Date: Oct 5, 2017 1:39 AM Author: zelos.malum@gmail.com Subject: Re: Irrefutable proofs that both Dedekind and Cauchy did not produce<br> any valid construction of the mythical "real" number 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, for fuck say you retarded bastard.

One of the criteria for a dedekinds cut of rational numbers is that if p is in L, and q is a rational number such that q<p, then q is ALSO in L, yet in all your L_n that property is false, cause I can always find a q that is not in them but less than a p, hey, yours even have a minimum and infinitum, neither of which exists in a dedekinds lower cut because of forementioned reason.

So how can yours satisfy the definition of dedekinds cuts, when dedekinds cuts say that for every rational q<p, with p in L, then q is in L, yet yours fail that miseribly? THat is the definition of a contradiction.