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<p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> faunjdikpe<br /> ==== type ====<br /> fu&#039;ivla<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Mon May 16 17:15:40 2016<br />  <br /> == English ==<br /> === Definition #68660 - Preferred ===<br />  <br /> ==== definition ====<br /> x&lt;sub&gt;1&lt;/sub&gt; (function) is the restriction of function x&lt;sub&gt;2&lt;/sub&gt; to domain set x&lt;sub&gt;3&lt;/sub&gt;<br /> ==== notes ====<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; should normally be a (strict) subset of the domain set 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;; however, for generality, any set is allowed, but &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; will be undefined everywhere except on/in the intersection of &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 domain set 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;. Outside of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt;, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; is undefined, even if &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. In/on &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt;, &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 identically equal everywhere. &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 a specific extension 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;. For the sense of restriction in which, instead of being undefined outside of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt;, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; is identically equal to the zero element of the space on the set exclusion of the domain 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; lacking &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; (and which is undefined everywhere not in the domain set 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;), try to use a product of a [[zdeltakronekre|zdeltakronekre]] function with &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 will be defined on the intersection of their two domain sets and will identically be 0 or &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; as specified. Be careful, concerning &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt;, when the domain set 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; is the Cartesian product ([[pi&#039;u|pi&#039;u]]) of sets; for example, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;R&lt;/i&gt;&lt;/span&gt; is not a subset of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;R&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;/span&gt;, even if it is isomorphic to one (actually, uncountably infinitely many in this case).<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/function restriction|function restriction]]&lt;/li&gt;&lt;li&gt;[[natlang/en/restriction|restriction ; of a function to a subset of its domain]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Mon May 16 17:15:40 2016<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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