From phma@ixazon.dynip.com Fri Aug 06 07:18:39 2004 Received: with ECARTIS (v1.0.0; list lojban-list); Fri, 06 Aug 2004 07:18:40 -0700 (PDT) Received: from [216.189.121.177] (helo=blackcat.ixazon.lan) by chain.digitalkingdom.org with esmtp (Exim 4.32) id 1Bt5YC-0006S0-W4 for lojban-list@lojban.org; Fri, 06 Aug 2004 07:18:29 -0700 Received: by blackcat.ixazon.lan (Postfix, from userid 1001) id 6793B4B06; Thu, 5 Aug 2004 02:36:10 +0000 (UTC) From: Pierre Abbat Organization: dis To: lojban-list@lojban.org Subject: [lojban] continuum hypothesis Date: Wed, 4 Aug 2004 22:36:09 -0400 User-Agent: KMail/1.5 MIME-Version: 1.0 Content-Disposition: inline Content-Type: text/plain; charset="iso-8859-1" Message-Id: <200408042236.09920.phma@phma.hn.org> X-archive-position: 8372 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: phma@phma.hn.org Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list I am the shepherd of {ci'i}. li ci'ino = aleph null, li ci'ipa = aleph one, etc. Those are cardinal numbers. Then there are ordinal numbers; the smallest ordinal with cardinality aleph null is called omega, but then you can add any natural number to omega and it still has cardinality aleph null, you can square omega, or raise it to any integer power, and it still has cardinality aleph null. The cardinality of the continuum is 2^(aleph null), which is the same as (aleph null)^(aleph null). It is denoted by 'c' in some particular font. The continuum hypothesis states that 2^(aleph null)=aleph one. For those (including me) who believe that the hypothesis is false, how should we call the cardinality of the continuum? How should we call the transfinite ordinals? phma -- li fi'u vu'u fi'u fi'u du li pa