From jay.kominek@colorado.edu Wed May 01 12:19:22 2002 Return-Path: X-Sender: kominek@ucsub.colorado.edu X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_3_1); 1 May 2002 19:19:22 -0000 Received: (qmail 50545 invoked from network); 1 May 2002 19:19:21 -0000 Received: from unknown (66.218.66.218) by m10.grp.scd.yahoo.com with QMQP; 1 May 2002 19:19:21 -0000 Received: from unknown (HELO ucsub.colorado.edu) (128.138.129.12) by mta3.grp.scd.yahoo.com with SMTP; 1 May 2002 19:19:21 -0000 Received: from ucsub.colorado.edu (kominek@ucsub.colorado.edu [128.138.129.12]) by ucsub.colorado.edu (8.11.6/8.11.2/ITS-5.0/student) with ESMTP id g41JJLJ24786 for ; Wed, 1 May 2002 13:19:21 -0600 (MDT) Date: Wed, 1 May 2002 13:19:21 -0600 (MDT) To: lojban@yahoogroups.com Subject: Re: [lojban] cipja'o In-Reply-To: <191.65c92d9.2a01940a@aol.com> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=utf-8 Content-Transfer-Encoding: QUOTED-PRINTABLE From: Jay Kominek X-Yahoo-Group-Post: member; u=20706630 X-Yahoo-Profile: jfkominek On Wed, 1 May 2002 pycyn@aol.com wrote: > Thanks; I really was unclear about the point. As for the right word, sin= ce I > forget the difference between irrational and transcendantal, I was happy = with > {nalfrinu} till now. Now, having three not obviously equivalent definiti= ons > of "transcendental" (just in mathematics), I am even less sure. suppose > what fits here it the old infinite non-repeating decimal expansion -- wh= ich > gives a horrible definition-type lujvo (though not as bad as "neither roo= t > nor quotient of rationals" or "not definable by an finite number of > rationally coefficiented equations") An irrational number is one which cannot be expressed as p/q where p and q are integers. A transcendental number is one which cannot be expressed as a polynomial with integer coefficients. All transcendental numbes are irrational. These are much simpler definitions than trying to refer to the decimal expansion. Further, they're correct. See http://mathworld.wolfram.com/ for all your math information needs. > Time for a good metaphor, which "beyond computing" just may be, though > it clearly sets off alarms in many people's belief webs. Whether or not you can compute a complete decimal expansion isn't terribly interesting, in general. Describing such a number as being "beyond computing" is describing a secondary characteristic, which doesn't even differentiate between irrational and transcendental numbers. > jay.kominek > expressed in algebraic terms.> > But this is about transcendental numbers, which, though presumably relate= d, > are not quite the same thing: the algebra seems OK here -- unless rationa= l > coefficients are required to call it algebra. The same expression for an appropriate Lojbanic word holds, just change fancu into namcu. In this case, integer coefficients are needed to call it algebra. > We don't, of course, have a word for algebra either (nor hardly any > other branch of mathematics -- or anything else). http://nuzban.wiw.org/wiki/?Math%20Terminology http://nuzban.wiw.org/wiki/?Terminology - Jay Kominek Plus =C3=A7a change, plus c'est la m=C3=AAme chose