Can't understand the meaning of some symbols

[shakgoku]

Homework Statement

This is an extract from elements of mechanics by giovanni.
I'[m unable to understand the meaning of $$R^d$$ and $$C^\infty$$

http://flic.kr/p/9K8P7p

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

hi shakgoku!

R^d is the same as Rⁿ …

i assume "d" stands for "dimension" ​

and C^∞ is the space of functions which are differentiable "infinitely many" times

 

[shakgoku]

Hey tiny-tim!

Thank you , now everything in the page makes sense to me! :)