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	<title>Comments on: Most elementray aha! moments</title>
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	<link>http://www.mathteacherctk.com/blog/2010/06/most-elementray-aha-moments/</link>
	<description>Thoughts on math education and related tidbits</description>
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		<title>By: A beautiful mathematical equality &#171; Chaitanya&#039;s Random Pages</title>
		<link>http://www.mathteacherctk.com/blog/2010/06/most-elementray-aha-moments/comment-page-1/#comment-1947</link>
		<dc:creator>A beautiful mathematical equality &#171; Chaitanya&#039;s Random Pages</dc:creator>
		<pubDate>Thu, 22 Jul 2010 10:31:44 +0000</pubDate>
		<guid isPermaLink="false">http://www.mathteacherctk.com/blog/?p=382#comment-1947</guid>
		<description>[...] A beautiful mathematical&#160;equality July 22, 2010 &#8212; ckrao   Here is an equality worth sharing, found at the CTK Insights blog here. [...]</description>
		<content:encoded><![CDATA[<p>[...] A beautiful mathematical&nbsp;equality July 22, 2010 &#8212; ckrao   Here is an equality worth sharing, found at the CTK Insights blog here. [...]</p>
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		<title>By: Radical Simplification &#124; CTK Insights</title>
		<link>http://www.mathteacherctk.com/blog/2010/06/most-elementray-aha-moments/comment-page-1/#comment-1942</link>
		<dc:creator>Radical Simplification &#124; CTK Insights</dc:creator>
		<pubDate>Mon, 19 Jul 2010 16:33:13 +0000</pubDate>
		<guid isPermaLink="false">http://www.mathteacherctk.com/blog/?p=382#comment-1942</guid>
		<description>[...] a related post I have shown that  Without resorting to this proof, I am going to show [...]</description>
		<content:encoded><![CDATA[<p>[...] a related post I have shown that  Without resorting to this proof, I am going to show [...]</p>
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		<title>By: admin</title>
		<link>http://www.mathteacherctk.com/blog/2010/06/most-elementray-aha-moments/comment-page-1/#comment-1928</link>
		<dc:creator>admin</dc:creator>
		<pubDate>Wed, 14 Jul 2010 18:18:23 +0000</pubDate>
		<guid isPermaLink="false">http://www.mathteacherctk.com/blog/?p=382#comment-1928</guid>
		<description>Here is in fact the same problem. Unless there is a reasonable definition of .999... there is no reason to assume that 10&#215;.999... = 9.999...

Assume x = 1 + &#916;. Then

10x = 10 + 10&#916;

Subtracting gives

9x = 9 + 9&#916;, or

x = 1 + &#916;,

which is nothing new.</description>
		<content:encoded><![CDATA[<p>Here is in fact the same problem. Unless there is a reasonable definition of .999... there is no reason to assume that 10&times;.999... = 9.999...</p>
<p>Assume x = 1 + &Delta;. Then</p>
<p>10x = 10 + 10&Delta;</p>
<p>Subtracting gives</p>
<p>9x = 9 + 9&Delta;, or</p>
<p>x = 1 + &Delta;,</p>
<p>which is nothing new.</p>
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