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Groups > sci.math > #424497 > unrolled thread

Universal quantification?

Started byWM <wolfgang.mueckenheim@hs-augsburg.de>
First post2018-09-29 01:33 -0700
Last post2018-10-01 12:29 -0700
Articles 20 on this page of 242 — 13 participants

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Contents

  Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-29 01:33 -0700
    Re: Universal quantification? Julio Di Egidio <julio@diegidio.name> - 2018-09-29 02:28 -0700
    Re: Universal quantification? bursejan@gmail.com - 2018-09-29 02:43 -0700
      Re: Universal quantification? bursejan@gmail.com - 2018-09-29 02:50 -0700
      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-29 06:03 -0700
        Re: Universal quantification? bursejan@gmail.com - 2018-09-29 06:20 -0700
          Re: Universal quantification? bursejan@gmail.com - 2018-09-29 06:28 -0700
            Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-29 12:01 -0700
              Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-01 00:22 -0700
                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-01 05:55 -0700
                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 06:40 -0700
                Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 06:38 -0700
          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-29 11:58 -0700
            Re: Universal quantification? bursejan@gmail.com - 2018-09-29 12:02 -0700
              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-29 12:19 -0700
                Re: Universal quantification? bursejan@gmail.com - 2018-09-29 12:45 -0700
                  Re: Universal quantification? 7777777 <jussir@yahoo.com> - 2018-09-29 23:26 -0700
                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-09-30 22:38 -0700
                      Re: Universal quantification? 7777777 <jussir@yahoo.com> - 2018-09-30 23:03 -0700
                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-09-30 23:20 -0700
                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-29 19:11 -0700
                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-30 02:04 -0700
                    Re: Universal quantification? bursejan@gmail.com - 2018-09-30 02:09 -0700
                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-30 02:30 -0700
                        Re: Universal quantification? bursejan@gmail.com - 2018-09-30 02:35 -0700
                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-30 20:16 -0700
                          Re: Universal quantification? FromTheRafters <erratic@nomail.afraid.org> - 2018-10-01 08:57 -0400
                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-01 06:35 -0700
                              Re: Universal quantification? FromTheRafters <erratic@nomail.afraid.org> - 2018-10-01 11:14 -0400
                            Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 07:00 -0700
                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 06:30 -0700
                            Re: Universal quantification? bursejan@gmail.com - 2018-10-01 09:52 -0700
                              Re: Universal quantification? bursejan@gmail.com - 2018-10-01 09:53 -0700
                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-01 22:43 -0700
                              Re: Universal quantification? transfinity01@gmail.com - 2018-10-02 02:42 -0700
                                Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-02 03:37 -0700
                                  Re: Universal quantification? transfinity01@gmail.com - 2018-10-02 11:20 -0700
                                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-02 11:27 -0700
                                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-03 02:53 -0700
                                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-03 03:48 -0700
                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-03 08:36 -0700
                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-03 22:55 -0700
                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-04 11:41 -0700
                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-05 02:53 -0700
                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-03 22:47 -0700
                                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-04 11:37 -0700
                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-04 22:36 -0700
                                          Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-05 02:50 -0700
                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-05 03:00 -0700
                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-05 03:59 -0700
                                              Re: Universal quantification? transfinity01@gmail.com - 2018-10-05 06:19 -0700
                                                Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-07 22:55 -0700
                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-08 09:10 -0700
                                                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-08 15:13 -0700
                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-09 01:38 -0700
                                                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-09 02:03 -0700
                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-09 02:57 -0700
                                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-09 03:19 -0700
                                                            Re: Universal quantification? bursejan@gmail.com - 2018-10-09 05:32 -0700
                                                              Re: Universal quantification? bursejan@gmail.com - 2018-10-09 05:34 -0700
                                                                Re: Universal quantification? bursejan@gmail.com - 2018-10-09 05:42 -0700
                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-08 22:29 -0700
                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-09 01:32 -0700
                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-09 05:23 -0700
                                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-09 09:17 -0700
                                                            Re: Universal quantification? bursejan@gmail.com - 2018-10-09 09:29 -0700
                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-10 22:29 -0700
                                                              Re: Universal quantification? transfinity01@gmail.com - 2018-10-10 23:09 -0700
                                                                Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-10 23:20 -0700
                                                                  Re: Universal quantification? transfinity01@gmail.com - 2018-10-11 02:14 -0700
                                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-11 03:00 -0700
                                                                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-12 03:40 -0700
                                                                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-12 07:47 -0700
                                                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-13 09:04 -0700
                                                                            Re: Universal quantification? bursejan@gmail.com - 2018-10-13 09:21 -0700
                                                                              Re: Universal quantification? bursejan@gmail.com - 2018-10-13 09:32 -0700
                                                                              Re: Universal quantification? transfinity01@gmail.com - 2018-10-14 02:11 -0700
                                                                                Re: Universal quantification? bursejan@gmail.com - 2018-10-14 04:54 -0700
                                                                                  Re: Universal quantification? transfinity01@gmail.com - 2018-10-14 12:32 -0700
                                                                                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-14 13:09 -0700
                                                                                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-15 02:47 -0700
                                                                                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-15 05:04 -0700
                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-14 22:43 -0700
                                                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-15 02:46 -0700
                                                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-15 05:16 -0700
                                                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-15 06:27 -0700
                                                                              Re: Universal quantification? transfinity01@gmail.com - 2018-10-15 11:45 -0700
                                                                                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-15 12:58 -0700
                                                                                  Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-15 22:30 -0700
                                                                                    Re: Universal quantification? transfinity01@gmail.com - 2018-10-16 03:30 -0700
                                                                                      Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-16 03:46 -0700
                                                                                  Re: Universal quantification? transfinity01@gmail.com - 2018-10-16 03:29 -0700
                                                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-16 03:31 -0700
                                                                                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-16 03:46 -0700
                                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-16 03:56 -0700
                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-16 04:07 -0700
                                                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-16 05:33 -0700
                                                                                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-16 08:11 -0700
                                                                                                Re: Universal quantification? bursejan@gmail.com - 2018-10-16 08:25 -0700
                                                                                                  Re: Universal quantification? bursejan@gmail.com - 2018-10-16 08:27 -0700
                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-16 08:58 -0700
                                                                                                    Re: Universal quantification? bursejan@gmail.com - 2018-10-16 10:52 -0700
                                                                                                      Re: Universal quantification? bursejan@gmail.com - 2018-10-16 10:57 -0700
                                                                                                    Re: Universal quantification? bursejan@gmail.com - 2018-10-16 11:12 -0700
                                                                                                Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-17 22:44 -0700
                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-18 11:27 -0700
                                                                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-18 22:22 -0700
                                                                                                      Re: Universal quantification? ich <dvhaus.dresden@gmail.com> - 2018-10-19 00:31 -0700
                                                                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-19 03:24 -0700
                                                                                                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-19 03:41 -0700
                                                                                                          Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-19 03:48 -0700
                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-19 12:33 -0700
                                                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-19 03:45 -0700
                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-19 12:32 -0700
                                                                                                            Re: Universal quantification? "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-19 21:24 -0500
                                                                                                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-20 00:45 -0700
                                                                                                                Re: Universal quantification? "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-21 16:41 -0500
                                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-22 02:59 -0700
                                                                                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-22 03:26 -0700
                                                                                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-22 04:43 -0700
                                                                                                                        Re: Universal quantification? bursejan@gmail.com - 2018-10-22 05:22 -0700
                                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-22 11:13 -0700
                                                                                                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-22 12:29 -0700
                                                                                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-22 22:25 -0700
                                                                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-22 05:32 -0700
                                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-22 11:14 -0700
                                                                                                                        Re: Universal quantification? Python <python@python.invalid> - 2018-10-22 15:26 +0200
                                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-22 11:21 -0700
                                                                                                                    Re: Universal quantification? "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-22 19:57 -0500
                                                                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-21 22:42 -0700
                                                                                                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-22 03:05 -0700
                                                                                                                Re: Universal quantification? Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-22 15:04 +0100
                                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-22 11:15 -0700
                                                                                                                    Re: Universal quantification? Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-23 14:36 +0100
                                                                                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-23 09:03 -0700
                                                                                                                        Re: Universal quantification? Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-23 17:17 +0100
                                                                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-24 22:44 -0700
                                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-25 03:28 -0700
                                                                                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-25 04:35 -0700
                                                                                                                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-25 05:09 -0700
                                                                                                                                Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-25 05:20 -0700
                                                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-25 06:33 -0700
                                                                                                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-25 22:37 -0700
                                                                                                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-26 13:38 -0700
                                                                                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-29 23:38 -0700
                                                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-30 04:36 -0700
                                                                                                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-30 04:52 -0700
                                                                                                                                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-30 11:06 -0700
                                                                                                                                                Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-30 23:27 -0700
                                                                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-31 02:28 -0700
                                                                                                                                                    Re: Universal quantification? bursejan@gmail.com - 2018-10-31 05:22 -0700
                                                                                                                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-10-31 23:36 -0700
                                                                                                                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-01 02:57 -0700
                                                                                                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-11-01 03:26 -0700
                                                                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-02 06:08 -0700
                                                                                                                                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-11-02 15:29 -0700
                                                                                                                                                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-03 03:16 -0700
                                                                                                                                                                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-11-03 06:53 -0700
                                                                                                                                                                  Re: Universal quantification? bursejan@gmail.com - 2018-11-03 07:02 -0700
                                                                                                                                                                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-11-03 07:32 -0700
                                                                                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-04 08:39 -0800
                                                                                                                                                                    Re: Universal quantification? bursejan@gmail.com - 2018-11-04 09:09 -0800
                                                                                                                                                                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-11-04 09:26 -0800
                                                                                                                                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-05 02:18 -0800
                                                                                                                                                                        Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-11-05 02:36 -0800
                                                                                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-05 05:17 -0800
                                                                                                                                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-11-05 05:29 -0800
                                                                                                                                                                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-06 02:32 -0800
                                                                                                                                                                                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-11-06 04:38 -0800
                                                                                                                                                                                Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-11-07 22:42 -0800
                                                                                                                                                                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-11-04 22:37 -0800
                                                                                                                                                                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-05 02:18 -0800
                                                                                                                                                            Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-11-04 22:34 -0800
                                                                                                                                                              Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-11-05 01:53 -0800
                                                                                                                                                                Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-11-05 02:18 -0800
                                                                                                                                Re: Universal quantification? ich <dvhaus.dresden@gmail.com> - 2018-10-30 05:02 -0700
                                                                                                                                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-30 11:52 -0700
                                                                                                        Re: Universal quantification? Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-19 11:46 +0100
                                                                                                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-19 12:55 -0700
                                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-05 03:12 -0700
                                  Re: Universal quantification? transfinity01@gmail.com - 2018-10-02 11:23 -0700
                                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-02 11:31 -0700
                                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-03 02:58 -0700
                                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-03 04:04 -0700
                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-03 08:36 -0700
                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-03 10:13 -0700
                                              Re: Universal quantification? transfinity01@gmail.com - 2018-10-04 11:48 -0700
                                                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-04 12:23 -0700
                                                  Re: Universal quantification? transfinity01@gmail.com - 2018-10-05 02:50 -0700
                                                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-05 03:29 -0700
                                                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-05 06:20 -0700
                                                        Re: Universal quantification? ich <dvhaus.dresden@gmail.com> - 2018-10-05 06:34 -0700
                                                          Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-05 07:42 -0700
                                                            Re: Universal quantification? bursejan@gmail.com - 2018-10-05 08:21 -0700
                                                        Re: Universal quantification? bursejan@gmail.com - 2018-10-05 06:35 -0700
                                                          Re: Universal quantification? bursejan@gmail.com - 2018-10-05 06:45 -0700
                                                            Re: Universal quantification? bursejan@gmail.com - 2018-10-05 06:53 -0700
                                                              Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-05 07:27 -0700
                                                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-06 08:12 -0700
                                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-06 09:08 -0700
                                                              Re: Universal quantification? bursejan@gmail.com - 2018-10-06 10:00 -0700
                                                                Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-07 08:21 -0700
                                                                  Re: Universal quantification? bursejan@gmail.com - 2018-10-07 08:27 -0700
                                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-03 19:54 -0700
                    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-09-30 22:46 -0700
                      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 06:35 -0700
                        Re: Universal quantification? ich <dvhaus.dresden@gmail.com> - 2018-10-01 06:44 -0700
                          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 07:06 -0700
                            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-01 10:14 -0700
                              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 11:36 -0700
                              Re: Universal quantification? transfinity01@gmail.com - 2018-10-01 13:33 -0700
                                Re: Universal quantification? bursejan@gmail.com - 2018-10-01 14:06 -0700
                                  Re: Universal quantification? bursejan@gmail.com - 2018-10-01 14:18 -0700
        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-29 17:48 -0700
        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-29 19:06 -0700
          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-30 02:04 -0700
            Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-30 04:33 -0700
              Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-30 10:53 -0700
                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-30 20:12 -0700
                  Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-01 06:30 -0700
    Re: Universal quantification? "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-09-29 18:57 -0500
      Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-30 02:04 -0700
        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-30 04:30 -0700
          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-30 10:53 -0700
        Re: Universal quantification? "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-09-30 11:15 -0500
          Re: Universal quantification? WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-09-30 11:02 -0700
            Re: Universal quantification? bursejan@gmail.com - 2018-09-30 14:44 -0700
              Re: Universal quantification? bursejan@gmail.com - 2018-09-30 15:03 -0700
            Re: Universal quantification? "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-02 19:06 -0500
              Re: Universal quantification? transfinity01@gmail.com - 2018-10-03 02:59 -0700
                Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-03 04:09 -0700
                  Re: Universal quantification? transfinity01@gmail.com - 2018-10-03 08:36 -0700
                    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-03 10:18 -0700
                      Re: Universal quantification? transfinity01@gmail.com - 2018-10-04 11:47 -0700
                        Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-10-04 12:26 -0700
                          Re: Universal quantification? transfinity01@gmail.com - 2018-10-05 02:49 -0700
                            Re: Universal quantification? Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-05 11:09 +0100
                Re: Universal quantification? "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-03 21:05 -0500
    Re: Universal quantification? me <dvhaus.dresden@gmail.com> - 2018-09-29 19:12 -0700
    Re: Universal quantification? Zelos Malum <zelos.malum@gmail.com> - 2018-09-30 22:34 -0700
    Re: Universal quantification? Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-10-01 12:24 -0700
    Re: Universal quantification? Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-10-01 12:29 -0700

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#424544

From"Shobe, Martin" <martin.shobe@yahoo.com>
Date2018-09-29 18:57 -0500
Message-ID<pop3i3$m61$1@dont-email.me>
In reply to#424497
On 9/29/2018 3:33 AM, WM wrote:
> 
> By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL.

No.

[snip nonsense]

Martin Shobe

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#424582

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-09-30 02:04 -0700
Message-ID<73a288c7-5dc2-4ad6-ae28-489fb14df09d@googlegroups.com>
In reply to#424544
Am Sonntag, 30. September 2018 01:58:01 UTC+2 schrieb Shobe, Martin:
> On 9/29/2018 3:33 AM, WM wrote:
> > 
> > By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL.
> 
> No.

Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as forall p/q exists n. Every n can be selected individually. Otherwise the statement is void.

Regards, WM 

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#424588

Fromme <dvhaus.dresden@gmail.com>
Date2018-09-30 04:30 -0700
Message-ID<7fad91db-f642-4c74-a9bc-a9caeba5837b@googlegroups.com>
In reply to#424582
Am Sonntag, 30. September 2018 11:04:51 UTC+2 schrieb WM:

> Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 
> 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as 
> forall p/q exists n. Every n can be selected individually. Otherwise the 
> statement is void.

If you say so.

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#424599

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-09-30 10:53 -0700
Message-ID<01c8ba33-fe3a-4c89-9265-14f6109a64b0@googlegroups.com>
In reply to#424588
Am Sonntag, 30. September 2018 13:30:50 UTC+2 schrieb me:
> Am Sonntag, 30. September 2018 11:04:51 UTC+2 schrieb WM:
> 
> > Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 
> > 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as 
> > forall p/q exists n. Every n can be selected individually. Otherwise the 
> > statement is void.
> 
> If you say so.

For Cantor's set theory individual accessibility is crucial. Otherwise there is no provable bijection. 

Well, set theorists are immune to such drawbacks. That are "minor problems" since almost all "real" numbers have been found to be inaccessible too.

Regards, WM

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#424595

From"Shobe, Martin" <martin.shobe@yahoo.com>
Date2018-09-30 11:15 -0500
Message-ID<poqsrv$2ab$1@dont-email.me>
In reply to#424582
On 9/30/2018 4:04 AM, WM wrote:
> Am Sonntag, 30. September 2018 01:58:01 UTC+2 schrieb Shobe, Martin:
>> On 9/29/2018 3:33 AM, WM wrote:
>>>
>>> By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL.
>>
>> No.
> 
> Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as forall p/q exists n. Every n can be selected individually. Otherwise the statement is void.

No. The bijection remains a bijection even if some members of n are 
inaccessible. Neither the universal quantifier nor FOL guarantee that 
any particular member can be accessed individually.

Martin Shobe

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#424600

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-09-30 11:02 -0700
Message-ID<b789b8ed-12df-4e05-be37-0b7bd66cb816@googlegroups.com>
In reply to#424595
Am Sonntag, 30. September 2018 18:16:07 UTC+2 schrieb Shobe, Martin:
> On 9/30/2018 4:04 AM, WM wrote:
> > Am Sonntag, 30. September 2018 01:58:01 UTC+2 schrieb Shobe, Martin:
> >> On 9/29/2018 3:33 AM, WM wrote:
> >>>
> >>> By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL.
> >>
> >> No.
> > 
> > Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as forall p/q exists n. Every n can be selected individually. Otherwise the statement is void.
> 
> No. The bijection remains a bijection even if some members of n are 
> inaccessible. Neither the universal quantifier nor FOL guarantee that 
> any particular member can be accessed individually.

For Cantor's set theory individual accessibility is crucial. Otherwise there is no provable bijection. 

Further your understatement is funny. There are not "some members" of |N inaccessible but almost all.

Well, set theorists are immune to such drawbacks. That are "minor problems" since almost all "real" numbers have been found to be inaccessible too.

Regards, WM

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#424618

Frombursejan@gmail.com
Date2018-09-30 14:44 -0700
Message-ID<a3c61f18-aacc-46eb-ae44-5a005a25f452@googlegroups.com>
In reply to#424600
So far you did not scratch any set theory. Your WM theorem
can be easily generalized to (for what set theory is for):

   λ limit ordinal =>
     forall β (β < λ => |ω| =< |{γ < λ | β < γ}| =< |λ|) 

Your WM special case is only λ=ω written with N instead
of ω. You then get:

     forall n in N (|{m in N|n < m}|=aleph_0)

What is a limit ordinal? See here:
https://en.wikipedia.org/wiki/Limit_ordinal

Am Sonntag, 30. September 2018 20:02:57 UTC+2 schrieb WM:
> Am Sonntag, 30. September 2018 18:16:07 UTC+2 schrieb Shobe, Martin:
> > On 9/30/2018 4:04 AM, WM wrote:
> > > Am Sonntag, 30. September 2018 01:58:01 UTC+2 schrieb Shobe, Martin:
> > >> On 9/29/2018 3:33 AM, WM wrote:
> > >>>
> > >>> By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL.
> > >>
> > >> No.
> > > 
> > > Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as forall p/q exists n. Every n can be selected individually. Otherwise the statement is void.
> > 
> > No. The bijection remains a bijection even if some members of n are 
> > inaccessible. Neither the universal quantifier nor FOL guarantee that 
> > any particular member can be accessed individually.
> 
> For Cantor's set theory individual accessibility is crucial. Otherwise there is no provable bijection. 
> 
> Further your understatement is funny. There are not "some members" of |N inaccessible but almost all.
> 
> Well, set theorists are immune to such drawbacks. That are "minor problems" since almost all "real" numbers have been found to be inaccessible too.
> 
> Regards, WM

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#424622

Frombursejan@gmail.com
Date2018-09-30 15:03 -0700
Message-ID<c70819e8-5f7c-475c-a502-ce826b87b61c@googlegroups.com>
In reply to#424618
If you take ω1
https://en.wikipedia.org/wiki/First_uncountable_ordinal

You get possibly uncountable many elements
following a segment:

    forall β (β < ω1 => |ω| =< |{γ < ω1 | β < ω1}| =< |ω1|)

Since ω1 is the first uncountable ordinal, every
β with β < ω1, is countable. Therefore I guess we 
even have now:

    forall β (β < ω1 => |{γ < ω1 | β < ω1}| = |ω1|)

Right?

Am Sonntag, 30. September 2018 23:44:44 UTC+2 schrieb burs...@gmail.com:
> So far you did not scratch any set theory. Your WM theorem
> can be easily generalized to (for what set theory is for):
> 
>    λ limit ordinal =>
>      forall β (β < λ => |ω| =< |{γ < λ | β < γ}| =< |λ|) 
> 
> Your WM special case is only λ=ω written with N instead
> of ω. You then get:
> 
>      forall n in N (|{m in N|n < m}|=aleph_0)
> 
> What is a limit ordinal? See here:
> https://en.wikipedia.org/wiki/Limit_ordinal
> 
> Am Sonntag, 30. September 2018 20:02:57 UTC+2 schrieb WM:
> > Am Sonntag, 30. September 2018 18:16:07 UTC+2 schrieb Shobe, Martin:
> > > On 9/30/2018 4:04 AM, WM wrote:
> > > > Am Sonntag, 30. September 2018 01:58:01 UTC+2 schrieb Shobe, Martin:
> > > >> On 9/29/2018 3:33 AM, WM wrote:
> > > >>>
> > > >>> By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL.
> > > >>
> > > >> No.
> > > > 
> > > > Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as forall p/q exists n. Every n can be selected individually. Otherwise the statement is void.
> > > 
> > > No. The bijection remains a bijection even if some members of n are 
> > > inaccessible. Neither the universal quantifier nor FOL guarantee that 
> > > any particular member can be accessed individually.
> > 
> > For Cantor's set theory individual accessibility is crucial. Otherwise there is no provable bijection. 
> > 
> > Further your understatement is funny. There are not "some members" of |N inaccessible but almost all.
> > 
> > Well, set theorists are immune to such drawbacks. That are "minor problems" since almost all "real" numbers have been found to be inaccessible too.
> > 
> > Regards, WM

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#424809

From"Shobe, Martin" <martin.shobe@yahoo.com>
Date2018-10-02 19:06 -0500
Message-ID<pp116o$for$1@dont-email.me>
In reply to#424600
On 9/30/2018 1:02 PM, WM wrote:
> Am Sonntag, 30. September 2018 18:16:07 UTC+2 schrieb Shobe, Martin:
>> On 9/30/2018 4:04 AM, WM wrote:
>>> Am Sonntag, 30. September 2018 01:58:01 UTC+2 schrieb Shobe, Martin:
>>>> On 9/29/2018 3:33 AM, WM wrote:
>>>>>
>>>>> By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL.
>>>>
>>>> No.
>>>
>>> Cantor's  approach of enumerating the fractions 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ... can be expressed as forall p/q exists n. Every n can be selected individually. Otherwise the statement is void.
>>
>> No. The bijection remains a bijection even if some members of n are
>> inaccessible. Neither the universal quantifier nor FOL guarantee that
>> any particular member can be accessed individually.
> 
> For Cantor's set theory individual accessibility is crucial. Otherwise there is no provable bijection.

We don't require individual accessibility to prove bijections.

[snip nonsense]

Martin Shobe

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#424845

Fromtransfinity01@gmail.com
Date2018-10-03 02:59 -0700
Message-ID<7d749d9f-63d6-4adb-877c-2a53fd186918@googlegroups.com>
In reply to#424809
Am Mittwoch, 3. Oktober 2018 02:06:53 UTC+2 schrieb Shobe, Martin:
> On 9/30/2018 1:02 PM, WM wrote:


> > For Cantor's set theory individual accessibility is crucial. Otherwise there is no provable bijection.
> 
> We don't require individual accessibility to prove bijections.
> 
Then you are outside of mathematics, sloppy and imprecise. In mathematics we have the term one-to-one mapping. And there we can check every single pair individually. Even in set theory this property has been accepted until now.

Regards, WM

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#424856

Fromme <dvhaus.dresden@gmail.com>
Date2018-10-03 04:09 -0700
Message-ID<c9d7acfe-16e1-4670-86b3-80e304b83982@googlegroups.com>
In reply to#424845
Am Mittwoch, 3. Oktober 2018 11:59:50 UTC+2 schrieb transf...@gmail.com:

> ... there we can check every single pair individually.

So you are able to execute infintely many tasks (one after another), really? :-)

I don't think so.

Anayway, at least in /set theory/ there's no need to _do_ that. :-)

> [nonsense deleted]

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#424874

Fromtransfinity01@gmail.com
Date2018-10-03 08:36 -0700
Message-ID<055273bd-c211-4056-9719-6ed60c2ae284@googlegroups.com>
In reply to#424856
Am Mittwoch, 3. Oktober 2018 13:09:07 UTC+2 schrieb me:
> Am Mittwoch, 3. Oktober 2018 11:59:50 UTC+2 schrieb transf...@gmail.com:
> 
> > ... there we can check every single pair individually.
> 
> So you are able to execute infintely many tasks (one after another), really?

No, but I can decide which to check.

> Anayway, at least in /set theory/ there's no need to _do_ that.

In Cantor's set theory there is. Its modern perverted version (perversion) does not need anything.

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

Regards, WM

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#424878

Fromme <dvhaus.dresden@gmail.com>
Date2018-10-03 10:18 -0700
Message-ID<48c95a58-86d6-4a6c-8603-44bae4e61ab2@googlegroups.com>
In reply to#424874
Am Mittwoch, 3. Oktober 2018 17:36:40 UTC+2 schrieb transf...@gmail.com:
> Am Mittwoch, 3. Oktober 2018 13:09:07 UTC+2 schrieb me:
> > Am Mittwoch, 3. Oktober 2018 11:59:50 UTC+2 schrieb transf...@gmail.com:
> > 
> > > ... there we can check every single pair individually.
> > 
> > So you are able to execute infintely many tasks (one after another),
> > really?
> 
> No [...]
> >
> > Anayway, at least in /set theory/ there's no need to _do_ that.
> >
> In Cantor's set theory there is.

No.

> Its modern perverted version (perversion) does not need anything.
> 
> "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und 
> vollständig, Element für Element, einander zuordnen lassen  ..." [Cantor,
> p. 119]

So you are suggesting that Cantor actually DID that in his papers (ore somewhere else)

      (I mean "check _every_ single pair _individually_")

when dealing with infinite sets, really? Wow, that's huge!

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#424939

Fromtransfinity01@gmail.com
Date2018-10-04 11:47 -0700
Message-ID<1196dd30-d430-4930-affd-36e8f888bed8@googlegroups.com>
In reply to#424878
Am Mittwoch, 3. Oktober 2018 19:18:30 UTC+2 schrieb me:

> > "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und 
> > vollständig, Element für Element, einander zuordnen lassen  ..." [Cantor,
> > p. 119]
> 
> So you are suggesting that Cantor actually DID that in his papers (ore somewhere else)

He said that the possibility is required. 

Regards, WM

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#424943

Fromme <dvhaus.dresden@gmail.com>
Date2018-10-04 12:26 -0700
Message-ID<ad112eb3-b517-46e8-bd53-10cc0aac8439@googlegroups.com>
In reply to#424939
Am Donnerstag, 4. Oktober 2018 20:47:12 UTC+2 schrieb transf...@gmail.com:
> Am Mittwoch, 3. Oktober 2018 19:18:30 UTC+2 schrieb me:
> > >
> > > "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und 
> > > vollständig, Element für Element, einander zuordnen lassen  ..." [Cantor,
> > > p. 119]
> > >
> > So you are suggesting that Cantor actually DID that in his papers (or
> > somewhere else)
> >
> He said that the possibility is required. 

No, he didn't. 

Again: He didn't SAY that.

When claiming that he actually MEANT that, that's just your OPINION. But, no one is willing to share that opinion, Mückenheim.

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#424992

Fromtransfinity01@gmail.com
Date2018-10-05 02:49 -0700
Message-ID<f5b30880-313d-4e3b-9ee7-b93de33284a7@googlegroups.com>
In reply to#424943
Am Donnerstag, 4. Oktober 2018 21:27:08 UTC+2 schrieb me:
> Am Donnerstag, 4. Oktober 2018 20:47:12 UTC+2 schrieb transf...@gmail.com:
> > Am Mittwoch, 3. Oktober 2018 19:18:30 UTC+2 schrieb me:
> > > >
> > > > "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und 
> > > > vollständig, Element für Element, einander zuordnen lassen  ..." [Cantor,
> > > > p. 119]
> > > >
> > > So you are suggesting that Cantor actually DID that in his papers (or
> > > somewhere else)
> > >
> > He said that the possibility is required. 
> 
> No, he didn't. 
> 
> Again: He didn't SAY that.

What he sais, "uniquely, completely, element by element" expresses precisely that. Further even today "well-defined" means that every element has its fixed place and can be checked there, namely as the first element of its subset.

Regards, WM

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#424998

FromAlan Smaill <smaill@SPAMinf.ed.ac.uk>
Date2018-10-05 11:09 +0100
Message-ID<fwe4le0iu1i.fsf@foxtrot.inf.ed.ac.uk>
In reply to#424992
transfinity01@gmail.com writes:

> Further even today "well-defined" means that every
> element has its fixed place and can be checked there, namely as the
> first element of its subset.

No, that's not what well-defined *means*.

  "In mathematics, an expression is called well-defined or unambiguous
   if its definition assigns it a unique interpretation or value."

Which expression formed from a  finite number of "s" followed by "1"
fails to correspond to a natural number?
Which two different expressions of this form correspond to the same
natural number?


>
> Regards, WM

-- 
Alan Smaill

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#424896

From"Shobe, Martin" <martin.shobe@yahoo.com>
Date2018-10-03 21:05 -0500
Message-ID<pp3si3$922$1@dont-email.me>
In reply to#424845
On 10/3/2018 4:59 AM, transfinity01@gmail.com wrote:
> Am Mittwoch, 3. Oktober 2018 02:06:53 UTC+2 schrieb Shobe, Martin:
>> On 9/30/2018 1:02 PM, WM wrote:
> 
> 
>>> For Cantor's set theory individual accessibility is crucial. Otherwise there is no provable bijection.
>>
>> We don't require individual accessibility to prove bijections.
>>
> Then you are outside of mathematics, sloppy and imprecise.

I have no problem "being outside" of what you call mathematics. What you 
call mathematics is inconsistent.

Martin Shobe

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#424553

Fromme <dvhaus.dresden@gmail.com>
Date2018-09-29 19:12 -0700
Message-ID<e99d91b3-f316-4373-b579-2db153ffbb46@googlegroups.com>
In reply to#424497
Am Samstag, 29. September 2018 10:33:41 UTC+2 schrieb WM:

> By means of the universal quantifier all aleph_0 natural numbers can be 
> selected individually. So says FOL.

Nonsense.

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#424653

FromZelos Malum <zelos.malum@gmail.com>
Date2018-09-30 22:34 -0700
Message-ID<2091c73a-4887-4716-a22d-1963d9cf22ac@googlegroups.com>
In reply to#424497
>By means of the universal quantifier all aleph_0 natural numbers can be selected individually. So says FOL. 

Incorrect, FOL is a formal language of logic that contains several types of symbols and rules on how to form sentences and words and then also how you deduce new ones.

Universal quantifier is just either one of the two quantifiers or a shorthand for ~Ex(~P(x)) so in a formal way, you are not selecting anything. You are just saying wether a sentence exist within the formal language or not.

But then again understanding these things would involve understanding logic, somethign you sorely do not.

>In fact every selected number belongs to a finite initial segment, that, according to set theory, is followed by aleph_0 not selected numbers. 

which is entirely irrelevant.

>In fact every putative user of the universal quantifier fails infinitely often and never succeeds. 

Incorrect, the fact that AnEsAx (n,x e |N & s c |N & (x=<n => x e s)) is a legitimate sentence in PA FOL does not mean Ax e |N(P(x)) is not a legitimate sentence in PA.

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