How much do you know? There is a common theorem which states that the set of all finite subsets of an infinite set is equipotent to the full set. Thus, $\mathcal{N}=\left\{E\subseteq\mathbb{N}:|S|<\infty \right\}$ has cardinality of $\aleph_0$. Then, if $\mathcal{G}$ is the set of all grammatical sentences we can clearly inject $\mathcal{G}\to\mathcal{N}$. Then, assuming that I understand a grammatical sentence the sentences $\text{hi},\text{hi hi},\text{hi hi hi},\cdots$ form an infinite subset of $\mathcal{G}$. It clearly follows that $|\mathcal{G}|=\aleph_0$.