ABSTRACT
The application of a numerical function f to arguments x1, . . . ,xn is usually written as f (x1, . . . ,xn) , which is an example of prefix notation where the function symbol comes first. There are other notational conventions used, such as + being placed between its arguments in infix notation, or the exponent appearing as a superscript. In the case of these functions, we think of numbers as a different sort of object than the sort the functions belong to. This distinction is reinforced by the set-theoretical understanding of functions. However, we saw in chapter 6 that the natural numbers themselves may be seen as functions, and at the same time, computable functions on N may be viewed as natural numbers. This suggests that f (n) could be thought of as an application of n to f — not only the other way around, an application of f to n .
