A graphic generalization of arithmetic

Details A graphic generalization of arithmetic A graphic generalization of arithmetic

2004-03-29

arxiv.org/abs/math/0403505v2

Mathematics

Combinatorics

31 pages, 17 figures

Scientific paper

In this paper, we extend the classical arithmetic defined over the set of natural numbers N, to the set of all finite directed connected multigraphs having a pair of distinct distinguished vertices. Specifically, we introduce a model F on the set of such graphs, and provide an interpretation of the language of arithmetic L={0,1,<=,+,x} inside F. The resulting model exhibits the property that the standard model on N embeds in F as a submodel, with the directed path of length n playing the role of the standard integer n. We will compare the theory of the larger structure F with classical arithmetic statements that hold in N. For example, we explore the extent to which F enjoys properties like the associativity and commutativity of + and x, distributivity, cancellation and order laws, and decomposition into irreducibles.

Affiliated with

Also associated with

No associations

Rating

A graphic generalization of arithmetic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A graphic generalization of arithmetic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A graphic generalization of arithmetic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-78778