Ordered Product of Ordered Sets

Letandwith

and

Let the ordering on A and B beandrespectively and let an ordering onbe given byWe need to determine whenwhereand

The elements of A times B can be ordered with respect to the sets A and B.

In fact, finite sets can be ordered in many different ways. Elements ofcan be arranged in 12! different ways, and this is equal to the number of ways in which elements ofcan be ordered.

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