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| − | [[Category:Glossary]] | + | *[[Distributed Space]] ''- Research on the kind of network space required by [[the project]]'' |
| − | *Organising some notes about spacetime fundamentals from pedia | + | *[[Conceptual Space]] ''- About the space of perceived experience referred to by [[w:Taoism|Taoism]] and [[w:Advaita vedanta|Advaita vedanta]]'' |
| | + | *[[Node Space]] ''- The first attempt at designing a network space for [[the project]]'' |
| | + | *[[Hilbert space]] |
| | + | *[[Space & Time]] |
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| − | | + | == See also == |
| − | ;The fundamental theorem of algebra
| + | *[[Sacred geometry]] |
| − | In [[w:mathematics|mathematics]], the [[w:fundamental theorem of algebra|fundamental theorem of algebra]] states that every complex [[w:polynomial|polynomial]] <math>p(z)</math> in one variable and of [[w:degree of a polynomial|degree]] <math>n</math> ≥ <math>1</math> has some complex [[w:root (mathematics)|root]]. In other words, the [[w:field (mathematics)|field]] of [[w:complex number|complex number]]s is [[w:algebraically closed field|algebraically closed]] and therefore, as for any other algebraically closed field, the equation <math>p(z)=0</math> has <math>n</math> roots ([[w:multiple roots of a polynomial|not necessarily distinct]]).
| + | *[http://tetryonics101.com/ Tetryonics] |
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| − | The name of the theorem is now considered a [[w:misnomer|misnomer]] by many mathematicians, since it is an instance of [[w:mathematical analysis|analysis]] rather than [[w:algebra|algebra]].
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| − | ;Algebraically closed field
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| − | In mathematics, a [[w:field (mathematics)|field]] <math>F</math> is said to be [[w:algebraically closed|algebraically closed]] if every polynomial in one variable of degree at least <math>1</math>, with [[w:coefficient|coefficient]]s in <math>F</math>, has a zero ([[w:root (mathematics)|root]]) in <math>F</math>.
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| − | ;What is a ''field''?
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| − | In [[w:abstract algebra|abstract algebra]], a [[w:field|field]] is an [[w:algebraic structure|algebraic structure]] in which the operations of addition, subtraction, multiplication and [[w:division (mathematics)|division]] (except division by zero) may be performed, and the same rules hold which are familiar from the [[w:arithmetic|arithmetic]] of ordinary [[w:number|number]]s.
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| − | The mathematical discipline concerned with the study of fields is called [[w:field theory (mathematics)|field theory]].
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| − | ;Abstract structure?
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| − | In [[w:universal algebra|universal algebra]], a branch of [[w:pure mathematics|pure mathematics]], an [[w:algebraic structure|algebraic structure]] consists of one or more [[w:set|set]]s [[w:Closure (mathematics)|closed]] under one or more [[w:operations|operations]], satisfying some [[w:axiom|axiom]]s. [[w:Abstract algebra|Abstract algebra]] is primarily the study of algebraic structures and their properties.
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| − | Abstractly, an "algebraic structure," is the collection of all possible [[w:model theory|model]]s of a given set of axioms. More concretely, an algebraic structure is any particular model of some set of axioms. For example, the [[w:monster group|monster group]] both "is" an algebraic structure in the concrete sense, and abstractly, "has" the group structure in common with all other [[w:group (mathematics)|group]]s. This article employs both meanings of "structure."
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| − | This definition of an algebraic structure should not be taken as restrictive. Anything that satisfies the axioms defining a structure is an instance of that structure, regardless of how many other axioms that instance happens to have. For example, all [[w:group (mathematics)|group]]s are also [[w:semigroup|semigroup]]s and [[w:magma (algebra)|magma]]s.
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