On Thursday, 27 February 2014 23:21:44 UTC+2, Sam Sung wrote: > firstname.lastname@example.org schrieb: > > > > >> 1, 10, 11, 100, 101, 110, 111, 1000, ... > > >> > > >> But it is a perfectly legitimate enumeration of members of N > > > > > > because the difference is always 1. > > > > The difference is ANY n in N in an unordered set, eg. (80769087,5, AGVZ, 2) > > > > On the other hand, as any set isomorphic (strukturgleich) to N > > contains each number exactly once, one can take ANY order of > > those sets as ordered by just a replacement of the symbols. > > > > That means that the function S(ANY) + UNITY = S(S(ANY)). > > > > Now get that already. > > > > Btw - the reals have got a different structure, as there > > is no successor function.