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, 16:08, 13 June 2009→Note 6: markup
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<pre>+ Ef<x_1, ..., x_k, dx_1, ..., dx_k>+ + = f<x_1 + dx_1, ..., x_k + dx_k>+ + = f<(x_1, dx_1), ..., (x_k, dx_k)>+
{| align="center" cellpadding="6" width="90%"
{| align="center" cellpadding="6" width="90%"
|
|
−<math>\begin{array}{cccl}
+<math>\begin{array}{lccl}
\text{Let} &
\text{Let} &
X
X
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\\[6pt]
\\[6pt]
&
&
−& = & X_1 \times \ldots \times X_k ~\times~ \operatorname{d}X_1 \times \ldots \times \operatorname{d}X_k.
+& = & X_1 \times \ldots \times X_k ~\times~ \operatorname{d}X_1 \times \ldots \times \operatorname{d}X_k
\end{array}</math>
\end{array}</math>
|}
|}
−For a proposition of the form <math>f : X_1 \times \ldots \times X_k \to \mathbb{B},</math> the ''(first order) enlargement'' of <math>f\!</math> is the proposition <math>\operatorname{E}f : \operatorname{E}X \to \mathbb{B}</math> that is defined by the following equation:
−For a proposition f : X_1 x ... x X_k -> B,
−the (first order) "enlargement" of f is the
−proposition Ef : EX -> B that is defined by:
−{| align="center" cellpadding="6" width="90%"
−|
−<math>\begin{array}{l}
−\operatorname{E}f(x_1, \ldots, x_k, \operatorname{d}x_1, \ldots, \operatorname{d}x_k)
−\\[6pt]
+= \quad f(x_1 + \operatorname{d}x_1, \ldots, x_k + \operatorname{d}x_k)
+\\[6pt]
+= \quad f( \texttt{(} x_1, \operatorname{d}x_1 \texttt{)}, \ldots, \texttt{(} x_k, \operatorname{d}x_k \texttt{)} )
+\end{array}</math>
+|}
+<pre>
It should be noted that the so-called "differential variables" dx_j
It should be noted that the so-called "differential variables" dx_j
are really just the same type of boolean variables as the other x_j.
are really just the same type of boolean variables as the other x_j.
