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	2023-04-21 17:12 -0400
Organization	A noiseless patient Spider
Message-ID	<4f345f96-938b-663c-2d74-d4bda0e6c6f2@att.net> (permalink)
References	(16 earlier) <e19a9620-fffc-4d0f-b21e-e54095334867n@googlegroups.com> <87mt32ufg2.fsf@bsb.me.uk> <9709a020-9a89-4c59-81eb-22aa1ebdc2e7n@googlegroups.com> <609371f4-a304-4876-a2b2-1b0c48e3d29cn@googlegroups.com> <3adbfe45-281d-48a8-81ca-6d4da0f2b868n@googlegroups.com>

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On 4/21/2023 3:52 PM, WM wrote:

> It is impossible to have
> NUF(x) = ℵ for all x > 0
> because
> NUF(x) > 1 for all x > 0
> is excluded by
> ∀n ∈ ℕ: 1/n - 1/(n+1) = 1/(n(n+1)) > 0.

∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

∀n ∈ ℕ: 1/n > 1/(n+1)

∀n ∈ ℕ:
x > 1/n  ⟹
x > 1/n > 1/(n+1)

NUF(x) > 0  ⟹
NUF(x) > 1

> What don't you understand?

Define ℝ such that
a jumping function is not all-continuous.

Define
f(x) := [NUF(x) > 0]

f() jumps,
thus f() is not all-continuous.

If
x > β  ∧  NUF(x) = 0
then
f() is continuous at β

If
y < β  ∧  NUF(x) > 0
then
f() is continuous at β

f() jumps,
thus f() is not all-continuous
thus a point β exists such that
x > β  ⟹  NUF(x) > 0
y < β  ⟹  NUF(x) = 0


If
NUF(2β) > 0
then
2β > 1/m₂ᵦ
(2β)/4 > (1/m₂ᵦ)/4  [!]
β/2 > 1/(4m₂ᵦ)
NUF(β/2) > 0

lemma.
If NUF(2β) > 0
then NUF(β/2) > 0


If β > 0
then
2β > β
NUF(2β) > 0
(and by lemma)
NUF(β/2) > 0

However,
if β > 0
then
β/2 < β
NUF(β/2) = 0
Contradiction.

Therefore, ¬(β > 0)

x > 0 ≥ β  ⟹  NUF(x) > 0

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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 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 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
            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

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