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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 19:38, 5 May 2008
, 19:38, 5 May 2008→Note 9: quotes -> italics
===Note 9===
===Note 9===
Another way of looking at this situation is by letting the (first order) differential features <math>\operatorname{d}u, \operatorname{d}v, \operatorname{d}w</math> be viewed as the features of another universe of discourse, called the "tangent universe to <math>X\!</math> with respect to the interpretation <math>c\!</math> " and represented as <math>\operatorname{d}X \cdot c</math> . In this setting, <math>\operatorname{D}q \cdot c</math> , the "difference proposition of <math>q\!</math> at the interpretation <math>c\!</math> ", where <math>c = u\ v\ w</math> , is marked by the shaded region in Figure 4.
Another way of looking at this situation is by letting the (first order) differential features <math>\operatorname{d}u, \operatorname{d}v, \operatorname{d}w</math> be viewed as the features of another universe of discourse, called the ''tangent universe'' to <math>X\!</math> with respect to the interpretation <math>c\!</math> and represented as <math>\operatorname{d}X \cdot c</math> . In this setting, <math>\operatorname{D}q \cdot c</math> , the ''difference proposition'' of <math>q\!</math> at the interpretation <math>c\!</math> , where <math>c = u\ v\ w</math> , is marked by the shaded region in Figure 4.
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