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<p class="MsoNormal">Perhaps it depends whether one cares about a special case, common case, or all instances?<o:p></o:p></p>
<p class="MsoNormal">And how many useful things can be proven for all instances without any specific semantics in mind.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><b>From:</b> Friam <friam-bounces@redfish.com> <b>On Behalf Of
</b>Jon Zingale<br>
<b>Sent:</b> Monday, October 25, 2021 5:17 PM<br>
<b>To:</b> friam@redfish.com<br>
<b>Subject:</b> Re: [FRIAM] stygmergy, CA's, and [biological] development<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Verdana",sans-serif;color:#333333">"""</span><span style="font-size:12.0pt;color:#333333"><o:p></o:p></span></p>
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<pre style="white-space:pre-wrap"><span style="font-family:"Verdana",sans-serif;color:black">An example of what Marcus is saying is that using the category definition<o:p></o:p></span></pre>
<pre><span style="font-family:"Verdana",sans-serif;color:black">of duality you can show that the dual space of the dual space is (is<o:p></o:p></span></pre>
<pre><span style="font-family:"Verdana",sans-serif;color:black">isomorphic to) the original space. That's easy to show without the added<o:p></o:p></span></pre>
<pre><span style="font-family:"Verdana",sans-serif;color:black">generality.</span><span style="color:black"><o:p></o:p></span></pre>
<pre style="white-space:pre-wrap"><span style="font-family:"Verdana",sans-serif;color:black">"""</span><span style="color:black"><o:p></o:p></span></pre>
<pre style="white-space:pre-wrap"><span style="font-family:"Verdana",sans-serif;color:black">Except for when that isn't true. Consider non-finite dimensional vector spaces.<o:p></o:p></span></pre>
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