\begin{definition}[Definition:Order Sum/Informal Interpretation]
We can consider the '''order sum''' $\struct {S \preccurlyeq} := \struct {S_1 \preccurlyeq_1} \oplus \struct {S_2 \preccurlyeq_2}$ as:
:First the set $S_1$, ordered by $\preccurlyeq_1$
:Then the set $S_2$, ordered by $\preccurlyeq_2$
Note that:
:$\forall x \in S_1, y \in S_2: \tuple {x, 0} \preccurlyeq \tuple {y, 1}$
That is, every element of $S_1$ is comparable with every element of $S_2$.
Category:Definitions/Order Sums
\end{definition}