# What it means to be infinitely differentiable

## Main Question or Discussion Point

<Moderator's note: Moved from a homework forum.>

1. Homework Statement

I am wondering if it is the same to say :

Function f is infinitely many times continuously differentiable
AND
Function f is infinitely many times differentiable

And if it is not the same, which one defines: C^infinity ?

## The Attempt at a Solution

mathman
Infinitely differential $$C^{\infty}$$ refers to a property at a particular point. However to get the nth derivative at that point, the (n-1)th derivative needs to be continuous at that point.

Stephen Tashi