The construction of real numbers does not need the axiom of choice in the sense that there are constructions of models of real numbers that do not need it. One

The construction of real numbers does not need the axiom of choice in the sense that there are constructions of models of real numbers that do not need it. One example of such construction is described on the Wikipedia page [1], look for "Edudoxus reals" there. [1] https://en.wikipedia.org/wiki/Construction_of_the_real_numbers https://en.wikipedia.org/wiki/Construction_of_the_real_numbe...