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Topic: Skepticism, mysticism, Jewish mathematics
Replies: 115   Last Post: Aug 7, 2006 1:30 AM

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Newberry

Posts: 207
Registered: 7/13/06
Re: Skepticism, mysticism, Jewish mathematics
Posted: Aug 6, 2006 1:31 PM
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> (1) This business with the nested intervals is generalized in a theorem
> which is called "Cantor's Theorem" in "Modern Theories of Integration"
> by H. Kestelman [1960]. IIRC, the statement of the theorem (in
> Chapter 1) is (pretty close to) this:
>
> For a [infinite] sequence of non-empty, closed, bounded point-sets {S}
> such that each S_n includes S_(n + 1), the intersection of all the
> sets in the sequence is non-empty. [The inclusions need not be proper.]
>


Well, 0 is the limit of both the point on the left and the points on
the right. Perhaps the result that the intersection is non-empty is
eqivalent to the fact that the limit exists.

I was puzzled by this result for a while because it seems devoid of any
meaning. I.e. if an interval has zero lenghth who cares if there is
anything in it or not? But the existence of a limit has a rather
significant meaning.



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7/25/06
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7/25/06
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7/26/06
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Mike Kelly
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7/26/06
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herbzet
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herbzet
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herbzet
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zr
8/1/06
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8/5/06
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7/28/06
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herbzet
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