a system 'n'

We will say that a system N is (this is Dedekind’s expression) simply infinite if there exists a transformation f of N within N that complies with the three following conditions:
• The application of f of N within N is a distinct application;
• N is the chain of one of its elements, which later Dedekind denotes as 1, and which he calls the base-element of N;
• The base-element 1 is not the correspondent through f of any element of N. In other words, for any n which is part of N, f(n) ≠ 1: the function f never “returns” to 1.  
A system N, structured by a function f which complies with these three conditions above, will be called “a system of numbers”, a site of the set of numbers.