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

Replies: 2   Last Post: Oct 5, 2017 9:47 AM

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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 5, 2017 9:47 AM
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Den onsdag 4 oktober 2017 kl. 20:52:33 UTC+2 skrev John Gabriel:
> On Wednesday, 4 October 2017 14:43:39 UTC-4, Markus Klyver wrote:
> > 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.

>
> Rubbish. My sets do meet the criteria.


They do not. 3.1 is in your cut, yes? Then -10000 should be in the cut as well, and so should 0.466468840107465. So your cuts are not Dedekind cuts.



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