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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Newsgroups | sci.math |
| Subject | Re: how (Aristotle says "potential is actual and actual is potential") |
| Date | 2024-06-10 00:46 -0400 |
| Organization | A noiseless patient Spider |
| Message-ID | <e37113ee-84bf-4ce2-a43d-026698bd9984@att.net> (permalink) |
| References | (16 earlier) <29qdneuOINDIO_77nZ2dnZfqnPWdnZ2d@giganews.com> <57baa734-3336-4b16-b6cb-92ff397618b5@att.net> <SySdnbrkHKiu5Pn7nZ2dnZfqnPSdnZ2d@giganews.com> <280516ab-e9d7-4eb2-b244-ee36a60c6644@att.net> <JnOdnQNHaufe2Pv7nZ2dnZfqnPGdnZ2d@giganews.com> |
On 6/9/2024 8:11 PM, Ross Finlayson wrote:
> On 06/08/2024 10:47 AM, Jim Burns wrote:
>> On 6/8/2024 11:28 AM, Ross Finlayson wrote:
>>> On 06/07/2024 10:35 PM, Jim Burns wrote:
>>>> It looks to me like
>>>> what you define the line.reals to be is
>>>> {0/d!,1/d!,…,d!/d!}.limit = ℚ∩[0,1]
>>>>
>>>> Yes,
>>>> {0/d!,1/d!,…,d!/d!}.limit is the continuum limit.
>>>>
>>>> "Continuum limit" means the distance between
>>>> nearest neighbors approaches 0, as it does in ℚ
>>>>
>>>> "Continuum limit" does not mean "continuum".
>>>
>>> I'm delighted that you note that the set ran(f)
>>> by its values, "doesn't not" meet the definition
>>> of least-upper-bound, then insofar as that it does.
>>
>> Whether ran(f) meets the definition depends upon
>> what ran(f) is.
>>
>> ℚ∩[0,1] my (JB's) best guess at your (RF's) ran(f)
>> _does not_ meet the definition.
>>
>> Is √½ = 0.70710678118... in ran(f) ?
>> Please explain.
>
> What ratios?
I refer to the ratios in my best guess at ran(f)
| This putative f
| called EF the equivalency function,
| f(n) = n/d, 0 <= n <= d, d -> oo
| in the continuum limit,
|
Date: Fri, 31 May 2024 18:37:34 -0700
I guess
| 0 <= n <= d
means
{0,1,…,d}
I guess
| f(n) = n/d, 0 <= n <= d
means
f{0,1,…,d} =
{0/d,1/d,…,d/d}
I guess
| f(n) = n/d, 0 <= n <= d, d -> oo
means
lim(d → ∞) f(n) = n/d, 0 <= n <= d =
lim(d → ∞) {0/d,1/d,…,d/d}
My guess is that
ran(f) = lim(d → ∞) {0/d,1/d,…,d/d}
Ross Finlayson,
is ran(f) = lim(d → ∞) {0/d,1/d,…,d/d} ?
While you (RF) ponder whether to perform
a simple, easy task which would greatly reduce
the uncertainty around what you are talking about,
I will carry on as though you had answered "yes".
I know what lim(d → ∞) {0/d,1/d,…,d/d} is,
forc reasonable values of "set limit":
lim(d → ∞) {0/d,1/d,…,d/d} =
⋂(0<dᵢ<∞) U(dᵢ<dᵤ<∞) {0/dᵤ,1/dᵤ,…,dᵤ/dᵤ) =
ℚ∩[0,1]
It is the same as the limit of
the sub.sequence of factorial.denominators,
which is a nested.set sequence, so
lim(d → ∞) {0/d!,1/d!,…,d!/d!} =
U(0<dᵤ<∞) {0/dᵤ!,1/dᵤ!,…,dᵤ!/dᵤ!) =
ℚ∩[0,1]
√½ ∉ ℚ∩[0,1]
>> Is √½ = 0.70710678118... in ran(f) ?
>> Please explain.
>>> I'm delighted that you note that
>>> the set ran(f) by its values, "doesn't not"
>>> meet the definition of least-upper-bound,
>>> then insofar as that it does.
If ran(f) = ℚ∩[0,1]
⎛ which, if it isn't, I'd like you to say it isn't,
⎝ and, if it is, I'd like you to say it is,
then ran(f) "doesn't not not" meet the definition
of having the least upper bound property.
> These are only integer fractions
> in the continuum limit, so the ordered field
> doesn't even exist yet.
| With the order defined above,
| ℚ is an ordered field that has no subfield
| other than itself,
| and is the smallest ordered field,
| in the sense that every ordered field contains
| a unique subfield isomorphic to ℚ
|
https://en.wikipedia.org/wiki/Rational_number
ℚ isn't the compete ordered field.
ℚ is the smallest ordered field.
ℚ is the continuum limit, but
the continuum limit is not the continuum.
> So, that
> elements of the complete ordered field in [0,1],
> like root two over two,
> have values that are real values that
> happen to equate to a value in ran(EF) in [0,1],
> a unique value, and that,
> there is no real value in [0,1] that
> is not an element of ran(EF),
> just has an existence result that
> of the infinitely many distinct integers, and
> the infinitely many distinct reals in [0,1],
> they're 1 to 1.
Please explain.
Does
| f(n) = n/d, 0 <= n <= , d -> oo
mean something else other than
| lim(d → ∞) {0/d,1/d,…,d/d}
?
Is your use of "limit" in
| lim(d → ∞) {0/d,1/d,…,d/d}
something else other than
| ⋂(0<dᵢ<∞) U(dᵢ<dᵤ<∞) {0/dᵤ,1/dᵤ,…,dᵤ/dᵤ)
?
If something else, then what else?
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Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-02 15:23 -0400
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Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-04 00:23 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-04 15:04 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-04 15:22 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-04 16:46 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-04 20:43 -0400
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Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-05 17:26 -0700
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Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-06 17:19 -0700
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Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-07 13:24 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-07 17:15 -0400
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Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-08 08:28 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-08 08:47 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-08 13:47 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-09 17:11 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-10 00:46 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-10 13:48 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-10 23:36 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-10 20:46 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-11 06:25 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-11 14:37 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-11 11:49 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-13 12:04 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-13 23:40 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-14 13:12 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-14 20:31 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-14 19:37 -0700
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Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-13 12:22 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-13 15:51 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-13 16:34 -0700
Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-14 11:34 -0700
Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-07 22:30 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-04 16:04 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-23 07:04 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-27 13:03 -0700
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-05-22 10:14 -0400
Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-05-22 06:23 -0400
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-17 19:03 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-19 15:52 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-20 12:08 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-17 19:29 -0400
Re: how Moebius <invalid@example.invalid> - 2024-05-19 03:10 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-08 12:19 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-19 15:46 +0000
Re: how Moebius <invalid@example.invalid> - 2024-05-19 18:49 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-19 16:28 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-20 20:08 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-21 11:50 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-21 16:55 +0000
Re: how Moebius <invalid@example.invalid> - 2024-05-21 22:35 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-21 19:27 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-22 19:13 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-22 16:48 -0400
Re: how Moebius <invalid@example.invalid> - 2024-05-22 23:44 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-23 13:44 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-26 18:40 +0000
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-26 20:02 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-27 14:14 +0000
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-23 12:10 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-23 15:52 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-26 18:53 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-26 17:44 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-27 14:09 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-27 13:46 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-27 20:10 +0000
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-27 19:00 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-28 08:20 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-28 15:42 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-29 17:11 +0000
Re: how Python <python@invalid.org> - 2024-05-29 19:30 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-29 18:19 +0000
Re: how Python <python@invalid.org> - 2024-05-29 21:20 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-29 14:29 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-30 07:44 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-30 16:24 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-31 17:15 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-05-31 15:15 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-01 15:15 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-03 04:57 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-03 11:58 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-03 14:34 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-03 19:50 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-03 22:07 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-04 14:10 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-04 17:31 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-05 10:43 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-05 13:21 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-05 20:32 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-05 22:54 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-05 17:08 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-05 12:03 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-05 20:33 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-05 22:56 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-05 15:28 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-05 20:39 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-05 17:31 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-06 13:27 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-06 15:44 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-06 16:04 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-06 16:05 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-06 14:35 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-06 20:14 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-07 14:00 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-07 19:21 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-07 17:00 -0400
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-07 22:34 -0700
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-08 07:21 -0400
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-08 13:25 -0400
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-08 12:13 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-08 18:49 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 13:26 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-10 15:57 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 16:39 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-10 18:45 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 17:37 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 14:20 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-10 23:34 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-10 13:09 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 17:45 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-10 15:18 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-10 22:05 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-10 16:50 -0400
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:25 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 00:33 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 16:06 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-11 14:36 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-11 16:50 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 12:28 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:22 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 00:27 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 16:02 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 01:16 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-11 01:18 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-08 12:42 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-08 14:16 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-08 22:20 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-08 18:47 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-09 00:59 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-09 11:53 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 13:38 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-10 14:02 -0400
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-08 20:40 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-09 04:28 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-09 06:19 -0400
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-09 12:38 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 16:33 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-10 16:16 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-10 22:29 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-11 14:45 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-11 16:59 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-11 18:56 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-11 22:30 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 10:24 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-12 14:29 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 18:22 +0000
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 16:40 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 20:44 +0000
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 16:51 -0400
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 14:22 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 14:23 -0700
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 19:46 -0400
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 19:37 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 01:44 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 20:00 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 02:21 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 20:37 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 02:45 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 18:55 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-13 04:23 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-13 06:09 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 13:57 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-15 00:24 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-14 21:06 -0400
Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-14 19:51 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-15 15:09 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-15 14:39 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-16 01:09 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-16 01:24 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-17 14:31 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-18 00:00 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-17 18:39 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-18 01:16 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-13 01:40 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-13 12:10 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-12 17:47 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 02:15 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 10:57 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-13 08:53 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 01:33 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 10:59 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 13:41 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 12:25 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-11 14:44 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-11 16:57 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-11 18:53 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-11 22:22 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 10:18 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-12 14:25 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 13:30 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 10:21 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 12:54 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-12 14:18 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 18:27 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-12 14:54 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 20:33 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-12 17:12 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 10:55 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-13 09:16 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 15:25 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 14:45 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 16:59 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-13 12:13 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-13 21:44 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-14 00:05 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-14 00:08 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-13 17:02 -0400
Re: how Tom Bola <Tom@bolamail.etc> - 2024-06-13 02:14 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-13 02:26 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 13:53 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 16:28 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 14:55 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 17:02 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 15:13 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 17:26 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-13 17:48 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 15:55 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 18:04 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-13 18:12 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-13 18:44 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 18:03 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 21:39 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-13 23:52 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 08:48 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-14 13:17 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 16:29 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-14 18:47 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 16:56 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-14 19:01 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-14 18:34 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 16:41 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-14 18:55 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 08:46 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-14 13:01 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-13 14:25 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 08:34 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-14 10:56 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 16:39 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-14 18:53 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-14 14:52 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-15 17:58 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-15 18:00 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-15 18:06 +0200
Re: how (point at infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-15 09:19 -0700
Re: how (point at infinity) Moebius <invalid@example.invalid> - 2024-06-15 18:35 +0200
Re: how (point at infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-15 09:45 -0700
Re: how (point at infinity) Moebius <invalid@example.invalid> - 2024-06-15 19:12 +0200
Re: how (point at infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-15 10:32 -0700
Re: how (point at infinity) Moebius <invalid@example.invalid> - 2024-06-15 19:14 +0200
Re: how (point at infinity) Jim Burns <james.g.burns@att.net> - 2024-06-15 13:30 -0400
Re: how (point at infinity) Moebius <invalid@example.invalid> - 2024-06-16 01:45 +0200
Re: how (point at infinity) Moebius <invalid@example.invalid> - 2024-06-16 01:50 +0200
Re: how (point at infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-16 05:56 -0700
Re: how (point at infinity) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-16 12:20 -0700
Re: how (point at infinity) Moebius <invalid@example.invalid> - 2024-06-16 21:46 +0200
Re: how (point at infinity) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-16 17:15 -0700
Re: how (point at infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-16 05:47 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-16 03:13 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-16 14:17 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-18 13:12 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-18 20:09 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-18 17:06 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-19 18:37 +0000
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-19 15:34 -0400
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-19 12:49 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-20 15:26 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-20 15:26 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-20 20:18 -0400
Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-20 18:36 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-21 17:01 -0400
Re: how (running constants in physics) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-22 15:26 -0700
Re: how (running constants in physics) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-24 17:56 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-21 06:59 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-21 13:32 -0400
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-21 15:13 -0400
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-22 07:58 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 16:31 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-22 14:20 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 20:19 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-22 13:22 -0700
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-22 18:17 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 12:11 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-22 13:34 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 20:12 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-22 17:04 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 21:30 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-23 13:58 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-23 20:04 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-24 13:18 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-24 18:41 +0000
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-22 18:21 -0400
Re: how Phil Carmody <pc+usenet@asdf.org> - 2024-06-23 01:25 +0300
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-23 19:52 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-22 12:09 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 20:23 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-22 14:16 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-22 14:18 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 21:35 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-22 14:41 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-22 17:25 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-22 21:34 +0000
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 13:45 +0000
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-13 08:22 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-13 14:50 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 14:39 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 16:53 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 15:07 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 17:23 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 14:28 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 16:40 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 15:01 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 17:09 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-13 17:35 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:38 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:39 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 13:44 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-10 15:58 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:33 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:37 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 00:47 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:49 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 01:09 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 16:15 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 03:28 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-11 03:41 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-11 03:43 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 12:31 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-12 01:33 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 16:20 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 01:28 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 16:54 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 03:07 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 12:41 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 12:43 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 13:00 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-12 01:24 +0200
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 06:50 -0400
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 06:49 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 13:33 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-10 16:03 +0200
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-10 13:43 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-10 17:50 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-10 22:14 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-10 15:40 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-11 00:50 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-06 10:52 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-07 10:59 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-07 11:59 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-07 12:00 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 13:18 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 20:38 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 13:51 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 13:57 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-12 21:01 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 04:37 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 14:04 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 16:32 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 14:56 +0000
Re: how Moebius <invalid@example.invalid> - 2024-06-13 17:00 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-13 15:10 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-13 11:57 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-13 11:56 -0700
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-14 08:41 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-14 11:30 -0700
Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-06-14 17:21 -0400
Re: how Moebius <invalid@example.invalid> - 2024-06-14 23:42 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-14 23:43 +0200
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-16 14:21 +0000
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-16 12:05 -0700
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-16 12:11 -0700
Re: how Moebius <invalid@example.invalid> - 2024-06-16 21:41 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-16 21:51 +0200
Re: how Moebius <invalid@example.invalid> - 2024-06-17 00:52 +0200
Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-16 17:11 -0700
Re: how Jim Burns <james.g.burns@att.net> - 2024-06-17 20:04 -0400
Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-06-18 20:13 +0000
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