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<section inlist="toc" xml:id="S1">
<tags>
<tag>1</tag>
<tag role="refnum">1</tag>
<tag role="typerefnum">§1</tag>
</tags>
<title><tag close=" ">1</tag>Basic math</title>
<para xml:id="S1.p1">
<equation xml:id="S1.Ex1">
<Math mode="display" tex="((a+b)-c)" text="(a + b) - c" xml:id="S1.Ex1.m1">
<XMath>
<XMDual>
<XMRef idref="S1.Ex1.m1.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S1.Ex1.m1.1">
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMDual>
<XMRef idref="S1.Ex1.m1.1.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S1.Ex1.m1.1.1">
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="ID">c</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S1.Ex2">
<Math mode="display" tex="(a+(b-c))" text="a + (b - c)" xml:id="S1.Ex2.m1">
<XMath>
<XMDual>
<XMRef idref="S1.Ex2.m1.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S1.Ex2.m1.1">
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMDual>
<XMRef idref="S1.Ex2.m1.1.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S1.Ex2.m1.1.1">
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
<XMTok font="italic" role="ID">c</XMTok>
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<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S2">
<tags>
<tag>2</tag>
<tag role="refnum">2</tag>
<tag role="typerefnum">§2</tag>
</tags>
<title><tag close=" ">2</tag>Intervals</title>
<para xml:id="S2.p1">
<equation xml:id="S2.Ex3">
<Math mode="display" tex="(a,b)" text="open-interval@(a, b)" xml:id="S2.Ex3.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="open-interval"/>
<XMRef idref="S2.Ex3.m1.1"/>
<XMRef idref="S2.Ex3.m1.2"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex3.m1.1">a</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex3.m1.2">b</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S2.Ex4">
<Math mode="display" tex="[a,b)" text="closed-open-interval@(a, b)" xml:id="S2.Ex4.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="closed-open-interval"/>
<XMRef idref="S2.Ex4.m1.1"/>
<XMRef idref="S2.Ex4.m1.2"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">[</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex4.m1.1">a</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex4.m1.2">b</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S2.Ex5">
<Math mode="display" tex="(a,b]" text="open-closed-interval@(a, b)" xml:id="S2.Ex5.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="open-closed-interval"/>
<XMRef idref="S2.Ex5.m1.1"/>
<XMRef idref="S2.Ex5.m1.2"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex5.m1.1">a</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex5.m1.2">b</XMTok>
<XMTok role="CLOSE" stretchy="false">]</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S2.Ex6">
<Math mode="display" tex="[a,b]" text="closed-interval@(a, b)" xml:id="S2.Ex6.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="closed-interval"/>
<XMRef idref="S2.Ex6.m1.1"/>
<XMRef idref="S2.Ex6.m1.2"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">[</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex6.m1.1">a</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="italic" role="ID" xml:id="S2.Ex6.m1.2">b</XMTok>
<XMTok role="CLOSE" stretchy="false">]</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S3">
<tags>
<tag>3</tag>
<tag role="refnum">3</tag>
<tag role="typerefnum">§3</tag>
</tags>
<title><tag close=" ">3</tag>Cases</title>
<para xml:id="S3.p1">
<equation xml:id="S3.Ex7">
<Math mode="display" tex="\left.\begin{array}[]{l}a\\ b\end{array}\right\}=\left\{\begin{array}[]{l}c\\ d\end{array}\right." text="cases@(Array[[a], [b]]) = cases@(Array[[c], [d]])" xml:id="S3.Ex7.m1">
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<XMApp>
<XMTok meaning="cases"/>
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<XMCell align="left">
<XMTok font="italic" role="ID">a</XMTok>
</XMCell>
</XMRow>
<XMRow>
<XMCell align="left">
<XMTok font="italic" role="ID">b</XMTok>
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<XMDual>
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<XMArray role="ARRAY" vattach="middle" xml:id="S3.Ex7.m1.2">
<XMRow>
<XMCell align="left">
<XMTok font="italic" role="ID">c</XMTok>
</XMCell>
</XMRow>
<XMRow>
<XMCell align="left">
<XMTok font="italic" role="ID">d</XMTok>
</XMCell>
</XMRow>
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<XMTok meaning="absent"/>
</XMWrap>
</XMDual>
</XMApp>
</XMath>
</Math>
</equation>
</para>
<para xml:id="S3.p2">
<equation xml:id="S3.Ex8">
<Math mode="display" tex="\left(\begin{array}[]{l}c\\ d\end{array}\right)" text="Array[[c], [d]]" xml:id="S3.Ex8.m1">
<XMath>
<XMDual>
<XMRef idref="S3.Ex8.m1.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMArray role="ARRAY" vattach="middle" xml:id="S3.Ex8.m1.1">
<XMRow>
<XMCell align="left">
<XMTok font="italic" role="ID">c</XMTok>
</XMCell>
</XMRow>
<XMRow>
<XMCell align="left">
<XMTok font="italic" role="ID">d</XMTok>
</XMCell>
</XMRow>
</XMArray>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S3.Ex9">
<Math mode="display" tex="(a+\left(\begin{array}[]{l}c\\ d\end{array}\right)+b)" text="a + Array[[c], [d]] + b" xml:id="S3.Ex9.m1">
<XMath>
<XMDual>
<XMRef idref="S3.Ex9.m1.2"/>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S3.Ex9.m1.2">
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMDual>
<XMRef idref="S3.Ex9.m1.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMArray role="ARRAY" vattach="middle" xml:id="S3.Ex9.m1.1">
<XMRow>
<XMCell align="left">
<XMTok font="italic" role="ID">c</XMTok>
</XMCell>
</XMRow>
<XMRow>
<XMCell align="left">
<XMTok font="italic" role="ID">d</XMTok>
</XMCell>
</XMRow>
</XMArray>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S4">
<tags>
<tag>4</tag>
<tag role="refnum">4</tag>
<tag role="typerefnum">§4</tag>
</tags>
<title><tag close=" ">4</tag>Atop</title>
<para xml:id="S4.p1">
<equation xml:id="S4.Ex10">
<Math mode="display" tex="a+{b\atop c}+d" text="a + b FRACOP c + d" xml:id="S4.Ex10.m1">
<XMath>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMApp>
<XMTok mathstyle="display" role="FRACOP" thickness="0pt"/>
<XMTok font="italic" role="ID">b</XMTok>
<XMTok font="italic" role="ID">c</XMTok>
</XMApp>
<XMTok font="italic" role="ID">d</XMTok>
</XMApp>
</XMath>
</Math>
</equation>
<equation xml:id="S4.Ex11">
<Math mode="display" tex="a+\left[b\atop c\right]+d" text="a + delimited-[]@(b FRACOP c) + d" xml:id="S4.Ex11.m1">
<XMath>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMDual>
<XMApp>
<XMTok meaning="delimited-[]"/>
<XMRef idref="S4.Ex11.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">[</XMTok>
<XMApp xml:id="S4.Ex11.m1.1">
<XMTok mathstyle="display" role="FRACOP" thickness="0pt"/>
<XMTok font="italic" role="ID">b</XMTok>
<XMTok font="italic" role="ID">c</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">]</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="ID">d</XMTok>
</XMApp>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S5">
<tags>
<tag>5</tag>
<tag role="refnum">5</tag>
<tag role="typerefnum">§5</tag>
</tags>
<title><tag close=" ">5</tag>Delimiters</title>
<para xml:id="S5.p1">
<equation xml:id="S5.Ex12">
<Math mode="display" tex="\left({a\over b}\right)" text="a / b" xml:id="S5.Ex12.m1">
<XMath>
<XMDual>
<XMRef idref="S5.Ex12.m1.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMApp xml:id="S5.Ex12.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex13">
<Math mode="display" tex="\left[{a\over b}\right]" text="delimited-[]@(a / b)" xml:id="S5.Ex13.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="delimited-[]"/>
<XMRef idref="S5.Ex13.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">[</XMTok>
<XMApp xml:id="S5.Ex13.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">]</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex14">
<Math mode="display" tex="\left[{a\over b}\right]" text="delimited-[]@(a / b)" xml:id="S5.Ex14.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="delimited-[]"/>
<XMRef idref="S5.Ex14.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">[</XMTok>
<XMApp xml:id="S5.Ex14.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">]</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex15">
<Math mode="display" tex="\left\{{a\over b}\right\}" text="set@(a / b)" xml:id="S5.Ex15.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="set"/>
<XMRef idref="S5.Ex15.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">{</XMTok>
<XMApp xml:id="S5.Ex15.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">}</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex16">
<Math mode="display" tex="\left\{{a\over b}\right\}" text="set@(a / b)" xml:id="S5.Ex16.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="set"/>
<XMRef idref="S5.Ex16.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">{</XMTok>
<XMApp xml:id="S5.Ex16.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">}</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex17">
<Math mode="display" tex="\left\lfloor{a\over b}\right\rfloor" text="floor@(a / b)" xml:id="S5.Ex17.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="floor"/>
<XMRef idref="S5.Ex17.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="lfloor" role="OPEN" stretchy="true">⌊</XMTok>
<XMApp xml:id="S5.Ex17.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok name="rfloor" role="CLOSE" stretchy="true">⌋</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex18">
<Math mode="display" tex="\left\lceil{a\over b}\right\rceil" text="ceiling@(a / b)" xml:id="S5.Ex18.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="ceiling"/>
<XMRef idref="S5.Ex18.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="lceil" role="OPEN" stretchy="true">⌈</XMTok>
<XMApp xml:id="S5.Ex18.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok name="rceil" role="CLOSE" stretchy="true">⌉</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex19">
<Math mode="display" tex="\left<{a\over b}\right>" text="delimited-⟨⟩@(a / b)" xml:id="S5.Ex19.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="delimited-⟨⟩"/>
<XMRef idref="S5.Ex19.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="langle" role="OPEN" stretchy="true">⟨</XMTok>
<XMApp xml:id="S5.Ex19.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok name="rangle" role="CLOSE" stretchy="true">⟩</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex20">
<Math mode="display" tex="\left\langle{a\over b}\right\rangle" text="delimited-⟨⟩@(a / b)" xml:id="S5.Ex20.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="delimited-⟨⟩"/>
<XMRef idref="S5.Ex20.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="langle" role="OPEN" stretchy="true">⟨</XMTok>
<XMApp xml:id="S5.Ex20.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok name="rangle" role="CLOSE" stretchy="true">⟩</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex21">
<Math mode="display" tex="\left|{a\over b}\right|" text="absolute-value@(a / b)" xml:id="S5.Ex21.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="absolute-value"/>
<XMRef idref="S5.Ex21.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">|</XMTok>
<XMApp xml:id="S5.Ex21.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">|</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex22">
<Math mode="display" tex="\left|{a\over b}\right|" text="absolute-value@(a / b)" xml:id="S5.Ex22.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="absolute-value"/>
<XMRef idref="S5.Ex22.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">|</XMTok>
<XMApp xml:id="S5.Ex22.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">|</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex23">
<Math mode="display" tex="\left\|{a\over b}\right\|" text="norm@(a / b)" xml:id="S5.Ex23.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="norm"/>
<XMRef idref="S5.Ex23.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">‖</XMTok>
<XMApp xml:id="S5.Ex23.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">‖</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex24">
<Math mode="display" tex="\left\|{a\over b}\right\|" text="norm@(a / b)" xml:id="S5.Ex24.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="norm"/>
<XMRef idref="S5.Ex24.m1.1"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">‖</XMTok>
<XMApp xml:id="S5.Ex24.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">‖</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex25">
<Math mode="display" tex="\left\uparrow{a\over b}\right\downarrow" text="delimited-↑↓@(a / b)" xml:id="S5.Ex25.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="delimited-↑↓"/>
<XMRef idref="S5.Ex25.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="uparrow" role="OPEN" stretchy="true">↑</XMTok>
<XMApp xml:id="S5.Ex25.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok name="downarrow" role="CLOSE" stretchy="true">↓</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex26">
<Math mode="display" tex="\left\Uparrow{a\over b}\right\Downarrow" text="delimited-⇑⇓@(a / b)" xml:id="S5.Ex26.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="delimited-⇑⇓"/>
<XMRef idref="S5.Ex26.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="Uparrow" role="OPEN" stretchy="true">⇑</XMTok>
<XMApp xml:id="S5.Ex26.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok name="Downarrow" role="CLOSE" stretchy="true">⇓</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex27">
<Math mode="display" tex="\left\updownarrow{a\over b}\right\Updownarrow" text="delimited-↕⇕@(a / b)" xml:id="S5.Ex27.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="delimited-↕⇕"/>
<XMRef idref="S5.Ex27.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="updownarrow" role="OPEN" stretchy="true">↕</XMTok>
<XMApp xml:id="S5.Ex27.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok name="Updownarrow" role="CLOSE" stretchy="true">⇕</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
<para xml:id="S5.p2">
<equation xml:id="S5.Ex28">
<Math mode="display" tex="a+\left\langle{b\over c}\right\rangle+d" text="a + delimited-⟨⟩@(b / c) + d" xml:id="S5.Ex28.m1">
<XMath>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMDual>
<XMApp>
<XMTok meaning="delimited-⟨⟩"/>
<XMRef idref="S5.Ex28.m1.1"/>
</XMApp>
<XMWrap>
<XMTok name="langle" role="OPEN" stretchy="true">⟨</XMTok>
<XMApp xml:id="S5.Ex28.m1.1">
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">b</XMTok>
<XMTok font="italic" role="ID">c</XMTok>
</XMApp>
<XMTok name="rangle" role="CLOSE" stretchy="true">⟩</XMTok>
</XMWrap>
</XMDual>
<XMTok font="italic" role="ID">d</XMTok>
</XMApp>
</XMath>
</Math>
</equation>
</para>
<para xml:id="S5.p3">
<equation xml:id="S5.Ex29">
<Math mode="display" tex="{a\over b}\left/{c\over d}\right." text="(a / b) / (c / d)" xml:id="S5.Ex29.m1">
<XMath>
<XMApp>
<XMTok role="MULOP" stretchy="true">/</XMTok>
<XMApp>
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMApp>
<XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
<XMTok font="italic" role="ID">c</XMTok>
<XMTok font="italic" role="ID">d</XMTok>
</XMApp>
</XMApp>
</XMath>
</Math>
</equation>
</para>
</section>
</document>