Nová infinitní matematika: I. Velká iluze matematiky 20. století

As early as 1899, Georg Cantor, the founder of the classical set theory, was aware of the fact that the class of all transfinite ordinal numbers cannot be expanded. That is, replaced by a set of all of these numbers. This is due to the fact that each set of ordinal numbers can be expanded by more numbers of this kind.
The presentation of the impossibility to expand the class of all natural numbers, contained in this book, is not a simple and easily accepted issue as in the case of transfinite ordinal numbers. Primarily because the field of infinite mathematics throughout the 20th century is based on the set of all natural numbers.
The scholar’s path to his intended goal takes Cantor’s theory to an ultra-product, which provides for a definition of an ultra-extension operator, which transforms the class of all sets and allows for an extension of the set of all natural numbers.