Hi!

I'm trying to show that the set of all complex valued continuous functions defined on the real line is an infinite-dimensional complex vector space.

Well I don't know where to start.. My first intuitive idea is to show that if we take the Taylor series of the function only up to n finite terms this sum will not be equal to the function, only in the limit . (Thinking as the function as a vector written as a linear combination of the elements of the basis)

Thanks in advance.