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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 6, 2017 1:34 AM




Re: Irrefutable proofs that both Dedekind and Cauchy did not produce any valid construction of the mythical "real" number
Posted:
Oct 6, 2017 1:34 AM


Den torsdag 5 oktober 2017 kl. 19:18:52 UTC+2 skrev John Gabriel: > On Thursday, 5 October 2017 09:47:24 UTC4, 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 UTC4, 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 UTC4, Markus Klyver wrote: > > > > > > Den fredag 29 september 2017 kl. 14:06:42 UTC+2 skrev John Gabriel: > > > > > > > https://drive.google.com/open?id=0BmOEooW03iLSTROakNyVXlQUEU > > > > > > > > > > > > > > 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 UTC4, John Gabriel wrote: > > > > > > https://drive.google.com/open?id=0BmOEooW03iLSTROakNyVXlQUEU > > > > > > > > > > > > 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!
So 2=4 in your world?



