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Extending du Bois-Reymond's Infinitesimal and Infinitary Calculus Theory

2015/02/15 by Chelton D. Evans, Evans, Chelton D., William K. Pattinson +1
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM

paper · pdf · doi:10.48550/arxiv.1502.06936

Resubmission of 6 other submissions. 99 pages

arxiv created 2015/04/06 · arxiv updated 2015/04/07

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.

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