From sbelknap@UIC.EDU Sun Mar 05 20:54:40 2000 Received: (qmail 1111 invoked from network); 6 Mar 2000 04:54:55 -0000 Received: from unknown (10.1.10.27) by m3.onelist.org with QMQP; 6 Mar 2000 04:54:55 -0000 Received: from unknown (HELO eeyore.cc.uic.edu) (128.248.171.51) by mta2.onelist.org with SMTP; 6 Mar 2000 04:54:55 -0000 Received: from [128.248.28.106] (slip4b-03.dialin.uic.edu [128.248.10.151]) by eeyore.cc.uic.edu (8.9.3/8.9.3) with ESMTP id WAA05448 for ; Sun, 5 Mar 2000 22:52:00 -0600 (CST) Mime-Version: 1.0 X-Sender: sbelknap@mailserv.uic.edu Message-Id: Date: Sun, 5 Mar 2000 22:54:08 -0600 To: lojban@onelist.com Subject: By George, I think I've got it. Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-eGroups-From: Steven Belknap From: Steven Belknap X-Yahoo-Message-Num: 2225 A student at Yale may belong to zero or more clubs. Some clubs are final clubs. A final club is defined as "a club such that membership in it precludes membership in any other final club". 1. Call a set, s, of clubs preclusive if being a member of any one of the clubs in s precludes being a member of any other club in s. 2. Call a set, m, of clubs maximally preclusive if it is preclusive and every proper superset of m is not preclusive. 3. There is one and only one nonempty set, m. (We are told that some clubs are final clubs. If there were no nonempty sets m, that would violate the conditions of the problem. If there were more than one set m, than it would not be possible to know which set m contained the final clubs, and a definition of final club would be impossible. Since the problem contains a definition, albeit a circular one, a definition must be possible and there must be only one nonempty set, m.) 4. Call a club, c, a final club iff it is a member of m. QED co'o mi'e stivn Steven Belknap, M.D. Assistant Professor of Clinical Pharmacology and Medicine University of Illinois College of Medicine at Peoria