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Re: Some results about unit fractions

From Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups sci.logic
Subject Re: Some results about unit fractions
Date 2023-04-14 00:00 +0100
Organization A noiseless patient Spider
Message-ID <87a5zbwfoy.fsf@bsb.me.uk> (permalink)
References (2 earlier) <879dfd49-219a-4503-a354-8b2e2d7b9f64n@googlegroups.com> <87ile0vqcz.fsf@bsb.me.uk> <f4b02250-fb38-4173-9c8e-e49f76c4b9f8n@googlegroups.com> <871qkovcf6.fsf@bsb.me.uk> <74e0e50e-adfe-4ebd-9d56-a433afab0435n@googlegroups.com>

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WM <askasker48@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des 
Unendlichen" at Hochschule Augsburg.) 

> Ben Bacarisse schrieb am Donnerstag, 13. April 2023 um 02:44:18 UTC+2:
>> WM <askas...@gmail.com> writes: 
>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des 
>> Unendlichen" at Hochschule Augsburg.) 
>> 
>> > Ben Bacarisse schrieb am Mittwoch, 12. April 2023 um 21:43:13 UTC+2: 
>> >> WM <askas...@gmail.com> writes: 
>> >> 
>> >> > Ben Bacarisse schrieb am Mittwoch, 12. April 2023 um 17:11:27 UTC+2: 
>> >> >> WM <askas...@gmail.com> writes: 
>> >> >> > NUF(x), the Number of Unit Fractions between 0 and x, increases in (0, 
>> >> >> > 1] from 0 to ℵo. 
>> >> >> No. NUF(x) is constant on (0,1]. 
>> >> > 
>> >> > Wrong. 
>> >> NUF(x) = ℵo for x > 0. NUF(x) has the same value over the whole 
>> >> interval (0,1]. It's hard to see anything you can be more obviously 
>> >> wrong about. 
>> > 
>> > Matheology may say so.
>> What's that? Mathematics says that NUF(x) = ℵo for x > 0.
>
> Yes, for every definable x, usually called eps, this is true.

Speculation about something in (0,1] for which NUF(x) =/= ℵo can be
ruled out because we know what kind of thing in is (0,1] and not one of
those things has a finite set of unit fractions between 0 and it.  We
know this by proving it.

If you were a mathematician, you would formally characterise everything
in (0,1] and prove ∃x in (0,1] with NUF(e) =/= ℵ₀.  I don't think you
can even do the first part of that.  You certainly can't do the second
because it's not true.

> But mathematics says also that all unit fractions sit at different
> places: ∀n ∈ ℕ: 1/n - 1/(n+1) = 1/(n(n+1)) > 0

Yes.

> and can appear in NUF only one by one.

No.  Infinitely many of them are in (0,x) for every x > 0.  They don't
appear or disappear, they don't come or go.  You have invented a
metaphorical view of them "appearing" which has confused you and which,
sadly, you will probably use to try to trick your students.

> Therefore there is only one way out of the apparent contradiction:
> Dark numbers.

We can define the basic properties possessed of every thing in (0,1]
(see the axioms of the reals).  Nothing else is in (0,1].  From those
basic properties we can prove x in (0,1] implies NUF(x) = ℵo.  That's
how mathematics works.  There isn't anything else in (0,1].  No unit
fractions appear anywhere.  Infinite unit fractions either are or are
not in (0,x).

>> The step change happens in WMaths too. UF(x) (the set of unit fractions 
>> between 0 and x) is empty when x = 0 and not finite for all x > 0. How 
>> is this possible when "never more than one unit fractions is added at a 
>> point"? 
>
> It is not possible.

So in WMaths ∃x in (0,1] and n in N with |UF(x)| = n.  Amazing.  Can you
show me such an x or is too dark to see?  Or are you relying on a
failure of logic in WMaths where ~∃x in S: P(x) does not imply ∀x in S:
P(x)?  You've had to rely on that nonsense in the past.

-- 
Ben.

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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 WM <askasker48@gmail.com> - 2023-04-22 06:49 -0700
                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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