- From: Tim Bray <tbray@textuality.com>
- Date: Wed, 28 Aug 2002 14:24:54 -0700
- To: "Roy T. Fielding" <fielding@apache.org>
- Cc: Graham Klyne <GK@NineByNine.org>, www-tag@w3.org
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
Received on Wednesday, 28 August 2002 17:24:53 UTC