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Groups > sci.logic > #345849 > unrolled thread
| Started by | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| First post | 2026-05-07 22:48 +0200 |
| Last post | 2026-07-02 16:01 -0700 |
| Articles | 20 on this page of 163 — 8 participants |
Back to article view | Back to sci.logic
An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-07 22:48 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-08 10:58 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-08 14:46 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-09 10:59 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-09 23:20 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-10 10:25 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-10 15:56 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-11 10:51 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-11 13:42 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-12 10:50 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-12 13:36 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-13 12:39 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-13 22:39 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-14 11:46 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-14 16:52 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-15 08:50 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-15 18:39 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-16 12:43 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-17 16:15 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-18 10:42 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-18 12:22 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-19 11:07 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-19 18:44 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-20 11:00 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-20 13:34 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-21 10:29 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-21 17:24 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-22 10:23 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-22 22:53 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-23 09:31 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-23 23:09 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-03 12:35 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-23 22:40 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-24 12:03 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-24 12:59 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-25 11:33 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-25 18:54 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-26 11:43 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-26 12:43 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-27 10:37 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-27 14:19 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-28 09:34 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-28 14:46 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-29 09:52 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-29 16:36 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-30 10:38 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-30 15:19 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-05-31 12:14 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-05-31 16:28 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-01 10:51 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-06-01 17:17 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-02 10:18 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-02 16:00 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-03 11:38 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-03 22:49 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-04 11:05 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-04 22:47 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-05 11:28 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-06-05 16:29 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-06 11:51 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-06 22:25 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-07 11:25 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-07 20:25 +0200
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-06 22:52 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-07 11:33 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-06-07 21:47 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-08 09:29 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-08 14:19 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-09 11:22 +0300
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-08 08:21 -0700
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-08 10:11 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-08 14:42 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-09 11:25 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 15:22 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 02:43 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 02:46 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 02:57 +0200
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-09 07:52 -0700
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 06:31 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 06:32 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 06:35 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-02 04:20 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-02 04:22 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-02 10:20 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-22 22:53 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-03 12:40 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-03 13:42 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-04 11:11 +0300
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-03 09:43 -0700
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-03 23:07 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-04 11:13 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-04 16:06 +0200
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-04 22:52 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-05 11:44 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-06-05 16:37 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-06 12:19 +0300
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-06-06 13:35 -0700
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-07 11:37 +0300
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-06-08 13:04 -0700
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-08 22:21 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-08 22:36 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-08 22:56 +0200
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-09 07:51 -0700
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-06-09 14:54 -0700
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 23:56 +0200
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-06-09 15:12 -0700
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-06-09 15:33 -0700
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-10 00:59 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-10 01:03 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-06 22:41 +0200
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-06 22:45 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-07 11:58 +0300
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-06-07 21:41 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-08 09:36 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-08 14:29 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-09 11:51 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 17:58 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 18:18 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-08 17:42 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-10 06:45 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-06 12:03 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-06 22:28 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-07 12:04 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-07 21:02 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 02:33 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-09 11:52 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-06 22:29 +0200
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-06 22:49 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-07 12:09 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-07 17:02 +0200
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-07 17:34 -0700
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-07 21:33 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-08 10:05 +0300
Re: An afterthought about the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2026-06-08 14:34 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-09 12:10 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-10 06:32 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-10 13:30 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-10 13:33 +0200
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-06-18 22:15 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-08 17:53 +0200
Re: An afterthought about the Binary Tree Mikko <mikko.levanto@iki.fi> - 2026-06-09 12:04 +0300
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 18:39 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 18:50 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 23:05 +0200
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-09 23:05 +0200
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-20 18:07 -0700
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-21 17:13 +0200
Re: An afterthought about the Binary Tree Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-02 13:52 +0100
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-02 08:50 -0700
Re: An afterthought about the Binary Tree Moebius <invalid@example.invalid> - 2026-05-08 14:57 +0200
Re: An afterthought about the Binary Tree wm <wolfgang.mueckenheim@tha.de> - 2026-05-08 15:16 +0200
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-08 10:16 -0700
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-09 11:02 -0700
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-08 09:58 -0700
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-08 10:47 -0700
Re: An afterthought about the Binary Tree Moebius <moebius@example.invalid> - 2026-06-06 04:35 +0200
Re: An afterthought about the Binary Tree Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-02 13:12 +0100
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-02 09:01 -0700
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-02 11:53 -0700
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-02 13:32 -0700
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-02 13:46 -0700
Re: An afterthought about the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-02 15:36 -0700
Re: An afterthought about the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-02 16:01 -0700
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-05-27 14:19 +0200 |
| Message-ID | <10v6nfs$2o9a0$1@dont-email.me> |
| In reply to | #346140 |
Am 27.05.2026 um 09:37 schrieb Mikko: > On 26/05/2026 13:43, WM wrote: >> Am 26.05.2026 um 10:43 schrieb Mikko: >>> The enumeration is called "complete" if everything intended to be in >>> the enumeration is in the enumeration. >> >> No. Everything intended is not enough. Everything existing is required. > > That is false. The definitions do not specify what shall be enumerated. > For example an enumeration of chess pieces can be complete without > mentioning cats although cats exist. An enumeration of fantasy animals > is not complete without dragons although dragons do not exist. > An enumeratiom of infinitely many steps is not complete if only every intended step is enumerated because most steps are dark and cannot be intended as individuals. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-05-28 09:34 +0300 |
| Message-ID | <10v8nl5$390tt$1@dont-email.me> |
| In reply to | #346143 |
On 27/05/2026 15:19, WM wrote: > Am 27.05.2026 um 09:37 schrieb Mikko: >> On 26/05/2026 13:43, WM wrote: >>> Am 26.05.2026 um 10:43 schrieb Mikko: > >>>> The enumeration is called "complete" if everything intended to be in >>>> the enumeration is in the enumeration. >>> >>> No. Everything intended is not enough. Everything existing is required. >> >> That is false. The definitions do not specify what shall be enumerated. >> For example an enumeration of chess pieces can be complete without >> mentioning cats although cats exist. An enumeration of fantasy animals >> is not complete without dragons although dragons do not exist. >> > An enumeratiom of infinitely many steps is not complete if only every > intended step is enumerated because most steps are dark and cannot be > intended as individuals. The intent need not be as individuals. But some intent is needed or the words "complete" and "incomplere" are meaningless when used about that enumeration. Of course every enumeration is complete in the sense that everthing that is enumerated is enoumerated. But that meaning is rarely useful. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-05-28 14:46 +0200 |
| Message-ID | <10v9dfr$3f07a$1@dont-email.me> |
| In reply to | #346152 |
Am 28.05.2026 um 08:34 schrieb Mikko: > On 27/05/2026 15:19, WM wrote: >> Am 27.05.2026 um 09:37 schrieb Mikko: >>> On 26/05/2026 13:43, WM wrote: >>>> Am 26.05.2026 um 10:43 schrieb Mikko: >> >>>>> The enumeration is called "complete" if everything intended to be in >>>>> the enumeration is in the enumeration. >>>> >>>> No. Everything intended is not enough. Everything existing is required. >>> >>> That is false. The definitions do not specify what shall be enumerated. >>> For example an enumeration of chess pieces can be complete without >>> mentioning cats although cats exist. An enumeration of fantasy animals >>> is not complete without dragons although dragons do not exist. >>> >> An enumeratiom of infinitely many steps is not complete if only every >> intended step is enumerated because most steps are dark and cannot be >> intended as individuals. > > The intent need not be as individuals. For enumeration purposes that is necessary, except in simple cases like enumerating ℕ by f(n) = n or f(n) = n + c. > But some intent is needed or the > words "complete" and "incomplere" are meaningless when used about that > enumeration. > > Of course every enumeration is complete in the sense that everthing that > is enumerated is enoumerated. But that meaning is rarely useful. Enumerating all rationals is impossible however. https://www.reddit.com/r/AspectsOfTheInfinite/comments/1tc6v1l/proof_of_the_existence_of_dark_numbers/ Regards, WM>
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-05-29 09:52 +0300 |
| Message-ID | <10vbd3r$3vl0s$2@dont-email.me> |
| In reply to | #346156 |
On 28/05/2026 15:46, WM wrote: > Am 28.05.2026 um 08:34 schrieb Mikko: >> On 27/05/2026 15:19, WM wrote: >>> Am 27.05.2026 um 09:37 schrieb Mikko: >>>> On 26/05/2026 13:43, WM wrote: >>>>> Am 26.05.2026 um 10:43 schrieb Mikko: >>> >>>>>> The enumeration is called "complete" if everything intended to be in >>>>>> the enumeration is in the enumeration. >>>>> >>>>> No. Everything intended is not enough. Everything existing is >>>>> required. >>>> >>>> That is false. The definitions do not specify what shall be enumerated. >>>> For example an enumeration of chess pieces can be complete without >>>> mentioning cats although cats exist. An enumeration of fantasy animals >>>> is not complete without dragons although dragons do not exist. >>>> >>> An enumeratiom of infinitely many steps is not complete if only every >>> intended step is enumerated because most steps are dark and cannot be >>> intended as individuals. >> >> The intent need not be as individuals. > > For enumeration purposes that is necessary, except in simple cases like > enumerating ℕ by f(n) = n or f(n) = n + c. In mathematics it does not matter whether f(n) is defined with a simple expression or a complicated set of conditions as long as it is well defined. Your "except" simply means that I was right and you were wrong. -- Mikko
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| From | wm <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-05-29 16:36 +0200 |
| Message-ID | <10vc89k$ba6g$2@solani.org> |
| In reply to | #346168 |
Am 29.05.2026 um 08:52 schrieb Mikko: > On 28/05/2026 15:46, WM wrote: >> Am 28.05.2026 um 08:34 schrieb Mikko: >>> On 27/05/2026 15:19, WM wrote: >>>> Am 27.05.2026 um 09:37 schrieb Mikko: >>>>> On 26/05/2026 13:43, WM wrote: >>>>>> Am 26.05.2026 um 10:43 schrieb Mikko: >>>> >>>>>>> The enumeration is called "complete" if everything intended to be in >>>>>>> the enumeration is in the enumeration. >>>>>> >>>>>> No. Everything intended is not enough. Everything existing is >>>>>> required. >>>>> >>>>> That is false. The definitions do not specify what shall be >>>>> enumerated. >>>>> For example an enumeration of chess pieces can be complete without >>>>> mentioning cats although cats exist. An enumeration of fantasy animals >>>>> is not complete without dragons although dragons do not exist. >>>>> >>>> An enumeratiom of infinitely many steps is not complete if only >>>> every intended step is enumerated because most steps are dark and >>>> cannot be intended as individuals. >>> >>> The intent need not be as individuals. >> >> For enumeration purposes that is necessary, except in simple cases >> like enumerating ℕ by f(n) = n or f(n) = n + c. > > In mathematics it does not matter whether f(n) is defined with a > simple expression or a complicated set of conditions as long as > it is well defined. That holds for visible numbers, not for dark numbers, and therefore not in actual infinity. Regards, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-05-30 10:38 +0300 |
| Message-ID | <10ve46g$mk00$1@dont-email.me> |
| In reply to | #346171 |
On 29/05/2026 17:36, wm wrote: > Am 29.05.2026 um 08:52 schrieb Mikko: >> On 28/05/2026 15:46, WM wrote: >>> Am 28.05.2026 um 08:34 schrieb Mikko: >>>> On 27/05/2026 15:19, WM wrote: >>>>> Am 27.05.2026 um 09:37 schrieb Mikko: >>>>>> On 26/05/2026 13:43, WM wrote: >>>>>>> Am 26.05.2026 um 10:43 schrieb Mikko: >>>>> >>>>>>>> The enumeration is called "complete" if everything intended to >>>>>>>> be in >>>>>>>> the enumeration is in the enumeration. >>>>>>> >>>>>>> No. Everything intended is not enough. Everything existing is >>>>>>> required. >>>>>> >>>>>> That is false. The definitions do not specify what shall be >>>>>> enumerated. >>>>>> For example an enumeration of chess pieces can be complete without >>>>>> mentioning cats although cats exist. An enumeration of fantasy >>>>>> animals >>>>>> is not complete without dragons although dragons do not exist. >>>>>> >>>>> An enumeratiom of infinitely many steps is not complete if only >>>>> every intended step is enumerated because most steps are dark and >>>>> cannot be intended as individuals. >>>> >>>> The intent need not be as individuals. >>> >>> For enumeration purposes that is necessary, except in simple cases >>> like enumerating ℕ by f(n) = n or f(n) = n + c. >> >> In mathematics it does not matter whether f(n) is defined with a >> simple expression or a complicated set of conditions as long as >> it is well defined. > That holds for visible numbers, not for dark numbers, and therefore not > in actual infinity. In mathematics there is no distinction between "visible" and "dark" numbers. All numbers is all numbers with no exception. -- Mikko
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-05-30 15:19 +0200 |
| Message-ID | <10veo5u$s378$1@dont-email.me> |
| In reply to | #346180 |
Am 30.05.2026 um 09:38 schrieb Mikko: > In mathematics there is no distinction between "visible" and "dark" > numbers. That's why modern mathematics is inconsistent. Example the nodes and paths of the Binary Tree. or such outrageous nonsense as countability of the rationals. Regards, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-05-31 12:14 +0300 |
| Message-ID | <10vgu4t$1e9dh$1@dont-email.me> |
| In reply to | #346187 |
On 30/05/2026 16:19, WM wrote: > Am 30.05.2026 um 09:38 schrieb Mikko: > >> In mathematics there is no distinction between "visible" and "dark" >> numbers. > > That's why modern mathematics is inconsistent. There is no known inconsistency in modern mathematics. Your inconsistent ideas are not a part of modern mathematics. > Example the nodes and paths of the Binary Tree. or such outrageous > nonsense as countability of the rationals. No known inconsistency there, only in your misconceptions about them. -- Mikko
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-05-31 16:28 +0200 |
| Message-ID | <10vhghr$1jcn3$1@dont-email.me> |
| In reply to | #346191 |
Am 31.05.2026 um 11:14 schrieb Mikko: > On 30/05/2026 16:19, WM wrote: >> Am 30.05.2026 um 09:38 schrieb Mikko: >> >>> In mathematics there is no distinction between "visible" and "dark" >>> numbers. >> >> That's why modern mathematics is inconsistent. > > There is no known inconsistency in modern mathematics. Your inconsistent > ideas are not a part of modern mathematics. If all contraditions are declared to be not a part of it, then set teory can forever remain consistent.> >> Example the nodes and paths of the Binary Tree. or such outrageous > > nonsense as countability of the rationals. > > No known inconsistency there, only in your misconceptions about them. Every node splits one sheaf off of the incoming sheaf --- not more and not less This sheaf goes undisturbed into the infinite. It passes infinitely many nodes, which split off further sheaves but do not change the passing sheaf. Therefore there are precisely as many sheaves differing by nodes as nodes, well one more. Nodes further down separate further but only to infinite subsets. (Mikko) Yes, we don't disagree on that. The number of sheafs (leading substrings, binary digits) is countable. (ceoln) There are countably many sheafs, but note that each is uncountable. (Alarming-Smoke1467) What makes infinite such paths which cannot be distinguished bny nodes? Regards,, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-01 10:51 +0300 |
| Message-ID | <10vjdm4$22v1j$1@dont-email.me> |
| In reply to | #346194 |
On 31/05/2026 17:28, WM wrote: > Am 31.05.2026 um 11:14 schrieb Mikko: >> On 30/05/2026 16:19, WM wrote: >>> Am 30.05.2026 um 09:38 schrieb Mikko: >>> >>>> In mathematics there is no distinction between "visible" and "dark" >>>> numbers. >>> >>> That's why modern mathematics is inconsistent. >> >> There is no known inconsistency in modern mathematics. Your inconsistent >> ideas are not a part of modern mathematics. > > If all contraditions are declared to be not a part of it, then set teory > can forever remain consistent. You are not allowed to declare someting to be not a part of modern mathematics. Each set theory either is constent or is not. If you can't prove either the consistency or inconsistency then you simply don't know. Above you claimed that modern mathematics is inconsistent but presented no reason to think you are not just lying. >>> Example the nodes and paths of the Binary Tree. or such outrageous >> > nonsense as countability of the rationals. >> >> No known inconsistency there, only in your misconceptions about them. > > Every node splits one sheaf off of the incoming sheaf --- not more and > not less This sheaf goes undisturbed into the infinite. It passes > infinitely many nodes, which split off further sheaves but do not change > the passing sheaf. Therefore there are precisely as many sheaves > differing by nodes as nodes, well one more. No inconsistency there. > Nodes further down separate further but only to infinite subsets. (Mikko) You failed to specify what nodes separate from what. It was specified in the original context of the quoted sentence. -- Mikko
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| From | wm <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-06-01 17:17 +0200 |
| Message-ID | <10vk7qa$6aof$2@solani.org> |
| In reply to | #346198 |
Am 01.06.2026 um 09:51 schrieb Mikko: > On 31/05/2026 17:28, WM wrote: >> Every node splits one sheaf off of the incoming sheaf --- not more and >> not less This sheaf goes undisturbed into the infinite. It passes >> infinitely many nodes, which split off further sheaves but do not >> change the passing sheaf. Therefore there are precisely as many >> sheaves differing by nodes as nodes, well one more. > > No inconsistency there. > >> Nodes further down separate further but only to infinite subsets. (Mikko) > > You failed to specify what nodes separate from what. The sheaves are countable, and nodes fail to separate their paths. Therefore there are only countably many distinct real numbers. Regards, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-02 10:18 +0300 |
| Message-ID | <10vm03v$2p1kf$1@dont-email.me> |
| In reply to | #346202 |
On 01/06/2026 18:17, wm wrote: > Am 01.06.2026 um 09:51 schrieb Mikko: >> On 31/05/2026 17:28, WM wrote: > >>> Every node splits one sheaf off of the incoming sheaf --- not more >>> and not less This sheaf goes undisturbed into the infinite. It passes >>> infinitely many nodes, which split off further sheaves but do not >>> change the passing sheaf. Therefore there are precisely as many >>> sheaves differing by nodes as nodes, well one more. >> >> No inconsistency there. >> >>> Nodes further down separate further but only to infinite subsets. >>> (Mikko) >> >> You failed to specify what nodes separate from what. > > The sheaves are countable, and nodes fail to separate their paths. > Therefore there are only countably many distinct real numbers. What does it mean that "nodes fail to separate their paths"? Doesn't the fact that for every pair of paths there is a node that is in one of the paths but not in the other imply that that node separate those two paths? Anyway, your "RTheerfore" is false. Your claim about nodes, no matter how it shall be interpreted, says nothing about real numbers. -- Mikko
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-06-02 16:00 +0200 |
| Message-ID | <10vmnl5$2vmfn$1@dont-email.me> |
| In reply to | #346217 |
Am 02.06.2026 um 09:18 schrieb Mikko: > On 01/06/2026 18:17, wm wrote: >> The sheaves are countable, and nodes fail to separate their paths. >> Therefore there are only countably many distinct real numbers. > > What does it mean that "nodes fail to separate their paths"? It means that all paths of a sheaf visit the same nodes. > Doesn't the fact that for every pair of paths there is a node that > is in one of the paths but not in the other imply that that node > separate those two paths? This is not a fact because nodes separate only to infinite subsets.> > Anyway, your "RTheerfore" is false. Your claim about nodes, no matter > how it shall be interpreted, says nothing about real numbers. > The paths are a representation of the real numbers within [0, 1). If nodes separate infinite sheaves only to infinite sets of paths, i.e., if onky countaby many different paths exist, then only countably many infinite digit sequences are seprated by digits. Regards, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-03 11:38 +0300 |
| Message-ID | <10vop74$3gh23$1@dont-email.me> |
| In reply to | #346229 |
On 02/06/2026 17:00, WM wrote: > Am 02.06.2026 um 09:18 schrieb Mikko: >> On 01/06/2026 18:17, wm wrote: > >>> The sheaves are countable, and nodes fail to separate their paths. >>> Therefore there are only countably many distinct real numbers. >> >> What does it mean that "nodes fail to separate their paths"? > > It means that all paths of a sheaf visit the same nodes. Which is false. Every path shares some finite number of nodes with another path (at least the root node) but no path shares all its nodes with another path. >> Doesn't the fact that for every pair of paths there is a node that >> is in one of the paths but not in the other imply that that node >> separate those two paths? > > This is not a fact because nodes separate only to infinite subsets. It is. If you see two paths that contain the same nodes you are seeng the same path as two. Perhaps you are drunk. >> Anyway, your "RTheerfore" is false. Your claim about nodes, no matter>> how it shall be interpreted, says nothing about real numbers. > The paths are a representation of the real numbers within [0, 1). That is not their real essense. And the most obvious association of paths to real numbers associates two paths to some real numbers. For example, both the path that goes first left and then always right and the path that goes forst right and then always left are both associated to the real number 1/2. > If nodes separate infinite sheaves only to infinite sets of paths, They do. No if about that. > i.e., if onky countaby many different paths exist, That "i.e." is false. Each of those sets is uncountble. > then only countably many infinite digit sequences are seprated by digits. Ex falso quodlibet. -- Mikko
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-06-03 22:49 +0200 |
| Message-ID | <10vq40u$3vjl1$1@dont-email.me> |
| In reply to | #346246 |
Am 03.06.2026 um 10:38 schrieb Mikko: > On 02/06/2026 17:00, WM wrote: >> Am 02.06.2026 um 09:18 schrieb Mikko: >>> On 01/06/2026 18:17, wm wrote: >> >>>> The sheaves are countable, and nodes fail to separate their paths. >>>> Therefore there are only countably many distinct real numbers. >>> >>> What does it mean that "nodes fail to separate their paths"? >> >> It means that all paths of a sheaf visit the same nodes. > > Which is false. It is fact. You had recognized it. > Every path shares some finite number of nodes with > another path (at least the root node) but no path shares all its > nodes with another path. That is true. But it would be wrong if more than countably many paths existed, because the nodes can separate only countably many paths - each node one additional path. > >> The paths are a representation of the real numbers within [0, 1). > > That is not their real essense. And the most obvious association of > paths to real numbers associates two paths to some real numbers. For > example, both the path that goes first left and then always right > and the path that goes forst right and then always left are both > associated to the real number 1/2. Such cases are possible but they are in the minority. > >> If nodes separate infinite sheaves only to infinite sets of paths, > > They do. No if about that. > >> i.e., if only countaby many different paths exist, > > That "i.e." is false. Each of those sets is uncountble. But those sets are not separated by nodes. Regards, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-04 11:05 +0300 |
| Message-ID | <10vrbjq$8678$1@dont-email.me> |
| In reply to | #346285 |
On 03/06/2026 23:49, WM wrote: > Am 03.06.2026 um 10:38 schrieb Mikko: >> On 02/06/2026 17:00, WM wrote: >>> Am 02.06.2026 um 09:18 schrieb Mikko: >>>> On 01/06/2026 18:17, wm wrote: >>> >>>>> The sheaves are countable, and nodes fail to separate their paths. >>>>> Therefore there are only countably many distinct real numbers. >>>> >>>> What does it mean that "nodes fail to separate their paths"? >>> >>> It means that all paths of a sheaf visit the same nodes. >> >> Which is false. > > It is fact. You had recognized it. You are equivocating. The usual meaning of "visit the same nodes" is that there is no node that all nodes in one path are also in the other path. But now you claim that you only intended that at least one of the nodes is common to them (the root node). >> Every path shares some finite number of nodes with >> another path (at least the root node) but no path shares all its >> nodes with another path. > > That is true. But it would be wrong if more than countably many paths > existed, because the nodes can separate only countably many paths - each > node one additional path. No node separates only one path. Instead it partitions the uncountable set of paths coming to it into two uncountable sets of paths leaving it, one to the left subnode and one to the right subnode. >>> The paths are a representation of the real numbers within [0, 1). >> >> That is not their real essense. And the most obvious association of >> paths to real numbers associates two paths to some real numbers. For >> example, both the path that goes first left and then always right >> and the path that goes forst right and then always left are both >> associated to the real number 1/2. > > Such cases are possible but they are in the minority. True, there are only a countable set of such cases but unconutably many other cases. >>> If nodes separate infinite sheaves only to infinite sets of paths, >> >> They do. No if about that. >> >>> i.e., if only countaby many different paths exist, >> >> That "i.e." is false. Each of those sets is uncountble. > > But those sets are not separated by nodes. They are but indirectly. Different sets are different because each contain a path that is different from every path in the other set. Different paths are different because no path contains all nodes that another path contains. -- Mikko
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-06-04 22:47 +0200 |
| Message-ID | <10vso9q$lr6r$1@dont-email.me> |
| In reply to | #346306 |
Am 04.06.2026 um 10:05 schrieb Mikko: > On 03/06/2026 23:49, WM wrote: >> But those sets are not separated by nodes. > > They are but indirectly. Different sets are different because each > contain a path that is different from every path in the other set. > Different paths are different because no path contains all nodes > that another path contains. Thdere are countably many sheaves (sets) separated by nodes. Whether one or more paths remain within a sheaf over the whole Binary Tree is irrelevant, Regards, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-05 11:28 +0300 |
| Message-ID | <10vu1b6$10c3q$1@dont-email.me> |
| In reply to | #346384 |
On 04/06/2026 23:47, WM wrote: > Am 04.06.2026 um 10:05 schrieb Mikko: >> On 03/06/2026 23:49, WM wrote: > >>> But those sets are not separated by nodes. >> >> They are but indirectly. Different sets are different because each >> contain a path that is different from every path in the other set. >> Different paths are different because no path contains all nodes >> that another path contains. > > Thdere are countably many sheaves (sets) separated by nodes. Whether one > or more paths remain within a sheaf over the whole Binary Tree is > irrelevant, Relevance is not relevant to mathematical truth. No matter now many times a sheaf cotaining uncountablyly many paths is split, every part is always a sheaf containing uncountably many paths. -- Mikko
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| From | wm <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2026-06-05 16:29 +0200 |
| Message-ID | <10vumfm$deov$1@solani.org> |
| In reply to | #346413 |
Am 05.06.2026 um 10:28 schrieb Mikko: > > No matter now many times a sheaf cotaining uncountablyly many paths is > split, every part is always a sheaf containing uncountably many paths. > No matter how many paths are within a sheaf, there are as many real numbers in the unit interval as are different sheaves in the Binary Tree. And their number is countable since the number of nodes is countable and every node adds one sheaf to the set of incoming sheaves. Regards, WM
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-06 11:51 +0300 |
| Message-ID | <1100n3g$1nmai$1@dont-email.me> |
| In reply to | #346420 |
On 05/06/2026 17:29, wm wrote: > Am 05.06.2026 um 10:28 schrieb Mikko: > >> >> No matter now many times a sheaf cotaining uncountablyly many paths is >> split, every part is always a sheaf containing uncountably many paths. >> > No matter how many paths are within a sheaf, there are as many real > numbers in the unit interval as are different sheaves in the Binary > Tree. And their number is countable since the number of nodes is > countable and every node adds one sheaf to the set of incoming sheaves. No, there are as many paths in a sheaf as there real numbers in the unit iterval. The number of paths in a sheaf is provably uncountable. In mathematics proofs matter but opinions don't. -- Mikko
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