We construct the dagger realization functor for analytic motives over nonarchimedean fields of mixed characteristic, as well as the Monsky-Washnitzer realization functor for algebraic motives over a discrete field of positive characteristic. In particular, the motivic language on the classic étale site provides a new direct definition of the overconvergent de Rham cohomology and rigid cohomology and shows that their finite dimensionality follows formally from one of Betti cohomology for smooth projective complex varieties. CONTENTS 1. Introduction 1 2. Overconvergent Rigid Varieties 3 3. Approximation Results 7 4. Dagger Rigid Motives 11 5. The Monsky-Washnitzer Realization Functor 17 Appendix A. Dagger Spaces and Inverse Limits of Adic Spaces 23 Acknowledgements 29 References 29