AC is an axiom (something assumed without proof) and not the result that would render mathematics itself inconsistent. Banach Tarski is not about AC, it is abo

AC is an axiom (something assumed without proof) and not the result that would render mathematics itself inconsistent. Banach Tarski is not about AC, it is about existence of some pathological sets that have no measure. Edit: AC is generally assumed to be true because rejecting it leads to even stranger paradoxes than that of Banach-Tarski.