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

SubjectAuthor
* Natural numbers and vases IIIWM
+* Re: Natural numbers and vases IIIFritz Feldhase
|+- Re: Natural numbers and vases IIIGus Gassmann
|`* Re: Natural numbers and vases IIIWM
| `- Re: Natural numbers and vases IIIsergi o
+* Re: Natural numbers and vases IIIsergi o
|`* Re: Natural numbers and vases IIIFromTheRafters
| +- Re: Natural numbers and vases IIIsergi o
| `* Re: Natural numbers and vases IIIWM
|  `* Re: Natural numbers and vases IIIsergi o
|   `- Re: Natural numbers and vases IIIsergi o
+* Re: Natural numbers and vases IIIWilliam
|`* Re: Natural numbers and vases IIIWM
| `* Re: Natural numbers and vases IIIWilliam
|  `* Re: Natural numbers and vases IIIWM
|   `* Re: Natural numbers and vases IIIWilliam
|    `* Re: Natural numbers and vases IIIWM
|     `* Re: Natural numbers and vases IIIWilliam
|      +* Re: Natural numbers and vases IIIWM
|      |`* Re: Natural numbers and vases IIIWilliam
|      | `* Re: Natural numbers and vases IIIWM
|      |  +* Re: Natural numbers and vases IIIWilliam
|      |  |+- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |+- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |+* Re: Natural numbers and vases IIIFritz Feldhase
|      |  ||`* Re: Natural numbers and vases IIIWM
|      |  || `* Re: Natural numbers and vases IIIsergi o
|      |  ||  `* Re: Natural numbers and vases IIIEram semper recta
|      |  ||   `- Re: Natural numbers and vases IIIEram semper recta
|      |  |`* Re: Natural numbers and vases IIIWM
|      |  | +- Re: Natural numbers and vases IIIsergi o
|      |  | `* Re: Natural numbers and vases IIIWilliam
|      |  |  +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |  |`* Re: Natural numbers and vases IIIWM
|      |  |  | +- Re: Natural numbers and vases IIIFromTheRafters
|      |  |  | `* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |  |  +* Re: Natural numbers and vases IIIWM
|      |  |  |  |`- Re: Natural numbers and vases IIIFromTheRafters
|      |  |  |  +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |  |  `- Re: Natural numbers and vases IIIGus Gassmann
|      |  |  `* Re: Natural numbers and vases IIIWM
|      |  |   +* Re: Natural numbers and vases IIIWilliam
|      |  |   |`* Re: Natural numbers and vases IIIWM
|      |  |   | +* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIIFromTheRafters
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||+* Re: Natural numbers and vases IIIFromTheRafters
|      |  |   | |||`- Re: Natural numbers and vases IIISurgio
|      |  |   | ||`* Re: Natural numbers and vases IIIJim Burns
|      |  |   | || +* Re: Natural numbers and vases IIIWM
|      |  |   | || |+- Re: Natural numbers and vases IIISergio
|      |  |   | || |`* Re: Natural numbers and vases IIIJim Burns
|      |  |   | || | `* Re: Natural numbers and vases IIIWM
|      |  |   | || |  `* Re: Natural numbers and vases IIISergio
|      |  |   | || |   `- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | || +* Re: Natural numbers and vases IIIWM
|      |  |   | || |`- Re: Natural numbers and vases IIISergio
|      |  |   | || +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || `- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISurgio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISurgio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`* Re: Natural numbers and vases IIISergio
|      |  |   | || +* Re: Natural numbers and vases IIIWM
|      |  |   | || |`* Re: Natural numbers and vases IIISergio
|      |  |   | || | +* Re: Natural numbers and vases IIIWM
|      |  |   | || | |`* Re: Natural numbers and vases IIISergio
|      |  |   | || | | `- Re: Natural numbers and vases IIIJim Africani
|      |  |   | || | `- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | || `- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | ||`- Re: Natural numbers and vases IIISergio
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIFredJeffries
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIFredJeffries
|      |  |   | |+* Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIFredJeffries
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWilliam
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+- Re: Natural numbers and vases IIIWM
|      |  |   | |+* Re: Natural numbers and vases IIIWM
|      |  |   | |`* Re: Natural numbers and vases IIIWM
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIEram semper recta
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +* Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +* Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
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|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
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|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIGus Gassmann
|      |  |   | +- Re: Natural numbers and vases IIIFritz Feldhase
|      |  |   | +- Re: Natural numbers and vases IIIzelos...@gmail.com
|      |  |   | +- 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 17:37 UTC

Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:20:46 UTC+2:
> 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.
>
> > He said that every step can be defined.
> No, he DIDN'T say that.

He gave the formula which allegedly does:

k = (m + n - 1)(m + n - 2)/2 + m

But he did not realize that this formula concerns ohne subjects to induction

|ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo

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

"That in every set (') of transfinite numbers there is a smallest one, can be shown as follows." [Cantor, p. 208, footnote by E. Zermelo]

"Every embodiment of different numbers of the first and the second number class has a smallest number, a minimum." [Cantor, p. 332]

"Here we use again and again the theorem [...] that every embodiment of numbers, i.e., every partial multitude of  has a minimum, a smallest number." [Cantor, p. 445]

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 17:44 UTC

William schrieb am Donnerstag, 11. August 2022 um 17:43:10 UTC+2:
> 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 all steps are made which can be denoted or described by induction ℵo numbers less than omega are not stepped.

> After each element of the set |N there are ℵo elements. each of which is subject to induction.

No. Try to comprehend the above equation. All subjects to induction leave ℵo elements which are not subjects to induction. Otherwise none were left.

> After the set |N there are no elements

Right. The set contains the subjects to induction and the ℵo dark numbers.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Thu, 11 Aug 2022 17:48:59 +0000
Content-Type: text/plain; charset="UTF-8"
 by: WM - Thu, 11 Aug 2022 17:48 UTC

Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 17:50:10 UTC+2:
> 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_,

Nonsense squared. omega does not belong to |N and is not |N, because it follows upon all natural numbers.

1 < 2 < 3 < ... < omega

> the statement
>
> IN < omega
>
> would be FALSE

because |N is a set of numbers while omega is a number.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Thu, 11 Aug 2022 17:55:12 +0000
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 by: WM - Thu, 11 Aug 2022 17:55 UTC

Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
> 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

Es wird daher zunächst der Anschein erweckt, als ob wir uns bei dieser Bildungsweise neuer ganzer bestimmt-unendlicher Zahlen ins Grenzenlose hin verlieren müßten, und daß wir außerstande seien, diesem endlosen Prozeß einen gewissen vorläufigen Abschluß zu geben,

und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.

Zeichen für die beim subjektiven Zählprozeß gezählten Einzeldinge sein sollen.

Man überzeugt sich, daß dieser Bildungsprozeß der Alefs und der ihnen entsprechenden Zahlenklassen des Systems  absolut grenzenlos ist.

Alles Cantor oder was?

Gruß, 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 17:57 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.
>
Does

|ℕ \ {1, 2, 3, ..., k}| < omega ==> |ℕ \ {1, 2, 3, ..., k, k+1}| < omega

mean that omega is subject to finite induction too?

Regards, WM

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 13:58:51 -0400
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 by: FromTheRafters - Thu, 11 Aug 2022 17:58 UTC

WM presented the following explanation :
> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:20:46 UTC+2:
>> 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.
>>
>>> He said that every step can be defined.
>> No, he DIDN'T say that.
>
> He gave the formula which allegedly does:
>
> k = (m + n - 1)(m + n - 2)/2 + m
>
> But he did not realize that this formula concerns ohne subjects to induction

Liar! Pairing does not imply steps.

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 17:59 UTC

Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 15:19:33 UTC+2:
> 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,

Es wird daher zunächst der Anschein erweckt, als ob wir uns bei dieser Bildungsweise neuer ganzer bestimmt-unendlicher Zahlen ins Grenzenlose hin verlieren müßten, und daß wir außerstande seien, diesem endlosen Prozeß einen gewissen vorläufigen Abschluß zu geben,

und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.

Zeichen für die beim subjektiven Zählprozeß gezählten Einzeldinge sein sollen.

Man überzeugt sich, daß dieser Bildungsprozeß der Alefs und der ihnen entsprechenden Zahlenklassen des Systems  absolut grenzenlos ist.

Alles Cantor oder was?

Gruß, 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 18:18 UTC

On Thursday, August 11, 2022 at 2:44:26 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 11. August 2022 um 17:43:10 UTC+2:
> > 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 all steps are made which can be denoted or described by induction ℵo numbers less than omega are not stepped.

Nope "all steps which can be denoted or described by induction" is the set |N. There are no elements of the set |N after the set |N
What is true is that each element of "all steps which can be denoted or described by induction" leaves ℵo numbers

> > After each element of the set |N there are ℵo elements. each of which is subject to induction.
> No. Try to comprehend the above equation. All subjects to induction leave [a different set of] ℵo elements

which are subject to induction. Each of the elements left "leaves" (i.e. is smaller than) ℵo elements each of which is subject to induction
Each element of the Peano set |N is subject to induction.

--
William Hughes

Re: Natural numbers and vases III

<td3hbb$a6a$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 13:21:29 -0500
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 by: Sergio - Thu, 11 Aug 2022 18:21 UTC

On 8/11/2022 12:37 PM, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:20:46 UTC+2:
>> 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.
>>
>>> He said that every step can be defined.
>> No, he DIDN'T say that.
>
> He gave the formula which allegedly does:
>
> k = (m + n - 1)(m + n - 2)/2 + m

gad, you totally misunderstand equations!

that is not step by step at all! it is called a mapping!!

this is step by step!!!

array k(1000,1000)
let n = 5
for m = 1 to 100 STEP 1
k = (m + n - 1)(m + n - 2)/2 + m
k(m,n) = k
next m
stop (or halt, end, quit)

*If you cant do the math dont post here*.

Go post in alt.fake.math.for.trolls

Why do you disparage Cantor, whilst referencing Cantor for your maths ?

You qUaCkErs!

>
> But he did not realize that this formula concerns ohne subjects to induction
>
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
>
>> "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen" [Cantor, p. 119]
>
> "That in every set (') of transfinite numbers there is a smallest one, can be shown as follows." [Cantor, p. 208, footnote by E. Zermelo]
>
> "Every embodiment of different numbers of the first and the second number class has a smallest number, a minimum." [Cantor, p. 332]
>
> "Here we use again and again the theorem [...] that every embodiment of numbers, i.e., every partial multitude of  has a minimum, a smallest number." [Cantor, p. 445]
>
> 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 18:21 UTC

On Thursday, 11 August 2022 at 14:59:35 UTC-3, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 15:19:33 UTC+2:
> > 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,
> Es wird daher zunächst der Anschein erweckt, als ob wir uns bei dieser Bildungsweise neuer ganzer bestimmt-unendlicher Zahlen ins Grenzenlose hin verlieren müßten, und daß wir außerstande seien, diesem endlosen Prozeß einen gewissen vorläufigen Abschluß zu geben,
>
> und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.
>
> Zeichen für die beim subjektiven Zählprozeß gezählten Einzeldinge sein sollen.
>
> Man überzeugt sich, daß dieser Bildungsprozeß der Alefs und der ihnen entsprechenden Zahlenklassen des Systems  absolut grenzenlos ist.
>
> Alles Cantor oder was?

It's easy to misinterpret hundred year-old prose, as you just amply demonstrated. Piss off.

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 18:24 UTC

On Thursday, August 11, 2022 at 2:57:49 PM UTC-3, WM wrote:

> Does
>
> |ℕ \ {1, 2, 3, ..., k}| < omega ==> |ℕ \ {1, 2, 3, ...., k, k+1}| < omega
>
> mean that omega is subject to finite induction too?
>

Nope. k and k+1 are both elements of |N, and are both less than omega.

--
William Hughes

Re: Natural numbers and vases III

<td3hr5$h3p$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 13:29:56 -0500
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 by: Sergio - Thu, 11 Aug 2022 18:29 UTC

On 8/11/2022 12:44 PM, WM wrote:
> William schrieb am Donnerstag, 11. August 2022 um 17:43:10 UTC+2:
>> 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 all steps are made which can be denoted or described by induction ℵo numbers less than omega are not stepped.

really ? then show us using Math. or are you just making stuff up ?

Hint: assume the number z has not been stepped, show that it has, by using your formula....

>
>> After each element of the set |N there are ℵo elements. each of which is subject to induction.
>
> No. Try to comprehend the above equation. All subjects to induction leave ℵo elements which are not subjects to induction.

you are the one that stopped at k, and k+1, go fix your own equation.

>
>> After the set |N there are no elements
>
> Right. The set contains the subjects to induction and the ℵo dark numbers.

The set contains the subjects to induction and the no dark numbers.

>
> Regards, WM

Re: Natural numbers and vases III

<td3hsn$h3p$2@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 11 Aug 2022 13:30:46 -0500
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 by: Sergio - Thu, 11 Aug 2022 18:30 UTC

On 8/11/2022 12:57 PM, 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.
>>
> Does
>
> |ℕ \ {1, 2, 3, ..., k}| < omega ==> |ℕ \ {1, 2, 3, ..., k, k+1}| < omega
>
> mean that omega is subject to finite induction too?

what do you think ? you can use google if you want...

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 11 Aug 2022 18:32 UTC

On Thursday, August 11, 2022 at 7:55:16 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
> > 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

NO ANSWER? WHY NOT?!

> > It's 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

HERE - YOU SILLY CRANK!!! IN THE QUOTE MENTIONED ABOVE!!!

Heilige Scheiße! WIE blöde kann man eigentlich sein Mückenheim?

Re: Natural numbers and vases III

<td3on3$1f9m$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 15:27:14 -0500
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 by: Sergio - Thu, 11 Aug 2022 20:27 UTC

On 8/11/2022 12:59 PM, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 15:19:33 UTC+2:
>> 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,
>
> Es wird daher zunächst der Anschein erweckt, als ob wir uns bei dieser Bildungsweise neuer ganzer bestimmt-unendlicher Zahlen ins Grenzenlose hin verlieren müßten, und daß wir außerstande seien, diesem endlosen Prozeß einen gewissen vorläufigen Abschluß zu geben,
>
> und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.
>
> Zeichen für die beim subjektiven Zählprozeß gezählten Einzeldinge sein sollen.
>
> Man überzeugt sich, daß dieser Bildungsprozeß der Alefs und der ihnen entsprechenden Zahlenklassen des Systems  absolut grenzenlos ist.
>
> Alles Cantor oder was?
>
> Gruß, WM

there is no step by step process described there. You made it up.

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)
Injection-Date: Fri, 12 Aug 2022 05:45:24 +0000
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 by: zelos...@gmail.com - Fri, 12 Aug 2022 05:45 UTC

torsdag 11 augusti 2022 kl. 14:52:35 UTC+2 skrev WM:
> 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. Can you see that ℵo remains ℵo for every subject of induction?

That does not mean that at all you fucking imbecile!

> > The set |N is not subject to induction
> The set is all its elements, most of which are outside of induction as induction proves.
> > 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. The implication is true, but the conclusion is wrong too.

You have not proven what you want to. You delude yourself

>
> Regards, WM

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)
Injection-Date: Fri, 12 Aug 2022 05:46:49 +0000
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 by: zelos...@gmail.com - Fri, 12 Aug 2022 05:46 UTC

torsdag 11 augusti 2022 kl. 15:01:00 UTC+2 skrev WM:
> 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.

which is meaningless as mathematics is not a process based thing.

> >
> > > |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?

Because of the fucking definitions. Why are you so retarded?

>
> 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, 12 Aug 2022 12:54 UTC

William schrieb am Donnerstag, 11. August 2022 um 20:25:01 UTC+2:
> On Thursday, August 11, 2022 at 2:57:49 PM UTC-3, WM wrote:
>
> > Does
> >
> > |ℕ \ {1, 2, 3, ..., k}| < omega ==> |ℕ \ {1, 2, 3, ...., k, k+1}| < omega
> >
> > mean that omega is subject to finite induction too?
> >
> Nope. k and k+1 are both elements of |N, and are both less than omega.

That was a mistake. What I wanted to say is this:

|{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.

It proves that less than ℵo numbers are subject to induction.

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, 12 Aug 2022 12:55 UTC

Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 20:22:00 UTC+2:
> On Thursday, 11 August 2022 at 14:59:35 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 15:19:33 UTC+2:
> > > 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,
> > Es wird daher zunächst der Anschein erweckt, als ob wir uns bei dieser Bildungsweise neuer ganzer bestimmt-unendlicher Zahlen ins Grenzenlose hin verlieren müßten, und daß wir außerstande seien, diesem endlosen Prozeß einen gewissen vorläufigen Abschluß zu geben,
> >
> > und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.
> >
> > Zeichen für die beim subjektiven Zählprozeß gezählten Einzeldinge sein sollen.
> >
> > Man überzeugt sich, daß dieser Bildungsprozeß der Alefs und der ihnen entsprechenden Zahlenklassen des Systems  absolut grenzenlos ist.
> >
> > Alles Cantor oder was?
> It's easy to misinterpret hundred year-old prose

The meaning of Cantor's sentences is obvious. No interpreter required.

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, 12 Aug 2022 13:01 UTC

Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 20:32:12 UTC+2:
> On Thursday, August 11, 2022 at 7:55:16 PM UTC+2, WM wrote:
> > Fritz Feldhase schrieb am Donnerstag, 11. August 2022 um 16:30:20 UTC+2:
> > > 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
> NO ANSWER? WHY NOT?!

1) there are no uncountable sets.
2) They can be counted too. Alle Mengen sind daher in einem erweiterten Sinne "abzählbar", im besonderen alle "Kontinua". [Cantor]

>
> > > It's 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
> IN THE QUOTE MENTIONED ABOVE!!!

Element für Element defined a process.

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, 12 Aug 2022 13:04 UTC

zelos...@gmail.com schrieb am Freitag, 12. August 2022 um 07:46:52 UTC+2:
> torsdag 11 augusti 2022 kl. 15:01:00 UTC+2 skrev WM:
> > 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.
>
> which is meaningless as mathematics is not a process based thing.

Bijecting with |N is a process. Up to every definable number it can be checked.
>
> > >
> > > > |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?
>
> Because of the fucking definitions. Why are you so retarded?

Why do they say so?

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 - Fri, 12 Aug 2022 13:08 UTC

On Friday, 12 August 2022 at 09:54:37 UTC-3, WM wrote:
> [...] What I wanted to say is this:
>
> |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>
> It proves that less than ℵo numbers are subject to induction.

It proves nothing of the sort. It proves that every FISON is finite, but it does not prove anything about the *number* of FISONs (which is ℵo), or the *set* of all FISONs or the *union* of all FISONs. We've been through this. You have no clue how induction works, nor that |N is not simply a list of all its elements (there are these tiny things that look like '{' and '}', you know), nor do you know *ANYTHING* about mathematics.

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 - Fri, 12 Aug 2022 13:09 UTC

On Friday, 12 August 2022 at 09:56:02 UTC-3, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 20:22:00 UTC+2:
> > On Thursday, 11 August 2022 at 14:59:35 UTC-3, WM wrote:
> > > Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 15:19:33 UTC+2:
> > > > 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,
> > > Es wird daher zunächst der Anschein erweckt, als ob wir uns bei dieser Bildungsweise neuer ganzer bestimmt-unendlicher Zahlen ins Grenzenlose hin verlieren müßten, und daß wir außerstande seien, diesem endlosen Prozeß einen gewissen vorläufigen Abschluß zu geben,
> > >
> > > und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.
> > >
> > > Zeichen für die beim subjektiven Zählprozeß gezählten Einzeldinge sein sollen.
> > >
> > > Man überzeugt sich, daß dieser Bildungsprozeß der Alefs und der ihnen entsprechenden Zahlenklassen des Systems  absolut grenzenlos ist.
> > >
> > > Alles Cantor oder was?
> > It's easy to misinterpret hundred year-old prose
> The meaning of Cantor's sentences is obvious. No interpreter required.

Evidently there is, if you think that Cantor talks abut a stepwise process here.

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, 12 Aug 2022 13:15 UTC

Gus Gassmann schrieb am Freitag, 12. August 2022 um 15:09:19 UTC+2:
> On Friday, 12 August 2022 at 09:56:02 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 20:22:00 UTC+2:
> > > On Thursday, 11 August 2022 at 14:59:35 UTC-3, WM wrote:
> > > > Gus Gassmann schrieb am Donnerstag, 11. August 2022 um 15:19:33 UTC+2:
> > > > > 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,
> > > > Es wird daher zunächst der Anschein erweckt, als ob wir uns bei dieser Bildungsweise neuer ganzer bestimmt-unendlicher Zahlen ins Grenzenlose hin verlieren müßten, und daß wir außerstande seien, diesem endlosen Prozeß einen gewissen vorläufigen Abschluß zu geben,
> > > >
> > > > und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.
> > > >
> > > > Zeichen für die beim subjektiven Zählprozeß gezählten Einzeldinge sein sollen.
> > > >
> > > > Man überzeugt sich, daß dieser Bildungsprozeß der Alefs und der ihnen entsprechenden Zahlenklassen des Systems  absolut grenzenlos ist.
> > > >
> > > > Alles Cantor oder was?
> > > It's easy to misinterpret hundred year-old prose
> > The meaning of Cantor's sentences is obvious. No interpreter required.
> Evidently there is, if you think that Cantor talks abut a stepwise process here.

und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.

How could a Stillstand be feared if there was no process, step by step, element by element?

Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Date: Fri, 12 Aug 2022 06:15:06 -0700 (PDT)
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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Fri, 12 Aug 2022 13:15 UTC

Gus Gassmann schrieb am Freitag, 12. August 2022 um 15:08:29 UTC+2:
> On Friday, 12 August 2022 at 09:54:37 UTC-3, WM wrote:
> > [...] What I wanted to say is this:
> >
> > |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
> >
> > It proves that less than ℵo numbers are subject to induction.
> It proves nothing of the sort. It proves that every FISON is finite, but it does not prove anything about the *number* of FISONs (which is ℵo), or the *set* of all FISONs or the *union* of all FISONs.

No. Induction proves that ℵo numberws are not swubject toinduction.
|ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.

Regards, WM

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

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