**Stephen P. King** (*stephenk1@home.com*)

*Sat, 10 Apr 1999 20:50:11 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 211] How to define length using LSs"**Previous message:**Hitoshi Kitada: "[time 209] Re: [time 208] Re: [time 204] Observation & Obler's Paradox"**In reply to:**Stephen P. King: "[time 203] Observation"**Next in thread:**Hitoshi Kitada: "[time 213] Re: [time 210] Re: [time 209] Observation & Obler's Paradox"

Dear Hitoshi,

I understand now. :) Thanks... A question: Is it sufficient to consider

all interactions to be representable in terms of pairs? What if

associativity fails?

Later,

Stephen

Hitoshi Kitada wrote:

*>
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*> Dear Stephen,
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*>
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*> Just on the following point:
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*>
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*> > > 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 the
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*> > > theory. This point might be related with Obler's paradox as I mention below.)
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*> > >
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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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*>
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*> The power set P of L={1,2,3} is
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*>
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*> P={ {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}
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*>
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*> that is different from Q. Q is the set of decomposition b of the set L. A
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*> decomposition b of L is a set defined as
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*>
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*> b={C1,C2,...,Ck},
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*>
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*> where Cj is a subset of L, which are mutually disjoint (i.e. Ci and Cj do not
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*> intersect when i is not equal to j), and the sum set of C1,...,Ck is equal to
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*> L. E.g.,
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*>
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*> b={{1,2}, {3}}, etc.
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*>
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*> Best wishes,
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*> Hitoshi
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**Next message:**Stephen P. King: "[time 211] How to define length using LSs"**Previous message:**Hitoshi Kitada: "[time 209] Re: [time 208] Re: [time 204] Observation & Obler's Paradox"**In reply to:**Stephen P. King: "[time 203] Observation"**Next in thread:**Hitoshi Kitada: "[time 213] Re: [time 210] Re: [time 209] Observation & Obler's Paradox"

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