\begin{definition}[Definition:Antilexicographic Order/General Definition]
Let $S_1, S_2, \ldots, S_n$ all be ordered sets.
Then we define $T_n$ as the '''antilexicographic order''' on $S_1, S_2, \ldots, S_n$ as:
:$\forall n \in \N_{>0}: T_n = \begin {cases}
S_1 & : n = 1 \\
T_{n - 1} \otimes^a S_n & : n > 1
\end {cases}$
\end{definition}