Let $f\in C([0,1],[0,1])$, such that: $$\forall x\in [0,1],\exists k\in \mathbb N, f^k(x)=0.$$
Is it true that $f$ nilpotent ?
PS : $f^2(x)=f\circ f (x)$
Nilpotent or not nilpotent
Dattier
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