User:Dfeuer/Definition:Product Order

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Definition

Let $\family {S_i, \preceq_i}$ be an ordered set for each $i \in I$.

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

$x \preceq y$ if and only if $x_i \preceq_i y_i$ for each $i \in I$.

Also see

User:Dfeuer/Product Order is Order