THE PROBLEM OF NEW PROPERTIES OF NUMBERS

Abstract

Background. The proposed work is devoted to research to clarify the axiomatization of arithmetic in connection with the presence of special assumptions in it. The conceptual problem of analyzing new properties of numbers is formulated under the assumption of the possibility of losing any initial premise. Materials and methods. A solution to the conceptual problem is given, followed by a logical analysis of the meaningful axiomatic theory of natural numbers, which led to the discovery of logical errors. An analysis of logical errors is given based on the meaningful axiomatic theory of natural numbers. It is shown that the properties of an established set of "finite real numbers", or positive real numbers contained in a given segment e, have the property of being discovered depending not only on the "requested numbers" of the actually infinite region, but also on real (positive) numbers infinite half-interval. Results. Conditions have been identified that allow us to establish new properties of numbers. Conclusions. The natural series N begins only with 1, there is no zero in it. It has been proven that modern arithmetic has an incorrect axiomatization and is subject to revision.

Keywords

• predicate
• inductive
• anti-inductive
• tetration
• abduction
• homomorphism
• referent
• srelatum
• dyadic relation
• recursion
• anti-recursion
• conceptual problem
• properties of natural numbers
• logical errors
• initial premises
• meaningful axiomatic theory