 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/22g/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Take

x_{n} = (- 1)^{n}

. Its shift is

- x

, so linearity and shift invariance give

ϕ (x) = ϕ (- x) = - ϕ (x) .

Thus every such functional assigns the common value

ϕ (x) = 0,

although the sequence does not converge.

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