I read this example
Example 3.33: Consider the Hermitian curve with equation $x^{r+1}=y^r+y$ over the field $\mathbb{F}_{r^2}$. Here $Q = (0:1:0)$ and $X = x/z$, $Y=y/z$ is a monomial generating set for $$R = \bigcup_{m=0}^\infty {L}(mQ).$$ It is obvious that the sets $\{X^iY^j\mid 0 \le i < r\}$ and $\{X^iY^j\mid 0 \le i < r+1\}$ each describes bases for $R$.
but I can't understand that why did the sets describe bases for $R$? Why are there two bases for $R$? But we know that base should be unique.