On 17 Mrz., 00:10, Virgil <vir...@ligriv.com> wrote: > In article > <489bd644-d0e7-41cb-8aca-18c916979...@bs5g2000vbb.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 16 Mrz., 16:10, fom <fomJ...@nyms.net> wrote: > > > > Borel was critical of the axiom of choice. > > > Very. > > > > According to most accounts, it had been determined > > > that much of his work had implicitly used the > > > axiom of choice.
Impossible. Borel worked in mathematics only. And he knew that uncountability is not a part of mathematics. In other instances AC is not required. > > > There is no problem. The axiom of choice as such is completely > > acceptable. What is inacceptable (because provably false) is the > > application of AC to uncountable sets. > > While the axiom of choice applied to solid spheres has led to an unusual > result, that result does not DISPROVE the axiom of choice, since the > sort of partitioning required is not guaranteed to preserve volumes,
So it is an insane partition, i.e., it is not a partition at all. However, the result is 1 = 2 and that is wrong in mathematics, with no regards of its generation.