Godel actually proved that there is no complete and consistent axiomatic formulation of arithmetic: in particular, there is no set of axioms for the structure of the natural numbers which both (1) allows the deduction of every true theorem in arithmetic, and (2) does not also allow the deduction of any false theorem in arithmetic. This is Godel's Theorem.

# arithmetic (idea)

See all of arithmetic, there is 1 more in this node.