\begin{section}{Common}
The function $f$ applied to $x$ is $f\of{x}$. We can group terms
- like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c - d}}$. Here's a
- set $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. The tuples go
- up to seven, for now:
+ like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c - d}}$. The tuples
+ go up to seven, for now:
%
\begin{itemize}
\begin{item}
\end{section}
\begin{section}{Set theory}
- The cardinality of the set $X \coloneqq \set{1,2,3}$ is $\card{X}
- = 3$, and its powerset is $\powerset{X}$.
+ Here's a set $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. The
+ cardinality of the set $X \coloneqq \set{1,2,3}$ is $\card{X} =
+ 3$, and its powerset is $\powerset{X}$.
We also have a few basic set operations, for example the union of
two or three sets: $\union{A}{B}$, $\unionthree{A}{B}{C}$. And of
% Group terms using square brackets.
\newcommand*{\sqty}[1]{ \left[{#1}\right] }
-% Create a set from the given elements
-\newcommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
-
-% A set comprehension, where the ``such that...'' bar is added
-% automatically. The bar was chosen over a colon to avoid ambiguity
-% with the L : V -> V notation. We can't leverage \set here because \middle
-% needs \left and \right present.
-\newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
-
% A pair of things.
\newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
\usepackage{mathtools}
\fi
+% Create a set from the given elements
+\newcommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
+
+% A set comprehension, where the ``such that...'' bar is added
+% automatically. The bar was chosen over a colon to avoid ambiguity
+% with the L : V -> V notation. We can't leverage \set here because \middle
+% needs \left and \right present.
+\newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
+
% The cardinality of a set. The |X| notation conflicts with the
% absolute value, and the meaning of card(X) is clear at once, so we