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<p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> fa&#039;ai<br /> ==== type ====<br /> experimental cmavo<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Mon Aug 4 20:44:23 2014<br />  <br /> == English ==<br /> === Definition #57188 - Preferred ===<br />  <br /> ==== selma&#039;o ====<br /> VUhU<br /> ==== definition ====<br /> <br /> mathematical ordered n-ary operator: (pointwise) functional left composition; MATH<br /> $X_1 \circ X_2$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;tt&gt;o&lt;/tt&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;.<br /> <br /> ==== notes ====<br /> <br /> Inputs must be appropriate functions; this outputs a function; follow by &quot;[[ku&#039;e|ku&#039;e]] ([[boi|boi]])&quot; in order to include/apply the output function to arguments (thereby producing a number). MATH<br /> $a_1 \circ a_2 \circ \dots \circ a_n = a_1(a_2(\dots(a_n(\cdot))\dots))$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;tt&gt;o&lt;/tt&gt;&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;tt&gt;o&lt;/tt&gt;...&lt;tt&gt;o&lt;/tt&gt;&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;n&lt;/sub&gt; = &lt;i&gt;a&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;(&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;(...(&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;n&lt;/sub&gt;(⋅))...))&lt;/span&gt; for any positive integer or countable infinity &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; and functions &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;a&lt;/i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/span&gt; for all integer &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt; &amp;lt; &lt;i&gt;n&lt;/i&gt; + 1&lt;/span&gt;. Replaces all of the inputs with a (possibly stripped, as appropriate) tuple; for replacing a single argument in a multivariate function with a function (either evaluated or not), use (partial) (e)valuation. Left compose multiple terms by separating the function names with &quot;[[boi|boi]]&quot;.<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/composition|composition ; pointwise function(al) left composition]]&lt;/li&gt;&lt;li&gt;[[natlang/en/functional composition|functional composition ; pointwise; left]]&lt;/li&gt;&lt;li&gt;[[natlang/en/functional power|functional power ; generalized; pointwise function(al) left composition]]&lt;/li&gt;&lt;li&gt;[[natlang/en/function composition|function composition ; pointwise, left]]&lt;/li&gt;&lt;li&gt;[[natlang/en/iterated function|iterated function ; pointwise function(al) left composition]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Sun Jan 21 04:35:56 2018<br /> <br /> [[comments.html?valsi=27178;definition=57188|[View<br /> Comments For This Definition]]] <br /> <br /> &lt;br/&gt;&lt;font size=&quot;+1&quot;&gt;Examples&lt;/font&gt;<br /> &lt;hr/&gt;<br /> &lt;dl&gt;<br /> &lt;/dl&gt;<br /> <br /> === Etymology ===</div>

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