Simple linear algebra notation queery:

[Zeth]

"Let S be a set. The set F(S,R) of all functions f : S → R from S to R
is a real vector space."

The above means that F is a collection of all possible functions that take some value, real or imaginary (or worse), and return a real number?

 

[EnumaElish]

It means F is the set of all functions from S to R.