As "the first generation of infinite set theory" is based on present classical infinite theory system, contradictory concepts of "potential infinite” and “actual infinite" make people unable to understand at all what the mathematical things being quantitative cognized in set theory are-------- are they "potential infinite things” or “actual infinite things " or the mixtures of both or none of both? People have been unable to understand at all what kind of relationship between the quantitative cognizing theory and the unavoidable concepts of "potential infinite, actual infinite" in set theory: If the mathematical things being quantitative cognized are "potential infinite”, what kind of "potential infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are "actual infinite”, what kind of "actual infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are the mixtures of both or none of both "potential infinite” and "actual infinite”, what kind of mixing cognizing idea, operations and results should people have? Is there "one to one correspondence" theories and operations for "potential infinite elements” or “actual infinite elements" or the mixtures of both or none of both? Why?
As it turns out, the quantitative cognizing theories and operations (including the theory and operations of one to one correspondence and limit theory) for those infinite related mathematical things in "the first generation of infinite set theory" are lack of scientific foundations: It is impossible to know at all what the relationship among all the quantitative cognizing behaviors in infinite set theory and the concepts of "potential infinite” and “actual infinite" is and how to carry out scientific and effective operations specifically to different kinds of infinite related mathematical things. Therefore, it is very free and arbitrary for people to conduct quantitative cognitions to any infinite related mathematical things in "the first generation of infinite set theory" : It can either be proved that there are as many elements in Rational Number Set as there are in Natural Number Set or that there are more elements in Rational Number Set than there are in Natural Number Set; the T = {x|x📷x}theory can either be used to create the Russell’s Paradox or to create "Power Set Theorem", make up the story of “the Hilbert Hotel forever with available rooms” ------- strictly make all the family members of the Russell's Paradox mathematicization and turn all the family members of Russell's Paradox into all kinds of Russell's Theorem; ... However, because it has nothing to do with applied mathematics, it is impossible to verify the scientificity of many practical quantitative cognitive operations and results in set theory. Therefore, there are far more unscientific contents in the quantitative cognitive process of present classical infinite set theory than in present classical mathematical analysis, because it can be more arbitrary！
Nothing wrong. All correct. Wrong are your attempts to find errors in this theory. Get busy, buddy!
Dear Mr. Aslanbek Naziev, thank you.
Would you please be so kind as to tell me your idea about my presentation in the topic -------anything wrong exactly in my presentation ?
Best,
Geng
Dear Geng Ouyang,
Read word by word, paragraph by paragraph, chapter by chapter the book "Set Theory and it's Logic" by Willard Van Orman Quine, and you will understand my reaction to your writings. Good luck!
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