Difference between revisions of "Hyperoperations Wiki"
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| − | The [[Hyperoperations Wiki]] is intended to complement [http://math.eretrandre.org/tetrationforum/ the Tetrationforum]. By creating a | + | The [[Hyperoperations Wiki]] is intended to complement [http://math.eretrandre.org/tetrationforum/ the Tetrationforum]. By creating a ''cartographic tool'' for the exploration done at the [[Tetrationforum]], keeping track of of definitions, terms, ideas, and bibliographic references; and to formally re-express all modern mathematical concepts from a preparatory viewpoint that is compatible with ''hyperoperative'' inquiry. |
[[File:hw.png|250px|center]] | [[File:hw.png|250px|center]] | ||
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[[File:hw_2.png|thumb|350px|right|The hyperoperations emerge from the investigation of the nature of [[arithmetical operations]].]] | [[File:hw_2.png|thumb|350px|right|The hyperoperations emerge from the investigation of the nature of [[arithmetical operations]].]] | ||
| − | The Hyperoperations Wiki serves as an online collaborative [[encyclopedia]] with a dual purpose. On one hand, it aims to map the [[definitions]] and [[relationships]] among the mathematical structures that emerge from and are connected to the [[abstract]] [[concept]] of [[hyperoperation]], thereby situating them within the landscape of modern and contemporary [[mathematics]]. On the other hand, to maintain a self-contained nature, the wiki seeks to provide all fundamental definitions—logical, set-theoretical, algebraic, and geometric— in a manner that makes them directly applicable to | + | The Hyperoperations Wiki serves as an online collaborative [[encyclopedia]] with a dual purpose. On one hand, it aims to map the [[definitions]] and [[relationships]] among the mathematical structures that emerge from and are connected to the [[abstract]] [[concept]] of [[hyperoperation]], thereby situating them within the landscape of modern and contemporary [[mathematics]]. On the other hand, to maintain a self-contained nature, the wiki seeks to provide all fundamental definitions—logical, set-theoretical, algebraic, and geometric— in a manner that makes them directly applicable to structures derived from hyperoperations, presenting them from what could be termed a '''''hyperoperational perspective ([[hPOV]]).''''' |
| − | Just like the concept of [[ring]], the concept of hyperoperation | + | Just like the concept of a [[ring]], the concept of hyperoperation serves as a potential avenue for exploring the conceptual nature of [[arithmetic operations]] through [[generalization]] and [[abstraction]]. The approach taken by the [[hPOV]] lies on the assumption that some relationships between addition and multiplication have a hierarchical nature. Certain relationships indicate a unidirectional increase in complexity and reveal pathways to explore further in those directions, '''''above and beyond''''', i.e. ''ὑπέρ ([[hyper]])'', '''''sums and products.''''' |
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| + | [[File:hw_3.png|thumb|600px|center|Intuition about extending the conceptual relationship between sum and product to the whole space of operations.]] | ||
===Useful pages=== | ===Useful pages=== | ||
[[Special:AllPages]] brings you to a list of all so far described terms. | [[Special:AllPages]] brings you to a list of all so far described terms. | ||
Revision as of 09:23, 10 May 2025
The Hyperoperations Wiki is intended to complement the Tetrationforum. By creating a cartographic tool for the exploration done at the Tetrationforum, keeping track of of definitions, terms, ideas, and bibliographic references; and to formally re-express all modern mathematical concepts from a preparatory viewpoint that is compatible with hyperoperative inquiry.
Idea
The Hyperoperations Wiki serves as an online collaborative encyclopedia with a dual purpose. On one hand, it aims to map the definitions and relationships among the mathematical structures that emerge from and are connected to the abstract concept of hyperoperation, thereby situating them within the landscape of modern and contemporary mathematics. On the other hand, to maintain a self-contained nature, the wiki seeks to provide all fundamental definitions—logical, set-theoretical, algebraic, and geometric— in a manner that makes them directly applicable to structures derived from hyperoperations, presenting them from what could be termed a hyperoperational perspective (hPOV).
Just like the concept of a ring, the concept of hyperoperation serves as a potential avenue for exploring the conceptual nature of arithmetic operations through generalization and abstraction. The approach taken by the hPOV lies on the assumption that some relationships between addition and multiplication have a hierarchical nature. Certain relationships indicate a unidirectional increase in complexity and reveal pathways to explore further in those directions, above and beyond, i.e. ὑπέρ (hyper), sums and products.
Useful pages
Special:AllPages brings you to a list of all so far described terms.