What does it mean for a set to be countable? Show that $\mathbb{Q} \times \mathbb{Q}$ is countable, and $\mathbb{R}$ is not countable.

Let $D$ be any set of non-trivial discs in a plane, any two discs being disjoint. Show that $D$ is countable.

Give an example of a set $C$ of non-trivial circles in a plane, any two circles being disjoint, which is not countable.