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<?xml version="1.0"?>
<!--This OMDoc document is generated from an sTeX-encoded one via LaTeXML, you may want to reconsider editing it.-->
<omdoc xmlns:omdoc="http://omdoc.org/ns" xmlns="http://omdoc.org/ns" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:stex="http://kwarc.info/ns/sTeX" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns" xmlns:om="http://www.openmath.org/OpenMath">
<omdoc:omgroup layout="sectioning" xml:id="sec.reals" about="#sec.reals" stex:srcref="reals.tex#textrange(from=1;0,to=16;13)">
<omdoc:metadata xml:id="sec.reals.metadata1" about="#sec.reals.metadata1" stex:srcref="reals.tex#textrange(from=1;0,to=15;12)">
<dc:title xml:id="sec.reals.metadata1.title1" about="#sec.reals.metadata1.title1" stex:srcref="reals.tex#textrange(from=1;0,to=16;13)">Real Numbers</dc:title>
</omdoc:metadata>
<theory xml:id="reals" about="#reals" stex:srcref="reals.tex#textrange(from=2;0,to=15;12)">
<imports from="../../../slides/extcds/omstd/arith1.omdoc#arith1"/>
<omdoc:symbol name="RealNumbers" xml:id="RealNumbers.sym" about="#RealNumbers.sym" stex:srcref="reals.tex#textrange(from=3;1,to=3;33)"/>
<omdoc:notation cd="reals" name="RealNumbers">
<omdoc:prototype>
<om:OMS cd="reals" name="RealNumbers"/>
</omdoc:prototype>
<omdoc:rendering>
<m:mi mathvariant="double-struck">R</m:mi>
</omdoc:rendering>
</omdoc:notation>
<omdoc:symbol name="absval" xml:id="absval.sym" about="#absval.sym" stex:srcref="reals.tex#textrange(from=4;1,to=4;43)"/>
<omdoc:notation cd="reals" name="absval">
<omdoc:prototype>
<om:OMA>
<om:OMS cd="reals" cr="fun" name="absval"/>
<omdoc:expr name="arg1"/>
</om:OMA>
</omdoc:prototype>
<omdoc:rendering precedence="2000">
<m:mrow>
<m:mo egroup="fence" fence="true">(</m:mo>
<m:mo cr="fun">|</m:mo>
<render name="arg1" precedence="2000"/>
<m:mo cr="fun">|</m:mo>
<m:mo egroup="fence" fence="true">)</m:mo>
</m:mrow>
</omdoc:rendering>
</omdoc:notation>
<omdoc:symbol name="rfrac" xml:id="rfrac.sym" about="#rfrac.sym" stex:srcref="reals.tex#textrange(from=5;1,to=5;33)"/>
<omdoc:notation cd="reals" name="rfrac">
<omdoc:prototype>
<om:OMA>
<om:OMS cd="reals" cr="fun" name="rfrac"/>
<omdoc:expr name="arg1"/>
<omdoc:expr name="arg2"/>
</om:OMA>
</omdoc:prototype>
<omdoc:rendering>
<m:mfrac>
<render name="arg1"/>
<render name="arg2"/>
</m:mfrac>
</omdoc:rendering>
</omdoc:notation>
<omdoc:symbol name="real-numbers" xml:id="real-numbers.def.sym" about="#real-numbers.def.sym" stex:srcref="reals.tex#textrange(from=7;0,to=10;16)"/>
<omdoc:definition for="real-numbers" xml:id="reals.def" about="#reals.def" stex:srcref="reals.tex#textrange(from=7;0,to=10;16)">
<omdoc:CMP xml:id="reals.def.CMP1" about="#reals.def.CMP1" stex:srcref="reals.tex#textrange(from=7;0,to=10;16)">
<p xmlns="http://www.w3.org/1999/xhtml" style="" class="p" id="reals.def.CMP1.p1">We denote the set of <omdoc:idx xml:id="reals.def.CMP1.p1.idx1" about="#reals.def.CMP1.p1.idx1" stex:srcref="reals.tex#textrange(from=7;27,to=8;44)"><omdoc:idt xml:id="reals.def.CMP1.p1.idx1.idt1" about="#reals.def.CMP1.p1.idx1.idt1" stex:srcref="reals.tex#textrange(from=7;27,to=8;44)"><omdoc:term cd="reals" name="real-numbers" role="definiendum" xml:id="reals.def.CMP1.p1.idx1.idt1.term1" about="#reals.def.CMP1.p1.idx1.idt1.term1" stex:srcref="reals.tex#textrange(from=7;27,to=8;44)">real numbers</omdoc:term></omdoc:idt><omdoc:ide index="default" xml:id="reals.def.CMP1.p1.idx1.ide2" about="#reals.def.CMP1.p1.idx1.ide2" stex:srcref="reals.tex#textrange(from=7;27,to=8;44)"><omdoc:idp>real</omdoc:idp><omdoc:idp>numbers</omdoc:idp></omdoc:ide></omdoc:idx> we all know and love with
<om:OMOBJ><om:OMS cd="reals" name="RealNumbers"/></om:OMOBJ>.</p>
</omdoc:CMP>
</omdoc:definition>
<omdoc:definition xml:id="absval.def" about="#absval.def" stex:srcref="reals.tex#textrange(from=12;0,to=14;16)">
<omdoc:CMP xml:id="absval.def.CMP1" about="#absval.def.CMP1" stex:srcref="reals.tex#textrange(from=12;0,to=14;16)">
<p xmlns="http://www.w3.org/1999/xhtml" style="" class="p" id="absval.def.CMP1.p1">The absolute value <om:OMOBJ><om:OMA><om:OMS cd="reals" name="absval"/><om:OMV name="r"/></om:OMA></om:OMOBJ> of a real number <om:OMOBJ><om:OMV name="r"/></om:OMOBJ>.</p>
</omdoc:CMP>
</omdoc:definition>
</theory>
</omdoc:omgroup>
</omdoc>
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