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COGNITIVE VISUALIZATION OF THE CONTINUUM

PROBLEM AND MIRROR SYMMETRIC PROOFS

IN THE TRANSFINITE NUMBERS THEORY


A.A.Zenkin

Computer Center of the Russian Academy of Sciences, Moscow

alexzen@com2com..ru

Table of content:

1. Introduction. Cognitive Visaulization of Number-Theoretical Abstractions

2. Different formulations of Continuum Hypothesis

3. Different Representations of the Real Numbers x Î [ 0, 1 ]

4. Cognitive Visualization of Continuum Problem

5. New Kind of Transfinite Integers

6. Some Mirror-Like Proofs of Mirror-Like Theorems

7. "Periodical system" of Hyper-Real Numbers

8. Mathematical Sciences Classification Based on the "Periodical System" of Hyper-Real Numbers

9. Conclusions

10. References



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