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hierarchy

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hierarchy

Not who you're looking for? Others named hierarchy: system of elements with multiple levels or tiers that are su · 2024 South Korean television series · In an undisclosed area of Texas after two adoptive brothers

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What's driving coverage of hierarchy right now?

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hierarchy across IJR

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Overview

In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets. The term pre-ordered set is unambiguous, and is always synonymous with a mathematical hierarchy. The term hierarchy is used to stress a hierarchical relation among the elements. Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers N is equipped with a natural pre-order structure, where whenever we can find some other number so that . That is, is bigger than only because we can get to from using . This idea can be applied to any commutative monoid. On the other hand, the set of integers Z requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation by writing . A mathematical hierarchy (a pre-ordered set) should not be confused with the more general concept of a hierarchy in the social realm, particularly when one is constructing computational models that are used to describe real-world social, economic or political systems. These hierarchies, or complex networks, are much too rich to be described in the category Set of sets. This is not just a pedantic claim; there are also mathematical hierarchies, in the general sense, that are not describable using set theory. Other natural hierarchies arise in computer science, where the word refers to partially ordered sets whose elements are classes of objects of increasing complexity. In that case, the preorder defining the hierarchy is the class-containment relation. Containment hierarchies are thus special cases of hierarchies.

From Wikipedia (CC BY-SA 4.0).

Notable quotes

“You moralistic dog—admitting a hierarchy in which you are subordinate, purely that you may have subordinates; licking the boots of a superior, that you may have yours in turn licked by an underling.”
— Kenneth Burke, Towards a Better Life (Berkeley: 1966), p. 9
“I think it only makes sense to seek out and identify structures of authority, hierarchy, and domination in every aspect of life, and to challenge them; unless a justification for them can be given, they are illegitimate, and should be dismantled, to increase the scope of human freedom.”
— Noam Chomsky, Language and Politics (1988) p. 775
“A movement, even a radical movement, is also an institution with its own set of leaders, power dynamics and hierarchy.”
— Melanie Kaye/Kantrowitz “Nine Suggestions For Radicals, or Lessons From the Gulf War” in The Issue is Power: Essays on Women, Jews, Violence and Resistance (1992)
“It has taken since time immemorial for us to organize ourselves, biologically and socially, into the functional hierarchies that both specify our perceptions and actions, and define our interactions with the natural and social world. Profound gratitude for that gift is the only proper response.”
— Jordan Peterson, Beyond Order (2021), p. 34
“Hierarchy has had six thousand years of trial. It will never succeed for long in any form.”
— George L. Jackson, Blood in My Eye (1971), p. 130
“The French want no-one to be their superior. The English want inferiors. The Frenchman constantly raises his eyes above him with anxiety. The Englishman lowers his beneath him with satisfaction.”
— Alexis de Tocqueville, Journeys to England and Ireland (1835)

Quotes via Wikiquote (CC BY-SA), each with its original source.

Notable quotes

“You moralistic dog—admitting a hierarchy in which you are subordinate, purely that you may have subordinates; licking the boots of a superior, that you may have yours in turn licked by an underling.”
— Kenneth Burke, Towards a Better Life (Berkeley: 1966), p. 9
“I think it only makes sense to seek out and identify structures of authority, hierarchy, and domination in every aspect of life, and to challenge them; unless a justification for them can be given, they are illegitimate, and should be dismantled, to increase the scope of human freedom.”
— Noam Chomsky, Language and Politics (1988) p. 775
“A movement, even a radical movement, is also an institution with its own set of leaders, power dynamics and hierarchy.”
— Melanie Kaye/Kantrowitz “Nine Suggestions For Radicals, or Lessons From the Gulf War” in The Issue is Power: Essays on Women, Jews, Violence and Resistance (1992)
“It has taken since time immemorial for us to organize ourselves, biologically and socially, into the functional hierarchies that both specify our perceptions and actions, and define our interactions with the natural and social world. Profound gratitude for that gift is the only proper response.”
— Jordan Peterson, Beyond Order (2021), p. 34
“Hierarchy has had six thousand years of trial. It will never succeed for long in any form.”
— George L. Jackson, Blood in My Eye (1971), p. 130
“The French want no-one to be their superior. The English want inferiors. The Frenchman constantly raises his eyes above him with anxiety. The Englishman lowers his beneath him with satisfaction.”
— Alexis de Tocqueville, Journeys to England and Ireland (1835)

Quotes via Wikiquote (CC BY-SA), each with its original source.

In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets. The term pre-ordered set is unambiguous, and is always synonymous with a mathematical hierarchy. The term hierarchy is used to stress a hierarchical relation among the elements.

Not who you're looking for? Others named hierarchy: system of elements with multiple levels or tiers that are su · 2024 South Korean television series · In an undisclosed area of Texas after two adoptive brothers

Overview

In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets. The term pre-ordered set is unambiguous, and is always synonymous with a mathematical hierarchy. The term hierarchy is used to stress a hierarchical relation among the elements. Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers N is equipped with a natural pre-order structure, where whenever we can find some other number so that . That is, is bigger than only because we can get to from using . This idea can be applied to any commutative monoid. On the other hand, the set of integers Z requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation by writing . A mathematical hierarchy (a pre-ordered set) should not be confused with the more general concept of a hierarchy in the social realm, particularly when one is constructing computational models that are used to describe real-world social, economic or political systems. These hierarchies, or complex networks, are much too rich to be described in the category Set of sets. This is not just a pedantic claim; there are also mathematical hierarchies, in the general sense, that are not describable using set theory. Other natural hierarchies arise in computer science, where the word refers to partially ordered sets whose elements are classes of objects of increasing complexity. In that case, the preorder defining the hierarchy is the class-containment relation. Containment hierarchies are thus special cases of hierarchies.

From Wikipedia (CC BY-SA 4.0).

hierarchy across IJR

Ask Genius by OpenServe about hierarchy Create in Studio Build a game Watch videos