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Let f(x)=lim(m->oo){lim(n->oo)cos^(2m)(n...

Let `f(x)=lim_(m->oo){lim_(n->oo)cos^(2m)(n !pix)},` where `x in Rdot` Then prove that `f(x)={1,`if x is rational` and 0, `if x is irrational``

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