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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 2023-04-16 01:28 +0100
Organization A noiseless patient Spider
Message-ID <87sfd0u0vc.fsf@bsb.me.uk> (permalink)
References (6 earlier) <74e0e50e-adfe-4ebd-9d56-a433afab0435n@googlegroups.com> <87a5zbwfoy.fsf@bsb.me.uk> <6b5e7753-cf00-468a-9fbc-bba1261034den@googlegroups.com> <87h6tiuhhf.fsf@bsb.me.uk> <a1758f59-1323-4ab6-80fb-36034bc6e6fdn@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 Samstag, 15. April 2023 um 02:17:05 UTC+2:
>> WM <askas...@gmail.com> writes:

...  Oh, I see you cut your mistake.  It would show some courage
had you left it and agreed that it was a mistake.  It's OK to be wrong
(I am often wrong -- check my post just yesterday) but it's shameful to
be intellectually dishonest.

For the record, your argument started with a false premise:

You: "If ℵ₀ unit fractions are smaller than all x in (0,1], ..."

Me: "But no unit fractions are smaller than all x in (0,1].  The only real
that is smaller than all x in (0,1] is zero and, as you know, that is
not a unit fraction."

You went on to repeat the error:

You: "..  then then you cannot distinguish them. If two of them, p and
     q, are distinct, then you have p > q > 0 and p is not in the set of
     ℵ₀ unit fractions smaller than every x > 0."

Me: "No unit fraction is smaller than every x > 0."


>> > I can show you mathematics if you were unable to see it yet: 
>> > ∀n ∈ ℕ: 1/n - 1/(n+1) = 1/(n(n+1)) > 0 
>> > All unit fractions have distances. They come as singles.
>> But, no, it seems you can't show such an x.
>
> Of course not. All unit fractions which start the game are dark

More dishonesty.  This part was about WMaths.  You cut from this reply
my asking:

Me: "So in WMaths ∃x in (0,1] and n in N with |UF(x)| = n."

To which you replied: "Yes" -- an extraordinary claim.  That
extraordinary claim was the context of my saying that you can't show
such an x.

So does WMaths now have dark numbers or have you abandoned all pretence
of intellectual honesty, switching away from WMaths when the questions
get hard?

To summarise (unless you want to retract C), these are the three great
(as yet unproven) theorems WMaths:

A.  There are sets P and E such that E ∈ P and P \ {E} = P.

B.  There is a bounded monotonic sequence of rationals that does not
    converge to a limit in R.

C.  ∃x in (0,1] with |UF(x)| ∈ N.  (NF(x) = {1/n < x with n ∈ N}.)

And I see no word of thanks for my helping to find these.  I can't help
with the proofs, of course, because you told me that you can't yet
define set membership, equality and difference in WMaths.  Apparently
the definitions in your textbook are simplifications for beginners.

-- 
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 JVR <jrennenkampff@googlemail.com> - 2023-04-22 15:30 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-23 06:31 -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 WM <askasker48@gmail.com> - 2023-04-22 11:56 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-22 13:29 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-22 16:36 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-23 06:30 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-23 15:23 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-23 13:43 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-24 00:35 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-22 15:03 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-22 15:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-22 15:07 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-23 06:57 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-04-23 14:45 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-24 07:25 -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 Jim Burns <james.g.burns@att.net> - 2023-04-22 15:24 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-23 06:22 -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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