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Re: Some results about unit fractions

Newsgroups sci.logic
Date 2023-05-19 11:36 -0700
References (14 earlier) <0985129a-230e-68c3-0619-c458e0be6025@att.net> <c13c3446-60c7-4a00-adc1-2a21e68efee4n@googlegroups.com> <844bbda2-a050-6624-1efa-f3fe8843ff2a@att.net> <6368303b-c51a-436c-83d4-616abdba7fa3n@googlegroups.com> <f5e2d1ef-af4a-ad95-2737-a7d2725d3297@att.net>
Message-ID <3b720ca7-7e41-46eb-b55a-1445ea695ca2n@googlegroups.com> (permalink)
Subject Re: Some results about unit fractions
From WM <askasker48@gmail.com>

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Jim Burns schrieb am Freitag, 19. Mai 2023 um 19:48:28 UTC+2:
> On 5/19/2023 8:40 AM, WM wrote: 
> > Jim Burns schrieb am Donnerstag, 
> > 18. Mai 2023 um 23:04:08 UTC+2:
> >> It seems to me that, for some things, 
> >> you and I agree that they exist. 
> >> 
> >> It's seems to me that, among these things, 
> >> there are ordered pairs ⟨x,y⟩, at least 
> >> one non-pair (for convenience, named 0), 
> >> and sets {x:P(x)} of a rather thin 
> >> set theory. 
> > 
> > No infinite set of pairs. 
> > No loss of Os.
> How does that work? 
> Does a 1×1 1-ended set of pairs 
> pop out of existence 

like Bob?

> when someone calls it "infinite"? 

No, it pops out of sight when larger than potential infinity. Then elements can no longer be attached to each other.
> 
> I'll make some claims and 
> wait for you to tell me when you see 
> things popping out of existence. 
> 
> If x and y exist, 
> ordered pair ⟨x,y⟩ exists. 
> 
> ⟨x,y⟩ = ⟨u,v⟩ 
> :⇔ 
> x = u and y = v 

Only if they are not dark. Most elements of infinite sets are dark:
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo = larger than the collection of definable numbers.

> 0 exists. 

Yes.
> 
> 0 is not an ordered pair. 
> 
> u ∈ {z| ∃x:z=⟨x,⟨x,0⟩⟩ } 
> :⇔ 
> ∃x:u=⟨x,⟨x,0⟩⟩ 

Yes. That mechanism yields a potentially infinite collection.
> 
> Has anything 
> popped out of existence yet? 

No.
> 
> I have not called anything "infinite" yet, 

There is nothing infinite yet. It is not bounded however. Therefore it is called potentially infinite.

> so maybe nothing will. 
> 
> 
> {y| ∃x:y=⟨x,⟨x,0⟩⟩ } is 
> a _construction_ of the successor '⁺⁺' 
> operation. 
> 
> I'm not claiming that I've _built_ it. 
> 
> I claim that it _exists_ and that 
> it has the properties we want for '⁺⁺' 

It exists and has properties. One of them is that it never covers an actually infinite set.
> 
> Define set '⁺⁺' 
> '⁺⁺' := {y| ∃x:y=⟨x,⟨x,0⟩⟩ } 

Better call it a collection.
> 
> Define 
> x⁺⁺ = y 
> :⇔ 
> ⟨x,y⟩ ∈ '⁺⁺' 
> 
> Successor i⁺⁺ is non-doppelgänger, 
> non-0, non-final, 
> which is what we want i⁺⁺ to be.
> > ..., why should it help to agree on 
> > ⟨x,y⟩, 0, {x:P(x)} ?
> If it's so unimportant, 
> why disagree?

I don't disagree that potentially infinite collections do exist. Examples are definable natnumbers, definable fractions, definable terms of the sequence
0.1
0.01
0.001
...

Regards, WM

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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 WM <askasker48@gmail.com> - 2023-05-07 07:17 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-07 23:50 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 06:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:04 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-08 14:59 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 13:59 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-08 21:02 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 05:45 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-09 11:46 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 13:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-10 08:47 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-10 06:07 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-10 13:58 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:10 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:13 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 10:19 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-08 15:32 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 13:13 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 14:02 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 13:57 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-08 13:54 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-08 14:24 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 05:49 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-09 12:41 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-09 14:03 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-09 17:09 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-10 06:05 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-10 09:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-10 13:05 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-10 13:21 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-11 04:37 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-11 09:51 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-12 05:31 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-11 14:00 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-12 05:31 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-12 15:37 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-13 06:22 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 14:30 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-13 11:41 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 23:24 -0400
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-05-14 02:20 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-14 14:04 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-14 14:44 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 03:29 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 05:59 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 10:15 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 13:49 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 17:14 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 08:03 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 09:33 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 11:11 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 12:08 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-18 08:39 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-18 12:23 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:33 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:41 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-18 12:47 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:53 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:59 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 13:02 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 10:24 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 13:50 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-15 17:16 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-13 15:44 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-14 14:09 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 19:41 -0400
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-13 23:41 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-14 14:11 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-14 18:17 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-14 16:16 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-14 20:48 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 03:28 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-15 10:08 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-15 13:46 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-15 18:59 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 07:31 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 09:32 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-16 11:08 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-16 12:01 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-17 05:44 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-17 08:17 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-17 05:53 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-17 14:48 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-18 12:20 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-18 12:52 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 05:43 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 08:56 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-18 17:02 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 05:40 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 08:51 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 09:54 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 10:42 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 11:26 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 12:09 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-19 13:47 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 11:36 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 12:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 12:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 12:50 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 13:16 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-20 09:36 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:39 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:43 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-19 20:36 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-20 09:20 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:38 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-20 09:42 -0700
                Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-20 23:40 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-21 01:56 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-21 02:00 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-20 17:55 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-22 06:51 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-22 07:02 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-22 10:05 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-22 10:19 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-22 11:01 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-22 11:56 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-22 12:30 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-22 13:27 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-23 10:56 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-23 11:13 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-24 07:44 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-23 14:45 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-24 07:33 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-05-24 17:46 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-25 05:56 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-05-26 02:11 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 04:44 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-05-27 01:39 +0100
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-05-26 23:51 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-27 10:19 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-27 10:58 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-27 13:22 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-25 06:41 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-05-26 02:00 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-26 04:44 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-05-27 01:47 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-27 10:14 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-27 10:59 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-27 13:26 -0700
                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 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> - 2023-05-26 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
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-05-18 17:57 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-05-19 05:29 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-19 08:43 -0700

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