The-State-of-the-Art in Mathematics
From: E. E. Escultura (escultur36_at_hotmail.com)
Date: 11/27/04
- Next message: Edward Green: "Kick classic in shins, win prizes"
- Previous message: E. E. Escultura: "Re Re Publication Scandal"
- Next in thread: Ross A. Finlayson: "Re: The-State-of-the-Art in Mathematics"
- Reply: Ross A. Finlayson: "Re: The-State-of-the-Art in Mathematics"
- Maybe reply: E. Escultura: "Re: The-State-of-the-Art in Mathematics"
- Messages sorted by: [ date ] [ thread ]
Date: Sat, 27 Nov 2004 13:16:07 +0000 (UTC)
Hi FolksI 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 concept) 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 th!
eorems 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 (in this ordering 0.99... < 1), 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 and a real number is well-defined only 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 natur!
al 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/
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 concept) 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 th!
eorems 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 (in this ordering 0.99... < 1), 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 and a real number is well-defined only 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 natur!
al 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/
- Next message: Edward Green: "Kick classic in shins, win prizes"
- Previous message: E. E. Escultura: "Re Re Publication Scandal"
- Next in thread: Ross A. Finlayson: "Re: The-State-of-the-Art in Mathematics"
- Reply: Ross A. Finlayson: "Re: The-State-of-the-Art in Mathematics"
- Maybe reply: E. Escultura: "Re: The-State-of-the-Art in Mathematics"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
