# Class of differentiability

smoothness class $C^k$, $0\leq k\leq\infty, a$
A concept characterizing differentiable mappings (in particular, functions). The class $C^0$ consists of all continuous functions, the class $C^k$ consists of functions with continuous derivatives of all orders not exceeding $k$ (in particular, $C^\infty$ is the class of functions with continuous derivatives of all orders), and the class $C^a$ consists of all real-analytic functions.
The notation $C^a$ ($a$ for analytic) is somewhat unusual. Instead one mostly uses $C^\omega$ ($\omega$ denotes the first transfinite ordinal number).