## Abstract

The success attained in the study of functions and curves with the help of set theory made it a full and equal member of the family of mathematical sciences. This recognition was acknowledged at the first international congress of mathematicians in Zurich in 1897. Hurwitz^{1} and Hadamard,^{2} the greatest experts in mathematical analysis, demonstrated in their lectures extremely varied applications of sets and disclosed their connection with the theory of so-called analytic functions. Three years later, at the next international mathematical congress, David Hilbert’s list of 23 of the most important unsolved mathematical problems included problems in set theory. In his lecture at the congress Henri Poincaré gave a high rating to Cantor’s works. Speaking of the role of intuition and logic in mathematics, he said that mathematics finds in set theory an absolutely permanent and reliable foundation, and now all that remains are the natural numbers and finite or infinite systems of such numbers. In his view, mathematics had become completely arithmetized and, finally, absolutely rigorous.

## Keywords

Classical Mathematic Continuum Hypothesis Existence Proof Decimal Digit Actual Infinite## Preview

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## References

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