Uergil
Posts:
433
Registered:
6/11/11
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Re: Matheology � 038
Posted:
Jun 14, 2012 3:59 PM
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In article
<cdea6df0-ebbb-48e5-8a2b-3669e1b74e97@f7g2000yqh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 14 Jun., 09:57, Jürgen R. <jurg...@arcor.de> wrote:
> > "WM" <mueck...@rz.fh-augsburg.de> schrieb im
> > Newsbeitragnews:d84ffa69-66ad-42b2-8904-a268c86d8a24@a16g2000vby.googlegroup
> > s.com...
> >
> > > Matheology § 038
> >
> > > One of the most often heard arguments in favour of transfinite set
> > > theory is the completeness requirement of |R and real functions. It is
> > > not true.
> >
> > > Well, then tell me, Herr Professor Doktor Mueckenheim, how do you
> > > solve the equation
> > > ih partial(du/dt) = H(u) [JR, Matheology § 022, sci.logic June 13,
> > > 2012]
> >
> > Evidently you misunderstood the question. The question is:
>
> Are there uncountably many real numbers.
> The answer is a resounding: No.
Then lets see WM count them!
> >
> > Is there in your version of mathematics such a thing as
> > "Calculus", i.e. "Mathematical Analysis"?
>
> Of course. Euler, Gauss, Cauchy, Weierstarss: They all knew how to do
> analysis.
> >
> > In particular:
> >
> > If there are at most countably many real numbers then
> > every (Lebesgue) integral vanishes. Is there such a
> > thing as an integral in your version of mathematics?
>
> No. It is a gross mistake to assume that the rational numbers could be
> counted.
That depends on one's definition of "counting".
It is certainly possible, and has been accomplished, to construct
bijections between the set of naturals and the set of rationals, as
well as both surjections and injections both ways.
> This is concluded from the correct observation that counting
> up to every rational number is possible. The conclusion is wrong
> because after every rational and every natural number, there are
> infinitely many others possible. No infinite set can be counted. Not
> even the natural numbers. The asserted bijection n - n is invalid,
> except for a small fraction of 0 % of possible natural numbers (not
> possible in MatheRealism, but possible in classical mathematics).
Thus WM claims that a set need not have the same 'number of members' as
itself.
>
> > If there are no more than countably many real numbers
> > it is unclear how the derivative of a function
> > can be well-defined.
>
> That depends on the defintion of "well- defined". But obviously there
> are not uncountably many real numbers and obviously no plane and no
> bridge have crashed for that reason.
What is so obvious to WM is not at all obvious to most mathematicians,
and even held to be false by them.
And mathematics is what mathematicians do.
>
> > Or are your considerations limited to operations with
> > numbers, i.e. to arithmetic?
>
> Mathematics uses numbers and limits, but only those which exist.
>
> We cannot sum all terms of any geometrical series. We can only
> determine supremum and infimum.
WM again shows his incompetence, as any decent mathematician can easily
sum all the terms of any geometric series with first term a and common
ratio r with |r| < 1.
>
> Cantor postulated an improper limit to be a proper limit - and failed.
Wm postulated that he knows more abut math than anyone else, and failed.
Anyone who has seen the things that WM presents as proofs can see that
WM is no mathematican.
--
"Ignorance is preferable to error, and he is less
remote from the- truth who believes nothing than
he who believes what is wrong.
Thomas Jefferson
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