Changes

==Note 26==

==Note 26==

If we follow the classical line that singles out linear functions as ideals of simplicity, then we may complete the analytic series of the proposition <math>f = pq : X \to \mathbb{B}</math> in the following way.

If we follow the classical line that singles out linear functions

as ideals of simplicity, then we may complete the analytic series

of the proposition f = pq : X -> B in the following way.

Figure 26-1 shows the differential proposition df = d[pq] : EX -> B

Figure&nbsp;26-1 shows the differential proposition <math>\operatorname{d}f = \operatorname{d}(pq) : \operatorname{E}X \to \mathbb{B}</math> that we get by extracting the cell-wise linear approximation to the difference map <math>\operatorname{D}f = \operatorname{D}(pq) : \operatorname{E}X \to \mathbb{B}.</math> This is the logical analogue of what would ordinarily be called ''the'' differential of <math>pq,\!</math> but since I've been attaching the adjective ''differential'' to just about everything in sight, the distinction tends to be lost. For the time being, I'll resort to using the alternative name ''tangent map'' for <math>\operatorname{d}f.\!</math>

that we get by extracting the cell-wise linear approximation to the

difference map Df = D[pq] : EX -> B.  This is the logical analogue

of what would ordinarily be called 'the' differential of pq, but

since I've been attaching the adjective "differential" to just

about everything in sight, the distinction tends to be lost.

For the time being, I'll resort to using the alternative

name "tangent map" for df.

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