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creepypasta13
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Homework Statement
let S' be the unit circle, C the set of complex numbers, R the set of real numbers, ||f|| = sqrt[integral(f^2) from -pi to pi] (the length or norm of f)
find a function f: S'->C (so f is 2-pi periodic) and a sequence of functions {f_n}:R->C so that
||f-f_n|| converges to 0 but we don't have f_n(x) converging to f(x) for ANY x in S'
Homework Equations
The Attempt at a Solution
i was thinking of (-1)^n for f_n, and 0=f(x), but then ||f-f_n|| converges to 1, not 0
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