Absorption (mathematics)

In algebra, absorption is a property of binary operations which reflects an underlying order relation.

Sometimes called the "absorption law", it is one of the defining properties of a lattice:


 * $$x \wedge (x \vee y) = x;~ x \vee (x \wedge y) = x . \,$$

Examples include
 * In set theory, intersection and union;
 * In propositional logic, conjunction (logical and) and disjunction (logical or);
 * In a distributive lattice, join and meet;
 * In a linearly ordered set, minimum and maximum;
 * In the integers, highest common factor and least common multiple;