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<?latexml searchpaths=".,../../sty,../../rnc,../../rnc/omdoc,../../sty/modules,../../sty/statements,../../sty/sproof,../../sty/omtext,../../sty/omdoc,../../sty/sref,../../sty/presentation,../../sty/dcm,../../sty/reqdoc,../../sty/omd,../../sty/mikoslides,../../sty/problem,../../sty/assignment,../../sty/etc,/Users/kohlhase/stc/stex/example/background"?>
<?latexml RelaxNGSchema="omdoc+ltxml"?>
<omdoc xmlns="http://omdoc.org/ns" xmlns:stex="http://kwarc.info/ns/sTeX" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:om="http://www.openmath.org/OpenMath" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:omdoc="http://omdoc.org/ns" stex:srcref="Anonymous String#textrange(from=1;1,to=1;17)" xml:id="reals.omdoc">
<omgroup layout="sectioning" xml:id="sec.reals" about="#sec.reals" stex:srcref="reals.tex#textrange(from=1;0,to=16;13)">
<metadata xml:id="sec.reals.p1" about="#sec.reals.p1" stex:srcref="reals.tex#textrange(from=1;0,to=15;12)">
<dc:title stex:srcref="reals.tex#textrange(from=1;0,to=16;13)" xml:id="sec.reals.p1.p1" about="#sec.reals.p1.p1">
<p xml:id="sec.reals.p1.p1.p1" about="#sec.reals.p1.p1.p1" stex:srcref="reals.tex#textrange(from=1;0,to=16;13)">Real Numbers</p>
</dc:title>
</metadata>
<theory xml:id="reals" about="#reals" stex:srcref="reals.tex#textrange(from=2;0,to=15;12)">
<symbol name="RealNumbers" xml:id="RealNumbers.sym" about="#RealNumbers.sym" stex:srcref="reals.tex#textrange(from=3;1,to=3;33)"/>
<notation cd="reals" name="RealNumbers">
<prototype>
<om:OMS cd="reals" name="RealNumbers"/>
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<rendering>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" xml:id="reals.m1" text="R">
<om:OMOBJ>
<om:OMV name="R"/>
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<m:math display="inline">
<m:mi mathvariant="double-struck">R</m:mi>
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</notation>
<symbol name="absval" xml:id="absval.sym" about="#absval.sym" stex:srcref="reals.tex#textrange(from=4;1,to=4;43)"/>
<notation cd="reals" name="absval">
<prototype>
<om:OMA>
<om:OMS cd="reals" cr="fun" name="absval"/>
<expr name="arg1"/>
</om:OMA>
</prototype>
<rendering argprec=" " precedence="2000">
<m:mrow>
<m:mo egroup="fence" fence="true">(</m:mo>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="\crossrefOp[fun]{|}" xml:id="reals.m2" text="CROSSREFOP@(|)">
<om:OMOBJ>
<om:OMA>
<om:OMV name=""/>
<om:OMV name="|"/>
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<m:math display="inline">
<m:mo cr="fun">|</m:mo>
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</Math>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="arg:1" xml:id="reals.m3" text="arg:1">
<om:OMOBJ>
<om:OMV name="arg:1"/>
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<m:math display="inline">
<m:mi>arg:1</m:mi>
</m:math>
</Math>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="\crossrefOp[fun]{|}" xml:id="reals.m4" text="CROSSREFOP@(|)">
<om:OMOBJ>
<om:OMA>
<om:OMV name=""/>
<om:OMV name="|"/>
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<m:math display="inline">
<m:mo cr="fun">|</m:mo>
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</Math>
<m:mo egroup="fence" fence="true">)</m:mo>
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<symbol name="rfrac" xml:id="rfrac.sym" about="#rfrac.sym" stex:srcref="reals.tex#textrange(from=5;1,to=5;33)"/>
<notation cd="reals" name="rfrac">
<prototype>
<om:OMA>
<om:OMS cd="reals" cr="fun" name="rfrac"/>
<expr name="arg1"/>
<expr name="arg2"/>
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<rendering>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" xml:id="reals.m5" text="arg:1 / arg:2">
<om:OMOBJ>
<om:OMA>
<om:OMS cd="latexml" name="divide"/>
<om:OMV name="arg:1"/>
<om:OMV name="arg:2"/>
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<m:math display="inline">
<m:mfrac>
<m:mi>arg:1</m:mi>
<m:mi>arg:2</m:mi>
</m:mfrac>
</m:math>
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</notation>
<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)"/>
<definition for="real-numbers" xml:id="reals.def" about="#reals.def" stex:srcref="reals.tex#textrange(from=7;0,to=10;16)">
<CMP xml:id="reals.def.p1" about="#reals.def.p1" stex:srcref="reals.tex#textrange(from=7;0,to=10;16)">
<p xml:id="reals.def.p1.p1" about="#reals.def.p1.p1" stex:srcref="reals.tex#textrange(from=7;0,to=10;16)">
We denote the set of <idx xml:id="reals.def.p1.p1.p1" about="#reals.def.p1.p1.p1" stex:srcref="reals.tex#textrange(from=7;27,to=8;47)"><idt><term cd="reals" name="real-numbers" role="definiendum" xml:id="reals.def.p1.p1.p1.p1" about="#reals.def.p1.p1.p1.p1" stex:srcref="reals.tex#textrange(from=7;27,to=8;47)">real numbers</term></idt><ide index="default"><idp><text xmlns="http://dlmf.nist.gov/LaTeXML">real</text></idp><idp><text xmlns="http://dlmf.nist.gov/LaTeXML">numbers</text></idp></ide></idx> we all know and love with
<Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="\RealNumbers" xml:id="reals.def.p1.p1.m1" text="RealNumbers"><om:OMOBJ><om:OMS cd="reals" name="RealNumbers"/></om:OMOBJ><m:math display="inline"><m:mi mathcolor="red">RealNumbers</m:mi></m:math></Math>.
</p>
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<CMP xml:id="absval.def.p1" about="#absval.def.p1" stex:srcref="reals.tex#textrange(from=12;0,to=14;16)">
<p xml:id="absval.def.p1.p1" about="#absval.def.p1.p1" stex:srcref="reals.tex#textrange(from=12;0,to=14;16)">
The absolute value <Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="\absval{r}" xml:id="absval.def.p1.p1.m1" text="absval@(r)"><om:OMOBJ><om:OMA><om:OMS cd="reals" name="absval"/><om:OMV name="r"/></om:OMA></om:OMOBJ><m:math display="inline"><m:mrow><m:mi mathcolor="red">absval</m:mi><m:mo></m:mo><m:mi>r</m:mi></m:mrow></m:math></Math> of a real number <Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="r" xml:id="absval.def.p1.p1.m2" text="r"><om:OMOBJ><om:OMV name="r"/></om:OMOBJ><m:math display="inline"><m:mi>r</m:mi></m:math></Math>.
</p>
</CMP>
</definition>
</theory>
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