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Re: Some results about unit fractions

Newsgroups sci.logic
Date 2023-04-25 11:26 -0700
References (15 earlier) <a379c92a-d667-47d2-b907-179e558f206cn@googlegroups.com> <0fc6bf2b-72e9-4174-9965-613540215d00n@googlegroups.com> <cbf377f0-d7a4-42a3-9a53-a91bb4f14cfdn@googlegroups.com> <46855194-6b79-42a7-853c-327f5125e468n@googlegroups.com> <d2d13be9-3f8f-de2e-df9e-7601cfa165fa@att.net>
Message-ID <a4a69ca6-9d4c-4962-b5d9-7debcba88cedn@googlegroups.com> (permalink)
Subject Re: Some results about unit fractions
From WM <askasker48@gmail.com>

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Jim Burns schrieb am Montag, 24. April 2023 um 21:51:35 UTC+2:
> On 4/24/2023 2:56 PM, WM wrote: 

> > NUF(x) is zero at x = 0 and 
> > ℵ for every eps that can be chosen. 
> 
> NUF(x) is zero at x = 0 and
> ℵ₀ for every eps > 0 which is 
> the between-point of a split of ℚ 

You  can split only in the visible range because dark numbers have no discernible order. But they have an existing order. All unit fractions are separated by finite positive intervals. Therefore NUF(x) grows in single steps of units.

> The minimum number of unit fractions in 
> any neighborhood of zero 
> is ℵ₀ 

Yes. (0, eps) contains ℵ unit fractions.
 
> x > 0 ⟹ NUF(x) = ℵ₀

Not every x. It is wrong by
∀n ∈ ℕ: 1/n - 1/(n+1) = 1/(n(n+1)) > 0

Can't you read this line? Can't you understand its meaning?

Regards, WM

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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 WM <askasker48@gmail.com> - 2023-04-24 07:35 -0700
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-24 07:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-24 12:59 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-24 12:15 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-24 17:00 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-25 11:44 -0700
                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 JVR <jrennenkampff@googlemail.com> - 2023-04-24 07:57 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-04-24 09:37 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-24 11:56 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-24 15:51 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-25 11:26 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-25 17:16 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-26 04:47 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-26 04:50 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-26 17:36 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-27 06:31 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-27 08:11 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-27 12:21 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-27 14:14 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-27 12:36 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-27 17:59 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-28 04:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-28 15:11 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-29 03:30 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-29 17:25 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-30 05:46 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-29 23:41 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-30 05:51 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-01 15:05 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 05:14 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-01 15:06 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-01 12:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 05:08 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 05:06 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-02 12:22 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-02 09:49 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-02 14:49 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-03 03:20 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-03 13:38 -0400
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-03 19:43 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-04 05:16 -0700
                Re: Some results about unit fractions Jeff Barnett <jbb@notatt.com> - 2023-05-04 09:43 -0600
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-05 05:01 -0700
                Re: Some results about unit fractions Jeff Barnett <jbb@notatt.com> - 2023-05-06 00:15 -0600
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 07:21 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-04 15:24 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-05 05:01 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-05 13:01 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 07:22 -0700
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-05-06 07:56 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 13:22 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-06 13:02 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-06 13:18 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-06 23:41 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-27 17:03 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-28 04:53 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-28 07:22 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-28 08:39 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-04-24 13:44 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-25 10:51 -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

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