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	<title>appendix &amp;laquo; WordPress.com Tag Feed</title>
	<link>http://en.wordpress.com/tag/appendix/</link>
	<description>Feed of posts on WordPress.com tagged "appendix"</description>
	<pubDate>Thu, 24 Dec 2009 08:26:00 +0000</pubDate>

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<title><![CDATA[It's probably not a good idea to cut out your own organs. I'll make an exception for my gall bladder.]]></title>
<link>http://bitemymoko.wordpress.com/2009/12/22/its-probably-not-a-good-idea-to-cut-out-your-own-organs-ill-make-an-exception-for-my-gall-bladder/</link>
<pubDate>Tue, 22 Dec 2009 09:10:02 +0000</pubDate>
<dc:creator>bitemymoko</dc:creator>
<guid>http://bitemymoko.wordpress.com/2009/12/22/its-probably-not-a-good-idea-to-cut-out-your-own-organs-ill-make-an-exception-for-my-gall-bladder/</guid>
<description><![CDATA[One night when I was in Grade 8, my parents returned from an outing to find me sitting at the kitche]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>One night when I was in Grade 8, my parents returned from an outing to find me sitting at the kitchen table, clad in my pajamas and poring over the first volume of our encyclopedia set.</p>
<p>I was studying the entry under Appendix and seeing if anything there applied to the searing pain in my abdomen. For some reason, my 13-year-old self had a profound fear of said organ rupturing one day and consequently sending me to my grave before I’d had the opportunity to fully appreciate the onslaught of puberty.</p>
<p>Turns out the pain in my side that had roused me from sleep and sent me downstairs to the bookshelf was not my appendix come calling with the ace of spades in hand but, rather, my spleen, having been bruised by a particularly robust tackle during a community football game I played that weekend.</p>
<p>A visit to the local hospital, a caution to stay off the cleats for a few days, and I was good as gold.</p>
<p>They say you can’t buy your health, which is a good thing considering my lack of fundage. Working in a seniors’ residence only reinforces that notion. Once Nature decides we are no longer of any use as far as perpetuating the species, our bodies quickly begin to deteriorate.</p>
<p>I’m touching wood as I write this, but I count myself lucky as far as health problems go. Oh sure, there was that stay in a hospital necessitated by a peptic ulcer, the result of taking full advantage of the employees-eat-for-free policy at the fried chicken joint where I was working.</p>
<p>I sprained both knees playing hockey and now no longer entertain any thoughts of running marathons. And an errant kidney stone once nearly brought me to my knees and resulted in yet another hospital stay. Only this one saw me being paid in full as part of my benefits package, so I read in bed for a week while women attended to my every need. So, yeah, totally worth the excruciating pain.</p>
<p>What’s now keeping me awake at night, literally, is my gall bladder. Or, rather, the gall stones that rattle around in said bladder, becoming more and more agitated as I shovel fatty substances into my pie hole, until one of the little bastards becomes jammed in the entrance.</p>
<p>This invariably happens at 1 a.m. and results in me on the bathroom floor, blinded by the light, fumbling under the sink for anything that will ease the pain.</p>
<p>A number of my relatives have had their gall bladders removed and report no adverse effects. But, unlike the abovementioned useless appendix, I’m pretty sure, when it’s not playing silly buggers, your gall bladder has a purpose.</p>
<p>Mine, for instance, is designed to remind me that eating Christmas cake is fine. Eating Christmas cake smothered in dollops of whipped cream? Not so much.</p>
<p>So, yeah, it’s been a rough start to my workday. I’m tired from a restless night and, unlike other attacks, this time my gall bladder is still throbbing well into the morning. In fact, I’ve just now returned from the toilet, where I recycled a bowl of cereal and fruit, along with several cups of perfectly decent coffee.</p>
<p>In my body’s haste to rid itself of anything that might be annoying my gall bladder, I managed to spew all over the floor, the door and my pant legs. It’s going to be a long, hot day here in the laundry room and I can only imagine the stench that will soon envelop me.</p>
<p>On second thought, maybe I will have the offending organ removed. In fact, if it gives me any more trouble today, I’m going to march straight down to the facility’s kitchen, borrow a steak knife and cut out the bastard myself.</p>
<p>And while I&#8217;m schlurping around in the old body cavity, I may even pay a visit to Mr. Appendix. A bit of payback, as it were, for scaring 13-year-old boys half to death.</p>
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<item>
<title><![CDATA[Appendix 4: z + n = n + z = n]]></title>
<link>http://sivaambi.wordpress.com/2009/12/20/appendix-4-z-n-n-z-n/</link>
<pubDate>Mon, 21 Dec 2009 04:33:35 +0000</pubDate>
<dc:creator>sivaambi</dc:creator>
<guid>http://sivaambi.wordpress.com/2009/12/20/appendix-4-z-n-n-z-n/</guid>
<description><![CDATA[To prove: Proof: We will first prove . By definition of addition, we have . By definition of , we ha]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><strong>To prove: </strong><img src='http://l.wordpress.com/latex.php?latex=z+%2B+n+%3D+n+%2B+z+%3D+n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + n = n + z = n' title='z + n = n + z = n' class='latex' /></p>
<p><strong>Proof:</strong></p>
<p>We will first prove <img src='http://l.wordpress.com/latex.php?latex=n+%2B+z+%3D+n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n + z = n' title='n + z = n' class='latex' />.</p>
<p>By definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=n+%2B+S%28z%29+%3D+S%28n%2Bz%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n + S(z) = S(n+z)' title='n + S(z) = S(n+z)' class='latex' />.</p>
<p>By definition of <img src='http://l.wordpress.com/latex.php?latex=z&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z' title='z' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28z%29+%3D+e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(z) = e' title='S(z) = e' class='latex' />.</p>
<p>By definition of addition, we know that <img src='http://l.wordpress.com/latex.php?latex=n+%2B+e+%3D+S%28n%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n + e = S(n)' title='n + e = S(n)' class='latex' />.</p>
<p>So we get, <img src='http://l.wordpress.com/latex.php?latex=S%28n%2Bz%29+%3D+n+%2B+S%28z%29+%3D+n+%2B+e+%3D+S%28n%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(n+z) = n + S(z) = n + e = S(n)' title='S(n+z) = n + S(z) = n + e = S(n)' class='latex' />.</p>
<p>Since the successor function is one-to-one, we get</p>
<p><img src='http://l.wordpress.com/latex.php?latex=n+%2B+z+%3D+n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n + z = n' title='n + z = n' class='latex' />.</p>
<p>Now, we will prove that <img src='http://l.wordpress.com/latex.php?latex=z+%2B+n+%3D+n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + n = n' title='z + n = n' class='latex' />.</p>
<p>This can be done by induction.</p>
<p>Let <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{S}' title='\mathbb{S}' class='latex' /> be the set of all <img src='http://l.wordpress.com/latex.php?latex=n+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n \in \mathbb{N}' title='n \in \mathbb{N}' class='latex' />, such that <img src='http://l.wordpress.com/latex.php?latex=z+%2B+n+%3D+n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + n = n' title='z + n = n' class='latex' />.</p>
<p><strong>First Step:</strong></p>
<p>Clearly, <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}' title='e \in \mathbb{S}' class='latex' />.</p>
<p>By definition of <img src='http://l.wordpress.com/latex.php?latex=z&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z' title='z' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28z%29+%3D+e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(z) = e' title='S(z) = e' class='latex' />.</p>
<p>By definition of addition, we get <img src='http://l.wordpress.com/latex.php?latex=z+%2B+e+%3D+S%28z%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + e = S(z)' title='z + e = S(z)' class='latex' />.</p>
<p>Hence <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}' title='e \in \mathbb{S}' class='latex' />.</p>
<p><strong>Second Step:</strong></p>
<p>Assume that <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}' title='k \in \mathbb{S}' class='latex' />. We need to prove that <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) \in \mathbb{S}' title='S(k) \in \mathbb{S}' class='latex' />.</p>
<p>By induction assumption, we get <img src='http://l.wordpress.com/latex.php?latex=z+%2B+k+%3D+k&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + k = k' title='z + k = k' class='latex' />.</p>
<p>By addition definition, we have <img src='http://l.wordpress.com/latex.php?latex=z+%2B+S%28k%29+%3D+S%28z%2Bk%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + S(k) = S(z+k)' title='z + S(k) = S(z+k)' class='latex' />.</p>
<p>So we get, <img src='http://l.wordpress.com/latex.php?latex=z+%2B+S%28k%29+%3D+S%28z%2Bk%29+%3D+S%28k%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + S(k) = S(z+k) = S(k)' title='z + S(k) = S(z+k) = S(k)' class='latex' />.</p>
<p>Hence, <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) \in \mathbb{S}' title='S(k) \in \mathbb{S}' class='latex' />.</p>
<p><strong>Final Step:</strong></p>
<p>So we have,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}' title='e \in \mathbb{S}' class='latex' /> and whenever <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}' title='k \in \mathbb{S}' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) \in \mathbb{S}' title='S(k) \in \mathbb{S}' class='latex' />.</p>
<p>Hence, by the principle of mathematical induction, we have</p>
<p><img src='http://l.wordpress.com/latex.php?latex=z+%2B+n+%3D+n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + n = n' title='z + n = n' class='latex' />, $\forall n \in \mathbb{N}$.</p>
<p>So, we get</p>
<p><img src='http://l.wordpress.com/latex.php?latex=z+%2B+n+%3D+n+%2B+z+%3D+n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='z + n = n + z = n' title='z + n = n + z = n' class='latex' />.</p>
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<title><![CDATA[Appendix 1 : Associativity of Addition over Natural Number]]></title>
<link>http://sivaambi.wordpress.com/2009/12/20/associativity-of-addition-over-natural-number/</link>
<pubDate>Sun, 20 Dec 2009 19:12:27 +0000</pubDate>
<dc:creator>sivaambi</dc:creator>
<guid>http://sivaambi.wordpress.com/2009/12/20/associativity-of-addition-over-natural-number/</guid>
<description><![CDATA[To prove: The line of thought is as follows: Let be the set of all numbers , such that ,  . We will ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><strong>To prove:</strong> <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29+%2B+c+%3D+a+%2B+%28b+%2B+c+%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b) + c = a + (b + c )' title='(a+b) + c = a + (b + c )' class='latex' /></p>
<p>The line of thought is as follows:</p>
<p>Let <img title="\mathbb{S}" src="http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D&#38;bg=ffffff&#38;fg=000000&#38;s=0" alt="\mathbb{S}" /> be the set of all numbers <img src='http://l.wordpress.com/latex.php?latex=c&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='c' title='c' class='latex' />, such that <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29+%2B+c+%3D+a+%2B+%28b+%2B+c+%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b) + c = a + (b + c )' title='(a+b) + c = a + (b + c )' class='latex' />,  <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+a%2Cb+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall a,b \in \mathbb{N}' title='\forall a,b \in \mathbb{N}' class='latex' />.</p>
<p>We will prove that <img src='http://l.wordpress.com/latex.php?latex=e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e' title='e' class='latex' /> is in the set <img title="\mathbb{S}" src="http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D&#38;bg=ffffff&#38;fg=000000&#38;s=0" alt="\mathbb{S}" /> and whenever <img title="k \in \mathbb{S}" src="http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D&#38;bg=ffffff&#38;fg=000000&#38;s=0" alt="k \in \mathbb{S}" />, we have <img title="S(k) \in \mathbb{S}" src="http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D&#38;bg=ffffff&#38;fg=000000&#38;s=0" alt="S(k) \in \mathbb{S}" />. Then by invoking Peano’s axiom (viz, the Principle Mathematical Induction), we state that <img title="\mathbb{S}=\mathbb{N}" src="http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D%3D%5Cmathbb%7BN%7D&#38;bg=ffffff&#38;fg=000000&#38;s=0" alt="\mathbb{S}=\mathbb{N}" /> and hence <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29+%2B+c+%3D+a+%2B+%28b+%2B+c+%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b) + c = a + (b + c )' title='(a+b) + c = a + (b + c )' class='latex' />,  <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+a%2Cb+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall a,b \in \mathbb{N}' title='\forall a,b \in \mathbb{N}' class='latex' />.</p>
<p><strong>Proof:</strong></p>
<p><strong>First Step:</strong></p>
<p>Clearly, <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}' title='e \in \mathbb{S}' class='latex' />. This is because of the definition of addition.</p>
<p><img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29%2Be+%3D+S%28a%2Bb%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b)+e = S(a+b)' title='(a+b)+e = S(a+b)' class='latex' /> and <img src='http://l.wordpress.com/latex.php?latex=a+%2B+S%28b%29+%3D+S%28a%2Bb%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='a + S(b) = S(a+b)' title='a + S(b) = S(a+b)' class='latex' /></p>
<p>Hence <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29%2Be+%3D+a+%2B+S%28b%29+%3D+a%2B+%28b%2Be%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b)+e = a + S(b) = a+ (b+e)' title='(a+b)+e = a + S(b) = a+ (b+e)' class='latex' /></p>
<p><strong>Second Step:</strong></p>
<p>Assume that the statement is true for some <img src='http://l.wordpress.com/latex.php?latex=k+%5C+in+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \ in \mathbb{N}' title='k \ in \mathbb{N}' class='latex' />.</p>
<p>Therefore, we have <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29%2Bk+%3D+a%2B%28b%2Bk%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b)+k = a+(b+k)' title='(a+b)+k = a+(b+k)' class='latex' />.</p>
<p>Now we need to prove, <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29+%2B+S%28k%29+%3D+a%2B%28b%2BS%28k%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b) + S(k) = a+(b+S(k))' title='(a+b) + S(k) = a+(b+S(k))' class='latex' />.</p>
<p>By definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29%2BS%28k%29+%3D+S%28%28a%2Bb%29+%2B+k%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b)+S(k) = S((a+b) + k)' title='(a+b)+S(k) = S((a+b) + k)' class='latex' /></p>
<p>By induction hypothesis, we have <img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29%2Bk+%3D+a%2B+%28b%2Bk%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b)+k = a+ (b+k)' title='(a+b)+k = a+ (b+k)' class='latex' /></p>
<p>By definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=b+%2B+S%28k%29+%3D+S%28b%2Bk%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='b + S(k) = S(b+k)' title='b + S(k) = S(b+k)' class='latex' /></p>
<p>By definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=a%2BS%28b%2Bk%29+%3D+S%28a%2B%28b%2Bk%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='a+S(b+k) = S(a+(b+k))' title='a+S(b+k) = S(a+(b+k))' class='latex' /></p>
<p>Hence, we get,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=%28a+%2B+b%29+%2B+S%28k%29+%3D+S%28%28a%2Bb%29+%2B+k%29+%3D+S%28a%2B+%28b%2Bk%29%29+%3D+a+%2B+S%28b%2Bk%29+%3D+a%2B+%28b+%2B+S%28k%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a + b) + S(k) = S((a+b) + k) = S(a+ (b+k)) = a + S(b+k) = a+ (b + S(k))' title='(a + b) + S(k) = S((a+b) + k) = S(a+ (b+k)) = a + S(b+k) = a+ (b + S(k))' class='latex' /></p>
<p>Hence, we get,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29+%2B+S%28k%29+%3D+a+%2B+%28b%2BS%28k%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b) + S(k) = a + (b+S(k))' title='(a+b) + S(k) = a + (b+S(k))' class='latex' /></p>
<p><strong>Final Step:</strong></p>
<p>So, we have <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}' title='e \in \mathbb{S}' class='latex' />. And whenever <img title="k \in \mathbb{S}" src="http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D&#38;bg=ffffff&#38;fg=000000&#38;s=0" alt="k \in \mathbb{S}" />, we have <img title="S(k) \in \mathbb{S}" src="http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D&#38;bg=ffffff&#38;fg=000000&#38;s=0" alt="S(k) \in \mathbb{S}" />.</p>
<p>Hence, by Principle of Mathematical Induction, we have the associativity of addition, viz,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=%28a%2Bb%29+%2B+c+%3D+a+%2B+%28b%2Bc%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='(a+b) + c = a + (b+c)' title='(a+b) + c = a + (b+c)' class='latex' /></p>
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<title><![CDATA[Appendix 2 : k + S(m) = S(k) + m]]></title>
<link>http://sivaambi.wordpress.com/2009/12/19/k-sm-sk-m/</link>
<pubDate>Sat, 19 Dec 2009 21:56:59 +0000</pubDate>
<dc:creator>sivaambi</dc:creator>
<guid>http://sivaambi.wordpress.com/2009/12/19/k-sm-sk-m/</guid>
<description><![CDATA[To prove: k + S(m) = S(k) + m This is done by induction on . Proof: Let be a set of all , such that ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><strong>To prove:</strong> k + S(m) = S(k) + m</p>
<p>This is done by induction on <img src='http://l.wordpress.com/latex.php?latex=m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m' title='m' class='latex' />.</p>
<p><strong>Proof:</strong></p>
<p>Let <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BT%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{T}' title='\mathbb{T}' class='latex' /> be a set of all <img src='http://l.wordpress.com/latex.php?latex=m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m' title='m' class='latex' />, such that <img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28m%29+%3D+S%28k%29+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(m) = S(k) + m' title='k + S(m) = S(k) + m' class='latex' />.</p>
<p><strong>Step 1:</strong></p>
<p><img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28e%29+%3D+S%28k%2Be%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(e) = S(k+e)' title='k + S(e) = S(k+e)' class='latex' /> (By definition of addition)</p>
<p><img src='http://l.wordpress.com/latex.php?latex=k%2Be+%3D+S%28k%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k+e = S(k)' title='k+e = S(k)' class='latex' /> (By definition of addition)</p>
<p><img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%2B+e+%3D+S%28S%28k%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) + e = S(S(k))' title='S(k) + e = S(S(k))' class='latex' /> (By definition of addition)</p>
<p>So we get,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28e%29+%3D+S%28k%2Be%29+%3D+S%28S%28k%29%29+%3D+S%28k%29+%2B+e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(e) = S(k+e) = S(S(k)) = S(k) + e' title='k + S(e) = S(k+e) = S(S(k)) = S(k) + e' class='latex' />.</p>
<p>Hence <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BT%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{T}' title='e \in \mathbb{T}' class='latex' /></p>
<p><strong>Step 2:</strong></p>
<p>Assume that <img src='http://l.wordpress.com/latex.php?latex=p+%5Cin+%5Cmathbb%7BT%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='p \in \mathbb{T}' title='p \in \mathbb{T}' class='latex' />. We have <img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28p%29+%3D+S%28k%29+%2B+p&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(p) = S(k) + p' title='k + S(p) = S(k) + p' class='latex' />.</p>
<p>Now we need to prove that <img src='http://l.wordpress.com/latex.php?latex=S%28p%29+%5Cin+%5Cmathbb%7BT%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(p) \in \mathbb{T}' title='S(p) \in \mathbb{T}' class='latex' />.</p>
<p><img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28S%28p%29%29+%3D+S%28k%2BS%28p%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(S(p)) = S(k+S(p))' title='k + S(S(p)) = S(k+S(p))' class='latex' /> (By definition of addition)</p>
<p><img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28p%29+%3D+S%28k%29+%2B+p&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(p) = S(k) + p' title='k + S(p) = S(k) + p' class='latex' /> (By induction hypothesis)</p>
<p><img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%2B+S%28p%29+%3D+S%28S%28k%29+%2B+p%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) + S(p) = S(S(k) + p)' title='S(k) + S(p) = S(S(k) + p)' class='latex' /> (By definition of addition)</p>
<p>So we get,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28S%28p%29%29+%3D+S%28k+%2B+S%28p%29%29+%3D+S%28S%28k%29%2Bp%29+%3D+S%28k%29+%2B+S%28p%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(S(p)) = S(k + S(p)) = S(S(k)+p) = S(k) + S(p)' title='k + S(S(p)) = S(k + S(p)) = S(S(k)+p) = S(k) + S(p)' class='latex' />.</p>
<p>Hence <img src='http://l.wordpress.com/latex.php?latex=S%28p%29+%5Cin+%5Cmathbb%7BT%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(p) \in \mathbb{T}' title='S(p) \in \mathbb{T}' class='latex' />, whenever <img src='http://l.wordpress.com/latex.php?latex=p+%5Cin+%5Cmathbb%7BT%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='p \in \mathbb{T}' title='p \in \mathbb{T}' class='latex' /></p>
<p>So we have <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BT%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{T}' title='e \in \mathbb{T}' class='latex' /> and whenever <img src='http://l.wordpress.com/latex.php?latex=m+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m \in \mathbb{N}' title='m \in \mathbb{N}' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28m%29+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(m) \in \mathbb{N}' title='S(m) \in \mathbb{N}' class='latex' />.</p>
<p>Hence by principle of mathematical induction, we have that <img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28m%29+%3D+S%28k%29+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(m) = S(k) + m' title='k + S(m) = S(k) + m' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+k%2Cm+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall k,m \in \mathbb{N}' title='\forall k,m \in \mathbb{N}' class='latex' /></p>
</div>]]></content:encoded>
</item>
<item>
<title><![CDATA[Appendix 3 : Commutativity of Addition over Natural Numbers]]></title>
<link>http://sivaambi.wordpress.com/2009/12/19/commutativity-of-addition-over-natural-numbers/</link>
<pubDate>Sat, 19 Dec 2009 20:55:57 +0000</pubDate>
<dc:creator>sivaambi</dc:creator>
<guid>http://sivaambi.wordpress.com/2009/12/19/commutativity-of-addition-over-natural-numbers/</guid>
<description><![CDATA[To prove: , . The line of thought for the proof is as follows. Let be the set of all numbers , such ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><strong>To prove:</strong> <img src='http://l.wordpress.com/latex.php?latex=m+%2B+n+%3D+n+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + n = n + m' title='m + n = n + m' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+m%2Cn+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall m,n \in \mathbb{N}' title='\forall m,n \in \mathbb{N}' class='latex' />.</p>
<p>The line of thought for the proof is as follows.</p>
<p>Let <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{S}' title='\mathbb{S}' class='latex' /> be the set of all numbers <img src='http://l.wordpress.com/latex.php?latex=n&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n' title='n' class='latex' />, such that <img src='http://l.wordpress.com/latex.php?latex=m+%2B+n+%3D+n+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + n = n + m' title='m + n = n + m' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+m+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall m \in \mathbb{N}' title='\forall m \in \mathbb{N}' class='latex' />.</p>
<p>We will prove that <img src='http://l.wordpress.com/latex.php?latex=e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e' title='e' class='latex' /> is in the set <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{S}' title='\mathbb{S}' class='latex' /> and whenever <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}' title='k \in \mathbb{S}' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) \in \mathbb{S}' title='S(k) \in \mathbb{S}' class='latex' />. Then by invoking Peano&#8217;s axiom (viz, the Principle Mathematical Induction), we state that <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D%3D%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{S}=\mathbb{N}' title='\mathbb{S}=\mathbb{N}' class='latex' /> and hence <img src='http://l.wordpress.com/latex.php?latex=m+%2B+n+%3D+n+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + n = n + m' title='m + n = n + m' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+m%2Cn+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall m,n \in \mathbb{N}' title='\forall m,n \in \mathbb{N}' class='latex' />.</p>
<p><strong>Proof:</strong></p>
<p><strong>First Step:</strong></p>
<p>We will prove that <img src='http://l.wordpress.com/latex.php?latex=m+%2B+e+%3D+e+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + e = e + m' title='m + e = e + m' class='latex' /> and hence <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}' title='e \in \mathbb{S}' class='latex' />.</p>
<p>The line of thought for the proof is as follows:</p>
<p>Let <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{S}_1' title='\mathbb{S}_1' class='latex' /> be the set of all numbers <img src='http://l.wordpress.com/latex.php?latex=m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m' title='m' class='latex' />, such that <img src='http://l.wordpress.com/latex.php?latex=m+%2B+e+%3D+e+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + e = e + m' title='m + e = e + m' class='latex' />.</p>
<p>We will prove that <img src='http://l.wordpress.com/latex.php?latex=e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e' title='e' class='latex' /> is in the set <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{S}_1' title='\mathbb{S}_1' class='latex' /> and whenever <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}_1' title='k \in \mathbb{S}_1' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) \in \mathbb{S}_1' title='S(k) \in \mathbb{S}_1' class='latex' />. Then by invoking Peano&#8217;s axiom (viz, the Principle Mathematical Induction), we state that <img src='http://l.wordpress.com/latex.php?latex=%5Cmathbb%7BS%7D_1%3D%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\mathbb{S}_1=\mathbb{N}' title='\mathbb{S}_1=\mathbb{N}' class='latex' /> and hence <img src='http://l.wordpress.com/latex.php?latex=m+%2B+e+%3D+e+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + e = e + m' title='m + e = e + m' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+m+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall m \in \mathbb{N}' title='\forall m \in \mathbb{N}' class='latex' />.</p>
<p>To prove: <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}_1' title='e \in \mathbb{S}_1' class='latex' /></p>
<p>Clearly, <img src='http://l.wordpress.com/latex.php?latex=e+%2B+e+%3D+e+%2B+e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e + e = e + e' title='e + e = e + e' class='latex' /> (We are adding the same elements on both sides)</p>
<p>Assume that <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}_1' title='k \in \mathbb{S}_1' class='latex' />. So we have <img src='http://l.wordpress.com/latex.php?latex=k+%2B+e+%3D+e+%2B+k&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + e = e + k' title='k + e = e + k' class='latex' />.</p>
<p>Now to prove <img src='http://l.wordpress.com/latex.php?latex=S%28k%29%2B+e+%3D+e+%2B+S%28k%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k)+ e = e + S(k)' title='S(k)+ e = e + S(k)' class='latex' />.</p>
<p>By the definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=e+%2B+S%28k%29+%3D+S%28e+%2B+k%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e + S(k) = S(e + k)' title='e + S(k) = S(e + k)' class='latex' /></p>
<p>By our induction step, we have <img src='http://l.wordpress.com/latex.php?latex=e+%2B+k+%3D+k+%2B+e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e + k = k + e' title='e + k = k + e' class='latex' />.</p>
<p>So we have <img src='http://l.wordpress.com/latex.php?latex=S%28e%2Bk%29+%3D+S%28k%2Be%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(e+k) = S(k+e)' title='S(e+k) = S(k+e)' class='latex' /></p>
<p>Again by definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=k+%2B+e+%3D+S%28k%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + e = S(k)' title='k + e = S(k)' class='latex' />.</p>
<p>Hence, we get <img src='http://l.wordpress.com/latex.php?latex=S%28k%2Be%29+%3D+S%28S%28k%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k+e) = S(S(k))' title='S(k+e) = S(S(k))' class='latex' />.</p>
<p>Again by definition of addition, <img src='http://l.wordpress.com/latex.php?latex=p+%2B+e+%3D+S%28p%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='p + e = S(p)' title='p + e = S(p)' class='latex' />.</p>
<p>So we gave <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%2B+e+%3D+S%28S%28k%29%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) + e = S(S(k))' title='S(k) + e = S(S(k))' class='latex' />.</p>
<p>Hence, we get <img src='http://l.wordpress.com/latex.php?latex=S%28k%2Be%29+%3D+S%28k%29+%2B+e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k+e) = S(k) + e' title='S(k+e) = S(k) + e' class='latex' />.</p>
<p>So we get,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=e+%2B+S%28k%29+%3D+S%28e%2Bk%29+%3D+S%28k%2Be%29+%3D+S%28S%28k%29%29+%3D+S%28k%29+%2B+e&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e + S(k) = S(e+k) = S(k+e) = S(S(k)) = S(k) + e' title='e + S(k) = S(e+k) = S(k+e) = S(S(k)) = S(k) + e' class='latex' />.</p>
<p>Hence, assuming that <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}_1' title='k \in \mathbb{S}_1' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D_1&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) \in \mathbb{S}_1' title='S(k) \in \mathbb{S}_1' class='latex' />.</p>
<p>Hence, by Principle of Mathematical Induction, we have <img src='http://l.wordpress.com/latex.php?latex=m+%2B+e+%3D+e+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + e = e + m' title='m + e = e + m' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+m+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall m \in \mathbb{N}' title='\forall m \in \mathbb{N}' class='latex' />.</p>
<p><strong>Second Step:</strong></p>
<p>Assume that <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}' title='k \in \mathbb{S}' class='latex' />. We need to prove now that <img src='http://l.wordpress.com/latex.php?latex=S%28k%29+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(k) \in \mathbb{S}' title='S(k) \in \mathbb{S}' class='latex' />.</p>
<p>Since <img src='http://l.wordpress.com/latex.php?latex=k+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k \in \mathbb{S}' title='k \in \mathbb{S}' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=m+%2B+k+%3D+k+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + k = k + m' title='m + k = k + m' class='latex' />.</p>
<p>To prove: <img src='http://l.wordpress.com/latex.php?latex=m+%2B+S%28k%29+%3D+S%28k%29+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + S(k) = S(k) + m' title='m + S(k) = S(k) + m' class='latex' />.</p>
<p>Proof:</p>
<p>By definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=m+%2B+S%28k%29+%3D+S%28m%2Bk%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + S(k) = S(m+k)' title='m + S(k) = S(m+k)' class='latex' />.</p>
<p>By induction hypothesis, we have <img src='http://l.wordpress.com/latex.php?latex=m+%2B+k+%3D+k+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + k = k + m' title='m + k = k + m' class='latex' />. Hence, we get <img src='http://l.wordpress.com/latex.php?latex=S%28m%2Bk%29+%3D+S%28k%2Bm%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(m+k) = S(k+m)' title='S(m+k) = S(k+m)' class='latex' />.</p>
<p>By definition of addition, we have <img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28m%29+%3D+S%28k%2Bm%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(m) = S(k+m)' title='k + S(m) = S(k+m)' class='latex' />.</p>
<p>Hence, we get <img src='http://l.wordpress.com/latex.php?latex=m+%2B+S%28k%29+%3D+S%28m%2Bk%29+%3D+S%28k%2Bm%29+%3D+k+%2B+S%28m%29&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + S(k) = S(m+k) = S(k+m) = k + S(m)' title='m + S(k) = S(m+k) = S(k+m) = k + S(m)' class='latex' />.</p>
<p>We are not done yet, since we want to prove, <img src='http://l.wordpress.com/latex.php?latex=m+%2B+S%28k%29+%3D+S%28k%29+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + S(k) = S(k) + m' title='m + S(k) = S(k) + m' class='latex' />.</p>
<p>So we are left to prove <img src='http://l.wordpress.com/latex.php?latex=k+%2B+S%28m%29+%3D+S%28k%29+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='k + S(m) = S(k) + m' title='k + S(m) = S(k) + m' class='latex' />.</p>
<p>This is done in <a href="http://sivaambi.wordpress.com/2009/12/19/k-sm-sk-m/" target="_blank">here</a>.</p>
<p>Hence, we get <img src='http://l.wordpress.com/latex.php?latex=m+%2B+S%28k%29+%3D+S%28k%29+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + S(k) = S(k) + m' title='m + S(k) = S(k) + m' class='latex' />.</p>
<p><strong>Final Step:</strong></p>
<p>So, we have <img src='http://l.wordpress.com/latex.php?latex=e+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='e \in \mathbb{S}' title='e \in \mathbb{S}' class='latex' />. And whenever <img src='http://l.wordpress.com/latex.php?latex=n+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n \in \mathbb{S}' title='n \in \mathbb{S}' class='latex' />, we have <img src='http://l.wordpress.com/latex.php?latex=S%28n%29+%5Cin+%5Cmathbb%7BS%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='S(n) \in \mathbb{S}' title='S(n) \in \mathbb{S}' class='latex' />.</p>
<p>Hence, by Principle of Mathematical Induction, we have the commutativity of addition, viz,</p>
<p><img src='http://l.wordpress.com/latex.php?latex=m+%2B+n+%3D+n+%2B+m&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='m + n = n + m' title='m + n = n + m' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%5Cforall+m%2Cn+%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\forall m,n \in \mathbb{N}' title='\forall m,n \in \mathbb{N}' class='latex' />.</p>
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<title><![CDATA[A very long week]]></title>
<link>http://llcall.wordpress.com/2009/12/18/a-very-long-week/</link>
<pubDate>Fri, 18 Dec 2009 21:10:21 +0000</pubDate>
<dc:creator>llcall</dc:creator>
<guid>http://llcall.wordpress.com/2009/12/18/a-very-long-week/</guid>
<description><![CDATA[Last night Neal told me, &#8220;I don&#8217;t like this week.&#8221;  If you know Neal&#8217;s calm,]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>Last night Neal told me, &#8220;I don&#8217;t like this week.&#8221;  If you know Neal&#8217;s calm, steady, quietly optimistic nature, you know that this is almost the equivalent of one of my <a href="http://llcall.wordpress.com/2009/12/16/back-home/" target="_blank">aforementioned teary meltdowns</a> (almost).  My poor guy is really at the end of his rope, the combined effect of the initial medical drama (and maybe too many people reminding him that if we lived in pioneer times, I&#8217;d be dead),  my constant need for help with basic life tasks like getting out of bed and picking things up, and the whirlwind of final projects, papers, and exams that should have been done by now if not for all these unexpected events.</p>
<p>Yesterday hit him with yet another blow: his computer crashed and in the process of whatever crazy things it was doing, also managed to reformat and erase his back-up hard drive.  Final film project (to which he had already devoted maybe 30-40 hours, and was due yesterday) = <span style="color:#ff0000;">GONE</span>.  All his other film footage for projects he&#8217;s been working on over the last two years = <span style="color:#ff0000;">GONE</span>.  Business documents, school documents = <span style="color:#ff0000;">GONE</span>.  We&#8217;ve got his computer and hard drive at two different repair shops, trying to determine if there is any recoverable data.</p>
<p>And yet there have been these constant reminders that God is really mindful of us.  I <a href="http://llcall.wordpress.com/2009/12/16/back-home/" target="_blank">mentioned before</a> that I was really grateful for my midwife&#8217;s insistence that they examine me for appendicitis.  Yesterday at our check-up appointment she told me the story from her perspective, starting out by saying that it was one of those experiences where you know God has just told you what to do.  She said that initially she had told the labor and delivery nurse that if my contractions were under control and I was hydrated, they could release me and she would call me later in the day to check in.  This was probably around 4:30 or 5 am.  She went back to sleep thinking that everything was under control, but at 6:00 am, she had a sort of lightning-bolt thought that she needed to talk to me immediately.  It was as she was talking to me that she realized appendicitis (even though, funny enough, when she talked to me on the phone she was still groggy enough that she couldn&#8217;t remember the name of the organ . . . our conversation went something like this: <span style="color:#0000ff;">Jana:</span> &#8220;You know that thing that can burst and it&#8217;s really bad.&#8221;  <span style="color:#ff00ff;">Me:</span> &#8220;Appendix?&#8221;  <span style="color:#0000ff;">Jana:</span> &#8220;Yeah, that&#8217;s it.  That&#8217;s what this is.&#8221;).  She called down to the ER immediately to let them know that this was absolutely urgent if we wanted to avoid a little preemie that day.  I marvel that even though she hadn&#8217;t even seen me or talked to me for more than a minute or two, she was exactly right.  The surgeon basically agreed that in a few more hours they would have had to deliver baby girl to preserve her health.  And Neal&#8217;s week would have been substantially more traumatic.</p>
<p>Another unexpected thing that we hardly know how to process at this moment also happened this week.  We were given a <em>very </em>generous anonymous Christmas gift.  All we were told is that the givers wanted to help a family in our ward at <a href="http://mormon.org/mormonorg/eng/" target="_blank">Church</a>, and that through prayer they learned that we were that family.  It is sort of an overwhelming thing to receive an envelope with cash in it, knowing that you are one of the truly blessed and most fortunate people on earth.  We couldn&#8217;t help but ask, <em>why us? </em> When the next day we found ourselves shelling out a couple hundred dollars that we weren&#8217;t planning on just to diagnose the problems with the computer and hard drive, I wondered if the money was a little tender mercy, mostly for Neal&#8217;s benefit, so that I wouldn&#8217;t hyperventilate about our monthly budget getting smashed (I tend to overreact about this type of thing; I am, afterall, my father&#8217;s stingy daughter).  But still I could hardly think that such an ultimately insignificant, very high-level &#8220;need&#8221; could merit that kind of attention when obviously there are people all around struggling to meet more basic needs.  We still keep asking ourselves, why should we be the recipients of so much generosity?  Is it to blunt the force of the last few months&#8217; medical bills?  Or something in the future that we still can&#8217;t foresee but God is preparing a way for us to handle?  (Neal has implored me not to contemplate the latter too much for obvious reasons.)</p>
<p>With all the question marks we still have, I am grateful that for now I am just dwelling on this feeling of gratitude.  Our baby girl is still safe and healthy.  My wounds are healing.  We&#8217;ll survive any and all computer crashes.  And Neal is taking a short break from all his heavy duties to do something that helps him unwind and relax: grocery shopping.  (And yes, I&#8217;m dead serious, walking the grocery aisles with his headphones on soothes his little soul.  He&#8217;s a weird dude, that one, but I love him.)</p>
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<title><![CDATA[Day 29 - 34 [Week 4 and 5] Appendectomy]]></title>
<link>http://operationcreate.wordpress.com/2009/12/13/day-29-34-week-4-and-5-appendectomy/</link>
<pubDate>Sun, 13 Dec 2009 11:40:55 +0000</pubDate>
<dc:creator>operationcreate</dc:creator>
<guid>http://operationcreate.wordpress.com/2009/12/13/day-29-34-week-4-and-5-appendectomy/</guid>
<description><![CDATA[Remember how my last post was something along the lines of, &#8220;Whine whine whine, I&#8217;m so s]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>Remember how my last post was something along the lines of, &#8220;Whine whine whine, I&#8217;m so sick&#8221;? Yeah. That turned out to be appendicitis. Went to the ER at 7pm Tuesday night and got admitted to the hospital. They removed my appendix at around 7:30pm Wednesday, and I finally got to go home Thursday night at 8pm.</p>
<p>I&#8217;m feeling better, obviously, since I don&#8217;t have a gut filled with infection anymore, but I do have three holes in my belly, and abdominal surgery is not the most comfortable thing in the world.</p>
<p>So, yeah. That&#8217;s where I&#8217;ve been.</p>
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<title><![CDATA["Then I will have an appendectomy"*]]></title>
<link>http://llcall.wordpress.com/2009/12/12/then-i-will-have-an-appendectomy/</link>
<pubDate>Sat, 12 Dec 2009 13:52:27 +0000</pubDate>
<dc:creator>llcall</dc:creator>
<guid>http://llcall.wordpress.com/2009/12/12/then-i-will-have-an-appendectomy/</guid>
<description><![CDATA[This is a really long post, probably mostly for my own benefit to remember what went on the last few]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><em>This is a really long post, probably mostly for my own benefit to remember what went on the last few days before all the drugs make it completely hazy.  I thought about posting some of the pictures the surgeon gave us of my innards to spice it up, but unless you&#8217;re a surgeon, you probably wouldn&#8217;t know what you were looking at anyway.</em></p>
<p>When I posted last week about <a href="http://llcall.wordpress.com/2009/12/01/im-in-stats-class-right-now/" target="_blank">finishing my last presentation and homework of grad school</a>, the end was so near, I could almost taste it.  But I still had one of those massive 3-part stats exams on my to-do list.  Although technically I had until Friday the 18th to finish, I felt totally driven to finish as soon as I could.  In fact, I gave myself a deadline of Wednesday the 9th (my professor allowed us to take it early if we wanted to).  It was interesting because a lot of people kept asking why I was imposing such an early deadline on myself, worrying that I was pushing myself too hard.  And it was a little hard . . . I mean, last Saturday I spent 10 hours straight camped out on the couch doing my take-home portion.  Intense, to say the least.</p>
<p>But for reasons that were not entirely clear to me, I just HAD to get my stats final done by Wednesday.  I wouldn&#8217;t say it felt like a spiritual prompting; I just felt like I needed to get it done by Wednesday.  And amazingly, shockingly (if you&#8217;ve been following my blog you know that I have not been the most productive person over the last several months) I finished exactly according to my plans.  As I left my stats class at 5:20 Wednesday evening, I could not have been more stoked because I actually made a plan and followed through with it.  A true Christmas miracle!  God bless us, everyone!</p>
<p>I was so ready to party that I even ordered my celebratory pizza on my laptop during class!  I brought the pizza home to share with dear Kaila, my friend that is in town for a short visit.  We inhaled it and then got all comfy and cozy to watch &#8220;Love Actually.&#8221;  It had the makings of a great night, until about 7:00 pm when I started having abdominal pain.  It wasn&#8217;t too bad at first and I thought it was just baby girl being a little mischievous.   But at the same time, the pain was in a place that made me ask out loud, <em>how on earth is baby girl kicking me there?!</em> <em> How can she even get to it?</em></p>
<p>Over the next couple of hours, the pain was intensifying but I just attributed it to digestive problems from over-consumption of delicious pizza.  I decided to go to bed early because I was feeling so crummy.  But sleep wouldn&#8217;t come and the pain kept getting worse.  Then vomiting started about 12:45 am.  I got Neal up about 1:30, and he woke my grandpa up, so that they could give me a blessing.  It was a very sweet moment, but not too long after it was becoming clear to me the pain was getting worse, the vomiting was getting worse, and it was time to book it to the emergency room.</p>
<p>Thankfully, there was no wait because they sent us straight up to labor and delivery.  They got me strapped to the fetal monitor and confirmed that I was having contractions.  They were not too intense according to their readings, but they were consistent and very close together.  The interesting thing though is that I wasn&#8217;t worried at all that I was going into preterm labor; it never even crossed my mind that baby girl would be born right then and there.</p>
<p>And she wasn&#8217;t.  They gave me medicine to relax my uterus and stop the contractions.  My blood work confirmed that I was very dehydrated, which they attributed to all the vomiting (I threw up in the hospital hallway as well . . . sorry Utah Valley janitorial staff), and they concluded that the dehydration started the contractions.  So labor and delivery is ready to discharge me, having stopped the contractions and given me an anti-nausea shot.  But thankfully, my midwife Jana called in to talk to me directly (she had been communicating with the nurses and ordering tests up to that point, about 6:30 am) and what I told her about the persistence of the pain made her think appendicitis.</p>
<p>So they trucked me down to the ER again to see an internal medicine specialist.  He also suspected appendicitis from my pain pattern and before I knew it, I was in the MRI machine so they could take a look at my insides.  Not the most pleasant 45 minutes ever&#8211;the noises are just deafening&#8211;but it wasn&#8217;t too bad compared to my last MRI because I got to go in feet first so my head didn&#8217;t feel quite so confined.  They were easily able to determine that my appendix was in bad shape.</p>
<p>Next I&#8217;m back to the ER where they begin prepping me for surgery, with everything from fetal heart monitoring to a Tylenol suppository (I&#8217;m sure you all know where suppositories go . . .  yuck!) to some wicked thing they called &#8220;bitter antacid.&#8221;  We met the surgeon at this point and he explained to us the possibility that this surgery would trigger labor and our baby would be born that day.  But of course, there was no choice.  So Neal and I had a few precious moments to contemplate this and some tears were shed.  And in case this isn&#8217;t a totally unexpected story already, the tears were Neal&#8217;s not mine.</p>
<p>Then I&#8217;m in &#8220;holding&#8221; while they finish getting me ready for the surgery.  Finally, the operating room where I don&#8217;t remember much before they knocked me out.  Then post-op . . . this was definitely the low point.  They said that the breathing tube they insert often irritates the throat so as I was coming to, I had the distinct feeling that 1) I could not breathe and 2) I could not swallow.  I was bordering on hysteria because I actually thought I was dying and that they weren&#8217;t helping to prevent it.  I asked for water and they said no.  I kept taking off the oxygen mask because I thought it was keeping me from breathing, and they kept putting it back on me.  I kept asking, <em>What did they do to my shoulder?</em> I was in extreme pain all over my abdomen, but the pain I felt in my shoulder area was the most surprising.  I distinctly remember wondering if they had taken a hammer to my shoulder just for spite.  Like I said, borderline hysteria. [The doctor has since explained to me that the shoulder pain is caused by the extra gas that they pumped into my abdomen so that they would have more space to maneuver].</p>
<p>It was also scary because this was the only time that baby girl was in distress.  Her heart rate was way too high, as was mine, and they kept trying to breathe with me and explain that I needed to relax so that the baby could relax too.  I distinctly remember feeling like a bad mother because although I was trying to calm down, I couldn&#8217;t figure out how to do it.  The room was spinning and I couldn&#8217;t see straight and I thought we were both dying.</p>
<p>After I was stabilized in post-op, they trucked me back up to labor and delivery, where I&#8217;ve been since Thursday around 4:00 pm.  For the record, I didn&#8217;t mind all this transporting from here to there because, guess what, you get to do it while laying down in bed.  It&#8217;s the only way to travel.  I&#8217;m probably spoiled for life!!</p>
<p>Based on the MRI, they couldn&#8217;t tell if my appendix had already ruptured or not, but luckily it had not.  Afterward the surgeon told us that he thought if we had been even ten hours later, it probably would have ruptured and caused even more serious problems.  So we just thank God that we were guided to go to the ER when we did, particularly in light of my great aversion to hospitals and the like.</p>
<p>Although they said there was a possibility of going home the day after the surgery, my white blood cell count is still elevated, showing that the infection persists even though my appendix is gone.  The surgeon said he could tell there was more infected fluid and tissue but because of the size of my uterus he couldn&#8217;t see the full extent nor get it all out.  I will be in the hospital until the white blood cells are back to normal because there is a danger of the infection getting into the uterus and causing either preterm labor or problems for the baby.  So far she seems to be handling it all like a champ . . . still kicking up a storm, although this feels less comforting to me than it normally does because she&#8217;s kicking places that were recently cut open.  I&#8217;ve been asking her very nicely to go to sleep, while Neal has been threatening her with groundings if she doesn&#8217;t behave more considerately.</p>
<p>In all my worst-case scenario worries, I definitely never saw this coming.  But the reason why I started with the story of my stats test is that Neal and I are both convinced that Heavenly Father certainly could foresee what we could not.  I just felt like I wanted to get done with my final quickly, but now I see that it was absolutely essential to give me the peace of mind that I feel right now.  I can focus entirely on my and baby girl&#8217;s health.  I can just move slowly and rest without worry about other things sliding.</p>
<p>So we thank God for his grace and mercy, and for family and friends that have offered every conceivable type of assistance.  These have been difficult days, but we&#8217;re glad that this baby is still safely tucked away.</p>
<p><strong><span style="color:#339966;">* If you&#8217;re wondering about the title of this post, I should explain that ironically enough, it is an inside joke that Neal and I have.  We&#8217;ve been joking about appendectomies for almost 5 years now.  It turns out they&#8217;re not as funny as we thought.</span></strong></p>
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<title><![CDATA[Internet and the Structure of Terrorism: The Underground Librarian Appendix]]></title>
<link>http://uprkermittfrog.wordpress.com/2009/12/09/internet-and-the-structure-of-terrorism-the-underground-librarian-appendix/</link>
<pubDate>Wed, 09 Dec 2009 21:08:03 +0000</pubDate>
<dc:creator>Tespid</dc:creator>
<guid>http://uprkermittfrog.wordpress.com/2009/12/09/internet-and-the-structure-of-terrorism-the-underground-librarian-appendix/</guid>
<description><![CDATA[Eco-Terrorism and Environmental Literacy Sunday, December 6, 2009   written by Meghan Wallace Kahn, ]]></description>
<content:encoded><![CDATA[Eco-Terrorism and Environmental Literacy Sunday, December 6, 2009   written by Meghan Wallace Kahn, ]]></content:encoded>
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<title><![CDATA[Needless Things]]></title>
<link>http://planetross.wordpress.com/2009/12/09/needless-things/</link>
<pubDate>Wed, 09 Dec 2009 14:06:03 +0000</pubDate>
<dc:creator>planetross</dc:creator>
<guid>http://planetross.wordpress.com/2009/12/09/needless-things/</guid>
<description><![CDATA[  3 things I have that I don&#8217;t really need bothering me eventually: &#8230; my tonsils, my app]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><strong><a href="http://planetross.wordpress.com/files/2009/12/november-25th-09-004.jpg"><img class="aligncenter size-medium wp-image-9270" title="&#34;this alarm will sound when you are severely incapable of doing anything&#34;" src="http://planetross.wordpress.com/files/2009/12/november-25th-09-004.jpg?w=285" alt="" width="285" height="300" /></a></strong></p>
<p><strong> </strong></p>
<p><strong>3 things I have that I don&#8217;t really need bothering me eventually: </strong></p>
<p><strong>&#8230; my tonsils, my appendix, and my conscience.</strong></p>
<p><strong> </strong></p>
<p><strong>note:</strong> I&#8217;m still waiting for that ice cream, jello, and no school payday!<br />
&#8230; stupid tonsils.</p>
<p><strong>double note:</strong> my appendix bothers me &#8230; what the hell did it used to do? &#8220;<strong><em>Scientists aren&#8217;t really studying the appendix in apes, wombats, and some rodents.</em></strong>&#8221; (wiki)<br />
What about the other rodents????</p>
<p><strong>triple note:</strong></p>
<p> &#8221;<em><strong>The most common explanation is that the human appendix is a vestigial structure which has lost its original function.</strong></em>&#8220;<br />
(wiki)</p>
<p>So that&#8217;s what <strong>Procol Harum</strong> was singing about!</p>
<p><strong><em>&#8220;But I wandered through my playing cards<br />
and would not let her be<br />
one of sixteen </em>vestigial <em>virgins<br />
who were leaving for the coast&#8221;</em></strong></p>
<p><strong><em></em></strong><br />
<strong>quadruple note:</strong> I thought I had nothing tonight, but this thought came through the door with me when I came home. Some milk came through the door with me too, but I put that in the fridge: I won&#8217;t share that.</p>
<p><strong>quintuple note:</strong> I talk like I write: random. It&#8217;s no mystery. A thousand monkeys on a thousand typewriters have nothing on me.</p>
<p><strong>sextuple note:</strong> I think <strong>Donald Diddams</strong> over at <a href="http://diddamsdigitalart.wordpress.com/"><strong> The Art of Digital Art</strong> </a> is the only one placing the cursor over the pictures on this blog.</p>
<p>.</p>
<p><strong><em><span style="text-decoration:underline;">notes to myself #78</span></em></strong></p>
<p>Eat more mince meat tarts, coconut marshmellow rolls, nanaimo bars, and homemade fruit cake while you have the chance! That stuff gets pretty rare later on in life.</p>
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<title><![CDATA[Shocker: The Appendix is the Storehouse for your Good Bacteria!]]></title>
<link>http://truthaboutprobiotics.com/2009/12/03/shocker-the-appendix-is-the-storehouse-for-your-good-bacteria/</link>
<pubDate>Thu, 03 Dec 2009 21:44:45 +0000</pubDate>
<dc:creator>Natasha Trenev</dc:creator>
<guid>http://truthaboutprobiotics.com/2009/12/03/shocker-the-appendix-is-the-storehouse-for-your-good-bacteria/</guid>
<description><![CDATA[http://www.livescience.com/health/090824-appendix-evolution.html Ever thought the appendix was usele]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://www.livescience.com/health/090824-appendix-evolution.html">http://www.livescience.com/health/090824-appendix-evolution.html</a></p>
<p>Ever thought the appendix was useless? Well, according to a recent article, you&#8217;re wrong!</p>
<p>The appendix recently has been found to be a storehouse for your good bacteria, and it even aides your body in fighting off infections! It is also connected to the immune system because it produces some of your white blood cells.</p>
<p>We felt that this was another compelling reason why the best health strategy is to consume beneficial good bacteria or probiotics on a daily basis because it is obvious to us the many systems in our body rely on this proper good bacteria replenishment. These good bacteria support our overall good health. Consuming a high-quality probiotic daily should be considered the foundation of your good health!</p>
<p>Tell TAP: What are your thoughts about the appendix?</p>
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<title><![CDATA[How Superhearing Works (12/2/09)]]></title>
<link>http://meagermedstudent.wordpress.com/2009/12/03/how-superhearing-works-12209/</link>
<pubDate>Thu, 03 Dec 2009 03:50:00 +0000</pubDate>
<dc:creator>joshpothen</dc:creator>
<guid>http://meagermedstudent.wordpress.com/2009/12/03/how-superhearing-works-12209/</guid>
<description><![CDATA[(Courtesy of www.smallvilleph.com) 7 AM. Finished eating breakfast. Decide to check Secure Exam scor]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><div id="attachment_754" class="wp-caption aligncenter" style="width: 310px"><a href="http://meagermedstudent.wordpress.com/files/2009/12/superhearingsmallvilleph.jpg"><img class="size-full wp-image-754" title="superhearing(smallvilleph)" src="http://meagermedstudent.wordpress.com/files/2009/12/superhearingsmallvilleph.jpg" alt="" width="300" height="168" /></a><p class="wp-caption-text">(Courtesy of www.smallvilleph.com)</p></div>
<p>7 AM. Finished eating breakfast. Decide to check Secure Exam score. Find out I passed. Thank goodness.</p>
<p>***</p>
<p>9 AM: Doctoring Skills. This week we&#8217;re learning how to do an abdominal exam. In the introductory lecture, Dr. Rubin asks whether anyone&#8217;s had various conditions. Lots of classmates have had heartburn. Only one of us has had their appendix removed. Dr. Rubin asks her why she had it taken out. &#8220;I got into a car accident in Spain,&#8221; she tells us. (Nothing major). &#8220;The hospital took it out without telling me. They wanted to take out my spleen too, but my Mom wouldn&#8217;t let them.&#8221; (Thank goodness.)</p>
<p> We break to meet with our SPs. We&#8217;re also doing a male genital exam, which is a tad awkward, but goes over well. The SPs are very gracious and helpful. </p>
<p>As part of it, we have to put our finger up the inguinal canal in the thigh to check for hernias. &#8220;Be careful not to go too fast, &#8221; our SP cautions. &#8220;If you go too far, I&#8217;ll have inguinal pain for two weeks.&#8221;</p>
<p>Thankfully, we didn&#8217;t.  </p>
<p>***</p>
<p>Wednesdays are nice because I get done around 11 AM. There is an embryology lecture later on that day, but aside from a secure exam review, that&#8217;s about it. So I get lots of time to study. I hang out with one of the Histology TAs during lunch during her office hours. Later, I grab a classroom and study. (I like to draw diagrams on the whiteboard or pretend-teach the lecture notes.)</p>
<p>One of my classmates stops in and tells me a fascinating story. Turns out on his flight back to Burlington at the end of Thanksgiving break, he met a woman who had an ear infection that had affected her tensor tympani muscle.</p>
<p>This muscle is responsible for dampening vibrations in the ear when you&#8217;re exposed to a really loud sound. Otherwise, you&#8217;ll hear them as, well, really loud sounds. Apparently hers couldn&#8217;t do its job effectively as a result of the infection, so her hearing was very sensitive. She couldn&#8217;t even eat food without hearing her jaws chewing as a painfully loud noise.</p>
<p>But this also gave her the ability to hear noises that were very far away. &#8220;She could hear the neighbors talking in the house next door!&#8221; he told me. &#8220;It&#8217;s like having a superpower!&#8221;</p>
<p>Now I know how superhearing works. I need to check if <a href="http://www.amazon.com/Science-Superman-Official-Guide-Krypton/dp/1596872683">The Science of Superman</a> says anything about control of the tensor tympani muscle.</p>
<p><strong>Josh Pothen (UVM&#8217;s Meager Med Student)</strong></p>
<p><em>Donate $1 to The Meager Med Student! </em><strong></strong><a href="https://www.paypal.com/cgi-bin/webscr?cmd=_donations&#38;business=R7HTGJ97CVZQQ&#38;lc=US&#38;item_name=Meager%20Med%20Student&#38;currency_code=USD&#38;bn=PP%2dDonationsBF%3abtn_donateCC_LG%2egif%3aNonHosted"><img src="https://www.paypal.com/en_US/i/btn/x-click-but04.gif" alt="Donate to The Meager Med Student" /></a></p>
<p><a href="http://www.stumbleupon.com/submit?url=http://meagermedstudent.wordpress.com/2009/12/03/how-superhearing-works-12209/%26title%3DThe%2BArticle%2BTitle"><img src="http://cdn.stumble-upon.com/images/120x20_thumb_blue.gif" border="0" alt="" /></a></p>
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<title><![CDATA[Bang on the Drum All Day (12/1/09)]]></title>
<link>http://meagermedstudent.wordpress.com/2009/12/02/bang-on-the-drum-all-day/</link>
<pubDate>Wed, 02 Dec 2009 03:43:16 +0000</pubDate>
<dc:creator>joshpothen</dc:creator>
<guid>http://meagermedstudent.wordpress.com/2009/12/02/bang-on-the-drum-all-day/</guid>
<description><![CDATA[(He knows all about the gut. from en.wikipedia.org) I wake up and check my grades. Only the Practica]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><div id="attachment_748" class="wp-caption aligncenter" style="width: 221px"><a href="http://meagermedstudent.wordpress.com/files/2009/12/colbertreport.jpg"><img class="size-medium wp-image-748" title="Colbertreport" src="http://meagermedstudent.wordpress.com/files/2009/12/colbertreport.jpg?w=211" alt="" width="211" height="300" /></a><p class="wp-caption-text">(He knows all about the gut. from en.wikipedia.org)</p></div>
<p>I wake up and check my grades. Only the Practical exam grade is available. I passed, but just marginally. Nevertheless, I have improved since the last test. This next block is supposedly easier, so perhaps I can excel here.</p>
<p>***</p>
<p>Time to return to the Gross Lab. Since this is the start of a new block, our table&#8217;s been assigned to a new cadaver.</p>
<p>Our table is broken into two groups: A and B. I&#8217;m in B. While the Bs were in Histo yesterday, As did dissection. So today, a rep from Group A comes in and teaches us in Group B about their dissection and the appropriate structures from 8-9. </p>
<p>At 9, we begin our work: opening the abdominal cavity to see the organs underneath, such as the small intestine, stomach, gallbladder, appendix, etc. Some of the bodies have clearly undergone surgeries where some of these organs have been removed. Since it&#8217;s mainly opening the cavity, we finish this one early.</p>
<p>***</p>
<p>Lunch time comes around. The CMDA has its Tuesday meeting, and this week they&#8217;ve asked me to lead the Bible study. I&#8217;ve prepared my own questions and lesson, and well, it goes as well as the other Bible studies. Fewer people this week, though. I realize I need to rehearse the study and questions a bit more next time.</p>
<p>***</p>
<p>1-3 lecture. Dr. Mawe talks about blood supply in the abdomen, as well as secretion, motility and control mechanisms in the gut.</p>
<p>There&#8217;s a lot of fascinating info here. You may have heard about the central nervous system (brain and spinal cord), but the gut has its own: the enteric nervous system. This means that when detached from the brain and the rest of the body, a piece of colon can still move something through it!</p>
<p>Dr. Mawe also informs us that there are more neurons in the gut than their are in the spinal cord. And just after I thought about of Stephen Colbert, he shows us <a href="http://www.colbertnation.com/the-colbert-report-videos/88460/june-11-2007/michael-gershon">an interview from the Colbert Report with  Dr. Michael Gershon</a>, who&#8217;s written a book about the gut called <a href="http://www.amazon.com/Second-Brain-Groundbreaking-Understanding-Disorders/dp/0060930721">&#8220;The Second Brain: A Groundbreaking New Understanding of Nervous Disorders of the Stomach and Intestines (Your Gut Has a Mind of Its Own)&#8221;</a> .</p>
<p>***</p>
<p>In MSLG this week, we&#8217;re discussing alternative and complementary medicine. So a craniosacral therapist comes in to discuss how he presses and rotates various areas to move fascia around and relieve cranial nerves. He even gives us a demo, and what he does seems harmless, since he barely moves the body around. He tells us he takes the approach that he&#8217;s interested in whatever cures the patient, whether it&#8217;s traditional allopathic medicine or another branch of alternative medicine.</p>
<p>Before that, though, we had our &#8220;check-in&#8221; time, which is essentially an ice-breaker/fun intro to whatever we do. It&#8217;s my turn to lead it this week. My idea: have everyone share a song they liked, and why.</p>
<p>We all go around and share our choices. (Mine was &#8220;Hello Hurricane&#8221; by Switchfoot.) When it&#8217;s the group leader&#8217;s turn, she suddenly pulls out an iPod and a speaker system. She plugs it in, plays &#8220;Bang On The Drum All Day&#8221; by Todd Rundgren, and urges us all to dance along to it with her. We do. We laugh very hard.</p>
<p><strong>Josh Pothen (UVM&#8217;s Meager Med Student)</strong></p>
<p><em>Donate $1 to The Meager Med Student! </em><strong></strong><a href="https://www.paypal.com/cgi-bin/webscr?cmd=_donations&#38;business=R7HTGJ97CVZQQ&#38;lc=US&#38;item_name=Meager%20Med%20Student&#38;currency_code=USD&#38;bn=PP%2dDonationsBF%3abtn_donateCC_LG%2egif%3aNonHosted"><img src="https://www.paypal.com/en_US/i/btn/x-click-but04.gif" alt="Donate to The Meager Med Student" /></a></p>
<p><a href="http://www.stumbleupon.com/submit?url=http://meagermedstudent.wordpress.com/2009/12/02/bang-on-the-drum-all-day/%26title%3DThe%2BArticle%2BTitle"><img src="http://cdn.stumble-upon.com/images/120x20_thumb_blue.gif" border="0" alt="" /></a></p>
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<title><![CDATA[Prayer Request]]></title>
<link>http://gubc.wordpress.com/2009/12/01/prayer-request-7/</link>
<pubDate>Tue, 01 Dec 2009 17:44:24 +0000</pubDate>
<dc:creator>Greg</dc:creator>
<guid>http://gubc.wordpress.com/2009/12/01/prayer-request-7/</guid>
<description><![CDATA[I found out this morning that the prayer-chain was activated for Bro. Dusten Bills last night. He wa]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>I found out this morning that the prayer-chain was activated for  Bro. Dusten Bills last night.  He was in the hospital with a lot of pain, possibly from his appendix.  (I was down yesterday and didn&#8217;t get the message until late, thus the slow posting of this information.)</p>
<p>Please keep him in your prayers. I&#8217;ll update when I know more.</p>
<p>UPDATE:</p>
<p>Dusten did have to have his appendix removed last night. He was released from the hospital this afternoon and is resting, as comfortably as possible, at home as of this posting (9:06pm).</p>
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<title><![CDATA['Oddities', Mister Brown? What 'Oddities'?]]></title>
<link>http://sjat.wordpress.com/2009/12/01/oddities-mister-brown-what-oddities/</link>
<pubDate>Tue, 01 Dec 2009 11:51:43 +0000</pubDate>
<dc:creator>SJAT</dc:creator>
<guid>http://sjat.wordpress.com/2009/12/01/oddities-mister-brown-what-oddities/</guid>
<description><![CDATA[Continuing my run of odd titles. Just a short list of random musings today. I worry that wifey might]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>Continuing my run of odd titles.</p>
<p>Just a short list of random musings today.</p>
<ol>
<li>I worry that wifey might get cheese poisoning if her cravings don&#8217;t start to vary a little more. A variety of cheese does not count as variety!</li>
<li>The area of South Wales called Glamorgan makes me chuckle, as it is, of course, Glam Organ. And that opens up a whole new line of thought.</li>
<li>Why don&#8217;t medical practitioners just make all appointments 20 minutes later than they do, and then we won&#8217;t have to wait the extra 20 minutes?</li>
<li>Sadly, the thing that I absolutely MOST want to do in my life is to find an inscription that confirms the name of a hirtherto unnamed Roman fort!</li>
<li>Why do different modern languages have different names for ancient people. Surely the pharaoh Khufu/Cheops only actually answered to one of those?</li>
<li>One day, someone will invent a biscuit (cookie) that can survive being dipped in coffee without leaving a sludgy deposit behind.</li>
<li>The love of Spongebob Squarepants may be the purest kind of love in the Universe, even defying religions&#8230;</li>
<li>Monkeys are inherently funny. Even the word. No other creature can fling poo and still be considered cute.</li>
<li>When I am super rich, the first thing I do will be to buy the roads out of our village, make them private and put a weight limit on them.</li>
<li>Sun is good. Snow is fun. Absolutely every weather in between can go suck! Sleet, rain, hail, ice. All go suck!</li>
<li>No thank you. I still do not want a fake rolex or a free college degree. And I am not going to send you 200,000, Mr. Nigerian General.</li>
<li>If brunch is the meal between breakfast and lunch, what is the meal between lunch and tea? Homer Simpson calls it Lupper. I like that.</li>
<li>If grit/salt stops roads getting icy, why don&#8217;t scientists invent a version of Tarmacadam for roads that <em>contains</em> said grit/salt permanently.</li>
<li>I&#8217;m still trying to work out what the T-shirt I saw that said &#8220;Kittens = Pop Tarts&#8221; actually meant. I find it disturbing and funny.</li>
<li>The themetune to Pinky and the Brain is made of glue. It gets stuck in your head and no amount of tugging will remove it.</li>
<li>Citrix was released upon the world by Satan, but designed by the IRS. No one else is wicked enough.</li>
<li>I will never understand why humans have an appendix when its only job appears to fill with crap, burst and then kill you.</li>
<li>Anything that goes &#8216;clunk&#8217; while you&#8217;re driving is worrying. Anything that goes &#8216;clunk&#8217; twice, or &#8216;clunk, rattle&#8217; needs stopping and checking.</li>
<li>I want to have my childhood toys again. I want my lego and my Star Wars figures. And I want to play. I am a kid.</li>
<li>Sperlunking does not sound like what it means. It still sounds like something I don&#8217;t want to do though. It sounds vaguely bottom-related to me.</li>
</ol>
<p>And that&#8217;s 20 thoughts that occurred to me this morning.</p>
<p>Oh, and because it&#8217;s been over a week since I mentioned the search terms and how people come across my little space in the cyber world, here are the last weeks&#8217; highlights on search terms:</p>
<p>man many arms &#8211; I know this is a reference to the Vitruvian man. Or possibly Doctor Octopus?</p>
<p>whistling walrus menu &#8211; I&#8217;ve know idea how this one ties in!</p>
<p>photo &#8220;the suspenders are killing me&#8221; &#8211; The mind boggles!</p>
<p>why is julian clary limping &#8211; And now I shall have to go and find out&#8230;</p>
<p>slimy beast claudius &#8211; Was he? I perhaps expected more &#8220;Why is Claudius limping?&#8221; It would make more sense.</p>
<p>wind blows dress up &#8211; I bet it does.</p>
<p>are there javelinas in san diego county &#8211; This for Poolie and Cocobean! Any answers there?</p>
<p>See you tomorrow.</p>
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<title><![CDATA[Lady Justice Is Only Blindfolded, Not Blind]]></title>
<link>http://goldenstate.wordpress.com/2009/11/30/lady-justice-is-only-blindfolded-not-blind/</link>
<pubDate>Mon, 30 Nov 2009 07:15:38 +0000</pubDate>
<dc:creator>goldenstate</dc:creator>
<guid>http://goldenstate.wordpress.com/2009/11/30/lady-justice-is-only-blindfolded-not-blind/</guid>
<description><![CDATA[&nbsp; The Chief Justice Deciding a Case We’re at the end, until the Court issues its decision in th]]></description>
<content:encoded><![CDATA[&nbsp; The Chief Justice Deciding a Case We’re at the end, until the Court issues its decision in th]]></content:encoded>
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<title><![CDATA[Inflamed appendix turns out to be baby]]></title>
<link>http://gaydutchnyc.wordpress.com/2009/11/28/inflamed-appendix-turns-out-to-be-baby/</link>
<pubDate>Sat, 28 Nov 2009 15:10:29 +0000</pubDate>
<dc:creator>gaydutchnyc</dc:creator>
<guid>http://gaydutchnyc.wordpress.com/2009/11/28/inflamed-appendix-turns-out-to-be-baby/</guid>
<description><![CDATA[A 37-year old waitress from Germany went into the hospital with extreme stomach pains. She assumed t]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>A 37-year old waitress from Germany went into the hospital with extreme stomach pains. She assumed the pain was from her appendix but at the hospital it turned out to be contractions. An hour later a healthy baby was born. They woman says she though she could not get pregnant and had not paid any attention to not getting her period anymore. Clearly not the smartest person and also how could you not notice??. Every now and then you hear a story like this and after asking female relative with kids about it, it&#8217;s just hardly possible to not notice. Maybe some psychological denial problems as well here.</p>
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<title><![CDATA[Jag är underbar!]]></title>
<link>http://paljettenq.wordpress.com/2009/11/26/jag-ar-underbar/</link>
<pubDate>Thu, 26 Nov 2009 21:51:43 +0000</pubDate>
<dc:creator>PaljettenQ</dc:creator>
<guid>http://paljettenq.wordpress.com/2009/11/26/jag-ar-underbar/</guid>
<description><![CDATA[Wow, vilken grej! Jag har fått mitt livs första  award!  ”I think you are an awesome girl”.  Av supe]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://paljettenq.wordpress.com/files/2009/11/thumbblog.jpg"><img class="alignnone size-full wp-image-2144" title="thumbblog" src="http://paljettenq.wordpress.com/files/2009/11/thumbblog.jpg" alt="" width="256" height="227" /></a></p>
<p>Wow, vilken grej! Jag har fått mitt livs första  award!  ”I think you are an awesome girl”.  Av supertjejen <a title="länk till Blogg Bureborn" href="http://bureborn.wordpress.com/2009/11/26/tio-saker-om-mig/">Sofia</a>,   Tack!</p>
<p>I titeln som fantastisk ingår uppgiften att dela ut priset och utmaningen till tre andra bloggerskor. Men även att jag ska berätta tio saker om mig själv&#8230; Att välja ut bara tre förunderligt bra tejer är ju svårt! Men jag väljer: <a href="http://blommaland.blogspot.com/">Blommaland</a>, <a title="grodår" href="http://wwwgrodar.blogspot.com/">Grodår</a> och <a href="http://livsglimtar.wordpress.com/">Livsglimten</a>. För de är underbart unika alla tre och förtjänar ett blingbling-må-bra-pris <img src='http://s.wordpress.com/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
<p><strong>Här är mina tio saker:</strong></p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/paljettenq-2008-paljett.jpg"><img class="alignnone size-full wp-image-2146" title="paljettenQ-2008-paljett" src="http://paljettenq.wordpress.com/files/2009/11/paljettenq-2008-paljett.jpg" alt="" width="39" height="40" /></a> 1. Jag äger en svart kort paljettkjol som egentligen är lite för kort för att jag ska känna mig bekväm i den.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/fruktstund-2009-paljettenq.jpg"><img class="alignnone size-thumbnail wp-image-2148" title="Fruktstund-2009-PaljettenQ" src="http://paljettenq.wordpress.com/files/2009/11/fruktstund-2009-paljettenq.jpg?w=112" alt="" width="49" height="67" /></a> 2. Jag är periodare då det kommer till att äta frukt, just nu är det apelsinjuice som gäller, givetvis egenpressad <img src='http://s.wordpress.com/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/almanacka-17-natter-2007web.jpg"><img class="alignnone size-thumbnail wp-image-2149" title="almanacka-17-nätter-2007web" src="http://paljettenq.wordpress.com/files/2009/11/almanacka-17-natter-2007web.jpg?w=150" alt="" width="50" height="52" /></a> 3. Nu är det två år sedan jag slutade att jobba vaken natt på ett korttidsboende. Nu är jag heltids konstnär och tror mig kunna leva på det minst ett och ett halvt år framåt, sedan vet jag inte hur det ser ut. Jag försöker lära mig att uppskatta ovissheten.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/sjojungfru2007-paljettenq.jpg"><img class="alignnone size-thumbnail wp-image-2150" title="sjöjungfru2007-PaljettenQ" src="http://paljettenq.wordpress.com/files/2009/11/sjojungfru2007-paljettenq.jpg?w=138" alt="" width="63" height="75" /></a>4.  Om jag kunde välja att bli en sagofigur skulle jag välja att bli en sjöjungfru, flaffa omkring med tuttarna i de blå haven.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/en-bra-lyssnare-2008-paljet.jpg"><img class="alignnone size-thumbnail wp-image-2151" title="En-bra-lyssnare-2008-Paljet" src="http://paljettenq.wordpress.com/files/2009/11/en-bra-lyssnare-2008-paljet.jpg?w=119" alt="" width="61" height="95" /></a> 5. Jag tycker inte att jag är en bra lyssnare. Rastlösheten kryper in på mig om jag inte är intresserad, men jag tror mig vara rätt tydlig när jag inte orkar höra mer. Som på Homer Simpson, en orkester börjar spela i huvudet på mig.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/pihjala-fazer-2009-paljette.jpg"><img class="alignnone size-thumbnail wp-image-2152" title="pihjala-fazer-2009-Paljette" src="http://paljettenq.wordpress.com/files/2009/11/pihjala-fazer-2009-paljette.jpg?w=150" alt="" width="93" height="54" /></a> 6. Jag är nog sockerberoende&#8230;  Jag äter det okontrollerat och blir arg om jag inte får äta i fred. Tänker er Kerberos vid skattkistan, den uppsynen har jag då någon närmar sig MITT godis.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/party-lordag-2008-paljet.jpg"><img class="alignnone size-thumbnail wp-image-2153" title="Party----lördag-2008-Paljet" src="http://paljettenq.wordpress.com/files/2009/11/party-lordag-2008-paljet.jpg?w=104" alt="" width="76" height="92" /></a> 7. Jag älskar att dansa. Det är riktigt roligt, men jag gör det sällan. Jag skulle vilja lära mig finsk tango.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/bird2008paljettenq.jpg"><img class="alignnone size-thumbnail wp-image-2154" title="bird2008PaljettenQ" src="http://paljettenq.wordpress.com/files/2009/11/bird2008paljettenq.jpg?w=150" alt="" width="62" height="61" /></a> 8. &#8220;Jag vill inte dö nyfiken&#8221;, det är en av mina deviser här i livet. Jag vill inte hämma mig till en grå präktighet och raspig håglöshet. Nej, jag tycker att det är bra att hålla nyfikenheten vaken.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/kanin-2009-paljettenq.jpg"><img class="alignnone size-thumbnail wp-image-2155" title="Kanin-2009-PaljettenQ" src="http://paljettenq.wordpress.com/files/2009/11/kanin-2009-paljettenq.jpg?w=97" alt="" width="59" height="97" /></a>9. Jag tycker det är roligt att träffa nya människor, men har ett fåtal vänner som får komma nära.</p>
<p><a href="http://paljettenq.wordpress.com/files/2009/11/hot-lips-2008-paljettenq.jpg"><img class="alignnone size-thumbnail wp-image-2156" title="hot-lips-2008-PaljettenQ" src="http://paljettenq.wordpress.com/files/2009/11/hot-lips-2008-paljettenq.jpg?w=99" alt="" width="59" height="78" /></a>10. Jag har inte så mycket fantasi men gillar att fnula med samma ämnen länge. Vrider och vänder dem så att själva knådandet blir en egen grej! Grundstommen är: &#8220; - Vad händer om jag gör så här?&#8221;</p>
<p>&#160;</p>
<p>&#160;</p>
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<title><![CDATA[Har du en säljande logga?]]></title>
<link>http://paljettenq.wordpress.com/2009/11/16/har-du-en-saljande-logga/</link>
<pubDate>Mon, 16 Nov 2009 21:43:34 +0000</pubDate>
<dc:creator>PaljettenQ</dc:creator>
<guid>http://paljettenq.wordpress.com/2009/11/16/har-du-en-saljande-logga/</guid>
<description><![CDATA[Efter en dag utan en tillstymmelse till att skapa bilder så fick jag ett plötsligt infall. Jag ville]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://paljettenq.wordpress.com/files/2009/11/mindmap-blogglogga-2009-pal.jpg"><img class="alignnone size-full wp-image-2128" title="mindmap-blogglogga-2009-Pal" src="http://paljettenq.wordpress.com/files/2009/11/mindmap-blogglogga-2009-pal.jpg" alt="" width="397" height="72" /></a></p>
<p>Efter en dag utan en tillstymmelse till att skapa bilder så fick jag ett plötsligt infall. Jag ville göra något utan anknytning till jobbet, så jag gjorde en låtsas logga till en fantasiblogg. Bara för  att leka lite och för att det inte fanns något roligt på TV. Det är lite som att spela spel en stund för att koppla av. Men är det endast en lek? Hur mycket tanke lägger vi ned på vår logotype?</p>
<p>Här på <a title="länk till ett exempel på hur det kan se ut på wordpress" href="http://botd.wordpress.com/top-posts/?lang=sv">WordPress har det blivit lite förändringar </a>de senaste månaderna. När man går in och tittar på det nya interface som fortfarande är under utveckling kan man se att loggornas betydelse har växt. Om du ingen logga har så blir tilldelad en svart ruta, dystert om något. Logga bör vara tydlig  i litet format.Första intrycket varar och den tvekande handen stannar till vid bilderna och vrakar. Har du en säljande logga gode bloggare?</p>
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<title><![CDATA[I went to church today for the first time in months]]></title>
<link>http://thescrapheap.wordpress.com/2009/11/15/i-went-to-church-today-for-the-first-time-in-months/</link>
<pubDate>Sun, 15 Nov 2009 09:23:45 +0000</pubDate>
<dc:creator>Jack</dc:creator>
<guid>http://thescrapheap.wordpress.com/2009/11/15/i-went-to-church-today-for-the-first-time-in-months/</guid>
<description><![CDATA[My wife is off traveling OS with the eldest&#8230; so I&#8217;ve got the 4 and 7 yr old, so I decide]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>My wife is off traveling OS with the eldest&#8230; so I&#8217;ve got the 4 and 7 yr old, so I decided to take them to church today&#8230;. for something to do&#8230;. And I decided I&#8217;d journal through the service&#8230; so here are my thoughts, hot off the press.</p>
<p>First up I notice the whole stage is done up&#8230; looks like they&#8217;ve spent maybe 10-15K on curtains, sound proofing and paint. Something I wanted to do for years but couldn&#8217;t scrape the money together. They&#8217;ve been saving lots on wages since over the last 12 months five staff have left. The worship doesn&#8217;t seem better or any more vibrant, despite people telling me that there&#8217;s a &#8220;move of God&#8221; because of the new pastor. It&#8217;s basically the same &#8211; although there was less people. But then I guess why would it be the same? Unless things fundamentally change the outward expression can&#8217;t.</p>
<p>Worship has started. The new guy is still busy shaking hands. He comes over and shakes mine, which I&#8217;m reluctant to do&#8230; then he said sorry for starting on the wrong foot. I said, it doesn&#8217;t matter (I mean &#8220;whatever&#8221;).</p>
<p>The fact that he froze me out and refused to meet me gave me heaps of grief and I&#8217;m slowly coming to terms with that. But then again looking on the positive side, maybe it just helped me face reality that I <em>am</em> useless and really <em>don&#8217;t</em> have anything to offer.</p>
<p>I am not needed and have nothing to contribute that someone else isn&#8217;t already contributing and anything I <em>could</em> do that isn&#8217;t being done is simply not important.</p>
<p>We&#8217;re up to the third song now. I&#8217;m singing and worshiping God because I love him, but at the same time I&#8217;m thinking it&#8217;s great to not have to make this service happen. There are times if its dead I would feel stress and feel like I&#8217;d have to do something to make something happen. There was always the worry that people will leave saying its dead and when word gets out that its dead it&#8217;s like poison.</p>
<p>I don&#8217;t know this last song&#8230; so I&#8217;m just kinda hanging with God. I don&#8217;t feel like I need to be singing. I&#8217;m not sure what people think I&#8217;m doing on my PDA&#8230; they probably think I&#8217;m texting someone! Who cares!</p>
<p>It&#8217;s just dawned on me&#8230;. I just figured out what part of the body of Christ i am &#8211; the appendix. No-one knows what it&#8217;s good for&#8230; and if it causes a problem or breaks, you don&#8217;t fix it&#8230; you surgically remove it and toss it on the scrapheap.</p>
<p>The next thing that dawns on me as the music is playing is the amazing thing is, God even loves stuff that isn&#8217;t useful&#8230; Like thunder, sunsets, the stars and planets, art, and poetry. I guess if we only view things through the lens of modernity, effectiveness, and usefulness then we are going to misunderstand a lot about God and His kingdom.</p>
<p>I always knew God didn&#8217;t need me&#8230; I&#8217;ve even preached it. But why did he have to use <em>this</em> church &#8211; <em>my</em> church, to teach me such a painful lesson?</p>
<p>I really enjoyed worship although for some reason, the kids don&#8217;t go to kids church until afterward, so my two were restless and a bit hyperactive. Not sure how parents are really supposed to engage with God if their kids are running around&#8230; but I guess pastors who have teenage kids don&#8217;t think about that&#8230;.</p>
<p>It is tough experiencing a modern church through post-modern eyes&#8230; For example, the pastor just jumped up and said something to the effect of &#8220;we are people of the book, etc&#8230; Believe the truth&#8230; The inspired Word of God&#8230; your emotions won&#8217;t set you free, the truth will&#8230;.blah blah blah.&#8221; But once we realise that the truth is in fact a person, not cold hard facts, but Jesus, and the word is Jesus and that it becomes law when the two are separated, it&#8217;s a bit hard to swallow.</p>
<p>I think i will one day find a way to serve God outside of the conventional church, but inside his kingdom.</p>
<p>I reckon that because we value mastery over mystery we elevate principles and in doing so we become legalistic and religious and don&#8217;t need the holy spirit. The enemy gets us with a double whammy.<br />
My former senior pastor and coach has flown in, and is preaching now, which is one of the reasons I decided to go to church today. He says the purpose of covenant is to bring us into union with God and into union with each other. He&#8217;s talking about something I believe deeply. That church is first and foremost relationship vertically, then relationship horizontally. I just wish there wasn&#8217;t so much baggage hanging off all that and it was much simpler. His son (a close friend of mine) who burned out a few years ago didn&#8217;t come&#8230; another victim in ministry.</p>
<p>It wasn&#8217;t bad but i was done by 90 minutes though with another half hour to go. What I listened to most was when my former coach talked about himself and when he gave an example of how he would pray the lord&#8217;s prayer, in fact I had goosebumps. The information side of things though (the hebrew definitions) I could do without.</p>
<p>Final thoughts&#8230; I guess i just love the church as it is, warts and all and to not be part of something one loves is really sad. I think that&#8217;s why its been so hard and painful. Yes, I know things need to change radically in the church, but that doesn&#8217;t stop me from loving what it is today.</p>
<p>Maybe i needed the pain to become disillusioned enough to look for something new and to truly see how crippled the church of today is.</p>
<p>On the upside, one good thing is that I don&#8217;t feel sick&#8230; just sad and useless&#8230; which is much better than sick!</p>
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<title><![CDATA[Appendicitis with Unusual Presentation]]></title>
<link>http://marilisa616.wordpress.com/2009/11/14/appendicitis-with-unusual-presentation/</link>
<pubDate>Sun, 15 Nov 2009 03:38:00 +0000</pubDate>
<dc:creator>marilisa616</dc:creator>
<guid>http://marilisa616.wordpress.com/2009/11/14/appendicitis-with-unusual-presentation/</guid>
<description><![CDATA[Appendicitis with Unusual Presentation: Mid-Abdominal Vs. Right Quadrant PainWith four children I]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><div class="separator" style="clear:both;text-align:center;"><a href="http://marilisa616.wordpress.com/files/2009/11/imagesca1odxa3.jpg" style="clear:left;float:left;margin-bottom:1em;margin-right:1em;"><img border="0" src="http://marilisa616.wordpress.com/files/2009/11/imagesca1odxa3.jpg?w=83" /></a></div>
<p><img border="0" height="0" src="http://counters.gigya.com/wildfire/IMP/CXNID=2000002.0NXC/bT*xJmx*PTEyNTgyNTUzNDgwMzcmcHQ9MTI1ODI1NTM*OTYxMiZwPTQxMTg2MSZkPSZnPTEmbz*4MjAzZWQzYTQ5MzQ*NjBjYmNiYmFlMWU1YTI4NTUxNyZvZj*w.gif" width="0" /><a href="http://www.associatedcontent.com/article/2381078/appendicitis_with_unusual_presentation.html"><b>Appendicitis with Unusual Presentation: Mid-Abdominal Vs. Right Quadrant Pain</b></a><br />With four children I&#8217;ve nursed many stomach aches. Three were caused by appendicitis. Appendicitis pain generally occurs on the right side. In the last bout, pain occurred in the LLQ and termed &#8216;appendicitis with unusual presentation.<br /><a href="http://www.associatedcontent.com/article/2381078/appendicitis_with_unusual_presentation.html">Read More</a></p>
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<title><![CDATA[Your Body’s Wonderful Sewer System]]></title>
<link>http://pavellas.wordpress.com/2009/11/11/your-body%e2%80%99s-wonderful-sewer-system/</link>
<pubDate>Tue, 10 Nov 2009 23:02:56 +0000</pubDate>
<dc:creator>Ron Pavellas</dc:creator>
<guid>http://pavellas.wordpress.com/2009/11/11/your-body%e2%80%99s-wonderful-sewer-system/</guid>
<description><![CDATA[No, I’m not talking about your alimentary canal. When your doctor (or Doctor Mom) checks to see if y]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>No, I’m not talking about your <a href="http://www.tutorvista.com/content/science/science-ii/nutrition/alimentary-canal.php">alimentary canal</a>.</p>
<p>When your doctor (or Doctor Mom) checks to see if your &#8220;glands&#8221; are swollen, it is your lymph nodes that are being checked—and they are not glands.</p>
<p>The lymph nodes, located throughout your body, are part of a <a href="http://www.bartleby.com/107/175.html">lymphatics circulatory system</a> which runs in parallel and in collaboration with your <a href="http://www.google.se/search?q=venous+blood+system&#38;ie=utf-8&#38;oe=utf-8&#38;aq=t&#38;rlz=1R1GGGL_en___SE323&#38;client=firefox-a">venous blood system</a>, as distinct from your <a href="http://www.google.se/search?q=venous+blood+system&#38;ie=utf-8&#38;oe=utf-8&#38;aq=t&#38;rlz=1R1GGGL_en___SE323&#38;client=firefox-a">arterial blood system</a>.<span style="color:white;font-size:xx-small;"><br />
∙<br />
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<a href="http://4.bp.blogspot.com/_kOEwIyKMNn8/SvLoPBU3yFI/AAAAAAAADlQ/wiEsosJGwgg/s1600-h/Venous_System.JPG"><img style="float:left;width:224.1px;height:360px;margin:0 10px 10px 0;" src="http://4.bp.blogspot.com/_kOEwIyKMNn8/SvLoPBU3yFI/AAAAAAAADlQ/wiEsosJGwgg/s400/Venous_System.JPG" border="0" alt="" /></a><a href="http://3.bp.blogspot.com/_kOEwIyKMNn8/SvLopNvSeQI/AAAAAAAADlY/ln5nVwerHcc/s1600-h/immune.gif"><img style="float:right;width:179.1px;height:360px;margin:0 0 10px 10px;" src="http://3.bp.blogspot.com/_kOEwIyKMNn8/SvLopNvSeQI/AAAAAAAADlY/ln5nVwerHcc/s400/immune.gif" border="0" alt="" /></a></p>
<p><a href="http://www.warriorpages.com/images/Venous_System.JPG">Venous Circulatory System</a><span style="color:white;font-size:xx-small;">∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙</span><a href="http://www.naturalhealthschool.com/img/immune.gif">Lymphatics Circulatory System</a><strong><span style="color:green;"><br />
</span></strong></p>
<p align="center"><strong><span style="color:green;">[Please click on the images to see the detail more clearly]</span></strong></p>
<p>So what do these lymph nodes have to do with the maladies I cite at the top of this page? They are protecting and defending your body by sensing, attacking, immobilizing, killing,  and flushing the remains of the bad critters that have invaded your otherwise pristine flesh. When thus engaged in dealing with the alien invaders, the lymph nodes ramp up their activities and become swollen with lymphatic fluid which contains the disease-eating organisms of your body—the <a href="http://en.wikipedia.org/wiki/Macrophage">macrophages</a> (literally, big eaters) and other defensive cells.</p>
<p>But, when the lymphatics system doesn&#8217;t work properly, bad things can happen—the sewer backs up. The result is a swelling of various tissues, a condition most commonly called lymphodema. There are other names for more serious problems associated with the dysfunction of the lymphatics system..</p>
<p><a href="http://4.bp.blogspot.com/_kOEwIyKMNn8/SvnrnoUObrI/AAAAAAAADmA/pt9_5Z9MOm0/s1600-h/macrophage.jpg"><img style="float:right;width:200px;height:158px;margin:0 0 10px 10px;" src="http://4.bp.blogspot.com/_kOEwIyKMNn8/SvnrnoUObrI/AAAAAAAADmA/pt9_5Z9MOm0/s200/macrophage.jpg" border="0" alt="" /></a><strong><span style="color:green;"> </span></strong></p>
<p align="right"><strong><span style="color:green;">A macrophage attacking infectious organisms</span></strong></p>
<p>I was reminded of all this, having remembered about &#8220;lymph&#8221; only vaguely from my biology classes in high school, by my friend Helena Janlöv-Remnerud. Helena is a trained nurse, entrepreneur, teacher and authority in lymphodema therapy. Because we have a mutual friend in the USA, we met several years ago and found we had interests in common.</p>
<p>What is lymphodema? And why does a person with this condition need therapy? So glad you asked.</p>
<p>The simplest way to describe lymphodema (or, more scientifically, <em>lymphodoema</em>) is an abnormal swelling of the limbs and other parts of the body. The most extreme example of this condition outside of a hospital will be the person whose legs seem like those of an elephant, hence the term <a href="http://en.wikipedia.org/wiki/Elephantiasis"><em>elephantiasis</em></a>, used in unusually serious cases where parasitic worms have invaded the lymphatics system, a disease usually found in the tropics.</p>
<p>Most commonly in the temperate zones, lymphodema is the result of acute trauma to the body, including deep surgical operations such as for cancer, and due to the effects other diseases such as diabetes.</p>
<p>Helena has had, for a number of years, her own lymphodema clinic in central Stockholm and is currently preparing for a move to a larger, multi-specialty clinic near a major medical center just north of the city center: <a href="http://oliviarehabilitering.se/">Olivia Rehabilitering</a> (click on &#8220;Lymfödemrehab&#8221; to see Helena&#8217;s clinic).</p>
<p><a href="http://2.bp.blogspot.com/_kOEwIyKMNn8/SvnuPygziuI/AAAAAAAADmQ/NxmChrGu6Zs/s1600-h/organsImmuneSystem.jpg"><img style="display:block;text-align:center;cursor:hand;width:346px;height:400px;margin:0 auto 10px;" src="http://2.bp.blogspot.com/_kOEwIyKMNn8/SvnuPygziuI/AAAAAAAADmQ/NxmChrGu6Zs/s400/organsImmuneSystem.jpg" border="0" /></a><B><FONT COLOR="green">
<p align="center">Your body&#8217;s immune system organs</B></FONT></p>
<p>I attended an open house for the clinic which will open for business in early 2010, and received a guided tour and lecture on the subject of Helena&#8217;s expertise. She likes to use the metaphor of a sewer system to describe the lymphatics system. This analogy appeals to me, my having been trained in public health and perceiving the hidden sewer systems of our cities and towns as the platform upon which we are able to successfully build our civilization. Think of the great water and sewer works <a href="http://en.wikipedia.org/wiki/Sanitation_in_ancient_Rome">built by the Ancient Romans</a>.</p>
<p>In helping this layman understand her metaphor, Helena told me:</p>
<blockquote><p>The lymphatic fluid takes all the waste products away from your tissues. As it moves toward its final destination in the blood stream, it passes through the analysis stations of the lymph nodes where bacteria and other harmful micro-organisms are detected. An alarm goes off in the lymph nodes that signals the production of warriors to attack them. The residue will be taken care of by the cleansing processes of the bloodstream: the liver, the kidneys and the spleen. All the output of the lymphatic system is poured into the venous blood system at two large veins under your collar bones, the subclavian veins. As the blood passes through the kidneys some waste products are done away with through bladder and the urine. When the blood passes through the liver other waste (like toxins) are discarded of through the bowel. The spleen mainly takes care of old erythrocytes (red blood cells); it also part of the immune system.</p></blockquote>
<p>Helena recently delivered a paper to <a href="http://www.svenskaodemforbundet.se/">Svenska Ödemförbundet</a> (Swedish Edema Association) on lymphoedema assessment and management in an <a href="http://www.flinders.sa.gov.au/lymphoedema/">Australian clinic</a> she visited, <a href="http://www.svenskaodemforbundet.se/files/forskning/Lymphoedema_assessment_and_management.pdf">which you can read in English, here</a>.</p>
<p><a href="http://1.bp.blogspot.com/_kOEwIyKMNn8/Svns5TZEN1I/AAAAAAAADmI/WduAGqMP0Uo/s1600-h/leg_swelling_lrg.jpg"><img style="float:left;width:140px;height:200px;margin:0 10px 10px 0;" src="http://1.bp.blogspot.com/_kOEwIyKMNn8/Svns5TZEN1I/AAAAAAAADmI/WduAGqMP0Uo/s200/leg_swelling_lrg.jpg" border="0" alt="" /></a>Another question you might ask is: how can the lymph fluids circulate if there is no &#8220;heart&#8221; attached to the system? There is <a href="http://www.google.se/search?hl=en&#38;safe=off&#38;client=firefox-a&#38;rlz=1R1GGGL_en___SE323&#38;num=50&#38;newwindow=1&#38;defl=en&#38;q=define:peristalsis&#38;ei=uOX5SpbOEs6z4QaXuKCyCw&#38;sa=X&#38;oi=glossary_definition&#38;ct=title&#38;ved=0CAcQkAE">peristaltic action</a> in the lymph vessels, but another vital method is through the movement of your body, especially the legs. This is one reason why walking is so important for your health—to keep the lymphatics flowing and flushing out the poisons and infectious residue from your body.</p>
<p>What I hope to leave you with is an appreciation for a seldom mentioned system of your body that deserves equal billing with your blood system.</p>
<p>Ask your doctor about it.</p>
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<title><![CDATA[Photo: The Chalkboard Explanation]]></title>
<link>http://the113project.wordpress.com/2009/11/06/photo-the-chalkboard-explanation/</link>
<pubDate>Fri, 06 Nov 2009 18:55:30 +0000</pubDate>
<dc:creator>eromedome22</dc:creator>
<guid>http://the113project.wordpress.com/2009/11/06/photo-the-chalkboard-explanation/</guid>
<description><![CDATA[Please take a look at this chalkboard.  IT&#8217;S ALL THERE.  Pay attention, people.]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><img class="alignnone size-full wp-image-28" title="11_3project Chalkboard" src="http://the113project.wordpress.com/files/2009/11/500x_stewartbeck1.jpg" alt="11_3project Chalkboard" width="500" height="374" /></p>
<p>Please take a look at this chalkboard.  IT&#8217;S ALL THERE.  Pay attention, people.</p>
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