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<channel>
	<title>norm &amp;laquo; WordPress.com Tag Feed</title>
	<link>http://en.wordpress.com/tag/norm/</link>
	<description>Feed of posts on WordPress.com tagged "norm"</description>
	<pubDate>Sat, 28 Nov 2009 10:44:20 +0000</pubDate>

	<generator>http://en.wordpress.com/tags/</generator>
	<language>en</language>

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<title><![CDATA[double trouble]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/27/double-trouble/</link>
<pubDate>Fri, 27 Nov 2009 04:42:28 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/27/double-trouble/</guid>
<description><![CDATA[there are times i feel so eager to please. i wish to give so much even beyond my ability. which leav]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>there are times i feel so eager to please. i wish to give so much even beyond my ability. which leaves me unable to please.. and on top of that, breaking my promise to be able to please.</p>
<p>social vulnerability, it haunts me.</p>
<p>&#160;</p>
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<title><![CDATA[it's a sign]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/24/its-a-sign/</link>
<pubDate>Tue, 24 Nov 2009 14:17:52 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/24/its-a-sign/</guid>
<description><![CDATA[warm day, warm night. WHY NO RAIN!? when im home the whole day.. wanted to show jo-lynn how the sky ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>warm day, warm night.<br />
WHY NO RAIN!? when im home the whole day..</p>
<p>wanted to show jo-lynn how the sky is one-toned so i cant tell if the sky is extremely clear or totally covered in dark clouds. ( we were guessing if it&#8217;ll rain in singapore tonight)</p>
<p>my hopeless 2mp nokia phone camera always leave me speechless.</p>
<p style="text-align:center;"><a href="http://thelittlefighter.wordpress.com/files/2009/11/24112009.jpg"><img class="aligncenter size-medium wp-image-452" src="http://thelittlefighter.wordpress.com/files/2009/11/24112009.jpg?w=300" alt="" width="270" height="203" /></a></p>
<p style="text-align:left;">WHAT IS THIS!?!?<br />
seriously, people would think my estate blacked-out.</p>
</div>]]></content:encoded>
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<item>
<title><![CDATA[)))):]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/24/451/</link>
<pubDate>Tue, 24 Nov 2009 14:10:40 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/24/451/</guid>
<description><![CDATA[warm day, warm night. WHY NO RAIN!? when im home the whole day.. wanted to show jo-lynn how the sky ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>warm day, warm night.<br />
WHY NO RAIN!? when im home the whole day..</p>
<p>wanted to show jo-lynn how the sky is one-toned, so i cant tell if the sky is extremely clear, or it&#8217;s totally covered in dark clouds. (we were guessing if it&#8217;ll rain tonight)</p>
<p style="text-align:left;">my hopeless 2mp nokia phone camera always leaves me speechless.<br />
<a href="http://thelittlefighter.wordpress.com/files/2009/11/24112009.jpg"><img class="aligncenter size-medium wp-image-452" src="http://thelittlefighter.wordpress.com/files/2009/11/24112009.jpg?w=300" alt="" width="270" height="203" /></a></p>
<p style="text-align:left;">WHAT IS THIS!?!?<br />
seriously, people would have thought my estate blacked-out!</p>
<p>&#160;</p>
</div>]]></content:encoded>
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<item>
<title><![CDATA[green is my colour]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/24/green-is-my-colour/</link>
<pubDate>Tue, 24 Nov 2009 07:23:03 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/24/green-is-my-colour/</guid>
<description><![CDATA[im envious,green-eyed, what have you. everyone&#8217;s going everywhere. and i wish i could too. i f]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>im envious,green-eyed, what have you.<br />
everyone&#8217;s going everywhere. and i wish i could too.</p>
<p>i find joy in their wonderful times abroad, yet it makes me sulk in jealousy.</p>
<p>im submerged, dwelling in stupid self-pity.</p>
</div>]]></content:encoded>
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<item>
<title><![CDATA[ageing]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/22/ageing/</link>
<pubDate>Sun, 22 Nov 2009 15:45:50 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/22/ageing/</guid>
<description><![CDATA[mommy fell, on the road, head first. my heart stopped. no car on the road, fortunately. how can anyo]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>mommy fell, on the road, head first.<br />
my heart stopped.<br />
no car on the road, fortunately.</p>
<p>how can anyone fall head first? it&#8217;s weird. her hands didnt even go forward to hold herself back.  she fell like how a display statue would fall. could it be a sign of ageing? that even the reflexes are getting a bit spastic.</p>
<p>noooo..i dont want my mom to age so soon!</p>
<p>she has a HUGE baluku on the side of the forehead now.<br />
yikes! she looks like a lohan fish.</p>
</div>]]></content:encoded>
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<item>
<title><![CDATA[Religious Identity and Economic Behavior]]></title>
<link>http://freemarketmojo.wordpress.com/2009/11/21/religious-identity-and-economic-behavior/</link>
<pubDate>Sat, 21 Nov 2009 12:02:08 +0000</pubDate>
<dc:creator>Ariel Goldring</dc:creator>
<guid>http://freemarketmojo.wordpress.com/2009/11/21/religious-identity-and-economic-behavior/</guid>
<description><![CDATA[Chris Blattman has linked to an interesting paper on religious identity and economic behavior publis]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://chrisblattman.com/2009/11/16/religious-identity-and-economic-behavior/" target="_blank">Chris Blattman</a> has linked to an interesting <a href="http://www.som.yale.edu/faculty/jjc83/religion.pdf" target="_blank">paper on religious identity and economic behavior</a> published a few months ago:</p>
<blockquote><p>We find that Protestantism increases contributions to public goods, and there is suggestive evidence that it increases employee reciprocity in a labor market with incomplete contracts. Catholicism decreases contributions to public goods, increases employee reciprocity, and decreases risk aversion. Judaism increases labor market reciprocity. There is some evidence that Christianity and Judaism increase employer wage offers. However, we find no evidence that religious identity affects discount rates or purely altruistic generosity.</p></blockquote>
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<title><![CDATA[ROFL.]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/19/oh-gawd/</link>
<pubDate>Wed, 18 Nov 2009 17:10:10 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/19/oh-gawd/</guid>
<description><![CDATA[u should see this click to see my new &#8216;friend&#8217; all of you. PRICELESS! for everything els]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>u should see this</p>
<p>click to see my new <a href="http://photos-h.ak.fbcdn.net/hphotos-ak-snc3/hs039.snc3/12668_1195420537168_1578093233_486495_8228805_n.jpg">&#8216;friend&#8217;</a></p>
<p>all of you.</p>
<p>PRICELESS!<br />
for everything else, you have&#8230;</p>
</div>]]></content:encoded>
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<item>
<title><![CDATA[Non-profits leaders: Learn the art of standing your ground while building consensus]]></title>
<link>http://pamelaziemann.wordpress.com/2009/11/17/non-profits-leaders-learn-the-art-of-standing-your-ground-while-building-consensus/</link>
<pubDate>Tue, 17 Nov 2009 00:34:48 +0000</pubDate>
<dc:creator>Pamela Ziemann</dc:creator>
<guid>http://pamelaziemann.wordpress.com/2009/11/17/non-profits-leaders-learn-the-art-of-standing-your-ground-while-building-consensus/</guid>
<description><![CDATA[Norm Rice, President &amp; CEO of The Seattle Foundation knows that being consistent helps people fe]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><span style="font-family:verdana, sans-serif;line-height:normal;font-size:small;white-space:pre-wrap;">Norm Rice, President &#38; CEO of The Seattle Foundation knows that being consistent helps people feel safe. Being consistent with his values and the way he approaches problems also helps people understand the best way to dialogue with him </span></p>
<div><span style="font-family:verdana, sans-serif;font-size:small;"><span style="line-height:normal;white-space:pre-wrap;">With that said however, Norm playfully added Ralph Waldo Emerson’s quote, “A <em>foolish</em> consistency is the hobgoblin of little minds.”
<p>&#160;</p>
<p>How do you know when to hold your ground and when holding your ground is for the wrong reasons? He offers 7 tips for non-profit leaders who want to create a solid foundation and make it to the finish line with success.</p>
<p><strong>1) </strong><strong>Are you in alignment?</strong></p>
<p>The moment you say yes to a new project, ask yourself if your individual values match what you’re trying to accomplish. You may be a skilled leader, but are you the right fit for the position?  Take time to understand what’s important to you and share your personal stories. As you take on a leadership role, people want to know about you as a person.</p>
<p>When asked to consider Presidency for The Seattle Foundation, Norm visited their website and read the 7 essential elements of a healthy community (environment, neighborhoods &#38; communities, arts &#38; culture, economy, education, health &#38; wellness and basic needs.) He recognized how their values were perfectly aligned with his and began the job with a solid foundation.</p>
<p><strong>2) Listen to hopes and aspirations. </strong></p>
<p>In this environment of change, people crave consensus, but don’t necessarily know how to do it. More than ever, non-profit leaders need to learn the art form of incorporating everyone’s values. When meeting people, Norm asks himself, “How can I meet their objectives and still come together with our overall goal?” One of his greatest compliments was from a woman who questioned him about the anti-bussing campaign. After 20 minutes, she still hadn’t come to a conclusion but told Norm she felt like she’d been heard. People may forget your words, but they’ll never forget how you made them feel. You don’t have to accept everything they say &#8211; it’s how you use what they say. You want to be able to say to people, “I made this decision because I heard you.”</p>
<p><strong>3) </strong><strong>Ask the right questions.</strong></p>
<p>The beauty of Social Media is that more people can get involved. Everyone has an opportunity to express themselves and feel like what they say matters. Ask the right questions and you’ll have fewer people who want to be anonymous. Using blogs and Facebook, Norm asks questions like “What do you think a 21<sup>st</sup> Century Seattle should look like?”  If your question is what’s wrong with schools, you’ll go off into a morass and never get an action plan. Rather than focusing on the barriers, frame all the information around your values and what you’d like to see happen.</p>
<p><strong>4) </strong><strong>Stay broad, but narrow enough to take action and reach your goals.</strong></p>
<p>Clearly articulate where you want to go with your non-profit. Listen as people express their aspirations, then let the collective creativity flow where it will. Capture their hopes and channel those hopes into an action plan for change.</p>
<p>Follow a step-by-step process by letting the creativity of the community carry you without being too prescriptive. What’s lacking with many non-profits is the willingness to accept what’s being developed. People want someone who can be a champion for their aspirations and help them carry it to the finish line.</p>
<p><strong>5) </strong><strong>Get a balanced perspective from your board.</strong></p>
<p>Maintain a diverse board that that will reinforce your strengths and help where you are weak. To have a strong foundation, enroll board members who aren’t like the leader. A healthy non-profit organization needs spirited discussions from people with many perspectives. The important thing is to bring all the different ideas back together at the end of each day and align them with your mission.<span style="font-size:small;"> </span></p>
<p><strong>6) </strong><strong>Can you find partners?</strong></p>
<p>At the risk of sounding cliché, Norm advises non-profits to look for acquisitions and mergers. Are there collaborations that will make you more successful? While not every non-profit should merge, be open to ways of working together. By non-profits aligning their goals, they can create more money. Norm says, “Yes, there’s gold in them thar hills, but it’s got to be mined differently!”</p>
<p><strong>7) </strong><strong>Keep assessing your mission.</strong></p>
<p>Sometimes you’ve gone as far as you can go. Non-profits have a tendency to say, “We’re it… We’ll be here forever.” Sometimes organizations can die from their own weight. You have to be nimble enough to know that NPOs are being looked at differently. People’s criteria for giving and their assessment after they’ve given have gotten even more rigorous. What does your non-profit deliver? Donors want to go online and see that they’ve made good giving decisions. Be able to walk away when you’ve had enough milestones to feel proud of your accomplishments. If you want a job because you need the job, you’ll start making the wrong decisions.<span style="font-size:small;"> </span></p>
<p>Norm’s skill of being grounded while able to change is something he’s developed over time. Pamela works with non-profit professionals to balance their natural abilities and use them more effectively.</p>
<p>&#160;</p>
<p></span></span></div>
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<title><![CDATA[A bound for matrix norm]]></title>
<link>http://mymbl.wordpress.com/2009/11/16/a-bound-for-matrix-norm/</link>
<pubDate>Mon, 16 Nov 2009 21:18:45 +0000</pubDate>
<dc:creator>mymbl</dc:creator>
<guid>http://mymbl.wordpress.com/2009/11/16/a-bound-for-matrix-norm/</guid>
<description><![CDATA[We wish to better the bounds for the norm of a matrix with scalar entries when it defines a linear m]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>
We wish to better the bounds for the norm of a matrix <img src='http://l.wordpress.com/latex.php?latex=%7BM+%3D+%28k%28i%2Cj%29%29%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{M = (k(i,j))}&amp;fg=000000&amp;s=-2' title='{M = (k(i,j))}&amp;fg=000000&amp;s=-2' class='latex' /> with scalar entries when it defines a linear map with from <img src='http://l.wordpress.com/latex.php?latex=%7Bl%5Ep%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{l^p}&amp;fg=000000&amp;s=-2' title='{l^p}&amp;fg=000000&amp;s=-2' class='latex' /> to <img src='http://l.wordpress.com/latex.php?latex=%7Bl%5Ep%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{l^p}&amp;fg=000000&amp;s=-2' title='{l^p}&amp;fg=000000&amp;s=-2' class='latex' />, that is the series ,
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++Mx%28i%29+%3D+%5Csum_%7Bj%3D1%7D%5E%5Cinfty+k_%7Bi%2Cj%7D+x%28j%29+%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  Mx(i) = \sum_{j=1}^\infty k_{i,j} x(j) &amp;fg=000000&amp;s=-2' title='\displaystyle  Mx(i) = \sum_{j=1}^\infty k_{i,j} x(j) &amp;fg=000000&amp;s=-2' class='latex' /></p>
<p> is convergent for each <img src='http://l.wordpress.com/latex.php?latex=%7Bi%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{i}&amp;fg=000000&amp;s=-2' title='{i}&amp;fg=000000&amp;s=-2' class='latex' /> and <img src='http://l.wordpress.com/latex.php?latex=%7BMx+%5Cin+l%5Ep%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{Mx \in l^p}&amp;fg=000000&amp;s=-2' title='{Mx \in l^p}&amp;fg=000000&amp;s=-2' class='latex' />. The standard bounds for matrix norm given in the <a href="http://books.google.co.in/books?id=BaEgbIoPTygC&#38;lpg=PT1&#38;ots=sz9VTTD64f&#38;dq=functional%20analysis%20Balmohan%20Limaye&#38;pg=PP1#v=onepage&#38;q=&#38;f=false">text</a>  for <img src='http://l.wordpress.com/latex.php?latex=%7Bp+%5Cgeq+2%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{p \geq 2}&amp;fg=000000&amp;s=-2' title='{p \geq 2}&amp;fg=000000&amp;s=-2' class='latex' />, are <img src='http://l.wordpress.com/latex.php?latex=%7B%5Calpha_1%5E%7B1%2Fp%7D+%5Calpha_%5Cinfty%5E%7B1%2Fq%7D%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\alpha_1^{1/p} \alpha_\infty^{1/q}}&amp;fg=000000&amp;s=-2' title='{\alpha_1^{1/p} \alpha_\infty^{1/q}}&amp;fg=000000&amp;s=-2' class='latex' /> and <img src='http://l.wordpress.com/latex.php?latex=%7B%5Cbeta_p%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\beta_p}&amp;fg=000000&amp;s=-2' title='{\beta_p}&amp;fg=000000&amp;s=-2' class='latex' />, for <img src='http://l.wordpress.com/latex.php?latex=%7Bl%5Ep%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{l^p}&amp;fg=000000&amp;s=-2' title='{l^p}&amp;fg=000000&amp;s=-2' class='latex' /> spaces. We give yet another bound using the power mean inequality: </p>
<p>
<p><b>1. <a href="http://en.wikipedia.org/wiki/Power_mean_inequality">Power Mean Inequality</a> : </b></p>
<p>Consider positive weights <img src='http://l.wordpress.com/latex.php?latex=%7Bp_k%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{p_k}&amp;fg=000000&amp;s=-2' title='{p_k}&amp;fg=000000&amp;s=-2' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%7Bk+%3D+1%2C+2%2C+%5Cldots%2C+%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{k = 1, 2, \ldots, }&amp;fg=000000&amp;s=-2' title='{k = 1, 2, \ldots, }&amp;fg=000000&amp;s=-2' class='latex' /> which have total mass <img src='http://l.wordpress.com/latex.php?latex=%7Bp_1+%2B+p_2+%2B+%5Cldots%3D+1%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{p_1 + p_2 + \ldots= 1}&amp;fg=000000&amp;s=-2' title='{p_1 + p_2 + \ldots= 1}&amp;fg=000000&amp;s=-2' class='latex' />, then for nonnegative real numbers <img src='http://l.wordpress.com/latex.php?latex=%7Bx_k%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{x_k}&amp;fg=000000&amp;s=-2' title='{x_k}&amp;fg=000000&amp;s=-2' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%7Bk+%3D+1%2C+2%2C%5Cldots+%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{k = 1, 2,\ldots }&amp;fg=000000&amp;s=-2' title='{k = 1, 2,\ldots }&amp;fg=000000&amp;s=-2' class='latex' /> and for all <img src='http://l.wordpress.com/latex.php?latex=%7B-%5Cinfty+%26%2360%3B+s+%26%2360%3B+t+%26%2360%3B+%5Cinfty%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{-\infty &lt; s &lt; t &lt; \infty}&amp;fg=000000&amp;s=-2' title='{-\infty &lt; s &lt; t &lt; \infty}&amp;fg=000000&amp;s=-2' class='latex' /> one has <a name="eq1">
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++%28%5Csum_%7Bk%3D1%7D%5E%5Cinfty+p_k+x_k%5Es%29%5E%7B1%2Fs%7D+%5Cleq+%28%5Csum_%7Bk%3D1%7D%5E%5Cinfty+p_k+x_k%5Et%29%5E%7B1%2Ft%7D+%5C+%5C+%5C+%5C+%5C+%281%29%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  (\sum_{k=1}^\infty p_k x_k^s)^{1/s} \leq (\sum_{k=1}^\infty p_k x_k^t)^{1/t} \ \ \ \ \ (1)&amp;fg=000000&amp;s=-2' title='\displaystyle  (\sum_{k=1}^\infty p_k x_k^s)^{1/s} \leq (\sum_{k=1}^\infty p_k x_k^t)^{1/t} \ \ \ \ \ (1)&amp;fg=000000&amp;s=-2' class='latex' /></p>
<p></a></p>
<p>
<p><b>2. Bound for matrix norm </b></p>
<p> Consider,
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++%5Cbegin%7Barray%7D%7Brcl%7D++%5Cleft+%26%23124%3B+%5Cleft+%26%23124%3B+Mx+%5Cright+%26%23124%3B+%5Cright+%26%23124%3B_p%5Ep+%26%2338%3B%3D+%5Csum_%7Bi%3D1%7D%5E%5Cinfty+%5Cleft%26%23124%3B%5Csum_%7Bj+%3D+1%7D%5E%5Cinfty+k_%7Bi%2Cj%7D+x%28j%29+%5Cright+%26%23124%3B%5Ep+%5C%5C+%26%2338%3B%5Cleq+%5Csum_%7Bi%3D1%7D%5E%5Cinfty+%5Cleft%28+%5Csum_%7Bj%3D1%7D%5E%5Cinfty+%5Cleft+%26%23124%3Bk_%7Bi%2Cj%7D+x%28j%29+%5Cright+%26%23124%3B+%5Cright+%29%5Ep+%5C%5C+%26%2338%3B%3D+%5Csum_%7Bi%3D1%2Cr_i+%5Cneq+0%7D%5E%5Cinfty+r_i%5Ep+%5Cleft+%28+%5Csum_%7Bj%3D1%7D%5E%5Cinfty+%5Cleft+%26%23124%3B%5Cfrac%7Bk_%7Bi%2Cj%7D%7D%7Br_i%7D+x%28j%29+%5Cright+%26%23124%3B+%5Cright+%29%5Ep+%5Cend%7Barray%7D+%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  \begin{array}{rcl}  \left &#124; \left &#124; Mx \right &#124; \right &#124;_p^p &amp;= \sum_{i=1}^\infty \left&#124;\sum_{j = 1}^\infty k_{i,j} x(j) \right &#124;^p \\ &amp;\leq \sum_{i=1}^\infty \left( \sum_{j=1}^\infty \left &#124;k_{i,j} x(j) \right &#124; \right )^p \\ &amp;= \sum_{i=1,r_i \neq 0}^\infty r_i^p \left ( \sum_{j=1}^\infty \left &#124;\frac{k_{i,j}}{r_i} x(j) \right &#124; \right )^p \end{array} &amp;fg=000000&amp;s=-2' title='\displaystyle  \begin{array}{rcl}  \left &#124; \left &#124; Mx \right &#124; \right &#124;_p^p &amp;= \sum_{i=1}^\infty \left&#124;\sum_{j = 1}^\infty k_{i,j} x(j) \right &#124;^p \\ &amp;\leq \sum_{i=1}^\infty \left( \sum_{j=1}^\infty \left &#124;k_{i,j} x(j) \right &#124; \right )^p \\ &amp;= \sum_{i=1,r_i \neq 0}^\infty r_i^p \left ( \sum_{j=1}^\infty \left &#124;\frac{k_{i,j}}{r_i} x(j) \right &#124; \right )^p \end{array} &amp;fg=000000&amp;s=-2' class='latex' /></p>
<p>
where for some fixed <img src='http://l.wordpress.com/latex.php?latex=%7Bs+%26%2362%3B+0%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{s &gt; 0}&amp;fg=000000&amp;s=-2' title='{s &gt; 0}&amp;fg=000000&amp;s=-2' class='latex' /> and <img src='http://l.wordpress.com/latex.php?latex=%7Bs+%26%2360%3B%3D+1%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{s &lt;= 1}&amp;fg=000000&amp;s=-2' title='{s &lt;= 1}&amp;fg=000000&amp;s=-2' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%7Br_i+%3D+%5Csum_%7Bj%3D1%7D%5E%5Cinfty+%26%23124%3Bk_%7Bi%2Cj%7D%5E%7Bs%7D%26%23124%3B%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{r_i = \sum_{j=1}^\infty &#124;k_{i,j}^{s}&#124;}&amp;fg=000000&amp;s=-2' title='{r_i = \sum_{j=1}^\infty &#124;k_{i,j}^{s}&#124;}&amp;fg=000000&amp;s=-2' class='latex' />.
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++%5Cbegin%7Barray%7D%7Brcl%7D++%5Cleft+%26%23124%3B+%5Cleft+%26%23124%3B+Mx+%5Cright+%26%23124%3B+%5Cright+%26%23124%3B_p%5Ep+%26%2338%3B+%5Cleq+%5Csum_%7Bi%3D1%2C+r_i+%5Cneq+0%7D%5E%5Cinfty+r_i%5Ep+%5Cleft+%28+%5Csum_%7Bj%3D1%7D%5E%5Cinfty+%5Cfrac%7B%5Cleft+%26%23124%3Bk_%7Bi%2Cj%7D%5E%7Bs%7D+%5Cright+%26%23124%3B%7D%7Br_i%7D+%5Cleft%26%23124%3Bk_%7Bi%2Cj%7D%5Cright%26%23124%3B%5E%7B1-s%7D%5Cleft%26%23124%3B+x%28j%29+%5Cright+%26%23124%3B+%5Cright+%29%5Ep+%5Cend%7Barray%7D+%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  \begin{array}{rcl}  \left &#124; \left &#124; Mx \right &#124; \right &#124;_p^p &amp; \leq \sum_{i=1, r_i \neq 0}^\infty r_i^p \left ( \sum_{j=1}^\infty \frac{\left &#124;k_{i,j}^{s} \right &#124;}{r_i} \left&#124;k_{i,j}\right&#124;^{1-s}\left&#124; x(j) \right &#124; \right )^p \end{array} &amp;fg=000000&amp;s=-2' title='\displaystyle  \begin{array}{rcl}  \left &#124; \left &#124; Mx \right &#124; \right &#124;_p^p &amp; \leq \sum_{i=1, r_i \neq 0}^\infty r_i^p \left ( \sum_{j=1}^\infty \frac{\left &#124;k_{i,j}^{s} \right &#124;}{r_i} \left&#124;k_{i,j}\right&#124;^{1-s}\left&#124; x(j) \right &#124; \right )^p \end{array} &amp;fg=000000&amp;s=-2' class='latex' /></p>
<p>
Now we use power mean inequality with <img src='http://l.wordpress.com/latex.php?latex=%7B%5Calpha%3D1%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\alpha=1}&amp;fg=000000&amp;s=-2' title='{\alpha=1}&amp;fg=000000&amp;s=-2' class='latex' /> { and } <img src='http://l.wordpress.com/latex.php?latex=%7B%5Cbeta+%3D+p%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\beta = p}&amp;fg=000000&amp;s=-2' title='{\beta = p}&amp;fg=000000&amp;s=-2' class='latex' />, <img src='http://l.wordpress.com/latex.php?latex=%7B+p_k+%3D+%5Cfrac%7B%26%23124%3Bk_%7Bi%2Cj%7D%5E%7Bs%7D%26%23124%3B%7D%7Br_i%7D%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{ p_k = \frac{&#124;k_{i,j}^{s}&#124;}{r_i}}&amp;fg=000000&amp;s=-2' title='{ p_k = \frac{&#124;k_{i,j}^{s}&#124;}{r_i}}&amp;fg=000000&amp;s=-2' class='latex' /> { and } <img src='http://l.wordpress.com/latex.php?latex=%7Bx_k+%3D+%26%23124%3B+k_%7Bi%2Cj%7D%5E%7B1-s%7D+x%28j%29%26%23124%3B%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{x_k = &#124; k_{i,j}^{1-s} x(j)&#124;}&amp;fg=000000&amp;s=-2' title='{x_k = &#124; k_{i,j}^{1-s} x(j)&#124;}&amp;fg=000000&amp;s=-2' class='latex' />. So,
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++%5Cbegin%7Barray%7D%7Brcl%7D++%5Cleft+%26%23124%3B+%5Cleft+%26%23124%3B+Mx+%5Cright+%26%23124%3B+%5Cright+%26%23124%3B_p%5Ep+%26%2338%3B%5Cleq+%5Csum_%7Bi%3D1%2Cr_i%5Cneq+0%7D%5E%5Cinfty+r_i%5Ep+%5Csum_%7Bj%3D1%7D%5E%5Cinfty+%5Cleft+%26%23124%3B+%5Cfrac%7B%26%23124%3Bk_%7Bi%2Cj%7D%5E%7Bs%7D%26%23124%3B%7D%7Br_i%7D+k_%7Bi%2Cj%7D%5E%7Bp%281-s%29%7Dx%28j%29%5Ep+%5Cright+%26%23124%3B+%5C%5C+%26%2338%3B%3D+%5Csum_%7Bi%3D1%7D%5E%5Cinfty%5Csum_%7Bj%3D1%7D%5E%5Cinfty+r_i%5E%7Bp-1%7D%5Cleft+%26%23124%3B+%7B+k_%7Bi%2Cj%7D%5E%7Bs%2Bp%281-s%29%7D%7D+%5Cright+%26%23124%3B+%5Cleft%26%23124%3Bx%28j%29%5Cright%26%23124%3B%5Ep+%5C%5C+%26%2338%3B+%3D+%5Csum_%7Bj%3D1%7D%5E%5Cinfty+%5Cleft%26%23124%3Bx%28j%29%5Cright%26%23124%3B%5Ep+%5Csum_%7Bi%3D1%7D%5E%5Cinfty+r_i%5E%7Bp-1%7D%5Cleft+%26%23124%3B+%7B+k_%7Bi%2Cj%7D%5E%7Bs%2Bp%281-s%29%7D%7D+%5Cright+%26%23124%3B+%5C%5C+%5Cend%7Barray%7D+%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  \begin{array}{rcl}  \left &#124; \left &#124; Mx \right &#124; \right &#124;_p^p &amp;\leq \sum_{i=1,r_i\neq 0}^\infty r_i^p \sum_{j=1}^\infty \left &#124; \frac{&#124;k_{i,j}^{s}&#124;}{r_i} k_{i,j}^{p(1-s)}x(j)^p \right &#124; \\ &amp;= \sum_{i=1}^\infty\sum_{j=1}^\infty r_i^{p-1}\left &#124; { k_{i,j}^{s+p(1-s)}} \right &#124; \left&#124;x(j)\right&#124;^p \\ &amp; = \sum_{j=1}^\infty \left&#124;x(j)\right&#124;^p \sum_{i=1}^\infty r_i^{p-1}\left &#124; { k_{i,j}^{s+p(1-s)}} \right &#124; \\ \end{array} &amp;fg=000000&amp;s=-2' title='\displaystyle  \begin{array}{rcl}  \left &#124; \left &#124; Mx \right &#124; \right &#124;_p^p &amp;\leq \sum_{i=1,r_i\neq 0}^\infty r_i^p \sum_{j=1}^\infty \left &#124; \frac{&#124;k_{i,j}^{s}&#124;}{r_i} k_{i,j}^{p(1-s)}x(j)^p \right &#124; \\ &amp;= \sum_{i=1}^\infty\sum_{j=1}^\infty r_i^{p-1}\left &#124; { k_{i,j}^{s+p(1-s)}} \right &#124; \left&#124;x(j)\right&#124;^p \\ &amp; = \sum_{j=1}^\infty \left&#124;x(j)\right&#124;^p \sum_{i=1}^\infty r_i^{p-1}\left &#124; { k_{i,j}^{s+p(1-s)}} \right &#124; \\ \end{array} &amp;fg=000000&amp;s=-2' class='latex' /></p>
<p> Now if we take,
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++%5Cgamma_s+%3D+%5Csup_j+%5Cleft+%5C%7B+%5Csum_%7Bi%3D1%7D%5E%5Cinfty+r_i%5E%7Bp-1%7D+%5Cleft%26%23124%3B+k_%7Bi%2Cj%7D%5E%7Bs+%2B+p%281-s%29%7D%5Cright%26%23124%3B+%5Cright+%5C%7D%5E%7B1%2Fp%7D+%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  \gamma_s = \sup_j \left \{ \sum_{i=1}^\infty r_i^{p-1} \left&#124; k_{i,j}^{s + p(1-s)}\right&#124; \right \}^{1/p} &amp;fg=000000&amp;s=-2' title='\displaystyle  \gamma_s = \sup_j \left \{ \sum_{i=1}^\infty r_i^{p-1} \left&#124; k_{i,j}^{s + p(1-s)}\right&#124; \right \}^{1/p} &amp;fg=000000&amp;s=-2' class='latex' /></p>
<p> Then we have <img src='http://l.wordpress.com/latex.php?latex=%7BMx+%5Cleq+%5Cgamma_s+%5Cleft%26%23124%3B+%5Cleft+%26%23124%3B+x+%5Cright+%26%23124%3B%5Cright+%26%23124%3B_p%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{Mx \leq \gamma_s \left&#124; \left &#124; x \right &#124;\right &#124;_p}&amp;fg=000000&amp;s=-2' title='{Mx \leq \gamma_s \left&#124; \left &#124; x \right &#124;\right &#124;_p}&amp;fg=000000&amp;s=-2' class='latex' />. So we have infinite number of bounds for the norm as we vary <img src='http://l.wordpress.com/latex.php?latex=%7Bs%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{s}&amp;fg=000000&amp;s=-2' title='{s}&amp;fg=000000&amp;s=-2' class='latex' /> among positive reals (of course, not all values of <img src='http://l.wordpress.com/latex.php?latex=%7Bs%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{s}&amp;fg=000000&amp;s=-2' title='{s}&amp;fg=000000&amp;s=-2' class='latex' /> might be useful )</p>
<p>
Example : Consider the matrix
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++A+%3D+%5Cbegin%7Bpmatrix%7D+1+%26%2338%3B+1%2F2%5E%7B3%7D+%26%2338%3B+1%2F3%5E3+%26%2338%3B+%5Cldots+%5C%5C+1%2F2+%26%2338%3B+1+%26%2338%3B+0+%26%2338%3B+%5Cldots+%5C%5C+1%2F3+%26%2338%3B+0+%26%2338%3B+1+%26%2338%3B+%5Cldots+%5C%5C+%5Cvdots+%26%2338%3B+%26%2338%3B+%26%2338%3B+%5Cvdots+%5C%5C+%5Cend%7Bpmatrix%7D+%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  A = \begin{pmatrix} 1 &amp; 1/2^{3} &amp; 1/3^3 &amp; \ldots \\ 1/2 &amp; 1 &amp; 0 &amp; \ldots \\ 1/3 &amp; 0 &amp; 1 &amp; \ldots \\ \vdots &amp; &amp; &amp; \vdots \\ \end{pmatrix} &amp;fg=000000&amp;s=-2' title='\displaystyle  A = \begin{pmatrix} 1 &amp; 1/2^{3} &amp; 1/3^3 &amp; \ldots \\ 1/2 &amp; 1 &amp; 0 &amp; \ldots \\ 1/3 &amp; 0 &amp; 1 &amp; \ldots \\ \vdots &amp; &amp; &amp; \vdots \\ \end{pmatrix} &amp;fg=000000&amp;s=-2' class='latex' /></p>
<p> For this matrix <img src='http://l.wordpress.com/latex.php?latex=%7B%5Calpha_1+%3D+%5Cinfty%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\alpha_1 = \infty}&amp;fg=000000&amp;s=-2' title='{\alpha_1 = \infty}&amp;fg=000000&amp;s=-2' class='latex' /> and <img src='http://l.wordpress.com/latex.php?latex=%7B%5Cbeta_2%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\beta_2}&amp;fg=000000&amp;s=-2' title='{\beta_2}&amp;fg=000000&amp;s=-2' class='latex' /> is also infinity, however <img src='http://l.wordpress.com/latex.php?latex=%7B%5Cgamma%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\gamma}&amp;fg=000000&amp;s=-2' title='{\gamma}&amp;fg=000000&amp;s=-2' class='latex' /> is finite with <img src='http://l.wordpress.com/latex.php?latex=%7Bs+%3D1%2F2%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{s =1/2}&amp;fg=000000&amp;s=-2' title='{s =1/2}&amp;fg=000000&amp;s=-2' class='latex' />. This is because <img src='http://l.wordpress.com/latex.php?latex=%7B%5Csup_i+r_i+%3D+%5Csum_n+%281%2Fn%5E3%29%5E%7B1%2F2%7D+%26%2360%3B+%5Cinfty+%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\sup_i r_i = \sum_n (1/n^3)^{1/2} &lt; \infty }&amp;fg=000000&amp;s=-2' title='{\sup_i r_i = \sum_n (1/n^3)^{1/2} &lt; \infty }&amp;fg=000000&amp;s=-2' class='latex' /> and <img src='http://l.wordpress.com/latex.php?latex=%7B%5Csup_%7Bi%7D+%5Csum_%7Bj%3D1%7D%5En+k_%7Bi%2Cj%7D%5E%7B%282%2B1%29%2F2%7D+%3D%5Csum_%7Bj%3D1%7D%5En+1%2Fn%5E%7B3%2F2%7D+%26%2360%3B+%5Cinfty%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\sup_{i} \sum_{j=1}^n k_{i,j}^{(2+1)/2} =\sum_{j=1}^n 1/n^{3/2} &lt; \infty}&amp;fg=000000&amp;s=-2' title='{\sup_{i} \sum_{j=1}^n k_{i,j}^{(2+1)/2} =\sum_{j=1}^n 1/n^{3/2} &lt; \infty}&amp;fg=000000&amp;s=-2' class='latex' />. Thus <img src='http://l.wordpress.com/latex.php?latex=%7B%5Cgamma_%7B2%7D+%5Cleq+%5Csup_i+r_i+%5Csup_i+%5Csum_%7Bj%3D1%7D%5En+k_%7Bi%2Cj%7D%5E%7B3%2F2%7D+%26%2360%3B+%5Cinfty%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\gamma_{2} \leq \sup_i r_i \sup_i \sum_{j=1}^n k_{i,j}^{3/2} &lt; \infty}&amp;fg=000000&amp;s=-2' title='{\gamma_{2} \leq \sup_i r_i \sup_i \sum_{j=1}^n k_{i,j}^{3/2} &lt; \infty}&amp;fg=000000&amp;s=-2' class='latex' />.</p>
<p>
You can further see that <img src='http://l.wordpress.com/latex.php?latex=%7B%5Cgamma_s%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\gamma_s}&amp;fg=000000&amp;s=-2' title='{\gamma_s}&amp;fg=000000&amp;s=-2' class='latex' /> is a better bound than <img src='http://l.wordpress.com/latex.php?latex=%7B%5Calpha_%5Cinfty%5E%7B1%2Fq%7D%5Calpha_1%5E%7B1%2Fp%7D%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{\alpha_\infty^{1/q}\alpha_1^{1/p}}&amp;fg=000000&amp;s=-2' title='{\alpha_\infty^{1/q}\alpha_1^{1/p}}&amp;fg=000000&amp;s=-2' class='latex' /> always, since if we take <img src='http://l.wordpress.com/latex.php?latex=%7Bs+%3D+1%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{s = 1}&amp;fg=000000&amp;s=-2' title='{s = 1}&amp;fg=000000&amp;s=-2' class='latex' /> and <img src='http://l.wordpress.com/latex.php?latex=%7Br+%3D+%5Cinfty%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{r = \infty}&amp;fg=000000&amp;s=-2' title='{r = \infty}&amp;fg=000000&amp;s=-2' class='latex' />, we have
<p align="center"><img src='http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle++%5Csup_j+%5Csum_%7Bi%3D1%7D%5E%5Cinfty+r_i%5E%7Bp-1%7D+%5Cleft%26%23124%3Bk_%7Bi%2Cj%7D%5E%7Bs+%2B+p%281-s%29%7D%5Cright%26%23124%3B+%3D+%5Csup_i+%7Br_i%5E%7Bp%2Fq%7D%7D+%5Csup_j+%5Csum_%7Bi%3D1%7D%5E%5Cinfty+%5Cleft+%26%23124%3Bk_%7Bi%2Cj%7D%5Cright%26%23124%3B+%5Cleq+%5Calpha_%5Cinfty%5E%7Bp%2Fq%7D+%5Calpha_1%2C+%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\displaystyle  \sup_j \sum_{i=1}^\infty r_i^{p-1} \left&#124;k_{i,j}^{s + p(1-s)}\right&#124; = \sup_i {r_i^{p/q}} \sup_j \sum_{i=1}^\infty \left &#124;k_{i,j}\right&#124; \leq \alpha_\infty^{p/q} \alpha_1, &amp;fg=000000&amp;s=-2' title='\displaystyle  \sup_j \sum_{i=1}^\infty r_i^{p-1} \left&#124;k_{i,j}^{s + p(1-s)}\right&#124; = \sup_i {r_i^{p/q}} \sup_j \sum_{i=1}^\infty \left &#124;k_{i,j}\right&#124; \leq \alpha_\infty^{p/q} \alpha_1, &amp;fg=000000&amp;s=-2' class='latex' /></p>
<p> where we have used the fact that <img src='http://l.wordpress.com/latex.php?latex=%7Bp-1+%3D+p%2Fq%7D%26%2338%3Bfg%3D000000%26%2338%3Bs%3D-2&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='{p-1 = p/q}&amp;fg=000000&amp;s=-2' title='{p-1 = p/q}&amp;fg=000000&amp;s=-2' class='latex' />. </p>
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<title><![CDATA[comfort food]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/16/comfort-food/</link>
<pubDate>Mon, 16 Nov 2009 07:26:17 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/16/comfort-food/</guid>
<description><![CDATA[lazy, rainy monday. rainy days always makes people sleepy or hungry. doesnt it? so today&#8217;s lun]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>lazy, rainy monday.</p>
<p>rainy days always makes people sleepy or hungry. doesnt it?</p>
<p style="text-align:center;">so today&#8217;s lunch is fresh cut potatoes! with home made sour cream and onions dip.<br />
whooooooooooppieeee!<br />
<img class="aligncenter size-medium wp-image-421" src="http://thelittlefighter.wordpress.com/files/2009/11/16112009002.jpg?w=300" alt="" width="240" height="180" /></p>
<p style="text-align:left;">no one&#8217;s cooking tonight ):<br />
strawberries for dinner.</p>
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<title><![CDATA[miuccia let-down]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/16/miuccia-let-down/</link>
<pubDate>Mon, 16 Nov 2009 04:11:28 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/16/miuccia-let-down/</guid>
<description><![CDATA[argh. so much anticipation for the miumiu sale. and hours before it commenced, it became 30% instead]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>argh.</p>
<p>so much anticipation for the miumiu sale. and hours before it commenced, it became 30% instead of a 40% discount. and just when i entered, all designs are in snake or croc skins. im really not into reptiles..</p>
<p>dis-a-point-ting.</p>
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<title><![CDATA[I think the U.S. is wack sometimes]]></title>
<link>http://mexecution.wordpress.com/2009/11/15/i-think-the-u-s-is-wack-sometimes/</link>
<pubDate>Sun, 15 Nov 2009 21:51:34 +0000</pubDate>
<dc:creator>mexecution</dc:creator>
<guid>http://mexecution.wordpress.com/2009/11/15/i-think-the-u-s-is-wack-sometimes/</guid>
<description><![CDATA[In the United States, although the Food and Drug Administration (FDA) does acknowledge that &#8220;t]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>In the United States, although the Food and Drug Administration (FDA) does acknowledge that &#8220;there has been considerable interest in its use for the treatment of a number of conditions, including glaucoma, AIDS wasting, neuropathic pain, treatment of spasticity associated with multiple sclerosis, and chemotherapy-induced nausea,&#8221; the agency has not approved &#8220;medical marijuana&#8221;. Anyways I got this statement from wikipedia and i just dont get why the fuck the USA doesnt make it legal.  What also sucks is that fact that ciggerates and alcohol are legal and they are more harmful than marijuana could ever be and I know for a fact that its because are companies making so much money off that they dont want to see profits to go down.  Among other things&#8230; Anyways it&#8217;s a fucking plant and shouldnt be so fucking ignorant about it start calling it a (drug) like it&#8217;s herion or some shit </p>
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<title><![CDATA[Cleanliness is next to... What's it to you?]]></title>
<link>http://eggfoojung.wordpress.com/2009/11/14/cleanliness/</link>
<pubDate>Sun, 15 Nov 2009 04:22:11 +0000</pubDate>
<dc:creator>Ramona W</dc:creator>
<guid>http://eggfoojung.wordpress.com/2009/11/14/cleanliness/</guid>
<description><![CDATA[My father&#8217;s off-again/on-again relationship with bathing is now off-again. My sister gave me s]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>My father&#8217;s off-again/on-again relationship with bathing is now off-again. My sister gave me such holy hell last time for keeping track of how close he was to breaking the record that this time I forgot to keep track. The record so far is two weeks just in case you were wondering. Last time he was thisclose to getting through the fourteenth day and I was kind of hoping that he would. Not hoping in the way that we hope to see the first Snowdrops and Crocuses in bloom in the spring because that would be kind of mean and he is my dad and I don&#8217;t want him to have his skin start breaking down or for him to get an infection of some kind. This was the kind of hoping that&#8217;s more like curiosity. You know when you&#8217;re watching a football game and the other team is made-up of players who look like they&#8217;re part giant and also part troll and they&#8217;re thirty-five points ahead of your team and your team is so bad you think maybe they brought in the Pop Warner kids to play instead of your team&#8217;s first or even second string? And somewhere around the time the other team gets another touchdown and the extra point so they&#8217;re forty-two points ahead, you&#8217;re thinking, &#8220;How many points can the other team score? Can they beat us by sixty points? Is this going to be one of those games that sets a record for how badly one team loses to the other?&#8221; Because if your team is going to lose anyway then wouldn&#8217;t it be much cooler to lose by 100 points instead of one touchdown and an extra point? It would look like your team played their very hardest but this team was obviously so phenomenal that there was nothing your team could have done and that would feel better than if your team had just tried a little harder they wouldn&#8217;t now be 1 and 3. That&#8217;s the kind of hoping I was doing on day fourteen of the non-bathing streak. Go big or go home essentially.</p>
<p>We don&#8217;t know why my father doesn&#8217;t want to take a bath. Or a shower. Cuz a shower would be just fine too. But he doesn&#8217;t want to take either one. And he can&#8217;t tell anyone why. I&#8217;m assuming the reason he can&#8217;t tell anyone is that he doesn&#8217;t know. The reason certainly isn&#8217;t because no one has asked him because everyone has asked him: me, my mother, my sister, my brother, his primary care physician, his therapist, his cardiologist. We don&#8217;t know why he doesn&#8217;t want to take either a bath or a shower but he doesn&#8217;t and the more people bug him about it the more it becomes one of those power thingies and the more he is determined- whatever the initial reason- to not take one because he is his own person by God and he does what he wants when he wants to do it.</p>
<p>My mother had decided that Friday the thirteenth was going to be The Day He Took A Bath and she announced this to him several days ahead of time. &#8220;Friday&#8217;s the day you&#8217;re going to be taking a bath,&#8221; she said. And he didn&#8217;t say anything one way or the other so it was considered to be stipulated.</p>
<p>She ran some bathwater for herself on Thursday and joked about him taking his bath a day early but he reminded her that it was not yet Friday and she had declared Friday to be bath-day. Many very reasonable people would consider his protesting taking a bath a day early to be acquiescence to taking a bath on Friday and those people would be well-intentioned but wrong.</p>
<p>Friday morning arrived and he did not indicated in any way that he wanted the water run for his bath. Morning was followed by afternoon and evening in their turns and still there was no bath. My mother reminded him that it was Friday and that meant it was bath-day. When he awoke from his afternoon nap and walked into the living room, I greeted him with &#8220;Here comes the bath-day boy!&#8221; He did not- as might have been expected- vomit but neither did he request that a bath be run. My mother said that he either needed to take a bath before bedtime or he would have to get up early and have one Saturday morning. You&#8217;re very intelligent and astute so you will have been quick to notice what happened here:</p>
<p>The bath cannot take place Thursday because the bath is going to take place Friday.</p>
<p>The bath is going to take place Friday.</p>
<p>The bath is going to take place Friday unless it doesn&#8217;t in which case it will take place on Saturday.</p>
<p>The bath did not take place Friday and my father did not rise sufficiently early to take a bath before company arrived . My mother announced that no one would be bringing him solid food until after he took a bath. He decided to get his own lunch since no one would bring him anything and opened some spaghetti and meatballs which he ate directly from the can with a fork.</p>
<p>In the meantime, my daughter, my sister, and I all went to the grocery store to assist my grandmother with her shopping. While we were at the store, my sister bought a package of Entenmann&#8217;s mixed donuts. As she brought them into the house, my father saw them. He announced that he would like me to bring him a glass of milk and two donuts.</p>
<p>I said, &#8220;No.&#8221;</p>
<p>He said, &#8220;Who the hell do you think you are and why aren&#8217;t you bringing me donuts?&#8221;</p>
<p>I replied that an agreement had been made and that no one was bringing him anything like that until he had a bath.</p>
<p>He demanded to know what business was it of mine.</p>
<p>I told him that it was the business of everyone because we all live in this house and everyone has to smell him and if he wants to be considered a member of society then he has to conform to some basic societal norms like taking a bath or shower at least once a week if the facilities are vailable and functional.</p>
<p>I consulted my mother who had made the decision in the first place and she said to go ahead because clearly he was not intending to take a bath so there was no point in holding out. I delivered the donuts and milk in a very thumping them down manner and said, &#8220;Congratulations! You outwaited your bath! You must be so proud!&#8221;</p>
<p>My question for you is: Why do I get so friggin&#8217; involved in all this? I have plugged up sinuses and am anosmic most of the time so I can only rely on my imagination to let me know how badly he smells. There were a couple of  times during the summer that my eyes started to sting if I was on the same side of the room as him so I guess I could say I can rely on my eyes as well as my nose  it&#8217;s winter now though and the rooms are a lot cooler. But why am I the last one in my immediate and extended family to give up and quit nagging? Why am I the one threatening him with MRSA or bedsores or yeast infections that never clear up and result in amputation of certain male endowments? Am I too stupid to know when to stop or can I just not stand to see someone succeed in being more stubborn than me?</p>
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<title><![CDATA[Amnesty International Pushes &quot;Gay Marriage&quot; Down Under]]></title>
<link>http://pbaptist.wordpress.com/2009/11/14/amnesty-international-pushes-gay-marriage-down-under/</link>
<pubDate>Fri, 13 Nov 2009 22:00:53 +0000</pubDate>
<dc:creator>Particular Kev</dc:creator>
<guid>http://pbaptist.wordpress.com/2009/11/14/amnesty-international-pushes-gay-marriage-down-under/</guid>
<description><![CDATA[By Piero A. Tozzi WASHINGTON, D.C., November 12, 2009 (LifeSiteNews.com) &#8211; Activist organizati]]></description>
<content:encoded><![CDATA[By Piero A. Tozzi WASHINGTON, D.C., November 12, 2009 (LifeSiteNews.com) &#8211; Activist organizati]]></content:encoded>
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<title><![CDATA[Norm Tüm Şarkılar Teker Teker]]></title>
<link>http://ottomanrap.wordpress.com/2009/11/13/norm-tum-sarkilar-teker-teker/</link>
<pubDate>Fri, 13 Nov 2009 14:17:32 +0000</pubDate>
<dc:creator>ottomanrap</dc:creator>
<guid>http://ottomanrap.wordpress.com/2009/11/13/norm-tum-sarkilar-teker-teker/</guid>
<description><![CDATA[NORM &#8211; KAFAM 1 MİLYON http://rapidshare.com/files/16976923&#8230;m_1_Milyon.rar NORM &#8211; R]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><strong><em><span style="color:green;">NORM &#8211; KAFAM 1 MİLYON</p>
<p><a href="http://rapidshare.com/files/169769234/Norm_-_Kafam_1_Milyon.rar" target="_blank">http://rapidshare.com/files/16976923&#8230;m_1_Milyon.rar</a></p>
<p>NORM &#8211; RAP DERSİ</p>
<p><a href="http://rapidshare.com/files/169769235/Norm_-_Rap_Dersi.rar" target="_blank">http://rapidshare.com/files/16976923&#8230;_Rap_Dersi.rar</a></p>
<p>NORM &#8211; SADECE DİNLE</p>
<p><a href="http://rapidshare.com/files/169769236/Norm_-_Sadece_Dinle.rar" target="_blank">http://rapidshare.com/files/16976923&#8230;dece_Dinle.rar</a></p>
<p>NORM &#8211; TRANSPARAN</p>
<p><a href="http://rapidshare.com/files/169769237/Norm_-_Transparan.rar" target="_blank">http://rapidshare.com/files/16976923&#8230;Transparan.rar</a></p>
<p>NORM &#8211; PLAYBOY</p>
<p><a href="http://rapidshare.com/files/169804381/10_-_Norm_-_Playboy.rar" target="_blank">http://rapidshare.com/files/16980438&#8230;_-_Playboy.rar</a></p>
<p>NORM BÖYLE 1 DÜNYA</p>
<p><a href="http://rapidshare.com/files/169804382/11_-_Norm_-_Boeyle_1_Duenya.rar" target="_blank">http://rapidshare.com/files/16980438&#8230;e_1_Duenya.rar</a></p>
<p>NORM &#8211; AJDAR DİSS</p>
<p><a href="http://rapidshare.com/files/169804383/12_-_Norm_-_Diss_Ajdar.rar" target="_blank">http://rapidshare.com/files/16980438&#8230;Diss_Ajdar.rar</a></p>
<p>NORM &#8211; AF YOK</p>
<p><a href="http://rapidshare.com/files/169804384/13_-_Norm_-_Af_Yok.rar" target="_blank">http://rapidshare.com/files/16980438&#8230;m_-_Af_Yok.rar</a></p>
<p>NORM EKSİK ETEK</p>
<p><a href="http://rapidshare.com/files/169804385/14_-_Norm_-_Eksik_Etek.rar" target="_blank">http://rapidshare.com/files/16980438&#8230;Eksik_Etek.rar</a></p>
<p>NORM &#8211; KAPALI GİŞE</p>
<p><a href="http://rapidshare.com/files/169804386/15_-_Norm_-_Kapal__305__Gi__351_e.rar" target="_blank">http://rapidshare.com/files/16980438&#8230;_Gi__351_e.rar</a></p>
<p>NORM İLLEGAL ŞAİR</p>
<p><a href="http://rapidshare.com/files/169811648/Norm_-_Illegal___350_air.rar" target="_blank">http://rapidshare.com/files/16981164&#8230;___350_air.rar</a></p>
<p>NORM &#8211; KADIKÖY ACİL</p>
<p><a href="http://rapidshare.com/files/169811650/Norm_-_Kad__305_koy_Acil.rar" target="_blank">http://rapidshare.com/files/16981165&#8230;5_koy_Acil.rar</a></p>
<p>NORM KİNİM</p>
<p><a href="http://rapidshare.com/files/169811651/Norm_-_Kinim.rar" target="_blank">http://rapidshare.com/files/169811651/Norm_-_Kinim.rar</a></p>
<p>NORM NOKTA KOY</p>
<p><a href="http://rapidshare.com/files/169811652/Norm_-_Nokta_Koy.rar" target="_blank">http://rapidshare.com/files/16981165&#8230;_Nokta_Koy.rar</a></p>
<p>NORM SAYKO</p>
<p><a href="http://rapidshare.com/files/169811653/Norm_-_Sayko.rar" target="_blank">http://rapidshare.com/files/169811653/Norm_-_Sayko.rar</a></p>
<p>NORM SON UYKU</p>
<p><a href="http://rapidshare.com/files/169811654/Norm_-_Son_Uyku.rar" target="_blank">http://rapidshare.com/files/16981165&#8230;-_Son_Uyku.rar</a></p>
<p>NORM TEKİR</p>
<p><a href="http://rapidshare.com/files/169811655/Norm_-_Tekir.rar" target="_blank">http://rapidshare.com/files/169811655/Norm_-_Tekir.rar</a></p>
<p>BONUS!!! (EKSİK ETEK BEAT)</p>
<p><a href="http://rapidshare.com/files/169834671/Eksik_Etek_Beat.rar" target="_blank">http://rapidshare.com/files/16983467&#8230;_Etek_Beat.rar</a></span></em></strong></p>
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<title><![CDATA[garlic bombay]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/13/garlic-bombay/</link>
<pubDate>Fri, 13 Nov 2009 02:47:27 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/13/garlic-bombay/</guid>
<description><![CDATA[it sucks to wake up to no breakfast. so i spun around the kitchen and gathered whatever i have. eggs]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>it sucks to wake up to no breakfast.</p>
<p>so i spun around the kitchen and gathered whatever i have.<br />
eggs.<br />
check.<br />
bread.<br />
check. (although it&#8217;s wholemeal)</p>
<p>and shoots. i committed one of the greatest sin anyone could commit while cooking.<br />
well, i did wash my hands..<br />
i just forgot to add seasoning.</p>
<p>and i thought of a brilliant idea to use butter to fry.. but i had none.<br />
the only alternative.. garlic spread.</p>
<p style="text-align:center;"><img class="aligncenter size-medium wp-image-408" src="http://thelittlefighter.wordpress.com/files/2009/11/13112009007.jpg?w=300" alt="" width="240" height="180" /></p>
<p style="text-align:left;">okay, it didnt taste bad. but i learnt it&#8217;s much better sweet than savoury.</p>
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<title><![CDATA[science discovery]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/11/science-discovery/</link>
<pubDate>Tue, 10 Nov 2009 16:15:06 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/11/science-discovery/</guid>
<description><![CDATA[omgoodnes. i had soy milk this afternoon. and conveniently forgot to clear my nearly finished cup. s]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>omgoodnes.</p>
<p>i had soy milk this afternoon. and conveniently forgot to clear my nearly finished cup. something interesting happened.</p>
<div id="attachment_400" class="wp-caption aligncenter" style="width: 250px"><img class="size-medium wp-image-400" src="http://thelittlefighter.wordpress.com/files/2009/11/10112009009.jpg?w=300" alt="tilted side ways" width="240" height="180" /><p class="wp-caption-text">tilted side ways</p></div>
<div id="attachment_401" class="wp-caption aligncenter" style="width: 250px"><img class="size-medium wp-image-401" src="http://thelittlefighter.wordpress.com/files/2009/11/10112009010.jpg?w=300" alt="" width="240" height="180" /><p class="wp-caption-text">diagonally upside down</p></div>
<p style="text-align:left;">how cool is that? my milk defied gravity!</p>
<p style="text-align:left;">so, curious about the texture. i dug it with a fork.</p>
<div id="attachment_402" class="wp-caption aligncenter" style="width: 250px"><img class="size-medium wp-image-402" src="http://thelittlefighter.wordpress.com/files/2009/11/11112009.jpg?w=300" alt="" width="240" height="180" /><p class="wp-caption-text">softer than tofu</p></div>
<p style="text-align:left;">the texture is just like panna cotta!</p>
<p style="text-align:left;">with an adventurous spirit of a scientist, i smelt it.. which is just like soy. and took a tiny bite. wow, i have a new invention &#8211; soy panna cotta!! it actually taste quite good!</p>
<p style="text-align:left;">oh wait.. is that how they make tau huay?</p>
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<title><![CDATA[little french encounter]]></title>
<link>http://thelittlefighter.wordpress.com/2009/11/10/little-french-encounter/</link>
<pubDate>Tue, 10 Nov 2009 05:28:18 +0000</pubDate>
<dc:creator>thelittlefighter</dc:creator>
<guid>http://thelittlefighter.wordpress.com/2009/11/10/little-french-encounter/</guid>
<description><![CDATA[last night, i watched Julie &amp; Julia. and this morning i woke up inspired to cook something frenc]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>last night, i watched Julie &#38; Julia.</p>
<p>and this morning i woke up inspired to cook something french. the problem is, i cant really cook. so i decided on egg. eggs are one of the best thing on earth, they taste good anyway u cook them! ..but please just cook them! the thought of the local ah peks who drink hot kopi or milo with a raw egg is rather..<br />
perturbing.</p>
<p>anyways, the only french egg dish i know is the omellete. so, out comes 2 eggs from the fridge and viola!</p>
<div id="attachment_391" class="wp-caption aligncenter" style="width: 250px"><img class="size-medium wp-image-391" src="http://thelittlefighter.wordpress.com/files/2009/11/10112009001.jpg?w=300" alt="beautiful creamy eggs" width="240" height="180" /><p class="wp-caption-text">beautiful creamy eggs</p></div>
<div id="attachment_394" class="wp-caption aligncenter" style="width: 250px"><img class="size-medium wp-image-394" src="http://thelittlefighter.wordpress.com/files/2009/11/101120090041.jpg?w=300" alt="yummm" width="240" height="180" /><p class="wp-caption-text">yummm</p></div>
<div id="attachment_395" class="wp-caption aligncenter" style="width: 250px"><img class="size-medium wp-image-395" src="http://thelittlefighter.wordpress.com/files/2009/11/101120090071.jpg?w=300" alt="look at the inside!" width="240" height="180" /><p class="wp-caption-text">look at the inside!</p></div>
<p style="text-align:left;">okay, my phone camera sucks. but the texture of the omellete was perfect!</p>
<p style="text-align:left;">blissfully munching away..</p>
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<title><![CDATA[Is Marcellus Shale too hot to handle?]]></title>
<link>http://wolverines.wordpress.com/2009/11/09/is-marcellus-shale-too-hot-to-handle/</link>
<pubDate>Mon, 09 Nov 2009 17:26:30 +0000</pubDate>
<dc:creator>Alan Gregory</dc:creator>
<guid>http://wolverines.wordpress.com/2009/11/09/is-marcellus-shale-too-hot-to-handle/</guid>
<description><![CDATA[Radioactivity &#8211; lots of it &#8211; found in wstewater samples from New York state drilling sit]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p><a href="http://www.timesunion.com/AspStories/story.asp?storyID=863369&#38;TextPage=1">Radioactivity</a> &#8211; lots of it &#8211; found in wstewater samples from New York state drilling sites. Not good. Just how much more natural land must be ruined to make us energy happy?</p>
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<title><![CDATA["Gender Abolition."]]></title>
<link>http://gendertranscendence.wordpress.com/2009/11/03/gender-abolition/</link>
<pubDate>Tue, 03 Nov 2009 17:58:43 +0000</pubDate>
<dc:creator>genderanarchy</dc:creator>
<guid>http://gendertranscendence.wordpress.com/2009/11/03/gender-abolition/</guid>
<description><![CDATA[I&#8217;ve heard this phrase thrown around in some conversations about gender. It&#8217;s sometimes ]]></description>
<content:encoded><![CDATA[<div class='snap_preview'><p>I&#8217;ve heard this phrase thrown around in some conversations about gender. It&#8217;s sometimes used to imply that gender itself should be abolished. Abolished, aka &#8220;done away with&#8221; [see slavery], which I don&#8217;t even think is possible. One can not easily just rid the world of something that&#8217;s been created as a conceptual norm in such mass numbers, and that many people agree with (and that some wouldn&#8217;t know how to even begin disagreeing with). People should be able to have the choice of being whoever they choose to be; that&#8217;s the freedom of choice we all should have.</p>
<p>Abolition of general gender is definitely not what I&#8217;m going for at all.  I believe that while the concept is understandable, gender abolition goes against my extreme love for freedom of choice (which should never be taken away, obviously). People define themselves through gender, and it&#8217;s fine as that. I would prefer a world without the gender binary in the conceptual sense, but that seems to be asking a lot out of our current state of things.</p>
<p>Gender isn&#8217;t necessarily bad, especially if the individual doesn&#8217;t think it is. Gender can be bad for those born into the wrong biological sex, who suffer because of the gender imposed upon them. That statement brings me to a critical point in which I digress that society is to blame. (*A.N.- I will forewarn readers that I hate society and often blame it, a lot of the time, but not always.) Society&#8217;s impositions of gender roles and assumptions are what erects barriers to the natural self.</p>
<p>When I speak of the &#8220;natural self&#8221; I tend to mean the self that we would be had we grown up in a society that wasn&#8217;t concerned with labeling our actions as masculine or feminine. I wholeheartedly agree with abolishing society&#8217;s imposed gender roles. This is not to say that I think biological females and males are not different. Of course they are; science confirms this, and as a Biology major you won&#8217;t see me arguing that point. What I want to raise hell about is the fact that society deems it appropriate to tell us how we should conform to our sex through a gender.</p>
<p>People have the right to be who they want to be. A sensitive and emotional guy, a tough chick that loves football and cars, a guy that loves to dress in &#8220;women&#8217;s&#8221; clothes, none of them should be seen as anything but an individual just being themselves. We don&#8217;t need masculine or feminine, expectations, or assumptions, etc. Let us just be.</p>
<p>So…(in my opinion):<br />
Gender abolition: Understandable, but unrealistic and unnecessary.<br />
Gender role abolition: Almost, if not fully, necessary.</p>
<p>Point: Just Be.</p>
<p>Imagine the female/male symbols, and take away the part that distinguishes them. I&#8217;d like if the new gender symbol was just a circle.</p>
<p>~Peace and Love~</p>
<p>*A.N.- Excuse me for the jumbled mess of thoughts. This is often how my posts will be presented. I wouldn&#8217;t be surprised if I go and fix this multiple times to clean it up a bit. This is a spill, and I&#8217;m never good at using words to describe my thoughts as completely and intelligently as I like.</p>
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