> > The unit square contains an infinite number of points. But is it
> > countably or uncountably infinite?
>
> Uncountable. Even the numbers between 0 and 1 are uncountable.

That depends on what numbers you are using. The number of points in the unit
square of rational numbers is countable, the number of points in the unit square
of irrational numbers is not.

By the way, IIRC, it is actually possible to constuct a bijection from [0,1]
onto the unit square, meaning there is actually the same number of points in the
unit square as there are points between 0 and 1.

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