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	<title>Felix&#039; Math Place &#187; Bessel&#8217;s inequality</title>
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	<description>Focussed on, but not limited to Computational Number Theory</description>
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		<title>Inequalities.</title>
		<link>http://math.fontein.de/2010/02/09/inequalities/</link>
		<comments>http://math.fontein.de/2010/02/09/inequalities/#comments</comments>
		<pubDate>Tue, 09 Feb 2010 06:29:04 +0000</pubDate>
		<dc:creator>Felix Fontein</dc:creator>
				<category><![CDATA[Algebra]]></category>
		<category><![CDATA[Analysis]]></category>
		<category><![CDATA[Bessel's inequality]]></category>
		<category><![CDATA[Cauchy-Schwarz inequality]]></category>
		<category><![CDATA[generalized mean inequality]]></category>
		<category><![CDATA[Gibb's inequality]]></category>
		<category><![CDATA[Hölder's inequality]]></category>
		<category><![CDATA[inequalities]]></category>
		<category><![CDATA[inequality of arithmetic and geometric mean]]></category>
		<category><![CDATA[inequality of weighted arithmetic and geometric mean]]></category>
		<category><![CDATA[Jensen's inequality]]></category>
		<category><![CDATA[log-sum inequality]]></category>
		<category><![CDATA[Maclaurin's inequality]]></category>
		<category><![CDATA[Mahler's inequality]]></category>
		<category><![CDATA[Minkowski's inequality]]></category>
		<category><![CDATA[Muirhead's inequality]]></category>
		<category><![CDATA[Newton's inequalities]]></category>
		<category><![CDATA[Parseval's identity]]></category>
		<category><![CDATA[Pythagorean means]]></category>
		<category><![CDATA[Rao-Blackwell Theorem]]></category>
		<category><![CDATA[triangle inequality]]></category>
		<category><![CDATA[Young's inequality (on numbers)]]></category>

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		<description><![CDATA[This post shows a diagram, listing a lot of inequalities and showing implications between them.]]></description>
			<content:encoded><![CDATA[<p>Inspired by a <a href="http://math.fontein.de/forward.php?r=http://twitter.com/ProbFact/statuses/8684799550">tweet</a>, I decided to play a bit with <a href="http://math.fontein.de/forward.php?r=http://www.graphviz.org/">Graphviz</a> to create a graph on which inequalities imply which ones. Here&#8217;s the result:<br />
<img src="http://math.fontein.de/wp-content/uploads/2010/02/inequalities-small.png" width="510" height="210" usemap="#ineqmap" border="0" alt="" /><br />
Click <a href="http://math.fontein.de/forward.php?r=http://math.fontein.de/wp-content/uploads/2010/02/inequalities-large.png">here</a> to obtain a larger version. Click any box on the image to obtain the <a href="http://math.fontein.de/forward.php?r=http://en.wikipedia.org/wiki/Main_Page">Wikipedia</a> page on the inequality.</p>
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