\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 $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. Here's a pair
- of things $\pair{1}{2}$ or a triple of them $\triple{1}{2}{3}$,
- and the factorial of the number $10$ is $\factorial{10}$.
+ set $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. The tuples go
+ up to seven, for now:
+ %
+ \begin{itemize}
+ \begin{item}
+ Pair: $\pair{1}{2}$,
+ \end{item}
+ \begin{item}
+ Triple: $\triple{1}{2}{3}$,
+ \end{item}
+ \begin{item}
+ Quadruple: $\quadruple{1}{2}{3}{4}$,
+ \end{item}
+ \begin{item}
+ Qintuple: $\quintuple{1}{2}{3}{4}{5}$,
+ \end{item}
+ \begin{item}
+ Sextuple: $\sextuple{1}{2}{3}{4}{5}{6}$,
+ \end{item}
+ \begin{item}
+ Septuple: $\septuple{1}{2}{3}{4}{5}{6}{7}$.
+ \end{item}
+ \end{itemize}
+ %
+ The factorial of the number $10$ is $\factorial{10}$.
The Cartesian product of two sets $A$ and $B$ is
$\cartprod{A}{B}$; if we take the product with $C$ as well, then
% A triple of things.
\newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
+% A four-tuple of things.
+\newcommand*{\quadruple}[4]{ \left({#1},{#2},{#3},{#4}\right) }
+
+% A five-tuple of things.
+\newcommand*{\quintuple}[5]{ \left({#1},{#2},{#3},{#4},{#5}\right) }
+
+% A six-tuple of things.
+\newcommand*{\sextuple}[6]{ \left({#1},{#2},{#3},{#4},{#5},{#6}\right) }
+
+% A seven-tuple of things.
+\newcommand*{\septuple}[7]{ \left({#1},{#2},{#3},{#4},{#5},{#6},{#7}\right) }
+
% The Cartesian product of two things.
\newcommand*{\cartprod}[2]{ {#1}\times{#2} }