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On Sun, 31 Dec 2006 17:02:17 +0900, ooo wrote:
> "Robert Maas, see http://tinyurl.com/uh3t"; <rem642b@xxxxxxxxx> wrote in
> message news:REM-2006dec30-001@xxxxxxxxxxxx
>> It gets more interesting if you talk about voids between sets of
>> real points instead of between two singleton real points. Given any
>> two sets, where all the points of one are strictly less than all
>> the points of the second set, there is at least one real point
>> "between" the two sets in the sense that it is either:
>> - The very greatest element of the set of lesser points.
>> - The very least element of the set of greater points.
>> - Strictly between the two sets.
> Abobe explanation is similler to a case that berween any two reals ,there
> exist at least one real ,even though not so much .
> Please cosider follouing question I intended to posr another place.
> These arguments ,including Cantor's diagonal, mention up to countable
> case,and assume that these argument hold for infinite numbers objects.
The axioms of set theory often allow us to reason about infinite sets
directly, without even considering a finite case. The proof of Cantor's
theorem (|X| < |P(X)|) is of this type. The proof applies to every X,
and the words "finite" or "infinite" do not even appear anywhere in the
proof. They don't need to.
> These arguments sometimes lead to confusion.
> In the question of vase and ball, argument is
> cardinarity of all added balls and that of removed balles is equevalent,
> hence at noon number of ball is 0 on the vase regardless process before
> then.
Your "hence" is misplaced. The vase and balls problem is not about
cardinality, because you can arrange to leave the vase nonempty at noon
without changing the cardinalities of the sets involved.
> Is it not the same with that cardinality of all naturas is equevalent with
> that of even numbers, so that naturals minus even numbers = 0.
> Why can it be ?
It isn't. You are talking nonsense.
--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
< www.mumia2000.org/">http://www.mumia2000.org/>
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