From lojbab@lojban.org Mon Jun 05 00:17:26 2000 Return-Path: Received: (qmail 23956 invoked from network); 5 Jun 2000 07:17:26 -0000 Received: from unknown (10.1.10.27) by m4.onelist.org with QMQP; 5 Jun 2000 07:17:26 -0000 Received: from unknown (HELO stmpy-5.cais.net) (205.252.14.75) by mta2 with SMTP; 5 Jun 2000 07:17:25 -0000 Received: from bob (54.dynamic.cais.com [207.226.56.54]) by stmpy-5.cais.net (8.10.1/8.9.3) with ESMTP id e557HOX90521 for ; Mon, 5 Jun 2000 03:17:25 -0400 (EDT) (envelope-from lojbab@lojban.org) Message-Id: <4.2.2.20000605031427.00afd250@127.0.0.1> X-Sender: vir1036/pop.cais.com@127.0.0.1 X-Mailer: QUALCOMM Windows Eudora Pro Version 4.2.2 Date: Mon, 05 Jun 2000 03:18:42 -0400 To: lojban@egroups.com Subject: Re: [lojban] Transfinite ordinals In-Reply-To: <00060421183101.20570@neofelis> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed From: "Bob LeChevalier (lojbab)" At 09:13 PM 06/04/2000 -0400, Pierre Abbat wrote: >I notice that Lojban has a word for transfinite cardinals, but not for >transfinite ordinals. > >Transfinite cardinals (denoted by Hebrew letters with subscripts) tell the >number of elements in a set; transfinite ordinals (denoted by Greek letters) >tell how it is ordered. For instance, the set of all positive integers has >cardinality aleph-null and ordinality omega. The set of all positive integers >and aleph-null still has cardinality aleph-null, but its ordinality is >omega+1. >The set of all ordered pairs of positive integers has ordinality omega*omega, >but its cardinality is still aleph-null. > >Anyone want to add a word for these? We are not adding new words; the language is baselined. (Other than lujvo which are more accurately described as built from existing pieces of the language, and borrowings which are taken from other languages, and are considered only semi-Lojban as a result). We have always assumed that an ordinal could be expressed by adding the ordinal suffix moi to a number (cardinal or otherwise - Lojban does not worry about the semantics). lojbab -- lojbab lojbab@lojban.org Bob LeChevalier, President, The Logical Language Group, Inc. 2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273 Artificial language Loglan/Lojban: http://www.lojban.org