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Maximum cardinality of an RDF model

From: Miles Sabin <MSabin@interx.com>
Date: Mon, 22 Jan 2001 14:23:44 -0000
Message-ID: <23CF4BF2C499D411907E00508BDC95E116FB84@ntmews_01.interx.com>
To: www-rdf-logic@w3.org
Working on the assumption that there's at most a countably
infinite set of URI(-refs) ... each is a finite sequence of
charaters drawn from a finite alphabet ... and similarly for
Literals, am I right to infer that,

1. there is at most a countable infinity of resources: because 
   every resource has a URI(-ref) and no two distinct resources 
   share a URI(-ref).

hence that,

2. the set Resources from rdfms 5.1, is at most countably
   infinite,

3. the set Properties from 5.3 is at most countably infinite:
   because a (proper) subset of Resources.

and hence that,

4. RDF models can contain at most countably many statements:
   becauce they're subsets of,

     Properties x Resources x (Resources U Literals)
    
   which is at most countably infinite because Properties,
   Resources and Literals are.

Cheers,


Miles

-- 
Miles Sabin                               InterX
Internet Systems Architect                5/6 Glenthorne Mews
+44 (0)20 8817 4030                       London, W6 0LJ, England
msabin@interx.com                         http://www.interx.com/
Received on Monday, 22 January 2001 09:24:20 GMT

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