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Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)

Revision as of 14:44, 31 May 2008

7,652 bytes added ,  14:44, 31 May 2008
→‎Work Area 1: abstract orbit table template
Line 3,480: Line 3,480:     
=Work Area 1=
 
=Work Area 1=
 +
 +
==Orbit Table Template==
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{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 +
|+ '''Orbit Table Template'''
 +
|- style="background:ghostwhite; height:36px"
 +
|  
 +
| <math>f\!</math>
 +
| <math>\operatorname{F}f|_{xy}</math>
 +
| <math>\operatorname{F}f|_{x(y)}</math>
 +
| <math>\operatorname{F}f|_{(x)y}</math>
 +
| <math>\operatorname{F}f|_{(x)(y)}</math>
 +
|- style="height:36px"
 +
| <math>f_{0}\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{1}\!</math>
 +
|-
 +
| height="36px" | <math>f_{2}\!</math>
 +
|-
 +
| height="36px" | <math>f_{4}\!</math>
 +
|-
 +
| height="36px" | <math>f_{8}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)(y)\!</math>
 +
|-
 +
| height="36px" | <math>(x)\ y\!</math>
 +
|-
 +
| height="36px" | <math>x\ (y)\!</math>
 +
|-
 +
| height="36px" | <math>x\ y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{3}\!</math>
 +
|-
 +
| height="36px" | <math>f_{12}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)\!</math>
 +
|-
 +
| height="36px" | <math>x\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{6}\!</math>
 +
|-
 +
| height="36px" | <math>f_{9}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x,\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x,\ y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{5}\!</math>
 +
|-
 +
| height="36px" | <math>f_{10}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(y)\!</math>
 +
|-
 +
| height="36px" | <math>y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
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|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{7}\!</math>
 +
|-
 +
| height="36px" | <math>f_{11}\!</math>
 +
|-
 +
| height="36px" | <math>f_{13}\!</math>
 +
|-
 +
| height="36px" | <math>f_{14}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x\ y)\!</math>
 +
|-
 +
| height="36px" | <math>(x\ (y))\!</math>
 +
|-
 +
| height="36px" | <math>((x)\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x)(y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|- style="height:36px"
 +
| <math>f_{15}\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
|}
 +
<br>
    
==Propositional Forms on Two Variables==
 
==Propositional Forms on Two Variables==
Line 3,786: Line 4,077:  
| <p><math>(~)\!</math></p>
 
| <p><math>(~)\!</math></p>
 
| <p><math>\operatorname{false}</math></p>
 
| <p><math>\operatorname{false}</math></p>
−
| <p><math>0\!</math></p>
+
| <p><math>1\!</math></p>
 
|-
 
|-
 
|
 
|
Line 4,409: Line 4,700:  
o------o------------o------------o------------o------------o------------o
 
o------o------------o------------o------------o------------o------------o
 
</pre>
 
</pre>
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 +
|+ '''Table 4.  <math>\operatorname{D}f</math> Expanded Over Ordinary Features <math>\{ x, y \}\!</math>'''
 +
|- style="background:ghostwhite; height:36px"
 +
| &nbsp;
 +
| <math>f\!</math>
 +
| <math>\operatorname{D}f|_{xy}</math>
 +
| <math>\operatorname{D}f|_{x(y)}</math>
 +
| <math>\operatorname{D}f|_{(x)y}</math>
 +
| <math>\operatorname{D}f|_{(x)(y)}</math>
 +
|- style="height:36px"
 +
| <math>f_{0}\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{1}\!</math>
 +
|-
 +
| height="36px" | <math>f_{2}\!</math>
 +
|-
 +
| height="36px" | <math>f_{4}\!</math>
 +
|-
 +
| height="36px" | <math>f_{8}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)(y)\!</math>
 +
|-
 +
| height="36px" | <math>(x)\ y\!</math>
 +
|-
 +
| height="36px" | <math>x\ (y)\!</math>
 +
|-
 +
| height="36px" | <math>x\ y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{3}\!</math>
 +
|-
 +
| height="36px" | <math>f_{12}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)\!</math>
 +
|-
 +
| height="36px" | <math>x\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{6}\!</math>
 +
|-
 +
| height="36px" | <math>f_{9}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x,\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x,\ y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{5}\!</math>
 +
|-
 +
| height="36px" | <math>f_{10}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(y)\!</math>
 +
|-
 +
| height="36px" | <math>y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{7}\!</math>
 +
|-
 +
| height="36px" | <math>f_{11}\!</math>
 +
|-
 +
| height="36px" | <math>f_{13}\!</math>
 +
|-
 +
| height="36px" | <math>f_{14}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x\ y)\!</math>
 +
|-
 +
| height="36px" | <math>(x\ (y))\!</math>
 +
|-
 +
| height="36px" | <math>((x)\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x)(y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|- style="height:36px"
 +
| <math>f_{15}\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
| <math>((~))\!</math>
 +
|}
 +
<br>
    
===Table 5===
 
===Table 5===
Jon Awbrey
12,080

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/67575"

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