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| Message-ID | <sZAwS4W-mGAVUndXZbpFKBdR4l4@jntp> (permalink) |
|---|---|
| Subject | Re: Question about unbounded infinite sets... |
| References | (5 earlier) <uqu2se$33rpu$3@i2pn2.org> <ES5dfcNfrhlcNPqO5VUV-PJGl34@jntp> <uqvhrd$36l0m$1@i2pn2.org> <NeuORAR9ug003aM2M7OHghS2yj0@jntp> <ur122u$38ebk$1@i2pn2.org> |
| Newsgroups | sci.math |
| Date | 2024-02-20 08:24 +0000 |
| Organization | Nemoweb |
| From | WM <wolfgang.mueckenheim@tha.de> |
Le 20/02/2024 à 03:17, Richard Damon a écrit :
> On 2/19/24 7:59 AM, WM wrote:
Measured by the number of points - there are always infinitely many
between two adjacent unit fractions.
>>>> If there is a set of real points with distances at the real axis,
>>>> then every point can be considered as the border between two subsets.
>>>> If it is impossible to reduce the left-hand subset to a finite
>>>> amount, then there is no point available dividing infinitely many
>>>> unit fractions. Then they sit at one point. That is impossible by ∀n
>>>> ∈ ℕ: 1/n - 1/(n+1) = d_n
>>>
>>> Why must the left side every become finite?
>>
>> If there are really existing real points, then each one can be used, in
>> principle, as the border.
>
> No, only the one ON the border would be the border, but for every one
> that you might want to think of as the border, there are more that are
> closer to the border.
That means they appear onlylater. That is potential infinity.
>
> Thus, there is NOT one (in the set) on the border, and thus there is no
> "first" (from the left) unit fraction, and thus NUF(x) isn't defined.
It is very well defined.
Further, if
∃^ℵ y ∈ {1/n : n ∈ ℕ} ∀x ∈ (0, 1]: 0 < y < x
is false, then there must be x > 0 which make it false, i.e., which have
fewer smaller unit fractions. Therefore
∀x ∈ (0, 1]: ∃^ℵ y ∈ {1/n : n ∈ ℕ}: 0 < y < x
cannot be true for all x > 0.
>
>>> I guess you agree that Achilles can't pass the Tortoise, or maybe only
>>> at some "dark" time that we can not see.
>>
>> Irrelevant for the present topic. But true that he overtakes in darkness.
>
> But he doesn't, he passes the Tortoise at a easily determined finite
> time (if we know the actual speeds).
Yes, the limit is well known, like the limit 0 of the unit fractions or
the limit ω of the natural numbers.
Regards, WM
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Why "not.first.false" Jim Burns <james.g.burns@att.net> - 2024-03-05 15:33 -0500
Re: Why "not.first.false" Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-05 19:42 -0800
Re: Why "not.first.false" Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-05 21:24 -0800
Re: Why "not.first.false" WM <wolfgang.mueckenheim@tha.de> - 2024-03-06 10:08 +0000
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Re: Why "not.first.false" Jim Burns <james.g.burns@att.net> - 2024-03-06 12:31 -0500
Re: Why "not.first.false" WM <wolfgang.mueckenheim@tha.de> - 2024-03-06 18:20 +0000
Re: Why "not.first.false" Jim Burns <james.g.burns@att.net> - 2024-03-06 14:30 -0500
Re: Why "not.first.false" WM <wolfgang.mueckenheim@tha.de> - 2024-03-07 10:44 +0000
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-05 14:07 -0800
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-03 15:56 -0800
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-04 09:44 +0000
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-04 13:26 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-03-04 17:53 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-05 10:09 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-03-05 06:36 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-06 10:00 +0000
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Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-03-08 09:14 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-08 15:32 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-03-08 12:43 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-08 19:02 +0000
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-08 09:37 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-03-08 14:26 -0500
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-08 12:29 -0800
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-08 12:41 -0800
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Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-08 08:33 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-03-08 11:52 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-08 18:52 +0000
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Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-04 12:49 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-03-04 16:39 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-05 09:57 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-03-05 06:40 -0500
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-05 08:15 -0800
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-06 10:04 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-03-04 16:52 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-03-05 10:07 +0000
Re: Question about unbounded infinite sets... FromTheRafters <FTR@nomail.afraid.org> - 2024-03-05 08:50 -0500
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 10:36 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-19 15:21 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-20 08:12 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-20 07:49 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-20 16:52 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-20 21:17 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-21 08:47 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-21 07:32 -0500
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-20 15:02 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-20 21:59 +0000
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-20 14:19 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-20 18:55 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-21 08:39 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-21 07:32 -0500
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-21 14:26 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 13:06 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-22 13:12 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-23 08:55 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-23 14:21 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-24 12:10 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-24 12:55 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-25 09:01 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-25 14:35 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-26 08:32 +0000
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-26 11:44 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-27 14:24 +0000
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-27 09:42 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-27 12:45 -0500
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:25 -0800
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:44 -0800
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-20 21:17 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-21 08:52 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-21 07:32 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 12:04 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-22 07:17 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 14:11 +0000
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:27 -0800
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-23 07:23 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-24 11:30 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-24 10:31 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-24 16:16 +0000
Re: Question about unbounded infinite sets... FromTheRafters <FTR@nomail.afraid.org> - 2024-02-24 11:29 -0500
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-24 11:47 -0500
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:26 -0800
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-21 10:27 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-21 15:02 -0500
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-21 12:59 -0800
Re: Question about unbounded infinite sets... Jim Burns <james.g.burns@att.net> - 2024-02-21 17:23 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-17 10:00 +0000
Re: Question about unbounded infinite sets... "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-18 20:00 -0800
Re: Question about unbounded infinite sets... Yecin Tcharushin Bazunov <inaah@htr.ru> - 2024-02-19 18:30 +0000
Re: Question about unbounded infinite sets... "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-19 19:19 -0800
Re: Question about unbounded infinite sets... "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-20 11:10 -0800
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-16 15:35 -0800
Re: Question about unbounded infinite sets... "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-16 18:48 -0800
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-16 19:34 -0800
Re: Question about unbounded infinite sets... Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-19 00:01 +0000
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-18 16:54 -0800
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-17 08:23 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-17 07:15 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-17 21:59 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-18 07:36 -0500
Re: Question about unbounded infinite sets... FromTheRafters <FTR@nomail.afraid.org> - 2024-02-18 11:49 -0500
Re: Question about unbounded infinite sets... Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-18 10:03 -0800
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-18 21:04 +0000
Re: Question about unbounded infinite sets... Erdélyi Szőke Komáromi <oikr@idrdls.hu> - 2024-02-16 21:44 +0000
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-16 15:07 -0800
Re: Question about unbounded infinite sets... x <x@x.org> - 2024-02-17 06:33 -0800
Re: Question about unbounded infinite sets... Burton Rabota Baidjanoff <nau@ninrbfbb.ru> - 2024-02-17 16:29 +0000
Re: Question about unbounded infinite sets... Trolidous <trolidous@go.com> - 2024-02-17 13:54 -0800
Re: Question about unbounded infinite sets... Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2024-02-16 21:45 +0000
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-16 15:12 -0800
Re: Question about unbounded infinite sets... FromTheRafters <FTR@nomail.afraid.org> - 2024-02-16 17:33 -0500
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-16 15:16 -0800
Re: Question about unbounded infinite sets... FromTheRafters <FTR@nomail.afraid.org> - 2024-02-17 06:33 -0500
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-20 11:59 -0800
Re: Question about unbounded infinite sets... "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-16 20:06 -0800
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-17 14:29 -0800
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