# Infinitely differentiable

Ratzinger
infinitely differentiable doesn't care if all the higher derivatives are zeroes (like for polynomials), it only has to be defined...correct?

$$f(x) = \left\{ \begin{array}{ll} 0 & x = 0 \\ e^{-1/x^2} \quad & x \neq 0 \end{array}$$