Comments on: Itty Bitty Intervals. Topic: Algebra/Sets. Level: Olympiad. http://wangsblog.com/jeffrey/?p=111 Serves a Daily Special and an All-You-Can-Eat Course in Problem Solving. Courtesy of me, Jeffrey Wang. Fri, 19 Dec 2008 19:04:11 -0800 http://wordpress.org/?v=2.9.2 hourly 1 By: RKinski http://wangsblog.com/jeffrey/?p=111&cpage=1#comment-4504 RKinski Wed, 22 Aug 2007 07:13:25 +0000 http://wangsblog.com/jeffrey/?p=111#comment-4504 <strong>Yahoo Database</strong> How add your blog to yahoo database? Yahoo Database

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]]> By: QC http://wangsblog.com/jeffrey/?p=111&cpage=1#comment-141 QC Sat, 18 Mar 2006 02:03:47 +0000 http://wangsblog.com/jeffrey/?p=111#comment-141 Proof 1: Pidgeonhole. Proof 2: Suppose that there do not exist two such numbers. Arrange them in increasing order as the sequence a_n. The successive difference from each a_k to each a_{k+1} must be greater than 1/(n-1), and there are (n-1) such successive pairs; hence, the interval must have length greater than 1. Contradiction. Proof 1: Pidgeonhole.

Proof 2: Suppose that there do not exist two such numbers. Arrange them in increasing order as the sequence a_n. The successive difference from each a_k to each a_{k+1} must be greater than 1/(n-1), and there are (n-1) such successive pairs; hence, the interval must have length greater than 1. Contradiction.

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