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Topic: Irrefutable proofs that both Dedekind and Cauchy did not produce
any valid construction of the mythical "real" number

Replies: 4   Last Post: Oct 4, 2017 2:43 PM

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Markus Klyver

Posts: 730
Registered: 5/26/17
Re: Irrefutable proofs that both Dedekind and Cauchy did not produce
any valid construction of the mythical "real" number

Posted: Oct 4, 2017 2:43 PM
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Den tisdag 3 oktober 2017 kl. 19:16:15 UTC+2 skrev John Gabriel:
> On Tuesday, 3 October 2017 12:32:26 UTC-4, Markus Klyver wrote:
> > Den fredag 29 september 2017 kl. 14:06:42 UTC+2 skrev John Gabriel:
> > > https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
> > >
> > > Comments are unwelcome and will be ignored.
> > >
> > > Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
> > >
> > > gilstrang@gmail.com (MIT)
> > > huizenga@psu.edu (HARVARD)
> > > andersk@mit.edu (MIT)
> > > david.ullrich@math.okstate.edu (David Ullrich)
> > > djoyce@clarku.edu
> > > markcc@gmail.com

> >
> > Those are not Dedekind cuts.

>
> Of course they are monkey!


No, they aren't. They don't satisfy the axioms a Dedekind cut should satisfy.

Den onsdag 4 oktober 2017 kl. 20:09:58 UTC+2 skrev John Gabriel:
> On Friday, 29 September 2017 08:06:42 UTC-4, John Gabriel wrote:
> > https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
> >
> > Comments are unwelcome and will be ignored.
> >
> > Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
> >
> > gilstrang@gmail.com (MIT)
> > huizenga@psu.edu (HARVARD)
> > andersk@mit.edu (MIT)
> > david.ullrich@math.okstate.edu (David Ullrich)
> > djoyce@clarku.edu
> > markcc@gmail.com

>
> Dedekind Cut: A set partition of the rational numbers into two nonempty subsets L and R, such that all members of L are less than those of R and such that L has no greatest member.
>
> Any cut of the form
>
> (m, k) U (k, n) where m < k and k < n
>
> is EQUIVALENT to
>
> (-oo, k) U (k, oo) where k is not a rational number.
>
> So I can rewrite the cut (-oo, k) U (k, oo) as:
>
> (-oo,m] U (m, k) U (k, n) U [n, oo)
>
> Since my proof deals only with (m, k) U (k, n), it does not matter that the tail parts (-oo,m) and (n, oo) are discarded because those parts are not used or affected by the proof. The union (m, k) U (k, n) can be chosen as I please with any rational numbers assigned to m and n.
>
> I suppose that if you morons had actually tried to understand the proof, you would have noticed I set an exercise for you to complete which helps explain the proof.


You forgot that a Dedekind cut must be closed downwards as well as upwards. Your sets fail this criteria.



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