https://wiki.lojban.io/index.php?action=history&feed=atom&title=utkaje utkaje - Revision history 2026-05-01T17:10:10Z Revision history for this page on the wiki MediaWiki 1.45.3 https://wiki.lojban.io/index.php?title=utkaje&diff=20451&oldid=prev Nalvaizmiku: Import words via API 2026-01-13T17:05:40Z <p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> utkaje<br /> ==== type ====<br /> fu&#039;ivla<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Thu Mar 7 04:45:14 2019<br />  <br /> == English ==<br /> === Definition #71314 - Preferred ===<br />  <br /> ==== definition ====<br /> x&lt;sub&gt;1&lt;/sub&gt; and x&lt;sub&gt;2&lt;/sub&gt; are path-linked by directed binary predicate x&lt;sub&gt;3&lt;/sub&gt; (ka) via intermediate steps x&lt;sub&gt;4&lt;/sub&gt; (ordered list; ce&#039;o) in graph x&lt;sub&gt;5&lt;/sub&gt;, such that (in the graph x&lt;sub&gt;5&lt;/sub&gt;) both (A) no other node exists to which x&lt;sub&gt;2&lt;/sub&gt; is connected in/by the same way/direction/relation and (B) no other node exists to which x&lt;sub&gt;1&lt;/sub&gt; is connected in/by the opposite/(anti)symmetric/reversed way/direction/relation.<br /> ==== notes ====<br /> <br /> Equivalent to &quot; MATH<br /> $x_1 \, x_2$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; fo MATH<br /> $x_4 \, x_5$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;4&lt;/sub&gt; &lt;i&gt;x&lt;/i&gt;&lt;sub&gt;5&lt;/sub&gt;&lt;/span&gt; .[[utkaro|utkaro]] fi &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; gi&#039;e se .utkaro fi MATH<br /> $x_&lt;a class=&quot;undefined&quot; href=&quot;../dict/3?bg=1;langidarg=2&quot;&gt;3&lt;/a&gt;^&lt;a class=&quot;undefined&quot; href=&quot;../dict/-1?bg=1;langidarg=2&quot;&gt;-1&lt;/a&gt;$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;-1&lt;/sup&gt;&lt;/span&gt;&quot;, where MATH<br /> $x_&lt;a class=&quot;undefined&quot; href=&quot;../dict/3?bg=1;langidarg=2&quot;&gt;3&lt;/a&gt;^&lt;a class=&quot;undefined&quot; href=&quot;../dict/-1?bg=1;langidarg=2&quot;&gt;-1&lt;/a&gt;$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;-1&lt;/sup&gt;&lt;/span&gt; is binary relation/predicate &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; with the order of its two arguments exchanged (basically: &quot;[[se|se]]&quot;-converted). Multiple paths may connect &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; and &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;. There may be peripheral branches extending from &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; which are acyclic (or cyclic) such that they contain a node which has a directed distance from &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; which exceeds that of any 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; 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;; it is just the case that for any path connecting &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; and &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 either direction, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; and &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; are root/leaf nodes thereof.<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/path connection with two endpoints|path connection with two endpoints]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Fri Jan 15 03:36:41 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> Nalvaizmiku