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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:41_1_1"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c1">a</font> is <a href="rat_1.html#V1" title="RAT_1:attr.1">irrational</a>
 ;<br/>

<b>assume </b><a NAME="E2:41_1_1"/>
<font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>

<a NAME="E3:41_1_1"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 1
 
;<br/>
<b>hence </b><a NAME="E4:41_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="borsuk_5.html#E1:41_1_1"><i><font color="Green" title="E24">A1</font></i></a></i>;<br/>


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