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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 2023-06-26 13:23 -0400
Organization A noiseless patient Spider
Message-ID <0e827a01-c898-0733-4ed8-812ad420b077@att.net> (permalink)
References (13 earlier) <33b8c197-a026-4076-bb5d-d2dc3126fd0bn@googlegroups.com> <1b79c668-4caf-5149-02f0-095368f87ba1@att.net> <f2a080d1-041f-4e48-97f1-36fda8b8b7f0n@googlegroups.com> <08a0d32f-fd24-7ea5-c786-42b70dae2149@att.net> <12682261-1178-4a93-9d74-7601bfd9b5f5n@googlegroups.com>

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On 6/26/2023 10:47 AM, WM wrote:
> Jim Burns schrieb am Sonntag,
> 25. Juni 2023 um 16:58:45 UTC+2:
>> On 6/25/2023 10:07 AM, WM wrote:

>>>> | Every infinite endsegment has
>>>> | an infinite set in common with
>>>> | every predecessor and
>>>> | every infinite successor.
>>
>> No.
>> The set in common with every successor
>> is empty, not infinite.
> 
> Since every successor is infinite,
> you need a successor having elements
> but not in common with all its predecessors.

In order for the set {common} of
elements in common with each end segment
to be empty
there must be no element in common
with each end segment.

In order for it to be empty,
we do not need anything _other than_
for no element to be in it.

The set ⋃⟨⟨0…k⟩⟩ has
only infinite end segments  and
an empty intersection of
all (infinite) end segments.

Each element j splits ⋃⟨⟨0…k⟩⟩
into ⟨0…j⟩∥⟨j⁺⁺…⟩
⟨j⁺⁺…⟩ 1×1 1-ended
⟨j⁺⁺…⟩ infinite.

Each element j splits ⋃⟨⟨0…k⟩⟩
into ⟨0…j⟩∥⟨j⁺⁺…⟩
j not-in ⟨j⁺⁺…⟩
j not-in {common}
{common} empty.

----
The complementary way to look at this
is that

each ⟨0…k⟩
⁺⁺ing 1×1 2-ended from 0
is finite.

each ⟨0…k⟩
is followed by ⟨0…k,k⁺⁺⟩
also ⁺⁺ing 1x1 2-ended from 0
and finite.

each ⟨0…k⟩
is non-final.

The set ⟨⟨0…k⟩⟩ of
⁺⁺ing 1×1 2-endeds from 0
is
1×1 1-ended from 0 (not finite)

The union ⋃⟨⟨0…k⟩⟩ of
⁺⁺ing 1×1 2-endeds from 0 (finites)
is
⁺⁺ing 1×1 1-ended from 0 (not finite)

Anything one step from a finite
is a finite.

Each finite ends.
Each finite does not end _the finites_

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Thread

Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-17 11:56 -0400
  Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-18 06:59 -0700
    Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-18 14:40 -0400
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-19 07:01 -0700
        Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 07:34 -0700
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-20 08:30 -0700
            Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:30 -0700
        Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-19 13:55 -0400
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-20 08:36 -0700
            Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:24 -0700
            Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-20 14:03 -0400
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-21 07:22 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-21 12:26 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-22 05:54 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-22 09:38 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 08:44 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-23 12:37 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 09:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-23 15:39 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-24 05:43 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-24 10:22 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-25 07:07 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-25 10:58 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 07:47 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-26 08:35 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-26 13:23 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-28 07:22 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-28 07:38 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-28 07:57 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-28 07:38 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-28 09:11 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-28 09:23 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-29 05:12 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-29 08:05 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-28 12:39 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-29 05:20 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-29 11:24 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 09:58 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:06 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 13:38 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 11:44 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-01 05:04 -0700

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