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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: ASYMPT_1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">e</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">e</font> &amp; <font color="Olive" title="b1">e</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 holds <br/> ex <font color="Olive" title="b2">s</font> being   <a href="asympt_0.html#V4" title="ASYMPT_0:attr.4">eventually-positive</a>  <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a> st <br/>( <font color="Olive" title="b2">s</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> (<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">e</font></span>)</span>,1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) &amp;  <a href="asympt_0.html#K6" title="ASYMPT_0:func.6">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> 8</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="asympt_0.html#K6" title="ASYMPT_0:func.6">Big_Oh</a> <font color="Olive" title="b2">s</font> &amp;  not  <a href="asympt_0.html#K6" title="ASYMPT_0:func.6">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> 8</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="asympt_0.html#K6" title="ASYMPT_0:func.6">Big_Oh</a> <font color="Olive" title="b2">s</font> )</div></div>
