Add \{big,small}scr commands (somewhat sadly).

self_repl_fns/kindle_template.tex

@@ -213,6 +213,9 @@
 \newcommand{\class}[1]{}
 \newcommand{\Rule}[3]{}
 \newcommand{\optquad}{\quad}
+\newcommand{\smallscrneg}{}
+\newcommand{\smallscr}[1]{}
+\newcommand{\smallscrbreak}{}
 
 % End custom, non-pandoc commands.
 

self_repl_fns/self_repl_fns.md

@@ -6,6 +6,8 @@
 \newcommand{\eqnset}[1]{\left.\mbox{$#1$}\;\;\right\rbrace\class{postbrace}{ }}
 \providecommand{\optquad}{\class{optquad}{}}
 \providecommand{\smallscrneg}{\class{smallscrneg}{ }}
+\providecommand{\bigscr}[1]{\class{bigscr}{#1}}
+\providecommand{\smallscr}[1]{\class{smallscr}{#1}}
 
 These are notes I'm creating for myself as I explore
 functions $f$ that can be written as a sum $f = g_1 + g_2$ where $g_1$ and $g_2$
@@ -514,11 +516,12 @@ $f$ must have the same value. To do that, it will be useful to define the
 *tail* of an expansion as a way to capture end-of-string behavior.
 More precisely, if $E$ is an expansion, then define $\tail(E)$ via
 
-$$\begin{array}{l}
-\tail(E) = \big\{\text{expansion }\eta \;\big|\;
+$$\bigscr{\tail(E) = \big\{\text{expansion }\eta \;\big|\;
+\exists\, j, k: 
+E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.}
+\smallscr{\begin{array}{l}\tail(E) = \big\{\text{expansion }\eta \;\big|\;
 \exists\, j, k: \\
-\quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.
-\end{array}$$
+\quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.\end{array}}$$
 
 Intuitively, $\tail(E)$ is the set of all numbers in $[0, 1]$ with
 the same final sequence of base-3 digits as $E$, ignoring any finite prefix

self_repl_fns/self_repl_fns.tex

@@ -90,6 +90,9 @@
 \newcommand{\class}[1]{}
 \newcommand{\Rule}[3]{}
 \newcommand{\optquad}{\quad}
+\newcommand{\smallscrneg}{}
+\newcommand{\smallscr}[1]{}
+\newcommand{\smallscrbreak}{}
 
 % End custom, non-pandoc commands.
 
@@ -100,6 +103,8 @@
 \newcommand{\eqnset}[1]{\left.\mbox{$#1$}\;\;\right\rbrace\class{postbrace}{ }}
 \providecommand{\optquad}{\class{optquad}{}}
 \providecommand{\smallscrneg}{\class{smallscrneg}{ }}
+\providecommand{\bigscr}[1]{\class{bigscr}{#1}}
+\providecommand{\smallscr}[1]{\class{smallscr}{#1}}
 
 These are notes I'm creating for myself as I explore functions \(f\)
 that can be written as a sum \(f = g_1 + g_2\) where \(g_1\) and \(g_2\)
@@ -647,11 +652,12 @@ \subsubsection{Characterizing one type of exactly self-replicating
 behavior. More precisely, if \(E\) is an expansion, then define
 \(\tail(E)\) via
 
-\[\begin{array}{l}
-\tail(E) = \big\{\text{expansion }\eta \;\big|\;
+\[\bigscr{\tail(E) = \big\{\text{expansion }\eta \;\big|\;
+\exists\, j, k: 
+E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.}
+\smallscr{\begin{array}{l}\tail(E) = \big\{\text{expansion }\eta \;\big|\;
 \exists\, j, k: \\
-\quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.
-\end{array}\]
+\quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.\end{array}}\]
 
 Intuitively, \(\tail(E)\) is the set of all numbers in \([0, 1]\) with
 the same final sequence of base-3 digits as \(E\), ignoring any finite

self_repl_fns/self_repl_fns_for_kindle.tex

@@ -90,6 +90,9 @@
 \newcommand{\class}[1]{}
 \newcommand{\Rule}[3]{}
 \newcommand{\optquad}{\quad}
+\newcommand{\smallscrneg}{}
+\newcommand{\smallscr}[1]{}
+\newcommand{\smallscrbreak}{}
 
 % End custom, non-pandoc commands.
 
@@ -100,6 +103,8 @@
 \newcommand{\eqnset}[1]{\left.\mbox{$#1$}\;\;\right\rbrace\class{postbrace}{ }}
 \providecommand{\optquad}{\class{optquad}{}}
 \providecommand{\smallscrneg}{\class{smallscrneg}{ }}
+\providecommand{\bigscr}[1]{\class{bigscr}{#1}}
+\providecommand{\smallscr}[1]{\class{smallscr}{#1}}
 
 These are notes I'm creating for myself as I explore functions \(f\)
 that can be written as a sum \(f = g_1 + g_2\) where \(g_1\) and \(g_2\)
@@ -647,11 +652,12 @@ \subsubsection{Characterizing one type of exactly self-replicating
 behavior. More precisely, if \(E\) is an expansion, then define
 \(\tail(E)\) via
 
-\[\begin{array}{l}
-\tail(E) = \big\{\text{expansion }\eta \;\big|\;
+\[\bigscr{\tail(E) = \big\{\text{expansion }\eta \;\big|\;
+\exists\, j, k: 
+E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.}
+\smallscr{\begin{array}{l}\tail(E) = \big\{\text{expansion }\eta \;\big|\;
 \exists\, j, k: \\
-\quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.
-\end{array}\]
+\quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.\end{array}}\]
 
 Intuitively, \(\tail(E)\) is the set of all numbers in \([0, 1]\) with
 the same final sequence of base-3 digits as \(E\), ignoring any finite

self_repl_fns/self_repl_fns_local.html

@@ -225,11 +225,12 @@ <h3 id="characterizing-one-type-of-exactly-self-replicating-function"><span clas
       {\lower1.8pt\hbox{$\smash{\scriptstyle 0}$}}
       {\lower1pt\hbox{$\smash{\scriptstyle 2}$}}$}\!\big\}}E_3) = f(1.E_3).{\class{smallscrneg}{ }}\qquad(7)\]</span></span></p>
       <p>We can expand on this idea to partition <span class="math inline">\((1,2) - G\)</span> into subsets on which <span class="math inline">\(f\)</span> must have the same value. To do that, it will be useful to define the <em>tail</em> of an expansion as a way to capture end-of-string behavior. More precisely, if <span class="math inline">\(E\)</span> is an expansion, then define <span class="math inline">\({\text{tail}}(E)\)</span> via</p>
-      <p><span class="math display">\[\begin{array}{l}
-      {\text{tail}}(E) = \big\{\text{expansion }\eta \;\big|\;
+      <p><span class="math display">\[{\class{bigscr}{{\text{tail}}(E) = \big\{\text{expansion }\eta \;\big|\;
+      \exists\, j, k: 
+      E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.}}
+      {\class{smallscr}{\begin{array}{l}{\text{tail}}(E) = \big\{\text{expansion }\eta \;\big|\;
       \exists\, j, k: \\
-      \quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.
-      \end{array}\]</span></p>
+      \quad E(j + m) = \eta(k + m) \,\forall\, m \ge 0\big\}.\end{array}}}\]</span></p>
       <p>Intuitively, <span class="math inline">\({\text{tail}}(E)\)</span> is the set of all numbers in <span class="math inline">\([0, 1]\)</span> with the same final sequence of base-3 digits as <span class="math inline">\(E\)</span>, ignoring any finite prefix of either expansion. For example, <span class="math inline">\(x=0.21021\overline{011}_3\)</span> and <span class="math inline">\(y=0.001\overline{011}_3\)</span> have <span class="math inline">\(\text{tail}(x) = \text{tail}(y)\)</span>.</p>
       <p>The following theorem builds on equation (7).</p>
       <p><strong>Theorem 2</strong> <span class="math inline">\(\;\)</span> <em>Suppose that <span class="math inline">\(f\)</span> is exactly self-replicating with functions <span class="math inline">\(s,\)</span> <span class="math inline">\(t_1,\)</span> and <span class="math inline">\(t_2\)</span> as given in (2). Also suppose that <span class="math inline">\(G\)</span> is defined as in (5). Then, for</em> <span class="math inline">\(x,y\in (1,2)-G,\)</span></p>

self_repl_fns/template.tex

@@ -212,6 +212,8 @@
 \newcommand{\Rule}[3]{}
 \newcommand{\optquad}{\quad}
 \newcommand{\smallscrneg}{}
+\newcommand{\smallscr}[1]{}
+\newcommand{\bigscr}[1]{#1}
 
 % End custom, non-pandoc commands.
 

self_repl_fns/tufte-edited.css

@@ -120,6 +120,18 @@ div.title { font-weight: 400;
   }
 }
 
+@media screen and (min-width: 761px) {
+  .MathJax .smallscr {
+    display: none;
+  }
+}
+
+@media screen and (max-width: 760px) {
+  .MathJax .bigscr {
+    display: none;
+  }
+}
+
 h1 { font-style: italic;
      font-weight: 400;
      margin-top: 3.2rem;