$f$ a smooth real valued map on $\mathbb{R}$ whose derivatives of all order vanish at 0. What is kind of mild condition can we add so that this map is constant in a neighborhood of $0$ ?
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1"analytic" - but that's far from mild, of course :) – Hagen von Eitzen Mar 30 '15 at 20:59
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@HagenvonEitzen Correct me if I'm wrong (I may be), but wouldn't that make $f$ identically zero? – GPerez Mar 30 '15 at 21:01
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@GPerez Yep, I admitted it's not mild :) – Hagen von Eitzen Mar 30 '15 at 21:24
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Have a look at this http://math.stackexchange.com/questions/240026/all-derivatives-zero-at-a-point-implies-constant-function – mfl Mar 30 '15 at 21:26