Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site uwvax.ARPA Path: utzoo!watmath!clyde!burl!ulysses!mhuxj!ihnp4!zehntel!hplabs!hao!seismo!uwvax!anderson From: anderson@uwvax.ARPA (David P. Anderson) Newsgroups: net.jokes Subject: All horses are black: inductive proof Message-ID: <433@uwvax.ARPA> Date: Fri, 28-Sep-84 02:33:24 EDT Article-I.D.: uwvax.433 Posted: Fri Sep 28 02:33:24 1984 Date-Received: Wed, 26-Sep-84 04:16:05 EDT Organization: U of Wisconsin CS Dept Lines: 20 <> In response to a recent request: Lemma: all horses are the same color. Proof: We will show by induction on n that in any set of n horses, no 2 are colored differently. This is clearly true for the empty set. Now assume it's true for n-1, and let X be a set of n horses. Let y be an element of X, and let Y be X with y removed. By induction all the horses in Y are of the same color. Similarly, choose z in X, z != y, and let Z be X with z removed. Again, Z is all of the same color. Let h be in the intersection of Y and Z; y and z are both the same color as h, so all the horses in X are the same color. Theorem: all horses are black. Proof: Clearly there exists a black horse. Now apply the Lemma. Now that that's settled: does anyone remember the proof that all functions are continuous?