From sentto-44114-2193-mark=kli.org@returns.onelist.com Sat Mar 04 13:23:55 2000 Return-Path: Delivered-To: shoulson-kli@meson.org Received: (qmail 31077 invoked from network); 4 Mar 2000 13:23:54 -0000 Received: from zash.lupine.org (205.186.156.18) by pi.meson.org with SMTP; 4 Mar 2000 13:23:54 -0000 Received: (qmail 21851 invoked by uid 40001); 4 Mar 2000 13:23:59 -0000 Delivered-To: kli-mark@kli.org Received: (qmail 21848 invoked from network); 4 Mar 2000 13:23:58 -0000 Received: from hh.egroups.com (208.48.218.10) by zash.lupine.org with SMTP; 4 Mar 2000 13:23:58 -0000 X-eGroups-Return: sentto-44114-2193-mark=kli.org@returns.onelist.com Received: from [10.1.10.37] by hh.egroups.com with NNFMP; 04 Mar 2000 13:23:52 -0000 Received: (qmail 22345 invoked from network); 4 Mar 2000 13:23:50 -0000 Received: from unknown (10.1.10.26) by m3.onelist.org with QMQP; 4 Mar 2000 13:23:50 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.171) by mta1.onelist.com with SMTP; 4 Mar 2000 13:23:50 -0000 Received: (qmail 85611 invoked by uid 0); 4 Mar 2000 13:23:50 -0000 Message-ID: <20000304132350.85610.qmail@hotmail.com> Received: from 200.41.247.53 by www.hotmail.com with HTTP; Sat, 04 Mar 2000 05:23:50 PST X-Originating-IP: [200.41.247.53] To: lojban@onelist.com MIME-Version: 1.0 Mailing-List: list lojban@onelist.com; contact lojban-owner@onelist.com Delivered-To: mailing list lojban@onelist.com Precedence: bulk List-Unsubscribe: Date: Sat, 04 Mar 2000 05:23:50 PST X-eGroups-From: "Jorge Llambias" From: "Jorge Llambias" Subject: [lojban] Final clubs - a basket demonstration Content-Type: text/plain Content-Transfer-Encoding: 8bit From: "Jorge Llambias" Here is a demonstration that for final clubs to be well defined by the circular "definition", it is necessary that all clubs be final clubs. Demonstration: We will divide all clubs into two baskets, one labeled "candidates for finality" and the other labeled "the rest". (If the clubs are too big to fit in the baskets, we can use little numbered balls to represent the clubs.) Choose any club whatsoever to start with and place it in the "candidates for finality" basket. Choose any of the remaining clubs and see whether it is incompatible with the first one you chose. If it is, put it in the "candidates" basket, else put it in the "the rest" basket. Choose any of the remaining clubs and test it for compatibility with all clubs in the "candidates" basket. If incompatible with all of them, put it there. Else drop it with "the rest". Repeat the preceding paragraph until there are no clubs remaining. Now, you can see that the "candidates for finality" are a possible set of final clubs. They are by construction incompatible with one another, and also by construction every club in "the rest" is compatible with at least one of them, so the "candidates" are a good set of final clubs. But the catch is that I could have started the whole procedure with any club whatsoever. So if there is any club in "the rest", I could have started with it and gotten a different but valid set of final clubs. Therefore, the only way for there to be a unique possible set of final clubs is that the "the rest" basket be empty. This means all clubs have to be final if final clubs are well defined. QED Please let me know if you find any holes in my argument. co'o mi'e xorxes ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com ------------------------------------------------------------------------ PERFORM CPR ON YOUR APR! Get a NextCard Visa, in 30 seconds! Get rates as low as 0.0% Intro or 9.9% Fixed APR and no hidden fees. Apply NOW! http://click.egroups.com/1/2121/1/_/17627/_/952176231/ ------------------------------------------------------------------------ To unsubscribe, send mail to lojban-unsubscribe@onelist.com