Hello, I've been reading Bishop & Crittenden's Geometry of Manifolds and I'm not sure why they say that F(M,m) is not a linear space where F(M,m) is the set of $\displaystyle C^\infty$ real-valued functions with domain a neighborhood of m (M is a differentiable manifold). Is it because addition of functions fail to be an abelian group due to the imposibility of defining a neutral element?