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Topic:
Irrefutable proofs that both Dedekind and Cauchy did not produce any valid construction of the mythical "real" number
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1
Last Post:
Oct 6, 2017 3:17 AM




Re: Irrefutable proofs that both Dedekind and Cauchy did not produce any valid construction of the mythical "real" number
Posted:
Oct 6, 2017 3:17 AM


On Wednesday, October 4, 2017 at 2:09:58 PM UTC4, 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?
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com Visit my Math Blog at http://www.dcproof.wordpress.com



