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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 7, 2017 4:50 AM

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zelos.malum@gmail.com

Posts: 1,066
Registered: 9/18/17
Re: Irrefutable proofs that both Dedekind and Cauchy did not produce
any valid construction of the mythical "real" number

Posted: Oct 7, 2017 4:50 AM
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Den fredag 6 oktober 2017 kl. 20:00:44 UTC+2 skrev John Gabriel:
> On Friday, 6 October 2017 10:37:35 UTC-4, Markus Klyver wrote:
> > Den fredag 6 oktober 2017 kl. 13:11:41 UTC+2 skrev John Gabriel:
> > > On Thursday, 5 October 2017 20:18:03 UTC-4, Markus Klyver wrote:
> > > > Den torsdag 5 oktober 2017 kl. 19:18:52 UTC+2 skrev John Gabriel:
> > > > > On Thursday, 5 October 2017 09:47:24 UTC-4, Markus Klyver wrote:
> > > > > > 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.

> > > > >
> > > > > They do you idiot.
> > > > >
> > > > > (-oo,m] U (m, k) U (k, n) U [n, oo)
> > > > >
> > > > > is the cut. My proof deals only with the subset (m, k) U (k, n) which includes the cut. I specifically chose a subset to make the proof easier to understand, but you are extremely dense!

> > > >
> > > > Those are four subsets. A Dedekind cut is a partition of ? into TWO sets.

> > >
> > > Chuckle. You are INCREDIBLY DENSE, DISHONEST and IGNORANT.
> > >
> > > (-oo,m] U (m, k) U (k, n) U [n, oo)
> > >
> > > IS THE SAME AS:
> > >
> > > ( (-oo,m] U (m, k) ) U ( (k, n) U [n, oo) )
> > >
> > > OR
> > >
> > > (-oo,k) U (k, oo)
> > >
> > >
> > > IDIOT!!!!

> >
> > (-?,m], (m, k), (k, n), [n, ?) are four sets. A Dedekind cut, as the Wikipedia definition goes, is a partition of ? into TWO sets.
> >
> > Den fredag 6 oktober 2017 kl. 13:16:45 UTC+2 skrev John Gabriel:

> > > On Friday, 6 October 2017 06:29:44 UTC-4, Markus Klyver wrote:
> > > > Den fredag 6 oktober 2017 kl. 07:35:28 UTC+2 skrev Zelos Malum:
> > > > > Den torsdag 5 oktober 2017 kl. 15:48:33 UTC+2 skrev Markus Klyver:
> > > > > > Den torsdag 5 oktober 2017 kl. 09:40:23 UTC+2 skrev Zelos Malum:
> > > > > > > Den torsdag 5 oktober 2017 kl. 09:33:08 UTC+2 skrev John Gabriel:
> > > > > > > >
> > > > > > > > Hee, hee. Dipshit. Nothing you say has any relevance. I have proved that my improved definition meets ALL the criteria. Go fuck yourself! You will be seen as the fucking moron that you are.

> > > > > > >
> > > > > > > that means it is YOUR definition not dedekind definition, ergo they are NOT dedekind cuts and hence your arguement against it is invalid.
> > > > > > >
> > > > > > > This is the definition of a strawman. You make up your own shit rather than adress the proper point.
> > > > > > >
> > > > > > > Your shit doesn't meet it because, again, why can I find rational numbers excluded? The definition says it shouldn't exist any excluded.

> > > > > >
> > > > > > Could you expand on this? Obviously every Dedekind cuts will not contain all the elements in ?.

> > > > >
> > > > > It depends a bit on how strict one has to be, using the more general notation it is so all is always contained. It is just that in some instances the upper (or lower, depending on which you choose to focus on) will have an infinitum (or supremum) in the given set.

> > > >
> > > > Right, that's what I was confused about.

> > >
> > > You're confused about everything.
> > >

> > > > Rudin only uses the lower set in his construction of the real numbers, which isn't a partition of ?.
> > >
> > > With respect to irrational numbers, this is all that matters you baboon. If it is a rational number, it is the GLB (greatest lower bound) of the upper set and not even necessary because rational numbers are well defined. Cuts were a failed attempt to define irrational numbers.
> > >
> > > Rudin was smart enough to understand what WLOG (without loss of generality) means. Evidently you are not. I used the same approach when I chose a subset because my proof does not require the entirety of the two partitions.
> > >

> > > > Of course his construction is equivalent anyway.
> > >
> > > Just as my construction/definition is equivalent also. Duhhhh!!!
> > >
> > > Grow a brain you idiot!

> >
> > With your method, we can complete [3, 4]. But [3, 4] is not ?.

>
> You've never understood my proof. It uses the EXACT Dedekind definition. You are just too stupid.


It doesn't, as pointed out many times to you, you are using strawmen arguements of dedekinds cuts.




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