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− | ==Formula Help==
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− | * [http://meta.wikimedia.org/wiki/Help:Displaying_a_formula Mathematical formulas]
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− | * [http://en.wikipedia.org/wiki/Wikipedia:Mathematical_symbols Mathematical symbols]
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− |
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− | ==Bytes & Parses==
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− |
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− | {| style="width:50%"
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− | | ∈
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− | | ∈
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− | |-
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− | | ε
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− | | ε
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− | |-
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− | | <nowiki><math>\in</math></nowiki>
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− | | <math>\in</math>
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− | |-
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− | | <nowiki><math>\in\!</math></nowiki>
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− | | <math>\in\!</math>
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− | |-
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− | | <nowiki><math>\epsilon</math></nowiki>
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− | | <math>\epsilon</math>
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− | |-
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− | | <nowiki><math>\epsilon\!</math></nowiki>
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− | | <math>\epsilon\!</math>
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− | |-
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− | | <nowiki><math>\varepsilon</math></nowiki>
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− | | <math>\varepsilon</math>
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− | |-
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− | | <nowiki><math>\varepsilon\!</math></nowiki>
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− | | <math>\varepsilon\!</math>
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− | |}
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− | <br>
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− |
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− | {| style="width:50%"
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− | | &eta;
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− | | η
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− | |-
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− | | <nowiki><math>\eta</math></nowiki>
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− | | <math>\eta</math>
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− | |-
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− | | <nowiki><math>\eta\!</math></nowiki>
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− | | <math>\eta\!</math>
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− | |}
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− | <br>
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− |
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− | {| style="width:50%"
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− | | &theta;
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− | | θ
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− | |-
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− | | <nowiki><math>\theta</math></nowiki>
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− | | <math>\theta</math>
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− | |-
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− | | <nowiki><math>\theta\!</math></nowiki>
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− | | <math>\theta\!</math>
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− | |-
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− | | <nowiki><math>\vartheta</math></nowiki>
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− | | <math>\vartheta</math>
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− | |-
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− | | <nowiki><math>\vartheta\!</math></nowiki>
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− | | <math>\vartheta\!</math>
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− | |}
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− | <br>
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− |
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− | {| style="width:50%"
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− | | &chi;
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− | | χ
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− | |-
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− | | <nowiki><math>\chi</math></nowiki>
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− | | <math>\chi</math>
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− | |-
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− | | <nowiki><math>\chi\!</math></nowiki>
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− | | <math>\chi\!</math>
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− | |}
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− | <br>
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− |
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− | ''x'' = ''x''<sub>''J''</sub> = ¢(''J'') = ''J''¢ = ''J'' ¢ = ''J''<sup>¢</sup> = ''J''<sup> ¢</sup>
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− |
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− | ''x'' = ''x''<sub>''J''</sub> = ¢(''J'') = ''J''¢ = ''J'' ¢ = ''J''<sup>¢</sup> = ''J''<sup> ¢</sup>
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− |
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− | ==Display==
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− |
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− | ===New===
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− |
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− | :{| cellpadding=1 style="height:40px"
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− | | <font face=georgia>'''W'''</font>
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− | | :
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− | | (
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− | | [
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− | | '''B'''<sup>''n''</sup>
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− | | ]
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− | | →
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− | | [
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− | | '''B'''<sup>''k''</sup>
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− | | ]
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− | | )
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− | |
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− | | →
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− | |
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− | | (
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− | | [
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− | | '''B'''<sup>''n''</sup>
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− | | ×
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− | | '''D'''<sup>''n''</sup>
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− | | ]
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− | | →
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− | | [
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− | | '''B'''<sup>''k''</sup>
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− | | ×
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− | | '''D'''<sup>''k''</sup>
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− | | ]
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− | | )
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− | | .
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− | |}
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− |
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− | :{| style="height:80px; text-align:center; width:90%"
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− | | align=left width=20%| Concrete type
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− | | width=8% | <math>\epsilon</math>
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− | | :
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− | | (
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− | | ''U''<sup>•</sup>
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− | | →
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− | | ''X''<sup>•</sup>
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− | | )
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− | | width=16% | →
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− | | (
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− | | E''U''<sup>•</sup>
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− | | →
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− | | ''X''<sup>•</sup>
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− | | )
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− | |-
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− | | align=left width=20%| Abstract type
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− | | width=8% | <math>\epsilon</math>
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− | | :
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− | | (
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− | | ['''B'''<sup>''n''</sup>]
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− | | →
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− | | ['''B'''<sup>''k''</sup>]
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− | | )
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− | | width=16% | →
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− | | (
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− | | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | →
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− | | ['''B'''<sup>''k''</sup>]
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− | | )
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− | |}
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− |
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− | :{| style="height:80px; text-align:center; width:90%"
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− | | align=left width=20%| Concrete type
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− | | width=8% | W
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− | | :
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− | | (
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− | | ''U''<sup>•</sup>
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− | | →
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− | | ''X''<sup>•</sup>
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− | | )
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− | | width=16% | →
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− | | (
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− | | E''U''<sup>•</sup>
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− | | →
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− | | d''X''<sup>•</sup>
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− | | )
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− | |-
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− | | align=left width=20%| Abstract type
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− | | width=8% | W
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− | | :
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− | | (
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− | | ['''B'''<sup>''n''</sup>]
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− | | →
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− | | ['''B'''<sup>''k''</sup>]
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− | | )
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− | | width=16% | →
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− | | (
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− | | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | →
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− | | ['''D'''<sup>''k''</sup>]
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− | | )
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− | |}
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− |
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− | :{| style="height:80px; text-align:center; width:90%"
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− | | width=6% | <math>\epsilon</math>''F''
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | E''U''<sup>•</sup>
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− | | width=4% | →
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− | | width=8% | ''X''<sup>•</sup>
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− | | width=4% | ⊆
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− | | width=8% | E''X''<sup>•</sup>
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− | | width=2% | )
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− | | width=4% | <math>\cong</math>
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− | | width=2% | (
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− | | width=16% | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | width=4% | →
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− | | width=8% | ['''B'''<sup>''k''</sup>]
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− | | width=4% | ⊆
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− | | width=16% | ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
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− | | width=2% | )
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− | |-
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− | | width=6% | W''F''
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | E''U''<sup>•</sup>
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− | | width=4% | →
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− | | width=8% | d''X''<sup>•</sup>
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− | | width=4% | ⊆
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− | | width=8% | E''X''<sup>•</sup>
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− | | width=2% | )
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− | | width=4% | <math>\cong</math>
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− | | width=2% | (
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− | | width=16% | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | width=4% | →
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− | | width=8% | ['''D'''<sup>''k''</sup>]
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− | | width=4% | ⊆
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− | | width=16% | ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
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− | | width=2% | )
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− | |}
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− |
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− | ===Old===
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− |
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− | :{| cellpadding=1 style="height:40px"
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− | | <font face=georgia>'''W'''</font>
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− | | :
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− | | (
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− | | [
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− | | '''B'''<sup>''n''</sup>
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− | | ]
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− | | →
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− | | [
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− | | '''B'''<sup>''k''</sup>
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− | | ]
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− | | )
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− | |
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− | | →
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− | |
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− | | (
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− | | [
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− | | '''B'''<sup>''n''</sup>
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− | | ×
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− | | '''D'''<sup>''n''</sup>
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− | | ]
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− | | →
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− | | [
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− | | '''B'''<sup>''k''</sup>
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− | | ×
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− | | '''D'''<sup>''k''</sup>
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− | | ]
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− | | )
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− | | .
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− | |}
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− |
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− | :{| style="height:80px; text-align:center; width:90%"
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− | | align=left width=20%| Concrete type
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− | | width=4% | <math>\epsilon</math>
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | ''U''<sup>•</sup>
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− | | width=4% | →
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− | | width=8% | ''X''<sup>•</sup>
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− | | width=2% | )
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− | | width=8% | →
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− | | width=2% | (
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− | | width=16% | E''U''<sup>•</sup>
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− | | width=4% | →
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− | | width=8% | ''X''<sup>•</sup>
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− | | width=2% | )
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− | |-
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− | | align=left width=20%| Abstract type
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− | | width=4% | <math>\epsilon</math>
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | ['''B'''<sup>''n''</sup>]
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− | | width=4% | →
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− | | width=8% | ['''B'''<sup>''k''</sup>]
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− | | width=2% | )
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− | | width=8% | →
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− | | width=2% | (
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− | | width=16% | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | width=4% | →
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− | | width=8% | ['''B'''<sup>''k''</sup>]
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− | | width=2% | )
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− | |}
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− |
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− | :{| style="height:80px; text-align:center; width:90%"
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− | | align=left width=20%| Concrete type
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− | | width=4% | W
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | ''U''<sup>•</sup>
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− | | width=4% | →
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− | | width=8% | ''X''<sup>•</sup>
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− | | width=2% | )
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− | | width=8% | →
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− | | width=2% | (
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− | | width=16% | E''U''<sup>•</sup>
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− | | width=4% | →
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− | | width=8% | d''X''<sup>•</sup>
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− | | width=2% | )
| |
− | |-
| |
− | | align=left width=20%| Abstract type
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− | | width=4% | W
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | ['''B'''<sup>''n''</sup>]
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− | | width=4% | →
| |
− | | width=8% | ['''B'''<sup>''k''</sup>]
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− | | width=2% | )
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− | | width=8% | →
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− | | width=2% | (
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− | | width=16% | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | width=4% | →
| |
− | | width=8% | ['''D'''<sup>''k''</sup>]
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− | | width=2% | )
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− | |}
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− |
| |
− | :{| style="height:80px; text-align:center; width:90%"
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− | | width=6% | <math>\epsilon</math>''F''
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | E''U''<sup>•</sup>
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− | | width=4% | →
| |
− | | width=8% | ''X''<sup>•</sup>
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− | | width=4% | ⊆
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− | | width=8% | E''X''<sup>•</sup>
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− | | width=2% | )
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− | | width=4% | <math>\cong</math>
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− | | width=2% | (
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− | | width=16% | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | width=4% | →
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− | | width=8% | ['''B'''<sup>''k''</sup>]
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− | | width=4% | ⊆
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− | | width=16% | ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
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− | | width=2% | )
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− | |-
| |
− | | width=6% | W''F''
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− | | width=2% | :
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− | | width=2% | (
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− | | width=8% | E''U''<sup>•</sup>
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− | | width=4% | →
| |
− | | width=8% | d''X''<sup>•</sup>
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− | | width=4% | ⊆
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− | | width=8% | E''X''<sup>•</sup>
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− | | width=2% | )
| |
− | | width=4% | <math>\cong</math>
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− | | width=2% | (
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− | | width=16% | ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>]
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− | | width=4% | →
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− | | width=8% | ['''D'''<sup>''k''</sup>]
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− | | width=4% | ⊆
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− | | width=16% | ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
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− | | width=2% | )
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− | |}
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− |
| |
− | ==Epitext==
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− |
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− | {| cellpadding=12 style="height:100px; width:100%; text-align:left"
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− | |-
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− | | <font color=red size="7">'''''Rosebud'''''</font>
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− | |}
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− |
| |
− | {| cellpadding=12 style="height:100px; width:100%; text-align:center"
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− | |-
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− | | <font color=red size="7">'''''Rosebud'''''</font>
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− | |}
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− |
| |
− | {| cellpadding=12 style="height:100px; width:100%; text-align:right"
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− | |-
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− | | <font color=red size="7">'''''Rosebud'''''</font>
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− | |}
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− |
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− | ==Gallery==
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− |
| |
− | <center>
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− | <font size=7>’</font>
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− |
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− | <font size=7>`´</font>
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− |
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− | <font size=7>′</font>
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− |
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− | ‹ ›
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− |
| |
− | 〈 〉
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− |
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− | <font face=system>( )</font>
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− |
| |
− | <font face=system>(</font> , <font face=system>)</font>
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− | </center>
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− |
| |
− |
| |
− | {| border=1 cellpadding=10 cellspacing=2 width=100%
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− | | <font face="lucida calligraphy">A</font> = {''a''<sub>''i''</sub>} = {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>}
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− | |-
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− | | ''A'' = 〈<font face="lucida calligraphy">A</font>〉 = 〈''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>〉= {‹''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>›}
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− | |-
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− | | ''A''^ = (''A'' → '''B''')
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− | |-
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− | | ''A''<sup>•</sup> = [<font face="lucida calligraphy">A</font>] = [''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>]
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− | |}
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− | <br>
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− |
| |
− | {| border=1 cellpadding=10 cellspacing=2 width=100%
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− | | d<font face="lucida calligraphy">A</font> = {d''a''<sub>''i''</sub>} = {d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>}
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− | |-
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− | | d''A'' = 〈d<font face="lucida calligraphy">A</font>〉 = 〈d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>〉= {‹d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>›}
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− | |-
| |
− | | d''A''^ = (d''A'' → '''B''')
| |
− | |-
| |
− | | d''A''<sup>•</sup> = [d<font face="lucida calligraphy">A</font>] = [d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>]
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− | |}
| |
− | <br>
| |
− |
| |
− | {| border=1 cellpadding=10 cellspacing=2 width=100%
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− | | E<font face="lucida calligraphy">A</font> = <font face="lucida calligraphy">A</font> ∪ d<font face="lucida calligraphy">A</font> = {''a''<sub>''i''</sub>} ∪ {d''a''<sub>''i''</sub>} = {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>, d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>}
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− | |-
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− | | E''A'' = 〈E<font face="lucida calligraphy">A</font>〉 = 〈''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>, d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>〉= {‹''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>, d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>›}
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− | |-
| |
− | | E''A''^ = (E''A'' → '''B''')
| |
− | |-
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− | | E''A''<sup>•</sup> = [E<font face="lucida calligraphy">A</font>] = [''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>, d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>]
| |
− | |}
| |
− | <br>
| |
− |
| |
− | {| border=1 cellpadding=10 cellspacing=2 width=100%
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− | | <font face="lucida calligraphy">X</font> = {''x''<sub>''i''</sub>} = {''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>}
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− | |-
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− | | ''X'' = 〈<font face="lucida calligraphy">X</font>〉 = 〈''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>〉= {‹''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>›}
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− | |-
| |
− | | ''X''^ = (''X'' → '''B''')
| |
− | |-
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− | | ''X''<sup>•</sup> = [<font face="lucida calligraphy">X</font>] = [''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>]
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− | |}
| |
− | <br>
| |
− |
| |
− | {| border=1 cellpadding=10 cellspacing=2 width=100%
| |
− | | d<font face="lucida calligraphy">X</font> = {d''x''<sub>''i''</sub>} = {d''x''<sub>1</sub>, …, d''x''<sub>''n''</sub>}
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− | |-
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− | | d''X'' = 〈d<font face="lucida calligraphy">X</font>〉 = 〈d''x''<sub>1</sub>, …, d''x''<sub>''n''</sub>〉= {‹d''x''<sub>1</sub>, …, d''x''<sub>''n''</sub>›}
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− | |-
| |
− | | d''X''^ = (d''X'' → '''B''')
| |
− | |-
| |
− | | d''X''<sup>•</sup> = [d<font face="lucida calligraphy">X</font>] = [d''x''<sub>1</sub>, …, d''x''<sub>''n''</sub>]
| |
− | |}
| |
− | <br>
| |
− |
| |
− | {| border=1 cellpadding=10 cellspacing=2 width=100%
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− | | <font face="lucida calligraphy"><u>X</u></font> = {<u>''x''</u><sub>''i''</sub>} = {<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>}
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− | |-
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− | | <u>''X''</u> = 〈<font face="lucida calligraphy"><u>X</u></font>〉 = 〈<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>〉= {‹<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>›}
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− | |-
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− | | <u>''X''</u>^ = (<u>''X''</u> → '''B''')
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− | |-
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− | | <u>''X''</u><sup>•</sup> = [<font face="lucida calligraphy"><u>X</u></font>] = [<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>]
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− | |}
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− | <br>
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− |
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− | ''f'' : '''B'''<sup>''k''</sup> → '''B'''
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− | ''f'' : '''B'''<sup>''n''</sup> → '''B'''
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− |
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− | ''f''<sup>–1</sup>
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− |
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− | <font face="lucida calligraphy">Pow</font>(''X'') = 2<sup>''X''</sup>
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− |
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− | {| cellpadding=6
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− | | Arbitrary
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− | | →
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− | | '''B'''<sup>''n''</sup> → '''B'''
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− | | ''X'' → '''B'''
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− | |-
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− | | Basic
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− | | <font face=symbol>'''¸>'''</font>
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− | | '''B'''<sup>''n''</sup> <font face=symbol>'''¸>'''</font> '''B'''
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− | | ''X'' <font face=symbol>'''¸>'''</font> '''B'''
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− | |-
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− | | Linear
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− | | <font face=symbol>'''+>'''</font>
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− | | '''B'''<sup>''n''</sup> <font face=symbol>'''+>'''</font> '''B'''
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− | | ''X'' <font face=symbol>'''+>'''</font> '''B'''
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− | |-
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− | | Positive
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− | | <font face=symbol>'''¥>'''</font>
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− | | '''B'''<sup>''n''</sup> <font face=symbol>'''¥>'''</font> '''B'''
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− | | ''X'' <font face=symbol>'''¥>'''</font> '''B'''
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− | |-
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− | | Singular
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− | | <font face=symbol>'''××>'''</font>
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− | | '''B'''<sup>''n''</sup> <font face=symbol>'''××>'''</font> '''B'''
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− | | ''X'' <font face=symbol>'''××>'''</font> '''B'''
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− | |}
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− |
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− | The ''linear propositions'', {hom : '''B'''<sup>''n''</sup> → '''B'''} = ('''B'''<sup>''n''</sup> <font face=symbol>'''+>'''</font> '''B'''), may be expressed as sums of the following form:
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− |
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− | : <math>\textstyle \sum_{i=1}^n e_i = e_1 + \ldots + e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = 0.</math>
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− |
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− | The ''positive propositions'', {pos : '''B'''<sup>''n''</sup> → '''B'''} = ('''B'''<sup>''n''</sup> <font face=symbol>'''¥>'''</font> '''B'''), may be expressed as products of the following form:
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− |
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− | : <math>\textstyle \prod_{i=1}^n e_i = e_1 \cdot \ldots \cdot e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = 1.</math>
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− |
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− | The ''singular propositions'', {''x'' : '''B'''<sup>''n''</sup> → '''B'''} = ('''B'''<sup>''n''</sup> <font face=symbol>'''××>'''</font> '''B'''), may be expressed as products of the following form:
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− | : <math>\textstyle \prod_{i=1}^n e_i = e_1 \cdot \ldots \cdot e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = (a_i) = \lnot a_i.</math>
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− |
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− | <font face="lucida calligraphy">I</font> = {1, …, ''n''}.
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− | ''J'' ⊆ <font face="lucida calligraphy">I</font>
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− |
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− | <font face="lucida calligraphy">J ⊆ I</font>
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− | <font face="lucida calligraphy">A</font><sub>''J''</sub>
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− | <font face="lucida calligraphy">A<sub>J</sub></font>
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− | <font face="mt extra">l</font><sub>''J''</sub> : '''B'''<sup>''k''</sup> → '''B'''
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− | <math>\ell_J : \mathbb{B}^k \to \mathbb{B}</math>
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− | θ : ('''K'''<sup>''n''</sup> → '''K''') → '''K'''
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− |
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− | <math>\theta</math> : ('''K'''<sup>''n''</sup> → '''K''') → '''K'''
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− |
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− | <math>\theta\!</math> : ('''K'''<sup>''n''</sup> → '''K''') → '''K'''
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− |
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− | <math>\vartheta</math> : ('''K'''<sup>''n''</sup> → '''K''') → '''K'''
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− | <math>\vartheta\!</math> : ('''K'''<sup>''n''</sup> → '''K''') → '''K'''
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− |
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− | <math>\chi\!</math> : ''X'' → <math>\bigcup_x \ \chi_x\!</math>
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− | <math>\chi\!</math> : '''K'''<sup>''n''</sup> → (('''K'''<sup>''n''</sup> → '''K''') → '''K''')
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− | <math>\chi\!</math> : ('''K'''<sup>''n''</sup> → '''K''') → ('''K'''<sup>''n''</sup> → '''K''')
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− |
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− | <math>\cong</math>
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− |
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− | <math>\lceil x \rceil</math>
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− |
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− | {| cellpadding=6
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− | | <u>''x''</u><sub>''i''</sub>(''x'')
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− | | χ(''x'' ∈ ''L''<sub>''i''</sub>)
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− | | <math>\lceil x \in L_i \rceil</math>
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− | | ''L''<sub>''i''</sub>(''x'')
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− | |-
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− | | <u>''x''</u><sub>''i''</sub>(''x'')
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− | | <math>\chi (x \in L_i)</math>
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− | | <math>\lceil x \in L_i \rceil</math>
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− | | ''L''<sub>''i''</sub>(''x'')
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− | |}
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− | {| cellpadding=4
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− | | ‹0, 0, 0›
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− | | <font face=system>‹0, 0, 0›</font>
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− | |-
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− | | ‹0, 0, 1›
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− | | <font face=system>‹0, 0, 1›</font>
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− | |-
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− | | ‹0, 1, 0›
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− | | <font face=system>‹0, 1, 0›</font>
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− | |-
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− | | ‹0, 1, 1›
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− | | <font face=system>‹0, 1, 1›</font>
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− | |-
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− | | ‹1, 0, 0›
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− | | <font face=system>‹1, 0, 0›</font>
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− | |-
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− | | ‹1, 0, 1›
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− | | <font face=system>‹1, 0, 1›</font>
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− | |-
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− | | ‹1, 1, 0›
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− | | <font face=system>‹1, 1, 0›</font>
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− | |-
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− | | ‹1, 1, 1›
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− | | <font face=system>‹1, 1, 1›</font>
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− | |}
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