Numbers and Sets | Part IA, 2005

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

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

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

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