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takeuchi
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Homework Statement
Let f:ℝ→ℝ an analytic function,i.e, f ∈ C^{∞}(ℝ) and for all a∈ℝ we have that
f:∑[tex]\infty[/tex]0((f⁽ⁿ⁾(a))/(n!))(x-a)ⁿ.
Suppose that for all x in ℝ:∃N=N_{x}∈ℕ:f^{(N)}(x)=0.
Show that F is a polynomial
Homework Equations
The Attempt at a Solution
I think that maybe the theorem of Baire's Categories is the key of exercise. So, I said:
Let A_{n}={x∈ℝ:f⁽ⁿ⁾(x)=0} and I want to show that for some n and for a uncountable x∈ℝ f⁽ⁿ⁾(x)=0...But I don't know how...
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