Product order

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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.

[edit] See also

• direct product of binary relationshttp://en.wikipedia.org../../../../articles/d/i/r/Direct_product.html#Direct_product_of_binary_relations
• examples of partial ordershttp://en.wikipedia.org../../../../articles/p/a/r/Partial_order.html#Examples
• orders on the Cartesian product of totally ordered setshttp://en.wikipedia.org../../../../articles/t/o/t/Total_order.html#Orders_on_the_Cartesian_product_of_totally_ordered_sets