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Re: An afterthought about the Binary Tree

From Mikko <mikko.levanto@iki.fi>
Newsgroups sci.logic
Subject Re: An afterthought about the Binary Tree
Date 2026-05-30 10:38 +0300
Organization A noiseless patient Spider
Message-ID <10ve46g$mk00$1@dont-email.me> (permalink)
References (27 earlier) <10v6nfs$2o9a0$1@dont-email.me> <10v8nl5$390tt$1@dont-email.me> <10v9dfr$3f07a$1@dont-email.me> <10vbd3r$3vl0s$2@dont-email.me> <10vc89k$ba6g$2@solani.org>

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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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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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