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## Main Question or Discussion Point

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

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 ?

1. Homework Statement1. 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 ?