So given that a taylor-series expansion is exact for an infinitely-times differentiable function, how does this constraint permit a bijective mapping of the function to a countable list of coefficients? How would you prove this is ok?
Additionally There exists several constraints that permit such a mapping, another example would be the Fourier coefficients for any periodic function. So to generalize the question is there a way to define the amount of information a function holds based off the constraints given?