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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="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"/>
not  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</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="c2">b</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</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="E3:40"/>
not  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">b</font> is <a href="rat_1.html#V1" title="RAT_1:attr.1">irrational</a>
 
;<br/>
<b>hence </b><a NAME="E4:40"/>
contradiction
 ;<br/>


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