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<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="asympt_1.html#K2" target="_self">seq_logn</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>;<br/>
<a NAME="E1:27"/>
( <a href="asympt_1.html#K2" target="_self">seq_logn</a>  <a href="seq_1.html#K19">/"</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K2" target="_self">seq_logn</a>  <a href="seq_1.html#K19">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="asympt_1.html#E23"><i><font color="Green">Lemma20</font></i></a></i>;<br/>
<a NAME="E2:27"/><b>then </b>
(  <a href="asympt_1.html#K2" target="_self">seq_logn</a>  <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K9">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> &amp; not  <a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K9">Big_Oh</a> <a href="asympt_1.html#K2" target="_self">seq_logn</a>  )
 
<b>by </b><i><a class="ref" href="asympt_0.html#T16">ASYMPT_0:16</a></i>;<br/>
<a NAME="E3:27"/><b>then </b>
(  <a href="asympt_1.html#K2" target="_self">seq_logn</a>  <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K9">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> &amp; not  <a href="asympt_1.html#K2" target="_self">seq_logn</a>  <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K10">Big_Omega</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="asympt_0.html#T19">ASYMPT_0:19</a></i>;<br/>
<b>hence </b><a NAME="E4:27"/>
(  <a href="asympt_0.html#K9">Big_Oh</a> <a href="asympt_1.html#K2" target="_self">seq_logn</a>  <a href="tarski.html#R1">c=</a>  <a href="asympt_0.html#K9">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> &amp; not  <a href="asympt_0.html#K9">Big_Oh</a> <a href="asympt_1.html#K2" target="_self">seq_logn</a>  <a href="hidden.html#R1">=</a>  <a href="asympt_0.html#K9">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="asympt_1.html#T4" target="_self">Th4</a></i>;<br/>


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