Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 (MU) 9/23/84; site munnari.OZ Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!mulga!munnari!lizs From: lizs@munnari.OZ (Liz Sonenberg) Newsgroups: net.math Subject: Re: Lists of points clarification Message-ID: <615@munnari.OZ> Date: Thu, 20-Dec-84 07:03:54 EST Article-I.D.: munnari.615 Posted: Thu Dec 20 07:03:54 1984 Date-Received: Mon, 24-Dec-84 03:10:43 EST References: <206@cmu-cs-g.ARPA> <614@munnari.OZ> Organization: Comp Sci, Melbourne Uni, Australia Lines: 13 > > I still don't see the problem. After an *evenly distributed* list of k points > has been chosen, exactly k of the subintervals > [0, 1/(k+1) ), [1/(k+1), 2/(k+1)), ... , [ k/(k+1), 1) will contain one of > the chosen points. By the pigeon-hole principle, there must be an interval > [i/(k+1), (i+1)/(k+1)) that doesn't contain one of the points. Choosing the > (k+1)th point in this interval will produce an *evenly distributed* list of > k+1 points, won't it ? OOPS. Sorry peoples, if I had seriously tried to answer my own question I ought to have seen my blunder immediately. David Wilson