<?xml version="1.0"?>
<div class="add">

<b>consider </b><font color="Maroon" title="c3">N</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:18_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">N</font> holds <br/><font color="Maroon" title="c2">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="asympt_0.html#D4" target="_self" title="ASYMPT_0:def.4">Def4</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">N</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="asympt_0.html#D4" target="_self" title="ASYMPT_0:def.4">ASYMPT_0:def 4</a><br/>

<b>let </b><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E3:18_1_1"/>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">N</font>
 ;<br/>

<a NAME="E4:18_1_1"/><b>then </b><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c2">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="asympt_0.html#E2:18_1_1"><i><font color="Green" title="E9">A1</font></i></a></i>;<br/>
<a NAME="E5:18_1_1"/>
 <a href="asympt_0.html#K2" title="ASYMPT_0:func.2">max</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">n</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></i>;<br/>
<b>hence </b><a NAME="E6:18_1_1"/>
<span class="p1">(<span class="default"><a href="asympt_0.html#K8" title="ASYMPT_0:func.8">max</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="asympt_0.html#E4:18_1_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="asympt_0.html#D10" target="_self" title="ASYMPT_0:def.10">Def10</a></i>;<br/>


</div>
