Re: Dead (but interesting) topic Re: URI denumerability

Am Donnerstag den, 29. August 2002, um 17:30, schrieb Tim Bray:

>
> Jeff Bone wrote:
>
>> Tim, I buy your argument.  But the problem then is that it 
>> implies that URI cannot represent the reals.  A proper subset of 
>> a denumerable set cannot stand in one-to-one correspondance with 
>> a non-denumerable set, right?  OTOH, it seems to me that, for any 
>> given real number, it is possible to construct a (or many - 
>> perhaps infinitely many) URIs that can stand for that real 
>> number...
>
> Er well my math degree is dated 1981, so the intuition is somewhat 
> rusty.  I believe, when you come right down to it, that the 
> problem is that there are lots of reals that have no names.  
> Clearly I could write URIs for well-known irrationals like e, pi, 
> and their friends.  It is obvious that there is no finite 
> representation of an irrational using a positional numeric 
> notation.  So unless you have some other way of getting at it 
> (ratio between circumference and diameter, integral of 1/x, square 
> root of 2) you'll never get a name, which means that it just isn't 
> a resource (a thing that has identity), so the world-view is kind 
> of consistent.

Well, you can give *any* real number a name, but you cannot give
*every* real number a name. (The amount of information represented by
the set of real numbers is greater than the amount of information
represented by an infinite set of finite words formed from a finite
alphabet.)

>
> Think of all those poor nameless reals... that's a special kind of 
> loneliness. -Tim

I donate a URI from http://greenbytes.de/ for the first number
you do not give one.

Or, look at the positive side: the amount of possible future top level
domains is numerable!

//Stefan