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Re: 10^7-ZFC
Posted:
May 3, 2012 9:31 PM
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On May 4, 9:51 am, MoeBlee <modem...@gmail.com> wrote:
> On May 3, 5:00 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > I don't expect you to be able to define an even number
>
> It is not a problem, even without the axiom of infinity, to define
> 'natural number' and '2' and multipication of natural numbers. And
> then the definition of 'even' is easy.
>
> MoeBlee
..but you can't use SETS of arithmetical objects, or anything large at
all.
The purpose of SET THEORY should be to use sets, not fall back to
solid ground Predicate Calculus every time you're asked to do anything
mathematical.
All the A X I O M S O F Z F C
are ad hoc tacked on to justify
XeY -> P(X,Y)
since
XeY <-> P(X,Y)
results in XeRS <-> X~eX
Can you define X and Y where
X e Y
and
Y e X
in ZFC?
It's another example of useless tacked on AXIOMS
Herc
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