fom
Posts:
1,968
Registered:
12/4/12


Re: ZFC is inconsistent
Posted:
Mar 18, 2013 4:00 AM


On 3/17/2013 3:25 AM, WM wrote: > On 17 Mrz., 00:10, Virgil <vir...@ligriv.com> wrote: >> In article >> <489bd644d0e741cb8aca18c916979...@bs5g2000vbb.googlegroups.com>, >> >> WM <mueck...@rz.fhaugsburg.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.
Actually, there is regard taken of its generation. On page 4 you will find the quote:
"The BanachTarski Paradox does not apply to finite sets, so it cannot be used to take a finite set and double it."
http://sdsudspace.calstate.edu/bitstream/handle/10211.10/292/Freiling_Eric.pdf?sequence=1

