 Since it is easy to see how the minimization operation can be used to define partial functions, the foregoing observations is expected. What is more surprising is that there are mathematically well-defined total functions which are not computable. Building on the discussion of the Entscheidungsproblem in  Section 1.7,  the most famous example of such a function derives from the so-called  Halting Problem (see entry on Turing machines)  for the Turing Machine model. This was originally formulated by Turing (1937) as follows: