About ACtheaxiomofchoice, the foundamentalfundamental theorem of Algebraalgebra, and real numbers
About foundamentalfundamental theorem of algebra, there is a large collection different demonstrations.
I ask: there is there some proof that avoidavoids AC (choiseaxiom)choiceaxiom)?
In a general topos (with natural number object) there are the two constructionconstructions of real numbers (generalizationgeneralizations of the classical Dedekind and Cauchy classicalconstructions) that are different.
In ZF theory, are the Dedekind and Cauchy constructions different? (inIn the "Cauchy" reals, operates on a real number $r$ through a choosechoice of a Cauchy sequence converging to $r$).r$.)