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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 2023-07-03 11:32 -0400
Organization A noiseless patient Spider
Message-ID <fa4ce064-cce0-0240-4645-772fb10e3d90@att.net> (permalink)
References (15 earlier) <bb1e1b3f-3451-4e7e-ad6f-67ccdb9e90e6n@googlegroups.com> <e4454fe7-51a5-57ce-5351-f9f6c90cb1b3@att.net> <d2ae8a07-68e3-4dd6-ba6a-0a8adf831c81n@googlegroups.com> <d356fd00-b026-8ba4-7f67-a01d0ea13fcc@att.net> <2875d178-5f00-4b96-9959-0f22b3fe2407n@googlegroups.com>

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On 7/3/2023 9:31 AM, WM wrote:
> Jim Burns schrieb am Montag,
> 3. Juli 2023 um 00:44:38 UTC+2:
>> On 7/2/2023 11:14 AM, WM wrote:

>>>> If Bob is in a cell, then
>>>> that cell has not had its last swap.
>>>
>>> If it is a visible cell.
>>
>> The word "visible" explains nothing.
>
> It is most important.
> There are invisible cells.

There are finitely accessible (FA) cells,
and finitely-accessible (FA) swaps.
FA swaps are only between FA cells.

Bob disappears without involving
non-FA cells or non-FA swaps.

The closes you'll come to finding magic
is here:
|
| For each FA cell,
| there is a last FA swap.
| Its last FA swap is FA
| and leaves an X in that FA cell.

Before any FA swap,
Bob Not-An-X is in a FA cell.

If Bob Not-An-X is in a FA cell,
then
its last X-leaving swap has not been swapped,
and not all swaps have been swapped.

By logic,
P ⇒ ¬Q  and  Q ⇒ ¬P
are either both true or both false.

| If Bob is in a FA cell,
| then
| not all FA swaps have been swapped.
|
is true.

| If all FA swaps have been swapped
| then
| Bob is not in a FA cell.
|
is true.

If all FA swaps have been swapped,
where is Bob?

We have seen that
he is not in a FA cell.

If Bob is in a non-FA cell,
he did not get there by
a FA swap between FA cells.

If all FA swaps have been swapped
either
Bob is somewhere, by magic,
or
Bob is nowhere, by logic.

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Thread

Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 01:34 +0100
  Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-20 08:34 -0700
    Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:09 -0700
      Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:18 -0700
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-21 07:17 -0700
        Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-21 16:52 +0200
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-22 05:48 -0700
            Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 13:20 -0700
    Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-22 00:51 +0100
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-22 05:58 -0700
        Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 01:05 +0100
          Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 17:17 -0700
            Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:26 +0100
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 09:01 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 01:59 +0100
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-06-26 04:42 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 14:42 +0100
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-06-26 15:22 -0700
                Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-27 01:14 +0200
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 08:12 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 07:59 -0700
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 08:53 -0700
            Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 09:52 -0700
            Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 02:05 +0100
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 08:05 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-29 01:34 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-29 05:31 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-29 16:37 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:18 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:21 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 13:52 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-29 19:15 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-30 14:27 +0100
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:03 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:09 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:15 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:21 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:26 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 02:05 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 09:04 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:56 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-30 16:47 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:15 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:20 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 02:13 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:59 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:34 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:55 -0700
                Re: Some results about unit fractions Python <python@invalid.org> - 2023-07-02 19:10 +0200
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 13:01 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:27 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 14:14 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 11:49 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 20:30 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-01 10:26 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 16:18 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 17:37 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 12:55 -0400
                Re: Some results about unit fractions Transfinity <transfinity01@gmail.com> - 2023-07-01 10:32 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 15:42 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:17 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 13:00 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 16:24 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:05 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:28 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 17:30 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:44 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 18:49 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 17:07 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-02 06:20 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 04:04 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:39 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:33 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:27 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 01:50 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:50 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:19 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 12:58 -0400
                Re: Some results about unit fractions Transfinity <transfinity01@gmail.com> - 2023-07-01 11:16 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 15:16 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:14 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-02 18:44 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-03 06:31 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-03 11:32 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:46 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-04 19:12 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-04 16:25 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-04 22:14 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-05 18:13 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-06 12:45 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-03 09:50 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:51 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-04 13:35 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-03 10:07 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:53 -0700

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