# Geng OuyangMinNan Normal University · mathematics

Geng Ouyang

## About

40

Publications

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80

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Citations since 2017

Introduction

Working hard for 45 years to solve some fundamental defects in infinite related areas disclosed by the “infinite related paradox syndrome complex”, a new infinite theory system with the “theory of abstract infinite concept carriers” is developed and the 2500 years old “infinite related paradoxes” black cloud over mathematics sky is to be removed. The “Infinite Mathematical Carrier Gene” and “Infinite Mathematical Carrier Measure” concepts are introduced, Quantum Mathematics is constructed.

Additional affiliations

September 1983 - February 2017

**mathematics**

Position

- Professor (Assistant)

August 1983 - January 2018

**mathematics**

Position

- Retired

July 1983 - July 2018

**mathematics**

Position

- Retired

## Publications

Publications (40)

In order to solve the fatal defects in the basic theory of the existing classical infinite theory system based on "actual infinite-potential infinite", we carry out scientific and systematic researches on the cognitive theory of "scientific abstract objects-the carriers of scientific abstract objects (abstract infinite concept-carriers of abstract...

In order to solve the fatal defects in the basic theory of the existing classical infinite theory system based on "actual infinite-potential infinite", we carry out scientific and systematic researches on the cognitive theory of "scientific abstract objects-the carriers of scientific abstract objects (abstract infinite concept-carriers of abstract...

In order to solve the fatal defects in the basic theory of the existing classical infinite theory system based on "actual infinite-potential infinite", we carry out scientific and systematic researches on the cognitive theory of "scientific abstract objects-the carriers of scientific abstract objects (abstract infinite concept-carriers of abstract...

The unavoidable defects of the basic theory of quantitative cognition in the existing mathematical analysis and set theory are analyzed and revealed from a new perspective. A clear conclusion is reached: it is the lack of "infinite carrier theory" in the existing classical infinite theory system that leads to the being of suspended "infinite parado...

The unavoidable defects of the basic theory of quantitative cognition in the existing mathematical analysis and set theory are analyzed and revealed from a new perspective. A clear conclusion is reached: it is the lack of "infinite carrier theory" in the existing classical infinite theory system that leads to the being of suspended "infinite parado...

The unavoidable defects of the basic theory of quantitative cognition in the existing mathematical analysis and set theory are analyzed and revealed from a new perspective. A clear conclusion is reached: it is the lack of "infinite carrier theory" in the existing classical infinite theory system that leads to the being of suspended "infinite parado...

Taking three outstanding paradoxes in the existing mathematical analysis and set theory as typical cases, the unavoidable defects of the basic theory of quantitative cognition in the existing mathematical analysis and set theory are analyzed and revealed from a new perspective. A clear conclusion has been reached: it is the lack of "infinite carrie...

Taking three outstanding paradoxes in the existing mathematical analysis and set theory as typical cases, the unavoidable defects of the basic theory of quantitative cognition in the existing mathematical analysis and set theory are analyzed and revealed from a new perspective. A clear conclusion has been reached: it is the lack of "infinite carrie...

Taking three outstanding paradoxes in the existing mathematical analysis and set theory as typical cases, the unavoidable defects of the basic theory of quantitative cognition in the existing mathematical analysis and set theory are analyzed and revealed from a new perspective. A clear conclusion has been reached: it is the lack of "infinite carrie...

Starting from the most primitive basis, our studies have proved that the un-scientific defined and contradictory concepts of “potential infinite, actual infinite” have been the foundation of present classical infinite theory system, this leads to the fact that both present classical mathematical analysis and set theory have exactly three same funda...

Starting from the most primitive basis, our studies have proved that the un-scientific defined and contradictory concepts of “potential infinite, actual infinite” have been the foundation of present classical infinite theory system, this leads to the fact that both present classical mathematical analysis and set theory have exactly three same funda...

Starting from the most primitive basis, our studies have proved that the un-scientific defined and contradictory concepts of “potential infinite, actual infinite” have been the foundation of present classical infinite theory system, this leads to the fact that both present classical mathematical analysis and set theory have exactly three same funda...

For thousands of years during the quantitative cognizing process to “infinite things”, many contradictory events which are non-self-justification in present science theory system have been frequently produced and they have been defined as paradoxes. Putting those suspended infinite relating paradox families (infinite relating paradoxes syndrome) to...

Combining concrete cases, the long neglected fatal defects in the foundation of present classical set theory and its quantitative cognizing tool of “one to one correspondence” are analyzed and studied. Two conclusions are drawn: (1) Present classical infinite idea is based on the concepts of “potential infinite” and “actual infinite” which have nev...

about my 37 papers titles and Abstracts for 2018 ICM

My 37 papers’ titles and Abstracts for 2018 ICM

The unavoidable mistakes and defects in quantitative cognizing activities to “infinite, infinitesimal, infinite great, infinite many” in present infinite set theory basing on present infinite theory system are analyzed and studied from a new angle. The researches and the ways solving those “eight challenging conundrums of quantitative cognitions to...

Taking the old and new members in “infinite related quantitative cognizing paradox families” in present classical mathematical analysis as typical examples, the newly discovered quantitative cognizing defects for “infinite things” in present classical “potential infinite--actual infinite” based mathematical analysis are further analyzed and studied...

The fundamental fatal defects on “infinite things’ quantitative cognitions” since antiquity in present classical infinite related science system disclosed by the suspended typical “’infinities—infinitesimals’ paradox families” are analyzed and studied, “fourteen challenging conundrums of ’infinities—infinitesimals’ quantitative cognitions” in moder...

The errors and defects in the “scientific-mathematical criterions of ‘infinite’ definition” in present classical infinite related science theory system are studied and disclosed; the inevitable relationships among these errors, defects, the quantitative cognizing obstacles to “infinite things” are analyzed and, the scientificity of new definition t...

Through three simple but fundamental cases, the theoretical and operational difficulties in the quantitative cognizing work of the “infinite things” resulted by the fatal defects in the foundation of “potential infinite--actual infinite” based present classical infinite related science theory system are analyzed: (1) mainly in present classical ana...

The 40 years work on five suspended typical defects in present classical infinite related science system disclosed by the newly discovered Harmonic Series Paradox of Zeno’s Paradoxes Family is summarized: the “time--space” absence defects in philosophy of mathematics, the defects in infinite conceptual system, the defects in limit theory, the defec...

Abstract: The long being defects disclosed by the suspended infinitude paradoxes family in three fundamental components in present traditional infinitude system are studied in a new way. Two conclusions are drown: 1) we should integrate the defects disclosed by all kinds of infinite paradoxes and pay much attention on the very fundamental research...

The fundamental defects in present traditional infinitude system disclosed by Zeno-Berkeley-Russell’s Paradoxes and the reasons of why the family members of these three paradoxes have been keeping increasing are investigated in a new working train of thought. Two conclusions are drown: （1） We should integrate the defects disclosed by all kinds of i...

Though with different forms, all of the infinite related mathematical things in human science are in the same family with the same root. Going on the fundamental research train of thought relating to “scientific cognition”, “the philosophy of mathematics” and “infinite”, we focus on the foundation of infinite related number system and the “scientif...

The specialized technique and theory of treating infinite numerical substances------ limit theory is analyzed and studied: what it is and how it behaves. Two new connotations of “theoretical infinite” and “applied infinite” are discovered and proposed and two defects in the foundation of present limit theory are disclosed. At the level of “system”,...

Abstract: Four mistakes in Cantor’s proofs on the uncountability of real number set are discovered and analyzed from the aspects of logic, infinite theory, limit theory, number system as well as the ideas and operations of the proofs. A conclusion is drown: because of the defects in the infinitude related foundation of mathematics, Cantor unavoidab...

As the twin paper of [7] and going on the fundamental research train of thought relating to “cognition”, “the philosophy of mathematics” and “infinite”, we extent our work to the foundation of infinite related set theory urged by the newly discovered fundamental defects, the relating paradoxes and cases in set theory. Three primary and basic substa...

Three different ways of treating infinitesimals in mathematical analysis (before limit theory, limit theory, non-standard analysis) are studied. A conclusion is drown: theoretically and operationally, the three ways are really perfect equivalences in nature, and all the problems and defects disclosed by the suspended infinitesimal paradox family ar...

## Questions

Questions (139)

Cantor turned an “infinite sequence of natural numbers +1” into a “super infinite sequence” with an absurd method of “super infinite number generation”-------- A person with a big axe, randomly find a reason to chop from front to back "natural number +1 infinite sequence”: each hack is called a "super infinite number generation method" to generate a "super infinite number" :

The first hack produces the first super infinite number, the second hack produces the second super infinite number, the third hack produces the third super infinite number, the fourth hack produces the fourth super infinite number, and the fifth hack produces the fifth infinite number,……

We human certainly need to develop “Quantitative Cognitions to “Infinite Things””, but we shouldn't create infinite super infinite numbers by chopping at random the “infinite sequence of natural numbers +1” with a big axe, as Cantor did.

**References：**

[1] OUYANG Geng. ON INFINITE PARADOXES AND NEW SOLUTIONS [M]．Xiamen: Xiamen UniversityPress. 2021-05-01 ISBN: 9787561582015

[2] OUYANG Geng. On the Quantitative Cognitions to “Infinite Things” (V) [J]．Journal of Kashgar University. 2018，39(3):30－41

[3] OUYANG Geng. On the Quantitative Cognitions to “Infinite Things” (VI) [J]．Journal of Kashgar University. 2019，40(3): 16－22

[4] OUYANG Geng. On the Quantitative Cognitions to “Infinite Things” (VII) [J]．Journal of Kashgar University. 2019，40(6): 8－14

[5] OUYANG Geng. On the Quantitative Cognitions to “Infinite Things” (VIII) [J]．Journal of Kashgar University. 2020，41(2): 5－11

It is generally accepted that the existing limit theory, which would deal exclusively with "infinitesimal number forms", may operate in one of following two ways:

（1） During the whole quantitative cognizing process to infinitesimal number forms, no one dare to say “let them be zero or get the limit or get the standard number”... So, the infinitesimals in the calculating operations would never be too small to be out of the quantitative cognizing process and the quantitative cognizing process would be carried our forever. This situation have been existing in mathematics since antiquity, only in Zeno’s time he created his Zeno’s Paradox to criticize this unscientific phenomenon bravely and sharply. As we know, all cases of such operations have formed a huge suspended Zeno’s Paradox Family (including the newly discovered "Harmonic Series Paradox").

（2）During the whole quantitative cognizing process to infinitesimal number forms, someone suddenly cries “let them be zero or get the limit or get the standard number”... So, all in a sudden the infinitesimals in the calculations become too small to stay in the quantitative cognizing process, they should disappear from (be out of) any relating quantitative cognizing process immediately. This situation have been existing in mathematics since antiquity, only in Berkeley’s time he created his Berkeley’s Paradox to criticize this unscientific phenomenon bravely and sharply. As we know, all cases of such operations have formed a huge suspended Berkeley’s Paradox Family.

When using the above first method of cognition to the “whether 0.9999999… equals to 1” argument, one is assured and bold with justice to get the result of 0.9999999… equals to 1

When using the above second method of cognition to the “whether 0.9999999… equals to 1” argument, one is assured and bold with justice to get the result of 0.9999999… does not equal to 1

So the debates of “whether 0.9999999… equals to 1” can go on endlessly and fruitlessly, but only with a variety of wordplay.

## Projects

Projects (3)

Our studies have proved that there have been two fundamental defects in present classical infinite theory system: (1) theoretically, confusion on the concepts of “potential infinite and actual infinite” in all the infinite relating science fields; (2) operationally, confusion on the scientific (especially mathematical) contents of “potential infinite and actual infinite”. And, these two very defects decide the unavoidable generation of infinite relating paradox families in present mathematical analysis and set theory--------the 2500 years old un-dispersed cloud of “infinite paradoxes syndrome” hanging over the sky of our science. As it turns out, the concepts of “potential infinite” and “actual infinite”, which are un-scientifically defined and mutually contradictory, must be abandoned; and the new infinite theory system basing on ““abstract things—the carriers of abstract things”, as well as the systematic theory of “infinite carriers” must be constructed and developed.
We call present classical infinite theory system basing on "potential infinite and actual infinite" concepts "the first generation of infinite theory system" and the new infinite theory system basing on "abstract things and the carriers of abstract things" concepts "the second generation of infinite theory system".

Beginning with the modern “strict mathematically proven” Zeno’s Achilles-Turtle Paradox: the newly discovered Harmonic Series Paradox, I have been working hard for 40 years to solve some major fundamental errors disclosed by the suspended infinite related paradoxes in present classical “actual infinite” and “potential infinite” related philosophy and mathematics.
A new infinite theory is pioneered, developed to remove the 2500 years old huge black cloud over mathematics sky.