Dimension of the space of rational functions of degree $\leq n$

Question

I am studying some theory of curves in order to associate them with codes and I have stuck in the following result. In my book (p. 362 for those who own the book), it says:

If $K$ is a field, for the field $K(x)$ the set of rational functions with order $\geq -n$ at $\infty$ is the vector space of rational functions of degree $\leq n$. This is infinite-dimensional.

Questions.

1. What does he mean by "the vector space of rational functions of degree $\leq n$"? Is this $$V:=\Bigg\{\frac{f(x)}{g(x)}\in K(x): \deg f,\deg g \leq n\Bigg\}.$$ In fact, what is the degree of a rational function?
2. If yes, why is this infinite dimensional?

Many thanks.