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Re: Some results about unit fractions

From Jim Burns <james.g.burns@att.net>
Newsgroups sci.logic
Subject Re: Some results about unit fractions
Date 2023-05-06 13:02 -0400
Organization A noiseless patient Spider
Message-ID <a61e2c27-f3f2-c97e-a313-707b1a3dc691@att.net> (permalink)
References (13 earlier) <4a001624-8eb3-414a-8499-edc6f9ca1b3an@googlegroups.com> <fb73f819-81a3-2b79-12d3-e43aeb0ac030@att.net> <9e201575-3f2e-4392-a7fb-8076d48c932en@googlegroups.com> <9e18c025-fa83-39b4-60ca-7e31862de5df@att.net> <7f09fd94-ca64-412c-b340-d4dcb4d0b02an@googlegroups.com>

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On 5/6/2023 10:22 AM, WM wrote:
> Jim Burns schrieb am Freitag,
> 5. Mai 2023 um 19:03:33 UTC+2:
>> On 5/5/2023 8:01 AM, WM wrote:
>>> Jim Burns schrieb am Donnerstag,
>>> 4. Mai 2023 um 21:24:56 UTC+2:

>>>> for each position p/q
>>>> the last exchange involving p/q
>>>> leaves an X (from k/1) at p/q.
>>>
>>> That is only provable for steps with
>>> more successors than predecessors.
>>
>> 1×1 1-ended successors are more than
>> 1×1 2-ended predecessors.
> 
> Your claim is only provable for steps
> with more successors than predecessors

A finite sequence of
correctly descriptive and 👁¬#1◇⊥ claims
(visibly not first possibly false)
only has claims which are true of
_that which is correctly described_
in that sequence.

Mathematics is certain.

However,
even galaxy-sized brains can, in
principle, make mistakes. It isn't
the brilliance of mathematicians which
makes mathematics _certain_

For what has been described, Mathematics
is certain. For other things, things not-
-described, the claims can be uncertain.

However, Mathematics, galaxy-brained
mathematicians, and I do not accept
responsibility for any incorrectness
of those claims when applied to
other things, things not-described.

The claims of Mathematics are certain
because we are very selective in
what we consider those claims to be.
It is _those_ claims which are certain.

> Your claim is only provable for steps
> with more successors than predecessors

for each position p/q
the last exchange involving p/q
leaves an X (from k/1) at p/q.

That claim is certain when applied to
all the positions Xs Os and exchanges
which I describe.

Those same words when applied to things
not-described are not my claim.

> Your claim is only provable for steps
> with more successors than predecessors
> - not for all.

No.
All.
All of that which is correctly described,
which is the only kind of claim which
you will ever see in mathematics.

For each split of row p/
between p/1 and p/q
some p/j is last-before
and p/j⁺⁺ is first-after.

For each split of column /q
between 1/q and p/q
some i/q is last-before
and i⁺⁺/q is first-after.

Initially, column /1, positions p/1
have X, and all other positions have O

For each split of the exchanges
between 1/1↔1/1 and p/q↔n/1
some i/j↔k/1 is last-before
and (j/=1? i⁺⁺/j⁻⁻: 1/i⁺⁺;)↔k⁺⁺/1
is first-after.

I borrow '? : ;' if-then-else operator
from PERL

for each of those positions p/q
the last of those exchanges involving p/q
leaves an X (from k/1) at p/q.

It is certain.

'Bye, Bob.

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Thread

Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-24 15:51 -0400
  Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-25 11:26 -0700
    Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-25 17:16 -0400
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-26 04:47 -0700
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-26 04:50 -0700
        Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-26 17:36 -0400
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-27 06:31 -0700
            Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-27 08:11 -0700
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-27 12:21 -0700
            Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-27 14:14 -0400
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-27 12:36 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-27 17:59 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-28 04:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-28 15:11 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-29 03:30 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-29 17:25 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-30 05:46 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-29 23:41 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-30 05:51 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-01 15:05 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 05:14 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-01 15:06 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-01 12:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 05:08 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 05:06 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-02 12:22 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 09:49 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-02 14:49 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-03 03:20 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-03 13:38 -0400
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-03 19:43 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-04 05:16 -0700
                Re: Some results about unit fractions Jeff Barnett <jbb@notatt.com> - 2023-05-04 09:43 -0600
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-05 05:01 -0700
                Re: Some results about unit fractions Jeff Barnett <jbb@notatt.com> - 2023-05-06 00:15 -0600
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 07:21 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-04 15:24 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-05 05:01 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-05 13:01 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 07:22 -0700
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-05-06 07:56 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 13:22 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-06 13:02 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 13:18 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-06 23:41 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-07 07:17 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-07 23:50 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 06:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:04 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-08 14:59 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 13:59 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-08 21:02 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 05:45 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-09 11:46 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 13:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-10 08:47 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-10 06:07 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-10 13:58 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:10 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:13 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:19 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-08 15:32 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 13:13 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 14:02 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 13:57 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 13:54 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 14:24 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 05:49 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-09 12:41 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 14:03 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-09 17:09 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-10 06:05 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-10 09:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-10 13:05 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-10 13:21 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-11 04:37 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-11 09:51 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-12 05:31 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-11 14:00 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-12 05:31 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-12 15:37 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-13 06:22 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 14:30 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-13 11:41 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 23:24 -0400
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-05-14 02:20 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-14 14:04 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-14 14:44 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 03:29 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 05:59 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 10:15 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 13:49 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 17:14 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 08:03 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 09:33 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 11:11 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 12:08 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-18 08:39 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-18 12:23 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:33 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:41 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-18 12:47 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:53 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:59 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 13:02 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 10:24 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 13:50 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 17:16 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-13 15:44 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-14 14:09 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 19:41 -0400
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 23:41 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-14 14:11 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-14 18:17 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-14 16:16 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-14 20:48 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 03:28 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-15 10:08 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 13:46 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-15 18:59 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 07:31 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 09:32 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 11:08 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 12:01 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-17 05:44 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-17 08:17 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-17 05:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-17 14:48 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-18 12:20 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:52 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 05:43 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 08:56 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-18 17:02 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 05:40 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 08:51 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 09:54 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 10:42 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 11:26 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 12:09 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-19 13:47 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 11:36 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 12:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 12:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 12:50 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 13:16 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-20 09:36 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:39 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:43 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-19 20:36 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-20 09:20 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:38 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:42 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-20 23:40 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-21 01:56 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-21 02:00 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-20 17:55 -0400
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-18 17:57 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 05:29 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 08:43 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-27 17:03 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-28 04:53 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-28 07:22 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-28 08:39 -0700

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