The studies to our infinite related science and mathematics history have proved that a new visible and tangible “infinite related mathematical carrier (called ‘infinite mathematical carrier’ or ‘infinite carrier’ for short following)” is needed in our science and mathematics to express and cognize quantitatively “infinite related mathematical things”. This special new “infinite carrier” is a new mathematical content (new mathematical manifestation, new mathematical entity) between “infinite things” and “finite things”, its emerging and existence decides the emerging and existence of “infinite related mathematical carrier theory”-------new manifestations of “mathematical carrier” (such as “inter-number，indistinct-number” and “inter-set，indistinct-set”) and their related quantitative cognizing and operating theory (such as limit theory and one-to-one coresponding theory) as well as new infinite related “number spectrum (number system)” and “set spectrum (set system)”. The developing of “infinite related mathematical carrier theory” leads us enter into a new and systematic cognizing field of infinite carrier, enables us to accomplish the scientific mission of “cognizing ‘abstract law’ with ‘concrete carriers’” efficently, systematically and scientifically (fully satisfied accurace with high deree of approximation) to all kinds of “infinite related mathematical things” in many quantitative cognizing situations.
The emerging and existence of new mathematical carrier “inter-number (indistinct-number)” has decided the generating of the new infinite related “number spectrum--------zero or absolutely none, infinitesimal, inter-small or indistinct-small, finite-number or distinct-number, inter-great or indistinct-great, infinity, yan or absolutely being" for solving the fatal fundamental defect of lacking “infinite mathematical carrier” in the process of quantitative cognizing to “infinite related number forms”; while the emerging and existence of new mathematical carrier “inter-set，indistinct-set” has decided the generating of the new infinite related “set spectrum---------empty set，finite-set, distinct-set，inter-set or indistinct-set，infinite set" for solving some other fatal fundamental defect of lacking “infinite mathematical carrier” in the process of quantitative cognizings to “different infinite things relating to set” since set theory was founded. Our studies proved that the abscence of the whole “infinite related mathematical carrier theory” is really one of the key factors for the emerging and existence of those suspended paradox families (‘infinite paradoxes’ symptom complex) in present set theory and analysis.
In previous discussion we have introduced the newly constructing “new infinite theory system as well as its related infinite mathematical carrier theory” basing on the accumulated quantitative cognizing fruits of thousands years work on “infinite related mathematical things” by our predecessors. As one of the infinite related mathematical carriers, the “inter-set” in “set spectrum” of new infinite set theory are new mathematical contents of visible and tangible “scientific carriers” (in fact, many infinite sets being quantitative cognized in present set theory are “inter-sets” which have very close relationship with their elements’ special “nature, existing condition, manifestation and relationship among each other”). And, with the related “quantitative treating theories of infinite related mathematical things” (such as those “carriers’ analysing and quantities reaching” theories to elements and number forms, limit theory, one-to-one coresponding theory, ...), we can cognize on “inter-sets” and attain our objective of scientific, systimatic cognitions to all kinds of sets in the infinite related new “set spectrum”.
it is because of the absence of the infinite related new number forms and set forms (infinite related things mathematical carriers) that makes us unable to treat “different beings of infinite related things” in mathematical analysis and set theory ever since.
Infinite refers to "infinite" or "infinite" or "unlimited" used in several different concepts but all of which combine one idea of "no end". In this sense, it is related to philosophy, mathematics, divinity, and life Daily also.
The first known symbol ()) for this expression was John Wallis in 1655 in his writings: De Sectionibus Conicis and Arithmetica Infinitorum.
In popular culture, infinity is usually something that can be likened to "as many as possible" or as far as possible. In many minds, the question remains: what is after infinity, but much is considered a question after infinity is absurd because infinity is a symbol of what can not be imagined Is greater than it.
In mathematics, infinity is used as a number to be measured by an unlimited quantity, symbolized by a letter ()). It is an entity different from any other numerical entity in its characteristics and behavior.
Thank you very much for your ideas dear Mr. ابتسام صاحب الزويني.
Yes, I agree with your ideas on infinite , but we need some “mathematical manifestation, mathematical entity” to conduct quantitative cognizing to “infinited things” in mathematics.
Thank you very much for your helpful ideas dear Mr. Peter Breuer.
I meant agree with Mr. ابتسام صاحب الزويني’s ideas on infinite, I have corrected the sentence.
Thank you again.
Sincerely yours,
Geng OUYANG
Five of my published papers have been up loaded onto RG to answer such questions:
1，On the Quantitative Cognitions to “Infinite Things” (I)
2，On the Quantitative Cognitions to “Infinite Things” (II)
3，On the Quantitative Cognitions to “Infinite Things” (III)
4 On the Quantitative Cognitions to “Infinite Things” (IV)
5 On the Quantitative Cognitions to “Infinite Things” (V)
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