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

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

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Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Sat, 13 Aug 2022 16:56 UTC

On Saturday, August 13, 2022 at 1:03:30 PM UTC-3, WM wrote:

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

Trivial. So what? Every element n of |N is followed by a set S(n) with cardinality ℵo. However, there is no single set S that works for each n (without exception) . An element that "remains" for "all n" would have to be in S(n) for each n (without exception). There is no such element..

--
William Hughes

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: Sat, 13 Aug 2022 13:27:33 -0400
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 by: FromTheRafters - Sat, 13 Aug 2022 17:27 UTC

WM was thinking very hard :
> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:
>
>>> But when following the process, which first has to establish this
>>> bijection, then it turns out that this claim is wrong.
>> The 'process' does not establish the bijection, the bijection is
>> already there.
>
> In your delusions but not in mathematics.

So, there is no bijection between {elephant, giraffe, aardvark} and
{jackrabbit, antelope, firetruck} ?

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 13 Aug 2022 12:45:17 -0500
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 by: Sergio - Sat, 13 Aug 2022 17:45 UTC

On 8/13/2022 11:03 AM, WM wrote:
> William schrieb am Freitag, 12. August 2022 um 18:57:03 UTC+2:
>> On Friday, August 12, 2022 at 1:41:21 PM UTC-3, WM wrote:
>>> William schrieb am Freitag, 12. August 2022 um 16:26:30 UTC+2:
>>>> On Friday, August 12, 2022 at 9:54:37 AM UTC-3, WM wrote:
>>>>
>>>>> |{1, 2, 3, ..., k}| < ℵo ==> |{1, 2, 3, ..., k, k+1}| < ℵo.
>>>>>
>>>>> It proves that less than ℵo numbers are subject to induction.
>>>>>
>>>> Nope, the finite value k can be any *element* of |N, and the infinite *set* |N contains ℵo *elements*.
>>>>
>>> The latter is true. But induction fails to cover ℕ.
>> Induction works for every *element* of |N
>>
> You may proclaim that again and again. It is like proclaiming 2 + 2 = 7.
> Every element of induction shows

Wrong, totally.

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

trivial, and it is not induction.

> and that will never change for any n subject to induction.

conclusion is also wrong as it is based upon wrong assumptions.

>
>> and as you note, |N contains ℵo *elements*.
>
> Yes. But most of them stay outside of induction because, according to Cantor, ω - n = ω.

Wrong, and wrong. Cantor is right. your loose neurons are misfiring...

>
> Regards, WM

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Natural numbers and vases III
Date: Sat, 13 Aug 2022 19:47:53 -0400
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 by: Jim Burns - Sat, 13 Aug 2022 23:47 UTC

On 8/13/2022 1:27 PM, FromTheRafters wrote:
> WM was thinking very hard :
>> FromTheRafters schrieb
>> am Freitag, 12. August 2022 um 19:27:37 UTC+2:

>>>> But when following the process, which
>>>> first has to establish this bijection,
>>>> then it turns out that this claim is wrong.
>>
>>
>>> The 'process' does not establish the bijection,
>>> the bijection is already there.
>>
>> In your delusions but not in mathematics.
>
> So, there is no bijection between
> {elephant, giraffe, aardvark} and
> {jackrabbit, antelope, firetruck} ?

If you match the aardvark to the firetruck,
you get road pizza.

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 - Sun, 14 Aug 2022 14:24 UTC

FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
> WM was thinking very hard :
> > FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:
> >
> >>> But when following the process, which first has to establish this
> >>> bijection, then it turns out that this claim is wrong.
> >> The 'process' does not establish the bijection, the bijection is
> >> already there.
> >
> > In your delusions but not in mathematics.
> So, there is no bijection between {elephant, giraffe, aardvark} and
> {jackrabbit, antelope, firetruck} ?

It is now, after you have processed the procedure.

Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Sun, 14 Aug 2022 14:29:30 +0000
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 by: WM - Sun, 14 Aug 2022 14:29 UTC

William schrieb am Samstag, 13. August 2022 um 18:57:01 UTC+2:
> On Saturday, August 13, 2022 at 1:03:30 PM UTC-3, WM wrote:
>
>
> > |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
> Trivial. So what? Every element n of |N is followed by a set S(n) with cardinality ℵo.

Not if you take all elements, the set.

> However, there is no single set S that works for each n (without exception) .

It is a set of some definable and ℵo undefinable natnumbers. The former is trivial, the latter is proven by induction. It works for every definable n.

> An element that "remains" for "all n" would have to be in S(n) for each n (without exception). There is no such element.

There is no such definable element. But there is a set of ℵo elements.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Sun, 14 Aug 2022 15:35 UTC

On Sunday, August 14, 2022 at 11:29:34 AM UTC-3, WM wrote:
> William schrieb am Samstag, 13. August 2022 um 18:57:01 UTC+2:

> > An element that "remains" for "all n" would have to be in S(n) for each n (without exception). There is no such element.
> There is no such [element of a finite set] element.

So if there is such and element it must be "dark". However, the Peano set |N does not contain "dark" elements.

--
William Hughes

Re: Natural numbers and vases III

<tdb5nc$15go$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 14 Aug 2022 10:52:10 -0500
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 by: Sergio - Sun, 14 Aug 2022 15:52 UTC

On 8/14/2022 9:24 AM, WM wrote:
> FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
>> WM was thinking very hard :
>>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:
>>>
>>>>> But when following the process, which first has to establish this
>>>>> bijection, then it turns out that this claim is wrong.
>>>> The 'process' does not establish the bijection, the bijection is
>>>> already there.
>>>
>>> In your delusions but not in mathematics.
>> So, there is no bijection between {elephant, giraffe, aardvark} and
>> {jackrabbit, antelope, firetruck} ?
>
> It is now, after you have processed the procedure.

what do you mean by "processed" ?

What do you mean by "procedure" ?

are you implying all functions in math require a process and procedure ?

>
> Regards, WM

Re: Natural numbers and vases III

<tdb692$36g3q$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 14 Aug 2022 12:01:36 -0400
Organization: Peripheral Visions
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 by: FromTheRafters - Sun, 14 Aug 2022 16:01 UTC

WM explained on 8/14/2022 :
> FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
>> WM was thinking very hard :
>>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:
>>>
>>>>> But when following the process, which first has to establish this
>>>>> bijection, then it turns out that this claim is wrong.
>>>> The 'process' does not establish the bijection, the bijection is
>>>> already there.
>>>
>>> In your delusions but not in mathematics.
>> So, there is no bijection between {elephant, giraffe, aardvark} and
>> {jackrabbit, antelope, firetruck} ?
>
> It is now, after you have processed the procedure.

What procedure are you imagining has been processed?

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 - Sun, 14 Aug 2022 16:50 UTC

William schrieb am Sonntag, 14. August 2022 um 17:35:50 UTC+2:
> On Sunday, August 14, 2022 at 11:29:34 AM UTC-3, WM wrote:
> > William schrieb am Samstag, 13. August 2022 um 18:57:01 UTC+2:
>
> > > An element that "remains" for "all n" would have to be in S(n) for each n (without exception). There is no such element.
> > There is no such [element of a finite set] element.
>
> So if there is such and element it must be "dark". However, the Peano set |N does not contain "dark" elements.
>
The Peano-"set" is not a set but a potentially infinite collection. This is proved by
∀n ∈ ℕ_Peano: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

But there are not two consecutive sets of card ℵo before ω. So all n which belong to Peano and have ℵo successors cannot form an ℵo-infinite set. The Peano-collection is only oo-infinite.

Regards, WM

Re: Natural numbers and vases III

<72272782-afc2-42ea-857e-ebeda90a4086n@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Sun, 14 Aug 2022 16:50 UTC

FromTheRafters schrieb am Sonntag, 14. August 2022 um 18:01:46 UTC+2:
> WM explained on 8/14/2022 :
> > FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
> >> WM was thinking very hard :
> >>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:
> >>>
> >>>>> But when following the process, which first has to establish this
> >>>>> bijection, then it turns out that this claim is wrong.
> >>>> The 'process' does not establish the bijection, the bijection is
> >>>> already there.
> >>>
> >>> In your delusions but not in mathematics.
> >> So, there is no bijection between {elephant, giraffe, aardvark} and
> >> {jackrabbit, antelope, firetruck} ?
> >
> > It is now, after you have processed the procedure.
> What procedure are you imagining has been processed?

You have written in some order.

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 - Sun, 14 Aug 2022 18:16 UTC

On Sunday, August 14, 2022 at 6:50:12 PM UTC+2, WM wrote:
> William schrieb am Sonntag, 14. August 2022 um 17:35:50 UTC+2:
> >
> The Peano-"set"

is usually called IN, you know. (See: https://de.wikipedia.org/wiki/Peano-Axiome)

> ∀n ∈ ℕ_Peano: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

With ℕ_Peano = IN (see comment above) this means:

∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo ,

you silly crank.

Re: Natural numbers and vases III

<tdbfgo$382ad$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=109147&group=sci.math#109147

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 14 Aug 2022 14:39:19 -0400
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 by: FromTheRafters - Sun, 14 Aug 2022 18:39 UTC

WM formulated the question :
> FromTheRafters schrieb am Sonntag, 14. August 2022 um 18:01:46 UTC+2:
>> WM explained on 8/14/2022 :
>>> FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
>>>> WM was thinking very hard :
>>>>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:
>>>>>
>>>>>>> But when following the process, which first has to establish this
>>>>>>> bijection, then it turns out that this claim is wrong.
>>>>>> The 'process' does not establish the bijection, the bijection is
>>>>>> already there.
>>>>>
>>>>> In your delusions but not in mathematics.
>>>> So, there is no bijection between {elephant, giraffe, aardvark} and
>>>> {jackrabbit, antelope, firetruck} ?
>>>
>>> It is now, after you have processed the procedure.
>> What procedure are you imagining has been processed?
>
> You have written in some order.

The roster form does not imply any particular order.

Maybe I pair up the elephant with the antelope because of the two Es,
the aardvark with the jackrabbit because of the two vowels and the two
consonants, and firetruck with giraffe because of the two R's and two
F's. Injective, surjective, the two sets have the same size.

Re: Natural numbers and vases III

<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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 by: William - Sun, 14 Aug 2022 19:51 UTC

On Sunday, August 14, 2022 at 1:50:12 PM UTC-3, WM wrote:

> The Peano-"set" is not a set

Piffle

>but a potentially infinite collection. This is proved by
> ∀n ∈ ℕ[]: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>
> But there are not two consecutive sets of card ℵo before ω.

Corect

>So all n which belong to [a] Peano [set[ and have ℵo successors

"all n which belong to a Peano set and have ℵo successors" is one set. There is no second set. "all n which belong to a Peano set and have ℵo successors " has cardinality ℵo.

--
William Hughes

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: Sun, 14 Aug 2022 19:01:29 -0500
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 by: Sergio - Mon, 15 Aug 2022 00:01 UTC

On 8/14/2022 11:50 AM, WM wrote:
> FromTheRafters schrieb am Sonntag, 14. August 2022 um 18:01:46 UTC+2:
>> WM explained on 8/14/2022 :
>>> FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
>>>> WM was thinking very hard :
>>>>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37 UTC+2:
>>>>>
>>>>>>> But when following the process, which first has to establish this
>>>>>>> bijection, then it turns out that this claim is wrong.
>>>>>> The 'process' does not establish the bijection, the bijection is
>>>>>> already there.
>>>>>
>>>>> In your delusions but not in mathematics.
>>>> So, there is no bijection between {elephant, giraffe, aardvark} and
>>>> {jackrabbit, antelope, firetruck} ?
>>>
>>> It is now, after you have processed the procedure.
>> What procedure are you imagining has been processed?
>
> You have written in some order.
>
> Regards, WM

We will never get a straight answer out of you.

Your continued avoidance leads most to believe that you are stupid at math.

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: Sun, 14 Aug 2022 19:03:35 -0500
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 by: Sergio - Mon, 15 Aug 2022 00:03 UTC

On 8/11/2022 12:48 PM, WM wrote:
> 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

if omega is a number, what number is it ?

Since you say is it a number then omega is an element of N, is that what you are saying ?

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 - Mon, 15 Aug 2022 01:41 UTC

On Thursday, August 11, 2022 at 7:49:03 PM UTC+2, WM wrote:
> 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". [Stop talking noonsense, William!]
> >
> > 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_,
> >
> omega [...] is not |N

Hör mal, Du Trottel, ich habe gerade gesagt:

___ In axiomatic set theory, say ZFC, IN = omega _by definition_. ___

Are you retarded?

Hence

> > the statement
> >
> > IN < omega
> >
> > would be FALSE [if uttered, stated in this context]

> <nonsense deleted>

Get lost, Mückenheim.

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 - Mon, 15 Aug 2022 01:59 UTC

On Friday, August 12, 2022 at 3:01:07 PM UTC+2, WM wrote:
> 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.

In set theory they are. Especially in Cantor's "transfinite set theory".

So how can the elements in two uncountable sets, say [-1, 1] and IR, in Cantor's theory be "related" step by step (in a one-to-one fashon)? You think that Cantor considered this possible? Please elaborate!

> 2) They can be counted too.

Ah, I see: they don't exist. But they can be counted too.Yeah, makes sense [in Mückenheim's psychotic world, that is].

Hint: 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 here at all.

> Element für Element defined a process.

Could please describe a stepwise process that relates all elements in [-1, 1] to all elements in IR (in a one-to-one fashon)?

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 - Mon, 15 Aug 2022 04:51 UTC

fredag 12 augusti 2022 kl. 14:54:37 UTC+2 skrev WM:
> 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
No it fucking doesn't, how retarded are you?

All it proves is that the cardinality of finite sets is...not infinite which we already knew by definition!

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: Mon, 15 Aug 2022 04:52:48 +0000
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 by: zelos...@gmail.com - Mon, 15 Aug 2022 04:52 UTC

fredag 12 augusti 2022 kl. 15:01:07 UTC+2 skrev WM:
> 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.

There is, R is uncountable

> 2) They can be counted too. Alle Mengen sind daher in einem erweiterten Sinne "abzählbar", im besonderen alle "Kontinua". [Cantor]

They can't by definitoin.

> >
> > > > 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: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Mon, 15 Aug 2022 04:53 UTC

fredag 12 augusti 2022 kl. 15:04:16 UTC+2 skrev WM:
> 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.

Nope, it is a function, not a process. MATHEMATICAL function.

>Up to every definable number it can be checked.

No one is checking each one, we just make a swift check of all AT ONCE that it is. My god you are retarded

> >
> > > >
> > > > > |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?

Because that is the most useful one for this.

>
> Regards, WM

Re: Natural numbers and vases III

<tdd1lo$3iac1$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 15 Aug 2022 04:55:17 -0400
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 by: FromTheRafters - Mon, 15 Aug 2022 08:55 UTC

After serious thinking WM wrote :
> 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.

Have you 'thrown out' the powerset axiom?

Re: Natural numbers and vases III

<cbbfc743-d141-4f13-8600-f1d3371a804an@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 15 Aug 2022 15:44 UTC

Fritz Feldhase schrieb am Sonntag, 14. August 2022 um 20:16:19 UTC+2:
> On Sunday, August 14, 2022 at 6:50:12 PM UTC+2, WM wrote:
> > William schrieb am Sonntag, 14. August 2022 um 17:35:50 UTC+2:
> > >
> > The Peano-"set"
>
> is usually called IN, you know. (See: https://de.wikipedia.org/wiki/Peano-Axiome)
> > ∀n ∈ ℕ_Peano: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> With ℕ_Peano = IN (see comment above) this means:
>
> ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo ,
>
For ℕ_Cantor nothing remains:
|ℕ \ ℕ_Cantor| = 0 ,
|ℕ_Cantor \ ℕ_Peano| = ℵo.

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 - Mon, 15 Aug 2022 15:50 UTC

Fritz Feldhase schrieb am Montag, 15. August 2022 um 03:59:25 UTC+2:
> On Friday, August 12, 2022 at 3:01:07 PM UTC+2, WM wrote:

> > 1) there are no uncountable sets.
> In set theory they are. Especially in Cantor's "transfinite set theory".

No, they are not existing.

> > 2) They can be counted too. Alle Mengen sind daher in einem erweiterten Sinne "abzählbar", im besonderen alle "Kontinua". [Cantor]

>
> Ah, I see: they don't exist. But they can be counted too.

According to Cantor!

> Hint: 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]

Element für Element = Schritt für Schritt.
>
> Actually, he didn't talk about a process here at all.

He did: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand".
>
> > Element für Element defined a process.
>
> Could please describe a stepwise process that relates all elements in [-1, 1] to all elements in IR (in a one-to-one fashon)?

I do not claim that possible.

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 - Mon, 15 Aug 2022 17:58 UTC

FromTheRafters schrieb am Montag, 15. August 2022 um 10:55:30 UTC+2:
> After serious thinking WM wrote :
> > 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.
> Have you 'thrown out' the powerset axiom?

For definable elements of sets yes. Simplest proof is the Binary Tree. In order to distinguish n Objects, you need at least n properties. For distinguishing n paths you need at least n properties. For n paths distinguishable by nodes you need n nodes. And if paths are not distinguishable by nodes then also Cantor's diagonal is not definable by digits.

Regards, WM

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

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