1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
|
<?xml version="1.0" encoding="UTF-8"?>
<?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"/>
</prototype>
<rendering>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" xml:id="reals.m1" text="R">
<XMath>
<XMTok role="UNKNOWN" font="blackboard">R</XMTok>
</XMath>
</Math>
</rendering>
</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@(|)">
<XMath>
<XMApp role="CROSSREFOP">
<XMTok cr="fun" role="CROSSREFOP"/>
<XMTok role="VERTBAR">|</XMTok>
</XMApp>
</XMath>
</Math>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="arg:1" xml:id="reals.m3" text="arg:1">
<XMath>
<XMTok role="ID">arg:1</XMTok>
</XMath>
</Math>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" mode="inline" tex="\crossrefOp[fun]{|}" xml:id="reals.m4" text="CROSSREFOP@(|)">
<XMath>
<XMApp role="CROSSREFOP">
<XMTok cr="fun" role="CROSSREFOP"/>
<XMTok role="VERTBAR">|</XMTok>
</XMApp>
</XMath>
</Math>
<m:mo egroup="fence" fence="true">)</m:mo>
</m:mrow>
</rendering>
</notation>
<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"/>
</om:OMA>
</prototype>
<rendering>
<Math xmlns="http://dlmf.nist.gov/LaTeXML" xml:id="reals.m5" text="arg:1 / arg:2">
<XMath>
<XMApp>
<XMTok meaning="divide" role="MULOP" style="text"/>
<XMTok role="ID">arg:1</XMTok>
<XMTok role="ID">arg:2</XMTok>
</XMApp>
</XMath>
</Math>
</rendering>
</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"><XMath><XMTok meaning="RealNumbers" name="RealNumbers" omcd="reals"/></XMath></Math>.
</p>
</CMP>
</definition>
<definition xml:id="absval.def" about="#absval.def" stex:srcref="reals.tex#textrange(from=12;0,to=14;16)">
<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)"><XMath><XMApp><XMTok meaning="absval" name="absval" omcd="reals"/><XMTok role="UNKNOWN" font="italic">r</XMTok></XMApp></XMath></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"><XMath><XMTok role="UNKNOWN" font="italic">r</XMTok></XMath></Math>.
</p>
</CMP>
</definition>
</theory>
</omgroup>
<!-- %%% Local Variables:
%%% mode: LaTeX
%%% TeX-master: "all"
%%% End:-->
</omdoc>
|