New Infinitary Mathematics

It is characteristic of twentieth-century mathematics that its mainstream exploration and application of infinity, albeit in bizarre ideal worlds, is based on the classical Cantor theory of infinite sets. The latter itself is based on the problematic assumption of the existence of the set of all natural numbers, whose only - and moreover theological - justification is often concealed and pushed into the collective unconscious. < br> < br> The book first examines the theological foundations from which classical set theory arose and on which it developed. The author warns against the dangers hidden in the construction of set theory, which can be traced in the works of some prominent mathematicians as well as in his own works. He then presents an argument for the absurdity of assuming the existence of the set of all natural numbers. < br> < br> However, the new infinite mathematics built by the author is not just a mere negation of current views and assumptions. On the contrary, his theory is guided by a cautious effort to cross the horizon of the ancient geometric world and pre-modern mathematics and to try to correspond more closely with the natural real world around us. The second half of the text is devoted to the rehabilitation of infinitesimal quantities and their fundamental role in mathematical analysis.