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"It is easier to fight for principles than to live up to them." -- Alfred Adler

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
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|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +* Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +* Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | `- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   `* Re: Natural numbers and vases IIIFromTheRafters
|      |  `* Re: Natural numbers and vases IIIzelos...@gmail.com
|      `* Re: Natural numbers and vases IIIFritz Feldhase
+* Re: Natural numbers and vases IIIzelos...@gmail.com
+* Re: Natural numbers and vases IIIEram semper recta
+- Re: Natural numbers and vases IIIEduardo Faqtardo
+- Re: Natural numbers and vases IIIEram semper recta
+- Re: Natural numbers and vases IIIArchimedes Plutonium
`- Re: Natural numbers and vases IIIArchimedes Plutonium

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Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Thu, 28 Jul 2022 21:49 UTC

On Thursday, 28 July 2022 at 17:31:29 UTC-3, WM wrote:
> William schrieb am Donnerstag, 28. Juli 2022 um 19:12:53 UTC+2:
> > On Thursday, July 28, 2022 at 11:21:44 AM UTC-3, WM wrote:
> > > William schrieb am Mittwoch, 27. Juli 2022 um 16:09:17 UTC+2:
> > > > On Wednesday, July 27, 2022 at 9:27:31 AM UTC-3, WM wrote:
> > > > >... The stepwise process never reaches a final state.
> > > >
> > > > And, as you note, a final state exists.
> > > >
> > > Yes,
> > >... but it can only be reached
> >
> > The important thing is it exists, "can be reached", but not by a stepwise process.
> Really a great insight. Now you have only to accept that every definable number can be defined (= reached by a stepwise process).

It seems like such a small step, and yet... It should be an equally small step to accept that every natural number has already been defined and is reached by a stepwise process. This has several advantages: No need to mark everything by "There be monsters" (aka "dark numbers" - woooooh). No need to re-verify the laws of arithmetic every time a new number is "defined" (in your asinine terminology). Any newly "defined" natural number already has a prime factorization (Why?), commutes (*automatically*) additively and multiplicatively with every other, previously "defined" natural number (Why?), has aleph_0 successors (Why?), etc. And there are no inconsistencies, if one understands that there *can* be discontinuous functions.

Your "model" (if I am allowed to use the term *very* loosely) of mathematics always reminds me of the geocentric model of the universe, prior to Copernicus and Kepler: Inconsistent, needlessly complicated, and patched up with new "epicycles" every time someone points out flaws in your "proofs". (And there are *MANY* flaws.) Your Math-surrealism is ridiculous ad-hockery that for some unfathomable reason you confuse with mathematics and inflict on your poor students.

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, 28 Jul 2022 21:53 UTC

On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:

> We still have that a "final state" exists

You are talking nonsense. And you know it, asshole!

The limit of a sequence is not a "final state" (of what?!).

And a "state" which is not REACHED by a process (sequence of steps) can hardly be termed a "final state" (OF WHAT?!). **sigh**

Seems that you are considering a "supertask". But supertasks are not part of mathematics, dumbo.

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

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, 28 Jul 2022 22:36 UTC

On Wednesday, July 27, 2022 at 2:24:45 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 26. Juli 2022 um 18:32:30 UTC+2:
> >
> > Proof (by induction). 1 is a natural number (by a Peano Axiom). If n is a natural number then n+1 is a natural number too (by a Peano Axiom and n + 1 = s(n)). Hence (by induction, another Peano Axiom) all natural numbers are natural numbers. qed
> >
> That i not provable by induction.

Huh?! Can you point out an error in the proof above, you silly asshole?

Why are you so full of shit, dumbo? You must have shit for brains!

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 28 Jul 2022 22:43 UTC

On Wednesday, July 27, 2022 at 2:32:52 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 26. Juli 2022 um 18:44:44 UTC+2:
> >
> > Better use a sequence of sets, say the sequence of intervalls (I_n) with I_n = (1, 1 + 1/n] for all n e IN.
> >
> > This sequence is inclusion monotonic (since I_(n+1) c I_n for all n e IN).The Intersection of the terms of this sequence is empty. INTERSECTION_(n e IN) I_n = { }.
> >
> Of course.

Right. This proves that an application of "quantifier shift" cannot be justified by the fact that a set sequence is "inclusion monotonic", dumbo.

Here we have

An e IN: Ex e IR: x e I_n.

But also

~Ex e IR: An e IN: x e I_n (i. e. the negation of the result of a quantifier shift).

In other words,

INTERSECTION_(n e IN) I_n = { }.

----------------------------------

Why are you so bad at math, Mückenheim?

Re: Natural numbers and vases III

<tbv3ll$1unm$1@gioia.aioe.org>

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Subject: Re: Natural numbers and vases III
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 by: Sergio - Thu, 28 Jul 2022 22:47 UTC

On 7/28/2022 4:53 PM, Fritz Feldhase wrote:
> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
>
>> We still have that a "final state" exists
>
> You are talking nonsense. And you know it, asshole!
>
> The limit of a sequence is not a "final state" (of what?!).
>
> And a "state" which is not REACHED by a process (sequence of steps) can hardly be termed a "final state" (OF WHAT?!). **sigh**
>
> Seems that you are considering a "supertask". But supertasks are not part of mathematics, dumbo.
>
> See: https://en.wikipedia.org/wiki/Supertask

these new Ants fit right in with, and exist because of, WMs maths;

Final State Ants

Final State of What Ants

Ants not part of mathematics, The Dumbo Ants.

Step wise sheeps counting Ants that never finish

The Final Ant that was "reached" by a step wise process.

(remember Reached Ants?)

Undefinable Ants that have been defined.

"Collective Action" Ants (belong to a Union)

"Individual Action" Ants (mostly members of a Union)

Brain dead pseudo wantabe dark-ish ants that do not know any math, and never will.

Ants which would remain.

Hence Elvis is alive Ants ?

at least half of all Ants cannot be individually defined

"The contradiction with the claim that all Ants can be individually defined is caused by the fact that not all Ants can be individually defined, but all
individually defined Ants have more successors Ants than predecessors Ants. So a very rough Ant-estimation shows that at least half of all Ants cannot
be individually defined Ants. Those individually defined Ants that are found will be required to take my individually defined class." - WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: fredjeff...@gmail.com (FredJeffries)
Injection-Date: Thu, 28 Jul 2022 23:18:09 +0000
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 by: FredJeffries - Thu, 28 Jul 2022 23:18 UTC

On Thursday, July 28, 2022 at 2:38:38 PM UTC-7, William wrote:
> On Thursday, July 28, 2022 at 5:31:29 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 28. Juli 2022 um 19:12:53 UTC+2:
> > > The important thing is [ a "final state"] exists, "can be reached", but not by a stepwise process.
> > Really a great insight. Now you have only to accept that every definable number can be defined (= reached by a stepwise process).

Don't do it! DON'T DO IT!!
It's a trick! He's trying to trick you!!!!!

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Fri, 29 Jul 2022 05:47 UTC

torsdag 28 juli 2022 kl. 22:31:29 UTC+2 skrev WM:
> William schrieb am Donnerstag, 28. Juli 2022 um 19:12:53 UTC+2:
> > On Thursday, July 28, 2022 at 11:21:44 AM UTC-3, WM wrote:
> > > William schrieb am Mittwoch, 27. Juli 2022 um 16:09:17 UTC+2:
> > > > On Wednesday, July 27, 2022 at 9:27:31 AM UTC-3, WM wrote:
> > > > >... The stepwise process never reaches a final state.
> > > >
> > > > And, as you note, a final state exists.
> > > >
> > > Yes,
> > >... but it can only be reached
> >
> > The important thing is it exists, "can be reached", but not by a stepwise process.
> Really a great insight. Now you have only to accept that every definable number can be defined (= reached by a stepwise process).
>
> Regards, WM
Which is again ALL NATURAL NUMBERS!

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Fri, 29 Jul 2022 13:57:07 +0000
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 by: WM - Fri, 29 Jul 2022 13:57 UTC

Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:33:32 UTC+2:
> On Thursday, July 28, 2022 at 10:31:29 PM UTC+2, WM wrote:
>
> > Now you have only to accept that every definable number can be defined (= reached by a stepwise process).
> EACH AND EVERY natural number can be "reached by a stepwise process",

Not by you! Define the largest number you can reach. I will surpass it.

> Hint: If n is natural number then, starting with 0, n applications of the successor operation (aka steps) suffice.

That will not suffice because always almost all numbers remain beyond that n, whatever you may choose, and even if you refrain from defining it further.

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, 29 Jul 2022 14:00 UTC

William schrieb am Donnerstag, 28. Juli 2022 um 23:38:38 UTC+2:
> On Thursday, July 28, 2022 at 5:31:29 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 28. Juli 2022 um 19:12:53 UTC+2:
> > > The important thing is [ a "final state"] exists, "can be reached", but not by a stepwise process.
> > Really a great insight. Now you have only to accept that every definable number can be defined (= reached by a stepwise process).
> So what? We still have that a "final state" exists (i.e there are methods, e.g. induction, that produce a "final state" exist)

Induction is doubtful because it shows that the final state cannot be reached. But Cantor's omega is sufficient.

> but a stepwise process cannot be used to prove that the "final state" does not exist.

No. We accept that the final state exists. But it cannot be reached by definable steps. If there is a completion then it is consisting of dark elements.

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, 29 Jul 2022 14:01 UTC

Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
>
> > We still have that a "final state" exists
> You are talking nonsense. And you know it, asshole!
>
> The limit of a sequence is not a "final state" (of what?!).

The completion of a set is the final state.
>
> And a "state" which is not REACHED by a process (sequence of steps) can hardly be termed a "final state" (OF WHAT?!). **sigh**

It is the completion of dark elements.
>
> Seems that you are considering a "supertask". But supertasks are not part of mathematics,

If set theory is correct, then supertasks are in it.

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, 29 Jul 2022 14:03 UTC

Fritz Feldhase schrieb am Freitag, 29. Juli 2022 um 00:36:27 UTC+2:
> On Wednesday, July 27, 2022 at 2:24:45 PM UTC+2, WM wrote:
> > Fritz Feldhase schrieb am Dienstag, 26. Juli 2022 um 18:32:30 UTC+2:
> > >
> > > Proof (by induction). 1 is a natural number (by a Peano Axiom). If n is a natural number then n+1 is a natural number too (by a Peano Axiom and n + 1 = s(n)). Hence (by induction, another Peano Axiom) all natural numbers are natural numbers. qed
> > >
> > That i not provable by induction.
> Huh?! Can you point out an error in the proof above

This proof proves that almost all natnumbers are following beyond every derfinable n.

Regards, WM

Re: Natural numbers and vases III

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 by: Sergio - Fri, 29 Jul 2022 14:08 UTC

On 7/29/2022 9:03 AM, WM wrote:
> Fritz Feldhase schrieb am Freitag, 29. Juli 2022 um 00:36:27 UTC+2:
>> On Wednesday, July 27, 2022 at 2:24:45 PM UTC+2, WM wrote:
>>> Fritz Feldhase schrieb am Dienstag, 26. Juli 2022 um 18:32:30 UTC+2:
>>>>
>>>> Proof (by induction). 1 is a natural number (by a Peano Axiom). If n is a natural number then n+1 is a natural number too (by a Peano Axiom and n + 1 = s(n)). Hence (by induction, another Peano Axiom) all natural numbers are natural numbers. qed
>>>>
>>> That i not provable by induction.
>> Huh?! Can you point out an error in the proof above
>
> This proof proves that almost all natnumbers are following beyond every derfinable n.
>
> Regards, WM

wrong. The proof does not contain the words, "almost" nor "derfinable", nor "following beyond"

go ahead and provide your own proof of what you claim.

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, 29 Jul 2022 09:11:12 -0500
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 by: Sergio - Fri, 29 Jul 2022 14:11 UTC

On 7/29/2022 8:57 AM, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:33:32 UTC+2:
>> On Thursday, July 28, 2022 at 10:31:29 PM UTC+2, WM wrote:
>>
>>> Now you have only to accept that every definable number can be defined (= reached by a stepwise process).
>> EACH AND EVERY natural number can be "reached by a stepwise process",
>
> Not by you! Define the largest number you can reach. I will surpass it.

red herring. Stick to the topic

>
>> Hint: If n is natural number then, starting with 0, n applications of the successor operation (aka steps) suffice.
>
> That will not suffice because always almost all numbers remain beyond that n, whatever you may choose, and even if you refrain from defining it further.

you deny induction.

>
> 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, 29 Jul 2022 09:13:08 -0500
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 by: Sergio - Fri, 29 Jul 2022 14:13 UTC

On 7/29/2022 9:01 AM, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
>> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
>>
>>> We still have that a "final state" exists
>> You are talking nonsense. And you know it, asshole!
>>
>> The limit of a sequence is not a "final state" (of what?!).
>
> The completion of a set is the final state.

how do you define "completion" ?

>>
>> And a "state" which is not REACHED by a process (sequence of steps) can hardly be termed a "final state" (OF WHAT?!). **sigh**
>
> It is the completion of dark elements.

Bogus.

>>
>> Seems that you are considering a "supertask". But supertasks are not part of mathematics,
>
> If set theory is correct, then supertasks are in it.

provide a URL, or you are just making stuff up.

>
> Regards, WM

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 29 Jul 2022 09:14:42 -0500
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 by: Sergio - Fri, 29 Jul 2022 14:14 UTC

On 7/29/2022 9:00 AM, WM wrote:
> William schrieb am Donnerstag, 28. Juli 2022 um 23:38:38 UTC+2:
>> On Thursday, July 28, 2022 at 5:31:29 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 28. Juli 2022 um 19:12:53 UTC+2:
>>>> The important thing is [ a "final state"] exists, "can be reached", but not by a stepwise process.
>>> Really a great insight. Now you have only to accept that every definable number can be defined (= reached by a stepwise process).
>> So what? We still have that a "final state" exists (i.e there are methods, e.g. induction, that produce a "final state" exist)
>
> Induction is doubtful because it shows that the final state cannot be reached. But Cantor's omega is sufficient.

Induction Ants
doubtful Ants
Final State Ants

>
>> but a stepwise process cannot be used to prove that the "final state" does not exist.
>
> No. We accept that the final state exists. But it cannot be reached by definable steps. If there is a completion then it is consisting of dark elements.

wrong. Dark Ants.

definable is bogus.

>
> Regards, WM

Re: Natural numbers and vases III

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 by: FromTheRafters - Fri, 29 Jul 2022 14:37 UTC

WM laid this down on his screen :
> Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
>> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
>>
>>> We still have that a "final state" exists
>> You are talking nonsense. And you know it, asshole!
>>
>> The limit of a sequence is not a "final state" (of what?!).
>
> The completion of a set is the final state.

A set is not a process, though it can be a function.

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 29 Jul 2022 15:17 UTC

FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> WM laid this down on his screen :
> > Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
> >> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
> >>
> >>> We still have that a "final state" exists
> >> You are talking nonsense. And you know it, asshole!
> >>
> >> The limit of a sequence is not a "final state" (of what?!).
> >
> > The completion of a set is the final state.
> A set is not a process, though it can be a function.

In ZFC everything is a set. Processes can be decribed by mathematics. Mathematics is based on ZFC. Conclusion: Processes are described as sets.

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, 29 Jul 2022 15:30 UTC

Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
> But supertasks are not part of mathematics..

Why?

> See: https://en.wikipedia.org/wiki/Supertask

Philosophers who reject their possibility tend not to reject them on grounds such as Thomson's but because they have qualms with the notion of infinity itself.

We do not.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Fri, 29 Jul 2022 15:48 UTC

On Friday, July 29, 2022 at 5:17:19 PM UTC+2, WM wrote:
> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> > WM laid this down on his screen :
> > > Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
> > > > On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
> > > > >
> > > > > We still have that a "final state" exists [...]
> > > > >
> > > > You are talking nonsense. And you know it, asshole!
> > > >
> > > > The limit of a sequence is not a "final state" (of what?!).
> > > >
> > > The completion of a set is the final state.
> > >
> > A set is not a process, though it can be a function.
> >
> In ZFC everything is a set. Processes can be decribed by mathematics. Mathematics is based on ZFC. Conclusion: Processes [can be] described as sets.

Did ANYONE claim otherwise, Mückenheim? :-)

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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, 29 Jul 2022 15:54 UTC

On Friday, July 29, 2022 at 5:30:53 PM UTC+2, WM wrote:

> Philosophers who reject their possibility tend not to reject them on grounds such as Thomson's but because they have qualms with the notion of infinity itself.
>
> We do not.

We? Huh?!

So you are claiming that you don't have qualms with the notion of actual infinity?

That's a rather amazing turn of events!

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Fri, 29 Jul 2022 12:10:43 -0400
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 by: FromTheRafters - Fri, 29 Jul 2022 16:10 UTC

WM wrote on 7/29/2022 :
> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
>> WM laid this down on his screen :
>>> Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
>>>> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
>>>>
>>>>> We still have that a "final state" exists
>>>> You are talking nonsense. And you know it, asshole!
>>>>
>>>> The limit of a sequence is not a "final state" (of what?!).
>>>
>>> The completion of a set is the final state.
>> A set is not a process, though it can be a function.
>
> In ZFC everything is a set.

Everything in ZFC is a set.

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 - Fri, 29 Jul 2022 16:37 UTC

On Friday, July 29, 2022 at 11:00:09 AM UTC-3, WM wrote:

>If there is a completion then it is consisting of dark elements.

Piffle. A "final state" cannot be reached by a stepwise process not because a "final state" contains "dark elements" but because the state changes at every step and there is no last step.

--
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 - Fri, 29 Jul 2022 16:53 UTC

On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
> WM wrote on 7/29/2022 :
> > FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> >> WM laid this down on his screen :
> >
> > In ZFC everything is a set.
> >
> Everything in ZFC is a set.

In ZFC: Everything is a set.

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, 29 Jul 2022 12:54:59 -0400
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 by: Jim Burns - Fri, 29 Jul 2022 16:54 UTC

On 7/29/2022 11:54 AM, Fritz Feldhase wrote:
> On Friday, July 29, 2022 at 5:30:53 PM UTC+2,
> WM wrote:

>> Philosophers who reject their possibility
>> tend not to reject them on grounds such as
>> Thomson's but because they have qualms with
>> the notion of infinity itself.
>>
>> We do not.
>
> We? Huh?!
>
> So you are claiming that you don't have qualms
> with the notion of actual infinity?
>
> That's a rather amazing turn of events!

Ask him what "actual infinity" means.

A WM-complete set cannot match a proper subset.

A WM-actual infinite set is
a WM-complete superset of a WM-incomplete subset.

WM-dark numbers, end segments, fractions
can be hypothetically added to a WM-incomplete
subset to produce a WM-complete set.

However,
if
a WM-dark number, end segment, fraction
can match _itself_
then
the WM-incomplete subset can match a proper
subset, the dark remainder can match itself,
and the superset is also WM-incomplete.

WM-completeness requires elements which
_cannot_ match themselves.

That is what WM has no qualms about.
So, don't open the champagne just yet.

Also, WM insists that _we_ have no qualms
about elements which cannot match themselves,
or else we are matheologians.

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 29 Jul 2022 14:23:48 -0400
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 by: FromTheRafters - Fri, 29 Jul 2022 18:23 UTC

Fritz Feldhase submitted this idea :
> On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
>> WM wrote on 7/29/2022 :
>>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
>>>> WM laid this down on his screen :
>>>
>>> In ZFC everything is a set.
>>>
>> Everything in ZFC is a set.
>
> In ZFC: Everything is a set.

Dark Numbers are not a set in ZFC.

In ZFC: Dark Numbers are not.

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

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