Cantor diagonalisation
Sure, that&#x27;s the story the government tells everyone. It sounds plausible enough, but is it the whole story?<p>* Apply Downward Lowenheim-Skolem to get a countable model of set theory<p>* Construct the reals using whichever technique you want.<p>* Since the base set theory is countable, so is the set of constructed reals.<p>The same technique can give you countably many groups, countably many rings, countably many points in the plane, etc. Everything is countable.