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infinite set: was Re: [ontolog-forum] puzzles

To: Chris Menzel <cmenzel@xxxxxxxx>, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Patrick Durusau <patrick@xxxxxxxxxxx>
Date: Tue, 02 May 2006 10:47:45 -0400
Message-id: <44577111.3030801@xxxxxxxxxxx>
Chris,    (01)

Thanks for the catch on the infinite sets!    (02)

Suspect that in intra-editor drafting posts we were always thinking 
"finite sets" but simply never said it.    (03)

I have started an intra-editor email to address your question about the 
cartesian product and labels. Initial reaction is agreement that it does 
look odd and perhaps unnecessary.    (04)

Hope you are having a great day!    (05)

Patrick    (06)

Chris Menzel wrote:    (07)

>On Sun, Apr 30, 2006 at 01:43:08PM -0500, Chris Menzel wrote:
>  
>
>>...
>>(1) Each label h in L corresponds to exactly one proxy and vice versa.
>>
>>(2) Let P = L x V.  P is the set of *properties*.
>>    
>>(3) A *proxy* is a finite set of properties.
>>
>>(4) The set X of all proxies is the set of all subsets of P, i.e., X is
>>    the power set of P.
>>...
>>Problem 1 can be avoided by (i) requiring the set L of labels and the
>>set V of values to be finite, or (ii) allowing infinite proxies, or
>>(iii) restricting the definition of the set X to the set of all
>>*finite* subsets of P.  Given that finitude is explicit in (4), 
>>    
>>
>
>Should be: (3),
>
>  
>
>>its omission from (5) 
>>    
>>
>
>Should be: (4).
>
>  
>
>>simply appears to be an oversight, so solution (iii) might be
>>preferred here.
>>    
>>
>
>-chris
>
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>  
>    (08)

-- 
Patrick Durusau
Patrick@xxxxxxxxxxx
Chair, V1 - Text Processing: Office and Publishing Systems Interface
Co-Editor, ISO 13250, Topic Maps -- Reference Model
Member, Text Encoding Initiative Board of Directors, 2003-2005    (09)

Topic Maps: Human, not artificial, intelligence at work!     (010)


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