Equation translation: $V=\{f\in C^0([0,1]);\ f(0)=f(1)=0\}$ What does this equation say in English? More specifically, what does $C^0([0,1])$ mean?
$V=\{f\in C^0([0,1]);\ f(0)=f(1)=0\}$
If it helps, this is a set that I need to prove whether or not is a vector space.
EDIT: Okay, I just read something that says,

Here we denote the set of all continuous functions on $I\subset \mathbb{R}$ by $C^0(I)$.

However, I'm still confused by what it means to say, $C^0([0,1])$.

$C^0([0,1])$ represents the set of continuous functions on the interval $[0,1]$. Therefore, $V$ is the set of continuous functions on the interval $[0,1]$ vanishing at the endpoints. For example, the functions $|x-\frac{1}{2}|-\frac{1}{2}$ and $\sin(\pi x)$ both belong to $V$.
More generally, the notation $C^n(A)$ represents the set of all $n$-times continuously differentiable functions on $A$.
