 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2010/p/p3/a/solution

x

from

U_{n}

u_{*} \in U_{n}

such that

∥ x - u_{*} ∥ = u \in U_{n} in f ∥ x - u ∥.

The definition requires attainment of the infimum. This finite-dimensional subspace does have such an approximation, as the explicit projection below shows; completeness of the whole inner-product space is unnecessary.

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