Manuscript VII-H@1 · VII-H.tex · example · d20d2a9f

Example: An infinitesimal catalogue can miss a finite difference

Physical matching and complete response ambiguity › Finite changes, not merely tangent directions · lines 372–381

Let $a, b \in E^{'}$ be linearly independent and consider

R^{θ} = R^{0} + θ a + θ^{2} b .

The derivative at $θ = 0$ detects only $a$ , but the span of all finite differences contains both $a$ and $b$ . A test annihilating $a$ alone need not give a prescription-independent value.

Displayed formulas in this passage

unlabeled · line 374
$R^{θ} = R^{0} + θ a + θ^{2} b .$

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section: Finite changes, not merely tangent directions