Re: The state-of-the-art in mathematics
From: Big Brother (ministry.ofLove_at_eurasia.com)
Date: 12/29/04
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Date: Wed, 29 Dec 2004 02:54:30 +0000 (UTC)
E.E.Escultura, consider this a challenge,
prove to me the following using an anti-tesis:
Let G=supE, and e>0. Then there exists a x belonging to E: x>G-e.
Why might I ask something so simple? Because I believe you will contradict one of your claims in this particular proof, show me, and everyone else, wrong and reply with a wellfounded proof by contradiction.
sincerly,
BB
On 27 Nov 2004, E. E. Escultura wrote:
>Hi Folks,
>
>I would like to share with you the latest findings on foundations,
>number theory and the real number system. They are all published in my
>papers but some of them have been resolved in MathForge.net and others
>are discussed in my websites..
> (1) The subject matter of mathematics cannot be the concepts of
>thought which are subjective; they must be symbols (I also call them
>concepts) well-defined by a set of axioms that specify the existence
>and properties of and operations on and relations among the concepts;
>the axioms must well-define the given mathematical space. To insure
>validity of proof the rules of inference or logic must be specific to
>the given mathematical space and well-defined by the axioms. In
>particular, universal rules of inference such as formal logic must be
>rejected. Moreover, ambiguous sets such as infinite sets must be
>avoided because they are sources of contradictions. Therefore, only
>finite spaces, which can be unbounded, are free from contradiction
>provided the axioms are consistent. It follows that distinct
>mathematical spaces are independent. Therefore, any propositions
>involving concepts from distinct spaces or mapping between them is
>nonsense. In this regard, Godel’s incompleteness theorems are
>nonsense.
> (2) With regards to number theory, the main defect is lack of valid
>axiomatization of the integers. I remedied this problem by embedding
>them in the new real number system that I have constructed. The new
>real number system is finite but unbounded, free from contradictions
>and paradoxes, has natural ordering, enriched by two new real numbers,
>namely, dark and unbounded numbers, and adequate for scientific and
>practical purposes.
> (3) The real numbers are decimals and it is well-defined if every
>digit is known or computable. Therefore, a nonperiodic real number or
>irrational is ill-defined or nonsense unless there is some algorithm
>for computing any of its digits. Other nonsense in the real number
>system includes classical curves and surfaces. Consequently, Wiles
>‘proof’ of FLT is wrong and his conclusion is also false because I
>have constructed countable counterexamples to FLT in several of my
>papers and in my websites. Curves and surfaces were fixed by L. C.
>Young in a series of papers from 1931 to 1969 where developed the
>theories of generalized curves and surfaces. Two of the axioms of the
>real number system see Royden’s Real Analysis, p. 31), namely, the
>completeness and dichotomy axioms, are false. Counterexamples to them
>were constructed by Banach-Tarski and Brouwer. Brouwer’ counterexample
>also implies that the irrationals are ill-defined and the real numbers
>have no natural ordering. In fact, these findings imply that the real
>number system is ill-defined, nonsense. The remedy is to reconstruct
>the real number system on finite set, namely, the set of basic
>integers 0, 1, …, 9, without these axioms using only three axioms. I
>have done this in several papers and part of it are posted in
>MathForge.net and discussed in my websites.
> (4) To illustrate how a wrong concept may wreck havoc on mathematics
>and physics, consider this Ullrich flip-flap: i = sqrt(-1) =
>sqrt(1/-1) = 1/i = -i or i = -i; dividing both sides of the last
>equation by i, I obtain 1 = -1 or 1 = 0 and the real number system
>goes down the drain. If I add i on both sides instead, I obtain 2i = 0
>or i = 0 and the complex number system vanishes in thin air. The
>remedy is to take i as an operator on plane vectors, that is, rotation
>of a vector by pi/2 radians counterclockwise. (This resolution is
>shown in my paper, Exact solutions of Fermat’s equations (Definitive
>resolution of FLT), Nonlinear, Studies, Vol. V, pp. 227 – 254) In
>physics this concept i has brought in such nonsense as negative or
>imaginary metric and energy.
>(5) My websites: http://www.users.bigpond.com/pidro/home.htm
>http://home.iprimus.com.au/pidro/
>
>E. E. Escultura
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