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Topic: ZFC is inconsistent
Replies: 54   Last Post: Mar 23, 2013 9:02 PM

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 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
>>
>> 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.

Actually, there is regard taken of its
generation. On page 4 you will find the
quote:

"The Banach-Tarski Paradox does not apply
to finite sets, so it cannot be used to
take a finite set and double it."

http://sdsu-dspace.calstate.edu/bitstream/handle/10211.10/292/Freiling_Eric.pdf?sequence=1

Date Subject Author
3/13/13 byron
3/13/13 Inverse 18 Mathematics
3/13/13 byron
3/13/13 YBM
3/23/13 Jesse F. Hughes
3/13/13 Frederick Williams
3/14/13 byron
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 YBM
3/15/13 Virgil
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 fom
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/17/13 Virgil
3/18/13 fom
3/16/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 fom
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/18/13 Virgil
3/18/13 fom
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/17/13 Virgil
3/16/13 Virgil