Set theory and analysis have brought us human tremendous achievements in our science, but so many suspended “infinite related paradox family members” strongly proved that there have been fatal defects in our “ontology-form” cognitions to "infinite" at least since Zeno’ time 2500 years ago ---------the fatal mistakes in the foundation of present classical infinite related science theory system.
2500-year is like a filliping in the long history of human beings, it is the right time for us human to integrate our works（achievements and faults）and look for a way out.
Our studies have proved that discard the contradictory, confusing, mistaken contents of “potential infinite and actual infinite” in the foundation of present classical science system and study and develop systematically all kinds of “infinite carriers” is the only way out; this is a step we should take sooner or later beyond our will. A newly constructed "infinite theory system" with newly discovered but having been long existing virgin land--------“the field of infinite carriers”, is waiting to be pioneered and developed.
Dear Waldemar Koczkodaj,
I sincerely admire your publications (excellent articles and interesting conclusions).
Yours sincerely,
Pavel
Dear Professor Waldemar Koczkodaj, thank you for your ideas from your work.
The "math nails": when facing “infinite things” in present classical infinite related science theory system, no one is sure whether they are “potential infinite things” or “actual infinite things” and are not sure how to treat them scientifically------- more and more suspended infinite related paradox families are produced by the “confusing of potential infinite and actual infinite” such as infinitesimal relating paradoxes in analysis, infinity relating paradoxes in set theory, both infinitesimal and infinity relating paradoxes in the ideas and skills of “Cantor’s diagonal-contradictory proofs and the conclusion on “Real Number Set has more elements than Natural Number Set (infinite elements in Real Number Set is more infinite than that in Natural Number Set-------Infinite R is more infinite than Infinite N)”, and these paradox family members are surely unsolvable in present classical infinite related mathematics where they were produced and nourished.
Yours,
Geng
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