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

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.

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