- From: Paul Grosso <pgrosso@arbortext.com>
- Date: Wed, 28 Aug 2002 16:19:52 -0500
- To: "Roy T. Fielding" <fielding@apache.org>, Graham Klyne <GK@NineByNine.org>
- Cc: www-tag@w3.org
At 13:57 2002 08 28 -0700, Roy T. Fielding wrote: >>At 06:45 PM 8/26/02 -0400, Ian B. Jacobs wrote: >>> Resolved: Move "Some resources do not have URIs. URIs are >>> denumerable, which means there are enough to give one to every >>> real number without collisions, for example." to footnote. >> >>Surely, this is wrong? [1] (The bit about giving one to every real number.) > >Yes, that was wrong -- denumerable would mean they are equivalent to >the set of natural numbers, not real numbers. We started off >discussing that and then fell down a rathole about it not belonging >in the document at all, and then further into the pits of despair >when I pointed out that URI are equivalent to real numbers anyway, >which means they are not denumerable. > >In any case, I agree that it should not be in the architecture document. > >>[1] http://www.math.utah.edu/~alfeld/math/sets/realproof.html > >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. The proof relies on the fact that the decimal representation of a real number can have an infinite number of digits. So the set of URIs is not denumerable if you allow a URI to have an infinite number of characters in its representation. paul
Received on Wednesday, 28 August 2002 17:20:55 UTC