# Definition:Smooth Real Function

## Definition

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

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

## Notes

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