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Topic: Matheology § 291
Replies: 28   Last Post: Jun 19, 2013 5:29 PM

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Posts: 8,833
Registered: 1/6/11
Re: Matheology � 291
Posted: Jun 18, 2013 4:42 PM
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In article <>, wrote:

> On Tuesday, 18 June 2013 20:46:40 UTC+2, Zeit Geist wrote:
> > On Tuesday, June 18, 2013 4:47:47 AM UTC-7,
> > wrote: > On Monday, 17 June 2013 21:46:17 UTC+2,

> > > In this case the question is whether the reals can be well-ordered - and
> > > absolutely nothing else! A theory that says yes and no does not
> > > contribute soemthing of value.

> > Yes, a theory that proves both "yes" and "no" as an answer to that question
> > would be of no value. However, we have a system that proves "yes", and and
> > another that proves "no". The former is invaluable in Real Analysis,
> > whereas the latter is useful in Game Theory. Both of the are useful to the
> > Sciences.

> Not at all. Both are completely useless.

Calculus is, if not impossible, at last considerably more difficult,
without a standard theory of real numbers a a basis.

And as far as I, or most of us here, can see, there is no part of
mathematics whatsoever that is improved by using WMytheology and many
parts are damaged by imposing it.

> And that which says the reals can be
> well-ordered is especially useless because, nevertheless, the reals cannot be
> wel-ordered.

In a system like WMytheology, in which WM claims that the rational can
be well-ordered in their standard order, one can also derive 2 = 1.
> > If the Scientist ( you ) wishes only to do his Science, then they need not
> > worry about the Mathematics that produces their formulae. They can just
> > ignore the Mathematical Black Box, and have faith that a formula, when
> > applied correctly, will yield the correct result.

> In order to have faith, we have to drop theories which predict false results.

Then, by all means, let us drop any system, like WMytheology, which
claims that the rationals can be well-ordered in their standard order
> > > Look, when I ask what is 5 + 5? You may answer, depending on the axioms,
> > > 10 or not 10, then your answer shows just the same kind of value as
> > > matheology. The only empty set that has a right to ebe considered is the
> > > story of success of set theory. > In the system of "Rope Arithmetic" or
> > > "Gap Arithmetic" we have the true equation, 5 + 5 = 11.

> That does not touch my example of common arithmetics and does not help to
> excuse the false results of set theory.

Nor the even far more false results of WMytheology.

The set whose members are {1}, {2}, {3}, ...
clearly has union set |N.

But WM claims, at lest within his WM's wild weird world of WMytheology
The set whose members are {1}, {1,2}, {1,2,3}, ...
must have a union set strictly less than |N.

What sort of set theory says things like that?

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