Editing Smoothness (section)

==== Example: analytic (''C''<sup>{{mvar|ω}}</sup>) ====
The [[exponential function]] <math>e^{x}</math> is [[Analytic function|analytic]], and hence falls into the class ''C''<sup>ω</sup> (where ω is the smallest [[transfinite ordinal]]). The [[trigonometric function]]s are also analytic wherever they are defined, because they are [[Trigonometric_functions#Euler's_formula_and_the_exponential_function | linear combinations of complex exponential functions]] <math>e^{ix}</math> and <math>e^{-ix}</math>.