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<div class="add">

<b>consider </b><font color="Maroon">x</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:10_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">n</font></span>)</span>
 ;<br/>
<a NAME="E3:10_1_1"/>
 ex <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">n</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">i</font> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">n</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
0
;<br/>

<b>thus </b><a NAME="E1:10_1_1_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">n</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">n</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="newton.html#T102">NEWTON:102</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:10_1_1"/>
not  <a href="urysohn1.html#K1" target="_self">dyadic</a> <font color="Maroon">n</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>;<br/>


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