  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
Ackermann's 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), it is shown that Escherian numbers are not
transitive. Then 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.
