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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Newsgroups | sci.logic |
| Subject | Re: Some results about unit fractions |
| Date | 2023-06-17 11:56 -0400 |
| Organization | A noiseless patient Spider |
| Message-ID | <7332a9ff-5d3f-bbe8-99f1-a7763c8a4cee@att.net> (permalink) |
| References | (12 earlier) <c14f72f7-21bd-4e1e-83c2-47ccff361d54n@googlegroups.com> <a4b94e13-7d86-4e25-a158-cfeaa15ec4aen@googlegroups.com> <f8313e7d-292b-48d5-bb1c-ad6212c42e9dn@googlegroups.com> <a968c1f2-41f5-0e5b-7f37-c3f6179391f2@att.net> <7c5b1af0-08cd-4289-be3f-0bc57e199e30n@googlegroups.com> |
On 6/17/2023 8:54 AM, WM wrote:
> Jim Burns schrieb am Freitag,
> 16. Juni 2023 um 18:37:25 UTC+2:
>> On 6/16/2023 9:41 AM, WM wrote:
>>> Fritz Feldhase schrieb am Freitag,
>>> 16. Juni 2023 um 15:22:02 UTC+2:
>>>> Die Menge der/aller Endsegmente ist
>>>> unendlich und jedes Endsegment ist selbst
>>>> eine unendliche Menge.
>
>>> That is a self-contradicting statement.
>>
>> Those are true statements
>
> Every infinite endsegment has
> an infinite set in common with
> every predecessor and
> every infinite successor.
No.
⟨finite⟩₀ ⁺⁺ing 1×1 2-ended from 0
Define ℕ := ⋃⟨finite⟩₀
For each j ∈ ℕ := ⋃⟨finite⟩₀
⟨finite⟩₀ exists
such that
j ∈ ⟨finite⟩₀
⟨semifinite⟩ⱼ₊₊ ⁺⁺ing 1×1 1-ended from j⁺⁺
¬(⟨semifinite⟩ⱼ₊₊ = ∅)
ℕ = ⟨semi-finite⟩₀
...because each j ∈ ℕ is non-final,
because each ⟨finite⟩₀ is non-final.
For each j ∈ ℕ := ⋃⟨finite⟩₀
a split ⟨finite⟩₀∥⟨semifinite⟩ⱼ₊₊ exists
such that
j ∈ ⟨finite⟩₀
¬(j ∈ ⟨semifinite⟩ⱼ₊₊)
¬(⟨semifinite⟩ⱼ₊₊ = ∅)
⟨semifinite⟩ⱼ₊₊ ⊇ {common}
¬(j ∈ {common})
For each j ∈ ℕ := ⋃⟨finite⟩₀
¬(j ∈ {common})
{common} = ∅
The set in common with
every predecessor and
every infinite successor
has no elements and
is not infinite.
> The set of indices ends at
> the minimum common infinite set.
The minimum common infinite set
is not infinite and
not-exists.
> An ending set is not infinite.
A description can exist of
something which not-exists.
An ending set not-exists.
>>> As long as the first set is finite,
>>> 1, 2, 3, ..., n | n, n+1, n+2, ...,
>>> the second set is infinite and
>>> larger than the first.
>
>>> The infinity of the endsegments prevents
>>> the infinity of their cardinal number.
>>
>> No.
>
> Yes.
No.
>> Each j ∈ ⟨0...⟩ splits ℕ into
>> ⟨0...j⟩∥⟨j⁺⁺...⟩
>> and
> each ⟨0...j⟩ is
non-final.
Also,
each ⟨j⁺⁺…⟩ is non-final.
⟨⟨1…⟩...⟩ is semifinite, not finite.
> finite. There is no exception.
> ∀j ∈ ⟨0...j⟩: |ℕ \ {1, 2, 3, ..., j}| = ℵo
Better: ∀j ∈ ⟨0...j′⟩:
{1,2,3,...,j} = ⟨finite⟩₁
ℕ⁺ := ⋃⟨finite⟩₁
ℕ⁺ = ⟨semifinite⟩₁
ℕ⁺\{1,2,3,...,j} = ⟨semifinite⟩ⱼ₊₊
¬(j ∈ ℕ⁺\{1,2,3,...,j})
¬(j ∈ {common})
{common} = ∅
>> A step from finite to infinite
>> not-exists,
>> because
>> anything which is a step from finite
>> is not infinite.
>
> That shows that
> all stepable sets are finite.
Each ⁺⁺ing 1×1 2-ended from 0
is finite.
The union of all (finite)
⁺⁺ing 1×1 2-endeds from 0 is
⁺⁺ing 1×1 1-ended from 0 and
is not finite
...because
each ⟨finite⟩₀ is non-final.
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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 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-18 02:09 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-18 07:15 -0700
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 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 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 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 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 Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-17 08:10 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-17 17:17 +0200
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-17 08:30 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-17 17:33 +0200
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
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