Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: $Revision: 1.6.2.13 $; site iuvax.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxj!ihnp4!inuxc!iuvax!dswise From: dswise@iuvax.UUCP Newsgroups: net.jokes Subject: Re: real transitional logic Message-ID: <7200035@iuvax.UUCP> Date: Tue, 18-Sep-84 10:31:00 EDT Article-I.D.: iuvax.7200035 Posted: Tue Sep 18 10:31:00 1984 Date-Received: Tue, 25-Sep-84 09:25:14 EDT References: <340@wxlvax.UUCP> Lines: 17 Nf-ID: #R:wxlvax:-34000:iuvax:7200035:000:721 Nf-From: iuvax!dswise Sep 18 09:31:00 1984 Theorem: No two horses are of the same color. PROOF (by simple induction): Simple induction is valid here because there are only a finite number of horses in the world. BASIS: A singleton set of horses vacuously satisfies the theorem. INDUCTION STEP: Assume the theorem is true of a set of n horses, and introduce an (n+1)st horse. 1. Now that you've introduced him, he knows all the other horses, and hence all horses know each other. (Whoops, wrong theorem.) 2. Try again. By a previous theorem, this (n+1)st horse has an infinite number of legs. Strange! That certainly is a horse of a different color. Thus, any two horses in the extended set are of different colors. ---acknowledgement to scs