  Arithmetic operations can be defined in various ways, even if one assumes
commutativity and associativity of addition and multiplication, and
distributivity of multiplication with respect to addition. In consequence,
whenever one encounters `plus' or `times' one has certain freedom of
interpreting this operation. This leads to some freedom in definitions of
derivatives, integrals and, thus, practically all equations occurring in
natural sciences. A change of realization of arithmetic, without altering the
remaining structures of a given equation, plays the same role as a symmetry
transformation. An appropriate construction of arithmetic turns out to be
particularly important for dynamical systems in fractal space-times. Simple
examples from classical and quantum, relativistic and nonrelativistic physics
are discussed, including the eigenvalue problem for a quantum harmonic
oscillator. It is explained why the change of arithmetic is not equivalent to
the usual change of variables, and why it may have implications for the Bell
theorem.
