Page "Constructivism (mathematics)" Paragraph 20

Still, one might expect that since T is a partial function from the natural numbers onto the real numbers, that therefore the real numbers are no more than countable.

And, since every natural number can be trivially represented as a real number, therefore the real numbers are no less than countable.

They are, therefore exactly countable.

However this reasoning is not constructive, as it still does not construct the required bijection.

In fact the cardinality of sets fails to be totally ordered ( see Cantor – Bernstein – Schroeder theorem ).