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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">b</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E2:40"/>
not <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font> is <a href="rat_1.html#V1" title="RAT_1:attr.1">irrational</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">c</font> = <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">a</font> as  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  ;<br/>
<a NAME="E4:40"/>
not <font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">a</font> is <a href="rat_1.html#V1" title="RAT_1:attr.1">irrational</a>
 
;<br/>
<b>hence </b><a NAME="E5:40"/>
contradiction
 <b>by </b><i><a class="txt" href="borsuk_5.html#E1:40"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/>


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