Thus, approximate and exact density-functionals are mathematically quite different. The noncomputability of the exact functional indicates that systematically improvable DFAs are probably possible, in the sense of mathematical a priori error estimationthat is, mathematical statements towards an approximation's accuracy in terms of its adjustable parameters, such as basis size. Therefore, I would like to go out on a limb and say that approximate density functionals are not really approximations to exact density functionals. They are instead largely independent and, to a variable extent, semiempirical models that have the common use of the density as a basic variable as a characteristic. The latter aspect is for me an answer to the question "What is DFT?" (2.1.6) Savin : Let me comment on the difficulty of obtaining exact functionals in a (semi)local form by choosing a simpler example. The Hartree density functional,