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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 2023-04-13 18:50 -0400
Organization A noiseless patient Spider
Message-ID <f7cdde30-d7d4-bf05-7840-68bd2e5c7aa6@att.net> (permalink)
References <5ecf2c26-d125-4ba6-ac58-55acd906e111n@googlegroups.com> <748daac7-4018-0b0b-d1d1-4d726d7c6ce0@att.net> <cfd17ed5-8981-4407-b49f-d3e04a57b41bn@googlegroups.com> <7b56caba-1e3e-1d8b-50bf-71cbf71afb77@att.net> <f9778e88-46b2-4dbe-b332-8776e86b5ed7n@googlegroups.com>

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On 4/13/2023 12:48 PM, WM wrote:
> Jim Burns schrieb am Donnerstag,
> 13. April 2023 um 00:32:21 UTC+2:

>> ∀n ∈ ℕ:
>> If x > 1/n
>> then x > 1/n > 1/(n+1) 
>>
>> If NUF(x) > 0
>> then NUF(x) > 1
>>
>> NUF(x) ≠ 1
> 
> This is true for all definable x.

It is true for all x which are
either x ≥ 1/n > 1/n⁺⁺ for some 1/n
or not x ≥ 1/n > 1/n⁺⁺ for some 1/n

> But
> ∀n ∈ ℕ:
> 1/n - 1/(n+1) = 1/(n(n+1)) > 0
> shows that never two unit fractions sit
> at the same place.
> Therefore they cannot be
> included in NUF(x) simultaneously.
> A first one must start.

No.
"A first one must start" _in a finite list_
However,
the unit fractions are not a finite list.

Each unit fraction u,
whether u is dark or visible,
is preceded by another unit fraction v
1/v = 1/u + 1
0 < v < u

Each unit fraction u,
whether u is dark or visible,
is _not first_

A finite list is 1×1 2-ended.
The unit fractions are 1×1 1-ended.
They are not a finite list.

> Therefore there are undefinable x.

The description is of a unit fraction,
whether visible or dark.

The not-first-possibly-false claims
augmenting the description refer to
a unit fraction, whether visible or dark.

Let's suppose being-undefinable
to be relevant to these facts equally true
of the definable and the undefinable.

It seems as though you've stopped
_just before_ you let us in on the
secret of _how it's relevant_

How is it relevant?

> It is simple to see:
> Every eps that you can choose
> contains almost all unit fractions.

That does not have the consequences
to which you feel entitled.

All 1×1 1-ended sets are the same size
(same cardinality, can match elements).

Split the unit fractions at eps > 0
m := ⌈1/eps⌉

⟨ ... 1/m ⟩  ⟨ 1/m⁻⁻ ... 1/1 ⟩

⟨ ... 1/m ⟩ is 1×1 1-ended.
It has the same cardinality as
1×1 1-ended UF = ⟨ ... 1/1 ⟩

----
Consider the two splits
⟨ ... 1/m⁺⁺ 1/m ⟩  ⟨ 1/m⁻⁻ ... 1/1 ⟩
⟨ ... 1/m⁺⁺ ⟩  ⟨ 1/m 1/m⁻⁻ ... 1/1 ⟩
1×1 1-ended,  1×1 2-ended
1×1 1-ended,  1×1 2-ended

|⟨ ... 1/m ⟩|  =
|⟨ ... 1/m⁺⁺ ⟩|

|⟨ 1/m⁻⁻ ... 1/1 ⟩|  <
|⟨ 1/m ... 1/1 ⟩|

Infinity is not
a reallyreallyreallyreallyreallyreally large
natural number.

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Thread

Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 07:06 -0700
  Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-12 07:42 -0700
    Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 07:49 -0700
      Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:26 -0700
      Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:27 -0700
      Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-12 23:55 -0700
        Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-13 09:44 -0700
  Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-12 16:11 +0100
    Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 09:37 -0700
      Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 09:56 -0700
      Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 09:58 -0700
        Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 14:22 -0700
      Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-12 20:43 +0100
        Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 14:20 -0700
          Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-13 01:44 +0100
            Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-13 09:44 -0700
              Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-13 10:47 -0700
              Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-14 00:00 +0100
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-13 18:04 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-14 21:27 +0100
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-14 19:25 -0700
                Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-15 00:12 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-15 11:19 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-16 01:29 +0100
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-15 18:50 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-16 05:41 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-16 22:30 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-17 12:02 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-18 02:50 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-18 05:05 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-21 03:39 +0100
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-21 03:41 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-21 13:20 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-21 06:42 -0700
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-21 08:34 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-21 12:52 -0700
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-21 13:08 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-22 06:45 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-04-22 06:48 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-21 17:12 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-16 06:02 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-16 07:28 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-16 16:50 +0100
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-16 09:15 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-16 17:26 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 07:38 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-15 01:17 +0100
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-14 19:30 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-15 11:31 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-16 01:28 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-16 05:29 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-16 22:30 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-17 12:23 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-17 13:17 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-18 02:49 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-18 04:58 -0700
                Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-18 05:06 -0700
                Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-18 05:07 -0700
                Re: Some results about unit fractions Mostowski Collapse <bursejan@gmail.com> - 2023-04-18 06:54 -0700
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-19 05:17 -0700
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-18 04:32 -0700
                Re: Some results about POLLUTING RETARDED CUNTS Julio Di Egidio <julio@diegidio.name> - 2023-04-18 04:48 -0700
        Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 14:24 -0700
          Re: Some results about unit fractions Python <python@invalid.org> - 2023-04-12 23:44 +0200
            Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-13 10:01 -0700
  Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:20 -0700
  Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:30 -0700
    Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 09:39 -0700
      Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 09:57 -0700
  Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-12 15:55 -0400
    Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 14:17 -0700
      Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-12 18:32 -0400
        Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-13 09:48 -0700
          Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-13 18:50 -0400
            Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 07:15 -0700
              Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 07:27 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 07:39 -0700
                Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 08:36 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 09:38 -0700
                Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 09:45 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 09:56 -0700
                Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 10:08 -0700

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