Changes

==Note 24==

==Note 24==

Now that we've introduced the field picture for thinking about propositions and their analytic series, a very pleasing way of picturing the relationship among a proposition <math>f : X \to \mathbb{B},</math> its enlargement or shift map <math>\operatorname{E}f : \operatorname{E}X \to \mathbb{B},</math> and its difference map <math>\operatorname{D}f : \operatorname{E}X \to \mathbb{B}</math> can now be drawn.

Now that we've introduced the field picture for thinking about

propositions and their analytic series, a very pleasing way of

picturing the relationship among a proposition f : X -> B, its

enlargement or shift map Ef : EX -> B, and its difference map

Df : EX -> B can now be drawn.

To illustrate this possibility, let's return to the differential

To illustrate this possibility, let's return to the differential analysis of the conjunctive proposition <math>f(p, q) = pq,\!</math> giving the development a slightly different twist at the appropriate point.

analysis of the conjunctive proposition f<p, q> = pq, giving the

development a slightly different twist at the appropriate point.

Figure 24-1 shows the proposition pq once again, which we now view

Figure&nbsp;24-1 shows the proposition <math>pq\!</math> once again, which we now view as a scalar field, in effect, a potential "plateau" of elevation 1 over the shaded region, with an elevation of 0 everywhere else.

as a scalar field, in effect, a potential "plateau" of elevation 1

over the shaded region, with an elevation of 0 everywhere else.

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