From cowan@ccil.org Thu Jan 24 19:27:43 2002 Return-Path: X-Sender: cowan@mercury.ccil.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_1_3); 25 Jan 2002 03:27:42 -0000 Received: (qmail 80469 invoked from network); 25 Jan 2002 03:27:42 -0000 Received: from unknown (216.115.97.167) by m10.grp.snv.yahoo.com with QMQP; 25 Jan 2002 03:27:42 -0000 Received: from unknown (HELO mercury.ccil.org) (192.190.237.100) by mta1.grp.snv.yahoo.com with SMTP; 25 Jan 2002 03:27:42 -0000 Received: from cowan by mercury.ccil.org with local (Exim 3.12 #1 (Debian)) id 16Tx1t-0003h9-00 for ; Thu, 24 Jan 2002 22:27:53 -0500 Subject: Re: lojban as a programming language [was Re: [lojban] Lojban for lay programmers] In-Reply-To: from Jim Carter at "Jan 24, 2002 02:15:22 pm" To: lojban@yahoogroups.com Date: Thu, 24 Jan 2002 22:27:53 -0500 (EST) X-Mailer: ELM [version 2.4ME+ PL66 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: X-eGroups-From: John Cowan From: John Cowan X-Yahoo-Group-Post: member; u=212516 X-Yahoo-Profile: johnwcowan Jim Carter scripsit: > In 64 bit IEEE float, let X = 1; Y = 1e-17 (and the LSB is about 2e-16). > If IEEE floats were closed under addition, the "first law" for groups, then > X+Y has to have a IEEE representation. Let Z = X+Y. But Z == 1; the sum > is truncated on the right to 56 bits. So we've just proved that Y == 0, > because 0 is the group member (provably unique) such that W + 0 == W for > every W in the group. Oops. Ah, but just because X + Y = X for some X, Y does not make Y the zero; for that to work, X + Y has to = X for *every* X. -- John Cowan http://www.ccil.org/~cowan cowan@ccil.org Please leave your values | Check your assumptions. In fact, at the front desk. | check your assumptions at the door. --sign in Paris hotel | --Miles Vorkosigan