Editing Primitive recursive function (section)

=== Operations on integers and rational numbers ===

By using [[Gödel numbering]]s, the primitive recursive functions can be extended to operate on other objects such as integers and [[rational number]]s.  If integers are encoded by Gödel numbers in a standard way, the arithmetic operations including addition, subtraction, and multiplication are all primitive recursive.  Similarly, if the rationals are represented by Gödel numbers then the [[Field (mathematics)|field]] operations are all primitive recursive.