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<p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> utkakpu<br /> ==== type ====<br /> fu&#039;ivla<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Thu Jan 17 18:48:52 2019<br />  <br /> == English ==<br /> === Definition #71273 - Preferred ===<br />  <br /> ==== definition ====<br /> x&lt;sub&gt;1&lt;/sub&gt; and x&lt;sub&gt;2&lt;/sub&gt; are path-connected by ordered binary relation/predicate x&lt;sub&gt;3&lt;/sub&gt; (ka), such that all paths which satisfy condition(s) x&lt;sub&gt;4&lt;/sub&gt; (ka; default: no additional conditions) in the relevant graph (x&lt;sub&gt;5&lt;/sub&gt;) linking nodes by said relation x&lt;sub&gt;3&lt;/sub&gt; in a directed manner and which contain x&lt;sub&gt;1&lt;/sub&gt; must also (later in the path) contain x&lt;sub&gt;2&lt;/sub&gt;.<br /> ==== notes ====<br /> <br /> All paths in the graph that pass through &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; must at some point also pass through &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;. Note that they may also contain &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; earlier; for example, cycles do this. It just must be the case that any path which at some point comes from &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; via relation &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; must, at some later point, go to &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; (and then they may continue on); in other words, the web from &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; &#039;bunches&#039; up at node &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; and no path from &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; does not eventually go to &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;. All other notes from &quot;.[[utka|utka]]&quot; apply, although &lt;span class=&quot;MATH&quot;&gt;.&lt;i&gt;utka&lt;/i&gt;&lt;sub&gt;4&lt;/sub&gt;&lt;/span&gt; is missing (and, thus, those notes are irrelevant), because it does not in general make sense to discuss intermediates nodes in this case (because no particular path is chosen). In a sense, this word captures the idea in the phrase &quot;All roads lead to Rome&quot;, except that it would be rephrased as &quot;All one-way roads from &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; lead to Rome&quot;. Diagrammatically, see: https://drive.google.com/file/d/14oSV_0ypJpIyKjEsOXVe684f6c-4jZBL/view?usp=drivesdk . The subgraph of paths from &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; &#039;bunches&#039; up at &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;; but this does not imply that it bunches up only at &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;, nor that &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; is the root node thereof, nor that the said subgraph does not have multiple paths out of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;. In other words, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; is the ancestor of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; in all possible ways/along all paths. This word is intended to be equivalent to &quot;[[.utkakpu|.utkakpu]]&quot;, which accidentally has a separate entry in this dictionary.<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/bunching point in subgraph|bunching point in subgraph]]&lt;/li&gt;&lt;li&gt;[[natlang/en/path-connection hub|path-connection hub]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Thu Jan 14 20:00:56 2021<br /> <br /> <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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