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

<b>thus </b><a NAME="E1:26_1_1"/>
 <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  is <a href="jct_misc.html#V1" title="JCT_MISC:attr.1">connected</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">r</font>, <font color="Maroon" title="c2">s</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="jct_misc.html#D1" title="JCT_MISC:def.1">JCT_MISC:def 1</a><br/>

<b>thus </b><a NAME="E1:26_1_1_1"/>
(  not <font color="Maroon" title="c1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  or  not <font color="Maroon" title="c2">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  or <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  )
 ;<br/>


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

<a NAME="E2:26_1_1"/>
(  <a href="limfunc1.html#K4" title="LIMFUNC1:func.4">right_open_halfline</a> 0 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp;  <a href="limfunc1.html#NK2" title="LIMFUNC1:NK.2">left_open_halfline</a> 0 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  )
 
;<br/>
<b>hence </b><a NAME="E3:26_1_1"/>
( not  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  is <a href="seq_4.html#V2" title="SEQ_4:attr.2">bounded_below</a> &amp; not  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  is <a href="seq_4.html#V1" title="SEQ_4:attr.1">bounded_above</a> )
 <b>by </b><i><a class="ref" href="rcomp_1.html#T3" title="RCOMP_1:th.3">RCOMP_1:3</a>, <a class="ref" href="rcomp_1.html#T4" title="RCOMP_1:th.4">RCOMP_1:4</a></i>;<br/>


</div>
