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Re: Some results about unit fractions

Newsgroups sci.logic
Date 2023-06-04 11:09 -0700
References (19 earlier) <97e48768-f2f0-1b05-884a-3c3d635d0cee@att.net> <a19a0048-d578-4a40-aaaf-3152604be791n@googlegroups.com> <544d1887-d13b-4ae0-b268-6c16234cec11n@googlegroups.com> <ebd936d0-17c3-4b56-8899-eb1a44965c38n@googlegroups.com> <4e29295e-1108-48e0-a388-5c126bea3986n@googlegroups.com>
Message-ID <82db1ca4-debc-4ad7-a5b9-a00e9322f6een@googlegroups.com> (permalink)
Subject Re: Some results about unit fractions
From Fritz Feldhase <franz.fritschee.ff@gmail.com>

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On Sunday, June 4, 2023 at 7:46:43 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 4. Juni 2023 um 19:18:04 UTC+2: 
> >
> > Not even ONE unit fraction fits between 0 and each and every x > 0.

~Eu e U: Ax > 0: u < x.

> So there are x with no unit fractions between themselves and 0. 

**sigh**

No, there aren't such x.

Hint: ~Eu e U: Ax > 0: u < x does NOT IMPLY Ex > 0: ~Eu e U: u < x.

See: https://en.wikipedia.org/wiki/Quantifier_shift 

> Therefore your theorem ∀x ∈ (0, 1]: NUF(x) = ℵo is wrong.

Ex falso quodlibet.

> NUF(D/2) < ℵo. 

Nope. If D e IR+, then D/2 e IR+ too. Hence NUF(D/2) = ℵo.

> NUF(x) is a fixed function, independent of what you consider. For every x there is a value. And there are x with no unit fractions between themselves and 0. 

No, there aren't such x e (0, 1].

Hint: If x e (0, 1], then 1/(ceil(1/x) + 1) is a unit fraction between 0 and x. Also gibt es mindestens einen Stammbruch zwischen 0 und x.

Wie DUMM kann man eigentlich sein, Mückenheim?

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Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-24 13:32 -0400
  Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-25 06:00 -0700
    Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-25 13:32 -0400
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-25 13:18 -0700
        Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-25 17:54 -0400
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 04:50 -0700
            Re: Some results about unit fractions Python <python@invalid.org> - 2023-05-26 13:58 +0200
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 06:05 -0700
            Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 12:10 -0400
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 10:57 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-26 12:01 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:56 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 15:52 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:58 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-28 05:11 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-28 07:04 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-28 18:47 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-29 11:15 -0700
            Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 14:36 -0400
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:47 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 16:25 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-27 13:44 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-28 05:37 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-28 07:00 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-29 16:08 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-30 06:45 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-30 09:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-31 07:41 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-30 18:18 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-31 07:45 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-31 15:00 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-01 12:00 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-01 16:13 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-02 05:40 -0700
                Re: Some results about unit fractions Jeff Barnett <jbb@notatt.com> - 2023-06-02 14:05 -0600
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 07:01 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-03 09:56 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 11:03 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-03 17:33 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-03 16:29 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-03 20:32 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:32 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 10:51 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 11:07 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:08 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 10:18 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:46 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 11:09 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 11:32 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 11:47 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-04 11:58 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 12:16 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-04 11:12 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 11:35 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-04 13:36 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-05 07:01 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-05 07:44 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 07:47 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 07:55 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-05 09:01 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 07:50 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 08:05 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:20 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-06 10:04 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:21 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-04 10:02 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-03 05:10 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 07:01 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-04 20:39 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-05 07:12 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-05 07:41 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 07:46 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 07:55 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-06 13:18 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 13:33 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-06 13:52 -0400
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-05 13:25 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-06 11:04 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-05 15:49 -0400
                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 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 08:53 -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 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
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-03 08:09 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 11:00 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-03 07:47 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-03 10:57 -0700
            Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 15:31 -0400
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 12:51 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-26 17:45 -0400

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