# Zeroth-rank operation and non transitive numbers. Nulranga operacio kaj netransitivaj nombroj. Operazione di rango zero e numeri non transitivi

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Observing the existing relationships between the elementary operations of addition, multiplication iteration of additions and exponentiation iteration of multiplications, a new operation named incrementation is defined, consistently with these laws and such that addition turns out to be an iteration of incrementations. Incrementation turns out to be consistent with Ackermanns function. After defining the inverse operation of incrementation named decrementation, we observe that R is not closed under it. So a new set of numbers is defined named E, Escherian numbers, such that decrementation is closed on it. After defining the concept of pseudoorder analogous to the order, but not transitive, addition and multiplication on E are analysed, and a correspondence between E and C is found. Finally, incrementation is extended to C, in such a way that decrementation is closed on C too. English keywords: hyper-operations, incrementation, zeration, Ackermann function, intransitive order, not transitive order, intransitive numbers, non transitive numbers, not transitive numbers, new number sets.

Autor: Cesco Reale

Fuente: https://archive.org/