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Groups > sci.math > #629778 > unrolled thread

Re: Replacement of Cardinality

Started byJim Burns <james.g.burns@att.net>
First post2024-07-27 13:34 -0400
Last post2024-07-29 17:59 +0200
Articles 20 on this page of 924 — 14 participants

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  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-27 13:34 -0400
    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-07-28 12:17 +0000
      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-28 14:17 -0400
        Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-28 16:25 -0700
          Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-28 16:32 -0700
            Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-28 16:42 -0700
              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-29 08:32 -0400
                Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-29 12:44 -0700
                  Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-29 12:46 -0700
                    Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-01 10:10 -0800
                      Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Jim Burns <james.g.burns@att.net> - 2025-01-01 16:14 -0500
                        Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-01 15:50 -0800
                          Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-01 16:28 -0800
                            Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Jim Burns <james.g.burns@att.net> - 2025-01-02 11:47 -0500
                              Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-02 11:04 -0800
                                Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Jim Burns <james.g.burns@att.net> - 2025-01-02 16:08 -0500
                          Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Jim Burns <james.g.burns@att.net> - 2025-01-02 12:35 -0500
                            Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-02 11:07 -0800
                              Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-02 11:14 -0800
                                Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-03 11:22 -0800
                              Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Jim Burns <james.g.burns@att.net> - 2025-01-02 16:55 -0500
                                Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-02 22:23 -0800
                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-29 17:12 -0400
                    Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-29 18:31 -0700
                      Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-29 18:32 -0700
                      Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-07-30 14:18 -0400
                        Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-30 13:56 -0700
                          Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-30 14:06 -0700
                          Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-07-31 16:21 -0400
                            Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-31 17:30 -0700
                              Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-01 07:23 -0400
                                Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-01 12:28 -0700
                                  Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-01 20:36 -0400
                                    Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-01 17:52 -0700
                                      Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-01 23:20 -0400
                                      Re: Replacement of Cardinality (ubiquitous ordinals) FromTheRafters <FTR@nomail.afraid.org> - 2024-08-02 06:39 -0400
                                        Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-02 12:55 -0700
                                          Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-03 15:08 -0400
                                            Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-03 18:08 -0700
                                              Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-03 23:45 -0400
                                                Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-03 20:51 -0700
                                                  Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-04 01:25 -0400
                                                    Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 07:36 -0700
                                                      Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-04 12:48 -0400
                                                        Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 10:44 -0700
                                                          Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-04 14:26 -0400
                                                            Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 11:38 -0700
                                                              Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-04 16:25 -0400
                                      Re: Replacement of Cardinality (ubiquitous ordinals) Jim Burns <james.g.burns@att.net> - 2024-08-02 08:54 -0400
                              Re: Replacement of Cardinality (ubiquitous ordinals) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-01-01 10:10 -0800
        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-07-29 13:23 +0000
          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-29 14:33 -0400
            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-07-30 17:30 +0000
              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-30 14:37 -0400
                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-07-31 00:49 +0200
                  Re: Replacement of Cardinality --- infinitesimal number system olcott <polcott333@gmail.com> - 2024-07-30 18:46 -0500
                    Re: Replacement of Cardinality --- infinitesimal number system Moebius <invalid@example.invalid> - 2024-07-31 01:54 +0200
                      Re: Replacement of Cardinality --- infinitesimal number system olcott <polcott333@gmail.com> - 2024-07-30 19:11 -0500
                        Re: Replacement of Cardinality --- infinitesimal number system "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-07-30 17:29 -0700
                        Re: Replacement of Cardinality --- infinitesimal number system Moebius <invalid@example.invalid> - 2024-07-31 03:19 +0200
                          Re: Replacement of Cardinality --- infinitesimal number system olcott <polcott333@gmail.com> - 2024-07-30 20:30 -0500
                            Re: Replacement of Cardinality --- infinitesimal number system Moebius <invalid@example.invalid> - 2024-07-31 03:33 +0200
                    Re: Replacement of Cardinality --- infinitesimal number system FromTheRafters <FTR@nomail.afraid.org> - 2024-07-30 20:22 -0400
                      Re: Replacement of Cardinality --- infinitesimal number system olcott <polcott333@gmail.com> - 2024-07-30 19:29 -0500
                      Re: Replacement of Cardinality --- infinitesimal number system Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-07-30 18:55 -0700
                    Re: Replacement of Cardinality --- infinitesimal number system Jim Burns <james.g.burns@att.net> - 2024-07-31 00:23 -0400
                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-07-31 14:05 +0000
                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-07-31 13:59 +0000
                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-31 13:33 -0400
                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-01 12:13 +0000
                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-01 14:12 -0400
                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-01 23:21 +0200
                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-02 15:36 +0000
                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-02 13:06 -0400
                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-02 19:31 +0200
                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-03 14:25 +0000
                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-03 17:42 +0000
                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-04 15:44 +0000
                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-04 13:59 -0400
                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-04 20:12 +0200
                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-03 14:51 -0700
                                  Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-03 17:59 -0400
                                    Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-03 18:14 -0700
                                      Re: Replacement of Cardinality (real-valued) FromTheRafters <FTR@nomail.afraid.org> - 2024-08-04 06:41 -0400
                                        Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 07:52 -0700
                                          Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 07:59 -0700
                                            Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 08:46 -0700
                                              Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 08:54 -0700
                                                Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 09:45 -0700
                                                Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 13:06 -0700
                                              Re: Replacement of Cardinality (real-valued) Jim Burns <james.g.burns@att.net> - 2024-08-07 16:06 -0400
                                                Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-07 18:03 -0700
                                                  Re: Replacement of Cardinality (real-valued) Jim Burns <james.g.burns@att.net> - 2024-08-08 15:00 -0400
                                                    Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-08 12:52 -0700
                                                      Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 20:07 -0700
                                      Re: Replacement of Cardinality (real-valued) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:00 -0800
                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-04 02:09 +0200
                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-04 15:32 +0000
                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-03 14:23 +0000
                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-03 15:54 -0400
                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-04 02:14 +0200
                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-04 02:15 +0200
                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-04 15:35 +0000
                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-04 11:53 -0400
                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-04 17:57 +0200
                                        Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-04 12:55 -0400
                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-04 17:55 +0000
                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-04 16:07 -0700
                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-05 02:24 +0200
                                        Re: Replacement of Cardinality (quantifier disambiguation) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 17:49 -0700
                                          Re: Replacement of Cardinality (quantifier disambiguation) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-04 18:41 -0700
                                            Re: Replacement of Cardinality (quantifier disambiguation) Jim Burns <james.g.burns@att.net> - 2024-08-05 09:01 -0400
                                              Re: Replacement of Cardinality (quantifier disambiguation) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-05 13:11 -0700
                                                Re: Replacement of Cardinality (quantifier disambiguation) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 20:07 -0700
                                            Re: Replacement of Cardinality (quantifier disambiguation) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:01 -0800
                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-04 23:44 -0700
                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-05 10:03 +0200
                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-05 10:12 +0200
                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-05 22:47 +0200
                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-05 23:25 +0200
                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-05 19:21 +0000
                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-05 18:35 -0400
                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-06 01:22 +0200
                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-06 08:35 +0000
                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-06 08:38 -0400
                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-06 13:55 +0000
                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-06 12:33 -0400
                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 12:31 +0000
                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-07 14:03 -0400
                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-07 20:15 +0200
                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 18:55 +0000
                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-07 17:16 -0400
                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 18:51 +0000
                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-07 12:11 -0700
                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-08 00:38 -0400
                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-08 08:00 +0000
                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-07 11:17 -0700
                                              Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-06 22:36 -0400
                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 13:05 +0000
                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-07 11:16 -0700
                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-07 20:20 +0200
                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 23:13 -0700
                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-07 14:49 -0400
                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 19:05 +0000
                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-07 12:12 -0700
                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-07 16:51 -0400
                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-04 15:29 +0000
                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-04 12:39 -0400
                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-04 19:28 +0200
                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-04 18:13 +0000
                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-04 16:16 -0400
                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-04 22:48 +0200
                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-05 19:12 +0000
                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-05 19:17 +0000
                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-05 01:12 +0200
                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-04 19:41 -0400
                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-05 02:03 +0200
                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-05 19:04 +0000
                                          Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-05 20:33 +0000
                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-06 09:03 +0000
                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-05 18:19 -0400
                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-06 03:55 +0200
                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-06 08:48 +0000
                                            Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-05 20:05 -0700
                                              Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Jim Burns <james.g.burns@att.net> - 2024-08-06 07:57 -0400
                                                Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-06 12:58 -0700
                                                  Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Jim Burns <james.g.burns@att.net> - 2024-08-06 20:27 -0400
                                                    Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Moebius <invalid@example.invalid> - 2024-08-07 02:37 +0200
                                                      Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-06 19:30 -0700
                                                        Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 20:07 -0700
                                                          Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Python <python@invalid.org> - 2024-08-13 05:10 +0200
                                                    Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Moebius <invalid@example.invalid> - 2024-08-07 02:38 +0200
                                                      Re: Replacement of Cardinality (defining numbers as half finite, half infinite) Moebius <invalid@example.invalid> - 2024-08-07 02:45 +0200
                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-06 08:26 +0000
                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-06 06:32 -0400
                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-06 13:52 +0000
                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-06 13:44 -0400
                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 12:38 +0000
                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-07 13:07 -0400
                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 17:47 +0000
                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-07 14:29 -0400
                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-07 19:01 +0000
                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-07 17:29 -0400
                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-07 23:55 +0200
                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-08 00:17 +0200
                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-08 08:05 +0000
                                                                    Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-08 06:30 -0400
                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-08 13:36 -0700
                                                                        Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-08 17:56 -0400
                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-08 15:14 -0700
                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-08 15:21 -0700
                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 02:07 +0200
                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 15:34 -0700
                                                                                  Re: Replacement of Cardinality (integral equations) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-10 16:45 -0700
                                                                                    Re: Replacement of Cardinality (integral equations) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:03 -0800
                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 02:04 +0200
                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-08 23:34 -0400
                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-09 06:23 -0400
                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-10 00:36 +0200
                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-10 15:59 +0000
                                                                              Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-10 13:15 -0400
                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-11 12:24 +0000
                                                                                  Re: Replacement of Cardinality (analytische bruecken) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-11 07:18 -0700
                                                                                  Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-11 12:11 -0400
                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-11 12:29 -0700
                                                                                  Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-15 16:17 +0000
                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 16:21 +0000
                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-16 12:48 -0400
                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 16:57 +0000
                                                                                          Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-16 14:02 -0400
                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:33 +0000
                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:34 -0700
                                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-10 13:39 -0400
                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-11 00:06 +0200
                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-11 14:09 +0000
                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-11 13:56 -0400
                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-12 13:47 +0000
                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-12 14:34 -0400
                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-13 14:27 +0000
                                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-13 12:26 -0400
                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-13 18:35 +0200
                                                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-13 13:42 -0400
                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:28 +0000
                                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-14 14:04 -0400
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-15 13:55 +0000
                                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-16 12:07 -0400
                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-14 12:01 -0700
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-15 13:57 +0000
                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-15 16:05 -0700
                                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:06 +0200
                                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-16 12:08 -0400
                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:22 -0700
                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:17 +0000
                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:09 +0000
                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:14 +0000
                                                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-14 13:35 -0400
                                                                                              Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-17 11:43 +0000
                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:42 +0000
                                                                                                  Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-17 10:15 -0400
                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:40 -0700
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:26 +0000
                                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-19 07:36 -0400
                                                                                                  Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-18 08:16 +0000
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:54 +0000
                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:12 -0700
                                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-19 21:43 -0400
                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:21 -0700
                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-13 22:16 +0200
                                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-13 17:02 -0400
                                                                                            Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-13 17:54 -0400
                                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-14 00:09 +0200
                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-14 12:04 -0700
                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 01:26 +0200
                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 01:28 +0200
                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 15:40 -0700
                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-11 00:47 +0200
                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 15:52 -0700
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-11 01:00 +0200
                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-11 01:03 +0200
                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:24 -0700
                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:25 -0700
                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-13 22:29 +0200
                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-14 12:02 -0700
                                                                                    Re: Replacement of Cardinality --- silliness olcott <polcott333@gmail.com> - 2024-08-10 18:12 -0500
                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-11 00:50 +0200
                                                                              Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-12 13:27 +0000
                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-12 14:07 +0000
                                                                                  Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-12 16:20 +0200
                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-13 14:15 +0000
                                                                                      Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-13 12:06 -0400
                                                                                  Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-12 22:34 +0000
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-13 00:39 +0200
                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-10 21:59 +0200
                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 01:59 +0200
                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 02:09 +0200
                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 02:27 +0200
                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-09 06:21 -0400
                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-09 17:37 -0700
                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-09 17:29 -0700
                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-10 02:42 +0200
                                                                      Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-08 17:26 -0700
                                                                        Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-09 00:01 -0400
                                                                          Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-10 00:31 +0200
                                                                        Re: Replacement of Cardinality (infinite middle) FromTheRafters <FTR@nomail.afraid.org> - 2024-08-09 06:25 -0400
                                                                          Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-09 12:17 -0700
                                                                            Re: Replacement of Cardinality (infinite middle) FromTheRafters <FTR@nomail.afraid.org> - 2024-08-09 18:22 -0400
                                                                              Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-09 16:25 -0700
                                                                            Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-10 14:02 -0400
                                                                              Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-10 21:46 +0200
                                                                                Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-10 17:22 -0400
                                                                                  Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-10 23:24 +0200
                                                                                    Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-10 23:33 +0200
                                                                                      Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-10 23:44 +0200
                                                                              Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-10 12:48 -0700
                                                                                Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-10 18:14 -0400
                                                                        Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 15:32 -0700
                                                                          Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-11 00:43 +0200
                                                                            Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 15:47 -0700
                                                                              Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-11 00:54 +0200
                                                                              Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-11 01:05 +0200
                                                                                Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 17:55 -0700
                                                                                  Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-11 03:19 +0200
                                                                                    Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-10 21:20 -0700
                                                                                      Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-11 18:10 +0200
                                                                                        Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-11 11:10 -0700
                                                                                          Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-11 17:38 -0400
                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-11 16:39 -0700
                                                                                              Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-12 00:44 -0400
                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 13:59 -0700
                                                                                                  Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 14:27 -0700
                                                                                                  Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-12 19:06 -0400
                                                                                                    Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-13 01:11 +0200
                                                                                                    Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 17:28 -0700
                                                                                                      Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 02:44 +0200
                                                                                                        Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-13 02:59 +0200
                                                                                                          Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 03:03 +0200
                                                                                                          Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 05:00 +0200
                                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 20:02 -0700
                                                                                                              Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 05:06 +0200
                                                                                                              Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-12 21:30 -0700
                                                                                                                Re: Replacement of Cardinality (infinite middle) FromTheRafters <FTR@nomail.afraid.org> - 2024-08-13 06:35 -0400
                                                                                                                  Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:29 -0700
                                                                                                                    Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-13 17:33 -0700
                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-13 12:19 -0700
                                                                                                        Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 18:06 -0700
                                                                                                          Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 03:09 +0200
                                                                                                          Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 18:16 -0700
                                                                                                            Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 03:24 +0200
                                                                                                            Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 04:47 +0200
                                                                                                              Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-12 19:50 -0700
                                                                                                                Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-13 04:53 +0200
                                                                                                      Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-13 00:25 -0400
                                                                                                        Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-13 18:03 -0700
                                                                                                          Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-13 23:37 -0400
                                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-16 19:28 -0700
                                                                                                              Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-16 20:57 -0700
                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-16 21:11 -0700
                                                                                                              Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-17 17:12 -0400
                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-18 07:17 -0700
                                                                                                                  Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-18 13:50 -0400
                                                                                                                    Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-18 14:22 -0700
                                                                                                                      Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-19 00:56 -0400
                                                                                                                        Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-19 12:27 -0700
                                                                                                                          Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-19 17:43 -0400
                                                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-19 15:02 -0700
                                                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-19 15:21 -0700
                                                                                                                              Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-20 00:25 +0200
                                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-19 16:01 -0700
                                                                                                                              Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-19 19:18 -0400
                                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-19 17:08 -0700
                                                                                                                                  Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-19 20:33 -0400
                                                                                                                                    Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-19 19:40 -0700
                                                                                                                                      Re: Replacement of Cardinality (infinite middle) Python <python@invalid.org> - 2024-08-20 08:19 +0200
                                                                                                                                        Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-20 12:36 -0700
                                                                                                                                    Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-24 08:18 -0700
                                                                                                                          Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-29 15:46 -0700
                                                                                                                            Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-29 19:32 -0400
                                                                                                                              Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-29 17:12 -0700
                                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-29 17:28 -0700
                                                                                                                                  Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-30 01:24 -0400
                                                                                                                                    Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-30 13:00 -0700
                                                                                                                                      Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-30 17:41 -0400
                                                                                                                                        Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-01 11:44 -0700
                                                                                                                                          Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-01 12:46 -0700
                                                                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:10 -0800
                                                                                                                                          Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-09-02 17:46 -0400
                                                                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-02 17:25 -0700
                                                                                                                                              Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-09-03 14:39 -0400
                                                                                                                                              Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-09-03 15:28 -0400
                                                                                                                                              Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-09-03 16:50 -0400
                                                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-05 12:57 -0700
                                                                                                                                                  Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-05 13:14 -0700
                                                                                                                                                    Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-09-06 15:40 -0400
                                                                                                                                                      Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-06 13:36 -0700
                                                                                                                                                        Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:12 -0800
                                                                                                                                                    Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:11 -0800
                                                                                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-02 19:47 -0700
                                                                                                                                              Re: Replacement of Cardinality (infinite middle) Mild Shock <janburse@fastmail.fm> - 2024-09-07 10:14 +0200
                                                                                                                                      Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:09 -0800
                                                                                                                                Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:08 -0800
                                                                                            Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-12 02:08 +0200
                                                                                        Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-11 12:29 -0700
                                                                                          Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-11 22:21 +0200
                                                                                Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-11 14:30 -0400
                                                                                  Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-11 11:39 -0700
                                                                                    Re: Replacement of Cardinality (infinite middle) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-11 12:30 -0700
                                                                                      Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-11 13:26 -0700
                                                                                        Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-11 13:40 -0700
                                                                                    Re: Replacement of Cardinality (infinite middle) Jim Burns <james.g.burns@att.net> - 2024-08-12 12:39 -0400
                                                                                      Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-12 19:22 +0200
                                                                                        Re: Replacement of Cardinality (infinite middle) Jeff Barnett <jbb@notatt.com> - 2024-08-12 12:37 -0600
                                                                                          Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-12 20:48 +0200
                                                                                            Re: Replacement of Cardinality (infinite middle) Jeff Barnett <jbb@notatt.com> - 2024-08-12 18:16 -0600
                                                                          Re: Replacement of Cardinality (infinite middle) Moebius <invalid@example.invalid> - 2024-08-11 01:37 +0200
                                                                            Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-10 16:51 -0700
                                                                              Re: Replacement of Cardinality (infinite middle) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:03 -0800
                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-10 15:26 +0000
                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-15 16:16 +0000
                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-08 08:20 +0000
                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-08 12:58 -0400
                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-08 13:44 -0700
                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 02:01 +0200
                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-08 13:13 -0400
                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 02:14 +0200
                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-08 20:32 -0400
                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 03:10 +0200
                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-09 03:12 +0200
                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-10 15:54 +0000
                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-10 13:28 -0400
                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-11 12:29 +0000
                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-11 13:56 -0400
                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-12 13:50 +0000
                                                                              Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-12 13:23 -0400
                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-13 14:17 +0000
                                                                                  Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-13 12:07 -0400
                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:13 -0700
                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:17 -0700
                                                                                        Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-13 17:11 -0400
                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-13 14:34 -0400
                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-13 14:39 -0400
                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:34 +0000
                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-14 16:04 -0400
                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-15 13:59 +0000
                                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-15 15:28 -0400
                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 21:37 +0200
                                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 23:25 +0200
                                                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-15 18:51 -0400
                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 00:59 +0200
                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-15 16:35 -0700
                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:39 +0200
                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:52 +0200
                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:53 +0200
                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 02:03 +0200
                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-15 17:22 -0700
                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-15 17:50 -0700
                                                                                                    Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-16 06:08 -0400
                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:11 +0200
                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:32 +0200
                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:36 +0200
                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-15 16:37 -0700
                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:57 +0200
                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:57 +0200
                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:16 +0200
                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:24 +0200
                                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-16 01:05 -0400
                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 07:50 +0200
                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 07:57 +0200
                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-15 23:48 -0700
                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 09:22 +0200
                                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-16 07:45 -0400
                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 00:55 +0200
                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:10 -0700
                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:15 -0700
                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:48 +0000
                                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-12 13:44 -0400
                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-12 20:24 +0200
                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-12 20:47 +0200
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-12 20:55 +0200
                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-13 14:25 +0000
                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-13 14:21 +0000
                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-13 13:02 -0400
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-13 19:32 +0200
                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:19 -0700
                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:26 +0000
                                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-14 13:43 +0000
                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-14 18:35 +0200
                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-15 13:49 +0000
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-13 19:47 +0200
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-13 19:51 +0200
                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:32 +0000
                                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-17 11:43 +0000
                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:46 +0000
                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-13 12:18 -0700
                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-14 12:23 +0000
                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-14 12:43 -0400
                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 01:04 +0200
                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-15 13:52 +0000
                                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-15 12:16 -0400
                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 16:19 +0000
                                                                                              Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-16 16:50 +0000
                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 17:00 +0000
                                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-16 13:54 -0400
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:30 +0000
                                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-17 10:17 -0400
                                                                                                        Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-17 11:56 -0400
                                                                                                          Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-17 12:21 -0400
                                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:43 -0700
                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:43 -0700
                                                                                                  Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-16 18:11 +0000
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:39 +0000
                                                                                                      Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-18 08:16 +0000
                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-18 11:52 -0700
                                                                                                          Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-18 14:15 -0700
                                                                                                            Re: Replacement of Cardinality (selective memory) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-18 17:42 -0700
                                                                                                              Re: Replacement of Cardinality (selective memory) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:04 -0800
                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:13 -0700
                                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:17 -0700
                                                                                                              Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-19 16:55 -0400
                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-20 12:35 -0700
                                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-20 15:36 -0700
                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-21 07:15 +0200
                                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-23 12:13 -0700
                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-23 23:16 +0200
                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:51 +0000
                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-16 11:44 -0700
                                                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-16 13:39 -0400
                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:28 +0000
                                                                                                  Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-17 10:29 -0400
                                                                                                    Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-17 17:02 +0200
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:32 +0000
                                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-19 20:40 -0400
                                                                                                        Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-20 06:31 -0400
                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:21 +0000
                                                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-20 17:25 -0400
                                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-20 15:19 -0700
                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 10:44 +0000
                                                                                                                Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-21 06:58 -0400
                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 12:24 +0000
                                                                                                                    Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-21 13:13 +0000
                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-21 15:51 +0200
                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 14:53 +0000
                                                                                                                          Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-21 12:21 -0400
                                                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 10:55 +0000
                                                                                                                              Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-22 13:37 +0000
                                                                                                                              Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-22 10:15 -0400
                                                                                                                          Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-21 18:15 +0000
                                                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-21 20:34 +0200
                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 12:16 +0000
                                                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-22 13:40 +0000
                                                                                                                                Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-23 18:04 -0400
                                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-24 02:05 +0200
                                                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-24 02:08 +0200
                                                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-24 00:30 -0400
                                                                                                                                      Re: Replacement of Cardinality (roots of zero, reciprocals of the multiplicative annihilator) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-24 07:57 -0700
                                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 00:04 +0200
                                                                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 03:05 +0200
                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 03:09 +0200
                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-24 14:11 +0000
                                                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-25 06:21 -0400
                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-25 19:35 +0000
                                                                                                                                        Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-25 17:18 -0400
                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 02:15 +0200
                                                                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 02:34 +0200
                                                                                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 02:43 +0200
                                                                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-27 19:36 +0000
                                                                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-27 13:07 -0700
                                                                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-27 22:08 +0200
                                                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-27 22:10 +0200
                                                                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 12:45 +0000
                                                                                                                                                  Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-28 10:00 -0400
                                                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:34 +0000
                                                                                                                                                      Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-29 12:05 -0400
                                                                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-29 12:02 -0700
                                                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 12:48 +0000
                                                                                                                                                          Re: Grey numbers (was: Replacement of Cardinality) joes <noreply@example.org> - 2024-08-30 14:35 +0000
                                                                                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:36 -0700
                                                                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-29 11:59 -0700
                                                                                                                                                        Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-29 15:47 -0400
                                                                                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-29 17:06 -0400
                                                                                                                                                      Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-30 07:21 +0000
                                                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 13:01 +0000
                                                                                                                                                          Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-30 09:20 -0400
                                                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:40 -0700
                                                                                                                                              Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-27 23:17 -0400
                                                                                                                                              Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-28 04:20 +0000
                                                                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 14:51 +0200
                                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-27 19:26 +0000
                                                                                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-27 19:06 -0400
                                                                                                                                              Re: Replacement of Cardinality (book-keeping sign) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-27 16:41 -0700
                                                                                                                                                Re: Replacement of Cardinality (book-keeping sign) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-27 16:53 -0700
                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 12:49 +0000
                                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-27 23:18 -0400
                                                                                                                                            Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-28 04:23 +0000
                                                                                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 15:05 +0200
                                                                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 13:16 +0000
                                                                                                                                                  Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-28 10:07 -0400
                                                                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 15:17 +0200
                                                                                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-26 16:19 +0000
                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 18:21 +0200
                                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 16:08 +0200
                                                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 16:23 +0200
                                                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-26 14:17 -0400
                                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 20:58 +0200
                                                                                                                                        Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-26 15:06 -0400
                                                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 11:09 +0000
                                                                                                                              Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-22 13:39 +0000
                                                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-22 17:59 +0200
                                                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-22 13:22 -0700
                                                                                                                              Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-22 10:19 -0400
                                                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-23 14:27 +0000
                                                                                                                                  Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-23 18:06 +0000
                                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-24 14:21 +0000
                                                                                                                                      Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-24 14:45 +0000
                                                                                                                                      Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-24 14:08 -0400
                                                                                                                                        Re: Replacement of Cardinality (effective bounds) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-24 13:50 -0700
                                                                                                                                          Re: Replacement of Cardinality (effective bounds) Jim Burns <james.g.burns@att.net> - 2024-08-24 18:39 -0400
                                                                                                                                            Re: Replacement of Cardinality (effective bounds) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-24 17:26 -0700
                                                                                                                                              Re: Replacement of Cardinality (effective bounds) Jim Burns <james.g.burns@att.net> - 2024-08-25 13:47 -0400
                                                                                                                                                Re: Replacement of Cardinality (effective bounds) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-25 13:31 -0700
                                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-25 19:41 +0000
                                                                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-25 12:55 -0700
                                                                                                                                          Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-25 16:11 -0400
                                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-21 12:32 -0700
                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 14:58 +0000
                                                                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-21 18:14 +0000
                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 11:07 +0000
                                                                                                                            Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-22 17:24 +0000
                                                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-22 13:31 -0700
                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-23 14:32 +0000
                                                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-23 18:08 +0000
                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-24 14:20 +0000
                                                                                                                                Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-23 14:42 -0400
                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-24 14:15 +0000
                                                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-24 16:16 -0400
                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-25 19:41 +0000
                                                                                                                                        Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-25 17:18 -0400
                                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-27 19:20 +0000
                                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-27 12:34 -0700
                                                                                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-27 22:01 +0200
                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-27 13:14 -0700
                                                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-27 22:27 +0200
                                                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 12:47 +0000
                                                                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-27 13:09 -0700
                                                                                                                                              Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-27 19:07 -0400
                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 12:51 +0000
                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-28 12:23 -0700
                                                                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-28 12:28 -0700
                                                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 22:38 +0200
                                                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:23 +0000
                                                                                                                                                      Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-29 12:09 -0400
                                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-27 23:24 -0400
                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 13:01 +0000
                                                                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-29 10:46 +0000
                                                                                                                                                  Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-29 07:00 -0400
                                                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:15 +0000
                                                                                                                                                      Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-29 15:38 +0000
                                                                                                                                                      Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-29 12:15 -0400
                                                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 12:51 +0000
                                                                                                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-30 13:18 -0400
                                                                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-29 11:53 -0700
                                                                                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-29 21:42 +0200
                                                                                                                                                          Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-29 15:52 -0400
                                                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-29 13:08 -0700
                                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:16 +0000
                                                                                                                                            Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-28 04:22 +0000
                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 13:07 +0000
                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-28 12:32 -0700
                                                                                                                                        Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-25 17:57 -0400
                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-26 00:20 +0200
                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-23 00:14 -0400
                                                                                                                    Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-21 12:20 -0400
                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 10:54 +0000
                                                                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-22 13:36 +0000
                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-22 17:58 +0200
                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-22 13:29 -0700
                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-23 14:24 +0000
                                                                                                                        Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-22 10:22 -0400
                                                                                                                          Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-22 12:49 -0700
                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-22 13:30 -0700
                                                                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-22 17:19 -0400
                                                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-22 13:28 -0700
                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-23 14:28 +0000
                                                                                                                            Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-23 16:32 +0200
                                                                                                                            Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-23 14:13 -0400
                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-24 14:17 +0000
                                                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-24 14:43 +0000
                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-24 15:24 +0000
                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-24 13:06 -0400
                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-24 13:06 -0400
                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-25 19:47 +0000
                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-25 17:28 -0400
                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-27 19:29 +0000
                                                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-27 12:34 -0700
                                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-27 22:03 +0200
                                                                                                                                    Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-27 22:08 -0400
                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 12:55 +0000
                                                                                                                                        Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-28 19:48 -0400
                                                                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-28 16:59 -0700
                                                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-28 13:15 -0400
                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:38 +0000
                                                                                                                                        Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-29 13:56 -0400
                                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 12:53 +0000
                                                                                                                                            Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-30 11:44 -0400
                                                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-26 16:16 +0000
                                                                                                                        Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-22 21:23 -0400
                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-23 14:49 +0000
                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-24 13:06 -0400
                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-25 19:45 +0000
                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-25 17:31 -0400
                                                                                                                                Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-26 20:06 -0400
                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-27 19:11 +0000
                                                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-27 12:22 -0700
                                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-27 21:31 +0200
                                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-27 19:57 +0000
                                                                                                                                          Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-27 22:16 -0400
                                                                                                                                          Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-28 04:20 +0000
                                                                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 14:47 +0200
                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 13:11 +0000
                                                                                                                                                Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-28 10:10 -0400
                                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:35 +0000
                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-28 12:10 -0700
                                                                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-29 10:48 +0000
                                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:13 +0000
                                                                                                                                                    Re: Replacement of Cardinality Richard Hachel <r.hachel@wanadou.fr> - 2024-08-29 13:23 +0000
                                                                                                                                                    Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-29 15:42 +0000
                                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 12:46 +0000
                                                                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 13:04 +0000
                                                                                                                                              Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-28 15:06 +0000
                                                                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:37 +0000
                                                                                                                                                  Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-30 07:21 +0000
                                                                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-30 12:13 +0200
                                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 12:59 +0000
                                                                                                                                                        Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-30 09:23 -0400
                                                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 15:29 +0000
                                                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-30 11:47 -0400
                                                                                                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-30 15:17 +0000
                                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-30 18:35 +0200
                                                                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:34 -0700
                                                                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:39 -0700
                                                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 13:02 +0000
                                                                                                                                                      Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-30 09:26 -0400
                                                                                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-30 13:31 -0400
                                                                                                                                    Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-27 22:13 -0400
                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 12:57 +0000
                                                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-28 12:06 -0700
                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 22:35 +0200
                                                                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:26 +0000
                                                                                                                                              Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-29 21:09 -0400
                                                                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 13:06 +0000
                                                                                                                                                  Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-30 09:28 -0400
                                                                                                                                        Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-28 19:48 -0400
                                                                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-28 17:02 -0700
                                                                                                                                            Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-28 18:49 -0700
                                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-29 13:27 +0000
                                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-29 11:51 -0700
                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 12:55 +0000
                                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-30 09:01 -0400
                                                                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:20 -0700
                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:18 -0700
                                                                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:22 -0700
                                                                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-09-01 01:26 +0200
                                                                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-31 19:56 -0700
                                                                                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-09-01 05:25 +0200
                                                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-09-01 01:19 +0200
                                                                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-31 19:54 -0700
                                                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-09-01 05:21 +0200
                                                                                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-09-01 05:27 +0200
                                                                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-01 12:09 -0700
                                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-09-01 21:18 +0200
                                                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-09-02 18:56 +0200
                                                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-09-02 13:13 -0400
                                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-09-03 13:19 +0200
                                                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-09-03 07:26 -0400
                                                                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-09-03 13:29 +0200
                                                                                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-03 13:00 -0700
                                                                                                                                                                    Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-09-03 17:11 -0400
                                                                                                                                                                    Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-09-03 22:47 -0400
                                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-09-03 13:31 +0200
                                                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-09-03 22:55 -0400
                                                                                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-04 14:07 -0700
                                                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-02 11:47 -0700
                                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-09-03 13:27 +0200
                                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-03 12:57 -0700
                                                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-09-03 23:04 -0400
                                                                                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-04 14:09 -0700
                                                                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-29 21:09 -0400
                                                                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-30 13:08 +0000
                                                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-30 09:32 -0400
                                                                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-30 15:15 +0000
                                                                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-30 18:34 +0200
                                                                                                                                                Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-30 12:09 -0400
                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:23 -0700
                                                                                                                                      Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-28 12:06 -0700
                                                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-28 02:13 -0400
                                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 13:25 +0000
                                                                                                                                        Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-28 15:30 +0200
                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 20:18 +0200
                                                                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-28 20:18 +0200
                                                                                                                                        Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-28 12:55 -0400
                                                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-28 17:12 +0000
                                                                                                                                            Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-28 14:41 -0400
                                                                                                                                      Re: Replacement of Cardinality Jeff Barnett <jbb@notatt.com> - 2024-08-28 13:04 -0600
                                                                                                                                        Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-28 16:10 -0400
                                                                                                                                          Re: Replacement of Cardinality Jeff Barnett <jbb@notatt.com> - 2024-08-28 20:36 -0600
                                                                                                                                            Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-29 16:09 -0400
                                                                                                                                              Re: Replacement of Cardinality Jeff Barnett <jbb@notatt.com> - 2024-08-29 22:20 -0600
                                                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-30 12:28 -0700
                                                                                                                                                  Re: Replacement of Cardinality Jeff Barnett <jbb@notatt.com> - 2024-08-30 13:45 -0600
                                                                                                                                                    Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-30 13:23 -0700
                                                                                                                                                Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-31 14:20 -0400
                                                                                                                                                  Re: Replacement of Cardinality Jeff Barnett <jbb@notatt.com> - 2024-08-31 12:44 -0600
                                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-21 12:32 -0700
                                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-29 15:21 -0700
                                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-21 07:32 -0400
                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 12:32 +0000
                                                                                                                    Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-21 20:10 -0400
                                                                                                                      Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-21 18:23 -0700
                                                                                                                        Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-21 21:49 -0400
                                                                                                                          Re: Replacement of Cardinality Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-21 19:15 -0700
                                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-22 12:17 -0700
                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 12:19 +0000
                                                                                                                        Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-22 21:23 -0400
                                                                                                                          Re: Replacement of Cardinality (natural infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-22 19:04 -0700
                                                                                                                            Re: Replacement of Cardinality (natural infinity) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-22 23:53 -0700
                                                                                                                              Re: Replacement of Cardinality (natural infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-23 15:02 -0700
                                                                                                                                Re: Replacement of Cardinality (natural infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-08-24 08:07 -0700
                                                                                                                                  Re: Replacement of Cardinality (natural infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:06 -0800
                                                                                                                            Re: Replacement of Cardinality (natural infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-12-29 18:05 -0800
                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:19 +0000
                                                                                                          Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-20 15:21 +0200
                                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:25 +0000
                                                                                                              Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-20 15:28 +0200
                                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:39 +0000
                                                                                                                  Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-20 15:41 +0200
                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:58 +0000
                                                                                                                      Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-20 16:04 +0200
                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 10:39 +0000
                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-20 12:33 -0700
                                                                                                          Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-20 22:02 -0400
                                                                                                      Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-22 07:35 +0000
                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 12:26 +0000
                                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-17 17:39 -0400
                                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-18 03:51 +0200
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:40 +0000
                                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-19 12:58 -0400
                                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-19 19:17 +0200
                                                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-19 14:12 -0400
                                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-19 21:43 +0200
                                                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:07 +0000
                                                                                                              Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-20 16:05 -0400
                                                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-21 02:16 +0200
                                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 10:47 +0000
                                                                                                                    Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-21 07:26 -0400
                                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 12:29 +0000
                                                                                                                Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-21 10:43 +0000
                                                                                                                  Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-21 07:31 -0400
                                                                                                                  Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-21 14:20 -0400
                                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 11:17 +0000
                                                                                                                      Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-22 13:28 +0200
                                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-22 12:27 +0000
                                                                                                                          Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-22 14:48 +0200
                                                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-22 14:38 -0400
                                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:20 -0700
                                                                                                            Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:22 -0700
                                                                                                              Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-19 17:12 -0400
                                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-20 15:42 -0700
                                                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-19 17:05 -0400
                                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:00 +0000
                                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 12:53 +0000
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 14:43 +0200
                                                                                      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-15 11:53 -0400
                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 18:38 +0200
                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 18:43 +0200
                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 18:44 +0200
                                                                                          Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-15 14:36 -0400
                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 23:34 +0200
                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 23:35 +0200
                                                                                            Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 23:36 +0200
                                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 23:43 +0200
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 18:57 +0200
                                                                                    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 19:01 +0200
                                                                                      Re: Replacement of Cardinality Python <python@invalid.org> - 2024-08-15 19:06 +0200
                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 19:35 +0200
                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-15 15:59 -0700
                                                                                          Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 01:04 +0200
                                                                                        Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 16:42 +0000
                                                                                          Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-16 12:57 -0400
                                                                                          Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-16 11:39 -0700
                                                                                            Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-16 17:56 -0400
                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:33 -0700
                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 19:31 +0200
                                                                                      Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 19:34 +0200
                                                                                        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-15 19:41 +0200
                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 16:45 +0000
                                                                                        Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-16 16:49 +0000
                                                                                          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 16:59 +0000
                                                                                            Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-16 14:03 -0400
                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-16 11:43 -0700
                                                                                            Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-16 14:10 -0400
                                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-16 11:44 -0700
                                                                                                Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-16 15:04 -0400
                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:35 -0700
                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:36 +0000
                                                                                                Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-17 17:44 -0400
                                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-18 04:01 +0200
                                                                                                    Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:46 +0000
                                                                                                      Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:11 -0700
                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:44 +0000
                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-19 15:06 -0400
                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:10 +0000
                                                                                            Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-16 18:11 +0000
                                                                                              Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-16 22:12 +0200
                                                                                              Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-16 16:38 -0400
                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:37 -0700
                                                                                              Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-08-16 18:05 -0400
                                                                                                Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:38 -0700
                                                                                              Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-17 13:37 +0000
                                                                                                Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-17 10:22 -0400
                                                                                                  Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-17 12:39 -0700
                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:29 +0000
                                                                                                    Re: Replacement of Cardinality Richard Damon <richard@damon-family.org> - 2024-08-19 07:34 -0400
                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:59 +0000
                                                                                                        Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:09 -0700
                                                                                                Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-18 09:30 +0000
                                                                                                  Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-19 11:57 +0000
                                                                                                    Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-08-19 15:33 -0400
                                                                                                    Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-19 13:10 -0700
                                                                                                      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-20 13:14 +0000
                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-12 13:54 -0700
                                                                              Re: Replacement of Cardinality "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-08-12 13:54 -0700
                                                                                Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-12 23:38 +0200
                                                                                  Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-08-12 23:43 +0200
                                                                          Re: Replacement of Cardinality joes <noreply@example.org> - 2024-08-15 16:18 +0000
                                                                            Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-08-16 16:22 +0000
        Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-07-29 19:16 +0200
    Re: Replacement of Cardinality Moebius <invalid@example.invalid> - 2024-07-29 02:04 +0200
      Re: Replacement of Cardinality Jim Burns <james.g.burns@att.net> - 2024-07-29 05:28 -0400
      Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-07-29 05:29 -0400
      Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-07-29 13:25 +0000
        Re: Replacement of Cardinality Tom Bola <Tom@bolamail.etc> - 2024-07-29 15:40 +0200
          Re: Replacement of Cardinality WM <wolfgang.mueckenheim@tha.de> - 2024-07-29 13:43 +0000
            Re: Replacement of Cardinality Tom Bola <Tom@bolamail.etc> - 2024-07-29 16:05 +0200
        Re: Replacement of Cardinality FromTheRafters <FTR@nomail.afraid.org> - 2024-07-29 11:52 -0400
          Re: Replacement of Cardinality Tom Bola <Tom@bolamail.etc> - 2024-07-29 17:59 +0200

Page 23 of 47 — ← Prev page 1 … 21 22 [23] 24 25 … 47  Next page →


#630407

FromMoebius <invalid@example.invalid>
Date2024-08-16 01:57 +0200
Message-ID<v9m4l2$14adh$8@dont-email.me>
In reply to#630396
Am 16.08.2024 um 01:11 schrieb Moebius:
> Am 16.08.2024 um 00:51 schrieb Jim Burns:
>> On 8/15/2024 3:37 PM, Moebius wrote:
>>> Am 15.08.2024 um 21:28 schrieb Jim Burns:
>>
>>>> Defining ⅟𝔊 to be the smallest unit fraction
>>>> isn't a claim that ⅟𝔊 exists.
>>>
>>> You need an existence proof [...]

and a proof of proof of uniqueness

>>> BEFORE stating a/the proper definition.
>>
>> Proving that [a unique] mimsy borogove exist[s]
>> before defining [the] mimsy borogove
>> seems like a pretty steep hill to climb.

Hint: That's exactly, what we have to do in math.

Seriously. :-)

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#630408

FromMoebius <invalid@example.invalid>
Date2024-08-16 01:57 +0200
Message-ID<v9m4m5$14adg$8@dont-email.me>
In reply to#630396
Am 16.08.2024 um 01:11 schrieb Moebius:
> Am 16.08.2024 um 00:51 schrieb Jim Burns:
>> On 8/15/2024 3:37 PM, Moebius wrote:
>>> Am 15.08.2024 um 21:28 schrieb Jim Burns:
>>
>>>> Defining ⅟𝔊 to be the smallest unit fraction
>>>> isn't a claim that ⅟𝔊 exists.
>>>
>>> You need an existence proof [...]

and a proof of uniqueness

>>> BEFORE stating a/the proper definition.
>>
>> Proving that [a unique] mimsy borogove exist[s]
>> before defining [the] mimsy borogove
>> seems like a pretty steep hill to climb.

Hint: That's exactly, what we have to do in math.

Seriously. :-)

[toc] | [prev] | [next] | [standalone]


#630397

FromMoebius <invalid@example.invalid>
Date2024-08-16 01:16 +0200
Message-ID<v9m28f$14adh$5@dont-email.me>
In reply to#630389
Am 16.08.2024 um 00:51 schrieb Jim Burns:

> Half or more of my proofs to WM say
> "Assume otherwise... However... Contradiction."

Yeah, to be precise a proof by contradiction assumes a STATEMENT/CLAIM.

> But maybe I'm crazy.

No, you aren't, I guess.

 > [nonsense deleted]

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#630398

FromMoebius <invalid@example.invalid>
Date2024-08-16 01:24 +0200
Message-ID<v9m2nv$14adg$3@dont-email.me>
In reply to#630397
Am 16.08.2024 um 01:16 schrieb Moebius:
> Am 16.08.2024 um 00:51 schrieb Jim Burns:
> 
>> Half or more of my proofs to WM say
>> "Assume otherwise... However... Contradiction."
> 
> Yeah, to be precise: a proof by contradiction assumes a STATEMENT/CLAIM and etc.

>> But maybe I'm crazy.
> 
> No, you aren't, I guess (or hope).
> 
>> [nonsense deleted]

Hint: If "√2" is not defined, the "statement" (rather expression)

      √2 is irrational

is not a meanigful statement (i.e. mathematical claim). (Got it?)

What you (most certainly) mean is:

      There is no rational number x such that x^2 = 2.

On the ohter hand, in the context of the real numbers we usually have 
defined "√2" (namely as the real number x > 0 such that x^2 = 2). Hence 
in this context we may claim

      √2 is irrational [i.e. not a rational number]

AND actually prove this claim.

Hope this helps.

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#630412

FromJim Burns <james.g.burns@att.net>
Date2024-08-16 01:05 -0400
Message-ID<80662980-e93e-4af4-9489-f17fad3097d1@att.net>
In reply to#630397
On 8/15/2024 7:16 PM, Moebius wrote:
> Am 16.08.2024 um 00:51 schrieb Jim Burns:

>> Half or more of my proofs to WM say
>> "Assume otherwise... However... Contradiction."
>
> Yeah, to be precise a proof by contradiction
> assumes a STATEMENT/CLAIM.

Many times, a false existence claim.

>> But maybe I'm crazy.
>
> No, you aren't, I guess.
>
>> [nonsense deleted]

Well.known, ancient proof undeleted (below).
If that is nonsense, everything is nonsense.

That proof uses properties such as
well.order and unique.prime.factorization
which p₂ and q₂ would have if they existed
in order to show that they don't exist.

Yes,
reasoning from those properties of p₂ and q₂
generates nonsense, contradiction.
However,
the nonsense is the point,
the reason that we conclude that p₂ and q₂ don't exist.


Another example.
ZFC+"An inaccessible ordinal exists"  proves
ZFC

In order to make that proof,
we need the _definition_ of 'inaccessible cardinal'.
https://en.wikipedia.org/wiki/Inaccessible_cardinal

You will not prove that an inaccessible cardinal _exists_
not from ZFC+"An inaccessible ordinal exists" --
or, if you do, Gödel shows that proves _inconsistency_

----
√2 is irrational.

⎛ Assume otherwise.
⎜ Assume p₃,q₃ ∈ ℕ₁:  p₃⋅p₃ = 2⋅q₃⋅q₃
⎜
⎜ p₃ ∈ {p ∈ ℕ₁: ∃q ∈ ℕ₁: p⋅p = 2⋅q⋅q}
⎜ p₂ = min.{p ∈ ℕ₁: ∃q ∈ ℕ₁: p⋅p = 2⋅q⋅q}
⎜ ∃q₂ ∈ ℕ₁: p₂⋅p₂ = 2⋅q₂⋅q₂
⎜ ¬∃p₁ < p₂: ∃q₁ ∈ ℕ₁: p₁⋅p₁ = 2⋅q₁⋅q₁
⎜
⎜ However,
⎜ p₂⋅p₂ = 2⋅q₂⋅q₂
⎜ 2 is prime.
⎜ 2|p₂ or 2|p₂
⎜ p₂ = 2⋅p₁
⎜ 2⋅p₁⋅2⋅p₁ = 2⋅q₂⋅q₂
⎜ 2⋅p₁⋅p₁ = q₂⋅q₂
⎜ 2|q₂ or 2|q₂
⎜ q₂ = 2⋅q₁
⎜ 2⋅p₁⋅p₁ = 2⋅q₁⋅2⋅q₁
⎜ p₁⋅p₁ = 2⋅q₁⋅q₁  and p₁ < p₂
⎝ Contradiction.

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#630413

FromMoebius <invalid@example.invalid>
Date2024-08-16 07:50 +0200
Message-ID<v9mpak$1b0t2$1@dont-email.me>
In reply to#630412
Am 16.08.2024 um 07:05 schrieb Jim Burns:
> On 8/15/2024 7:16 PM, Moebius wrote:
>> Am 16.08.2024 um 00:51 schrieb Jim Burns:
> 
>>> Half or more of my proofs to WM say
>>> "Assume otherwise... However... Contradiction."
>>
>> Yeah, to be precise a proof by contradiction
>> assumes a STATEMENT/CLAIM.
> 
> Many times, a false existence claim.

Right.

> √2 is irrational.

This statement is just nonsense, _if_ "√2" is not already defined.*)

> ⎛ Assume otherwise.

Nope. You clearly don't assume

       √2 is rational ,

but:

> ⎜ Assume p₃,q₃ ∈ ℕ₁:  p₃⋅p₃ = 2⋅q₃⋅q₃
:
> ⎝ Contradiction.

________________________________

*) Of course, _if_ we already have introduced the real numbers (i.e. IR) 
we may define

       √2 = the real number x such that x*x = 2 ,    (*)

_after_ we have shown that that there is exactly one x e IR such that 
x*x = 2.

 From (*) we get immediately: √2*√2 = 2.

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#630414

FromMoebius <invalid@example.invalid>
Date2024-08-16 07:57 +0200
Message-ID<v9mpo7$1b0t3$1@dont-email.me>
In reply to#630413
Am 16.08.2024 um 07:50 schrieb Moebius:

> Of course, _if_ we already have introduced the real numbers (i.e. IR) 
> we may define
> 
>        √2 = the real number x such that x^2 = 2 ,    (*)
> 
> _after_ we have shown that that there is exactly one x e IR such that 
> x^2 = 2.
> 
> From (*) we get immediately: (√2)^2 = 2

Now we may assume that there are natural numbers n,m such that √2 = n/m.

(...)

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#630415

From"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Date2024-08-15 23:48 -0700
Message-ID<v9msnt$1bjlj$1@dont-email.me>
In reply to#630414
On 8/15/2024 10:57 PM, Moebius wrote:
> Am 16.08.2024 um 07:50 schrieb Moebius:
> 
>> Of course, _if_ we already have introduced the real numbers (i.e. IR) 
>> we may define
>>
>>        √2 = the real number x such that x^2 = 2 ,    (*)
>>
>> _after_ we have shown that that there is exactly one x e IR such that 
>> x^2 = 2.
>>
>> From (*) we get immediately: (√2)^2 = 2
> 
> Now we may assume that there are natural numbers n,m such that √2 = n/m.
> 
> (...)

The infinite convergents of continuous fractions can describe sqrt(2) up 
to any desired precision?

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#630416

FromMoebius <invalid@example.invalid>
Date2024-08-16 09:22 +0200
Message-ID<v9muof$1brsi$1@dont-email.me>
In reply to#630415
Am 16.08.2024 um 08:48 schrieb Chris M. Thomasson:
> On 8/15/2024 10:57 PM, Moebius wrote:
>> Am 16.08.2024 um 07:50 schrieb Moebius:
>>
>>> Of course, _if_ we already have introduced the real numbers (i.e. IR) 
>>> we may define
>>>
>>>        √2 = the real number x such that x^2 = 2 ,    (*)
>>>
>>> _after_ we have shown that there is exactly one x e IR such that 
>>> x^2 = 2.
>>>
>>> From (*) we get immediately: (√2)^2 = 2
>>
>> Now we may assume that there are natural numbers n,m such that √2 = n/m.
>>
>> (...)
> 
> The infinite convergents of continuous fractions can describe sqrt(2) up 
> to any desired precision?

Sure.

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#630418

FromJim Burns <james.g.burns@att.net>
Date2024-08-16 07:45 -0400
Message-ID<a19e3518-863c-4d2a-a196-e5821d5c473c@att.net>
In reply to#630413
On 8/16/2024 1:50 AM, Moebius wrote:
> Am 16.08.2024 um 07:05 schrieb Jim Burns:
>> On 8/15/2024 7:16 PM, Moebius wrote:
>>> Am 16.08.2024 um 00:51 schrieb Jim Burns:
>>>> On 8/15/2024 3:37 PM, Moebius wrote:
>>>>> Am 15.08.2024 um 21:28 schrieb Jim Burns:

>>>>>> Defining ⅟𝔊 to be the smallest unit fraction
>>>>>> isn't a claim that ⅟𝔊 exists.
>>>>>
>>>>> You need an existence proof [...]
>>>>> BEFORE stating a/the proper definition.

>>>> Half or more of my proofs to WM say
>>>> "Assume otherwise... However... Contradiction."
>>>
>>> Yeah, to be precise a proof by contradiction
>>> assumes a STATEMENT/CLAIM.
>>
>> Many times, a false existence claim.
>
> Right.

About things without an existence proof.

>> √2 is irrational.
>
> This statement is just nonsense,
> _if_ "√2" is not already defined.*)

Delete less.

>> ⎛ Assume otherwise.
>
> Nope. You clearly don't assume
> 
>> √2 is rational ,
>
> but:
>
>> ⎜ Assume p₃,q₃ ∈ ℕ₁:  p₃⋅p₃ = 2⋅q₃⋅q₃
> :
>> ⎝ Contradiction.

I assume a statement equivalent to
⎜ Rational √2 exists.

> ________________________________
> 
> *) Of course,
> _if_ we already have introduced the real numbers
> (i.e. IR) 
> we may define
>
> √2 = the real number x such that x*x = 2 ,    (*)
>
> _after_ we have shown that that
> there is exactly one x e IR such that x*x = 2.

Upthread is not a proof that real √2 exists.

Upthread is a proof that rational √2 not.exists,
which never mentions Dedekind completeness,
a never.mentioning which shows that,
whether or not real √2 exists,
rational √2 not.exists.

No, I am not proving that, here.
It makes my proof weaker and less focused, here.

>  From (*) we get immediately: √2*√2 = 2.

You're complaining I didn't show you √2*√2 = 2.

Consider it left as an exercise for the reader.




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#630390

FromMoebius <invalid@example.invalid>
Date2024-08-16 00:55 +0200
Message-ID<v9m11q$14adg$1@dont-email.me>
In reply to#630381
Am 15.08.2024 um 21:28 schrieb Jim Burns:

> A definition isn't a claim something exists.
Yeah, if you define a "property", say,

       x is a /Mückenheim number/ iff x e IR & x * 0 = 1.

Using symols:

       WM(x) :<-> x e IR & x * 0 = 1 .

THEN we can prove:

      ~Ex(WM(x)).  (*)

But this "approach" does not work for constants (or "functions").

We may express (*) (using normal language) the following way:

      There are no Mückenheim numbers.

But this "approach" does not work for say, the "Mückenheim number" WM:

      WM = the smallest unit fraction ,

SINCE THERE IS NO /smallest unit fraction/.

Again, we may define the property /smallest unit fraction/:

      WM(x) :<-> x e SB & Ay e SB: x <= y.
     "x is a smallest unit fraction."

Then we can prove:

      ~Ex(WM(x)).
      "There is no smallest unit fraction."

HENCE we CAN'T define:

      WM = ix(x e SB & Ay e SB: x <= y)
      "WM is the smallest unit fraction."

The rules concerning "proper definitions" do not allow for such a 
definition.

Hope this helps.

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#630299

From"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Date2024-08-13 12:10 -0700
Message-ID<v9gb32$1g5h$1@dont-email.me>
In reply to#630284
On 8/13/2024 7:17 AM, WM wrote:
> Le 12/08/2024 à 19:23, Richard Damon a écrit :
>> On 8/12/24 9:50 AM, WM wrote:
> 
>>>> What causes an exception: nₓ ∈ ℕ:
>>>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>>>
>>> The end of the positive axis.
>>
>> Which, by the definition of the Natural Numbers, doesn't exist.
> 
> The end of the positive axis exists.

Nope. Just like there is no end to the negative x axis. Oh, there is no 
end to the y axis as well. The z axis, the w axis, on and on wrt n-ary 
axes... :^)

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#630301

From"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Date2024-08-13 12:15 -0700
Message-ID<v9gbcn$1g5h$3@dont-email.me>
In reply to#630299
On 8/13/2024 12:10 PM, Chris M. Thomasson wrote:
> On 8/13/2024 7:17 AM, WM wrote:
>> Le 12/08/2024 à 19:23, Richard Damon a écrit :
>>> On 8/12/24 9:50 AM, WM wrote:
>>
>>>>> What causes an exception: nₓ ∈ ℕ:
>>>>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>>>>
>>>> The end of the positive axis.
>>>
>>> Which, by the definition of the Natural Numbers, doesn't exist.
>>
>> The end of the positive axis exists.
> 
> Nope. Just like there is no end to the negative x axis. Oh, there is no 
> end to the y axis as well. The z axis, the w axis, on and on wrt n-ary 
> axes... :^)
> 

Well, let me add a correction:

(...)<--(-1)<--(-0+)-->(+1)-->(...)

So, there is an "end" wrt the transition from positive to negative at 
zero. Sorry about that.

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#630338

FromWM <wolfgang.mueckenheim@tha.de>
Date2024-08-14 12:48 +0000
Message-ID<rOuxeA2Qgu5seCK_U-I-thsffNc@jntp>
In reply to#630299
Le 13/08/2024 à 21:10, "Chris M. Thomasson" a écrit :
> On 8/13/2024 7:17 AM, WM wrote:
>> Le 12/08/2024 à 19:23, Richard Damon a écrit :
>>> On 8/12/24 9:50 AM, WM wrote:
>> 
>>>>> What causes an exception: nₓ ∈ ℕ:
>>>>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>>>>
>>>> The end of the positive axis.
>>>
>>> Which, by the definition of the Natural Numbers, doesn't exist.
>> 
>> The end of the positive axis exists.
> 
> Nope. 

It exists and is an element of the open interval (0, oo).

Regards, WM

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#630234

FromJim Burns <james.g.burns@att.net>
Date2024-08-12 13:44 -0400
Message-ID<fcd3f5f1-fd6e-44ac-823d-fa567d5fb9ba@att.net>
In reply to#630228
On 8/12/2024 9:50 AM, WM wrote:
> Le 11/08/2024 à 19:56, Jim Burns a écrit :
>> On 8/11/2024 8:29 AM, WM wrote:
>>> Le 10/08/2024 à 19:28, Jim Burns a écrit :

>>>> What causes an exception:
>>>> nₓ ∈ ℕ without ⅟(nₓ+1) ?
>>>
>>> The end of the positivee axis.
>>
>>>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
>>
>> ∀n ∈ ℕ: 1/n > 1/(n+1) > 0
> 
> If 1/(n+1) exists.

>>>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
asserts 1/(n+1) exists, '∀n ∈ ℕ'
along with asserting other things.

>> Each positive unit fraction is not
>> the first positive unit fraction.
>>
>> What causes an exception: nₓ ∈ ℕ:
>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>
> The end of the positive axis.

There is no ⅟nₓ before the end of the positive axis
without ⅟(nₓ+1) before the end of the positive axis.

⎛ Assume otherwise.
⎜ Assume ⅟nₓ > 0 ≥ ⅟(nₓ+1)
⎜
⎜ nₓ⋅⅟nₓ = 1
⎜ ⅟nₓ > 0  ∧  1 > 0  ⇒  nₓ > 0
⎜ nₓ > 0  ⇒  nₓ+1 > 0
⎜ (nₓ+1)⋅⅟(nₓ+1) = 1
⎜ nₓ+1 > 0  ∧  1 > 0  ⇒  ⅟(nₓ+1) > 0
⎝ Contradiction.

There is no exception to not.being the lower end.

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#630235

FromMoebius <invalid@example.invalid>
Date2024-08-12 20:24 +0200
Message-ID<v9dk04$3dc99$1@dont-email.me>
In reply to#630234
Am 12.08.2024 um 19:44 schrieb Jim Burns:
> On 8/12/2024 9:50 AM, WM wrote:
>> Le 11/08/2024 à 19:56, Jim Burns a écrit :

>>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 (*) [WM]
>>>>
>>> ∀n ∈ ℕ: 1/n > 1/(n+1) > 0 (**) [JB]
>>
>> If 1/(n+1) exists. [WM]

Mückenheim, wenn Du meinst, dass das eine Voraussetzung für (**) ist, 
dann ist es doch auch eine für (*). Warum hast Du das VORHER nicht dazu 
gesagt? Du redest wirklich nur saudummen Scheißdreck daher, Mückenheim.

In der Mathematik ist es so:

Es gibt das allgemein akzeptierte Peano-Axiom:

       An e IN: s(n) e IN.

Daraus folgt zusammen mit der Definition

       n+1 =df s(n)    (n e IN)

sofort:

       An e IN: s+1 e IN.

Und daraus natürlich:

       An e IN: Em e IN: m = n+1 .

       "Mückensprech: (for each and every n in IN) n+1 exists and is an 
element in IN."

Mit der (üblichen) Definition

       n < m =df Ek e IN: n+k = m

ergibt sich zusammen mit dem ebenfalls allgemein akzeptierte Peano-Axiom:

       1 e IN

auch

       An e IN: n+1 e IN & n < n+1 .

Daraus folgt dann im Kontext der rationalen Zahlen (Q):

       An e IN: 1/(n+1) < 1/n .

Man kann natürlich ebenso gut beweisen:

       An e IN: Eq,q' e Q: q = 1/n & q' = 1/(n+1) & q' < q ,

oder auch nur:

       An e IN: Eq e Q: q = 1/(n+1) & q < 1/n .

       "Mückensprech: (for each and every n in IN) 1/(n+1) exists and is 
an element in Q."

Was genau verstehst Du daran nicht?

Also ja:

>>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0

> asserts 1/(n+1) exists, '∀n ∈ ℕ'
> along with asserting other things.

Right.

Wie schon ZIG mal erwähnt, Mückenheim: Wenn 1/(n+1) nicht für jedes n e 
IN definiert wäre (also existieren würde), dann dürftest Du es in einer 
einschlägigen Behauptung wie

        ∀n ∈ ℕ: 1/n - 1/(n+1) > 0

gar nicht verwenden, Depp.

"Ebensogut" könntest Du behaupten:

        ∀x ∈ IR: |1/x| >= 0 .   (***)

Nur ist 1/x für x = 0 nicht definiert, daher ist der Ausdruck (***) als 
Behauptung nicht zulässig (da 0 e IR ist).

Um aber zum eigentlichen Thema zurück zu kommen:

>>> Each positive unit fraction is not
>>> the first positive unit fraction. 
>>>
>>> What causes an exception: nₓ ∈ ℕ:
>>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>>
>> The end of the positive axis.

Nö. Natürlich nicht. Denn es gilt: An e IN: 0 < 1/(n+1) < 1/n.

Dass also die "positive axis" bei 0 "aufhört", ist KEIN Problem.

> There is no ⅟nₓ before the end of the positive axis
> without ⅟(nₓ+1) before the end of the positive axis.
> 
> ⎛ Assume otherwise.
> ⎜ Assume ⅟nₓ > 0 ≥ ⅟(nₓ+1)
> ⎜
> ⎜ nₓ⋅⅟nₓ = 1
> ⎜ ⅟nₓ > 0  ∧  1 > 0  ⇒  nₓ > 0
> ⎜ nₓ > 0  ⇒  nₓ+1 > 0
> ⎜ (nₓ+1)⋅⅟(nₓ+1) = 1
> ⎜ nₓ+1 > 0  ∧  1 > 0  ⇒  ⅟(nₓ+1) > 0
> ⎝ Contradiction.
> 
> There is no exception to not.being the lower end.

Jep. Außer in Mückenheims Wahnwelt. :-)

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#630238

FromMoebius <invalid@example.invalid>
Date2024-08-12 20:47 +0200
Message-ID<v9dlb8$3dc99$2@dont-email.me>
In reply to#630235
Am 12.08.2024 um 20:24 schrieb Moebius:
> Am 12.08.2024 um 19:44 schrieb Jim Burns:
>> On 8/12/2024 9:50 AM, WM wrote:
>>> Le 11/08/2024 à 19:56, Jim Burns a écrit :

>>>> Each positive unit fraction is not
>>>> the first positive unit fraction.
>>>> What causes an exception: nₓ ∈ ℕ:
>>>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>>>
>>> The end of the positive axis.
> 
> Nö. Natürlich nicht. Denn es gilt: An e IN: 0 < 1/(n+1) < 1/n.
> 
> Dass also die "positive axis" bei 0 "aufhört", ist KEIN Problem.

Ist jetzt seit kurzem die Menge {1/n : n e IN} wieder endlich, 
Mückenheim? Oder wollen Sie behaupten, dass es ein n e IN gibt, so dass 
1/n NICHT größer als 0 ist? <faceplam>

Jedenfalls erlaubt *ihre* Behauptung

         ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 ,

sofort auf

         ∀n ∈ ℕ: 1/(n+1) < 1/n

zu schließen.

Und - wegen Ak e IN: 0 < 1/k - damit auch auf

         ∀n ∈ ℕ: 0 < 1/(n+1) < 1/n ,

wie von JB behauptet. (Wie schon erwähnt, gilt in der Mathematik ja An e 
IN: n+1 e IN.)

Es gibt dazu eine schöne Entsprechung, die die natürlichen Zahlen (statt 
den Stammbrüchen) betrifft:

          ∀n ∈ ℕ: omega > n+1 > n .

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#630240

FromMoebius <invalid@example.invalid>
Date2024-08-12 20:55 +0200
Message-ID<v9dlr2$3dc99$4@dont-email.me>
In reply to#630238
Am 12.08.2024 um 20:47 schrieb Moebius:

> Jedenfalls erlaubt *ihre* Behauptung
> 
>          ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 ,
> 
> sofort auf
> 
>          ∀n ∈ ℕ: 1/(n+1) < 1/n
> 
> zu schließen.
> 
> Und - wegen Ak e IN: 0 < 1/k - damit auch auf
> 
>          ∀n ∈ ℕ: 0 < 1/(n+1) < 1/n ,
> 
> wie von JB behauptet. (Wie schon erwähnt, gilt in der Mathematik ja An e 
> IN: n+1 e IN.)
> 
> Es gibt dazu eine schöne Entsprechung, die die natürlichen Zahlen (statt 
> den Stammbrüchen) betrifft:
> 
>           ∀n ∈ ℕ: omega > n+1 > n .

Ein Unterschied zwischen den beiden Folgen (n)_(n e IN) und (1/n)_(n e 
IN) besteht natürlich darin, dass die Abstände zwischen zwei aufeinander 
folgenden Folgengliedern im einem Fall konstant sind, im anderen aber 
eine Nullfolge bilden. D. h. die natürlichen Zahlen "bevölkern" das 
Intervall [0, oo), während für die Stammbrüche das Intervall (0, 1] 
ausreicht. Iw. scheinen Sie mit diesem (an sich trivialen) Sachverhalt 
überfordert zu sein, Mückenheim.

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#630286

FromWM <wolfgang.mueckenheim@tha.de>
Date2024-08-13 14:25 +0000
Message-ID<kFiFazyPsjTBWAsYZU_81p__Z9I@jntp>
In reply to#630235
Le 12/08/2024 à 20:24, Moebius a écrit :

> In der Mathematik ist es so:
> 
> Es gibt das allgemein akzeptierte Peano-Axiom:
> 
>        An e IN: s(n) e IN.

Und alle paar tausend Jahre kommt eine neue Idee und wirft den 
verkrusteten Trödel um.

Gruß, WM

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#630285

FromWM <wolfgang.mueckenheim@tha.de>
Date2024-08-13 14:21 +0000
Message-ID<t_rVz7RU7M3aHZTB1TQJS59Ez0I@jntp>
In reply to#630234
Le 12/08/2024 à 19:44, Jim Burns a écrit :
> On 8/12/2024 9:50 AM, WM wrote:
>> Le 11/08/2024 à 19:56, Jim Burns a écrit :

>>> What causes an exception: nₓ ∈ ℕ:
>>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
>>
>> The end of the positive axis.
> 
> There is no ⅟nₓ before the end of the positive axis
> without ⅟(nₓ+1) before the end of the positive axis.

You cannot see it. It is dark. The function NUF(x) is a step-function. It 
can increase from 0 at x = 0 to greater values, either in a step of size 1 
or in a step of size more than 1. But increase by more than 1 is excluded 
by the gaps between unit fractions. (Note the universal quantifier there, 
according to which never – in no limit and in no accumulation point – 
two unit fractions occupy the same point x.) Therefore the step size can 
only be 1, resulting in a real coordinate x with NUF(x) = 1.

Regards, WM

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