Re: what RDF is not (was ...)

From: Mark Baker <distobj@acm.org>
Subject: Re: what RDF is not (was ...)
Date: Fri, 4 Jan 2002 09:51:20 -0500 (EST)

> > This isn't necessarily a _practical_ problem, but it certainly
> > undercuts any suggestion that RDF(S) is capable of representing
> > "everything".
> 
> Anything with identity can be represented on the Web.  
> 
> Real numbers are not countable, but that isn't the same thing as not
> being identifiable.  It just means that, given one real, there's no
> "next largest" real.

Wrong.

> For example, here's some possible URIs for some transcendentals;
> 
> http://numbers.example.org/transcendental/pi
> http://numbers.example.org/transcendental/e

Sure, but there are only countably many of such URIs, so not all reals can
have such indentifiers.


> > Well, if you baulk at things as intangible as real numbers, how about
> > points on a line,
> 
> No problem.  Pick one and I'll give you a URI for it.  8-) I can give
> you a URI for the whole line too, or for a segment of it, or anything
> else identifiable about it.


OK, here goes.  This is for real numbers themselves, but points on a real
line would work as well.


First one assumption:

A URI is a finite sequence of unicode characters.



Order all finite sequences of unicode characters.  Any ordering will
do, in particular you could order them by the lexicographic ordering of
their standard encoding in ASCII.   The nth such sequence will be referred
to as U(n).

Now we identify the following real number by describing the fractional part
of its decimal expansion.   The number is between 0 and 1, so its integral
part is just the character 0.

The nth element of the fractional part will be 
1 if U(n) is a URI that represents a real number that has the nth element
  of the fractional part of its decimal expansion anything but 1
2 otherwise

This real number is different from all the real numbers represented by
URIs.



peter

Received on Friday, 4 January 2002 10:48:56 UTC