On the Boundaries of Constructive Definability in Arithmetic
The Fundamental Limit of the Natural Number Sequence
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Abstract:
This paper introduces the concept of a natural number ("Numerus Apoptosis" or "Apoptonumerus"), the attainment of which leads to a fundamental collapse of arithmetic properties. It is proven that any attempt to define a natural number exceeding this value results in a logical contradiction within the framework of standard set theory axioms. The proposed object establishes an absolute set-theoretical limit for the concept of a "natural number."
This paper introduces the concept of a natural number ("Numerus Apoptosis" or "Apoptonumerus"), the attainment of which leads to a fundamental collapse of arithmetic properties. It is proven that any attempt to define a natural number exceeding this value results in a logical contradiction within the framework of standard set theory axioms. The proposed object establishes an absolute set-theoretical limit for the concept of a "natural number."
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