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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 2023-06-25 10:58 -0400
Organization A noiseless patient Spider
Message-ID <08a0d32f-fd24-7ea5-c786-42b70dae2149@att.net> (permalink)
References (13 earlier) <90f5d0bc-5c3a-416a-8ca0-860a05f719e0n@googlegroups.com> <364a6a02-ecd1-5dbc-3bd3-e4564453d69d@att.net> <33b8c197-a026-4076-bb5d-d2dc3126fd0bn@googlegroups.com> <1b79c668-4caf-5149-02f0-095368f87ba1@att.net> <f2a080d1-041f-4e48-97f1-36fda8b8b7f0n@googlegroups.com>

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On 6/25/2023 10:07 AM, WM wrote:
> Jim Burns schrieb am Samstag,
> 24. Juni 2023 um 16:22:12 UTC+2:
>> On 6/24/2023 8:43 AM, WM wrote:

>>> Show one *infinite* successor that has
>>> no element in common with some predecessor.
>>
>> That is not your claim.
>
> No,

Your claim is below.

> it would be sufficient to show
> one *infinite* successor that has
> at least one element not in common with
> at least one predecessor.
>
>> This is your claim.
>> | Every infinite endsegment has
>> | an infinite set in common with
>> | every predecessor and
>> | every infinite successor.
>
> Of course.

⟨6.02214076×10²³…⟩ is a counter-example.

>> ⟨6.02214076×10²³…⟩ does not have
>> an infinite set in common with
>> every predecessor and
>> every infinite successor.
>
> It is not an endsegment.

⟨6.02214076×10²³…⟩ is the end segment of ℕ
which starts at 6.02214076×10²³

> ⟨6.02214076×10²³, 6.02214076×10²³ + 1, …⟩
> is an endsegment

⟨6.02214076×10²³, 6.02214076×10²³ + 1, …⟩
= ⟨6.02214076×10²³…⟩
= {i|6.02214076×10²³≤i} ⊆ N

> ⟨6.02214076×10²³, 6.02214076×10²³ + 1, …⟩
> is an endsegment and obeys my claim.

6.02214076×10²³ is not in
⟨6.02214076×10²³+1, 6.02214076×10²³+2, …⟩
and is not in common with
each infinite successor of
⟨6.02214076×10²³, 6.02214076×10²³+1, …⟩

6.02214076×10²³+1 is not in
⟨6.02214076×10²³+2, 6.02214076×10²³+3, …⟩
and is not in common with
each infinite successor of
⟨6.02214076×10²³, 6.02214076×10²³+1, …⟩

6.02214076×10²³+2 is not in
⟨6.02214076×10²³+3, 6.02214076×10²³+4, …⟩
and is not in common with
each infinite successor of
⟨6.02214076×10²³, 6.02214076×10²³+1, …⟩

for each j in
⟨6.02214076×10²³, 6.02214076×10²³+1, …⟩
j is not in ⟨j+1, j+2, …⟩
and is not in common with
each infinite successor of
⟨6.02214076×10²³, 6.02214076×10²³+1, …⟩

> ⟨6.02214076×10²³, 6.02214076×10²³ + 1, …⟩
> is an endsegment and obeys my claim.

>> | 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.

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Thread

Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-17 05:54 -0700
  Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-17 08:46 -0700
    Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-18 06:57 -0700
  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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