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## Homework Statement

Hello, this is not a problem but I want some clarification with the following paragraph (starting my linear algebra course!):

Let S be any nonempty set and F be any field*, and let

*F*(S,F) denote the

set of all functions from S to F. Two functions f and g in

*F*(S, F) are called

equal if f(s) = g(s) for each s in S. The set

*F*(S,F) is a vector space with

the operations of addition and scalar multiplication defined for f, g in

*F*(S, F)

and c in F by

(f + g)(s)=f(s)+g(s) and (cf)(s)=c[f(s)]

for each s in S. Note that these are the familiar operations of addition and

scalar multiplication for functions used in algebra and calculus.

*my prof said we can assume the field is R, all real numbers

## Homework Equations

## The Attempt at a Solution

What does it mean "from S to F"?

Does it mean that any function in

*F*(S,F) can take in any values of S and produce a value in F?

I'm also confused about notation that my professor uses.

R

^{X}to denote the set {f, X->R} where R is all reals and X is some non-empty set of numbers. Does this also mean the same thing as

*F*(X,R)?