On Tuesday, April 8, 2014 11:47:13 PM UTC-4, William Elliot wrote: > On Mon, 7 Apr 2014, Dan Christensen wrote: > > > > > > Naive Finite Arithmetic > > > > > > Let N be a set, 0,m two elements and S|N -> N a function. > > > > > > Axioms for naive finite arithmetic: > > > > > > 0, m in N; Sm = m > > > > > m should have no successor. Perhaps a partial function S on N? > > > > Naive finite arithmetic is not your finite arithmetic. > > > > S is a full function to banish the pests of your system. > > > Inventing a successor for the maximum number seems a bit weird to me. > > It fits much better than not having one. >
We have a finite succession of objects with a beginning and an end. The first element, by definition has no predecessor. The last element, by definition has no successor. I'd say your work-around isn't up to spec.