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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
|      |  |   | +- 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 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 IIIzelos...@gmail.com
|      |  |   | +- 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 IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- 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 IIIzelos...@gmail.com
|      |  |   | +- 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 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

<dc20d51e-f609-4ad3-8446-e681807c4bban@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Fri, 02 Sep 2022 13:32:56 +0000
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 by: WM - Fri, 2 Sep 2022 13:32 UTC

Jim Burns schrieb am Donnerstag, 1. September 2022 um 20:52:33 UTC+2:
> 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 (โŠ‡) 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_

No, it has come down from ancient mathematics, Cantor, and modern mathematics.

> If it arises from our description that
> all the end segments are infinite and
> the intersection of all the end segments
> is empty,

This is a contradiction, because endsegments are decreasing. But before they have decreaed to the empty set, they contain what all predecessors contain.

> This description does immediately not rule out
> your dark numbers and dark end segments.
> Dark numbers could conceivably be in ๐ธ
> which are > each i in โ‹ƒ๐“•\๐ธ
>
> However,
> this description requires ๐ธ subset โ‹ƒ๐“•

That is a wrong desription.

Regards, WM

Re: Natural numbers and vases III

<tet1o7$1lvr$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 2 Sep 2022 08:51:01 -0500
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 by: Sergio - Fri, 2 Sep 2022 13:51 UTC

On 9/2/2022 8:32 AM, WM wrote:
> Jim Burns schrieb am Donnerstag, 1. September 2022 um 20:52:33 UTC+2:
>> 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 (โŠ‡) 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_
>
> No, it has come down from ancient mathematics
No, it is not used at all today. You use it to mislead people.

>
>> If it arises from our description that
>> all the end segments are infinite and
>> the intersection of all the end segments
>> is empty,
>
> This is a contradiction,

Wrong, we have proved it mathematically many times to you in this forum, troll, it is consistent.

>
>> This description does immediately not rule out
>> your dark numbers and dark end segments.
>> Dark numbers could conceivably be in ๐ธ
>> which are > each i in โ‹ƒ๐“•\๐ธ
>>
>> However,
>> this description requires ๐ธ subset โ‹ƒ๐“•
>
>
> Regards, WM

Re: Natural numbers and vases III

<tet1qm$2hqpg$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: Fri, 02 Sep 2022 09:52:16 -0400
Organization: Peripheral Visions
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 by: FromTheRafters - Fri, 2 Sep 2022 13:52 UTC

WM formulated on Friday :
> Jim Burns schrieb am Donnerstag, 1. September 2022 um 20:52:33 UTC+2:
>> 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 (โŠ‡) 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_
>
> No, it has come down from ancient mathematics, Cantor, and modern
> mathematics.
>
>> If it arises from our description that
>> all the end segments are infinite and
>> the intersection of all the end segments
>> is empty,
>
> This is a contradiction, because endsegments are decreasing.

How are they decreasing? What do you mean here by decreasing? There
being a sequence of subsets of subsets does not mean any set changes
size. Each successive subset has one fewer symbol to 'match' or
'intersect' with some other 'later' subset. The 'intersection' is
'decreasing' by that same notion, so your analogy fails. The
intersection is 'heading' for the emptyset by the same mental mechanism
from which you build your fantasy.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 2 Sep 2022 14:14 UTC

Archimedes Plutonium schrieb am Donnerstag, 1. September 2022 um 21:18:19 UTC+2:
> WM take your mindless bs to sci.logic,

You prefer mindful bs?

> since you are a failure of math for your (1) slant cut of cone is ellipse when actually it is a oval

Sorry, I cannot agree. The ellipse is proved in my book
W. Mรผckenheim: "Mathematik fรผr die ersten Semester", 4th ed., De Gruyter, Berlin (2015).
(And it was already proved so in the first edition - unfortunately not for the first time.)

> (2) your crazy logic is Boole of 2 OR 1 = 3 with AND as subtraction

I never said so.

(3) you are a failure of math never recognizing calculus is geometry and never able to see FTC needs a geometry proof

I prefer geometrical proofs wherever applicable.

> (4) but worst of all, you cannot even ask the question which is the atom's true electron-- the muon or 0.5MeV particle.

Sorry, I have detected more that 997567 electron-positron annihilations during my career and always found the 511 keV detected in the detectors.
>
> You waste everyone's time with your endless insane dark number bullshit

Can you explain how by exchanging X's and O's in the matrix

XOOO...
XOOO...
XOOO...
XOOO...
....

all O's will be removed from the matrix?

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: Fri, 2 Sep 2022 09:35:12 -0500
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 by: Sergio - Fri, 2 Sep 2022 14:35 UTC

On 9/2/2022 9:14 AM, WM wrote:
> Archimedes Plutonium schrieb am Donnerstag, 1. September 2022 um 21:18:19 UTC+2:
>> WM take your mindless bs to sci.logic,
>
> You prefer mindful bs?
>
>> since you are a failure of math for your (1) slant cut of cone is ellipse when actually it is a oval
>
> Sorry, I cannot agree. The ellipse is proved in my book
> W. Mรผckenheim: "Mathematik fรผr die ersten Semester", 4th ed., De Gruyter, Berlin (2015).
> (And it was already proved so in the first edition - unfortunately not for the first time.)
>
>> (2) your crazy logic is Boole of 2 OR 1 = 3 with AND as subtraction
>
> I never said so.
>
> (3) you are a failure of math never recognizing calculus is geometry and never able to see FTC needs a geometry proof
>
> I prefer geometrical proofs wherever applicable.
>
>> (4) but worst of all, you cannot even ask the question which is the atom's true electron-- the muon or 0.5MeV particle.
>
> Sorry, I have detected more that 997567 electron-positron annihilations during my career and always found the 511 keV detected in the detectors.
>>
>> You waste everyone's time with your endless insane dark number bullshit
>
> Can you explain how by exchanging X's and O's in the matrix
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> all O's will be removed from the matrix?
>
> Regards, WM

just count them and find out

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 - Fri, 2 Sep 2022 14:44 UTC

On Friday, September 2, 2022 at 3:33:01 PM UTC+2, WM wrote:
> Jim Burns schrieb am Donnerstag, 1. September 2022 um 20:52:33 UTC+2:
>
> endsegments are decreasing.

No, not the endsegments re decreasing, but the _sequence_ of endsegments (E_n)_(neIN) defined with E_n = {m e IN: m >= n} for all n e IN.

***sigh***

No brain, no math.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 2 Sep 2022 15:45 UTC

Fritz Feldhase schrieb am Freitag, 2. September 2022 um 16:44:51 UTC+2:
> On Friday, September 2, 2022 at 3:33:01 PM UTC+2, WM wrote:
> > Jim Burns schrieb am Donnerstag, 1. September 2022 um 20:52:33 UTC+2:
> >
> > endsegments are decreasing.
>
> No, not the endsegments re decreasing, but the _sequence_ of endsegments

The number of people going home decreases slowly after 6 pm.
https://ell.stackexchange.com/questions/86340/people-decrease-or-the-number-of-people-decrease

Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 2 Sep 2022 15:57 UTC

FromTheRafters schrieb am Freitag, 2. September 2022 um 15:52:32 UTC+2:
> WM formulated on Friday :

> > This is a contradiction, because endsegments are decreasing.
> How are they decreasing?

Verymuch liek the states of water flowing out of a bathub. They will never have an empty intersection before the bathtub is empty. "Mathematics" contradicting this basic principle is rubbish.

> What do you mean here by decreasing? There
> being a sequence of subsets of subsets does not mean any set changes
> size.

That's a matter of language. The number of people going home decreases slowly after 6 pm. https://ell.stackexchange.com/questions/86340/people-decrease-or-the-number-of-people-decrease

> Each successive subset has one fewer symbol to 'match' or
> 'intersect' with some other 'later' subset.

Exactly.
One less!
โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}

> The 'intersection' is
> 'decreasing' by that same notion, so your analogy fails.

On the contrary. It is true.

> The
> intersection is 'heading' for the emptyset

but will not reach it unless the empty et is reached by the endsegments producing the intersection.

Before coming down this forum I would never have believed in the existence of such foolish thinking as I encountered here.

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 - Fri, 2 Sep 2022 16:12 UTC

Jim Burns schrieb am Mittwoch, 31. August 2022 um 19:41:04 UTC+2:

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

As soon as there is no longer an infinite set, the next state of affairs is a finite set by the very definition of endsegments, i.e., simple mathematics: โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

To overlook this shows incompetence in mathematics and logic.

To deny it by the analogy that
โˆ€k โˆˆ โ„• โˆƒm โˆˆ โ„•: k < m ==> โˆƒm โˆˆ โ„• โˆ€k โˆˆ โ„•: k < m
is an invalid conclusion and shows naivety.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 2 Sep 2022 16:15 UTC

Jim Burns schrieb am Mittwoch, 31. August 2022 um 19:41:04 UTC+2:

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

As soon as there is no longer an infinite set, the next state of affairs is a finite set by the very definition of endsegments, i.e., simple mathematics: โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

To overlook this shows incompetence in mathematics and logic.

To deny it by the analogy that
โˆ€k โˆˆ โ„• โˆƒm โˆˆ โ„•: k < m ==> โˆƒm โˆˆ โ„• โˆ€k โˆˆ โ„•: k < m
is an invalid conclusion, is an invalid conclusion and shows naivety.

Regards, WM

Re: Natural numbers and vases III

<tetari$2iq8m$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: Fri, 02 Sep 2022 12:26:20 -0400
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 by: FromTheRafters - Fri, 2 Sep 2022 16:26 UTC

WM presented the following explanation :
> FromTheRafters schrieb am Freitag, 2. September 2022 um 15:52:32 UTC+2:
>> WM formulated on Friday :
>
>>> This is a contradiction, because endsegments are decreasing.
>> How are they decreasing?
>
> Verymuch liek the states of water flowing out of a bathub. They will never
> have an empty intersection before the bathtub is empty. "Mathematics"
> contradicting this basic principle is rubbish.
>
>> What do you mean here by decreasing? There
>> being a sequence of subsets of subsets does not mean any set changes
>> size.
>
> That's a matter of language. The number of people going home decreases slowly
> after 6 pm.
> https://ell.stackexchange.com/questions/86340/people-decrease-or-the-number-of-people-decrease
>
>> Each successive subset has one fewer symbol to 'match' or
>> 'intersect' with some other 'later' subset.
>
> Exactly.
> One less!
> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}
>
>> The 'intersection' is
>> 'decreasing' by that same notion, so your analogy fails.
>
> On the contrary. It is true.
>
>> The
>> intersection is 'heading' for the emptyset
>
> but will not reach it unless the empty et is reached by the endsegments
> producing the intersection.
>
> Before coming down this forum I would never have believed in the existence of
> such foolish thinking as I encountered here.

Many of us are thinking the same thing.

Re: Natural numbers and vases III

<aa6f4474-f249-1d73-ce7c-25b112ea9404@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 2 Sep 2022 13:22:07 -0400
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 by: Jim Burns - Fri, 2 Sep 2022 17:22 UTC

On 9/2/2022 9:32 AM, WM wrote:
> Jim Burns schrieb am Donnerstag,
> 1. September 2022 um 20:52:33 UTC+2:

>> If it arises from our description that
>> all the end segments are infinite and
>> the intersection of all the end segments
>> is empty,
>
> This is a contradiction,
> because endsegments are decreasing.

Each non-โˆ… end segment of โ‹ƒ๐“• is infinite.

NO n exists in any FISON ๐นโ‚™ such that
n+1 is NOT in some FISON ๐นโ‚™โˆชโŸจn+1โŸฉ

NO n exists in โ‹ƒ๐“• such that
n+1 is NOT in โ‹ƒ๐“•
== โ‹ƒ๐“• is infinite.

For each non-โˆ… end segment ๐ธ of โ‹ƒ๐“•,
NO n exists in ๐ธ such that
n+1 is NOT in ๐ธ
== ๐ธ is infinite.

----
The intersection of all non-โˆ… end segments
of โ‹ƒ๐“• is โˆ….

For each FISON ๐น
its complement โ‹ƒ๐“•\๐น is a non-โˆ… end segment.

If
n is in each non-โˆ… end segment ๐ธ,
then
n is not-in ๐น

If
n is not-in each FISON ๐น,
then
n is not in โ‹ƒ๐“•
and
n is not-in each non-โˆ… end segment ๐ธ โŠ† โ‹ƒ๐“•
and
n is not in the intersection โ‹‚๐“” of
all non-โˆ… end segments of โ‹ƒ๐“•

Only elements which aren't in โ‹‚๐“”
can be in โ‹‚๐“”
โ‹‚๐“” = โˆ…

> But before they have decreased to
> the empty set, they contain
> what all predecessors contain.

If there is one non-โˆ… end segment which
n is not in, then n is not in their
intersection.

>> This description does immediately not rule out
>> your dark numbers and dark end segments.
>> Dark numbers could conceivably be in ๐ธ
>> which are > each i in โ‹ƒ๐“•\๐ธ
>>
>> However,
>> this description requires ๐ธ subset โ‹ƒ๐“•
>
> That is a wrong desription.

No.
The end segments of a set are subsets
of that set.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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 by: Sergio - Fri, 2 Sep 2022 17:39 UTC

On 9/2/2022 10:57 AM, WM wrote:
> FromTheRafters schrieb am Freitag, 2. September 2022 um 15:52:32 UTC+2:
>> WM formulated on Friday :
>
>>> This is a contradiction, because endsegments are decreasing.
>> How are they decreasing?
>
> Verymuch liek the states of water flowing out of a bathub. They will never have an empty intersection before the bathtub is empty. "Mathematics" contradicting this basic principle is rubbish.

still Wrong. you just do not/can not understand that "intersection" is an operator on sets.

endsegments are not like water in bathtub at all.

>
>> What do you mean here by decreasing? There
>> being a sequence of subsets of subsets does not mean any set changes
>> size.
>
> That's a matter of language. The number of people going home decreases slowly after 6 pm. https://ell.stackexchange.com/questions/86340/people-decrease-or-the-number-of-people-decrease

another red herring.

>
>> Each successive subset has one fewer symbol to 'match' or
>> 'intersect' with some other 'later' subset.
>
> Exactly.
> One less!
> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k}
>
>> The 'intersection' is
>> 'decreasing' by that same notion,

wrong, there is no decreasing. "intersection" is an operator on sets, it finds the common elements.

>
>> The
>> intersection is 'heading' for the emptyset

nope, intersection is infinite with finite number of endsegments, then empty if you include All endsegments

a step function (not step by step)

>
> but will not reach it unless the empty et is reached by the endsegments producing the intersection.

wrong.

>
> Before coming down this forum I would never have believed in the existence of such foolish thinking as I encountered here.
>
> Regards, WM

you bring the foolish thinking with you, you have it in spades

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: Fri, 2 Sep 2022 13:39:24 -0500
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 by: Sergio - Fri, 2 Sep 2022 18:39 UTC

On 9/2/2022 11:12 AM, WM wrote:
> Jim Burns schrieb am Mittwoch, 31. August 2022 um 19:41:04 UTC+2:
>
>> | For each natural k,
>> and
>> | there is an infinite set E,
>> are swapped.
>> It is an invalid step.
>
> As soon as there is no longer an infinite set, the next state of affairs is a finite set by the very definition of endsegments, i.e., simple mathematics: โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

that is not a step by step equation.

It is relationship of two adjacent endsegments, that is all.

but you know this.

>
> To overlook this shows incompetence in mathematics and logic.

corrected: "To agree with WM shows incompetence in mathematics and logic."

>
> Regards, 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: Fri, 2 Sep 2022 14:48:47 -0400
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 by: Jim Burns - Fri, 2 Sep 2022 18:48 UTC

On 9/2/2022 12:15 PM, WM wrote:
> Jim Burns schrieb am Mittwoch,
> 31. August 2022 um 19:41:04 UTC+2:

>> | For each natural k,
>> and
>> | there is an infinite set E,
>> are swapped.
>> It is an invalid step.
>
> As soon as there is no longer an infinite set,
> the next state of affairs is
> a finite set by the very definition of
> endsegments, i.e., simple mathematics:
> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

Consider some set ๐”ป of dark numbers
appended to the set โ‹ƒ๐“• of FISON-ends.
I'll write ๐”ป appended to โ‹ƒ๐“• as (โ‹ƒ๐“•)โŠ•๐”ป

Everything in โ‹ƒ๐“• < everything in ๐”ป
โ‹ƒ๐“• and ๐”ป keep the same order internally.
You (WM) want ๐”ป to have no internal order.
Correct? ๐”ป keeps its no-internal-order.

> As soon as there is no longer an infinite set,

There is always an infinite set.

It doesn't matter what's in ๐”ป
For each element n of โ‹ƒ๐“•,
there is an infinite set after n _in โ‹ƒ๐“•_

For each FISON ๐นโ‚™, ๐นโ‚™โˆชโŸจn+1โŸฉ is a FISON too.
Each FISON-end is not the last FISON-end.
There is no last FISON-end.

----
There is nothing that can be appended to โ‹ƒ๐“•
in ๐”ป which is able to make anything after โ‹ƒ๐“•
accessible from โ‹ƒ๐“•.
It doesn't matter what is in ๐”ป

โ‹ƒ๐“• and ๐”ป are a split of (โ‹ƒ๐“•)โŠ•๐”ป
By 'โŠ•',
everything in โ‹ƒ๐“• < everything in ๐”ป
A split.

No step in (โ‹ƒ๐“•)โŠ•๐”ป begins
before that split and ends after it.

No matter what is in ๐”ป,
the answer is the same.
No step begins before and ends after,
because
each step that begins before (in โ‹ƒ๐“•)
ends before (in โ‹ƒ๐“•).

And that's because ๐นโ‚™โˆชโŸจn+1โŸฉ is a FISON.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 2 Sep 2022 19:54 UTC

Jim Burns schrieb am Freitag, 2. September 2022 um 20:48:57 UTC+2:
> On 9/2/2022 12:15 PM, WM wrote:
> You (WM) want ๐”ป to have no internal order.
> Correct? ๐”ป keeps its no-internal-order.

There is no chance to distinguish the dark elements although for every visible element n also n^n^n^n^n is a vsible element.

> > As soon as there is no longer an infinite set,
> There is always an infinite set.

Then there is no empty intersection.
>
> It doesn't matter what's in ๐”ป
> For each element n of โ‹ƒ๐“•,
> there is an infinite set after n _in โ‹ƒ๐“•_

Yes, the terms below n^n^n^n^n^n^n are all visible.
But if Cantor is right, then the dark terms are many,many more than all visisble terms. They cannot be exhausted.
>
> For each FISON ๐นโ‚™, ๐นโ‚™โˆชโŸจn+1โŸฉ is a FISON too.
> Each FISON-end is not the last FISON-end.
> There is no last FISON-end.

Right. But that makes the collection of visisble elements not larger tan every natural number.
>
> ----
> There is nothing that can be appended to โ‹ƒ๐“•
> in ๐”ป which is able to make anything after โ‹ƒ๐“•
> accessible from โ‹ƒ๐“•.
> It doesn't matter what is in ๐”ป

That is correct. ๐”ป does not matter in mathematics.
>
> โ‹ƒ๐“• and ๐”ป are a split of (โ‹ƒ๐“•)โŠ•๐”ป
> By 'โŠ•',
> everything in โ‹ƒ๐“• < everything in ๐”ป

That is obvious because everything in โ‹ƒ๐“• is smaller than the largest element. Nevertheless no single dark element can be defined.

> A split.
>
> No step in (โ‹ƒ๐“•)โŠ•๐”ป begins
> before that split and ends after it.

Correct.
>
> No matter what is in ๐”ป,
> the answer is the same.
> No step begins before and ends after,
> because
> each step that begins before (in โ‹ƒ๐“•)
> ends before (in โ‹ƒ๐“•).

That is correct.
>
> And that's because ๐นโ‚™โˆชโŸจn+1โŸฉ is a FISON.

Even ๐นโ‚™โˆช{1, 2, 3, ..., n^n^n^n^n^n^n} is a FISON..
That is called potential infinity.

But if all endsegments are existing, then (and only then) all elements can be removed such that none remains, but by the very definition of endsegments, only one per endsegment.:
โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

All infinite endsegments have an infinite set in common.
To deny it by the analogy that
โˆ€k โˆˆ โ„• โˆƒm โˆˆ โ„•: k < m ==> โˆƒm โˆˆ โ„• โˆ€k โˆˆ โ„•: k < m
is an invalid conclusion, is an invalid conclusion and shows naivety.

Regards, WM

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 2 Sep 2022 17:21:05 -0400
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 by: Jim Burns - Fri, 2 Sep 2022 21:21 UTC

On 9/2/2022 3:54 PM, WM wrote:
> Jim Burns schrieb am Freitag,
> 2. September 2022 um 20:48:57 UTC+2:
>> On 9/2/2022 12:15 PM, WM wrote:

>>> As soon as there is no longer an infinite set,
>>
>> There is always an infinite set.
>
> Then there is no empty intersection.

Consider some set ๐”ป of dark numbers
appended to the set โ‹ƒ๐“• of FISON-ends.
I'll write ๐”ป appended to โ‹ƒ๐“• as (โ‹ƒ๐“•)โŠ•๐”ป

There is always an infinite set.

If
there exists _any_ n โˆˆ โ‹ƒ๐“• such that
E(n)โˆฉ(โ‹ƒ๐“•) _cannot_ match โ‹ƒ๐“•
then
there exists a _first_ n1 โˆˆ โ‹ƒ๐“• such that
E(nโ‚)โˆฉ(โ‹ƒ๐“•) _cannot_ match โ‹ƒ๐“•
but
E(nโ‚-1)โˆฉ(โ‹ƒ๐“•) _can_ match โ‹ƒ๐“•

However,
E(nโ‚-1)โˆฉ(โ‹ƒ๐“•) _can_ match E(nโ‚)โˆฉ(โ‹ƒ๐“•)
Thus,
E(nโ‚)โˆฉ(โ‹ƒ๐“•) _can_ match โ‹ƒ๐“•
Contradiction.

Therefore,
there doesn't exist _any_ n โˆˆ โ‹ƒ๐“• such that
E(n)โˆฉ(โ‹ƒ๐“•) _cannot_ match โ‹ƒ๐“•
and
there is always an infinite set.

----
> Then there is no empty intersection.

No.

Let ๐“” be the set of all end segments of (โ‹ƒ๐“•)โŠ•๐”ป

No element in โ‹ƒ๐“• is in all ๐ธ in ๐“”

The intersection โ‹‚๐“” of all end segments
is a subset of ๐”ป
โ‹‚๐“” โŠ† ๐”ป

From above,
each end segment of (โ‹ƒ๐“•)โŠ•๐”ป is infinite
no matter what is in ๐”ป

If ๐”ป = โˆ…, then _still_
each end segment of (โ‹ƒ๐“•)โŠ•๐”ป is infinite,
but โ‹‚๐“” โŠ† โˆ…
so โ‹‚๐“” = โˆ…

>> For each FISON ๐นโ‚™, ๐นโ‚™โˆชโŸจn+1โŸฉ is a FISON too.
>> Each FISON-end is not the last FISON-end.
>> There is no last FISON-end.
>
> Right.
> But that makes the collection of
> visisble elements not larger tan
> every natural number.

No, the opposite of that.
For each FISON-end n,
there are more FISON-ends than in ๐นโ‚™

For each FISON ๐นโ‚™, ๐นโ‚™โˆชโŸจn+1โŸฉ is a FISON 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: Fri, 2 Sep 2022 16:21:50 -0500
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 by: Sergio - Fri, 2 Sep 2022 21:21 UTC

On 9/2/2022 1:48 PM, Jim Burns wrote:
> On 9/2/2022 12:15 PM, WM wrote:
>> Jim Burns schrieb am Mittwoch,
>> 31. August 2022 um 19:41:04 UTC+2:
>
>>> | For each natural k,
>>> and
>>> | there is an infinite set E,
>>> are swapped.
>>> It is an invalid step.
>>
>> As soon as there is no longer an infinite set,
>> the next state of affairs is
>> a finite set by the very definition of
>> endsegments, i.e., simple mathematics:
>> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .
>
> Consider some set ๐”ป of dark numbers

there are no sets of dark numbers, as dark numbers cannot be elements, silly.

Re: Natural numbers and vases III

<tetsgf$1if1$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: Fri, 2 Sep 2022 23:27:39 +0200
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 by: Tom Bola - Fri, 2 Sep 2022 21:27 UTC

Sergio schrieb:
> On 9/2/2022 1:48 PM, Jim Burns wrote:
>> On 9/2/2022 12:15 PM, WM wrote:
>>> Jim Burns schrieb am Mittwoch,
>>> 31. August 2022 um 19:41:04 UTC+2:
>>
>>>> | For each natural k,
>>>> and
>>>> | there is an infinite set E,
>>>> are swapped.
>>>> It is an invalid step.
>>>
>>> As soon as there is no longer an infinite set,
>>> the next state of affairs is
>>> a finite set by the very definition of
>>> endsegments, i.e., simple mathematics:
>>> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .
>>
>> Consider some set ๏ฟฝ๏ฟฝ of dark numbers
>
>
> there are no sets of dark numbers, as dark numbers cannot be elements, silly.

LOL,
yep, that's by one's will (you cannot visualize the
very idea that nature is not made by some ONE's will)...

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: Fri, 2 Sep 2022 17:42:11 -0400
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 by: Jim Burns - Fri, 2 Sep 2022 21:42 UTC

On 9/2/2022 5:21 PM, Sergio wrote:
> On 9/2/2022 1:48 PM, Jim Burns wrote:
>> On 9/2/2022 12:15 PM, WM wrote:
>>> Jim Burns schrieb am Mittwoch,
>>> 31. August 2022 um 19:41:04 UTC+2:

>>>> | For each natural k,
>>>> and
>>>> | there is an infinite set E,
>>>> are swapped.
>>>> It is an invalid step.
>>>
>>> As soon as there is no longer an infinite set,
>>> the next state of affairs is
>>> a finite set by the very definition of
>>> endsegments, i.e., simple mathematics:
>>> โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .
>>
>> Consider some set ๐”ป of dark numbers
>
> there are no sets of dark numbers,
> as dark numbers cannot be elements,
> silly.

I am a silly person. So I've been told IRL.

๐”ป is so far the best I can do to
characterize WM's dark numbers.

I will fall short at some point, of course.
His dark numbers are nonsense.
Making sense of them misses what they are.

But I am silly, so it amuses me to try.

Re: Natural numbers and vases III

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From: Tom...@bolamail.etc (Tom Bola)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 2 Sep 2022 23:52:08 +0200
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 by: Tom Bola - Fri, 2 Sep 2022 21:52 UTC

Jim Burns

[๏ฟฝ๏ฟฝ - Dark Numbers]

> Making sense of them misses what they are.

Bingo Bolero!

That's the final way to idealize these... but you never know ;)

However, WM is an abhoring asshole...

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 3 Sep 2022 20:15 UTC

Jim Burns schrieb am Freitag, 2. September 2022 um 19:22:17 UTC+2:
> On 9/2/2022 9:32 AM, WM wrote:
> > Jim Burns schrieb am Donnerstag,
> > 1. September 2022 um 20:52:33 UTC+2:
> >> If it arises from our description that
> >> all the end segments are infinite and
> >> the intersection of all the end segments
> >> is empty,
> >
> > This is a contradiction,
> > because endsegments are decreasing.
> Each non-โˆ… end segment of โ‹ƒ๐“• is infinite.

Wrong. As soon as there is no longer an infinite common set, the next state of affairs is a finite set by the very definition of endsegments, i.e., simple mathematics: โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

To deny it by the analogy that
โˆ€k โˆˆ โ„• โˆƒm โˆˆ โ„•: k < m ==> โˆƒm โˆˆ โ„• โˆ€k โˆˆ โ„•: k < m
is an invalid conclusion, is an invalid conclusion and shows naivety.

> > But before they have decreased to
> > the empty set, they contain
> > what all predecessors contain.
> If there is one non-โˆ… end segment which
> n is not in, then n is not in their
> intersection.

There is no definable n in the intersection. Nevertheless the intersection of infinite endsegments is infinite.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 3 Sep 2022 20:21 UTC

Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:

> Consider some set ๐”ป of dark numbers

Consider a bathtub. That makes all your arguments rubbish. Therefore I have deleted them and will no longer read them.

All states of a leaking bathtub which is not empty have a non-empty intersection.

Regards, WM

Re: Natural numbers and vases III

<tf0dc6$1ap4$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 3 Sep 2022 15:27:49 -0500
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 by: Sergio - Sat, 3 Sep 2022 20:27 UTC

On 9/3/2022 3:15 PM, WM wrote:
> Jim Burns schrieb am Freitag, 2. September 2022 um 19:22:17 UTC+2:
>> On 9/2/2022 9:32 AM, WM wrote:
>>> Jim Burns schrieb am Donnerstag,
>>> 1. September 2022 um 20:52:33 UTC+2:
>>>> If it arises from our description that
>>>> all the end segments are infinite and
>>>> the intersection of all the end segments
>>>> is empty,
>>>
>>> This is a contradiction,
>>> because endsegments are decreasing.
>> Each non-โˆ… end segment of โ‹ƒ๐“• is infinite.
>
> Wrong. As soon as there is no longer an infinite common set, the next state of affairs is a finite set by the very definition of endsegments, i.e., simple mathematics: โˆ€k โˆˆ โ„•: E(k+1) = E(k) \ {k} .

that is only the relationship between adjacent endsegments.
It is not a step by step, that requires MORE, but you do not know how to do it.

>
> To deny it by the analogy that
> โˆ€k โˆˆ โ„• โˆƒm โˆˆ โ„•: k < m ==> โˆƒm โˆˆ โ„• โˆ€k โˆˆ โ„•: k < m
> is an invalid conclusion, is an invalid conclusion and shows naivety.

Red herring.

>
>>> But before they have decreased to
>>> the empty set, they contain
>>> what all predecessors contain.
>> If there is one non-โˆ… end segment which
>> n is not in, then n is not in their
>> intersection.
>
> There is no definable n in the intersection. Nevertheless the intersection of infinite endsegments is infinite.

Wrong. Prove it using Math, lazy bones.

>
> 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: Sat, 3 Sep 2022 15:29:00 -0500
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 by: Sergio - Sat, 3 Sep 2022 20:29 UTC

On 9/3/2022 3:21 PM, WM wrote:
> Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
>
>> Consider some set ๐”ป of dark numbers
>
> Consider a bathtub. That makes all your arguments rubbish. Therefore I have deleted them and will no longer read them.
>
> All states of a leaking bathtub which is not empty have a non-empty intersection.

Prove it using Math, blowhard.

What is in the intersection ? a common core ?

>
> Regards, WM

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

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