However, only one student seemed to have this facility. Pip wanted C to be the real numbers, but Sam talked him into using {0}. It is plausible that Pip’s past experience of functions which have the reals as the domain has led to R being treated as a prototypical function domain. We also note here the shift from a general class to finding a single counterexample, and Sam seemed to want formulae for g and h even though A, B and C could only have 1 or 2 values. It is possible that Sam’s PES of functions consists of formulae