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

Revision as of 19:52, 18 June 2008

12 bytes removed ,  19:52, 18 June 2008
→‎Detail of Calculation for the Difference Map: fill table
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| height="60px" |
 
| height="60px" |
 
<math>\begin{smallmatrix}
 
<math>\begin{smallmatrix}
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   & x  &  y & \operatorname{d}x & \operatorname{d}y \\
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   &   x  &  y   & \operatorname{d}x & \operatorname{d}y \\
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+ & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\
+
+ & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\
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= &     &     & \operatorname{d}x & \operatorname{d}y \\
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   &  x  & (y) & \operatorname{d}x & \operatorname{d}y \\
 
   &  x  & (y) & \operatorname{d}x & \operatorname{d}y \\
 
+ & (x) &  y  & \operatorname{d}x & \operatorname{d}y \\
 
+ & (x) &  y  & \operatorname{d}x & \operatorname{d}y \\
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= &     &     & \operatorname{d}x & \operatorname{d}y \\
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= & (x, & y) & \operatorname{d}x & \operatorname{d}y \\
 
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   & (x) &  y  & \operatorname{d}x & \operatorname{d}y \\
 
   & (x) &  y  & \operatorname{d}x & \operatorname{d}y \\
 
+ &  x  & (y) & \operatorname{d}x & \operatorname{d}y \\
 
+ &  x  & (y) & \operatorname{d}x & \operatorname{d}y \\
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= &     &     & \operatorname{d}x & \operatorname{d}y \\
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| height="60px" |
 
| height="60px" |
 
<math>\begin{smallmatrix}
 
<math>\begin{smallmatrix}
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   & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\
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   & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\
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+ & x  &  y & \operatorname{d}x & \operatorname{d}y \\
+
+ &   x  &  y   & \operatorname{d}x & \operatorname{d}y \\
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= &     &     & \operatorname{d}x & \operatorname{d}y \\
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= & ((x, & y)) & \operatorname{d}x & \operatorname{d}y \\
 
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Line 4,564: Line 4,564:  
   &  x  & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
   &  x  & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\
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= &    &     & \operatorname{d}x & (\operatorname{d}y) \\
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= &    & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
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Line 4,571: Line 4,571:  
   &  x  &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
   &  x  &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & (x) &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & (x) &  y  & \operatorname{d}x & (\operatorname{d}y) \\
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= &    &     & \operatorname{d}x & (\operatorname{d}y) \\
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Line 4,578: Line 4,578:  
   & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
   & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
+ &  x  & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
+ &  x  & (y) & \operatorname{d}x & (\operatorname{d}y) \\
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= &    &     & \operatorname{d}x & (\operatorname{d}y) \\
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   & (x) &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
   & (x) &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
+ &  x  &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
+ &  x  &  y  & \operatorname{d}x & (\operatorname{d}y) \\
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= &    &     & \operatorname{d}x & (\operatorname{d}y) \\
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= &    & y  & \operatorname{d}x & (\operatorname{d}y) \\
 
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Line 4,595: Line 4,595:  
   & (x) &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
   & (x) &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\
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= &     &    & (\operatorname{d}x) & \operatorname{d}y \\
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|-
 
|-
Line 4,602: Line 4,602:  
   & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
   & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & (x) &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & (x) &  y  & (\operatorname{d}x) & \operatorname{d}y \\
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= &     &    & (\operatorname{d}x) & \operatorname{d}y \\
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|-
 
|-
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   &  x  &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
   &  x  &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
+ &  x  & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
+ &  x  & (y) & (\operatorname{d}x) & \operatorname{d}y \\
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= &     &    & (\operatorname{d}x) & \operatorname{d}y \\
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|-
 
|-
Line 4,616: Line 4,616:  
   &  x  & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
   &  x  & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
+ &  x  &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
+ &  x  &  y  & (\operatorname{d}x) & \operatorname{d}y \\
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= &     &    & (\operatorname{d}x) & \operatorname{d}y \\
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Line 4,624: Line 4,624:  
| height="60px" |
 
| height="60px" |
 
<math>\begin{smallmatrix}
 
<math>\begin{smallmatrix}
−
   & (x) & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
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   & (x) (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
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+ & (x) & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+
+ & (x) (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
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= &     &    & (\operatorname{d}x) & (\operatorname{d}y) \\
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|-
 
|-
 
| height="60px" |
 
| height="60px" |
 
<math>\begin{smallmatrix}
 
<math>\begin{smallmatrix}
−
   & (x) &  y  & (\operatorname{d}x) & (\operatorname{d}y) \\
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   & (x)\ y  & (\operatorname{d}x) & (\operatorname{d}y) \\
−
+ & (x) &  y  & (\operatorname{d}x) & (\operatorname{d}y) \\
+
+ & (x)\ y  & (\operatorname{d}x) & (\operatorname{d}y) \\
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= &     &    & (\operatorname{d}x) & (\operatorname{d}y) \\
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|-
 
|-
 
| height="60px" |
 
| height="60px" |
 
<math>\begin{smallmatrix}
 
<math>\begin{smallmatrix}
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   &  x & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
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   &  x\ (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−
+ &  x & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+
+ &  x\ (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−
= &     &    & (\operatorname{d}x) & (\operatorname{d}y) \\
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|-
 
|-
 
| height="60px" |
 
| height="60px" |
 
<math>\begin{smallmatrix}
 
<math>\begin{smallmatrix}
−
   &  x & y  & (\operatorname{d}x) & (\operatorname{d}y) \\
+
   &  x\ y  & (\operatorname{d}x) & (\operatorname{d}y) \\
−
+ &  x & y  & (\operatorname{d}x) & (\operatorname{d}y) \\
+
+ &  x\ y  & (\operatorname{d}x) & (\operatorname{d}y) \\
−
= &     &    & (\operatorname{d}x) & (\operatorname{d}y) \\
+
= &   0    & (\operatorname{d}x) & (\operatorname{d}y) \\
 
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Line 4,665: Line 4,665:  
   &  x  & & \operatorname{d}x & \operatorname{d}y \\
 
   &  x  & & \operatorname{d}x & \operatorname{d}y \\
 
+ & (x) & & \operatorname{d}x & \operatorname{d}y \\
 
+ & (x) & & \operatorname{d}x & \operatorname{d}y \\
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= &     & & \operatorname{d}x & \operatorname{d}y \\
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= & 1  & & \operatorname{d}x & \operatorname{d}y \\
 
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|-
 
|-
Line 4,672: Line 4,672:  
   & (x) & & \operatorname{d}x & \operatorname{d}y \\
 
   & (x) & & \operatorname{d}x & \operatorname{d}y \\
 
+ &  x  & & \operatorname{d}x & \operatorname{d}y \\
 
+ &  x  & & \operatorname{d}x & \operatorname{d}y \\
−
= &     & & \operatorname{d}x & \operatorname{d}y \\
+
= & 1  & & \operatorname{d}x & \operatorname{d}y \\
 
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|}
Line 4,682: Line 4,682:  
   &  x  & & \operatorname{d}x & (\operatorname{d}y) \\
 
   &  x  & & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & (x) & & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & (x) & & \operatorname{d}x & (\operatorname{d}y) \\
−
= &     & & \operatorname{d}x & (\operatorname{d}y) \\
+
= & 1  & & \operatorname{d}x & (\operatorname{d}y) \\
 
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|-
 
|-
Line 4,689: Line 4,689:  
   & (x) & & \operatorname{d}x & (\operatorname{d}y) \\
 
   & (x) & & \operatorname{d}x & (\operatorname{d}y) \\
 
+ &  x  & & \operatorname{d}x & (\operatorname{d}y) \\
 
+ &  x  & & \operatorname{d}x & (\operatorname{d}y) \\
−
= &     & & \operatorname{d}x & (\operatorname{d}y) \\
+
= & 1  & & \operatorname{d}x & (\operatorname{d}y) \\
 
\end{smallmatrix}</math>
 
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|}
 
|}
Line 4,699: Line 4,699:  
   & (x) & & (\operatorname{d}x) & \operatorname{d}y \\
 
   & (x) & & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & (x) & & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & (x) & & (\operatorname{d}x) & \operatorname{d}y \\
−
= &     & & (\operatorname{d}x) & \operatorname{d}y \\
+
= & 0  & & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
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|-
 
|-
Line 4,706: Line 4,706:  
   &  x  & & (\operatorname{d}x) & \operatorname{d}y \\
 
   &  x  & & (\operatorname{d}x) & \operatorname{d}y \\
 
+ &  x  & & (\operatorname{d}x) & \operatorname{d}y \\
 
+ &  x  & & (\operatorname{d}x) & \operatorname{d}y \\
−
= &     & & (\operatorname{d}x) & \operatorname{d}y \\
+
= & 0  & & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
Line 4,716: Line 4,716:  
   & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
   & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\
−
= &     & & (\operatorname{d}x) & (\operatorname{d}y) \\
+
= & 0  & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
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   &  x  & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
   &  x  & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ &  x  & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ &  x  & & (\operatorname{d}x) & (\operatorname{d}y) \\
−
= &     & & (\operatorname{d}x) & (\operatorname{d}y) \\
+
= & 0  & & (\operatorname{d}x) & (\operatorname{d}y) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
Jon Awbrey
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