Difference between revisions of "User:Jon Awbrey/GRAPHICS"
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& + & (p) & \cdot & (q) & \cdot & ~\operatorname{d}p~~\operatorname{d}q~\end{array}</math> | & + & (p) & \cdot & (q) & \cdot & ~\operatorname{d}p~~\operatorname{d}q~\end{array}</math> | ||
| + | |} | ||
| + | |||
| + | {| align="center" cellspacing="10" style="text-align:center" | ||
| + | | [[Image:Field Picture PQ Difference Conjunction.jpg|500px]] | ||
| + | |- | ||
| + | | <math>\text{Figure 22-c. Difference}~ \operatorname{D}(pq) : \operatorname{E}X \to \mathbb{B}</math> | ||
| + | |- | ||
| + | | | ||
| + | <math>\begin{array}{rcccccc} | ||
| + | \operatorname{D}(pq) | ||
| + | & = & p & \cdot & q & \cdot & ((\operatorname{d}p)(\operatorname{d}q)) | ||
| + | \\[4pt] | ||
| + | & + & p & \cdot & (q) & \cdot & ~(\operatorname{d}p)~\operatorname{d}q~~ | ||
| + | \\[4pt] | ||
| + | & + & (p) & \cdot & q & \cdot & ~~\operatorname{d}p~(\operatorname{d}q)~ | ||
| + | \\[4pt] | ||
| + | & + & (p) & \cdot & (q) & \cdot & ~~\operatorname{d}p~~\operatorname{d}q~~ | ||
| + | \end{array}</math> | ||
|} | |} | ||
Revision as of 19:48, 16 June 2009
Differential Logic
ASCII Graphics
o-------------------------------------------------o | | | | | o-------------o o-------------o | | / \ / \ | | / o \ | | / /%\ \ | | / /%%%\ \ | | o o%%%%%o o | | | |%%%%%| | | | | P |%%%%%| Q | | | | |%%%%%| | | | o o%%%%%o o | | \ \%%%/ / | | \ \%/ / | | \ o / | | \ / \ / | | o-------------o o-------------o | | | | | o-------------------------------------------------o | f = p q | o-------------------------------------------------o Figure 22-a. Conjunction pq : X -> B |
o-------------------------------------------------o | | | | | o-------------o o-------------o | | / \ / \ | | / P o Q \ | | / /%\ \ | | / /%%%\ \ | | o o.->-.o o | | | p(q)(dp)dq |%\%/%| (p)q dp(dq) | | | | o---------------|->o<-|---------------o | | | | |%%^%%| | | | o o%%|%%o o | | \ \%|%/ / | | \ \|/ / | | \ o / | | \ /|\ / | | o-------------o | o-------------o | | | | | | | | | | | o | | (p)(q) dp dq | | | o-------------------------------------------------o | f = p q | o-------------------------------------------------o | | | Ef = p q (dp)(dq) | | | | + p (q) (dp) dq | | | | + (p) q dp (dq) | | | | + (p)(q) dp dq | | | o-------------------------------------------------o Figure 22-b. Enlargement E[pq] : EX -> B |
o-------------------------------------------------o | | | | | o-------------o o-------------o | | / \ / \ | | / P o Q \ | | / /%\ \ | | / /%%%\ \ | | o o%%%%%o o | | | (dp)dq |%%%%%| dp(dq) | | | | o<--------------|->o<-|-------------->o | | | | |%%^%%| | | | o o%%|%%o o | | \ \%|%/ / | | \ \|/ / | | \ o / | | \ /|\ / | | o-------------o | o-------------o | | | | | | | | v | | o | | dp dq | | | o-------------------------------------------------o | f = p q | o-------------------------------------------------o | | | Df = p q ((dp)(dq)) | | | | + p (q) (dp) dq | | | | + (p) q dp (dq) | | | | + (p)(q) dp dq | | | o-------------------------------------------------o Figure 22-c. Difference D[pq] : EX -> B |
JPEG Graphics
|
| \(\text{Figure 22-a. Conjunction}~ pq : X \to \mathbb{B}\) |
|
| \(\text{Figure 22-b. Enlargement}~ \operatorname{E}(pq) : \operatorname{E}X \to \mathbb{B}\) |
|
\(\begin{array}{rcccccc} \operatorname{E}(pq) & = & p & \cdot & q & \cdot & (\operatorname{d}p)(\operatorname{d}q) \\[4pt] & + & p & \cdot & (q) & \cdot & (\operatorname{d}p)~\operatorname{d}q~ \\[4pt] & + & (p) & \cdot & q & \cdot & ~\operatorname{d}p~(\operatorname{d}q) \\[4pt] & + & (p) & \cdot & (q) & \cdot & ~\operatorname{d}p~~\operatorname{d}q~\end{array}\) |
|
| \(\text{Figure 22-c. Difference}~ \operatorname{D}(pq) : \operatorname{E}X \to \mathbb{B}\) |
|
\(\begin{array}{rcccccc} \operatorname{D}(pq) & = & p & \cdot & q & \cdot & ((\operatorname{d}p)(\operatorname{d}q)) \\[4pt] & + & p & \cdot & (q) & \cdot & ~(\operatorname{d}p)~\operatorname{d}q~~ \\[4pt] & + & (p) & \cdot & q & \cdot & ~~\operatorname{d}p~(\operatorname{d}q)~ \\[4pt] & + & (p) & \cdot & (q) & \cdot & ~~\operatorname{d}p~~\operatorname{d}q~~ \end{array}\) |
