In the "second generation of infinite set theory" based on the new infinite theory system, the "infinite carrier theory" is the basic theory for quantitative cognitions and studies of many "mathematical things related to infinite" in infinite set. The generation and existence of the new mathematical carrier “interim-set, Non-Definite-Set 📷” determines the generation and existence of the new system of set types (Set Spectrum) --------- Empty Set 📷; Finite-Set 📷; Interim-Set (Non-Definite-Set) 📷; Infinite Set 📷, Yan Set 📷. In this newly constructed infinite related Set Spectrum: "zero quantity" is the only quantitative cognizing result of the “Empty Set 📷” since there are no elements contained in such set, which determines that people do not need or can not conduct any more quantitative cognitions and studies on the number of elements contained in such set.; many different finite sets contain different number of elements since Finite-Set 📷 since the elements contained in such sets are the “finite numbers with cognizable quantitative nature (Archimedean Property)" and people must conduct quantitative cognitions and various studies on the number of elements contained in such sets; people are bound to conduct quantitative cognitions and various studies on the number of elements contained in Interim-Set (Non-Definite-Set) 📷 since the elements contained in such sets are the “infinite law carriers with cognizable quantitative properties (Half Archimedean Property)”.
Dear Geng Ouyang
You are using unusual terms to describe the set theory:
(first generation, second generation, etc.). What is the philosophy behind your classification?
In the mathematical language, one needs to show and define a set of consistent axioms to construct a new model. And next, compare the old model with the new one. I think that it is challenging to add any new axiom for the current model.
To talk about the advantages and some new numerical analysis techniques is a different issue. Where the global vision can be analyzed locally using different approaches, but all should be performed under the same umbrella of the main mother set theory.
Best regards
Dear Issam Kaddoura
I agree with you that it is really not easy to understand this question only by a few lines. But I have uploaded 20 papers about this project to introduce my work from the aspects of philosophy and mathematics, especially 8 papers of ----- .
The emergence of the new infinite theory system determines the emergence of the second generation of infinite set theory and the fourth generation of mathematical analysis------- we call present classical infinite set theory basing on present classical infinite theory system “the first generation of infinite set theory (the old infinite set theory)" and the new infinite set theory basing on the new infinite theory system the second generation of infinite set theory"; we call "the first, second and third generations of mathematical analysis (before standard analysis, standard analysis and non-standard analysis) " basing on present classical infinite theory system “the present classical mathematical analysis (the old mathematical analysis) " and the new mathematical analysis basing on the new infinite theory system the fourth generation of mathematical analysis".
Thank you.
Sincerely yours,
Geng
it is extremely unlikely that there is a new theory of infinite sets that is not contained in the current one; your exposition does not define any of its terms, so there is no way to evaluate its correctness
i started to read On the Quantitative Cognitions to “Infinite Things” (I)
the first error i found is in conflating / confusing the notions of science and mathematics, and thereby claiming that since there are no demonstrably infinite objects in science, the same must be true for mathematics; that is simply incorrect, as more than a hundred years of mathematics has shown
so items 1 and 1.1 in the very first paper are wrong (``generally accepted'' was true until cantor showed that the equivalence was nonsense, and has not been true since)
and you really better define what a carrier is if you want to claim a new theory
Dear Mr. Christopher Landauer ,
I believe that some of the phenomenon being mentioned in your above post have been discussed in my uploaded paper of 《On the Quantitative Cognitions to “Infinite Things” (IV) 》.
Thank you very much for your good comments and ideas and I am now on the way to make things “better”.
Sincerely yours,
Geng
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