Let f: R->R. If f is infinitely differentiable and analytic on a dense set is f analytic? Is this true if we restric f to [0,1]?(adsbygoogle = window.adsbygoogle || []).push({});

note: by analytic I mean the radius of convergence of the taylor expansion is non-zero about every point.

Maybe this is simple but I was thinking about it and can't figure it out

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# If f is infinitely differentiable and analytic on a dense set is f analytic?

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