In mathematics, given two ordered sets A and B, one can induce an ordering on the Cartesian product A × B. Given two pairs (a₁,b₁) and (a₂,b₂) in A × B, one sets

(a₁,b₁) ≤ (a₂,b₂)

if and only if a₁ ≤ a₂ and b₁ ≤ b₂.

This ordering is called the product order. Another possible ordering on A × B is the lexicographical order.

See also

• direct product of binary relationshttp://en.wikipedia.org/wiki/Direct_product#Direct_product_of_binary_relations
• examples of partial ordershttp://en.wikipedia.org/wiki/Partial_order#Examples
• orders on the Cartesian product of totally ordered setshttp://en.wikipedia.org/wiki/Total_order#Orders_on_the_Cartesian_product_of_totally_ordered_sets

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