(1) An "infinite set" is consisted by a kind of "infinite elements (infinite carriers)" ------- there will be no "infinite set" without "infinite carriers".
(2) The unique characteristics (special properties, special existing conditions, special form of expression and the special relationship between and among each other) of each kind of “infinite carriers (infinite elements)” constitute each "unique infinite set"-------- there will be no variety of different infinite sets without "different kinds of special infinite elements ('infinite carriers' with unique characteristics)".
Well, I guess that makes sense. Then you talk about an infinite set of __ . Fill in the blank. Otherwise I guess there would just be one infinite set of a hodgepodge of everything. Is that the point? It seems intuitive, unless that isn't what was meant.
Thank you dear Mr. James R Knaub,
The new definition of infinite set affirms the set elements’ uniqueness, scientificity and importance which have been long neglected.
Sincerely yours,
Geng
Our studies have proved that the "tangible, visible, and reachable actual infinite" that people have been talking about and using for thousands of years basing on their senses and without any justification, should have been a set of "New Infinite Carrier Theory System (Actual Infinite Theory System)" that includes following new mathematical things which are closely related to the concept of "infinite": the new number form, the new Number Spectrum, the new definition for infinite set, the new definition for the elements of infinite set, the new “set – elements” relationship, the new Set Spectrum, the new “Semi-Archimedean Character”, the new “number character”, the new “set character”, the new Infinite Mathematical Carrier, the new Infinite Mathematical Carrier Gene, the new Infinite Mathematical Carrier Measure, the new limit theory and its operation, the new one to one correspondence theory and its operation, ...". The new infinite theory system (especially the newly developed "infinite mathematical carrier theory") lays a solid and scientific foundation for the second generation of set theory and the fourth generation of mathematical analysis for human to scientifically carry out the qualitative and quantitative cognitions of infinite mathematical things. We should cherish and inherit the infinite related wealth of knowledge gained by our predecessors, but we should also correct mistakes produced by the unscientific classical infinite theory system and open up new fields.
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