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The autodecrement is not magical. -- Larry Wall in the perl man page

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 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

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Thu, 11 Aug 2022 12:53 UTC


Gus Gassmann schrieb am Mittwoch, 10. August 2022 um 20:46:32 UTC+2:
> On Wednesday, 10 August 2022 at 14:06:51 UTC-3, Fritz Feldhase wrote:
> > On Wednesday, August 10, 2022 at 6:56:22 PM UTC+2, Gus Gassmann wrote:
> > > On Wednesday, 10 August 2022 at 12:32:16 UTC-3, WM wrote:
> > > > Gus Gassmann schrieb am Dienstag, 9. August 2022 um 14:15:21 UTC+2:
> > > > > On Tuesday, 9 August 2022 at 07:51:27 UTC-3, WM wrote:
> > > > > >
> > > > > > XOOOO...
> > > > > > XOOOO...
> > > > > > XOOOO...
> > > > > > XOOOO...
> > > > > > XOOOO...
> > > > > > ...
> > > > > >
> > > > > > will never become
> > > > > >
> > > > > > XXX...
> > > > > > XXX...
> > > > > > XXX...
> > > > > > ...
> > > > > >
> > > > > > by exchanges of X and O.
> > > > >
> > > > > Because you say so?

Because it is correct. You see, that your approach is not even accepted by matheologians. You are wrong!

> > > > >
> > > > No, because never an O will disappear.
> > > >
> > > Hence, because you say so.
> > No, because he is right.
> > Hint: If there is an O in the matrix A then there's an O in the matrix swap(i,j;k,l)(A).
> > > I talked about a *limit* [...]
> >
> > In contrast to WM.
> >
> > Starting with the "original" matrix NO swap will "result in" the limit matrix. Right?
> In the sense that the matrix of all X is one of the matrices in the sequence of exchanges, of course not. But that does not, of course, invalidate the Cantor enumeration of the positive rationals,

The enumeration would appear completely in the sequence of exchanges. Every term is one enumeration. How many enumerations are reserved for the limit?

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, 11 Aug 2022 12:55 UTC

Gus Gassmann schrieb am Mittwoch, 10. August 2022 um 20:55:33 UTC+2:
> On Wednesday, 10 August 2022 at 14:06:51 UTC-3, Fritz Feldhase wrote:

> > Starting with the "original" matrix NO swap will "result in" the limit matrix. Right?
> >
> > (You see, I don't think that we should talk about "supertasks" in this context.)
> Is the taking of a limit a "supertask"? I happen to think not, and I do not want to give anybody any cover to try to claim that taking the limit of 1/n as n-->oo is a supertask and hence not possible.

That is not a super task. That is possible and correct. But you are confusing many things.

> Maybe I am a radical, but when I see a map from |N to A, I always try to visualize a limiting expression or object.

That is wrong. Try to visiualize the truth.

> With any of WM's processes that he claims prove the inconsistency of ZFC, the limit is self-evident.

It is self-evident that your limit cannot be correct by enumerating fractions. That would mean that by exchanging X and O the matrix
XOOOO...
XOOOO...
XOOOO...
XOOOO...
XOOOO...
....
loses all its O's.

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, 11 Aug 2022 12:56 UTC

Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 02:02:26 UTC+2:
> On Wednesday, August 10, 2022 at 8:55:33 PM UTC+2, Gus Gassmann wrote:

> > > Starting with the "original" matrix NO swap will "result in" the limit matrix. Right?
> > >
No indexing will complete the task.

> > Is the taking of a limit a "supertask"?
> Of course not.

It is simply nonsens, to write the desired matrix and to believe it was a limit.
But Cantor's enumeration is a super task.

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, 11 Aug 2022 07:59:23 -0500
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 by: Sergio - Thu, 11 Aug 2022 12:59 UTC

On 8/11/2022 7:50 AM, WM wrote:
> Fritz Feldhase schrieb am Mittwoch, 10. August 2022 um 19:06:51 UTC+2:
>> On Wednesday, August 10, 2022 at 6:56:22 PM UTC+2, Gus Gassmann wrote:
>>> On Wednesday, 10 August 2022 at 12:32:16 UTC-3, WM wrote:
>>>> Gus Gassmann schrieb am Dienstag, 9. August 2022 um 14:15:21 UTC+2:
>>>>> On Tuesday, 9 August 2022 at 07:51:27 UTC-3, WM wrote:
>>>>>>
>>>>>> XOOOO...
>>>>>> XOOOO...
>>>>>> XOOOO...
>>>>>> XOOOO...
>>>>>> XOOOO...
>>>>>> ...
>>>>>>
>>>>>> will never become
>>>>>>
>>>>>> XXX...
>>>>>> XXX...
>>>>>> XXX...
>>>>>> ...
>>>>>>
>>>>>> by exchanges of X and O.
>>>>>
>>>>> Because you say so?
>>>>>
>>>> No, because never an O will disappear.
>>>>
>>> Hence, because you say so.
>> No, because he is right.
>> Hint: If there is an O in the matrix A then there's an O in the matrix swap(i,j;k,l)(A).
>>> I talked about a *limit* [...]
>>
>> In contrast to WM.
>>
>> Starting with the "original" matrix NO swap will "result in" the limit matrix. Right?
>>
>> (You see, I don't think that we should talk about "supertasks" in this context.)
>
> Cantor used it. He said that every step can be defined. "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen" [Cantor, p. 119]

1. your reference is only about simple one to one mapping
2. Here you reference Cantors work as good, however you disparage Cantors work.
3. your swaparoo matrix ignores Math, that's why it is wrong.

>
> 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, 11 Aug 2022 13:00 UTC

Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 02:17:38 UTC+2:

> It's nice to see that we can actually get
>
> > > > > > XXX...
> > > > > > XXX...
> > > > > > XXX...
> > > > > > ...
> > > > > >
>
> as the limit of this sequence

It is not the limit.

> (decribed by Mückenheim).

The sequence has been described first by Cantor.
>
> But what do we GAIN by that? Cantor's "argument" does not need this fact. It does not refer to a "limit of a sequence" descibing the results of swaps).

Very correct! All must happen element by element, i.e., as steps of a super task.
>
> Cantor just defined a certain sequence (and proved certain properies of that sequence), that's all.

Not quite. He proved certain properties in the _finite_ case.

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, 11 Aug 2022 13:00 UTC

Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 04:31:28 UTC+2:
> On Wednesday, 10 August 2022 at 21:17:38 UTC-3, Fritz Feldhase wrote:
> [...]
> > It's nice to see that we can actually get
> >
> > > > > > > XXX...
> > > > > > > XXX...
> > > > > > > XXX...
> > > > > > > ...
> > > > > > >
> >
> > as the limit of this sequence (decribed by Mückenheim).
> >
> > But what do we GAIN by that? Cantor's "argument" does not need this fact. It does not refer to a "limit of a sequence" descibing the results of swaps).

Correct. But most matheologians have not yet grasped that fact.

> I like to use it to stick another pin into WM's balloon.

You have none.

> I did not invent the matrix sequence, but WM used it to convince himself that it disproves Cantor. I am trying to show him that you can get results from it that agree with Cantor.

But not in the way Cantor prescribed. Therefore you fail.

> > Cantor just defined a certain sequence (and proved certain properies of that sequence), that's all.

And he proved that every step can be checked. But only finitely many. And never a new X appears.

> But he accepts limits, at least in some forms, so my hope was/is that by making him look at the limiting behaviour of other sequences he'd actually figure something out.

Cantor did not use any limit. He said that every step can be defined. "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen" [Cantor, p. 119] No limits involved.

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, 11 Aug 2022 13:00 UTC

zelos...@gmail.com schrieb am Donnerstag, 11. August 2022 um 07:10:35 UTC+2:
> onsdag 10 augusti 2022 kl. 17:41:55 UTC+2 skrev WM:
> > zelos...@gmail.com schrieb am Mittwoch, 10. August 2022 um 07:52:19 UTC+2:
> > > tisdag 9 augusti 2022 kl. 13:54:44 UTC+2 skrev WM:
> >
> > > > Of course. All intersections with definable endsegments are finite. The infinite intersection contains endsegments which are not individually definable.
> > > >
> > > Your "definable" is meaningless.
> >
> > The set can only be subtracted collectively.
> your "collectively" is meaningless

It means as a whole and not by successively omittig elements.
>
> > |ℕ \ ℕ| = 0
>
> Correct
> > Every element or FISON subtracted will leave almost all of the set remaining.
> > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > Can you guess why?
> Because that is how cardinal arithmetic fucking works.

Why does it work that way and not other?

Regards, WM

Re: Natural numbers and vases III

<td2upf$1pnv$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
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 by: Sergio - Thu, 11 Aug 2022 13:04 UTC

On 8/11/2022 7:49 AM, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 10. August 2022 um 18:56:22 UTC+2:
>> On Wednesday, 10 August 2022 at 12:32:16 UTC-3, WM wrote:
>>> Gus Gassmann schrieb am Dienstag, 9. August 2022 um 14:15:21 UTC+2:
>>>> On Tuesday, 9 August 2022 at 07:51:27 UTC-3, WM wrote:
>>>>> XOOOO...
>>>>> XOOOO...
>>>>> XOOOO...
>>>>> XOOOO...
>>>>> XOOOO...
>>>>> ...
>>>>>
>>>>> will never become
>>>>>
>>>>> XXX...
>>>>> XXX...
>>>>> XXX...
>>>>> ...
>>>>>
>>>>> by exchanges of X and O.
>>>> Because you say so?
>>> No, because never an O will disappear.
>> Hence, because you say so.
>
> No, because an exchange of X and O will never delete anything.

too shallow, and what is your swapadoodle algroithum ?

>
>> I talked about a*limit*,
>
> Cantor did not. His enumeration happens step by step. How many exchanges are left for the "limit"?

you fail to understand induction and limits.

>
>> which you clearly are too
>
> intelligent to accept that inconsistent delusion. Like many others.

insults will not drive people into accepting your obvious bad math, it simply reinforces that your's is bad math.

>
> Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 11 Aug 2022 08:09:17 -0500
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 by: Sergio - Thu, 11 Aug 2022 13:09 UTC

On 8/11/2022 7:52 AM, WM wrote:
> William schrieb am Mittwoch, 10. August 2022 um 19:32:32 UTC+2:
>> On Wednesday, August 10, 2022 at 12:36:31 PM UTC-3, WM wrote:
>>> William schrieb am Dienstag, 9. August 2022 um 16:33:59 UTC+2:
>> Each element of the set |N is subject to induction.
>
> No.
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
> This means induction shows that almost all elements, namely ℵo, are remaining outside of induction.

Liar. you cannot read equations, you don't know what induction is, you dont know what a limit is.

These are all cured by taking a class in Algebra.

> Can you see that ℵo remains ℵo for every subject of induction?

your logic;
a man has two legs
a monkey has two legs
therefore all men are monkeys.

>
>> The set |N is not subject to induction
>
> The set is all its elements, most of which are outside of induction as induction proves.

Liar.

>
>> And since each element of |N is subject to induction, |N does not contain a "dark" element.
>
> The premise has been proven wrong by induction above.

wrong, and there is no proof.

>
> Regards, WM
>

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Thu, 11 Aug 2022 13:19 UTC

On Thursday, 11 August 2022 at 10:00:39 UTC-3, WM wrote:
[...]
> Cantor did not use any limit. He said that every step can be defined. "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen" [Cantor, p. 119] No limits involved.

Quite so, and not a stepwise process, either. As soon as *YOU* invent a step-by-step interpretation of Cantor's map,you ere no longer following Cantor, and *YOU* have to be clear about the implications of what happens as the number of steps gets larger and larger. You have no clue about how mathematics works. But that's not new, either.

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 11 Aug 2022 09:34:46 -0400
Organization: Peripheral Visions
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 by: FromTheRafters - Thu, 11 Aug 2022 13:34 UTC

WM presented the following explanation :
> zelos...@gmail.com schrieb am Donnerstag, 11. August 2022 um 07:10:35 UTC+2:
>> onsdag 10 augusti 2022 kl. 17:41:55 UTC+2 skrev WM:
>>> zelos...@gmail.com schrieb am Mittwoch, 10. August 2022 um 07:52:19 UTC+2:
>>>> tisdag 9 augusti 2022 kl. 13:54:44 UTC+2 skrev WM:
>>>>> Of course. All intersections with definable endsegments are finite. The
>>>>> infinite intersection contains endsegments which are not individually
>>>>> definable.
>>>>>
>>>> Your "definable" is meaningless.
>>>
>>> The set can only be subtracted collectively.
>> your "collectively" is meaningless
>
> It means as a whole and not by successively omittig elements.
>>
>>>> ℕ \ ℕ| = 0
>>
>> Correct
>>> Every element or FISON subtracted will leave almost all of the set
>>> remaining. ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>>> Can you guess why?
>> Because that is how cardinal arithmetic fucking works.
>
> Why does it work that way and not other?

By design!

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, 11 Aug 2022 08:44:40 -0500
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 by: Sergio - Thu, 11 Aug 2022 13:44 UTC

On 8/11/2022 7:56 AM, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 02:02:26 UTC+2:
>> On Wednesday, August 10, 2022 at 8:55:33 PM UTC+2, Gus Gassmann wrote:
>
>>>> Starting with the "original" matrix NO swap will "result in" the limit matrix. Right?
>>>>
> No indexing will complete the task.

Liar and wrong, use the natural numbers it is an infinite set, or did you stop at k again ?

>
> Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 11 Aug 2022 08:46:31 -0500
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 by: Sergio - Thu, 11 Aug 2022 13:46 UTC

On 8/11/2022 7:55 AM, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 10. August 2022 um 20:55:33 UTC+2:
>> On Wednesday, 10 August 2022 at 14:06:51 UTC-3, Fritz Feldhase wrote:
>
>>> Starting with the "original" matrix NO swap will "result in" the limit matrix. Right?
>>>
>>> (You see, I don't think that we should talk about "supertasks" in this context.)
>> Is the taking of a limit a "supertask"? I happen to think not, and I do not want to give anybody any cover to try to claim that taking the limit of 1/n as n-->oo is a supertask and hence not possible.
>
> That is not a super task. That is possible and correct. But you are confusing many things.
>
>> Maybe I am a radical, but when I see a map from |N to A, I always try to visualize a limiting expression or object.
>
> That is wrong. Try to visiualize the truth.
>
>> With any of WM's processes that he claims prove the inconsistency of ZFC, the limit is self-evident.
>
> It is self-evident that your limit cannot be correct by enumerating fractions. That would mean that by exchanging X and O the matrix
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> ...
> loses all its O's.

it is self evident that your way fails, and is a hoax.

>
> Regards, WM
>
>

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Thu, 11 Aug 2022 13:47 UTC

On Thursday, August 11, 2022 at 9:52:35 AM UTC-3, WM wrote:
> William schrieb am Mittwoch, 10. August 2022 um 19:32:32 UTC+2:
> > On Wednesday, August 10, 2022 at 12:36:31 PM UTC-3, WM wrote:
> > > William schrieb am Dienstag, 9. August 2022 um 16:33:59 UTC+2:
> > Each element of the set |N is subject to induction.
> No.
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
> This means induction shows that almost all elements, namely ℵo, are remaining outside of induction.

No it means that after each element subject to induction are ℵo elements subject to induction.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 14:17 UTC

On Thursday, August 11, 2022 at 2:49:25 PM UTC+2, WM wrote:

> Cantor['s] enumeration happens step by step.

Idiot. In mathematics things don't "happen".

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 14:20 UTC

On Thursday, August 11, 2022 at 2:50:14 PM UTC+2, WM wrote:

> > I don't think that we should talk about "supertasks" in this context. [FF]
> >
> Cantor used it.

Nonsense. You are delusional.

> He said that every step can be defined.

No, he DIDN'T say that.

"Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen" [Cantor, p. 119]

As you can see: he didn't say that, you silly crank.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 14:23 UTC

On Thursday, August 11, 2022 at 2:56:07 PM UTC+2, WM wrote:

> It is simply nonsens, to write the desired matrix and to believe it was a limit.

We do not (just) "believe" that, you silly crank. It can be PROVED.

> But Cantor's enumeration is a super task.

Du hast einen Sprung in der Schüssel, Mann.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 14:30 UTC

On Thursday, August 11, 2022 at 3:00:07 PM UTC+2, WM wrote:

> Very correct! All must happen element by element, i.e., as steps of a super task.

Du hast einen Riesensprung in der Schüssel.

Please elaborate how this could be done for uncountable sets. (Say, [-1, 1] and IR.)

See: https://en.wikipedia.org/wiki/Uncountable_set

It'sc clear that Cantor DID NOT talk about a "stepwise process" here:

"Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen [...]" [Cantor, p. 119]

Actually, he didn't talk about a process at all, you silly crank!

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 14:35 UTC

On Thursday, August 11, 2022 at 3:00:07 PM UTC+2, WM wrote:

> > Cantor just defined a certain sequence (and proved certain properies of that sequence), that's all.
> >
> Not quite. He proved certain properties in the _finite_ case.

Huh?! He invented TRANSFINITE set theory and used its methods to prove "certain properties in the _finite_ case".

Holy shit!

You mad as a hatter, man. A complete crank.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 14:37 UTC

On Thursday, August 11, 2022 at 3:00:39 PM UTC+2, WM wrote:
>
> Cantor [...] said that every step can be defined.

Huh?! WHERE DID HE SAY THAT --- HERE:

"Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen [...]" [Cantor, p. 119]

Du phantasierst. (You are delusional.)

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 14:41 UTC

On Thursday, August 11, 2022 at 3:09:27 PM UTC+2, Sergio wrote:

> [...] you cannot read equations, you don't know what induction is, you dont know what a limit is.
>
> These are all cured by taking a class in Algebra.

Certainly not in Mückenheim's case. There's simply no cure for him.

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, 11 Aug 2022 15:08 UTC

William schrieb am Donnerstag, 11. August 2022 um 15:47:45 UTC+2:
> On Thursday, August 11, 2022 at 9:52:35 AM UTC-3, WM wrote:
> > William schrieb am Mittwoch, 10. August 2022 um 19:32:32 UTC+2:
> > > On Wednesday, August 10, 2022 at 12:36:31 PM UTC-3, WM wrote:
> > > > William schrieb am Dienstag, 9. August 2022 um 16:33:59 UTC+2:
> > > Each element of the set |N is subject to induction.
> > No.
> > |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
> > This means induction shows that almost all elements, namely ℵo, are remaining outside of induction.
> No it means that after each element subject to induction are ℵo elements subject to induction.

No, all steps are made. n can denote every natural number which can be denoted. ℵo elements are remaining.

Regards, WM

Re: Natural numbers and vases III

<td37k6$383$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 11 Aug 2022 10:35:33 -0500
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 by: Sergio - Thu, 11 Aug 2022 15:35 UTC

On 8/11/2022 10:08 AM, WM wrote:
> William schrieb am Donnerstag, 11. August 2022 um 15:47:45 UTC+2:
>> On Thursday, August 11, 2022 at 9:52:35 AM UTC-3, WM wrote:
>>> William schrieb am Mittwoch, 10. August 2022 um 19:32:32 UTC+2:
>>>> On Wednesday, August 10, 2022 at 12:36:31 PM UTC-3, WM wrote:
>>>>> William schrieb am Dienstag, 9. August 2022 um 16:33:59 UTC+2:
>>>> Each element of the set |N is subject to induction.
>>> No.
>>> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
>>> This means induction shows that almost all elements, namely ℵo, are remaining outside of induction.
>> No it means that after each element subject to induction are ℵo elements subject to induction.
>
> No, all steps are made. n can denote every natural number which can be denoted. ℵo elements are remaining.
>
> Regards, WM

Wrong, your equations state you stop at k, and k+1

|ℕ \ {1, 2, 3, ..., k}| = ℵo

|ℕ \ {1, 2, 3, ...}| = 0

most math trolls only bicker over nomenclature, cause they suck at math.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Thu, 11 Aug 2022 15:43:06 +0000
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 by: William - Thu, 11 Aug 2022 15:43 UTC

On Thursday, August 11, 2022 at 12:08:15 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 11. August 2022 um 15:47:45 UTC+2:
> > On Thursday, August 11, 2022 at 9:52:35 AM UTC-3, WM wrote:
> > > William schrieb am Mittwoch, 10. August 2022 um 19:32:32 UTC+2:
> > > > On Wednesday, August 10, 2022 at 12:36:31 PM UTC-3, WM wrote:
> > > > > William schrieb am Dienstag, 9. August 2022 um 16:33:59 UTC+2:
> > > > Each element of the set |N is subject to induction.
> > > No.
> > > |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
> > > This means induction shows that almost all elements, namely ℵo, are remaining outside of induction.
> > No it means that after each element subject to induction are ℵo elements subject to induction.
> No, all steps are made. n can denote every natural number which can be denoted.

After "all steps are made", i.e, after the set |N, there are no elements. After each element of the set |N there are ℵo elements. each of which is subject to induction. After the set |N there are no elements

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Thu, 11 Aug 2022 15:50:05 +0000
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 by: Fritz Feldhase - Thu, 11 Aug 2022 15:50 UTC

On Thursday, August 11, 2022 at 5:43:10 PM UTC+2, William wrote:

> After "all steps are made", i.e, after the set |N, there are no elements.

There is no "after the set IN".

There's only a "after all natural numbers":

0 < 1 < 2 < 3 < ... < omega < omega+1 < omega+2 < ...

omega is larger than each and every natural number.

An e IN: n < omega.

While, on the other hand,

IN < omega

is nonsense. Even worse, since in axiomatic set theory, say ZFC, IN = omega _by definition_, the statement

IN < omega

would be FALSE (after all ~(omega < omega)!

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

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