Re: URI denumerability

Roy T. Fielding wrote:

> Just out of curiosity, could someone please explain why that same
> proof cannot be used to prove that URI are not denumerable?  Just
> replace the real numbers in the proof with their equivalent
> representation as a URI.

Aha, mathematical fun.  A URI is a finite-length string with each 
position having a maximum number of values (let's assume 97 for ascii). 
  Thus you can organize all possible URIs in a list sorted lexically. 
You can number the list.  There are no URIs that don't get a number. 
Thus they can be matched up 1-for-1 with integers and are denumerable. 
If you could arrange for a finite-length way to encode irrational 
numbers (aside from special cases such as e and pi) you'd be right, but 
I'm pretty sure that in principle you can't.  Because if you could then 
they'd be denumerable just like URIs. -Tim