I'm working through Axler's linear algebra textbook and in it he says that $F^n$, the set of n-tuples with elements in $\mathbb{R}$ or $\mathbb{C}$, as well as $F^\infty$, are specific cases of $F^S$ - the set of functions mapping from $S$ to $F$. He states that we can think of $F^n$ as $F^{\{1,2,...,n\}}$ and analogously for $F^\infty$.
I am having trouble understanding how the set of all points (vectors) in n-dimensions (i.e., $F^n$) is equivalent to the set of all functions mapping the first $n$ natural numbers to $F$.