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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)

Revision as of 20:02, 12 November 2012

3,417 bytes added ,  20:02, 12 November 2012
→‎6.27. Differential Logic and Group Operations: format tables
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<br>
 
<br>
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<pre>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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Table 43.1 The Differential Group G = V4
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|+ style="height:30px" |
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Abstract Logical Active Active Genetic
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<math>\text{Table 71.1} ~~ \text{The Differential Group} ~ G = V_4\!</math>
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Element Element List Term Element
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|- style="background:#f0f0ff"
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1 (dm)(dn) <d!> d! 1
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| width="16%" | <math>\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}</math>
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r dm (dn) <dm> dm! dm
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| width="36%" | <math>\begin{matrix} \text{Logical}  \\ \text{Element} \end{matrix}</math>
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s (dm) dn <dn> dn! dn
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| width="16%" | <math>\begin{matrix} \text{Active}  \\ \text{List}    \end{matrix}</math>
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t dm  dn <d*> d* dm*dn
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| width="16%" | <math>\begin{matrix} \text{Active}  \\ \text{Term}    \end{matrix}</math>
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</pre>
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| width="16%" | <math>\begin{matrix} \text{Genetic}  \\ \text{Element} \end{matrix}</math>
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|-
 +
| valign="bottom" |
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<math>\begin{matrix}
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1
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\\[4pt]
 +
r
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\\[4pt]
 +
s
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\\[4pt]
 +
t
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\end{matrix}</math>
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| valign="bottom" |
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<math>\begin{matrix}
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(\operatorname{d}\text{m})
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(\operatorname{d}\text{n})
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\\[4pt]
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~\operatorname{d}\text{m}~
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(\operatorname{d}\text{n})
 +
\\[4pt]
 +
(\operatorname{d}\text{m})
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~\operatorname{d}\text{n}~
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\\[4pt]
 +
~\operatorname{d}\text{m}~
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~\operatorname{d}\text{n}~
 +
\end{matrix}</math>
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| valign="bottom" |
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<math>\begin{matrix}
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\langle\operatorname{d}!\rangle
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\\[4pt]
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\langle\operatorname{d}\text{m}\rangle
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\\[4pt]
 +
\langle\operatorname{d}\text{n}\rangle
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\\[4pt]
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\langle\operatorname{d}*\rangle
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\end{matrix}</math>
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| valign="bottom" |
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<math>\begin{matrix}
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\operatorname{d}!
 +
\\[4pt]
 +
\operatorname{d}\text{m}!
 +
\\[4pt]
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\operatorname{d}\text{n}!
 +
\\[4pt]
 +
\operatorname{d}*
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\end{matrix}</math>
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| valign="bottom" |
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<math>\begin{matrix}
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1
 +
\\[4pt]
 +
\operatorname{d}_{\text{m}}
 +
\\[4pt]
 +
\operatorname{d}_{\text{n}}
 +
\\[4pt]
 +
\operatorname{d}_{\text{m}} * \operatorname{d}_{\text{n}}
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\end{matrix}</math>
 +
|}
   −
<pre>
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<br>
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Table 43.2  Cosets of Gm in G
  −
Group Logical Logical Group
  −
Coset Coset Element Element
  −
Gm (dm) (dm)(dn) 1
  −
(dm) dn dn
  −
Gm*dm dm dm (dn) dm
  −
dm  dn dn*dm
  −
</pre>
     −
<pre>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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Table 43.3  Cosets of Gn in G
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|+ style="height:30px" |
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Group Logical Logical Group
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<math>\text{Table 71.2} ~~ \text{Cosets of} ~ G_\text{m} ~ \text{in} ~ G\!</math>
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Coset Coset Element Element
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|- style="background:#f0f0ff"
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Gn (dn) (dm)(dn) 1
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| width="25%" | <math>\text{Group Coset}\!</math>
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dm (dn) dm
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| width="25%" | <math>\text{Logical Coset}\!</math>
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Gn*dn dn (dm) dn dn
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| width="25%" | <math>\text{Logical Element}\!</math>
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dm  dn dm*dn
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| width="25%" | <math>\text{Group Element}\!</math>
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</pre>
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|-
 +
| <math>G_\text{m}\!</math>
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| <math>(\operatorname{d}\text{m})\!</math>
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|
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<math>\begin{matrix}
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(\operatorname{d}\text{m})(\operatorname{d}\text{n})
 +
\\[4pt]
 +
(\operatorname{d}\text{m})~\operatorname{d}\text{n}~
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\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
1
 +
\\[4pt]
 +
\operatorname{d}_\text{n}
 +
\end{matrix}</math>
 +
|-
 +
| <math>G_\text{m} * \operatorname{d}_\text{m}\!</math>
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| <math>\operatorname{d}\text{m}\!</math>
 +
|
 +
<math>\begin{matrix}
 +
~\operatorname{d}\text{m}~(\operatorname{d}\text{n})
 +
\\[4pt]
 +
~\operatorname{d}\text{m}~~\operatorname{d}\text{n}~
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
\operatorname{d}_\text{m}
 +
\\[4pt]
 +
\operatorname{d}_\text{n} * \operatorname{d}_\text{m}
 +
\end{matrix}</math>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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|+ style="height:30px" |
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<math>\text{Table 71.3} ~~ \text{Cosets of} ~ G_\text{n} ~ \text{in} ~ G\!</math>
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|- style="background:#f0f0ff"
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| width="25%" | <math>\text{Group Coset}\!</math>
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| width="25%" | <math>\text{Logical Coset}\!</math>
 +
| width="25%" | <math>\text{Logical Element}\!</math>
 +
| width="25%" | <math>\text{Group Element}\!</math>
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|-
 +
| <math>G_\text{n}\!</math>
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| <math>(\operatorname{d}\text{n})\!</math>
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|
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<math>\begin{matrix}
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(\operatorname{d}\text{m})(\operatorname{d}\text{n})
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\\[4pt]
 +
~\operatorname{d}\text{m}~(\operatorname{d}\text{n})
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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1
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\\[4pt]
 +
\operatorname{d}_\text{m}
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\end{matrix}</math>
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|-
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| <math>G_\text{n} * \operatorname{d}_\text{n}\!</math>
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| <math>\operatorname{d}\text{n}\!</math>
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|
 +
<math>\begin{matrix}
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(\operatorname{d}\text{m})~\operatorname{d}\text{n}~
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\\[4pt]
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~\operatorname{d}\text{m}~~\operatorname{d}\text{n}~
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\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
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\operatorname{d}_\text{n}
 +
\\[4pt]
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\operatorname{d}_\text{m} * \operatorname{d}_\text{n}
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\end{matrix}</math>
 +
|}
 +
 
 +
<br>
    
===6.28. The Bridge : From Obstruction to Opportunity===
 
===6.28. The Bridge : From Obstruction to Opportunity===
Jon Awbrey
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