Split the indicator section into one div per subfile

_subfiles/indicator-functions/_def-indicator-function.qmd

@@ -0,0 +1,18 @@
+:::{#def-indicator-function}
+#### Indicator function, set indicator
+
+For any subset $A \subseteq \universe$ of a universal set $\universe$,
+the **indicator function** of $A$,
+[@wikipedia_indicator_function]
+or **set indicator**,
+is the function
+$\indic{A} : \universe \to \{0, 1\}$ defined by:
+
+$$
+\indic{A}(x) \eqdef \begin{cases}
+1, & x \in A \\
+0, & x \notin A
+\end{cases}
+$$
+
+:::

_subfiles/indicator-functions/_def-iverson-bracket.qmd

@@ -0,0 +1,15 @@
+:::{#def-iverson-bracket}
+#### Iverson bracket
+
+For any logical proposition $P$,
+the **Iverson bracket** of $P$ is
+[@wikipedia_iverson_bracket]
+
+$$
+[P] \eqdef \begin{cases}
+1, & \text{if } P \text{ is true} \\
+0, & \text{if } P \text{ is false}
+\end{cases}
+$$
+
+:::

_subfiles/indicator-functions/_def-kronecker-delta.qmd

@@ -0,0 +1,15 @@
+:::{#def-kronecker-delta}
+#### Kronecker delta
+
+For integers $i$ and $j$,
+the **Kronecker delta** is
+[@wikipedia_kronecker_delta]
+
+$$\kron_{ij} \eqdef [i = j]$$
+
+that is,
+$\kron_{ij} = 1$ when $i = j$
+and $\kron_{ij} = 0$ when $i \neq j$
+(@def-iverson-bracket).
+
+:::

_subfiles/indicator-functions/_def-predicate-indicator.qmd

@@ -0,0 +1,17 @@
+:::{#def-predicate-indicator}
+#### Predicate indicator
+
+For any logical proposition or predicate $P$,
+the **indicator** of $P$,
+or **predicate indicator**,
+takes the value $1$ when $P$ is true
+and $0$ when $P$ is false:
+
+$$
+\indicp{P} \eqdef \begin{cases}
+1, & \text{if } P \text{ is true} \\
+0, & \text{if } P \text{ is false}
+\end{cases}
+$$
+
+:::

_subfiles/indicator-functions/_exm-indicator-numerical.qmd

@@ -0,0 +1,22 @@
+:::{#exm-indicator-numerical}
+#### Evaluating set and predicate indicators
+
+Consider the real line $\universe = \reals$,
+the set of nonnegative numbers $A = [0, \infty)$,
+and a continuous
+[random variable](https://morrison-lab.github.io/pds/random-variables.html#def-random-variable)
+$Y$ (defined in the Morrison Lab's probability notes).
+
+1. Set indicator $\indic{A}(x)$:
+   - For $x = 3.5$: since $3.5 \in [0, \infty)$, $\indic{A}(3.5) = 1$.
+   - For $x = -2.1$: since $-2.1 \notin [0, \infty)$, $\indic{A}(-2.1) = 0$.
+
+2. Predicate indicator $\indicp{Y > 5}$:
+   - If an observation yields $Y = 7.2$,
+     the predicate $7.2 > 5$ is true,
+     so $\indicp{7.2 > 5} = 1$.
+   - If an observation yields $Y = 4.1$,
+     the predicate $4.1 > 5$ is false,
+     so $\indicp{4.1 > 5} = 0$.
+
+:::

_subfiles/indicator-functions/_exm-iverson-bracket.qmd

@@ -0,0 +1,8 @@
+:::{#exm-iverson-bracket}
+#### Evaluating Iverson brackets
+
+- $[3 > 2] = 1$, because $3 > 2$ is true.
+- $[2 > 3] = 0$, because $2 > 3$ is false.
+- $[4 \in \cb{1, 2}] = 0$, because $4$ is not an element of $\cb{1, 2}$.
+
+:::

_subfiles/indicator-functions/_exm-kronecker-delta.qmd

@@ -0,0 +1,32 @@
+:::{#exm-kronecker-delta}
+#### Evaluating the Kronecker delta
+
+- $$
+  \begin{aligned}
+  \kron_{11} &= [1 = 1] \\
+  &= 1.
+  \end{aligned}
+  $$
+
+- $$
+  \begin{aligned}
+  \kron_{12} &= [1 = 2] \\
+  &= 0.
+  \end{aligned}
+  $$
+
+- $$
+  \begin{aligned}
+  \kron_{22} &= [2 = 2] \\
+  &= 1.
+  \end{aligned}
+  $$
+
+- $$
+  \begin{aligned}
+  \kron_{23} &= [2 = 3] \\
+  &= 0.
+  \end{aligned}
+  $$
+
+:::

_subfiles/indicator-functions/_sec-indicator-functions.qmd

@@ -23,69 +23,15 @@ This section summarizes the principal notational conventions.
 
 {{< slidebreak >}}
 
-:::{#def-indicator-function}
-#### Indicator function, set indicator
-
-For any subset $A \subseteq \universe$ of a universal set $\universe$,
-the **indicator function** of $A$,
-[@wikipedia_indicator_function]
-or **set indicator**,
-is the function
-$\indic{A} : \universe \to \{0, 1\}$ defined by:
-
-$$
-\indic{A}(x) \eqdef \begin{cases}
-1, & x \in A \\
-0, & x \notin A
-\end{cases}
-$$
-
-:::
+{{< include mds/_subfiles/indicator-functions/_def-indicator-function.qmd >}}
 
 {{< slidebreak >}}
 
-:::{#def-predicate-indicator}
-#### Predicate indicator
-
-For any logical proposition or predicate $P$,
-the **indicator** of $P$,
-or **predicate indicator**,
-takes the value $1$ when $P$ is true
-and $0$ when $P$ is false:
-
-$$
-\indicp{P} \eqdef \begin{cases}
-1, & \text{if } P \text{ is true} \\
-0, & \text{if } P \text{ is false}
-\end{cases}
-$$
-
-:::
+{{< include mds/_subfiles/indicator-functions/_def-predicate-indicator.qmd >}}
 
 {{< slidebreak >}}
 
-:::{#exm-indicator-numerical}
-#### Evaluating set and predicate indicators
-
-Consider the real line $\universe = \reals$,
-the set of nonnegative numbers $A = [0, \infty)$,
-and a continuous
-[random variable](https://morrison-lab.github.io/pds/random-variables.html#def-random-variable)
-$Y$ (defined in the Morrison Lab's probability notes).
-
-1. Set indicator $\indic{A}(x)$:
-   - For $x = 3.5$: since $3.5 \in [0, \infty)$, $\indic{A}(3.5) = 1$.
-   - For $x = -2.1$: since $-2.1 \notin [0, \infty)$, $\indic{A}(-2.1) = 0$.
-
-2. Predicate indicator $\indicp{Y > 5}$:
-   - If an observation yields $Y = 7.2$,
-     the predicate $7.2 > 5$ is true,
-     so $\indicp{7.2 > 5} = 1$.
-   - If an observation yields $Y = 4.1$,
-     the predicate $4.1 > 5$ is false,
-     so $\indicp{4.1 > 5} = 0$.
-
-:::
+{{< include mds/_subfiles/indicator-functions/_exm-indicator-numerical.qmd >}}
 
 {{< slidebreak >}}
 
@@ -173,32 +119,11 @@ the Iverson bracket
 
 {{< slidebreak >}}
 
-:::{#def-iverson-bracket}
-#### Iverson bracket
-
-For any logical proposition $P$,
-the **Iverson bracket** of $P$ is
-[@wikipedia_iverson_bracket]
-
-$$
-[P] \eqdef \begin{cases}
-1, & \text{if } P \text{ is true} \\
-0, & \text{if } P \text{ is false}
-\end{cases}
-$$
-
-:::
+{{< include mds/_subfiles/indicator-functions/_def-iverson-bracket.qmd >}}
 
 {{< slidebreak >}}
 
-:::{#exm-iverson-bracket}
-#### Evaluating Iverson brackets
-
-- $[3 > 2] = 1$, because $3 > 2$ is true.
-- $[2 > 3] = 0$, because $2 > 3$ is false.
-- $[4 \in \cb{1, 2}] = 0$, because $4$ is not an element of $\cb{1, 2}$.
-
-:::
+{{< include mds/_subfiles/indicator-functions/_exm-iverson-bracket.qmd >}}
 
 {{< slidebreak >}}
 
@@ -232,56 +157,11 @@ $$
 
 {{< slidebreak >}}
 
-:::{#def-kronecker-delta}
-#### Kronecker delta
-
-For integers $i$ and $j$,
-the **Kronecker delta** is
-[@wikipedia_kronecker_delta]
-
-$$\kron_{ij} \eqdef [i = j]$$
-
-that is,
-$\kron_{ij} = 1$ when $i = j$
-and $\kron_{ij} = 0$ when $i \neq j$
-(@def-iverson-bracket).
-
-:::
+{{< include mds/_subfiles/indicator-functions/_def-kronecker-delta.qmd >}}
 
 {{< slidebreak >}}
 
-:::{#exm-kronecker-delta}
-#### Evaluating the Kronecker delta
-
-- $$
-  \begin{aligned}
-  \kron_{11} &= [1 = 1] \\
-  &= 1.
-  \end{aligned}
-  $$
-
-- $$
-  \begin{aligned}
-  \kron_{12} &= [1 = 2] \\
-  &= 0.
-  \end{aligned}
-  $$
-
-- $$
-  \begin{aligned}
-  \kron_{22} &= [2 = 2] \\
-  &= 1.
-  \end{aligned}
-  $$
-
-- $$
-  \begin{aligned}
-  \kron_{23} &= [2 = 3] \\
-  &= 0.
-  \end{aligned}
-  $$
-
-:::
+{{< include mds/_subfiles/indicator-functions/_exm-kronecker-delta.qmd >}}
 
 ### Strengths and limitations of the Iverson bracket