A linear order is a type of ordering relation on a set where every pair of elements is comparable, meaning for any two elements 'a' and 'b', either 'a' is less than 'b', 'b' is less than 'a', or they are equal. This relation satisfies the properties of reflexivity, antisymmetry, and transitivity. Linear orders are crucial in understanding more complex structures, such as partially ordered sets, since they represent a complete ranking of elements.
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