From pycyn@aol.com Mon Jun 05 01:56:38 2000 Return-Path: Received: (qmail 3806 invoked from network); 5 Jun 2000 08:56:37 -0000 Received: from unknown (10.1.10.26) by m4.onelist.org with QMQP; 5 Jun 2000 08:56:37 -0000 Received: from unknown (HELO imo16.mx.aol.com) (152.163.225.6) by mta1 with SMTP; 5 Jun 2000 08:56:37 -0000 Received: from Pycyn@aol.com by imo16.mx.aol.com (mail_out_v27.9.) id a.9c.4543288 (4230) for ; Mon, 5 Jun 2000 04:56:33 -0400 (EDT) Message-ID: <9c.4543288.266cc540@aol.com> Date: Mon, 5 Jun 2000 04:56:32 EDT Subject: Re: [lojban] Transfinite ordinals To: lojban@egroups.com MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Mailer: AOL 3.0 16-bit for Windows sub 41 From: pycyn@aol.com In a message dated 00-06-04 21:20:26 EDT, you write: << 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? >> Will we do better than <.o'obu>? Adding all the paraphenalia of subscripts and the like, can get most of these. And, of course, there are all those other order types than the well-ordering (I forget the main ones: eta? and iota? for dense and continuous?) and even the extreme well-orderings -- of omegas and then the inaccessibles. If we ever need those (and I hope it is rarely) we will get the signs we need for them.