(1) In mathematics, among the various "infinite related number forms with cognizable quantitative properties (such as infinitesimal variables and monads in present classical mathematical analysis)", some are with Half Archimedean Property, while others are not ------- this determines that people need to carry out various necessary qualitative cognitions and studies on them [14-28].
(2) In mathematics, certain infinite related Half Archimedean number forms (such as infinitesimal variables and monads in present classical mathematical analysis) sometimes can join any quantitative calculation process (formula) with “mathematical contents with Archimedean property (such as finite number forms)”, but sometimes can not --------- this determines that during the necessary qualitative cognizing process to them, people sometimes need to put this kind of "Half Archimedean number forms" together with "mathematical contents with Archimedean property (finite number forms)" on the same quantity calculation process (formula), and carry out many calculations of “mathematical contents with Archimedean property” but sometimes need to use certain "scientific reasons" suddenly to drive such quantitative forms out of the exactly same quantitative calculation process (formula) to terminate the very calculation for the "differential" operation results (unfortunately, the fatal defects in the basic theory has been preventing mankind from finding this "scientific reason" for more than 2,500 years). Otherwise, there would be no the subject mathematical analysis in our science.
Not familiar with the terminology, can you give some example? With infinitesimals I could guess, but monad is more a philosophical entity, I think.
If you think some numbers are matrices, you can do more with real alone.
For example i may be
0 -1
1 0
Dear Mr. Juan Weisz ,
For “monad”, I mean the term from Non-Standard Analysis.
Sincerely yours,
Geng
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