  This paper presents a new representation of natural numbers and discusses its
consequences for computability and computational complexity. The paper argues
that the introduction of the first Peano axiom in the traditional definition of
natural numbers is not essential. It claims that natural numbers remain usable
in traditional ways without assuming the existence of at least one natural
number. However, the uncertainty about the existence of natural numbers
translates into every computation and introduces intrinsic uncertainty that
cannot be avoided. The uncertainty in the output of a computation can be
reduced, though, at the expense of a longer runtime and thus higher complexity.
For the new representation of natural numbers, the paper claims that, with the
first Peano axiom, P is equal to NP, and that without the first Peano axiom, P
becomes a proper subset of NP.
