Polymultisets, Multisuccessors, and Multidimensional Peano Arithmetics
General Mathematics
2012-01-10 v1
Abstract
The goal of this paper is introduction of a concept of natural multidimensional numbers and to construct a generalized Peano arithmetic of these multidimensional numbers. For this purpose we define a polymultiset as a special set-like form of m-ary multirelation. In addition, multisuccessor and multipredecessor functions on polymultisets are determined. By introducing Peano-like axioms for natural multidimensional numbers, we build a commutative semiring of 2-numbers <P2, +, \cdot, 02, 100>.
Cite
@article{arxiv.1201.1820,
title = {Polymultisets, Multisuccessors, and Multidimensional Peano Arithmetics},
author = {Alexander Chunikhin},
journal= {arXiv preprint arXiv:1201.1820},
year = {2012}
}
Comments
13 pages