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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 2026-06-03 11:38 +0300
Organization A noiseless patient Spider
Message-ID <10vop74$3gh23$1@dont-email.me> (permalink)
References (26 earlier) <10vhghr$1jcn3$1@dont-email.me> <10vjdm4$22v1j$1@dont-email.me> <10vk7qa$6aof$2@solani.org> <10vm03v$2p1kf$1@dont-email.me> <10vmnl5$2vmfn$1@dont-email.me>

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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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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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