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		<id>https://www.explainxkcd.com/wiki/index.php?action=history&amp;feed=atom&amp;title=1208%3A_Footnote_Labyrinths</id>
		<title>1208: Footnote Labyrinths - Revision history</title>
		<link rel="self" type="application/atom+xml" href="https://www.explainxkcd.com/wiki/index.php?action=history&amp;feed=atom&amp;title=1208%3A_Footnote_Labyrinths"/>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;action=history"/>
		<updated>2026-05-02T03:34:17Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=324002&amp;oldid=prev</id>
		<title>172.70.90.221: It's officially identified as Title Text, around here. If you change this, you'd need to change almost *every* Explanation page, and possibly one or more templates. (And the device I'm on, here, has no mouse.)</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=324002&amp;oldid=prev"/>
				<updated>2023-09-20T03:57:49Z</updated>
		
		<summary type="html">&lt;p&gt;It&amp;#039;s officially identified as Title Text, around here. If you change this, you&amp;#039;d need to change almost *every* Explanation page, and possibly one or more templates. (And the device I&amp;#039;m on, here, has no mouse.)&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 03:57, 20 September 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l25&quot; &gt;Line 25:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 25:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;mouse-over &lt;/del&gt;suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;title text &lt;/ins&gt;suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] also plays on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] also plays on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>172.70.90.221</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=323991&amp;oldid=prev</id>
		<title>172.71.146.198 at 19:21, 19 September 2023</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=323991&amp;oldid=prev"/>
				<updated>2023-09-19T19:21:54Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 19:21, 19 September 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l25&quot; &gt;Line 25:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 25:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The mouse over suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The mouse&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;-&lt;/ins&gt;over suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] also plays on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] also plays on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>172.71.146.198</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=323990&amp;oldid=prev</id>
		<title>172.71.146.199 at 19:21, 19 September 2023</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=323990&amp;oldid=prev"/>
				<updated>2023-09-19T19:21:31Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 19:21, 19 September 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l25&quot; &gt;Line 25:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 25:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;title text &lt;/del&gt;suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;mouse over &lt;/ins&gt;suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] also plays on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] also plays on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>172.71.146.199</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=320799&amp;oldid=prev</id>
		<title>172.71.146.213: /* Explanation */ correct tense</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=320799&amp;oldid=prev"/>
				<updated>2023-08-13T05:34:59Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Explanation: &lt;/span&gt; correct tense&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 05:34, 13 August 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l27&quot; &gt;Line 27:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 27:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The title text suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The title text suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;is &lt;/del&gt;also &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;playing &lt;/del&gt;on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The comic [[1184: Circumference Formula]] also &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;plays &lt;/ins&gt;on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Transcript==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Transcript==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>172.71.146.213</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=306572&amp;oldid=prev</id>
		<title>172.70.211.92: /*The last explanation implied going from the bottom up, which was confusing. I expanded the interpretation which verifies the &quot;no solution&quot; answer via supertask. I know it's long, but I can't shorten it. I hope it's an interesting contribution! Tysm!*/</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=306572&amp;oldid=prev"/>
				<updated>2023-02-21T06:41:22Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;The last explanation implied going from the bottom up, which was confusing. I expanded the interpretation which verifies the &amp;quot;no solution&amp;quot; answer via supertask. I know it&amp;#039;s long, but I can&amp;#039;t shorten it. I hope it&amp;#039;s an interesting contribution! Tysm!&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 06:41, 21 February 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l19&quot; &gt;Line 19:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 19:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;;Interpreting nested footnotes as footnotes on footnotes, right-associative&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;;Interpreting nested footnotes as footnotes on footnotes, right-associative&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1 + 2&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;. We turn to the definition of &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, which is &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;not true&amp;lt;sup&amp;gt;3 + 2&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;not true&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1 + 2&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;. We turn to the definition of &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, which is &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;not true&amp;lt;sup&amp;gt;3 + 2&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;not true&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Now &amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt; is &amp;quot;true&amp;lt;sup&amp;gt;2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot;. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;The &lt;/del&gt;6 &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;says that &lt;/del&gt;the 2 &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;footnote &lt;/del&gt;is &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;really &lt;/del&gt;1&amp;lt;sup&amp;gt;2&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; = &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;1&lt;/del&gt;&amp;lt;sup&amp;gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;(4&lt;/del&gt;. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;ibid&lt;/del&gt;.&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;)&lt;/del&gt;&amp;lt;/sup&amp;gt; = 1&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;but &lt;/del&gt;the 3 &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;tells us &lt;/del&gt;that the &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;6 &lt;/del&gt;is &amp;quot;not true&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;&amp;quot;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;, getting us into an infinite loop, meaning &lt;/del&gt;there is no solution.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Now &amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt; is &amp;quot;true&amp;lt;sup&amp;gt;2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot;. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Going from top down accordingly, the 3 tells us that the 6 is &amp;quot;not true&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;&amp;quot;, getting us into an infinite loop, and if we are restricted to only following the footnotes step-by-step, then we will never reach a solution.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;:Suppose we ignore infinity momentarily, we can say there must be only two possibilities (though we have to be wary of paradoxes) for the meaning of &amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;: either &amp;lt;sup&amp;gt;&lt;/ins&gt;6&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/sup&amp;gt; is true, and thus &lt;/ins&gt;the 2 is &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;actually a &lt;/ins&gt;1 &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;(ibid.), or &amp;lt;sup&amp;gt;6&lt;/ins&gt;&amp;lt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&lt;/ins&gt;sup&amp;gt; &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;is false or ignored, and thus the &lt;/ins&gt;2 &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;remains a 2. In the latter case, the resolution we see is &amp;quot;true&lt;/ins&gt;&amp;lt;sup&amp;gt;2&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;/ins&gt;&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot; &lt;/ins&gt;= &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;true&amp;lt;sup&amp;gt;2&lt;/ins&gt;&amp;lt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&lt;/ins&gt;sup&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;. It is meaningless to increment a phrase by 2, so if we also require actions to have meaning, then footnote 2 must change to a 1&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;:Consequently, 6 must be true&lt;/ins&gt;. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;We can finally resolve &amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt; = &amp;quot;true&amp;lt;sup&amp;gt;2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&lt;/ins&gt;&amp;lt;/sup&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot; &lt;/ins&gt;= &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;true&amp;lt;sup&amp;gt;&lt;/ins&gt;1&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/sup&amp;gt;&amp;quot; is ignored. Since we now know that footnote 5 is ignored, we then go back to the definition of &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, which we found was &amp;quot;not true&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;not true&amp;quot;.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;:Before returning to &amp;quot;no&lt;/ins&gt;&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;&lt;/ins&gt;, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;we see that this conclusion contradicts our previous assumption that 6 is true. In &lt;/ins&gt;the &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;definition of &amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;, we found that it is ignored since we imposed &amp;quot;true&amp;lt;sup&amp;gt;2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;&lt;/ins&gt;3&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;true&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, but we also found &lt;/ins&gt;that the &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;definition of &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; &lt;/ins&gt;is &amp;quot;not true&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;; therefore, &lt;/ins&gt;&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt; &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;= &lt;/ins&gt;&amp;quot;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;true&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;quot; since it is not true that 2 is actually 1. Now we have reached our contradiction. The upshot is &lt;/ins&gt;there &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;really &lt;/ins&gt;is no solution &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;if we restrict footnotes to have only one meaning/definition (in other words, a footnote cannot be both true and not true)&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The title text suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The title text suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations &amp;quot;minus one, modulo 6, plus 1&amp;quot; to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt;&amp;quot; = &amp;quot;no&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;&amp;quot;, so we ignore the &amp;quot;no&amp;quot; and the correct statement is &amp;quot;we found evidence for the data.&amp;quot; Meanwhile, &amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; becomes &amp;quot;not true&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;quot;, an {{w|infinite recursion}}, and since 2&amp;lt;sup&amp;gt;6&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&amp;lt;/sup&amp;gt; mod 6 = 4, we just get &amp;quot;ibid&amp;quot; and the 5 refers back to the 3. Footnote 6 is equivalent to 1&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt; = 1 = &amp;quot;ignore this&amp;quot;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>172.70.211.92</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=300976&amp;oldid=prev</id>
		<title>172.71.158.216: Footnote category</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=300976&amp;oldid=prev"/>
				<updated>2022-12-09T21:47:14Z</updated>
		
		<summary type="html">&lt;p&gt;Footnote category&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 21:47, 9 December 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l38&quot; &gt;Line 38:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 38:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{comic discussion}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{comic discussion}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:My Hobby]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:My Hobby]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Footnotes]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>172.71.158.216</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=276207&amp;oldid=prev</id>
		<title>Jacky720: Reverted edits by Xray Kilo Charlie Delta (talk) to last revision by Vandalbane</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=276207&amp;oldid=prev"/>
				<updated>2022-05-23T18:39:30Z</updated>
		
		<summary type="html">&lt;p&gt;Reverted edits by &lt;a href=&quot;/wiki/index.php/Special:Contributions/Xray_Kilo_Charlie_Delta&quot; title=&quot;Special:Contributions/Xray Kilo Charlie Delta&quot;&gt;Xray Kilo Charlie Delta&lt;/a&gt; (&lt;a href=&quot;/wiki/index.php?title=User_talk:Xray_Kilo_Charlie_Delta&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User talk:Xray Kilo Charlie Delta (page does not exist)&quot;&gt;talk&lt;/a&gt;) to last revision by &lt;a href=&quot;/wiki/index.php/User:Vandalbane&quot; title=&quot;User:Vandalbane&quot;&gt;Vandalbane&lt;/a&gt;&lt;/p&gt;
&lt;a href=&quot;//www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;amp;diff=276207&amp;amp;oldid=275293&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Jacky720</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=275293&amp;oldid=prev</id>
		<title>Xray Kilo Charlie Delta: Reverted vandalism with User:CRLF/OneClickUndo.js</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=275293&amp;oldid=prev"/>
				<updated>2022-05-23T18:26:51Z</updated>
		
		<summary type="html">&lt;p&gt;Reverted vandalism with &lt;a href=&quot;/wiki/index.php/User:CRLF/OneClickUndo.js&quot; title=&quot;User:CRLF/OneClickUndo.js&quot;&gt;User:CRLF/OneClickUndo.js&lt;/a&gt;&lt;/p&gt;
&lt;a href=&quot;//www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;amp;diff=275293&amp;amp;oldid=274199&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Xray Kilo Charlie Delta</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=274199&amp;oldid=prev</id>
		<title>Vandalbane: Reverted vandalism with User:CRLF/OneClickUndo.js</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=274199&amp;oldid=prev"/>
				<updated>2022-05-23T18:12:31Z</updated>
		
		<summary type="html">&lt;p&gt;Reverted vandalism with &lt;a href=&quot;/wiki/index.php/User:CRLF/OneClickUndo.js&quot; title=&quot;User:CRLF/OneClickUndo.js&quot;&gt;User:CRLF/OneClickUndo.js&lt;/a&gt;&lt;/p&gt;
&lt;a href=&quot;//www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;amp;diff=274199&amp;amp;oldid=274000&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Vandalbane</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&amp;diff=274000&amp;oldid=prev</id>
		<title>Xray Kilo Charlie Delta: haha your js cant stop my js</title>
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				<updated>2022-05-23T18:10:03Z</updated>
		
		<summary type="html">&lt;p&gt;haha your js cant stop my js&lt;/p&gt;
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		<author><name>Xray Kilo Charlie Delta</name></author>	</entry>

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