Groups | Search | Server Info | Login | Register
| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Newsgroups | sci.logic |
| Subject | Re: Some results about unit fractions |
| Date | 2023-06-05 15:49 -0400 |
| Organization | A noiseless patient Spider |
| Message-ID | <62ebdf2f-12bd-d326-2fb9-4ef61098324a@att.net> (permalink) |
| References | (13 earlier) <c3ddc370-f619-4825-a62a-20ecfeaac644n@googlegroups.com> <ca516a7b-0726-72d4-7d55-0317ffc175e3@att.net> <839be6ce-13c6-47b2-9de3-fb09b0a3e9c8n@googlegroups.com> <597bb9d5-5e15-d2f6-426d-8c2f68515d8e@att.net> <eea9a633-0556-4039-a4af-48d9e34235e5n@googlegroups.com> |
On 6/5/2023 10:12 AM, WM wrote:
> Jim Burns schrieb am Montag,
> 5. Juni 2023 um 02:39:36 UTC+2:
[...]
> I know that
> for every x that you can name,
> there are ℵ₀ unit fractions smaller than x
> - one and the same core of unit fractions,
> much smaller than every definable number.
> That is not a question, but proven.
> It follows from the fact, that
> every set suitable as the core
> for the smallest chosen number
> is also suitable
> for all larger numbers.
"Every set suitable" assumes that
a suitable set exists.
_That is what you want to prove_
| assumption ⟹ assumption
is 👁¬#1◇⊥ (valid) but
doesn't support "assumption"
Better:
| assumption ⭯
----
For each unit fraction ⅟n
⟨...,⅟n⁺⁺⟩, ⟨⅟n,...,⅟1⟩ exist.
and
{core} ⊆ ⟨...,⅟n⁺⁺⟩
⅟n ∉ ⟨...,⅟n⁺⁺⟩
⅟n ∉ {core}
For each unit fraction ⅟n
⅟n ∉ {core}
Therefore,
{core} = ∅
----
For each unit fraction 1/n
⟨...,⅟n⁺⁺⟩, ⟨⅟n,...,⅟1⟩ exist,
and
⟨1,...,n⟩, ⟨n⁺⁺,...⟩ exist.
For each ⟨1,...,n⟩ ⁺⁺ing 1x1 2-ended,
⟨1,...,n,n⁺⁺⟩ ⁺⁺ing 1x1 2-ended
exists.
For each split
⟨1,...,i⟩, ⟨i⁺⁺,...,n⟩
i,i⁺⁺ are ⁺⁺ing last-before,first-after
of ⟨1,...,i⟩, ⟨i⁺⁺,...,n,n⁺⁺⟩
Those are all-but-one of the splits
of ⟨1,...,n,n⁺⁺⟩
There is also ⟨1,...,n⟩, ⟨n⁺⁺⟩
n,n⁺⁺ are ⁺⁺ing last-before,first-after
for that last split.
Therefore,
each split of ⟨1,...,n,n⁺⁺⟩ has
⁺⁺ing last-before,first-after
because
each split of ⟨1,...,n⟩ has
⁺⁺ing last-before,first-after.
⟨1,...,n,n⁺⁺⟩ is ⁺⁺ing 1x1 2-ended
because
⟨1,...,n⟩ is ⁺⁺ing 1x1 2-ended
THEREFORE,
each n ∈ ⟨1,...⟩ is non-final and
each ⟨1,...,n⟩, ⟨n⁺⁺,...⟩ is
⁺⁺ing 1x1 2-ended,1-ended
and
{core} = ∅
> Same with endsegments.
> All infinite endsegments have
> one and the same infinite core
> because
> they never acquire new elements.
They all have
one and the same _empty_ core
because
they never acquire fourth ends.
Back to sci.logic | Previous | Next — Previous in thread | Next in thread | Find similar
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-25 13:32 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-25 13:18 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-25 17:54 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 04:50 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-05-26 13:58 +0200
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 06:05 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 12:10 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 10:57 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-26 12:01 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:56 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 15:52 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:58 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-28 05:11 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-28 07:04 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-28 18:47 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-29 11:15 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 14:36 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:47 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 16:25 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-27 13:44 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-28 05:37 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-28 07:00 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-29 16:08 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-30 06:45 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-30 09:19 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-31 07:41 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-30 18:18 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-31 07:45 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-31 15:00 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-01 12:00 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-01 16:13 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-02 05:40 -0700
Re: Some results about unit fractions Jeff Barnett <jbb@notatt.com> - 2023-06-02 14:05 -0600
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 07:01 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-03 09:56 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 11:03 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-03 17:33 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-03 16:29 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-03 20:32 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:32 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 10:51 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 11:07 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:08 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 10:18 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:46 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 11:09 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 11:32 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 11:47 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 11:58 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 12:16 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-04 11:12 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 11:35 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-04 13:36 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-05 07:01 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-05 07:44 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 07:47 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 07:55 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-05 09:01 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 07:50 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 08:05 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:20 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-06 10:04 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:21 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:02 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-03 05:10 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 07:01 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-04 20:39 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-05 07:12 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-05 07:41 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 07:46 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 07:55 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:06 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 13:18 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 13:33 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-06 13:52 -0400
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-05 13:25 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:04 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-05 15:49 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:11 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-07 12:25 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-08 03:46 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-08 04:13 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-08 05:51 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-08 07:15 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-08 09:34 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-08 16:48 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-08 16:50 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-09 03:43 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-08 14:48 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-08 13:50 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-08 18:39 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-09 03:48 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-09 12:26 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-09 13:36 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-09 18:25 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-10 05:05 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-10 15:10 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-11 06:47 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-11 10:24 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-11 11:37 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-11 11:53 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-11 13:24 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-11 15:21 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-11 15:38 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-12 11:52 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-12 11:52 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-12 13:16 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-12 14:03 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-12 14:45 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-13 07:20 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-13 07:35 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-13 14:02 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-13 14:50 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-13 20:12 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-12 14:48 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-11 15:11 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-11 13:28 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-11 17:12 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-12 11:52 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-13 13:25 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-13 14:07 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-13 20:11 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-14 04:55 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-14 05:58 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-14 11:30 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-14 12:55 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-15 04:53 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-15 13:22 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-15 05:40 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:17 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-16 06:32 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-16 16:27 +0200
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-15 06:01 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-15 09:26 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-15 09:52 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-15 10:59 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-15 12:40 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-16 06:07 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-16 06:22 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-16 06:41 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-16 08:54 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-16 12:37 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-17 05:54 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-16 08:53 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-15 17:06 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-16 06:18 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-16 06:53 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-16 06:25 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-14 08:03 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-14 10:58 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-14 18:30 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-15 04:51 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-09 14:18 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-03 08:09 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 11:00 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-03 07:47 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 10:57 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 15:31 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:51 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 17:45 -0400
csiph-web