We have understood from the studies of infinite related mathematics’ history that present classical infinite theory system is based on the concepts of "potential infinite and actual infinite", which cannot be defined scientifically and contradict each other. This fatal flaw in the basic theory deeply affects the scientific nature of mathematical behavior of mathematical workers in the field related to the concept of "infinite". So, one cannot escape the constraint of the two false concepts of "potential infinite and actual infinite", and one cannot stop the emergence of various infinite related paradoxes. In addition, these paradoxes must exist in the form of "family (infinite paradox syndrome)". In different historical periods, the constantly emerging paradox family members repeatedly reveal the fundamental defects in the classical infinite theory system from different perspectives and call on people to solve these very defects. The fatal fundamental defects in present classical infinite theory system are the source of the second and the third mathematical crisis: more than 2500 years, no one can get rid of a kind of disease in the infinite related fields of mathematics --------- a diseases produced by the confusion of "potential infinite and actual infinite" concepts in set theory diagnosed clearly by Poincare, Frege, and Weyl more than 100 years ago. Studies have proved that this is the common "disease" existing in many infinite related mathematical disciplines with the foundation of present classical infinite theory system: the various "number and non--number mathematical things” -------- “variables of not only potential infinite but also actual infinite (the ‘ghost’ disappearing and reappearing at any time?)" for all the family members of Zeno's Paradox and Berkeley's Paradox in mathematical analysis [1-6]; the mathematical things with the property of "elements belonging and not belonging to a set ---------- T = {x|x📷x} (variable elements of not only potential infinite but also actual infinite: the ‘ghost’ disappearing and reappearing at any time?) " for all the family members of Russell paradox in set theory；…
This is why we are so sure to say that the Third Mathematical Crisis in present scientific theory system is unsolvable and the Third Mathematical Crisis is another manifestation of the Second Mathematical Crisis in set theory. They are "twins".
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Again and again you start a question basing on my research. When I give you an answer you neither argue against my assertions nor you accept my research.
This is not how scientific discussion works. It´s more near or like plagiating the research of others — mine!
Read it and discuss or leave it. You do not have the authorship of these questions, so you have to name the sources (me / the address), because you know.
Since 2016 the papers on Cantor are at my homepage (www.mathe-neu.de) avaiable for free. Some days ago also at RG (https://www.researchgate.net/project/Logic-of-Formalism-How-physics-raises-math-to-a-natural-science). See articles 03 / 04 / 05.
Regards, Peter
Dear Mr. Peter Kepp,
I began the infinite related project 45 years ago, and my first paper on this project was published in 1995 and my first paper on set theory was published in 1998.
Would you please check my published papers on the net of CNKI and those I uploaded on RG?
I am very sorry to say we two have totally different working thought and different results.
Thank you.
Sincerely yours,
Geng
Answer see parallel-topic. (Why two at the same time?). Please no answer here.
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