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

<b>thus </b><a NAME="E1:35_1_1"/>
 <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  is <a href="jct_misc.html#V1">connected</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">s</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="jct_misc.html#D1">JCT_MISC:def 1</a><br/>

<b>thus </b><a NAME="E1:35_1_1_1"/>
(  not <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  or  not <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  or <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a>  <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  )
 ;<br/>


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

<a NAME="E2:35_1_1"/>
(  <a href="limfunc1.html#K4">right_open_halfline</a> 0 <a href="tarski.html#R1">c=</a>  <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  &amp;  <a href="limfunc1.html#NK2" target="_self">left_open_halfline</a> 0 <a href="tarski.html#R1">c=</a>  <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  )
 
;<br/>
<b>hence </b><a NAME="E3:35_1_1"/>
( not  <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  is <a href="seq_4.html#V2">bounded_below</a> &amp; not  <a href="subset_1.html#K2">[#]</a> <a href="numbers.html#K1">REAL</a>  is <a href="seq_4.html#V1">bounded_above</a> )
 <b>by </b><i><a class="ref" href="rcomp_1.html#T3">RCOMP_1:3</a>, <a class="ref" href="rcomp_1.html#T4">RCOMP_1:4</a></i>;<br/>


</div>
