W3C home > Mailing lists > Public > www-tag@w3.org > August 2002

URI denumerability

From: Roy T. Fielding <fielding@apache.org>
Date: Wed, 28 Aug 2002 13:57:33 -0700
Cc: www-tag@w3.org
To: Graham Klyne <GK@NineByNine.org>
Message-Id: <C5EB2415-BAC8-11D6-AB80-000393753936@apache.org>

> 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.

Received on Wednesday, 28 August 2002 17:00:32 UTC

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