Difference between revisions of "Multigrade operator"

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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
 
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
  
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In [[logic]] and [[mathematics]], a '''multigrade operator''' <math>\Omega</math> is a ''[[parametric operator]]'' with ''parameter'' ''k'' in the set '''N''' of non-negative integers.
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A '''multigrade operator''' <math>\Omega\!</math> is a ''[[parametric operator]]'' with ''parameter'' <math>k\!</math> in the set <math>\mathbb{N}\!</math> of non-negative integers.
  
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The application of a multigrade operator <math>\Omega</math> to a finite sequence of operands (''x''<sub>1</sub>,&nbsp;…,&nbsp;''x''<sub>''k''</sub>) is typically denoted with the parameter ''k'' left tacit, as the appropriate application is implicit in the number of operands listed.  Thus <math>\Omega</math>(''x''<sub>1</sub>,&nbsp;…,&nbsp;''x''<sub>''k''</sub>) may be taken for <math>\Omega</math><sub>''k''</sub>(''x''<sub>1</sub>,&nbsp;…,&nbsp;''x''<sub>''k''</sub>).
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The application of a multigrade operator <math>\Omega\!</math> to a finite sequence of operands <math>(x_1, \ldots, x_k)\!</math> is typically denoted with the parameter <math>k\!</math> left tacit, as the appropriate application is implicit in the number of operands listed.  Thus <math>\Omega (x_1, \ldots, x_k)\!</math> may be taken for <math>\Omega_k (x_1, \ldots, x_k).\!</math>
  
 
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* [http://intersci.ss.uci.edu/wiki/index.php/Multigrade_operator Multigrade Operator @ InterSciWiki]
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* [http://mywikibiz.com/Multigrade_operator Multigrade Operator @ MyWikiBiz]
 
* [http://mywikibiz.com/Multigrade_operator Multigrade Operator @ MyWikiBiz]
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* [http://mathweb.org/wiki/Multigrade_operator Multigrade Operator @ MathWeb Wiki]
 
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* [http://netknowledge.org/wiki/Multigrade_operator Multigrade Operator @ NetKnowledge]
 
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* [http://wiki.oercommons.org/mediawiki/index.php/Multigrade_operator Multigrade Operator @ OER Commons]
 
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* [http://p2pfoundation.net/Multigrade_Operator Multigrade Operator @ P2P Foundation]
 
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* [http://semanticweb.org/wiki/Multigrade_operator Multigrade Operator @ SemanticWeb]
 
 
* [http://ref.subwiki.org/wiki/Multigrade_operator Multigrade Operator @ Subject Wikis]
 
* [http://ref.subwiki.org/wiki/Multigrade_operator Multigrade Operator @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity Beta]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, &ldquo;Semiotic Information&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
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* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
 
  
 
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Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
 
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
  
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* [http://intersci.ss.uci.edu/wiki/index.php/Multigrade_operator Multigrade Operator], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Multigrade_operator Multigrade Operator], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Multigrade_operator Multigrade Operator], [http://mywikibiz.com/ MyWikiBiz]
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* [http://mathweb.org/wiki/Multigrade_operator Multigrade Operator], [http://mathweb.org/wiki/ MathWeb Wiki]
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* [http://planetmath.org/MultigradeOperator Multigrade Operator], [http://planetmath.org/ PlanetMath]
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* [http://planetmath.org/encyclopedia/MultigradeOperator.html Multigrade Operator], [http://planetmath.org/ PlanetMath]
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* [http://wikinfo.org/w/index.php/Multigrade_operator Multigrade Operator], [http://wikinfo.org/w/ Wikinfo]
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* [http://planetphysics.org/encyclopedia/MultigradeOperator.html Multigrade Operator], [http://planetphysics.org/ PlanetPhysics]
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* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity]
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* [http://proofwiki.org/wiki/Definition:Multigrade_Operator Multigrade Operator], [http://proofwiki.org/ ProofWiki]
 
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* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://getwiki.net/-Parametric_Operator&r=multigrade_operator Multigrade Operator], [http://getwiki.net/ GetWiki]
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* [http://web.archive.org/web/20060913000000/http://en.wikipedia.org/wiki/Multigrade_operator Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]
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* [http://wikinfo.org/index.php/Multigrade_operator Multigrade Operator], [http://wikinfo.org/ Wikinfo]
 
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* [http://textop.org/wiki/index.php?title=Multigrade_operator Multigrade Operator], [http://textop.org/wiki/ Textop Wiki]
 
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* [http://en.wikipedia.org/w/index.php?title=Multigrade_operator&oldid=40451309 Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]
 
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Latest revision as of 04:12, 7 November 2015

☞ This page belongs to resource collections on Logic and Inquiry.

A multigrade operator \(\Omega\!\) is a parametric operator with parameter \(k\!\) in the set \(\mathbb{N}\!\) of non-negative integers.

The application of a multigrade operator \(\Omega\!\) to a finite sequence of operands \((x_1, \ldots, x_k)\!\) is typically denoted with the parameter \(k\!\) left tacit, as the appropriate application is implicit in the number of operands listed. Thus \(\Omega (x_1, \ldots, x_k)\!\) may be taken for \(\Omega_k (x_1, \ldots, x_k).\!\)

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Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

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