From phma@oltronics.net Sun Jun 04 18:18:48 2000 Return-Path: Received: (qmail 16244 invoked from network); 5 Jun 2000 01:18:28 -0000 Received: from unknown (10.1.10.26) by m3.onelist.org with QMQP; 5 Jun 2000 01:18:28 -0000 Received: from unknown (HELO mail.oltronics.net) (204.213.85.8) by mta1 with SMTP; 5 Jun 2000 01:18:26 -0000 Received: from neofelis (i019-1.clt-nc.oltronics.net [207.15.133.19]) by mail.oltronics.net (8.9.3/8.9.3) with SMTP id VAA01607 for ; Sun, 4 Jun 2000 21:18:23 -0400 To: lojban@egroups.com Subject: Transfinite ordinals Date: Sun, 4 Jun 2000 21:13:18 -0400 X-Mailer: KMail [version 1.0.28] Content-Type: text/plain MIME-Version: 1.0 Message-Id: <00060421183101.20570@neofelis> Content-Transfer-Encoding: 8bit From: Pierre Abbat 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? phma