<?xml version="1.0" encoding="UTF-8"?>
<?latexml class="article"?>
<?latexml package="amsmath"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML" class="ltx_authors_1line">
<resource src="LaTeXML.css" type="text/css"/>
<resource src="ltx-article.css" type="text/css"/>
<title>The perverse timing of stepping the equation counter</title>
<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>Equations</title>
<para xml:id="S1.p1">
<p>Note how equations increment the equation counter at the <emph font="italic">beginning</emph>,
even if later on, the equation tag is removed or set explicitly!</p>
</para>
<para xml:id="S1.p2">
<p>Normal (w/eq=0)</p>
<equation xml:id="S1.E1">
<tags>
<tag>(1)</tag>
<tag role="refnum">1</tag>
</tags>
<Math mode="display" tex="N=\mbox{1}" text="N = [1]" xml:id="S1.E1.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>1</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>Nonumber before (w/eq=1)</p>
<equation xml:id="S1.Ex1">
<Math mode="display" tex="N=\mbox{1}" text="N = [1]" xml:id="S1.Ex1.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>1</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>Nonumber after (w/eq=1)</p>
<equation xml:id="S1.Ex2">
<Math mode="display" tex="N=\mbox{2}" text="N = [2]" xml:id="S1.Ex2.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>2</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>Numbered, Tag before (w/eq=1)</p>
<equation xml:id="S1.Ex3">
<tags>
<tag>(1<sup><text font="italic">′</text></sup>)</tag>
<tag role="refnum">1<sup><text font="italic">′</text></sup></tag>
</tags>
<Math mode="display" tex="N=\mbox{1}" text="N = [1]" xml:id="S1.Ex3.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>1</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>Numbered, Tag after (w/eq=1)</p>
<equation xml:id="S1.Ex4">
<tags>
<tag>(1<sup><text font="italic">′′</text></sup>)</tag>
<tag role="refnum">1<sup><text font="italic">′′</text></sup></tag>
</tags>
<Math mode="display" tex="N=\mbox{2}" text="N = [2]" xml:id="S1.Ex4.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>2</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>Other variations:</p>
<equation xml:id="S1.Ex5">
<tags>
<tag>(1<text font="typewriter"> primed</text>)</tag>
<tag role="refnum">1<text font="typewriter"> primed</text></tag>
</tags>
<Math mode="display" tex="N=\mbox{2}" text="N = [2]" xml:id="S1.Ex5.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>2</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<equation xml:id="S1.Ex6">
<tags>
<tag>(1 in text)</tag>
<tag role="refnum">1 in text</tag>
</tags>
<Math mode="display" tex="N=\mbox{2}" text="N = [2]" xml:id="S1.Ex6.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>2</XMText>
</XMApp>
</XMath>
</Math>
</equation>
</para>
<para xml:id="S1.p3">
<p>UnNumbered (w/eq=1)</p>
<equation xml:id="S1.Ex7">
<Math mode="display" tex="N=\mbox{1}" text="N = [1]" xml:id="S1.Ex7.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>1</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>UnNumbered, Tag before (w/eq=1)</p>
<equation xml:id="S1.Ex8">
<tags>
<tag>(1<sup><text font="italic">′′′</text></sup>)</tag>
<tag role="refnum">1<sup><text font="italic">′′′</text></sup></tag>
</tags>
<Math mode="display" tex="N=\mbox{1}" text="N = [1]" xml:id="S1.Ex8.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>1</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>UnNumbered, Tag after (w/eq=1)</p>
<equation xml:id="S1.Ex9">
<tags>
<tag>(1<sup><text font="italic">′′′′</text></sup>)</tag>
<tag role="refnum">1<sup><text font="italic">′′′′</text></sup></tag>
</tags>
<Math mode="display" tex="N=\mbox{1}" text="N = [1]" xml:id="S1.Ex9.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>1</XMText>
</XMApp>
</XMath>
</Math>
</equation>
<p>Now (w/eq=1).</p>
</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>Eqnarrays</title>
<para xml:id="S2.p1">
<p>Note how eqnarrays <emph font="italic">also</emph> increment at the beginning!
<emph font="italic">Even</emph> eqnarray*!</p>
</para>
<para xml:id="S2.p2">
<p>Mostly numbered, unnumbered before and after (w/eq=1)</p>
<equationgroup class="ltx_eqn_eqnarray" xml:id="S3.EGx1">
<equation xml:id="S2.E2">
<tags>
<tag>(2)</tag>
<tag role="refnum">2</tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{2}" text="N = [2]" xml:id="S2.E2.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText class="ltx_markedasmath">2</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<tr>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S2.E2.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S2.E2.m2">
<XMath>
<XMTok meaning="equals" role="RELOP">=</XMTok>
</XMath>
</Math></td>
<td align="left"><text class="ltx_markedasmath">2</text></td>
</tr>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S2.E3">
<tags>
<tag>(3)</tag>
<tag role="refnum">3</tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{3}" text="N = [3]" xml:id="S2.E3.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText class="ltx_markedasmath">3</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<tr>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S2.E3.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S2.E3.m2">
<XMath>
<XMTok meaning="equals" role="RELOP">=</XMTok>
</XMath>
</Math></td>
<td align="left"><text class="ltx_markedasmath">3</text></td>
</tr>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S2.Ex10">
<MathFork>
<Math tex="\displaystyle N=\mbox{4}" text="N = [4]" xml:id="S2.Ex10.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText class="ltx_markedasmath">4</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<tr>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S2.Ex10.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S2.Ex10.m2">
<XMath>
<XMTok meaning="equals" role="RELOP">=</XMTok>
</XMath>
</Math></td>
<td align="left"><text class="ltx_markedasmath">4</text></td>
</tr>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S2.Ex11">
<MathFork>
<Math tex="\displaystyle N=\mbox{4}" text="N = [4]" xml:id="S2.Ex11.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText class="ltx_markedasmath">4</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<tr>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S2.Ex11.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S2.Ex11.m2">
<XMath>
<XMTok meaning="equals" role="RELOP">=</XMTok>
</XMath>
</Math></td>
<td align="left"><text class="ltx_markedasmath">4</text></td>
</tr>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S2.E4">
<tags>
<tag>(4)</tag>
<tag role="refnum">4</tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{4}" text="N = [4]" xml:id="S2.E4.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText class="ltx_markedasmath">4</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<tr>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S2.E4.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S2.E4.m2">
<XMath>
<XMTok meaning="equals" role="RELOP">=</XMTok>
</XMath>
</Math></td>
<td align="left"><text class="ltx_markedasmath">4</text></td>
</tr>
</MathBranch>
</MathFork>
</equation>
</equationgroup>
</para>
<para xml:id="S2.p3">
<p>Unnumbered (w/eq=4)</p>
<equationgroup class="ltx_eqn_eqnarray" xml:id="S3.EGx2">
<equation xml:id="S2.Ex12">
<MathFork>
<Math tex="\displaystyle N=\mbox{5}" text="N = [5]" xml:id="S2.Ex12.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText class="ltx_markedasmath">5</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<tr>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S2.Ex12.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S2.Ex12.m2">
<XMath>
<XMTok meaning="equals" role="RELOP">=</XMTok>
</XMath>
</Math></td>
<td align="left"><text class="ltx_markedasmath">5</text></td>
</tr>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S2.Ex13">
<MathFork>
<Math tex="\displaystyle N=\mbox{5}" text="N = [5]" xml:id="S2.Ex13.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText class="ltx_markedasmath">5</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<tr>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S2.Ex13.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S2.Ex13.m2">
<XMath>
<XMTok meaning="equals" role="RELOP">=</XMTok>
</XMath>
</Math></td>
<td align="left"><text class="ltx_markedasmath">5</text></td>
</tr>
</MathBranch>
</MathFork>
</equation>
</equationgroup>
<p>Now (w/eq=4).</p>
</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>AMS alignments</title>
<para xml:id="S3.p1">
<p>However, note how AMS alignments <emph font="italic">defer</emph> incrementing the equation counter
until the end of line mark!</p>
</para>
<para xml:id="S3.p2">
<p>Align numbered, some unnumbered before, after, some tagged before, after (w/eq=4)</p>
<equationgroup class="ltx_eqn_align" xml:id="S3.EGx3">
<equation xml:id="S3.E5">
<tags>
<tag>(5)</tag>
<tag role="refnum">5</tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{4}" text="N = [4]" xml:id="S3.E5.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>4</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.E5.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{4}" text="absent = [4]" xml:id="S3.E5.m2">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>4</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.E6">
<tags>
<tag>(6)</tag>
<tag role="refnum">6</tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{5}" text="N = [5]" xml:id="S3.E6.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>5</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.E6.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{5}" text="absent = [5]" xml:id="S3.E6.m2">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>5</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.Ex14">
<MathFork>
<Math tex="\displaystyle N=\mbox{6}" text="N = [6]" xml:id="S3.Ex14.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>6</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex14.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{6}" text="absent = [6]" xml:id="S3.Ex14.m2">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>6</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.Ex15">
<MathFork>
<Math tex="\displaystyle N=\mbox{6}" text="N = [6]" xml:id="S3.Ex15.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>6</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex15.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{6}" text="absent = [6]" xml:id="S3.Ex15.m2">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>6</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.E7">
<tags>
<tag>(7)</tag>
<tag role="refnum">7</tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{6}" text="N = [6]" xml:id="S3.E7.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>6</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.E7.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{6}" text="absent = [6]" xml:id="S3.E7.m2">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>6</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.Ex16">
<tags>
<tag>(7<sup><text font="italic">′</text></sup>)</tag>
<tag role="refnum">7<sup><text font="italic">′</text></sup></tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{7}" text="N = [7]" xml:id="S3.Ex16.m5">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex16.m3">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{7}" text="absent = [7]" xml:id="S3.Ex16.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.Ex17">
<tags>
<tag>(7<sup><text font="italic">′′</text></sup>)</tag>
<tag role="refnum">7<sup><text font="italic">′′</text></sup></tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{7}" text="N = [7]" xml:id="S3.Ex17.m5">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex17.m3">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{7}" text="absent = [7]" xml:id="S3.Ex17.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
</equationgroup>
</para>
<para xml:id="S3.p3">
<p>Align numbered, some tagged before, after (w/eq=7)</p>
<equationgroup class="ltx_eqn_align" xml:id="S3.EGx4">
<equation xml:id="S3.Ex18">
<MathFork>
<Math tex="\displaystyle N=\mbox{7}" text="N = [7]" xml:id="S3.Ex18.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex18.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{7}" text="absent = [7]" xml:id="S3.Ex18.m2">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.Ex19">
<tags>
<tag>(7<sup><text font="italic">′′′</text></sup>)</tag>
<tag role="refnum">7<sup><text font="italic">′′′</text></sup></tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{7}" text="N = [7]" xml:id="S3.Ex19.m5">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex19.m3">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{7}" text="absent = [7]" xml:id="S3.Ex19.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.Ex20">
<tags>
<tag>(7<sup><text font="italic">′′′′</text></sup>)</tag>
<tag role="refnum">7<sup><text font="italic">′′′′</text></sup></tag>
</tags>
<MathFork>
<Math tex="\displaystyle N=\mbox{7}" text="N = [7]" xml:id="S3.Ex20.m5">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex20.m3">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{7}" text="absent = [7]" xml:id="S3.Ex20.m4">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
<equation xml:id="S3.Ex21">
<MathFork>
<Math tex="\displaystyle N=\mbox{7}" text="N = [7]" xml:id="S3.Ex21.m3">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math>
<MathBranch>
<td align="right"><Math mode="inline" tex="\displaystyle N" text="N" xml:id="S3.Ex21.m1">
<XMath>
<XMTok font="italic" role="UNKNOWN">N</XMTok>
</XMath>
</Math></td>
<td align="left"><Math mode="inline" tex="\displaystyle=\mbox{7}" text="absent = [7]" xml:id="S3.Ex21.m2">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok meaning="absent"/>
<XMText>7</XMText>
</XMApp>
</XMath>
</Math></td>
</MathBranch>
</MathFork>
</equation>
</equationgroup>
<p>Now (w/eq=7).</p>
</para>
</section>
</document>