
Re: Two Finite Arithmetics
Posted:
Apr 8, 2014 11:57 PM


On Tuesday, April 8, 2014 11:47:13 PM UTC4, William Elliot wrote: > On Mon, 7 Apr 2014, Dan Christensen wrote: > > > > > > Naive Finite Arithmetic > > > > > > Let N be a set, 0,m two elements and SN > 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 workaround isn't up to spec.
Dan Download my DC Proof 2.0 software at http://www.dcproof.com Visit my new math blog at http://www.dcproof.wordpress.com

