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Directory:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 15:54, 17 June 2009
, 15:54, 17 June 2009→Note 22: use \texttt{...} for logical ops
<math>\begin{array}{rcccccc}
<math>\begin{array}{rcccccc}
\operatorname{E}(pq)
\operatorname{E}(pq)
& = & p & \cdot & q & \cdot & (\operatorname{d}p)(\operatorname{d}q)
& = &
p
& \cdot &
q
& \cdot &
\texttt{(} \operatorname{d}p \texttt{)}
\texttt{(} \operatorname{d}q \texttt{)}
\\[4pt]
\\[4pt]
& + & p & \cdot & (q) & \cdot & (\operatorname{d}p)~\operatorname{d}q~
& + &
p
& \cdot &
\texttt{(} q \texttt{)}
& \cdot &
\texttt{(} \operatorname{d}p \texttt{)}
\texttt{~} \operatorname{d}q \texttt{~}
\\[4pt]
\\[4pt]
& + & (p) & \cdot & q & \cdot & ~\operatorname{d}p~(\operatorname{d}q)
& + &
\texttt{(} p \texttt{)}
& \cdot &
q
& \cdot &
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{(} \operatorname{d}q \texttt{)}
\\[4pt]
\\[4pt]
& + & (p) & \cdot & (q) & \cdot & ~\operatorname{d}p~~\operatorname{d}q~\end{array}</math>
& + &
\texttt{(} p \texttt{)}
& \cdot &
\texttt{(} q \texttt{)}
& \cdot &
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{~} \operatorname{d}q \texttt{~}
\end{array}</math>
|}
|}
<math>\begin{array}{rcccccc}
<math>\begin{array}{rcccccc}
\operatorname{D}(pq)
\operatorname{D}(pq)
& = & p & \cdot & q & \cdot & ((\operatorname{d}p)(\operatorname{d}q))
& = &
p
& \cdot &
q
& \cdot &
\texttt{(}
\texttt{(} \operatorname{d}p \texttt{)}
\texttt{(} \operatorname{d}q \texttt{)}
\texttt{)}
\\[4pt]
\\[4pt]
& + & p & \cdot & (q) & \cdot & ~(\operatorname{d}p)~\operatorname{d}q~~
& + &
p
& \cdot &
\texttt{(} q \texttt{)}
& \cdot &
\texttt{~}
\texttt{(} \operatorname{d}p \texttt{)}
\texttt{~} \operatorname{d}q \texttt{~}
\texttt{~}
\\[4pt]
\\[4pt]
& + & (p) & \cdot & q & \cdot & ~~\operatorname{d}p~(\operatorname{d}q)~
& + &
\texttt{(} p \texttt{)}
& \cdot &
q
& \cdot &
\texttt{~}
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{(} \operatorname{d}q \texttt{)}
\texttt{~}
\\[4pt]
\\[4pt]
& + & (p) & \cdot & (q) & \cdot & ~~\operatorname{d}p~~\operatorname{d}q~~
& + &
\texttt{(} p \texttt{)}
& \cdot &
\texttt{(}q \texttt{)}
& \cdot &
\texttt{~}
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{~} \operatorname{d}q \texttt{~}
\texttt{~}
\end{array}</math>
\end{array}</math>
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|}