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Observing the existing relationships between the elementary operations ofaddition, multiplication (iteration of additions) and exponentiation (iterationof multiplications), a new operation (named incrementation) is defined,consistently with these laws and such that addition turns out to be aniteration of incrementations. Incrementation turns out to be consistent withAckermann's function. After defining the inverse operation of incrementation(named decrementation), we observe that R is not closed under it. So a new setof numbers is defined (named E, Escherian numbers), such that decrementation isclosed on it. After defining the concept of pseudoorder (analogous to theorder, but not transitive), it is shown that Escherian numbers are nottransitive. Then addition and multiplication on E are analysed, and acorrespondence between E and C is found. Finally, incrementation is extended toC, in such a way that decrementation is closed on C too. English keywords:hyper-operations, incrementation, zeration, Ackermann function, intransitiveorder, not transitive order, intransitive numbers, non transitive numbers, nottransitive numbers, new number sets.

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