What is the linear space C^∞?

In my linear algebra text, a problem says: "Let V be the span of cos(x) and sin(x) in C^∞ (C with superscript infinity). What exactly is this space? I haven't heard of it before and there is no definition in the book.

What is the linear space C^∞?
C^0 = space of continuous functions


C^1 = space of continuous and derivable functions so that the derivative is continuous





C^(infinity) = set of functions u so that


d^n u/dx^n (n-th derivative of u) is continuous


for all n.
Reply:C^infinity is the set of all infinte dimensioned vectors with components from the complex numbers. V is maybe the subspace of linear combinations of sines and cosines of all tuples from C^infinity.
Reply:They are talking about the projection of the complex vector space onto the Riemann sphere as a form of stereographic projection. The north pole of the Riemann sphere is defined as "infinity". We donate this as the extended complex plane.





At least that is what I think they're talking about...