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| Subject | Re: Cardinalities of sets |
|---|---|
| Newsgroups | sci.math, sci.physics.relativity, sci.electronics.design |
| References | (19 earlier) <10na9a8$kc8a$1@dont-email.me> <10nabhd$k7kl$1@dont-email.me> <10nci9d$7c6h$2@gwaiyur.mb-net.net> <z6acnXqIZ5dpRAT0nZ2dnZfqnPidnZ2d@giganews.com> <IWednWDVRZ8SQAT0nZ2dnZfqnPadnZ2d@giganews.com> |
| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
| Date | 2026-02-21 08:51 -0800 |
| Message-ID | <uw2dnRC5M6oafwT0nZ2dnZfqn_idnZ2d@giganews.com> (permalink) |
Cross-posted to 3 groups.
On 02/21/2026 08:30 AM, Ross Finlayson wrote:
> On 02/21/2026 08:14 AM, Ross Finlayson wrote:
>> On 02/21/2026 07:16 AM, Thomas 'PointedEars' Lahn wrote:
>>> [X-Post & F'up2 sci.math]
>>>
>>> Jeroen Belleman wrote:
>>>> On 2/20/26 19:31, Bill Sloman wrote:
>>>>> I know enough to know that the infinite number of integers is a
>>>>> smaller
>>>>> number than the infinite number of rational numbers,
>>>
>>> "One of the great challenges in this world is knowing enough about
>>> a subject to think you're right, but not enough about the subject
>>> to know you're wrong."
>>>
>>> --Neil deGrasse Tyson, astrophysicist and science communicator
>>> (in his MasterClass promotion video:
>>> <https://www.youtube.com/watch?v=io6QdGcoWMU>)
>>>
>>> (SCNR)
>>>
>>>>> but I don't get excited about it.
>>>>
>>>> I don't think that is correct. Both the sets of natural and rational
>>>> numbers are aleph-0 in size,
>>>
>>> More precisely, their _cardinality_ is ℵ₀ (strictly: _alef_-0).
>>>
>>>> because it's possible to create a one-to-one mapping of every rational
>>>> number to every integer.
>>>
>>> Otherwise correct (as purportedly proven by Georg Cantor at the end of
>>> the
>>> 19th/beginning of the 20th century): |ℤ| = |ℚ| = ℵ₀.
>>>
>>> The misconception that this would not be so can arise from the
>>> assumption
>>> that ℚ = ℤ × ℤ. But actually, ℚ ⊊ ℤ × ℤ since e.g. 2/2 = 1/1 and
>>> ℤ/0 ∉ ℚ as ℚ := {p/q : p, q ∈ ℤ, q > 0}.
>>>
>>> But then |ℚ| < |ℤ × ℤ|; and while |ℤ| < |ℤ × ℤ|, |ℤ| < |ℚ| does NOT
>>> follow,
>>> and is fact false: |ℤ| = |ℚ| < |ℤ × ℤ|.
>>>
>>> ISTM that Bill Sloman's statement would be true when comparing the
>>> cardinalities of ℤ (or ℚ) and ℝ, the set of _real_ numbers, instead.
>>> ℤ (and
>>> ℚ) is/are countable (countably infinite), while ℝ is uncountable
>>> (uncountably infinite, as also purportedly proven by Cantor). |ℤ| =
>>> |ℚ| =
>>> ℵ₀; |ℝ| = 2^ℵ₀, and (ISTM uncontroversial that) ℵ₀ < 2^ℵ₀, so then
>>> |ℤ| = |ℚ| < |ℝ|.
>>>
>>> <https://en.wikipedia.org/wiki/Aleph_number>
>>>
>>
>>
>> Cardinality is rather _less precise_ than other matters
>> of size relation like, for example, asymptotic density.
>>
>> Or, "half of the integers are even".
>>
>> Cardinality establishes a transitive inequality among sets,
>> where "cardinals" themselves as equivalence classes of sets
>> having any transitive bijective relation, are, besides zero,
>> rather too large to be sets in ordinary set theories like ZF(C).
>>
>> Cardinality is rather specific to sets, and, set theory
>> rather _describes_ numbers than _is_ numbers,
>> that though "descriptive set theory" is a great account
>> of formalization in mathematics.
>>
>> Emil duBois-Reymond discovered various arguments for
>> the uncountability of reals, later Cantor wrote them
>> in set theory.
>>
>>
>> About the Continuum Hypothesis of G. Cantor, there's
>> that Goedel showed it consistent one way and von Neumann
>> another, then P. Cohen added an axiom to make it
>> independent instead of inconsistent, set theory.
>>
>>
>>
>
> As one might imagine, that's a bit messy, since then
> thusly one may derive contradictions in set theory
> itself, and not even talking about how to derive
> contradictions in set theory about description of
> other theories of one relation, like ordinals for
> order theory or about class/set distinction, or
> about theories of other objects like those of
> geometry or number theory, as modeled in
> ordinary set theory.
>
>
Or, I suppose that was Paul if not Emil
duBois-Reymond, mea culpa.
It's also for duBois-Reymond the idea of
all the expressions of real-valued variables,
in the language of those then and by their
differences in the asymptotic, then that
these each cross the line at zero the abscissa,
the "long line" of duBois-Reymond, is only everywhere
crossing the line itself, so is a continuous domain,
while though its cardinally larger than the usual
definition of the Archimedean complete ordered field,
usually written "R" in blackboard-bold font.
Then, that the "line-reals" or "drawing the line",
"line-drawing", is the usual account of that
drawing a line makes a line segment each as of
points, in a line: these "iota-values" are
also a continuous domain, with extent density
completeness measure, though, that's countable,
not uncountable.
How then that's not inconsistent according to
set theory's models of these as different sets
that have the same topological properties,
is simply enough for line-reals the function
establishing them, a "natural/unit equivalency
function" for their cardinal equivalency or equipollency,
is simply enough not a Cartesian function, then
that besides itself falling out of the results otherwise
for un-countability as not disqualified and rejected,
then as non-Cartesian isn't connected transitively,
to be disqualified and rejected as a bijection between
ordinary naturals and a bounded continuous domain.
This isn't usually brought up in class, yet,
it's an exercise you can verify yourself.
For example, I regularly have put it to
large, competent, conscientious, co-operative reasoners.
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Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 12:40 +0100
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Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 15:15 +0100
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Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-03 09:53 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-03 23:14 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-05 11:57 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-06 01:43 +1100
Re: energy and mass Jeroen Belleman <jeroen@nospam.please> - 2026-03-05 16:03 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-05 08:48 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-05 22:03 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-05 18:20 -0800
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-03-06 11:01 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-07 16:48 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-05 08:42 -0800
Re: energy and mass "Don" <g@crcomp.net> - 2026-03-05 18:48 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-05 12:32 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-06 05:57 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-03-01 13:13 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 06:51 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 07:06 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-01 17:05 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-01 10:46 +0100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-28 10:03 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-01 00:17 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-01 10:26 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-01 21:03 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-03 10:06 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-03 23:40 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-03 13:47 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-04 16:25 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-04 02:52 -0800
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-06 09:37 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-07 00:36 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-06 07:47 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-03-01 12:49 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-27 04:05 +1100
Re: energy and mass "Don" <g@crcomp.net> - 2026-02-28 15:06 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 07:27 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-05 08:54 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-06 06:12 +1100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-28 16:31 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 07:49 -0800
Re: energy and mass Python <python@cccp.invalid> - 2026-02-28 16:01 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 08:13 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 08:37 -0800
Re: energy and mass Maciej Woźniak <mlwozniak@wp.pl> - 2026-02-28 18:18 +0100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-28 17:59 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 09:06 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-28 19:10 +0100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-28 18:01 +0100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-01 10:59 +0100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-03 09:19 +0100
Re: energy and mass "Don" <g@crcomp.net> - 2026-02-28 23:02 +0000
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-01 00:12 +0100
Re: energy and mass "Don" <g@crcomp.net> - 2026-03-01 00:33 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 16:52 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-01 02:30 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-28 22:50 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-01 17:06 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 09:08 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-02 02:04 +0100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-02 02:08 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 19:00 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-02 02:13 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 19:39 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-05 08:50 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 10:22 -0800
Re: energy and mass Taylor Mészáros <motor@orkzmm.hu> - 2026-03-01 21:17 +0000
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-02 01:53 +0100
Re: energy and mass Winford Balabolkin <od@dnwi.ru> - 2026-03-02 10:37 +0000
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-02 02:00 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 18:59 -0800
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-03 10:18 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-03 03:21 -0800
Re: energy and mass "Don" <g@crcomp.net> - 2026-03-01 07:09 +0000
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-01 02:13 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-03-01 10:45 +0100
Re: energy and mass Maciej Woźniak <mlwozniak@wp.pl> - 2026-03-01 23:57 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-03-01 10:45 +0100
Re: energy and mass Maciej Woźniak <mlwozniak@wp.pl> - 2026-03-01 23:53 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-03-01 10:45 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-25 08:32 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 18:52 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 02:45 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 12:40 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-25 00:32 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 15:15 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-25 02:31 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 20:34 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 14:53 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-27 17:42 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-27 10:43 +0100
Re: energy and mass Jovany Márton <md@jjryoto.hu> - 2026-02-27 17:33 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 09:17 -0800
Re: energy and mass "Don" <g@crcomp.net> - 2026-02-24 18:41 +0000
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 20:34 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 08:56 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-23 21:08 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-23 22:27 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 12:40 +0100
Re: energy and mass Jeroen Belleman <jeroen@nospam.please> - 2026-02-19 14:36 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-19 07:56 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-20 03:00 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-19 07:49 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-20 05:30 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-19 07:46 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-20 05:40 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-19 21:41 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-19 15:52 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-20 15:22 +0100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-19 11:27 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-19 21:41 +0100
Re: energy and mass The Starmaker <starmaker@ix.netcom.com> - 2026-02-19 17:48 -0800
Re: energy and mass The Starmaker <starmaker@ix.netcom.com> - 2026-02-20 01:35 -0800
Re: energy and mass Arie de Muijnck <noreply@ademu.nl> - 2026-02-20 08:19 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-20 11:35 +0100
Re: energy and mass Jeroen Belleman <jeroen@nospam.please> - 2026-02-19 22:11 +0100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-19 23:57 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-19 15:49 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-19 20:45 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-19 07:44 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-20 06:19 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-19 21:41 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-19 15:48 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-20 18:45 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 08:47 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-21 05:31 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 10:52 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 11:13 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-21 16:11 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 21:41 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 21:52 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-21 23:56 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 05:20 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 05:34 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-22 15:47 +1100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-22 15:37 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-22 20:34 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 17:27 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-22 22:50 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 23:44 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-23 08:54 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 18:04 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 00:38 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-23 12:28 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 02:27 +1100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-21 23:35 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 05:08 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-21 12:46 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-22 15:52 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-22 20:34 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-22 11:46 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 17:30 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-23 12:28 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 23:58 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-23 21:08 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-23 22:16 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 18:12 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 12:40 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-25 00:09 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 15:15 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-25 03:03 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-24 20:34 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-26 17:07 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-26 11:21 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-27 04:29 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-26 21:39 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-27 17:48 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-27 10:43 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-28 04:19 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-27 21:48 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-28 17:14 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-26 10:22 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-27 05:08 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-26 09:52 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-27 04:54 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-28 10:28 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-01 00:52 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-03-01 10:39 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-03-01 21:35 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 08:43 -0800
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-03-01 10:45 -0800
Re: energy and mass athel.cb@gmail.com <user12588@newsgrouper.org.invalid> - 2026-03-01 19:53 +0000
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-03-01 12:53 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-01 20:31 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 12:59 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-02 01:59 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-21 15:56 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 22:03 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 22:12 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-22 00:08 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 05:40 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-22 15:58 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 23:25 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-22 11:25 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 02:55 +1100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-22 00:01 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-21 12:46 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-22 16:06 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-22 11:25 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 03:20 +1100
Re: energy and mass nospam@de-ster.demon.invalid (J. J. Lodder) - 2026-02-22 22:38 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-22 14:10 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 17:46 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-22 23:12 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-22 23:26 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-23 17:40 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-22 22:53 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-23 12:28 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 00:17 +1100
Re: energy and mass Jeroen Belleman <jeroen@nospam.please> - 2026-02-20 20:09 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 11:21 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-21 16:16 +0100
Cardinalities of sets (was: energy and mass) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-21 16:16 +0100
Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 08:14 -0800
Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 08:30 -0800
Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 08:51 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-20 21:47 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-20 18:48 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-21 11:19 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 04:52 -0800
Re: energy and mass "Don" <g@crcomp.net> - 2026-02-23 14:36 +0000
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 03:57 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-23 09:08 -0800
Re: energy and mass liz@poppyrecords.invalid.invalid (Liz Tuddenham) - 2026-02-23 18:16 +0000
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-23 21:49 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-23 22:28 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 18:15 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 00:42 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-25 18:54 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-25 11:34 -0800
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-25 23:01 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-25 20:51 -0800
Re: energy and mass Esequiel Stamatelos <staa@qeaesm.gr> - 2026-02-25 19:54 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-25 18:38 -0800
Re: energy and mass Emette Totolos <molle@mtt.gr> - 2026-02-26 13:56 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-26 06:07 -0800
Re: energy and mass The Starmaker <starmaker@ix.netcom.com> - 2026-02-26 20:33 -0800
Re: energy and mass Keelyn Imagawa <ewaeaaa@aiy.jp> - 2026-02-27 17:27 +0000
Re: energy and mass The Starmaker <starmaker@ix.netcom.com> - 2026-02-27 12:25 -0800
Re: energy and mass Chadwick Katsukawa <iu@aah.jp> - 2026-02-27 21:44 +0000
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-26 21:22 +0100
Re: energy and mass Mohammad Fukumitsu <afuimo@sismu.jp> - 2026-02-26 20:41 +0000
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-23 21:08 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-24 18:19 +1100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-23 23:33 +0100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-23 15:03 -0800
Re: energy and mass ram@zedat.fu-berlin.de (Stefan Ram) - 2026-02-24 17:26 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 09:38 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 10:09 -0800
business administration book? (Re: energy and mass) Mild Shock <janburse@fastmail.fm> - 2026-02-24 21:26 +0100
Re: business administration book? (Re: energy and mass) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 15:01 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-24 18:04 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-25 10:17 +0100
Re: energy and mass ram@zedat.fu-berlin.de (Stefan Ram) - 2026-02-24 21:50 +0000
Re: energy and mass "Don" <g@crcomp.net> - 2026-02-24 15:53 +0000
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-25 14:48 +0100
Re: energy and mass "Don" <g@crcomp.net> - 2026-02-25 15:54 +0000
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-25 17:48 +0100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-20 08:29 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-17 23:28 +1100
Re: energy and mass liz@poppyrecords.invalid.invalid (Liz Tuddenham) - 2026-02-14 10:19 +0000
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-11 23:09 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-11 14:11 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-12 11:12 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-12 08:43 -0800
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-12 09:41 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-13 11:27 +0100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-13 10:14 -0800
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-11 14:39 -0800
Re: energy and mass Martin Brown <'''newspam'''@nonad.co.uk> - 2026-02-12 09:39 +0000
Re: energy and mass Jan Panteltje <alien@comet.invalid> - 2026-02-12 13:42 +0000
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-12 16:20 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 04:10 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-13 23:40 +0100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-13 15:15 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-18 21:26 +1100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-12 07:38 -0800
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-12 08:21 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 04:26 +1100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-13 10:00 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 15:27 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-13 23:40 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-12 19:39 +0100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-12 11:11 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-12 22:29 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 04:19 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-13 10:03 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-13 11:59 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 04:41 +1100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-13 20:57 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-13 23:40 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 15:22 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-13 23:40 +0100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-14 11:17 +0100
Re: energy and mass Python <python@cccp.invalid> - 2026-02-14 10:20 +0000
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 23:11 +1100
Re: energy and mass Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-14 14:21 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-15 02:59 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-17 09:45 +0100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-15 10:07 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-15 23:44 +1100
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-15 07:34 -0800
Re: energy and mass "Don" <g@crcomp.net> - 2026-02-15 18:41 +0000
Re: energy and mass Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-15 13:18 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-15 21:48 +0100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-17 10:16 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-17 23:41 +1100
Re: energy and mass Thomas Heger <ttt_heg@web.de> - 2026-02-18 16:39 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-19 03:38 +1100
Re: energy and mass athel.cb@gmail.com <user12588@newsgrouper.org.invalid> - 2026-02-17 16:45 +0000
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-17 09:04 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-17 22:31 +0100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-17 14:56 -0800
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-18 10:37 +0100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-18 07:35 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-19 03:49 +1100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-18 09:00 -0800
Re: energy and mass Gerhard Hoffmann <dk4xp@arcor.de> - 2026-02-18 18:35 +0100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-12 11:12 +0100
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 04:01 +1100
Re: energy and mass nospam@de-ster.demon.nl (J. J. Lodder) - 2026-02-13 23:40 +0100
Re: energy and mass john larkin <jl@glen--canyon.com> - 2026-02-13 15:24 -0800
Re: energy and mass Bill Sloman <bill.sloman@ieee.org> - 2026-02-14 15:39 +1100
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