How should I understand $\mathbf F^\mathbf n$? I am trying to go through Axler's Linear Algebra Done Right. I am stuck in the first few pages because I can't wrap my head around fields. 
The definition of $\mathbf F^\mathbf n$ was given as:
the set of all lists of length $\mathbf n $ of elements of $\mathbf F$.
okay, for simple cases such as $\mathbf n$ = 2 or 3, I think I understand it 
$  \mathbf R^\mathbf 2 = \{(x_1, x_2): x_1, x_2 \in \mathbf R \} $ is basically any point on a plane, if n = 3, it's a point in a space and so on, but I can't understand expressions such as 
1) $\mathbf R^{[0,1]}$
2) $\mathbf R^{\mathbf R}$
how should I understand these expressions? 
1) seems to be any R between zero and one is that correct?
2) how is this different from plain R? 

$A^B$ where $B$ is a set means all functions from $B$ to $A$.  Your ${\bf R}^2$ corresponds to ${\bf R}^{\{1,2\}}$, i.e. a member $(x_1, x_2)$ of ${\bf R}^2$ corresponds to the function $f$ from $\{1,2\}$ to $\bf R$ with $f(1) = x_1$ and $f(2) = x_2$.  In the case of ${\bf R}^{[0,1]}$, your function $f$ goes from $[0,1]$ to $\bf R$, i.e. it has to specify a value $f(x)$ for every 
real number $x$ from $0$ to $1$.
