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<p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> fancysuksa<br /> ==== type ====<br /> lujvo<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Wed Apr 16 21:53:52 2014<br />  <br /> == English ==<br /> === Definition #56447 - Preferred ===<br />  <br /> ==== definition ====<br /> function f&lt;sub&gt;1&lt;/sub&gt; is discontinuous/abrupt/sharply changes locally (in output) on/at s&lt;sub&gt;2&lt;/sub&gt; (set), with abruptness of type x&lt;sub&gt;3&lt;/sub&gt; (default: 1)<br /> ==== notes ====<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;s&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; should be a set within some open subset of definition of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;f&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt;, or a set on which &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;f&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; is not defined at all. For &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt;, an argument of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; (number) corresponds to a differentiability class of order &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt;, to which &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;f&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; does NOT belong at points in set &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;s&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;; notice that such an &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; makes no implications about the truth value of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;f&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; belonging to any given differentiability classes of order &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;m&lt;/i&gt; &amp;lt; &lt;i&gt;n&lt;/i&gt;&lt;/span&gt;, but &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;f&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; cannot belong to differentiability classes of order &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;m&lt;/i&gt; &amp;gt; &lt;i&gt;n&lt;/i&gt;&lt;/span&gt;; &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt; = 0&lt;/span&gt; implies that the function is not continuous on that set (lack of definition there is sufficient for such a claim); a function that is discontinuous or which has a cusp or sharp &#039;corner&#039; in its graph/plot (meaning that its derivative is discontinuous) at points in &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;s&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; will have &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;≤1&lt;/span&gt;. For now at least, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; can be a non-negative integer; generalizations may eventually be defined. This lujvo is not perfectly algorithmic/predictable.<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/discontinuous function|discontinuous function]]&lt;/li&gt;&lt;li&gt;[[natlang/en/non-smooth function|non-smooth function]]&lt;/li&gt;&lt;li&gt;[[natlang/en/sharp corner|sharp corner ; of a function]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 3<br /> <br /> ==== time ====<br /> Sun Jul 12 14:00:41 2020<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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