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<a NAME="E1:3_1_1"/>
 <a href="rsspace.html#K2">seq_id</a> <a href="rsspace.html#K6">Zeroseq</a>  is <a href="series_1.html#V2">absolutely_summable</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>1</sub></font> =  <a href="rsspace.html#K2">seq_id</a> <a href="rsspace.html#K6">Zeroseq</a>  as   <a href="seq_1.html#NM1">Real_Sequence</a> ;<br/>
<a NAME="E2:3_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="rsspace.html#D6">RSSPACE:def 6</a></i>;<br/>
<b>hence </b><a NAME="E3:3_1_1_1"/>
 <a href="rsspace.html#K2">seq_id</a> <a href="rsspace.html#K6">Zeroseq</a>  is <a href="series_1.html#V2">absolutely_summable</a>
 <b>by </b><i><a class="ref" href="comseq_3.html#T3">COMSEQ_3:3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:3_1_1"/>
not  <a href="rsspace3.html#K1" target="_self">the_set_of_l1RealSequences</a>  is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="rsspace3.html#D1" target="_self">Def1</a></i>;<br/>


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