Definition:Smooth Real Function

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A real function is smooth if it is of differentiability class $C^\infty$.

That is, if it admits of continuous derivatives of all orders.


Sometimes authors refer to functions that have only a continuous first derivative as smooth. If the particular usage is potentially ambiguous, make sure to specify exactly what you mean.

My brother Esau is an hairy man, but I am a smooth man. -- Take A Pew