  In this paper, we answer the question: "what is the qth Fibonacci number,
where q is a positive rational?". The answer is the codenominator function,
which is an integral-valued map. It is defined via a pair of functional
equations. Many Fibonacci identities in the literature are valid for the
codenominator. It is related to the recently introduced involution Jimm and to
the outer automorphism of PGL(2,Z)
