Maybe a silly question, but in some books (like "Differential Geometry - Manifolds, Curves, Surfaces - Gostiaux and Berger"), when differentiable maps of class $C^s$ are defined, we have something like:
"Let $f:M \rightarrow N$ a map between $C^k$ manifolds. We say that $f$ is a $C^s$ map (with $s \leq k$) if (...)"
Why (a priori) it's required that "$s \leq k$" ? I tried to find a pathological case, but I had no progress.
Thanks in advance.