM, WM wrote:
> Jim Burns schrieb am Mittwoch,
> 31. August 2022 um 18:12:28 UTC+2:

>> No end segment is last (⊇) of all
>> end segments.
>
> True.
> The reason is this:
> The infinite, definable endsegments are
> potentially infinite.

Your use of "potentially infinite" is a
_virtus dormitiva_

https://alexcabuz.wordpress.com/2010/02/10/virtus-dormitiva/
| | In the play, a character is asked to explain
| why opium causes sleep. He answers that opium
| contains a “dormitive principle” which is at
| the origin of its ability to cause sleep.
| In the original text the phrase is in latin:
| "virtus dormitiva".
| | It is evident that the explanation does not
| explain anything, but only replaces one
| poorly understood phenomenon with another.
| The interlocutor is in no way wiser after
| the explanation than before it.

> The empty endsegment is not discernible
> among all infinite and finite dark endsegments.

Describe an end segment 𝐸 of the set ⋃𝓕
of FISON-ends, conceivably infinite, finite,
empty, discernible, or indiscernible.

If we are satisfied with the description,
we won't need to change the domain.

If it arises from our description that
all the end segments are infinite and
the intersection of all the end segments
is empty, then then entire point of
all this rigamarole that we use is that
we will know that that is how it is.

If we then _change_ the description in order
for some _other_ claims to arise from the
_changed_ description, then that isn't
a description of or claim about the same
domain, the same end segments. Hence, "change".

----
Describe an end segment 𝐸 of the set ⋃𝓕
of FISON-ends.

| 𝐸 and ⋃𝓕\𝐸 is a split of ⋃𝓕
| (or, trivially, 𝐸 = ⋃𝓕).
| | For each i ∈ ⋃𝓕\𝐸, each j ∈ 𝐸, i < j
| | 𝐸 ⊆ ⋃𝓕, ⋃𝓕\𝐸 ⊆ ⋃𝓕
| 𝐸 ∪ ⋃𝓕\𝐸 = ⋃𝓕
| 𝐸 ≠ ∅
| 𝐸 ≠ ⋃𝓕 -> ⋃𝓕\𝐸 ≠ ∅

This description does immediately not rule out
your dark numbers and dark end segments.
Dark numbers could conceivably be in 𝐸
which are > each i in ⋃𝓕\𝐸

However,
this description requires 𝐸 subset ⋃𝓕
Each j in 𝐸 is in ⋃𝓕
Each j in ⋃𝓕 is in some FISON 𝐹
Each j in any FISON 𝐹 is not dark.

Each end segment 𝐸 of ⋃𝓕 has no dark numbers.

Also,
each end segment 𝐸 of ⋃𝓕 is infinite.

Also,
the intersection of all the end segments
is empty.

>> The intersection of all (infinite)
>> end segments is not an (infinite)
>> end segment.
>
> Either the intersection is infinite
> or it is not existing.

Either the intersection is infinite
or it is not an end segment.

It is not an end segment.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: plutoniu...@gmail.com (Archimedes Plutonium)
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 by: Archimedes Plutonium - Thu, 1 Sep 2022 19:18 UTC

WM take your mindless bs to sci.logic, since you are a failure of math for your (1) slant cut of cone is ellipse when actually it is a oval, (2) your crazy logic is Boole of 2 OR 1 = 3 with AND as subtraction (3) you are a failure of math never recognizing calculus is geometry and never able to see FTC needs a geometry proof (4) but worst of all, you are such a arsewipe of science you cannot even ask the question which is the atom's true electron-- the muon or 0.5MeV particle.

You waste everyone's time with your endless insane dark number bullshit-- go to sci. logic, leave sci.math for you insanely failed math.

Re: Natural numbers and vases III
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Archimedes Plutonium
Aug 31, 2022, 11:55:37 AM (yesterday)



to
Take this bullshit failed ignorance to sci.logic, you do not deserve to post in sci.math.
On Monday, July 18, 2022 at 4:29:37 PM UTC-5, WM wrote:

Take this bullshit over to sci.logic, for you are a math failure-- Your AND connector is subtraction with 2 OR 1 = 3. You do not even know a geometry proof of Fundamental Theorem of Calculus. You are a failure in geometry for your slant cut in cone is a ellipse when actually that is a oval. But worst of all-- your so stupid in science you cannot even ask the question which is the atom's true electron-- 0.5MeV particle or the muon stuck inside a 840 MeV proton torus.

You do not deserve to post in sci.math with your failed ignorance of math.

3rd published book

AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
by Archimedes Plutonium (Author)

Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.

Product details
• ASIN ‏ : ‎ B07PLSDQWC
• Publication date ‏ : ‎ March 11, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 1621 KB
• Text-to-Speech ‏ : ‎ Enabled
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Not Enabled
• Print length ‏ : ‎ 20 pages
• Lending ‏ : ‎ Enabled

Proofs Ellipse is never a Conic section, always a Cylinder section and a Well Defined Oval definition//Student teaches professor series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 14May2022. This is AP's 68th published book of science.

Preface: A similar book on single cone cut is a oval, never a ellipse was published in 11Mar2019 as AP's 3rd published book, but Amazon Kindle converted it to pdf file, and since then, I was never able to edit this pdf file, and decided rather than struggle and waste time, decided to leave it frozen as is in pdf format. Any new news or edition of ellipse is never a conic in single cone is now done in this book. The last thing a scientist wants to do is wade and waddle through format, when all a scientist ever wants to do is science itself. So all my new news and thoughts of Conic Sections is carried out in this 68th book of AP. And believe you me, I have plenty of new news.

In the course of 2019 through 2022, I have had to explain this proof often on Usenet, sci.math and sci.physics. And one thing that constant explaining does for a mind of science, is reduce the proof to its stripped down minimum format, to bare bones skeleton proof. I can prove the slant cut in single cone is a Oval, never the ellipse in just a one sentence proof. Proof-- A single cone and oval have just one axis of symmetry, while a ellipse requires 2 axes of symmetry, hence slant cut is always a oval, never the ellipse..

Product details
• ASIN ‏ : ‎ B081TWQ1G6
• Publication date ‏ : ‎ November 21, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 827 KB
• Simultaneous device usage ‏ : ‎ Unlimited
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Not Enabled
• Print length ‏ : ‎ 51 pages
• Lending ‏ : ‎ Enabled

#12-2, 11th published book

World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 15Dec2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.

Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". And very surprising that most math professors cannot tell the difference between a "proving something" and that of "analyzing something". As if an analysis is the same as a proof. We often analyze various things each and every day, but few if none of us consider a analysis as a proof. Yet that is what happened in the science of mathematics where they took an analysis and elevated it to the stature of being a proof, when it was never a proof.

To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?

Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.

Product details
ASIN ‏ : ‎ B07PQTNHMY
Publication date ‏ : ‎ March 14, 2019
Language ‏ : ‎ English
File size ‏ : ‎ 1309 KB
Text-to-Speech ‏ : ‎ Enabled
Screen Reader ‏ : ‎ Supported
Enhanced typesetting ‏ : ‎ Enabled
X-Ray ‏ : ‎ Not Enabled
Word Wise ‏ : ‎ Not Enabled
Print length ‏ : ‎ 154 pages
Lending ‏ : ‎ Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)

On Thursday, September 1, 2022 at 8:16:47 AM UTC-5, WM wrote:
> Jim Burns schrieb am Mittwoch, 31. August 2022 um 18:12:28 UTC+2:
> > On 8/31/2022 9:06 AM, WM wrote:
>
> > No end segment is last (⊇) of all
> > end segments.
>
> True. The reason is this: The infinite, definable endsegments are potentially infinite. The empty endsegment is not discernible among all infinite and finite dark endsegments.
> >
> > The intersection of all (infinite)
> > end segments is not an (infinite)
> > end segment.
>
> Either the intersection is infinite or it is not existing.
>
> In every case the states of a nonempty bathtub have a non-empty intersection. Likewise the intervals [0, 1+1/n] have a non-empty intersection. The existence of infinitely many states is not an argument for an empty intersection.
>
> Regards, WM


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

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