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Revision as of 15:24, 13 June 2009
, 15:24, 13 June 2009→Note 6: markup
The ''enlargement'' or ''shift'' operator <math>\operatorname{E}</math> exhibits a wealth of interesting and useful properties in its own right, so it pays to examine a few of the more salient features that play out on the surface of our initial example, <math>f(p, q) = pq.\!</math>
The ''enlargement'' or ''shift'' operator <math>\operatorname{E}</math> exhibits a wealth of interesting and useful properties in its own right, so it pays to examine a few of the more salient features that play out on the surface of our initial example, <math>f(p, q) = pq.\!</math>
A suitably generic definition of the extended universe of discourse is afforded by the following set-up:
definition of the extended universe of discourse:
{| align="center" cellpadding="6" width="90%"
|
<math>\begin{array}{cccl}
\text{Let} &
X
& = &
X_1 \times \ldots \times X_k.
\\[6pt]
\text{Let} &
\operatorname{d}X
& = &
\operatorname{d}X_1 \times \ldots \times \operatorname{d}X_k.
\\[6pt]
\text{Then} &
\operatorname{E}X
& = &
X \times \operatorname{d}X
\\[6pt]
&
& = & X_1 \times \ldots \times X_k ~\times~ \operatorname{d}X_1 \times \ldots \times \operatorname{d}X_k.
\end{array}</math>
|}
<pre>
For a proposition f : X_1 x ... x X_k -> B,
For a proposition f : X_1 x ... x X_k -> B,
the (first order) "enlargement" of f is the
the (first order) "enlargement" of f is the
