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<a NAME="E1:3_1_1"/>
 <a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <a href="rsspace.html#K3" title="RSSPACE:func.3">Zeroseq</a> is  <a href="series_1.html#V2" title="SERIES_1:attr.2">absolutely_summable</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c1">rseq</font> =  <a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <a href="rsspace.html#K3" title="RSSPACE:func.3">Zeroseq</a> as   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a> ;<br/>
<a NAME="E2:3_1_1_1"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c1">rseq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:3_1_1_1"/>
 <a href="rsspace.html#K2" title="RSSPACE:func.2">seq_id</a> <a href="rsspace.html#K3" title="RSSPACE:func.3">Zeroseq</a> is  <a href="series_1.html#V2" title="SERIES_1:attr.2">absolutely_summable</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="comseq_3.html#T3" onmouseover="rs('comseq_3/T3')" onmouseout="rh()">COMSEQ_3:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:3_1_1"/>
 not  <a href="rsspace3.html#K1" title="RSSPACE3:func.1">the_set_of_l1RealSequences</a>  is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rsspace3.html#D1" target="_self" onmouseover="rs('rsspace3/D1')" onmouseout="rh()">Def1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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