Definition:Smooth Real Function
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Definition
A real function is smooth if and only if it is of differentiability class $C^\infty$.
That is, if and only if it admits of continuous derivatives of all orders.
 | Work In Progress In particular: Subdefine whether differentiable at a point or on an interval. Refer to the fascinating fact that the concept is so much simpler in the complex plane. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by completing it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{WIP}} from the code. |
Also defined as
Some sources define a smooth function as a real function which has a continuous first derivative everywhere.
$\mathsf{Pr} \infty \mathsf{fWiki}$ does not endorse this definition.
Also see
- My brother Esau is an hairy man, but I am a smooth man. -- Take A Pew
- Results about smooth real functions can be found here.
Sources
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): smooth