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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 6:39 PM

On 3/18/2013 4:57 PM, WM wrote:
> On 18 Mrz., 20:32, Virgil <vir...@ligriv.com> wrote:
>

>>> On the contrary. I am looking for any applications of infinite set
>>> theory. But hitherto I could not find anything serious.

>>
>> Standard calculus is based on the infiniteness of the real number line
>> and the infiniteness of the Cartesian plan.

>
> Yes, but many matheologians are unable to recognize that infinity is
> not finished and that. and that calculus has been existing long before
> Cantor.

Yes. Since Newton and Leibniz.

Berkeley had been the original critic of Newton's
introduction of the infinite into mathematics. He,
legitimately, compared the convergence of ratios to
a set of accounting books out of balance equally and
oppositely on the different sides of the ledgers.

Today that is referred to in the definition of differentials
as the error approaching to 0 faster than the function
approaching its limit.

There is just one minor issue with that view. It is
based on prior knowledge of the derivative function and
it is said in relation to a fixed point of the domain.

The debates begun by Berkeley occurred during the period
when numerical techniques were being developed to approximate
the solutions to problems of the infinitesimal calculus.
This, in turn, set up the conditions for "solving" the problem
of infinitesimals arithmetically. That would, if I recall
correctly, be attributed to Lagrange and Cauchy.

Whoops! New problem: what *exactly* does it mean to be continuous?

Well, thanks to Lobachevsky, one could not turn to familiar
geometry anymore.

So, Dedekind showed us how to represent the continuity of
our functions through an arithmetical continuity on our
domains.

Then, as noted before, there is Leibniz' statement of
the principle of identity of indiscernibles linking
nested logical domains with geometric intuition. I
could be wrong, but it seems a lot like Cantor's
intersection theorem stating that a nested sequence of
closed non-empty sets with vanishing diameter is
non-empty.

In other words, the only reason you can complain
about Cantor today is because Berkeley complained

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