```Date: Oct 6, 2017 3:17 AM
Author: Dan Christensen
Subject: Re: Irrefutable proofs that both Dedekind and Cauchy did not produce<br> any valid construction of the mythical "real" number

On Wednesday, October 4, 2017 at 2:09:58 PM UTC-4, John Gabriel wrote:> 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.> Yes. Sets L and R are both subsets of Q. L and R are disjoint. L U R = Q. > Any cut of the form > >     (m, k) U  (k, n)  where m < k and k < n > Are you really suggesting that (m, k) and (k, n) comprise a Dedekind cut??? They are both subsets of Q, but they are NOT disjoint (k is common to both sets) and their union is NOT Q (n+1 is in neither set). So, they do not comprise a Dedekind cut.> is EQUIVALENT to > >     (-oo, k) U (k, oo)   where k is not a rational number. >Huh? If k is not a rational number, then whatever (-oo, k) might be, it is NOT a subset of Q. Likewise for (k, oo).Have a look at https://en.wikipedia.org/wiki/Dedekind_cut before you go any further, Troll Boy. As usual, you are in way over your head. > 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...You have banned all axioms and the rules of logic in your goofy system, Troll Boy. Recall, you wrote:"There are no postulates or axioms in mathematics." -- Feb. 6, 2017 "There are no rules in mathematics."-- March 17, 2015   How can you possibly write a proof if you believe this nonsense?DanDownload my DC Proof 2.0 software at http://www.dcproof.comVisit my Math Blog at http://www.dcproof.wordpress.com
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