Is complement of diagonal language countable?
A language is a set of finite strings over some finite alphabet&nbsp;$\Sigma$. Therefore, every language is countable. You can see this by considering $\Sigma = \{0, \dots, d\}$ for some $d\in\mathbb{N}$ and now you can associate any string with a natural number written in base&nbsp;$d$.  To avoid the problem that, e.g., $0$ and $000$ denote the same number (and I guess $\epsilon$&nbsp;counts as zero, too), we actually associate the string $x_1\dots x_n$ with the number $1x_1\dots x_n$. Thus, we have an injection from $\Sigma^*$ to&nbsp;$\mathbb{N}$, so $\Sigma^*$&nbsp;is countable and so are all its subsets.