Let f(x)=(lim)n∞{(lim)n∞cos2m(n!πx)}, where x∈R˙ Then prove that f(x)={1,ifξsrational0,ifξsirrational

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Question

Let $f (x) = (lim)_{n \infty} {(lim)_{n \infty} cos^{2 m} (n! π x)},$ where $x \in R ˙$ Then prove that $f (x) = {1, if ξ s r a t i o n a l 0, if ξ s i r r a t i o n a l$

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Let

f (x) = (lim)_{n \infty} {(lim)_{n \infty} cos^{2 m} (n! π x)},

where

x \in R ˙

Then prove that

f (x) = {1, if ξ s r a t i o n a l 0, if ξ s i r r a t i o n a l

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Question Text

Let

f (x) = (lim)_{n \infty} {(lim)_{n \infty} cos^{2 m} (n! π x)},

where

x \in R ˙

Then prove that

f (x) = {1, if ξ s r a t i o n a l 0, if ξ s i r r a t i o n a l