# Product order

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Product order

In mathematics, given two ordered sets A and B, one can induce a partial 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 a1a2 and b1b2.

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

The Cartesian product with product order is the categorical product in the category of partially ordered sets with monotone functions.

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