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| Date | 2023-06-30 10:15 -0700 |
| References | (17 earlier) <87ttuv3uek.fsf@bsb.me.uk> <cab30405-2b70-4052-84da-6aa07f094bdcn@googlegroups.com> <878rc33y4n.fsf@bsb.me.uk> <5bf3786a-17a4-403b-94f8-de8343ecd263n@googlegroups.com> <87mt0h2bpu.fsf@bsb.me.uk> |
| Message-ID | <e4e49f8a-1973-4037-be68-ed3a4777883dn@googlegroups.com> (permalink) |
| Subject | Re: Some results about unit fractions |
| From | WM <askasker48@gmail.com> |
Ben Bacarisse schrieb am Freitag, 30. Juni 2023 um 17:48:02 UTC+2:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
> > Ben Bacarisse schrieb am Donnerstag, 29. Juni 2023 um 02:34:04 UTC+2:
> >> WM <askas...@gmail.com> writes:
> >
> >> > I did it. E(1), E(2), ..., { }. Have you overlooked it?
> >> No, that is not "an inclusion-monotonic sequence (M_n): M(n) ⊇ M(n+1)
> >> which have no element in common".
> >
> > It is inclusion-monotonic with no doubt.
> > The terms have no element in common.
> But it's not a sequence (M_n). Such things are functions from N. See
> any introductory textbook like, oh, I don't know... your own!
Such a sequence is potentially infinite. What remains between the definable terms and the limit is dark. Same with the endsegments.
These are the definable terms of the sequence:
∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀
This is the limit:
∩{E(k) : k ∈ ℕ} = { }
In between there is a decrease from ℵ₀ to empty by dark terms.
> >> If {} is in the sequence, what index
> >> is it at?
> >
> > For all definable terms, where we can give the index, we have
> > ∀k ∈ ℕ_def: |∩{E(1), E(2), ..., E(k)}| = ℵ₀.
> So what n in N has M_n = {}? None.
It is the limit, after all dark terms.
> It's not a sequence (M_n). Are you
> this dishonest when your students see you've made a mistake?
Try to understand the difference between the potentially infinite classical mathematics and actual infinity. Try at least to grasp that actually infinite endsegments cannot be actually infinitely many.
Regards, WM
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Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 01:34 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-20 08:34 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:09 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:18 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-21 07:17 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-21 16:52 +0200
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-22 05:48 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 13:20 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-22 00:51 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-22 05:58 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 01:05 +0100
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 17:17 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:26 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 09:01 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 01:59 +0100
Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-06-26 04:42 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 14:42 +0100
Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-06-26 15:22 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-27 01:14 +0200
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 08:12 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 07:59 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 08:53 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 09:52 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 02:05 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 08:05 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-29 01:34 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-29 05:31 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-29 16:37 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:18 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:21 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 13:52 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-29 19:15 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-30 14:27 +0100
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:03 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:06 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:09 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:15 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:21 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:26 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 02:05 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 09:04 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:56 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-30 16:47 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:15 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:20 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 02:13 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:59 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:34 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:55 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-07-02 19:10 +0200
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 13:01 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:27 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 14:14 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 11:49 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 20:30 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-01 10:26 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 16:18 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 17:37 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 12:55 -0400
Re: Some results about unit fractions Transfinity <transfinity01@gmail.com> - 2023-07-01 10:32 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 15:42 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:17 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 13:00 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 16:24 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:05 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:28 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 17:30 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:44 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 18:49 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 17:07 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-02 06:20 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 04:04 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:39 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:33 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:27 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 01:50 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:50 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:19 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 12:58 -0400
Re: Some results about unit fractions Transfinity <transfinity01@gmail.com> - 2023-07-01 11:16 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 15:16 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:14 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-02 18:44 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-03 06:31 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-03 11:32 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:46 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-04 19:12 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-04 16:25 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-04 22:14 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-05 18:13 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-06 12:45 -0400
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-03 09:50 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:51 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-04 13:35 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-03 10:07 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:53 -0700
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