- 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
- $\triple{1}{2}{3}$. The Cartesian product of two sets $A$ and $B$
- is $\cartprod{A}{B}$; if we take the product with $C$ as well,
- then we obtain $\cartprodthree{A}{B}{C}$. The direct sum of $V$
- and $W$ is $\directsum{V}{W}$ 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
+ we obtain $\cartprodthree{A}{B}{C}$. The direct sum of $V$ and $W$
+ is $\directsum{V}{W}$. Or three things,
+ $\directsumthree{U}{V}{W}$. How about more things? Like
+ $\directsummany{k=1}{\infty}{V_{k}} \ne
+ \cartprodmany{k=1}{\infty}{V_{k}}$. Those direct sums and
+ cartesian products adapt nicely to display equations:
+ %
+ \begin{equation*}
+ \directsummany{k=1}{\infty}{V_{k}} \ne \cartprodmany{k=1}{\infty}{V_{k}}.
+ \end{equation*}