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2. Show that if A is real, but not rational, then there is no integer q 4: 0 so that f; (:r + 21m) =

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2. Show that if A is real, but not rational, then there is no integer q 4: 0 so that f; (:r + 21m) = fatter) for all a: E (00, 00). However, show too that f; is \"almost periodic\" for a multiple of 2a in the following sense: for any tolerance E > 0, there is an integer gs at 0 so that \"AGE + 21rqe)- fx(w)| 0, there is a :1 so that 827\")\"; lies in the segment 5(5) of the unit circle 5(6) := {82\"}; :y E (6,6)}. L N

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