# Definition:Smooth Real Function

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## Contents

## 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.

## Also defined as

Some sources define a **smooth function** as a real function which has a continuous first derivative everywhere.

## Also see

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

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**smooth**:**1.** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**smooth**