Definition
Given two partially ordered sets A and B, the lexicographical order on the Cartesian product A × B is defined as
- (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′).
The result is a partial order. If A and B are totally ordered, then the result is a total order as well.
More generally, one can define the lexicographic order on the Cartesian product of n ordered sets, on the Cartesian product of a countably infinite family of ordered sets, and on the union of such sets.
Read more about this topic: Lexicographical Order
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