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

<b>reconsider </b><font color="Maroon">A</font> = <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">0</span><a href="seq_4.html#K1">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  ;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>thus </b><a NAME="E2:59_1_1"/>
not <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>thus </b><a NAME="E3:59_1_1"/>
<font color="Maroon">A</font> is <a href="seq_4.html#V1">bounded_above</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
0
; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D1">SEQ_4:def 1</a><br/>

<b>let </b><font color="Maroon">t</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:59_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>hence </b><a NAME="E2:59_1_1_1"/>
not 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>

<b>take </b>
0
; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D2">SEQ_4:def 2</a><br/>

<b>let </b><font color="Maroon">t</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E4:59_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>hence </b><a NAME="E5:59_1_1"/>
not <font color="Maroon">t</font> <a href="xxreal_0.html#R1">&lt;</a> 0
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
