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| Date | 2023-07-01 17:07 -0700 |
| References | (16 earlier) <c8698cf3-2f57-e92b-60d8-89b3ceab1188@att.net> <9b94bfca-626b-423e-89b1-7bccaa961971n@googlegroups.com> <31b7ebdf-8279-701b-603e-22f55f29a22d@att.net> <ea023641-d45f-4262-8038-00bfa479fa9cn@googlegroups.com> <5cf34130-a303-fc0b-4798-1b05bd35fd6f@att.net> |
| Message-ID | <16bc3298-eb1e-4a1c-a693-67bc540d4d73n@googlegroups.com> (permalink) |
| Subject | Re: Some results about unit fractions |
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
On Sunday, July 2, 2023 at 12:49:57 AM UTC+2, Jim Burns wrote:
> On 7/1/2023 5:44 PM, Fritz Feldhase wrote:
> > On Saturday, July 1, 2023
> > at 11:30:53 PM UTC+2, Jim Burns wrote:
> > >
> > > Each cell is visible.
> > > Each swap is visible.
> > > Each swap is between visible cells.
> > >
> > How do/did you define visible?
> >
> Essentially, "visible" == "finitely accessible"
Errr...
Well, for each and every natural number n: The set {m e IN : m <= n} (aka {1, ..., n}) is finite,
Hence I'd say that each and every natural number is "finitely accessible", ok? [Finitely many steps CAN BE perfomed "in principle". At least Chuck Norris could do it!]
MOREOVER, in the context of set theory, where (usually) "the natural numbers" are defined due to von Neumann, we have An e IN: n = {m e IN : m < n}.
You see:
0 = { }
1 = {0}
2 = {0, 1}
3 = {0, 1, 2
:
n = {0, 1, 2, ..., n-1} (with n e IN, n > 3)
:
... which AGAIN seems to imply that each and every natural number is "finitely accessible". Ok?
> There are many ways to describe "finite".
Indeed! Actually a quite interesting topic. (Really!)
There are quite surprising ways to achieve this!
> I have been leaning heavily on
> | (Paul Stäckel) S can be given a total
> | ordering which is well-ordered both forwards
> | and backwards. That is, every non-empty
> | subset of S has both a least and a greatest
> | element in the subset.
> |
> https://en.wikipedia.org/wiki/Finite_set
Seems intuitively reasonable.
> Each natural k is visible: k ends a sequence ⟨0…k⟩
Well... In this case (see comments above) each and every natural number is "visible", I'd say.
So the notion is "redundant" and can (or should) be avoided. (See: https://en.wikipedia.org/wiki/Occam%27s_razor)
Or would you consider claims like
For all natural numbers n _with n >= 0_, bla bla bla
sensible?
> > I'm quite sure that we can do
> > math/set theory without that notion.
> >
> I'm quite sure of the same.
See?!
> Even better: I have done math/set theory
> without "visible" for many years.
Hear, hear! :-)
> It's WM's "visible", more or less.
I already told you: "WM's psychotic babbling is of no interest here."
At least for me.
To be continued [or not]. Stay tuned!
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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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