Absorption (mathematics): Difference between revisions
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In [[algebra]], '''absorption''' is a property of [[binary operation]]s which reflects an underlying [[order (relation)|order relation]]. | In [[algebra]], '''absorption''' is a property of [[binary operation]]s which reflects an underlying [[order (relation)|order relation]]. | ||
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Examples include | Examples include | ||
* In [[set theory]], [[intersection]] and [[union]]; | * In [[set theory]], [[intersection]] and [[union]]; | ||
* In [[propositional logic]], [[conjunction | * In [[propositional logic]], [[Conjunction (logical and)|conjunction (logical and)]] and [[disjunction]] (logical or); | ||
* In a [[distributive lattice]], [[join]] and [[meet]]; | * In a [[distributive lattice]], [[join]] and [[meet]]; | ||
* In a [[linear order|linearly ordered]] set, [[minimum]] and [[maximum]]; | * In a [[linear order|linearly ordered]] set, [[minimum]] and [[maximum]]; | ||
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==References== | ==References== | ||
* {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=0-521-09695-2 | pages=76 }} | * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=0-521-09695-2 | pages=76 }}[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 16:00, 5 July 2024
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:
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;
References
- A.G. Howson (1972). A handbook of terms used in algebra and analysis. Cambridge University Press, 76. ISBN 0-521-09695-2.