Inconsistency of all formal systems that include N (natural numbers set)
Enrico Pier Giorgio Cadeddu · Zenodo (CERN European Organization for Nuclear Research) · 2023
Considering the set of natural numbers N, then in the context of the axiom of infinity and Peano axioms, we find a fundamental contradiction. This is not a finitist proof but its invalidity would imply that of the axiom of infinity, together the existence of not all natural numbers. With the axiom of infinity in fact all natural numbers exist and then they have to be reachable.