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<div><span class="kw">theorem </span><a NAME="T24"><span class="comment"><font color="firebrick">:: DIOPHAN1:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a><br/>  for <font color="Olive" title="b2">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b2">r</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>  &amp; <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b3">p</font> where <font color="Olive" title="b3">p</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  : <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b3">p</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 2</span>)</span> </span> } </span>  holds <br/><font color="Olive" title="b1">S</font> is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> </div></div>
