Extending du Bois-Reymond's Infinitesimal and Infinitary Calculus Theory
General Mathematics
2015-04-07 v2
Abstract
The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and little-o/big-O defined with the Gossamer number system, and the relations algebra is explored. A comparison of function algebra is developed. A transfer principle more general than Non-Standard-Analysis is developed, hence a two-tier system of calculus is described. Non-reversible arithmetic is proved, and found to be the key to this calculus and other theory. Finally sequences are partitioned between finite and infinite intervals.
Keywords
Cite
@article{arxiv.1502.06936,
title = {Extending du Bois-Reymond's Infinitesimal and Infinitary Calculus Theory},
author = {Chelton D. Evans and William K. Pattinson},
journal= {arXiv preprint arXiv:1502.06936},
year = {2015}
}
Comments
Resubmission of 6 other submissions. 99 pages