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

Revision as of 21:02, 18 June 2008

24 bytes removed ,  21:02, 18 June 2008
→‎Detail of Calculation for the Difference Map: finish table
Line 4,817: Line 4,817:  
   & &  y  & \operatorname{d}x & \operatorname{d}y \\
 
   & &  y  & \operatorname{d}x & \operatorname{d}y \\
 
+ & & (y) & \operatorname{d}x & \operatorname{d}y \\
 
+ & & (y) & \operatorname{d}x & \operatorname{d}y \\
−
= & &     & \operatorname{d}x & \operatorname{d}y \\
+
= & & 1  & \operatorname{d}x & \operatorname{d}y \\
 
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|-
 
|-
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   & & (y) & \operatorname{d}x & \operatorname{d}y \\
 
   & & (y) & \operatorname{d}x & \operatorname{d}y \\
 
+ & &  y  & \operatorname{d}x & \operatorname{d}y \\
 
+ & &  y  & \operatorname{d}x & \operatorname{d}y \\
−
= & &     & \operatorname{d}x & \operatorname{d}y \\
+
= & & 1  & \operatorname{d}x & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
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   & & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
   & & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & & (y) & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & & (y) & \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 4,841: Line 4,841:  
   & &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
   & &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & &  y  & \operatorname{d}x & (\operatorname{d}y) \\
 
+ & &  y  & \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 4,851: Line 4,851:  
   & &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
   & &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & & (y) & (\operatorname{d}x) & \operatorname{d}y \\
−
= & &     & (\operatorname{d}x) & \operatorname{d}y \\
+
= & & 1  & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,858: Line 4,858:  
   & & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
   & & (y) & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & &  y  & (\operatorname{d}x) & \operatorname{d}y \\
 
+ & &  y  & (\operatorname{d}x) & \operatorname{d}y \\
−
= & &     & (\operatorname{d}x) & \operatorname{d}y \\
+
= & & 1  & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
Line 4,868: Line 4,868:  
   & & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
 
   & & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ & & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ & & (y) & (\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 4,875: Line 4,875:  
   & &  y  & (\operatorname{d}x) & (\operatorname{d}y) \\
 
   & &  y  & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ & &  y  & (\operatorname{d}x) & (\operatorname{d}y) \\
 
+ & &  y  & (\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 4,897: Line 4,897:  
   & ((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 \\
+
= & ((x, & y)) & \operatorname{d}x & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,904: Line 4,904:  
   & ((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 \\
+
= & (x, & y)  & \operatorname{d}x & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,911: Line 4,911:  
   &  (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 \\
+
= & (x, & y)  & \operatorname{d}x & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,918: Line 4,918:  
   &  (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 \\
+
= & ((x, & y)) & \operatorname{d}x & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
Line 4,928: Line 4,928:  
   & ((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) \\
+
= &      & y  & \operatorname{d}x & (\operatorname{d}y) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,935: Line 4,935:  
   & ((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) \\
+
= &      & (y)  & \operatorname{d}x & (\operatorname{d}y) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,942: Line 4,942:  
   &  (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) \\
+
= &      & y  & \operatorname{d}x & (\operatorname{d}y) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,949: Line 4,949:  
   &  (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) \\
+
= &      & (y)  & \operatorname{d}x & (\operatorname{d}y) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
Line 4,959: Line 4,959:  
   & (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 \\
+
= & x  &      & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,966: Line 4,966:  
   & (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 \\
+
= & x  &      & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,973: Line 4,973:  
   & ((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 \\
+
= & (x) &      & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
Line 4,980: Line 4,980:  
   & ((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 \\
+
= & (x) &      & (\operatorname{d}x) & \operatorname{d}y \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
Line 4,988: Line 4,988:  
| 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) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
 
| 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) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
 
| 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) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|-
 
|-
 
| 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) \\
 
\end{smallmatrix}</math>
 
\end{smallmatrix}</math>
 
|}
 
|}
Jon Awbrey
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