**Hitoshi Kitada** (*hitoshi@kitada.com*)

*Sun, 11 Apr 1999 08:24:52 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 210] Re: [time 209] Observation & Obler's Paradox"**Previous message:**Stephen P. King: "[time 208] Re: [time 204] Observation & Obler's Paradox"**In reply to:**Stephen P. King: "[time 203] Observation"**Next in thread:**Stephen P. King: "[time 210] Re: [time 209] Observation & Obler's Paradox"

Dear Stephen,

Just on the following point:

*> > E.g., consider a set L={1,2,3}. (In the case of the universe, L may be an
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*> > infinite set. At this point, to use the notion "cluster decomposition" b
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*> > concerning the universe may be an abuse at least at the present stage of
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the

*> > theory. This point might be related with Obler's paradox as I mention
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below.)

*> >
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*> > Then the set Q is
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*> >
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*> > Q={ {{1},{2},{3}},
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*> > {{1},{2,3}}, {{1,2},{3}}, {{1,3},{2}},
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*> > {{1,2,3}} },
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*> >
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*> > consisting of 5 elements. b varies over those elements.
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*>
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*> Forgive my mathematical naivete, but is Q here an example of a power
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*> set?
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The power set P of L={1,2,3} is

P={ {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}

that is different from Q. Q is the set of decomposition b of the set L. A

decomposition b of L is a set defined as

b={C1,C2,...,Ck},

where Cj is a subset of L, which are mutually disjoint (i.e. Ci and Cj do not

intersect when i is not equal to j), and the sum set of C1,...,Ck is equal to

L. E.g.,

b={{1,2}, {3}}, etc.

Best wishes,

Hitoshi

**Next message:**Stephen P. King: "[time 210] Re: [time 209] Observation & Obler's Paradox"**Previous message:**Stephen P. King: "[time 208] Re: [time 204] Observation & Obler's Paradox"**In reply to:**Stephen P. King: "[time 203] Observation"**Next in thread:**Stephen P. King: "[time 210] Re: [time 209] Observation & Obler's Paradox"

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