Can't understand the meaning of some symbols

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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

 
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hi shakgoku! :smile:

Rd is the same as Rn

i assume "d" stands for "dimension" :biggrin:

and C is the space of functions which are differentiable "infinitely many" times
 
Hey tiny-tim!

Thank you , now everything in the page makes sense to me! :)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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