Primitive recursive functions. II
Raphael M. Robinson · Proceedings of the American Mathematical Society · 1955
In this note, we shall prove two theorems which are modifications of a result of PRF.1 The second of these is used by the author in another paper.2In PRF, we made much use of pairing functions, that is, of functionsbut no fixed choice of pairing functions was made.In this note, we shall use only the Cantor pairing functions.Here 2/(«, ») = (« + v)2 + 3u + o.In this case, the formula x = J(u, v) establishes a one-to-one correspondence between pairs of natural numbers (u, v) and all natural numbers x.K and A are defined as the inverse functions.Notice that Ax is the excess of x over a triangular number.In addition to the previous formulas, we also have J(Kx, Ax) =x.