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arXiv · 1502.06936

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

Chelton D. Evans·William K. Pattinson
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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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Chelton D. Evans, William K. Pattinson. 2015-02-15. Extending du Bois-Reymond's Infinitesimal and Infinitary Calculus Theory. https://arxiv.org/abs/1502.06936

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