User:Dfeuer/Definition:Product Order

Definition
Let $\left({S_i,\preceq_i}\right)$ be an ordered set for each $i \in I$.

Then the product order, $\preceq$, on $S = \displaystyle \prod_{i \mathop\in I} S_i$ is defined thus:

$x \preceq y$ iff $x_i \preceq_i y_i$ for each $i\in I$.