\begin{definition}[Definition:Orthogonal Latin Squares]
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
Let $\mathbf A$ and $\mathbf B$ be Latin squares of order $n$.
Let $\left[{a}\right]_{i j}$ and $\left[{b}\right]_{i j}$ be the elements of $\mathbf A$ and $\mathbf B$ respectively whose indices are $i$ and $j$.
Then $\mathbf A$ and $\mathbf B$ are '''orthogonal''' {{iff}}:
:for all $i$ and $j$, the ordered pairs $\left({\left[{a}\right]_{i j}, \left[{b}\right]_{i j}}\right)$ are distinct.
That is, {{iff}} $\left({\left[{a}\right]_{i j}, \left[{b}\right]_{i j}}\right)$ appears no more than once for every ordered pair $\left({i, j}\right)$.
\end{definition}