I'm going through my assignments for this week, and I have a problem understanding the (notation of?) this exercise:
Let $S$ be a nonempty set and $F$ a field. Prove that for any $s_0 \in S$, $\{f \in F(S,F):f(s_0)=0\}$, is a subspace of $F(S,F)$. ($F(S,F)$ being the set of all functions).
Now what I'm wondering is what exactly is $s_0$, why the $_0$, and how should I understand the $f(s_0)=0$ part of the subspace?
Thanks for any help :)