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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> ;<br/>

<b>assume </b><a NAME="E1:100"/><i><font color="Green" title="E73">A1</font></i>: 
<font color="Maroon" title="c1">F</font> is <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>
 ;<br/>

<b>assume </b><a NAME="E2:100"/>
 ex <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">F</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 ;<br/>

<a NAME="E3:100"/><b>then </b>
not  <a href="supinf_2.html#K20" title="SUPINF_2:func.20">SUM</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> 
 
<b>by </b><i><a class="txt" href="supinf_2.html#E1:100"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="supinf_2.html#T64" target="_self" title="SUPINF_2:th.64">Th64</a>, <a class="ref" href="supinf_1.html#T1" title="SUPINF_1:th.1">SUPINF_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:100"/>
not <font color="Maroon" title="c1">F</font> is <a href="supinf_2.html#V7" title="SUPINF_2:attr.7">summable</a>
 <b>by </b><i><a class="ref" href="supinf_2.html#D24" target="_self" title="SUPINF_2:def.24">Def24</a></i>;<br/>


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