I'm trying to work through William Coppels Number Theory book, and I'm having a hard time with notation. In the section defining the natural numbers he gives this proposition:
Given a set A, and element a1 of A and a map T: A->A, there exists exactly one map p:N->A such that: p(1) = a1 and p(S(n)) = Tp(n) for every n that is a member of N Where S(n) is a function that gives the next element in a set after n and N are the natural numbers.
My question is: What is Tp(n)? Is that the same as T(p(n))? The notation is somewhat confusing (to me).