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<div><span class="kw">theorem </span><a NAME="T14"><span class="comment"><font color="firebrick">:: DIOPHAN2:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>  <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  holds <span class="p1"> { <span class="default"> <font color="Olive" title="b2">q</font> where <font color="Olive" title="b2">q</font> is   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</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="b1">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b2">q</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="square_1.html#K3" title="SQUARE_1:func.3">sqrt</a> 5</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1" title="RAT_1:func.1">denominator</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 2</span>)</span></span>)</span> </span> } </span>  is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> </div></div>
