  Let K be an expansion of either an ordered field or a valued field. Given a
definable set X $\subseteq$ K<sup>m</sup> let C(X) be the ring of continuous
definable functions from X to K. Under very mild assumptions on the geometry of
X and on the structure K, in particular when K is o-minimal or P-minimal, or an
expansion of a local field, we prove that the ring of integers Z is
interpretable in C(X). If K is o-minimal and X is definably connected of pure
dimension 2, then C(X) defines the subring Z. If K is P-minimal and X has no
isolated points, then there is a discrete ring Z contained in K and naturally
isomorphic to Z, such that the ring of functions f $\in$ C(X) which take values
in Z is definable in C(X).
