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

Thanks Bill ... I think! I didn't realise that there were larger and smaller
infinities!

But if there is a natural number:

	.6775746636352

I still don't understand why we can't we have a URI:

	http://www.schema.org/datatypes/natural#.6775746636352

In other words, for every natural number there is a URI.

Whether that URI 'pre-exists' is another matter, but I wasn't commenting on
whether there would be a database that contains every URI, one for each
natural number, since obviously that would be impossible. I more had in mind
something like the much discussed rdf:aboutEachPrefix attribute, where you
might say that any object identified with the prefix:

	http://www.schema.org/datatypes/double#

was a floating point number (for example). Then you wouldn't need to define
every single float, you would just create URIs for the numbers that you were
dealing with at any one time.

(I don't want to mix up two debates here. I wasn't actually commenting on
data typing in my initial posting, I was merely asking why Peter was saying
that there were a finite number of URIs. I think we may have been talking at
cross purposes. I am saying that whilst there are of course a finite number
of URIs at any one time, there are an infinite number of _possible_ URIs.
The problem is not in finding enough, but in coming up with a convenient way
of creating them as and when they are needed.)

Mark

> -----Original Message-----
> From: Bill de hOra [mailto:bdehora@interx.com]
> Sent: 04 January 2002 14:23
> To: 'Mark Birbeck'
> Subject: RE: what RDF is not (was ...) 
> 
> 
> Hi Mark,
> 
> Countably (or denumerably) infinite means that a set has a 121
> correspondance between its members and at least one of its subsets, ie
> there is a 121 correspondance between the natural numbers and the
> squares of the natural numbers:
> 
> 1  2  3 ...
> 1  4  9 ...
> 
> A denumerable infinity is the smallest sort of infinity (sometimes
> marked as X0 or Aleph nought). Aleph nought is synonomous with the
> natural numbers.
> 
> Finite sets do not have such correspondances with any of their subsets
> (this property actually defines then as finite).
> 
> However the set of all sets (or the power set) of X0 are uncountably
> infinite (there exists a proof). That any set has a power set 
> is usually
> accepted as the Power Set Axiom. In general a power set always has a
> greater cardinal number that the set itself (Cantor's theorem, which
> shows that there is never ending succession of different and greater
> infinities).
> 
> Essentially there are not enough URIs to correspond onto the real
> numbers, just as there are not enough natural numbers to 
> correspond onto
> the real numbers (for example it's provable that there is no 121
> correspondance between the natural numbers and the reals ranging from
> 0-1, thus the reals are uncountably infinite). 
> 
> There are not enough URIs to denote all resources (ie there aren't
> enough URIs to denote the points on a line, or to denote the power set
> of the set of URIs), but there are close enough to enough for 
> government
> use.
> 
> regards,
> Bill de hÓra
> 
> 
> 
> > -----Original Message-----
> > From: Mark Birbeck [mailto:Mark.Birbeck@x-port.net] 
> > Sent: 04 January 2002 13:50
> > To: 'Peter F. Patel-Schneider'
> > Cc: www-rdf-interest@w3.org
> > Subject: RE: what RDF is not (was ...) 
> > 
> > 
> > > How many URIs are there?  Only countably infinite.   How many 
> > > real numbers
> > > are there?  Uncountably infinite.  QED.
> > 
> > Mmm ... I'm not a mathematician so I may be missing 
> > something, but if there
> > are infinite numbers 'n', then there must be infinite strings 
> > 'xn' - i.e.,
> > some prefix on any number.
> > 
> > Mark
> > 
> > 
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Received on Friday, 4 January 2002 10:35:43 UTC