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Groups > sci.math > #412942 > unrolled thread
| Started by | David Petry <davidlpetry@gmail.com> |
|---|---|
| First post | 2018-05-11 11:20 -0700 |
| Last post | 2018-05-17 12:29 -0700 |
| Articles | 20 on this page of 227 — 16 participants |
Back to article view | Back to sci.math
The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-11 11:20 -0700
Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-11 19:33 +0000
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-11 13:16 -0700
Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-11 16:48 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-11 18:31 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-11 18:46 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-11 18:49 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 00:59 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 02:20 -0700
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 12:43 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 14:09 -0700
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 12:40 -0700
Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-12 20:48 +0000
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 14:50 -0700
Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-13 01:00 +0000
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-13 15:10 -0700
Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-14 17:33 +0000
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-14 21:09 -0700
Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-15 19:19 +0000
Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-15 13:50 -0700
Re: The fundamental theorem of set theory is problematic "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-15 21:34 -0500
Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 09:10 -0700
Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 09:15 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 05:33 -0700
Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-12 19:02 -0400
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 01:38 -0700
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-14 21:40 -0700
Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-15 05:22 -0400
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 01:31 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-13 03:51 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 05:18 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-13 06:59 -0700
Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-13 11:02 +0000
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 05:37 -0700
Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-13 21:57 +0100
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-14 04:44 -0700
Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-14 13:29 +0100
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-14 07:42 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 09:36 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 09:42 -0700
Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-14 18:29 +0100
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 12:03 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 12:06 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 12:10 -0700
Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-15 13:44 -0700
Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-14 18:16 +0100
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 05:44 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 06:38 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 17:58 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 18:04 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 18:19 -0700
Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-15 09:14 -0700
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-15 10:07 -0700
Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 09:26 -0700
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-16 11:18 -0700
Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 12:26 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 14:06 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-16 15:53 -0700
Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-16 19:07 -0400
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 01:17 -0700
Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-17 09:42 -0400
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-16 17:40 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 11:06 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 01:05 -0700
Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 12:57 -0700
Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-13 00:20 +0000
Re: The fundamental theorem of set theory is problematic "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-11 20:03 -0500
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 00:59 -0700
Re: The fundamental theorem of set theory is problematic Julio Di Egidio <julio@diegidio.name> - 2018-05-12 01:59 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 02:55 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:04 -0700
Re: The fundamental theorem of set theory is problematic Julio Di Egidio <julio@diegidio.name> - 2018-05-12 03:06 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:09 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:13 -0700
Re: The fundamental theorem of set theory is problematic Julio Di Egidio <julio@diegidio.name> - 2018-05-12 03:20 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:28 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:24 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 01:14 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-13 09:07 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 11:08 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-13 12:05 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 12:53 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 11:02 -0700
Re: The fundamental theorem of set theory is problematic j4n bur53 <janburse@fastmail.fm> - 2018-05-15 21:13 +0200
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 11:30 -0700
Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-16 12:23 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 14:00 -0700
Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-16 16:18 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-16 16:27 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 05:01 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-17 08:34 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 09:34 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-17 10:12 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 10:57 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 11:56 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 12:00 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 12:29 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-17 13:38 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-18 08:12 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-18 12:23 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-19 04:53 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-19 07:21 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 09:11 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 03:20 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-20 04:48 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 05:19 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-20 10:09 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 13:26 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-20 18:10 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-21 06:05 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-21 07:24 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-21 08:59 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-21 11:48 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 05:45 -0700
Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-22 14:51 +0200
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-22 06:31 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 13:26 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-22 14:22 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 06:06 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-23 07:19 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 11:56 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-23 12:08 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 13:22 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-23 18:11 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 02:47 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-24 06:00 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 07:43 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-24 08:10 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 09:37 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-24 09:45 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-25 09:05 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-25 11:09 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-25 15:26 -0700
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-25 23:14 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-26 03:23 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-26 06:37 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-26 06:50 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-26 07:30 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-26 08:39 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-26 09:15 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-27 05:37 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-27 08:58 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-28 03:53 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-28 05:04 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-28 05:10 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-28 05:19 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-29 04:53 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-29 06:22 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-29 06:36 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-29 07:12 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-29 08:35 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-29 08:52 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-30 04:25 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-30 04:50 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-31 06:17 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-31 07:05 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-31 09:53 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-31 11:47 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-01 03:58 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-06-01 05:07 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-01 05:24 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-06-01 06:27 -0700
Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-01 10:21 -0700
Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-02 14:04 -0700
Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-02 16:27 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-02 07:23 -0700
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-06-04 00:11 -0700
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-27 23:12 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-23 12:49 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-23 12:51 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 13:24 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-24 02:09 -0700
Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-22 19:09 +0100
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 13:29 -0700
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-23 22:32 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 03:57 -0700
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-24 04:48 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 07:29 -0700
Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-24 16:39 +0200
Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-18 01:19 +0200
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-18 08:14 -0700
Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-18 17:31 +0200
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-18 10:09 -0700
Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-18 10:53 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 13:54 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 13:55 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:09 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:19 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:23 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:37 -0700
Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-18 14:33 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-19 04:58 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:28 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:34 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:36 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:46 -0700
Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-19 09:00 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 03:21 -0700
Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-19 02:01 +0200
Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-21 16:40 +0100
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-21 09:06 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-21 13:52 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 05:45 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-22 08:27 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 13:29 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-22 13:43 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-22 13:52 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 06:06 -0700
Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-22 17:30 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 06:06 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-15 17:14 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 11:26 -0700
Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-16 16:35 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 05:03 -0700
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-17 05:33 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 09:31 -0700
Re: The fundamental theorem of set theory is problematic Sergio <invalid@invalid.com> - 2018-05-13 12:40 -0500
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-13 22:36 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-14 04:49 -0700
Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-17 01:34 -0700
Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 05:08 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:03 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:06 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:19 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:26 -0700
Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:30 -0700
Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-17 12:29 -0700
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-05-18 08:14 -0700 |
| Message-ID | <65563251-b837-4d92-9bf7-f40a9623d03c@googlegroups.com> |
| In reply to | #413286 |
Am Freitag, 18. Mai 2018 01:19:43 UTC+2 schrieb Python: > Doktor Frankenheim wrote: > > Am Donnerstag, 17. Mai 2018 19:12:19 UTC+2 schrieb wpih...@gmail.com: > >> On Thursday, May 17, 2018 at 1:34:48 PM UTC-3, WM wrote: > >> > >> > >>> Stop evading the issue. If every number is computable, then computing > >>> and storing every number gives a computed list of computed numbers. > >>> > >> Nope. Each number in the sequence is the output of a Turing machine. > > > > It is irrelevant how a number is computed. Best it should be done by a > > modern computer and not by a machine from the stone-age. > > Oh dear Herr Mueckenheim, this is bad... You do not know what is > meant by "Turing machine"! See https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, 2.3 The halting problem Regards, WM
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| From | Python <python@python.invalid> |
|---|---|
| Date | 2018-05-18 17:31 +0200 |
| Message-ID | <5afef1d1$0$3866$426a74cc@news.free.fr> |
| In reply to | #413325 |
Doktor Frankenheim wrote: > Am Freitag, 18. Mai 2018 01:19:43 UTC+2 schrieb Python: >> Doktor Frankenheim wrote: >>> Am Donnerstag, 17. Mai 2018 19:12:19 UTC+2 schrieb wpih...@gmail.com: >>>> On Thursday, May 17, 2018 at 1:34:48 PM UTC-3, WM wrote: >>>> >>>> >>>>> Stop evading the issue. If every number is computable, then computing >>>>> and storing every number gives a computed list of computed numbers. >>>>> >>>> Nope. Each number in the sequence is the output of a Turing machine. >>> >>> It is irrelevant how a number is computed. Best it should be done by a >>> modern computer and not by a machine from the stone-age. >> >> Oh dear Herr Mueckenheim, this is bad... You do not know what is >> meant by "Turing machine"! Snipped part restored here: >> You certainly believe that it relates to >> the Colossus machine at Bletchley Park, don't you? >> >> It is no surprise that your levels of incompetence are as >> high in CS than in math by the way.. --- > See https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, 2.3 The halting problem So either you were drunk dead when you posted this HUGE blunder about "machine from the stone-age" or you are just parroting, without understanding a word of it, standard CS description of the halting problem. Note that these two hypothesis are not contradictory. Moreover the 2.3 section of you utterly crappy pdf does not lead to any kind of contradiction neither in Set Theory nor in Turing article. There is not a single word in this part supporting you silly sophistry, one may even wonder what is the purpose of this part in your idiotic document.
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-05-18 10:09 -0700 |
| Message-ID | <ca009433-5e4f-459b-9215-7042cf6330bd@googlegroups.com> |
| In reply to | #413326 |
Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > Note that these two hypothesis are not contradictory. Moreover the 2.3 > section of your pdf does not lead to any kind of > contradiction neither in Set Theory nor in Turing article. Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity. > There is not > a single word in this part supporting you, one may > even wonder what is the purpose of this part in your document. Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI. Regards, WM
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| From | FredJeffries <fredjeffries@gmail.com> |
|---|---|
| Date | 2018-05-18 10:53 -0700 |
| Message-ID | <f0b05f20-d19c-47d7-a1b1-06325b0a5100@googlegroups.com> |
| In reply to | #413341 |
On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. https://en.wikipedia.org/wiki/Axiom_schema_of_specification
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-18 13:54 -0700 |
| Message-ID | <69d396a0-3900-4813-832a-b5e1215cbb6f@googlegroups.com> |
| In reply to | #413341 |
If you have only P_fin(N), and if you cannot do something with your potential infinite N, which is not actual infinite, then question is whether you can do any math at all in Volkswagen Omlette. Do you have mathematical induction for your potential infinite N. Do you have a predicates, some language to make statements about N. If this is all missing, I guess Volkswagen Omlette is not math. Its more Robinson sticks and stones. Nothing useful. Am Freitag, 18. Mai 2018 19:09:39 UTC+2 schrieb WM: > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > section of your pdf does not lead to any kind of > > contradiction neither in Set Theory nor in Turing article. > > Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity. > > > There is not > > a single word in this part supporting you, one may > > even wonder what is the purpose of this part in your document. > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI. > > Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-18 13:55 -0700 |
| Message-ID | <68e510d4-e2de-48e9-ab39-1e127f5829f6@googlegroups.com> |
| In reply to | #413351 |
Can you show there are, well lets say, potentially infinite many prime numbers. How would you do it in Volkswagen Omlette. Put the finger in the sky and look whether its windy? Am Freitag, 18. Mai 2018 22:54:14 UTC+2 schrieb burs...@gmail.com: > If you have only P_fin(N), and if you cannot do something > with your potential infinite N, which is not actual infinite, > then question is whether you can do any math at > > all in Volkswagen Omlette. Do you have mathematical > induction for your potential infinite N. Do you have > a predicates, some language to make > > statements about N. If this is all missing, I guess > Volkswagen Omlette is not math. Its more Robinson > sticks and stones. Nothing useful. > > Am Freitag, 18. Mai 2018 19:09:39 UTC+2 schrieb WM: > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > > section of your pdf does not lead to any kind of > > > contradiction neither in Set Theory nor in Turing article. > > > > Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity. > > > > > There is not > > > a single word in this part supporting you, one may > > > even wonder what is the purpose of this part in your document. > > > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI. > > > > Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-18 14:09 -0700 |
| Message-ID | <864fb280-2f62-4386-bdcb-312c09e97b30@googlegroups.com> |
| In reply to | #413353 |
What is your PDF useful for. It doesn't contain
any math, since in Volkswagen Omlette you can
only do Robinson sticks and stones.
So what is your PDF useful. I think the following
you wrote "Chapter II is a summary of set theory,
essentially without critism",
is also not true, your axiom of infinity on
page 45 of your PDF is still wrong. What you write
there is not an axiom of infinity of any sort.
So your Chapter II is bad copy pasta nonsense.
The axiom of choice is also syntaxtically wrong,
you wrote, only the inner part after the implication sign:
exists F: T -> UT /\ forall X in T: F(X) in X
The above is syntactically wrong, you should either write:
exists F: T -> UT : forall X in T: F(X) in X
or then you should write:
exists F (F: T -> UT /\ forall X in T: F(X) in X)
Otherwise the scoping is not correct. Similar like
in the wrong axiom of infinity, you put to much quantifier
play into a simple propositional connective,
here the problem is the conjunction /\. What you wrote
would be read as follows:
(exists F: T -> UT) /\ (forall X in T: F(X) in X)
Which is not the axiom of choice. You can also check
wiki, there is no conjunction /\, but a bound quantifier:
https://en.wikipedia.org/wiki/Axiom_of_choice#Statement
Am Freitag, 18. Mai 2018 22:55:56 UTC+2 schrieb burs...@gmail.com:
> Can you show there are, well lets say, potentially
> infinite many prime numbers. How would you do it
> in Volkswagen Omlette.
>
> Put the finger in the sky and
> look whether its windy?
>
> Am Freitag, 18. Mai 2018 22:54:14 UTC+2 schrieb burs...@gmail.com:
> > If you have only P_fin(N), and if you cannot do something
> > with your potential infinite N, which is not actual infinite,
> > then question is whether you can do any math at
> >
> > all in Volkswagen Omlette. Do you have mathematical
> > induction for your potential infinite N. Do you have
> > a predicates, some language to make
> >
> > statements about N. If this is all missing, I guess
> > Volkswagen Omlette is not math. Its more Robinson
> > sticks and stones. Nothing useful.
> >
> > Am Freitag, 18. Mai 2018 19:09:39 UTC+2 schrieb WM:
> > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python:
> > >
> > >
> > > > Note that these two hypothesis are not contradictory. Moreover the 2.3
> > > > section of your pdf does not lead to any kind of
> > > > contradiction neither in Set Theory nor in Turing article.
> > >
> > > Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity.
> > >
> > > > There is not
> > > > a single word in this part supporting you, one may
> > > > even wonder what is the purpose of this part in your document.
> > >
> > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI.
> > >
> > > Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-18 14:19 -0700 |
| Message-ID | <47761321-fac4-4f3e-ba27-3dff18d4393e@googlegroups.com> |
| In reply to | #413354 |
Well would be read is also wrong, its simply
not a WFF in modern terms, if you put a conjunction
after a bound quantifier, and not directly the formula.
Although in some corners of the world this might be
in use, but wiki doesn't do it. Proof wiki also
doesn't do it, they also use a bound quantifier:
https://proofwiki.org/wiki/Axiom:Axiom_of_Choice#Formulation_1
But bound quantifiers have always the problem,
that you need a convention which one is the bound
variable, like if you write:
exists P(x) A(x)
How do you know inside P(x) which one is the x? So
recommendation, maybe refrain from it. And simply
use unbounded quantifiers, like:
exists x (P(x) /\ A(x))
Am Freitag, 18. Mai 2018 23:09:27 UTC+2 schrieb burs...@gmail.com:
> What is your PDF useful for. It doesn't contain
> any math, since in Volkswagen Omlette you can
> only do Robinson sticks and stones.
>
> So what is your PDF useful. I think the following
> you wrote "Chapter II is a summary of set theory,
> essentially without critism",
>
> is also not true, your axiom of infinity on
> page 45 of your PDF is still wrong. What you write
> there is not an axiom of infinity of any sort.
>
> So your Chapter II is bad copy pasta nonsense.
>
> The axiom of choice is also syntaxtically wrong,
> you wrote, only the inner part after the implication sign:
>
> exists F: T -> UT /\ forall X in T: F(X) in X
>
> The above is syntactically wrong, you should either write:
>
> exists F: T -> UT : forall X in T: F(X) in X
>
> or then you should write:
>
> exists F (F: T -> UT /\ forall X in T: F(X) in X)
>
> Otherwise the scoping is not correct. Similar like
> in the wrong axiom of infinity, you put to much quantifier
> play into a simple propositional connective,
>
> here the problem is the conjunction /\. What you wrote
> would be read as follows:
>
> (exists F: T -> UT) /\ (forall X in T: F(X) in X)
>
> Which is not the axiom of choice. You can also check
> wiki, there is no conjunction /\, but a bound quantifier:
>
> https://en.wikipedia.org/wiki/Axiom_of_choice#Statement
>
> Am Freitag, 18. Mai 2018 22:55:56 UTC+2 schrieb burs...@gmail.com:
> > Can you show there are, well lets say, potentially
> > infinite many prime numbers. How would you do it
> > in Volkswagen Omlette.
> >
> > Put the finger in the sky and
> > look whether its windy?
> >
> > Am Freitag, 18. Mai 2018 22:54:14 UTC+2 schrieb burs...@gmail.com:
> > > If you have only P_fin(N), and if you cannot do something
> > > with your potential infinite N, which is not actual infinite,
> > > then question is whether you can do any math at
> > >
> > > all in Volkswagen Omlette. Do you have mathematical
> > > induction for your potential infinite N. Do you have
> > > a predicates, some language to make
> > >
> > > statements about N. If this is all missing, I guess
> > > Volkswagen Omlette is not math. Its more Robinson
> > > sticks and stones. Nothing useful.
> > >
> > > Am Freitag, 18. Mai 2018 19:09:39 UTC+2 schrieb WM:
> > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python:
> > > >
> > > >
> > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3
> > > > > section of your pdf does not lead to any kind of
> > > > > contradiction neither in Set Theory nor in Turing article.
> > > >
> > > > Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity.
> > > >
> > > > > There is not
> > > > > a single word in this part supporting you, one may
> > > > > even wonder what is the purpose of this part in your document.
> > > >
> > > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI.
> > > >
> > > > Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-18 14:23 -0700 |
| Message-ID | <7ff08d2b-1032-4a7b-8394-06a88ecdceb6@googlegroups.com> |
| In reply to | #413355 |
Actually I like the parenthesis in proof wiki.
And I retract that its not a WFF. The following
is actually a WFF:
exists F : A -> B
And it could mean something totally different. For
example A and B could be propositional variables.
And then its an unbounded quantification.
So your text could be effectively read even as follows,
which is also not a good reading:
exists F : T -> (UT /\ ....)
Am Freitag, 18. Mai 2018 23:19:46 UTC+2 schrieb burs...@gmail.com:
> Well would be read is also wrong, its simply
> not a WFF in modern terms, if you put a conjunction
> after a bound quantifier, and not directly the formula.
>
> Although in some corners of the world this might be
> in use, but wiki doesn't do it. Proof wiki also
> doesn't do it, they also use a bound quantifier:
>
> https://proofwiki.org/wiki/Axiom:Axiom_of_Choice#Formulation_1
>
> But bound quantifiers have always the problem,
> that you need a convention which one is the bound
> variable, like if you write:
>
> exists P(x) A(x)
>
> How do you know inside P(x) which one is the x? So
> recommendation, maybe refrain from it. And simply
> use unbounded quantifiers, like:
>
> exists x (P(x) /\ A(x))
>
> Am Freitag, 18. Mai 2018 23:09:27 UTC+2 schrieb burs...@gmail.com:
> > What is your PDF useful for. It doesn't contain
> > any math, since in Volkswagen Omlette you can
> > only do Robinson sticks and stones.
> >
> > So what is your PDF useful. I think the following
> > you wrote "Chapter II is a summary of set theory,
> > essentially without critism",
> >
> > is also not true, your axiom of infinity on
> > page 45 of your PDF is still wrong. What you write
> > there is not an axiom of infinity of any sort.
> >
> > So your Chapter II is bad copy pasta nonsense.
> >
> > The axiom of choice is also syntaxtically wrong,
> > you wrote, only the inner part after the implication sign:
> >
> > exists F: T -> UT /\ forall X in T: F(X) in X
> >
> > The above is syntactically wrong, you should either write:
> >
> > exists F: T -> UT : forall X in T: F(X) in X
> >
> > or then you should write:
> >
> > exists F (F: T -> UT /\ forall X in T: F(X) in X)
> >
> > Otherwise the scoping is not correct. Similar like
> > in the wrong axiom of infinity, you put to much quantifier
> > play into a simple propositional connective,
> >
> > here the problem is the conjunction /\. What you wrote
> > would be read as follows:
> >
> > (exists F: T -> UT) /\ (forall X in T: F(X) in X)
> >
> > Which is not the axiom of choice. You can also check
> > wiki, there is no conjunction /\, but a bound quantifier:
> >
> > https://en.wikipedia.org/wiki/Axiom_of_choice#Statement
> >
> > Am Freitag, 18. Mai 2018 22:55:56 UTC+2 schrieb burs...@gmail.com:
> > > Can you show there are, well lets say, potentially
> > > infinite many prime numbers. How would you do it
> > > in Volkswagen Omlette.
> > >
> > > Put the finger in the sky and
> > > look whether its windy?
> > >
> > > Am Freitag, 18. Mai 2018 22:54:14 UTC+2 schrieb burs...@gmail.com:
> > > > If you have only P_fin(N), and if you cannot do something
> > > > with your potential infinite N, which is not actual infinite,
> > > > then question is whether you can do any math at
> > > >
> > > > all in Volkswagen Omlette. Do you have mathematical
> > > > induction for your potential infinite N. Do you have
> > > > a predicates, some language to make
> > > >
> > > > statements about N. If this is all missing, I guess
> > > > Volkswagen Omlette is not math. Its more Robinson
> > > > sticks and stones. Nothing useful.
> > > >
> > > > Am Freitag, 18. Mai 2018 19:09:39 UTC+2 schrieb WM:
> > > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python:
> > > > >
> > > > >
> > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3
> > > > > > section of your pdf does not lead to any kind of
> > > > > > contradiction neither in Set Theory nor in Turing article.
> > > > >
> > > > > Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity.
> > > > >
> > > > > > There is not
> > > > > > a single word in this part supporting you, one may
> > > > > > even wonder what is the purpose of this part in your document.
> > > > >
> > > > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI.
> > > > >
> > > > > Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-18 14:37 -0700 |
| Message-ID | <efb6f460-6c8f-443b-8496-46e7673b92c9@googlegroups.com> |
| In reply to | #413356 |
Also one more question? Why on earth would somebody
make a heading "2.17 Partial models of ZFC",
and then explain Gödels L?
Thats just debilated nonsense. Either something is
a model of ZFC or it is not. What do you mean by
partial model?
L is a supposed to be model, but not a partial model.
Did you think because L appears in connection with
Gödel, and since Gödel has an incompletness
theorem, that some models are partial? Or that incompletness
of a logical system means partial models? Thats just
complete nonsese. If a logical system like ZFC is
incomplete, this only means there are sentences A,
such that neither:
ZFC |- A /* not provable */
nor this:
ZFC |- ~A /* not provable */
But this doesn't mean that models are partial. It
means that theories are incomplete, but not that
models are partial.
Why do you call models partial?
You also write "to summarize: A partial model M of
ZFC has to be extended by a generic set G such that M[G]
has the desired properties."
In my opinion a partial model is an oxymoron:
https://en.wikipedia.org/wiki/Oxymoron
And this needs some rephrasing. Either into "models
of subtheories of ZFC, or then not models at all but
other things. Basically in forcing you
get anyway two models V and V[G], otherwise there would
be no point in doing forcing. You can then for example
hope for V |= A and V[G] |= ~A for some special A,
eh voila you get your incompletness.
Am Freitag, 18. Mai 2018 23:23:22 UTC+2 schrieb burs...@gmail.com:
> Actually I like the parenthesis in proof wiki.
> And I retract that its not a WFF. The following
> is actually a WFF:
>
> exists F : A -> B
>
> And it could mean something totally different. For
> example A and B could be propositional variables.
> And then its an unbounded quantification.
>
> So your text could be effectively read even as follows,
> which is also not a good reading:
>
> exists F : T -> (UT /\ ....)
>
> Am Freitag, 18. Mai 2018 23:19:46 UTC+2 schrieb burs...@gmail.com:
> > Well would be read is also wrong, its simply
> > not a WFF in modern terms, if you put a conjunction
> > after a bound quantifier, and not directly the formula.
> >
> > Although in some corners of the world this might be
> > in use, but wiki doesn't do it. Proof wiki also
> > doesn't do it, they also use a bound quantifier:
> >
> > https://proofwiki.org/wiki/Axiom:Axiom_of_Choice#Formulation_1
> >
> > But bound quantifiers have always the problem,
> > that you need a convention which one is the bound
> > variable, like if you write:
> >
> > exists P(x) A(x)
> >
> > How do you know inside P(x) which one is the x? So
> > recommendation, maybe refrain from it. And simply
> > use unbounded quantifiers, like:
> >
> > exists x (P(x) /\ A(x))
> >
> > Am Freitag, 18. Mai 2018 23:09:27 UTC+2 schrieb burs...@gmail.com:
> > > What is your PDF useful for. It doesn't contain
> > > any math, since in Volkswagen Omlette you can
> > > only do Robinson sticks and stones.
> > >
> > > So what is your PDF useful. I think the following
> > > you wrote "Chapter II is a summary of set theory,
> > > essentially without critism",
> > >
> > > is also not true, your axiom of infinity on
> > > page 45 of your PDF is still wrong. What you write
> > > there is not an axiom of infinity of any sort.
> > >
> > > So your Chapter II is bad copy pasta nonsense.
> > >
> > > The axiom of choice is also syntaxtically wrong,
> > > you wrote, only the inner part after the implication sign:
> > >
> > > exists F: T -> UT /\ forall X in T: F(X) in X
> > >
> > > The above is syntactically wrong, you should either write:
> > >
> > > exists F: T -> UT : forall X in T: F(X) in X
> > >
> > > or then you should write:
> > >
> > > exists F (F: T -> UT /\ forall X in T: F(X) in X)
> > >
> > > Otherwise the scoping is not correct. Similar like
> > > in the wrong axiom of infinity, you put to much quantifier
> > > play into a simple propositional connective,
> > >
> > > here the problem is the conjunction /\. What you wrote
> > > would be read as follows:
> > >
> > > (exists F: T -> UT) /\ (forall X in T: F(X) in X)
> > >
> > > Which is not the axiom of choice. You can also check
> > > wiki, there is no conjunction /\, but a bound quantifier:
> > >
> > > https://en.wikipedia.org/wiki/Axiom_of_choice#Statement
> > >
> > > Am Freitag, 18. Mai 2018 22:55:56 UTC+2 schrieb burs...@gmail.com:
> > > > Can you show there are, well lets say, potentially
> > > > infinite many prime numbers. How would you do it
> > > > in Volkswagen Omlette.
> > > >
> > > > Put the finger in the sky and
> > > > look whether its windy?
> > > >
> > > > Am Freitag, 18. Mai 2018 22:54:14 UTC+2 schrieb burs...@gmail.com:
> > > > > If you have only P_fin(N), and if you cannot do something
> > > > > with your potential infinite N, which is not actual infinite,
> > > > > then question is whether you can do any math at
> > > > >
> > > > > all in Volkswagen Omlette. Do you have mathematical
> > > > > induction for your potential infinite N. Do you have
> > > > > a predicates, some language to make
> > > > >
> > > > > statements about N. If this is all missing, I guess
> > > > > Volkswagen Omlette is not math. Its more Robinson
> > > > > sticks and stones. Nothing useful.
> > > > >
> > > > > Am Freitag, 18. Mai 2018 19:09:39 UTC+2 schrieb WM:
> > > > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python:
> > > > > >
> > > > > >
> > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3
> > > > > > > section of your pdf does not lead to any kind of
> > > > > > > contradiction neither in Set Theory nor in Turing article.
> > > > > >
> > > > > > Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity.
> > > > > >
> > > > > > > There is not
> > > > > > > a single word in this part supporting you, one may
> > > > > > > even wonder what is the purpose of this part in your document.
> > > > > >
> > > > > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI.
> > > > > >
> > > > > > Regards, WM
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| From | Zeit Geist <Tucsondrew@me.com> |
|---|---|
| Date | 2018-05-18 14:33 -0700 |
| Message-ID | <bc8a6f75-938e-4aa6-8b3d-bafbe73e7f9f@googlegroups.com> |
| In reply to | #413341 |
On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > section of your pdf does not lead to any kind of > > contradiction neither in Set Theory nor in Turing article. > > Not necessary to argue about that. Take the set of all definable real numbers Wait! Wail! Stop right there. We are not talking about “definable” numbers; we are talking about “computable” numbers. The “definable real numbers” Is a superset of the “computable real numbers”. See the Wikipedia article I sighted. I will take, from this point on, that “definable” means “computable”, and proceed forward. > which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity. You are incorrect. Yes, the well ordering exists, since every countable set of reals can well-ordered, even without the Axiom of Choice. However, there exists noTuring machine which can compute the ordering of the list. Thus, the LIST is non-computable. Hence, if we take that list, which exists because of your argument above; then the resulting diagonal number is a actual real number. However, this number will be non-computable. > > There is not > > a single word in this part supporting you, one may > > even wonder what is the purpose of this part in your document. > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI. > Regards, WM ZG
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-05-19 04:58 -0700 |
| Message-ID | <57211441-0f25-426b-b5fa-181567e7d367@googlegroups.com> |
| In reply to | #413357 |
Am Freitag, 18. Mai 2018 23:33:34 UTC+2 schrieb Zeit Geist: > On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > > section of your pdf does not lead to any kind of > > > contradiction neither in Set Theory nor in Turing article. > > > > Not necessary to argue about that. Take the set of all definable real numbers > > Wait! Wail! Stop right there. We are not talking about “definable” numbers I am. > The “definable real numbers” Is a superset of the “computable real numbers”. See the Wikipedia article I sighted. I will take, from this point on, that “definable” means “computable”, and proceed forward. Simply use definable as it is used elsewhere too. Note Hilbert's statement: "Working with the infinite can only be secured by the finite." [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 190] Well, in the finite every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by its finite name (because an object of mathematics has no other form of existence). This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it. Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-19 05:28 -0700 |
| Message-ID | <271f1c0c-ee17-4349-99e8-772467085ff5@googlegroups.com> |
| In reply to | #413382 |
Definable has subcategories. You can define something simply and more complex, like you can have a simple Sigma^0 sentence, or more complex sentences see also: https://en.wikipedia.org/wiki/Arithmetical_hierarchy#Extensions_and_variations For example if you define less than in peano, as follows: x < y :<=> exists z(x+z = y) Then the above is a Sigma^0 defintion. Right? Computable has subcategories. Computable has also a lot of subcategories, for example the primitive functions and the recursive functions are not the same. There is a link between definable and computable, you can some subcategories of definable identify with some subcategories of computable. But the subcategories of definable are much more, see also this picture: https://en.wikipedia.org/wiki/Arithmetical_hierarchy#/media/File:Arithmetic_hierarchy.svg Am Samstag, 19. Mai 2018 13:58:52 UTC+2 schrieb WM: > Am Freitag, 18. Mai 2018 23:33:34 UTC+2 schrieb Zeit Geist: > > On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > > > section of your pdf does not lead to any kind of > > > > contradiction neither in Set Theory nor in Turing article. > > > > > > Not necessary to argue about that. Take the set of all definable real numbers > > > > Wait! Wail! Stop right there. We are not talking about “definable” numbers > > I am. > > > The “definable real numbers” Is a superset of the “computable real numbers”. See the Wikipedia article I sighted. I will take, from this point on, that “definable” means “computable”, and proceed forward. > > Simply use definable as it is used elsewhere too. > > Note Hilbert's statement: "Working with the infinite can only be secured by the finite." [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 190] Well, in the finite every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by its finite name (because an object of mathematics has no other form of existence). This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it. > > Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-19 05:34 -0700 |
| Message-ID | <4641ab3c-904e-4140-b101-5093c2959eee@googlegroups.com> |
| In reply to | #413383 |
For example the real numbers pi, e, etc.. are all definable (in ZFC). Whereby its irrelevant how you define them, as digit sequences or otherwise. For example metamath defines pi not as a digit sequence, but as an inverse of a trigonometric function: Define pi = 3.14159..., which is the smallest positive number whose sine is zero. http://us.metamath.org/mpegif/df-pi.html What kind of definition is "smallest"? Sigma^0, Pi^0, etc..? How do you express that x is the smallest y such that P(y). P(x) & forall y (P(y) => x =< y) So on the surface it has a Pi form. But maybe it is equivalent to some Sigma form. Who knows? Am Samstag, 19. Mai 2018 14:29:04 UTC+2 schrieb burs...@gmail.com: > Definable has subcategories. You can define > something simply and more complex, like you > can have a simple Sigma^0 sentence, or more > complex sentences see also: > https://en.wikipedia.org/wiki/Arithmetical_hierarchy#Extensions_and_variations > > For example if you define less than in peano, > as follows: > > x < y :<=> exists z(x+z = y) > > Then the above is a Sigma^0 defintion. Right? > > Computable has subcategories. Computable > has also a lot of subcategories, for example > the primitive functions and the recursive functions > are not the same. > > There is a link between definable and computable, > you can some subcategories of definable identify > with some subcategories of computable. But the > subcategories of definable are much more, > > see also this picture: > > https://en.wikipedia.org/wiki/Arithmetical_hierarchy#/media/File:Arithmetic_hierarchy.svg > > Am Samstag, 19. Mai 2018 13:58:52 UTC+2 schrieb WM: > > Am Freitag, 18. Mai 2018 23:33:34 UTC+2 schrieb Zeit Geist: > > > On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > > > > > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > > > > section of your pdf does not lead to any kind of > > > > > contradiction neither in Set Theory nor in Turing article. > > > > > > > > Not necessary to argue about that. Take the set of all definable real numbers > > > > > > Wait! Wail! Stop right there. We are not talking about “definable” numbers > > > > I am. > > > > > The “definable real numbers” Is a superset of the “computable real numbers”. See the Wikipedia article I sighted. I will take, from this point on, that “definable” means “computable”, and proceed forward. > > > > Simply use definable as it is used elsewhere too. > > > > Note Hilbert's statement: "Working with the infinite can only be secured by the finite." [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 190] Well, in the finite every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by its finite name (because an object of mathematics has no other form of existence). This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it. > > > > Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-19 05:36 -0700 |
| Message-ID | <1e33e661-0322-4d72-b1bf-05bbace1580d@googlegroups.com> |
| In reply to | #413384 |
To get the full account of this pi definition, you need also consider how sin is defined. So possibly sin is some limit, so in the end, you get a much higher up definition of pi. But still its a definition... Am Samstag, 19. Mai 2018 14:34:48 UTC+2 schrieb burs...@gmail.com: > For example the real numbers pi, e, etc.. are > all definable (in ZFC). Whereby its irrelevant > how you define them, as digit sequences or > > otherwise. For example metamath defines pi > not as a digit sequence, but as an inverse of > a trigonometric function: > > Define pi = 3.14159..., which is the smallest > positive number whose sine is zero. > http://us.metamath.org/mpegif/df-pi.html > > What kind of definition is "smallest"? Sigma^0, > Pi^0, etc..? How do you express that x is > the smallest y such that P(y). > > P(x) & forall y (P(y) => x =< y) > > So on the surface it has a Pi form. But maybe > it is equivalent to some Sigma form. Who knows? > > Am Samstag, 19. Mai 2018 14:29:04 UTC+2 schrieb burs...@gmail.com: > > Definable has subcategories. You can define > > something simply and more complex, like you > > can have a simple Sigma^0 sentence, or more > > complex sentences see also: > > https://en.wikipedia.org/wiki/Arithmetical_hierarchy#Extensions_and_variations > > > > For example if you define less than in peano, > > as follows: > > > > x < y :<=> exists z(x+z = y) > > > > Then the above is a Sigma^0 defintion. Right? > > > > Computable has subcategories. Computable > > has also a lot of subcategories, for example > > the primitive functions and the recursive functions > > are not the same. > > > > There is a link between definable and computable, > > you can some subcategories of definable identify > > with some subcategories of computable. But the > > subcategories of definable are much more, > > > > see also this picture: > > > > https://en.wikipedia.org/wiki/Arithmetical_hierarchy#/media/File:Arithmetic_hierarchy.svg > > > > Am Samstag, 19. Mai 2018 13:58:52 UTC+2 schrieb WM: > > > Am Freitag, 18. Mai 2018 23:33:34 UTC+2 schrieb Zeit Geist: > > > > On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > > > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > > > > > > > > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > > > > > section of your pdf does not lead to any kind of > > > > > > contradiction neither in Set Theory nor in Turing article. > > > > > > > > > > Not necessary to argue about that. Take the set of all definable real numbers > > > > > > > > Wait! Wail! Stop right there. We are not talking about “definable” numbers > > > > > > I am. > > > > > > > The “definable real numbers” Is a superset of the “computable real numbers”. See the Wikipedia article I sighted. I will take, from this point on, that “definable” means “computable”, and proceed forward. > > > > > > Simply use definable as it is used elsewhere too. > > > > > > Note Hilbert's statement: "Working with the infinite can only be secured by the finite." [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 190] Well, in the finite every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by its finite name (because an object of mathematics has no other form of existence). This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it. > > > > > > Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-05-19 05:46 -0700 |
| Message-ID | <212e3406-d553-455d-bda1-7b72cb0513a3@googlegroups.com> |
| In reply to | #413385 |
If you accept definitions, and definitions are your criteria for "good" objects, then you should also accept limits. Since in ZFC a limit is a simple FOL formula. But I guess this might be not your "good" objects. Since in your PDF you write: Epilogue: About mathematics and reality and this book "The mathematician who is merely equipped with an abacus has access to integers only." and then you cite "The natural numbers of today are not the same as the natural numbers of yesterday". https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf So I guess none of definable or computable matches any of what you are heading for with Volkswagen Omlette. Definitions are much too powerful. And computations are also much too powerful. In your Augsburg Crank institute world there will be NOT infinitely many prime numbers. There will be only these prime numbers that have been found today. And tomorrow there will be maybe more prime numbers. So all of math is out of reach for Volkswagen Omlette... Am Samstag, 19. Mai 2018 14:36:18 UTC+2 schrieb burs...@gmail.com: > To get the full account of this pi definition, > you need also consider how sin is defined. So > > possibly sin is some limit, so in the end, > you get a much higher up definition of pi. > > But still its a definition... > > Am Samstag, 19. Mai 2018 14:34:48 UTC+2 schrieb burs...@gmail.com: > > For example the real numbers pi, e, etc.. are > > all definable (in ZFC). Whereby its irrelevant > > how you define them, as digit sequences or > > > > otherwise. For example metamath defines pi > > not as a digit sequence, but as an inverse of > > a trigonometric function: > > > > Define pi = 3.14159..., which is the smallest > > positive number whose sine is zero. > > http://us.metamath.org/mpegif/df-pi.html > > > > What kind of definition is "smallest"? Sigma^0, > > Pi^0, etc..? How do you express that x is > > the smallest y such that P(y). > > > > P(x) & forall y (P(y) => x =< y) > > > > So on the surface it has a Pi form. But maybe > > it is equivalent to some Sigma form. Who knows? > > > > Am Samstag, 19. Mai 2018 14:29:04 UTC+2 schrieb burs...@gmail.com: > > > Definable has subcategories. You can define > > > something simply and more complex, like you > > > can have a simple Sigma^0 sentence, or more > > > complex sentences see also: > > > https://en.wikipedia.org/wiki/Arithmetical_hierarchy#Extensions_and_variations > > > > > > For example if you define less than in peano, > > > as follows: > > > > > > x < y :<=> exists z(x+z = y) > > > > > > Then the above is a Sigma^0 defintion. Right? > > > > > > Computable has subcategories. Computable > > > has also a lot of subcategories, for example > > > the primitive functions and the recursive functions > > > are not the same. > > > > > > There is a link between definable and computable, > > > you can some subcategories of definable identify > > > with some subcategories of computable. But the > > > subcategories of definable are much more, > > > > > > see also this picture: > > > > > > https://en.wikipedia.org/wiki/Arithmetical_hierarchy#/media/File:Arithmetic_hierarchy.svg > > > > > > Am Samstag, 19. Mai 2018 13:58:52 UTC+2 schrieb WM: > > > > Am Freitag, 18. Mai 2018 23:33:34 UTC+2 schrieb Zeit Geist: > > > > > On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > > > > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > > > > > > > > > > > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > > > > > > section of your pdf does not lead to any kind of > > > > > > > contradiction neither in Set Theory nor in Turing article. > > > > > > > > > > > > Not necessary to argue about that. Take the set of all definable real numbers > > > > > > > > > > Wait! Wail! Stop right there. We are not talking about “definable” numbers > > > > > > > > I am. > > > > > > > > > The “definable real numbers” Is a superset of the “computable real numbers”. See the Wikipedia article I sighted. I will take, from this point on, that “definable” means “computable”, and proceed forward. > > > > > > > > Simply use definable as it is used elsewhere too. > > > > > > > > Note Hilbert's statement: "Working with the infinite can only be secured by the finite." [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 190] Well, in the finite every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by its finite name (because an object of mathematics has no other form of existence). This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it. > > > > > > > > Regards, WM
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| From | Zeit Geist <Tucsondrew@me.com> |
|---|---|
| Date | 2018-05-19 09:00 -0700 |
| Message-ID | <5fe53698-c038-4255-80f2-3c8a31994917@googlegroups.com> |
| In reply to | #413382 |
On Saturday, May 19, 2018 at 4:58:52 AM UTC-7, WM wrote: > Am Freitag, 18. Mai 2018 23:33:34 UTC+2 schrieb Zeit Geist: > > On Friday, May 18, 2018 at 10:09:39 AM UTC-7, WM wrote: > > > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > > > > > > > > > Note that these two hypothesis are not contradictory. Moreover the 2.3 > > > > section of your pdf does not lead to any kind of > > > > contradiction neither in Set Theory nor in Turing article. > > > > > > Not necessary to argue about that. Take the set of all definable real numbers > > > > Wait! Wail! Stop right there. We are not talking about “definable” numbers > > I am. > > > The “definable real numbers” Is a superset of the “computable real numbers”. See the Wikipedia article I sighted. I will take, from this point on, that “definable” means “computable”, and proceed forward. > > Simply use definable as it is used elsewhere too. > Note Hilbert's statement: "Working with the infinite can only be secured by the finite." [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 190] Well, in the finite every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by its finite name (because an object of mathematics has no other form of existence). This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it. You talking that out of context. He means that even when discussing infinite objects we restrict ourself to finite proofs. Also, you entirely snipped where I show why you are wrong about the list of computable numbers being computable. What? No answer? > Regards, WM ZG
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| From | WM <wolfgang.mueckenheim@hs-augsburg.de> |
|---|---|
| Date | 2018-05-20 03:21 -0700 |
| Message-ID | <eab5490a-77d8-48ad-a379-c19fd5906b33@googlegroups.com> |
| In reply to | #413391 |
Am Samstag, 19. Mai 2018 18:00:32 UTC+2 schrieb Zeit Geist: > On Saturday, May 19, 2018 at 4:58:52 AM UTC-7, WM wrote: > > > Simply use definable as it is used elsewhere too. > > > Note Hilbert's statement: "Working with the infinite can only be secured by the finite." [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 190] Well, in the finite every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by its finite name (because an object of mathematics has no other form of existence). This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it. > > You talking that out of context. He means that even when discussing infinite objects we restrict ourself to finite proofs. No, he means what he says in this fully quoted paragraph: Finally we will remember our original topic and draw the conclusion. On balance the complete result of all our investigations about the infinite is this: The infinite is nowhere realized; it is neither present in nature nor admissible as the foundation of our rational thinking – a remarkable harmony between being and thinking. [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) 161-190] > we restrict ourself to finite proofs. You are wrong. "The infinite is nowhere realized". Therefore finite proofs proving is are wrong. > > Also, you entirely snipped where I show why you are wrong about the list of computable numbers being computable. "Countable" may differently be interpreted. But we don't need argue about its "true" definition. Simply take definable. There your objections vanish. Regards, WM
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| From | Python <python@python.invalid> |
|---|---|
| Date | 2018-05-19 02:01 +0200 |
| Message-ID | <5aff6950$0$5202$426a74cc@news.free.fr> |
| In reply to | #413341 |
Doktor Frankenheim wrote: > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > >> Note that these two hypothesis are not contradictory. Moreover the 2.3 >> section of your pdf does not lead to any kind of >> contradiction neither in Set Theory nor in Turing article. > > Not necessary to argue about that. Take the set of all definable real numbers which exists according to set theory since every subset of |R exists, even when ZFC is unable to define definability. This set can be well-ordered, like every set. This order is even a sequence because the set is a subset of a countable set. This sequence is defined and has a defined diagonal which contradicts something - in fact the assumption of actual infinity. > >> There is not >> a single word in this part supporting you "supporting your silly sophistry" Not joking, Herr Mueckenheim: refrain from editing posts your answering too, this is called dishonesty, especially when editing IN THE MIDDLE OF A SENTENCE. We all know how dishonest you are in general, do not add this disgrace to your own infamy. >>, one may >> even wonder what is the purpose of this part in your document. > > Chapter II is a summary of set theory, essentially without critism, in order to educate the reader to the point where she can understand chapter VI. > > Regards, WM Danke shön Herr Mueckenheim, but I wasn't asking for a sensible reason for your book-of-fallacies to be, in addition, badly written and organised.
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-05-21 16:40 +0100 |
| Message-ID | <fwer2m510gp.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #413341 |
WM <wolfgang.mueckenheim@hs-augsburg.de> writes: > Am Freitag, 18. Mai 2018 17:31:36 UTC+2 schrieb Python: > > >> Note that these two hypothesis are not contradictory. Moreover the 2.3 >> section of your pdf does not lead to any kind of >> contradiction neither in Set Theory nor in Turing article. > > Not necessary to argue about that. Take the set of all definable real > numbers which exists according to set theory since every subset of |R > exists, even when ZFC is unable to define definability. Can WM define definability for us? Otherwise I have no idea what a definable real is. Can we at least take it that if a real is definable, then it is a consequence of the definition that a digit expansion is uniquely defined at each index, for arbitrarily large indices? > Regards, WM > -- Alan Smaill
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