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

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: ZFC is inconsistent
Posted: Mar 15, 2013 5:30 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 13 Mrz., 18:40, Frederick Williams <freddywilli...@btinternet.com>
wrote:
> Some mathematicians do reject the
> axiom of choice, but I do not know if any have done so because of
> Banach-Tarski.


Every mathematician does so! Notwithstanding any intermediate
abracadabra the result is that v = 2V and that is wrong in
mathematics.
>
> I suspect that a good many, on first hearing of the Banach-Tarski
> paradox, thought 'Wow! How about that! Isn't mathematics fun?'  And
> perhaps: 'So what happens if Choice is false? Do any loopy things happen
> in that case?'  Meanwhile, note that if set theory is consistent, one
> may safely assume either Choice or its negation.


ZF is not consistent if this result is correct.

Proof: With axiom of choice it is possible to choose uncountably many
elements out of uncountably many sets. But non-material elements
cannot be chosen other than by defining them. Further it is undisputed
that only countably many definitions are available and that
"uncountable" is larger than "countable".

These things are well-known to every mathematician who deserves this
name. We have no choice.

Regards, WM


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

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