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Directory:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 23:38, 17 June 2009
, 23:38, 17 June 2009→Note 26: markup
To understand the extended interpretations, that is, the conjunctions of basic and differential features that are being indicated here, it may help to note the following equivalences:
To understand the extended interpretations, that is, the conjunctions of basic and differential features that are being indicated here, it may help to note the following equivalences:
<pre>
{| align="center" cellspacing="10" style="text-align:center"
|
<math>\begin{matrix}
\texttt{(}
\operatorname{d}p
\texttt{,}
</pre>
\operatorname{d}q
\texttt{)}
& = &
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{(} \operatorname{d}q \texttt{)}
& + &
\texttt{(} \operatorname{d}p \texttt{)}
\texttt{~} \operatorname{d}q \texttt{~}
\\[4pt]
dp
& = &
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{~} \operatorname{d}q \texttt{~}
& + &
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{(} \operatorname{d}q \texttt{)}
\\[4pt]
\operatorname{d}q
& = &
\texttt{~} \operatorname{d}p \texttt{~}
\texttt{~} \operatorname{d}q \texttt{~}
& + &
\texttt{(} \operatorname{d}p \texttt{)}
\texttt{~} \operatorname{d}q \texttt{~}
\end{matrix}</math>
|}
Capping the series that analyzes the proposition <math>pq\!</math> in terms of succeeding orders of linear propositions, Figure 26-2 shows the remainder map <math>\operatorname{r}(pq) : \operatorname{E}X \to \mathbb{B},</math> that happens to be linear in pairs of variables.
Capping the series that analyzes the proposition <math>pq\!</math> in terms of succeeding orders of linear propositions, Figure 26-2 shows the remainder map <math>\operatorname{r}(pq) : \operatorname{E}X \to \mathbb{B},</math> that happens to be linear in pairs of variables.